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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Sustain. Food Syst.</journal-id>
<journal-title>Frontiers in Sustainable Food Systems</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Sustain. Food Syst.</abbrev-journal-title>
<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.2023.1237844</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Sustainable Food Systems</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Rural industrial convergence, urbanization development, and farmers&#x2019; income growth &#x2013; evidence from the Chinese experience</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Yang</surname>
<given-names>Juan</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/2374033/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Chen</surname>
<given-names>Lingming</given-names>
</name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x002A;</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/1514734/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Yadong</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
</contrib>
</contrib-group>
<aff id="aff1"><sup>1</sup><institution>School of Business, Hunan University of Science and Technology</institution>, <addr-line>Xiangtan, Hunan Province</addr-line>, <country>China</country></aff>
<aff id="aff2"><sup>2</sup><institution>School of Business, Loudi Vocational and Technical College</institution>, <addr-line>Loudi, Hunan Province</addr-line>, <country>China</country></aff>
<aff id="aff3"><sup>3</sup><institution>School of Economics and Management, Xinyu University</institution>, <addr-line>Xinyu, Jiangxi Province</addr-line>, <country>China</country></aff>
<author-notes>
<fn id="fn0002" fn-type="edited-by"><p>Edited by: Sendhil R., Pondicherry University, India</p></fn>
<fn id="fn0003" fn-type="edited-by"><p>Reviewed by: Wonder Agbenyo, Sichuan Agricultural University, China; Sara Javed, Beijing University of International Business and Economics, China</p></fn>
<corresp id="c001">&#x002A;Correspondence: Lingming Chen, <email>lingming1016@mail.hnust.edu.cn</email></corresp>
</author-notes>
<pub-date pub-type="epub">
<day>16</day>
<month>11</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>7</volume>
<elocation-id>1237844</elocation-id>
<history>
<date date-type="received">
<day>14</day>
<month>06</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>31</day>
<month>10</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x00A9; 2023 Yang, Chen and Zhang.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Yang, Chen and Zhang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). 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.</p>
</license>
</permissions>
<abstract>
<p>Farmers&#x2019; income growth is a significant social problem, which has a bearing on the building of a moderately prosperous society in an all-round way. The convergence of rural industries based on agricultural development has become a meaningful way to solve the problem. The convergence of rural industries cannot be separated from the construction of urbanisation because the aggregation of population resources and the optimisation of industrial structures need the support of urbanisation. Based on the panel data of 29 provinces in China from 2004 to 2020, this paper makes an empirical study on the interaction between rural industrial agglomeration, urbanisation level, and farmers&#x2019; income using the theories of &#x201C;intermediate role&#x201D; and &#x201C;threshold effect.&#x201D; The results show that rural industrial agglomeration significantly affects farmers&#x2019; economic development, among which the eastern, western, and central regions have the most substantial positive effect. The level of urbanisation development is the mediating variable of the impact of rural industrial convergence on farmers&#x2019; income growth, which indirectly promotes farmers&#x2019; income growth, and the mediating effect is significant. Lastly, the level of urbanisation development is the threshold variable for the impact of rural industrial convergence on farmers&#x2019; income growth, and the coefficient of rural industrial convergence on farmers&#x2019; income growth is highest when the level of urbanisation is between 0.7960 and 0.8500. Therefore, in order to achieve sustainable growth in farmers&#x2019; operating income, wage income and financial transfer income, the country should give full play to the advantages of rural industrial integration, build a modernised industrial system for agriculture, expand the functions of agriculture in the secondary and tertiary sectors, and make good use of the policies that benefit the people in rural industrial development. At the same time, with the opportunity of county urbanisation, a rural industrial development system with the county as the centre of development has been established, guiding the rational flow and effective integration of urban and rural industrial resource elements and realising the integrated development of urbanisation and rural industry. Given the differences in industrial development in the eastern, central and western regions, the State should also promote rural industrial integration policies by stage, region and strategy to raise the level of farmers&#x2019; income.</p>
</abstract>
<kwd-group>
<kwd>rural industrial convergence</kwd>
<kwd>urbanization</kwd>
<kwd>farmers&#x2019; income growth</kwd>
<kwd>mediating effect</kwd>
<kwd>threshold effect</kwd>
</kwd-group>
<contract-num rid="cn1">22B1057</contract-num>
<contract-sponsor id="cn1">Hunan Provincial Education Department</contract-sponsor>
<counts>
<fig-count count="2"/>
<table-count count="11"/>
<equation-count count="4"/>
<ref-count count="71"/>
<page-count count="14"/>
<word-count count="10500"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Land, Livelihoods and Food Security</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="sec1">
<label>1.</label>
<title>Introduction</title>
<p>Farmers&#x2019; income growth is related to building a well-off society in an all-around way, and it is an unavoidable problem that promotes the sustainable growth of farmers&#x2019; income in the process of socialist modernisation. How to effectively increase farmers&#x2019; income is of great concern to the academic community. Farmers&#x2019; income growth is affected by many factors. One is the natural environment, such as rice farmers&#x2019; income, which is affected by weather, temperature, precipitation and other climatic influences (<xref ref-type="bibr" rid="ref44">Ojo and Baiyegunhi, 2021</xref>). In Iran, climate change can also lead to changes in groundwater mineralisation that pose a risk to farmers&#x2019; incomes (<xref ref-type="bibr" rid="ref1">Akbari et al., 2020</xref>), and Philippine smallholder agro-forestry composite farmers are adopting adaptive strategies in response to climate change in a bid to improve farm incomes (<xref ref-type="bibr" rid="ref22">Landicho et al., 2016</xref>). Second, government policy. Agriculture is a declining industry when agricultural products rely on the world market, and the U.S. government&#x2019;s transfer payment mechanism can enhance the competitiveness of agricultural products (<xref ref-type="bibr" rid="ref41">Miljkovic et al., 2008</xref>). China has used PES programmes to create some non-farm jobs and relies on non-agricultural employment to increase the incomes of small and medium-sized farmers (<xref ref-type="bibr" rid="ref48">Sheng and Wang, 2022</xref>) while increasing forestry subsidies to raise farmers&#x2019; incomes (<xref ref-type="bibr" rid="ref37">Lu et al., 2020</xref>). Third, the level of economic development. Regional economic development impacts farmers&#x2019; incomes, and transport infrastructure is crucial in economic development, especially in China, where the supply of rural roads has an inverted U-shaped effect on inter-provincial farmers&#x2019; income disparities (<xref ref-type="bibr" rid="ref61">Weng et al., 2021</xref>). The impact of infrastructure on rural&#x2013;urban income inequality is also present in other Asian countries (<xref ref-type="bibr" rid="ref42">Mishra and Agarwal, 2019</xref>). Fourth, the development of urbanization equally affects farmers&#x2019; income growth (<xref ref-type="bibr" rid="ref42">Mishra and Agarwal, 2019</xref>). Nigeria&#x2019;s agricultural labour market is centred on towns and cities, making it easy for job-seekers to find work (<xref ref-type="bibr" rid="ref55">Tiffen, 2018</xref>). China&#x2019;s large surplus of rural labour has also increased the farmer&#x2019;s income through urbanization, but it has resulted in the agricultural modernisation level lagging behind urbanisation (<xref ref-type="bibr" rid="ref64">Yuan et al., 2018</xref>). Fifth, production technology improvement. Science and technology innovations have had a more significant impact on farmers&#x2019; income growth, with Indian regions bridging the rice yield gap through soda soil management techniques (<xref ref-type="bibr" rid="ref49">Sheoran et al., 2021</xref>), Nigerian smallholder maize producers further improving farmers&#x2019; income through knowledge innovations such as improving traditional farming techniques (<xref ref-type="bibr" rid="ref3">Ayanwale et al., 2023</xref>), and China applying internet technology to farmers&#x2019; income growth, which increases farmers&#x2019; income through entrepreneurial effects and the availability of non-farm jobs (<xref ref-type="bibr" rid="ref68">Zhou et al., 2020</xref>). Sixth, agricultural economic co-operation organisations. Farmers&#x2019; production and management companies in India (<xref ref-type="bibr" rid="ref2">Anirban et al., 2018</xref>), farmers&#x2019; economic cooperation organisations and levels of agricultural specialisation in China (<xref ref-type="bibr" rid="ref63">Yang and Liu, 2012</xref>), and agribusiness supermarket pacts in Kenya (<xref ref-type="bibr" rid="ref43">Ogutu et al., 2020</xref>) have all played an essential role in improving farmers&#x2019; incomes. The above studies have provided solutions for farmers&#x2019; income growth and laid a sound research foundation. However, researchers seldom combine two or more of these influences to examine their impact on farmers&#x2019; income growth. As science and technology continue to progress, productivity levels rise, and urbanisation accelerates, the development trend expands the agricultural industry chain, increases farmers&#x2019; non-agricultural income and improves the structure of farmers&#x2019; income. Nowadays, especially in the context of constructing China&#x2019;s agricultural powerhouse, it is necessary to speed up the pace of agricultural modernization, do an excellent job of extending the agricultural industry chain and take the road of rural industrial convergence. At the same time, China has stepped into the stage of county urbanisation, and it is worth trying to put the convergence of rural industries, urbanisation development, and farmers&#x2019; income growth into a research framework by taking advantage of the momentum of <italic>in situ</italic> urbanisation development. Indeed, some theoretical literature has confirmed that rural industrial convergence is an effective way to increase farmers&#x2019; income (<xref ref-type="bibr" rid="ref65">Zhang et al., 2020</xref>), and it promotes the efficiency of factor allocation through the cross-border penetration and cross-convergence of capital, labour, and technology (<xref ref-type="bibr" rid="ref38">Luo and Wei, 2022</xref>); rural industrial convergence can achieve farmers&#x2019; income increase through accelerating urbanisation as a mediating variable (<xref ref-type="bibr" rid="ref33">Li and Ran, 2019</xref>). The faster the urbanisation process, the higher the farmers&#x2019; income (<xref ref-type="bibr" rid="ref17">Huang, 2016</xref>). The convergence of rural industries can contribute to urbanisation and the rapid growth of farmers&#x2019; incomes by acting as a catalyst.</p>
