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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Earth Sci.</journal-id>
<journal-title>Frontiers in Earth Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Earth Sci.</abbrev-journal-title>
<issn pub-type="epub">2296-6463</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">872806</article-id>
<article-id pub-id-type="doi">10.3389/feart.2022.872806</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Earth Science</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>The Widening Wealth Inequality as a Contributor to Increasing Household Carbon Emissions</article-title>
<alt-title alt-title-type="left-running-head">Qin et&#x20;al.</alt-title>
<alt-title alt-title-type="right-running-head">Wealth Inequality and Carbon Emissions</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Qin</surname>
<given-names>Xiaodi</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1672918/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Wu</surname>
<given-names>Haitao</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Xiaofang</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Wang</surname>
<given-names>Wei</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>School of Business Administration</institution>, <institution>Zhongnan University of Economics and Law</institution>, <addr-line>Wuhan</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>College of Management</institution>, <institution>Sichuan Agricultural University</institution>, <addr-line>Ya&#x27;an</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/1496727/overview">Shaoquan Liu</ext-link>, Institute of Mountain Hazards and Environment (CAS), China</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/1673726/overview">Zhi Chen</ext-link>, Hubei Academy of Social Sciences, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1676134/overview">Zhiqiang Li</ext-link>, Nanjing University of Information Science and Technology, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Haitao Wu, <email>wuhan_haitao@aliyun.com</email>; Wei Wang, <email>wangwei@sicau.edu.cn</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Interdisciplinary Climate Studies, a section of the journal Frontiers in Earth Science</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>18</day>
<month>03</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>872806</elocation-id>
<history>
<date date-type="received">
<day>10</day>
<month>02</month>
<year>2022</year>
</date>
<date date-type="accepted">
<day>16</day>
<month>02</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Qin, Wu, Zhang and Wang.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Qin, Wu, Zhang 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&#x20;terms.</p>
</license>
</permissions>
<abstract>
<p>The Sustainable Development Goals call for taking urgent action to combat climate change and reduce inequalities. However, the related actions have not been effective. Global CO2 emissions in 2021 are projected to rebound to approaching the 2018&#x2013;2019 peak, and wealth inequality has been increasing at the very top of the distribution resulting from the COVID-19 pandemic. To test whether a trade-off exists between social and environmental benefits, this study calculates county-level wealth inequality with the Gini coefficient and consumption-based household carbon emissions with the emissions coefficient method and input&#x2013;output modeling. Data are collected from the China Family Panel Studies, the Visible Infrared Imaging Radiometer Suite, the Chinese National Bureau of Statistics and Carbon Emission Account and Datasets in 2014, 2016 and 2018. In addition, a high-dimensional fixed-effects model, an instrumental variable model and causal mediation analysis are adopted to empirically test how wealth inequality influences household carbon emissions and explore the underlying mechanisms. The results show that county-level wealth inequality has a positive impact on household carbon emissions per capita. This means that policies designed to narrow the wealth gap can help reduce carbon emissions, making progress toward multiple SDGs. Moreover, the study reveals that the social norms of the Veblen effect and short-termism play an important role in mediating the relationship between wealth inequality and consumption-based household carbon emissions. This finding provides a new perspective to understand the mechanism behind wealth inequality and household carbon emissions related to climate change.</p>
</abstract>
<kwd-group>
<kwd>wealth inequality</kwd>
<kwd>household carbon emissions</kwd>
<kwd>climate change</kwd>
<kwd>veblen effect</kwd>
<kwd>short-termism</kwd>
</kwd-group>
<contract-sponsor id="cn001">National Office for Philosophy and Social Sciences<named-content content-type="fundref-id">10.13039/501100012325</named-content>
</contract-sponsor>
<contract-sponsor id="cn002">National Bureau of Statistics of China<named-content content-type="fundref-id">10.13039/100009376</named-content>
</contract-sponsor>
<contract-sponsor id="cn003">Ministry of Education<named-content content-type="fundref-id">10.13039/100010002</named-content>
</contract-sponsor>
<contract-sponsor id="cn004">Central Universities in China<named-content content-type="fundref-id">10.13039/501100012429</named-content>
</contract-sponsor>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>Extreme weather events around the world are becoming increasingly frequent, posing a serious threat to the survival of humankind, especially for the poor. Increasing carbon emissions, contributing greatly to global warming and climate change, have therefore become a matter of global concern (IPCC, 2018). The household sector has been one of the largest contributors to carbon emissions due to the direct energy consumption and indirect consumption activities of households (<xref ref-type="bibr" rid="B19">Hertwich and Peters, 2009</xref>; <xref ref-type="bibr" rid="B26">Li et&#x20;al., 2019</xref>). Households consume 29% of global energy and are responsible for 21% of the total carbon emissions<sup>1</sup> In the case of China, the largest emitter, the household sector accounts for over 40% of the total carbon emissions and maintains stable growth (<xref ref-type="bibr" rid="B14">Fan et&#x20;al., 2013</xref>; <xref ref-type="bibr" rid="B41">Shi et&#x20;al., 2016</xref>; <xref ref-type="bibr" rid="B42">Shigetomi,2018</xref>). 12In May 2020, the Chinese government proposed the <italic>domestic-international dual circulation</italic> model, which prioritizes domestic consumption to achieve sustainable economic development. The dual circulation plan may further increase the proportion of consumption-based carbon emissions from the household sector.</p>
<p>The increasing significance of consumption-based carbon emissions leads us to rethink the driving factors for household consumption to find effective paths to achieving the carbon-neutral goals outlined in the Paris Agreement (<xref ref-type="bibr" rid="B38">Rogelj et&#x20;al., 2019</xref>). Among the driving factors, the role of inequality, another important SDG and climate action, has also gained great attention from researchers (<xref ref-type="bibr" rid="B6">Piketty and Chancel, 2015</xref>; <xref ref-type="bibr" rid="B21">Jorgenson et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B39">Rojas-Vallejos and Lastuka, 2020</xref>).</p>
<p>Past research has suggested a relationship between income inequality and carbon emissions but failed to achieve consensus (<xref ref-type="bibr" rid="B17">Guo, 2014</xref>; <xref ref-type="bibr" rid="B44">Uddin et&#x20;al., 2020</xref>). <xref ref-type="bibr" rid="B37">Ravallion et&#x20;al. (2000)</xref> investigated the relationship between income inequality and carbon emissions from production and proposed that higher inequality comes with less emissions. <xref ref-type="bibr" rid="B40">Sager (2019)</xref> further studied the relationship between income inequality and consumption-based carbon emissions using input&#x2013;output analysis and found that lower income inequality contributes to higher consumption-based carbon emissions. Other researchers insist that income inequality is positively related to carbon emissions (<xref ref-type="bibr" rid="B16">Golley &#x26; Meng, 2012</xref>; <xref ref-type="bibr" rid="B62">Zhu et&#x20;al., 2018</xref>).</p>
<p>A limitation of these studies is that they have only focused on income inequality and fail to consider the role of wealth inequality. However, wealth is much more concentrated than income because wealth can accumulate over time (<xref ref-type="bibr" rid="B20">Jones, 2015</xref>). More importantly, income inequality has declined over the past years, but wealth inequality is worsening following the rapid growth and transformation in China (<xref ref-type="bibr" rid="B47">Wan et&#x20;al., 2018</xref>; <xref ref-type="bibr" rid="B46">Wan et&#x20;al., 2021</xref>). According to the Global Wealth Report in 2021 by Credit Suisse, the Gini coefficient of wealth for China was 0.599 in 2000, rose quickly to 0.636 in 2005 and reached 0.704 in 2020 (see <xref ref-type="fig" rid="F1">Figure&#x20;1</xref>). It is therefore imperative to investigate how wealth inequality influences consumption-based carbon emissions.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Gini coefficient of wealth in China during 2000-2020.</p>
</caption>
<graphic xlink:href="feart-10-872806-g001.tif"/>
</fig>
