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<journal-id journal-id-type="publisher-id">Front. Environ. Sci.</journal-id>
<journal-title>Frontiers in Environmental Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Environ. Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-665X</issn>
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<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-id pub-id-type="publisher-id">1630688</article-id>
<article-id pub-id-type="doi">10.3389/fenvs.2025.1630688</article-id>
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<subj-group subj-group-type="heading">
<subject>Environmental Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Talent agglomeration and carbon emissions in China: promotive effect or inhibitory effect? analysis on heterogeneous bilateral stochastic frontier model</article-title>
<alt-title alt-title-type="left-running-head">Zhang et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fenvs.2025.1630688">10.3389/fenvs.2025.1630688</ext-link>
</alt-title>
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<contrib-group>
<contrib contrib-type="author" corresp="yes" equal-contrib="yes">
<name>
<surname>Zhang</surname>
<given-names>Yue</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>&#x2020;</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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<contrib contrib-type="author" equal-contrib="yes">
<name>
<surname>Yang</surname>
<given-names>Xin</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="author-notes" rid="fn001">
<sup>&#x2020;</sup>
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<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Qun</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
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<contrib contrib-type="author">
<name>
<surname>Liu</surname>
<given-names>Chao</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
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<contrib contrib-type="author">
<name>
<surname>Ren</surname>
<given-names>Yangjun</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Ting</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
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<aff id="aff1">
<sup>1</sup>
<institution>Business School, Hohai University</institution>, <addr-line>Nanjing</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>The People&#x2019;s Hospital of Danyang, Affiliated Danyang Hospital of Nantong University</institution>, <addr-line>Danyang</addr-line>, <country>China</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>School of Management Engineering, Nanjing Institute of Technology</institution>, <addr-line>Nanjing</addr-line>, <country>China</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>School of Public Administration, Hohai University</institution>, <addr-line>Nanjing</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/734151/overview">Irina Georgescu</ext-link>, Bucharest Academy of Economic Studies, Romania</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2176331/overview">Jani Kinnunen</ext-link>, &#xc5;bo Akademi University, Finland</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3096661/overview">Chang Mei</ext-link>, Sichuan University, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Yue Zhang, <email>zytokio@hhu.edu.cn</email>
</corresp>
<fn fn-type="equal" id="fn001">
<label>
<sup>&#x2020;</sup>
</label>
<p>These authors have contributed equally to this work and share first authorship</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>17</day>
<month>09</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>13</volume>
<elocation-id>1630688</elocation-id>
<history>
<date date-type="received">
<day>21</day>
<month>05</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>20</day>
<month>08</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Zhang, Yang, Wang, Liu, Ren and Wang.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Zhang, Yang, Wang, Liu, Ren and Wang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>As the dual imperatives of carbon reduction and economic expansion gain prominence, the pursuit of high-quality development has taken on greater urgency, with talent agglomeration emerging as a critical driving force. Yet its specific impact on carbon emissions remains unclear. To address this question, this study employs a two-tier stochastic frontier model using panel data from 30 Chinese provinces spanning 2013&#x2013;2023, enabling the identification and decomposition of the dual effects of talent agglomeration on carbon emissions. The results show that talent agglomeration exerts asymmetric bilateral impacts, with the inhibitory effect dominating the promotive effect and producing an overall decline in emissions. Specifically, the promotive channel increased emissions by 16.2%, while the inhibitory channel reduced them by 43.8%, resulting in a net decrease of 27.6% relative to the frontier level. The net inhibitory effect became more pronounced after 2020 following a brief uptick in 2014, and spatial heterogeneity was evident, with the largest reductions occurring in the western region, followed by the central and eastern regions. Further heterogeneity analysis indicates that larger net reductions occur at higher levels of talent agglomeration (&#x2265;40%), higher economic development (70%&#x2013;100%), and under stricter environmental regulation, whereas in the early stages of urbanization the promotive effect dominates but gradually shifts toward inhibition as urbanization deepens. These findings demonstrate that although talent agglomeration has dual channels of influence, its overall impact is to reduce emissions, thereby providing more precise guidance for carbon reduction policies that reconcile economic growth with environmental sustainability.</p>
</abstract>
<kwd-group>
<kwd>talent agglomeration</kwd>
<kwd>carbon emissions</kwd>
<kwd>bilateral stochastic frontier model</kwd>
<kwd>promotive effect</kwd>
<kwd>heterogeneous characteristics</kwd>
</kwd-group>
<counts>
<page-count count="15"/>
</counts>
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<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Environmental Economics and Management</meta-value>
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</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>China is undergoing a transformative period aimed at achieving high-quality and sustainable development (<xref ref-type="bibr" rid="B33">Wang and Han, 2023</xref>). One of the most major dilemma in this transition lies in reducing carbon emissions while maintaining progress in industrialization and urbanization (<xref ref-type="bibr" rid="B28">Shi et al., 2018</xref>). In response, the State Council launched the &#x201c;Beautiful China&#x201d; initiative to foster a low-carbon innovation system, underscoring the importance of talent as a driver of emission reduction and sustainable growth. Building on this agenda, regional governments have increasingly adopted measures to attract and concentrate high-level talent, positioning it as a cornerstone of innovation and economic transformation. Measures such as improving foundational infrastructure, reforming the household registration system, and enhancing the business climate have been implemented to create favorable environments conducive to both innovation and sustainability (<xref ref-type="bibr" rid="B20">Meyers et al., 2020</xref>; <xref ref-type="bibr" rid="B32">Wang and Chen, 2023</xref>). As high technical and scientific talent has facilitated technological advancement and industrial restructuring (<xref ref-type="bibr" rid="B36">Wang L. et al., 2020</xref>), it is necessary to achieve synergistic effects that align both economic and environmental goals. Consequently, clarifying the dual impacts of talent agglomeration and identifying ways to reinforce its dominant inhibitory effect have become pressing concerns for both policymakers and scholars during this transitional phase.</p>
<p>While substantial evidence highlights the link between economic development and environmental outcomes, there remains a critical need to integrate talent mobility into low-carbon innovation strategies. Existing studies show that R&#x26;D talent plays a pivotal role in promoting sustainable development at multiple levels (<xref ref-type="bibr" rid="B5">Crowley-Henry and Al Ariss, 2018</xref>; <xref ref-type="bibr" rid="B16">Lin et al., 2021</xref>). Compared to other factors, talent agglomeration shaped by population mobility significantly influences industrial innovation competitiveness and supports sustainable economic progress, offering multifaceted economic, social, and environmental value (<xref ref-type="bibr" rid="B36">Wang L. et al., 2020</xref>; <xref ref-type="bibr" rid="B27">Shi and Lai, 2023</xref>). As a concentration of high-quality human capital, talent agglomeration is essential for innovation. It also generates knowledge spillovers that promote regional industrial development and facilitate green technology diffusion (<xref ref-type="bibr" rid="B17">Liu and Zhang, 2021</xref>). However, some studies have indicated that excessive agglomeration, especially when combined with regional development imbalances or mismatches in industrial layout, can exacerbate environmental pollution, thus hindering emission reduction efforts (<xref ref-type="bibr" rid="B17">Liu and Zhang, 2021</xref>; <xref ref-type="bibr" rid="B25">Shen and Peng, 2021</xref>). Moreover, the inhibitory effects from technological innovation and industrial upgrading induced by talent agglomeration do not fully offset the promotive effects arising from congestion and urbanization, yielding only limited net reductions in carbon emissions. Consequently, this study examines the synergistic effects of talent agglomeration on the environment to clarify its role in supporting China&#x2019;s carbon reduction strategies and sustainable development goals.</p>
<p>The contributions of this research are fourfold. First, this research introduces a comparative framework that evaluates both the promotive and inhibitory effects of talent agglomeration on carbon emissions, moving beyond the traditional one-dimensional perspective and addressing biases in existing literature. Second, it develops a robust analytical model that captures regional variations in economic development, urbanization, and policy conditions, thereby enriching current research that often isolates factors such as technological innovation or policy design. Third, it offers empirical evidence on the environmental impacts of talent agglomeration, particularly in the context of China&#x2019;s diverse regional economies. Fourth, the findings indicate that in most regions&#x2014;especially in eastern provinces&#x2014;the restraining effect of talent agglomeration on carbon emissions outweighs its stimulative effect, offering policymakers practical guidance on leveraging talent strategies to support both carbon reduction and sustainable economic growth.</p>
<p>The subsequent content of this study is organized in the following way: <xref ref-type="sec" rid="s2">Section 2</xref> discusses relevant literature and formulates the hypotheses. <xref ref-type="sec" rid="s3">Section 3</xref> introduces the models and research data. <xref ref-type="sec" rid="s4">Section 4</xref> describes the empirical process and results, followed by the conclusion, policy implications, and suggestions for further study in the final section.</p>
</sec>
<sec id="s2">
<title>2 Literature review and hypothesis development</title>
<sec id="s2-1">
<title>2.1 Literature review</title>
<p>At present, there has been little investigation into the environmental effects of scientific and technological talent agglomeration. The overwhelming majority of the literature has examined the relationship between socioeconomic dynamics, such as industrial agglomeration and urbanization, on carbon emissions, arguing that these factors significantly enhance regional energy efficiency and environmental protection while highlighting the unintended negative consequences of neglecting a comprehensive approach (<xref ref-type="bibr" rid="B50">Zhang Y. et al., 2024</xref>). Some research shows that regional agglomeration of population and industry increases energy demand and carbon emission (<xref ref-type="bibr" rid="B46">York, 2007</xref>; <xref ref-type="bibr" rid="B15">Li et al., 2022</xref>). Nonetheless, when examining the agglomeration effects, researchers have largely found substantial evidence supporting improved public infrastructure efficiency, thereby reducing energy emission intensity (<xref ref-type="bibr" rid="B8">Glaeser and Kerr, 2009</xref>; <xref ref-type="bibr" rid="B41">Wuyts and Dutta, 2014</xref>).</p>
<p>Research supporting the first view contends that agglomeration can effectively reduce carbon emissions. This is because industrial agglomeration facilitates the scaling of regional industries, which helps lower production costs and promotes resource sharing, thereby improving energy efficiency and supporting environmental protection (<xref ref-type="bibr" rid="B54">Zou et al., 2024</xref>). Using panel data at the provincial level spanning 1991 to 2016, <xref ref-type="bibr" rid="B47">Zhang et al. (2017)</xref> demonstrated that regional industrial agglomeration can directly enhance regional production efficiency in the short term. High human capital not only promotes knowledge sharing and collaboration, driving process innovation and product quality improvement in enterprises (<xref ref-type="bibr" rid="B6">Dost and Badir, 2018</xref>), but also contributes to promoting sustainable practices through low-carbon policies, green technological innovation, and industrial optimization (<xref ref-type="bibr" rid="B43">Yang et al., 2022</xref>). High human capital promotes knowledge sharing and collaboration, significantly driving process innovation and product quality improvement in enterprises Regional industrial and population agglomeration has been recognized as a crucial strategy advancing environmental sustainability and fostering a green economy (<xref ref-type="bibr" rid="B36">Wang et al., 2020b</xref>).</p>
<p>In contrast, other research suggests that regional industrial and population agglomeration can exacerbate environmental degradation. On one hand, regional industrial and population agglomeration significantly increases energy demand, complicates the acquisition of resources such as land and energy, and leads to higher emissions of industrial pollutants (<xref ref-type="bibr" rid="B1">Andersson and L&#xf6;&#xf6;f, 2011</xref>). On the other hand, while agglomeration can improve accessibility in urban areas, it may also generate large volumes of waste and further raise energy consumption (<xref ref-type="bibr" rid="B45">Yi et al., 2022</xref>). For example, a study using urban population density and <italic>per capita</italic> energy consumption in China found a positive correlation between the two (<xref ref-type="bibr" rid="B37">Wang et al., 2024</xref>). Moreover, in highly agglomerated regions, the productivity gains associated with concentration may be accompanied by higher carbon emissions (<xref ref-type="bibr" rid="B22">Oliveira et al., 2014</xref>).</p>
