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<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Ecol. Evol.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Ecology and Evolution</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Ecol. Evol.</abbrev-journal-title>
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<issn pub-type="epub">2296-701X</issn>
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<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-meta>
<article-id pub-id-type="doi">10.3389/fevo.2026.1753076</article-id>
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<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Promote or inhibit: how climate policy uncertainty may shape extreme weather&#x2019;s impact on grain production</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Zhang</surname><given-names>Xiaojun</given-names></name>
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<name><surname>Zhang</surname><given-names>Ming</given-names></name>
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<name><surname>Shi</surname><given-names>Ziyi</given-names></name>
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<contrib contrib-type="author" corresp="yes">
<name><surname>Luo</surname><given-names>Yixuan</given-names></name>
<xref ref-type="corresp" rid="c001"><sup>*</sup></xref>
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<aff id="aff1"><institution>School of Economics and Management, Fuzhou University</institution>, <city>Fuzhou</city>,&#xa0;<country country="cn">China</country></aff>
<author-notes>
<corresp id="c001"><label>*</label>Correspondence: Yixuan Luo, <email xlink:href="mailto:lois_luo@fzu.edu.cn">lois_luo@fzu.edu.cn</email></corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-02-11">
<day>11</day>
<month>02</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2026</year>
</pub-date>
<volume>14</volume>
<elocation-id>1753076</elocation-id>
<history>
<date date-type="received">
<day>24</day>
<month>11</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>23</day>
<month>01</month>
<year>2026</year>
</date>
<date date-type="rev-recd">
<day>18</day>
<month>01</month>
<year>2026</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2026 Zhang, Zhang, Shi and Luo.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Zhang, Zhang, Shi and Luo</copyright-holder>
<license>
<ali:license_ref start_date="2026-02-11">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<sec>
<title>Introduction</title>
<p>While existing research recognizes that policy conditions can influence the link between climate change and agricultural output, a critical question has long been overlooked&#x2014;even if policy direction is correct, if policies are volatile and unpredictable, they can themselves become a source of risk. How this policy uncertainty alters the relationship between climate change and agricultural production lacks in-depth exploration in academia. This study aims to fill this critical gap by specifically revealing how Climate Policy Uncertainty (CPU) moderates the effects of temperature and precipitation on grain yields.</p>
</sec>
<sec>
<title>Methods</title>
<p>This study employs panel data from 286 prefecture-level cities in China spanning 2001&#x2013;2020. Based on the C-D production function, it adopts an economic-climate interaction model, incorporates CPU as a moderating variable, and conducts empirical tests using regression method.</p>
</sec>
<sec>
<title>Results</title>
<p>There exists a significant inverse U-shaped relationship between climatic factors and grain yields. However, when CPU increases, this relationship curve becomes significantly steeper, meaning the negative impact of extreme climate on grain yields is amplified. In other words, policy instability may exacerbate the destructive force of climate change. Further regional analysis reveals that this &#x201c;amplification effect&#x201d; of CPU is more prominent in non-major grain-producing areas: in the north, it primarily intensifies the precipitation-yield relationship, while in the south, it amplifies the temperature-yield relationship. It is noteworthy that in non-climate adaptation pilot cities, CPU exhibits a more pronounced negative moderating effect.</p>
</sec>
<sec>
<title>Discussion</title>
<p>The core implication of this research is that in the face of climate change, the clarity, coherence, and predictability of policies are themselves a crucial form of adaptive capacity. Ensuring policy stability can effectively stabilize farmers&#x2019; production expectations and incentivize long-term investments to combat climate risks. Further, the results also underscore the necessity of driving systemic transformation to convert external risks into endogenous drivers, then CPUs&#x2019; responses can be internalized as assets against future extreme weather within a risk framework in the future. Ultimately, anchoring climate-policy regimes in stable, Nature-Based Solutions&#x2014;especially by advancing them across the Global South&#x2014;offers a scalable pathway to turn policy uncertainty into ecological and social resilience.</p>
</sec>
</abstract>
<kwd-group>
<kwd>climate change</kwd>
<kwd>inverted-U shape</kwd>
<kwd>climate policy uncertainty</kwd>
<kwd>grain yields</kwd>
<kwd>moderating effect</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the Fujian Province Innovation Strategy Research Plan Project (Grant No. 2024R0015).</funding-statement>
</funding-group>
<counts>
<fig-count count="3"/>
<table-count count="9"/>
<equation-count count="4"/>
<ref-count count="238"/>
<page-count count="27"/>
<word-count count="15015"/>
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<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Conservation and Restoration Ecology</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec id="s1" sec-type="intro">
<label>1</label>
<title>Introduction</title>
<p>Grain is the basis for human survival and development, which affects political, economic and social stability and has received widespread global attention (<xref ref-type="bibr" rid="B13">Bi et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B20">&#xc7;akir et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B32">Clapp et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B146">Pandey and Mishra, 2024</xref>). Grain production is the core support for food security (<xref ref-type="bibr" rid="B106">Li and Lin, 2022</xref>; <xref ref-type="bibr" rid="B218">Yan et&#xa0;al., 2023</xref>). However, in the 21st century, extreme weather events such as high temperatures, floods, droughts and cold waves have occurred frequent (<xref ref-type="bibr" rid="B4">Almazroui et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B219">Yan et&#xa0;al., 2022</xref>), severely impacting the global grain production environment (<xref ref-type="bibr" rid="B95">Lee and Zhao, 2023</xref>; <xref ref-type="bibr" rid="B236">Zheng et&#xa0;al., 2018</xref>). Both the Food and Agriculture Organization of the United Nations (FAO) and the United Nations Intergovernmental Panel on Climate Change (IPCC) have clearly pointed out that agriculture is one of the industries most significantly and vulnerably affected by the risks under climate change (<xref ref-type="bibr" rid="B77">Intergovernmental Panel On Climate Change (IPCC), 2022</xref>). Among these, developing countries, which are highly dependent on grain production for their livelihoods and face a lack of technological innovation and climate adaptation strategies, are far more affected than developed countries (<xref ref-type="bibr" rid="B2">Abbas et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B201">Warsame et&#xa0;al., 2021</xref>).</p>
<p>China is one of the countries with the most significant global climate change and frequentmeteorological disasters (<xref ref-type="bibr" rid="B200">Wang W. et&#xa0;al., 2024</xref>). Theseabnormal climate changes have severely impacted the stability and sustainability of China&#x2019;s grain production, and their most direct and obvious manifestation on grain production is the fluctuation of grain yields (<xref ref-type="bibr" rid="B104">Li D. et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B215">Xiao et&#xa0;al., 2013</xref>). It is predicted that climate change could lead to a reduction in China&#x2019;s wheat, rice and corn production by about 20%, which in turn has potential impacts on international grain trade (<xref ref-type="bibr" rid="B217">Xuan et&#xa0;al., 2021</xref>). As the world&#x2019;s largest agricultural producer (<xref ref-type="bibr" rid="B22">Carter et&#xa0;al., 2012</xref>), it is of great significance to explore the impact of climate change on Chinese agriculture. In recent years, scholars have conducted a large number of studies in this area, and have found that climate change, especially rising temperatures and changing precipitation patterns, has a significant impact on China&#x2019;s grain yields (<xref ref-type="bibr" rid="B48">Gao R. et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B72">Holst et&#xa0;al., 2013</xref>; <xref ref-type="bibr" rid="B105">Li et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B158">Saud et&#xa0;al., 2022</xref>).</p>
<p>Referring to the existing literature, agricultural climate balance and even stability of global grain yields were continuously threatening by aforementioned climate change risks (<xref ref-type="bibr" rid="B122">Luqman et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B206">Wheeler and Von Braun, 2013</xref>). Without an effective response in the coming decades, it will systematically jeopardize grain yields, destabilize food security systems and undermine the foundations of agricultural livelihoods (<xref ref-type="bibr" rid="B64">Hao W. et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B151">Ray et&#xa0;al., 2015</xref>). This highlight that coherent and stable climate policies are essential to provide grain producers with technical support, financial security and risk insurance to enhance their capacity to cope with climate risks (<xref ref-type="bibr" rid="B155">Rodr&#xed;guez-Barillas et&#xa0;al., 2024</xref>). However, the formulation, deliberation and implementation of climate policies generally face significant uncertainties (<xref ref-type="bibr" rid="B114">Liu G. et&#xa0;al., 2023</xref>). The root causes of uncertainty are diverse, covering multiple dimensions such as public attitudes, policy environments, interest group games, and urgency of the problem (<xref ref-type="bibr" rid="B91">Kysel&#xe1; et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B167">Sharp et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B207">Wood et&#xa0;al., 2014</xref>). Against this background, <xref ref-type="bibr" rid="B52">Gavriilidis (2021)</xref> proposes a new assessment methodology, called the Climate Policy Uncertainty (CPU) Index, to quantify the uncertainty that is closely associated with climate policy. Although the CPU index is a relatively new concept, it has attracted increasing attention from the academic community and has been applied in many studies (<xref ref-type="bibr" rid="B38">Ding et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B89">Kong et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B153">Ren et&#xa0;al., 2023</xref>).</p>
<p>However, there is still limited exploration related to the extension of CPU research to the closely related agricultural sector. In fact, the high dependence of the agricultural sector on climatic conditions and the institutional environment makes it more vulnerable to CPU (<xref ref-type="bibr" rid="B94">Lee et&#xa0;al., 2024</xref>). The climate policy environment not only profoundly affects the equilibrium of supply and demand and price fluctuations in agricultural markets (<xref ref-type="bibr" rid="B177">Sun et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B214">Xiao et&#xa0;al., 2019</xref>), but also directly shapes the risk-averse decision-making process of farmers and agribusinesses (<xref ref-type="bibr" rid="B6">Ant&#xf3;n et&#xa0;al., 2013</xref>; <xref ref-type="bibr" rid="B190">Waldman et&#xa0;al., 2020</xref>). In a context of relatively stable climate policies, grain producers are able to plan their planting, select varieties and organize their farming schedules more effectively, based on climate patterns and policy guidance (<xref ref-type="bibr" rid="B54">Grigorieva et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B142">Osbahr et&#xa0;al., 2008</xref>). A stable policy environment also encourages producers to manage climate risks by introducing new technologies and diversifying cropping patterns (<xref ref-type="bibr" rid="B36">De Laporte et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B186">Vermeulen et&#xa0;al., 2012</xref>), and to have the confidence to make long-term investments, including improving soil and building water facilities, in order to increase the stability and resilience of grain production (<xref ref-type="bibr" rid="B204">Wei et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B221">Yang et&#xa0;al., 2007</xref>). However, the high level of CPU may be like a fog, seriously disrupting the expectations of future climate conditions and supporting policies. As it is difficult to predict the direction of policies (such as carbon emission limits, adjustment of agricultural subsidies), grain producers tend to be conservative and cautious in their decision-making (<xref ref-type="bibr" rid="B144">Ouattara et&#xa0;al., 2018</xref>). In the face of climate change (fluctuations in temperature and precipitation, etc.), they may avoid expanding grain production readily out of concern for potential policy adjustment risks (<xref ref-type="bibr" rid="B220">Yang et&#xa0;al., 2023</xref>). Simultaneously, long-term agricultural investment relies on a stable policy environment, and the CPU may create ambiguity in grain producers&#x2019; expectations of future returns, which inhibits their incentives to invest in production (<xref ref-type="bibr" rid="B76">Huang and Sun, 2024</xref>). Once climate variables deviate from the appropriate range for grain growth, grain yields are at risk of a sharp decline. Therefore, it is important to incorporate consideration of the role of CPU when examining the impact of climate change on grain yields. Especially in developing countries, policy uncertainty often accompanies rapid industrialization and frequent policy adjustments. The behavioral responses triggered by such uncertainty may further weaken the already limited climate resilience of agricultural systems, creating a cycle of &#x201c;unclear policies &#x2192; insufficient investment &#x2192; weak adaptation&#x201d;.</p>
<p>This study makes several contributions to the literature. First, this study employs a modified Cobb-Douglas (<xref ref-type="bibr" rid="B33">Cobb and Douglas, 1928</xref>) production function that incorporates climatic elements to construct an economic-climate model (C-D-C) and incorporate a quadratic term at the empirical level. From an economic perspective, it verifies that the impact of climate change impacts on grain production exhibits complex nonlinear characteristics involving multiple interacting factors. This establishes an empirical foundation for quantifying the economic costs of climate risks and optimizing food security response strategies. Second, while some studies suggest that policy conditions could moderate the relationship between climate change and grain yields (<xref ref-type="bibr" rid="B49">Gao et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B74">Hua et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B237">Zhu et&#xa0;al., 2024</xref>), the underlying mechanisms require further elaboration. This study employs empirical economic methods, incorporating CPU as a moderating variable within the &#x201c;climate-agriculture&#x201d; analytical framework, to reveal the role of policy uncertainty in mediating the relationship between climate change and grain production. The implications may extend beyond China to offer insights for various international contexts facing similar policy challenges, with a view to enhancing global climate change adaptation capacity and risk management capabilities. Finally, by analyzing data across multiple regional dimensions&#x2014;including major grain-producing and non-major grain producing areas, northern regions and southern regions, and climate-adapted and non-climate-adapted cities&#x2014;this study reveals the spatial heterogeneity of climate impacts and policy moderation effects. It provides decision-making references for countries worldwide in addressing food shortages and malnutrition, holding particular significance for nations currently facing food crises.</p>
<p>The subsequent structure of this study is as follows. Section 2 presents the literature review and theoretical analysis. Section 3 focuses on the model, describing variables and data. Section 4 introduces our empirical findings. Section 5 serves as the discussion section, providing an in-depth analysis of the empirical results. Section 6 concludes the study and offers corresponding policy recommendations.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Literature review and research hypotheses</title>
<sec id="s2_1">
<label>2.1</label>
<title>Climate change and grain yields</title>
<p>Grain production is highly dependent on the climatic environment (<xref ref-type="bibr" rid="B25">Chandio et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B179">Teng et&#xa0;al., 2023</xref>), and climatic factors are not only critical to the sustainability of agricultural production activities (<xref ref-type="bibr" rid="B19">Cabas et&#xa0;al., 2010</xref>; <xref ref-type="bibr" rid="B24">Chandio et&#xa0;al., 2024</xref>), but also key drivers of grain growth and yield in a given region (<xref ref-type="bibr" rid="B11">Baig et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B69">Herath and Thirumarpan, 2017</xref>; <xref ref-type="bibr" rid="B145">Panda et&#xa0;al., 2019</xref>). In this context, climate change has become a major force reshaping agroecosystems (<xref ref-type="bibr" rid="B5">Altieri et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B164">Semeraro et&#xa0;al., 2023</xref>). There is a global consensus that climate change has far-reaching implications for agricultural production (<xref ref-type="bibr" rid="B162">Schlenker and Roberts, 2009</xref>; <xref ref-type="bibr" rid="B226">Yuan et&#xa0;al., 2024</xref>), temperature and precipitation are the core influencing factors (<xref ref-type="bibr" rid="B90">Kukal and Irmak, 2018</xref>).</p>
<p>Evidences of significant impacts on grain yields have been found in many regions of the world (<xref ref-type="bibr" rid="B117">Lobell and Field, 2007</xref>; <xref ref-type="bibr" rid="B199">Wang et&#xa0;al., 2018</xref>). Some studies have shown that rising temperatures may have a positive impact on agricultural production in some developed countries such as the United State and Germany (<xref ref-type="bibr" rid="B37">Desch&#xea;nes and Greenstone, 2007</xref>; <xref ref-type="bibr" rid="B109">Li et&#xa0;al., 2011</xref>; <xref ref-type="bibr" rid="B112">Lippert et&#xa0;al., 2009</xref>). <xref ref-type="bibr" rid="B1">Abbas (2022)</xref> investigated the dynamics between grain yields and precipitation in Pakistan from 2000 to 2019 and found that increased precipitation has a significant positive impact on grain yields. Conversely, a study by <xref ref-type="bibr" rid="B180">Tetteh et&#xa0;al. (2022)</xref> revealed that high temperatures have jeopardized overall grain production in Ghana. Similarly, <xref ref-type="bibr" rid="B211">Wu et&#xa0;al. (2021)</xref> found through their study that increased temperatures have harmed maize production in China from 1979 to 2016. <xref ref-type="bibr" rid="B99">Li (2023)</xref> suggested that increased precipitation has negatively impacted rice production in Japan. Overall, temperature and precipitation are the core influencing factors (<xref ref-type="bibr" rid="B90">Kukal and Irmak, 2018</xref>), and the relationship between them and grain yields may not be a simple linear pattern, but a complex and non-linear one (<xref ref-type="bibr" rid="B18">Burke et&#xa0;al., 2015</xref>). Regarding nonlinear effects, <xref ref-type="bibr" rid="B107">Li C. et&#xa0;al. (2024)</xref> used panel data from China&#x2019;s major grain-producing regions between 1978 and 2018, finding a nonlinear relationship between precipitation, temperature, and rice yields, which is characterized by an inverted U-shaped pattern. <xref ref-type="bibr" rid="B3">Agnolucci et&#xa0;al. (2020)</xref> research indicates that grain yields do not follow a simple linear relationship with temperature but instead displays a nonlinear pattern centered around an &#x201c;optimal temperature window.&#x201d; Based on the literature, studies examining the nonlinear relationship between temperature and precipitation and grain yields are still relatively limited compared to those focusing on linear relationships.</p>