<p>There have been several attempts to study the relationship between wealth inequality and consumption-based carbon emissions. One study, by <xref ref-type="bibr" rid="B25">Knight et&#x20;al. (2017)</xref>, reveals that wealth inequality is positively connected with consumption-based carbon emissions in high-income countries. Another study, by <xref ref-type="bibr" rid="B2">Aye (2020)</xref>, found that wealth inequality has positive effects on carbon emissions. A limitation of these two studies is that they use the top decile of the wealth share to measure wealth inequality. The top decile of the wealth share is easy to calculate but fails to consider the whole wealth distribution. In addition, these studies are limited in that they only use the concentration of political and economic power to explain how wealth inequality influences carbon emissions. However, as some scholars have argued, social norms, including the Veblen effect and short-termism, may also link inequality to consumption-based household carbon emissions, which needs to be verified from the perspective of wealth inequality (<xref ref-type="bibr" rid="B4">Berthe &#x26; Elie, 2015</xref>; <xref ref-type="bibr" rid="B29">Liobikien, 2020</xref>). Moreover, most of the existing studies use mediation analysis to test the mediating mechanism but fail to ensure accurate causal estimation of the relation between the mediator and dependent variable. <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fpsyg.2020.02067/full">Mayer et&#x20;al. (2014</ext-link>) and <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fpsyg.2020.02067/full">Kisbu-Sakarya et&#x20;al.(2020</ext-link>) proposed causal mediation analysis to address this problem.</p>
<p>Against this background, we focus on how wealth inequality influences household carbon emissions and make the following contributions. First, we utilize the Gini coefficient of wealth to measure wealth inequality at the county level. The Gini coefficient can capture variation in the head and tail of the wealth distribution. Moreover, wealth inequality is measured at the county level, while most previous studies focus on the provincial or municipality level. County-level wealth inequality has special links tbo consumer behavior given the similar norms within a county. Besides, as a global problem, carbon emissions decision-making may come from global, national, provincial or municipality strata, but is tangibly implemented at county levels. Therefore, county-level wealth inequality can better reveal the impact of wealth inequality on consumption-based carbon emissions and enrich the limited literature regarding wealth inequality in China. Second, we calculate direct and indirect consumption-based household carbon emissions based on a household survey spanning from 2014 to 2018 in China. This supplements the most recent data on consumption-based carbon emissions in China. Third, we use the instrumental variable method and causal mediation analysis to address the endogeneity problem when evaluating how wealth inequality influences household carbon emissions. Finally, there is no study explaining the influencing mechanism of wealth inequality on consumption-based household carbon emissions based on the role of social norms, including the Veblen effect and short-termism. Our study aims to fill this gap and enriches the literature regarding the specific mechanisms that may link wealth inequality to emissions.</p>
</sec>
<sec id="s2">
<title>Data and Methods</title>
<p>To determine how wealth inequality influences household carbon emissions, we apply four databases: 1) Samples of China households from the China Family Panel Studies (CFPS) in 2014, 2016 and 2018; 2) The county-level Night Light Development Index (NLDI) from the multitemporal dataset of the Visible Infrared Imaging Radiometer Suite (VIIRS) in 2014, 2016 and 2018; 3) China&#x2019;s Input&#x2013;Output Tables (IOTs) in 42 economic sectors from the Chinese National Bureau of Statistics (CNBS) in 2015, 2017 and 2018; and 4) Sectoral emission factor information Carbon Emission Account &#x26; Datasets (CEADs) in 2014, 2016 and&#x20;2018.</p>
<p>The CFPS and VIIRS: wealth, expenditure, demographics and county features.</p>
<p>The CFPS dataset, launched by Peking University, collects household data on the economic and noneconomic information and wellbeing of the Chinese population at the individual, family, and community levels. It covers 25 provinces/municipalities/autonomous regions in China and does not include Hong Kong, Macao, Taiwan, Xinjiang, Tibet, Qinghai, Inner Mongolia, Ningxia and Hainan (<xref ref-type="bibr" rid="B51">Xie &#x26; Lu, 2015</xref>). The stratified, three-stage, and probability-proportionate-to-size sampling approach is adopted to improve the randomness and representativeness of the CFPS dataset. First, we feature household wealth by collecting total net assets in the CFPS. Wealth is defined as all household assets minus liabilities, including net housing assets, net financial assets, nonhousing debt, fixed productive assets, land assets, consumer durables and other assets. Second, to calculate indirect household carbon emissions, we collect consumption expenditures in the CFPS. Referring to the classification of household expenditures in the CNBS, consumption expenditures are classified into seven categories of expenditures on food; clothing; residence; household facilities and services; health care and medical services; transportation and telecommunication; and education, culture and recreation.<sup>2</sup> However, the classification of expenditures in the CFPS does not directly match the 42 economic sectors in the CNBS. To match the two datasets, we disaggregate the consumption expenditure in the CFPS into corresponding sectors in the CNBS, based on the proportion of urban and rural households&#x2019; output in 42 economic sectors in IOTs. Third, to measure direct household carbon emissions, we collect expenditures on cooking with fuel, heating with fuel and driving with petrol in the CFPS. Fourth, some scholars assert that conspicuous consumption is the representative case of the Veblen effect. Therefore, referring to <xref ref-type="bibr" rid="B22">Kaus (2013)</xref>, <xref ref-type="bibr" rid="B4">Berthe &#x26; Elie (2015)</xref>, and <xref ref-type="bibr" rid="B60">Zhou et&#x20;al. (2018)</xref>, the Veblen effect is defined as the total household consumption expenditures and proportion of consumption on clothing, residence, transportation and telecommunication to the total expenditure in the CFPS. In addition, the CFPS dataset collects people&#x2019;s attitudes toward the severity of the environmental problem in China, with scores from 0 to 10. &#x201c;0&#x201d; represents &#x201c;not severe&#x201d;, while &#x201c;10&#x201d; represents &#x201c;extremely severe&#x201d;. <xref ref-type="bibr" rid="B12">Echavarren (2017)</xref> proposes that people are more likely to emphasize environmental awareness and engage in low-carbon consumption when they perceive the severity of environmental pollution. As those who are short-sighted usually lack environmental awareness and tend to score low for that question (<xref ref-type="bibr" rid="B53">Xu et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B52">Xu et&#x20;al., 2019</xref>; <xref ref-type="bibr" rid="B10">Cruz &#x26; Manata, 2020</xref>), low scores are used to represent the weakening environmental awareness of households caused by short-termism. Fifth, we collect data on household demographic variables, including the child and elderly dependency ratio, proportion of healthy people, log of adult per capita income, access to the internet, and household location. In addition, we capture the characteristic variables of the head of household, such as gender, membership, medicare, age, squared age, marital status and qualifications. Finally, we collect NLDI data in 2014, 2016 and 2018 from the VIIRS to depict county-level economic activities (<xref ref-type="bibr" rid="B7">Chen &#x26; Nordhaus, 2015</xref>; <xref ref-type="bibr" rid="B50">Wu et&#x20;al., 2018</xref>; <xref ref-type="bibr" rid="B54">Xu et&#x20;al., 2020</xref>; <xref ref-type="bibr" rid="B61">Zhou et&#x20;al., 2021</xref>). These characteristic variables have significant effects on wealth and consumption-based carbon emissions. The definitions of the key variables are displayed in <xref ref-type="table" rid="T1">Table&#x20;1</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Variable definition.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Variable</th>
<th align="center">Variable definition</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Wealth inequality at county level</td>
<td align="left">County-level Gini coefficient of wealth</td>
</tr>
<tr>
<td align="left">HCEs_total</td>
<td align="left">Household total carbon emissions per capita (ton)</td>
</tr>
<tr>
<td align="left">HCEs_diect</td>
<td align="left">Household total direct carbon emissions per capita (ton)</td>
</tr>
<tr>
<td align="left">HCEs_indiect</td>
<td align="left">Household total indirect carbon emissions per capita (ton)</td>
</tr>
<tr>
<td align="left">Child_r</td>
<td align="left">Child dependency ratio of a household</td>
</tr>
<tr>
<td align="left">Old_r</td>
<td align="left">Elderly dependency ratio of a household</td>
</tr>
<tr>
<td align="left">Health_r</td>
<td align="left">Proportion of healthy people of a household</td>
</tr>
<tr>
<td align="left">Fami_size</td>
<td align="left">Family size</td>
</tr>
<tr>
<td align="left">Ln_pinc</td>
<td align="left">Log of adult per capita income (yuan)</td>
</tr>
<tr>
<td align="left">Inter_access</td>
<td align="left">Access to the internet (yes &#x3d; 1, no &#x3d; 0)</td>
</tr>
<tr>
<td align="left">Rural</td>
<td align="left">Household&#xa0;location (rural &#x3d; 1, urban &#x3d; 0)</td>
</tr>
<tr>
<td align="left">Gender</td>