<p>Nonetheless, certain research has suggested that the relationship between agglomeration economies and carbon emissions is nonlinear (<xref ref-type="bibr" rid="B35">Wang F. et al., 2020</xref>). Some researcher noted that there is significant difference across countries at different stages of development. While some scholars found that agglomeration in low-income countries effectively reduces carbon emissions, others observed the opposite trend in high-income countries, with an increase in carbon emissions. As demonstrated by <xref ref-type="bibr" rid="B34">Wang and Wang (2019)</xref>, agglomeration is linked to environmental pollution in a manner that follows an inverted U-shaped trajectory. Initially, agglomeration generates sizable innovation and knowledge spillovers; once density surpasses a critical level, congestion and crowding erode these benefits, so the spillover gains weaken and may vanish. Only when surpassing a specific threshold does agglomeration begin to positively contribute to reducing pollution emissions (<xref ref-type="bibr" rid="B35">Wang F. et al., 2020</xref>; <xref ref-type="bibr" rid="B40">Wu et al., 2021</xref>). The research identified a positive N-shaped relationship between agglomeration and carbon emissions, suggesting that after surpassing an inefficient level of agglomeration, further agglomeration can theoretically mitigate carbon emissions (<xref ref-type="bibr" rid="B15">Li et al., 2022</xref>). Over extended periods, this relationship consistently exhibits a positive N shape, indicating that, theoretically, beyond certain levels of inefficiency, agglomeration can again contribute to reducing carbon emissions.</p>
<p>Despite the importance of talent agglomeration, research on this topic remains superficial, and the heterogeneous characteristics of these impacts have not been comprehensively explored. Therefore, this study further expands in three aspects: First, it establishes a bilateral analytical framework for assessing the effect of talent agglomeration on carbon emissions and evaluates this relationship across 30 provinces in China. Second, it investigates the twofold impact of talent agglomeration on regional carbon emissions and empirically explores its spatiotemporal evolution and changing patterns. Third, the study explores the differential impacts of urbanization and economic development at different levels of development and investigates practical paths to reinforce the inhibitory effects of talent agglomeration on emissions.</p>
</sec>
<sec id="s2-2">
<title>2.2 Hypothesis</title>
<p>The agglomeration of elements within a region can enhance the quality and flow direction of these elements, thereby achieving economies of scale and generating economic benefits (<xref ref-type="bibr" rid="B44">Ye et al., 2022</xref>). But are the environmental impacts of spatial agglomeration the same? Agglomeration can promote the sharing of public facilities and technologies within a region, reduce pollution, and enhance collaborative innovation, thereby improving ecological efficiency (<xref ref-type="bibr" rid="B31">Tian et al., 2024</xref>). The increase in regional energy consumption and exacerbation of congestion caused by agglomeration place significant pressure on the sustainable development of the regional ecological environment (<xref ref-type="bibr" rid="B19">Martin and Sunley, 2006</xref>). As an essential prerequisite for innovation, scientific and technological talent extends urbanization and industrial agglomeration in regional development. Thus, its dynamics have two opposing effects on carbon utilization.</p>
<sec id="s2-2-1">
<title>2.2.1 The inhibition impact of talent agglomeration on carbon emission</title>
<p>Talent agglomeration strengthens knowledge exchange and collaboration, catalyzing green innovation and accelerating the adoption, diffusion, and assimilation of low-energy technologies, thereby reducing carbon emissions. High-value knowledge and skills serve as the primary drivers of innovation, directly enhancing regional innovation capacity under supportive policies and favorable environmental conditions (<xref ref-type="bibr" rid="B52">Zhou et al., 2018</xref>). By fostering innovation and creativity, talent agglomeration can facilitate the regional adoption of low-energy technologies, thereby reducing carbon emissions while simultaneously improving energy efficiency (<xref ref-type="bibr" rid="B34">Wang and Wang, 2019</xref>). Moreover, regions with abundant knowledge and specialized skills tend to drive the practical implementation of innovation that reduces carbon emissions. Talent agglomeration enhances technological assimilation by translating individual innovations into practical applications and facilitating the sharing and absorption of technologies within the region, thereby lowering carbon emissions (<xref ref-type="bibr" rid="B38">Wingreen and Blanton, 2018</xref>).</p>
<p>The gathering and concentration of R&#x26;D talent facilitate the development of green industries, thus driving cleaner industrial restructuring. The foundation for regional adjustments and upgrades lies in restructuring labor markets with scientific and technological talent, which reduces the costs and risks of technological advancements for businesses and facilitates emissions reduction (<xref ref-type="bibr" rid="B4">Cheng et al., 2021</xref>). Green technologies, which optimize energy consumption, improve resource efficiency, and enable sustainable energy systems, rely heavily on the support of scientific and technological talent, thereby cutting carbon emissions. Moreover, the diffusion of talent across regions supports further reductions in carbon emissions and advances progress toward sustainable development goals (Wang et al., 2022).</p>
<p>Talent agglomeration process involves the improvement of regional public services, enhancing service quality and advancing decarbonization. Regions with well-developed public services and living infrastructure are more likely to attract scientific and technological talent while simultaneously reducing carbon emissions. Owing to the improved urban living environment, regions are more likely to attract talent and enhance public services, which supports emissions reduction (<xref ref-type="bibr" rid="B10">Jiang et al., 2020</xref>). Additionally, the agglomeration process raises overall environmental awareness, driven by higher standards for environmental quality and stronger preferences for low-carbon living, thereby curbing emissions (<xref ref-type="bibr" rid="B49">Zhang P. et al., 2024</xref>).</p>
<p>
<statement content-type="hypothesis" id="Hypothesis_1">
<label>Hypothesis 1</label>
<p>Talent agglomeration can inhibit regional carbon emissions.</p>
</statement>
</p>
</sec>
<sec id="s2-2-2">
<title>2.2.2 The promotion impact of talent agglomeration on carbon emission</title>
<p>Some researchers argue that agglomeration acts as a contributing factor to China&#x2019;s carbon emissions. The degree of agglomeration will lead to modifications in production equipment capacity (<xref ref-type="bibr" rid="B24">Robertson and Gatignon, 1986</xref>). As the scale of talent agglomeration grows, competition intensifies and resource allocation becomes increasingly unequal, particularly hindering the diffusion of innovative green technologies. Intense competitive pressures diminish collaboration and create technological barriers, restricting the dissemination of green technologies. In addition, the consolidation of existing production structures reinforces carbon-intensive practices, thereby aggravating environmental pressures.</p>
<p>In China, severe distortions in resource allocation influence corporate investment preferences and production behaviors, resulting in environmental damage (<xref ref-type="bibr" rid="B23">Peng et al., 2021</xref>). The substantial costs associated with acquiring scientific and technological talent drive enterprises to scale up production, boost output, and redirect resources away from technological innovation, thereby impeding advancements in production technology (<xref ref-type="bibr" rid="B2">Cao et al., 2023</xref>). This path dependency exacerbates resource misallocation, leading to higher levels of environmental pollution. Moreover, talent agglomeration tends to raise regional living and production costs, contributing to increased greenhouse gas emissions and crowding effects (<xref ref-type="bibr" rid="B9">Han et al., 2018</xref>). The agglomeration of scientific and technological talents accelerates urban expansion, which results in infrastructure congestion and subsequent environmental degradation. Such non-productive consumptions significantly elevate the levels of direct carbon emissions. These non-productive consumptions substantially increase direct carbon emission levels.</p>
<p>
<statement content-type="hypothesis" id="Hypothesis_2">
<label>Hypothesis 2</label>
<p>Talent agglomeration can promote regional carbon emissions.</p>
<p>Building on the two streams of talent agglomeration&#x2019;s impact on carbon emissions, we analyzed the bilateral effects through the mechanism illustrated in <xref ref-type="fig" rid="F1">Figure 1</xref>.</p>
</statement>
</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Mechanism analysis of the effects of talent agglomeration on carbon emissions.</p>
</caption>
<graphic xlink:href="fenvs-13-1630688-g001.tif">
<alt-text content-type="machine-generated">Diagram illustrating the relationship between talent agglomeration and carbon emissions. Positive factors include technological innovation, industrial upgrading, and public services, supporting urbanization, economic development, and environmental regulation. Negative factors include consolidated misallocation, industrial mismatch, and environmental crowding. Hypotheses H1 and H2 connect these elements to carbon emissions.</alt-text>
</graphic>
</fig>
</sec>
</sec>
</sec>
<sec id="s3">
<title>3 Methodology and research data</title>
<sec id="s3-1">
<title>3.1 The two-tier stochastic frontier model</title>
<p>To measure the bilateral relationship between talent agglomeration and carbon emissions, we follow the two-tier stochastic frontier model of <xref ref-type="bibr" rid="B12">Kumbhakar and Parmeter (2009)</xref>. As shown in <xref ref-type="disp-formula" rid="e1">Equation 1</xref>:<disp-formula id="e1">
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<mml:mi mathvariant="normal">&#x3b4;</mml:mi>
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<mml:mi mathvariant="normal">&#x3c9;</mml:mi>
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<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">&#x3b5;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2a;</mml:mo>
<mml:mi mathvariant="normal">&#x3b4;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>As shown in <xref ref-type="disp-formula" rid="e1">Equation 1</xref>, <inline-formula id="inf1">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>f</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the carbon emission boundary, and <inline-formula id="inf2">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>x</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes a set of control variables influencing regional carbon emissions, specifically urbanization, industrialization, energy structure and environmental regulation; <inline-formula id="inf3">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the inefficiency component related to carbon emissions, <inline-formula id="inf4">
<mml:math id="m5">
<mml:mrow>
<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> denotes the stochastic error term capturing other unobservable factors affecting carbon emissions. <inline-formula id="inf5">
<mml:math id="m6">
<mml:mrow>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes the vector of parameters that require estimation The composite residual term <inline-formula id="inf6">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is defined <inline-formula id="inf7">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<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>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf8">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is a normally distributed random error term<inline-formula id="inf9">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x223c;</mml:mo>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:msup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, accounting for deviations in the carbon emission gap.</p>
<p>Given that <inline-formula id="inf10">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>&#x3be;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> may not equal zero, relying on Ordinary Least Squares (OLS) estimates would result in bias. Therefore, the parameters are estimated using Maximum Likelihood Estimation (MLE) to ensure more accurate results. This model helps isolate the impact of talent agglomeration on the carbon emission gap, considering regional disparities in key economic and environmental factors. If <inline-formula id="inf11">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2a7e;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, it indicates a positive effect of the concentration of technological talent on the carbon emission gap. Conversely, if <inline-formula id="inf12">
<mml:math id="m13">
<mml:mrow>
<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>&#x2a7d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, it signifies a negative effect on the regional innovation efficiency gap, indicating a hindrance. When <inline-formula id="inf13">
<mml:math id="m14">
<mml:mrow>
<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>&#x2a7d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf14">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> or <inline-formula id="inf15">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2a7e;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf16">
<mml:math id="m17">
<mml:mrow>
<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>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, the model constitutes a unilateral stochastic frontier model.</p>
<p>If <inline-formula id="inf17">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<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>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, the model reduces to an OLS model, which would be biased if <inline-formula id="inf18">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is non-zero. Therefore, MLE is applied to mitigate this bias and ensure more reliable estimates (<xref ref-type="bibr" rid="B13">Lei et al., 2024</xref>). The residuals <inline-formula id="inf19">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are assumed to follow a normal distribution with a mean of zero and variance <inline-formula id="inf20">
<mml:math id="m21">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3b5;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>, i.e., <inline-formula id="inf21">
<mml:math id="m22">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x223c;</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3b5;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>It is assumed that both <inline-formula id="inf22">
<mml:math id="m23">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf23">
<mml:math id="m24">
<mml:mrow>
<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> are follow exponential distributions, specifically, <inline-formula id="inf24">
<mml:math id="m25">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x223c;</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>E</mml:mi>
