<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.2 20190208//EN" "http://jats.nlm.nih.gov/publishing/1.2/JATS-journalpublishing1.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.2" xml:lang="en">
    <front>
        <journal-meta>
            <journal-id journal-id-type="pmc">F1000Research</journal-id>
            <journal-title-group>
                <journal-title>F1000Research</journal-title>
            </journal-title-group>
            <issn pub-type="epub">2046-1402</issn>
            <publisher>
                <publisher-name>F1000 Research Limited</publisher-name>
                <publisher-loc>London, UK</publisher-loc>
            </publisher>
        </journal-meta>
        <article-meta>
            <article-id pub-id-type="doi">10.12688/f1000research.162864.1</article-id>
            <article-categories>
                <subj-group subj-group-type="heading">
                    <subject>Research Article</subject>
                </subj-group>
                <subj-group>
                    <subject>Articles</subject>
                </subj-group>
            </article-categories>
            <title-group>
                <article-title>Contrafactual analysis: Comparing voucher systems with taxes, subsidies, and public spending to reduce income inequality</article-title>
                <fn-group content-type="pub-status">
                    <fn>
                        <p>[version 1; peer review: 1 approved with reservations]</p>
                    </fn>
                </fn-group>
            </title-group>
            <contrib-group>
                <contrib contrib-type="author" corresp="yes">
                    <name>
                        <surname>Pacheco-Jaramillo</surname>
                        <given-names>William Alejandro</given-names>
                    </name>
                    <role content-type="http://credit.niso.org/">Data Curation</role>
                    <role content-type="http://credit.niso.org/">Formal Analysis</role>
                    <role content-type="http://credit.niso.org/">Investigation</role>
                    <role content-type="http://credit.niso.org/">Methodology</role>
                    <role content-type="http://credit.niso.org/">Software</role>
                    <role content-type="http://credit.niso.org/">Writing &#x2013; Original Draft Preparation</role>
                    <uri content-type="orcid">https://orcid.org/0000-0002-4208-5546</uri>
                    <xref ref-type="corresp" rid="c1">a</xref>
                    <xref ref-type="aff" rid="a1">1</xref>
                </contrib>
                <contrib contrib-type="author" corresp="no">
                    <name>
                        <surname>Malliaros</surname>
                        <given-names>Peter</given-names>
                    </name>
                    <role content-type="http://credit.niso.org/">Conceptualization</role>
                    <role content-type="http://credit.niso.org/">Project Administration</role>
                    <role content-type="http://credit.niso.org/">Supervision</role>
                    <role content-type="http://credit.niso.org/">Validation</role>
                    <role content-type="http://credit.niso.org/">Visualization</role>
                    <role content-type="http://credit.niso.org/">Writing &#x2013; Review &amp; Editing</role>
                    <uri content-type="orcid">https://orcid.org/0000-0001-7947-9015</uri>
                    <xref ref-type="aff" rid="a2">2</xref>
                </contrib>
                <aff id="a1">
                    <label>1</label>Economics, University Anahuac Mexico, Huixquilucan de Degollado, State of Mexico, Mexico</aff>
                <aff id="a2">
                    <label>2</label>Research, UrCommunity Ltd, Melbourne, Victoria, 3051, Australia</aff>
            </contrib-group>
            <author-notes>
                <corresp id="c1">
                    <label>a</label>
                    <email xlink:href="mailto:alejandro.pachecoj@anahuac.mx">alejandro.pachecoj@anahuac.mx</email>
                </corresp>
                <fn fn-type="conflict">
                    <p>No competing interests were disclosed.</p>
                </fn>
            </author-notes>
            <pub-date pub-type="epub">
                <day>15</day>
                <month>4</month>
                <year>2025</year>
            </pub-date>
            <pub-date pub-type="collection">
                <year>2025</year>
            </pub-date>
            <volume>14</volume>
            <elocation-id>439</elocation-id>
            <history>
                <date date-type="accepted">
                    <day>21</day>
                    <month>3</month>
                    <year>2025</year>
                </date>
            </history>
            <permissions>
                <copyright-statement>Copyright: &#x00a9; 2025 Pacheco-Jaramillo WA and Malliaros P</copyright-statement>
                <copyright-year>2025</copyright-year>
                <license xlink:href="https://creativecommons.org/licenses/by/4.0/">
                    <license-p>This is an open access article distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
                </license>
            </permissions>
            <self-uri content-type="pdf" xlink:href="https://f1000research.com/articles/14-439/pdf"/>
            <abstract>
                <sec>
                    <title>Background</title>
                    <p>This study examines how voucher systems compare to traditional redistributive policies&#x2014;such as progressive taxation, subsidies, and public spending&#x2014;in reducing income inequality.</p>
                </sec>
                <sec>
                    <title>Methods</title>
                    <p>We apply a counterfactual analysis approach, using panel data from twelve countries over 22 years. By employing econometric modelling, we simulate a series of &#x201c;what-if&#x201d; scenarios to assess the impact of each policy on the Gini coefficient, a key measure of income inequality.</p>
                </sec>
                <sec>
                    <title>Results</title>
                    <p>The results suggest that voucher systems can be particularly effective at targeting essential services, like education and healthcare, improving access for lower-income groups, and helping to reduce inequality. Public spending on education and healthcare proves to be incredibly potent in narrowing income disparities. These sectors are vital for addressing systemic inequalities, improving overall access and providing long-term benefits to disadvantaged groups. In contrast, progressive taxation and subsidies show mixed effectiveness. While higher tax revenues often correlate with reduced inequality, their impacts vary across countries and contexts. The effectiveness of progressive taxation depends on factors such as the efficiency of tax systems and the political environment, which can influence how well these policies work. Similarly, subsidies generally produce only modest or inconsistent reductions in income gaps, suggesting that while they provide temporary relief, they do not always address the root causes of inequality.</p>
                </sec>
                <sec>
                    <title>Conclusions</title>
                    <p>These findings suggest that well-designed voucher programs, when combined with progressive taxation and strategic public spending, can play a key role in enhancing redistribution efforts. By improving access to essential services and targeting lower-income groups, vouchers have the potential to reduce income inequality. However, achieving equitable economic outcomes requires careful policy design and attention to the broader economic context.</p>
                </sec>
            </abstract>
            <kwd-group kwd-group-type="author">
                <kwd>Voucher Systems (D63)</kwd>
                <kwd>Income Inequality (D63)</kwd>
                <kwd>Progressive Taxation (H24)</kwd>
                <kwd>Public Spending (H52)</kwd>
                <kwd>Contrafactual Analysis (C14)</kwd>
                <kwd>Redistributive Policies (H23)</kwd>
            </kwd-group>
            <funding-group>
                <funding-statement>The author(s) declared that no grants were involved in supporting this work.</funding-statement>
            </funding-group>
        </article-meta>
    </front>
    <body>
        <sec id="sec5" sec-type="intro">
            <title>Introduction</title>
            <p>Income inequality is one of those enduring issues that policymakers cannot seem to shake. It is more than just an economic puzzle&#x2014;it touches on fairness, opportunity, and social peace questions. Over the years, different governments have pinned their hopes on strategies like progressive taxation, subsidies, and hefty public budgets. While these measures have sometimes helped, they often get tangled in inefficiencies, miss their targets, or do not reach enough people.</p>
            <p>That is where voucher programs come into play. They offer a more precise way to deliver resources straight to the areas where they are needed&#x2014;think education, healthcare, or housing. Unlike general cash transfers or scattered subsidies, vouchers ensure funds go directly to school tuition or necessary supplies. By design, that is supposed to cut down on waste and make a more significant dent in inequality. However, vouchers work best when they are one part of a broader plan. Progressive taxes can supply the revenue needed for social programs, while public spending and subsidies tackle the more profound inequalities woven into the system.</p>
            <p>This paper investigates the relationships among vouchers, taxation, public spending, and subsidies in reducing income inequality. We examine data from a dozen countries over two decades (22 years) and use the Gini coefficient to gauge inequality levels. Through contrafactual analysis, we test different &#x201c;what if&#x201d; scenarios: What if more voucher programs were rolled out? Would targeted subsidies boost their effect? Our goal is to give policymakers solid, evidence-based insights they can use to create change. Inequality is not just about statistics. It is about ensuring people have access to the fundamentals&#x2014;like a good education or a decent healthcare system&#x2014;that open the door to upward mobility. Smartly designed subsidies can quickly fix households under pressure, while vouchers help ensure resources land where they should. When we combine these tools thoughtfully, we can tackle inequality from many angles.</p>
            <p>The stakes could not be higher. Persistent inequality stirs social unrest, chokes economic progress, and prevents people from reaching their full potential. On the other hand, well-crafted policies can spark development, tighten social bonds, and create a sense that everyone is part of the progress. This paper aims to illuminate which policy combos work best and explore vouchers as vital to a bigger redistribution puzzle.</p>
            <p>This paper also examines Universal Basic Income (UBI) as another potential tool for redistributing wealth. However, we will not crunch numbers or perform detailed measurements, mainly because there is insufficient solid data on how UBI is implemented. Instead, we focus on its possible upsides and downsides and compare it to other policy options.</p>
        </sec>
        <sec id="sec6">
            <title>Theoretical framework</title>
            <p>Let us start with vouchers; imagine getting a voucher instead of cash&#x2014;this voucher can only be used for things like education, healthcare, or housing. In other words, a voucher is a government subsidy earmarked for specific needs, ensuring that the money goes directly toward essential services. This method prevents funds from being spent on anything else and even allows recipients to choose among approved providers. This choice can spark competition, leading to higher quality and more efficient services (
                <xref ref-type="bibr" rid="ref16">Hastings, Kane, &amp; Staiger, 2006</xref>).</p>
            <p>Which many praises for their pinpoint precision. Broader public spending can sometimes get diverted, but vouchers directly assist the essentials&#x2014;food, housing, education, or healthcare. Rather than handing out cash that might be used for other things, vouchers steer the funds to their intended purposes. Research by 
                <xref ref-type="bibr" rid="ref11">Currie and Gahvari (2008)</xref> supports the idea that this kind of targeted help reduces the drawbacks of general cash transfers. Meanwhile, 
                <xref ref-type="bibr" rid="ref17">Hoynes and Schanzenbach (2018)</xref> show how food vouchers improve diets and lighten financial pressure on needy families. This makes it more challenging to misuse funds, ensuring the support goes where it should. Similarly, 
                <xref ref-type="bibr" rid="ref41">Fiszbein and Schady (2009)</xref> emphasise the long-term gains in skills and well-being from conditional transfers linked to education or healthcare.</p>
            <p>Public spending has traditionally been a go-to method for battling inequality. The logic is straightforward: invest in education so people can earn more in the future and put money into healthcare to stay healthy and remain productive. Evidence supports the link between more significant investment in these areas and lower inequality rates. 
                <xref ref-type="bibr" rid="ref14">Gupta et al. (2002)</xref> found that healthcare spending in developing countries considerably narrows income gaps. 
                <xref ref-type="bibr" rid="ref8">Blanden et al. (2005)</xref> show how more education funding boosts social mobility, letting individuals climb the economic ladder. The 
                <xref ref-type="bibr" rid="ref54">OECD (2021)</xref> even reports that countries putting more GDP into education tend to have smaller Gini coefficients. However, access is not always uniform&#x2014;rural and low-income areas can still lag. In Mexico, for instance, 
                <xref ref-type="bibr" rid="ref48">Barber and Gertler (2010)</xref> observed that targeted funding for rural clinics reduced infant mortality and improved health outcomes. This is a reminder that targeted programs, like vouchers, can bolster broad public spending to ensure all groups benefit.</p>
            <p>Subsidies are another puzzle piece, but they can also be problematic. They are designed to make essentials such as energy, food, or transport more affordable, yet they often fail to reach the poorest groups. 
                <xref ref-type="bibr" rid="ref10">Clements et al. (2013)</xref> note that energy subsidies, for example, can help wealthier households more simply because they use more electricity.</p>
            <p>Still, subsidies can do a world of good if they are carefully thought out. 
                <xref ref-type="bibr" rid="ref1">Alderman and Yemtsov (2014)</xref> discuss how targeted food subsidies can boost nutrition and lighten the economic burden on low-income families. 
                <xref ref-type="bibr" rid="ref32">Ravallion (2016)</xref> takes it further, arguing that subsidies explicitly aimed at groups like rural households can make a real dent in income inequality. Technology is also shifting how subsidies work. In parts of Sub-Saharan Africa, digital payments have cut corruption and made subsidies more accurate, as 
                <xref ref-type="bibr" rid="ref46">Aker et al. (2016)</xref> report.</p>
            <p>Combining vouchers, subsidies, and public spending gives you a more holistic way to address income inequality. Each tool tackles a different angle: vouchers target specific needs, subsidies offer short-term relief, and public spending lays the groundwork through infrastructure and accessible services. 
                <xref ref-type="bibr" rid="ref51">Thaler and Sunstein (2008)</xref> describe vouchers as &#x201c;nudges&#x201d; that guide people toward better choices, but those nudges mean little without well-funded schools and healthcare. 
                <xref ref-type="bibr" rid="ref43">Banerjee and Duflo (2019)</xref> back this up, pointing out that the best results come when demand-side interventions, like vouchers, are paired with investments that ensure quality services.</p>
            <p>The evidence is on their side. 
                <xref ref-type="bibr" rid="ref44">Bastagli et al. (2016)</xref> show in a meta-analysis that a mix of vouchers, subsidies, and public investments has a more significant impact on cutting poverty and inequality than any tool alone. Brazil&#x2019;s Bolsa Fam&#x00ed;lia program is a classic example: it blends cash transfers, food subsidies, and healthcare incentives to improve how income is distributed significantly and to boost general well-being (
                <xref ref-type="bibr" rid="ref33">Soares et al., 2010</xref>). Besides poverty being a massive global challenge, it is not the only one. In many cases, the gap between the wealthiest and everyone else can lead to problems&#x2014;such as social unrest, slower economic growth, and political polarisation (
                <xref ref-type="bibr" rid="ref52">Alvaredo et al., 2018</xref>; 
                <xref ref-type="bibr" rid="ref5">Atkinson, 2015</xref>). That is why addressing income inequality is just as important as fighting poverty. Economists agree that significant income gaps can undermine long-term progress (
                <xref ref-type="bibr" rid="ref7">Bartels, 2016</xref>). 
                <xref ref-type="bibr" rid="ref35">Stiglitz (2018)</xref> points out that when wealth becomes too concentrated, societies risk weaker democratic institutions and diminished social trust. Over time, these trends can drag down overall development, even for people not technically living in poverty (
                <xref ref-type="bibr" rid="ref54">OECD, 2021</xref>).</p>
            <p>Thanks to these concerns, countries known for their liberal traditions&#x2014;like the United States&#x2014;have rolled out social programs to narrow the income divide (
                <xref ref-type="bibr" rid="ref7">Bartels, 2016</xref>; 
                <xref ref-type="bibr" rid="ref35">Stiglitz, 2018</xref>). Efforts range from progressive taxation to direct transfers and other safety nets. The main idea is to ensure economic growth lifts as many people as possible rather than benefiting just a tiny group at the top. This study aims to continue the previous research by 
                <xref ref-type="bibr" rid="ref21">Malliaros and Pacheco-Jaramillo (2025)</xref>, which explores how reducing income inequality is not only about fairness or ideology but also about creating a more stable and cohesive society. When wealth is shared more evenly, communities see stronger civic engagement, better health outcomes, and healthier economic performance in the long run.</p>
            <p>Right now, one popular way to tackle income inequality is through voucher systems (
                <xref ref-type="bibr" rid="ref4">Angrist et al., 2002</xref>). However, they are not the only strategy out there. Governments and policymakers use cash transfers, universal basic income (UBI), and direct subsidies to help redistribute wealth (
                <xref ref-type="bibr" rid="ref22">Moffitt, 2015</xref>). Although our econometric model does not include UBI (mainly because it is not yet widespread and lacks extensive data), it is still important to discuss how UBI compares to vouchers and other social support measures (
                <xref ref-type="bibr" rid="ref29">OECD, 2017</xref>).</p>
            <sec id="sec7">
                <title>Advantages and disadvantages of Universal Basic Income (UBI)</title>
                <p>What exactly is UBI? It is a plan to give everyone a regular, no-strings-attached cash payment, regardless of their income level or job status (
                    <xref ref-type="bibr" rid="ref36">Van Parijs &amp; Vanderborght, 2017</xref>). This sounds simple, but it has some interesting upsides. For starters, UBI cuts down on the red tape you see with need-based programs. Since everyone gets it, there is no heavy screening process to determine who qualifies. Another benefit is that it offers a guaranteed safety net for everyone, which can lower poverty rates, boost financial security, and make people more flexible in their economic choices (
                    <xref ref-type="bibr" rid="ref23">Murray, 2006</xref>). However, there is more. First, UBI could reduce administrative costs because you would not need different agencies to track who is eligible for which benefit (
                    <xref ref-type="bibr" rid="ref34">Standing, 2017</xref>). Second, it might spark new ideas and businesses since people might be willing to take more significant risks or try out entrepreneurial ventures when they know they have a regular income to fall back on (
                    <xref ref-type="bibr" rid="ref37">Widerquist &amp; Sheahen, 2012</xref>).</p>
                <p>On the flip side, UBI has some real hurdles. The most significant sticking point is the enormous price tag. Funding a program that covers everyone can be a serious challenge, especially for larger populations. Unlike vouchers that focus on needs&#x2014;like education or healthcare&#x2014;UBI broadly spreads money. That approach makes some policymakers question whether it is truly efficient and worry about the effects of the labour market. There is also a chance that UBI could cause inflationary pressures, mainly if consumer demand shoots up without enough goods or services to match (
                    <xref ref-type="bibr" rid="ref36">Van Parijs &amp; Vanderborght, 2017</xref>). Finally, some folks fear it might discourage work, particularly those who already earn low wages and might choose not to seek employment if they can rely on a guaranteed monthly check (
                    <xref ref-type="bibr" rid="ref22">Moffitt, 2015</xref>).</p>
                <p>Another argument for the UBI is that it could soften the blow of automation. As machines and AI take over more tasks, displaced workers might at least have a basic income to help them transition to new careers or learn fresh skills (
                    <xref ref-type="bibr" rid="ref34">Standing, 2017</xref>). Another plus is how UBI might reduce social stigma. Since there is no means test, it sidesteps the label of &#x201c;welfare&#x201d; and ensures everyone gets some level of support, regardless of their background or situation (
                    <xref ref-type="bibr" rid="ref36">Van Parijs &amp; Vanderborght, 2017</xref>).</p>
                <p>Financing UBI can be tricky. Often, it calls for raising taxes or introducing new ones, which can shrink people&#x2019;s disposable income and, ultimately, slow spending (
                    <xref ref-type="bibr" rid="ref22">Moffitt, 2015</xref>). Governments pulling money from other public services or imposing significant tax hikes could spark political pushback or citizen outrage. There is also the issue of a single payment fitting different regions. What might be enough in a cheaper area might fall short where living costs are much higher, making &#x201c;one size fits all&#x201d; less than ideal.</p>
                <p>From a political feasibility standpoint, vouchers offer a more practical and widely accepted approach to redistribution compared to Universal Basic Income (UBI). UBI proposals often face strong resistance from policymakers across the ideological spectrum due to concerns over fiscal sustainability, labour disincentives, and potential inflationary effects. In contrast, vouchers have been more successful in gaining legislative approval because they are structured as targeted interventions that support specific sectors such as education, healthcare, and food security. Countries such as the United States, Brazil, and India have implemented large-scale voucher programs with bipartisan support because they help while maintaining market-based price signals. Moreover, vouchers align with existing social safety net structures, making them easier to integrate without requiring a complete overhaul of public finance systems. This makes them a politically palatable alternative that balances economic efficiency with social protection.</p>
                <p>All in all, UBI is a fascinating concept with real potential&#x2014;and real pitfalls. Whether it is more effective than vouchers or other welfare strategies depends on how it is designed and funded. As more pilot programs pop up and researchers collect more data, we will hopefully get a clearer picture of UBI&#x2019;s impact and whether it is worth adopting on a big scale.</p>
            </sec>
            <sec id="sec8">
                <title>Contrafactual analysis of redistributive policies</title>
                <p>When it comes to shaping economic policy, one of the most valuable tools is contrafactual analysis. This approach helps us see what could happen if we made different policy choices&#x2014;essentially comparing the real world with a hypothetical version where redistributive policies take a new direction (
                    <xref ref-type="bibr" rid="ref42">Rubin, 1974</xref>; 
                    <xref ref-type="bibr" rid="ref47">Angrist &amp; Pischke, 2009</xref>). It is like asking, what if we increased public spending on education? What if subsidies were expanded? By exploring these &#x201c;what if&#x201d; scenarios, policymakers can test the waters before making real-world decisions.</p>
                <p>Think of the Baseline Scenario as the economic status quo. It reflects how things are right now, with existing redistributive policies&#x2014;like education funding, healthcare subsidies, and social support programs&#x2014;remaining at their current levels. This baseline gives us a starting point to measure against (
                    <xref ref-type="bibr" rid="ref49">Cameron &amp; Trivedi, 2005</xref>).</p>
                <p>The Contrafactual Scenario, in contrast, imagines an alternative path. What if government spending on education and healthcare increased to 4% of GDP? What if voucher programs were doubled? These hypothetical changes allow us to estimate how adjustments in public spending might impact income inequality, social mobility, and overall economic well-being (
                    <xref ref-type="bibr" rid="ref50">Heckman &amp; Vytlacil, 2007</xref>).</p>
                <p>To make this analysis meaningful, we rely on a few core assumptions:
                    <list list-type="bullet">
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Using Data from Real-World Cases: We draw insights from empirical studies in emerging and developed countries to understand how redistributive policies have worked in different economic settings (
                                <xref ref-type="bibr" rid="ref45">Duflo &amp; Banerjee, 2011</xref>). These cases provide a strong foundation for estimating potential outcomes.</p>
                        </list-item>
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Reallocating Public Resources: The analysis assumes a certain percentage of GDP is redistributed through subsidies, vouchers, and direct public spending. The goal is to evaluate how shifting funds within the system affect inequality and access to services (
                                <xref ref-type="bibr" rid="ref50">Heckman &amp; Vytlacil, 2007</xref>).</p>
                        </list-item>
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Beyond Just Money Transfers: Financial redistribution alone is not the whole story. We also consider secondary effects, such as better access to education, improved healthcare, and increased social mobility&#x2014;factors that contribute to long-term economic equity (
                                <xref ref-type="bibr" rid="ref49">Cameron &amp; Trivedi, 2005</xref>).</p>
                        </list-item>
                    </list>
                </p>
                <p>We can identify what works best to reduce inequality by simulating different policy scenarios. One key takeaway? Redistributive policies are most effective when combined rather than applied in isolation (
                    <xref ref-type="bibr" rid="ref47">Angrist &amp; Pischke, 2009</xref>). Vouchers, subsidies, and public investment work better together, reinforcing each other&#x2019;s impact.</p>
                <p>At the same time, this approach helps policymakers anticipate unintended consequences before rolling out large-scale reforms. Instead of a trial-and-error approach, contrafactual analysis offers a strategic way to fine-tune policies&#x2014;leading to more innovative, more effective interventions that genuinely make a difference.</p>
                <p>When considering how redistributive policies can help lower income inequality, we must recognise that different countries use different social programs. Each nation&#x2019;s approach to welfare, taxation, and public spending depends on its economic situation, budget strength, and policy priorities.</p>
                <p>Take developed countries like the United States, Germany, Japan, and Australia. They offer broad social protection programs, including universal healthcare, pension systems, and targeted subsidies. Meanwhile, emerging economies such as India, Mexico, China, and South Africa often focus on conditional cash transfers and employment subsidies. However, they can run into challenges with how progressive their taxes are or how much money they must work with. Developing nations&#x2014;like Peru, the Philippines, Colombia, and Ecuador&#x2014;use a mix of direct social transfers and indirect subsidies. However, their fiscal structures are not as robust, so they sometimes struggle to fund these programs effectively. By exploring these scenarios, we better understand which policy tools dent inequality and how different approaches to vouchers, taxes, and public spending shape overall income distribution. Comparing these country-specific strategies helps us see the bigger picture and reveals which methods are most effective in moving toward more equitable economic outcomes (see 
                    <xref ref-type="table" rid="T1">
Table 1</xref>).</p>
                <table-wrap id="T1" orientation="portrait" position="float">
                    <label>
Table 1. </label>
                    <caption>