<p>According to the threshold theory in agronomy (AT), crop responses to environmental or biologicalfactors are often nonlinear. When factors exceed a critical value (threshold), yields decline rapidly or disaster risks rise significantly (<xref ref-type="bibr" rid="B75">Huang et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B121">Luo, 2011</xref>). Simultaneously, the law of diminishing marginal returns (DMR) in agricultural production functions indicates that, when other inputs (such as land and technology) remain constant, continuously increasing a single variable factor (like labor, fertilizer, or water) results in marginal productivity (the output increment per additional unit of that factor) first rising and then declining, ultimately following a diminishing trend (<xref ref-type="bibr" rid="B79">Just and Peterson, 2003</xref>; <xref ref-type="bibr" rid="B93">Layson, 2015</xref>). Currently, some studies have extended this theoretical logic to the analysis of how climate factors influence agricultural production reveals: when the climate variables are in the appropriate range, their resource attributes are dominant, and they contribute to grain yields by optimizing photosynthesis, ensuring cumulative temperatures and land moisture (<xref ref-type="bibr" rid="B65">Hao S. et&#xa0;al., 2024</xref>); once the ecological threshold is exceeded, they turn into stress factors, which inhibit physiology disturb the ecological balance, and induce disasters, leading to a decrease in grain yields (<xref ref-type="bibr" rid="B131">Mir&#xf3;n et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B172">Skarb&#xf8; and VanderMolen, 2016</xref>). Overall, the relationship between temperature and precipitation and grain yields may not be a simple linear pattern, but could exist a potential complex nonlinear relationship (<xref ref-type="bibr" rid="B18">Burke et&#xa0;al., 2015</xref>).</p>
<p>Specifically, from a temperature perspective, when temperatures fall below the appropriate range,grain growth slows down or even stops. Low temperatures hinder cellular metabolism by inhibiting enzyme activity (<xref ref-type="bibr" rid="B191">Wang H. et&#xa0;al., 2023</xref>), and extreme low temperatures can cause frost damage that destroys cellular structure and interferes with nutrient transportation, leading to a reduction in grain yields (<xref ref-type="bibr" rid="B110">Lin et&#xa0;al., 2023</xref>). As temperatures gradually rise, grain yields increase. Increased temperatures accelerate physiological processes such as photosynthesis, respiration and nutrient conversion (<xref ref-type="bibr" rid="B137">Niu et&#xa0;al., 2023</xref>), creating conditions for seed development and activating soil microbial activity to release more nutrients (<xref ref-type="bibr" rid="B194">Wang M. et&#xa0;al., 2024</xref>). However, when temperatures exceed certain thresholds, grain yields decline. High temperatures and heat waves can exacerbate the volatilization of pesticides and fertilizers, increasing the risk of pests and diseases (<xref ref-type="bibr" rid="B225">Yin et&#xa0;al., 2023</xref>), while at the same time accelerating respiratory depletion but inhibiting photosynthesis at the physiological level, leading to a lack of net photosynthetically active product accumulation resulting in a reduction in grain yields (<xref ref-type="bibr" rid="B233">Zhang et&#xa0;al., 2022</xref>).</p>
<p>From a precipitation perspective, when the precipitation is insufficient, the lack of soil moisture will directly cause the physiological activities of the grain to be hindered (<xref ref-type="bibr" rid="B127">Mares and Mrva, 2014</xref>), which is manifested by the wilting of leaves, the decrease of photosynthetic efficiency and the restriction of root growth, which will ultimately lead to the reduction of grain yields (<xref ref-type="bibr" rid="B51">Garg et&#xa0;al., 2020</xref>). With the increase of precipitation, the improvement of soil moisture can guarantee the absorption of water and fertilizer to meet the needs of grain growth period, thus promoting the yields of grain (<xref ref-type="bibr" rid="B149">Qiu et&#xa0;al., 2022</xref>). However, when precipitation exceeds the capacity of grain crops, soil water saturation and deterioration of aeration lead to root hypoxia, which inhibits respiration and normal physiological functions, threatening grain growth and yields (<xref ref-type="bibr" rid="B83">Khalil et&#xa0;al., 2020</xref>). In addition, extreme flooding can even destroy farmland, which can be devastating to grain production (<xref ref-type="bibr" rid="B168">Shehzad, 2023</xref>).</p>
<p>Based on the above literature review and theoretical analysis, this study proposes.</p>
<p><bold>Hypothesis 1a:</bold> The relationship between temperature and grain yields follows an inverted U-shaped curve.</p>
<p><bold>Hypothesis 1b:</bold> There exists an inverted U-shaped relationship between precipitation and the grain yields.</p>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Moderating effect of climate policy uncertainty</title>
<p>CPU refers to the uncertainty and lack of clarity inherent in government policies and regulationsrelated to climate change mitigation and adaptation strategies, which makes it difficult for policy participants (such as businesses, agricultural producers, investors, etc.) to accurately predict the direction of the policy and the impacts it will bring (<xref ref-type="bibr" rid="B181">Tian and Li, 2023</xref>). Currently, the measurement of CPU relies on mining news texts, which are processed using word frequency statistics and machine learning algorithms (<xref ref-type="bibr" rid="B124">Ma et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B138">Noailly et&#xa0;al., 2022</xref>). The existing discussions on CPU mainly focus on three levels. First of all, at the level of economic risk, CPU will increase the operating costs and risks of enterprises, make their investment decisions more prudent, and then inhibit the expansion of investment scale and cut international trade flows (<xref ref-type="bibr" rid="B137">Niu et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B230">Zhang Z. et&#xa0;al., 2025</xref>). Secondly, in terms of environmental risks, CPUs could undermine investment in green technologies, lead to a mismatch of resources and an inability to effectively channel financial flows to key environmental sectors, and slow down the green transition process (<xref ref-type="bibr" rid="B50">Gao D. et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B205">Wei et&#xa0;al., 2024</xref>). Finally, in terms of social risk, CPU may exacerbate social inequality and undermine public trust in climate policy (<xref ref-type="bibr" rid="B42">Emami Meybodi and Owjimehr, 2024</xref>; <xref ref-type="bibr" rid="B87">Kitt et&#xa0;al., 2021</xref>).</p>
<p>In the agricultural sector, frequent weather extremes, exacerbated by global warming, have severely disrupted grain growth cycles (<xref ref-type="bibr" rid="B45">Fatima et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B140">Onyeaka et&#xa0;al., 2024</xref>). Climate policies are designed to provide farmers with guidelines and safeguards against climate risks (<xref ref-type="bibr" rid="B84">Khan et&#xa0;al., 2023</xref>), and to buffer climate shocks and enhance system resilience through adaptive measures (<xref ref-type="bibr" rid="B9">Assan et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B85">Khan and Roberts, 2013</xref>). However, due to the complexity of the climate and the need to balance economic growth and carbon reduction, policy formulation and implementation are often characterized by discontinuity or ambiguity (<xref ref-type="bibr" rid="B94">Lee et&#xa0;al., 2024</xref>), making it difficult for agricultural actors to anticipate changes in the policy environment (<xref ref-type="bibr" rid="B196">Wang J. et&#xa0;al., 2024</xref>). For example, frequent adjustments in agricultural subsidies, irrigation investments or emission reduction targets further confuse expectations (<xref ref-type="bibr" rid="B128">Masud and Khan, 2024</xref>). While existing studies have separately highlighted the economic costs of CPU, its drag on the green transition, and the threats climate change poses to agriculture, empirical examinations of how CPU interacts with natural climate risks and analyses of regional vulnerability differences remain relatively limited.</p>
<p>The theory of real options (RO) represents the extension and application of financial option concepts and analytical tools within the real economy. This theory posits that investment opportunities held by enterprises can be viewed as options based on physical assets (<xref ref-type="bibr" rid="B88">Kogut and Kulatilaka, 2001</xref>; <xref ref-type="bibr" rid="B183">Trigeorgis and Reuer, 2017</xref>). The higher the level of uncertainty in the external environment, the greater the value of such options typically becomes. Consequently, from the perspective of real options, the CPU increases the &#x201c;waiting value&#x201d; of producers (<xref ref-type="bibr" rid="B57">Guo et&#xa0;al., 2023</xref>). This &#x201c;waiting value&#x201d; makes grain producers, especially risk averse farmers, more inclined to delay the implementation of countermeasures in response to climate risks, maintain the status quo, and avoid attempting to introduce new technologies or new varieties that may bring uncertainty, so as to accumulate more information and avoid potential risk (<xref ref-type="bibr" rid="B96">Lei et&#xa0;al., 2024</xref>). In addition, according to the Adaptive Capacity (AC) theory, which refers to the ability of socio-ecological systems, institutions, humans, and other organisms to adjust in order to reduce potential harm, seize opportunities, or cope with consequences (<xref ref-type="bibr" rid="B26">Chapagain et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B163">Seaborn et&#xa0;al., 2021</xref>). Therefore, under high CPU load, agricultural entities find themselves caught in a dilemma of dual uncertainties stemming from both climate and policy (<xref ref-type="bibr" rid="B132">Mittenzwei et&#xa0;al., 2017</xref>),and their adaptive behavior is degraded from &#x201c;forward-looking investment&#x201d; to &#x201c;passive response&#x201d; (<xref ref-type="bibr" rid="B130">Menapace et&#xa0;al., 2013</xref>), which significantly weakens the adaptive capacity of the system.</p>
<p>The potential risks posed by CPU is that it may systematically reconfigures the slope of themarginal effect of the inverted U-shaped relationship between climate variables and grain yields.The moderating effect could be mainly concluded in three dimensions, which could increase the&#x201c;waiting value&#x201d; and decrease the adaptive capacity. The first is the weakening of risk response and agricultural inputs, CPU makes the management behavior of grain producers tend to be conservative (<xref ref-type="bibr" rid="B165">Shah and Alharthi, 2022</xref>; <xref ref-type="bibr" rid="B171">Singh et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B227">Yuan et&#xa0;al., 2021</xref>), such as farmers worrying about the loss of policy changes and sticking to the traditional planting pattern (<xref ref-type="bibr" rid="B17">Brock and Haden, 2024</xref>), which hinders the improvement of grain climate resilience. At the same time, the willingness to invest in the long term will also contract (<xref ref-type="bibr" rid="B73">Hong et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B115">Liu et&#xa0;al., 2024</xref>), for example, delaying the upgrading of irrigation systems and the introduction of resilient varieties due to uncertainty about the direction of future climate policy support (<xref ref-type="bibr" rid="B59">Hallegatte, 2009</xref>; <xref ref-type="bibr" rid="B198">Wang S. et&#xa0;al., 2019</xref>). This could result in a lag in agricultural transformation and a weakening of grain system stability (<xref ref-type="bibr" rid="B102">Li et&#xa0;al., 2017</xref>). Second is the rigidity of production and business decisions, with CPUs interfering with market signals, exacerbating grain price volatility (<xref ref-type="bibr" rid="B114">Liu G. et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B193">Wang K. H. et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B224">Yin and Cao, 2024</xref>), and constraining grain producers from forming rational expectations (<xref ref-type="bibr" rid="B238">Zou et&#xa0;al., 2024</xref>). This leads to a tendency for farmers&#x2019; production decisions to be short-term risk averse, such as discarding high-risk, high-yield crops and conservatively adjusting acreage (<xref ref-type="bibr" rid="B46">Findlater et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B124">Ma et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B182">Tong et&#xa0;al., 2019</xref>). This significantly limits the flexibility of the grain system to respond to climate fluctuations and magnifies the negative impacts of temperature and precipitation changes on grain yields (<xref ref-type="bibr" rid="B135">Nam, 2021</xref>). The third is technology iteration and infrastructure blockage, as CPU increases the risk of sunk costs in agricultural technology development and inhibits the willingness of innovation agents to invest, especially when the technology may face policy rollbacks (<xref ref-type="bibr" rid="B173">Snitker et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B176">Sun et&#xa0;al., 2024</xref>), which will result in a delay in the diffusion of adaptation technologies. At the same time, because CPU increases the difficulty of risk assessment, financial institutions will tighten credit (<xref ref-type="bibr" rid="B60">Han et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B61">Hansen, 2022</xref>) and limit financial support for agricultural infrastructure and technological innovation (<xref ref-type="bibr" rid="B113">Liu Y. et&#xa0;al., 2023</xref>; <xref ref-type="bibr" rid="B141">Osabutey and Jackson, 2024</xref>), making grain production more vulnerable in the face of extreme weather.</p>
<p>Based on the above literature review and theoretical analysis, this study proposes.</p>
<p>Hypothesis 2a: CPU enhances the relationship between temperature and grain yields, that is, the higher the CPU, the steeper the inverted U-shaped relationship between temperature and grain yields.</p>
<p>Hypothesis 2b: The relationship between precipitation and grain yields is reinforced by CPU, with greater CPU levels translating into a steeper inverted U-shaped pattern.</p>
<p>Based on a progressive, sub-thematic literature review and analysis of relevant theories, we constructed the core theoretical framework and corresponding hypothesis mechanism diagram for our study. This provides a clarified presentation of our research approach and theoretical application process (<xref ref-type="fig" rid="f1"><bold>Figure&#xa0;1</bold></xref>). As shown in <xref ref-type="fig" rid="f1"><bold>Figure&#xa0;1</bold></xref>, the potential contribution of our research lies in two aspects. First, building upon the inverted U-shaped relationship between temperature and precipitation observed in existing literature, we employ an empirical model from an economic perspective to validate this agronomic principle, aligning with AT and DMR theories. Second, we further explore the possible moderating role of CPU in this inverted U effect&#x2014;examining its potential amplifying or diminishing influence and the potential nonlinearity of its role&#x2014;while attempting to construct a theoretical framework centered on AC and RO theories to analyze such potential phenomena.</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p>Theoretical mechanism diagram.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fevo-14-1753076-g001.tif">
<alt-text content-type="machine-generated">Diagram illustrating the relationship between temperature, precipitation, and grain production. It features an inverted U-shape curve, indicating positive effects predominate initially, then negative. Key theories include AT and DMR, and AC and RO, emphasizing suitable and related higher temperatures and precipitation effects. The hypothesis section discusses the inverted U-shape's impact on grain production and the modulation by Climate Policy Uncertainty. Elements include photosynthesis, nutrient absorption, soil moisture, and risk response. The C-D-C production function denotes variables K, L, and T.</alt-text>
</graphic></fig>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Research design</title>
<sec id="s3_1">
<label>3.1</label>
<title>Model construction</title>
<sec id="s3_1_1">
<label>3.1.1</label>
<title>C-D model</title>
<p>The Cobb-Douglas production function model (C-D model) (<xref ref-type="bibr" rid="B33">Cobb and Douglas, 1928</xref>) is widely recognized in economics as the classic model reflecting the relationship between production factors and output (<xref ref-type="bibr" rid="B185">Vasyl&#x2019;Yeva, 2021</xref>). Compared to other models, the C-D production function model can more accurately depict the process of agricultural input-output and enable in-depth analysis in conjunction with other economic indicators (<xref ref-type="bibr" rid="B30">Chou et&#xa0;al., 2021</xref>). Its basic form is:</p>
<disp-formula id="eq1"><label>(1)</label>
<mml:math display="block" id="M1"><mml:mrow><mml:mi>Q</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mi>L</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:msup><mml:mi>K</mml:mi><mml:mi>&#x3b1;</mml:mi></mml:msup><mml:msup><mml:mi>L</mml:mi><mml:mi>&#x3b2;</mml:mi></mml:msup></mml:mrow></mml:math>
</disp-formula>
<p>In <xref ref-type="disp-formula" rid="eq1">Equation 1</xref>, <inline-formula>
<mml:math display="inline" id="im1"><mml:mi>Q</mml:mi></mml:math></inline-formula> represents output; <inline-formula>
<mml:math display="inline" id="im2"><mml:mi>L</mml:mi></mml:math></inline-formula> and <inline-formula>
<mml:math display="inline" id="im3"><mml:mi>K</mml:mi></mml:math></inline-formula> denote the quantities of labor and capital inputs, respectively; A indicates the level of technology; <inline-formula>
<mml:math display="inline" id="im4"><mml:mi>&#x3b1;</mml:mi></mml:math></inline-formula> and <inline-formula>
<mml:math display="inline" id="im5"><mml:mi>&#x3b2;</mml:mi></mml:math></inline-formula> are the output elasticity coefficients for labor and capital, respectively.</p>
</sec>
<sec id="s3_1_2">
<label>3.1.2</label>
<title>&#x201c;Economic-Climate&#x201d; model</title>
<p>Since grain yields is constrained not only by factors of production such as land, labor, and fertilizer, but also directly influenced by climatic elements like temperature and precipitation (<xref ref-type="bibr" rid="B192">Wang P. et&#xa0;al., 2019</xref>). To enhance the applicability and explanatory power of the C-D production function model, agricultural economists have undertaken innovative efforts. They incorporate climate elements like temperature and precipitation as crucial production factors into the traditional C-D production function, forming an &#x201c;economic-climate&#x201d; model (C-D-C) that comprehensively considers both climate factors and agricultural input resource (<xref ref-type="bibr" rid="B31">Chou and Ye, 2006</xref>; <xref ref-type="bibr" rid="B39">Dong et&#xa0;al., 2007</xref>). The C-D-C model integrates both climatic and economic factors, treating climatic parameters under average climate conditions while accounting for long-term trends in climatic variables (<xref ref-type="bibr" rid="B56">Guo et&#xa0;al., 2024</xref>). Its specific form is:</p>
<disp-formula id="eq2"><label>(2)</label>
<mml:math display="block" id="M2"><mml:mrow><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mi>L</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>C</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>
</disp-formula>
<p>In <xref ref-type="disp-formula" rid="eq2">Equation 2</xref>, <inline-formula>
<mml:math display="inline" id="im6"><mml:mi>Y</mml:mi></mml:math></inline-formula> represents grain yields; <inline-formula>
<mml:math display="inline" id="im7"><mml:mi>L</mml:mi></mml:math></inline-formula> and <inline-formula>
<mml:math display="inline" id="im8"><mml:mi>K</mml:mi></mml:math></inline-formula> denote labor and capital inputs, respectively; T signifies technological progress; and C represents climate variables.</p>
</sec>
<sec id="s3_1_3">
<label>3.1.3</label>
<title>Quadratic form model</title>