<td align="left">Gender of the head of household (male &#x3d; 1, female &#x3d; 0)</td>
</tr>
<tr>
<td align="left">Party</td>
<td align="left">CPC member of the head of household (yes &#x3d; 1, no &#x3d; 0)</td>
</tr>
<tr>
<td align="left">Medicare</td>
<td align="left">Covered by medicare of the head of household (yes &#x3d; 1, no &#x3d; 0)</td>
</tr>
<tr>
<td align="left">Age</td>
<td align="left">Age of the head of household</td>
</tr>
<tr>
<td align="left">SAge</td>
<td align="left">Squared age of the head of household</td>
</tr>
<tr>
<td align="left">Married</td>
<td align="left">Marital status of the head of household (married &#x3d; 1, unmarried &#x3d; 0)</td>
</tr>
<tr>
<td align="left">Qualification</td>
<td align="left">Qualifications (junior middle school or above &#x3d; 1, primary school or below)</td>
</tr>
<tr>
<td align="left">ANLI</td>
<td align="left">Average&#xa0;nighttime&#xa0;light&#xa0;index&#xa0;at county level</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>CNBS and CEADs, IOTs and sectoral carbon emissions intensity.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>To apply the I-O approach to calculate consumption-based household carbon emissions, we need to integrate household consumption expenditures into IOTs in the CNBS dataset and sectoral carbon emission factors in the CEADs dataset. Given that the CNBS dataset only provides IOTs in 42 economic sectors in 2015, 2017 and 2018, we match IOTs from the CNBS dataset in 2015 and 2017 to corresponding data from the CFPS and CEADs datasets in 2014 and 2016, respectively. Sector classifications are almost the same in the CNBS and CEADs datasets, which greatly reduces the bias due to data matching. With these two datasets, we can calculate the Leontief inverse matrix, which is essential for measuring indirect household carbon emissions and emissions derived from sectoral IOTs and per-yuan carbon emission factors.</p>
<sec id="s2-1">
<title>Calculation of Wealth Inequality</title>
<p>Following <xref ref-type="bibr" rid="B25">Knight et&#x20;al. (2017)</xref>, <xref ref-type="bibr" rid="B30">Liu et&#x20;al. (2019)</xref> and <xref ref-type="bibr" rid="B46">Wan et&#x20;al. (2021)</xref>, we adopt the commonly used Gini coefficient to measure wealth inequality at the county level. The Gini coefficient evolves from the Lorenz curve framework and can measure the wealth distribution within a population. It has the benefit of providing an all-inclusive measure of wealth inequality and capturing changes in the head and tail of the wealth spectrum. The Gini coefficient of wealth can be simply expressed as follows:<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:mi mathvariant="bold-italic">Gini</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mn>1</mml:mn>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msup>
<mml:mi mathvariant="bold-italic">n</mml:mi>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi mathvariant="bold-italic">h</mml:mi>
<mml:mn>1</mml:mn>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi mathvariant="bold-italic">n</mml:mi>
</mml:munderover>
<mml:munderover>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mrow>
<mml:mi mathvariant="bold-italic">h</mml:mi>
<mml:mn>2</mml:mn>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi mathvariant="bold-italic">n</mml:mi>
</mml:munderover>
<mml:mo>&#x7c;</mml:mo>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">h</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="bold-italic">W</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">h</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>&#x7c;</mml:mo>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>where <inline-formula id="inf1">
<mml:math id="m2">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denotes the county-level Gini coefficient of wealth per adult; <inline-formula id="inf2">
<mml:math id="m3">
<mml:mi>n</mml:mi>
</mml:math>
</inline-formula> denotes the number of households in the county; and <inline-formula id="inf3">
<mml:math id="m4">
<mml:mi>&#x3bc;</mml:mi>
</mml:math>
</inline-formula> denotes the average per adult household wealth of all households in the county. <inline-formula id="inf4">
<mml:math id="m5">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf5">
<mml:math id="m6">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> represent the per adult wealth of households <inline-formula id="inf6">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf7">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>h</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Theoretically, <inline-formula id="inf8">
<mml:math id="m9">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> ranges from 0 (complete equality) to 1 (complete inequality), which means that the higher <inline-formula id="inf9">
<mml:math id="m10">
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is, the greater the wealth inequality&#x20;is.</p>
</sec>
<sec id="s2-2">
<title>Calculation of Direct and Indirect HCEs</title>
<p>As expressed in <xref ref-type="disp-formula" rid="e2">Eq. 2</xref>, the total consumption-based carbon emissions <inline-formula id="inf10">
<mml:math id="m11">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi>t</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for households consist of the direct carbon emissions <inline-formula id="inf11">
<mml:math id="m12">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and the indirect carbon emissions <inline-formula id="inf12">
<mml:math id="m13">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. We use the emissions coefficient method (ECM) from the IPCC (2006) to calculate the direct carbon emissions <inline-formula id="inf13">
<mml:math id="m14">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for households and input&#x2013;output modeling (IOM) to calculate the indirect carbon emissions <inline-formula id="inf14">
<mml:math id="m15">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.<disp-formula id="e2">
<mml:math id="m16">
<mml:mrow>
<mml:mi mathvariant="bold-italic">HCE</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">s</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi mathvariant="bold-italic">total</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="bold-italic">HCE</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">s</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi mathvariant="bold-italic">direct</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="bold-italic">HCE</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">s</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi mathvariant="bold-italic">indirect</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>
</p>
<sec id="s2-2-1">
<title>Emissions Coefficient Method (ECM)</title>
<p>The ECM has been widely used to calculate direct carbon emissions in previous studies (<xref ref-type="bibr" rid="B35">Munksgaard et&#x20;al., 2000</xref>; <xref ref-type="bibr" rid="B48">Wiedenhofer et&#x20;al., 2017</xref>; <xref ref-type="bibr" rid="B59">Zhang, et&#x20;al., 2020</xref>). The direct carbon emissions <inline-formula id="inf15">
<mml:math id="m17">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> for households are calculated as follows:<disp-formula id="e3">
<mml:math id="m18">
<mml:mrow>
<mml:mi mathvariant="bold-italic">HCE</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">s</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi mathvariant="bold-italic">direct</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:munder>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
</mml:mstyle>
<mml:mi mathvariant="bold-italic">j</mml:mi>
</mml:munder>
<mml:msub>
<mml:mi mathvariant="bold-italic">f</mml:mi>
<mml:mi mathvariant="bold-italic">j</mml:mi>
</mml:msub>
<mml:mi mathvariant="bold-italic">Energ</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">ji</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>where <inline-formula id="inf16">
<mml:math id="m19">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>g</mml:mi>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the energy <italic>j</italic> consumed by the household and <inline-formula id="inf17">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the carbon emissions factor from energy source <italic>j</italic>. In the CFPS, there are three main sources of energy consumed by the household: cooking with fuel, heating with fuel and driving with petrol. First, the CFPS dataset classifies cooking fuel into electricity, natural gas, LNG, coal, solar energy and others. Carbon emissions from electricity consumption are usually regarded as indirect HCEs, and emissions from solar energy and others are negligible. Therefore, we calculate energy consumption from cooking fuel based on expenditure and price on natural gas, LNG and coal. Second, given that urban residents in China usually depend on central heating to heat a house, the HCEs of urban households are regarded as indirect carbon emissions, relying on the sector of &#x201c;Electricity, gas, steam and air conditioning supply&#x201d;. Because rural residents in China depend on coal for heating, we calculate the energy consumption from heating fuel in rural areas based on the expenditure on heating and the price of coal. Third, local transportation expenses are split into expenditures on public transportation and petrol for self-driving, according to the ratio of urban and rural households&#x2019; output in the sectors of &#x201c;Transportation, Storage, Post and Telecommunication Services&#x201d; and &#x201c;Petroleum Processing and Coking&#x201d; in IOTs. We consider consumption on public transportation as indirect HCEs and calculate the energy consumption from driving petrol from petrol expenditures and prices. We can calculate the direct HCEs by multiplying the direct consumption by the corresponding emissions factors and sum up the results.</p>
