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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.2025.1633290</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>Do agricultural services contribute to grain production? The heterogeneity analysis based on service categories and service sources</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Zhu</surname>
<given-names>Weijing</given-names>
</name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/3228169/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/resources/"/>
<role content-type="https://credit.niso.org/contributor-roles/software/"/>
<role content-type="https://credit.niso.org/contributor-roles/validation/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-review-editing/"/>
<role content-type="https://credit.niso.org/contributor-roles/visualization/"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Sun</surname>
<given-names>Xiaoyu</given-names>
</name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<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/3076003/overview"/>
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<role content-type="https://credit.niso.org/contributor-roles/writing-review-editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Qi</surname>
<given-names>Zhenhui</given-names>
</name>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
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<aff id="aff1"><sup>1</sup><institution>School of International Education, Wuhan Business University</institution>, <addr-line>Wuhan</addr-line>, <country>China</country></aff>
<aff id="aff2"><sup>2</sup><institution>Collage of Economics and Management, Hubei University of Technology</institution>, <addr-line>Wuhan</addr-line>, <country>China</country></aff>
<aff id="aff3"><sup>3</sup><institution>Research Center of Hubei Rural Social Management Innovation</institution>, <addr-line>Wuhan</addr-line>, <country>China</country></aff>
<aff id="aff4"><sup>4</sup><institution>Hontye Intelligence Land Technology Consulting Company Limited</institution>, <addr-line>Wuhan</addr-line>, <country>China</country></aff>
<author-notes>
<fn id="fn0001" fn-type="edited-by"><p>Edited by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1968011/overview">Muhammad Asad Ur Rehman Naseer</ext-link>, Bahauddin Zakariya University, Pakistan</p></fn>
<fn id="fn0002" fn-type="edited-by"><p>Reviewed by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1203918/overview">Xuetao Sun</ext-link>, Ocean University of China, China</p>
<p><ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3009336/overview">Guanqiu Yin</ext-link>, Shenyang Agricultural University, China</p></fn>
<corresp id="c001">&#x002A;Correspondence: Xiaoyu Sun, <email>20241097@hbut.edu.cn</email></corresp>
</author-notes>
<pub-date pub-type="epub">
<day>14</day>
<month>10</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>9</volume>
<elocation-id>1633290</elocation-id>
<history>
<date date-type="received">
<day>22</day>
<month>05</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>26</day>
<month>09</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x00A9; 2025 Zhu, Sun and Qi.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Zhu, Sun and Qi</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>
<sec id="sec1">
<title>Introduction</title>
<p>Agricultural services have a substitution effect on agricultural labor. But few studies have considered the impact of agricultural services on grain production from the perspective of heterogeneity in services categories and sources. Therefore, this study examines the impact of agricultural services on grain production in China and explores its heterogeneous effects.</p>
</sec>
<sec id="sec2">
<title>Methods</title>
<p>Utilizing data from the 2018 China Labor-force Dynamics Survey (CLDS2018), this study examines the impact of agricultural services on grain production through the PSM method. Secondly, robustness and endogeneity checks were conducted using IPWRA and IV-probit models, respectively. Finally, heterogeneity analysis was conducted on service categories and sources.</p>
</sec>
<sec id="sec3">
<title>Results</title>
<p>Agricultural services can contribute to grain production; the robustness and endogeneity tests also confirmed this finding. However, there are heterogeneous effects in the service categories and service sources. In detail, machinery service and technical service have positive effect on grain production except agricultural materials supply service. And the positive effect of agricultural services was significant when the supplier of the services is government or voluntary organizations.</p>
</sec>
<sec id="sec4">
<title>Discussion</title>
<p>Based on the above findings, promoting the development of service markets and establishing a favorable market environment will enhance the positive impact of agricultural services on grain production, thereby contributing to ensure food security in developing countries with millions of small households.</p>
</sec>
</abstract>
<kwd-group>
<kwd>food security</kwd>
<kwd>agricultural services</kwd>
<kwd>grain production</kwd>
<kwd>service categories</kwd>
<kwd>service sources</kwd>
</kwd-group>
<counts>
<fig-count count="3"/>
<table-count count="11"/>
<equation-count count="2"/>
<ref-count count="49"/>
<page-count count="13"/>
<word-count count="8560"/>
</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="sec5">
<label>1</label>
<title>Introduction</title>
<p>Food security is an important goal in achieving the United Nations 2030 Sustainable Development Goals. According to the latest issue of the State of Food Security and Nutrition in the World report, countries need to make great efforts and take immediate action to promote the transformation of the agricultural food system to realize the commitment to eradicate hunger by 2030. The safety and sustainable development of food supply all over the world has always been a concern (<xref ref-type="bibr" rid="ref15">Lambin and Meyfroidt, 2010</xref>). Since <xref ref-type="bibr" rid="ref3">Brown (1995)</xref> published <italic>Who Will Feed China?</italic> China&#x2019;s grain security has become a worldwide concern.</p>
<p>Grain production is a key link to ensure grain security. In 2024, China&#x2019;s total grain output reached 706.499 million tons, an increase of 1.6% over the previous year. It exceeded 700 million tons for the first time, on the basis of nine consecutive years of stabilization above 650 million tons.</p>
<p>There are numerous factors that affect the grain production, and the exiting studies focus on macro or micro level. At the macro level, the existing literatures focused on the impact of climate change (<xref ref-type="bibr" rid="ref17">Li et al., 2020</xref>; <xref ref-type="bibr" rid="ref11">Ha et al., 2021</xref>; <xref ref-type="bibr" rid="ref10">Feng et al., 2025</xref>), economic development (<xref ref-type="bibr" rid="ref38">Wang et al., 2025</xref>), urbanization (<xref ref-type="bibr" rid="ref36">Shen et al., 2024</xref>), land use change (<xref ref-type="bibr" rid="ref19">Liu et al., 2015</xref>; <xref ref-type="bibr" rid="ref20">Lu et al., 2024</xref>; <xref ref-type="bibr" rid="ref48">Zhou and Fu, 2025</xref>), and policy (<xref ref-type="bibr" rid="ref39">Wang et al., 2007</xref>; <xref ref-type="bibr" rid="ref21">Lu et al., 2013</xref>; <xref ref-type="bibr" rid="ref9001">Yi et al., 2015</xref>; <xref ref-type="bibr" rid="ref9">Fan et al., 2023</xref>) on grain production. At the micro level, the existing literatures focused on the impact of off-farm employment, land transfer and grain subsidy on rural household&#x2019;s grain production. Research has indicated that off-farm employment has been a dominant effect of farm exit (<xref ref-type="bibr" rid="ref45">Zhan et al., 2012</xref>), thus it can constrain the grain production (<xref ref-type="bibr" rid="ref25">McCarthy et al., 2009</xref>; <xref ref-type="bibr" rid="ref8">De Brauw, 2010</xref>). However, some literatures had demonstrated that off-farm employment did not significantly affect the grain production (<xref ref-type="bibr" rid="ref41">Wu and Meng, 1996</xref>). Because off-farm employment loosens the household budget constrain by remittances, which allows households to improve their agricultural productivity (<xref ref-type="bibr" rid="ref35">Rozelle et al., 1999</xref>). In addition, <xref ref-type="bibr" rid="ref43">Yang et al. (2020)</xref> found the effect of off-farm employment on grain production was non-liner, and it had an inverted-U relationship. At the same time, due to high land rents, farmers prefer planting crops and reducing grain production (<xref ref-type="bibr" rid="ref47">Zhao et al., 2017</xref>). Therefore, land transfer negatively affects grain production (<xref ref-type="bibr" rid="ref6">Chen et al., 2014</xref>; <xref ref-type="bibr" rid="ref27">Otsuka et al., 2016</xref>). In contrast, several studies have shown that land renting-in has positive effect on grain production (<xref ref-type="bibr" rid="ref18">Liu et al., 2018</xref>), especially when there is less labor available for agriculture (<xref ref-type="bibr" rid="ref30">Qiu et al., 2020</xref>).</p>
<p>In recent years, against the background of massive migration of agricultural labor and rising labor costs, agricultural services have a substitution effect on agricultural labor and alleviate agricultural labor constraints. Hence, another line of research has focused on the impact of agricultural services on grain production recently in China. Agricultural services have a positive impact on grain production area, and contribute to enhancing the production efficiency (<xref ref-type="bibr" rid="ref16">Li et al., 2024</xref>; <xref ref-type="bibr" rid="ref28">Qiao, 2020</xref>; <xref ref-type="bibr" rid="ref42">Xu et al., 2025</xref>). In other parts of Asia and Africa, agricultural services also have a significant impact on food production. In rural areas of Southeast Asia, agricultural services are widely utilized in grain production (<xref ref-type="bibr" rid="ref13">Justice and Biggs, 2020</xref>; <xref ref-type="bibr" rid="ref2">Belton et al., 2021</xref>). Agricultural machinery services significantly contribute to food security and farm incomes in Bangladesh (<xref ref-type="bibr" rid="ref26">Mottaleb et al., 2017</xref>). And agricultural services play an important role in raising farm incomes in South Africa (<xref ref-type="bibr" rid="ref1">Baiyegunhi et al., 2019</xref>).</p>
