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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.2022.773728</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>Fiscal Decentralization, Public Health Expenditure and Public Health&#x02013;Evidence From China</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name><surname>Xu</surname> <given-names>Wangzi</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x0002A;</sup></xref>
<xref ref-type="author-notes" rid="fn002"><sup>&#x02020;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1459858/overview"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Lin</surname> <given-names>Jia</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="author-notes" rid="fn002"><sup>&#x02020;</sup></xref>
<uri xlink:href="http://loop.frontiersin.org/people/1758497/overview"/>
</contrib>
</contrib-group>
<aff id="aff1"><sup>1</sup><institution>School of Public Health, Xiamen University</institution>, <addr-line>Xiamen</addr-line>, <country>China</country></aff>
<aff id="aff2"><sup>2</sup><institution>International School, Jinan University</institution>, <addr-line>Guangzhou</addr-line>, <country>China</country></aff>
<author-notes>
<fn fn-type="edited-by"><p>Edited by: Mihajlo Jakovljevic, Hosei University, Japan</p></fn>
<fn fn-type="edited-by"><p>Reviewed by: Mariela Deliverska, Medical University Sofia, Bulgaria; Naiefa Rashied, University of Johannesburg, South Africa; Morro Touray, University of Surrey, United Kingdom</p></fn>
<corresp id="c001">&#x0002A;Correspondence: Wangzi Xu <email>xuwangzi1016&#x00040;163.com</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>
<fn fn-type="equal" id="fn002"><p>&#x02020;These authors share first authorship</p></fn></author-notes>
<pub-date pub-type="epub">
<day>18</day>
<month>05</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>773728</elocation-id>
<history>
<date date-type="received">
<day>10</day>
<month>09</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>25</day>
<month>04</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x000A9; 2022 Xu and Lin.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Xu and Lin</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>Since the beginning of the COVID-19 outbreak and the launch of the &#x0201C;Healthy China 2030&#x0201D; strategy in 2019, public health has become a relevant topic of discussion both within and outside China. The provision of public health services, which is determined by public health expenditure, is critical to the regional public health sector. Fiscal decentralization provides local governments with more financial freedom, which may result in changes to public health spending; thus, fiscal decentralization may influence public health at the regional level. In order to study the effects of fiscal decentralization on local public health expenditure and local public health levels, we applied a two-way fixed effect model as well as threshold regression and intermediate effect models to 2008&#x02013;2019 panel data from China&#x00027;s 30 mainland provinces as well as from four municipalities and autonomous regions to study the effects of fiscal decentralization on public health. The study found that fiscal decentralization has a positive effect on increasing public health expenditure. Moreover, fiscal decentralization can promote improvements in regional public health by increasing public health expenditure and by improving the availability of regional medical public service resources. In addition, fiscal decentralization has a non-linear effect on public health.</p></abstract>
<kwd-group>
<kwd>public health expenditure</kwd>
<kwd>public health</kwd>
<kwd>fiscal decentralization</kwd>
<kwd>intermediary effect test</kwd>
<kwd>threshold regression analysis</kwd>
</kwd-group>
<counts>
<fig-count count="6"/>
<table-count count="9"/>
<equation-count count="9"/>
<ref-count count="59"/>
<page-count count="12"/>
<word-count count="7804"/>
</counts>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>Introduction</title>
<p>Since the beginning of the COVID-19 outbreak, China&#x00027;s public health system has become an essential contributor to the protection of public health and to the promotion of economic and social development. Public health is valued by society and the government because it is underpinned by individual health. In 2020, the Health Committee of China received an 11.3% increment in its budget allocation from state finances relative to what it received in 2019. China&#x00027;s &#x0201C;Healthy China 2030&#x0201D; strategy, which was launched in 2016, emphasized health as an inevitable requirement for human survival and development as well as the foundation for economic development (<xref ref-type="bibr" rid="B1">1</xref>). It also regards health as a significant symbol of national prosperity and economic rejuvenation. China&#x00027;s president, Xi Jinping, also attaches great importance to public health and places the protection of individual health as a development priority. He promoted the reform of China&#x00027;s health system, increased the amount of reimbursement received from health insurance, and ensured access to affordable and effective medical treatment (<xref ref-type="bibr" rid="B2">2</xref>). Improving the public health care system, increasing government health expenditure, and promoting public health are essential to ensuring stable and sustainable economic development. In this public health and improvement drive, China introduced fiscal decentralization programs to foster resources that are efficiently managed to ensure the delivery of effective public health care.</p>
<p>A fiscal decentralization system involves shifting revenue and expenditure to lower levels of government, something that is currently applied in the Chinese context (<xref ref-type="bibr" rid="B3">3</xref>) China&#x00027;s fiscal decentralization began in the 1980s (<xref ref-type="bibr" rid="B4">4</xref>). Lin and Zhou (<xref ref-type="bibr" rid="B5">5</xref>), Akai and Sakata (<xref ref-type="bibr" rid="B6">6</xref>), and Zhang and Zou (<xref ref-type="bibr" rid="B7">7</xref>) have studied the effects of different aspects of fiscal decentralization on economic growth and environmental pollution (<xref ref-type="bibr" rid="B8">8</xref>). However, studies on fiscal decentralization in the context of public health care are limited. The classical theory of fiscal decentralization is based on the tenet that local governments know more about their local situation than the central government does (<xref ref-type="bibr" rid="B9">9</xref>). Therefore, under a decentralized system, local governments can better provide public goods in an effective, efficient, and timely manner. However, some studies present different views (<xref ref-type="bibr" rid="B10">10</xref>). For example, Fu and Zhang (<xref ref-type="bibr" rid="B11">11</xref>) believe that Chinese decentralization distorts the public expenditure structure of local governments and that as fiscal decentralization increases, most local governments focus on effective capital construction investment while ignoring investment in education, culture and health. In addition, local corruption has increased government investment expenditure and reduced expenditure targeting livelihoods such as education and health care (<xref ref-type="bibr" rid="B12">12</xref>). Thus, in the fiscal expenditure structure, economic public goods crowd out non-economic livelihood-related public goods, such as public health services.</p>
<p>Considering the possible non-linear relationship, the introduction of a quadratic term and the use of threshold effect regression and other non-linear regression models can capture the possible structural changes that take place in the model and the non-linear relationship between variables more appropriately. Therefore, this paper adopts a non-linear regression model when analyzing the impacts of fiscal decentralization on public health. The main aim of this paper is to analyze the impacts of fiscal decentralization on public health. We employed a two-way fixed effect model as well as threshold regression and intermediate effect models for the analyses. First, using 2008&#x02013;2019 panel data from 30 provinces in China, the paper examines the effects of fiscal decentralization on public health expenditure and public health outcomes. Second, after establishing that the impact of fiscal decentralization on public health is non-linear through introduction of a quadratic term [as in Wang and Wang (<xref ref-type="bibr" rid="B13">13</xref>)], this paper further utilizes a threshold regression model [as in Li et al. (<xref ref-type="bibr" rid="B14">14</xref>)] to study the non-linear relationship between fiscal decentralization and public health. Finally, with respect to policy recommendations for the government, the paper also discusses the influence mechanism through an intermediary effect test.</p>
</sec>
<sec sec-type="materials and methods" id="s2">
<title>Materials and Methods</title>
<sec>
<title>Variable Selection</title>
<sec>
<title>Explanatory and Response Variables</title>
<p>Scholars around the world have different opinions on how to measure fiscal decentralization (<xref ref-type="bibr" rid="B15">15</xref>, <xref ref-type="bibr" rid="B16">16</xref>). This paper uses fiscal revenue decentralization (FD) and fiscal expenditure decentralization (FED) to represent the level of local fiscal decentralization (<xref ref-type="bibr" rid="B17">17</xref>). The calculation formula is presented below in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap position="float" id="T1">
<label>Table 1</label>
<caption><p>Variables of interest.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Classification</bold></th>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="left"><bold>Variable definitions</bold></th>
<th valign="top" align="left"><bold>Outcome measure /Computing method</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Response</td>
<td valign="top" align="left">PH</td>
<td valign="top" align="left">Public health</td>
<td valign="top" align="left">Population mortality</td>
</tr>
<tr>
<td valign="top" align="left">variables</td>
<td valign="top" align="left">PS</td>
<td valign="top" align="left">Public health expenditure</td>
<td valign="top" align="left">Logarithm of public health expenditure in each province</td>
</tr>
<tr>
<td valign="top" align="left">Explanatory</td>