<p>Based on the theoretical analysis of the above literature, what is the relationship between the convergence of rural industries, urbanisation, and farmers&#x2019; income growth from an empirical perspective? Is there a direct and indirect transmission mechanism between each other? Is there a linear relationship between the impact of rural industrial convergence on farmers&#x2019; income growth? With doubts, based on the panel data of 29 provinces and cities in China from 2004 to 2020, this study uses principal component analysis to measure rural industrial convergence, empirically analyses the transmission mechanism of rural industrial convergence affecting farmers&#x2019; income increase, and uses the level of urbanisation development as a threshold variable to examine the non-linear relationship between rural industrial convergence and farmers&#x2019; income growth, to provide theoretical and practical guidance for the scientific implementation of the convergence of rural industries, urbanisation development and the positive interaction with farmers&#x2019; income growth in China.</p>
<p>The rest of the paper is organised as follows: Part II briefly reviews and critiques the relevant literature; Part III presents the theoretical mechanisms and research hypotheses; Part IV reports mainly on the model, variables, and data descriptions; Part V analyses and discusses the empirical results; and Part VI presents the research conclusions and policy implications.</p>
</sec>
<sec id="sec2">
<label>2.</label>
<title>Literature review</title>
<sec id="sec3">
<label>2.1.</label>
<title>Rural industrial convergence and farmers&#x2019; income growth</title>
<p>The theory of rural industrial convergence can be traced back to the &#x201C;six industries &#x201C;theory advocated by Japanese scholar Imamura in the 1990s. He believes that to enhance the added value of agricultural products and increase farmers&#x2019; income, it is necessary to rely on agriculture to do a good job in the integrated development of agricultural &#x201C;production, processing and marketing&#x201D; to resolve the dilemma of Japanese agricultural development (<xref ref-type="bibr" rid="ref32">Li et al., 2020</xref>). The central idea of the &#x201C;six industrialisation concept&#x201D; highlights the essential role of agriculture and reflects the importance of rural industrial convergence for regional economic benefits (<xref ref-type="bibr" rid="ref45">Qi et al., 2021</xref>). Rural industrial convergence is essential for China to implement a rural revitalisation strategy and achieve shared prosperity (<xref ref-type="bibr" rid="ref12">Fu et al., 2022</xref>). In January 2016, the General Office of the State Council officially issued the document &#x201C;Guiding Opinions on Promoting the Convergence and Development of Rural Primary, Secondary, and Tertiary Industries&#x201D; (<xref ref-type="bibr" rid="ref7">Central People&#x2019;s Government of the People&#x2019;s Republic of China Network, 2016</xref>). At this point, the convergence of rural industries has become a critical development way to sustain farmers&#x2019; income in China. Currently, the literature on rural industrial integration and farmers &#x2018;income growth focuses on the following two aspects:</p>
<p>First, the impact of rural industrial integration on farmers&#x2019; income growth. One hand, rural industrial convergence has a significant positive impact on farmers&#x2019; income (<xref ref-type="bibr" rid="ref58">Wang and Li, 2019</xref>). The convergence of rural industries helps alleviate farmers&#x2019; poverty vulnerability (<xref ref-type="bibr" rid="ref31">Li and Lu, 2019</xref>). It promotes farmers&#x2019; income growth by extending the agricultural industry chain, giving full play to agricultural versatility, and promoting the integrated development of agricultural service industries (<xref ref-type="bibr" rid="ref53">Tang and Hu, 2017</xref>). The income of the subjects participating in the convergence of rural industries has increased significantly (<xref ref-type="bibr" rid="ref14">Guo et al., 2019</xref>; <xref ref-type="bibr" rid="ref32">Li et al., 2020</xref>). In particular, the average gross and operating incomes of farm households involved in rural industrial convergence are significantly higher than those of households not involved in rural industrial convergence (<xref ref-type="bibr" rid="ref62">Yang and Ding, 2019</xref>). The micro-survey data of farmers&#x2019; households also confirmed that compared with the traditional agricultural development model, the income increase effect of farmers participating in rural industrial convergence is as high as 50% (<xref ref-type="bibr" rid="ref29">Li et al., 2017</xref>).</p>
<p>On the other hand, there is heterogeneity in the impact of rural industrial convergence on farmers. The impact of rural industrial convergence on farmers is not the same, and the effect of low-income farmers&#x2019; income increase is more prominent (<xref ref-type="bibr" rid="ref45">Qi et al., 2021</xref>). In addition, due to the differences in location conditions, resource conditions, development foundations and other factors between rural areas (<xref ref-type="bibr" rid="ref26">Li J. J., 2021</xref>), the impact of rural industrial integration on farmers&#x2019; income between different regions is also heterogeneous (<xref ref-type="bibr" rid="ref58">Wang and Li, 2019</xref>).</p>
<p>Second, rural industrial convergence helps to narrow the income gap between urban and rural areas and can lead farmers to shared prosperity. Agricultural industrialisation is the focus of rural industrial convergence. It is a crucial breakthrough to narrow the urban&#x2013;rural income gap (<xref ref-type="bibr" rid="ref8">Chen, 2005</xref>). The critical reason for the increasing urban&#x2013;rural income gap in Hunan Province is that agricultural industrialisation is not high (<xref ref-type="bibr" rid="ref50">Song, 2011</xref>). The impact of urban&#x2013;rural income gap changes in the Yangtze River Economic Belt is also in developing rural industrial convergence (<xref ref-type="bibr" rid="ref28">Li, 2022</xref>). Promoting agricultural industrialisation, improving land and labour productivity, and increasing farmers&#x2019; operating income will help narrow the urban&#x2013;rural income gap (<xref ref-type="bibr" rid="ref21">Lai, 2012</xref>).</p>
</sec>
<sec id="sec4">
<label>2.2.</label>
<title>Rural industrial convergence and urbanization development</title>
<p>When it comes to industrial convergence, it is necessary to analyse urbanisation construction because industrial development and urbanisation are interactive, and industrial employment structure can significantly affect the urbanisation rate (<xref ref-type="bibr" rid="ref36">Long et al., 2015</xref>). In the early days, <xref ref-type="bibr" rid="ref23">Lewis (1954)</xref> found that the industrial sector absorbed surplus labour from the agricultural sector and played an essential role in increasing the income of rural labour. Rural workers are usually affected by the expected income gap to decide whether to migrate from rural to urban areas (<xref ref-type="bibr" rid="ref56">Todaro, 1969</xref>). Urbanisation is gathering population and resources into cities and towns, promoting social and cultural convergence and economic structure optimisation (<xref ref-type="bibr" rid="ref35">Liu et al., 2023</xref>). With the continuous improvement of the economy and industrial structure, farmers&#x2019; income has been increasing. The literature research on rural industrial convergence and urbanisation development mainly focuses on the following:</p>
<p>First, rural industrial convergence and urbanisation development have a promoting effect. <xref ref-type="bibr" rid="ref40">Michaels et al. (2008)</xref> believe that with the advancement of urbanisation, the specialisation of the labour force improves production efficiency and promotes the improvement of technological innovation level and the aggregation of emerging industries, which leads to the adjustment of industrial structure. <xref ref-type="bibr" rid="ref9">Duan (2017)</xref> found that the key to the success of urbanisation is to realise the upgrading of industrial structure through the improvement of production efficiency; the adjustment of industrial structure, especially the change of the proportion of employment structure, is the reason for the increase of urbanisation rate (<xref ref-type="bibr" rid="ref52">Sun and Chai, 2012</xref>; <xref ref-type="bibr" rid="ref16">Hong, 2013</xref>). Similarly, urbanisation can promote the transformation of industrial and employment structures (<xref ref-type="bibr" rid="ref24">Li, 2011</xref>).</p>
<p>Second, there is a negative correlation between rural industrial convergence and urbanisation development. <xref ref-type="bibr" rid="ref11">Farhana et al. (2014)</xref> found that due to the division of labour under urbanisation, developing countries promote urbanisation in an extensive development mode, which inhibits the adjustment and optimisation of industrial structures. When the level of new urbanization does not match the relative amount of industrial transfer, such as industrial transfer lags behind the development of new urbanization, and the development of new urbanization inhibits the transfer of industrial structure (<xref ref-type="bibr" rid="ref69">Zhou et al., 2019</xref>). With regard to urbanization, different countries and regions have different impacts on their industrial structure in developing countries. There is no significant impact on its industrial structure in Africa (<xref ref-type="bibr" rid="ref13">Gollin et al., 2015</xref>). In addition, urbanization will also have a negative impact on some industries. For example, urbanization will have a specific crowding-out effect on manufacturing (<xref ref-type="bibr" rid="ref18">Huang and Qiu, 2017</xref>). At the same time, other factors (such as the level of financial support for agriculture) will also restrict the effect of urbanisation on the development of rural industrial convergence (<xref ref-type="bibr" rid="ref27">Li X. L., 2021</xref>).</p>
<p>Based on the current literature review, it is found that most researchers focus on the analysis of the single factor influence of rural industrial convergence or urbanisation development level on farmers&#x2019; income or directly discuss the developing relationship between rural industrial convergence and urbanisation. Few people include rural industrial convergence, urbanisation development level, and farmers&#x2019; income growth in a research framework. Therefore, it is one of the marginal contributions of this paper to integrate the above three into an analytical framework and use the level of urbanisation development as an intermediary variable and threshold variable to carry out empirical research on the intermediary effect and threshold effect. The second marginal contribution is constructing the index system of rural industrial convergence and using the principal component analysis method to objectively measure rural industrial convergence development.</p>
</sec>
</sec>
<sec id="sec5">
<label>3.</label>
<title>Theoretical mechanism and research hypothesis</title>
<sec id="sec6">
<label>3.1.</label>
<title>The direct influence mechanism of rural industrial convergence on farmers&#x2019; income increase</title>