</sec>
<sec id="s2-2-2">
<title>Input-Output modeling (IOM)</title>
<p>IOM has also been widely used to calculate the indirect carbon emissions of households (<xref ref-type="bibr" rid="B16">Golley and Meng, 2012</xref>; <xref ref-type="bibr" rid="B48">Wiedenhofer et&#x20;al., 2017</xref>), which is similar to the consumer lifestyle approach (CLA). Both IOM and LCA are closely linked to the consumption patterns of the household, while IOM has the unparalleled advantage of systematically covering all the indirect linkages between different industrial sectors. We can use IOM to calculate the indirect carbon emissions <inline-formula id="inf18">
<mml:math id="m21">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> as follows:<disp-formula id="e4">
<mml:math id="m22">
<mml:mrow>
<mml:mi mathvariant="bold-italic">HCE</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">s</mml:mi>
<mml:mrow>
<mml:mi mathvariant="bold-italic">i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi mathvariant="bold-italic">indirect</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mi mathvariant="bold-italic">D</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="bold-italic">I</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="bold-italic">A</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mi mathvariant="bold-italic">Ex</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">p</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>where <inline-formula id="inf19">
<mml:math id="m23">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the row vector of emission factors for sector <italic>i</italic>. <inline-formula id="inf20">
<mml:math id="m24">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>I</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>, called the Leontief inverse matrix, is essential to the calculation of <inline-formula id="inf21">
<mml:math id="m25">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mrow>
<mml:mi>i</mml:mi>
<mml:mo>_</mml:mo>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>r</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>c</mml:mi>
<mml:mi>t</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> through the IOM method, where <inline-formula id="inf22">
<mml:math id="m26">
<mml:mi>I</mml:mi>
</mml:math>
</inline-formula> denotes an identity matrix and <inline-formula id="inf23">
<mml:math id="m27">
<mml:mi>A</mml:mi>
</mml:math>
</inline-formula> denotes a matrix of direct requirements coefficients. <inline-formula id="inf24">
<mml:math id="m28">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>x</mml:mi>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is a column vector of expenditure on commodities and services for the household. First, we calculate <inline-formula id="inf25">
<mml:math id="m29">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> by <inline-formula id="inf26">
<mml:math id="m30">
<mml:mrow>
<mml:msub>
<mml:mi>D</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>/</mml:mo>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, where <inline-formula id="inf27">
<mml:math id="m31">
<mml:mrow>
<mml:mtext>&#xa0;</mml:mtext>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the total carbon emissions and <inline-formula id="inf28">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the total output for sector <italic>i.</italic> We can obtain <inline-formula id="inf29">
<mml:math id="m33">
<mml:mrow>
<mml:msub>
<mml:mi>E</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> from the CEADs database and <inline-formula id="inf30">
<mml:math id="m34">
<mml:mrow>
<mml:msub>
<mml:mi>V</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> from the Chinese National Bureau of Statistics. Second, we multiply <inline-formula id="inf31">
<mml:math id="m35">
<mml:mrow>
<mml:mo>&#xa0;</mml:mo>
<mml:mi>D</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> by the Leontief inverse matrix <inline-formula id="inf32">
<mml:math id="m36">
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> and obtain the total sectoral carbon emission intensity matrix <inline-formula id="inf33">
<mml:math id="m37">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>I</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula>. Third, we multiply the desired expenditure <inline-formula id="inf34">
<mml:math id="m38">
<mml:mrow>
<mml:mi>E</mml:mi>
<mml:mi>x</mml:mi>
<mml:msub>
<mml:mi>p</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> by <inline-formula id="inf35">
<mml:math id="m39">
<mml:mrow>
<mml:mi>D</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi>I</mml:mi>
<mml:mo>&#x2212;</mml:mo>
<mml:mi>A</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> and obtain the consumption-based indirect carbon emissions by sector. Finally, we classify the sectoral indirect carbon emissions and summarize them by the classification of individual consumption to obtain the indirect carbon emissions for the household. In summary, by applying the CAEDs database, we reduce uncertainty as much as possible. Matching the CEADs database, Chinese National Bureau of Statistics and CFPS database greatly helps us increase the accuracy of the calculation of indirect HCEs (<xref ref-type="bibr" rid="B59">Zhang, et&#x20;al., 2020</xref>).</p>
</sec>
<sec id="s2-2-3">
<title>High-Dimensional Fixed-Effects Model</title>
<p>To evaluate the influence of widening wealth inequality on household carbon emissions, we apply the high-dimensional fixed-effects (HDFE) model. With the HDFE model, it is possible to examine the influence of multiple levels of fixed effects. The household carbon emissions (HCEs) as a function of wealth inequality (WealthInequality) at the county level are represented as follows:<disp-formula id="e5">
<mml:math id="m40">
<mml:mrow>
<mml:mi mathvariant="bold-italic">HCE</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">s</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mi mathvariant="bold-italic">WealthInequalit</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">X</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b2;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mi mathvariant="bold-italic">j</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c5;</mml:mi>
<mml:mi mathvariant="bold-italic">t</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>
</p>
<p>In this equation, the HDFE model uses control variables (<inline-formula id="inf36">
<mml:math id="m41">
<mml:mrow>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>)</bold> as well as the dependent variable of household carbon emissions and the explanatory variable of wealth inequality. <inline-formula id="inf37">
<mml:math id="m42">
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>C</mml:mi>
<mml:mi>E</mml:mi>
<mml:msub>
<mml:mi>s</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes consumption-based carbon emissions of the <italic>ith</italic> household, and <inline-formula id="inf38">
<mml:math id="m43">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> denotes the Gini coefficient of wealth in the county where the <italic>ith</italic> household is located. <inline-formula id="inf39">
<mml:math id="m44">
<mml:mrow>
<mml:msub>
<mml:mi>X</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is a vector of control variables, including features of the household, head of the household and county. Household features refer to the child and elderly dependency ratio, proportion of healthy people, family size, household income per capita, access to the internet and household location. Features of head of the household refer to gender, party, medicare, age, squared age, marital status and qualification. The county feature refers to socioeconomic activities, which is represented by the average nighttime light index at the county level. Region-invariance and time-invariance are captured by the fixed effects, which are <inline-formula id="inf40">
<mml:math id="m45">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mi>j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf41">
<mml:math id="m46">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c5;</mml:mi>
<mml:mi>t</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. Finally, <inline-formula id="inf42">
<mml:math id="m47">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bc;</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the error&#x20;term.</p>
</sec>
<sec id="s2-2-4">
<title>Instrumental Variable Model</title>
<p>Although we use the HDFE model to improve the robustness of the estimation results, reverse causality and omitted variable bias may occur and cause endogeneity problems. To address such an endogeneity problem, we further use an instrumental variable model (IV) and choose rainfall as an instrumental variable. Rainfall may influence agricultural production and physical assets, especially in rural China. Therefore, rainfall may affect county-level wealth inequality and consumption-based household carbon emissions. Rainfall may not directly influence household carbon emissions, which is an exogenous variable (<xref ref-type="bibr" rid="B56">Yang and Choi, 2007</xref>; <xref ref-type="bibr" rid="B1">Akobeng, 2017</xref>; <xref ref-type="bibr" rid="B34">Mulubrhan et&#x20;al., 2018</xref>; <xref ref-type="bibr" rid="B58">Zeng et&#x20;al., 2021</xref>). Using the IV, HCEs as a function of wealth inequality can be expressed as:<disp-formula id="e6">
<mml:math id="m48">
<mml:mrow>
