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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Public Health</journal-id>
<journal-title>Frontiers in Public Health</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Public Health</abbrev-journal-title>
<issn pub-type="epub">2296-2565</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fpubh.2022.838733</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Public Health</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Can Basic Medical Insurance Reduce Elderly Family Income Inequality in China?</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name><surname>Pu</surname> <given-names>Xiaohong</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1255192/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Wang</surname> <given-names>Yilong</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1636197/overview"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name><surname>Zhang</surname> <given-names>Weike</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x0002A;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1249915/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Zeng</surname> <given-names>Ming</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1656845/overview"/>
</contrib>
</contrib-group>
<aff id="aff1"><sup>1</sup><institution>School of Public Administration, Sichuan University</institution>, <addr-line>Chengdu</addr-line>, <country>China</country></aff>
<aff id="aff2"><sup>2</sup><institution>School of Management, Northwest Minzu University</institution>, <addr-line>Lanzhou</addr-line>, <country>China</country></aff>
<author-notes>
<fn fn-type="edited-by"><p>Edited by: Chi Wei Su, Qingdao University, China</p></fn>
<fn fn-type="edited-by"><p>Reviewed by: Wei Zhou, Yunnan University of Finance and Economics, China; Leiyu Sun, University of Malaya, Malaysia</p></fn>
<corresp id="c001">&#x0002A;Correspondence: Weike Zhang <email>zhangwk&#x00040;scu.edu.cn</email></corresp>
<fn fn-type="other" id="fn001"><p>This article was submitted to Health Economics, a section of the journal Frontiers in Public Health</p></fn></author-notes>
<pub-date pub-type="epub">
<day>15</day>
<month>02</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>838733</elocation-id>
<history>
<date date-type="received">
<day>18</day>
<month>12</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>14</day>
<month>01</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x000A9; 2022 Pu, Wang, Zhang and Zeng.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Pu, Wang, Zhang and Zeng</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>Basic medical insurance is the critical medical security system to realize common prosperity in China. This study explores the impact of basic medical insurance on elderly family income inequality in China using the China Family Panel Studies (CFPS) data in 2018. Our finding shows that basic medical insurance is significantly negatively correlated with elderly family income inequality, indicating basic medical insurance has a positive impact on narrowing the elderly family income inequality. The heterogeneity analysis shows that basic medical insurance has a more significant reduction effect among the eastern elderly and the younger elderly family. The results also suggest that health performance significantly mediates the relationship between basic medical insurance and elderly family income inequality. This study implies that the Chinese government should increase the proportion of basic medical insurance reimbursement and expand the scope of reimbursement for basic medical insurance to realize income fairness among elderly families.</p></abstract>
<kwd-group>
<kwd>basic medical insurance</kwd>
<kwd>elderly income inequality</kwd>
<kwd>Kakwani index</kwd>
<kwd>health performance</kwd>
<kwd>China</kwd>
</kwd-group>
<counts>
<fig-count count="0"/>
<table-count count="6"/>
<equation-count count="4"/>
<ref-count count="45"/>
<page-count count="8"/>
<word-count count="6567"/>
</counts>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>Introduction</title>
<p>China has been experiencing rapid aging over the past few decades. According to the seventh population census released by China&#x00027;s National Bureau of Statistics in 2021, the number of people aged 60 and above in China reaches 190 million by 2020, including 35.8 million aged 80 and above and accounting for 2.54 percent of the total population<xref ref-type="fn" rid="fn0001"><sup>1</sup></xref>. The World Health Organization predicts that by 2050, China will have 300 million people over 65 years old, accounting for 30 percent of the total population (<xref ref-type="bibr" rid="B1">1</xref>). An aging society will have a significant negative impact on China&#x00027;s economic growth and place a heavy burden on society as a whole in terms of the elderly family (<xref ref-type="bibr" rid="B2">2</xref>).</p>
<p>As the core of China&#x00027;s medical insurance system, basic medical insurance plays an essential role in preventing and resolving significant health risks and preventing sustained catastrophic medical and health expenditures (<xref ref-type="bibr" rid="B3">3</xref>). One of the fundamental stated goals of basic medical insurance is to reduce the impact of health shocks on family income and reduce poverty due to illness for the overall population, especially for the poor subgroups (<xref ref-type="bibr" rid="B4">4</xref>). Basic medical insurance is closely related to medical expenses and income distribution of the elderly family, and unreasonable and unfair medical insurance will aggravate elderly family income inequality (<xref ref-type="bibr" rid="B5">5</xref>). As the leading group vulnerable to diseases, the elderly spend a high proportion of their family income on medical care (<xref ref-type="bibr" rid="B6">6</xref>). Medical expenses and medical insurance are important factors affecting elderly family income<xref ref-type="fn" rid="fn0001"><sup>1</sup></xref> inequality. In particular, concerning major diseases, the increased risk of disability and the high cost of post-care significantly impact elderly families, especially those with low income (<xref ref-type="bibr" rid="B7">7</xref>). Besides, the medical expenses of the elderly can affect the disposable income of the elderly and the whole family, and elderly family income inequality related to basic medical insurance can increase the risk of inter-generational income inequality transmission (<xref ref-type="bibr" rid="B8">8</xref>). Therefore, it is an exciting topic to explore whether basic medical insurance influences elderly family income inequality in China.</p>