                        <title>Comparison of social programs and fiscal policies across selected countries.</title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Country</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Category</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Social programs</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Universal health coverage</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">UBI experiments</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Tax system</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">United States</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developed</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Medicare, Medicaid, SNAP, Social Security</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">No</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Small-scale pilot programs</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Progressive, with earned income tax credits</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Germany</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developed</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Universal healthcare, child benefits, pensions</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Yes</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Limited trials</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Highly progressive, strong social welfare system</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Japan</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developed</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">National healthcare, pensions, unemployment insurance</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Yes</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Minimal</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Moderate progressive taxation, high VAT</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Australia</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developed</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Medicare, Centrelink benefits, pensions</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Yes</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">None</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Progressive, strong welfare support</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">India</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Emerging</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Food subsidies, rural employment schemes, health insurance</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">No</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Limited pilot programs</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Regressive, heavy indirect taxes (GST)</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Mexico</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Emerging</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Opportunities (now Prospera), healthcare subsidies</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Partial</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">None</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Moderate, high VAT impact on lower incomes</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">China</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Emerging</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Social insurance, rural health programs, pensions</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Yes</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">None</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Mixed, growing direct taxation system</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Colombia</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Emerging</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Conditional cash transfers, health subsidies</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Partial</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">None</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Regressive, high indirect taxation</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Peru</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developing</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Juntos cash transfers, food programs</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Partial</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">None</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Regressive, limited tax collection</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Philippines</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developing</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">4Ps (cash transfers), health subsidies</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Partial</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">None</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Regressive, high reliance on indirect taxation</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">South Africa</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developing</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Social grants, free healthcare for low-income groups</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Partial</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Proposed but not implemented</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Progressive, high corporate tax rates</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Ecuador</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developing</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Human Development transfer, public healthcare</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Partial</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">None</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">Mixed, firm reliance on indirect taxation</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>Sources: World Bank (WDI) For public expenditure, social protection, and taxation data; OECD For tax structures and social spending in developed countries; IMF Fiscal Monitor For government expenditure and taxation data. National Statistics Agencies: For country-specific social programs. WHO &amp; ILO: For healthcare and employment-related social benefits.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>Developed countries (USA, Germany, Japan, and Australia) are grouped because their robust fiscal structures and extensive social protection systems provide a benchmark for advanced redistributive policies (
                    <xref ref-type="bibr" rid="ref31">Piketty, 2014</xref>). Emerging economies (India, Mexico, China, and South Africa) are included due to their focus on conditional cash transfers and employment subsidies amid challenges with progressive taxation and limited fiscal resources (
                    <xref ref-type="bibr" rid="ref5">Atkinson, 2015</xref>). Developing nations (Peru, the Philippines, Colombia, and Ecuador) rely on direct transfers and indirect subsidies, highlighting the difficulties in effectively funding redistributive programs under constrained fiscal environments.</p>
            </sec>
            <sec id="sec9">
                <title>Descriptive analysis</title>
                <p>Our primary measure for gauging income inequality is the Gini coefficient. Some countries show real progress in closing the gap thanks to well-planned social policies (
                    <xref ref-type="bibr" rid="ref2">Alvaredo et al., 2022</xref>). Others, however, keep seeing those gaps widen. In many developing nations, the index stays stubbornly high even when their economies grow, suggesting that economic expansion alone does not always help those at the bottom. Instead, progressive taxes and robust social support systems can make a more meaningful dent in inequality. We also notice that major downturns&#x2014;such as the 2008 financial crisis or the 2020 COVID-19 pandemic&#x2014;tend to knock vulnerable groups hardest and drive up inequality in the short term (
                    <xref ref-type="bibr" rid="ref18">IMF, 2022</xref>). These episodes remind us that solid fiscal measures are critical for cushioning the blow during tough times.</p>
                <p>A few things become apparent when you dig into the correlation analysis (see 
                    <xref ref-type="fig" rid="f1">
Figure 1</xref>). Subsidies, for instance, play a significant role in reducing poverty and inequality. The numbers show that when governments spend more on subsidies, it often leads to fairer income distribution and fewer people in extreme poverty. On the other hand, poverty and inequality seem tightly connected&#x2014;when poverty levels rise, inequality often does too.</p>
                <fig fig-type="figure" id="f1" orientation="portrait" position="float">
                    <label>
Figure 1. </label>
                    <caption>
                        <title>Correlation matrix.</title>
                    </caption>
                    <graphic id="gr1" orientation="portrait" position="float" xlink:href="https://f1000research-files.f1000.com/manuscripts/179131/e7fb0213-5f67-4127-9b70-4a489b129652_figure1.gif"/>
                </fig>
                <p>However, here is the interesting part: economic growth does not significantly impact inequality. The data shows almost no correlation, suggesting that growth alone cannot tackle income disparities. Taxes tell a similar story. While there is a slight link between tax revenue and inequality, it is not strong enough to suggest that current tax systems are doing enough to reduce disparities.</p>
                <p>So, what does all this mean? It highlights the importance of targeted policies, like subsidies and social programs. Relying only on growth or broad fiscal measures will not cut it. If the goal is to create a fairer society, redistributive policies must be front and centre.</p>
                <p>
                    <xref ref-type="fig" rid="f2">
Figure 2</xref> reveals that GDP per capita growth does not guarantee a reduction in inequality, as measured by the Gini index. Countries like Japan and Germany maintain low inequality (Gini index of 30-35) through effective redistributive policies, even with moderate economic growth. In contrast, South Africa exhibits high inequality (Gini index of 55-65) despite low growth, reflecting persistent structural disparities. In Latin America, countries such as Mexico, Colombia, and Peru face high inequality levels (Gini index of 45-55) with limited improvements, indicating challenges in redistributive policies. Meanwhile, China experiences rapid growth (up to 10%) but with varying levels of inequality, and the United States maintains moderate-to-high inequality (Gini index of 40-45), with economic growth having a limited impact on reducing income disparities.</p>
                <fig fig-type="figure" id="f2" orientation="portrait" position="float">
                    <label>
Figure 2. </label>
                    <caption>
                        <title>GDP per capita growth vs Gini index.</title>
                    </caption>
                    <graphic id="gr2" orientation="portrait" position="float" xlink:href="https://f1000research-files.f1000.com/manuscripts/179131/e7fb0213-5f67-4127-9b70-4a489b129652_figure2.gif"/>
                </fig>
                <p>Next, poverty indicators shed light on a related but distinct issue. Looking at the proportion of people living on $2.15 a day (in 2017 PPP terms), extreme poverty remains a serious concern in many developing regions (
                    <xref ref-type="bibr" rid="ref39">World Bank, 2022</xref>). In some places, targeted welfare programs have slowly brought these numbers down. In others, poverty is stuck at high levels or even climbing. When healthcare is pricey, and coverage is thin, getting sick can be financially devastating. This finding points to well-funded health systems&#x2019; importance in protecting low-income households from economic free fall.</p>
                <p>Government spending patterns, meanwhile, offer more clues about how inequality evolves. The share of government expenditure relative to GDP shows how much a country invests in public services and social protection. Generally, countries that devote much of their budgets to social transfers&#x2014;like cash assistance and subsidies&#x2014;tend to have lower inequality. Still, pouring money into these areas does not guarantee success if corruption or mismanagement undermines the process. In contrast, when governments allocate limited resources to social programs, market forces often fail to keep inequality in check (
                    <xref ref-type="bibr" rid="ref55">OECD, 2023</xref>).</p>
                <p>Tax policies also shape the income landscape. One measure in the data, tax revenue as a percentage of GDP, reflects a government&#x2019;s ability to fund redistributive programs. Places with higher tax revenues can afford broader social services, though how taxes are structured matters greatly. Progressive systems, which ask higher earners to pay a more significant share, often help narrow income gaps. However, regressive taxes&#x2014;such as sales taxes&#x2014;can harder hit those with lower incomes. A related indicator, &#x201c;taxes minus subsidies on products,&#x201d; shows whether subsidies make up for the burden placed by indirect taxes. If they do not, people at the lower income scale may face even tighter finances. Corporate taxes also play a role by influencing how wealth is concentrated since high corporate tax rates can fund social initiatives, whereas lower rates might leave gaps in the budget.</p>
                <p>Economic growth, measured here by GDP per capita growth, has a varied relationship with inequality. Strong growth sometimes lifts everyone&#x2019;s income, causing inequality to drop. In other contexts, however, growth primarily benefits the wealthiest, and the gap widens. This divide can come from changes in labour markets&#x2014;like automation and global shifts&#x2014;where skilled workers reap most of the rewards, leaving others behind (
                    <xref ref-type="bibr" rid="ref18">IMF, 2022</xref>). To address such imbalances, wage subsidies and job protections can help ensure that economic gains trickle down to broader segments of society.</p>
                <p>Education and healthcare spending play a longer-term role in shaping equality. Governments investing heavily in education tend to see better social mobility over time. Access to good schools can give young people from low-income backgrounds a fighting chance to improve their prospects (
                    <xref ref-type="bibr" rid="ref2">Alvaredo et al., 2022</xref>). Meanwhile, whether you measure it per capita or as a share of GDP, health expenditure helps reveal how much a society prioritises broad, affordable healthcare. Countries with more comprehensive coverage typically display lower inequality since medical bills financially ruin fewer individuals. By contrast, underfunded health systems can deepen disparities and leave low-income groups at greater risk.</p>
                <p>Looking at the big picture, no single factor single-handedly determines a country&#x2019;s level of income inequality. Instead, a mix of economic structures, targeted policies, and outside shocks all shape outcomes. Nations that embrace progressive taxes, strong social spending, and thoughtful investment in human capital usually enjoy more balanced and resilient growth. On the other hand, those who expect the market to do all the heavy lifting often see persistent or worsening inequality. Taken as a whole, this evidence can guide policymakers in devising strategies that support inclusive development and share the benefits of growth more widely.</p>
                <p>
                    <xref ref-type="table" rid="T2">
Table 2</xref> presents key statistics for the Gini coefficient, including the mean, median, standard deviation, minimum, and maximum values.</p>
                <table-wrap id="T2" orientation="portrait" position="float">
                    <label>
Table 2. </label>
                    <caption>
                        <title>Gini coefficient (Income inequality).</title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Group</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Mean</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Median</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Std. Dev.</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">
Min</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">
Max</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developed</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">36.2</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">35.8</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">4.1</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">28.9</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">41.5</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Emerging</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">45.6</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">44.6</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">7.3</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">35.7</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">64.8</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Developing</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">47.1</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">46.5</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">5.9</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">40.1</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">58.4</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>By the Authors.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>Developed countries exhibit lower inequality (mean Gini = 36.2) compared to emerging (45.6) and developing (47.1). South Africa (ZAF) is an outlier in the emerging group (Gini = 64.8 in 2003).</p>
            </sec>
            <sec id="sec10">
                <title>Correlation matrix for developed countries (USA, Germany, Australia, Japan)</title>
                <p>In developed countries, higher health expenditure moderately reduces inequality, while subsidies have a weaker redistributive effect. Poverty remains a strong driver of inequality, even in wealthy nations, and economic growth alone shows no significant impact on reducing income inequality (see 
                    <xref ref-type="table" rid="T3">
Table 3</xref>).</p>
                <table-wrap id="T3" orientation="portrait" position="float">
                    <label>
Table 3. </label>
                    <caption>
                        <title>Correlation matrix for developed countries (USA, Germany, Australia, Japan).</title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Variable</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Gini</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Subsidies</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Education Expenditure</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Health Expenditure</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">GDP Growth</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Tax Revenue</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Poverty Rate</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Gini</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.35</bold>
</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.40</bold>
</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.10</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.25</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.60</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Subsidies</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.35</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.30</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.45</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.30</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Education Expenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.30</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.20</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.05</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.35</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.10</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Health Expenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.40</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.20</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.20</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.50</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.55</bold>
</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">GDP Growth</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.10</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.05</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.20</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.05</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.05</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Tax Revenue</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.25</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.45</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.35</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.50</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.05</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.20</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Poverty Rate</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.60</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.30</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.10</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.05</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.20</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>By the Authors.</p>
                    </table-wrap-foot>
                </table-wrap>
                <table-wrap id="T4" orientation="portrait" position="float">
                    <label>
Table 4. </label>
                    <caption>
                        <title>Correlation matrix for developed countries (Mexico, South Africa, China, India).</title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Variable</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Gini</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Subsidies</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Education Expenditure</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Health Expenditure</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">GDP Growth</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Tax Revenue</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Poverty Rate</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Gini</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.70</bold>
</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.55</bold>
</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.75</bold>
</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.60</bold>
</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.45</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>0.85</bold>
</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Subsidies</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.70</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.65</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.80</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.50</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.60</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.65</bold>
</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Education Expenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.65</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.50</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.40</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.50</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Health Expenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.75</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.80</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.50</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.70</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.80</bold>
</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">GDP Growth</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.60</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.50</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.40</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.30</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.55</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Tax Revenue</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.45</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.60</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.70</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.30</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.40</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Poverty Rate</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.85</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.65</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.50</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.80</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.40</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>By the Authors.</p>
                    </table-wrap-foot>
                </table-wrap>
            </sec>
            <sec id="sec11">
                <title>Correlation matrix for emerging countries (Mexico, South Africa, China, India)</title>
                <p>Health expenditure shows the strongest negative correlation with inequality, highlighting its critical role (e.g., China&#x2019;s healthcare reforms). Subsidies also significantly reduce inequality, as seen in India&#x2019;s welfare programs. Poverty rates are tightly linked to inequality, making poverty reduction essential. GDP growth helps lower inequality, especially when combined with effective social programs.</p>
            </sec>
            <sec id="sec12">
                <title>Correlation matrix for developing countries (Colombia, Ecuador, Peru, Philippines)</title>
                <p>Below is the correlation matrix for key variables in developing countries.</p>
                <p>Higher health expenditure and subsidies are strongly linked to lower income inequality, while education spending shows a weaker connection. Poverty rates closely align with higher inequality, but increased health spending helps reduce poverty. Additionally, higher tax revenue supports more significant health investments, highlighting the importance of fiscal capacity in funding social programs.</p>
                <p>Since vouchers are not directly measured in the dataset. The correlation analysis shows that targeted transfers&#x2014;like the subsidies and other transfers we are measuring&#x2014;have a stronger association with lower inequality than tax revenue. In our discussion, vouchers are considered a policy alternative that operates similarly to these targeted transfers. Thus, the correlation analysis suggests that investing in healthcare has the strongest link to reducing inequality. While subsidies also help make a difference, their impact is not as strong as that of healthcare spending. Given the strong correlation between healthcare spending and reduced inequality, we will incorporate two health variables into our econometric model. Tax revenue is minor, showing only a modest connection to lowering inequality. This is why, in the context of our counterfactual analysis, we posit that voucher systems could potentially yield better outcomes, as supported by the theoretical literature.</p>
            </sec>
        </sec>
        <sec id="sec13" sec-type="methods">
            <title>Methods</title>
            <p>This study employs a panel data econometric model to evaluate the relationship between redistributive policies and income inequality. We will start by looking at the dependent variable and then dive into the independent and control variables that help paint a fuller picture of inequality. The best indicator here is the Gini index because we are zeroing in on income inequality. It is a standard go-to measure because it lets us compare inequality across countries and track how it changes over time. Economists frequently use the Gini index to check if policies aimed at redistributing income (like subsidies or taxes) are making a real difference.</p>
            <sec id="sec30">
                <title>Independent and control variables</title>
                <p>We use six independent and control variables to capture how policy decisions and broader economic forces shape inequality.
                    <list list-type="order">
                        <list-item>
                            <label>1.</label>
                            <p>Poverty (Headcount Ratio at $2.15 a Day). Poverty is a key piece of the puzzle. We look at the percentage of the population living on $2.15 (2017 PPP) a day or less. This simple measure tells us how severe extreme poverty is and how likely it is that people at the lowest end of the income scale can meet their basic needs.</p>
                        </list-item>
                        <list-item>
                            <label>2.</label>
                            <p>Subsidies and Other Transfers (% of Expense). We also look at how much of government spending goes toward social transfers. Higher subsidies often boost lower-income households, potentially reducing inequality.</p>
                        </list-item>
                        <list-item>
                            <label>3.</label>
                            <p>GDP per Capita Growth (Annual %). Economic growth can cut inequality or worsen it, depending on who benefits from it. So, we track GDP per capita growth as a control factor, capturing positive and negative growth swings.</p>
                        </list-item>
                        <list-item>
                            <label>4.</label>
                            <p>Tax Revenue (% of GDP). Taxes are crucial for funding social programs. This variable shows how much fiscal &#x201c;firepower&#x201d; a government must invest in redistributive policies.</p>
                        </list-item>
                        <list-item>
                            <label>5.</label>
                            <p>Government Expenditure on Education (% of GDP). Education spending is a big deal when it comes to long-term inequality. Better education can open opportunities, often leading to a more balanced income distribution in the long run.</p>
                        </list-item>
                        <list-item>
                            <label>6.</label>
                            <p>Domestic Government Health Expenditure (% of GDP): This measure of public health spending as a share of GDP is based on WHO&#x2019;s SHA 2011 framework for standardised cross-country comparisons and sourced from the WHO Global Health Expenditure Database (April 15, 2024).</p>
                        </list-item>
                    </list>
                </p>
                <p>These variables offer a solid framework for analysing how redistributive policies shape income inequality, capturing key channels&#x2014;extreme poverty, social transfers, fiscal capacity (via tax revenue), public spending on education and health, and overall economic conditions&#x2014;that together determine how income is spread across a society (
                    <xref ref-type="bibr" rid="ref5">Atkinson, 2015</xref>; 
                    <xref ref-type="bibr" rid="ref31">Piketty, 2014</xref>). By incorporating these measures and GDP per capita growth as a control, we can explore the complex interplay of economic growth and fiscal policies in affecting inequality while allowing for an interaction term between vouchers and taxes to assess their combined effects (
                    <xref ref-type="bibr" rid="ref25">OECD, 2015</xref>). Ultimately, this approach helps us understand the real-world impact of different policy strategies on people&#x2019;s livelihoods and overall social equity, ensuring robustness by accounting for multiple factors influencing income distribution.</p>
            </sec>
            <sec id="sec14">
                <title>Incorporating contrafactual analysis for vouchers</title>
                <p>In this part of the study, we zoom in on three countries&#x2014;the United States, India, and Mexico&#x2014;to see how voucher-type programs might work. Each one offers a unique setting, which helps us capture a broader range of possible outcomes. The United States, for instance, has a long track record with housing vouchers and specific educational programs (
                    <xref ref-type="bibr" rid="ref9">Center on Budget and Policy Priorities, 2022</xref>). An emerging economy, India implements what is often considered a &#x201c;quasi-voucher&#x201d; food subsidy through its Public Distribution System (
                    <xref ref-type="bibr" rid="ref38">World Bank, 2021</xref>). Meanwhile, Mexico blends conditional cash transfers with health and education support (
                    <xref ref-type="bibr" rid="ref30">OECD, 2020</xref>). We cover developed and emerging contexts by picking these three examples, giving us a more robust foundation for our counterfactual modelling.</p>
                <p>From the data we gathered, spending on these voucher-like initiatives usually spans about 0.2% to 1.0% of a country&#x2019;s GDP. For simplicity&#x2019;s sake, we will use an average figure of about 0.5% of GDP in our simulations. The idea is to see how the Gini coefficient might shift if it went into a voucher system instead of devoting that slice of public spending to direct subsidies. Following the approach suggested by 
                    <xref ref-type="bibr" rid="ref22">Moffitt (2015)</xref>, this counterfactual method lets us explore potential changes in income distribution&#x2014;even when we do not have exact, country-by-country data.
                    <list list-type="order">
                        <list-item>
                            <label>1.</label>
                            <p>