<p>A review of the relevant literature reveals that most studies focus on the economic impacts of agricultural services, such as their effects on production efficiency and farmer income, while fewer literatures explore the influence of agricultural services on farmers&#x2019; crop structure. Secondly, much of the literature emphasizes the impact of agricultural machinery services on agricultural production (<xref ref-type="bibr" rid="ref26">Mottaleb et al., 2017</xref>; <xref ref-type="bibr" rid="ref29">Qing et al., 2019</xref>; <xref ref-type="bibr" rid="ref5">Chaya et al., 2019</xref>; <xref ref-type="bibr" rid="ref32">Qiu et al., 2021a</xref>,<xref ref-type="bibr" rid="ref31">b</xref>,<xref ref-type="bibr" rid="ref33">c</xref>). However agricultural services represent a comprehensive services system encompassing various agricultural production processes, <xref ref-type="bibr" rid="ref37">Tang et al. (2018)</xref> clarified agricultural services into three phases and five categories: pre-production (agricultural materials supply services), medium-production (including financial services, technical services and machinery services) and post-production (processing and sales services). Furthermore, agricultural services also involve different service suppliers, such as agricultural enterprises, government services, agricultural universities, rural cooperatives, and agricultural specialists. In this study, agricultural services involve farmers delegating some or all of the agricultural production process to service suppliers, who then provide services to farmers on a fee-for-service basis. Due to data limitations, this article only focuses on three service categories (machinery services, technical services, and agricultural materials supply services) and three services sources (government, voluntary organizations, and agricultural enterprises). Except for <xref ref-type="bibr" rid="ref16">Li et al. (2024)</xref> and <xref ref-type="bibr" rid="ref33">Qiu et al. (2021c)</xref>, fewer studies have examined the impact of service categories heterogeneity. However, these literatures primarily focus on the heterogeneity of medium-production services (such as plowing, sowing, medicating, fertilizing, irrigation, harvesting services). The heterogeneous effects of agricultural services on crop structures from the perspectives of service categories and service sources is under-analyzed.</p>
<p>To fill the literature gap, in this study, we investigated two main research questions through empirical analysis: (1) Do agricultural services promote or inhibit the production of grain crops? (2) Can it be applied equally among the different service categories and the different service sources?</p>
<p>The answers to the above questions have important theoretical value and practical significance. The results of this research could serve to develop the agricultural services market, promote the grain production, and ensure China&#x2019;s longer-term food security. Our study also has important implications for developing countries with similar characteristics in agriculture to China.</p>
</sec>
<sec id="sec6">
<label>2</label>
<title>Background and theoretical framework</title>
<sec id="sec7">
<label>2.1</label>
<title>Background: grain crops vs. cash crops</title>
<p>To explore farmers&#x2019; crop choice decisions, it is necessary to analyze the characteristics of factor requirement for grain crops and cash crops. As shown in <xref ref-type="table" rid="tab1">Table 1</xref>.</p>
<table-wrap position="float" id="tab1">
<label>Table 1</label>
<caption><p>The characteristics of factor requirement for grain crops and cash crops.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Crop types</th>
<th align="center" valign="top">Labor requirements</th>
<th align="center" valign="top">Technology requirements</th>
<th align="center" valign="top">Mechanical operation difficulty</th>
<th align="center" valign="top">Probability of adopting agricultural services</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">Grain crops</td>
<td align="center" valign="top">Low</td>
<td align="center" valign="top">Low</td>
<td align="center" valign="top">Low</td>
<td align="center" valign="top">High</td>
</tr>
<tr>
<td align="left" valign="top">Cash crops</td>
<td align="center" valign="top">High</td>
<td align="center" valign="top">High</td>
<td align="center" valign="top">High</td>
<td align="center" valign="top">Low</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>Source(s): Author&#x2019;s own compilation.</p>
</table-wrap-foot>
</table-wrap>
<p>Firstly, the two crops have different requirements for labor. Rural China&#x2019;s agricultural production still heavily relies on labor input (<xref ref-type="bibr" rid="ref14">Kung, 2002</xref>). According to the National Agricultural Product Cost and Income Data Compilation, the average acreage of labor used was 4.44 for the three grain crops (rice, wheat, and maize) and 2.37 for soybeans. And the average acreage of labor used for peanuts, rapeseed and cotton was 7.62, 6.11 and 10.94, respectively. At the same time, there is a clear seasonality of labor inputs in food production. On the contrary, most cash crops have a relatively even demand for labor at different times of the year. This shows that cash crops have a much higher degree of labor demand than grain crops and are labor intensive.</p>
<p>Secondly, the two crops have different requirements of technology. Cash crops have a higher level of demand for technology and, conversely, grain crops have a lower level of demand for technology. As a result, grain crops are better suited to specialization.</p>
<p>Thirdly, there are differences in the difficulty of mechanical operations between the two crops. According to the data from China Agricultural Machinery Industry Yearbook, in 2023, the comprehensive mechanization rates of wheat, rice, and corn were 97.81, 88.03, and 91.67%, respectively. Conversely, the rates of rapeseed, potatoes, and peanuts were 67.80, 56.89, and 68.25%, respectively. That is to say, compares to cash crops, grains crops have lower difficulty in adopting mechanized operations.</p>
<p>As mentioned above, grain crops have lower requirements for labor and technology, and the difficulty of mechanical operations is relatively low. Due to the substitution effect of agricultural services on labor and technology, farmers who grow grain crops are more likely to adopt agricultural services. Cash crops, on the other hand, are characterized by high labor and high technology requirements, so farmers rarely adopt agricultural services in the production of cash crops.</p>
</sec>
<sec id="sec8">
<label>2.2</label>
<title>Theoretical framework</title>
<p>In the context of the massive migrant of rural labors, labor cost is one of the major factors driving up the agricultural production cost in China (<xref ref-type="bibr" rid="ref22">Luo, 2018</xref>). As a result, agricultural services are widely emerging in rural China. According to the China Rural Policy and Reform Statistics Annual Report 2020, the total number of agricultural service organizations was 955 thousand, an increase of 6.9% over the previous year, with a total service operating income of 166.36 billion yuan.</p>
<p>In the actual production process, as the basic unit of agricultural operation, farmers often analyze the feasibility and convenience of grain production according to the maximization of income and their own resource endowment. Cash crops offer high profit margins but require high-tech planting techniques, the lengthy growth cycle and a significant number of manual labor inputs at the early stages of production, which result in higher capital and time costs when purchasing agricultural services. In contrast, grain crops have relatively low labor and technology requirements, and agricultural machinery has a stronger substitution effect on labor (<xref ref-type="bibr" rid="ref46">Zhang et al., 2023</xref>). That is to say, the current grain cultivation has a more mature and perfect production technology and operational processes that facilitate large-scale batch operation of machinery (<xref ref-type="bibr" rid="ref49">Zhou et al., 2023</xref>). This is conducive to the services suppliers undertaking a wider range of grain growers in the production service business. Overall, as the market for agricultural services improves, grain crops can reduce the cost of production services through more concentrated labor hours and more labor substitution. Therefore, farmers who have a demand for agricultural services tend to choose grain crops with lower costs and risks and are more adaptable to the characteristics of service supply in order to realize their expected returns (<xref ref-type="bibr" rid="ref16">Li et al., 2024</xref>). Based on the above inference, the following hypothesis is put forward in this study:</p>
<disp-quote>
<p><italic>H1.</italic> Agricultural services promote the farmers&#x2019; grain production.</p>
</disp-quote>
<p>With the development of agricultural services market, the agricultural services had appeared throughout the whole process of grain production (<xref ref-type="bibr" rid="ref37">Tang et al., 2018</xref>). In the pre-production phase, it mainly includes agricultural materials supply service. In the medium-production phase, it mainly includes financial service, technical service (including irrigation, disease and pest control, and technical training), and machinery service (including ploughing, seeding, transplanting, and harvesting). And in the post-production phase, it mainly includes processing and sales service. There are also differences in the contribution of agricultural services to grain production for different service categories. Hence, this study put forward the following hypothesis:</p>
<disp-quote>
<p><italic>H2.</italic> The positive effect of agricultural services on grain production is heterogeneous across service categories.</p>
</disp-quote>
<p>Agricultural services have different suppliers for different categories of agricultural services. The government is the primary supplier of agricultural services, mainly providing public agricultural services. The agricultural materials companies, agricultural machinery companies, agricultural enterprises and rural credit cooperatives mainly provide commercial agricultural services. While farmer cooperatives, research institutes and agricultural technology service stations are organizations with dual quality of public and private interests, providing semi-public agricultural services.</p>