<mml:mi>X</mml:mi>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf25">
<mml:math id="m26">
<mml:mrow>
<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>&#x223c;</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>E</mml:mi>
<mml:mi>X</mml:mi>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf26">
<mml:math id="m27">
<mml:mrow>
<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>&#x223c;</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>E</mml:mi>
<mml:mi>X</mml:mi>
<mml:mi>P</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, with the residual terms being mutually independent and uncorrelated with inter-provincial characteristic factors. Given these distributional assumptions, the probability density function is derived, as shown in <xref ref-type="disp-formula" rid="e2">Equation 2</xref>:<disp-formula id="e2">
<mml:math id="m28">
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>exp</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>exp</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:msubsup>
<mml:mo>&#x222b;</mml:mo>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mi>&#x221e;</mml:mi>
</mml:msubsup>
<mml:mtext>&#x200a;</mml:mtext>
<mml:mi>&#x3c6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>d</mml:mi>
<mml:mi>x</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>exp</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>exp</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mi>&#x3c6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
<p>Within this framework, <inline-formula id="inf27">
<mml:math id="m29">
<mml:mrow>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mo>&#xb7;</mml:mo>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf28">
<mml:math id="m30">
<mml:mrow>
<mml:mi>&#x3c6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mo>&#xb7;</mml:mo>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> denote the cumulative distribution function (CDF) and the probability density function (PDF) of the standard normal distribution, respectively, and the reparameterizations are defined in <xref ref-type="disp-formula" rid="e3">Equation 3</xref>:<disp-formula id="e3">
<mml:math id="m31">
<mml:mrow>
<mml:mtable columnalign="left">
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>;</mml:mo>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>;</mml:mo>
</mml:mrow>
</mml:mtd>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
</p>
<p>The log-likelihood to be maximized is given by <xref ref-type="disp-formula" rid="e4">Equation 4</xref>:<disp-formula id="e4">
<mml:math id="m32">
<mml:mrow>
<mml:mi>ln</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mo>;</mml:mo>
<mml:mi>&#x3c0;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>n</mml:mi>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>ln</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mo>&#x2061;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi>n</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:mtext>&#x200a;</mml:mtext>
<mml:mi>ln</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:msup>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b3;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msup>
<mml:mi>e</mml:mi>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:msup>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>
</p>
<p>Within this framework, let <inline-formula id="inf29">
<mml:math id="m33">
<mml:mrow>
<mml:mi>&#x3c0;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>. Consequently, the values for all parameters can be explicitly obtained via Maximum Likelihood Estimation (MLE). Furthermore, it is necessary to estimate <inline-formula id="inf30">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf31">
<mml:math id="m35">
<mml:mrow>
<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>, thus necessitating the further derivation of the conditional density function, as shown in <xref ref-type="disp-formula" rid="e5">Equations 5</xref>, <xref ref-type="disp-formula" rid="e6">6</xref>:<disp-formula id="e5">
<mml:math id="m36">
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2223;</mml:mo>
<mml:msub>
<mml:mi>&#x3be;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi>exp</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c9;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>exp</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="[" close="]" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>exp</mml:mi>
<mml:mo>&#x2061;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mi>&#x3b2;</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
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<label>(6)</label>
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<p>Based on <xref ref-type="disp-formula" rid="e5">Equations 5</xref>, <xref ref-type="disp-formula" rid="e6">6</xref>, the conditional expectations follow from <xref ref-type="disp-formula" rid="e7">Equations 7</xref>, <xref ref-type="disp-formula" rid="e8">8</xref>:<disp-formula id="e7">
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<label>(7)</label>
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<label>(8)</label>
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<p>The conditional expectations are used to quantify the absolute deviations of regional carbon utilization gaps from the frontier, representing positive and negative effects. For ease of subsequent discussion and comparison, these conditional expectations are further converted into percentages that represent deviations from the frontier level. <xref ref-type="disp-formula" rid="e9">Equations 9</xref>, <xref ref-type="disp-formula" rid="e10">10</xref> transform these expectations into percentage deviations from the frontier:<disp-formula id="e9">
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<label>(10)</label>
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</p>
<p>Finally, the net effect is defined in <xref ref-type="disp-formula" rid="e11">Equation 11</xref>:<disp-formula id="e11">
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<label>(11)</label>
</disp-formula>
</p>
<p>Herein, <inline-formula id="inf34">
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</inline-formula> represents the difference between the facilitating and hindering effects. If <inline-formula id="inf35">
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</inline-formula> &#x3e;0, it indicates that the facilitating effects are stronger than the hindering effects, thus playing a dominant role. Conversely, if <inline-formula id="inf36">
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</inline-formula> &#x3c;0, it signifies that the hindering effects are predominant.</p>
</sec>
<sec id="s3-2">
<title>3.2 Data source and sample selection</title>
<p>Referring to the conceptual and empirical framework, and considering data availability, Chinese provincial panel data spanning 2013 to 2023 were used to investigate the effect of scientific and technological talent concentration on interprovincial atmospheric pollution. Owing to data constraints, the regions of Tibet, Hong Kong, Macao, and Taiwan were excluded from this study. All variables involving price factors were adjusted for inflation using 2010 as the base year.</p>
<sec id="s3-2-1">
<title>3.2.1 Variable selection</title>
<sec id="s3-2-1-1">
<title>3.2.1.1 Carbon emission</title>
<p>As specified in <xref ref-type="disp-formula" rid="e12">Equation 12</xref>, a carbon emission calculation method is derived from the guidelines of the Intergovernmental Panel on Climate Change (IPCC), which serves as a standard approach for estimating greenhouse gas emissions. This approach is commonly applied in environmental studies to estimate emissions from various energy sources. Additionally, based on prior literature (<xref ref-type="bibr" rid="B18">Liu et al., 2023</xref>; <xref ref-type="bibr" rid="B11">Kuang et al., 2024</xref>)., the emissions are calculated using data from eight key energy sources&#x2014;coke, gasoline, natural gas, raw coal, fuel oil, crude oil, kerosene, and diesel&#x2014;factored into end-use consumption:<disp-formula id="e12">
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<mml:mrow>
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<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mn>6</mml:mn>
</mml:munderover>
</mml:mstyle>
<mml:mtext>&#x200a;</mml:mtext>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>O</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>3.67</mml:mn>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>
</p>
<p>Among these, <inline-formula id="inf37">
<mml:math id="m49">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> represents the total emissions of <inline-formula id="inf38">
<mml:math id="m50">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf39">
<mml:math id="m51">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes the type of energy consumed. <inline-formula id="inf40">
<mml:math id="m52">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> refers to the total consumption of the <inline-formula id="inf41">
<mml:math id="m53">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> th type of energy in each province. <inline-formula id="inf42">
<mml:math id="m54">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>C</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> signifies the calorific value, <inline-formula id="inf43">
<mml:math id="m55">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> indicates the carbon content, and <inline-formula id="inf44">
<mml:math id="m56">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>O</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the oxidation factor.</p>
<p>
<inline-formula id="inf45">
<mml:math id="m57">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>O</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the carbon emission factor, while <inline-formula id="inf46">
<mml:math id="m58">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>C</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>C</mml:mi>
<mml:mi>O</mml:mi>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>3.67</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> denotes the carbon dioxide emission factor. Since there is an order of magnitude difference between the carbon emissions of each region and other variables, combined with the experience of previous studies, the logarithm of carbon emissions is taken for calculation in this study <xref ref-type="bibr" rid="B40">Wu et al. (2021)</xref>.</p>
</sec>
<sec id="s3-2-1-2">
<title>3.2.1.2 Talent agglomeration</title>
<p>The degree of talent agglomeration is the clustering phenomenon formed by the same type of talent gathering in a certain area, with strong spatial characteristics (<xref ref-type="bibr" rid="B26">Shi and Lai, 2019</xref>). Building on previous research, this study employs the location entropy index to measure the level of talent agglomeration. Specifically, as shown in <xref ref-type="disp-formula" rid="e13">Equation 13</xref>:<disp-formula id="e13">
<mml:math id="m59">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>A</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi>T</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>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
<label>(13)</label>
</disp-formula>
</p>
<p>In this model, <inline-formula id="inf47">
<mml:math id="m60">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>A</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the density of talent agglomeration of in region i for the year&#xa0;t. This ratio is calculated by dividing the number of R&#x26;D personnel (<inline-formula id="inf48">
<mml:math id="m61">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) by the total number of employed individuals (<inline-formula id="inf49">
<mml:math id="m62">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>) in the region. <inline-formula id="inf50">
<mml:math id="m63">
<mml:mrow>
<mml:msub>
<mml:mi>T</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represents the national full-time equivalent of R&#x26;D personnel, while <inline-formula id="inf51">
<mml:math id="m64">
<mml:mrow>
<mml:msub>
<mml:mi>L</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> refers to the total national employment. A <inline-formula id="inf52">
<mml:math id="m65">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>A</mml:mi>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> value exceeding 1 signifies a higher level of talent agglomeration within the area, whereas a value below 1 implies a lower level of agglomeration.</p>
</sec>
<sec id="s3-2-1-3">
<title>3.2.1.3 Other inter-provincial characteristic variables</title>
<p>Drawing on existing research, it has been identified that carbon emission is influenced not only by talent agglomeration but also by urbanization, industrialization and local governance (<xref ref-type="bibr" rid="B30">Taskin and Zaim, 2001</xref>). Following the approach of <xref ref-type="bibr" rid="B29">Sun and Huang (2020)</xref>, urbanization is represented by the non-agricultural population ratio (lnUrb). And the level of economic development (lnPGdp) and environmental regulation (ER) are selected as control variables (<xref ref-type="bibr" rid="B18">Liu et al., 2023</xref>). Environmental regulation is evaluated by the ratio of industrial pollution control investment to GDP, indicating the government&#x2019;s prioritization of environmental sustainability (<xref ref-type="bibr" rid="B48">Zhang et al., 2022</xref>).</p>
</sec>
</sec>
<sec id="s3-2-2">
<title>3.2.2 Research area and data source</title>
<p>Given the notable regional disparities in socioeconomic development, governance capacity, and environmental complexity, as well as unique challenges in implementing talent agglomeration policies on carbon emissions in China (<xref ref-type="bibr" rid="B14">Li and Ramanathan, 2018</xref>; <xref ref-type="bibr" rid="B39">Wu et al., 2020</xref>) we address these differences effectively by dividing the research area into eastern, central, and western regions. <xref ref-type="fig" rid="F2">Figure 2a</xref> delineates this regionalization, while <xref ref-type="fig" rid="F2">Figure 2b</xref> reports provincial mean carbon emissions for 2013&#x2013;2023. Overall, a clear spatial gradient emerges, with emissions decreasing from north to south and from east to west, and the eastern region consistently recording the highest totals, followed by the central region.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Provinces and regions covered with average carbon emissions during the study period.</p>
</caption>
<graphic xlink:href="fenvs-13-1630688-g002.tif">
<alt-text content-type="machine-generated">Two maps of China display regional information. Map (a) shows regions divided into Eastern, Central, and Western, with a section labeled as no data. Map (b) illustrates carbon emissions, using varying shades to indicate different emission levels, ranging from twenty-five thousand to forty-five thousand units, with some regions marked as no data. A compass rose is present in both maps, and a scale bar indicates distances in kilometers.</alt-text>
</graphic>
</fig>