                                <bold>Establishing Baseline vs. Contrafactual Scenarios</bold>
                            </p>
                            <p>The baseline scenario represents the current policy environment, where vouchers may either be absent or account for only a tiny percentage of government spending. This scenario is reflected in the existing dataset without any policy changes. The contrafactual scenario imagines a scenario where vouchers are expanded significantly. This can be operationalised in two ways:</p>
                            <list list-type="bullet">
                                <list-item>
                                    <label>&#x2022;</label>
                                    <p>Simulating an increase in vouchers as a percentage of government spending (vouchers account for 0.5% of GDP).</p>
                                </list-item>
                                <list-item>
                                    <label>&#x2022;</label>
                                    <p>Testing an alternative allocation where vouchers replace a portion of subsidies or other redistributive expenditures.</p>
                                </list-item>
                            </list>
                        </list-item>
                        <list-item>
                            <label>2.</label>
                            <p>

                                <bold>Modifying the Econometric Model</bold>
                            </p>
                            <p>The existing model already includes taxation, subsidies, and public expenditures. To incorporate vouchers, we introduce a voucher spending variable and an interaction term between vouchers and taxes.</p>
                        </list-item>
                    </list>
                </p>
            </sec>
            <sec id="sec15">
                <title>Revised model specification</title>
                <p>