<p>Due to the characteristic of agricultural services, there are differences in the agricultural services provided by different supplier, which in turn lead to differences in the impact effects on grain production. Therefore, the following hypothesis was formulated:</p>
<disp-quote>
<p><italic>H3.</italic> The positive effect of agricultural services on grain production is heterogeneous across service sources.</p>
</disp-quote>
<p>The conceptual framework of this stated relationship is shown in <xref ref-type="fig" rid="fig1">Figure 1</xref>.</p>
<fig position="float" id="fig1">
<label>Figure 1</label>
<caption><p>Conceptual framework.</p></caption>
<graphic xlink:href="fsufs-09-1633290-g001.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">Flowchart illustrating the relationship between agricultural services and grain production. An arrow labeled H1 points from agricultural services to grain production. Above is a box labeled heterogeneity, including service categories and service sources, with arrows labeled H2 and H3 impacting the flow towards grain production.</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec sec-type="methods" id="sec9">
<label>3</label>
<title>Methodology</title>
<sec id="sec10">
<label>3.1</label>
<title>Data</title>
<p>This study draws data from the 2018 China Labor-Force Dynamics Survey (CLDS2018). The survey was conducted by the Centre for Social Science Survey at Sun Yat-Sen University, China. The CLDS dataset involves relatively rich information about households in China, including the basic structure of the family, economic condition, agricultural production, land use and other aspects. It has been recognized as one of the most nationally representative surveys in China. This paper focuses on studying the impact of the agricultural services on grain production. Furthermore, considering that there are numerous factors affecting the grain production, we also retained relevant variables such as individual characteristics, household characteristics and village characteristics. However, considering that not every household provided all the information on the above variables, we deleted the samples of farm households who did not participate in agricultural production, and we deleted the missing values of key variables, such as the agricultural services, farm size, and so on. In the end, we got a cross-sectional data of 4,011 farm households covering 214 villages in 26 provinces across the country.</p>
</sec>
<sec id="sec11">
<label>3.2</label>
<title>Variables and descriptive statistics</title>
<sec id="sec12">
<label>3.2.1</label>
<title>Dependent variable</title>
<p>Grain production. Following the previous literatures, we defined grain production as dummy variable (<xref ref-type="bibr" rid="ref44">Yi and Chen, 2010</xref>; <xref ref-type="bibr" rid="ref23">Luo et al., 2018</xref>). Specifically, the grain production variable takes the value of 1 if household planted the grain crops and 0 otherwise.</p>
</sec>
<sec id="sec13">
<label>3.2.2</label>
<title>Independent variable</title>
<p>Agricultural services. According to <xref ref-type="bibr" rid="ref12">Huan et al. (2022)</xref>, the agricultural services is a binary indicator, where the value of 1 signifies that the household adopted the agricultural services, and 0 otherwise.</p>
</sec>
<sec id="sec14">
<label>3.2.3</label>
<title>Control variables</title>
<p>According to the existing studies, our paper mainly controls for individual, household, and village characteristics, which are deemed to influence both agricultural services and grain production (<xref ref-type="bibr" rid="ref41">Wu and Meng, 1996</xref>; <xref ref-type="bibr" rid="ref30">Qiu et al., 2020</xref>; <xref ref-type="bibr" rid="ref43">Yang et al., 2020</xref>; <xref ref-type="bibr" rid="ref9">Fan et al., 2023</xref>). The detailed definitions of the variables are presented in <xref ref-type="table" rid="tab2">Table 2</xref>.</p>
<table-wrap position="float" id="tab2">
<label>Table 2</label>
<caption><p>Variable definition and descriptive statistics.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Variable</th>
<th align="left" valign="top">Definition</th>
<th align="center" valign="top">All samples (1)</th>
<th align="center" valign="top">Farmers adopted services(2)</th>
<th align="center" valign="top">Farmers did not adopt services (3)</th>
<th align="center" valign="top">Differences (2)&#x2013;(3)<break/>(4)</th>
<th align="center" valign="top">Test for Diff.&#x202F;=&#x202F;0 (5)</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" colspan="2">Dependent variable</td>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">Grain production</td>
<td align="left" valign="top">Whether to plant grain crops (1 if yes 0 otherwise)</td>
<td align="center" valign="top">0.860</td>
<td align="center" valign="top">0.887</td>
<td align="center" valign="top">0.802</td>
<td align="center" valign="top">0.085</td>
<td align="center" valign="top">&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top" colspan="7">Independent variable</td>
</tr>
<tr>
<td align="left" valign="top">Agricultural services</td>
<td align="left" valign="top">Whether to adopt agricultural services (1 if yes 0 otherwise)</td>
<td align="center" valign="top">0.686</td>
<td align="center" valign="top">&#x2014;</td>
<td align="center" valign="top">&#x2014;</td>
<td align="center" valign="top">&#x2014;</td>
<td align="center" valign="top">&#x2014;</td>
</tr>
<tr>
<td align="left" valign="top" colspan="7">Individual characteristics</td>
</tr>
<tr>
<td align="left" valign="top">Age</td>
<td align="left" valign="top">Age of the householder (year)</td>
<td align="center" valign="top">55.175</td>
<td align="center" valign="top">55.618</td>
<td align="center" valign="top">54.209</td>
<td align="center" valign="top">1.408</td>
<td align="center" valign="top">&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top">Education</td>
<td align="left" valign="top">Education of the householder (year)</td>
<td align="center" valign="top">7.105</td>
<td align="center" valign="top">7.226</td>
<td align="center" valign="top">6.842</td>
<td align="center" valign="top">0.384</td>
<td align="center" valign="top">&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top" colspan="7">Household characteristics</td>
</tr>
<tr>
<td align="left" valign="top">Agricultural labor</td>
<td align="left" valign="top">The proportion of family labor engaged in agricultural production</td>
<td align="center" valign="top">0.453</td>
<td align="center" valign="top">0.447</td>
<td align="center" valign="top">0.467</td>
<td align="center" valign="top">&#x2212;0.020</td>
<td align="center" valign="top">&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top">Pop. younger than 16</td>
<td align="left" valign="top">The proportion of the population younger than 16&#x202F;years old</td>
<td align="center" valign="top">0.128</td>
<td align="center" valign="top">0.126</td>
<td align="center" valign="top">0.132</td>
<td align="center" valign="top">&#x2212;0.006</td>
<td/>
</tr>
<tr>
<td align="left" valign="top">Pop. older than 70</td>
<td align="left" valign="top">The proportion of the population older than 70&#x202F;years old</td>
<td align="center" valign="top">0.077</td>
<td align="center" valign="top">0.081</td>
<td align="center" valign="top">0.069</td>
<td align="center" valign="top">0.012</td>
<td align="center" valign="top">&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top">Machine assets</td>
<td align="left" valign="top">The amount of the self-owned agricultural machines (piece)</td>
<td align="center" valign="top">0.244</td>
<td align="center" valign="top">0.248</td>
<td align="center" valign="top">0.236</td>
<td align="center" valign="top">0.012</td>
<td/>
</tr>
<tr>
<td align="left" valign="top">Farm size</td>
<td align="left" valign="top">The total area of land of the household (mu)</td>
<td align="center" valign="top">9.020</td>
<td align="center" valign="top">9.144</td>
<td align="center" valign="top">8.750</td>
<td align="center" valign="top">0.394</td>
<td/>
</tr>
<tr>
<td align="left" valign="top">Grain subsidy</td>
<td align="left" valign="top">Whether to receive grain subsidy (1 if yes 0 otherwise)</td>
<td align="center" valign="top">0.512</td>
<td align="center" valign="top">0.527</td>
<td align="center" valign="top">0.478</td>
<td align="center" valign="top">0.049</td>
<td align="center" valign="top">&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top" colspan="7">Village characteristics</td>
</tr>
<tr>
<td align="left" valign="top">Village economy</td>
<td align="left" valign="top">The per capita disposable annual income (thousand yuan)</td>
<td align="center" valign="top">10.730</td>
<td align="center" valign="top">11.341</td>
<td align="center" valign="top">9.397</td>
<td align="center" valign="top">1.944</td>
<td align="center" valign="top">&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top">Village landform</td>
<td align="left" valign="top">Whether the village is located on plain (1 if yes 0 otherwise)</td>
<td align="center" valign="top">0.461</td>
<td align="center" valign="top">0.512</td>
<td align="center" valign="top">0.351</td>
<td align="center" valign="top">0.161</td>
<td align="center" valign="top">&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top">Village location</td>
<td align="left" valign="top">The distance from the village to the nearest town (km)</td>
<td align="center" valign="top">5.924</td>
<td align="center" valign="top">5.300</td>
<td align="center" valign="top">7.285</td>
<td align="center" valign="top">&#x2212;1.985</td>
<td align="center" valign="top">&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top">Near a city</td>
<td align="left" valign="top">Whether the village is located on the suburb of a large or medium-sized city (1 if yes 0 otherwise)</td>
<td align="center" valign="top">0.054</td>
<td align="center" valign="top">0.068</td>
<td align="center" valign="top">0.024</td>
<td align="center" valign="top">0.044</td>
<td align="center" valign="top">&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top">Sample size (<italic>N</italic>)</td>
<td/>
<td align="center" valign="top">4,011</td>
<td align="center" valign="top">2,750</td>
<td align="center" valign="top">1,261</td>
<td align="center" valign="top">&#x2014;</td>