<p>Several studies have found an association between basic medical insurance and income inequality. Specifically, some researchers have shown that basic medical insurance has a significant reduction effect on income inequality. For example, Fan et al. consider that the integration of social medical insurance policy has a positive impact on improving the rate of inpatient health services utilization. And both urban and rural catastrophic health expenditures all show a decreasing trend (<xref ref-type="bibr" rid="B9">9</xref>). Lu et al. report that UEBMI (Urban Employee Basic Medical Insurance) and URBMI (Urban Resident Basic Medical Insurance) significantly increase the monthly net income of agriculture migrants, especially in the lower-income group (<xref ref-type="bibr" rid="B10">10</xref>). In contrast, some researchers have demonstrated that basic medical insurance cannot significantly reduce income inequality. For example, Wang et al. suggest that URRBMI (Urban-Rural Resident Basic Medical Insurance) does not reduce the overall catastrophic health expenditures of residents effectively (<xref ref-type="bibr" rid="B11">11</xref>). Liu et al. suggest that there is no significant decrease in actual medical expenses after participating in basic medical insurance (<xref ref-type="bibr" rid="B12">12</xref>). Zhang et al. find that basic medical insurance is not essential in reducing income inequality among patients (<xref ref-type="bibr" rid="B13">13</xref>). So far, however, there has been little discussion about its impact on elderly family income inequality. Therefore, this study set out to explore the impact of basic medical insurance on elderly family income inequality in China.</p>
<p>This study uses the China Family Panel Studies (CFPS) data in 2018 to investigate how basic medical insurance affects elderly family income inequality in China. Besides, this study examines the mediation effect of health performance on the relationship between basic medical insurance and elderly family income inequality. The main contributions of this study are presented in three aspects. First, this study aims to contribute to this growing area of research by exploring the impact of basic medical insurance on elderly family income inequality. Second, this study analyzes the heterogeneous influence of basic medical insurance on elderly family income inequality from the perspectives of different regions and ages, and provides some important insights into elderly family income inequality. Finally, this study adopts the mediation effect model to examine the influence mechanism between basic medical insurance and elderly family income inequality through the mediating effect of health performance.</p>
<p>The remainder of this study is organized as follows. Section 2 proposes the research hypothesis. Section 3 presents the data sources and empirical models. Section 4 presents the empirical results and further analysis, and finally, Section 5 offers the research conclusions and policy recommendations.</p></sec>
<sec id="s2">
<title>Research Hypothesis</title>
<p>For a long time, China&#x00027;s basic medical insurance system has suffered from systemic fragmentation and disparities between urban and rural areas (<xref ref-type="bibr" rid="B14">14</xref>), which results in the apparent &#x0201C;pro-rich&#x0201D; characteristics of the basic medical insurance system (<xref ref-type="bibr" rid="B3">3</xref>). In other words, the higher-income group can enjoy higher reimbursement rates and better quality medical treatment than the lower-income group (<xref ref-type="bibr" rid="B7">7</xref>). Since 2013, the Chinese government has carried out a series of medical insurance reforms to guarantee fairness for various income groups (<xref ref-type="bibr" rid="B15">15</xref>). For example, the Chinese government has integrated the basic medical insurance system for urban and rural residents to narrow the urban-rural differences in medical insurance (<xref ref-type="bibr" rid="B16">16</xref>). After the integration, basic medical insurance has effectively reduced the incidence of income poverty among the lower-income group and the widening income gap between urban and rural residents (<xref ref-type="bibr" rid="B17">17</xref>). Of course, basic medical insurance coverage can effectively reduce the catastrophic health expenditures among the elderly family, thus narrowing the reimbursement gap and the income gap between the high- and low-income of the elderly family (<xref ref-type="bibr" rid="B18">18</xref>). This effectively guarantees the fairness of basic medical insurance and can sufficiently reduce the elderly family income inequality.</p>
<p>Based on the above analysis, this study proposes the following hypothesis:</p>
<list list-type="simple">
<list-item><p><bold>H1:</bold> Basic medical insurance can reduce elderly family income inequality in China.</p></list-item>
</list>
<p>Basic medical insurance policies vary from region to region, province to province, and even city to city (<xref ref-type="bibr" rid="B19">19</xref>). Compared with central and western regions, the eastern region of China is more economically developed, and the local governments provide more subsidies for basic medical insurance (<xref ref-type="bibr" rid="B20">20</xref>). In medical treatment for the elderly, the reimbursement rate is generally higher in the eastern regions than that in the central and western regions (<xref ref-type="bibr" rid="B21">21</xref>, <xref ref-type="bibr" rid="B22">22</xref>). The economic development of the central and western regions as a whole is less developed than that of the eastern regions (<xref ref-type="bibr" rid="B23">23</xref>), and the financial subsidies for basic medical insurance are not as strong as that of the local governments in the eastern regions (<xref ref-type="bibr" rid="B24">24</xref>). In general, compared with the central and western regions, basic medical insurance has a more significant inhibitory effect on the family income inequality of the elderly in the eastern regions.</p>
<p>The life cycle theory explains the objective fact that the incidence of disease increases significantly with age. China has entered an aging society, and the aging population mainly concentrates on the younger elderly of 60&#x02013;80 years old (<xref ref-type="bibr" rid="B25">25</xref>). While some in this group remain in good health, there are apparent gaps in health status (<xref ref-type="bibr" rid="B26">26</xref>). This group has become the largest user and beneficiary group of basic medical insurance (<xref ref-type="bibr" rid="B27">27</xref>). Compared to the general reliance on basic medical insurance to compensate for the cost of treatment for illnesses suffered by aged 80 and above, basic medical insurance has a more remarkable dampening effect on the widening income deprivation of the younger elderly family of 60&#x02013;80 years old (<xref ref-type="bibr" rid="B28">28</xref>).</p>
<p>Based on the above analysis, this study proposes the following hypotheses:</p>
<list list-type="simple">
<list-item><p><bold>H2a:</bold> The impact of basic medical insurance on elderly family income inequality in the eastern regions is more significant than in the central and western regions.</p></list-item>
<list-item><p><bold>H2b:</bold> The impact of basic health insurance on the younger family income inequality is more significant than that of the advanced elderly family.</p></list-item>
</list>