<p>The influence mechanism of rural industrial convergence on farmers&#x2019; income is as follows: First, rural industrial convergence is conducive to developing agricultural industrialisation and improving comprehensive agricultural income. <xref ref-type="bibr" rid="ref19">Jiang (2017)</xref> believes that agricultural industrialisation is the source and main content of the convergence and development of rural industries. Agricultural industrialisation focuses on the radiation and driving role of leading enterprises and realises the endogenous development of rural areas and the multi-functional development of agriculture (<xref ref-type="bibr" rid="ref66">Zhao, 2015</xref>). In particular, the convergence of primary, secondary, and tertiary industries led by farmers&#x2019; professional cooperatives can enhance the potential of agriculture itself, realise the increase of agricultural added value and sustainable development, and increase farmers&#x2019; income (<xref ref-type="bibr" rid="ref30">Li and Liu, 2019</xref>). Second, the convergence of rural industries is conducive to broadening the channels for farmers to increase their income and build a non-agricultural employment platform. (<xref ref-type="bibr" rid="ref46">Rhodes, 1993</xref>) believes that industrial convergence makes the production and sales stages of agricultural products and other related products more integrated, forming an orderly chain from the supply of production materials to the processing and retail of products so that farmers can obtain the profits of industrialisation. China&#x2019;s rural industrial convergence development practice models mainly include leading agricultural enterprises, industrial and commercial capital, vertical convergence management, and &#x2018;Internet + agriculture&#x2019; e-commerce platforms (<xref ref-type="bibr" rid="ref39">Lv and Liu, 2017</xref>). These platforms save production transaction costs and create conditions for realising local non-agricultural employment and household utility maximisation (<xref ref-type="bibr" rid="ref6">Cai et al., 2020</xref>). The income of farmers has increased steadily in the development trend of rural industrial convergence. Because of this, this paper proposes hypothesis 1.</p>
<disp-quote>
<p><italic>Hypothes</italic>is <italic>1</italic>: Rural industrial convergence promotes the increase of farmers&#x2019; income.</p>
</disp-quote>
</sec>
<sec id="sec7">
<label>3.2.</label>
<title>The indirect mechanism of rural industrial convergence to promote farmers&#x2019; income</title>
<p>The level of urbanisation development is an indirect mechanism for rural industrial convergence to promote farmers&#x2019; income increase. It is proposed to optimise the industrial structure based on urbanisation (<xref ref-type="bibr" rid="ref54">Tian and Abdurezak, 2010</xref>), and the convergence of rural industries can also promote the development of local urbanisation (<xref ref-type="bibr" rid="ref34">Li and Zhao, 2017</xref>). In the long run, there is a positive interaction between urbanisation development and farmers&#x2019; income growth (<xref ref-type="bibr" rid="ref51">Song and Xiao, 2005</xref>). The impact of urbanisation development on farmers&#x2019; income growth: First, urbanisation development is conducive to improving the operating income of rural households. Population urbanisation is an essential manifestation of urbanisation development. With the migration of agricultural surplus labour, the requirements of agricultural production for agricultural production are also increased, thus increasing the operating income of farmers (<xref ref-type="bibr" rid="ref25">Li, 2016</xref>). At the same time, by transferring farmers&#x2019; land use rights, we can expand the scale of farmers, thus creating new development opportunities for farmers to increase their income. Second, the development of urbanisation is conducive to improving the wage income of rural residents. Urbanisation helps to increase farmers&#x2019; wage income (<xref ref-type="bibr" rid="ref59">Wang and Peng, 2013</xref>). Urbanisation development provides farmers with many employment opportunities, and the transfer of rural labour force employment increases wage income (<xref ref-type="bibr" rid="ref10">Fang and Zhang, 2015</xref>). Thirdly, urbanisation development is conducive to improving farmers&#x2019; financial transfer payment income. Urbanisation development is closely related to local economic growth. &#x2018;As urbanisation enters a stage of rapid development, a large number of rural surplus labour force pours into cities and towns, the level of industrialisation continues to increase, and economic growth accelerates simultaneously (<xref ref-type="bibr" rid="ref5">Cai et al., 2023</xref>). When a region&#x2019;s economy develops to a certain extent, its funds for supporting agriculture will be adequately guaranteed. Simultaneously, there will be more capital inflows of transfer payments to rural areas. Based on this, this paper proposes Hypothesis 2.</p>
<disp-quote>
<p><italic>Hypothes</italic>is 2: Rural industrial convergence promotes farmers&#x2019; income through urbanisation.</p>
</disp-quote>
</sec>
<sec id="sec8">
<label>3.3.</label>
<title>The influence mechanism of non-linear relationship between rural industrial convergence and farmers&#x2019; income growth</title>
<p>The proportion of the urban population is significantly related to the industrial structure and distribution (<xref ref-type="bibr" rid="ref36">Long et al., 2015</xref>) and plays an essential role in the city&#x2019;s economic development. Of course, there is a non-linear relationship between industrial integration and regional economic development. For example, the convergence of cultural and tourism industries can positively promote economic growth in ethnic areas, and its impact has non-linear characteristics. There is an optimal level of convergence of cultural and tourism industries that promotes economic growth (<xref ref-type="bibr" rid="ref67">Zhao and Wang, 2022</xref>). In addition, urbanisation development also has a threshold effect on farmers&#x2019; income growth. Since the mid-1980s, farmers&#x2019; income has been developing in an unstable and discontinuous trend, and the growth has been prolonged (<xref ref-type="bibr" rid="ref29">Li et al., 2017</xref>). In recent years, due to the fluctuation of economic development and the weak occupational stability of migrant workers, the difficulty of increasing farmers&#x2019; income and the risk of partial reduction have increased significantly (<xref ref-type="bibr" rid="ref20">Jiang and Lu, 2017</xref>). Therefore, this paper proposes hypothesis 3.</p>
<disp-quote>
<p><italic>Hypothes</italic>is <italic>3</italic>: There is a non-linear relationship between the impact of agricultural industry convergence on farmers&#x2019; income.</p>
</disp-quote>
</sec>
</sec>
<sec sec-type="materials|methods" id="sec9">
<label>4.</label>
<title>Materials and methods</title>
<sec id="sec10">
<label>4.1.</label>
<title>Model construction</title>
<p>On this basis, this paper examines the relationship between the degree of urbanisation on rural industrial agglomeration and the increase in farmers&#x2019; income, examines the regulatory effect of the degree of urbanisation on rural industrial agglomeration and peasant household income, and takes urbanisation as an intermediary variable. This part mainly refers to the literature of <xref ref-type="bibr" rid="ref4">Baron and Kenny (1986)</xref> and <xref ref-type="bibr" rid="ref60">Wen et al. (2004)</xref>, then introduces the stepwise test method to construct the intermediary effect model.</p>
<disp-formula id="EQ1"><label>(1)</label><mml:math id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Income</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B2;</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B2;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>Industry</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B2;</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Z</mml:mi><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B5;</mml:mi><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
<disp-formula id="EQ2"><label>(2)</label><mml:math id="M2"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Urban</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>Industry</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B1;</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Z</mml:mi><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B5;</mml:mi><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
<disp-formula id="EQ3"><label>(3)</label><mml:math id="M3"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Income</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03BB;</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03BB;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>Industry</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03BB;</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>Urban</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03BB;</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Z</mml:mi><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B5;</mml:mi><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>
<p>In equation (1), <italic>Income<sub>i,t</sub></italic> refers to the disposable income of farmers in <italic>i</italic> province during the <italic>t</italic> period, <italic>Industry<sub>i,t</sub></italic> refers to the development level of rural industrial integration in i province during the t period, <italic>Z<sub>i,t</sub></italic> is a group of control variables,<italic>&#x2107;<sub>i,t</sub></italic> is a random disturbance term. Based on the test of the influence coefficient of rural industrial convergence development level <italic>Industry<sub>i,t</sub></italic> on farmers&#x2019; income increase <italic>Income<sub>i,t</sub></italic>, <italic>&#x03B2;<sub>1</sub></italic> in <xref ref-type="disp-formula" rid="EQ1">Eq. 1</xref>. The linear regression equation of rural industrial convergence development level <italic>Industry<sub>i,t</sub></italic> to the intermediary variable urbanisation development level <italic>Urban<sub>i,t</sub></italic> is constructed (such as <xref ref-type="disp-formula" rid="EQ2">Eq. 2</xref>). Finally, the linear regression equation of <italic>Industry<sub>i,t</sub></italic> and intermediary variable <italic>Urban<sub>i,t</sub></italic> to <italic>Income<sub>i,t</sub></italic> (such as formula 3) was constructed, and the significance of regression coefficients such as <italic>&#x03B1;<sub>1</sub>, &#x03BB;<sub>1</sub></italic>, and <italic>&#x03BB;<sub>2</sub></italic> judged the existence of the intermediary effect. In addition, to further explore the non-linear effect of agricultural industry convergence on farmers&#x2019; income due to urbanisation development, a threshold effect model of agricultural industry convergence on farmers&#x2019; income under the background of urbanisation construction is constructed to verify Hypothesis 3. This paper draws on <xref ref-type="bibr" rid="ref15">Hansen (1999)</xref>, <xref ref-type="bibr" rid="ref57">Wang (2015)</xref> and other threshold research experience, combined with the actual data, to set up a double threshold model; the particular assumptions are as follows:</p>
<disp-formula id="EQ4"><label>(4)</label><mml:math id="M4"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mtext>Income</mml:mtext><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03BC;</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B7;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mtext>Industry</mml:mtext><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>Urban</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B3;</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi mathvariant="normal">&#x03B7;</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mtext>Industry</mml:mtext><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi mathvariant="normal">&#x03B3;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>&#x003C;</mml:mo><mml:msub><mml:mrow><mml:mtext>Urban</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B3;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mi mathvariant="normal">&#x03B7;</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mtext>Industry</mml:mtext><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>Urban</mml:mtext></mml:mrow><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>&#x003E;</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B3;</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="normal">&#x03B8;</mml:mi><mml:msub><mml:mi mathvariant="normal">Z</mml:mi><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="normal">&#x03B5;</mml:mi><mml:mrow><mml:mi mathvariant="normal">i</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p><italic>i</italic> represents the region, <italic>t</italic> represents the year, <italic>Income<sub>i,t</sub></italic> is the explained variable, &#x03BC;<italic><sub>i</sub></italic> is used to reflect the individual effect of the region, <italic>Urban<sub>i,t</sub></italic> represents the threshold variable, <italic>&#x03B3;</italic> as the specific threshold value, <italic>I(.)</italic> is the indicative function, and the true and false are determined according to the results of 0 and 1 in the brackets. <italic>Z<sub>i,t</sub></italic> is a set of control variables, <italic>&#x03B8;</italic> is the corresponding coefficient vector and <italic>&#x2107;<sub>i,t</sub></italic> is the random disturbance term.</p>