<td align="center" valign="top">&#x2014;</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>1mu&#x202F;=&#x202F;1/15 hectare. &#x002A;&#x002A;&#x002A;, &#x002A;&#x002A;, &#x002A; denote significance at 1% level, 5% level, and 10% level, respectively.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec15">
<label>3.2.4</label>
<title>Descriptive statistics</title>
<p><xref ref-type="table" rid="tab2">Table 2</xref> also shows the descriptive statistics stratified by the farms whether to adopted agricultural services. T-tests and chi-square tests are applied to assess whether difference between the farms who adopted agricultural services group and farms who did not adopt agricultural services group are statistically significant. On average, the 68% of farm households adopted the agricultural services. And our final samples consist of 2,750 farm households that adopted agricultural services and 1,261 farm households that did not adopt agricultural services. In addition, we also found that grain production, age, education, agricultural labor, Pop. older than 70, grain subsidy, village economy, village landform, village location, and near a city were significantly different between the two groups.</p>
</sec>
</sec>
<sec id="sec16">
<label>3.3</label>
<title>Estimation strategy</title>
<p>In order to accurately estimate the effect of agricultural services on the farmers&#x2019; grain production. Let <inline-formula><mml:math id="M1"><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup></mml:math></inline-formula> be the grain production of farmer <inline-formula><mml:math id="M2"><mml:mi>i</mml:mi></mml:math></inline-formula> if the farmer adopted the agricultural services (&#x201C;treated&#x201D;), and <inline-formula><mml:math id="M3"><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup></mml:math></inline-formula> the grain production of the same farmer <inline-formula><mml:math id="M4"><mml:mi>i</mml:mi></mml:math></inline-formula> if the farmer did not adopt the agricultural services (&#x201C;control&#x201D;). According to <xref ref-type="bibr" rid="ref34">Rosenbaum and Rubin (1983)</xref>, the treatment effect of adopting agricultural services can be simply defined as:</p>
<disp-formula id="EQ1"><label>(1)</label><mml:math id="M5"><mml:msub><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup></mml:math></disp-formula>
<p>In estimating <xref ref-type="disp-formula" rid="EQ1">Equation 1</xref>, a problem arises because we can observe either <inline-formula><mml:math id="M6"><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup></mml:math></inline-formula> or <inline-formula><mml:math id="M7"><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup></mml:math></inline-formula>, but not both of them for each individual farmer <inline-formula><mml:math id="M8"><mml:mi>i</mml:mi></mml:math></inline-formula> at the same time. This is a classical impact evaluation problem, which is also known as a missing data (counterfactual) problem.</p>
<p>Propensity score matching (PSM) was developed to address this missing data problem. In our case, having data from both farmers who adopted agricultural services (<inline-formula><mml:math id="M9"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math></inline-formula>) and farmers who did not adopt agricultural services (<inline-formula><mml:math id="M10"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math></inline-formula>) allows one to compute <inline-formula><mml:math id="M11"><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:math></inline-formula>, which can be easily decomposed into <inline-formula><mml:math id="M12"><mml:mi>E</mml:mi><mml:mo stretchy="true">[</mml:mo><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo stretchy="true">)</mml:mo><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">]</mml:mo></mml:math></inline-formula> and <inline-formula><mml:math id="M13"><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:math></inline-formula> by adding and subtracting a same term, <inline-formula><mml:math id="M14"><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:math></inline-formula>. The details see the <xref ref-type="disp-formula" rid="EQ2">Equation 2</xref>.</p>
<disp-formula id="EQ2"><label>(2)</label><mml:math id="M15"><mml:mtable displaystyle="true"><mml:mtr><mml:mtd><mml:msub><mml:mi>T</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo><mml:mo>+</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">[</mml:mo><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo><mml:mo stretchy="true">]</mml:mo><mml:mo>+</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>The term <inline-formula><mml:math id="M16"><mml:mi>E</mml:mi><mml:mo stretchy="true">[</mml:mo><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi>S</mml:mi></mml:msubsup><mml:mo>&#x2212;</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo stretchy="true">)</mml:mo><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">]</mml:mo></mml:math></inline-formula> is the average treatment effect on the treated (ATT), which is what we want. The other term, <inline-formula><mml:math id="M17"><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="true">)</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="true">(</mml:mo><mml:msubsup><mml:mi>Y</mml:mi><mml:mi>i</mml:mi><mml:mi mathvariant="italic">NS</mml:mi></mml:msubsup><mml:mo>&#x2223;</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="true">)</mml:mo></mml:math></inline-formula>, is the selection bias. Except for the case where the farmers who adopted agricultural services and the farmers who did not adopt agricultural services are assigned randomly, the selection bias is unlikely to be zero. The PSM method is developed to minimize the selection bias.</p>
<p>The basic idea of PSM method is to find a large group of farmers that did not adopt the agricultural services who are similar to the farmers that adopted the agricultural services in all relevant pre-treatment characteristics. And then match farmers who adopted agricultural services to farmers who did not adopt according to the propensity scores. In the present study, we adopted the kernel-based matching to calculate the ATT. And we used the IPWRA and IV-probit methods for robustness and endogeneity checks. In addition, the reliability of the matching estimates is largely dependent on the quality of matching. Both criteria will be checking in this paper.</p>
</sec>
</sec>
<sec sec-type="results" id="sec17">
<label>4</label>
<title>Results</title>
<sec id="sec18">
<label>4.1</label>
<title>Logit model on determinants of farmers&#x2019; agricultural services adoption</title>
<p>The determinants of farmers&#x2019; agricultural services adoption are estimated with a logit model to obtain the propensity scores used for matching. However, the multicollinearity problem makes it difficult to accurately estimate the model, especially in cross-sectional data. Hence, before the logit model, we test the variance inflation factor (VIF) of each explanatory variable. All the VIFs are less than 10, suggesting that the estimated model is free of any serious multicollinearity.</p>
<p>The logit model and marginal effect results are reported in <xref ref-type="table" rid="tab3">Table 3</xref>. On the individual level, the age and education of the householder were positively related to farmers&#x2019; agricultural services adoption at the 1% level. And for each unit increase in education and age, the probability of farmers adopting agricultural services increased by 0.3 and 0.7%, respectively.</p>
<table-wrap position="float" id="tab3">
<label>Table 3</label>
<caption><p>Logit model results of factors determining farmers&#x2019; agricultural services adoption.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" rowspan="3">Variable</th>
<th align="center" valign="top" colspan="4">Farmer&#x2019;s agricultural services adoption</th>
</tr>
<tr>
<th align="center" valign="top" colspan="2">Logit model</th>
<th align="center" valign="top" colspan="2">Marginal effect</th>
</tr>
<tr>
<th align="center" valign="top">Coefficient</th>
<th align="center" valign="top">SE</th>
<th align="center" valign="top">Coefficient</th>
<th align="center" valign="top">SE</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle" colspan="5">Individual characteristics</td>
</tr>
<tr>
<td align="left" valign="middle">Age</td>
<td align="center" valign="middle">0.013&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.003</td>
<td align="center" valign="middle">0.003&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.001</td>
</tr>
<tr>
<td align="left" valign="middle">Education</td>
<td align="center" valign="middle">0.035&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.011</td>
<td align="center" valign="middle">0.007&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.002</td>
</tr>
<tr>
<td align="left" valign="middle" colspan="5">Household characteristics</td>
</tr>
<tr>
<td align="left" valign="middle">Agricultural labor</td>
<td align="center" valign="middle">&#x2212;0.496&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.147</td>
<td align="center" valign="middle">&#x2212;0.100&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.029</td>
</tr>
<tr>
<td align="left" valign="middle">Pop. younger than 16</td>
<td align="center" valign="middle">&#x2212;0.330</td>
<td align="center" valign="middle">0.248</td>
<td align="center" valign="middle">&#x2212;0.066</td>
<td align="center" valign="middle">0.050</td>
</tr>
<tr>
<td align="left" valign="middle">Pop. older than 70</td>
<td align="center" valign="middle">0.251</td>
<td align="center" valign="middle">0.213</td>
<td align="center" valign="middle">0.051</td>
<td align="center" valign="middle">0.043</td>
</tr>
<tr>
<td align="left" valign="middle">Machine assets</td>
<td align="center" valign="middle">0.016</td>
<td align="center" valign="middle">0.071</td>
<td align="center" valign="middle">0.003</td>
<td align="center" valign="middle">0.014</td>
</tr>
<tr>
<td align="left" valign="middle">Farm size</td>
<td align="center" valign="middle">0.002</td>
<td align="center" valign="middle">0.002</td>
<td align="center" valign="middle">0.000</td>
<td align="center" valign="middle">0.000</td>
</tr>
<tr>
<td align="left" valign="middle">Grain subsidy</td>
<td align="center" valign="middle">0.136&#x002A;</td>
<td align="center" valign="middle">0.072</td>
<td align="center" valign="middle">0.027&#x002A;</td>
<td align="center" valign="middle">0.014</td>
</tr>
<tr>
<td align="left" valign="middle" colspan="5">Village characteristics</td>
</tr>
<tr>
<td align="left" valign="middle">Village economy</td>