<td valign="top" align="left">FD</td>
<td valign="top" align="left">Fiscal Revenue Decentralization</td>
<td valign="top" align="left">Per capita provincial fiscal revenue/(per capita provincial fiscal revenue &#x0002B; per capita central fiscal revenue)</td>
</tr>
<tr>
<td valign="top" align="left">variables</td>
<td valign="top" align="left">FED</td>
<td valign="top" align="left">Fiscal expenditure decentralization</td>
<td valign="top" align="left">Per capita provincial fiscal expenditure/(per capita provincial fiscal expenditure &#x0002B; per capita central fiscal expenditure)</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">lnGDPave</td>
<td valign="top" align="left">Real per capita GDP</td>
<td valign="top" align="left">The logarithm of nominal per capita GDP multiplied by GDP index divided by 100</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Industry</td>
<td valign="top" align="left">Industrial structure</td>
<td valign="top" align="left">Added value of secondary industry/added value of tertiary industry</td>
</tr>
<tr>
<td valign="top" align="left">Control</td>
<td valign="top" align="left">Patent</td>
<td valign="top" align="left">Scientific/technological level</td>
<td valign="top" align="left">Regional authorized patents</td>
</tr>
<tr>
<td valign="top" align="left">Variables</td>
<td valign="top" align="left">Market</td>
<td valign="top" align="left">Marketization index</td>
<td valign="top" align="left">2008&#x02013;2016 from the report, 2017&#x02013;2019 forecasted by trends</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Trade</td>
<td valign="top" align="left">Import and export trade</td>
<td valign="top" align="left">Total imports and exports/nominal GDP</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Pop</td>
<td valign="top" align="left">Resident population</td>
<td valign="top" align="left">The logarithm of permanent residents in each region</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Urban Pollution</td>
<td valign="top" align="left">Urbanization rate aAir pollution</td>
<td valign="top" align="left">Urban population/resident population Industrial SO2 emissions take logarithm</td>
</tr>
<tr>
<td valign="top" align="left">Mediating</td>
<td valign="top" align="left">Bed</td>
<td valign="top" align="left">Number of beds</td>
<td valign="top" align="left">Number of beds in regional medical institutions</td>
</tr>
<tr>
<td valign="top" align="left">Variables</td>
<td valign="top" align="left">Tech</td>
<td valign="top" align="left">Hygienic personnel</td>
<td valign="top" align="left">Number of health workers per thousand people</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In addition, the core of Chinese fiscal decentralization is the distribution of tax revenue between the central and local governments, which is essentially fiscal revenue decentralization. Therefore, this paper takes FD as the core explanatory variable and uses FED as a robustness test to ensure the robustness of the regression results. <xref ref-type="fig" rid="F1">Figure 1</xref> illustrates the annual changes in the degree of average FD in China in the period of 2008&#x02013;2019.</p>
<fig id="F1" position="float">
<label>Figure 1</label>
<caption><p>Annual average degree of FD in the period of 2008&#x02013;2019.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fpubh-10-773728-g0001.tif"/>
</fig>
<p>The response variable for public health is a multi-dimensional and macro concept. Some literature and government reports use life expectancy per capita, infant mortality, and maternal mortality to measure public health interventions (<xref ref-type="bibr" rid="B18">18</xref>), but the most frequently used indicator in scientific research is population mortality. Therefore, this paper uses population mortality as the measure of public health interventions. Thus, the lower the population mortality, the higher the level of public health interventions. <xref ref-type="fig" rid="F2">Figure 2</xref> shows the annual average population mortality in China from 2008 to 2019.</p>
<fig id="F2" position="float">
<label>Figure 2</label>
<caption><p>Annual average population mortality in China in the period of 2008&#x02013;2019.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fpubh-10-773728-g0002.tif"/>
</fig>
<p>Public health expenditure is another response variable as well as a vital intermediary variable. The data were obtained directly from each province&#x00027;s statistical year book. <xref ref-type="fig" rid="F3">Figure 3</xref> demonstrates the trend of China&#x00027;s average annual total health expenditure from 2008 to 2019. In fact, due to the increase in outpatient costs, rising drug prices, and more individualized medical care, health spending has continued to grow at an alarming rate worldwide (<xref ref-type="bibr" rid="B19">19</xref>). Hence, it can be seen from <xref ref-type="fig" rid="F3">Figure 3</xref> that China&#x00027;s average health expenditure is continuously increasing.</p>
<fig id="F3" position="float">
<label>Figure 3</label>
<caption><p>Average annual public health spending in the period of 2008&#x02013;2019.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fpubh-10-773728-g0003.tif"/>
</fig>
<p>The trend observed in the three figures above suggests that there may be a correlation between the degree of fiscal decentralization, public health, and public health expenditure.</p>
</sec>
<sec>
<title>Variable Definition</title>
<p><xref ref-type="table" rid="T1">Table 1</xref> provides the definitions and calculation methods of all variables in this paper.</p>
<p>The control variables are variables other than explanatory variables that may affect population health. Economic development, scientific and technological advancement, degree of urbanization, international trade and air pollution are closely related to public health improvements (<xref ref-type="bibr" rid="B20">20</xref>&#x02013;<xref ref-type="bibr" rid="B22">22</xref>). The number of hospital beds and the density and distribution health workers are important embodiments of the resource level of the public healthcare system (<xref ref-type="bibr" rid="B23">23</xref>) and are confounding factors of public health. Public health spending also directly affects the public health level (<xref ref-type="bibr" rid="B24">24</xref>); thus, the mediating variables are Bed, Tech, and PS.</p>
</sec>
<sec>
<title>Data Sources</title>
<p>Due to the lack of some data, the regions of Taiwan and Tibet have been excluded. All data are sourced from the China Statistical Year book, the Finance Year book of China and the China Statistical Year book on Environment. The descriptive statistics of all of the variables 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>Variable</bold></th>
<th valign="top" align="center"><bold>Sample size</bold></th>
<th valign="top" align="center"><bold>Average value</bold></th>
<th valign="top" align="center"><bold>Standard deviation</bold></th>
<th valign="top" align="center"><bold>Minimum value</bold></th>
<th valign="top" align="center"><bold>Maximum value</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">FD</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">0.590</td>
<td valign="top" align="center">0.469</td>
<td valign="top" align="center">0.199</td>
<td valign="top" align="center">2.727</td>
</tr>
<tr>
<td valign="top" align="left">FED</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">0.9996</td>
<td valign="top" align="center">0.437</td>
<td valign="top" align="center">0.515</td>
<td valign="top" align="center">2.938</td>
</tr>
<tr>
<td valign="top" align="left">PS</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">5.472</td>
<td valign="top" align="center">0.802</td>
<td valign="top" align="center">2.84</td>
<td valign="top" align="center">7.365</td>
</tr>
<tr>
<td valign="top" align="left">PH</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">6.042</td>
<td valign="top" align="center">0.763</td>
<td valign="top" align="center">4.21</td>
<td valign="top" align="center">7.57</td>
</tr>
<tr>
<td valign="top" align="left">Tech</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">5.737</td>
<td valign="top" align="center">1.874</td>
<td valign="top" align="center">1</td>
<td valign="top" align="center">15.46</td>
</tr>
<tr>
<td valign="top" align="left">Pollution</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">12.5932</td>
<td valign="top" align="center">1.2142</td>
<td valign="top" align="center">6.7799</td>
<td valign="top" align="center">14.3033</td>
</tr>
<tr>
<td valign="top" align="left">Pop</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">4521.672</td>
<td valign="top" align="center">2711.412</td>
<td valign="top" align="center">554</td>
<td valign="top" align="center">11521</td>
</tr>
<tr>
<td valign="top" align="left">Bed</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">21.205</td>
<td valign="top" align="center">13.785</td>
<td valign="top" align="center">1.735</td>
<td valign="top" align="center">64.01</td>
</tr>
<tr>
<td valign="top" align="left">lnGDPave</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">10.57</td>
<td valign="top" align="center">0.512</td>
<td valign="top" align="center">9.196</td>
<td valign="top" align="center">11.77</td>
</tr>
<tr>
<td valign="top" align="left">Market</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">6.44</td>
<td valign="top" align="center">1.948</td>
<td valign="top" align="center">2.33</td>
<td valign="top" align="center">11.518</td>
</tr>
<tr>
<td valign="top" align="left">Industry</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">0.956</td>
<td valign="top" align="center">0.309</td>
<td valign="top" align="center">0.191</td>
<td valign="top" align="center">1.897</td>
</tr>
<tr>
<td valign="top" align="left">Patent</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">43371.06</td>
<td valign="top" align="center">68928.77</td>
<td valign="top" align="center">228</td>
<td valign="top" align="center">5,27,390</td>
</tr>
<tr>
<td valign="top" align="left">Urban</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">55.801</td>
<td valign="top" align="center">13.044</td>
<td valign="top" align="center">29.11</td>
<td valign="top" align="center">89.6</td>
</tr>
<tr>
<td valign="top" align="left">Trade</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">0.282</td>
<td valign="top" align="center">0.329</td>