                    <disp-formula id="e1">

                        <mml:math display="block">
                            <mml:mtext>Gini</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b1;</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                            <mml:mn>1</mml:mn>
                            <mml:mo>&#x2217;</mml:mo>
                            <mml:mtext>Vouchers</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                            <mml:mn>2</mml:mn>
                            <mml:mo>&#x2217;</mml:mo>
                            <mml:mtext>Taxes</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                            <mml:mn>3</mml:mn>
                            <mml:mo>&#x2217;</mml:mo>
                            <mml:mtext>Subsidies</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                            <mml:mn>4</mml:mn>
                            <mml:mo>&#x2217;</mml:mo>
                            <mml:mtext>Expense</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                            <mml:mn>5</mml:mn>
                            <mml:mo>&#x2217;</mml:mo>
                            <mml:mtext>GDPgrowth</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                            <mml:mn>6</mml:mn>
                            <mml:mo>&#x2217;</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mtext>Vouchers</mml:mtext>
                                <mml:mo>_</mml:mo>
                                <mml:mi>it</mml:mi>
                                <mml:mo>&#x2217;</mml:mo>
                                <mml:mtext>Taxes</mml:mtext>
                                <mml:mo>_</mml:mo>
                                <mml:mi>it</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>+</mml:mo>
                            <mml:mi>&#x03b3;X</mml:mi>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03bc;</mml:mi>
                            <mml:mo>_</mml:mo>
                            <mml:mi mathvariant="normal">i</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b5;</mml:mi>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                        </mml:math>
</disp-formula>
                </p>
                <p>&#x2192; New variable indicating government spending on voucher programs (0,5 % of GDP).</p>
                <p>&#x2192; Interaction term to capture whether tax-funded voucher programs have a more significant redistributive effect.</p>
                <p>Other variables &#x2192; Poverty, subsidies, public expenses, economic growth, education, and healthcare spending remain unchanged as controls.
                    <list list-type="order">
                        <list-item>
                            <label>3.</label>
                            <p>

                                <bold>Contrafactual Policy Simulation</bold>
                            </p>
                        </list-item>
                    </list>
                </p>
                <p>To test the effect of vouchers, we simulate different levels of voucher expenditure:</p>
                <p>Scenario 1 (Baseline): No voucher programs or minimal spending.</p>
                <p>Scenario 2 (Moderate Voucher Expansion): 0.5% of GDP allocated to vouchers.</p>
                <p>Scenario 3 (Significant Voucher Expansion): 1% of GDP allocated to vouchers, funded by a mix of tax revenue and subsidy reallocation.</p>
                <p>By comparing these scenarios, we estimate the potential reduction in the Gini index under different levels of voucher spending.
                    <list list-type="order">
                        <list-item>
                            <label>4.</label>
                            <p>

                                <bold>Expected Findings &amp; Interpretation</bold>
                            </p>
                        </list-item>
                    </list>
                </p>
                <p>If &#x2192; Increased voucher spending reduces inequality.</p>
                <p>If &#x2192; Vouchers complement taxation, tax-funded vouchers are more effective than taxation alone.</p>
                <p>If &#x2192; Traditional subsidies alone may not be as effective as vouchers in reducing inequality.</p>
                <p>By integrating contrafactual analysis, we go beyond measuring past effects and predict the potential impact of expanding vouchers. This approach allows policymakers to compare vouchers with other redistributive policies, such as taxes and subsidies, and make informed decisions about structuring social spending for maximum equity.</p>
            </sec>
        </sec>
        <sec id="sec16">
            <title>Results from the econometric model</title>
            <sec id="sec17">
                <title>Panel data analysis of redistributive policies and income inequality</title>
                <p>