<td align="center" valign="middle">0.012&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.004</td>
<td align="center" valign="middle">0.002&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.001</td>
</tr>
<tr>
<td align="left" valign="middle">Village landform</td>
<td align="center" valign="middle">0.550&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.074</td>
<td align="center" valign="middle">0.111&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.015</td>
</tr>
<tr>
<td align="left" valign="middle">Village location</td>
<td align="center" valign="middle">&#x2212;0.055&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.006</td>
<td align="center" valign="middle">&#x2212;0.011&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.001</td>
</tr>
<tr>
<td align="left" valign="middle">Near a city</td>
<td align="center" valign="middle">1.119&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.205</td>
<td align="center" valign="middle">0.225&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.041</td>
</tr>
<tr>
<td align="left" valign="middle">Constant</td>
<td align="center" valign="middle">&#x2212;0.071</td>
<td align="center" valign="middle">0.251</td>
<td align="center" valign="middle">&#x2014;</td>
<td align="center" valign="middle">&#x2014;</td>
</tr>
<tr>
<td align="left" valign="middle"><italic>N</italic></td>
<td align="center" valign="middle" colspan="2">4,011</td>
<td align="center" valign="middle" colspan="2">4,011</td>
</tr>
<tr>
<td align="left" valign="middle">Pseudo-<italic>R</italic><sup>2</sup></td>
<td align="center" valign="middle" colspan="2">0.054</td>
<td align="center" valign="middle" colspan="2">&#x2014;</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>&#x002A;&#x002A;&#x002A;, &#x002A;&#x002A;, &#x002A; denote significance at 1% level, 5% level, and 10% level, respectively.</p>
</table-wrap-foot>
</table-wrap>
<p>In terms of household characteristics, agricultural labor had negative effect on the farmers&#x2019; agricultural services adoption at the 1% level. And the probability of the agricultural services adoption decreased by 10% for each unit increased in agricultural labor. Grain subsidy had positive effect on the farmers&#x2019; agricultural services adoption at the 10% level. In other words, compared to household who do not receive grain subsidies, household who receive grain subsidies have a 2.7 percentage point higher probability of adopting agricultural services.</p>
<p>Regarding the village characteristics, the village economy, village landform and near a city had positive effects on adoption of agricultural services at the 1% level. For each unit increase in village economy, the probability of farmers adopting agricultural services increased by 0.2%. Farmers in the plain were 11.1% more likely to adopt agricultural services than farmers in non-plain areas. And farmers in suburban areas of large and medium-sized cities were 22.5% more likely to adopt agricultural services than farmers in non-suburban areas. Moreover, the village location had negative effect on the farmers&#x2019; agricultural services adoption at the 1% level. And the probability of the agricultural services adoption decreased by 1.1% for each unit increased in the distance from the village to the nearest town.</p>
</sec>
<sec id="sec19">
<label>4.2</label>
<title>Matching quality</title>
<p>Before we present the matching estimates on the effect of agricultural services on grain production, it is important to check the quality of the kernel-based matching.</p>
<p>Firstly, the distribution of predicted propensity scores shows a large common support of propensity scores between the farmers adopted agricultural services and farmers did not adopt agricultural services. As a result, only 22 observations off support in control group and 6 observations off support in treatment group, and all the 28 observations not in the common support region were excluded from the analysis (the details see the <xref ref-type="table" rid="tab4">Table 4</xref>). <xref ref-type="table" rid="tab4">Table 4</xref> shows a significant overlap between the two distributions with very few off-support observations, confirming high common support. This means that the common support assumption is satisfied.</p>
<table-wrap position="float" id="tab4">
<label>Table 4</label>
<caption><p>Matched observations in control group and treatment groups.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" rowspan="2">Treatment assignment</th>
<th align="center" valign="top" colspan="2">Common support</th>
<th align="center" valign="top" rowspan="2">Total</th>
</tr>
<tr>
<th align="center" valign="top">Off support</th>
<th align="center" valign="top">On support</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle">Control</td>
<td align="center" valign="middle">22</td>
<td align="center" valign="middle">1,229</td>
<td align="center" valign="middle">1,261</td>
</tr>
<tr>
<td align="left" valign="middle">Treated</td>
<td align="center" valign="middle">6</td>
<td align="center" valign="middle">2,744</td>
<td align="center" valign="middle">2,750</td>
</tr>
<tr>
<td align="left" valign="middle">Total</td>
<td align="center" valign="middle">28</td>
<td align="center" valign="middle">3,983</td>
<td align="center" valign="middle">4,011</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Secondly, the pseudo-R<sup>2</sup> and the mean bias were lower after matching than before. Before matching, the pseudo-R<sup>2</sup> and the mean bias were 0.054 and 13.4, respectively. But they were reduced after matching (0.005 and 4.0, respectively).</p>
<p>Finally, the PSM quality indicators before and after matching are reported in <xref ref-type="table" rid="tab5">Table 5</xref>. Except for the machine assets variable, the bias of all variables after matching decreased substantially. In addition, the variables including age, education, agricultural labor, Pop. older than 70, grain subsidy, and village location were significantly different at the 1% between the control group and treatment group before the matching, and all of them were insignificant after matching. Meanwhile, according to the <xref ref-type="app" rid="app1">Figure A1</xref>, the distribution of standardized deviations of each variable before matching was relatively discrete. However, after applying the kernel-based matching method, the standardized deviations of each variable were less than 10%, and most of them were near the 0 value, which shows a significant reduction compared with the pre-matching period.</p>
<table-wrap position="float" id="tab5">
<label>Table 5</label>
<caption><p>PSM quality indicators before and after matching.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" rowspan="2">Variable</th>
<th align="center" valign="top">Unmatched</th>
<th align="center" valign="top" colspan="2">Mean</th>
<th align="center" valign="top" rowspan="2">Bias (%)</th>
<th align="center" valign="top" rowspan="2">Bias reduction (%)</th>
<th align="center" valign="top" rowspan="2"><italic>t</italic>-test<break/><italic>p</italic>&#x202F;&#x003E;&#x202F;|t|</th>
</tr>
<tr>
<th align="center" valign="top">Matched</th>
<th align="center" valign="top">Treated</th>
<th align="center" valign="top">Control</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" rowspan="2">Age</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">55.618</td>
<td align="center" valign="top">54.209</td>
<td align="center" valign="top">12.6</td>
<td/>
<td align="center" valign="top">0.000&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">55.592</td>
<td align="center" valign="top">55.266</td>
<td align="center" valign="top">2.9</td>
<td align="center" valign="top">76.9</td>
<td align="center" valign="top">0.275</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Education</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">7.226</td>
<td align="center" valign="top">6.842</td>
<td align="center" valign="top">11.6</td>
<td/>
<td align="center" valign="top">0.001&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">7.221</td>
<td align="center" valign="top">7.300</td>
<td align="center" valign="top">&#x2212;2.4</td>
<td align="center" valign="top">79.5</td>
<td align="center" valign="top">0.374</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Agricultural labor</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">0.447</td>
<td align="center" valign="top">0.467</td>
<td align="center" valign="top">&#x2212;7.8</td>
<td/>
<td align="center" valign="top">0.022&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">0.447</td>
<td align="center" valign="top">0.457</td>
<td align="center" valign="top">&#x2212;3.6</td>
<td align="center" valign="top">53.7</td>
<td align="center" valign="top">0.182</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Pop. younger than 16</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">0.126</td>
<td align="center" valign="top">0.132</td>
<td align="center" valign="top">&#x2212;3.6</td>
<td/>
<td align="center" valign="top">0.285</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">0.126</td>
<td align="center" valign="top">0.126</td>
<td align="center" valign="top">0.2</td>
<td align="center" valign="top">93.3</td>
<td align="center" valign="top">0.927</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Pop. older than 70</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">0.081</td>
<td align="center" valign="top">0.069</td>
<td align="center" valign="top">6.9</td>
<td/>
<td align="center" valign="top">0.046&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">0.081</td>
<td align="center" valign="top">0.075</td>
<td align="center" valign="top">3.3</td>
<td align="center" valign="top">52.4</td>
<td align="center" valign="top">0.242</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Machine assets</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">0.248</td>
<td align="center" valign="top">0.236</td>
<td align="center" valign="top">2.3</td>
<td/>
<td align="center" valign="top">0.493</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">0.248</td>
<td align="center" valign="top">0.263</td>
<td align="center" valign="top">&#x2212;2.9</td>
<td align="center" valign="top">&#x2212;25.5</td>
<td align="center" valign="top">0.288</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Farm size</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">9.144</td>
<td align="center" valign="top">8.750</td>
<td align="center" valign="top">2.1</td>
<td/>