<td valign="top" align="center">0.0127</td>
<td valign="top" align="center">1.698</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The data set covers the period 2008 to 2019 (inclusive). Since this paper includes 30 Chinese provinces, the use of panel data can address endogeneity problems caused by unobservable heterogeneity, because the fixed effect model using panel data can control the time-invariant missing variables that change with individuals. Moreover, panel data provide the characteristics of each province&#x00027;s respective regional dynamic behaviors, making the results more buoyant (<xref ref-type="bibr" rid="B25">25</xref>).</p>
</sec>
</sec>
<sec>
<title>Model Development</title>
<sec>
<title>Benchmark Regression Models</title>
<p>Three models were developed for the benchmark regression analysis. Model 1 is used to test the impact of fiscal decentralization on public health expenditure:</p>
<disp-formula id="E1"><label>(1)</label><mml:math id="M1"><mml:mtable class="eqnarray" columnalign="right center left"><mml:mtr><mml:mtd><mml:msub><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mi>P</mml:mi><mml:mi>S</mml:mi></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mstyle></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B2;</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mn>0</mml:mn></mml:mstyle></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B2;</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mn>1</mml:mn></mml:mstyle></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mi>F</mml:mi><mml:mi>D</mml:mi></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mstyle></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B2;</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mn>2</mml:mn></mml:mstyle></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mi>X</mml:mi></mml:mstyle></mml:mrow><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mstyle></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003BC;</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mi>i</mml:mi></mml:mstyle></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B4;</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mi>t</mml:mi></mml:mstyle></mml:mrow></mml:msub><mml:mo>&#x0002B;</mml:mo><mml:msub><mml:mrow><mml:mi>&#x003B5;</mml:mi></mml:mrow><mml:mrow><mml:mstyle mathvariant="bold-italic"><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mstyle></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where PS<sub>it</sub> is public health expenditure; FD<sub>it</sub> is fiscal revenue decentralization and can be replaced by fiscal expenditure decentralization; and X<sub>it</sub> represents a series of control variables, including the regional economic level, industrial structure, degree of urbanization degree, imports and exports, level of scientific and technological development, and degree of marketization. &#x003BC;<sub>i</sub> is the provincial fixed effect, &#x003B4;<sub>t</sub> is the time fixed effect, and &#x003B5;<sub>it</sub> is a random error term. The Chi<sup>2</sup> value of Hausman&#x00027;s test is 8.28 (<italic>P</italic> = 0.0159). Therefore, the original hypothesis indicating the use of the random effect model is rejected, and Model 1 can be analyzed using a two-way fixed effect model.</p>
<p>Model 2 was used to study the impact of fiscal decentralization on public health. The quadratic term of the explanatory variable is added to test whether there is a non-linear relationship between the explanatory variables and response variables, that is, whether there is a U-shaped or n-shaped relationship. Even if the quadratic term of the explanatory variable is added, the relationship between the explanatory variable and each parameter is still linear. Since fiscal decentralization has a non-linear relationship with public health, the quadratic term for the FD variable was introduced to test the non-linear relationship between FD and PH [as in Jin et al. (<xref ref-type="bibr" rid="B26">26</xref>)]. If the results show that the coefficients of FD<sup>2</sup> and FD are both significant, then the relationship between FD and PH is non-linear.</p>
<disp-formula id="E2"><label>(2)</label><mml:math id="M2"><mml:mtable class="eqnarray" columnalign="right center left"><mml:mtr><mml:mtd><mml:mrow><mml:mi>P</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mtext>&#x003B1;</mml:mtext><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mtext>&#x003B1;</mml:mtext><mml:mn>1</mml:mn></mml:msub><mml:mi>F</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mtext>&#x003B1;</mml:mtext><mml:mn>2</mml:mn></mml:msub><mml:mi>F</mml:mi><mml:msubsup><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mtext>&#x003B1;</mml:mtext><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003BC;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mtext>&#x003B4;</mml:mtext><mml:mi>t</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003B5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where FD<sup>2</sup> is the squared term of FD; PH<sub>it</sub> represents public health measured by population mortality; X<sub>it</sub> is the control variable with confounding effects on PH (as in Model 1); &#x003BC;<sub>i</sub> is the provincial fixed effect; &#x003B4;<sub>t</sub> is the time-fixed effect; and &#x003B5;<sub>it</sub> is a random error term and is independently identically distributed.</p>
<p>Model 3 was used to further analyze whether PS affects the effect of FD on PH; in this model, we selected public health expenditure as an intermediary variable and introduced the interactive terms FD &#x000D7; PS to verify whether fiscal decentralization influences public health by affecting public health expenditure or otherwise.</p>
<disp-formula id="E3"><label>(3)</label><mml:math id="M3"><mml:mtable class="eqnarray" columnalign="right center left"><mml:mtr><mml:mtd><mml:mtable columnalign='left'><mml:mtr><mml:mtd><mml:mi>P</mml:mi><mml:msub><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mtext>&#x000A0;</mml:mtext><mml:mo>=</mml:mo><mml:msub><mml:mi>&#x003B2;</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003B1;</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>F</mml:mi><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003B1;</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi>P</mml:mi><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003B1;</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mi>F</mml:mi><mml:mi>D</mml:mi><mml:mo>&#x000D7;</mml:mo><mml:mi>P</mml:mi><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003B1;</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003BC;</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003B4;</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>&#x003B5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where FD &#x000D7; PS<sub>it</sub> is the interaction between fiscal decentralization and public health expenditure. In order to eliminate the influence of multicollinearity and make the coefficients comparable, the variables FD and PS are centralized (<xref ref-type="bibr" rid="B27">27</xref>). The explanations of other variables are the same as in previous equations.</p>
</sec>
<sec>
<title>Threshold Regression Models</title>
<p>The quadratic term is introduced into Model (2) to preliminarily study the non-linear relationship between FD and PH, but Model (2) cannot confirm whether the relationship is U-shaped or n-shaped, so threshold regression is needed to further explore the non-linear relationship between fiscal decentralization and public health. In reference to Wang and Wang (<xref ref-type="bibr" rid="B13">13</xref>), this paper uses the threshold effect model for further analysis. First, taking fiscal decentralization itself as the threshold variable, a double threshold model, Model (4), is established (<xref ref-type="bibr" rid="B28">28</xref>).</p>
<disp-formula id="E4"><label>(4)</label><mml:math id="M4"><mml:mtable class="eqnarray" columnalign="right center left"><mml:mtr><mml:mtd><mml:msub><mml:mtext>PH</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mtext>=&#x003B2;</mml:mtext><mml:mtext>0</mml:mtext></mml:msub><mml:msub><mml:mtext>+&#x003B2;</mml:mtext><mml:mtext>1</mml:mtext></mml:msub><mml:msub><mml:mtext>FD</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000D7;I</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>FD</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mo>&#x02264;</mml:mo><mml:msub><mml:mtext>&#x003B3;</mml:mtext><mml:mtext>1</mml:mtext></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:msub><mml:mtext>+&#x003B2;</mml:mtext><mml:mtext>2</mml:mtext></mml:msub><mml:msub><mml:mtext>FD</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000D7;I</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mtext>&#x003B3;</mml:mtext><mml:mtext>1</mml:mtext></mml:msub><mml:msub><mml:mrow><mml:mtext>&#x0003C;FD</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mo>&#x02264;</mml:mo><mml:msub><mml:mtext>&#x003B3;</mml:mtext><mml:mtext>2</mml:mtext></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;</mml:mtext></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;+&#x003B2;</mml:mtext><mml:mtext>3</mml:mtext></mml:msub><mml:msub><mml:mtext>FD</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000D7;I</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mtext>&#x003B3;</mml:mtext><mml:mtext>2</mml:mtext></mml:msub><mml:msub><mml:mrow><mml:mtext>&#x0003C;FD</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:msub><mml:mtext>+&#x003B2;</mml:mtext><mml:mtext>4</mml:mtext></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mtext>+&#x003BC;</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mtext>+&#x003B4;</mml:mtext><mml:mtext>t</mml:mtext></mml:msub><mml:msub><mml:mtext>+&#x003B5;</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where I(&#x000B7;) is a characteristic function, and the value of I(&#x000B7;) is 1 if the corresponding condition is true and is 0 otherwise. &#x003B3;<sub>1</sub> and &#x003B3;<sub>2</sub> are threshold values. &#x003B2;<sub>1</sub>, &#x003B2;<sub>2</sub>, and &#x003B2;<sub>3</sub> represent the impact of fiscal decentralization on public health under different levels of threshold variables. The other variables are as they were in the previous models.</p>
<p>However, the non-linear relationship between fiscal decentralization and public health may also be a single threshold effect, so the estimated model can be modified, such as in Model (5) below.</p>