<p>To further verify whether a nonlinear relationship exists between climate change and grain yields, this study extends the C-D-C model by introducing a quadratic term for climate factors. In agronomy, threshold theory (AT) emphasizes that crop growth exhibits a three-stage response to key environmental factors: &#x201c;minimum threshold - optimal range - maximum threshold.&#x201d; Regarding temperature: The minimum threshold is the base temperature required for seed germination and enzyme activation; The optimal range is the temperature interval where processes like photosynthesis achieve maximum efficiency; The maximum threshold is the temperature causing protein denaturation and a sharp increase in respiratory consumption. Regarding precipitation: The minimum threshold is the basic water requirement for sustaining cellular photosynthesis; The optimal range is the equilibrium point between water deficiency and waterlogging; while the maximum threshold represents the critical point for root rot due to waterlogging (<xref ref-type="bibr" rid="B23">Challinor et&#xa0;al., 2015</xref>). This indicates that the impact may rise initially (minimum threshold to optimal range), peak at the optimal range, and then decline (optimal range to maximum threshold), forming an inverted U-shaped influence curve. Therefore, integrating agronomic theory with economic modeling, we incorporate a quadratic term into the model to characterize the impact of climate on crop production.</p>
<p>Thus, the C-D-C model is transformed logarithmically, and its log-linear form is selected as the analytical framework for this study:</p>
<disp-formula id="eq3"><label>(3)</label>
<mml:math display="block" id="M3"><mml:mrow><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x3b1;</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi>&#x3b2;</mml:mi><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b3;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3bc;</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3f5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im9"><mml:mi>y</mml:mi></mml:math></inline-formula> denotes total grain yields; climate denotes climate change factor; x denotes the control variable (This study selects control variables based on the three core factors of capital, labor, and technological progress within the C-D production function, while accounting for agricultural production characteristics: &#x2460;Capital Input Dimension: Crop planting area, fertilizer application volume, and government fiscal expenditure are selected, representing the land capital base, physical capital investment, and public capital investment sources for agricultural production, respectively. &#x2461;Labor Input Dimension: The number of persons employed in the primary sector is selected to reflect the scale of labor input in agricultural production. &#x2462;Technological progress dimension: The number of agricultural patents is selected as a quantitative indicator of agricultural technological invention and innovation output.); constant term is denoted by <inline-formula>
<mml:math display="inline" id="im10"><mml:mi>&#x3b1;</mml:mi></mml:math></inline-formula>, <inline-formula>
<mml:math display="inline" id="im11"><mml:mrow><mml:msub><mml:mi>&#x3f5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> denotes random error term; <inline-formula>
<mml:math display="inline" id="im12"><mml:mrow><mml:msub><mml:mi>&#x3b3;</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> denotes individual fixed effect; <inline-formula>
<mml:math display="inline" id="im13"><mml:mrow><mml:msub><mml:mi>&#x3bc;</mml:mi><mml:mi>t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> denotes time fixed effect, <inline-formula>
<mml:math display="inline" id="im14"><mml:mi>i</mml:mi></mml:math></inline-formula> denotes city; <inline-formula>
<mml:math display="inline" id="im15"><mml:mi>t</mml:mi></mml:math></inline-formula> denotes year. In agricultural production, the yield-increasing effect of marginal inputs (such as fertilizers, water, and labor) diminishes progressively as input quantities accumulate, rather than maintaining a constant rate of increase. The logarithmic form accurately captures this nonlinear relationship where &#x201c;incremental inputs gradually decouple from incremental outputs,&#x201d; aligning with the actual response characteristics of factor inputs in agricultural production (<xref ref-type="bibr" rid="B100">Li and Geng, 2013</xref>; <xref ref-type="bibr" rid="B118">Lobell et&#xa0;al., 2013</xref>).</p>
</sec>
<sec id="s3_1_4">
<label>3.1.4</label>
<title>CPU moderation model</title>
<p>Theoretical analyses have shown that CPU has a moderating effect of any input factor (including climatic factors) is typically not constant. Introducing a on the relationship between climate change factors and grain yields. Therefore, On the basis of model (3), the moderating effect model (4) of curvilinear regression is constructed by adding CPU and <inline-formula>
<mml:math display="inline" id="im16"><mml:mrow><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>*</mml:mo><mml:mi>C</mml:mi><mml:mi>P</mml:mi><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, the interaction term between CPU and climate change factors, as well as <inline-formula>
<mml:math display="inline" id="im17"><mml:mrow><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>*</mml:mo><mml:mi>C</mml:mi><mml:mi>P</mml:mi><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, the interaction term between CPU and the squared term (<inline-formula>
<mml:math display="inline" id="im18"><mml:mrow><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:msup><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) after taking the logarithm effectively captures this &#x201c;initially increasing, then decreasing&#x201d; nonlinear relationship, which aligns mathematically with threshold theory in agronomy.Furthermore, the logarithmic form effectively mitigates the heteroskedasticity issue of the model (<xref ref-type="bibr" rid="B208">Wooldridge, 2020</xref>). The climate change factors remain consistent with the previous specification, while the rest of the control variables are the same as those in model (3):</p>
<disp-formula id="eq4"><label>(4)</label>
<mml:math display="block" id="M4"><mml:mrow><mml:mtable><mml:mtr><mml:mtd columnalign="left"><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x3b1;</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mi>C</mml:mi><mml:mi>P</mml:mi><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd columnalign="left"><mml:mo>*</mml:mo><mml:mi>C</mml:mi><mml:mi>P</mml:mi><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>e</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>*</mml:mo><mml:mi>C</mml:mi><mml:mi>P</mml:mi><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>&#x3b2;</mml:mi><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3b3;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3bc;</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x3f5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math>
</disp-formula>
<p>If the sign of the coefficient of the quadratic term is the same as that of the coefficient of the quadratic interaction term, there is an enhancement effect; if the sign is opposite, there is a weakening effect (<xref ref-type="bibr" rid="B58">Haans et&#xa0;al., 2016</xref>). If hypothesis H<sub>1</sub> holds, the coefficient of the squared term in model (1) is significantly negative, then a significantly negative <inline-formula>
<mml:math display="inline" id="im19"><mml:mrow><mml:mo>&#xa0;</mml:mo><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mrow><mml:mn>5</mml:mn><mml:mo>&#xa0;</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> may indicate that CPU strengthens the relationship between climate change factors and grain yields, while a significantly positive <inline-formula>
<mml:math display="inline" id="im20"><mml:mrow><mml:msub><mml:mi>&#x3b2;</mml:mi><mml:mn>5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> indicates that CPU weakens the relationship between the two.</p>
</sec>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Variable selection</title>
<list list-type="simple">
<list-item>
<p>(1) Core explanatory variable: grain yields (Y). Grain yields is measured as the total amount of grain products, mainly including the annual production of rice, wheat, corn, soybean, tuber and other crops (at prefecture-level).</p></list-item>
<list-item>
<p>(2) Explained variable: Climate change. The impact of climate on agricultural production is primarily reflected in temperature and precipitation (<xref ref-type="bibr" rid="B90">Kukal and Irmak, 2018</xref>; <xref ref-type="bibr" rid="B126">Maitah et&#xa0;al., 2021</xref>). Considering that the annual mean temperature comprehensively reflects the heat accumulation status during the grain growing season and before sowing, it determines whether grain can complete their growth cycle normally and influences the selection of sowing dates (<xref ref-type="bibr" rid="B7">Arshad et&#xa0;al., 2021</xref>). Annual total precipitation reflects the overall level of water supply throughout the year, meeting the water requirements of the grain growing season while also affecting soil moisture conditions, thereby influencing the determination of sowing periods and seedling emergence rates (<xref ref-type="bibr" rid="B40">Drebenstedt et&#xa0;al., 2023</xref>). Both metrics also serve as macro indicators representing fundamental regional climate characteristics, thereby avoiding the cumulative climatic effects and prior influences that might be overlooked when selecting data from a single growing season period (<xref ref-type="bibr" rid="B188">Vogel et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B222">Yang et&#xa0;al., 2020</xref>). Therefore, this study employs annual mean temperature (TP) and annual total precipitation (RF) as climate indicators to assess their impact on grain production (at prefecture-level).</p></list-item>
<list-item>
<p>(3) Moderating variable: CPU. This study employs the China Prefecture-Level CPU Index calculated using the MacBERT model. This index, based on data from <xref ref-type="bibr" rid="B124">Ma et&#xa0;al. (2023)</xref> covering six major Chinese news outlets&#x2014;including the People&#x2019;s Daily, Guangming Daily, Economic Daily, Global Times, Science and Technology Daily, and China News Service. It employs the China Prefecture-Level CPU Index calculated using the MacBERT model, which encompasses uncertainties across all dimensions of climate policy: the entities responsible for policy formulation (who formulates climate policies), the timing and content of policy implementation (when and what types of policies are implemented), and the consequences of climate policy actions (the outcomes of climate policy actions). (See Appendix 1 for the data processing procedure).</p></list-item>
<list-item>
<p>(4) Control variables: Based on the three factors of capital (K), labor (L), and technological progress (T) in the C-D production function, and considering both literature conventions and data availability, this study sets the corresponding control variables as follows: Considering the characteristics of agricultural production, the area sown with crops determines the land size for grain production and is the agricultural capital base dimension; fertilizer application represents mobile physical capital and affects soil fertility and yields; and government fiscal expenditure is the main source of public capital inputs such as agricultural infrastructure and agricultural subsidies. Therefore, capital input is represented by area sown with crops (AC), fertilizer application (FER), and government fiscal expenditure (GE). The number of employees in primary industry directly reflects the scale of labor input into agricultural production. Therefore, labor input is measured by the number of employees in primary industry (LAB). The number of agricultural patents serves as a direct, quantifiable indicator of technological inventions and innovation output within the agricultural sector. Therefore, technological progress is reflected by the number of agricultural patents (TE). The specific definitions of the above variables are shown in <xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>.</p></list-item>
</list>
<table-wrap id="T1" position="float">
<label>Table&#xa0;1</label>
<caption>
<p>Definition of variables.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="center">Variable type</th>
<th valign="top" align="center">Variable definition</th>
<th valign="top" align="center">Variable symbol</th>
<th valign="top" align="center">Variable unit</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="center">Explained variable</td>
<td valign="top" align="center">Grain yields</td>
<td valign="top" align="center">Y</td>
<td valign="top" align="center">Ten thousand tons</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">Explanatory variable</td>
<td valign="top" align="center">Average annual temperature</td>
<td valign="top" align="center">TP</td>
<td valign="top" align="center">degrees centigrade</td>
</tr>
<tr>
<td valign="top" align="center">Total annual precipitation</td>
<td valign="top" align="center">RF</td>
<td valign="top" align="center">millimetre</td>
</tr>
<tr>
<td valign="top" align="center">Adjusting variable</td>
<td valign="top" align="center">Climate policy uncertainty</td>
<td valign="top" align="center">CPU</td>
<td valign="top" align="center">/</td>
</tr>
<tr>
<td valign="top" rowspan="5" align="center">Control variable</td>
<td valign="top" align="center">Area sown with crops</td>
<td valign="top" align="center">AC</td>
<td valign="top" align="center">thousands of hectares</td>
</tr>
<tr>
<td valign="top" align="center">Fertilizer application</td>
<td valign="top" align="center">FER</td>
<td valign="top" align="center">Ten thousand tons</td>
</tr>
<tr>
<td valign="top" align="center">Number of employees in primary industry</td>
<td valign="top" align="center">LAB</td>
<td valign="top" align="center">ten thousand people</td>
</tr>
<tr>
<td valign="top" align="center">Number of agricultural patents</td>
<td valign="top" align="center">TE</td>
<td valign="top" align="center">item</td>
</tr>
<tr>
<td valign="top" align="center">Government fiscal expenditure</td>
<td valign="top" align="center">GE</td>
<td valign="top" align="center">billions</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3_3">
<label>3.3</label>
<title>Data sources and data processing</title>
<p>In this study, we select the panel data of 286 prefecture-level cities in China from 2001 to 2020, and the data of the above explanatory variables and all control variables are from the National Bureau of Statistics of China, China&#x2019;s official statistical yearbooks, and the work reports of local governments issued by the governments of each prefecture-level city at the end of the year. The missing data of a small number of prefecture-level cities are added and processed by linear interpolation in this study. (Linear interpolation can fill in missing values based on the linear relationship between adjacent known data points while maximally preserving the trend characteristics of the original data. It causes minimal disturbance to the original data and is suitable for statistical materials with relatively stable data quality over extended time spans (<xref ref-type="bibr" rid="B208">Wooldridge, 2020</xref>), such as panel data from prefecture-level cities.) The data source for the explanatory variables climate change factors (mean annual temperature and total annual precipitation) is the National Center for Environmental Information (NCEI) under the U.S. National Oceanic and Atmospheric Administration (NOAA) (See Appendix 1 for the data processing procedure). The CPU index is available for download from the ISETS Energy Finance Network website. In this study, all continuous variables are shrink-tailed at the 1% and 99% levels to minimize the effect of outliers. A statistical description of the sample intervals is presented in <xref ref-type="table" rid="T2"><bold>Table&#xa0;2</bold></xref>.</p>
<table-wrap id="T2" position="float">
<label>Table&#xa0;2</label>
<caption>
<p>Descriptive statistics of variables.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="left">Variable</th>
<th valign="middle" align="left">&#x2003;Obs.</th>
<th valign="middle" align="left">&#x2003;Mean</th>
<th valign="middle" align="left">&#x2003;S.D.</th>
<th valign="middle" align="left">&#x2003;Min.</th>
<th valign="middle" align="left">&#x2003;Max</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="left">&#x2003;lnY</td>
<td valign="middle" align="left">5720</td>
<td valign="middle" align="left">4.823</td>
<td valign="middle" align="left">1.046</td>
<td valign="middle" align="left">1.065</td>
<td valign="middle" align="left">6.957</td>
</tr>
<tr>
<td valign="middle" align="left">&#x2003;lnTP</td>
<td valign="middle" align="left">5720</td>
<td valign="middle" align="left">2.594</td>
<td valign="middle" align="left">0.459</td>
<td valign="middle" align="left">0.841</td>
<td valign="middle" align="left">3.175</td>
</tr>
<tr>
<td valign="middle" align="left">&#x2003;lnRF</td>
<td valign="middle" align="left">5720</td>
<td valign="middle" align="left">6.875</td>
<td valign="middle" align="left">0.552</td>
<td valign="middle" align="left">5.262</td>
<td valign="middle" align="left">7.842</td>
</tr>
<tr>
<td valign="middle" align="left">&#x2003;lnAC</td>
<td valign="middle" align="left">5720</td>
<td valign="middle" align="left">5.878</td>
<td valign="middle" align="left">0.905</td>
<td valign="middle" align="left">2.832</td>
<td valign="middle" align="left">7.554</td>
</tr>
<tr>
<td valign="middle" align="left">&#x2003;lnFER</td>
<td valign="middle" align="left">5720</td>
<td valign="middle" align="left">2.486</td>
<td valign="middle" align="left">0.944</td>
<td valign="middle" align="left">-0.598</td>
<td valign="middle" align="left">4.419</td>
</tr>
<tr>
<td valign="middle" align="left">&#x2003;lnLAB</td>
<td valign="middle" align="left">5720</td>
<td valign="middle" align="left">-1.102</td>
<td valign="middle" align="left">1.476</td>
<td valign="middle" align="left">-4.605</td>
<td valign="middle" align="left">2.707</td>
</tr>
<tr>
<td valign="middle" align="left">&#x2003;lnTE</td>
<td valign="middle" align="left">5440</td>
<td valign="middle" align="left">4.245</td>
<td valign="middle" align="left">1.834</td>
<td valign="middle" align="left">0.693</td>
<td valign="middle" align="left">8.32</td>
</tr>
<tr>
<td valign="middle" align="left">&#x2003;lnGE</td>
<td valign="middle" align="left">5720</td>
<td valign="middle" align="left">4.818</td>
<td valign="middle" align="left">1.2</td>
<td valign="middle" align="left">2.153</td>
<td valign="middle" align="left">7.58</td>
</tr>
<tr>
<td valign="middle" align="left">&#x2003;CPU</td>
<td valign="middle" align="left">5720</td>
<td valign="middle" align="left">1.086</td>
<td valign="middle" align="left">0.638</td>
<td valign="middle" align="left">0.053</td>
<td valign="middle" align="left">2.742</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Empirical test and results analysis</title>
<sec id="s4_1">
<label>4.1</label>
<title>Baseline regression results</title>
<p>Based on <xref ref-type="disp-formula" rid="eq3">Equation 3</xref> in the model construction, we conducted regression analysis to investigate the relationship between temperature, precipitation, and grain yields. The relevant results are summarized in <xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>. Model (1) indicates that, without controlling for other variables, temperature exerts a positive effect on grain yields at the 5% significance level, while its squared term exerts a negative effect at the 5% significance level. Based on this, Model (3) incorporates economic input as a control variable. The results remain significant: the coefficient for lnTP is 0.544, the quadratic coefficient for lnTP is -0.150, revealing a nonlinear relationship between the two variables. By differentiating <xref ref-type="disp-formula" rid="eq3">Equation 3</xref> and incorporating the coefficients from the baseline regression results presented in <xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>, calculations reveal that within the sample range, when temperature reaches its minimum value, the slope of the curve is 0.292, indicating that a 1% increase in temperature leads to a 0.292% increase in grain yields. When temperature reaches its maximum value, the slope of the curve is -0.409, indicating that a 1% increase in temperature leads to a 0.409% decrease in grain yields. The inflection point of the curve is 1.813<xref ref-type="fn" rid="fn1"><sup>1</sup></xref>, indicating that there is an inverted U-shape relationship between temperature and grain yields, which is &#x201c;promoted first, then suppressed&#x201d;. This indicates that when the temperature is lower than a turning point, increasing temperature can increase grain yields. However, when the temperature rises to the turning point, the continuous increase in temperature will lead to a decrease in grain yields, which aligns with the findings of <xref ref-type="bibr" rid="B71">Hogan and Schlenker (2024)</xref>, validating the universality of the inverted U-shaped relationship between temperature and grain yields. The reason for this is that an appropriate increase in temperature accelerates physiological processes such as photosynthesis and creates favorable conditions for grain growth, thus increasing grain yields. However, when the temperature is too high, it will not only increase the volatilization of pesticides and fertilizers in the farmland, leading to an increase in pests and diseases, but will also lead to a decrease in the activity of photosynthesis enzymes, a decrease in the accumulation of organic matter in grain crops, and ultimately a decrease in yields.</p>