<mml:mi mathvariant="bold-italic">WealthInequalit</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mi mathvariant="bold-italic">Rainfal</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">l</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">X</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b2;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mi mathvariant="bold-italic">j</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c5;</mml:mi>
<mml:mi mathvariant="bold-italic">t</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>
<disp-formula id="e7">
<mml:math id="m49">
<mml:mrow>
<mml:mi mathvariant="bold-italic">HCE</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">s</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi mathvariant="bold-italic">WealthInequalit</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="true">&#x5e;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">X</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b2;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mi mathvariant="bold-italic">j</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c5;</mml:mi>
<mml:mi mathvariant="bold-italic">t</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>where parameter <inline-formula id="inf43">
<mml:math id="m50">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is estimated by standard 2SLS estimation. <inline-formula id="inf44">
<mml:math id="m51">
<mml:mrow>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="true">&#x5e;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> stands for the estimated values of <inline-formula id="inf45">
<mml:math id="m52">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in the first stage. The instrumental variable, <inline-formula id="inf46">
<mml:math id="m53">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, denotes the average annual precipitation in the county where the <italic>ith</italic> household is located.</p>
</sec>
<sec id="s2-2-5">
<title>Causal Mediation Analysis</title>
<p>To disentangle the mechanisms underlying the association between wealth inequality and household carbon emissions, we need to use mediation analysis. However, typical mediation analysis is essentially a causal model and depends on assumptions that are not consistent with causal conclusions. Therefore, we use mediation analysis (CMA) to improve the accuracy of causal estimation (<xref ref-type="bibr" rid="B33">Mayer et&#x20;al., 2014</xref>; <xref ref-type="bibr" rid="B11">Dippel et&#x20;al., 2020</xref>; <xref ref-type="bibr" rid="B23">Kisbu-Sakarya et&#x20;al., 2020</xref>). The estimation procedure of CMA to identify all linear coefficients is as follows:</p>
<p>1) Under linearity and with the instrument, parameter <inline-formula id="inf47">
<mml:math id="m54">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b1;</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is identified by standard 2SLS estimation, described by <xref ref-type="disp-formula" rid="e8">Eq. 8</xref> and <xref ref-type="disp-formula" rid="e9">Eq. 9</xref>. <inline-formula id="inf48">
<mml:math id="m55">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf49">
<mml:math id="m56">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
<mml:mi>u</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>t</mml:mi>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> have the same meanings as above.<disp-formula id="e8">
<mml:math id="m57">
<mml:mrow>
<mml:mi mathvariant="bold-italic">WealthInequalit</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mi mathvariant="bold-italic">Rainfal</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">l</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">X</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b2;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mi mathvariant="bold-italic">j</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c5;</mml:mi>
<mml:mi mathvariant="bold-italic">t</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
<disp-formula id="e9">
<mml:math id="m58">
<mml:mrow>
<mml:mi mathvariant="bold-italic">Mediato</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">r</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b1;</mml:mi>
<mml:mn>3</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi mathvariant="bold-italic">WealthInequalit</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="true">&#x5e;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">X</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
<mml:mi mathvariant="bold-italic">&#x3b2;</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bb;</mml:mi>
<mml:mi mathvariant="bold-italic">j</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3c5;</mml:mi>
<mml:mi mathvariant="bold-italic">t</mml:mi>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>
<list list-type="simple">
<list-item>
<p>2) Then, we use <inline-formula id="inf50">
<mml:math id="m59">
<mml:mrow>
<mml:mi>R</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>f</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:msub>
<mml:mi>l</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> as an instrument for <inline-formula id="inf51">
<mml:math id="m60">
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>o</mml:mi>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, when conditioned on <inline-formula id="inf52">
<mml:math id="m61">
<mml:mrow>
<mml:mi>W</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>h</mml:mi>
<mml:mi>I</mml:mi>
<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
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</inline-formula>, by the following 2SLS model:</p>
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<disp-formula id="e10">
<mml:math id="m62">
<mml:mrow>
<mml:mi mathvariant="bold-italic">Mediato</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">r</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
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<mml:msub>
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<mml:mn>0</mml:mn>
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<mml:msub>
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<mml:mrow>
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<mml:msub>
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<mml:mi mathvariant="bold-italic">wi</mml:mi>
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</mml:msub>
<mml:mi mathvariant="bold-italic">WealthInequalit</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
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<mml:mi mathvariant="bold-italic">i</mml:mi>
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<mml:mi mathvariant="bold-italic">i</mml:mi>
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</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
<disp-formula id="e11">
<mml:math id="m63">
<mml:mrow>
<mml:mi mathvariant="bold-italic">HCE</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">s</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
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<mml:mn>5</mml:mn>
<mml:mi mathvariant="bold-italic">m</mml:mi>
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</mml:msub>
<mml:mrow>
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<mml:mrow>
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<mml:msub>
<mml:mi mathvariant="bold-italic">r</mml:mi>
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<mml:mi mathvariant="bold-italic">wi</mml:mi>
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</mml:msub>
<mml:mi mathvariant="bold-italic">WealthInequalit</mml:mi>
<mml:msub>
<mml:mi mathvariant="bold-italic">y</mml:mi>
<mml:mi mathvariant="bold-italic">i</mml:mi>
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<mml:mi mathvariant="bold-italic">i</mml:mi>
</mml:msub>
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</mml:math>
<label>(11)</label>
</disp-formula>where parameters <inline-formula id="inf53">
<mml:math id="m64">
<mml:mrow>
<mml:msub>
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</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the expected values of the estimators of a 2SLS regression where <inline-formula id="inf55">
<mml:math id="m66">
<mml:mrow>
<mml:mi>W</mml:mi>
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<mml:mi>n</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>q</mml:mi>
<mml:mi>u</mml:mi>
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</inline-formula> plays the role of a conditioning variable. <inline-formula id="inf56">
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<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
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<mml:mi>t</mml:mi>
<mml:mi>o</mml:mi>
<mml:msub>
<mml:mi>r</mml:mi>
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</mml:mrow>
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</mml:mover>
</mml:mrow>
</mml:math>
</inline-formula> is the estimated value of <inline-formula id="inf57">
<mml:math id="m68">
<mml:mrow>
<mml:mi>M</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>d</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>a</mml:mi>
<mml:mi>t</mml:mi>
<mml:mi>o</mml:mi>
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<mml:mi>r</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in the first&#x20;stage.</p>
</sec>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>Results</title>
<sec id="s3-1">
<title>Descriptive Statistics</title>
<p>