</sec>
<sec id="sec11">
<label>4.2.</label>
<title>Variable description</title>
<sec id="sec12">
<label>4.2.1.</label>
<title>Explained variable</title>
<p>Farmers&#x2019; income, variable symbol marked as <italic>Income</italic>. The growth of rural residents&#x2019; income is measured by the logarithm of the <italic>per capita</italic> disposable income of rural residents.</p>
</sec>
<sec id="sec13">
<label>4.2.2.</label>
<title>Core explanatory variable</title>
<p>This paper takes the rural industrial convergence evaluation index as the core explanatory variable, and the variable symbol is marked as <italic>Industry</italic>. Rural industrial convergence is a comprehensive indicator, including two secondary and six tertiary indicators (as shown in <xref ref-type="table" rid="tab1">Table 1</xref>). This index is mainly processed by principal component analysis.</p>
<table-wrap position="float" id="tab1">
<label>Table 1</label>
<caption><p>Rural industry convergence index system description.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">First grade indexes</th>
<th align="center" valign="top">Level 2 indicators</th>
<th align="center" valign="top">Three levels indicators</th>
<th align="center" valign="top">Index calculation and description</th>
<th align="center" valign="top">Attribute</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle" rowspan="14">The comprehensive development level of rural industrial convergence</td>
<td align="left" valign="middle" rowspan="8">Convergence behaviour</td>
<td align="left" valign="middle" rowspan="2">Agricultural Industry</td>
<td align="left" valign="middle">Agricultural production and processing level (%): The primary income of agricultural and sideline food products processing / Total output value of agriculture, forestry, fishery, and animal husbandry; Symbol D1</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle">Agricultural commodity rate (%): commercial agricultural output / total value of farm product; Symbol D2</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="3">Agricultural Multi-purpose</td>
<td align="left" valign="middle">The ratio of rural population to the added value of agriculture, forestry, animal husbandry, and fishery per 10,000 people (yuan/person): G.D.P. of primary industry / Rural population; Symbol D3</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle">Fertiliser application rate per unit area (tons/ha); Fertiliser application amount/crop planting area measurement; Symbol D4</td>
<td align="left" valign="middle">Negative</td>
</tr>
<tr>
<td align="left" valign="middle">Percentage of non-agricultural employment (%): Rural individual employment + rural private enterprise employment / Rural employees; Symbol D5</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="3">Industrial Support</td>
<td align="left" valign="middle">Four highway mileage (km); Symbol D6</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle">Rural delivery route (km); Symbol D7</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle">Mobile telephone switch capacity (ten thousand); Symbol D8</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="6">Fusion Result</td>
<td align="left" valign="middle" rowspan="2">Strong Farming</td>
<td align="left" valign="middle">increased agricultural production: Total grain output <italic>per capita</italic> (kg/person); Symbol D9</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle">Modernisation of agricultural production: Agricultural machinery total power (kilowatts); Symbol D10</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="2">Rich People</td>
<td align="left" valign="middle">Rural retail sales (billion yuan); Symbol D11</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle">Rural residents &#x2018;consumption expenditure (yuan/person); Symbol D12</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle" rowspan="2">Strong Village</td>
<td align="left" valign="middle">Fixed asset investment and housing construction of rural households (billion yuan); Symbol D13</td>
<td align="left" valign="middle">Positive</td>
</tr>
<tr>
<td align="left" valign="middle">Rural solar water heater (ten thousand square meters); Symbol D14</td>
<td align="left" valign="middle">Positive</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="sec14">
<label>4.2.3.</label>
<title>Threshold or intermediary variable</title>
<p>This paper selects the level of urbanisation development as an intermediary and threshold variable, measured by the ratio of the urban and variable symbol marks <italic>Urban</italic>.</p>
</sec>
<sec id="sec15">
<label>4.2.4.</label>
<title>Control variables</title>
<p>(1) Government support, the variable symbol mark <italic>Government</italic>, measured by budget expenditure. (2) Scientific and technological innovation, variable symbol mark <italic>Innovations</italic>, take the logarithm of patent authorisation. (3) the degree of opening to the outside world, variable symbol mark <italic>Open</italic>, measured by the total import and export. (4) The level of domestic tourism development, the variable symbol mark <italic>Tourism</italic>, with the total domestic tourism consumption to measure (see <xref ref-type="table" rid="tab2">Table 2</xref>).</p>
<table-wrap position="float" id="tab2">
<label>Table 2</label>
<caption><p>Variable description.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Variable type</th>
<th align="left" valign="top">Variable symbol</th>
<th align="left" valign="top">Name of indicator</th>
<th align="left" valign="top">Index calculation</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">Explained variable</td>
<td align="left" valign="top"><italic>Income</italic></td>
<td align="left" valign="top">Rural income</td>
<td align="left" valign="top"><italic>Per capita</italic> disposable income of rural residents</td>
</tr>
<tr>
<td align="left" valign="top">Core explanatory variable</td>
<td align="left" valign="top"><italic>Industry</italic></td>
<td align="left" valign="top">The comprehensive development level of rural industrial convergence</td>
<td align="left" valign="top">P.C.A</td>
</tr>
<tr>
<td align="left" valign="top">Mediation /Threshold variable</td>
<td align="left" valign="top"><italic>Urban</italic></td>
<td align="left" valign="top">Urbanisation development</td>
<td align="left" valign="top">Population urbanisation rate</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="4">Control variables</td>
<td align="left" valign="top"><italic>Government</italic></td>
<td align="left" valign="top">Support from government</td>
<td align="left" valign="top">Budgetary fiscal expenditure</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Innovation</italic></td>
<td align="left" valign="top">Science and technology innovation</td>
<td align="left" valign="top">Patent grants</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Open</italic></td>
<td align="left" valign="top">Degree of openness to foreign trade</td>
<td align="left" valign="top">Total export&#x2013;import volume</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Tourism</italic></td>
<td align="left" valign="top">Domestic tourism consumption level</td>
<td align="left" valign="top">The total domestic tourism consumption</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="sec16">
<label>4.3.</label>
<title>Data sources and data processing</title>
<sec id="sec17">
<label>4.3.1.</label>
<title>Data source</title>
<p>Considering the accessibility of data, this paper uses the panel data of 29 provinces or municipals from 2004 to 2020, excluding Tibet, Xinjiang, Taiwan, Macao, and Hong Kong in China. The data in this paper mainly come from the National Bureau of Statistics, China Statistical Yearbook, China Industry Statistical Yearbook, China Rural Development Yearbook, China Agriculture and Rural Development Database, and China Economic and Social Big Data Research Platform. Part is from annual reports on the national economic and social development of China and its provinces and municipalities and yearbooks for each province and municipality.</p>
</sec>
<sec id="sec18">
<label>4.3.2.</label>
<title>Data processing</title>
<p>First, the missing value of the indicator data is filled by the moving average method. Second, the index lacks value in dealing with two methods. On the one hand, the average value is obtained by adding the annual growth rate of the index. On the other hand, the data without relevant index refers to the literature of <xref ref-type="bibr" rid="ref70">Zhu and Xu (2003)</xref> in the Economic Research magazine, such as the amount of investment completed in industrial pollution control is processed using the calculation index (0.55&#x002A; Consumer Price Index +0.45 &#x002A; Fixed Asset Investment Price Index). Third, the income of statistical indicators is deflated with 2004 as the base year to eliminate the impact of inflation on the value.</p>
</sec>
</sec>
<sec id="sec19">
<label>4.4.</label>
<title>Statistical description of variables</title>
<p>There are 493 observed variables in this paper, and the descriptive statistics of variables are shown in <xref ref-type="table" rid="tab3">Table 3</xref>. Among them, the mean value of the explained variable farmers&#x2019; income is 42.53329, the standard deviation is 16.35281, the minimum value is 17.96, and the maximum is 98.68276. These data show that the income gap between provinces is narrowing with the steady growth of farmers&#x2019; <italic>per capita</italic> disposable income. The mean value of the comprehensive development level of rural industrial integration is 1.1, the standard deviation is 0.5671242, the minimum value is 0.0965812, and the maximum value is 3.784256. This means that the comprehensive development level of China&#x2019;s rural industrial integration has a large gap between provinces, with a difference of 39 times between the maximum and the minimum. The development of rural industrial integration still has a long way to go. In addition, the development of urbanization is relatively balanced. Still, the maximum and minimum values of variables such as government financial support, scientific and technological innovation, domestic tourism development level, and opening up are far from each other.</p>
<table-wrap position="float" id="tab3">
<label>Table 3</label>
<caption><p>Statistical description of variables.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="middle">Variable symbol</th>
<th align="center" valign="middle">Name of indicator</th>
<th align="center" valign="middle">Number of observations</th>
<th align="center" valign="middle">Mean value</th>
<th align="center" valign="middle">Standard deviation</th>
<th align="center" valign="middle">Minimum value</th>
<th align="center" valign="middle">Maximum value</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle"><italic>Income</italic></td>
<td align="left" valign="middle">Rural income</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">42.5333</td>
<td align="center" valign="top">16.3528</td>
<td align="center" valign="top">17.9600</td>
<td align="center" valign="top">98.6828</td>
</tr>
<tr>
<td align="left" valign="middle"><italic>Industry</italic></td>