                    <bold>Group 1: Advanced Economies</bold>
                </p>
                <p>In advanced economies, public investments in education and health show strong, statistically significant negative relationships with the Gini index, indicating that these expenditures effectively reduce income inequality. High Tax Revenue further enhances this inequality-reducing effect. Although the impact of subsidies and GDP Growth is insignificant, the Poverty Rate has a positive and significant effect, underscoring that even in developed countries, higher poverty is linked with increased inequality (see 
                    <xref ref-type="table" rid="T6">
Table 6</xref>).</p>
                <table-wrap id="T5" orientation="portrait" position="float">
                    <label>
Table 5. </label>
                    <caption>
                        <title>Correlation matrix for developing countries (Colombia, Ecuador, Peru, Philippines).</title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Variable</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Gini</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Subsidies</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Education Expenditure</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Health Expenditure</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">GDP Growth</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Tax Revenue</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Poverty Rate</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Gini</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.52</bold>
</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.28</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.61</bold>
</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.18</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.35</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>0.78</bold>
</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Subsidies</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.52</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.45</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.60</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.20</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.48</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Education Expenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.28</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.45</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.30</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.40</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.25</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Health Expenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.61</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.60</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.30</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.25</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.65</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">
                                    <bold>-0.68</bold>
</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">GDP Growth</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.18</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.20</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.25</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.10</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.15</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Tax Revenue</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.35</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.55</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.40</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.65</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.10</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.40</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Poverty Rate</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.78</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.48</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.25</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.68</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.40</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.00</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>By the Authors.</p>
                    </table-wrap-foot>
                </table-wrap>
                <table-wrap id="T6" orientation="portrait" position="float">
                    <label>
Table 6. </label>
                    <caption>
                        <title>Advanced economies (USA, DEU, JPN, AUS).</title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Variable</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Coefficient</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Robust SE</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">t</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">P&gt;|t|</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">95% Conf. Interval</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Subsidies</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.05</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.1</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.5</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.62</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.15, 0.25]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">EducationExpenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.3</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.08</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-3.75</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.001</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.46, -0.14]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">HealthExpenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.4</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.12</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-3.33</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.002</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.64, -0.16]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">GDPgrowth</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.29, 0.29]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">TaxRevenue</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.65</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.18</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-3.61</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.001</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-1.01, -0.29]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">PovertyRate</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.2</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.08</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">2.5</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.02</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[0.04, 0.36]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Constant</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">43</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">8</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">5.38</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[27.00, 59.00]</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>By the Authors.</p>
                    </table-wrap-foot>
                </table-wrap>
                <table-wrap id="T7" orientation="portrait" position="float">
                    <label>
Table 7. </label>
                    <caption>
                        <title>Emerging markets (IND, MEX, CHN, South Africa).</title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Variable</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Coefficient</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Robust SE</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">t</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">P&gt;|t|</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">95% Conf. Interval</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Subsidies</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.12</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.11</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.09</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.28</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.10, 0.34]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">EducationExpenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.22</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.1</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-2.2</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.03</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.42, -0.02]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">HealthExpenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.28</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.12</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-2.33</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.022</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.52, -0.04]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">GDPgrowth</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.25</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-1.67</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.105</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.55, 0.05]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">TaxRevenue</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.52</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.16</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-3.25</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.005</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.84, -0.20]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">PovertyRate</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.38</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.08</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">4.75</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.001</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[0.22, 0.54]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Constant</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">44.5</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">9.5</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">4.71</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[25.50, 63.50]</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>By the Authors.</p>
                    </table-wrap-foot>
                </table-wrap>
                <table-wrap id="T8" orientation="portrait" position="float">
                    <label>
Table 8. </label>
                    <caption>
                        <title>Developing economies (ECU, PER, COL, Philippines).</title>
                    </caption>
                    <table content-type="article-table" frame="hsides">
                        <thead>
                            <tr>
                                <th align="left" colspan="1" rowspan="1" valign="top">Variable</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Coefficient</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">Robust SE</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">t</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">P&gt;|t|</th>
                                <th align="left" colspan="1" rowspan="1" valign="top">95% Conf. Interval</th>
                            </tr>
                        </thead>
                        <tbody>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Subsidies</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.25</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">1.67</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.11</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.05, 0.55]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">EducationExpenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.18</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.12</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-1.5</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.15</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.42, 0.06]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">HealthExpenditure</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.22</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.14</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-1.57</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.13</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.50, 0.06]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">GDPgrowth</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.35</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.18</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-1.94</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.06</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.70, 0.00]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">TaxRevenue</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-0.47</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.17</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">-2.76</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.01</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[-0.81, -0.13]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">PovertyRate</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.45</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.09</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">5</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0.001</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[0.27, 0.63]</td>
                            </tr>
                            <tr>
                                <td align="left" colspan="1" rowspan="1" valign="top">Constant</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">46</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">10</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">4.6</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">0</td>
                                <td align="left" colspan="1" rowspan="1" valign="top">[26.00, 66.00]</td>
                            </tr>
                        </tbody>
                    </table>
                    <table-wrap-foot>
                        <p>By the Authors.</p>
                    </table-wrap-foot>
                </table-wrap>
                <p>

                    <bold>Group 2: Emerging Markets (IND, MEX, CHN, South Africa)</bold>
                </p>
                <p>Higher government expenditure on education and health in this group reduces income inequality. Specifically, a one-unit increase in Education Expenditure is associated with a 0.22-point reduction in the Gini index, while an increase in Health Expenditure is linked to a 0.28-point reduction. Tax Revenue remains a substantial and statistically significant factor (coefficient = &#x2013;0.52) in lowering inequality. Conversely, the positive coefficient on Poverty Rate (0.38) indicates that higher poverty levels are strongly associated with increased inequality. Subsidies, while positive, are not statistically significant in this group. With a negative sign, GDP Growth suggests a potential inequality-reducing effect; however, its impact does not reach conventional significance. Overall, the evidence from emerging markets suggests that targeted public spending and efficient tax collection can play key roles in mitigating inequality, although poverty remains a critical challenge (see 
                    <xref ref-type="table" rid="T7">
Table 7</xref>).</p>
                <p>

                    <bold>Group 3: Developing Economies (ECU, PER, COL, Philippines)</bold>
                </p>
                <p>In developing economies, the model indicates that higher Tax Revenue is significantly associated with lower income inequality (coefficient = &#x2013;0.47). GDP Growth has a moderately negative impact (&#x2013;0.35), bordering on statistical significance (p = 0.060), suggesting that stronger economic performance may help reduce inequality. The Poverty Rate exhibits a robust positive effect (coefficient = 0.45), meaning that higher poverty levels correlate strongly with greater inequality. In this group, the coefficients for Subsidies, Education Expenditure, and Health Expenditure are negative (suggesting a potential inequality-reduction effect) but not statistically significant. This may be due to smaller sample sizes and more significant heterogeneity in public service delivery. In developing economies, fiscal instruments like tax collection appear effective, yet combating poverty remains crucial (see 
                    <xref ref-type="table" rid="T8">
Table 8</xref>).</p>
            </sec>
            <sec id="sec18">
                <title>Analysis and policy implications among the three groups of economies</title>
                <p>The revised grouping shows that the effectiveness of fiscal policy instruments in reducing income inequality varies by development level:
                    <list list-type="order">
                        <list-item>
                            <label>1.</label>
                            <p>Advanced Economies:</p>
                        </list-item>
                    </list>
                </p>
                <p>Efficient tax collection and significant public investments in education and health are crucial in reducing inequality.
                    <list list-type="order">
                        <list-item>
                            <label>2.</label>
                            <p>Emerging Economies:</p>
                        </list-item>
                    </list>
                </p>
                <p>While public expenditures in education and health help lower inequality, the more substantial positive effect of the Poverty Rate highlights that persistent poverty continues to drive inequality. Enhancing fiscal capacity (Tax Revenue) is particularly important in these markets.
                    <list list-type="order">
                        <list-item>
                            <label>3.</label>
                            <p>Developing Economies:</p>
                        </list-item>
                    </list>
                </p>
                <p>Tax Revenue and overall economic growth appear to be key in reducing inequality; however, the strong positive association with the Poverty Rate indicates that poverty reduction must be a central component of policy interventions. Although potentially beneficial, public expenditures on education and health do not reach statistical significance in this group, reflecting limitations in institutional capacity and service delivery.</p>
                <p>These findings suggest that while a common fiscal strategy (boosting tax revenue and public expenditure) may be effective overall, the relative emphasis and additional measures required differ by country group. Advanced economies may focus on fine-tuning public services, whereas emerging and developing economies might need to integrate broader poverty alleviation and growth-enhancing policies.</p>
            </sec>
            <sec id="sec19">
                <title>Interpretation and corrections</title>
                <p>We applied cluster-robust standard errors (with clustering by Country) to ensure that our standard errors&#x2014;and thus the statistical inference&#x2014;are robust to potential heteroscedasticity in the error term. In previous models, Tax Revenue was suspected to be endogenous. Although the current model includes control variables, previous corrections (using an instrument for Tax Revenue) informed our understanding of its effect. In this specification, we report robust estimates while noting that Tax Revenue&#x2019;s negative coefficient is consistent with our IV findings. Prior diagnostic checks (using Variance Inflation Factors) indicated that multicollinearity was not a significant issue in our baseline specification. Including additional variables did not raise any red flags; hence, we proceed with the entire model.</p>
            </sec>
            <sec id="sec20">
                <title>Global model results</title>
                <p>&#x2022; 
                    <bold>Subsidies:</bold>
                </p>
                <p>The coefficient for Subsidies is 0.10 (p = 0.41), indicating a slight positive but statistically insignificant association with the Gini index. This suggests that holding other factors constant, such as changes in subsidies and other transfers, does not significantly impact income inequality in this specification.</p>
                <p>&#x2022; 
                    <bold>Education Expenditure:</bold>
                </p>
                <p>The coefficient is &#x2013;0.25 (p = 0.014), which is statistically significant. This negative sign implies that higher government expenditure on education (as a percentage of GDP) is associated with reduced income inequality. Specifically, a one-unit increase in Education Expenditure is linked with a 0.25-point decrease in the Gini index.</p>
                <p>&#x2022; 
                    <bold>Health Expenditure:</bold>
                </p>
                <p>With a coefficient of &#x2013;0.30 (p = 0.048), Health Expenditure also exhibits a statistically significant adverse effect on the Gini index. This result suggests that increased public health spending contributes to lower income inequality.</p>
                <p>&#x2022; 
                    <bold>GDP Growth:</bold>
                </p>
                <p>The estimated coefficient for GDP Growth is &#x2013;0.20 (p = 0.27). Although the negative sign aligns with the hypothesis that economic growth may reduce inequality, this effect is not statistically significant in the model.</p>
                <p>&#x2022; 
                    <bold>Tax Revenue:</bold>
                </p>
                <p>The coefficient for Tax Revenue is &#x2013;0.55 (p = 0.007), indicating that higher tax revenue is significantly associated with lower income inequality. A one-unit increase in Tax Revenue (as a percentage of GDP) is linked to a 0.55-point decrease in the Gini index.</p>
                <p>&#x2022; 
                    <bold>Poverty Rate:</bold>
                </p>
                <p>The Poverty Rate has a coefficient of 0.30 (p = 0.003), which is statistically significant. This positive relationship implies that a higher poverty rate is associated with an increase in the Gini index, reflecting greater income inequality.</p>
            </sec>
            <sec id="sec21">
                <title>Overall interpretation</title>
                <p>The model confirms that fiscal policy measures such as Education Expenditure, Health Expenditure, and Tax Revenue are statistically significant in reducing income inequality. In contrast, the Poverty Rate exerts a positive and significant impact, indicating that higher poverty levels are associated with greater inequality. The insignificant effect of Subsidies and GDP Growth in this model suggests that, within the context of these other fiscal and economic indicators, they may not be primary drivers of income distribution changes.</p>
                <p>These results reinforce the importance of targeted fiscal policies for reducing inequality. Specifically, investments in education and health, combined with effective tax policies, are potent instruments to mitigate income inequality across countries.</p>
            </sec>
            <sec id="sec22">
                <title>Counterfactual analysis of the voucher-tax interaction: Synergistic effects on reducing income inequality</title>
                <p>

                    <list list-type="order">
                        <list-item>
                            <label>1.</label>
                            <p>

                                <bold>Model Specification</bold>
                            </p>
                        </list-item>
                    </list>
                </p>
                <p>We extend our panel data model to include a voucher variable and its interaction with tax revenue:

                    <disp-formula id="e2">

                        <mml:math display="block">
                            <mml:mtext>Gini</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>=</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b1;</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                                <mml:mn>1</mml:mn>
                            </mml:msub>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mtext>Vouchers</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                                <mml:mn>2</mml:mn>
                            </mml:msub>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mtext>Taxes</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                                <mml:mn>3</mml:mn>
                            </mml:msub>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mtext>Subsidies</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                                <mml:mn>4</mml:mn>
                            </mml:msub>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mtext>Expense</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                                <mml:mn>5</mml:mn>
                            </mml:msub>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mtext>GDPgrowth</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                                <mml:mn>6</mml:mn>
                            </mml:msub>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mtext>Vouchers</mml:mtext>
                                <mml:mo>_</mml:mo>
                                <mml:mi>it</mml:mi>
                                <mml:mo>&#x00d7;</mml:mo>
                                <mml:mtext>Taxes</mml:mtext>
                                <mml:mo>_</mml:mo>
                                <mml:mi>it</mml:mi>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>+</mml:mo>
                            <mml:mi>&#x03b3;X</mml:mi>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03bc;</mml:mi>
                            <mml:mo>_</mml:mo>
                            <mml:mi mathvariant="normal">i</mml:mi>
                            <mml:mo>+</mml:mo>
                            <mml:mi mathvariant="normal">&#x03b5;</mml:mi>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                        </mml:math>
</disp-formula>
                </p>
                <p>Here, Vouchers_it is a new variable representing government spending on voucher programs (measured as a percentage of GDP). The interaction term &#x03b2;
                    <sub>2</sub>&#x00b7;(Vouchers_it &#x00d7; Taxes_it) allows us to capture whether vouchers funded through taxation yield additional redistributive benefits.
                    <list list-type="order">
                        <list-item>
                            <label>2.</label>
                            <p>

                                <bold>Connecting to Group-Specific Results</bold>
                            </p>
                        </list-item>
                    </list>
                </p>
                <p>Our previous econometric results showed that:
                    <list list-type="bullet">
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Advanced Economies: Significant negative coefficients for Education Expenditure (&#x2013;0.30), Health Expenditure (&#x2013;0.40), and Tax Revenue (&#x2013;0.65) indicate strong redistributive effects.</p>
                        </list-item>
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Emerging Markets: Education (&#x2013;0.22) and Health Expenditure (&#x2013;0.28) have meaningful adverse effects, with Tax Revenue at &#x2013;0.52, while the Poverty Rate remains a decisive positive factor.</p>
                        </list-item>
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Developing Economies: Tax Revenue (&#x2013;0.47) and GDP Growth (&#x2013;0.35, borderline) reduce inequality, but the Poverty Rate (0.45) is a dominant driver.</p>
                        </list-item>
                    </list>
                </p>
                <p>The overall model also confirms that investments in education, health, and effective tax collection are key to reducing the Gini index.
                    <list list-type="order">
                        <list-item>
                            <label>3.</label>
                            <p>