<disp-formula id="E5"><label>(5)</label><mml:math id="M5"><mml:mtable columnalign='left'><mml:mtr><mml:mtd><mml:msub><mml:mtext>PH</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mtext>=&#x003B2;</mml:mtext><mml:mtext>0</mml:mtext></mml:msub><mml:msub><mml:mtext>+&#x003B2;</mml:mtext><mml:mtext>1</mml:mtext></mml:msub><mml:msub><mml:mtext>FD</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000D7;I</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>FD</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mo>&#x02264;</mml:mo><mml:mtext>&#x003B3;</mml:mtext></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:msub><mml:mtext>+&#x003B2;</mml:mtext><mml:mtext>2</mml:mtext></mml:msub><mml:msub><mml:mtext>FD</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000D7;I</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>&#x003B3;&#x000A0;&#x0003C;FD</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mtext>&#x000A0;&#x000A0;</mml:mtext></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;+&#x003B2;</mml:mtext><mml:mtext>3</mml:mtext></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mtext>+&#x003BC;</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mtext>+&#x003B4;</mml:mtext><mml:mtext>t</mml:mtext></mml:msub><mml:msub><mml:mtext>+&#x003B5;</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>Similarly, Model (6) is obtained by taking the variable PS as the threshold variable, and the interpretation of each variable is the same as that in Model (5).</p>
<disp-formula id="E6"><label>(6)</label><mml:math id="M6"><mml:mtable class="eqnarray" columnalign="right center left"><mml:mtr><mml:mtd><mml:msub><mml:mtext>PH</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mtext>=&#x003B2;</mml:mtext><mml:mtext>0</mml:mtext></mml:msub><mml:msub><mml:mtext>+&#x003B2;</mml:mtext><mml:mtext>1</mml:mtext></mml:msub><mml:msub><mml:mtext>FD</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000D7;I</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>PS</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mo>&#x02264;</mml:mo><mml:mtext>&#x000A0;&#x003B3;</mml:mtext></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:msub><mml:mtext>+&#x003B2;</mml:mtext><mml:mtext>2</mml:mtext></mml:msub><mml:msub><mml:mtext>FD</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000D7;I</mml:mtext><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mtext>&#x003B3;&#x000A0;&#x0003C;PS</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mtext>&#x000A0;&#x000A0;</mml:mtext></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msub><mml:mtext>&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;&#x000A0;+&#x003B2;</mml:mtext><mml:mtext>3</mml:mtext></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mtext>+&#x003BC;</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mtext>+&#x003B4;</mml:mtext><mml:mtext>t</mml:mtext></mml:msub><mml:msub><mml:mtext>+&#x003B5;</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
</sec>
<sec>
<title>Mechanism Analysis Models</title>
<p>In Equation (3) above, we used the interaction term between public health expenditure and fiscal decentralization as the intermediary variable to obtain results determining whether or not it has a positive impact on public health. To achieve this, mediating effect analysis is adopted to analyze the mechanism. Intermediary effect analysis is a method that tests whether a variable becomes an intermediary variable and to what extent it plays an intermediary role in the process. Generally speaking, if variable X affects variable Y by affecting variable M, then variable M is an intermediary variable (<xref ref-type="bibr" rid="B29">29</xref>). Testing the product of coefficients is the core principal of the intermediary effect tests and assumes that coefficient &#x0201C;a&#x0201D; is the effect of the independent variable on the intermediate variable and that coefficient &#x0201C;b&#x0201D; is the impact of the intermediate variable on the dependent variable after controlling the influence of the independent variable. The Sobel test is a coefficient product test. It checks the existence of the mediating effect by calculating Sobel statistics &#x0201C;z&#x0201D;. &#x0201C;z&#x0201D; is computed by &#x0201C;ab&#x0201D; divided by the standard error of &#x0201C;ab,&#x0201D; which examines whether the product of &#x0201C;a, b&#x0201D; is significantly or not (<xref ref-type="bibr" rid="B30">30</xref>). Therefore, we constructed models based on the concept of the intermediary effect and utilized the Sobel test to verify whether public health as the intermediary variable produces an intermediary effect. At the same time, the number of beds in regional medical institutions and the number of medical practitioners per 1,000 people are introduced as intermediary variables, lnGDPave, Patent, and Urban are adopted as control variables to determine how the fiscal decentralization mechanism affects public health. Based on the theory and benchmark models above, the models for the mediating effect test are constructed below (<xref ref-type="bibr" rid="B31">31</xref>):</p>
<disp-formula id="E7"><label>(7)</label><mml:math id="M7"><mml:mtable class="eqnarray" columnalign="right center left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mtext>M</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000A0;=&#x000A0;</mml:mtext><mml:msub><mml:mtext>&#x003B2;</mml:mtext><mml:mtext>0</mml:mtext></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003B2;</mml:mtext></mml:mrow><mml:mtext>1</mml:mtext></mml:msub><mml:msub><mml:mrow><mml:mtext>FD</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003B2;</mml:mtext></mml:mrow><mml:mtext>2</mml:mtext></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000A0;+&#x000A0;</mml:mtext><mml:msub><mml:mtext>&#x003BC;</mml:mtext><mml:mtext>i</mml:mtext></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003C6;</mml:mtext></mml:mrow><mml:mtext>t</mml:mtext></mml:msub><mml:mtext>&#x000A0;+&#x000A0;</mml:mtext><mml:msub><mml:mi>&#x003B5;</mml:mi><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E8"><label>(8)</label><mml:math id="M8"><mml:mtable class="eqnarray" columnalign="right center left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mrow><mml:mtext>PH</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000A0;=&#x000A0;</mml:mtext><mml:msub><mml:mtext>&#x003B2;</mml:mtext><mml:mtext>0</mml:mtext></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003B2;</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mtext>M</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003B2;</mml:mtext></mml:mrow><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000A0;+&#x000A0;</mml:mtext><mml:msub><mml:mtext>&#x003BC;</mml:mtext><mml:mtext>i</mml:mtext></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003C6;</mml:mtext></mml:mrow><mml:mtext>t</mml:mtext></mml:msub><mml:mtext>&#x000A0;+&#x000A0;</mml:mtext><mml:msub><mml:mi>&#x003B5;</mml:mi><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<disp-formula id="E9"><label>(9)</label><mml:math id="M9"><mml:mtable class="eqnarray" columnalign="right center left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mrow><mml:mtext>PH</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mtext>&#x000A0;=&#x000A0;</mml:mtext><mml:msub><mml:mtext>&#x003B2;</mml:mtext><mml:mtext>0</mml:mtext></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003B2;</mml:mtext></mml:mrow><mml:mn>5</mml:mn></mml:msub><mml:msub><mml:mtext>M</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003B2;</mml:mtext></mml:mrow><mml:mn>6</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>FD</mml:mtext></mml:mrow><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003B2;</mml:mtext></mml:mrow><mml:mn>7</mml:mn></mml:msub><mml:msub><mml:mtext>X</mml:mtext><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mtext>&#x000A0;</mml:mtext><mml:msub><mml:mtext>&#x003BC;</mml:mtext><mml:mtext>i</mml:mtext></mml:msub><mml:msub><mml:mrow><mml:mtext>+&#x003C6;</mml:mtext></mml:mrow><mml:mtext>t</mml:mtext></mml:msub><mml:mtext>&#x000A0;+&#x000A0;</mml:mtext><mml:msub><mml:mi>&#x003B5;</mml:mi><mml:mrow><mml:mtext>it</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>
<p>where M is the intermediary variables PS, Tech, and Bed, X<sub>it</sub> represents a series of control variables consistent with those in the benchmark regression, FD<sub>it</sub> is fiscal revenue decentralization degree in province <italic>i</italic> and year <italic>t</italic> and PH<sub>it</sub> is the population mortality in province <italic>i</italic> and year <italic>t</italic>. If &#x003B2;<sub>1</sub>, &#x003B2;<sub>3</sub>, and &#x003B2;<sub>5</sub> are all significant, it suggests that fiscal decentralization promotes public health by affecting those intermediary variables.</p>
<p>Stata16 (of StataCorp, 4905 Lakeway Dr. College Station, TX77845, United States) was the statistical software used for all the analyses in this paper.</p>
</sec>
</sec>
</sec>
<sec sec-type="results" id="s3">
<title>Results</title>
<sec>
<title>Benchmark Regression</title>
<p><xref ref-type="table" rid="T3">Table 3</xref> illustrates the benchmark regression results of Equation (1) for public health expenditure (PS) and the results of Equations (2) to (3), which measured public health according to population mortality (PH).</p>
<table-wrap position="float" id="T3">
<label>Table 3</label>
<caption><p>Benchmark regression results.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th/>
<th valign="top" align="center" style="border-bottom: thin solid #000000;" colspan="2"><bold>PS</bold></th>
<th valign="top" align="center" style="border-bottom: thin solid #000000;" colspan="3"><bold>PH</bold></th>
</tr>
<tr>
<th/>
<th valign="top" align="center"><bold>Column (1) Model (1)</bold></th>
<th valign="top" align="center"><bold>Column (2) Model (1)</bold></th>
<th valign="top" align="center"><bold>Column (3) Model (2)</bold></th>
<th valign="top" align="center"><bold>Column (4) Model (2)</bold></th>
<th valign="top" align="center"><bold>Column (5) Model (3)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">FD</td>
<td valign="top" align="center">204.7639<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (4.36)</td>
<td valign="top" align="center">175.1637<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;</sup></xref> (2.03)</td>