<td align="left" valign="middle">The comprehensive development level of rural industrial convergence</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">1.1000</td>
<td align="center" valign="top">0.5671</td>
<td align="center" valign="top">0.0966</td>
<td align="center" valign="top">3.7843</td>
</tr>
<tr>
<td align="left" valign="middle"><italic>Urban</italic></td>
<td align="left" valign="middle">Urbanisation development</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">0.5498</td>
<td align="center" valign="top">0.1436</td>
<td align="center" valign="top">0.2571</td>
<td align="center" valign="top">0.9215</td>
</tr>
<tr>
<td align="left" valign="middle"><italic>Government</italic></td>
<td align="left" valign="middle">Support from government</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">3591.4410</td>
<td align="center" valign="top">2905.7450</td>
<td align="center" valign="top">123.0200</td>
<td align="center" valign="top">17430.7900</td>
</tr>
<tr>
<td align="left" valign="middle"><italic>Innovations</italic></td>
<td align="left" valign="middle">Science and technology innovation</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">70122.2200</td>
<td align="center" valign="top">120460.1000</td>
<td align="center" valign="top">124</td>
<td align="center" valign="top">967204</td>
</tr>
<tr>
<td align="left" valign="middle"><italic>Open</italic></td>
<td align="left" valign="middle">Degree of opening to the outside world</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">1.13e+08</td>
<td align="center" valign="top">1.95e+08</td>
<td align="center" valign="top">332,800</td>
<td align="center" valign="top">1.09e+09</td>
</tr>
<tr>
<td align="left" valign="middle"><italic>Tourism</italic></td>
<td align="left" valign="middle">Domestic tourism development level</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">10588.6000</td>
<td align="center" valign="top">19067.2000</td>
<td align="center" valign="top">30.0662</td>
<td align="center" valign="top">153831.2000</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>Data source: The data in the table are calculated by STATA 15.0.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec20">
<label>4.5.</label>
<title>Co-linearity analysis</title>
<p>This paper verifies the multivariate collinearity among the explanatory variables by using the expansion factor. The judgment method is based on the V.I.F. of the explanatory variable. When the V.I.F. exceeds 10, the multiple correlations are higher. The maximum value of V.I.F. is 6.16 from the detected value of the variation expansion factor in <xref ref-type="table" rid="tab4">Table 4</xref>. It can be seen that there is no significant multivariate co-linearity among the explanatory variables. In addition, to prove that each variable is related to the other, this paper has carried out the correlation coefficient test, which also has a specific correlation.</p>
<table-wrap position="float" id="tab4">
<label>Table 4</label>
<caption><p>Expansion factor test results.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Variables</th>
<th align="center" valign="top">VIF</th>
<th align="center" valign="top">1/VIF</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="bottom"><italic>Industry</italic></td>
<td align="center" valign="bottom">3.43</td>
<td align="center" valign="bottom">0.2919</td>
</tr>
<tr>
<td align="left" valign="bottom"><italic>Urban</italic></td>
<td align="center" valign="bottom">1.51</td>
<td align="center" valign="bottom">0.6604</td>
</tr>
<tr>
<td align="left" valign="bottom"><italic>Government</italic></td>
<td align="center" valign="bottom">6.16</td>
<td align="center" valign="bottom">0.1623</td>
</tr>
<tr>
<td align="left" valign="bottom"><italic>Innovation</italic></td>
<td align="center" valign="bottom">5.26</td>
<td align="center" valign="bottom">0.1901</td>
</tr>
<tr>
<td align="left" valign="bottom"><italic>Open</italic></td>
<td align="center" valign="bottom">3.40</td>
<td align="center" valign="bottom">0.2937</td>
</tr>
<tr>
<td align="left" valign="bottom"><italic>Tourism</italic></td>
<td align="center" valign="bottom">1.30</td>
<td align="center" valign="bottom">0.7714</td>
</tr>
<tr>
<td align="left" valign="bottom">Mean VIF</td>
<td align="center" valign="bottom">3.51</td>
<td/>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>Data source: The data in the table are calculated by STATA 15.0.</p>
</table-wrap-foot>
</table-wrap>
</sec>
</sec>
<sec sec-type="results" id="sec21">
<label>5.</label>
<title>Results</title>
<sec id="sec22">
<label>5.1.</label>
<title>Analysis of benchmark estimation results</title>
<p>This paper estimates the panel data by ordinary least squares linear estimation (O.L.S.). Firstly, it empirically studies the relationship between industrial convergence and farmers&#x2019; income. On this basis, the control variables are added sequentially, and finally, the mode of (1)&#x2009;~&#x2009;(5) is obtained. As shown in <xref ref-type="table" rid="tab5">Table 5</xref>, the regression analysis of the model (5) shows that for rural industrial integration, each additional 1 percentage point will bring 17.32 percentage points of growth to farmers. Therefore, rural residents&#x2019; <italic>per capita</italic> disposable income will increase with the improvement of rural industrial integration. This result confirms that the &#x201C;rural industry integration&#x201D; mentioned in Hypothesis 1 plays a positive role in promoting the economic development of farmers. Among the control variables, the degree of government support, openness, and the development of domestic tourism is most closely related to the economic income of farmers. Among them, the opening-up index is positive, indicating that the degree of openness of enterprises is higher, and the degree of internationalisation of their products is higher; the development of enterprises has improved, and farmers have obtained more jobs; their treatment has been better guaranteed, and their quality of life has been further improved. In addition, the coefficient of domestic <italic>per capita</italic> tourism consumption is positive, which shows that under the influence of the improvement of domestic <italic>per capita</italic> tourism consumption and the policy of &#x2018;tourism +&#x2019; industrial integration, farmers&#x2019; income will also rise gradually.</p>
<table-wrap position="float" id="tab5">
<label>Table 5</label>
<caption><p>Benchmark O.L.S. regression results.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="top">Variables</th>
<th align="center" valign="top" colspan="5"><italic>Income</italic></th>
</tr>
<tr>
<th/>
<th align="center" valign="top">(1)</th>
<th align="center" valign="top">(2)</th>
<th align="center" valign="top">(3)</th>
<th align="center" valign="top">(4)</th>
<th align="center" valign="top">(5)</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top"><italic>Industry</italic></td>
<td align="center" valign="top">16.69<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">18.31<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">19.95<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">17.47<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">17.32<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(15.73)</td>
<td align="center" valign="top">(9.66)</td>
<td align="center" valign="top">(11.15)</td>
<td align="center" valign="top">(10.22)</td>
<td align="center" valign="top">(10.19)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Government</italic></td>
<td/>
<td align="center" valign="top">&#x2212;0.0003</td>
<td align="center" valign="top">&#x2212;0.0028<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">&#x2212;0.0022<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">&#x2212;0.0025<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td/>
<td align="center" valign="top">(&#x2212;1.03)</td>
<td align="center" valign="top">(&#x2212;6.24)</td>
<td align="center" valign="top">(&#x2212;5.14)</td>
<td align="center" valign="top">(&#x2212;5.64)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Innovation</italic></td>
<td/>
<td/>
<td align="center" valign="top">0.0000<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.0000</td>
<td align="center" valign="top">0.0000</td>
</tr>
<tr>
<td/>
<td/>
<td/>
<td align="center" valign="top">(8.20)</td>
<td align="center" valign="top">(1.35)</td>
<td align="center" valign="top">(1.32)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Open</italic></td>
<td/>
<td/>
<td/>
<td align="center" valign="top">3.74e-08<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">3.89e-08<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td/>
<td/>
<td/>
<td align="center" valign="top">(8.13)</td>
<td align="center" valign="top">(8.45)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Tourism</italic></td>
<td/>
<td/>
<td/>
<td/>
<td align="center" valign="top">0.0000<sup>&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td/>
<td/>
<td/>
<td/>
<td align="center" valign="top">(2.68)</td>
</tr>
<tr>
<td align="left" valign="top">_cons</td>
<td align="center" valign="top">24.17<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">23.76<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">26.30<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">26.30<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">26.42<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(18.41)</td>
<td align="center" valign="top">(17.32)</td>
<td align="center" valign="top">(19.85)</td>
<td align="center" valign="top">(21.14)</td>
<td align="center" valign="top">(21.35)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>N</italic></td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">493</td>
</tr>
<tr>
<td align="left" valign="top"><italic>R</italic><sup>2</sup></td>
<td align="center" valign="top">0.34</td>
<td align="center" valign="top">0.34</td>
<td align="center" valign="top">0.42</td>
<td align="center" valign="top">0.49</td>
<td align="center" valign="top">0.49</td>
</tr>
<tr>
<td align="left" valign="top">Adj. <italic>R</italic><sup>2</sup></td>
<td align="center" valign="top">0.33</td>
<td align="center" valign="top">0.33</td>
<td align="center" valign="top">0.41</td>
<td align="center" valign="top">0.48</td>
<td align="center" valign="top">0.49</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p><italic>t</italic> statistics in parentheses.<sup>&#x002A;</sup> <italic>p</italic> &#x003C;&#x2009;0.1, <sup>&#x002A;&#x002A;</sup> <italic>p</italic> &#x003C;&#x2009;0.05, <sup>&#x002A;&#x002A;&#x002A;</sup> <italic>p</italic> &#x003C;&#x2009;0.01, One star shows 10% significance, two stars show 5% significance, and three stars show 1% significance.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec23">
<label>5.2.</label>
<title>Analysis of mediating effect results</title>
<p>This paper draws on <xref ref-type="bibr" rid="ref4">Baron and Kenny (1986)</xref> and <xref ref-type="bibr" rid="ref60">Wen et al. (2004)</xref> three-step method to analyse the intermediary effect empirically and find an indirect transmission mechanism between rural industrial convergence and farmers&#x2019; income. Urbanisation is the intermediary variable between the two, and the result is significant. The mediating effect test is divided into three steps: the first step, through the <italic>&#x03B2;<sub>1</sub></italic> coefficient in equation 1 to represent the total effect of rural industrial convergence on farmers&#x2019; income, is clear that the <italic>&#x03B2;<sub>1</sub></italic> coefficient is significantly positive. In the second stage, an empirical analysis was conducted to analyse the impact of rural industrial integration on urbanisation development according to <xref ref-type="disp-formula" rid="EQ2">Eq. 2</xref>. Model (6) shows that the variable Urban is significantly positive at 1%, indicating that rural industrial convergence is rising and urbanisation development is gradually accelerating. The third step is to test whether the results of rural industrial convergence (<italic>Industry</italic>) variables in Formula 3 are significant. Model (7) shows that the empirical results of rural industrial convergence (<italic>Industry</italic>) are significant, and the correlation coefficient decreases, which indicates that there is a partial mediating effect between urbanisation development (<italic>Urban</italic>) and rural industrial convergence (<italic>Industry</italic>). The Sobel test was carried out simultaneously for the validity of the above results. It was found that the Sobel test <italic>p</italic> value was 0.0004, the Z value was 3.485, and the p value of the test results was less than 0.001. In addition, the two significance tests of Goodman1 and Goodman2 also meet the requirements, which are significant at 1%. Alternatively, the proportion of mediating effect to total effect is 28.52%, and the empirical conclusion supports Hypothesis 2 (see <xref ref-type="table" rid="tab6">Table 6</xref>).</p>