<p>According to existing research, basic medical insurance has a positive effect on improving the health performance of the elderly (<xref ref-type="bibr" rid="B29">29</xref>). On the one hand, basic medical insurance can improve health awareness and health care knowledge of the elderly (<xref ref-type="bibr" rid="B30">30</xref>). On the other hand, basic medical insurance provides the elderly with protection against illness (<xref ref-type="bibr" rid="B31">31</xref>), which increases the enthusiasm of the elderly to seek medical care and prevents minor illnesses from becoming serious ones (<xref ref-type="bibr" rid="B32">32</xref>). Meanwhile, the improved health performance of the elderly is conducive to reducing elderly family income inequality. The underlying reason is that the elderly family with low income is more sensitive to health expenditures than the high-income elderly family. The improved health performance has led to a significant reduction in health expenditures and narrowing income gaps among elderly families (<xref ref-type="bibr" rid="B33">33</xref>). Hence, basic medical insurance may reduce elderly family income inequality by promoting health performance.</p>
<p>Based on the above analysis, this study proposes the following hypothesis.</p>
<list list-type="simple">
<list-item><p><bold>H3</bold>: Health performance mediates the impact of basic medical insurance on elderly family income inequality in China.</p></list-item>
</list></sec>
<sec id="s3">
<title>Data, Variables, and Empirical Model</title>
<sec>
<title>Data</title>
<p>This study set out to examine the impact of basic medical insurance on elderly family income inequality using the China Family Panel Studies (CFPS) in 2018. The CFPS data was launched in 2010, which tracks more than 16,000 respondents from different parts of China every 1 or 2 years. CFPS focuses on the economic and non-economic wellbeing of China&#x00027;s population and a number of research topics, including economic activity, educational outcomes, family relations and family dynamics, population migration, health, etc. It is a national, large-scale, multidisciplinary social tracking survey project.</p>
<p>In addition, we choose CFPS data from 2018 for empirical analysis because only CFPS data from 2018 contain detailed variables of basic health insurance, income, and health performance, which are the basis for this analysis. Following China&#x00027;s current statutory retirement age, 60 is used as the starting age for older adults. Hence, we select the samples aged over 60 and under 100 years. After removing the samples with missing values of key variables, we finally gain 4,521 samples.</p></sec>
<sec>
<title>Variables</title>
<sec>
<title>Dependent Variable</title>
<p>The dependent variable of this study is elderly family income inequality (<italic>Inequality</italic>). Most literature uses the relative deprivation index to reflect the degree of income inequality, which can be recognized as a suitable measuring method. This study uses the Kakwani index, an excellent relative deprivation index with dimensionless characteristics, to measure elderly family income inequality in China.</p>
<p>Referring to previous studies (<xref ref-type="bibr" rid="B34">34</xref>, <xref ref-type="bibr" rid="B35">35</xref>), Kakwani index is defined as follows:</p>
<disp-formula id="E1"><label>(1)</label><mml:math id="M1"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:mi>R</mml:mi><mml:mi>D</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mtext>&#x000A0;</mml:mtext><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:msub><mml:mrow><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mi>X</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mstyle displaystyle="true"><mml:munderover accentunder="false" accent="false"><mml:mrow><mml:mo>&#x02211;</mml:mo></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mi>j</mml:mi><mml:mo>&#x0002B;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:munderover></mml:mstyle><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mtext>&#x000A0;</mml:mtext><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>&#x0003C;</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>&#x0003C;</mml:mo><mml:mo>&#x02026;</mml:mo><mml:mo>&#x0003C;</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>Where <italic>RD</italic>(<italic>x, x</italic><sub><italic>j</italic></sub>) is the Kakwani index of a given elderly family <italic>j</italic>; <italic>x</italic> represents the elderly family income; <italic>u</italic><sub><italic>X</italic></sub> is the average elderly family income in all samples; and <italic>n</italic> represents the number of elderly families.</p>
<p>China&#x00027;s endowment pattern is mainly family-based, and the living conditions of the elderly are not entirely determined by their income but the family income (<xref ref-type="bibr" rid="B36">36</xref>). In other words, the life of the elderly after retirement is mainly supported by their children in China. Hence, we calculate the Kakwani index of the elderly using their total family income (<italic>Inequality_tot</italic>) and average family income (<italic>Inequality_avg</italic>). We take <italic>Inequality_tot</italic> as the main proxy variable of elderly family income inequality and adopt <italic>Inequality_avg</italic> to conduct our robust test.</p></sec>
<sec>
<title>Independent Variable</title>
<p>The independent variable of this study is basic medical insurance (<italic>Insurance</italic>). We assign 1 to <italic>Insurance</italic> if the elderly have basic medical insurance reimbursement, otherwise 0.</p></sec>
<sec>
<title>Control Variables</title>
<p>Referring to the previous literature (<xref ref-type="bibr" rid="B37">37</xref>&#x02013;<xref ref-type="bibr" rid="B39">39</xref>), we control the following variables: gender (<italic>Gender</italic>), education level (<italic>Educ</italic>), marriage (<italic>Marriage</italic>), retirement (<italic>Retirement</italic>), political outlook (<italic>Outlook</italic>), household size (<italic>Size</italic>), cash deposits (<italic>Cash</italic>), life satisfaction (<italic>Satisfaction</italic>), happiness level (<italic>Happiness</italic>), medical condition (<italic>Condition</italic>), and internet use (<italic>Internet</italic>). All control variables and their definitions are shown in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap position="float" id="T1">
<label>Table 1</label>
<caption><p>The definitions of all variables.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="left"><bold>Symbols</bold></th>
<th valign="top" align="left"><bold>Definitions</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left" colspan="3"><bold>Dependent variable</bold></td>
</tr>
<tr>
<td valign="top" align="left">Elderly family income inequality</td>
<td valign="top" align="left">Inequality_tot</td>
<td valign="top" align="left">The Kakwani index of the elderly based on total family income.</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Inequality_avg</td>
<td valign="top" align="left">The Kakwani index of the elderly based on average family income.</td>
</tr>
<tr>
<td valign="top" align="left" colspan="3"><bold>Independent variable</bold></td>
</tr>
<tr>
<td valign="top" align="left">Basic medical insurance</td>
<td valign="top" align="left">Insurance</td>
<td valign="top" align="left"><italic>Insurance</italic> is equal to 1 if the elderly have basic medical insurance reimbursement, and otherwise 0.</td>
</tr>
<tr>
<td valign="top" align="left" colspan="3"><bold>Mediating variable</bold></td>
</tr>
<tr>
<td valign="top" align="left">Health performance</td>