<td valign="top" align="center">&#x02212;1.775053<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.97)</td>
<td valign="top" align="center">&#x02212;1.635604<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.63)</td>
<td valign="top" align="center">0.254947 (0.85)</td>
</tr>
<tr>
<td valign="top" align="left">lnGDPave</td>
<td/>
<td valign="top" align="center">118.4329 (0.67)</td>
<td/>
<td valign="top" align="center">1.387735<xref ref-type="table-fn" rid="TN3"><sup>&#x0002A;</sup></xref> (2.32)</td>
<td valign="top" align="center">0.9316115 (1.53)</td>
</tr>
<tr>
<td valign="top" align="left">Industry</td>
<td/>
<td valign="top" align="center">&#x02212;111.4985<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.36)</td>
<td/>
<td valign="top" align="center">&#x02212;0.13067 (&#x02212;0.83)</td>
<td valign="top" align="center">&#x02212;0.1142591 (&#x02212;0.66)</td>
</tr>
<tr>
<td valign="top" align="left">Urban</td>
<td/>
<td valign="top" align="center">15.9217<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (4.22)</td>
<td/>
<td valign="top" align="center">&#x02212;0.0386917<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.43)</td>
<td valign="top" align="center">&#x02212;0.060338<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;3.30)</td>
</tr>
<tr>
<td valign="top" align="left">Market</td>
<td/>
<td valign="top" align="center">44.14284<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (3.31)</td>
<td/>
<td valign="top" align="center">&#x02212;0.031523 (&#x02212;0.68)</td>
<td valign="top" align="center">&#x02212;0.017638 (-0.36)</td>
</tr>
<tr>
<td valign="top" align="left">Trade</td>
<td/>
<td valign="top" align="center">&#x02212;296.9658<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.89)</td>
<td/>
<td valign="top" align="center">0.0585157 (0.27)</td>
<td valign="top" align="center">&#x02212;0.066019 (&#x02212;0.32)</td>
</tr>
<tr>
<td valign="top" align="left">Patent</td>
<td/>
<td valign="top" align="center">&#x02212;57.82005<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.48)</td>
<td/>
<td valign="top" align="center">&#x02212;0.1169984 (&#x02212;1.33)</td>
<td valign="top" align="center">&#x02212;0.1752133<xref ref-type="table-fn" rid="TN2"><sup>&#x0002A;&#x0002A;</sup></xref> (&#x02212;1.94)</td>
</tr>
<tr>
<td valign="top" align="left">FD<sup>2</sup></td>
<td/>
<td/>
<td valign="top" align="center">0.6677871<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (4.04)</td>
<td valign="top" align="center">0.5963655<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (3.38)</td>
<td/>
</tr>
<tr>
<td valign="top" align="left">PS</td>
<td/>
<td/>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.0000269 (&#x02212;1.38)</td>
</tr>
<tr>
<td valign="top" align="left">FD &#x000D7; PS</td>
<td/>
<td/>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.001067<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.06)</td>
</tr>
<tr>
<td valign="top" align="left">Constant term</td>
<td valign="top" align="center">194.7079<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (6.99)</td>
<td valign="top" align="center">&#x02212;1460.97 (&#x02212;0.85)</td>
<td valign="top" align="center">6.710703<xref ref-type="table-fn" rid="TN1"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (25.13)</td>
<td valign="top" align="center">&#x02212;4.390332 (&#x02212;0.75)</td>
<td valign="top" align="center">4.979367 (0.82)</td>
</tr>
<tr>
<td valign="top" align="left">Samples</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">360</td>
<td valign="top" align="center">360</td>
</tr>
<tr>
<td valign="top" align="left">Control variables</td>
<td valign="top" align="center">Not controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Not controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
</tr>
<tr>
<td valign="top" align="left">Year and province effect</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
</tr>
<tr>
<td valign="top" align="left"><italic>R</italic><sup>2</sup></td>
<td valign="top" align="center">0.86</td>
<td valign="top" align="center">0.88</td>
<td valign="top" align="center">0.85</td>
<td valign="top" align="center">0.86</td>
<td valign="top" align="center">0.85</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="TN1"><p><italic>The columns report n(z-values); n refers to the coefficient of each term, z-values are in parentheses, and <sup>&#x0002A;&#x0002A;&#x0002A;</sup>p &#x0003C; 0.01</italic>,</p></fn>
<fn id="TN2"><label>&#x0002A;&#x0002A;</label><p><italic>p &#x0003C; 0.05</italic>,</p></fn> 
<fn id="TN3"><label>&#x0002A;</label><p><italic>p &#x0003C; 0.1</italic>.</p></fn> 
<p><italic>Control variables include lnGDPave, Industry, Urban, Market, Trade, and Patent</italic>.</p>
</table-wrap-foot>
</table-wrap>
<p>As presented in <xref ref-type="table" rid="T3">Table 3</xref>, regardless of whether the control variable is introduced or not, the coefficient of the effects of fiscal decentralization on public health expenditure is significantly positive at the 1% level (which means that there is a probability that the coefficient is false and is &#x0003C;1%), indicating that fiscal decentralization promotes the government public health expenditure. Additionally, it can be seen from Column (3) and (4) that fiscal decentralization has a significant negative effect on population mortality (at the level of 1%), which further proves the promotion effect that fiscal decentralization has on public health. The coefficient of FD is negative, but in contrast to the FD coefficient, the coefficient of the quadratic term of FD is significantly positive (at the 1% level). And the absolute value of the coefficient of FD<sup>2</sup> is smaller than that of FD, demonstrating the non-linear feature of the impact of fiscal decentralization on public health. In Column (5), the negative coefficients of the interaction terms in Equation (3) are significant, illustrating that fiscal decentralization can advance public health through increasing public health expenditure.</p>
</sec>
<sec>
<title>Robustness Check</title>
<p>In order to verify the robustness of the above regression results, the following robustness tests were conducted. Firstly, FED was used as an explanatory variable to replace FD to estimate Equations (1), (2), and (3). The results are demonstrated in <xref ref-type="table" rid="T4">Table 4</xref>. Secondly, we used the feasible generalized least squares (FGLS) estimation to deal with the problem of heteroscedasticity for the robustness test. The results are shown in columns (1), (3), and (4) of <xref ref-type="table" rid="T5">Table 5</xref>. Other studies emphasize the negative impact of air pollution on public health (<xref ref-type="bibr" rid="B32">32</xref>, <xref ref-type="bibr" rid="B33">33</xref>). However, environmental pollution can be represented by many existing control variables, such as industry and because population may also be affected by lnGDPave. However, in order to make the results more robust, we introduced air pollution and population as control variables into all of the models, and the results are illustrated in Columns (2), (5), and (6) in <xref ref-type="table" rid="T5">Table 5</xref>.</p>
<table-wrap position="float" id="T4">
<label>Table 4</label>
<caption><p>Robustness check results.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th/>
<th valign="top" align="center" style="border-bottom: thin solid #000000;" colspan="2"><bold>PS</bold></th>
<th valign="top" align="center" style="border-bottom: thin solid #000000;" colspan="3"><bold>PH</bold></th>
</tr>
<tr>
<th/>
<th valign="top" align="center"><bold>Column (1) Model (1)</bold></th>
<th valign="top" align="center"><bold>Column (2) Model (1)</bold></th>
<th valign="top" align="center"><bold>Column (3) Model (2)</bold></th>
<th valign="top" align="center"><bold>Column (4) Model (2)</bold></th>
<th valign="top" align="center"><bold>Column (5) Model (3)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">FED</td>
<td valign="top" align="center">154.0399<xref ref-type="table-fn" rid="TN4"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (3.09)</td>
<td valign="top" align="center">119.0458<xref ref-type="table-fn" rid="TN5"><sup>&#x0002A;&#x0002A;</sup></xref> (1.57)</td>
<td valign="top" align="center">&#x02212;2.081253<xref ref-type="table-fn" rid="TN4"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;3.14)</td>
<td valign="top" align="center">&#x02212;1.975881<xref ref-type="table-fn" rid="TN4"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.92)</td>
<td valign="top" align="center">0.0554069 (0.22)</td>
</tr>
<tr>
<td valign="top" align="left">FED<sup>2</sup></td>
<td/>
<td/>
<td valign="top" align="center">0.652546<xref ref-type="table-fn" rid="TN4"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (4.07)</td>
<td valign="top" align="center">0.621215<xref ref-type="table-fn" rid="TN4"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (3.74)</td>
<td/>
</tr>
<tr>
<td valign="top" align="left">FED &#x000D7; PS</td>
<td/>
<td/>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.001783<xref ref-type="table-fn" rid="TN4"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.80)</td>
</tr>
<tr>
<td valign="top" align="left">Control variables</td>
<td valign="top" align="center">Not controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Not controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
</tr>
<tr>
<td valign="top" align="left">Year and province effect</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
</tr>
<tr>
<td valign="top" align="left"><italic>R</italic><sup>2</sup></td>
<td valign="top" align="center">0.88</td>
<td valign="top" align="center">0.88</td>
<td valign="top" align="center">0.85</td>
<td valign="top" align="center">0.86</td>
<td valign="top" align="center">0.85</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="TN4"><p><italic>The columns report n (z-values); n refers to coefficient of each term, z-values are in parentheses, and <sup>&#x0002A;&#x0002A;&#x0002A;</sup>p &#x0003C; 0.01</italic>,</p></fn> 
<fn id="TN5"><label>&#x0002A;&#x0002A;</label><p><italic>p &#x0003C; 0.05</italic>,</p></fn> 
<p><italic><sup>&#x0002A;</sup>p &#x0003C; 0.1</italic>.</p> 
<p><italic>Control variables include lnGDPave, Industry, Urban, Market, Trade, and Patent</italic>.</p>
</table-wrap-foot>
</table-wrap>
<table-wrap position="float" id="T5">
<label>Table 5</label>
<caption><p>More control variable results using FGLS.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th/>