<table-wrap position="float" id="tab6">
<label>Table 6</label>
<caption><p>Mediating effect test results.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="center" valign="top">Variables</th>
<th align="center" valign="top"><italic>Income</italic></th>
<th align="center" valign="top"><italic>Urban</italic></th>
<th align="center" valign="top"><italic>Income</italic></th>
</tr>
</thead>
<tbody>
<tr>
<td/>
<td align="center" valign="top"><bold>(5)</bold></td>
<td align="center" valign="top"><bold>(6)</bold></td>
<td align="center" valign="top"><bold>(7)</bold></td>
</tr>
<tr>
<td align="left" valign="top"><italic>Industry</italic></td>
<td align="center" valign="top">17.32<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.0597<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">12.38<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(10.19)</td>
<td align="center" valign="top">(3.50)</td>
<td align="center" valign="top">(12.85)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Government</italic></td>
<td align="center" valign="top">&#x2212;0.0025<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.0000</td>
<td align="center" valign="top">&#x2212;0.0025<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(&#x2212;5.64)</td>
<td align="center" valign="top">(0.09)</td>
<td align="center" valign="top">(&#x2212;10.22)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Innovation</italic></td>
<td align="center" valign="top">0.0000</td>
<td align="center" valign="top">&#x2212;0.0000<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.0000<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(1.32)</td>
<td align="center" valign="top">(&#x2212;2.78)</td>
<td align="center" valign="top">(6.42)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Open</italic></td>
<td align="center" valign="top">3.89e-08<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">4.29e-10<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">3.47e-09</td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(8.45)</td>
<td align="center" valign="top">(9.29)</td>
<td align="center" valign="top">(1.24)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Tourism</italic></td>
<td align="center" valign="top">0.0000<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.0000</td>
<td align="center" valign="top">0.0000<sup>&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(2.68)</td>
<td align="center" valign="top">(1.63)</td>
<td align="center" valign="top">(2.37)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Urban</italic></td>
<td/>
<td/>
<td align="center" valign="top">82.69<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td/>
<td/>
<td align="center" valign="top">(32.69)</td>
</tr>
<tr>
<td align="left" valign="top">_cons</td>
<td align="center" valign="top">26.42<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.448<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">&#x2212;10.65<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(21.35)</td>
<td align="center" valign="top">(36.14)</td>
<td align="center" valign="top">(&#x2212;8.02)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>N</italic></td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">493</td>
<td align="center" valign="top">493</td>
</tr>
<tr>
<td align="left" valign="top"><italic>R</italic><sup>2</sup></td>
<td align="center" valign="top">0.49</td>
<td align="center" valign="top">0.34</td>
<td align="center" valign="top">0.84</td>
</tr>
<tr>
<td align="left" valign="top">Adj. <italic>R</italic><sup>2</sup></td>
<td align="center" valign="top">0.49</td>
<td align="center" valign="top">0.33</td>
<td align="center" valign="top">0.84</td>
</tr>
<tr>
<td align="left" valign="top">Sobel test</td>
<td align="center" valign="top" colspan="3">0.0004<sup>&#x002A;&#x002A;&#x002A;</sup>(z&#x2009;=&#x2009;3.485)</td>
</tr>
<tr>
<td align="left" valign="top">Goodman test 1</td>
<td align="center" valign="top" colspan="3">0.0004<sup>&#x002A;&#x002A;&#x002A;</sup>(z&#x2009;=&#x2009;3.483)</td>
</tr>
<tr>
<td align="left" valign="top">Goodman test 2</td>
<td align="center" valign="top" colspan="3">0.0004<sup>&#x002A;&#x002A;&#x002A;</sup>(z&#x2009;=&#x2009;3.486)</td>
</tr>
<tr>
<td align="left" valign="top">Mediation effect coefficient</td>
<td align="center" valign="middle" colspan="3">0.0004<sup>&#x002A;&#x002A;&#x002A;</sup>(z&#x2009;=&#x2009;3.485)</td>
</tr>
<tr>
<td align="left" valign="top">Direct effect coefficient</td>
<td align="center" valign="top" colspan="3">0.0000<sup>&#x002A;&#x002A;&#x002A;</sup> (z&#x2009;=&#x2009;12.854)</td>
</tr>
<tr>
<td align="left" valign="top">Total effect coefficient</td>
<td align="center" valign="top" colspan="3">0.0000<sup>&#x002A;&#x002A;&#x002A;</sup> (z&#x2009;=&#x2009;10.190)</td>
</tr>
<tr>
<td align="left" valign="top">The proportion of the mediating effect</td>
<td align="center" valign="middle" colspan="3">0.2852</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p><italic>t</italic> statistics in parentheses.<sup>&#x002A;</sup> <italic>p</italic> &#x003C;&#x2009;0.1, <sup>&#x002A;&#x002A;</sup> <italic>p</italic> &#x003C;&#x2009;0.05, <sup>&#x002A;&#x002A;&#x002A;</sup> <italic>p</italic> &#x003C;&#x2009;0.01, One star shows 10% significance, two stars show 5% significance, and three stars show 1% significance.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec24">
<label>5.3.</label>
<title>Panel threshold effect analysis</title>
<p>Using the development degree of urbanisation as the threshold variable and the panel threshold regression method, this paper examines the internal relationship between rural industrial convergence and the increase in farmers&#x2019; income. It reveals the mechanism of rural industrial convergence on increasing peasant household income. To estimate all the parameters of the threshold model, the research should first test the number of thresholds and credibility. Firstly, the number of threshold values of the model is searched and determined, and the <italic>F</italic> value and p value of a single threshold and two thresholds are obtained, as shown in <xref ref-type="table" rid="tab7">Table 7</xref>. It can be seen from <xref ref-type="table" rid="tab7">Table 7</xref> that the single threshold is not significant, the double threshold effect is significant at the level of 10%, and the corresponding <italic>p</italic> values are 0.0940. Therefore, this paper selects the double threshold model for analysis.</p>
<table-wrap position="float" id="tab7">
<label>Table 7</label>
<caption><p>The result of the threshold effect test.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Threshold</th>
<th align="center" valign="top">RSS</th>
<th align="center" valign="top">MSE</th>
<th align="center" valign="top">Fstat</th>
<th align="center" valign="top">Prob</th>
<th align="center" valign="top">Crit10</th>
<th align="center" valign="top">Crit5</th>
<th align="center" valign="top">Crit1</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">Single</td>
<td align="center" valign="top">2626.6767</td>
<td align="center" valign="top">5.51821</td>
<td align="center" valign="top">35.77</td>
<td align="center" valign="top">0.1860</td>
<td align="center" valign="top">44.5128</td>
<td align="center" valign="top">52.8291</td>
<td align="center" valign="top">70.5220</td>
</tr>
<tr>
<td align="left" valign="top">Double</td>
<td align="center" valign="top">2451.4985</td>
<td align="center" valign="top">5.1502</td>
<td align="center" valign="top">34.01</td>
<td align="center" valign="top">0.0940</td>
<td align="center" valign="top">33.4835</td>
<td align="center" valign="top">38.2559</td>
<td align="center" valign="top">55.2367</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>To detect the authenticity of the threshold value, we construct a confidence interval to judge. This paper uses a double threshold estimate, and the result is inferred by a 95% confidence interval (as shown in <xref ref-type="table" rid="tab8">Table 8</xref>). The paper also uses likelihood ratio function graphs, such as <xref ref-type="fig" rid="fig1">Figures 1</xref>, <xref ref-type="fig" rid="fig2">2</xref>. Since there are two threshold values, it is a segmented display, which can help us understand the threshold value&#x2019;s estimation and the confidence interval&#x2019;s construction process. The estimated value of the threshold parameter refers to the value of &#x03B3; when the likelihood ratio test statistic L.R. = 0, which is 0.7960 (<xref ref-type="fig" rid="fig1">Figure 1</xref>) and 0.8500 (<xref ref-type="fig" rid="fig2">Figure 2</xref>) in the double threshold model of this study.</p>
<table-wrap position="float" id="tab8">
<label>Table 8</label>
<caption><p>Double threshold estimation results.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="middle">Threshold types</th>
<th align="center" valign="middle">Threshold</th>
<th align="center" valign="middle">95% Confidence interval</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">The first threshold</td>
<td align="center" valign="top">0.7960</td>
<td align="center" valign="top">(0.7761,0.8046)</td>
</tr>
<tr>
<td align="left" valign="top">The second threshold</td>
<td align="center" valign="top">0.8500</td>
<td align="center" valign="top">(0.8471,0.8593)</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig position="float" id="fig1">
<label>Figure 1</label>
<caption><p>Estimation of the first threshold and likelihood ratio function.</p></caption>
<graphic xlink:href="fsufs-07-1237844-g001.tif"/>
</fig>
<fig position="float" id="fig2">
<label>Figure 2</label>
<caption><p>Estimate of the second threshold and likelihood ratio function diagram.</p></caption>
<graphic xlink:href="fsufs-07-1237844-g002.tif"/>
</fig>
<p>From the threshold effect regression result in <xref ref-type="table" rid="tab9">Table 9</xref>, it can be seen that the impact of rural industrial convergence on farmers&#x2019; income changes in three intervals. Rural industrial convergence positively impacts farmers&#x2019; income growth by acting on urbanisation, which verifies hypothesis 3. According to the double threshold test value of urbanisation, rural industrial convergence&#x2019;s impact on farmers&#x2019; income growth is significantly positive when urbanisation is less than or equal to 0.7960 (Urban &#x2264;0.7960). For every point of growth in rural industrial convergence, farmers&#x2019; income will rise by 6.311 points; when the level of urbanisation is between 0.7960 and 0.8500 (0.7960&#x2009;&#x003C;&#x2009;<italic>Urban</italic>&#x2009;&#x2264;&#x2009;0.8500), the income of farmers will rise by 8.831 points for every increase in rural industrial convergence. Indeed, as the fundamental driving force to promote the development of urbanisation, the Industry creates opportunities for farmers&#x2019; employment through industrial agglomeration, industrial chain extension, and industrial multi-functional expansion (<xref ref-type="bibr" rid="ref71">Zhu and Zhang, 2022</xref>). The flow of farmers accelerates urbanisation construction, and at the same time, the disposable income of farmers increases. In addition, from Model (8), it can be seen that the influence coefficient of rural industrial convergence on farmers&#x2019; income increases first and then decreases. When the urbanisation level is between 0.7960 and 0.8500, the coefficient of rural industrial convergence affecting farmers&#x2019; income growth is the highest.</p>