<td valign="top" align="left">Health</td>
<td valign="top" align="left"><italic>Health</italic> is equal to 1&#x02013;3, representing unhealthy, fair, healthy, respectively.</td>
</tr>
<tr>
<td valign="top" align="left" colspan="3"><bold>Control variables</bold></td>
</tr>
<tr>
<td valign="top" align="left">Gender</td>
<td valign="top" align="left">Gender</td>
<td valign="top" align="left"><italic>Gender</italic> is equal 1 if the elderly are male, and otherwise 0.</td>
</tr>
<tr>
<td valign="top" align="left">Education level</td>
<td valign="top" align="left">Educ</td>
<td valign="top" align="left"><italic>Educ</italic> is 1&#x02013;7, indicating that education is unschooling, primary school, middle school, high school, bachelor&#x00027;s, master&#x00027;s and doctor&#x00027;s degree, respectively.</td>
</tr>
<tr>
<td valign="top" align="left">Marriage</td>
<td valign="top" align="left">Marriage</td>
<td valign="top" align="left"><italic>Marriage</italic> is equal 1 if the elderly are in marriage period, and otherwise 0.</td>
</tr>
<tr>
<td valign="top" align="left">Retirement</td>
<td valign="top" align="left">Retirement</td>
<td valign="top" align="left"><italic>Retirement</italic> is equal 1 if the elderly are retiring, and otherwise 0.</td>
</tr>
<tr>
<td valign="top" align="left">Political outlook</td>
<td valign="top" align="left">Outlook</td>
<td valign="top" align="left"><italic>Outlook</italic> is equal 1 if the elderly are party member, and otherwise 0.</td>
</tr>
<tr>
<td valign="top" align="left">Household size</td>
<td valign="top" align="left">Size</td>
<td valign="top" align="left"><italic>Size</italic> represents the number of the elderly family members.</td>
</tr>
<tr>
<td valign="top" align="left">Cash deposits</td>
<td valign="top" align="left">Cash</td>
<td valign="top" align="left"><italic>Cash</italic> represents the logarithm of cash deposits for the elderly family.</td>
</tr>
<tr>
<td valign="top" align="left">Life satisfaction</td>
<td valign="top" align="left">Satisfaction</td>
<td valign="top" align="left"><italic>Satisfaction</italic> is equal to 1&#x02013;5 scale, representing the elderly life satisfaction, respectively.</td>
</tr>
<tr>
<td valign="top" align="left">Happiness level</td>
<td valign="top" align="left">Happiness</td>
<td valign="top" align="left"><italic>Happiness</italic> is to 1&#x02013;10 sacle, representing the elderly happiness level, respectively.</td>
</tr>
<tr>
<td valign="top" align="left">Medical condition</td>
<td valign="top" align="left">Condition</td>
<td valign="top" align="left"><italic>Condition</italic> is 1&#x02013;5, representing the elderly medical conditions are very bad, bad, fair, good, and very good, respecitvely.</td>
</tr>
<tr>
<td valign="top" align="left">Internet use</td>
<td valign="top" align="left">Internet</td>
<td valign="top" align="left">Internet is equal 1 if the elderly are using internet, and otherwise 0.</td>
</tr>
</tbody>
</table>
</table-wrap></sec>
<sec>
<title>Mediating Variable</title>
<p>This study aims to explore the mediating effect of health performance (<italic>Health</italic>) between basic medical insurance and elderly family income inequality. We measure the health performance of the elderly based on the question of &#x0201C;Health status.&#x0201D; Referring to the previous literature (<xref ref-type="bibr" rid="B40">40</xref>), we assign 1 to <italic>Health</italic> if the elderly answer unhealthy, 2 for fair, and 3 for healthy.</p>
<p>The above variables and their definitions are presented in <xref ref-type="table" rid="T1">Table 1</xref>, and their descriptive statistics are shown in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
<table-wrap position="float" id="T2">
<label>Table 2</label>
<caption><p>Descriptive statistics.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="center"><bold>Obs</bold></th>
<th valign="top" align="center"><bold>Mean</bold></th>
<th valign="top" align="center"><bold>S.D</bold>.</th>
<th valign="top" align="center"><bold>Min</bold></th>
<th valign="top" align="center"><bold>Max</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Inequality_tot</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">0.54</td>
<td valign="top" align="center">0.26</td>
<td valign="top" align="center">0.01</td>
<td valign="top" align="center">1.00</td>
</tr>
<tr>
<td valign="top" align="left">Inequality_avg</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">0.56</td>
<td valign="top" align="center">0.23</td>
<td valign="top" align="center">0.00</td>
<td valign="top" align="center">1.00</td>
</tr>
<tr>
<td valign="top" align="left">Insurance</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">0.51</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.00</td>
<td valign="top" align="center">1.00</td>
</tr>
<tr>
<td valign="top" align="left">Gender</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">0.46</td>
<td valign="top" align="center">0.50</td>
<td valign="top" align="center">0.00</td>
<td valign="top" align="center">1.00</td>
</tr>
<tr>
<td valign="top" align="left">Educ</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">1.92</td>
<td valign="top" align="center">1.07</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">7.00</td>
</tr>
<tr>
<td valign="top" align="left">Marriage</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">0.82</td>
<td valign="top" align="center">0.38</td>
<td valign="top" align="center">0.00</td>
<td valign="top" align="center">1.00</td>
</tr>
<tr>
<td valign="top" align="left">Retirement</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">0.17</td>
<td valign="top" align="center">0.38</td>
<td valign="top" align="center">0.00</td>
<td valign="top" align="center">1.00</td>
</tr>
<tr>
<td valign="top" align="left">Outlook</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">0.01</td>
<td valign="top" align="center">0.07</td>
<td valign="top" align="center">0.00</td>
<td valign="top" align="center">1.00</td>
</tr>
<tr>
<td valign="top" align="left">Size</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">3.81</td>
<td valign="top" align="center">2.13</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">21.00</td>
</tr>
<tr>
<td valign="top" align="left">Cash</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">9.75</td>
<td valign="top" align="center">2.02</td>
<td valign="top" align="center">1.10</td>
<td valign="top" align="center">15.32</td>
</tr>
<tr>
<td valign="top" align="left">Satisfaction</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">4.23</td>
<td valign="top" align="center">0.92</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">5.00</td>
</tr>
<tr>
<td valign="top" align="left">Happiness</td>
<td valign="top" align="center">4521</td>
<td valign="top" align="center">7.74</td>
<td valign="top" align="center">2.20</td>
<td valign="top" align="center">0.00</td>
<td valign="top" align="center">10.00</td>
</tr>
<tr>
<td valign="top" align="left">Condition</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">2.49</td>
<td valign="top" align="center">0.67</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">3.00</td>
</tr>
<tr>
<td valign="top" align="left">Internet</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">0.03</td>