<xref ref-type="table" rid="T2">Table&#x20;2</xref> displays the summary statistics of county-level wealth inequality, household carbon emissions per capita, and control variables. As <xref ref-type="table" rid="T2">Table&#x20;2</xref> shows, wealth inequality shows an average value of 0.54 and holds steady with the growth of wealth. In addition, we obtain the average total, direct and indirect household carbon emissions per capita in China during 2014-2018 by means of the application of ECM and IOM. The average total household carbon emissions per capita are 2.8 tons. The total direct carbon emissions per capita are 0.28 tons, which is much smaller than the total indirect carbon emissions per capita of 2.52 tons. <xref ref-type="table" rid="T1">Table&#x20;1</xref> also displays the direct and indirect household carbon emissions per capita across different years. The total, direct and indirect carbon emissions per capita show a stable increment from 2014 to 2018. Most control variables fluctuate slightly throughout the year. Log income per adult in the household increases stably.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Description of county-level wealth inequality, household carbon emissions per capital and control variables. Source: Calculated by the authors based on CFPS, IOTs and CEADs in 2014-2018.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Variable</th>
<th rowspan="2" align="center">Mean</th>
<th colspan="3" align="center">Year</th>
</tr>
<tr>
<th align="center">2014</th>
<th align="center">2016</th>
<th align="center">2018</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Wealth inequality at county level</td>
<td align="char" char=".">0.54</td>
<td align="char" char=".">0.52</td>
<td align="char" char=".">0.55</td>
<td align="char" char=".">0.54</td>
</tr>
<tr>
<td align="left">HCEs_total</td>
<td align="char" char=".">2.84</td>
<td align="char" char=".">2.61</td>
<td align="char" char=".">2.69</td>
<td align="char" char=".">3.22</td>
</tr>
<tr>
<td align="left">HCEs_diect</td>
<td align="char" char=".">0.28</td>
<td align="char" char=".">0.31</td>
<td align="char" char=".">0.27</td>
<td align="char" char=".">0.28</td>
</tr>
<tr>
<td align="left">HCEs_indiect</td>
<td align="char" char=".">2.55</td>
<td align="char" char=".">2.3</td>
<td align="char" char=".">2.42</td>
<td align="char" char=".">2.95</td>
</tr>
<tr>
<td align="left">Child_r</td>
<td align="char" char=".">0.23</td>
<td align="char" char=".">0.22</td>
<td align="char" char=".">0.23</td>
<td align="char" char=".">0.25</td>
</tr>
<tr>
<td align="left">Old_r</td>
<td align="char" char=".">0.23</td>
<td align="char" char=".">0.22</td>
<td align="char" char=".">0.24</td>
<td align="char" char=".">0.25</td>
</tr>
<tr>
<td align="left">Health_r</td>
<td align="char" char=".">0.5</td>
<td align="char" char=".">0.64</td>
<td align="char" char=".">0.63</td>
<td align="char" char=".">0.23</td>
</tr>
<tr>
<td align="left">Fami_size</td>
<td align="char" char=".">3.78</td>
<td align="char" char=".">3.8</td>
<td align="char" char=".">3.8</td>
<td align="char" char=".">3.74</td>
</tr>
<tr>
<td align="left">Ln_pinc</td>
<td align="char" char=".">0.49</td>
<td align="char" char=".">0.14</td>
<td align="char" char=".">0.54</td>
<td align="char" char=".">0.78</td>
</tr>
<tr>
<td align="left">Inter_access</td>
<td align="char" char=".">0.56</td>
<td align="char" char=".">0.44</td>
<td align="char" char=".">0.58</td>
<td align="char" char=".">0.65</td>
</tr>
<tr>
<td align="left">Rural</td>
<td align="char" char=".">0.52</td>
<td align="char" char=".">0.53</td>
<td align="char" char=".">0.52</td>
<td align="char" char=".">0.51</td>
</tr>
<tr>
<td align="left">Gender</td>
<td align="char" char=".">0.55</td>
<td align="char" char=".">0.6</td>
<td align="char" char=".">0.51</td>
<td align="char" char=".">0.52</td>
</tr>
<tr>
<td align="left">Party</td>
<td align="char" char=".">0.1</td>
<td align="char" char=".">0.1</td>
<td align="char" char=".">0.1</td>
<td align="char" char=".">0.11</td>
</tr>
<tr>
<td align="left">Medicare</td>
<td align="char" char=".">0.91</td>
<td align="char" char=".">0.91</td>
<td align="char" char=".">0.92</td>
<td align="char" char=".">0.9</td>
</tr>
<tr>
<td align="left">Age</td>
<td align="char" char=".">51.79</td>
<td align="char" char=".">51.79</td>
<td align="char" char=".">51.41</td>
<td align="char" char=".">52.18</td>
</tr>
<tr>
<td align="left">SAge</td>
<td align="char" char=".">28.82</td>
<td align="char" char=".">28.62</td>
<td align="char" char=".">28.51</td>
<td align="char" char=".">29.34</td>
</tr>
<tr>
<td align="left">Married</td>
<td align="char" char=".">0.84</td>
<td align="char" char=".">0.87</td>
<td align="char" char=".">0.84</td>
<td align="char" char=".">0.82</td>
</tr>
<tr>
<td align="left">Qualification</td>
<td align="char" char=".">0.5</td>
<td align="char" char=".">0.5</td>
<td align="char" char=".">0.47</td>
<td align="char" char=".">0.53</td>
</tr>
<tr>
<td align="left">ANLI</td>
<td align="char" char=".">18.86</td>
<td align="char" char=".">19.04</td>
<td align="char" char=".">18.3</td>
<td align="char" char=".">19.23</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Gini coefficient of wealth per adult by province in 2018.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<sec id="s3-1-1">
<title>Gini Coefficient of Wealth per Adult by Province in 2018</title>
<p>In addition, <xref ref-type="fig" rid="F2">Figure&#x20;2</xref> displays wealth inequality measured by the Gini coefficient of wealth per adult by province in 2018. Both Zhejiang and Heilongjiang obtain relatively low Gini coefficients of wealth per adult, scoring between 0.48 and 0.52 and representing low wealth inequality. The Gini coefficient of Chongqing is much higher, with a score reaching 0.83, followed by Guizhou, Gansu, Hebei, Guangdong, Shandong, Fujian, Sichuan, Jilin and Shaanxi, with scores ranging from 0.62 to&#x20;0.7.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Gini coefficient of wealth per adult by province in&#x20;2018.</p>
</caption>
<graphic xlink:href="feart-10-872806-g002.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F3">Figure&#x20;3</xref> shows the average direct and indirect carbon emissions structure during 2014-2018. We classify the carbon emissions in <xref ref-type="table" rid="T2">Table&#x20;2</xref> into 7 main categories generated by consumption from food; clothing; residence; household facilities and services; health care and medical services; transportation and telecommunication; and education, culture and recreation. The pie chart shows that indirect carbon emissions per capita account for 90.04%, far more than direct carbon emissions.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Household carbon emissions across wealth percentiles.</p>
</caption>
<graphic xlink:href="feart-10-872806-g003.tif"/>
</fig>
</sec>
<sec id="s3-1-2">
<title>Direct and Indirect Carbon Emissions Structure</title>
<p>
<xref ref-type="fig" rid="F4">Figure&#x20;4</xref> displays the total, direct and indirect household carbon emissions per capita across different wealth percentiles. Both the direct and indirect carbon emissions per capita first show a slight decrease and then increase with household wealth. These results preliminarily reveal the relationship between household carbon emissions and wealth inequality. However, how wealth inequality influences household carbon emissions needs to be further explored by means of the HDFE and CMA models.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>The estimated results of regression of the total, direct and indirect household carbon emissions based on HDFE and IV&#x20;model.</p>
</caption>
<graphic xlink:href="feart-10-872806-g004.tif"/>
</fig>
</sec>
</sec>
<sec id="s3-2">
<title>Results of HDFE and IV Models</title>
<p>
<xref ref-type="table" rid="T3">Table&#x20;3</xref> provides the estimated results based on the HDFE and IV models. Columns 1) and 3) in <xref ref-type="table" rid="T3">Table&#x20;3</xref> display the estimation results without the control variables. To reduce the confounding impact of irrelevant variables, we further control for variables at the individual, family, and county levels in Columns 2) and (4). The estimated results of these two columns show that wealth inequality has a significantly positive effect on total household carbon emissions per capita, with coefficients of 1.384 in the HDFE model and 12.615 in the IV model at the <italic>p</italic>&#x20;&#x3d; 0.01 level. For the control variables, we find a significantly negative correlation between the child and elderly dependency ratio and household carbon emissions per capita in both models. This means that a higher dependency ratio may reduce household carbon emissions per capita. In addition, other variables, including Ln_pinc, Inter_Access, Party, Qualifications and ANLI, have a significantly positive effect on household carbon emissions per capita in both models. These findings indicate that higher income, easier access to the internet, being a CPC member, higher qualifications and faster socioeconomic development may help increase the total carbon emissions per capita of the household.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Estimation results: HDFE and IV regression for HCEs_<sub>total</sub> during 2014-2018.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left"/>
<th align="center">(1) HDFE</th>
<th align="center">(2) HDFE</th>
<th align="center">(3) IV</th>
<th align="center">(4) IV</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Wealth Inequality</td>
<td align="center">0.148</td>
<td align="center">1.384<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="char" char=".">23.336<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="center">12.615<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Child_r</td>
<td align="left"/>
<td align="center">&#x2212;1.607<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="left"/>