<table-wrap position="float" id="tab9">
<label>Table 9</label>
<caption><p>Regression results of urbanization development threshold effect of rural Industrial convergence on farmers&#x2019; income.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="middle" rowspan="2">Variables</th>
<th align="center" valign="middle" colspan="2"><italic>Income</italic></th>
</tr>
<tr>
<th align="center" valign="middle" colspan="2">(8)</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle" rowspan="3"><italic>Industry</italic></td>
<td align="center" valign="middle"><italic>Urban</italic> &#x2264;&#x2009;0.7960</td>
<td align="center" valign="middle">6.311<sup>&#x002A;&#x002A;&#x002A;</sup> (0.748)</td>
</tr>
<tr>
<td align="center" valign="middle">0.7960&#x2009;&#x003C; <italic>Urban</italic> &#x2264;&#x2009;0.8500</td>
<td align="center" valign="middle">13.76<sup>&#x002A;&#x002A;&#x002A;</sup> (1.009)</td>
</tr>
<tr>
<td align="center" valign="middle"><italic>Urban</italic> &#x003E;&#x2009;0.8500</td>
<td align="center" valign="middle">8.831<sup>&#x002A;&#x002A;&#x002A;</sup> (0.815)</td>
</tr>
<tr>
<td align="left" valign="middle">Constant</td>
<td align="center" valign="middle" colspan="2">30.16&#x002A;&#x002A;&#x002A; (0.473)</td>
</tr>
<tr>
<td align="left" valign="top">Control variables</td>
<td align="center" valign="top" colspan="2">Controlled</td>
</tr>
<tr>
<td align="left" valign="top">Observations</td>
<td align="center" valign="top" colspan="2">493</td>
</tr>
<tr>
<td align="left" valign="top">Number of ids</td>
<td align="center" valign="top" colspan="2">29</td>
</tr>
<tr>
<td align="left" valign="top">R-squared</td>
<td align="center" valign="top" colspan="2">0.855</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>Standard errors are in parentheses. &#x002A;<italic>p</italic> &#x003C;&#x2009;0.1, &#x002A;&#x002A;<italic>p</italic> &#x003C;&#x2009;0.05, &#x002A;&#x002A;&#x002A;<italic>p</italic> &#x003C;&#x2009;0.01, One star shows 10% significance, two stars show 5% significance, and three stars show 1% significance.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec25">
<label>5.4.</label>
<title>Regional heterogeneity analysis</title>
<p>Based on the national and regional development strategy and the geographical location of each province, drawing on <xref ref-type="bibr" rid="ref47">Shen et al. (2021)</xref>, three groups of regional division criteria for eastern, central, and western<xref ref-type="fn" rid="fn0001"><sup>1</sup></xref>. This paper presents a comparative study of 29 provinces in eastern, central, and western China. As can be seen from models (9) to (11), the results of the impact of the integration of the &#x201C;three industries&#x201D; in rural areas on farmers&#x2019; income growth are significant at the 1% level in both the eastern and western regions. At the same time, they are significant at the 10% level in the central region. Among the three regions, the eastern region has the best result for the impact of the integration of rural &#x201C;three industries&#x201D; on farmers&#x2019; income, which is related to its good agricultural industry base; the western region ranks second, which mainly depends on the strong support from the Chinese government to the western region; the coefficient of the central region is relatively low, which indicates that there is still room for development in the impact of rural industrial convergence on farmers&#x2019; growth. Besides, the coefficient ranking of urbanisation development affecting farmers&#x2019; income growth is consistent with the coefficient ranking of the impact of rural industrial convergence. For the control variable, its impact on farmers&#x2019; income is not consistent in different models (see <xref ref-type="table" rid="tab10">Table 10</xref>).</p>
<table-wrap position="float" id="tab10">
<label>Table 10</label>
<caption><p>Regional heterogeneity regression results.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th/>
<th align="center" valign="middle" colspan="3"><italic>Income</italic></th>
</tr>
<tr>
<th align="left" valign="middle">Variables</th>
<th align="center" valign="middle">East</th>
<th align="center" valign="middle">West</th>
<th align="center" valign="middle">Central</th>
</tr>
</thead>
<tbody>
<tr>
<td/>
<td align="center" valign="top"><bold>(9)</bold></td>
<td align="center" valign="top"><bold>(10)</bold></td>
<td align="center" valign="top"><bold>(11)</bold></td>
</tr>
<tr>
<td align="left" valign="top"><italic>Industry</italic></td>
<td align="center" valign="top">16.80<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">10.80<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1.564<sup>&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(8.21)</td>
<td align="center" valign="top">(8.99)</td>
<td align="center" valign="top">(2.05)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Urban</italic></td>
<td align="center" valign="top">96.96<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">41.37<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">16.19<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(19.07)</td>
<td align="center" valign="top">(16.89)</td>
<td align="center" valign="top">(4.30)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Government</italic></td>
<td align="center" valign="top">&#x2212;0.0052<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">&#x2212;0.0010<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.0001</td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(&#x2212;7.28)</td>
<td align="center" valign="top">(&#x2212;2.89)</td>
<td align="center" valign="top">(0.29)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Innovation</italic></td>
<td align="center" valign="top">0.0001<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">&#x2212;0.0000<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.0000</td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(6.37)</td>
<td align="center" valign="top">(&#x2212;2.78)</td>
<td align="center" valign="top">(1.06)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Open</italic></td>
<td align="center" valign="top">3.16e-09</td>
<td align="center" valign="top">9.77e-08<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">2.33e-08</td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(0.63)</td>
<td align="center" valign="top">(8.23)</td>
<td align="center" valign="top">(0.84)</td>
</tr>
<tr>
<td align="left" valign="top">Tourism</td>
<td align="center" valign="top">0.0000</td>
<td align="center" valign="top">0.0000</td>
<td align="center" valign="top">0.0000</td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(1.03)</td>
<td align="center" valign="top">(0.38)</td>
<td align="center" valign="top">(0.68)</td>
</tr>
<tr>
<td align="left" valign="top">FE</td>
<td align="center" valign="top">Yes</td>
<td align="center" valign="top">Yes</td>
<td align="center" valign="top">Yes</td>
</tr>
<tr>
<td align="left" valign="top"><italic>N</italic></td>
<td align="center" valign="top">187</td>
<td align="center" valign="top">170</td>
<td align="center" valign="top">136</td>
</tr>
<tr>
<td align="left" valign="top"><italic>R</italic><sup>2</sup></td>
<td align="center" valign="top">0.80</td>
<td align="center" valign="top">0.94</td>
<td align="center" valign="top">0.90</td>
</tr>
<tr>
<td align="left" valign="top">Adj. <italic>R</italic><sup>2</sup></td>
<td align="center" valign="top">0.77</td>
<td align="center" valign="top">0.93</td>
<td align="center" valign="top">0.88</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p><italic>t</italic> statistics in parentheses. <sup>&#x002A;</sup><italic>p</italic> &#x003C;&#x2009;0.1, <sup>&#x002A;&#x002A;</sup><italic>p</italic> &#x003C;&#x2009;0.05, <sup>&#x002A;&#x002A;&#x002A;</sup><italic>p</italic> &#x003C;&#x2009;0.01, One star shows 10% significance, two stars show 5% significance, and three stars show 1% significance.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec26">
<label>5.5.</label>
<title>Robustness test</title>
<p>In the empirical robustness study, we use a model about the fixed effect of the relationship between industrial convergence and farmers&#x2019; income (as shown in <xref ref-type="table" rid="tab11">Table 11</xref>), as follows: First, it adjusts the sample size and deletes the municipalities to carry out the robustness test. Since Shanghai, Beijing, Chongqing, and Tianjin are municipalities directly under the central government, there are differences between urban volume and provinces. Thus, this paper directly excludes these four municipalities for regression. Model (12) shows that the impact of rural industrial convergence on farmers&#x2019; income is still significant. Second, The study is robust by lagging the explanatory variables one period; the lag of one explanatory variable, L.industry in the model (13), passes the significance test at the 1% level, and the coefficient is positive, close to the benchmark result. Third, robustness is measured by replacing control variables. In model (14), the degree of economic development (<italic>Economy</italic>), the degree of human capital (<italic>Capital</italic>), and foreign investment (<italic>FDI</italic>) are added. Through linear regression analysis of the explanatory variables, the regression coefficients are robust and remain significantly positive at the 1% level. In terms of the control variables, the level of G.D.P. <italic>per capita</italic> (<italic>Economy</italic>) has a significant effect on farmers&#x2019; income with a positive coefficient; the number of college students per 100 people (<italic>Capital</italic>) also has a significant effect on farmers&#x2019; income with a negative coefficient; The effect of foreign investment, i.e., total investment in foreign enterprises, on farmers&#x2019; income is significantly positive. The results of this study are robust through the above three methods.</p>
<table-wrap position="float" id="tab11">
<label>Table 11</label>
<caption><p>Robustness test results.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th/>
<th align="center" valign="middle" colspan="3"><italic>Income</italic></th>
</tr>
<tr>
<th align="left" valign="middle">Variables</th>
<th align="center" valign="middle">Delete municipalities</th>
<th align="center" valign="middle">Lag one phase explanatory variable</th>
<th align="center" valign="middle">Replace control variables</th>
</tr>
</thead>
<tbody>
<tr>
<td/>
<td align="center" valign="top"><bold>(12)</bold></td>
<td align="center" valign="top"><bold>(13)</bold></td>
<td align="center" valign="top"><bold>(14)</bold></td>
</tr>
<tr>
<td align="left" valign="top"><italic>Industry</italic></td>
<td align="center" valign="top">10.70<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td/>
<td align="center" valign="top">3.580<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(10.32)</td>
<td/>
<td align="center" valign="top">(4.86)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Urban</italic></td>
<td align="center" valign="top">63.91<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">89.03<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">23.97<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td align="center" valign="top">(13.35)</td>
<td align="center" valign="top">(27.66)</td>
<td align="center" valign="top">(4.61)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>Government</italic></td>
<td align="center" valign="top">&#x2212;0.0024<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">&#x2212;0.0020<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td/>
</tr>
<tr>
<td/>
<td align="center" valign="top">(&#x2212;6.72)</td>
<td align="center" valign="top">(&#x2212;5.47)</td>
<td/>
</tr>
<tr>
<td align="left" valign="top"><italic>Innovation</italic></td>