<p>The scope of this research encompasses the provinces of China over the years 2013&#x2013;2023, excluding Tibet, Hong Kong, Macao, and Taiwan due to data limitations. Data concerning energy were extracted from the China Energy Statistics Yearbook, while information from other domains was drawn from the China Statistical Yearbook and the China Statistical Yearbook of Science and Technology. The energy consumption data for 2018 were projected using linear regression, while interpolation techniques were employed to address other missing data. Descriptive statistical results for all variables can be found in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Descriptive statistics of variables.</p>
</caption>
<table>
<thead valign="top">
<tr style="background-color:#A6A6A6">
<th align="center">Variables</th>
<th align="center">Symbols</th>
<th align="center">N</th>
<th align="center">Mean</th>
<th align="center">Std.dev</th>
<th align="center">Min</th>
<th align="center">Max</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Carbon Emissions</td>
<td align="center">lnCo2</td>
<td align="center">330</td>
<td align="center">10.2972</td>
<td align="center">0.7538</td>
<td align="center">8.1161</td>
<td align="center">12.2170</td>
</tr>
<tr>
<td align="center">Talent agglomeration</td>
<td align="center">lnTa</td>
<td align="center">330</td>
<td align="center">0.1052</td>
<td align="center">0.6035</td>
<td align="center">&#x2212;1.3445</td>
<td align="center">1.6381</td>
</tr>
<tr>
<td align="center">Urbanization</td>
<td align="center">lnUrb</td>
<td align="center">330</td>
<td align="center">&#x2212;0.5608</td>
<td align="center">0.2314</td>
<td align="center">&#x2212;1.4848</td>
<td align="center">&#x2212;0.1100</td>
</tr>
<tr>
<td align="center">GDP <italic>per capita</italic>
</td>
<td align="center">lnPGdp</td>
<td align="center">330</td>
<td align="center">10.7829</td>
<td align="center">0.4770</td>
<td align="center">9.4636</td>
<td align="center">12.1417</td>
</tr>
<tr>
<td align="center">Environment Regulation</td>
<td align="center">ER</td>
<td align="center">330</td>
<td align="center">8.0808</td>
<td align="center">6.1310</td>
<td align="center">2.5763</td>
<td align="center">36.0529</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
</sec>
<sec id="s4">
<title>4 Empirical analysis</title>
<sec id="s4-1">
<title>4.1 Estimation of bilateral stochastic frontier model</title>
<sec id="s4-1-1">
<title>4.1.1 Analysis of factors influencing carbon emission</title>
<p>The dual impacts of agglomeration on carbon emissions are estimated using <xref ref-type="disp-formula" rid="e12">Equation 12</xref>. The results are presented in <xref ref-type="table" rid="T2">Table 2</xref>, with column 2 displaying the OLS estimates that exclude deviation effects, column 3 to column 5 report maximum-likelihood estimates from the two-tier stochastic frontier model. Specification M2 includes year fixed effects only, M3 includes regional fixed effects only, and M4 includes both sets of fixed effects. In M4, urbanization (lnUrb &#x3d; 0.166&#x2a;,Z &#x3d; 63.21) and environmental regulation (ER &#x3d; 0.294&#x2a;,Z &#x3d; 17.29) are positively associated with carbon emissions, whereas per-capita GDP (lnPGdp &#x3d; &#x2212;0.029&#x2a;, Z &#x3d; &#x2212;57.28) is negatively associated; relative to the OLS baseline, these sign and significance reversals indicate that explicitly modeling inefficiency within the two-tier stochastic frontier model yields materially different inferences.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>The basic estimation of the two-tier stochastic frontier model.</p>
</caption>
<table>
<thead valign="top">
<tr style="background-color:#A6A6A6">
<th align="center">Variables</th>
<th align="center">OLS</th>
<th align="center">M 2</th>
<th align="center">M 3</th>
<th align="center">M 4</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="center">lnUrb</td>
<td align="center">0.695&#x2a;&#x2a;</td>
<td align="center">0.638&#x2a;&#x2a;&#x2a;</td>
<td align="center">0.086&#x2a;&#x2a;&#x2a;</td>
<td align="center">0.166&#x2a;&#x2a;&#x2a;</td>
</tr>
<tr>
<td align="center">(2.47)</td>
<td align="center">(28.28)</td>
<td align="center">(12.68)</td>
<td align="center">(63.21)</td>
</tr>
<tr>
<td rowspan="2" align="center">lnPGdp</td>
<td align="center">&#x2212;0.031</td>
<td align="center">0.059&#x2a;&#x2a;&#x2a;</td>
<td align="center">0.039&#x2a;&#x2a;&#x2a;</td>
<td align="center">&#x2212;0.029&#x2a;&#x2a;&#x2a;</td>
</tr>
<tr>
<td align="center">(-0.72)</td>
<td align="center">(5.28)</td>
<td align="center">(15.09)</td>
<td align="center">(-57.28)</td>
</tr>
<tr>
<td rowspan="2" align="center">ER</td>
<td align="center">&#x2212;0.342&#x2a;&#x2a;&#x2a;</td>
<td align="center">0.169&#x2a;&#x2a;&#x2a;</td>
<td align="center">0.128&#x2a;&#x2a;&#x2a;</td>
<td align="center">0.294&#x2a;&#x2a;&#x2a;</td>
</tr>
<tr>
<td align="center">(-3.02)</td>
<td align="center">(6.38)</td>
<td align="center">(18.29)</td>
<td align="center">(17.29)</td>
</tr>
<tr>
<td align="center">Constant</td>
<td align="center">3.267 (1.21)</td>
<td align="center">1.390&#x2a;&#x2a;&#x2a; (7.18)</td>
<td align="center">4.221&#x2a;&#x2a;&#x2a; (14.39)</td>
<td align="center">2.109&#x2a;&#x2a;&#x2a; (72.17)</td>
</tr>
<tr>
<td align="center">Constant item</td>
<td align="left"/>
<td align="center">&#x2212;10.421&#x2a;&#x2a;&#x2a; (&#x2212;15.16)</td>
<td align="center">&#x2212;12.753&#x2a;&#x2a;&#x2a; (&#x2212;14.28)</td>
<td align="center">&#x2212;17.808&#x2a;&#x2a;&#x2a; (&#x2212;18.62)</td>
</tr>
<tr>
<td align="center">Inhibitory effect</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2212;7.021&#x2a;&#x2a;&#x2a; (&#x2212;12.19)</td>
</tr>
<tr>
<td align="center">Promotive effects</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
<td align="center">1.288&#x2a;&#x2a;&#x2a; (5.20)</td>
</tr>
<tr>
<td align="center">Constant item</td>
<td align="left"/>
<td align="left"/>
<td align="center">&#x2212;1.697&#x2a;&#x2a;&#x2a; (&#x2212;12.10)</td>
<td align="center">&#x2212;5.281&#x2a;&#x2a;&#x2a; (&#x2212;23.29)</td>
</tr>
<tr>
<td align="center">R-squared</td>
<td align="center">0.667</td>
<td align="left"/>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="center">Log-L</td>
<td align="center">133.91</td>
<td align="center">253.71</td>
<td align="center">263.22</td>
<td align="center">281.31</td>
</tr>
<tr>
<td align="center">pro fixed</td>
<td align="center">No</td>
<td align="center">No</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="center">Year fixed</td>
<td align="center">No</td>
<td align="center">Yes</td>
<td align="center">No</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="center">N</td>
<td align="center">330</td>
<td align="center">330</td>
<td align="center">330</td>
<td align="center">330</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Note: &#x2a;&#x2a;&#x2a;, &#x2a;&#x2a;, and &#x2a; denote significance at the 1%, 5%, and 10% levels, respectively, with the corresponding Z statistics provided in parentheses. This notation is used consistently throughout the text.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="s4-1-2">
<title>4.1.2 Variance decomposition: analyzing the impact coefficients of bilateral effects</title>
<p>The results demonstrate that talent agglomeration exerts a net inhibitory effect on carbon emissions, primarily by improving energy efficiency. As shown in <xref ref-type="table" rid="T3">Table 3</xref>, talent agglomeration exerts both promotive and inhibitory effects on carbon emissions, with the inhibitory effect measured at 0.438, significantly exceeding the promotive effect of 0.162. The results confirm the coexistence of bilateral effects, while further indicating that the inhibitory effect dominates, thereby supporting both theoretical assumptions. Overall, the impact on emission reduction is positive, with E (<inline-formula id="inf53">
<mml:math id="m66">
<mml:mrow>
<mml:mi>&#x3c9;</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>u</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>) &#x3d; <inline-formula id="inf54">
<mml:math id="m67">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>-<inline-formula id="inf55">
<mml:math id="m68">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> &#x3d; &#x2212;0.276], reflecting the dominance of the inhibitory effect.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Variance decomposition of the impact of talent agglomeration.</p>
</caption>
<table>
<thead valign="top">
<tr style="background-color:#A6A6A6">
<th align="center">Meaning</th>
<th align="center">Variance meaning</th>
<th align="center">Symbols</th>
<th align="left">Measurements coefficients</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="3" align="center">Impacts</td>
<td align="center">Random error term</td>
<td align="center">
<inline-formula id="inf56">
<mml:math id="m69">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.104</td>
</tr>
<tr>
<td align="center">Promotive effect</td>
<td align="center">
<inline-formula id="inf57">
<mml:math id="m70">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.162</td>
</tr>
<tr>
<td align="center">Inhibitory effect</td>
<td align="center">
<inline-formula id="inf58">
<mml:math id="m71">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.438</td>
</tr>
<tr>
<td rowspan="4" align="center">Variance decomposition</td>
<td align="center">Random total error term</td>
<td align="center">
<inline-formula id="inf59">
<mml:math id="m72">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.229</td>
</tr>
<tr>
<td align="center">The weight of the two effects</td>
<td align="center">
<inline-formula id="inf60">
<mml:math id="m73">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.953</td>
</tr>
<tr>
<td align="center">Promotive effect weight</td>
<td align="center">
<inline-formula id="inf61">
<mml:math id="m74">
<mml:mrow>
<mml:mfrac>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.121</td>
</tr>
<tr>
<td align="center">Inhibitory effect weight</td>
<td align="center">
<inline-formula id="inf62">
<mml:math id="m75">
<mml:mrow>
<mml:mfrac>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.879</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Further analysis reveals that the combined bilateral component accounts for 95.3% of the variance in carbon emissions. As shown in <xref ref-type="table" rid="T3">Table 3</xref>, within this component, the promotive effect accounts for only 12.1%, whereas the inhibitory effect accounts for 87.9%, further evidencing the leading role of the inhibitory effect in emission reduction.</p>
</sec>
<sec id="s4-1-3">
<title>4.1.3 Frontier-level examination analyzing the bilateral effect</title>
<p>Based on <xref ref-type="disp-formula" rid="e9">Equations 9</xref>&#x2013;<xref ref-type="disp-formula" rid="e11">11</xref>, the promotive, inhibitory, and net effects of talent agglomeration on carbon emissions were estimated as percentages. As shown in <xref ref-type="table" rid="T4">Table 4</xref>, talent agglomeration increases emissions by 16.2% and reduces them by 43.8%, producing a net reduction of 27.6% relative to the frontier level. This finding suggests that, with the coexistence of both promotive and inhibitory effects of talent agglomeration, assuming the frontier carbon emission is 100%, the final emission level would be 72.4%.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Estimation of the net effect of talent agglomeration on carbon emissions (%).</p>
</caption>
<table>
<thead valign="top">
<tr style="background-color:#A6A6A6">
<th align="center">Variable</th>
<th align="center">mean</th>
<th align="center">Sd</th>
<th align="center">p25</th>
<th align="center">p50</th>
<th align="center">p75</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">thepromotive effect</td>
<td align="center">0.26</td>
<td align="center">0.14</td>
<td align="center">0.17</td>
<td align="center">0.20</td>
<td align="center">0.27</td>
</tr>
<tr>
<td align="center">the inhibitory effect</td>
<td align="center">0.44</td>
<td align="center">0.24</td>
<td align="center">0.21</td>
<td align="center">0.40</td>
<td align="center">0.63</td>
</tr>
<tr>
<td align="center">the net effect</td>
<td align="center">&#x2212;0.18</td>
<td align="center">0.34</td>
<td align="center">&#x2212;0.46</td>
<td align="center">&#x2212;0.22</td>
<td align="center">0.08</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="table" rid="T4">Table 4</xref> demonstrates the variations in the promotive, inhibitory, and net effects of talent agglomeration on carbon emissions. Specifically, at the 25th percentile, the combined effects result in a 28.6% reduction in actual carbon emissions across one-quarter of the regions. At the 50th percentile, the combined effects lead to a 4.2% reduction, while at the 75th percentile, there is a 38.8% increase in carbon emissions. This finding further substantiates the overall inhibitory effect of scientific talent agglomeration on regional carbon emissions. Further analysis reveals that at the second percentile, the impact of environmental regulation decreases by 23.4% compared to the first percentile, whereas at the third percentile, the effect of environmental regulation increases instead of decreasing. This further corroborates the conclusion that talent agglomeration plays a positive environmental role by reducing carbon emissions.</p>
<p>The distribution of the promotive, inhibitory, and net effects of talent agglomeration on carbon emissions is presented in <xref ref-type="fig" rid="F3">Figure 3</xref>, based on province&#x2013;year estimates for 2013&#x2013;2023. As shown in <xref ref-type="fig" rid="F3">Figure 3a</xref>, the promotive effect exhibits a right-tailed distribution: most observations lie below 15%, and the frequency drops sharply beyond 20%. This pattern suggests that the emissions-increasing channel is typically weak but occasionally exhibits spikes in a small subset of observations, which may be consistent with short-run scale effects. As shown in <xref ref-type="fig" rid="F3">Figure 3b</xref>, the inhibitory effect has a heavier right tail than the promotion distribution: most observations are at low percentages, with occasional large reductions, which may reflect the lagged materialization of efficiency and regulation gains. As shown in <xref ref-type="fig" rid="F3">Figure 3c</xref>, the net-effect distribution is concentrated on negative values and positive observations are rare, indicating the dominance of the reducing mechanism. This distribution highlights that the inhibitory effect is both more frequent and more substantial than the promotive effect. Overall, these distributions confirm that talent agglomeration exerts a net inhibitory impact on carbon emissions, consistent with our theoretical analysis.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Characteristics of the net effect of talent agglomeration on regional carbon emissions (%).</p>
</caption>
<graphic xlink:href="fenvs-13-1630688-g003.tif">
<alt-text content-type="machine-generated">Three histograms show distribution effects. (a) Promotion effect histogram peaks around 0% with a sharp decline. (b) Inhibition effect histogram also peaks near 0%, declining quickly. (c) Net effect histogram is centered near 0%, with symmetric distribution.</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec id="s4-2">
<title>4.2 Spatial characteristics in the effect of talent agglomeration on regional carbon emissions</title>