<table-wrap id="T3" position="float">
<label>Table&#xa0;3</label>
<caption>
<p>Baseline regression results of the impact of climate change on grain yields.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" rowspan="3" align="center">Variable</th>
<th valign="top" colspan="2" align="center">Exclude control variables</th>
<th valign="top" colspan="2" align="center">Include control variables</th>
</tr>
<tr>
<th valign="top" align="center">(1)</th>
<th valign="top" align="center">(2)</th>
<th valign="top" align="center">(3)</th>
<th valign="top" align="center">(4)</th>
</tr>
<tr>
<th valign="top" align="center">Baseline-TP</th>
<th valign="top" align="center">Baseline-RF</th>
<th valign="top" align="center">Baseline-TP</th>
<th valign="top" align="center">Baseline-RF</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" rowspan="2" align="center">lnTP</td>
<td valign="top" align="center">0.908**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.544*</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(2.303)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.670)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup></td>
<td valign="top" align="center">-0.243**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.150*</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(-2.511)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.848)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF</td>
<td valign="top" align="center"/>
<td valign="top" align="center">2.455***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">2.069***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(9.502)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(8.768)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup></td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.170***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.143***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(-9.087)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-8.364)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">Constant</td>
<td valign="top" align="center">4.153***</td>
<td valign="top" align="center">-3.972***</td>
<td valign="top" align="center">3.151***</td>
<td valign="top" align="center">-3.927***</td>
</tr>
<tr>
<td valign="top" align="center">(10.533)</td>
<td valign="top" align="center">(-4.444)</td>
<td valign="top" align="center">(8.957)</td>
<td valign="top" align="center">(-4.776)</td>
</tr>
<tr>
<td valign="top" align="center">Control</td>
<td valign="top" align="center">No</td>
<td valign="top" align="center">No</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Entity FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Time FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">N</td>
<td valign="top" align="center">5720</td>
<td valign="top" align="center">5720</td>
<td valign="top" align="center">5720</td>
<td valign="top" align="center">5720</td>
</tr>
<tr>
<td valign="top" align="center">R<sup>2</sup></td>
<td valign="top" align="center">0.003</td>
<td valign="top" align="center">0.048</td>
<td valign="top" align="center">0.152</td>
<td valign="top" align="center">0.185</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in parentheses are t statistics. ***, **, and * indicate significance at the confidence levels of&lt;0.01,&lt;0.05, and&lt; 0.1. &#x201c;Control Yes&#x201d; indicates the inclusion of control variables in the regression.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>Model (2) (see <xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>) indicates that, without controlling for other variables, precipitation exerts a positive effect on grain yields at the 1% significance level, while its squared term exerts a negative effect on grain yields at the 1% significance level. Based on this, Model (4) incorporates economic input as a control variable. The results remain significant: the coefficient for lnRF is 2.096, the quadratic coefficient for lnRF is -0.143, indicating a nonlinear relationship between the two variables. Similarly, by differentiating <xref ref-type="disp-formula" rid="eq3">Equation 3</xref> and incorporating the coefficients from the baseline regression results presented in <xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>, calculations reveal that within the sample range, when precipitation reaches its minimum value, the slope of the curve is 0.564. This indicates that at this point, a 1% increase in precipitation leads to a 0.564% increase in grain yields. When precipitation reaches its maximum value, the slope of the curve is -0.174, indicating that a 1% increase in precipitation leads to a 0.174% decrease in grain yields. The inflection point of the curve is 7.391, indicating that there is an inverted U-shape relationship between precipitation and grain yields (when the precipitation is low, increasing precipitation can improve the yields; however, when precipitation increases to a turning point, continuing to increase precipitation will lead to a reduction in yields). This conclusion aligns with the findings of <xref ref-type="bibr" rid="B157">Saei et&#xa0;al. (2018)</xref>, validating the universality of the inverted U-shaped relationship between precipitation and grain yields. The reason for this is that drought and low rainfall can inhibit the growth and development of grain. Moderate increase in precipitation is good for increasing grain set and hence grain yields. However, when precipitation is too high, it can lead to over-wetting of farmland, collapse of grain crops, and even bring about flooding, which washes away farmland and results in reduced grain yields.</p>
<p>As a result, this study reveals an inverted U-shaped relationship between temperature, precipitation, and grain yields. This finding aligns with <xref ref-type="bibr" rid="B70">Hoffman et&#xa0;al. (2018)</xref> research on the nonlinear association between climatic factors and grain yields, while also corroborating the threshold theory within the field of agronomy (<xref ref-type="bibr" rid="B121">Luo, 2011</xref>; <xref ref-type="bibr" rid="B213">Xiao et&#xa0;al., 2022</xref>). It should be noted that the inverted U-shaped relationship belongs to a special curvilinear relationship, in order to further ensure the reliability of the results of the above inverted U-shaped relationship, this study draws on the method of <xref ref-type="bibr" rid="B111">Lind and Mehlum (2010)</xref>, and utilizes the &#x201c;utest&#x201d; command to test the regression (3) and (4). The test results show that the overall t-value is significant at the statistical level of 1%, and the slope of the set model has both positive and negative values, and the location of the extreme point falls within the sample interval, which indicates that the inverted U-shaped relationship is valid. Hypothesis H1 is verified.</p>
</sec>
<sec id="s4_2">
<label>4.2</label>
<title>Moderating effects</title>
<p>The above analysis shows that there is an inverted U-shaped relationship between climate change factors and grain yields. Based on the above, we expect that CPU enhancement may amplify the negative effect of climate change factors, i.e., strengthen the inverted U-shaped relationship between the two. To empirically verify the moderating effect of CPU, we introduced the interaction term between CPU and the squared term of climate change factors to construct the moderating model (<xref ref-type="disp-formula" rid="eq4">Equation 4</xref>) The regression results are summarized in <xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>. The Model (3) tests the positive moderating effect of CPU on the relationship between temperature and grain yields. The results show that the coefficient of the quadratic cross-multiplier term between temperature and grain yields is significantly negative at the 5% level, indicating that CPU further strengthens the inverted U-shaped relationship between temperature and grain yields, that is the inverted U-shaped relationship between temperature and grain yields is steeper when CPU is higher. Similarly, model (4) (see <xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>) tests the positive moderating effect of CPU on the relationship between precipitation and grain yields. The results show that the coefficient of the quadratic cross-multiplier term between precipitation and grain yields is significantly negative at the 5% level, indicating that CPU likewise further strengthens the inverted U-shaped relationship between precipitation and grain yields, that is the inverted U-shape relationship between precipitation and grain yields is steeper when CPU is higher.</p>
<table-wrap id="T4" position="float">
<label>Table&#xa0;4</label>
<caption>
<p>Regression results of moderating effect of <inline-formula>
<mml:math display="inline" id="im21"><mml:mrow><mml:mtext>CPU</mml:mtext></mml:mrow></mml:math></inline-formula> on the relationship between climate change and grain yields.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" rowspan="3" align="center">Variable</th>
<th valign="middle" colspan="2" align="center">Exclude control variables</th>
<th valign="middle" colspan="2" align="center">Include control variables</th>
</tr>
<tr>
<th valign="middle" align="center">(1)</th>
<th valign="middle" align="center">(2)</th>
<th valign="middle" align="center">(3)</th>
<th valign="middle" align="center">(4)</th>
</tr>
<tr>
<th valign="middle" align="center">Moderation-TP/CPU</th>
<th valign="middle" align="center">Moderation-RF/CPU</th>
<th valign="middle" align="center">Moderation-TP/CPU</th>
<th valign="middle" align="center">Moderation-RF/CPU</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" rowspan="2" align="center">lnTP</td>
<td valign="middle" align="center">1.102***</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.733**</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">(2.839)</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(2.200)</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">lnTP*CPU</td>
<td valign="middle" align="center">0.131</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.300***</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">(1.161)</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(3.108)</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">(lnTP)<sup>2</sup></td>
<td valign="middle" align="center">-0.254***</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">-0.166**</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">(-2.690)</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(-2.027)</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">(lnTP)<sup>2</sup>*CPU</td>
<td valign="middle" align="center">-0.082***</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">-0.111***</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" align="center">(-3.401)</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(-5.306)</td>
<td valign="middle" align="center"/>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">CPU</td>
<td valign="middle" align="center">-0.037***</td>
<td valign="middle" align="center">-0.034***</td>
<td valign="middle" align="center">-0.024***</td>
<td valign="middle" align="center">-0.021***</td>
</tr>
<tr>
<td valign="middle" align="center">(-5.339)</td>
<td valign="middle" align="center">(-5.227)</td>
<td valign="middle" align="center">(-3.730)</td>
<td valign="middle" align="center">(-3.373)</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">lnRF</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">1.701***</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">1.419***</td>
</tr>
<tr>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(6.689)</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(6.161)</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">lnRF*CPU</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.240</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">0.251</td>
</tr>
<tr>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(1.226)</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(1.398)</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">lnRF<sup>2</sup></td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">-0.115***</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">-0.096***</td>
</tr>
<tr>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(-6.229)</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(-5.714)</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">(lnRF)<sup>2</sup>*CPU</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">-0.029**</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">-0.029**</td>
</tr>
<tr>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(-2.020)</td>
<td valign="middle" align="center"/>
<td valign="middle" align="center">(-2.185)</td>
</tr>
<tr>
<td valign="middle" rowspan="2" align="center">Constant</td>
<td valign="middle" align="center">3.765***</td>
<td valign="middle" align="center">-1.341</td>
<td valign="middle" align="center">2.788***</td>
<td valign="middle" align="center">-1.653**</td>
</tr>
<tr>
<td valign="middle" align="center">(9.545)</td>
<td valign="middle" align="center">(-1.536)</td>
<td valign="middle" align="center">(7.677)</td>
<td valign="middle" align="center">(-2.069)</td>
</tr>
<tr>
<td valign="middle" align="center">Control</td>
<td valign="middle" align="center">No</td>
<td valign="middle" align="center">No</td>
<td valign="middle" align="center">Yes</td>
<td valign="middle" align="center">Yes</td>
</tr>
<tr>
<td valign="middle" align="center">Entity FE</td>
<td valign="middle" align="center">Yes</td>
<td valign="middle" align="center">Yes</td>
<td valign="middle" align="center">Yes</td>
<td valign="middle" align="center">Yes</td>
</tr>
<tr>
<td valign="middle" align="center">Time FE</td>
<td valign="middle" align="center">Yes</td>
<td valign="middle" align="center">Yes</td>
<td valign="middle" align="center">Yes</td>
<td valign="middle" align="center">Yes</td>
</tr>
<tr>
<td valign="middle" align="center">N</td>
<td valign="middle" align="center">5720</td>
<td valign="middle" align="center">5720</td>
<td valign="middle" align="center">5720</td>
<td valign="middle" align="center">5720</td>
</tr>
<tr>
<td valign="middle" align="center">R<sup>2</sup></td>
<td valign="middle" align="center">0.099</td>
<td valign="middle" align="center">0.109</td>
<td valign="middle" align="center">0.223</td>
<td valign="middle" align="center">0.233</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in parentheses are t statistics. ***, **, and * indicate significance at the confidence levels of&lt;0.01,&lt;0.05, and&lt; 0.1. &#x201c;Control Yes&#x201d; indicates the inclusion of control variables in the regression.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>The findings suggest that the CPU indeed amplifies the adverse effects of climate change on grain yields, implying that the challenges originally posed by climate change may be further amplified against the backdrop of an uncertain and unstable policy environment, making agricultural production more difficult. This amplification effect may be more pronounced in agricultural production scenarios within developing countries, as their agricultural producers often have limited resources and lower resilience to policy fluctuations, making it difficult for them to cope with the combined impacts of climate risks and policy volatility. This aligns with the core argument proposed by <xref ref-type="bibr" rid="B203">Webber et&#xa0;al. (2020)</xref> that non-climatic stresses may exacerbate climate-induced yields losses. However, this argument extends the existing literature by treating policy uncertainty as an independent and understudied amplifying factor, rather than a generic contextual factor. Moreover, unlike previous studies such as <xref ref-type="bibr" rid="B81">Kan et&#xa0;al. (2023)</xref>, which primarily examined the direct effects of policy adjustments on agricultural input allocation, our findings reveal a more complex and indirect pathway: policy volatility interacts with climate risks to exert compounding pressures on grain production systems.</p>
<p>The moderating effect of CPU is demonstrated more clearly in <xref ref-type="fig" rid="f2"><bold>Figures&#xa0;2</bold></xref>, <xref ref-type="fig" rid="f3"><bold>3</bold></xref>, where a steeper inverted U-shaped relationship between climate factors and grain yields can be seen for high CPU. Thus, hypothesis 2 is verified. According to the theoretical analysis above, for the main body of grain production, CPU amplifies their risk in climate change (it is difficult to accurately predict the direction of the climate and quickly respond to the related risks) and market risk (fluctuations in the price of agricultural products as well as changes in the market demand), which makes them more cautious and conservative in the process of production decision-making, which affects the efficiency of grain production, restricts the improvement of grain yields, and further amplifies the conflict between climate change and grain yields. This study confirms the core finding from existing research that the climate policy environment influences agricultural producers&#x2019; operational decisions (<xref ref-type="bibr" rid="B44">Fanchone et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B170">Singh et&#xa0;al., 2016</xref>). This also aligns with the conclusion that policy interventions can alter the relationship between climate change and grain production (<xref ref-type="bibr" rid="B66">Harkness et&#xa0;al., 2023</xref>). Notably, while previous studies have primarily focused on the regulatory effects of policies themselves (<xref ref-type="bibr" rid="B50">Gao D. et&#xa0;al., 2025</xref>), this research innovatively reveals the moderating role of the climate policy environment&#x2014;it can influence the relationship between climate change and grain production by affecting agricultural producers&#x2019; operational decisions.</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p>The inverted U-shaped curve diagram regarding lnTP and lnY.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fevo-14-1753076-g002.tif">
<alt-text content-type="machine-generated">A plot shows three parabolic curves representing grain yield as a function of temperature in logarithmic scales. The equations are \( y = a_1(\ln TP)^2 \) with no CPU, and \( y = (a_2 + b \text{CPU})(\ln TP)^2 \) with CPU. Parameters \( a_1, a_2, \) and \( b \) have specified ranges. The legend indicates that the curves correspond to no CPU, low CPU (\(\text{CPU} - \sigma\)), and high CPU (\(\text{CPU} + \sigma\)), shown in black and green.</alt-text>
</graphic></fig>
<fig id="f3" position="float">
<label>Figure&#xa0;3</label>
<caption>
<p>The inverted U-shaped curve diagram regarding lnRF and lnY. (&#x3c3; denotes the standard deviation).</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fevo-14-1753076-g003.tif">
<alt-text content-type="machine-generated">Graph depicting the relationship between logarithm of grain yields and precipitation. The curve represents equations with and without climate potential units (CPU). No CPU is a black line, low CPU is a light green line, and high CPU is a bright green line. The equations and parameter ranges are displayed. The x-axis shows logarithm of precipitation, and the y-axis shows logarithm of grain yields.</alt-text>
</graphic></fig>
<p>Therefore, to mitigate the negative impacts of climate change on grain yields and ensure the sustainability of agricultural production, policymakers must not only establish stable, transparent, and consistent climate policy frameworks but also respond promptly to challenges posed by uncertainty. This approach prevents CPU from disrupting the adaptation rhythm of grain production systems to climate change, thereby avoiding the vicious cycle of &#x201c;reduced grain yields &#x2192; worsening poverty.&#x201d; Further, this finding also underscores the necessity of driving systemic transformation to convert external risks into endogenous drivers (<xref ref-type="bibr" rid="B187">Vermeulen et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B228">Zagaria et&#xa0;al., 2021</xref>). By deeply integrating climate adaptation with green agricultural development and industrial upgrading&#x2014;including promoting water-saving, energy-efficient, and pollution-reducing green production technologies (<xref ref-type="bibr" rid="B119">Loboguerrero et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B197">Wang et&#xa0;al., 2025</xref>)&#x2014;and cultivating enhanced agricultural climate resilience as a new competitive advantage for regional agriculture (<xref ref-type="bibr" rid="B80">Kabato et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B152">Regmi and Paudel, 2024</xref>) (e.g., developing climate-smart agriculture that combines adaptation actions with resource efficiency improvements), CPUs&#x2019; responses can be internalized as assets against future extreme weather within a risk framework (<xref ref-type="bibr" rid="B169">Simpson et&#xa0;al., 2023</xref>).</p>