<td valign="top" align="center">0.16</td>
<td valign="top" align="center">0.00</td>
<td valign="top" align="center">1.00</td>
</tr>
<tr>
<td valign="top" align="left">Health</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">2.30</td>
<td valign="top" align="center">0.56</td>
<td valign="top" align="center">1.00</td>
<td valign="top" align="center">3.00</td>
</tr>
</tbody>
</table>
</table-wrap></sec></sec>
<sec>
<title>Empirical Model</title>
<p>Referring to the previous literature (<xref ref-type="bibr" rid="B13">13</xref>, <xref ref-type="bibr" rid="B38">38</xref>, <xref ref-type="bibr" rid="B41">41</xref>), we construct the following model to test the impact of basic medical insurance on elderly family income inequality.</p>
<disp-formula id="E2"><label>(2)</label><mml:math id="M2"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><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:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x003B1;</mml:mi><mml:mo>&#x0002B;</mml:mo><mml:mi>&#x003B2;</mml:mi><mml:mi>I</mml:mi><mml:mi>n</mml:mi><mml:mi>s</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:mi>&#x003B4;</mml:mi><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>s</mml:mi><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>Inequality</italic> is the dependent variable of elderly family income inequality; <italic>Insurance</italic> is the independent variable of basic medical insurance; <italic>Controls</italic> represents the control variables, including <italic>Gender, Educ, Marriage, Retirement, Outlook, Size, Cash, Satisfaction, Happiness, Condition</italic>, and <italic>Internet</italic>; &#x003B1; denotes the intercepted item; &#x003B2; is the coefficient of interest; &#x003B4; denotes the coefficients of the control variables; <italic>i</italic> represents the elderly individual, and &#x003B5;<sub>i</sub> is a normally distributed random error vector.</p>
<p>We run Formulas (2) based on the OLS regression. As we can see, &#x003B2; is the coefficient of the variable of interest. If &#x003B2; is smaller than 0, it indicates that the bigger <italic>Insurance</italic> is, the smaller <italic>Inequality</italic> is. In other words, basic medical insurance reduces elderly family income inequality. If so, H1 is verified by the data. In contrast, if &#x003B2; is bigger than 0, it indicates that basic medical insurance worsens elderly family income inequality. If so, H1 doesn&#x00027;t stand according to our data.</p></sec></sec>
<sec id="s4">
<title>Empirical Results and Analysis</title>
<sec>
<title>Benchmark Regression Results</title>
<p>In this section, we conduct the empirical analysis by using Model (<xref ref-type="bibr" rid="B1">1</xref>) and report the results in <xref ref-type="table" rid="T3">Table 3</xref>. Among them, Column (1) reports the results without control variables, and Column (2) reports the results with control variables. We can find that all the coefficients of <italic>Insurance</italic> are significant and negative at the 1% level. These results indicate that basic medical insurance can reduce elderly family income inequality in China and support our H1. In other words, basic medical insurance coverage can effectively reduce the catastrophic health expenditures among the elderly family, and narrow the reimbursement gap and the income gap between the high- and low-income of the elderly family, which effectively guarantees the welfare of the family.</p>
<table-wrap position="float" id="T3">
<label>Table 3</label>
<caption><p>The benchmark regression result.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="center"><bold>(1)</bold></th>
<th valign="top" align="center"><bold>(2)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Insurance</td>
<td valign="top" align="center">&#x02212;0.052<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">&#x02212;0.022<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td valign="top" align="center">(0.008)</td>
<td valign="top" align="center">(0.006)</td>
</tr>
<tr>
<td valign="top" align="left">Gender</td>
<td/>
<td valign="top" align="center">0.035<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.006)</td>
</tr>
<tr>
<td valign="top" align="left">Educ</td>
<td/>
<td valign="top" align="center">&#x02212;0.027<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.003)</td>
</tr>
<tr>
<td valign="top" align="left">Marriage</td>
<td/>
<td valign="top" align="center">0.017&#x0002A;&#x0002A;</td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.007)</td>
</tr>
<tr>
<td valign="top" align="left">Retirement</td>
<td/>
<td valign="top" align="center">&#x02212;0.133<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.008)</td>
</tr>
<tr>
<td valign="top" align="left">Outlook</td>
<td/>
<td valign="top" align="center">0.004<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.040)</td>
</tr>
<tr>
<td valign="top" align="left">Size</td>
<td/>
<td valign="top" align="center">&#x02212;0.043<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.001)</td>
</tr>
<tr>
<td valign="top" align="left">Cash</td>
<td/>
<td valign="top" align="center">&#x02212;0.058<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.001)</td>
</tr>
<tr>
<td valign="top" align="left">Satisfaction</td>
<td/>
<td valign="top" align="center">0.003</td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.003)</td>
</tr>
<tr>
<td valign="top" align="left">Happiness</td>
<td/>
<td valign="top" align="center">&#x02212;0.005<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.001)</td>
</tr>
<tr>
<td valign="top" align="left">Condition</td>
<td/>
<td valign="top" align="center">&#x02212;0.006</td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.004)</td>
</tr>
<tr>
<td valign="top" align="left">Internet</td>
<td/>
<td valign="top" align="center">&#x02212;0.104<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td/>
<td valign="top" align="center">(0.018)</td>
</tr>
<tr>
<td valign="top" align="left">Constant</td>
<td valign="top" align="center">0.564<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">1.344<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td valign="top" align="center">(0.006)</td>
<td valign="top" align="center">(0.023)</td>
</tr>
<tr>
<td valign="top" align="left">Observations</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">4,521</td>
</tr>
<tr>
<td valign="top" align="left">R-squared</td>
<td valign="top" align="center">0.010</td>
<td valign="top" align="center">0.487</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="TN1">
<label>&#x0002A;&#x0002A;&#x0002A;</label>
<p><italic>p &#x02264; 0.01; Standard errors are in parentheses</italic>.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>In terms of the control variables, most of the estimates are in agreement with theoretical expectations. Specifically speaking, the coefficients of <italic>Gender, Marriage</italic>, and <italic>Outlook</italic> are significantly positive at the traditional statistic levels, indicating that elderly family income inequality is more significant among males, married people, and party members. The coefficients of <italic>Edu, Retirement, Size, Cash, Happiness</italic> and <italic>Internet</italic> are all significantly negative at the traditional statistic levels. These results suggest that the elderly family income inequality can be narrowed as education levels rise. The number of cash deposits, household size, happiness level, and internet use can reduce elderly family income inequality.</p></sec>