<p>Subsequently, we examine the spatial variation in the emission-reducing effects of talent agglomeration across China&#x2019;s three major regions: Eastern, Central, and Western. Overall, talent agglomeration generates both promotive and inhibitory effects across regions, with the inhibitory effect consistently prevailing and leading to net emission reductions. These results suggest that while talent agglomeration consistently contributes to carbon emission reductions, the magnitude of its impact varies significantly by region.</p>
<p>In the western regions, where infrastructure and technological development levels are relatively low, the technological advancements and government policy support, including talent-rewarding policies and improvements in infrastructure, financial development, and credit optimization, driven by talent agglomeration can substantially improve carbon emission efficiency (<xref ref-type="bibr" rid="B53">Zhuo and Deng, 2020</xref>; <xref ref-type="bibr" rid="B51">Zheng et al., 2022</xref>). These measures strengthen innovation capacity and energy efficiency, ensuring that the inhibitory effect outweighs the promotive effect and produces the greatest emission reduction in the western region. In the central region, although energy-intensive industries still account for a larger share of the industrial structure (<xref ref-type="bibr" rid="B7">Fan et al., 2011</xref>), recent policy-driven talent agglomeration has enhanced efficiency improvements and management upgrading, leading to significant emission reductions (<xref ref-type="bibr" rid="B42">Yang et al., 2021</xref>). In the eastern regions, with better infrastructure and technological conditions, and a focus on technology industries and services, talent agglomeration primarily promotes management optimization and technological innovation (<xref ref-type="bibr" rid="B3">Chen et al., 2020</xref>). The overall evidence suggests that although both promotive and inhibitory effects coexist in all three regions, the inhibitory effect consistently dominates, producing regionally differentiated but uniformly negative net effects on carbon emissions.</p>
<p>
<xref ref-type="table" rid="T5">Table 5</xref> displays the frequency distributions of the promotive, inhibitory, and net effects of talent agglomeration on carbon emissions. The inhibitory effect exhibits a pronounced right-tailed distribution, extending beyond the 90th percentile, indicating that in certain provinces carbon emissions indicating that in certain provinces, large reductions occur as talent agglomeration increases. In contrast, the promotive effect weakens beyond the 90th percentile and remains below the inhibitory effect, underscoring its secondary role. The comparative distributions show that while both effects coexist, the inhibitory effect is more frequent and more substantial, consistently dominating the promotive effect. Accordingly, the overall distribution of effects is concentrated on the left half-axis below zero, with higher frequencies than on the right half-axis, confirming that the net impact of talent agglomeration is negative at most quantile points. These findings confirm the dominance of the inhibitory effect and underscore the need for region-specific emission reduction strategies.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Characteristics of the net effect of talent agglomeration on regional carbon emissions (%).</p>
</caption>
<table>
<thead valign="top">
<tr style="background-color:#A6A6A6">
<th align="center">Province and region</th>
<th align="center">Net effect mean value</th>
<th align="center">p25</th>
<th align="center">p50</th>
<th align="center">p75</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">Beijing</td>
<td align="center">&#x2212;0.13</td>
<td align="center">&#x2212;0.45</td>
<td align="center">&#x2212;0.04</td>
<td align="center">0.12</td>
</tr>
<tr>
<td align="center">Tianjin</td>
<td align="center">&#x2212;0.14</td>
<td align="center">&#x2212;0.43</td>
<td align="center">&#x2212;0.05</td>
<td align="center">0.08</td>
</tr>
<tr>
<td align="center">Hebei</td>
<td align="center">&#x2212;0.24</td>
<td align="center">&#x2212;0.53</td>
<td align="center">&#x2212;0.19</td>
<td align="center">&#x2212;0.01</td>
</tr>
<tr>
<td align="center">Liaoning</td>
<td align="center">&#x2212;0.15</td>
<td align="center">&#x2212;0.45</td>
<td align="center">&#x2212;0.09</td>
<td align="center">0.1</td>
</tr>
<tr>
<td align="center">Shanghai</td>
<td align="center">&#x2212;0.01</td>
<td align="center">&#x2212;0.28</td>
<td align="center">0.13</td>
<td align="center">0.33</td>
</tr>
<tr>
<td align="center">Jiangsu</td>
<td align="center">0.03</td>
<td align="center">&#x2212;0.21</td>
<td align="center">0.17</td>
<td align="center">0.37</td>
</tr>
<tr>
<td align="center">Zhejiang</td>
<td align="center">&#x2212;0.01</td>
<td align="center">&#x2212;0.3</td>
<td align="center">0.1</td>
<td align="center">0.34</td>
</tr>
<tr>
<td align="center">Fujian</td>
<td align="center">&#x2212;0.19</td>
<td align="center">&#x2212;0.39</td>
<td align="center">&#x2212;0.3</td>
<td align="center">0.02</td>
</tr>
<tr>
<td align="center">Shandong</td>
<td align="center">&#x2212;0.1</td>
<td align="center">&#x2212;0.34</td>
<td align="center">&#x2212;0.12</td>
<td align="center">0.08</td>
</tr>
<tr>
<td align="center">Guangdong</td>
<td align="center">&#x2212;0.19</td>
<td align="center">&#x2212;0.27</td>
<td align="center">&#x2212;0.31</td>
<td align="center">&#x2212;0.04</td>
</tr>
<tr>
<td align="center">Guangxi</td>
<td align="center">&#x2212;0.08</td>
<td align="center">&#x2212;0.51</td>
<td align="center">&#x2212;0.38</td>
<td align="center">&#x2212;0.09</td>
</tr>
<tr>
<td align="center">Hainan</td>
<td align="center">&#x2212;0.24</td>
<td align="center">&#x2212;0.55</td>
<td align="center">&#x2212;0.38</td>
<td align="center">&#x2212;0.12</td>
</tr>
<tr>
<td align="center">Shanxi</td>
<td align="center">&#x2212;0.25</td>
<td align="center">&#x2212;0.53</td>
<td align="center">&#x2212;0.23</td>
<td align="center">&#x2212;0.06</td>
</tr>
<tr>
<td align="center">Neimenggu</td>
<td align="center">&#x2212;0.24</td>
<td align="center">&#x2212;0.52</td>
<td align="center">&#x2212;0.21</td>
<td align="center">0.02</td>
</tr>
<tr>
<td align="center">Jilin</td>
<td align="center">&#x2212;0.31</td>
<td align="center">&#x2212;0.56</td>
<td align="center">&#x2212;0.33</td>
<td align="center">&#x2212;0.04</td>
</tr>
<tr>
<td align="center">Heilongjiang</td>
<td align="center">&#x2212;0.29</td>
<td align="center">&#x2212;0.51</td>
<td align="center">&#x2212;0.28</td>
<td align="center">0</td>
</tr>
<tr>
<td align="center">Anhui</td>
<td align="center">&#x2212;0.17</td>
<td align="center">&#x2212;0.44</td>
<td align="center">&#x2212;0.11</td>
<td align="center">0.15</td>
</tr>
<tr>
<td align="center">Jiangxi</td>
<td align="center">&#x2212;0.29</td>
<td align="center">&#x2212;0.48</td>
<td align="center">&#x2212;0.38</td>
<td align="center">&#x2212;0.14</td>
</tr>
<tr>
<td align="center">Henan</td>
<td align="center">&#x2212;0.31</td>
<td align="center">&#x2212;0.45</td>
<td align="center">&#x2212;0.29</td>
<td align="center">&#x2212;0.11</td>
</tr>
<tr>
<td align="center">Hubei</td>
<td align="center">&#x2212;0.15</td>
<td align="center">&#x2212;0.4</td>
<td align="center">&#x2212;0.22</td>
<td align="center">&#x2212;0.03</td>
</tr>
<tr>
<td align="center">Hunan</td>
<td align="center">&#x2212;0.31</td>
<td align="center">&#x2212;0.43</td>
<td align="center">&#x2212;0.29</td>
<td align="center">0.23</td>
</tr>
<tr>
<td align="center">Chongqing</td>
<td align="center">&#x2212;0.32</td>
<td align="center">&#x2212;0.44</td>
<td align="center">&#x2212;0.38</td>
<td align="center">0.06</td>
</tr>
<tr>
<td align="center">Sichuan</td>
<td align="center">&#x2212;0.21</td>
<td align="center">&#x2212;0.48</td>
<td align="center">&#x2212;0.26</td>
<td align="center">0.2</td>
</tr>
<tr>
<td align="center">Guizhou</td>
<td align="center">&#x2212;0.18</td>
<td align="center">&#x2212;0.54</td>
<td align="center">&#x2212;0.47</td>
<td align="center">0.05</td>
</tr>
<tr>
<td align="center">Yunnan</td>
<td align="center">&#x2212;0.18</td>
<td align="center">&#x2212;0.46</td>
<td align="center">&#x2212;0.26</td>
<td align="center">0.2</td>
</tr>
<tr>
<td align="center">Shaanxi</td>
<td align="center">&#x2212;0.18</td>
<td align="center">&#x2212;0.33</td>
<td align="center">&#x2212;0.11</td>
<td align="center">0.1</td>
</tr>
<tr>
<td align="center">Gansu</td>
<td align="center">&#x2212;0.24</td>
<td align="center">&#x2212;0.48</td>
<td align="center">&#x2212;0.34</td>
<td align="center">0.07</td>
</tr>
<tr>
<td align="center">Qinghai</td>
<td align="center">&#x2212;0.32</td>
<td align="center">&#x2212;0.54</td>
<td align="center">&#x2212;0.41</td>
<td align="center">0.05</td>
</tr>
<tr>
<td align="center">Ningxia</td>
<td align="center">&#x2212;0.21</td>
<td align="center">&#x2212;0.47</td>
<td align="center">&#x2212;0.32</td>
<td align="center">0.05</td>
</tr>
<tr>
<td align="center">Xinjiang</td>
<td align="center">&#x2212;0.18</td>
<td align="center">&#x2212;0.47</td>
<td align="center">&#x2212;0.3</td>
<td align="center">0.2</td>
</tr>
<tr>
<td align="center">Eastern Region</td>
<td align="center">&#x2212;0.18</td>
<td align="center">&#x2212;0.46</td>
<td align="center">&#x2212;0.22</td>
<td align="center">0.08</td>
</tr>
<tr>
<td align="center">Central Region</td>
<td align="center">&#x2212;0.12</td>
<td align="center">&#x2212;0.39</td>
<td align="center">&#x2212;0.12</td>
<td align="center">0.10</td>
</tr>
<tr>
<td align="center">Western Region</td>
<td align="center">&#x2212;0.22</td>
<td align="center">&#x2212;0.47</td>
<td align="center">&#x2212;0.32</td>
<td align="center">0.11</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4-3">
<title>4.3 Temporal characteristics of talent agglomeration impacts on carbon emissions</title>
<p>Different from the linear or nonlinear regression methods used in other literature, the approach in this paper can be used to decompose the bilateral effects of talent agglomeration on carbon emissions for different years, and then analyze the trend characteristics of this impact over time. <xref ref-type="fig" rid="F4">Figure 4</xref> shows the annual variations in the promotive, inhibitory, and net effects. The results indicate that while both effects coexist, the inhibitory effect generally dominates, keeping the net effect negative in all years except 2014, when a temporary surge in promotion (46.27%) produced a positive net outcome (25.39%). The inhibitory effect peaked in 2013 (71.08%) and again in 2021 (67.80%), while the promotive effect reached its lowest in 2020 (19.90%). This produced a sizable negative net effect in 2020 (&#x2212;17.36%), which deepened further by 2023 (&#x2212;27.06%). These patterns suggest that while agglomeration may temporarily raise emissions in the early phase (e.g., 2014), its maturation strengthens the inhibitory channel through efficiency gains and structural upgrading, leading to persistently negative net effects that intensify after 2020.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Temporal trends of the bilateral effects of scientific and technological talent agglomeration.</p>
</caption>
<graphic xlink:href="fenvs-13-1630688-g004.tif">
<alt-text content-type="machine-generated">Line graph showing Promotion, Inhibition, and Net Effects from 2013 to 2023. The Promotion Effect fluctuates between 21.17% and 26.89%. The Inhibition Effect peaks at 71.08% in 2013 and declines to 35.47% in 2023. The Net Effect ranges from -48.95% in 2013 to -27.06% in 2023, with notable fluctuations.</alt-text>
</graphic>
</fig>
<p>In summary, the net effect of talent agglomeration on carbon emissions was predominantly negative during 2013&#x2013;2023. Drawing on China&#x2019;s practice, implementation exhibits a phased transition and lagged cumulative effects: an early and temporary scale-up (e.g., 2014), a near-neutral middle stage around 2018&#x2013;2019, and a post-2020 efficiency-dominated phase in which the inhibitory channel strengthens with a lag (promotion bottoming in 2020&#xa0;at 19.90%, inhibition peaking in 2021 at 67.80%). This shows that the impact of talent agglomeration on carbon emissions exhibits stage-specific dynamics and lagged materialization.</p>
</sec>
<sec id="s4-4">
<title>4.4 Heterogeneity test of the net effect of talent agglomeration on carbon emission</title>
<p>Drawing from the preceding mechanism analysis, this study hypothesizes that the effects of talent agglomeration on carbon emissions are twofold. The promotive effects may increase energy consumption and emissions through urban expansion, energy-intensive industrial structures and resource misallocation, while the inhibitory effects may enhance energy efficiency and reduce carbon intensity through knowledge exchange, green innovation and industrial upgrading. To examine the heterogeneous effects of talent agglomeration on carbon emissions, this study categorizes regions by urbanization, economic development, and environmental regulation levels, and tests the impacts across different percentiles. The results are presented in <xref ref-type="table" rid="T6">Table 6</xref>.</p>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>Differences of the bilateral effects under various talent agglomeration levels (%).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Percentage range</th>
<th rowspan="2" align="center">Effects</th>
<th colspan="2" align="center">Talent agglomeration</th>
<th colspan="2" align="center">Urbanization</th>
<th colspan="2" align="center">Economic</th>
<th colspan="2" align="center">Environmental regulation</th>
</tr>
<tr>
<th align="center">Mean</th>
<th align="center">SD</th>
<th align="center">Mean</th>
<th align="center">SD</th>
<th align="center">Mean</th>
<th align="center">SD</th>
<th align="center">Mean</th>
<th align="center">SD</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="3" align="center">10%&#x2013;40%</td>
<td align="center">Promotive effect</td>
<td align="center">0.316</td>
<td align="center">0.126</td>
<td align="center">0.27</td>
<td align="center">0.14</td>
<td align="center">0.26</td>
<td align="center">0.13</td>
<td align="center">0.348</td>
<td align="center">0.147</td>
</tr>
<tr>
<td align="center">Inhibitory effect</td>
<td align="center">0.299</td>
<td align="center">0.214</td>
<td align="center">0.44</td>
<td align="center">0.25</td>
<td align="center">0.46</td>
<td align="center">0.27</td>
<td align="center">0.341</td>
<td align="center">0.271</td>
</tr>
<tr>
<td align="center">Net effect</td>
<td align="center">0.016</td>
<td align="center">0.358</td>
<td align="center">0.17</td>
<td align="center">0.35</td>
<td align="center">&#x2212;0.21</td>
<td align="center">0.36</td>
<td align="center">0.007</td>
<td align="center">0.36</td>
</tr>
<tr>
<td rowspan="3" align="center">40%&#x2013;70%</td>
<td align="center">Promotive effect</td>
<td align="center">0.262</td>
<td align="center">0.107</td>
<td align="center">0.24</td>
<td align="center">0.14</td>
<td align="center">0.23</td>
<td align="center">0.13</td>
<td align="center">0.307</td>
<td align="center">0.124</td>
</tr>
<tr>
<td align="center">Inhibitory effect</td>
<td align="center">0.428</td>
<td align="center">0.29</td>
<td align="center">0.44</td>
<td align="center">0.24</td>
<td align="center">0.46</td>
<td align="center">0.23</td>
<td align="center">0.479</td>
<td align="center">0.309</td>
</tr>
<tr>
<td align="center">Net effect</td>
<td align="center">&#x2212;0.166</td>
<td align="center">0.333</td>
<td align="center">&#x2212;0.2</td>