<td align="center">&#x2212;1.755<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Old_r</td>
<td align="left"/>
<td align="center">&#x2212;0.001</td>
<td align="left"/>
<td align="center">&#x2212;0.018</td>
</tr>
<tr>
<td align="left">Health_r</td>
<td align="left"/>
<td align="center">&#x2212;0.188</td>
<td align="left"/>
<td align="center">&#x2212;0.234</td>
</tr>
<tr>
<td align="left">Fami_size</td>
<td align="left"/>
<td align="center">&#x2212;0.314<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="left"/>
<td align="center">&#x2212;0.315<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Ln_pinc</td>
<td align="left"/>
<td align="center">0.931<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="left"/>
<td align="center">0.943<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Inter_Access</td>
<td align="left"/>
<td align="center">0.173<sup>&#x2a;&#x2a;</sup>
</td>
<td align="left"/>
<td align="center">0.197<sup>&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Rural</td>
<td align="left"/>
<td align="center">&#x2212;0.026</td>
<td align="left"/>
<td align="center">&#x2212;0.042</td>
</tr>
<tr>
<td align="left">Gender</td>
<td align="left"/>
<td align="center">0.074</td>
<td align="left"/>
<td align="center">0.027</td>
</tr>
<tr>
<td align="left">Party</td>
<td align="left"/>
<td align="center">0.356<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="left"/>
<td align="center">0.368<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Medicare</td>
<td align="left"/>
<td align="center">0.115</td>
<td align="left"/>
<td align="center">0.143</td>
</tr>
<tr>
<td align="left">Age</td>
<td align="left"/>
<td align="center">&#x2212;0.027</td>
<td align="left"/>
<td align="center">&#x2212;0.019</td>
</tr>
<tr>
<td align="left">SAge</td>
<td align="left"/>
<td align="center">0.007</td>
<td align="left"/>
<td align="center">&#x2212;0.002</td>
</tr>
<tr>
<td align="left">Married</td>
<td align="left"/>
<td align="center">&#x2212;0.139</td>
<td align="left"/>
<td align="center">&#x2212;0.154</td>
</tr>
<tr>
<td align="left">Qualifications</td>
<td align="left"/>
<td align="center">0.261<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="left"/>
<td align="center">0.353<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">ANLI</td>
<td align="left"/>
<td align="center">0.009<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="left"/>
<td align="center">0.015<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Year-fixed effect</td>
<td align="left"/>
<td align="center">Yes</td>
<td align="left"/>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">Region-fixed effect</td>
<td align="left"/>
<td align="center">Yes</td>
<td align="left"/>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">Constant</td>
<td align="center">2.724<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="center">4.404<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="char" char=".">&#x2212;9.675<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="center">&#x2212;1.951</td>
</tr>
<tr>
<td align="left">Cragg-Donald Wald F</td>
<td align="center">&#x2014;</td>
<td align="center">&#x2014;</td>
<td align="char" char=".">331.514</td>
<td align="center">682.216</td>
</tr>
<tr>
<td align="left">Observations</td>
<td align="center">37,070</td>
<td align="center">28,814</td>
<td align="char" char=".">31,593</td>
<td align="center">28,814</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Significance relationships are shown as indicated by <italic>p</italic>-values: <sup>&#x2a;</sup>
<italic>p</italic>&#x20;&#x3c; 0.10, <sup>&#x2a;&#x2a;</sup>
<italic>p</italic>&#x20;&#x3c; 0.05, <sup>&#x2a;&#x2a;&#x2a;</sup>
<italic>p</italic>&#x20;&#x3c; 0.01.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>To further capture the relationship between wealth inequality and household carbon emissions, we describe the estimated results of the regression of the total, direct and indirect household carbon emissions based on the HDFE and IV models in <xref ref-type="fig" rid="F4">Figure&#x20;4</xref>. As it shows, wealth inequality increases household carbon emissions per capita mainly by promoting indirect household carbon emissions. These impacts can be seen in both the HDFE and IV models with significantly positive coefficients. On the other hand, wealth inequality may reduce direct household carbon emissions per capita, with the estimated coefficient being significantly negative in the IV model and insignificantly close to 0 in the HDFE&#x20;model.</p>
</sec>
<sec id="s5-1">
<title>The Role of Social Norms</title>
<p>To study the role of social norms from the perspective of the Veblen effect and short-termism, the IV and CMA models are adopted to test the mediating role of the Veblen effect and short-termism, and the results are displayed in <xref ref-type="table" rid="T4">Tables 4</xref>, <xref ref-type="table" rid="T5">5</xref>, respectively.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Estimation results: IV model for mediator.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left"/>
<th align="center">(1) IV Total consumption</th>
<th align="center">(2) IV Conspicuous consumption ratio</th>
<th align="center">(3) IV Environmental awareness</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Wealth Inequality</td>
<td align="center">4.378<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="center">&#x2212;0.777<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="center">&#x2212;18.803<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Conspicuous consumption ratio</td>
<td align="center">&#x2212;0.210<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="left"/>
<td align="left"/>
</tr>
<tr>
<td align="left">Total consumption</td>
<td align="left"/>
<td align="center">&#x2212;0.007<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="left"/>
</tr>
<tr>
<td align="left">Family-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">Household-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">County-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">Year-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">Region-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">Constant</td>
<td align="center">7.612<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="center">0.816<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="center">17.802<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Cragg-Donald Wald F</td>
<td align="center">683.093</td>
<td align="center">657.250</td>
<td align="center">665.252</td>
</tr>
<tr>
<td align="left">Observations</td>
<td align="center">27,283</td>
<td align="center">27,283</td>
<td align="center">28,416</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Significance relationships are shown as indicated by <italic>p</italic>-values: <sup>&#x2a;</sup>
<italic>p</italic>&#x20;&#x3c; 0.10, <sup>&#x2a;&#x2a;</sup>
<italic>p</italic>&#x20;&#x3c; 0.05, <sup>&#x2a;&#x2a;&#x2a;</sup>
<italic>p</italic>&#x20;&#x3c; 0.01.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Estimation results: CMA model for mediator.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left"/>
<th align="center">(1) CMA Total consumption</th>
<th align="center">(2) CMA Conspicuous consumption ratio</th>
<th align="center">(3) CMA Environmental awareness</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Indirect Effect</td>
<td align="center">26.508<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
<td align="center">&#x2212;3.25</td>
<td align="center">11.543<sup>&#x2a;&#x2a;&#x2a;</sup>
</td>
</tr>
<tr>
<td align="left">Family-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">Household-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">County-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">Year-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">Region-fixed effect</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
<td align="center">Yes</td>
</tr>
<tr>
<td align="left">1st-stage F statistic</td>
<td align="center">706.052</td>
<td align="center">681.112</td>
<td align="center">705.033</td>
</tr>
<tr>
<td align="left">2nd-stage F statistic</td>
<td align="center">160.82</td>
<td align="center">111.27</td>
<td align="center">199.284</td>
</tr>
<tr>
<td align="left">Observations</td>
<td align="center">27,283</td>
<td align="center">27,283</td>
<td align="center">28,416</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Significance relationships are shown as indicated by <italic>p</italic>-values: <sup>&#x2a;</sup>
<italic>p</italic>&#x20;&#x3c; 0.10, <sup>&#x2a;&#x2a;</sup>
<italic>p</italic>&#x20;&#x3c; 0.05, <sup>&#x2a;&#x2a;&#x2a;</sup>
<italic>p</italic>&#x20;&#x3c; 0.01.</p>
</fn>
</table-wrap-foot>
</table-wrap>
<p>Column 1) in <xref ref-type="table" rid="T4">Table&#x20;4</xref> reveals that wealth inequality can give rise to the growth of total consumption expenditure. Column 1) in <xref ref-type="table" rid="T5">Table&#x20;5</xref> indicates that the growth of total consumption expenditures that accompanies wealth inequality plays a mediating role in intensifying household carbon emissions per capita. Column 2) in <xref ref-type="table" rid="T4">Tables 4</xref>, <xref ref-type="table" rid="T5">5</xref> indicates that wealth inequality reduces the conspicuous consumption ratio instead of increasing it. No evidence is found for the role of the conspicuous consumption ratio in wealth inequality increasing household carbon emissions per capita.</p>
<p>As shown in <xref ref-type="table" rid="T4">Table&#x20;4</xref>, Column 3) indicates that the wealth gap can weaken the environmental awareness of households. Column 3) in <xref ref-type="table" rid="T5">Table&#x20;5</xref> further reveals that greater wealth inequality can increase household carbon emissions per capita by weakening the environmental awareness of households caused by short-termism.</p>