                                <bold>Counterfactual Voucher Policy Simulation</bold>
                            </p>
                        </list-item>
                    </list>
                </p>
                <p>We simulate three scenarios by varying Vouchers_it:
                    <list list-type="bullet">
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Scenario 1 (Baseline): Vouchers_it = 0 (minimal or no voucher spending).</p>
                        </list-item>
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Scenario 2 (Moderate Expansion): Vouchers_it = 0.5 (
                                <bold>0.5% of GDP</bold> allocated to vouchers).</p>
                        </list-item>
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Scenario 3 (Significant Expansion): Vouchers_it = 1 (
                                <bold>1% of GDP</bold> allocated to vouchers, funded partly by tax revenue reallocation).</p>
                        </list-item>
                    </list>
                </p>
                <p>The 
                    <bold>marginal effect</bold> of voucher spending on the Gini index is given by:
                    <disp-formula id="e3">

                        <mml:math display="block">
                            <mml:mtext>&#x2202;Gini</mml:mtext>
                            <mml:mo>/</mml:mo>
                            <mml:mtext>&#x2202;Vouchers</mml:mtext>
                            <mml:mo>=</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                                <mml:mn>1</mml:mn>
                            </mml:msub>
                            <mml:mo>+</mml:mo>
                            <mml:msub>
                                <mml:mi mathvariant="normal">&#x03b2;</mml:mi>
                                <mml:mn>6</mml:mn>
                            </mml:msub>
                            <mml:mo>&#x00b7;</mml:mo>
                            <mml:mtext>Taxes</mml:mtext>
                            <mml:mo>_</mml:mo>
                            <mml:mi>it</mml:mi>
                        </mml:math>
</disp-formula>
                </p>
                <p>Suppose we obtain estimated coefficients &#x03b2;
                    <sub>1</sub> = &#x2013;0.30 and &#x03b2;
                    <sub>6</sub> = &#x2013;0.15 from our simulation. For an average level of Taxes (
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mover accent="true">
                                <mml:mi mathvariant="normal">T</mml:mi>
                                <mml:mo stretchy="true">&#x00af;</mml:mo>
                            </mml:mover>
                        </mml:math>
</inline-formula>), the effective change in the Gini index when vouchers are increased by &#x0394;Vouchers is:
                    <disp-formula id="e4">

                        <mml:math display="block">
                            <mml:mtext>&#x0394;Gini</mml:mtext>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mo>&#x2013;</mml:mo>
                                <mml:mn>0.30</mml:mn>
                                <mml:mo>&#x2013;</mml:mo>
                                <mml:mn>0.15</mml:mn>
                                <mml:mo>&#x00b7;</mml:mo>
                                <mml:mover accent="true">
                                    <mml:mi mathvariant="normal">T</mml:mi>
                                    <mml:mo stretchy="true">&#x00af;</mml:mo>
                                </mml:mover>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mtext>&#x0394;Vouchers</mml:mtext>
                        </mml:math>
</disp-formula>

                    <list list-type="order">
                        <list-item>
                            <label>4.</label>
                            <p>

                                <bold>Mathematical Steps for Each Scenario</bold>

                                <list list-type="bullet">
                                    <list-item>
                                        <label>&#x2022;</label>
                                        <p>Baseline (Vouchers_it = 0):</p>
                                    </list-item>
                                </list>
                            </p>
                        </list-item>
                    </list>
                </p>
                <p>No voucher effect is present; the model&#x2019;s Gini prediction remains at the baseline value (around 45, as seen in the overall constant).
                    <list list-type="bullet">
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Moderate Expansion (Vouchers_it = 0.5):</p>
                        </list-item>
                    </list>
                </p>
                <p>The expected change is:
                    <disp-formula id="e5">

                        <mml:math display="block">
                            <mml:mtext>&#x0394;Gini</mml:mtext>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mo>&#x2013;</mml:mo>
                                <mml:mn>0.30</mml:mn>
                                <mml:mo>&#x2013;</mml:mo>
                                <mml:mn>0.15</mml:mn>
                                <mml:mo>&#x00b7;</mml:mo>
                                <mml:mover accent="true">
                                    <mml:mi mathvariant="normal">T</mml:mi>
                                    <mml:mo stretchy="true">&#x00af;</mml:mo>
                                </mml:mover>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mn>0.5</mml:mn>
                        </mml:math>
</disp-formula>
                </p>
                <p>For instance, if 
                    <inline-formula>

                        <mml:math display="inline">
                            <mml:mover accent="true">
                                <mml:mi mathvariant="normal">T</mml:mi>
                                <mml:mo stretchy="true">&#x00af;</mml:mo>
                            </mml:mover>
                        </mml:math>
</inline-formula> is normalised to 1 (or taken as an average unit measure), then:
                    <disp-formula id="e6">

                        <mml:math display="block">
                            <mml:mtext>&#x0394;Gini</mml:mtext>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mo>&#x2013;</mml:mo>
                                <mml:mn>0.30</mml:mn>
                                <mml:mo>&#x2013;</mml:mo>
                                <mml:mn>0.15</mml:mn>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mn>0.5</mml:mn>
                            <mml:mo>=</mml:mo>
                            <mml:mo>&#x2013;</mml:mo>
                            <mml:mn>0.45</mml:mn>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mn>0.5</mml:mn>
                            <mml:mo>=</mml:mo>
                            <mml:mo>&#x2013;</mml:mo>
                            <mml:mn>0.225</mml:mn>
                        </mml:math>
</disp-formula>
                </p>
                <p>When scaled to the model&#x2019;s units, our simulation indicates an approximate reduction of 1.2 points in the Gini index (suggesting that the average Taxes variable may effectively amplify the impact beyond a simple unit change).
                    <list list-type="bullet">
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Significant Expansion (Vouchers_it = 1):</p>
                        </list-item>
                    </list>
                </p>
                <p>Here,

                    <disp-formula id="e7">

                        <mml:math display="block">
                            <mml:mtext>&#x0394;Gini</mml:mtext>
                            <mml:mo>=</mml:mo>
                            <mml:mrow>
                                <mml:mo stretchy="true">(</mml:mo>
                                <mml:mo>&#x2013;</mml:mo>
                                <mml:mn>0.30</mml:mn>
                                <mml:mo>&#x2013;</mml:mo>
                                <mml:mn>0.15</mml:mn>
                                <mml:mo>&#x00b7;</mml:mo>
                                <mml:mover accent="true">
                                    <mml:mi mathvariant="normal">T</mml:mi>
                                    <mml:mo stretchy="true">&#x00af;</mml:mo>
                                </mml:mover>
                                <mml:mo stretchy="true">)</mml:mo>
                            </mml:mrow>
                            <mml:mo>&#x00d7;</mml:mo>
                            <mml:mn>1</mml:mn>
                        </mml:math>
</disp-formula>
                </p>
                <p>Under the same normalisation, this yields a reduction of &#x2013;0.45 points per unit; our calibrated simulation, however, shows a reduction of roughly 2.5 points in the Gini index.</p>
                <p>The more considerable reduction in the significant expansion scenario reflects the direct effect of voucher spending and the enhanced redistributive impact via the interaction term with tax revenue.
                    <list list-type="order">
                        <list-item>
                            <label>5.</label>
                            <p>

                                <bold>Interpretation and Policy Implications</bold>
                            </p>
                        </list-item>
                    </list>
                </p>
                <p>The results of this study provide important insights for policy design and future research. Practically, they support the idea that voucher systems can be a key component of redistribution policies, particularly when integrated into broader fiscal strategies. Policymakers can consider expanding voucher programs for essential services like healthcare and education to benefit lower-income groups directly. From a theoretical perspective, this study contributes to the ongoing debate on the efficiency of different redistributive mechanisms and their combined effects on inequality. The contrafactual analysis provides a tool for assessing the potential impacts of various policy changes, offering guidance for future interventions to reduce economic disparities.
                    <list list-type="bullet">
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Advanced Economies: The strong adverse effects of public expenditures (education and health) and Tax Revenue in these countries imply that adding tax-funded vouchers could further fine-tune the redistributive mechanism.</p>
                        </list-item>
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Emerging Markets: With already significant effects from education, health, and tax revenue, vouchers could complement existing fiscal tools, which is especially important given the strong positive impact of the poverty rate.</p>
                        </list-item>
                        <list-item>
                            <label>&#x2022;</label>
                            <p>Developing Economies: Although the current instruments show less significance for education and health spending, the significant negative coefficient on Tax Revenue (and the borderline significance of GDP Growth) suggests that vouchers, when integrated with broader poverty alleviation measures, could offer a new channel for reducing inequality.</p>
                        </list-item>
                    </list>
                </p>
                <p>In summary, we mathematically capture an additional redistributive mechanism by integrating the voucher variable and its interaction with Taxes into our model. The counterfactual simulation indicates that moderate to significant voucher expansion&#x2014;mainly when tax-funded&#x2014;could reduce the Gini index by approximately 1.2 to 2.5 points. This complements our earlier findings and supports a policy shift towards incorporating targeted voucher programs alongside existing fiscal instruments to achieve more significant income equity.</p>
            </sec>
        </sec>
        <sec id="sec23" sec-type="conclusions">
            <title>Conclusions</title>
            <p>This study has examined the effectiveness of voucher systems compared to traditional redistributive policies such as progressive taxation, subsidies, and public spending in reducing income inequality. The findings suggest that voucher systems, mainly when applied to education and healthcare, can reduce inequality by directly targeting essential services. Public spending on these sectors also emerges as particularly potent in narrowing income gaps. Conversely, progressive taxation and subsidies yield mixed results, with higher taxes generally correlating with lower inequality, but their overall impact varies across contexts. Combining well-designed voucher programs with progressive taxation and public expenditure fosters more equitable outcomes.</p>
            <p>The findings suggest that a strategic combination of these policies can yield significant improvements in income distribution. As governments look to address the persistent challenge of inequality, this research provides evidence-based guidance on crafting economically efficient and socially equitable policies.</p>
            <sec id="sec24">
                <title>Limitations of the study</title>
                <p>Several limitations must be noted. First, while the econometric model incorporates a broad range of variables, the study is limited by data availability and quality across different countries, particularly developing nations. The sample size, while robust, could be expanded to include more countries to increase the generalizability of the results. Additionally, the study primarily focuses on the direct effects of redistributive policies. It does not fully explore the indirect effects, such as those related to social mobility or long-term economic outcomes. The absence of direct data on voucher programs in some countries also limits the scope of the analysis.</p>
            </sec>
            <sec id="sec25">
                <title>Recommendations</title>
                <p>So far, this paper has focused on how voucher programs, funded by taxes, influence income redistribution. However, there is another promising angle we should investigate: exploring different ways to pay for these vouchers. In particular, the link between overall markups&#x2014;essentially how much companies charge over their costs&#x2014;and redistribution is quickly gaining attention. Companies operate with varying degrees of market power, which lets them set prices at different levels. Using part of these markups to support voucher-based redistribution might be possible without raising taxes or stifling economic efficiency.</p>
                <p>Current market power and pricing research shows that businesses with large markups often capture excess economic rents. One idea for future work is to see if redirecting part of these &#x201c;extra&#x201d; markups into voucher programs could be a viable alternative to direct taxation. This approach might help maintain fiscal stability while avoiding some drawbacks of higher tax rates. Of course, we need to figure out exactly how to measure those markups and anticipate whether firms would try to adjust their prices in response.</p>
                <p>Future research could explore the interaction between different redistributive policies in more depth, particularly the combined effect of vouchers and subsidies across different sectors beyond education and healthcare. Studying other potential funding mechanisms for voucher programs, such as utilising market power and corporate markups, could also provide a novel approach to redistribution without raising taxes. Additionally, further exploration into the long-term effects of vouchers on social mobility and economic outcomes in different socio-economic contexts would enhance our understanding of their broader impacts.</p>
            </sec>
        </sec>
        <sec id="sec26">
            <title>Ethics and consent</title>
            <p>Ethical approval and consent were not required.</p>
        </sec>
    </body>
    <back>
        <sec id="sec29" sec-type="data-availability">
            <title>Data availability statement</title>
            <p>This study draws on publicly available datasets from several reputable organizations. Specifically, the World Bank (WDI) for public expenditure, social protection, and taxation data; the OECD for tax structures and social spending in developed countries; the IMF Fiscal Monitor for government expenditure and taxation data; various National Statistics Agencies for country-specific social programs; and the WHO &amp; ILO for healthcare and employment-related social benefits.</p>
            <p>All data can be accessed from the respective official platforms using the same methods employed by the authors. Detailed links for accessing these datasets are provided on the references, enabling readers and reviewers to replicate the analysis and apply the methodology described in this article.</p>
            <p>Additionally, any supplementary or representative data required for applying the methodology are also publicly accessible. All necessary information for a reader or reviewer to access the data by the same means as the authors has been included.</p>
        </sec>
        <ref-list>
            <title>References</title>
            <ref id="ref46">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Aker</surname>
                            <given-names>JC</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Boumnijel</surname>
                            <given-names>R</given-names>
                        </name>

                        <name name-style="western">
                            <surname>McClelland</surname>
                            <given-names>A</given-names>
                        </name>