<sec>
<title>Robustness Test</title>
<p>Following the previous literature (<xref ref-type="bibr" rid="B7">7</xref>), we use <italic>Inequality_avg</italic> as the alternative measure of elderly family income inequality to conduct the robustness test. The results are presented in Columns (1,2) of <xref ref-type="table" rid="T4">Table 4</xref>. As can be seen, all the coefficients of <italic>Insurance</italic> are significantly negative at the 1% level, which indicates that basic medical insurance significantly lowers elderly family income inequality. This result is consistent with the above findings and further supports our conclusions.</p>
<table-wrap position="float" id="T4">
<label>Table 4</label>
<caption><p>Results of robustness test and endogeneity test.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="center" colspan="2" style="border-bottom: thin solid #000000;"><bold>Robustness test</bold></th>
<th valign="top" align="center" colspan="2" style="border-bottom: thin solid #000000;"><bold>Endogeneity test</bold></th>
</tr>
<tr>
<th/>
<th valign="top" align="center"><bold>(1)</bold></th>
<th valign="top" align="center"><bold>(2)</bold></th>
<th valign="top" align="center"><bold>(3)</bold></th>
<th valign="top" align="center"><bold>(4)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Insurance</td>
<td valign="top" align="center">&#x02212;0.050<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">&#x02212;0.018<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td/>
<td valign="top" align="center">&#x02212;0.031 <xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td valign="top" align="center">(0.007)</td>
<td valign="top" align="center">(0.005)</td>
<td/>
<td valign="top" align="center">(0.048)</td>
</tr>
<tr>
<td valign="top" align="left">Institution</td>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.022<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td/>
</tr>
<tr>
<td/>
<td/>
<td/>
<td valign="top" align="center">(0.006)</td>
<td/>
</tr>
<tr>
<td valign="top" align="left">Constant</td>
<td valign="top" align="center">0.590<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">1.081<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">1.344<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">1.402<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td valign="top" align="center">(0.005)</td>
<td valign="top" align="center">(0.020)</td>
<td valign="top" align="center">(0.022)</td>
<td valign="top" align="center">(0.030)</td>
</tr>
<tr>
<td valign="top" align="left">Control variables</td>
<td valign="top" align="center">No</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="left">Observations</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">4,521</td>
<td valign="top" align="center">4,521</td>
</tr>
<tr>
<td valign="top" align="left">R-squared</td>
<td valign="top" align="center">0.012</td>
<td valign="top" align="center">0.425</td>
<td valign="top" align="center">0.487</td>
<td valign="top" align="center">0.191</td>
</tr>
<tr>
<td valign="top" align="left">Phase I F-value</td>
<td/>
<td/>
<td valign="top" align="center">58.75</td>
<td/>
</tr>
<tr>
<td valign="top" align="left">DWH test <italic>p</italic>-value</td>
<td/>
<td/>
<td/>
<td valign="top" align="center">0.000</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="TN2">
<label>&#x0002A;&#x0002A;&#x0002A;</label>
<p><italic>p &#x02264; 0.01; Standard errors are in parentheses</italic>.</p></fn>
</table-wrap-foot>
</table-wrap></sec>
<sec>
<title>Endogeneity Test</title>
<p>Although we control for many factors affecting elderly family income inequality, there is still an endogenous problem. Hence, we use the two-stage least square method (2 SLS) to minimize the impact of the endogenous problem. To carry out the 2 SLS method, we construct an instrumental variable (denoted as <italic>Institution</italic>), and set <italic>Institution</italic> as 1 to 5, representing general hospitals, specialized hospitals, specialized community health centers or rural health centers, community health service stations or village health offices, and clinics, respectively. In the first-stage regression model, <italic>Insurance</italic> is the dependent variable, and <italic>Institution</italic> is the independent variable. While in the second-stage regression model, the dependent variable is <italic>Inequality_tot</italic>, and the independent variable is the fitted value of <italic>Insurance</italic> in the first-stage regression.</p>
<p>Furthermore, we choose <italic>Institution</italic> as the instrumental variable of <italic>Insurance</italic> for the following reasons. First, the supervision level of medical institutions in China is different, and the elderly are likely to pay various medical expenses in various medical institutions. Thus, the payment of basic health insurance for the elderly is related to the institutions they visit. Second, the elderly&#x00027;s choice of medical institutions has no direct impact on the elderly family income inequality. Besides, the result of the F-value [see Column (3) of <xref ref-type="table" rid="T4">Table 4</xref>] shows that there is no weak instrumental variable problem with <italic>Institution</italic>. Hence, <italic>Institution</italic> is an appropriate instrumental variable for <italic>Insurance</italic>.</p>
<p>The results of the endogeneity test are presented in Column (4) of <xref ref-type="table" rid="T4">Table 4</xref>. The estimated coefficient of the fitted value of <italic>Insurance</italic> is significantly negative, which is consistent with the above findings and further suggests that the conclusion is still robust.</p></sec>
<sec>
<title>Heterogeneity Analysis</title>
<p>This section examines the heterogeneous impact of basic medical insurance on elderly family income inequality from the differences of region and age. The regression results are reported in <xref ref-type="table" rid="T5">Table 5</xref>. Columns (1-3) are the results of eastern region, central region and western region, respectively. Column (4) is the results of younger elderly, and Column (5) is the results of advanced elderly.</p>
<table-wrap position="float" id="T5">
<label>Table 5</label>
<caption><p>Results of heterogeneous analysis.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="center" colspan="3" style="border-bottom: thin solid #000000;"><bold>Region difference</bold></th>
<th valign="top" align="center" colspan="2" style="border-bottom: thin solid #000000;"><bold>Age difference</bold></th>
</tr>
<tr>
<th/>
<th valign="top" align="center" style="border-bottom: thin solid #000000;"><bold>Eastern</bold></th>
<th valign="top" align="center" style="border-bottom: thin solid #000000;"><bold>Central</bold></th>
<th valign="top" align="center" style="border-bottom: thin solid #000000;"><bold>Western</bold></th>
<th valign="top" align="center" style="border-bottom: thin solid #000000;"><bold>Younger elderly</bold></th>
<th valign="top" align="center" style="border-bottom: thin solid #000000;"><bold>Advanced elderly</bold></th>
</tr>