<th valign="top" align="center" style="border-bottom: thin solid #000000;" colspan="2"><bold>PS</bold></th>
<th valign="top" align="center" style="border-bottom: thin solid #000000;" colspan="3"><bold>PH</bold></th>
</tr>
<tr>
<th/>
<th valign="top" align="center"><bold>Column (1) Model (1)</bold></th>
<th valign="top" align="center"><bold>Column (2) Model (1)</bold></th>
<th valign="top" align="center"><bold>Column (3) Model (2)</bold></th>
<th valign="top" align="center"><bold>Column (4) Model (3)</bold></th>
<th valign="top" align="center"><bold>Column (5) Model (2)</bold></th>
<th valign="top" align="center"><bold>Column (6) Model (3)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">FD</td>
<td valign="top" align="center">17.65036<xref ref-type="table-fn" rid="TN7"><sup>&#x0002A;&#x0002A;</sup></xref> (1.88)</td>
<td valign="top" align="center">174.2401<xref ref-type="table-fn" rid="TN6"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (2.74)</td>
<td valign="top" align="center">&#x02212;1.08911<xref ref-type="table-fn" rid="TN6"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;3.78)</td>
<td valign="top" align="center">0.27909 (1.79)</td>
<td valign="top" align="center">&#x02212;1.168549<xref ref-type="table-fn" rid="TN7"><sup>&#x0002A;&#x0002A;</sup></xref> (&#x02212;1.97)</td>
<td valign="top" align="center">0.3031356 (1.02)</td>
</tr>
<tr>
<td valign="top" align="left">FD<sup>2</sup></td>
<td/>
<td/>
<td valign="top" align="center">0.413459<xref ref-type="table-fn" rid="TN6"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (3.82)</td>
<td/>
<td valign="top" align="center">0.451718<xref ref-type="table-fn" rid="TN6"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (2.51)</td>
<td/>
</tr>
<tr>
<td valign="top" align="left">FD &#x000D7; PS</td>
<td/>
<td/>
<td/>
<td valign="top" align="center">&#x02212;0.00209<xref ref-type="table-fn" rid="TN6"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;6.21)</td>
<td/>
<td valign="top" align="center">&#x02212;0.00108<xref ref-type="table-fn" rid="TN7"><sup>&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.19)</td>
</tr>
<tr>
<td valign="top" align="left">Control</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
</tr>
<tr>
<td valign="top" align="left">variables</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="TN6"><p><italic>The columns report n(z-values); n refers to coefficient of each term, z-values are in parentheses, and <sup>&#x0002A;&#x0002A;&#x0002A;</sup>p &#x0003C; 0.01</italic>,</p></fn> 
<fn id="TN7"><label>&#x0002A;&#x0002A;</label><p><italic>p &#x0003C; 0.05</italic>,</p></fn> 
<p><italic><sup>&#x0002A;</sup>p &#x0003C; 0.1</italic>.</p>
<p><italic>Control variables in Columns (1), (3), and (4) include lnGDPave, Industry, Urban, Market, Trade, and Patent, and the control variables in (2), (5), and (6) include lnGDPave, Industry, Urban, Market, Trade, Patent, Pop, and Pollution</italic>.</p>
</table-wrap-foot>
</table-wrap>
<p>As indicated in <xref ref-type="table" rid="T4">Tables 4</xref>, <xref ref-type="table" rid="T5">5</xref>, no matter which method is used to test the robustness of benchmark regression, the magnitude and sign of the coefficients of the main explanatory variables are the same as those of the benchmark regression, showing that fiscal decentralization has positive effect on public health expenditure, that fiscal decentralization also exerts a non-linear favorable effect on public health. Fiscal decentralization can affect public health by increasing public health expenditure. The benchmark regression passed the robustness test and thus, the results are considered valid.</p>
</sec>
<sec>
<title>Mechanism Analysis</title>
<p>The results of the Sobel test are presented in <xref ref-type="table" rid="T6">Table 6</xref>.</p>
<table-wrap position="float" id="T6">
<label>Table 6</label>
<caption><p>Sobel test results.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Variable</bold></th>
<th valign="top" align="left"><bold>Project</bold></th>
<th valign="top" align="center"><bold>coefficient</bold></th>
<th valign="top" align="center"><bold>standard deviation</bold></th>
<th valign="top" align="center"><bold><italic>Z</italic>-value/<italic>T</italic>-value</bold></th>
<th valign="top" align="center"><bold><italic>P</italic>&#x0003E;|<italic>Z</italic>|/<italic>P</italic>&#x0003E;|<italic>t</italic>|</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">PS</td>
<td valign="top" align="left">Sobel value</td>
<td valign="top" align="center">&#x02212;0.276338</td>
<td valign="top" align="center">0.03416027</td>
<td valign="top" align="center">&#x02212;8.089</td>
<td valign="top" align="center">6.661e-16</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Direct effect</td>
<td valign="top" align="center">&#x02212;0.28588</td>
<td valign="top" align="center">0.1533915</td>
<td valign="top" align="center">&#x02212;1.86</td>
<td valign="top" align="center">0.063</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Total effect</td>
<td valign="top" align="center">&#x02212;0.56222</td>
<td valign="top" align="center">0.1569531</td>
<td valign="top" align="center">&#x02212;3.58</td>
<td valign="top" align="center">0.000</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Proportion of intermediary effect</td>
<td valign="top" align="center" colspan="4">49.15%</td>
</tr>
<tr>
<td valign="top" align="left">Bed</td>
<td valign="top" align="left">Sobel value</td>
<td valign="top" align="center">&#x02212;0.338111</td>
<td valign="top" align="center">0.01692059</td>
<td valign="top" align="center">&#x02212;19.98</td>
<td valign="top" align="center">0.000</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Direct effect</td>
<td valign="top" align="center">&#x02212;0.493609</td>
<td valign="top" align="center">0.1192244</td>
<td valign="top" align="center">&#x02212;4.14</td>
<td valign="top" align="center">0.000</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Total effect</td>
<td valign="top" align="center">&#x02212;0.83172</td>
<td valign="top" align="center">0.1202742</td>
<td valign="top" align="center">&#x02212;6.92</td>
<td valign="top" align="center">0.000</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Proportion of intermediary effect</td>
<td valign="top" align="center" colspan="4">40.65%</td>
</tr>
<tr>
<td valign="top" align="left">Tech</td>
<td valign="top" align="left">Sobel value</td>
<td valign="top" align="center">&#x02212;0.017398</td>
<td valign="top" align="center">0.00677149</td>
<td valign="top" align="center">&#x02212;2.569</td>
<td valign="top" align="center">0.010</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Direct effect</td>
<td valign="top" align="center">&#x02212;0.544824</td>
<td valign="top" align="center">0.1573193</td>
<td valign="top" align="center">&#x02212;3.46</td>
<td valign="top" align="center">0.001</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Total effect</td>
<td valign="top" align="center">&#x02212;0.562221</td>
<td valign="top" align="center">0.1569531</td>
<td valign="top" align="center">&#x02212;3.58</td>
<td valign="top" align="center">0.000</td>
</tr>
<tr>
<td/>
<td valign="top" align="left">Proportion of intermediary effect</td>
<td valign="top" align="center" colspan="4">3.09%</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>As shown in <xref ref-type="table" rid="T6">Table 6</xref>, the three intermediary variables passed the intermediary effect test at the 1% level, with the intermediary variables having a negative impact on population mortality. The intermediary effect of public health expenditure accounts for its largest proportion, up to 49.15%, which is significantly mutually confirmed with the previous interaction term in Equation (3). Similarly, the number of medical beds account for 40.65%, and the number of medical practitioners also have a significant impact, accounting for 3.09%. <xref ref-type="fig" rid="F4">Figure 4</xref> illustrates the flow of the mechanism effects.</p>
<fig id="F4" position="float">
<label>Figure 4</label>
<caption><p>Mechanism flow chart.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fpubh-10-773728-g0004.tif"/>
</fig>
</sec>
<sec>
<title>Heterogeneity Analysis</title>
<p><xref ref-type="fig" rid="F5">Figures 5</xref>, <xref ref-type="fig" rid="F6">6</xref> show regional distribution differences in terms of provincial population mortality and the fiscal decentralization level in China in 2008 and 2019, respectively. No data were available for Tibet and Taiwan. The darker the color, the higher the population mortality, and the worse the public health level.</p>
<fig id="F5" position="float">
<label>Figure 5</label>
<caption><p>Provincial differences in PH and FD in 2008.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fpubh-10-773728-g0005.tif"/>
</fig>
<fig id="F6" position="float">
<label>Figure 6</label>
<caption><p>Provincial differences in PH and FD in 2019.</p></caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fpubh-10-773728-g0006.tif"/>
</fig>
<p><xref ref-type="fig" rid="F5">Figures 5</xref>, <xref ref-type="fig" rid="F6">6</xref> suggest that there are differences in the population mortality and degree of fiscal decentralization between coastal and inland cities. Therefore, we categorized the 30 provinces into coastal and inland areas. Coastal areas include Hebei, Liaoning, Tianjin, Shandong, Zhejiang, Shanghai, Fujian, Jiangsu, Guangdong, Hainan, and Guangxi. In addition, according to the traditional east&#x02013;west division method, we also divided them into east (Tianjin, Beijing, Hebei, Shanghai, Liaoning, Jiangsu, Fujian, Zhejiang, Shandong, Hainan and Guangdong), west (Sichuan, Gansu, Qinghai, Yunnan, Guizhou, Chongqing, Shaanxi, Xinjiang, Ningxia, Guangxi, Inner Mongolia) and central (Shanxi, Heilongjiang, Anhui, Henan, Hunan, Hubei, Hebei, Jiangxi) regions (<xref ref-type="bibr" rid="B34">34</xref>). Using these categorizations, we applied Equation 2 for regression. The regression results are shown in <xref ref-type="table" rid="T7">Table 7</xref>.</p>
<table-wrap position="float" id="T7">
<label>Table 7</label>
<caption><p>Regional regression results.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th/>
<th valign="top" align="center"><bold>Coastal areas</bold></th>
<th valign="top" align="center"><bold>Inland areas</bold></th>
<th valign="top" align="center"><bold>Eastern regions</bold></th>