<td align="center">0.33</td>
<td align="center">&#x2212;0.23</td>
<td align="center">0.32</td>
<td align="center">&#x2212;0.172</td>
<td align="center">0.306</td>
</tr>
<tr>
<td rowspan="3" align="center">70%&#x2013;100%</td>
<td align="center">Promotive effect</td>
<td align="center">0.29</td>
<td align="center">0.184</td>
<td align="center">0.27</td>
<td align="center">0.14</td>
<td align="center">0.29</td>
<td align="center">0.15</td>
<td align="center">0.305</td>
<td align="center">0.157</td>
</tr>
<tr>
<td align="center">Inhibitory effect</td>
<td align="center">0.517</td>
<td align="center">0.238</td>
<td align="center">0.43</td>
<td align="center">0.24</td>
<td align="center">0.39</td>
<td align="center">0.23</td>
<td align="center">0.68</td>
<td align="center">0.262</td>
</tr>
<tr>
<td align="center">Net effect</td>
<td align="center">&#x2212;0.226</td>
<td align="center">0.372</td>
<td align="center">&#x2212;0.17</td>
<td align="center">0.35</td>
<td align="center">&#x2212;0.1</td>
<td align="center">0.33</td>
<td align="center">&#x2212;0.375</td>
<td align="center">0.366</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>First, this study tested the effects of different degrees of talent agglomeration on emissions. In the 10%&#x2013;40% range, emissions show a significant increase, followed by a decrease beyond 40%. This inverted U shape identifies a 40% agglomeration degree as the inflection point, demonstrating a substantial impact on sustainable development. However, regional disparities in China make it challenging for all areas to attract talent equally due to varying conditions for talent attraction.</p>
<p>Next, the study examined the urbanization level, a crucial element of the macroeconomic environment that is highly correlated with regional population structure and production methods (<xref ref-type="bibr" rid="B21">Nathaniel et al., 2021</xref>). At low levels of urbanization, the promotive effect dominates, as increased infrastructure construction and energy demand temporarily raise emissions. As urbanization advances, however, the inhibitory effect strengthens and overtakes the promotive effect, resulting in a net reduction in emissions. This pattern indicates that while both effects coexist, the balance shifts toward inhibition as urbanization deepens. In the 70%&#x2013;100% range, the inhibitory effect becomes dominant, reducing emissions relative to lower levels of economic development. This further confirms the inverted U-shaped relationship, with promotive effects stronger at early stages and inhibitory effects prevailing as economic development advances.</p>
<p>Finally, we examined the relationship between talent agglomeration and carbon emissions under different levels of environmental regulation. At low levels of regulation (bottom 40%), the promotive effect dominates, and emissions increase. By contrast, in regions with stricter regulation, the inhibitory effect overtakes the promotive effect, resulting in significant net reductions. This further supports the view that emissions are more effectively reduced through environmental regulation than through other measures.</p>
</sec>
<sec id="s4-5">
<title>4.5 Robustness</title>
<p>Three verification methods were adopted to ensure the robustness of the results.</p>
<p>First, considering that potential reverse causality may exist, in which talent agglomeration may affect carbon emissions while carbon emissions may also affect talent agglomeration, this paper adopts the instrumental variable (IV) approach to address the endogeneity problem. Based on this consideration, the first lag of talent agglomeration variable is selected as the instrumental variable, and a two-stage least squares (2SLS) estimation is conducted under the framework of province and year two-way fixed effects. The regression results are reported in Models M5 and M6 of <xref ref-type="table" rid="T7">Table 7</xref>. In M6, the Cragg&#x2013;Donald Wald F statistic is 40.5, and the Kleibergen&#x2013;Paap rk Wald F statistic is 35.2 (p &#x3c; 0.001), indicating that the selected instrumental variable satisfies the relevance condition. As shown in M6, the impact of talent agglomeration on carbon emissions remains significantly negative, which is consistent with the main conclusions of the baseline regression and the bilateral frontier decomposition, suggesting that the findings of this paper are not driven by endogeneity due to reverse causality.</p>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>Endogeneity test results of the impact of talent agglomeration on carbon emissions.</p>
</caption>
<table>
<thead valign="top">
<tr style="background-color:#A6A6A6">
<th align="center">Indicators</th>
<th align="center">M 5</th>
<th align="center">M6</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="center">TA</td>
<td align="center">&#x2212;0.12&#x2a;&#x2a;</td>
<td align="center">&#x2212;0.11&#x2a;&#x2a;</td>
</tr>
<tr>
<td align="center">(-4.81)</td>
<td align="center">(-4.50)</td>
</tr>
<tr>
<td align="center">Cragg&#x2013;Donald Wald F</td>
<td align="left"/>
<td align="center">40.5</td>
</tr>
<tr>
<td align="center">Kleibergen&#x2013;Paap rk Wald F</td>
<td align="center">-</td>
<td align="center">&#x3c7;<sup>2</sup> &#x3d; 35.2 (p &#x3c; 0.001)</td>
</tr>
<tr>
<td align="center">Kleibergen&#x2013;Paap rk LM</td>
<td align="center">-</td>
<td align="center">24.7</td>
</tr>
<tr>
<td align="center">N</td>
<td align="center">300</td>
<td align="center">300</td>
</tr>
<tr>
<td align="center">Province FE</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="center">Year FE</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Then replacing the proportion of total city RCE to GDP as a proxy for carbon emissions still confirmed the existence of bilateral effects. The findings show that the promoting effect is 0.5590, while the inhibiting effect stands at 0.9486. This result confirms the statistical significance of talent agglomeration on carbon emissions and clarifies that talent agglomeration has bilateral effects on carbon emissions, consistent with the findings mentioned above.</p>
<p>Moreover, based on the impact weights, the promoting and inhibiting effects of talent agglomeration account for 9.2% and 90.8%, respectively. This indicates that over the years, the inhibiting effect has been dominant, which is consistent with the study&#x2019;s conclusions. The variations in the inhibiting, net, and promoting effects were re-estimated, and these results are illustrated in <xref ref-type="table" rid="T8">Table 8</xref>. The study found that as the degree of talent agglomeration increases, its promoting effect raises carbon emissions, while the inhibiting effect curbs regional carbon emissions. The net effect leads to actual carbon emissions falling below the frontier level, aligning with the conclusions.</p>
<table-wrap id="T8" position="float">
<label>TABLE 8</label>
<caption>
<p>Robustness test for the deviation of talent agglomeration&#x2019;s impacts on regional carbon emissions (%).</p>
</caption>
<table>
<thead valign="top">
<tr style="background-color:#A6A6A6">
<th align="center">Meaning</th>
<th align="center">Variance meaning</th>
<th align="center">Symbols</th>
<th align="center">Measurements coefficients</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="3" align="center">Impacts</td>
<td align="center">Random error term</td>
<td align="center">
<inline-formula id="inf63">
<mml:math id="m76">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.094</td>
</tr>
<tr>
<td align="center">Promotive effect</td>
<td align="center">
<inline-formula id="inf64">
<mml:math id="m77">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.136</td>
</tr>
<tr>
<td align="center">Inhibitory effect</td>
<td align="center">
<inline-formula id="inf65">
<mml:math id="m78">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>&#x3c9;</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.427</td>
</tr>
<tr>
<td rowspan="4" align="center">Variance decomposition</td>
<td align="center">Random total error term</td>
<td align="center">
<inline-formula id="inf66">
<mml:math id="m79">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> &#x2b;<inline-formula id="inf67">
<mml:math id="m80">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>w</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> &#x2b;<inline-formula id="inf68">
<mml:math id="m81">
<mml:mrow>
<mml:msubsup>
<mml:mi>&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.210</td>
</tr>
<tr>
<td align="center">The weight of the two effects</td>
<td align="center">
<inline-formula id="inf69">
<mml:math id="m82">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>w</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>w</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>v</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.958</td>
</tr>
<tr>
<td align="center">Promotive effect weight</td>
<td align="center">
<inline-formula id="inf70">
<mml:math id="m83">
<mml:mrow>
<mml:mfrac>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>w</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.092</td>
</tr>
<tr>
<td align="center">Inhibitory effect weight</td>
<td align="center">
<inline-formula id="inf71">
<mml:math id="m84">
<mml:mrow>
<mml:mfrac>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>w</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>u</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
<mml:mo>&#x2b;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">&#x3c3;</mml:mi>
<mml:mi>w</mml:mi>
<mml:mn>2</mml:mn>
</mml:msubsup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">0.908</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s5">
<title>5 Conclusion and policy implications</title>
<sec id="s5-1">
<title>5.1 Conclusion</title>
<p>This study proposed a decomposition approach to examine the bilateral effects of talent agglomeration on carbon emissions. Utilizing panel data from 30 Chinese provinces from 2013 to 2023 and applying a two-tier stochastic frontier model, the study empirically decomposed the promotive and inhibitory effects of talent agglomeration and assessed their net impact. It further investigated the temporal, regional, and contextual heterogeneity of these effects.</p>
<p>The empirical findings reveal the following: (1) Talent agglomeration exhibits asymmetric bilateral effects on regional carbon emissions, with an overall inhibitory impact. On average, it increases emissions by 16.2% through the promotive channel but reduces them by 43.8% through the inhibitory channel, leading to a net reduction of 27.6% relative to the frontier level. (2) The net effect of talent agglomeration on carbon emissions is predominantly negative across different periods. After a brief increase in 2014, the inhibitory effect strengthened, particularly after 2020. (3) Regional heterogeneity is evident: the western region achieves significantly larger net reductions than the central and eastern regions. (4) Heterogeneity analysis shows that regions with higher talent agglomeration (&#x2265;40%), advanced economic development (70%&#x2013;100%), and stricter environmental regulation experience greater net reductions in emissions, whereas at low urbanization stages the promotive effect dominates but shifts toward inhibition as urbanization deepens.</p>
</sec>
<sec id="s5-2">
<title>5.2 Policy implications</title>
<p>For policymakers aiming to harness talent agglomeration as a mechanism to promote sustainable development, our findings provide essential guidance, highlighting that while both promotive and inhibitory effects coexist, the inhibitory effects dominate overall, leading to a net reduction in carbon emissions. Tailoring strategies to fit specific regional conditions is therefore crucial to fully leverage talent&#x2019;s role in emission reduction.</p>
<p>First, policymakers should adopt a demand-oriented approach to talent agglomeration, ensuring that talent attraction is closely aligned with local industrial development and environmental needs. Our findings demonstrate that enhancing the degree of talent agglomeration contributes significantly to effective emission reductions, if strategies are tailored to fit specific regional conditions. Accordingly, the identification and prioritization of key demands in industrial upgrading, R&#x26;D, and technology transfer is proposed, along with policies to guide the precise agglomeration of talent to address these needs. By aligning talent policies with local economic and environmental priorities, regions can foster multi-stakeholder collaboration and build sustainable innovation ecosystems that amplify the environmental benefits of talent agglomeration.</p>
<p>Second, the optimization of the spatial layout of talent agglomeration and the strengthening of cross-regional cooperation are advocated to enhance overall emission reduction. Empirical evidence shows that the inhibitory effect has strengthened since 2020, with the western region demonstrating greater emission reductions than the central and eastern regions. Regional cooperation should proceed along two complementary paths. Promoting local and neighboring talent exchange is anticipated to mitigate the negative spillover effects of over-agglomeration; meanwhile, cooperation and technical support with economically similar regions&#x2014;through interregional talent cooperation funds, joint R&#x26;D, and technology transfer platforms&#x2014;can unlock positive spillover potential and ensure that inhibitory effects dominate, resulting in net emission reductions. Ultimately, building cross-regional complementary innovation networks is essential to generate synergistic effects among regions, thereby enhancing national carbon reduction benefits and promoting high-quality economic development.</p>
<p>Finally, it is necessary to tailor talent agglomeration strategies to distinct regional conditions to strengthen the inhibitory effects on carbon emissions. Establish flexible, region-specific policies that align with the economic development stage, industrial structure, and existing talent levels in each area. Developed regions should consolidate the energy-efficiency gains of talent agglomeration, whereas less-developed regions should focus on building the foundations to enhance its inhibitory effects. In practice, this requires creating supportive platforms and career opportunities for talent retention&#x2014;such as establishing region-specific priority projects and improving compensation schemes&#x2014;so that talent agglomeration can more effectively contribute to carbon reduction and environmental sustainability across regions. These tailored strategies will ensure that talent agglomeration contributes effectively to carbon reduction and environmental sustainability in each region.</p>
</sec>
<sec id="s5-3">
<title>5.3 Research limitation and future work</title>
<p>These findings open the door to future longitudinal research linking the bilateral effects of talent agglomeration on carbon emissions by showing that such agglomeration might be generally viewed as related to significant environmental outcomes, thus supplementing and extending previous studies. Like any other study, this study is not free from limitations. Owing to data constraints, this study analyzes the bilateral effects of talent agglomeration on carbon emissions from a macro perspective and does not account for the impact of micro-level enterprises and individual talent contributions on regional energy conservation and emission reduction. Ideally, these findings should be replicated in a study that explores a wider variety of environmental pollutants, including carbon dioxide emissions, wastewater contamination, and solid waste pollution. This approach would yield a more comprehensive understanding of how scientific and technological talent agglomeration impacts the environment.</p>