<tr>
<th/>
</tr>
<tr>
<th/>
<th valign="top" align="center"><bold>(1)</bold></th>
<th valign="top" align="center"><bold>(2)</bold></th>
<th valign="top" align="center"><bold>(3)</bold></th>
<th valign="top" align="center"><bold>(4)</bold></th>
<th valign="top" align="center"><bold>(5)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Basic medical insurance</td>
<td valign="top" align="center">&#x02212;0.027<xref ref-type="table-fn" rid="TN3"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">&#x02212;0.015</td>
<td valign="top" align="center">&#x02212;0.004</td>
<td valign="top" align="center">&#x02212;0.023<xref ref-type="table-fn" rid="TN3"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">&#x02212;0.013</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">(0.008)</td>
<td valign="top" align="center">(0.010)</td>
<td valign="top" align="center">(0.012)</td>
<td valign="top" align="center">(0.006)</td>
<td valign="top" align="center">(0.028)</td>
</tr>
<tr>
<td valign="top" align="left">Control variables</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
<td valign="top" align="center">Yes</td>
</tr>
<tr>
<td valign="top" align="left">Constant</td>
<td valign="top" align="center">1.369<xref ref-type="table-fn" rid="TN3"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">1.333<xref ref-type="table-fn" rid="TN3"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">1.240<xref ref-type="table-fn" rid="TN3"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">1.351<xref ref-type="table-fn" rid="TN3"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
<td valign="top" align="center">1.233<xref ref-type="table-fn" rid="TN3"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref></td>
</tr>
<tr>
<td/>
<td valign="top" align="center">(0.033)</td>
<td valign="top" align="center">(0.040)</td>
<td valign="top" align="center">(0.048)</td>
<td valign="top" align="center">(0.023)</td>
<td valign="top" align="center">(0.119)</td>
</tr>
<tr>
<td valign="top" align="left">Observations</td>
<td valign="top" align="center">2,159</td>
<td valign="top" align="center">1,258</td>
<td valign="top" align="center">1,104</td>
<td valign="top" align="center">4,317</td>
<td valign="top" align="center">204</td>
</tr>
<tr>
<td valign="top" align="left">R&#x02013;squared</td>
<td valign="top" align="center">0.395</td>
<td valign="top" align="center">0.362</td>
<td valign="top" align="center">0.263</td>
<td valign="top" align="center">0.367</td>
<td valign="top" align="center">0.475</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="TN3">
<label>&#x0002A;&#x0002A;&#x0002A;</label>
<p><italic>p &#x02264; 0.01; Standard errors are in parentheses</italic>.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>For the region differences, as can be seen from Columns (1-3) in <xref ref-type="table" rid="T5">Table 5</xref>, the coefficient of <italic>Insurance</italic> for the eastern regions is significantly negative at the 1% level, while it is not significant for central and western regions. That is, basic medical insurance can reduce elderly family income inequality in the eastern regions, but it has no effect in the central and western regions. Hence, the findings confirm H2a. Economically developed areas are mostly located in the eastern regions, where the reimbursement of basic medical insurance for the elderly is higher, and the proportion of medical costs borne by the elderly is lower. However, the economic development of central and western regions lags behind that of the eastern regions, and there is a severe imbalance in regional development. The reimbursement of basic medical insurance for the elderly varies significantly among regions. Therefore, basic medical insurance can significantly reduce eastern elderly family income inequality, but this effect does not exist for the central and western regions.</p>
<p>In terms of the age difference, 60&#x02013;80 years old is defined as the younger elderly, and 80&#x02013;100 years old is defined as the advanced elderly. As can be seen from Columns (4) and (5) in <xref ref-type="table" rid="T5">Table 5</xref>, the coefficient of <italic>Insurance</italic> for younger elderly is significantly negative at the 1% level, while it is not significant for advanced elderly. These results indicate that basic medical insurance can reduce the family income inequality of the younger elderly, but it has no effect on the advanced elderly family and confirms H2b. These results may be explained by the fact that the current elderly population in China is mainly concentrated in the younger elderly group, which accounts for 70% of the total elderly people, and this group uses basic medical insurance more frequently and intensively than the advanced elderly. Another possible explanation for this might be that the significant health disparities between the younger and advanced elderly, basic medical insurance is more effective in reducing family income inequality among the younger elderly due to illness shocks.</p></sec>
<sec>
<title>Mediating Effect of Health Performance</title>
<p>Health performance is directly related to the applications of basic health insurance and elderly family income inequality, which may affect the relationship between them. Therefore, we examine the mediating role of health performance on the relationship between basic health insurance and elderly family income inequality in China.</p>
<p>Most studies adopt the stepwise causal test proposed by Baron et al. to test the mediating effect. However, there may be insufficient sample number or non-normal sample distribution for the data obtained from social surveys due to the limitations of research conditions, and the mediation effect may be biased using the stepwise causal test (<xref ref-type="bibr" rid="B42">42</xref>). Therefore, this study uses the Bootstrap method proposed by Hayes (<xref ref-type="bibr" rid="B43">43</xref>) to test the mediating effect of health performance, and the model is constructed as follows:</p>
<disp-formula id="E3"><label>(3)</label><mml:math id="M3"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><mml:mi>H</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mtd><mml:mtd><mml:mo>=</mml:mo></mml:mtd><mml:mtd><mml:mi>&#x003B1;</mml:mi><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B2;</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>I</mml:mi><mml:mi>n</mml:mi><mml:mi>s</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:mi>&#x003B4;</mml:mi><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:msub><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E4"><label>(4)</label><mml:math id="M4"><mml:mtable class="eqnarray" columnalign="left"><mml:mtr><mml:mtd><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:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>&#x003B1;</mml:mi><mml:mo>&#x0002B;</mml:mo><mml:mi>&#x003B2;</mml:mi><mml:mi>I</mml:mi><mml:mi>n</mml:mi><mml:mi>s</mml:mi><mml:mi>u</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>c</mml:mi><mml:msub><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mtext>&#x000A0;</mml:mtext><mml:mtext class="textrm" mathvariant="normal">&#x0002B;</mml:mtext><mml:mtext>&#x000A0;</mml:mtext><mml:msub><mml:mrow><mml:mi>&#x003B2;</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mi>H</mml:mi><mml:mi>e</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:mi>&#x003B4;</mml:mi><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:msub><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:mtext>&#x000A0;</mml:mtext><mml:msub><mml:mrow><mml:mi>&#x003B5;</mml:mi></mml:mrow><mml:mrow><mml:mi>i</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where <italic>Health</italic> represents the mediator variable of health performance, and the other variables are the same with the Model (<xref ref-type="bibr" rid="B1">1</xref>). The Bootstrap method can directly test whether &#x003B2;<sub>1</sub> &#x000D7; &#x003B2;<sub>2</sub> is significantly different from 0. If its coefficient is significantly different from 0, indicating that health performance has a mediating effect between basic medical insurance and elderly family income inequality.</p>