</sec>
<sec id="s4_3">
<label>4.3</label>
<title>Robustness tests</title>
<p>This study conducts robustness tests on the main regression results from three perspectives to ensure the reliability of the findings: (1) Lagged impact of policy; (2) Exclusion of municipalities; (3) Special year removal.</p>
<sec id="s4_3_1">
<label>4.3.1</label>
<title>Lagged impact of policy</title>
<p>Based on the above analysis, the full impact of CPU on agricultural production may not be immediately apparent. By including a one-period lag term for CPU in the regression model, this study aims to capture the delayed response of farmers and agricultural systems. This allows for a more accurate assessment of how policy changes actually affect grain yields over time, rather than assuming instantaneous effects. The regression results are shown in <xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref> for models (1) and (2): the squared terms of temperature and precipitation and the interaction term of CPU both remain stable at a negative significant level of 1%, proving that CPU still reinforces the inverted U-shape relationship between climatic factors and grain yields, affirming the empirical results above and passing the robustness test.</p>
<table-wrap id="T5" position="float">
<label>Table&#xa0;5</label>
<caption>
<p>Robustness tests results.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" rowspan="3" align="center">Variable</th>
<th valign="top" colspan="2" align="center">Lagged impact of policy</th>
<th valign="top" colspan="2" align="center">Exclusion of municipalities</th>
<th valign="top" colspan="2" align="center">Special year removal</th>
</tr>
<tr>
<th valign="top" align="center">(1)</th>
<th valign="top" align="center">(2)</th>
<th valign="top" align="center">(3)</th>
<th valign="top" align="center">(4)</th>
<th valign="top" align="center">(5)</th>
<th valign="top" align="center">(6)</th>
</tr>
<tr>
<th valign="top" align="center">Robust-TP</th>
<th valign="top" align="center">Robust-RF</th>
<th valign="top" align="center">Robust-TP</th>
<th valign="top" align="center">Robust-RF</th>
<th valign="top" align="center">Robust-TP</th>
<th valign="top" align="center">Robust-RF</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" rowspan="2" align="center">lnTP</td>
<td valign="top" align="center">0.536*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.671**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.857**</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(1.720)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.025)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.418)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup></td>
<td valign="top" align="center">-0.116</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.156*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.205**</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(-1.491)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.915)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.383)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnTP*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.325***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.330***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(4.005)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(3.915)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup>*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.112***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.115***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-6.363)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-6.309)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.009</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.005</td>
<td valign="top" align="center">-0.012**</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.474)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.766)</td>
<td valign="top" align="center">(-2.016)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnTP*L.CPU</td>
<td valign="top" align="center">0.171</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">1.538***</td>
</tr>
<tr>
<td valign="top" align="center">(1.617)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(5.963)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup>*L.CPU</td>
<td valign="top" align="center">-0.082***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.105***</td>
</tr>
<tr>
<td valign="top" align="center">(-3.680)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-5.551)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">L.CPU</td>
<td valign="top" align="center">-0.029***</td>
<td valign="top" align="center">-0.030***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.015***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.461***</td>
</tr>
<tr>
<td valign="top" align="center">(-4.754)</td>
<td valign="top" align="center">(-5.004)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.604)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(3.087)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.582***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.411***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.044***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(7.390)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(6.122)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-3.904)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup></td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.112***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.096***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(-7.281)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-5.704)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.388***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.720)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup>*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.038***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-3.530)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF*L.CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.244</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.474)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup>*L.CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.027**</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.234)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">Constant</td>
<td valign="top" align="center">3.097***</td>
<td valign="top" align="center">-1.858**</td>
<td valign="top" align="center">2.803***</td>
<td valign="top" align="center">-1.647**</td>
<td valign="top" align="center">2.632***</td>
<td valign="top" align="center">-2.126**</td>
</tr>
<tr>
<td valign="top" align="center">(9.131)</td>
<td valign="top" align="center">(-2.450)</td>
<td valign="top" align="center">(7.701)</td>
<td valign="top" align="center">(-2.061)</td>
<td valign="top" align="center">(6.668)</td>
<td valign="top" align="center">(-2.392)</td>
</tr>
<tr>
<td valign="top" align="center">Control</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Entity FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Time FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">N</td>
<td valign="top" align="center">5434</td>
<td valign="top" align="center">5434</td>
<td valign="top" align="center">5640</td>
<td valign="top" align="center">5640</td>
<td valign="top" align="center">5148</td>
<td valign="top" align="center">5148</td>
</tr>
<tr>
<td valign="top" align="center">R<sup>2</sup></td>
<td valign="top" align="center">0.218</td>
<td valign="top" align="center">0.215</td>
<td valign="top" align="center">0.234</td>
<td valign="top" align="center">0.237</td>
<td valign="top" align="center">0.243</td>
<td valign="top" align="center">0.246</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in parentheses are t statistics. ***, **, and * indicate significance at the confidence levels of&lt;0.01,&lt;0.05, and&lt; 0.1. &#x201c;Control Yes&#x201d; indicates the inclusion of control variables in the regression.</p></fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="s4_3_2">
<label>4.3.2</label>
<title>Exclusion of municipalities</title>
<p>Considering that municipalities directly under the central government are obviously different from other prefecture-level cities in terms of their agricultural economic methods and production and business activities, they have unique administrative structures, economic priorities, and resource allocations, which may distort the relationship between climatic factors and grain yields. In this study, the samples of four municipalities, namely Beijing, Tianjin, Shanghai and Chongqing, are excluded from the regression process and the regression is re-run using the remaining samples. The results of the basic regression are shown in <xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref> for models (3) and (4): the quadratic and linear coefficients of temperature and precipitation on grain yields are significant, exhibiting an inverted U-shaped relationship. Meanwhile, the significance and positivity of the interaction terms of squared terms of temperature and precipitation with CPU remain unchanged, consistent with previous analyses, suggesting that the main conclusions of this study are well robust.</p>
</sec>
<sec id="s4_3_3">
<label>4.3.3</label>
<title>Special year removal</title>
<p>The 2008 snowstorms in the south and the 2016 flooding events in the middle and lower reaches of the Yangtze River had severe and unusual impacts on grain production in China. To prevent the events in exceptional years from masking the potential relationship between regular climate change and grain yields. In this study, data from 2008 and 2016 are excluded and the regression is rerun using the remaining samples to mitigate the impact of extreme weather events. The regression results are displayed in <xref ref-type="table" rid="T5"><bold>Table&#xa0;5</bold></xref> for models (5) and (6): The coefficient values and significance levels of the coefficients of the base regression results and the moderated effects regression results are basically the same as those of the regression results above, which indicates that the results of the study are robust and reliable.</p>
</sec>
</sec>
<sec id="s4_4">
<label>4.4</label>
<title>Endogeneity test</title>
<p>In identifying endogenous variables, grain yields may also influence CPU, such as low yields potentially prompting governments to revise climate policies. Thus, a bidirectional causal endogenous relationship between CPU and grain yields is highly probable. Simultaneously, CPU may be associated with unobserved local economic or environmental shocks that also affect yields, implying potential omitted variable bias. To mitigate endogeneity issues arising from the above factors, this study employs three sequential approaches for endogeneity testing: two-stage least squares (2SLS) with instrumental variables (IV), system GMM, and the inclusion of additional control variables. For instrument selection, the study adheres to the principles of correlation and exogeneity, choosing two indicators as IVs for CPU: the lagged political cycle (one year) and the lagged CPU variable L.CPU. The political cycle is measured following <xref ref-type="bibr" rid="B216">Xu and Ma (2019)</xref>, using changes in government officials as its proxy variable. Specifically, if a city mayor changes between January and June, it is recorded as a change in the current year; if between July and December, it is recorded as a change in the following year. When a mayor changes, cycle is coded as 1; otherwise, it is coded as 0.</p>
<p>The first four columns in <xref ref-type="table" rid="T6"><bold>Table&#xa0;6</bold></xref> present regression results based on the two-stage least squares method. Notably, DWH yields a p-value of 0.00, indicating endogeneity issues with CPU in the model. Based on the results from columns (1) and (3) in the first stage, it is evident that both instrumental variables are significantly correlated with CPU. Moreover, the Cragg-Donald Wald F-statistics for identifying weak instrumental variables exceed the 10% critical value, confirming the absence of weak instruments and validating the instrumental variable correlation assumption. The P-values for the Sargan statistics in the over-identification test are all greater than 0.05, verifying the exogeneity of the instrumental variables. Furthermore, as shown in columns (2) and (4), the coefficients for the interaction terms between CPU and the linear and quadratic terms of precipitation and temperature exhibit no significant differences compared to those in <xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>. This further substantiates the negative moderating effect of CPU on the relationship between climate risk and grain yields.</p>
<table-wrap id="T6" position="float">
<label>Table&#xa0;6</label>
<caption>
<p>Regression results of endogeneity tests.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" rowspan="3" align="center">Variable</th>
<th valign="middle" colspan="2" align="center">2sls-TP</th>
<th valign="middle" colspan="2" align="center">2sls-RF</th>
<th valign="middle" align="center">GMM-TP</th>
<th valign="middle" align="center">GMM-RF</th>
<th valign="middle" align="center">Add control -TP</th>
<th valign="middle" align="center">Add control -RF</th>
</tr>
<tr>
<th valign="middle" align="center">(1)</th>
<th valign="middle" align="center">(2)</th>
<th valign="middle" align="center">(3)</th>
<th valign="middle" align="center">(4)</th>
<th valign="middle" align="center">(5)</th>
<th valign="middle" align="center">(6)</th>
<th valign="middle" align="center">(7)</th>
<th valign="middle" align="center">(8)</th>
</tr>
<tr>
<th valign="middle" align="center">CPU</th>
<th valign="middle" align="center">lnY</th>
<th valign="middle" align="center">CPU</th>
<th valign="middle" align="center">lnY</th>
<th valign="middle" align="center">lnY</th>
<th valign="middle" align="center">lnY</th>
<th valign="middle" align="center">lnY</th>
<th valign="middle" align="center">lnY</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" rowspan="2" align="center">CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.350***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.248***</td>
<td valign="top" align="center">-0.001***</td>
<td valign="top" align="center">0.004***</td>
<td valign="top" align="center">-0.020***</td>
<td valign="top" align="center">-0.017***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(-9.863)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-6.551)</td>
<td valign="top" align="center">(-3.089)</td>
<td valign="top" align="center">(5.461)</td>
<td valign="top" align="center">(-3.338)</td>
<td valign="top" align="center">(-2.955)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnTP</td>
<td valign="top" align="center">-0.063</td>
<td valign="top" align="center">-0.366***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.124***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.348</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(-0.710)</td>
<td valign="top" align="center">(-3.450)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-25.396)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.157)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup></td>
<td valign="top" align="center">-0.001</td>
<td valign="top" align="center">-0.043*</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.008***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.045</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(-0.040)</td>
<td valign="top" align="center">(-1.819)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(7.823)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.599)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnTP*CPU</td>
<td valign="top" align="center">-0.224</td>
<td valign="top" align="center">0.623***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.229***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.469***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(-1.110)</td>
<td valign="top" align="center">(3.747)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(30.204)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(5.286)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup>*CPU</td>
<td valign="top" align="center">0.038</td>
<td valign="top" align="center">-0.174***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.043***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.143***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(0.830)</td>
<td valign="top" align="center">(-4.695)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-26.873)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-7.405)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.644***</td>
<td valign="top" align="center">3.376***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.165***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.258***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.750)</td>
<td valign="top" align="center">(13.023)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-7.693)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(5.927)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup></td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.045**</td>
<td valign="top" align="center">-0.265***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.008***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.086***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.580)</td>
<td valign="top" align="center">(-13.676)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(4.714)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-5.576)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.180</td>
<td valign="top" align="center">0.695*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.499***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.248</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.350)</td>
<td valign="top" align="center">(1.721)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(20.890)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.452)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup>*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.013</td>
<td valign="top" align="center">-0.059*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.034***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.029**</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(0.350)</td>
<td valign="top" align="center">(-1.956)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-18.402)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.305)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">Cycle</td>
<td valign="top" align="center">-0.048***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.047***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(-3.660)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-3.590)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">L.CPU</td>
<td valign="top" align="center">0.414***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.417***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(30.370)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(30.630)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">L.lnY</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.744***</td>
<td valign="top" align="center">0.764***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(532.935)</td>
<td valign="top" align="center">(359.579)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">L2.lnY</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.208***</td>
<td valign="top" align="center">0.211***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(192.369)</td>
<td valign="top" align="center">(103.144)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">Constant</td>
<td valign="top" align="center">-0.001</td>
<td valign="top" align="center">3.166***</td>
<td valign="top" align="center">2.119***</td>
<td valign="top" align="center">-8.478***</td>
<td valign="top" align="center">0.325***</td>
<td valign="top" align="center">0.763***</td>
<td valign="top" align="center">1.776***</td>
<td valign="top" align="center">-2.175***</td>
</tr>
<tr>
<td valign="top" align="center">(0.010)</td>
<td valign="top" align="center">(25.144)</td>
<td valign="top" align="center">(2.710)</td>
<td valign="top" align="center">(-9.985)</td>
<td valign="top" align="center">(34.500)</td>
<td valign="top" align="center">(10.822)</td>
<td valign="top" align="center">(5.119)</td>