<td align="center" valign="top">0.563</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">9.152</td>
<td align="center" valign="top">9.476</td>
<td align="center" valign="top">&#x2212;1.7</td>
<td align="center" valign="top">17.8</td>
<td align="center" valign="top">0.544</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Grain subsidy</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">0.527</td>
<td align="center" valign="top">0.478</td>
<td align="center" valign="top">9.8</td>
<td/>
<td align="center" valign="top">0.004&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">0.527</td>
<td align="center" valign="top">0.542</td>
<td align="center" valign="top">&#x2212;3.1</td>
<td align="center" valign="top">68.2</td>
<td align="center" valign="top">0.249</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Village economy</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">11.341</td>
<td align="center" valign="top">9.397</td>
<td align="center" valign="top">15.0</td>
<td/>
<td align="center" valign="top">0.000&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">11.341</td>
<td align="center" valign="top">12.327</td>
<td align="center" valign="top">&#x2212;7.6</td>
<td align="center" valign="top">49.3</td>
<td align="center" valign="top">0.044&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Village landform</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">0.512</td>
<td align="center" valign="top">0.351</td>
<td align="center" valign="top">32.9</td>
<td/>
<td align="center" valign="top">0.000&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">0.511</td>
<td align="center" valign="top">0.536</td>
<td align="center" valign="top">&#x2212;5.0</td>
<td align="center" valign="top">84.6</td>
<td align="center" valign="top">0.067&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Village location</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">5.300</td>
<td align="center" valign="top">7.285</td>
<td align="center" valign="top">&#x2212;34.8</td>
<td/>
<td align="center" valign="top">0.000&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">5.308</td>
<td align="center" valign="top">5.396</td>
<td align="center" valign="top">&#x2212;1.6</td>
<td align="center" valign="top">95.5</td>
<td align="center" valign="top">0.469</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Near a city</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">0.068</td>
<td align="center" valign="top">0.024</td>
<td align="center" valign="top">21.2</td>
<td/>
<td align="center" valign="top">0.000&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">0.066</td>
<td align="center" valign="top">0.037</td>
<td align="center" valign="top">13.8</td>
<td align="center" valign="top">35.1</td>
<td align="center" valign="top">0.000&#x002A;&#x002A;&#x002A;</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>&#x002A;&#x002A;&#x002A;, &#x002A;&#x002A;, &#x002A; denote significance at 1% level, 5% level, and 10% level, respectively.</p>
</table-wrap-foot>
</table-wrap>
<p>Furthermore, <xref ref-type="fig" rid="fig2">Figure 2</xref> illustrates the kernel density functions of the treatment group and the control group based on pre- and post-matching of the two groups, respectively. The kernel density functions of the two groups were significantly different before matching. After matching, the kernel density functions of the two groups were a lot closer, indicating that the characteristics of the variables were similar in the two groups after matching. This means that there was no systematic difference between the treatment and control groups after matching, thus satisfying the balance test.</p>
<fig position="float" id="fig2">
<label>Figure 2</label>
<caption><p>Kernel density of the treatment and control groups.</p></caption>
<graphic xlink:href="fsufs-09-1633290-g002.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">Two density plots compare propensity scores for treated and control groups before and after matching. Before matching, the treated group is a solid line, while the control is a dashed line. After matching, both distributions align more closely, with both peaks around 0.5.</alt-text>
</graphic>
</fig>
<p>The overall evidence suggests that the matching process successfully achieved covariate balance by eliminating potential bias between the treatment groups and control groups arising from observed variables. Next, we estimate the treatment effect of agricultural services on grain production.</p>
</sec>
<sec id="sec20">
<label>4.3</label>
<title>Overall effect across propensity scores</title>
<p>The kernel-based matching method was used to estimate the effect of agricultural services on grain production (see <xref ref-type="table" rid="tab6">Table 6</xref>). The analysis based on the entire sample shows that agricultural services significantly increased farmers&#x2019; likelihood to plant grain crops in all respects. Specifically, agricultural services will contribute to increasing the probability of planting grain crops by about 4.8%. This indicates that agricultural services can contribute to grain production. Thus, the H1 was supported.</p>
<table-wrap position="float" id="tab6">
<label>Table 6</label>
<caption><p>The ATT of agricultural services on grain production.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" rowspan="2">Matching method</th>
<th align="center" valign="top" rowspan="2">Unmatched matched</th>
<th align="center" valign="top" colspan="2">Mean</th>
<th align="center" valign="top" rowspan="2">ATT</th>
<th align="center" valign="top" rowspan="2">S.E.</th>
<th align="center" valign="top" rowspan="2"><italic>T</italic> value</th>
</tr>
<tr>
<th align="center" valign="top">Treatment</th>
<th align="center" valign="top">Control</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" rowspan="2">Kernel-based matching</td>
<td align="center" valign="top">U</td>
<td align="center" valign="top">0.887</td>
<td align="center" valign="top">0.802</td>
<td align="center" valign="top">0.085&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="top">0.012</td>
<td align="center" valign="top">7.23</td>
</tr>
<tr>
<td align="center" valign="top">M</td>
<td align="center" valign="top">0.887</td>
<td align="center" valign="top">0.839</td>
<td align="center" valign="top">0.048&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="top">0.014</td>
<td align="center" valign="top">3.85</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>&#x002A;&#x002A;&#x002A;, &#x002A;&#x002A;, &#x002A; denote significance at 1% level, 5% level, and 10% level, respectively.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec21">
<label>4.4</label>
<title>Robustness and endogeneity checks</title>
<sec id="sec22">
<label>4.4.1</label>
<title>Robustness check</title>
<p>Robustness check is conducted by modifying the model specification. Drawing on existing studies (<xref ref-type="bibr" rid="ref24">Ma et al., 2024</xref>; <xref ref-type="bibr" rid="ref4">Cao et al., 2024</xref>), the PSM might omit certain samples, and it relies heavily on the assumption that the treatment model specification is appropriately specified and overlooks the correct specification of the outcome model. According to <xref ref-type="bibr" rid="ref40">Wooldridge (2003)</xref>, IPWRA estimates would be consistent even if the treatment or outcome were not specified correctly. Therefore, we employ the IPWRA estimator to check the robustness of the estimates obtained from the PSM, considering that it has a double-robust property that relaxes the strong assumption of the PSM model.</p>
<p>The IPWRA results estimating the treatment effects of agricultural services on grain production are presented in <xref ref-type="table" rid="tab7">Table 7</xref>. The potential-outcomes means (POMS) for farmers who adopted agricultural services and those who did not were 0.881 and 0.825, respectively, both of which were significant at the 1% level. The average treatment effect (ATE) of agricultural services on grain production was 0.056. Thus, households that adopted agricultural services had grain production of 5.6% higher than non-agricultural services. These results were consistent with the findings shown in <xref ref-type="table" rid="tab6">Table 6</xref>, thereby reinforcing the robustness of our conclusions.</p>
<table-wrap position="float" id="tab7">
<label>Table 7</label>
<caption><p>Impact of agricultural services on grain production: robustness check from the IPWRA estimates.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th/>
<th align="center" valign="top">POMS</th>
<th align="center" valign="top">ATE</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" rowspan="2">Agricultural services</td>
<td align="center" valign="top">0.881&#x002A;&#x002A;&#x002A;</td>
<td/>
</tr>
<tr>
<td align="center" valign="top">(0.006)</td>
<td align="center" valign="top">0.056&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Non-agricultural services</td>
<td align="center" valign="top">0.825&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="top">(0.014)</td>
</tr>
<tr>
<td align="center" valign="top">(0.012)</td>
<td/>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>&#x002A;&#x002A;&#x002A;, &#x002A;&#x002A;, &#x002A; denote significance at 1% level, 5% level, and 10% level, respectively; standard errors in parentheses.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec23">
<label>4.4.2</label>
<title>Endogeneity check</title>
<p>To address potential endogeneity concerns, we also used the IV-probit model to examine the effect of agricultural services on grain production. The instrumental variable must be strongly correlated with the adoption of agricultural services but must not directly influence the household&#x2019;s grain production. Consequently, the average number of agricultural services adopted by other farmers in the village was selected as the instrumental variable. A household&#x2019;s decision to adopt the agricultural services is likely to be affected by the agricultural services adopt status of their neighbors. But the mimicry on agricultural services is less likely to directly influence the household&#x2019;s decision to plant cash crops or grain crops. As shown in <xref ref-type="table" rid="tab8">Table 8</xref>, the first stage F-statistic was 456.08, well above the critical value of 10, thereby rejecting the hypothesis of weak instruments and confirming that selected instrumental variable effectively addressed endogeneity concerns. Additionally, the IV-Probit model successfully passed the Wald test, indicating that the instrumental variable was valid and the parameter estimates were reliable. The second-stage results showed that the coefficient for the effect of agricultural services on grain production was 0.322 (significant at the 1% level). This finding supported the argument that agricultural services contribute to grain production, thereby confirming the robustness of the study&#x2019;s conclusions.</p>