<th valign="top" align="center"><bold>Central/western regions</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">FD</td>
<td valign="top" align="center">&#x02212;0.4044268<xref ref-type="table-fn" rid="TN8"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.89)</td>
<td valign="top" align="center">&#x02212;0.579207<xref ref-type="table-fn" rid="TN8"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;3.86)</td>
<td valign="top" align="center">&#x02212;1.056453<xref ref-type="table-fn" rid="TN8"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;67.82)</td>
<td valign="top" align="center">&#x02212;0.1241495 (&#x02212;0.42)</td>
</tr>
<tr>
<td valign="top" align="left">Control variable</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
</tr>
<tr>
<td valign="top" align="left">Province and time effect</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Controlled</td>
</tr>
<tr>
<td valign="top" align="left">Number of samples</td>
<td valign="top" align="center">132</td>
<td valign="top" align="center">228</td>
<td valign="top" align="center">132</td>
<td valign="top" align="center">228</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p><italic>z-values are in parentheses</italic>,</p>
<fn id="TN8"><label>&#x0002A;&#x0002A;&#x0002A;</label><p><italic>p &#x0003C; 0.01</italic>,</p></fn><p><italic><sup>&#x0002A;&#x0002A;</sup>p &#x0003C; 0.05</italic>,</p> 
<p><italic><sup>&#x0002A;</sup>p &#x0003C; 0.1</italic>.</p>
</table-wrap-foot>
</table-wrap>
<p>The results illustrate that fiscal decentralization in inland cities plays a larger role in improving the level of public health compared to coastal areas. However, no significant differences were observed in the impacts of fiscal decentralization on the level of public health between eastern and western cities.</p>
<p>Unexpectedly, the fiscal decentralization of inland provinces better inhibits population mortality compared to coastal regions. The reasons for this may be that the economies of coastal cities are relatively more developed and that the fiscal decentralization level is better established. During the threshold effect analysis (further explained below), we found that when fiscal decentralization reaches a certain degree, its promotion effect on local public health will be weakened. Another important factor to highlight is that the populations of inland Chinese regions are generally smaller than those found in other parts of the country, so the population mortality statistics may be biased (<xref ref-type="bibr" rid="B35">35</xref>). For the central and western regions, the coefficient is not significant. This is because eastern regions and coastal areas were at the forefront of the reform and opening up (which has been one of China&#x00027;s national policies since 1978), resulting in a stronger economic foundation. The central and western cities have a lower population density and lower industrial aggregation, so the role that fiscal decentralization plays in public health may be weaker.</p>
</sec>
<sec>
<title>Threshold Effect Analysis</title>
<p>In addition to the verification of a non-linear relationship between fiscal decentralization and public health in the previous sections, a threshold effect analysis was conducted on FD and PS to further understand the non-linear effect of fiscal decentralization on public health. The results of the threshold effect test are presented in <xref ref-type="table" rid="T8">Table 8</xref>.</p>
<table-wrap position="float" id="T8">
<label>Table 8</label>
<caption><p>Threshold existence test.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Threshold variables</bold></th>
<th valign="top" align="center"><bold>Threshold number</bold></th>
<th valign="top" align="center"><bold>Threshold estimator</bold></th>
<th valign="top" align="center"><bold>Bootstrap times</bold></th>
<th valign="top" align="center"><bold>F-stat</bold></th>
<th valign="top" align="center"><bold>prob</bold></th>
<th valign="top" align="center" style="border-bottom: thin solid #000000;" colspan="3"><bold>Critical value</bold></th>
</tr>
<tr>
<th/>
<th/>
<th/>
<th/>
<th/>
<th/>
<th valign="top" align="center"><bold>1%</bold></th>
<th valign="top" align="center"><bold>5%</bold></th>
<th valign="top" align="center"><bold>10%</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">FD</td>
<td valign="top" align="center">Single</td>
<td valign="top" align="center">2.0361</td>
<td valign="top" align="center">500</td>
<td valign="top" align="center">30.35</td>
<td valign="top" align="center">0.004</td>
<td valign="top" align="center">36.0683</td>
<td valign="top" align="center">27.5463</td>
<td valign="top" align="center">22.7376</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">Double</td>
<td valign="top" align="center">1.1932</td>
<td valign="top" align="center">500</td>
<td valign="top" align="center">18.46</td>
<td valign="top" align="center">0.170</td>
<td valign="top" align="center">71.3974</td>
<td valign="top" align="center">44.3315</td>
<td valign="top" align="center">27.9452</td>
</tr>
<tr>
<td valign="top" align="left">PS</td>
<td valign="top" align="center">Single</td>
<td valign="top" align="center">135.1796</td>
<td valign="top" align="center">500</td>
<td valign="top" align="center">41.37</td>
<td valign="top" align="center">0.008</td>
<td valign="top" align="center">38.8815</td>
<td valign="top" align="center">28.5789</td>
<td valign="top" align="center">24.2140</td>
</tr>
<tr>
<td/>
<td valign="top" align="center">Double</td>
<td valign="top" align="center">140.4184</td>
<td valign="top" align="center">500</td>
<td valign="top" align="center">&#x02212;0.32</td>
<td valign="top" align="center">1.000</td>
<td valign="top" align="center">37.2183</td>
<td valign="top" align="center">27.2670</td>
<td valign="top" align="center">22.1377</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>As is illustrated in <xref ref-type="table" rid="T8">Table 8</xref>, there is a single threshold effect with both variables FD and PS acting as threshold variables. Therefore, threshold effect regression was applied on Models (5) and (6), as shown in <xref ref-type="table" rid="T9">Table 9</xref>.</p>
<table-wrap position="float" id="T9">
<label>Table 9</label>
<caption><p>Results of the panel threshold effect regression test.</p></caption>
<table frame="hsides" rules="groups">
<thead><tr>
<th valign="top" align="left"><bold>Variables</bold></th>
<th valign="top" align="center"><bold>Model (5)</bold></th>
<th valign="top" align="center"><bold>Variables</bold></th>
<th valign="top" align="center"><bold>Model (6)</bold></th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">FD (FD &#x02264;2.0361)</td>
<td valign="top" align="center">&#x02212;2.240428<xref ref-type="table-fn" rid="TN9"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;4.89)</td>
<td valign="top" align="center">FD (PS &#x02264;135.1796)</td>
<td valign="top" align="center">&#x02212;1.252698<xref ref-type="table-fn" rid="TN9"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;2.66)</td>
</tr>
<tr>
<td valign="top" align="left">FD (2.0361 &#x0003C; FD)</td>
<td valign="top" align="center">&#x02212;2.740643<xref ref-type="table-fn" rid="TN9"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;5.63)</td>
<td valign="top" align="center">FD (135.1796 &#x0003C; PS)</td>
<td valign="top" align="center">&#x02212;1.608206<xref ref-type="table-fn" rid="TN9"><sup>&#x0002A;&#x0002A;&#x0002A;</sup></xref> (&#x02212;3.52)</td>
</tr>
<tr>
<td valign="top" align="left">Control variable</td>
<td valign="top" align="center">Controlled</td>
<td valign="top" align="center">Control variable</td>
<td valign="top" align="center">Controlled</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="TN9"><p><italic>z-values are in parentheses, <sup>&#x0002A;&#x0002A;&#x0002A;</sup>p &#x0003C; 0.01</italic>,</p></fn> 
<p><italic><sup>&#x0002A;&#x0002A;</sup>p &#x0003C; 0.05</italic>,</p> 
<p><italic><sup>&#x0002A;</sup>p &#x0003C; 0.1</italic>.</p>
</table-wrap-foot>
</table-wrap>
<p><xref ref-type="table" rid="T9">Table 9</xref> indicates that regardless of whether FD or PS is adopted as the threshold variable, after crossing a certain value, that is, when FD is &#x0003E;2.0361 or PS is &#x0003E;135.1796, the absolute value of the coefficient of core explanatory variable FD becomes larger, implying that FD can inhibit population mortality. On the other hand, the results of the threshold effect regression test also indicate that regardless of the level of FD and PS, FD always shows a negative correlation with population mortality, which again verifies that providing further fiscal decentralization to local governments will promote the improvement of local health.</p>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>Discussion</title>
<p>In recent years, scholars have conducted a lot of research on the impacts of fiscal decentralization on economic development. However, there is little research on the impact of fiscal decentralization on public health. The impact of fiscal decentralization on public goods has been a contested topic since it was first proposed. It was first proposed by Tiebout (<xref ref-type="bibr" rid="B36">36</xref>) and Oates (<xref ref-type="bibr" rid="B37">37</xref>), who formulated &#x0201C;voting by foot&#x0201D; theory, where residents can freely choose to settle in places where their public goods and tax burden needs are better provided by local governments. These scholars believed that local governments understand the preferences of local residents better than the central government, making them better positioned to provide public goods and services to their populations. However, scholars such as Weingast (<xref ref-type="bibr" rid="B38">38</xref>) believe that fiscal decentralization has an adverse impact on the supply of public goods (<xref ref-type="bibr" rid="B39">39</xref>). That is, fiscal decentralization enables local governments to compete for scarce capital and labor, increase the number of economic public goods, and then squeezes out the expenditure of non-economic public goods (<xref ref-type="bibr" rid="B40">40</xref>). Such decentralization skeptics worry that there would be destructive interregional competition among local governments, which may reduce expenditure or relax regulations; hence, they might not be able to fully provide basic public services (<xref ref-type="bibr" rid="B41">41</xref>). Despite these arguments, other scholars such as Khaleghian (<xref ref-type="bibr" rid="B42">42</xref>), Cantarero and Pascual (<xref ref-type="bibr" rid="B43">43</xref>), and Uchimura and J&#x000FC;tting (<xref ref-type="bibr" rid="B44">44</xref>) argue that fiscal decentralization could improve access to health services. In recent years, some studies in the literature have examined the impact of fiscal decentralization on various population health indicators, such as infant mortality, life expectancy, or immunization coverage, and found that fiscal decentralization had a beneficial impact on public health (<xref ref-type="bibr" rid="B45">45</xref>). In addition, Uchimura and J&#x000FC;tting (<xref ref-type="bibr" rid="B44">44</xref>) found that county-level fiscal decentralization in China was significantly associated with low infant mortality from 1995 to 2001.</p>