</sec>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec sec-type="author-contributions" id="s7">
<title>Author contributions</title>
<p>YZ: Writing &#x2013; original draft, Validation, Conceptualization. XY: Conceptualization, Funding acquisition, Resources, Writing &#x2013; original draft, Formal analysis. QW: Writing &#x2013; review and editing, Supervision, Project administration. CL: Writing &#x2013; review and editing, Validation, Supervision, Conceptualization. YR: Validation, Methodology, Software, Writing &#x2013; review and editing. TW: Visualization, Writing &#x2013; review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s8">
<title>Funding</title>
<p>The author(s) declare that no financial support was received for the research and/or publication of this article.</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s10">
<title>Generative AI statement</title>
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<ref-list>
<title>References</title>
<ref id="B1">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Andersson</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>L&#xf6;&#xf6;f</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2011</year>). <article-title>Agglomeration and productivity: evidence from firm-level data</article-title>. <source>Ann. Reg. Sci.</source> <volume>46</volume>, <fpage>601</fpage>&#x2013;<lpage>620</lpage>. <pub-id pub-id-type="doi">10.1007/s00168-009-0352-1</pub-id>
</citation>
</ref>
<ref id="B2">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Cao</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Yan</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Does perfect regional innovation ecosystem curb carbon emissions? A measure based on the niche fitness</article-title>. <source>Environ. Impact Assess. Rev.</source> <volume>102</volume>, <fpage>107219</fpage>. <pub-id pub-id-type="doi">10.1016/j.eiar.2023.107219</pub-id>
</citation>
</ref>
<ref id="B3">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Chen</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Shi</surname>
<given-names>A.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Carbon emission curbing effects and influencing mechanisms of China&#x2019;s emission trading scheme: the mediating roles of technique effect, composition effect and allocation effect</article-title>. <source>J. Clean. Prod.</source> <volume>264</volume>, <fpage>121700</fpage>. <pub-id pub-id-type="doi">10.1016/j.jclepro.2020.121700</pub-id>
</citation>
</ref>
<ref id="B4">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Cheng</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Yin</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Shen</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>G.</given-names>
</name>
<etal/>
</person-group> (<year>2021</year>). <article-title>Behavioral decision-making in power demand-side response management: a multi-population evolutionary game dynamics perspective</article-title>. <source>Int. J. Electr. Power Energy Syst.</source> <volume>129</volume>, <fpage>106743</fpage>. <pub-id pub-id-type="doi">10.1016/j.ijepes.2020.106743</pub-id>
</citation>
</ref>
<ref id="B5">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Crowley-Henry</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Al Ariss</surname>
<given-names>A.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Talent management of skilled migrants: propositions and an agenda for future research</article-title>. <source>Int. J. Hum. Resour. Manag.</source> <volume>29</volume>, <fpage>2054</fpage>&#x2013;<lpage>2079</lpage>. <pub-id pub-id-type="doi">10.1080/09585192.2016.1262889</pub-id>
</citation>
</ref>
<ref id="B6">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Dost</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Badir</surname>
<given-names>Y. F.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Generation or adoption? The role of social capital</article-title>. <source>Manag. Decis.</source> <volume>57</volume>, <fpage>1457</fpage>&#x2013;<lpage>1471</lpage>. <pub-id pub-id-type="doi">10.1108/MD-11-2017-1108</pub-id>
</citation>
</ref>
<ref id="B7">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Fan</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Kanbur</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2011</year>). <article-title>China&#x2019;s regional disparities: experience and policy</article-title>. <source>Rev. Dev. Finance</source> <volume>1</volume>, <fpage>47</fpage>&#x2013;<lpage>56</lpage>. <pub-id pub-id-type="doi">10.1016/j.rdf.2010.10.001</pub-id>
</citation>
</ref>
<ref id="B8">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Glaeser</surname>
<given-names>E. L.</given-names>
</name>
<name>
<surname>Kerr</surname>
<given-names>W. R.</given-names>
</name>
</person-group> (<year>2009</year>). <article-title>Local industrial conditions and entrepreneurship: how much of the spatial distribution can we explain?</article-title> <source>J. Econ. Manag. Strateg.</source> <volume>18</volume>, <fpage>623</fpage>&#x2013;<lpage>663</lpage>. <pub-id pub-id-type="doi">10.1111/j.1530-9134.2009.00225.x</pub-id>
</citation>
</ref>
<ref id="B9">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Han</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Xie</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Lu</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Fang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>The effects of urban agglomeration economies on carbon emissions: evidence from Chinese cities</article-title>. <source>J. Clean. Prod.</source> <volume>172</volume>, <fpage>1096</fpage>&#x2013;<lpage>1110</lpage>. <pub-id pub-id-type="doi">10.1016/j.jclepro.2017.09.273</pub-id>
</citation>
</ref>
<ref id="B10">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Jiang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Fu</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>G.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Can the improvement of living environment stimulate urban innovation? Analysis of high-quality innovative talents and foreign direct investment spillover effect mechanism</article-title>. <source>J. Clean. Prod.</source> <volume>255</volume>, <fpage>120212</fpage>. <pub-id pub-id-type="doi">10.1016/j.jclepro.2020.120212</pub-id>
</citation>
</ref>
<ref id="B11">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kuang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Fan</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Bin</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Fan</surname>
<given-names>M.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Impact of the digital economy on carbon dioxide emissions in resource-based cities</article-title>. <source>Sci. Rep.</source> <volume>14</volume>, <fpage>16514</fpage>. <pub-id pub-id-type="doi">10.1038/s41598-024-66005-0</pub-id>
<pub-id pub-id-type="pmid">39019973</pub-id>
</citation>
</ref>
<ref id="B12">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Kumbhakar</surname>
<given-names>S. C.</given-names>
</name>
<name>
<surname>Parmeter</surname>
<given-names>C. F.</given-names>
</name>
</person-group> (<year>2009</year>). <article-title>The effects of match uncertainty and bargaining on labor market outcomes: evidence from firm- and worker-specific estimates</article-title>. <source>J. Prod. Anal.</source> <volume>31</volume>, <fpage>1</fpage>&#x2013;<lpage>14</lpage>. <pub-id pub-id-type="doi">10.1007/s11123-008-0117-3</pub-id>
</citation>
</ref>
<ref id="B13">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Lei</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Cai</surname>
<given-names>Q.</given-names>
</name>
<name>
<surname>Jiang</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Assessing the impact of environmental regulation on enterprise high-quality development in China: a two-tier stochastic frontier model</article-title>. <source>Energy Econ.</source> <volume>133</volume>, <fpage>107502</fpage>. <pub-id pub-id-type="doi">10.1016/j.eneco.2024.107502</pub-id>
</citation>
</ref>
<ref id="B14">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Ramanathan</surname>
<given-names>R.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Exploring the relationships between different types of environmental regulations and environmental performance: evidence from China</article-title>. <source>J. Clean. Prod.</source> <volume>196</volume>, <fpage>1329</fpage>&#x2013;<lpage>1340</lpage>. <pub-id pub-id-type="doi">10.1016/j.jclepro.2018.06.132</pub-id>
</citation>
</ref>
<ref id="B15">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Li</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Meng</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Study on the mechanism of haze pollution affected by urban population agglomeration</article-title>. <source>Atmosphere</source> <volume>13</volume>, <fpage>278</fpage>. <pub-id pub-id-type="doi">10.3390/atmos13020278</pub-id>
</citation>
</ref>
<ref id="B16">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Lin</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Ren</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Wu</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Xiao</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Housing price, talent movement, and innovation output: evidence from Chinese cities</article-title>. <source>Rev. Dev. Econ.</source> <volume>25</volume>, <fpage>76</fpage>&#x2013;<lpage>103</lpage>. <pub-id pub-id-type="doi">10.1111/rode.12705</pub-id>
</citation>
</ref>
<ref id="B17">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Industrial agglomeration, technological innovation and carbon productivity: evidence from China</article-title>. <source>Resour. Conserv. Recycl.</source> <volume>166</volume>, <fpage>105330</fpage>. <pub-id pub-id-type="doi">10.1016/j.resconrec.2020.105330</pub-id>
</citation>
</ref>
<ref id="B18">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Liu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Ding</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Teng</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Ye</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>The bilateral effects of digital economy on regional carbon emissions in China</article-title>. <source>Front. Environ. Sci.</source> <volume>11</volume>, <fpage>1287811</fpage>. <pub-id pub-id-type="doi">10.3389/fenvs.2023.1287811</pub-id>
</citation>
</ref>
<ref id="B19">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Martin</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Sunley</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2006</year>). <article-title>Path dependence and regional economic evolution</article-title>. <source>J. Econ. Geogr.</source> <volume>6</volume>, <fpage>395</fpage>&#x2013;<lpage>437</lpage>. <pub-id pub-id-type="doi">10.1093/jeg/lbl012</pub-id>
</citation>
</ref>
<ref id="B20">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Meyers</surname>
<given-names>M. C.</given-names>
</name>
<name>
<surname>van Woerkom</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Paauwe</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Dries</surname>
<given-names>N.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>HR managers&#x2019; talent philosophies: prevalence and relationships with perceived talent management practices</article-title>. <source>Int. J. Hum. Resour. Manag.</source> <volume>31</volume>, <fpage>562</fpage>&#x2013;<lpage>588</lpage>. <pub-id pub-id-type="doi">10.1080/09585192.2019.1579747</pub-id>
</citation>
</ref>
<ref id="B21">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Nathaniel</surname>
<given-names>S. P.</given-names>
</name>
<name>
<surname>Nwulu</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Bekun</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Natural resource, globalization, urbanization, human capital, and environmental degradation in Latin American and Caribbean countries</article-title>. <source>Environ. Sci. Pollut. Res.</source> <volume>28</volume>, <fpage>6207</fpage>&#x2013;<lpage>6221</lpage>. <pub-id pub-id-type="doi">10.1007/s11356-020-10850-9</pub-id>
<pub-id pub-id-type="pmid">32989704</pub-id>
</citation>
</ref>
<ref id="B22">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Oliveira</surname>
<given-names>E. A.</given-names>
</name>
<name>
<surname>Andrade</surname>
<given-names>J. S.</given-names>
</name>
<name>
<surname>Makse</surname>
<given-names>H. A.</given-names>
</name>
</person-group> (<year>2014</year>). <article-title>Large cities are less green</article-title>. <source>Sci. Rep.</source> <volume>4</volume>, <fpage>4235</fpage>. <pub-id pub-id-type="doi">10.1038/srep04235</pub-id>
<pub-id pub-id-type="pmid">24577263</pub-id>
</citation>
</ref>
<ref id="B23">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Peng</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Shen</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Ying</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>Q.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Can environmental regulation directly promote green innovation behavior? Based on situation of industrial agglomeration</article-title>. <source>J. Clean. Prod.</source> <volume>314</volume>, <fpage>128044</fpage>. <pub-id pub-id-type="doi">10.1016/j.jclepro.2021.128044</pub-id>
</citation>
</ref>
<ref id="B24">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Robertson</surname>
<given-names>T. S.</given-names>
</name>
<name>
<surname>Gatignon</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>1986</year>). <article-title>Competitive effects on technology diffusion</article-title>. <source>J. Mark.</source> <volume>50</volume>, <fpage>1</fpage>&#x2013;<lpage>12</lpage>. <pub-id pub-id-type="doi">10.1177/002224298605000301</pub-id>
</citation>
</ref>
<ref id="B25">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shen</surname>
<given-names>N.</given-names>
</name>
<name>
<surname>Peng</surname>
<given-names>H.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Can industrial agglomeration achieve the emission-reduction effect?</article-title> <source>Socioecon. Plann. Sci.</source> <volume>75</volume>, <fpage>100867</fpage>. <pub-id pub-id-type="doi">10.1016/j.seps.2020.100867</pub-id>
</citation>
</ref>
<ref id="B26">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shi</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Lai</surname>
<given-names>W.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Incentive factors of talent agglomeration: a case of high-tech innovation in China</article-title>. <source>Int. J. Innov. Sci.</source> <volume>11</volume>, <fpage>561</fpage>&#x2013;<lpage>582</lpage>. <pub-id pub-id-type="doi">10.1108/IJIS-05-2019-0048</pub-id>
</citation>
</ref>
<ref id="B27">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shi</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Lai</surname>