<td valign="top" align="center">(-2.931)</td>
</tr>
<tr>
<td valign="top" align="center">Control</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
<td valign="top" align="center">YES</td>
</tr>
<tr>
<td valign="top" align="center">Pvalue of DWH</td>
<td valign="top" colspan="2" align="center">0.000</td>
<td valign="top" colspan="2" align="center">0.000</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">P value of Sargan</td>
<td valign="top" colspan="2" align="center">0.812</td>
<td valign="top" colspan="2" align="center">0.469</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">Cragg-D F(10%)</td>
<td valign="top" colspan="2" align="center">528.380(19.93)</td>
<td valign="top" colspan="2" align="center">538.265(19.93)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">AR(1)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.000</td>
<td valign="top" align="center">0.000</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">AR(2)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.636</td>
<td valign="top" align="center">0.672</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">Hansen</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">1.000</td>
<td valign="top" align="center">0.997</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">N</td>
<td valign="top" align="center"/>
<td valign="top" align="center">5434</td>
<td valign="top" align="center"/>
<td valign="top" align="center">5434</td>
<td valign="top" align="center">5148</td>
<td valign="top" align="center">5148</td>
<td valign="top" align="center">5720</td>
<td valign="top" align="center">5720</td>
</tr>
<tr>
<td valign="top" align="center">R<sup>2</sup></td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.783</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.758</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.972</td>
<td valign="top" align="center">0.973</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>***p&lt;0.01&#x201d;, &#x201c;**p&lt;0.05&#x201d;, &#x201c;*p&lt;0.10. Z-values are indicated in parentheses in columns (2) and (4)-(6), while t-values are indicated in parentheses in the remaining columns.&#x201d;Control Yes&#x201d; indicates the inclusion of control variables in the regression.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>Columns (5) and (6) in <xref ref-type="table" rid="T6"><bold>Table&#xa0;6</bold></xref> present the estimation results of the dynamic GMM model. Given the persistence characteristics of grain yields over time, this study further incorporates lagged terms l.lncl and l2.lncf to isolate potential unobservable factors. First, AR tests indicate first-order serial correlation but no second-order serial correlation, confirming no significant serial correlation in the original model&#x2019;s error term. Second, Hansen tests yield P-values exceeding 0.05, confirming the validity of the over-identification constraint. Estimation results show that the direction and significance of interaction coefficients align with the main model, indicating that CPU&#x2019;s negative regulatory effect remains reliable after mitigating endogeneity issues.</p>
<p>The final two columns in <xref ref-type="table" rid="T6"><bold>Table&#xa0;6</bold></xref> present the estimation results after incorporating additional control variables. This study selected four indicators&#x2014;livestock manure utilization rate, effective irrigated area, total agricultural machinery power, and GDP growth rate&#x2014;from four perspectives that may influence grain production: soil quality, irrigation coverage, agricultural technology, and economic shocks. These were included in the control variable set. Based on the interaction term coefficients, the reliability of the moderation effect results was further validated.</p>
</sec>
<sec id="s4_5">
<label>4.5</label>
<title>Heterogeneity test</title>
<p>The above studies show that two major factors of climate change significantly affect grain yields, and that the CPU can exacerbate the negative impacts of climate change on grain yields. China is a vast country with different scales across the country. On this basis, the scope of the study is further subdivided to investigate the different impacts of climate change as well as the moderating effect of CPU on grain yields in different regions, which can help to more accurately predict and evaluate the potential risks in agricultural production. Based on previous studies, the heterogeneity analysis will be carried out in terms of both major grain-producing and non-major grain-producing regions, as well as southern and northern regions, while this study also incorporates the heterogeneity analysis of climate-adaptive policy pilot cities and non-climate-adaptive policy pilot cities.</p>
<sec id="s4_5_1">
<label>4.5.1</label>
<title>Heterogeneity between major grain-producing and non-major grain-producing regions</title>
<p>Based on the agricultural resource endowments, crop structure characteristics, and primary grain production functions of China&#x2019;s various provinces, the Ministry of Finance issued the &#x201c;Opinions on Reforming and Improving Comprehensive Agricultural Development Policies&#x201d; in 2003, categorizing China&#x2019;s 31 provinces into two main types: primary grain-producing regions and non-primary grain-producing regions (<xref ref-type="bibr" rid="B120">Lu et&#xa0;al., 2020</xref>). Given the differences in agricultural production conditions and policy allocations between the two regions, we explore the heterogeneity of climate and CPU fluctuations in these regions through subsample regression analysis.</p>
<p>From <xref ref-type="table" rid="T7"><bold>Table&#xa0;7</bold></xref>, it can be seen that there is a significant inverted U-shaped relationship between climatic factors (temperature and precipitation) and grain yields in both major grain-producing and non-major grain-producing areas in China, with the relationship of &#x201c;promoting first and suppressing later&#x201d;. However, the coefficients of the quadratic cross-multipliers of CPU with temperature and precipitation in grain-producing areas are not significant, but the coefficients of the quadratic cross-multipliers of CPU with precipitation in non-major grain-producing areas are significantly negative at 1%, indicating that CPU in non-major grain-producing areas further strengthens the inverted U-shape relationship between climate change and grain yields, and magnifies the systemic risk of climate change.</p>
<table-wrap id="T7" position="float">
<label>Table&#xa0;7</label>
<caption>
<p>Heterogeneity test results for major grain-producing and non-major grain producing regions.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" rowspan="3" align="center">Variable</th>
<th valign="middle" colspan="4" align="center">Major grain producing regions</th>
<th valign="middle" colspan="4" align="center">Non-major rain producing regions</th>
</tr>
<tr>
<th valign="middle" align="center">(1)</th>
<th valign="middle" align="center">(2)</th>
<th valign="middle" align="center">(3)</th>
<th valign="middle" align="center">(4)</th>
<th valign="middle" align="center">(5)</th>
<th valign="middle" align="center">(6)</th>
<th valign="middle" align="center">(7)</th>
<th valign="middle" align="center">(8)</th>
</tr>
<tr>
<th valign="middle" align="center">Baseline -TP</th>
<th valign="middle" align="center">Baseline -RF</th>
<th valign="middle" align="center">Moderate -TP/CPU</th>
<th valign="middle" align="center">Moderate -RF/CPU</th>
<th valign="middle" align="center">Baseline -TP</th>
<th valign="middle" align="center">Baseline -RF</th>
<th valign="middle" align="center">Moderate -TP/CPU</th>
<th valign="middle" align="center">Moderate-RF/CPU</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" rowspan="2" align="center">lnTP</td>
<td valign="top" align="center">0.473</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.595*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">2.238***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.913***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(1.481)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.812)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.968)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.814)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup></td>
<td valign="top" align="center">-0.185**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.199**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.513***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.471***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(-2.200)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.319)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-3.014)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-3.048)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnTP*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.179*</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.689***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.859)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(3.711)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup>*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.022</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.186***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(0.985)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-5.045)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.002</td>
<td valign="top" align="center">-0.010</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.027**</td>
<td valign="top" align="center">0.010</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.266)</td>
<td valign="top" align="center">(-1.409)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.335)</td>
<td valign="top" align="center">(1.023)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF</td>
<td valign="top" align="center"/>
<td valign="top" align="center">2.096***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.635***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.764***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.133***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(6.673)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(5.187)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(5.630)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(3.776)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup></td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.146***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.112***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.121***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.075***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(-6.345)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-4.828)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-5.452)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-3.506)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.225</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.047</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.168)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.226)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup>*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.023</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.005</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.570)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.349)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">Constant</td>
<td valign="top" align="center">4.149***</td>
<td valign="top" align="center">-3.385***</td>
<td valign="top" align="center">3.868***</td>
<td valign="top" align="center">-1.913*</td>
<td valign="top" align="center">0.848</td>
<td valign="top" align="center">-3.333***</td>
<td valign="top" align="center">1.404*</td>
<td valign="top" align="center">-1.162</td>
</tr>
<tr>
<td valign="top" align="center">(12.472)</td>
<td valign="top" align="center">(-3.166)</td>
<td valign="top" align="center">(11.312)</td>
<td valign="top" align="center">(-1.784)</td>
<td valign="top" align="center">(0.944)</td>
<td valign="top" align="center">(-2.922)</td>
<td valign="top" align="center">(1.737)</td>
<td valign="top" align="center">(-1.082)</td>
</tr>
<tr>
<td valign="top" align="center">Control</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Entity FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Time FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">N</td>
<td valign="top" align="center">3180</td>
<td valign="top" align="center">3180</td>
<td valign="top" align="center">3180</td>
<td valign="top" align="center">3180</td>
<td valign="top" align="center">2540</td>
<td valign="top" align="center">2540</td>
<td valign="top" align="center">2540</td>
<td valign="top" align="center">2540</td>
</tr>
<tr>
<td valign="top" align="center">R<sup>2</sup></td>
<td valign="top" align="center">0.262</td>
<td valign="top" align="center">0.298</td>
<td valign="top" align="center">0.282</td>
<td valign="top" align="center">0.315</td>
<td valign="top" align="center">0.090</td>
<td valign="top" align="center">0.112</td>
<td valign="top" align="center">0.199</td>
<td valign="top" align="center">0.174</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in parentheses are t statistics. ***, **, and * indicate significance at the confidence levels of&lt;0.01,&lt;0.05, and&lt; 0.1. &#x201c;Control Yes&#x201d; indicates the inclusion of control variables in the regression.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>The possible reason of such heterogeneity between major grain-producing and non-major grain-producing regions may be that grain-producing regions have well-developed infrastructure, rich experience in coping with climate change, strong policy support, and sound market regulation mechanisms, which can effectively buffer the impacts of CPU and safeguard the stability of grain yields. However, in non-major grain-producing areas where agricultural infrastructure is weak and most of the local small-scale farmers have limited funds, an increase in the CPU will lead to a lack of guaranteed sustained investment in agricultural infrastructure construction in the region, affecting grain output. At the same time, local agricultural products are more dependent on external markets, and CPUs will interfere with market expectations and prices, making it difficult for farmers to adjust production in a timely manner, weakening their ability to resist risks and affecting the stable supply of grain. Under the dual risks of extreme weather and CPU constraints, the comparative advantage of major grain-producing regions over non- major grain-producing regions lies in their long-term, stable national policies that have invested in building a multidimensional resilient ecosystem (<xref ref-type="bibr" rid="B166">Shangguan et&#xa0;al., 2025</xref>). This result of CPU&#x2019;s heterogeneous effect underscores that future policy priorities in grain-producing regions should focus on upgrading from &#x201c;yield resilience&#x201d; to &#x201c;green industrial chain resilience,&#x201d; while leveraging their radiating influence to drive development in non-grain-producing areas (<xref ref-type="bibr" rid="B154">Ren et&#xa0;al., 2025</xref>).</p>
</sec>
<sec id="s4_5_2">
<label>4.5.2</label>
<title>Heterogeneity between the northern and southern regions</title>
<p>China&#x2019;s climate exhibits a pronounced north-south differentiation across natural zones, with the division between northern and southern regions primarily based on the Qinling-Huaihe Line as a natural geographical boundary. The climatic differences between the north and the south are mainly reflected in rainfall, temperature and seasons (<xref ref-type="bibr" rid="B97">Lei et&#xa0;al., 2023</xref>). The south has abundant and relatively stable precipitation, warm temperatures, and is prone to high temperatures in summer; the north has less total precipitation and uneven seasonal distribution, and moderate temperatures. This climatic difference leads to differences in the climate dependence of agriculture between the north and the south.</p>
<p>As can be seen from <xref ref-type="table" rid="T8"><bold>Table&#xa0;8</bold></xref>, the primary terms of temperature and precipitation in both the southern and northern regions of China significantly and positively affect grain yields, and their squared terms significantly and negatively affect grain yields, suggesting that the climatic factors (temperature and precipitation) in both regions have an inverted U-shaped relationship with grain yields. The coefficients of the quadratic cross-multiplication terms of CPU and temperature were significant at the 1% level in the southern region, while the quadratic cross-multiplication terms of precipitation were not significant. The probable reason is that precipitation is abundant and stable in the south, so the grain water demand is guaranteed and less affected by the fluctuation of precipitation, and at the same time, the water conservancy facilities in the south are perfect, and the ability to cope with the changes of precipitation is strong. However, with the intensification of climate warming, summer high temperature events in the South have become more frequent and more intense, resulting in significant fluctuations in grain yields. Measures to cope with temperature changes in the South are more influenced by policies, such as the construction of sunshades and the adoption of heat-resistant crop varieties that require policy and financial support, making them more vulnerable to CPU. At the same time, in the face of CPU, farmers will choose a more conservative production strategy and may reduce agricultural inputs in areas at risk of high temperatures, thus affecting grain production. The coefficient of the quadratic cross-multiplier term between CPU and precipitation is significant at the 1% level in the northern region, while the quadratic cross-multiplier term for temperature is not significant. The probable reason for this is the higher latitude of the northern region, where grain yields is relatively less affected by the increase in temperature due to warming. With relatively low total precipitation and uneven seasonal distribution in the northern region, grain growth is susceptible to the risk of water shortage. Simultaneously, the lack of investment in water infrastructure to meet the needs of agricultural production, and the CPU&#x2019;s further constraints on the maintenance and upgrading of facilities, the promotion of new irrigation technologies, and the ability to prevent flooding and drainage in the event of a sudden downpour make grain production capacity even more vulnerable in the face of extreme precipitation.</p>
<table-wrap id="T8" position="float">
<label>Table&#xa0;8</label>
<caption>
<p>Heterogeneity test results for the south region and the north region.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" rowspan="3" align="center">Variable</th>
<th valign="middle" colspan="4" align="center">North region</th>
<th valign="middle" colspan="4" align="center">South region</th>
</tr>
<tr>
<th valign="middle" align="center">(1)</th>
<th valign="middle" align="center">(2)</th>
<th valign="middle" align="center">(3)</th>
<th valign="middle" align="center">(4)</th>
<th valign="middle" align="center">(5)</th>
<th valign="middle" align="center">(6)</th>
<th valign="middle" align="center">(7)</th>
<th valign="middle" align="center">(8)</th>
</tr>
<tr>
<th valign="middle" align="center">Baseline -TP</th>
<th valign="middle" align="center">Baseline -RF</th>
<th valign="middle" align="center">Moderate -TP/CPU</th>
<th valign="middle" align="center">Moderate -RF/CPU</th>
<th valign="middle" align="center">Baseline -TP</th>
<th valign="middle" align="center">Baseline -RF</th>
<th valign="middle" align="center">Moderate -TP/CPU</th>
<th valign="middle" align="center">Moderate-RF/CPU</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" rowspan="2" align="center">lnTP</td>
<td valign="top" align="center">0.637*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.769**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">4.276*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">7.130***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(1.842)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.142)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.916)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.945)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup></td>
<td valign="top" align="center">-0.222**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.243**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.754*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-1.278***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(-2.362)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.518)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.872)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.949)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnTP*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.345***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">5.441***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.809)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(9.345)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup>*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.062**</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-1.023***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.074)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-9.873)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.008</td>