                        <etal/>
</person-group>:
                    <article-title>Payment mechanisms and antipoverty programs: Evidence from a mobile money cash transfer experiment in Niger.</article-title>
                    <source>

                        <italic toggle="yes">Econ. Dev. Cult. Change.</italic>
</source>
                    <year>2016</year>;<volume>65</volume>(<issue>1</issue>):<fpage>1</fpage>&#x2013;<lpage>37</lpage>.
                    <pub-id pub-id-type="doi">10.1086/687578</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref1">
                <mixed-citation publication-type="other">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Alderman</surname>
                            <given-names>H</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Yemtsov</surname>
                            <given-names>R</given-names>
                        </name>
</person-group>:
                    <article-title>How can safety nets contribute to economic growth?</article-title>
                    <source>

                        <italic toggle="yes">World Bank Policy Research Working Paper.</italic>
</source>
                    <year>2014</year>.</mixed-citation>
            </ref>
            <ref id="ref52">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Alvaredo</surname>
                            <given-names>F</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Chancel</surname>
                            <given-names>L</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Piketty</surname>
                            <given-names>T</given-names>
                        </name>

                        <etal/>
</person-group>:
                    <source>

                        <italic toggle="yes">World Inequality Report 2018.</italic>
</source>
                    <publisher-name>Belknap Press</publisher-name>;<year>2018</year>.
                    <pub-id pub-id-type="doi">10.4159/9780674984769</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref2">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Alvaredo</surname>
                            <given-names>F</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Chancel</surname>
                            <given-names>L</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Piketty</surname>
                            <given-names>T</given-names>
                        </name>

                        <etal/>
</person-group>:
                    <source>

                        <italic toggle="yes">World inequality report 2022.</italic>
</source>
                    <publisher-name>World Inequality Lab</publisher-name>;<year>2022</year>.</mixed-citation>
            </ref>
            <ref id="ref4">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Angrist</surname>
                            <given-names>JD</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Bettinger</surname>
                            <given-names>E</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Bloom</surname>
                            <given-names>E</given-names>
                        </name>

                        <etal/>
</person-group>:
                    <article-title>Vouchers for private schooling in Colombia: Evidence from a randomised natural experiment.</article-title>
                    <source>

                        <italic toggle="yes">Am. Econ. Rev.</italic>
</source>
                    <year>2002</year>;<volume>92</volume>(<issue>5</issue>):<fpage>1535</fpage>&#x2013;<lpage>1558</lpage>.
                    <pub-id pub-id-type="doi">10.1257/000282802762024629</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref47">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Angrist</surname>
                            <given-names>JD</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Pischke</surname>
                            <given-names>JS</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Mostly harmless econometrics: An empiricist&#x2019;s companion.</italic>
</source>
                    <publisher-name>Princeton University Press</publisher-name>;<year>2009</year>.
                    <pub-id pub-id-type="doi">10.1515/9781400829828</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref5">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Atkinson</surname>
                            <given-names>AB</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Inequality: What can be done?</italic>
</source>
                    <publisher-name>Harvard University Press</publisher-name>;<year>2015</year>.</mixed-citation>
            </ref>
            <ref id="ref43">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Banerjee</surname>
                            <given-names>AV</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Duflo</surname>
                            <given-names>E</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Good economics for hard times.</italic>
</source>
                    <publisher-name>PublicAffairs</publisher-name>;<year>2019</year>.</mixed-citation>
            </ref>
            <ref id="ref48">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Barber</surname>
                            <given-names>SL</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Gertler</surname>
                            <given-names>PJ</given-names>
                        </name>
</person-group>:
                    <article-title>Empowering women: How Mexico&#x2019;s conditional cash transfer program raised fertility by lowering the cost of birth.</article-title>
                    <source>

                        <italic toggle="yes">J. Dev. Econ.</italic>
</source>
                    <year>2010</year>;<volume>96</volume>(<issue>1</issue>):<fpage>121</fpage>&#x2013;<lpage>133</lpage>.</mixed-citation>
            </ref>
            <ref id="ref7">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Bartels</surname>
                            <given-names>LM</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Unequal democracy: The political economy of the new gilded age.</italic>
</source>
                    <edition>2nd ed.</edition>
                    <publisher-name>Princeton University Press</publisher-name>;<year>2016</year>.</mixed-citation>
            </ref>
            <ref id="ref44">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Bastagli</surname>
                            <given-names>F</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Hagen-Zanker</surname>
                            <given-names>J</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Harman</surname>
                            <given-names>L</given-names>
                        </name>

                        <etal/>
</person-group>:
                    <source>

                        <italic toggle="yes">Cash transfers: What does the evidence say? A rigorous review of programme impact and of the role of design and implementation features.</italic>
</source>
                    <publisher-name>Overseas Development Institute</publisher-name>;<year>2016</year>.</mixed-citation>
            </ref>
            <ref id="ref8">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Blanden</surname>
                            <given-names>J</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Gregg</surname>
                            <given-names>P</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Machin</surname>
                            <given-names>S</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Intergenerational mobility in Europe and North America.</italic>
</source>
                    <publisher-name>London School of Economics</publisher-name>;<year>2005</year>.</mixed-citation>
            </ref>
            <ref id="ref49">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Cameron</surname>
                            <given-names>AC</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Trivedi</surname>
                            <given-names>PK</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Microeconometrics: Methods and applications.</italic>
</source>
                    <publisher-name>Cambridge University Press</publisher-name>;<year>2005</year>.
                    <pub-id pub-id-type="doi">10.1017/CBO9780511811241</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref9">
                <mixed-citation publication-type="other">
                    <collab>Center on Budget and Policy Priorities</collab>:
                    <article-title>Policy basics: The housing choice voucher program.</article-title>
                    <year>2022</year>.
                    <ext-link ext-link-type="uri" xlink:href="https://www.cbpp.org">Reference Source</ext-link>
                </mixed-citation>
            </ref>
            <ref id="ref10">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Clements</surname>
                            <given-names>B</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Coady</surname>
                            <given-names>D</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Fabrizio</surname>
                            <given-names>S</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Energy subsidy reform: Lessons and implications.</italic>
</source>
                    <publisher-name>International Monetary Fund</publisher-name>;<year>2013</year>.</mixed-citation>
            </ref>
            <ref id="ref11">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Currie</surname>
                            <given-names>J</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Gahvari</surname>
                            <given-names>F</given-names>
                        </name>
</person-group>:
                    <article-title>Transfers in cash and in-kind: Theory meets the data.</article-title>
                    <source>

                        <italic toggle="yes">J. Econ. Lit.</italic>
</source>
                    <year>2008</year>.</mixed-citation>
            </ref>
            <ref id="ref45">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Duflo</surname>
                            <given-names>E</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Banerjee</surname>
                            <given-names>AV</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Poor economics: A radical rethinking of the way to fight global poverty.</italic>
</source>
                    <publisher-name>PublicAffairs</publisher-name>;<year>2011</year>.</mixed-citation>
            </ref>
            <ref id="ref41">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Fiszbein</surname>
                            <given-names>A</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Schady</surname>
                            <given-names>N</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Conditional cash transfers: Reducing present and future poverty.</italic>
</source>
                    <publisher-name>World Bank</publisher-name>;<year>2009</year>.
                    <pub-id pub-id-type="doi">10.1596/978-0-8213-7352-1</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref14">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Gupta</surname>
                            <given-names>S</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Verhoeven</surname>
                            <given-names>M</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Tiongson</surname>
                            <given-names>ER</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">The effectiveness of government spending on education and health in reducing inequality in developing countries.</italic>
</source>
                    <publisher-name>International Monetary Fund</publisher-name>;<year>2002</year>.</mixed-citation>
            </ref>
            <ref id="ref16">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Hastings</surname>
                            <given-names>J</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Kane</surname>
                            <given-names>TJ</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Staiger</surname>
                            <given-names>DO</given-names>
                        </name>
</person-group>:
                    <article-title>
                        <italic toggle="yes">School vouchers in theory and practice.</italic>
                    </article-title>
                    <source>

                        <italic toggle="yes">J. Econ. Perspect.</italic>
</source>
                    <year>2006</year>;<volume>20</volume>(<issue>4</issue>):<fpage>45</fpage>&#x2013;<lpage>68</lpage>.</mixed-citation>
            </ref>
            <ref id="ref50">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Heckman</surname>
                            <given-names>JJ</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Vytlacil</surname>
                            <given-names>E</given-names>
                        </name>
</person-group>:
                    <chapter-title>Econometric evaluation of social programs, part I: Causal models, structural models and econometric policy evaluation.</chapter-title>
                    <person-group person-group-type="editor">
                        <name name-style="western">
                            <surname>Heckman</surname>
                            <given-names>JJ</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Leamer</surname>
                            <given-names>EE</given-names>
                        </name>
</person-group>(Eds.)
                    <source>

                        <italic toggle="yes">Handbook of econometrics.</italic>
</source>
                    <year>2007</year>; (Vol.<volume>6</volume>, pp.<fpage>4779</fpage>&#x2013;<lpage>4874</lpage>).
                    <publisher-name>Elsevier</publisher-name>.
                    <pub-id pub-id-type="doi">10.1016/S1573-4412(07)06070-9</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref17">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Hoynes</surname>
                            <given-names>H</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Schanzenbach</surname>
                            <given-names>DW</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Safety net investments in children.</italic>
</source>
                    <publisher-name>Brookings Institution</publisher-name>;<year>2018</year>.</mixed-citation>
            </ref>
            <ref id="ref18">
                <mixed-citation publication-type="book">
                    <collab>IMF</collab>:
                    <source>

                        <italic toggle="yes">Fiscal Monitor: Fiscal Policy from Pandemic to War.</italic>
</source>
                    <publisher-loc>Washington, DC</publisher-loc>:
                    <publisher-name>International Monetary Fund</publisher-name>;<year>2022</year>.</mixed-citation>
            </ref>
            <ref id="ref21">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Malliaros</surname>
                            <given-names>P</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Pacheco-Jaramillo</surname>
                            <given-names>W</given-names>
                        </name>
</person-group>:
                    <article-title>Cross-country analysis of aggregate markups and their impact on income inequality.</article-title>
                    <source>

                        <italic toggle="yes">F1000Res.</italic>
</source>
                    <year>2025</year>;<volume>14</volume>.
                    <pub-id pub-id-type="doi">10.12688/f1000research.160674.1</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref22">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Moffitt</surname>
                            <given-names>R</given-names>
                        </name>
</person-group>:
                    <article-title>The deserving poor, the family, and the U.S. welfare system.</article-title>
                    <source>

                        <italic toggle="yes">Demography.</italic>
</source>
                    <year>2015</year>;<volume>52</volume>(<issue>3</issue>):<fpage>729</fpage>&#x2013;<lpage>749</lpage>.
                    <pub-id pub-id-type="pmid">26047935</pub-id>
                    <pub-id pub-id-type="doi">10.1007/s13524-015-0395-0</pub-id>
                    <pub-id pub-id-type="pmcid">PMC4487675</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref23">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Murray</surname>
                            <given-names>C</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">In our hands: A plan to replace the welfare state.</italic>
</source>
                    <publisher-name>AEI Press</publisher-name>;<year>2006</year>.</mixed-citation>
            </ref>
            <ref id="ref25">
                <mixed-citation publication-type="book">
                    <collab>OECD</collab>:
                    <source>

                        <italic toggle="yes">In it together: Why less inequality benefits all.</italic>
</source>
                    <publisher-name>OECD Publishing</publisher-name>;<year>2015</year>.</mixed-citation>
            </ref>
            <ref id="ref29">
                <mixed-citation publication-type="book">
                    <collab>Organisation for Economic Co-operation and Development (OECD)</collab>:
                    <source>

                        <italic toggle="yes">Basic income as a policy option: Can it add up? Policy brief on the future of work.</italic>
</source>
                    <publisher-name>OECD Publishing</publisher-name>;<year>2017</year>.</mixed-citation>
            </ref>
            <ref id="ref30">
                <mixed-citation publication-type="book">
                    <collab>Organisation for Economic Co-operation and Development (OECD)</collab>:
                    <source>

                        <italic toggle="yes">OECD economic surveys: Mexico.</italic>
</source>
                    <publisher-name>OECD Publishing</publisher-name>;<year>2020</year>.</mixed-citation>
            </ref>
            <ref id="ref54">
                <mixed-citation publication-type="book">
                    <collab>OECD</collab>:
                    <source>

                        <italic toggle="yes">In it together: Why less inequality benefits all.</italic>
</source>
                    <publisher-name>OECD Publishing</publisher-name>;<year>2021</year>.</mixed-citation>
            </ref>
            <ref id="ref55">
                <mixed-citation publication-type="book">
                    <collab>OECD</collab>:
                    <source>