<td align="center" valign="top">0.0000<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.0000<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td/>
</tr>
<tr>
<td/>
<td align="center" valign="top">(9.60)</td>
<td align="center" valign="top">(6.07)</td>
<td/>
</tr>
<tr>
<td align="left" valign="top"><italic>Open</italic></td>
<td align="center" valign="top">&#x2212;5.66e-09</td>
<td align="center" valign="top">&#x2212;8.45e-10</td>
<td/>
</tr>
<tr>
<td/>
<td align="center" valign="top">(&#x2212;1.72)</td>
<td align="center" valign="top">(&#x2212;0.25)</td>
<td/>
</tr>
<tr>
<td align="left" valign="top"><italic>Tourism</italic></td>
<td align="center" valign="top">0.0000<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.0000<sup>&#x002A;&#x002A;</sup></td>
<td/>
</tr>
<tr>
<td/>
<td align="center" valign="top">(3.60)</td>
<td align="center" valign="top">(2.70)</td>
<td/>
</tr>
<tr>
<td align="left" valign="top"><italic>L.industry</italic></td>
<td/>
<td align="center" valign="top">11.40<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td/>
</tr>
<tr>
<td/>
<td/>
<td align="center" valign="top">(10.39)</td>
<td/>
</tr>
<tr>
<td align="left" valign="top"><italic>Economy</italic></td>
<td/>
<td/>
<td align="center" valign="top">0.109<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td/>
<td/>
<td align="center" valign="top">(15.10)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>lncapital</italic></td>
<td/>
<td/>
<td align="center" valign="top">&#x2212;2.955<sup>&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td/>
<td/>
<td align="center" valign="top">(&#x2212;2.82)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>lnfdi</italic></td>
<td/>
<td/>
<td align="center" valign="top">1.381<sup>&#x002A;&#x002A;&#x002A;</sup></td>
</tr>
<tr>
<td/>
<td/>
<td/>
<td align="center" valign="top">(4.15)</td>
</tr>
<tr>
<td align="left" valign="top">FE</td>
<td align="center" valign="top">Yes</td>
<td align="center" valign="top">Yes</td>
<td align="center" valign="top">Yes</td>
</tr>
<tr>
<td align="left" valign="top"><italic>N</italic></td>
<td align="center" valign="top">425</td>
<td align="center" valign="top">464</td>
<td align="center" valign="top">493</td>
</tr>
<tr>
<td align="left" valign="top"><italic>R</italic><sup>2</sup></td>
<td align="center" valign="top">0.77</td>
<td align="center" valign="top">0.84</td>
<td align="center" valign="top">0.90</td>
</tr>
<tr>
<td align="left" valign="top">Adj. <italic>R</italic><sup>2</sup></td>
<td align="center" valign="top">0.75</td>
<td align="center" valign="top">0.84</td>
<td align="center" valign="top">0.89</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p><italic>t</italic> statistics in parentheses. <sup>&#x002A;</sup><italic>p</italic> &#x003C;&#x2009;0.1, <sup>&#x002A;&#x002A;</sup><italic>p</italic> &#x003C;&#x2009;0.05, <sup>&#x002A;&#x002A;&#x002A;</sup><italic>p</italic> &#x003C;&#x2009;0.01, One star shows 10% significance, two stars show 5% significance, and three stars show 1% significance.</p>
</table-wrap-foot>
</table-wrap>
</sec>
</sec>
<sec id="sec27">
<label>6.</label>
<title>Conclusions and policy implications</title>
<sec id="sec28">
<label>6.1.</label>
<title>Conclusion</title>
<p>This study conducted empirical research on developing rural industrial integration in 29 provinces (municipals) in China from 2004 to 2020. Least squares, mediation models, and panel threshold models were used to investigate the intrinsic relationship between the development of rural industrial integration and urbanisation and farmers&#x2019; income growth. The research conclusions are: (1) Rural industrial convergence is essential to increase farmers&#x2019; income. In addition, the empirical results are still robust by deleting the samples of municipalities, lagging one-period explanatory variables, and replacing control variables. (2) The degree of urbanisation as an intermediary variable of rural industrial convergence development affecting farmers&#x2019; income increase indirectly promotes the growth of farmers&#x2019; income, and the intermediary effect is significant. (3) The level of rural industrial convergence development has a non-linear impact on farmers&#x2019; income. The degree of urbanisation development is the threshold variable and passes the double threshold test. The impact of rural industrial convergence development on farmers&#x2019; income increases first and then decreases. When the level of urbanisation is between 0.7960 and 0.8500, rural industrial convergence development has the highest impact on farmers&#x2019; income. (4) Rural industrial integration on the increase of farmers&#x2019; income has regional differences. The contribution of rural industrial integration to farmers&#x2019; income growth was significantly positive at the 1% level in both the eastern and western regions, with the highest coefficient of influence in the eastern region and the second highest in the western region. Provinces in the central region were significantly positive at the 10% level.</p>
</sec>
<sec id="sec29">
<label>6.2.</label>
<title>Policy implications</title>
<p>Based on the above research conclusions, it can get the following policy implications:</p>
<p>First, it&#x2019;s necessary to give full play to the advantages of rural industrial convergence to improve the income structure of farmers and provide sustainable development momentum for farmers&#x2019; income growth. One is that it should highlight the essential functions of agriculture, develop modern agriculture, and increase farmers&#x2019; operating income. Each region should develop a modern industrial system of agricultural products according to local conditions in combination with regional resource endowment differences, not only to ensure the adequate supply of agricultural products but also to avoid the homogenisation of agricultural industry development, form a reasonable layout of the agricultural industry and agricultural characteristic brand, and realise the steady increase of farmers&#x2019; operating income. The other is it should strengthen the function expansion of the secondary and tertiary industries of agriculture and broaden the wage income of farmers. Fine agricultural industry division of labour, extending the industrial chain through the rich agricultural production, processing, sales, circulation, and another modern agricultural support system, using rural cooperatives or leading agricultural enterprises and other organisations to radiate the leading role of non-agricultural jobs for farmers. Another is to improve the national financial support for agriculture and agricultural policies and increase farmers&#x2019; financial transfer payment income.</p>
<p>Second, it should use the advantages of &#x201C;city-industry convergence&#x201D; and take the opportunity of county urbanisation construction to provide new development impetus for farmers&#x2019; income increase. According to the National Bureau of Statistics of China&#x2019;s urbanization rate of 0.6522 in 2022, the impact of China&#x2019;s urbanization development level on farmers&#x2019; income growth has not yet reached the optimal level. At present, China&#x2019;s urbanization development strategy has shifted from the provincial level to the county level. Therefore, it is essential to strengthen the integrated development of county urbanisation and rural industry, guide the rational flow and effective convergence of urban and rural industrial resource elements, and establish a rural industrial development system with the county as the development centre. One of them is it should create a relaxed industrial development environment in the process of county urbanisation construction, break through the bottleneck of rural industrial convergence development, and create a good development environment for farmers&#x2019; income increase. The second one is it should resolve the dilemma of lagging transformation of rural industrial production and processing, resource and environmental constraints, financial and insurance support, and market channel development with new ideas, new methods, and new measures. Then, it needs to take the opportunity of <italic>in-situ</italic> urbanisation development in the county to provide farmers with more non-agricultural jobs and expand farmers&#x2019; income channels.</p>
<p>Third, it is essential to give full play to the advantages of industrial development in the eastern, central, and western regions and formulate diversified and differentiated policies for increasing farmers&#x2019; income. At first, It should learn from advanced model experience. The eastern region has a good industrial foundation and preferential regional development policies. The impact coefficient of rural industrial convergence on farmers&#x2019; income growth is the highest. So, summarising the typical experience of the impact of rural industrial convergence on farmers&#x2019; income growth in the eastern region provides a reference for the central and western regions. The second is to stimulate the development potential of the central region. Most of the agricultural provinces in the central region are innovative in the mechanism of rural industrial convergence in the central region, giving full play to the advantages of resource endowments in the central agricultural provinces, taking the road of convergence of the three industries in the agricultural provinces, and maximising the disposable income of rural residents. Lastly, it should use the advantages of the Western development policy to store the growth momentum of farmers&#x2019; income in the Western region.</p>
<p>Fourth, It is essential to rely on information technology to promote the convergence of rural industries and broaden the channels of increasing farmers&#x2019; income in any way. The rapid development of science and technology promotes the improvement of agricultural production efficiency and broadens the channels for the growth of farmers&#x2019; agricultural and non-agricultural income. Based on this, on the one hand, It should complete the construction of agricultural modernization as soon as possible with the help of information technology and increase farmers&#x2019; income through scale, organization and intensification; on the other hand, it should extend the agricultural chain using the communication function of information technology (such as live broadcast, small video, etc.), meanwhile making use of &#x2018;rural tourism +&#x2019; policy to expand the function of agricultural, and steadily increase farmers&#x2019; income.</p>
</sec>
</sec>
<sec sec-type="data-availability" id="sec30">
<title>Data availability statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec sec-type="author-contributions" id="sec31">
<title>Author contributions</title>
<p>YZ and JY: conceptualisation. JY: methodology and writing&#x2014;review and editing. JY and LC: software, formal analysis, resources, data curation, and writing&#x2014;original draft preparation. YZ and LC: supervision. All authors contributed to the article and approved the submitted version.</p>
</sec>
</body>
<back>
<sec sec-type="funding-information" id="sec32">
<title>Funding</title>
<p>This study is funded by the Excellent Youth Project of Scientific Research of the Hunan Provincial Education Department, grant number 22B1057.</p>
</sec>
<ack>
<p>I would like to express our gratitude to all those who helped us while writing this article.</p>
</ack>
<sec sec-type="COI-statement" id="sec33">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec id="sec100" sec-type="disclaimer">
<title>Publisher&#x2019;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>
</sec>
<fn-group>
<fn id="fn0001"><p><sup>1</sup>The eastern group includes Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Hainan; the central group includes Shanxi, Jilin, Heilongjiang, Henan, Hubei, Hunan, Anhui, Jiangxi; the western group includes Inner Mongolia, Chongqing, Sichuan, Guangxi, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia.</p></fn>
</fn-group>
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