</sec>
</sec>
<sec id="s4">
<title>Discussion, Conclusion and Future Research</title>
<p>In this study, we have introduced the Gini coefficient to measure wealth inequality at the county level to display the all-inclusive wealth distribution. The ECM and IOM are used to calculate the direct and indirect HCEs with the most recent large-scale data from the CFPS, CNBS and CEADs spanning 2014 to 2018 in China, making it possible to estimate consumption-based household carbon emissions over time though household-level data. HDFE, IV and CAM are applied to effectively test the impact of wealth inequality on household carbon emissions and the role of social norms of the Veblen effect and short-termism.</p>
<p>The main findings reveal that higher county-level wealth inequality has similar positive influences on household carbon emissions per capita by promoting indirect household carbon emissions as income inequality. The positive impact of income inequality on household carbon emissions has been proven by previous studies (<xref ref-type="bibr" rid="B3">Baek &#x26; Gweisah, 2013</xref>; <xref ref-type="bibr" rid="B31">Lutz, 2019</xref>). This finding is also consistent with the findings of (<xref ref-type="bibr" rid="B25">Knight et&#x20;al., 2017</xref>), who also focuses on wealth inequality. However, (<xref ref-type="bibr" rid="B24">Knight et&#x20;al., 2016</xref>), does not exploit data at the county level and tries to explain the mechanism with political economy theories instead of social norms. Our study aims to fill this gap using a dataset from the CFPS, VIIRS, CNBS and CEADs in 2014, 2016 and&#x20;2018.</p>
<p>The second important finding indicates that wealth inequality may increase consumption-based household carbon emissions through the Veblen effect. This finding is consistent with previous studies (<xref ref-type="bibr" rid="B4">Berthe &#x26; Elie, 2015</xref>; <xref ref-type="bibr" rid="B36">Nielsen et&#x20;al., 2021</xref>). These previous scholars state that consumption is far more than a simple factor of individual utility, but it also plays an important role as social value. Greater wealth inequality in a society means greater differences in social status, therefore causing fierce competition. Such competition is commonly represented by conspicuous consumption, not only in the total consumption level but also in the consumption structure. The middle and lower classes are inspired to copy the consumption patterns of the rich, who tend to overconsume and prefer carbon-intensive products, such as central air conditioning. The Veblen effect highlights the emulative influence of people with high socioeconomic status on increasing household carbon emissions. However, it also offers solutions for reducing household carbon emissions and climate damages if people with high socioeconomic status can assume social responsibilities by reducing unnecessary consumption and consuming low-carbon products.</p>
<p>Another important finding is that wealth inequality has positive effects on consumption-based household carbon emissions by aggravating the short-termism of consumers. This finding also confirms the results of a previous study by <xref ref-type="bibr" rid="B5">Boyce (1994)</xref>, who proposes that growing wealth inequality may induce short-termism among the rich, middle class and the poor. In such a case, the poor focus on short-term material concerns and are particularly vulnerable to consumerism. They may fail to consider the long-term environmental consequences of their consumption. This means that they may lack environmental awareness and are not inclined to adopt pro-environmental behavior and are prone to carbon-intensive consumption. The rich and middle class may also become trapped in short-termism due to the fear of being caught up with by the lower class in consumption. In this way, wider wealth inequality also raises household carbon emissions through short-termism (<xref ref-type="bibr" rid="B43">Slawinski et&#x20;al., 2017</xref>). This finding highlights the important role of short-termism and adds to a growing body of literature on how wealth inequality influences household carbon consumption.</p>
<p>In addition, this article notes that the total indirect carbon emissions are usually much larger than the direct carbon emissions. In fact, the total indirect carbon emissions are usually much larger than the direct carbon emissions, which is in line with previous studies (<xref ref-type="bibr" rid="B15">Feng et&#x20;al., 2011</xref>; <xref ref-type="bibr" rid="B57">Yang et&#x20;al., 2017</xref>). Compared with previous studies, the calculation results of carbon emissions are similar to the findings of <xref ref-type="bibr" rid="B59">Zhang, et&#x20;al. (2020)</xref>, who reported total household carbon emissions ranging from 2.32 to 3.37 during 2012-2016. In addition, as shown in <xref ref-type="table" rid="T1">Table&#x20;1</xref>, the residential sector is the largest indirect carbon emissions sector in China, which supports evidence from a previous study (<xref ref-type="bibr" rid="B26">Li et&#x20;al., 2019</xref>; <xref ref-type="bibr" rid="B8">Cheng, et&#x20;al., 2020</xref>).</p>
<p>Finally, it is worth noting that both Zhejiang and Heilongjiang obtain similarly low Gini indices of wealth per adult (see <xref ref-type="fig" rid="F1">Figure&#x20;1</xref>), but they represent totally different stories. Zhejiang, as the demonstration zone for achieving common prosperity in China, has ensured both fairness and efficiency by realizing low wealth inequality accompanied by a high speed of economic growth. Heilongjiang, one of the northeast old industrial bases in China, lost the benefit of the high speed of GDP growth in 1949-1978 and currently fails to achieve efficiency even with low wealth inequality. These findings are similar to those reported by <xref ref-type="bibr" rid="B28">Liang et&#x20;al. (2021)</xref> and <xref ref-type="bibr" rid="B27">Li (2021)</xref>, who owe the success of Zhejiang to the rural reforms of homestead land, arable land transfer and land expropriation.</p>
<p>In summary, considering the constant attention to climate change and wealth inequality around the world and in China, we refine the understanding of how county-level wealth inequality influences consumption-based household carbon emissions from the perspective of social norms, including the Veblen effect and short-termism. These findings provide useful information for addressing the challenges of climate change and wealth inequality, both of which are key goals of the SDGs. Social and environmental benefits can be achieved at the same time because policies targeted at reducing wealth inequality can also help reduce household carbon emissions. In addition, the impact of the Veblen effect can be used, and consumption-driven short-termism should be prevented to achieve the carbon neutral target in&#x20;2030.</p>
<p>Although we have figured out the effect and mechanisms of the wealth inequality on the consumption-based household carbon emissions with empirical models, there are some limitations in this study. First, this article mainly focused on how county-level wealth inequality on the consumption-based household carbon emissions and the underlying mechanisms, we did not consider the efforts made by Chinese government in environmental protection in recent years, such as energy cleaning, which can directly affect household carbon emissions. Future research can explore the impact and mechanism of Chinese government in environmental protection on household carbon emissions in depth. Second, due to limited availability of quality data, we fail to figure out the relationship and mechanisms between wealth inequality and household carbon emissions for many countries and years. Future research can concentrate on this topic if better data can be available.</p>
</sec>
</body>
<back>
<sec id="s5">
<title>Data Availability Statement</title>
<p>Publicly available datasets were analyzed in this study. This data can be found here: <ext-link ext-link-type="uri" xlink:href="https://opendata.pku.edu.cn/">https://opendata.pku.edu.cn/</ext-link> <ext-link ext-link-type="uri" xlink:href="https://earthdata.nasa.gov/learn/backgrounders/nighttime-lights">https://earthdata.nasa.gov/learn/backgrounders/nighttime-lights</ext-link> <ext-link ext-link-type="uri" xlink:href="http://www.stats.gov.cn/">http://www.stats.gov.cn/</ext-link> <ext-link ext-link-type="uri" xlink:href="https://www.ceads.net.cn/">https://www.ceads.net.cn/</ext-link>.</p>
</sec>
<sec id="s6">
<title>Author Contributions</title>
<p>XQ contributed to data collection, statistical analysis and the manuscript edition. HW significantly contributed in design of study and revise of the manuscript. XZ lead writing and compilation of figures and tables. WW helped in the conceptualization of the work and final overview.</p>
</sec>
<sec id="s7">
<title>Funding</title>
<p>This research was funded by National Social Science Foundation of China (grant number. 19ZDA151), National Statistical Research Project (grant number. 2020LY065), Humanities and Social Sciences Youth Foundation (grant number. 19YJC790126) and Special Funding for Basic Scientific Research Business Expenses of Central Universities (grant number. 202211001).</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<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="disclaimer" id="s9">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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