<p>The main argument surrounding fiscal decentralization theory is whether fiscal decentralization can improve public welfare. The first generation of decentralization theories hold that local governments are more efficient in supplying certain public goods, improving public welfare levels (<xref ref-type="bibr" rid="B46">46</xref>). Starting from public choice theory, the second generation of fiscal decentralization theories hold that the government does not start with the goal of maximizing resident welfare (<xref ref-type="bibr" rid="B47">47</xref>, <xref ref-type="bibr" rid="B48">48</xref>), and that especially in countries with an imperfect democratic constitutional system, the competition between local governments under fiscal decentralization cannot improve the level of public welfare and may instead lead to a decline in or even the deterioration of the level of public welfare (<xref ref-type="bibr" rid="B49">49</xref>).</p>
<p>Jim&#x000E9;nez-Rubio et al. (<xref ref-type="bibr" rid="B45">45</xref>) used infant mortality as the public health index and drew the conclusion that fiscal decentralization can only have a significant positive impact on public health if local governments are provided with a large amount of financial autonomy. Hao et al. (<xref ref-type="bibr" rid="B50">50</xref>) used panel data from 23 provinces in China from 2002 to 2012 and using a simultaneous equation model to analyze the data, found that fiscal decentralization has both direct and indirect negative impacts on public health. However, the 2002&#x02013;2012 panel data used by Hao et al. (<xref ref-type="bibr" rid="B50">50</xref>) was based on the economic development that took place when local Chinese governments were placing emphasis on GDP and ignoring expenditure on public goods.</p>
<p>The primary aim of this study was to investigate the (non-linear) effect of fiscal decentralization on public health. The empirical results verified that fiscal decentralization plays a significant role in promoting public health expenditure. With greater financial autonomy, local governments have the capacity to directly increase expenditure in the public health areas that are relevant to the needs of the people in each region since local governments have a better understanding of local issues. Additionally, when the interaction terms of fiscal decentralization and public health spending are introduced, the results show that the coefficient of the interaction term is negative, even though the coefficient of FD is always insignificant in the results. Therefore, what is important is the coefficient of the interaction term. We also established that fiscal decentralization does promote public health by increasing public health expenditure. Based on these results, the intermediary test and threshold effect analysis outcomes show that fiscal decentralization promotes public health through public health expenditure and improves local medical services. At the same time, the effect of fiscal decentralization on public health presents non-linear changes with the changes in the threshold variables of fiscal decentralization and public health expenditure.</p>
<p>The results of this study are different from those obtained in previous studies. Other literature suggests that fiscal decentralization has a negative effect on public health outcomes (<xref ref-type="bibr" rid="B51">51</xref>). No previous studies have examined the non-linear relationship between fiscal decentralization and public health. The awareness that Chinese people have about public health and public health measures has improved significantly (<xref ref-type="bibr" rid="B52">52</xref>). The performance criteria of local governments are now not only focused on simple economic indicators such as GDP, but also on other indicators such as environmental pollution (<xref ref-type="bibr" rid="B53">53</xref>). The Central Committee and the central government of China now pay more attention to people&#x00027;s livelihoods, especially the health of the people in the country (<xref ref-type="bibr" rid="B54">54</xref>). Local governments have also paid more attention to public health issues and have created interventions with stricter monitoring measures (<xref ref-type="bibr" rid="B55">55</xref>). Since fiscal decentralization has brought greater economic autonomy to local governments, the local governments have consequently paid more attention to public health intervention programs that have been largely developed in response to the demands of local residents for a better quality of health.</p>
<p>A number of research limitations have been identified in this study. First, in the robustness test, indicators such as maternal mortality [which is also a widely used indicator to measure public health (<xref ref-type="bibr" rid="B56">56</xref>)] were not used to replace population mortality as a measurement of public health. Second, other models, such as panel smooth transition regression (PSTR), were not used to study the non-linear relationship, so there may be bias in terms of model selection. Thirdly, using the commonly used intermediary effect test in mechanism analysis means that many of the key mechanisms of fiscal decentralization affecting public health are likely to be missed. Fourthly, compared to the city-level or county-level panel data, the sample used in the present study is not representative of the population. Micro-level panel data in the regions would have more accuracy. Finally, the results obtained from the heterogeneity analysis cannot be explained. Since various robustness tests were conducted, these shortcomings have essentially been attenuated if not eliminated. In future research, we can further study the impact of fiscal decentralization on public health at the city or at more micro levels or the impact of fiscal decentralization on specific types of diseases, such as chronic conditions, particularly non-communicable diseases. The control and prevention of chronic diseases may be closely related to local health expenditure. In addition, we can examine the impact of fiscal decentralization on the differences in the public health level between urban and rural areas. It will also be interesting to determine whether fiscal decentralization aggravates the unequal distribution of healthcare resources to study the connection between fiscal decentralization and the supply of public health and local health resources.</p>
</sec>
<sec id="s5">
<title>Conclusions and Policy Recommendations</title>
<p>Based on the above results, this paper draws the following conclusions: (1) fiscal decentralization can increase the level of regional fiscal health expenditure; (2) fiscal decentralization promotes public health by increasing public health expenditure and improving regional medical resources, such as beds in medical institutions and medical personnel; and (3) the positive effect of fiscal decentralization on public health is non-linear and is affected by fiscal decentralization and public expenditure.</p>
<p>There are several policy implications for the findings of this study: China&#x00027;s public health expenditure still does not comply with the requirements of the WHO (<xref ref-type="bibr" rid="B57">57</xref>). The WHO health expenditure targets require an upper-middle-income country to ensure financial health protection at an adequate level, meaning that at least 6.7% of GDP should be allocated to public health spending (<xref ref-type="bibr" rid="B58">58</xref>). However, based on the WHO&#x00027;s Global Health Expenditure Database (<xref ref-type="bibr" rid="B59">59</xref>), during 2008&#x02013;2019, China, an upper-middle-income country, does not exceed 5% of GDP. The government should therefore continue to increase its public health expenditure, and, when necessary, legislate to clarify the proportion of GDP required for public health investment, as is the case for education. Post Covid-19, the public health system still needs to be continuously improved to adequately respond to all major challenges. The central government should continue to increase and protect fiscal decentralization. For example, it should improve the degree of decentralization through fiscal and taxation tools. When promoting fiscal decentralization, the government should refine the scope of its central and local expenditure responsibilities, create an environment for fairness and openness, and refine the responsibilities of local government in terms of public service expenditure in the process of fiscal decentralization. In the process of deepening fiscal decentralization and expanding local fiscal autonomy, local governments should be thoroughly invested in serving the people and should listen to the real needs of the people. Additionally, financial resources should be used to continuously improve people&#x00027;s living conditions as well as to improve people&#x00027;s health.</p>
</sec>
<sec sec-type="data-availability" id="s6">
<title>Data Availability Statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.</p>
</sec>
<sec id="s7">
<title>Author Contributions</title>
<p>WX conceived the concept, designed and conducted empirical analysis, and wrote the paper. JL collected data and helped conducting the empirical research revising and editing the paper as well as making the graphs and tables. All authors read, revised, and approved to the submitted version of the manuscript.</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="s8">
<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>
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