<p><xref ref-type="table" rid="T6">Table 6</xref> reports the results of the mediation analysis. We can find that the indirect and direct effects of health performance are significant at the 1% level (the coefficients are &#x02212;0.002 and &#x02212;0.049, respectively), and the proportion of indirect effect is 4.1%. These results indicate that health performance partly mediates the relationships between basic medical insurance and elderly family income inequality in China and confirms H3. The possible reason is that the reimbursement of basic medical insurance promotes the timely access of the elderly to medical services and prevents the deterioration of their health status. Thus, it is beneficial to decrease the risk of medical expenses for major diseases of the elderly and ultimately reduce elderly family income inequality.</p>
<table-wrap position="float" id="T6">
<label>Table 6</label>
<caption><p>Results of mediating effect.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Types</bold></th>
<th valign="top" align="center"><bold>Observed coefficient</bold></th>
<th valign="top" align="center"><bold>Bootstrap standard error</bold></th>
<th valign="top" align="center"><bold><italic>P</italic>-value</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Indirect effect</td>
<td valign="top" align="center">&#x02212;0.002</td>
<td valign="top" align="center">0.001</td>
<td valign="top" align="center">0.012</td>
</tr>
<tr>
<td valign="top" align="left">Direct effect</td>
<td valign="top" align="center">&#x02212;0.049</td>
<td valign="top" align="center">0.008</td>
<td valign="top" align="center">0.000</td>
</tr>
<tr>
<td valign="top" align="left" colspan="3">The proportion of indirect effect</td>
<td valign="top" align="center">4.1%</td>
</tr>
</tbody>
</table>
</table-wrap></sec></sec>
<sec id="s5">
<title>Conclusion and Implications</title>
<p>This study has examined the influence of basic medical insurance on elderly family income inequality in China through using the CFPS data in 2018 and also discussed the heterogeneity of region and age differences and the mediating effect of health performance.</p>
<p>This study adds to the growing body of researches about the impact of basic medical insurance on elderly family income inequality. Our empirical results show that basic medical insurance significantly reduces elderly family income inequality in China. In other words, basic medical insurance reduces the burden of the elderly and their families through medical expenses reimbursement, thus reducing the family income inequality of the elderly. We also find that the impact of basic medical insurance on elderly family income inequality varies with the differences of region and age. Specifically, basic health insurance plays a more significant role in reducing elderly family income inequality in the eastern regions than in the central and western regions. Besides, compared with the advanced elderly, the effect of basic medical insurance on reducing younger elderly family income inequality is more pronounced. Finally, we provide additional evidence that health performance plays a mediating effect between the relationship between basic medical insurance and elderly family income inequality in China.</p>
<p>The above conclusions have several important policy implications for China to promote the realization of the goal of &#x0201C;fair medical insurance&#x0201D; and the common prosperity of the elderly during the Fourth 5-Year Plan period (<xref ref-type="bibr" rid="B44">44</xref>). As a crucial medical security system design in China, basic medical insurance has a series of tasks such as adjusting the income distribution gap, guaranteeing health rights, and maintaining health justice (<xref ref-type="bibr" rid="B45">45</xref>). This study proposes that basic medical insurance can reduce elderly family income inequality and play a key role in maintaining welfare utility, which aligns with the original intention of institutional design to ensure fairness and promote stability. However, considering the impact of basic medical insurance on medical expenses and the income distribution of the elderly family, it is necessary to re-examine the basic medical insurance system in China. First, the Chinese government should narrow regional disparities in basic medical insurance reimbursement and compensation to ensure the fairness and sustainability of basic medical insurance. Second, the Chinese government should further integrate the basic medical insurance for urban and rural residents and the basic medical insurance for urban employees to reduce elderly family income inequality caused by participating in different types of basic medical insurance. Finally, the Chinese government should improve the design of basic medical insurance policies. Specifically, the government should optimize the welfare policy of medical insurance, such as providing more medical subsidies to the advanced elderly, including physical examination into the category of medical reimbursement, reducing the threshold line or increasing the reimbursement ratio.</p></sec>
<sec sec-type="data-availability" id="s6">
<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/dataverse/CFPS">https://opendata.pku.edu.cn/dataverse/CFPS</ext-link>.</p></sec>
<sec id="s7">
<title>Author Contributions</title>
<p>XP: writing&#x02014;original draft, data collection, and literature search. YW: conceptualization, writing&#x02014;original draft, and software. WZ: writing&#x02014;reviewing and editing and supervision. MZ: data collection. All authors contributed to the article and approved the submitted version.</p></sec>
<sec sec-type="funding-information" id="s8">
<title>Funding</title>
<p>This work was supported by the Key Project of National Social Science Foundation of China (17ASH009), the Planning Project of Gansu Province Philosophy and Social Science (2021YB027), the 2021 Innovation and Entrepreneurship Reform Funds in Northwest Minzu University (4), the Education Department Innovation Funds in Gansu Province (2020B-074), and the Fundamental Research Funds for central universities in Northwest Minzu University (31920190117).</p></sec>
<sec sec-type="COI-statement" id="conf1">
<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&#x00027;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> </body>
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