<table-wrap position="float" id="tab8">
<label>Table 8</label>
<caption><p>Instrumental variable estimation.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Variable</th>
<th align="center" valign="top">First stage: agricultural services</th>
<th align="center" valign="top">Second stage: grain production</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" rowspan="2">Agricultural services</td>
<td align="center" valign="top">-</td>
<td align="center" valign="top">0.322&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">-</td>
<td align="center" valign="top">(0.084)</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Instrumental variable</td>
<td align="center" valign="top">0.322&#x002A;&#x002A;&#x002A;</td>
<td/>
</tr>
<tr>
<td align="center" valign="top">(0.004)</td>
<td/>
</tr>
<tr>
<td align="left" valign="top">Individual characteristics</td>
<td align="center" valign="top">Yes</td>
<td align="center" valign="top">Yes</td>
</tr>
<tr>
<td align="left" valign="top">Household characteristics</td>
<td align="center" valign="top">Yes</td>
<td align="center" valign="top">Yes</td>
</tr>
<tr>
<td align="left" valign="top">Village characteristics</td>
<td align="center" valign="top">Yes</td>
<td align="center" valign="top">Yes</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="2">Constant</td>
<td align="center" valign="top">0.259&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="top">0.781&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="center" valign="top">(0.034)</td>
<td align="center" valign="top">(0.200)</td>
</tr>
<tr>
<td align="left" valign="top"><italic>F</italic>-statistic</td>
<td align="center" valign="top" colspan="2">456.08</td>
</tr>
<tr>
<td align="left" valign="top">Wald test</td>
<td align="center" valign="top" colspan="2">14.86&#x002A;&#x002A;&#x002A;</td>
</tr>
<tr>
<td align="left" valign="top">Observations</td>
<td align="center" valign="top">4,007</td>
<td align="center" valign="top">4,007</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>&#x002A;&#x002A;&#x002A;, &#x002A;&#x002A;, &#x002A; denote significance at 1% level, 5% level, and 10% level, respectively; standard errors in parentheses.</p>
</table-wrap-foot>
</table-wrap>
</sec>
</sec>
<sec id="sec24">
<label>4.5</label>
<title>Heterogeneity analysis</title>
<sec id="sec25">
<label>4.5.1</label>
<title>Heterogenous effects across the service categories</title>
<p>The definition of agricultural services in <xref ref-type="table" rid="tab2">Table 2</xref> was whether to adopt agricultural services. This definition may omit some important information about the different services contents. According to <xref ref-type="bibr" rid="ref37">Tang et al. (2018)</xref>, we clarified agricultural services into three categories: machinery services, technical services, and agricultural materials supply services. Specifically, the contents of machinery services include machinery ploughing, sowing, and harvesting. The contents of technical services include irrigation, disease, and pest control. And the contents of agricultural materials supply services include supply of seeds (seedlings), chemical fertilizers, pesticides, and agricultural films. Consequently, following the PSM model, we re-estimate the impact of agricultural services on grain production by separating the machinery, technical, and agricultural materials supply services. The results are presented in <xref ref-type="table" rid="tab9">Table 9</xref>.</p>
<table-wrap position="float" id="tab9">
<label>Table 9</label>
<caption><p>Heterogenous effects across the service categories (Kernel-based matching).</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Service categories</th>
<th align="center" valign="top">Treatment</th>
<th align="center" valign="top">Control</th>
<th align="center" valign="top">ATT</th>
<th align="center" valign="top">S.E.</th>
<th align="center" valign="top"><italic>T</italic> value</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle" colspan="6">Machinery services vs. non-agricultural services (<italic>N</italic>&#x202F;=&#x202F;2,837)</td>
</tr>
<tr>
<td align="left" valign="middle">Unmatched</td>
<td align="center" valign="middle">0.911</td>
<td align="center" valign="middle">0.802</td>
<td align="center" valign="middle">0.109&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.013</td>
<td align="center" valign="middle">8.45</td>
</tr>
<tr>
<td align="left" valign="middle">Matched</td>
<td align="center" valign="middle">0.910</td>
<td align="center" valign="middle">0.850</td>
<td align="center" valign="middle">0.061&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.018</td>
<td align="center" valign="middle">3.45</td>
</tr>
<tr>
<td align="left" valign="middle" colspan="6">Technical services vs. non-agricultural services (<italic>N</italic>&#x202F;=&#x202F;3,652)</td>
</tr>
<tr>
<td align="left" valign="middle">Unmatched</td>
<td align="center" valign="middle">0.880</td>
<td align="center" valign="middle">0.802</td>
<td align="center" valign="middle">0.079&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.012</td>
<td align="center" valign="middle">6.42</td>
</tr>
<tr>
<td align="left" valign="middle">Matched</td>
<td align="center" valign="middle">0.880</td>
<td align="center" valign="middle">0.836</td>
<td align="center" valign="middle">0.044&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.015</td>
<td align="center" valign="middle">2.95</td>
</tr>
<tr>
<td align="left" valign="middle" colspan="6">Agricultural materials supply services vs. non-agricultural services (<italic>N</italic>&#x202F;=&#x202F;1,573)</td>
</tr>
<tr>
<td align="left" valign="middle">Unmatched</td>
<td align="center" valign="middle">0.875</td>
<td align="center" valign="middle">0.802</td>
<td align="center" valign="middle">0.073&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.024</td>
<td align="center" valign="middle">3.00</td>
</tr>
<tr>
<td align="left" valign="middle">Matched</td>
<td align="center" valign="middle">0.875</td>
<td align="center" valign="middle">0.887</td>
<td align="center" valign="middle">&#x2212;0.012</td>
<td align="center" valign="middle">0.023</td>
<td align="center" valign="middle">&#x2212;0.52</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>&#x002A;&#x002A;&#x002A;, &#x002A;&#x002A;, &#x002A; denote significance at 1% level, 5% level, and 10% level, respectively.</p>
</table-wrap-foot>
</table-wrap>
<p>After matching, machinery services and technical services were statistically significant at the 1% level and had a positive impact on grain crops plantation. The contribution effect of machinery services to grain production was 6.1%. The contribution effect of technical services to grain production was 4.4%, slightly smaller than the contribution effect of machinery services. However, agricultural materials supply services had not a significantly impact on grain production. Thus, the H2 was supported. Furthermore, we applied IPWRA to examine the heterogenous effects across the services categories (see <xref ref-type="app" rid="app1">Table A1</xref>). The estimation results of IPWRA showed that agricultural machinery services had the greatest promoting effect on grain production, followed by technical services, and the agricultural materials supply services was not significant. These results were consistent with the findings shown in <xref ref-type="table" rid="tab9">Table 9</xref>, thereby reinforcing the robustness of our conclusions.</p>
</sec>
<sec id="sec26">
<label>4.5.2</label>
<title>Heterogenous effects across the service sources</title>
<p>Regarding the sources of agricultural services, we clarified the supplier of agricultural services into three categories: government, voluntary organizations (including research institutions, higher education institutions and so on), and agricultural enterprises. Following the PSM model, we re-estimate the impact of agricultural services on grain production by separating the contributions of government, voluntary organizations, and agricultural enterprises. The results are presented in <xref ref-type="table" rid="tab10">Table 10</xref>.</p>
<table-wrap position="float" id="tab10">
<label>Table 10</label>
<caption><p>Heterogenous effects across the service sources (Kernel-based matching).</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Service sources</th>
<th align="center" valign="top">Treatment</th>
<th align="center" valign="top">Control</th>
<th align="center" valign="top">ATT</th>
<th align="center" valign="top">S.E.</th>
<th align="center" valign="top"><italic>T</italic> value</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle" colspan="6">Government vs. Non-agricultural services (<italic>N</italic>&#x202F;=&#x202F;3,528)</td>
</tr>
<tr>
<td align="left" valign="middle">Unmatched</td>
<td align="center" valign="middle">0.875</td>
<td align="center" valign="middle">0.802</td>
<td align="center" valign="middle">0.073&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.013</td>
<td align="center" valign="middle">5.86</td>
</tr>
<tr>
<td align="left" valign="middle">Matched</td>
<td align="center" valign="middle">0.875</td>
<td align="center" valign="middle">0.834</td>
<td align="center" valign="middle">0.041&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.015</td>
<td align="center" valign="middle">2.82</td>
</tr>
<tr>
<td align="left" valign="middle" colspan="6">Voluntary organizations vs. non-agricultural services (<italic>N</italic>&#x202F;=&#x202F;1,448)</td>
</tr>
<tr>
<td align="left" valign="middle">Unmatched</td>
<td align="center" valign="middle">0.893</td>
<td align="center" valign="middle">0.802</td>
<td align="center" valign="middle">0.091&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.030</td>
<td align="center" valign="middle">3.00</td>
</tr>
<tr>
<td align="left" valign="middle">Matched</td>
<td align="center" valign="middle">0.897</td>
<td align="center" valign="middle">0.829</td>
<td align="center" valign="middle">0.068&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.032</td>
<td align="center" valign="middle">2.11</td>
</tr>
<tr>