<td valign="top" align="center">-0.092***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.157***</td>
<td valign="top" align="center">0.028</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.653)</td>
<td valign="top" align="center">(-5.498)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-5.771)</td>
<td valign="top" align="center">(1.590)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.117***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.611</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.493**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.792</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.972)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.575)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.351)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.194)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup></td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.075***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.035</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.101**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.053</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.593)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.157)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.312)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.167)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">1.312***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.081</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(4.746)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.119)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup>*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.112***</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.002</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-4.963)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.047)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">Constant</td>
<td valign="top" align="center">3.843***</td>
<td valign="top" align="center">0.079</td>
<td valign="top" align="center">3.612***</td>
<td valign="top" align="center">1.649</td>
<td valign="top" align="center">-3.330</td>
<td valign="top" align="center">-2.801</td>
<td valign="top" align="center">-7.015**</td>
<td valign="top" align="center">-0.155</td>
</tr>
<tr>
<td valign="top" align="center">(10.321)</td>
<td valign="top" align="center">(0.064)</td>
<td valign="top" align="center">(9.444)</td>
<td valign="top" align="center">(1.300)</td>
<td valign="top" align="center">(-1.053)</td>
<td valign="top" align="center">(-1.207)</td>
<td valign="top" align="center">(-2.026)</td>
<td valign="top" align="center">(-0.064)</td>
</tr>
<tr>
<td valign="top" align="center">Control</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Entity FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Time FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">N</td>
<td valign="top" align="center">2600</td>
<td valign="top" align="center">2600</td>
<td valign="top" align="center">2600</td>
<td valign="top" align="center">2600</td>
<td valign="top" align="center">3120</td>
<td valign="top" align="center">3120</td>
<td valign="top" align="center">3120</td>
<td valign="top" align="center">3120</td>
</tr>
<tr>
<td valign="top" align="center">R<sup>2</sup></td>
<td valign="top" align="center">0.143</td>
<td valign="top" align="center">0.167</td>
<td valign="top" align="center">0.165</td>
<td valign="top" align="center">0.188</td>
<td valign="top" align="center">0.175</td>
<td valign="top" align="center">0.175</td>
<td valign="top" align="center">0.262</td>
<td valign="top" align="center">0.193</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in parentheses are t statistics. ***, **, and * indicate significance at the confidence levels of&lt;0.01,&lt;0.05, and&lt; 0.1.&#x201d;Control Yes&#x201d; indicates the inclusion of control variables in the regression.</p></fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="s4_5_3">
<label>4.5.3</label>
<title>Heterogeneity between climate-adapted and non-climate-adapted cities</title>
<p>To address the challenges posed by climate change, China launched the first batch of pilot projects for building climate- adapted cities in 2017, aiming to comprehensively enhance the capacity of cities to adapt to climate change. Twenty-eight cities were selected for the first batch of pilot projects, covering three regions: eastern, central and western (<xref ref-type="bibr" rid="B67">He et&#xa0;al., 2025</xref>). To explore whether climate resilience policies have a positive impact on climate resilience of grain production, we conducted a subsample regression analysis. It is worth noting that the development of climate-resilient cities in China remains at an early stage, with a relatively limited overall number of such cities. This directly resulted in a sample size of only 100 climate-resilient cities (N = 100) being included in the sub-sample regression analysis of this study. The limitations of the sample size may to some extent reduce the statistical power and robustness of the regression results.</p>
<p><xref ref-type="table" rid="T9"><bold>Table&#xa0;9</bold></xref> shows that the coefficients of the quadratic cross-multiplier terms of CPU with both temperature and precipitation in climate-adapted cities are not significant, but the coefficients of the quadratic cross-multiplier terms of CPU with temperature and precipitation in non-climate-adapted cities are significant and negative at the 1% level, indicating that CPU in non-climate-adapted cities further strengthens the inverted U-shaped relationship between climate change and grain yields, amplifying the systematic risk of climate change, whereas CPU does not significantly affect the climate resilience of grain yields in climate-adapted cities. The likely reason for this is that non-adapted cities could merely implement climate-resilient policies and may have unstable policy support systems (including agricultural insurance, disaster subsidies, and technology extension), which brought risks posed by CPU. However, long-term implementation of climate adaptation policies may enable farmers to accumulate a wealth of coping experience and develop a strong adaptive capacity, which enables them to adjust their production measures in response to changes in temperature and precipitation in a timely manner, and to minimize the negative impacts of CPUs on grain yields. This finding provides crucial evidence for new insights into the theory of agricultural adaptation in grain production. Against the backdrop of increasingly frequent extreme weather events, shifting from passive responses&#x2014;such as attempting to reduce CPU while adapting to extreme weather&#x2014;to proactive development transforms climate resilience into an endogenous driver for agricultural green upgrading (<xref ref-type="bibr" rid="B12">Bailey-Serres et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B235">Zheng et&#xa0;al., 2024</xref>). Merely defending against risks is static and passive. The long-term goal should leverage stability to transition agricultural systems toward more productive and sustainable forms (<xref ref-type="bibr" rid="B147">Pretty et&#xa0;al., 2018</xref>).</p>
<table-wrap id="T9" position="float">
<label>Table&#xa0;9</label>
<caption>
<p>Heterogeneity test results for climate-adapted and non-climate-adapted cities.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" rowspan="3" align="center">Variable</th>
<th valign="middle" colspan="4" align="center">Adapted cities</th>
<th valign="middle" colspan="4" align="center">Non&#x2013;adapted cities</th>
</tr>
<tr>
<th valign="middle" align="center">(1)</th>
<th valign="middle" align="center">(2)</th>
<th valign="middle" align="center">(3)</th>
<th valign="middle" align="center">(4)</th>
<th valign="middle" align="center">(5)</th>
<th valign="middle" align="center">(6)</th>
<th valign="middle" align="center">(7)</th>
<th valign="middle" align="center">(8)</th>
</tr>
<tr>
<th valign="middle" align="center">Baseline -TP</th>
<th valign="middle" align="center">Baseline -RF</th>
<th valign="middle" align="center">Moderate -TP/CPU</th>
<th valign="middle" align="center">Moderate -RF/CPU</th>
<th valign="middle" align="center">Baseline -TP</th>
<th valign="middle" align="center">Baseline -RF</th>
<th valign="middle" align="center">Moderate -TP/CPU</th>
<th valign="middle" align="center">Moderate-RF/CPU</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" rowspan="2" align="center">lnTP</td>
<td valign="top" align="center">-5.487**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-5.348**</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.531</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.659**</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(-2.382)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-2.203)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.621)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.986)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup></td>
<td valign="top" align="center">1.027*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.994</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.148*</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.154*</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center">(1.738)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.618)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.804)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.877)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnTP*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.643</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.325***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.701)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(3.990)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnTP)<sup>2</sup>*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.137</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.112***</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(0.709)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-6.352)</td>
<td valign="top" align="center"/>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.033</td>
<td valign="top" align="center">-0.001</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.007</td>
<td valign="top" align="center">-0.013**</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(1.148)</td>
<td valign="top" align="center">(-0.058)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-1.167)</td>
<td valign="top" align="center">(-2.390)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.492</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.815</td>
<td valign="top" align="center"/>
<td valign="top" align="center">2.070***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">1.405***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.465)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.663)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(8.714)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(6.094)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup></td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.040</td>
<td valign="top" align="center"/>
<td valign="top" align="center">0.065</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.143***</td>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.096***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center">(0.529)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(0.737)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-8.328)</td>
<td valign="top" align="center"/>
<td valign="top" align="center">(-5.687)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">lnRF*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.850</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">0.404***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(0.408)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(2.828)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">(lnRF)<sup>2</sup>*CPU</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.062</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">-0.039***</td>
</tr>
<tr>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-0.421)</td>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center"/>
<td valign="top" align="center">(-3.634)</td>
</tr>
<tr>
<td valign="top" rowspan="2" align="center">Constant</td>
<td valign="top" align="center">12.660***</td>
<td valign="top" align="center">6.864</td>
<td valign="top" align="center">12.334***</td>
<td valign="top" align="center">7.998*</td>
<td valign="top" align="center">3.155***</td>
<td valign="top" align="center">-3.933***</td>
<td valign="top" align="center">2.791***</td>
<td valign="top" align="center">-1.652**</td>
</tr>
<tr>
<td valign="top" align="center">(4.865)</td>
<td valign="top" align="center">(1.652)</td>
<td valign="top" align="center">(4.368)</td>
<td valign="top" align="center">(1.683)</td>
<td valign="top" align="center">(8.956)</td>
<td valign="top" align="center">(-4.751)</td>
<td valign="top" align="center">(7.724)</td>
<td valign="top" align="center">(-2.067)</td>
</tr>
<tr>
<td valign="top" align="center">Control</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Entity FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">Time FE</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="center">N</td>
<td valign="top" align="center">100</td>
<td valign="top" align="center">100</td>
<td valign="top" align="center">100</td>
<td valign="top" align="center">100</td>
<td valign="top" align="center">5620</td>
<td valign="top" align="center">5620</td>
<td valign="top" align="center">5620</td>
<td valign="top" align="center">5620</td>
</tr>
<tr>
<td valign="top" align="center">R<sup>2</sup></td>
<td valign="top" align="center">0.191</td>
<td valign="top" align="center">0.134</td>
<td valign="top" align="center">0.207</td>
<td valign="top" align="center">0.142</td>
<td valign="top" align="center">0.153</td>
<td valign="top" align="center">0.186</td>
<td valign="top" align="center">0.239</td>
<td valign="top" align="center">0.241</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The values in parentheses are t statistics. ***, **, and * indicate significance at the confidence levels of&lt;0.01,&lt;0.05, and&lt; 0.1.&#x201d;Control Yes&#x201d; indicates the inclusion of control variables in the regression.</p></fn>
</table-wrap-foot>
</table-wrap>
</sec>
</sec>
</sec>
<sec id="s5" sec-type="discussion">
<label>5</label>
<title>Discussion</title>
<p>Against the backdrop of escalating climate threats to global food security, this study employs an economic-climate model (C-D-C) to systematically validate a significant inverted U-shaped relationship between climate factors (temperature, precipitation) and total grain yields. The findings corroborate previous literature on the nonlinear relationship between climate and yields (<xref ref-type="bibr" rid="B27">Chen et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B55">Guntukula, 2020</xref>; <xref ref-type="bibr" rid="B161">Schlenker et&#xa0;al., 2006</xref>), aligning with principles of agronomy and ecology (<xref ref-type="bibr" rid="B160">Schauberger et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B174">Song et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B184">Tschurr et&#xa0;al., 2023</xref>). Additionally, it provides empirical insights into how policy uncertainty shapes extreme temperatures&#x2019; impact on grain productio&#x2014;while scholars have noted institutional conditions&#x2019; direct effects on grain production (<xref ref-type="bibr" rid="B49">Gao et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B74">Hua et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B237">Zhu et&#xa0;al., 2024</xref>), research on institutional role in moderating the climate-grain production relationship remains limited, with existing studies indicating that agricultural infrastructure and insurance subsidies can mitigate climate adverse impacts (<xref ref-type="bibr" rid="B195">Wang et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B210">Wu et&#xa0;al., 2019</xref>) and agricultural R&amp;D investment enhances crop adaptability (<xref ref-type="bibr" rid="B14">Bollington et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B21">Carter et&#xa0;al., 2021</xref>).</p>
<p>What sets this study apart is its integration of CPU as a moderating variable within the climate-agriculture framework, emphasizing policy quality and stability over mere existence, and ambiguous or discontinuous climate policies may act as &#x201c;institutional barriers&#x201d; to agricultural adaptation (<xref ref-type="bibr" rid="B139">Oberlack, 2017</xref>). Specifically, high CPU exposes farmers to dual climate and policy uncertainties (<xref ref-type="bibr" rid="B132">Mittenzwei et&#xa0;al., 2017</xref>), which increases the &#x201c;waiting value&#x201d; of investments (<xref ref-type="bibr" rid="B223">Yanore et&#xa0;al., 2023</xref>) and delays adaptive adoption. Consistent with RO theory, CPU enhances the option value of waiting for future information, leading farmers to delay irreversible long-term investments (e.g., drip irrigation) amid policy ambiguities and leaving systems vulnerable to climate risks (<xref ref-type="bibr" rid="B34">Dai, 2025</xref>; <xref ref-type="bibr" rid="B53">Ginbo et&#xa0;al., 2021</xref>). From the perspective of AC theory, CPU erodes key elements&#x2014;resource availability and action freedom&#x2014;thereby reducing farmers&#x2019;ability to manage risks via consistent resource access and planning (<xref ref-type="bibr" rid="B98">Lennert et&#xa0;al., 2024</xref>). In summary, CPU amplifies climate impacts through dual mechanisms: raising the &#x201c;waiting premium&#x201d; on long-term investments and weakening immediate &#x201c;action capacity.&#x201d; Notably, CPU&#x2019;s moderating effect also presents spatially heterogeneous. In detail, non-major grain-producing areas are more sensitive to CPU shocks due to weaker infrastructure, insufficient institutional support, and higher market dependency, which supports the &#x201c;institutional buffer&#x201d; hypothesis (<xref ref-type="bibr" rid="B136">Nilsson et&#xa0;al., 2012</xref>). In contrast, climate adaptation pilot cities show reduced grain yields sensitivity to CPU, underscoring the role of policy credibility in boosting agricultural resilience (<xref ref-type="bibr" rid="B10">Awokuse et&#xa0;al., 2024</xref>), while regionally, southern areas are more sensitive to CPU-temperature interactions and northern regions are more susceptible to CPU-precipitation interactions, reflecting differences in agricultural climate exposure and adaptive capacity (<xref ref-type="bibr" rid="B108">Li et&#xa0;al., 2016</xref>). Furthermore, three theoretical sub-pathways can explain how CPU amplifies extreme weather&#x2019;s impact on grain production: firstly, farmers adopt precautionary strategies to prepare for policy changes, curtailing adaptive inputs for climate risks; secondly, CPU reduces long-term signal reliability, leading to short-term experience reliance and slower, narrower system adjustments; thirdly, CPU prompts caution in public goods supply and long-term financing and reduces long-term adaptive technology R&amp;D, though adaptive cities and staple grain regions can mitigate these issues via stable policies, forming resilient assets unaffected by CPU. Through aforementioned results, we further contend that policies enhancing the climate resilience of agricultural systems should not only focus on infrastructure and subsidies, but also incorporate Nature-based Solutions into their core strategy. By harnessing natural processes, Nature-based Solutions can deliver critical regulatory services&#x2014;such as temperature regulation, water retention, and carbon sequestration&#x2014;in a more cost-effective and synergistic manner. Crucially, once established, many Nature-based Solutions measures exhibit robust self-sustaining ecosystem service functions with reduced subsequent fiscal dependency. This capacity can partially buffer the disruption caused by CPU to long-term agricultural investments.</p>