<given-names>W.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Fuzzy AHP approach to evaluate incentive factors of high-tech talent agglomeration</article-title>. <source>Expert Syst. Appl.</source> <volume>212</volume>, <fpage>118652</fpage>. <pub-id pub-id-type="doi">10.1016/j.eswa.2022.118652</pub-id>
</citation>
</ref>
<ref id="B28">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Shi</surname>
<given-names>K.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>C.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>Spatiotemporal variations of urban CO<sub>2</sub> emissions in China: a multiscale perspective</article-title>. <source>Appl. Energy</source> <volume>211</volume>, <fpage>218</fpage>&#x2013;<lpage>229</lpage>. <pub-id pub-id-type="doi">10.1016/j.apenergy.2017.11.042</pub-id>
</citation>
</ref>
<ref id="B29">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Sun</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>C.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>How does urbanization affect carbon emission efficiency? Evidence from China</article-title>. <source>J. Clean. Prod.</source> <volume>272</volume>, <fpage>122828</fpage>. <pub-id pub-id-type="doi">10.1016/j.jclepro.2020.122828</pub-id>
</citation>
</ref>
<ref id="B30">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Taskin</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Zaim</surname>
<given-names>O.</given-names>
</name>
</person-group> (<year>2001</year>). <article-title>The role of international trade on environmental efficiency: a DEA approach</article-title>. <source>Econ. Model.</source> <volume>18</volume>, <fpage>1</fpage>&#x2013;<lpage>17</lpage>. <pub-id pub-id-type="doi">10.1016/S0264-9993(00)00025-0</pub-id>
</citation>
</ref>
<ref id="B31">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Tian</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Zhu</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Co-agglomeration, technological innovation and haze pollution: an empirical research based on the middle reaches of the yangtze river urban agglomeration</article-title>. <source>Ecol. Indic.</source> <volume>158</volume>, <fpage>111492</fpage>. <pub-id pub-id-type="doi">10.1016/j.ecolind.2023.111492</pub-id>
</citation>
</ref>
<ref id="B32">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>L.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>Impacts of digital economy agglomeration on carbon emission: a two-tier stochastic frontier and spatial decomposition analysis of China</article-title>. <source>Sustain. Cities Soc.</source> <volume>95</volume>, <fpage>104624</fpage>. <pub-id pub-id-type="doi">10.1016/j.scs.2023.104624</pub-id>
</citation>
</ref>
<ref id="B33">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Han</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2023</year>). <article-title>The impact of industrial agglomeration on urban green land use efficiency in the yangtze river economic belt</article-title>. <source>Sci. Rep.</source> <volume>13</volume>, <fpage>974</fpage>. <pub-id pub-id-type="doi">10.1038/s41598-023-28250-7</pub-id>
<pub-id pub-id-type="pmid">36653473</pub-id>
</citation>
</ref>
<ref id="B34">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2019</year>). <article-title>Does industrial agglomeration facilitate environmental performance: new evidence from urban China?</article-title> <source>J. Environ. Manage.</source> <volume>248</volume>, <fpage>109244</fpage>. <pub-id pub-id-type="doi">10.1016/j.jenvman.2019.07.015</pub-id>
<pub-id pub-id-type="pmid">31310937</pub-id>
</citation>
</ref>
<ref id="B35">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Fan</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>G.</given-names>
</name>
<name>
<surname>Chai</surname>
<given-names>W.</given-names>
</name>
</person-group> (<year>2020a</year>). <article-title>The effect of urbanization and spatial agglomeration on carbon emissions in urban agglomeration</article-title>. <source>Environ. Sci. Pollut. Res.</source> <volume>27</volume>, <fpage>24329</fpage>&#x2013;<lpage>24341</lpage>. <pub-id pub-id-type="doi">10.1007/s11356-020-08597-4</pub-id>
<pub-id pub-id-type="pmid">32306267</pub-id>
</citation>
</ref>
<ref id="B36">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Xue</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Chang</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Xie</surname>
<given-names>C.</given-names>
</name>
</person-group> (<year>2020b</year>). <article-title>Macroeconomic determinants of high-tech migration in China: the case of yangtze river Delta urban agglomeration</article-title>. <source>Cities</source> <volume>107</volume>, <fpage>102888</fpage>. <pub-id pub-id-type="doi">10.1016/j.cities.2020.102888</pub-id>
</citation>
</ref>
<ref id="B37">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wang</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Du</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Zhong</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Xu</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Zhao</surname>
<given-names>Y.</given-names>
</name>
<etal/>
</person-group> (<year>2024</year>). <article-title>Unveiling the impact mechanism of urban resilience on carbon dioxide emissions of the pearl river Delta urban agglomeration in China</article-title>. <source>Environ. Impact Assess. Rev.</source> <volume>105</volume>, <fpage>107422</fpage>. <pub-id pub-id-type="doi">10.1016/j.eiar.2024.107422</pub-id>
</citation>
</ref>
<ref id="B38">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wingreen</surname>
<given-names>S. C.</given-names>
</name>
<name>
<surname>Blanton</surname>
<given-names>J. E.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>IT professionals&#x2019; person&#x2013;organization fit with IT training and development priorities</article-title>. <source>Inf. Syst. J.</source> <volume>28</volume>, <fpage>294</fpage>&#x2013;<lpage>317</lpage>. <pub-id pub-id-type="doi">10.1111/isj.12135</pub-id>
</citation>
</ref>
<ref id="B39">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wu</surname>
<given-names>H.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Hao</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Ren</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>P.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>Environmental decentralization, local government competition, and regional green development: evidence from China</article-title>. <source>Sci. Total Environ.</source> <volume>708</volume>, <fpage>135085</fpage>. <pub-id pub-id-type="doi">10.1016/j.scitotenv.2019.135085</pub-id>
<pub-id pub-id-type="pmid">31812397</pub-id>
</citation>
</ref>
<ref id="B40">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wu</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Jia</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Gao</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Effects of population flow on regional carbon emissions: evidence from China</article-title>. <source>Environ. Sci. Pollut. Res.</source> <volume>28</volume>, <fpage>62628</fpage>&#x2013;<lpage>62639</lpage>. <pub-id pub-id-type="doi">10.1007/s11356-021-15131-7</pub-id>
<pub-id pub-id-type="pmid">34196868</pub-id>
</citation>
</ref>
<ref id="B41">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Wuyts</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Dutta</surname>
<given-names>S.</given-names>
</name>
</person-group> (<year>2014</year>). <article-title>Benefiting from alliance portfolio diversity: the role of past internal knowledge creation strategy</article-title>. <source>J. Manag.</source> <volume>40</volume>, <fpage>1653</fpage>&#x2013;<lpage>1674</lpage>. <pub-id pub-id-type="doi">10.1177/0149206312442339</pub-id>
</citation>
</ref>
<ref id="B42">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Ren</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Ran</surname>
<given-names>Q.</given-names>
</name>
</person-group> (<year>2021</year>). <article-title>Can the new energy demonstration city policy reduce environmental pollution? Evidence from a quasi-natural experiment in China</article-title>. <source>J. Clean. Prod.</source> <volume>287</volume>, <fpage>125015</fpage>. <pub-id pub-id-type="doi">10.1016/j.jclepro.2020.125015</pub-id>
</citation>
</ref>
<ref id="B43">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yang</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>W.</given-names>
</name>
<name>
<surname>Feng</surname>
<given-names>D.</given-names>
</name>
<name>
<surname>Lu</surname>
<given-names>J.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Impact of pilot environmental policy on urban eco-innovation</article-title>. <source>J. Clean. Prod.</source> <volume>341</volume>, <fpage>130858</fpage>. <pub-id pub-id-type="doi">10.1016/j.jclepro.2022.130858</pub-id>
</citation>
</ref>
<ref id="B44">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Ye</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Wan</surname>
<given-names>Q.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Yao</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Huang</surname>
<given-names>D.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>How do R&#x26;D agglomeration and economic policy uncertainty affect the innovative performance of Chinese high-tech industry?</article-title> <source>Technol. Soc.</source> <volume>69</volume>, <fpage>101957</fpage>. <pub-id pub-id-type="doi">10.1016/j.techsoc.2022.101957</pub-id>
</citation>
</ref>
<ref id="B45">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Yi</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Qi</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Chen</surname>
<given-names>D.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>Impact of population agglomeration in big cities on carbon emissions</article-title>. <source>Environ. Sci. Pollut. Res.</source> <volume>29</volume>, <fpage>86692</fpage>&#x2013;<lpage>86706</lpage>. <pub-id pub-id-type="doi">10.1007/s11356-022-21722-9</pub-id>
<pub-id pub-id-type="pmid">35799006</pub-id>
</citation>
</ref>
<ref id="B46">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>York</surname>
<given-names>R.</given-names>
</name>
</person-group> (<year>2007</year>). <article-title>Demographic trends and energy consumption in european union nations, 1960&#x2013;2025</article-title>. <source>Soc. Sci. Res.</source> <volume>36</volume>, <fpage>855</fpage>&#x2013;<lpage>872</lpage>. <pub-id pub-id-type="doi">10.1016/j.ssresearch.2006.06.007</pub-id>
</citation>
</ref>
<ref id="B47">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>Z.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>M.</given-names>
</name>
<name>
<surname>Tian</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>W.</given-names>
</name>
</person-group> (<year>2017</year>). <article-title>Research on the development efficiency of regional high-end talent in China: a complex network approach</article-title>. <source>PLoS One</source> <volume>12</volume>, <fpage>e0188816</fpage>. <pub-id pub-id-type="doi">10.1371/journal.pone.0188816</pub-id>
<pub-id pub-id-type="pmid">29272286</pub-id>
</citation>
</ref>
<ref id="B48">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Mu</surname>
<given-names>R.</given-names>
</name>
<name>
<surname>Zhan</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>J.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>L.</given-names>
</name>
<name>
<surname>Yu</surname>
<given-names>Y.</given-names>
</name>
<etal/>
</person-group> (<year>2022</year>). <article-title>Digital economy, energy efficiency, and carbon emissions: evidence from provincial panel data in China</article-title>. <source>Sci. Total Environ.</source> <volume>852</volume>, <fpage>158403</fpage>. <pub-id pub-id-type="doi">10.1016/j.scitotenv.2022.158403</pub-id>
<pub-id pub-id-type="pmid">36057314</pub-id>
</citation>
</ref>
<ref id="B49">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>P.</given-names>
</name>
<name>
<surname>Qian</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>2024a</year>). <article-title>Can technological talent agglomeration improve carbon emission efficiency? Evidence from China</article-title>. <source>Environ. Dev. Sustain</source>. <pub-id pub-id-type="doi">10.1007/s10668-024-04909-7</pub-id>
</citation>
</ref>
<ref id="B50">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhang</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Wang</surname>
<given-names>T.</given-names>
</name>
<name>
<surname>Zhang</surname>
<given-names>X.</given-names>
</name>
</person-group> (<year>2024b</year>). <article-title>Do all roads lead to rome? Conditions and configurations of digital economy on carbon emission efficiency</article-title>. <source>J. Environ. Manage.</source> <volume>371</volume>, <fpage>123154</fpage>. <pub-id pub-id-type="doi">10.1016/j.jenvman.2024.123154</pub-id>
<pub-id pub-id-type="pmid">39527873</pub-id>
</citation>
</ref>
<ref id="B51">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zheng</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Deng</surname>
<given-names>F.</given-names>
</name>
<name>
<surname>Li</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Yang</surname>
<given-names>Z.</given-names>
</name>
</person-group> (<year>2022</year>). <article-title>The impact of China&#x2019;s Western development strategy on energy conservation and emission reduction</article-title>. <source>Environ. Impact Assess. Rev.</source> <volume>94</volume>, <fpage>106743</fpage>. <pub-id pub-id-type="doi">10.1016/j.eiar.2022.106743</pub-id>
</citation>
</ref>
<ref id="B52">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhou</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Guo</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Liu</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2018</year>). <article-title>High-level talent flow and its influence on regional unbalanced development in China</article-title>. <source>Appl. Geogr.</source> <volume>91</volume>, <fpage>89</fpage>&#x2013;<lpage>98</lpage>. <pub-id pub-id-type="doi">10.1016/j.apgeog.2017.12.023</pub-id>
</citation>
</ref>
<ref id="B53">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zhuo</surname>
<given-names>C.</given-names>
</name>
<name>
<surname>Deng</surname>
<given-names>F.</given-names>
</name>
</person-group> (<year>2020</year>). <article-title>How does China&#x2019;s Western development strategy affect regional green economic efficiency?</article-title> <source>Sci. Total Environ.</source> <volume>707</volume>, <fpage>135939</fpage>. <pub-id pub-id-type="doi">10.1016/j.scitotenv.2019.135939</pub-id>
<pub-id pub-id-type="pmid">31864002</pub-id>
</citation>
</ref>
<ref id="B54">
<citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname>Zou</surname>
<given-names>S.</given-names>
</name>
<name>
<surname>Fan</surname>
<given-names>X.</given-names>
</name>
<name>
<surname>Zhou</surname>
<given-names>Y.</given-names>
</name>
<name>
<surname>Cui</surname>
<given-names>Y.</given-names>
</name>
</person-group> (<year>2024</year>). <article-title>Achieving collaborative pollutant and carbon emissions reduction through digital governance: evidence from Chinese enterprises</article-title>. <source>Environ. Res.</source> <volume>263</volume>, <fpage>120197</fpage>. <pub-id pub-id-type="doi">10.1016/j.envres.2024.120197</pub-id>
<pub-id pub-id-type="pmid">39427948</pub-id>
</citation>
</ref>
</ref-list>
</back>
</article>