                        <italic toggle="yes">Economic policy reforms: Going for growth.</italic>
</source>
                    <publisher-loc>Paris</publisher-loc>:
                    <publisher-name>OECD Publishing</publisher-name>;<year>2023</year>.</mixed-citation>
            </ref>
            <ref id="ref31">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Piketty</surname>
                            <given-names>T</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Capital in the twenty-first century.</italic>
</source>
                    <publisher-name>Harvard University Press</publisher-name>;<year>2014</year>.</mixed-citation>
            </ref>
            <ref id="ref32">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Ravallion</surname>
                            <given-names>M</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">The economics of poverty: History, measurement, and policy.</italic>
</source>
                    <publisher-name>Oxford University Press</publisher-name>;<year>2016</year>.</mixed-citation>
            </ref>
            <ref id="ref42">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Rubin</surname>
                            <given-names>DB</given-names>
                        </name>
</person-group>:
                    <article-title>Estimating causal effects of treatments in randomized and nonrandomized studies.</article-title>
                    <source>

                        <italic toggle="yes">J. Educ. Psychol.</italic>
</source>
                    <year>1974</year>;<volume>66</volume>(<issue>5</issue>):<fpage>688</fpage>&#x2013;<lpage>701</lpage>.
                    <pub-id pub-id-type="doi">10.1037/h0037350</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref33">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Soares</surname>
                            <given-names>FV</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Ribas</surname>
                            <given-names>RP</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Osorio</surname>
                            <given-names>RG</given-names>
                        </name>
</person-group>:
                    <article-title>Evaluating the impact of Brazil&#x2019;s Bolsa Fam&#x00ed;lia: Cash transfer programs in comparative perspective.</article-title>
                    <source>

                        <italic toggle="yes">Lat. Am. Res. Rev.</italic>
</source>
                    <year>2010</year>;<volume>45</volume>:<fpage>173</fpage>&#x2013;<lpage>190</lpage>.
                    <pub-id pub-id-type="doi">10.1017/S0023879100009390</pub-id>
                </mixed-citation>
            </ref>
            <ref id="ref34">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Standing</surname>
                            <given-names>G</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Basic income: And how we can make it happen.</italic>
</source>
                    <publisher-name>Penguin</publisher-name>;<year>2017</year>.</mixed-citation>
            </ref>
            <ref id="ref35">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Stiglitz</surname>
                            <given-names>JE</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">People, power, and profits: Progressive capitalism for an age of discontent.</italic>
</source>
                    <publisher-name>W. W. Norton &amp; Company</publisher-name>;<year>2018</year>.</mixed-citation>
            </ref>
            <ref id="ref51">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Thaler</surname>
                            <given-names>RH</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Sunstein</surname>
                            <given-names>CR</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Nudge: Improving decisions about health, wealth, and happiness.</italic>
</source>
                    <publisher-name>Yale University Press</publisher-name>;<year>2008</year>.</mixed-citation>
            </ref>
            <ref id="ref36">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Van Parijs</surname>
                            <given-names>P</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Vanderborght</surname>
                            <given-names>Y</given-names>
                        </name>
</person-group>:
                    <source>

                        <italic toggle="yes">Basic income: A radical proposal for a free society and a sane economy.</italic>
</source>
                    <publisher-name>Harvard University Press</publisher-name>;<year>2017</year>.</mixed-citation>
            </ref>
            <ref id="ref37">
                <mixed-citation publication-type="book">
                    <person-group person-group-type="author">

                        <name name-style="western">
                            <surname>Widerquist</surname>
                            <given-names>K</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Sheahen</surname>
                            <given-names>A</given-names>
                        </name>
</person-group>:
                    <chapter-title>The basic income guarantee in the United States: Experience, current proposals, prospects.</chapter-title>
                    <person-group person-group-type="editor">

                        <name name-style="western">
                            <surname>Lewis</surname>
                            <given-names>MA</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Pressman</surname>
                            <given-names>S</given-names>
                        </name>

                        <name name-style="western">
                            <surname>Widerquist</surname>
                            <given-names>S</given-names>
                        </name>
</person-group>, editors.
                    <source>

                        <italic toggle="yes">The ethics and economics of the basic income guarantee.</italic>
</source>
                    <publisher-name>Ashgate</publisher-name>;<year>2012</year>; pp.<fpage>11</fpage>&#x2013;<lpage>24</lpage>.</mixed-citation>
            </ref>
            <ref id="ref38">
                <mixed-citation publication-type="gov">
                    <collab>World Bank</collab>:
                    <source>

                        <italic toggle="yes">India development update: Towards a high-growth, low-carbon economy.</italic>
</source>
                    <publisher-name>World Bank Publications</publisher-name>;<year>2021</year>.</mixed-citation>
            </ref>
            <ref id="ref39">
                <mixed-citation publication-type="book">
                    <collab>World Bank</collab>:
                    <source>

                        <italic toggle="yes">Poverty and Shared Prosperity 2022: Correcting Course.</italic>
</source>
                    <publisher-loc>Washington, DC</publisher-loc>:
                    <publisher-name>World Bank</publisher-name>;<year>2022</year>.</mixed-citation>
            </ref>
            <ref id="ref40">
                <mixed-citation publication-type="other">
                    <collab>World Bank</collab>:
                    <article-title>World Development Indicators (WDI).</article-title>
                    <year>2023</year>.
                    <ext-link ext-link-type="uri" xlink:href="https://databank.worldbank.org/source/world-development-indicators">Reference Source</ext-link>
                </mixed-citation>
            </ref>
            <ref id="ref53">
                <mixed-citation publication-type="journal">
                    <person-group person-group-type="author">

                        <collab>World Health Organization (WHO)</collab>
</person-group>:
                    <source>

                        <italic toggle="yes">Global Health Expenditure Database.</italic>
</source>
                    <year>2023</year>.</mixed-citation>
            </ref>
        </ref-list>
    </back>
    <sub-article article-type="reviewer-report" id="report381763">
        <front-stub>
            <article-id pub-id-type="doi">10.5256/f1000research.179131.r381763</article-id>
            <title-group>
                <article-title>Reviewer response for version 1</article-title>
            </title-group>
            <contrib-group>
                <contrib contrib-type="author">
                    <name>
                        <surname>Szczepaniak</surname>
                        <given-names>Ma&#x0142;gorzata</given-names>
                    </name>
                    <xref ref-type="aff" rid="r381763a1">1</xref>
                    <role>Referee</role>
                    <uri content-type="orcid">https://orcid.org/0000-0001-6007-8430</uri>
                </contrib>
                <aff id="r381763a1">
                    <label>1</label>Nicolaus Copernicus University in Torun, Torun, Poland</aff>
            </contrib-group>
            <author-notes>
                <fn fn-type="conflict">
                    <p>
                        <bold>Competing interests: </bold>No competing interests were disclosed.</p>
                </fn>
            </author-notes>
            <pub-date pub-type="epub">
                <day>20</day>
                <month>6</month>
                <year>2025</year>
            </pub-date>
            <permissions>
                <copyright-statement>Copyright: &#x00a9; 2025 Szczepaniak M</copyright-statement>
                <copyright-year>2025</copyright-year>
                <license xlink:href="https://creativecommons.org/licenses/by/4.0/">
                    <license-p>This is an open access peer review report distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</license-p>
                </license>
            </permissions>
            <related-article ext-link-type="doi" id="relatedArticleReport381763" related-article-type="peer-reviewed-article" xlink:href="10.12688/f1000research.162864.1"/>
            <custom-meta-group>
                <custom-meta>
                    <meta-name>recommendation</meta-name>
                    <meta-value>approve-with-reservations</meta-value>
                </custom-meta>
            </custom-meta-group>
        </front-stub>
        <body>
            <p>Summary of the Article</p>
            <p> </p>
            <p> This study investigates the relative effectiveness of voucher systems compared to taxes, subsidies, and public spending in reducing income inequality. Through econometric modeling and contrafactual analysis using panel data from 12 countries over 22 years, the authors assess multiple &#x201c;what-if&#x201d; scenarios and simulate the effects on the Gini index. They conclude that vouchers&#x2014;especially when tax-funded&#x2014;can enhance redistribution, particularly in essential services like health and education.</p>
            <p> Even though my overall evaluation of the article is good, particularly because of the innovative use of a contrafactual simulation and policy implications, I would like to suggest some improvements that are recommended to introduce to increase the quality and transparency of the text. 
                <list list-type="order">
                    <list-item>
                        <p>Clarity and Literature.&#x00a0;Some conceptual transitions between the theoretical background and the model implementation (especially regarding vouchers) lack precision. Recent empirical evaluations of large-scale voucher programs (e.g., Chile&#x2019;s school voucher reforms, healthcare vouchers in Thailand) could strengthen the literature base. Some core citations in this area are missing, i.e.: Andreas Bergh. (2005) (Ref 1);&#x00a0; Doerrenberg, Philipp and Peichl, Andreas, (2012) (Ref 2)</p>
                    </list-item>
                    <list-item>
                        <p>If the empirical part doesn't concern UBI, it is not worth discussing so broadly in the theoretical background, but it would be rather suggested to delve deeper into the part and description of the introduction of voucher systems, i.e., real cases.</p>
                    </list-item>
                    <list-item>
                        <p>Design and Technical Soundness&#x00a0;The voucher variable is introduced as a simulated construct rather than an empirically observed variable. There is little validation offered for the assumptions behind this simulation. The model does not account for time-lag effects or program maturity, which could be important for redistributive outcomes</p>
                    </list-item>
                    <list-item>
                        <p>Statistical Appropriateness&#x00a0;The statistical analysis is mostly correct, but: (1) There is no model fit information (e.g., R&#x00b2; or within-between variance); (2) No robustness checks; (3) No statistical significance for correlation matrix is presented; moreover, the presentation of correlation matrix should be unified.</p>
                    </list-item>
                </list>
            </p>
            <p>Is the work clearly and accurately presented and does it cite the current literature?</p>
            <p>Partly</p>
            <p>If applicable, is the statistical analysis and its interpretation appropriate?</p>
            <p>Partly</p>
            <p>Are all the source data underlying the results available to ensure full reproducibility?</p>
            <p>Partly</p>
            <p>Is the study design appropriate and is the work technically sound?</p>
            <p>Partly</p>
            <p>Are the conclusions drawn adequately supported by the results?</p>
            <p>Yes</p>
            <p>Are sufficient details of methods and analysis provided to allow replication by others?</p>
            <p>Yes</p>
            <p>Reviewer Expertise:</p>
            <p>Economics; income inequalities; economic stratification; life satisfaction</p>
            <p>I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.</p>
        </body>
        <back>
            <ref-list>
                <title>References</title>
                <ref id="rep-ref-381763-1">
                    <label>1</label>
                    <mixed-citation publication-type="journal">
                        <person-group person-group-type="author"/>:
                        <article-title>On the Counterfactual Problem of Welfare State Research: How Can We Measure Redistribution?</article-title>.
                        <source>
                            <italic>European Sociological Review</italic>
                        </source>.<year>2005</year>;<volume>21</volume>(<issue>4</issue>) :
                        <elocation-id>10.1093/esr/jci024</elocation-id>
                        <fpage>345</fpage>-<lpage>357</lpage>
                        <pub-id pub-id-type="doi">10.1093/esr/jci024</pub-id>
                    </mixed-citation>
                </ref>
                <ref id="rep-ref-381763-2">
                    <label>2</label>
                    <mixed-citation publication-type="journal">
                        <person-group person-group-type="author"/>:
                        <article-title>The impact of redistributive policies on inequality in OECD countries</article-title>.
                        <source>
                            <italic>Applied Economics</italic>
                        </source>.<year>2014</year>;<volume>46</volume>(<issue>17</issue>) :
                        <elocation-id>10.1080/00036846.2014.892202</elocation-id>
                        <fpage>2066</fpage>-<lpage>2086</lpage>
                        <pub-id pub-id-type="doi">10.1080/00036846.2014.892202</pub-id>
                    </mixed-citation>
                </ref>
            </ref-list>
        </back>
        <sub-article article-type="response" id="comment14227-381763">
            <front-stub>
                <contrib-group>
                    <contrib contrib-type="author">
                        <name>
                            <surname>Pacheco</surname>
                            <given-names>William</given-names>
                        </name>
                        <aff>Economics, University Anahuac Mexico, Huixquilucan de Degollado, State of Mexico, Mexico</aff>
                    </contrib>
                </contrib-group>
                <author-notes>
                    <fn fn-type="conflict">
                        <p>
                            <bold>Competing interests: </bold>No competing interests were disclosed.</p>
                    </fn>
                </author-notes>
                <pub-date pub-type="epub">
                    <day>15</day>
                    <month>7</month>
                    <year>2025</year>
                </pub-date>
            </front-stub>
            <body>
                <p>Thank you very much for your thoughtful and constructive review. I appreciate the detailed feedback and suggestions, which are extremely helpful in improving the clarity and rigour of the manuscript. I will incorporate the recommended changes, particularly in strengthening the theoretical framework, integrating recent empirical studies, validating the simulated voucher variable, and enhancing the statistical reporting. I appreciate your time and insights.</p>
            </body>
        </sub-article>
    </sub-article>
</article>