<td align="left" valign="middle" colspan="6">Agricultural enterprises vs. non-agricultural services (<italic>N</italic>&#x202F;=&#x202F;1,496)</td>
</tr>
<tr>
<td align="left" valign="middle">Unmatched</td>
<td align="center" valign="middle">0.860</td>
<td align="center" valign="middle">0.802</td>
<td align="center" valign="middle">0.058&#x002A;&#x002A;</td>
<td align="center" valign="middle">0.028</td>
<td align="center" valign="middle">2.08</td>
</tr>
<tr>
<td align="left" valign="middle">Matched</td>
<td align="center" valign="middle">0.858</td>
<td align="center" valign="middle">0.855</td>
<td align="center" valign="middle">0.003</td>
<td align="center" valign="middle">0.028</td>
<td align="center" valign="middle">0.12</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>&#x002A;&#x002A;&#x002A;, &#x002A;&#x002A;, &#x002A; denote significance at 1% level, 5% level, and 10% level, respectively.</p>
</table-wrap-foot>
</table-wrap>
<p>When the primary supplier of agricultural services was government, the positive effect of agricultural services on grain production was 0.041. Meanwhile, the effect of agricultural services on grain production was 0.068 when the primary supplier of agricultural services was voluntary organizations. And there are statistically significant at the 1 and 5% level, respectively. However, when the primary supplier was agricultural enterprises, the effect of agricultural services was insignificant. The reasons why it was not significant are: agricultural services market suffer from the market failures. More specifically, some agricultural services in the market have the attributes of public goods. And the agricultural services provided by agricultural enterprises do not cover all the phases of agricultural production (including pre-production, medium-production, and post-production). It thus has a limited effect on grain production. Thus, the H3 was supported. Combining the three primary suppliers mentioned above, agricultural services provided by voluntary organizations had the greatest positive effect on grain production, following by the government, and the impact effect generated by agricultural enterprises was not significant. Similarly, we applied IPWRA to examine the heterogenous effects across the services sources (see <xref ref-type="app" rid="app1">Table A1</xref>). These findings were consistent with the results shown in <xref ref-type="table" rid="tab10">Table 10</xref>, thereby confirming the robustness of the study&#x2019;s conclusions.</p>
</sec>
</sec>
</sec>
<sec id="sec27">
<label>5</label>
<title>Conclusion and policy implications</title>
<p>This study applied the PSM method to examine the effect of agricultural services on grain production. The empirical results proved that agricultural services have positive effect on grain production. Robustness test and endogeneity check also confirmed this finding. Furthermore, this study presented the heterogenous analysis of the positive effect of agricultural services based on the service categories and service sources. The results clearly indicated that machinery service and technical service have positive effect on grain production except agricultural materials supply service. The positive effect of agricultural services was significant when the supplier of the services is government or voluntary organizations.</p>
<p>Several policy implications emerge from this study. First, to ensure food security, policymakers could focus on the agricultural services&#x2019; positive effect on the grain production. Municipalities should facilitate the growth of the agricultural services market and make timely adjustments to the cultivation structure in order to ensure food security via policy mechanisms. Policies to maximize the favorable effects of the agricultural service market on grain cultivation. Concurrently, prioritize the farmers in agricultural services guidance and publicity, ensure that they are the primary force behind all types of new agricultural management, and fortify their favorable attitude toward agricultural services. Second, consider the positive impact of agricultural services on grain production, it is imperative that policymakers establish a favorable market environment for the majority of agricultural services. Optimize pertinent policies and regulations, augment production subsidies for diverse service organizations, enhance and compensate for the deficiencies of each service provision link. Encourage diverse service organizations to provide an agricultural service model with a wider range of services and more comprehensive coverage. Additionally, strengthening market oversight is crucial to prevent opportunistic behavior and ensure continuous improvements in service quality and effectiveness.</p>
<p>This study has important implications for China&#x2019;s food security. The findings of this study can deepen the understanding of relationship between agricultural services and grain production. Agricultural services contribute to grain production, which is an important path for the developing countries to accelerate the realization of agricultural modernization and improve agricultural production efficiency, and also has a positive impact on the China&#x2019;s food security. Secondly, the results of this study also have implications for other developing countries, especially those with millions of small households. Based on this study, developing countries with millions of small households, such as India and some African countries, might need to encourage the development of agricultural services, and thereby promote grain production and ensure national food security. Meanwhile, the heterogeneous effects of agricultural services on food production indicate that developing countries should, based on their own resource endowments and industrial structures, actively develop diverse agricultural services and cultivate a multi-principal service supplier.</p>
<p>However, several aspects warrant further improvement. Firstly, this study is based on cross-sectional data from 2018, whereas smallholder farmers&#x2019; participation in agricultural services is dynamic. Future research should incorporate long-term tracking of smallholder farmers and consider various factors such as policy changes and technological advancements to yield more scientific, rigorous, dan accurate results. Secondly, agricultural services encompass a wide range of services across pre-production, medium-production, and post-production stages. Due to the data limitations, this study primarily focuses on the impact of pre-production and medium-production services on grain production, it does not address the effect of post-production services.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="sec28">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="sec29">
<title>Author contributions</title>
<p>WZ: Conceptualization, Data curation, Formal analysis, Methodology, Resources, Software, Validation, Writing &#x2013; original draft, Writing &#x2013; review &#x0026; editing, Visualization. XS: Conceptualization, Funding acquisition, Supervision, Writing &#x2013; original draft, Writing &#x2013; review &#x0026; editing. ZQ: Methodology, Software, Visualization, Writing &#x2013; review &#x0026; editing.</p>
</sec>
<sec sec-type="funding-information" id="sec30">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article. This research was supported by the National Natural Science Foundation of China (71904150), and the Hubei University of Technology Doctoral Research Initiation Foundation (XJ2024004702).</p>
</sec>
<sec sec-type="COI-statement" id="sec31">
<title>Conflict of interest</title>
<p>ZQ was employed by the Hontye Intelligence Land Technology Consulting Company Limited.</p>
<p>The remaining 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 sec-type="ai-statement" id="sec32">
<title>Generative AI statement</title>
<p>The authors declare that no Gen AI was used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
</sec>
<sec sec-type="disclaimer" id="sec33">
<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>
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</ref-list>
<app-group>
<app id="app1">
<title>Appendix</title>
<table-wrap position="float" id="tab11">
<label>Table A1</label>
<caption><p>Heterogenous effects based on IPWRA estimates.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th rowspan="2"/>
<th align="center" valign="top" colspan="3">Heterogenous effects across the service categories</th>
</tr>
<tr>
<th align="center" valign="top">Machinery services</th>
<th align="center" valign="top">Technical services</th>
<th align="center" valign="top">Agricultural materials supply services</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" rowspan="2">ATE</td>
<td align="center" valign="top">0.079&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="top">0.053&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="top">&#x2212;0.007</td>
</tr>
<tr>
<td align="center" valign="top">(0.016)</td>
<td align="center" valign="top">(0.015)</td>
<td align="center" valign="top">(0.021)</td>
</tr>
</tbody>
</table>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th rowspan="2"/>
<th align="center" valign="top" colspan="3">Heterogenous effects across the service sources</th>
</tr>
<tr>
<th align="center" valign="top">Government</th>
<th align="center" valign="top">Voluntary organizations</th>
<th align="center" valign="top">Agricultural enterprise</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" rowspan="2">ATE</td>
<td align="center" valign="top">0.047&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="top">0.104&#x002A;&#x002A;&#x002A;</td>
<td align="center" valign="top">0.022</td>
</tr>
<tr>
<td align="center" valign="top">(0.014)</td>
<td align="center" valign="top">(0.034)</td>
<td align="center" valign="top">(0.028)</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig position="float" id="fig3">
<label>Figure A1</label>
<caption><p>Standardized % bias across covariates.</p></caption>
<graphic xlink:href="fsufs-09-1633290-g003.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">Dot and cross plot showing standardized percentage bias across covariates. Variables like "Village landform," "Near a city," and "Age" are plotted on the y-axis. Bias ranges from negative forty to forty on the x-axis. Unmatched biases are marked by dots, and matched by crosses. Most unmatched biases are higher than matched ones.</alt-text>
</graphic>
</fig>
</app>
</app-group>
</back>
</article>