<p>The findings of this paper provide significant implications for China and nations worldwide. FromChina&#x2019;s standpoint, as a leading global grain producer and consumer (<xref ref-type="bibr" rid="B68">He et&#xa0;al., 2022</xref>), its energy and agricultural transformation is steered by the &#x201c;dual carbon&#x201d; objectives (achieving carbon peak by 2030 and carbon neutrality by 2060) (<xref ref-type="bibr" rid="B28">Chen et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B35">Dang et&#xa0;al., 2025</xref>). While this policy ensures long-term sustainability and fosters green transition, short-term adjustments may entail some challenges (<xref ref-type="bibr" rid="B62">Hao et&#xa0;al., 2022</xref>). Based on previous research and our findings, three key approaches can be summarized to mitigate the impact of policy uncertainty on grain producers who may be affected in the short term. Firstly, long-term expectations for this policy should be stabilized to reduce systemic risks in agricultural production (<xref ref-type="bibr" rid="B103">Li J. et&#xa0;al., 2024</xref>). Uncertainty in climate policies hinders producers&#x2019; investment in green agricultural innovations and sustainable agricultural machinery (<xref ref-type="bibr" rid="B92">Lai et&#xa0;al., 2026</xref>; <xref ref-type="bibr" rid="B176">Sun et&#xa0;al., 2024</xref>). Therefore, the design of the &#x201c;dual carbon&#x201d; policy should establish a clear long-term pathway, reduce frequent adjustments, and create stable fiscal and financial support tailored for agriculture (<xref ref-type="bibr" rid="B229">Zhai and Hu, 2024</xref>). This will stabilize expectations for small and micro agricultural producer, preventing policy volatility from undermining their adaptive capacity (<xref ref-type="bibr" rid="B231">Zhang X. et&#xa0;al., 2025</xref>). Second, promote the strengthening of adaptation capacity (based on the AC theory) among agricultural entities to mitigate the inverted U-shaped risks posed by extreme weather (<xref ref-type="bibr" rid="B29">Chepkoech et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B82">Kangogo et&#xa0;al., 2020</xref>). Building on the established inverted U-shaped relationship with climate change, supporting policies for &#x201c;dual carbon&#x201d; should invest in climate-resilient infrastructure and promote adaptive agricultural technologies (<xref ref-type="bibr" rid="B41">Elahi et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B134">Mthembu et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B202">Webb et&#xa0;al., 2017</xref>), which will enhance the agricultural system&#x2019;s capacity to withstand climate fluctuations, flatten the inverted U-shaped curve (reducing the slope in <xref ref-type="fig" rid="f2"><bold>Figures&#xa0;2</bold></xref>, <xref ref-type="fig" rid="f3"><bold>3</bold></xref>). Third, implement differentiated policies by region to avoid a one-size-fits-all approach(<xref ref-type="bibr" rid="B101">Li L. et&#xa0;al., 2023</xref>). Tailored emission reductiontargets, technology promotion lists, and compensation mechanisms should be established based on each region&#x2019;s position on the inverted U-curve, variations in green production efficiency, and agricultural carbon emission characteristics (<xref ref-type="bibr" rid="B212">Xia et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B234">Zhang X. et&#xa0;al., 2023</xref>). Moreover, in line with the rural revitalization policy requirements (the &#x201c;Comprehensive Plan for Promoting Rural Revitalization (2024-2027)&#x201d;, it is imperative to establish market-driven incentive mechanisms, such as agricultural carbon sink markets and horizontal ecological compensation, harmonizing the &#x201c;dual carbon&#x201d; goals with rural revitalization aspirations (<xref ref-type="bibr" rid="B175">Song et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B178">Tang et&#xa0;al., 2023</xref>). Additionally, leveraging international experience, a 10&#x2013;15 year cross-cycle plan should be formulated, integrating fiscal support with climate resilience enhancement and emission reduction and carbon sequestration targets, thereby converting inverted U-shaped risks into stable income streams (<xref ref-type="bibr" rid="B16">Br&#xe9;chet et&#xa0;al., 2013</xref>; <xref ref-type="bibr" rid="B47">Fodha and Yamagami, 2025</xref>).</p>
<p>From an international standpoint, extending the relevant analysis to other developing nations, such as rice-producing countries in Southeast Asia and smallholder economies in Africa, uncovers inherent instability within their policy frameworks (<xref ref-type="bibr" rid="B8">Aryal et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B116">Liu et&#xa0;al., 2020</xref>). Variables like fluctuations in international climate financing and domestic government transitions intensify CPU (<xref ref-type="bibr" rid="B125">Ma et&#xa0;al., 2024</xref>; <xref ref-type="bibr" rid="B133">Monasterolo et&#xa0;al., 2019</xref>), prompting resource-constrained agricultural producers to opt for conservative survival strategies rather than climate-adaptive innovative investments. This creates a vicious cycle of &#x201c;policy uncertainty &#x2192; inadequate investment &#x2192; diminished adaptability &#x2192; declining grain production &#x2192; worsening poverty&#x201d;. The primary finding of this study is that CPU significantly undermines the climate resilience of grain production systems. This challenge is particularly pronounced in developing countries experiencing rapid industrialization and policy shift (<xref ref-type="bibr" rid="B15">Borsetta et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B43">Fahad and Hossain, 2025</xref>), offering valuable insights for regions with comparable global climate conditions and developmental stages to tackle climate change and safeguard food security. Moreover, it is imperative to further investigate methods for balancing short-term, medium-term, and long-term policy interests within a framework that ensures positive social externalities, while steering clear of policy discontinuity (<xref ref-type="bibr" rid="B129">Medina Hidalgo et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B189">Vogt-Schilb and Hallegatte, 2017</xref>).</p>
<p>In a word, in addition to extend the application of <xref ref-type="bibr" rid="B52">Gavriilidis (2021)</xref> CPU concept to the agricultural sector, the study also provides a critical theoretical lens for understanding the complex decision-making environment faced by developing countries under the triple pressures of &#x201c;development-emission reduction-adaptation.&#x201d; Our findings underscore the critical importance of establishing stable, transparent, and continuous climate policy frameworks for developing countries&#x2014;particularly for advancing Nature-based Solutions to address the impacts of climate change within the Global South, where policy stability could unlock the potential of ecological approaches to enhance agricultural resilience. For China, this implies that while advancing macro-level climate strategies, it must provide clear, predictable implementation guidelines and long-term incentives in the agricultural sector to stabilize producer confidence (<xref ref-type="bibr" rid="B78">Ju et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B209">Wu, 2023</xref>). For the international community, it means providing financial and technical assistance to help vulnerable developing countries build more resilient policy systems and implementation capacities (<xref ref-type="bibr" rid="B150">Rauniyar et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B159">Savvidou et&#xa0;al., 2021</xref>).</p>
</sec>
<sec id="s6" sec-type="conclusions">
<label>6</label>
<title>Conclusions and policy implications</title>
<p>This study examines the nonlinear effects of climate change factors (temperature and precipitation) on grain yields and innovatively explores the moderating role of CPU in this relationship, using panel data for 286 prefecture-level cities in China from 2001 to 2020. The study draws the following conclusions: (1) Climate change factors (temperature and precipitation) have a significant inverted U-shaped relationship with grain yields. Moderate increases in temperature and precipitation initially boost grain yields, but exceeding ecological thresholds may have adverse effects, leading to yield declines. (2) CPU exacerbates the negative impacts of climate extremes by enabling farmers to invest less in adaptation and make conservative production decisions. the higher the level of CPU, the steeper the inverted U-shape curve, indicating that the adverse impacts of climate change on grain yields are more pronounced in high CPU environments. (3) The impact of the CPU exhibits regional heterogeneity. Specifically, non-major grain-producing regions are more susceptible to CPU-amplified climate risks due to weaker agricultural infrastructure; precipitation fluctuates widely in the north, and precipitation extremes are more likely to be amplified by CPU effects; hot weather is frequent in the south, and temperature extremes are more likely to be amplified by CPU effects; and non-climate-adapted cities without adaptive climates aren&#x2019;t able to mitigate the CPU effects by stabilizing policies and infrastructure.</p>
<p>Based on the research findings, this study proposes the following policy recommendations using China as an example, aiming to provide insights and references for national grain systems&#x2014;particularly those in developing countries with high gain system vulnerability&#x2014;to address climate change and extreme weather events.</p>
<p>First, strengthen the capacity building of agriculture to adapt to climate change: on the one hand, the government should increase the construction of advanced climate monitoring and early-warning system facilities to provide accurate and timely climate data and early-warning information, and to help farmers to make informed decisions and optimize the use of their resources under the changing climate conditions, reduce potential losses and enhance the resilience of the grain system. For instance, enhance the integrated digital support platform for &#x201c;monitoring-early warning-decision-making,&#x201d; leveraging digital technologies to develop disaster warning modules for crops such as rice, wheat, and corn (e.g., high-temperature heat damage, drought, and waterlogging warnings) (<xref ref-type="bibr" rid="B156">Rojas, 2021</xref>; <xref ref-type="bibr" rid="B232">Zhang W. et&#xa0;al., 2023</xref>). Utilize channels like mobile apps to achieve simultaneous, precise delivery of warning information alongside adaptive cultivation techniques (e.g., irrigation and fertilizer adjustments). On the other hand, the promotion of drought- and flood-tolerant crop varieties, the improvement of water-saving irrigation techniques, as well as the optimization of the layout of agricultural production and the allocation of resources, will increase the adaptive capacity of agriculture to climate change. Disaster-avoidance cropping systems (such as adjusting planting dates and developing conservation tillage) could be enhanced by establishing county-level demonstration farms and implementing subsidy programs.</p>
<p>Second, enhancing climate resilience through policy stabilization: Governments should strive to reduce the uncertainty of climate policy and provide a stable policy environment for agricultural production, while actively advancing Nature-based Solutions to address the impacts of climate change within the Global South. The agricultural departments could lead the development of a medium-to-long-term action plan for agricultural adaptation to climate change. By 2030 and 2060, a phased approach may be established to achieve emission reduction and carbon sequestration targets, build adaptive capacity indicators, promote key technologies, and establish a central government funding framework. Moreover, annual progress reports shall be published in accordance with the plan and stable &#x201c;ecological subsidies&#x201d; will directly benefit farmers implementing adaptation measures. Through these measures, the Government can help farmers anticipate and adapt to climate and policy changes, minimize the adverse impacts of the CPU, and encourage long-term investment in climate change mitigation and technological innovation (<xref ref-type="bibr" rid="B86">Khatri-Chhetri et&#xa0;al., 2021</xref>).</p>
<p>Third, develop targeted regional strategies:</p>
<list list-type="simple">
<list-item>
<p>(1) for non-major grain-producing regions that are subject to greater fluctuations in CPU, the Government should take measures to buffer the impact of CPU and increase the resilience of the grain system by strengthening infrastructure, improving water resource management and providing specialized agricultural extension services (<xref ref-type="bibr" rid="B143">Osumba et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B148">Priya et&#xa0;al., 2025</xref>). By encouraging leading agricultural enterprises in major grain-producing regions to form partnerships with leading enterprises in non-major grain-producing regions, and through methods such as contract farming and technical management services, non-grain-producing production areas can benefit from the resilient production models and market channels of major grain-producing regions. In non-major grain-producing regions, funds promoting production resilience can be established. By linking funding to improvements in local climate resilience indicators, these funds can incentivize local agricultural producers&#x2014;including small-scale farmers and agricultural cooperatives&#x2014;to implement measures addressing climate risks.</p></list-item>
<list-item>
<p>(2) Accurate policy implementation should be tailored to regional variations. Southern China could establish medium-to-long-term protection mechanisms against high-temperature disasters, including a special long-term fiscal program for &#x201c;heat-adaptive planting technologies.&#x201d; This would ensure the continuity and predictability of support for heat-tolerant varieties, shade structures, and related resources (<xref ref-type="bibr" rid="B63">Hao and He, 2025</xref>; <xref ref-type="bibr" rid="B123">Ma et&#xa0;al., 2022</xref>). while innovating financial instruments to diversify high-temperature production risks (e.g., heatwave insurance) that automatically trigger payouts when consecutive high temperatures reach specific thresholds. these instruments stabilize farmers&#x2019; income expectations while countering their tendency to reduce investments due to concerns over policy uncertainty risks. In northern China, combining conservation tillage and dryland farming with the restoration of native vegetation to comprehensively enhance soil health and water retention capacity (Nature-based Solutions). Simultaneously, promoting long-term maintenance agreements for water conservancy facilities can partially insulate against CPU disruptions by contractually locking in the attention and responsibilities of government and social capital. Moreover, in financial instruments, developing &#x201c;dual drought and flood insurance&#x201d; enhances farmers&#x2019; confidence in weathering precipitation fluctuations in the context of CPU risks.</p></list-item>
<list-item>
<p>(3) The scope of climate adaptation pilot projects could be further expanded. Building upon the ongoing advancement of pilot climate-adaptive cities, and drawing on the advanced experience of adaptive cities (such as establishing high-density meteorological observation networks and utilizing smart platforms for precise disaster early warning&#x2014;a typical example is Shenzhen City&#x2019;s &#x201c;electronic water gauge&#x201d; flood warning system), develop and train a &#x201c;Climate Adaptive Grain Production Decision Support System&#x201d; tailored for non-adaptive cities. In the long run, this system could contribute to integrating localized climate forecasts, resilient technical solutions, and policy tool information, while enhancing adaptation tools such as urban climate change health risk monitoring and assessment, and comprehensive indicators for heat island, rain island, drought island, and smog island effects. Thus, those successful practices, technologies and experiences that have already yielded significant results in climate-resilient cities will be systematically replicated in other regions.</p></list-item>
</list>
<p>This study still has limitations that require further refinement in subsequent research. Although this study selected annual mean temperature and annual total precipitation as climate factors, which may have obscured the effects of water and heat stress on grain crops during their critical growth stages. Future research should refine climate indicators by focusing on crop critical growth stages and employing more precise metrics such as accumulated temperature, days of extreme temperatures, and precipitation concentration to achieve accurate analysis of the climate-yield relationship. The research unit could be extended to the county level, utilizing county-level grain production data and policy text data to improve variable matching. In this study, we have employed two-stage least squares and system GMM methods to address endogeneity issues. Moving forward, we will utilize more cutting-edge approaches such as machine learning to mitigate endogeneity concerns. Additionally, this study introduces the moderating effect of CPU into the field of grain production, and future research could introduce CPU into other areas of agricultural sector research, such as agro-ecosystem services, rural economic development, and agricultural supply chain management, in order to comprehensively assess the impacts of CPU on the sustainable development of agriculture in various aspects.</p>
</sec>
</body>
<back>
<sec id="s7" sec-type="data-availability">
<title>Data availability statement</title>
<p>The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/<xref ref-type="supplementary-material" rid="SM1"><bold>Supplementary Material</bold></xref>.</p></sec>
<sec id="s8" sec-type="author-contributions">
<title>Author contributions</title>
<p>XZ: Formal analysis, Writing &#x2013; original draft, Writing &#x2013; review &amp; editing, Project administration, Supervision, Conceptualization, Validation, Investigation. MZ: Visualization, Formal analysis, Validation, Data curation, Writing &#x2013; review &amp; editing, Methodology, Writing &#x2013; original draft. ZS: Formal analysis, Writing &#x2013; review &amp; editing, Methodology, Data curation, Visualization, Investigation, Validation. YL: Validation, Supervision, Methodology, Funding acquisition, Resources, Writing &#x2013; review &amp; editing, Project administration.</p></sec>
<sec id="s10" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p></sec>
<sec id="s11" sec-type="ai-statement">
<title>Generative AI statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p></sec>
<sec id="s12" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p></sec>
<sec id="s13" sec-type="supplementary-material">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fevo.2026.1753076/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fevo.2026.1753076/full#supplementary-material</ext-link></p>
<supplementary-material xlink:href="DataSheet1.pdf" id="SM1" mimetype="application/pdf"/></sec>
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<fn id="n1" fn-type="custom" custom-type="edited-by">
<p>Edited by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/912857">Oyetola Oyebanji</ext-link>, Botanical Research Institute of Texas, United States</p></fn>
<fn id="n2" fn-type="custom" custom-type="reviewed-by">
<p>Reviewed by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/287272">Alban Kuriqi</ext-link>, University of Lisbon, Portugal</p>
<p><ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1921416">Raza Ali Tunio</ext-link>, Sichuan Agricultural University, China</p>
<p><ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3307166">Zhou Shiwei</ext-link>, Anhui Provincial Institute of Water Resources Science, China</p></fn>
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<fn-group>
<fn id="fn1"><label>1</label>
<p>It is worth noting that the turning point calculated in our model represents a &#x201c;macro-statistical optimum for economic output,&#x201d; rather than the &#x201c;micro-physiological optimum for individual crops&#x201d; often cited in the literature. Macro-aggregated data incorporates complex factors such as crop structure, cropping systems, regional variations, and non-growing season periods. We based our analysis on prefecture-level city-level data for annual, multi-crop (rice, wheat, corn, soybean, tuber and other crops.) mixed yields, using annual average temperature and precipitation. Thus, the turning point number calculated reflects the &#x201c;climate-economic equilibrium point&#x201d; that maximizes total annual grain output across all regions under China's current multi-crop planting structure, geographic distribution, and agricultural scheduling&#x2014;not the optimal physiological temperature for any single crop at any specific stage.</p></fn>
</fn-group>
</back>
</article>