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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">JEF</journal-id>
<journal-title-group>
<journal-title>Journal of Economic and Financial Sciences</journal-title>
</journal-title-group>
<issn pub-type="ppub">1995-7076</issn>
<issn pub-type="epub">2312-2803</issn>
<publisher>
<publisher-name>AOSIS</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">JEF-18-1056</article-id>
<article-id pub-id-type="doi">10.4102/jef.v18i1.1056</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Linking wealth and household head traits via quantile multilevel models in South Africa</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6428-8814</contrib-id>
<name>
<surname>Mulamba</surname>
<given-names>Kabeya C.</given-names>
</name>
<xref ref-type="aff" rid="AF0001">1</xref>
</contrib>
<aff id="AF0001"><label>1</label>South African Research Chair in Industrial Development, School of Economics, College of Business and Economics, University of Johannesburg, Johannesburg, South Africa</aff>
</contrib-group>
<author-notes>
<corresp id="cor1"><bold>Corresponding author:</bold> Kabeya Mulamba, <email xlink:href="cmulamba@uj.ac.za">cmulamba@uj.ac.za</email></corresp>
</author-notes>
<pub-date pub-type="epub"><day>31</day><month>08</month><year>2025</year></pub-date>
<pub-date pub-type="collection"><year>2025</year></pub-date>
<volume>18</volume>
<issue>1</issue>
<elocation-id>1056</elocation-id>
<history>
<date date-type="received"><day>26</day><month>05</month><year>2025</year></date>
<date date-type="accepted"><day>23</day><month>07</month><year>2025</year></date>
</history>
<permissions>
<copyright-statement>&#x00A9; 2025. The Author</copyright-statement>
<copyright-year>2025</copyright-year>
<license license-type="open-access" xlink:href="https://creativecommons.org/licenses/by/4.0/">
<license-p>Licensee: AOSIS. This work is licensed under the Creative Commons Attribution License.</license-p>
</license>
</permissions>
<abstract>
<sec id="st1">
<title>Orientation</title>
<p>This study explored how household wealth in South Africa relates to key socioeconomic traits of household heads, against the backdrop of persistent inequality and growing scholarly interest in wealth as a driver of well-being and mobility.</p>
</sec>
<sec id="st2">
<title>Research purpose</title>
<p>The study aimed to answer two central questions: (1) Are household head characteristics associated with different points of household wealth distribution across South African districts? (2) Is there greater variation in wealth within districts than between districts in these associations?</p>
</sec>
<sec id="st3">
<title>Motivation of the study</title>
<p>Despite growing literature on wealth, few studies use micro-level data in developing countries. South Africa&#x2019;s unequal context and the clustered nature of the National Income Dynamic Study (NIDS) data highlight the need for methods that capture distributional and geographic variation.</p>
</sec>
<sec id="st4">
<title>Research approach/design and method</title>
<p>This study applied linear quantile multilevel modelling (LQMM) to Wave 5 NIDS data, accounting for district-level clustering and capturing how household head traits affect wealth across its distribution.</p>
</sec>
<sec id="st5">
<title>Main findings</title>
<p>Household head characteristics &#x2013; particularly age, education, marital status, gender and ethnicity &#x2013; are significantly associated with household wealth. Importantly, these relationships vary across different quantiles of the wealth distribution, and there is substantial variation in wealth within and between districts.</p>
</sec>
<sec id="st6">
<title>Practical/managerial implications</title>
<p>Given the heterogeneity in wealth outcomes, policies aimed at improving economic well-being in South Africa should consider both the geographic context (district-level disparities) and the distributional effects of household head characteristics. One-size-fits-all approaches may fail to address deeper inequalities.</p>
</sec>
<sec id="st7">
<title>Contribution/value-add</title>
<p>This study advances the literature by using LQMM to model wealth across districts and distribution levels, emphasising district-level wealth disparities and deepening understanding of how socioeconomic traits shape wealth in unequal, post-apartheid South Africa. This model captures differences in effects across quantiles but does not correct for endogeneity from things such as omitted variables or measurement error.</p>
</sec>
</abstract>
<kwd-group>
<kwd>household</kwd>
<kwd>wealth</kwd>
<kwd>South Africa</kwd>
<kwd>Districts</kwd>
<kwd>LQMM</kwd>
</kwd-group>
<funding-group>
<funding-statement><bold>Funding information</bold> This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.</funding-statement>
</funding-group>
</article-meta>
</front>
<body>
<sec id="s0001">
<title>Introduction</title>
<p>This study uses Wave 5 of the National Income Dynamics Study (NIDS) (Southern Africa Labour and Development Research Unit <xref ref-type="bibr" rid="CIT0033">2018</xref>), which is a nationally representative survey that is part of a longitudinal survey of individuals and their households on income, expenditure, wealth and other socioeconomic measures in South Africa, to answer two research questions: (1) <italic>Are household heads&#x2019; characteristics associated with the distribution points of household wealth differently across districts in South Africa</italic>? and (2) <italic>Is there a significant difference in the variability of household wealth distribution within districts compared to that of between districts in the aforementioned associations</italic>?</p>
<p>The investigation of wealth and other related phenomena continues to attract particular attention in economics and other social sciences, both in developed and developing countries (Balestra &#x0026; Tonkin <xref ref-type="bibr" rid="CIT0001">2018</xref>; Branson et al. <xref ref-type="bibr" rid="CIT0003">2024</xref>; Chatterjee, Czajka &#x0026; Gethin <xref ref-type="bibr" rid="CIT0008">2020</xref>, <xref ref-type="bibr" rid="CIT0009">2022</xref>; Chelwa, Maboshe &#x0026; Hamilton <xref ref-type="bibr" rid="CIT0010">2024</xref>; Jin &#x0026; Xie <xref ref-type="bibr" rid="CIT0017">2017</xref>; Joubert &#x0026; Van der Merwe <xref ref-type="bibr" rid="CIT0019">2021</xref>; Mojsejov&#x00E1; &#x0026; Marcinov&#x00E1; <xref ref-type="bibr" rid="CIT0021">2023</xref>; Muyanga, Jayne &#x0026; Burke <xref ref-type="bibr" rid="CIT0024">2013</xref>; Schmidt &#x0026; Sevak <xref ref-type="bibr" rid="CIT0027">2006</xref>; Shifa et al. <xref ref-type="bibr" rid="CIT0029">2023</xref>; Sierminska, Frick &#x0026; Grabka <xref ref-type="bibr" rid="CIT0030">2010</xref>; Soseco <xref ref-type="bibr" rid="CIT0032">2021</xref>; Vo et al. <xref ref-type="bibr" rid="CIT0039">2023</xref>; Vo &#x0026; Ho <xref ref-type="bibr" rid="CIT0038">2023</xref>). One reason for such interest is that, beyond providing a financial cushion for households during economic hardships, wealth, particularly in the form of physical assets such as land or real estate or investments such as shares, can also serve as a channel for intergenerational mobility. Chelwa et al. (<xref ref-type="bibr" rid="CIT0010">2024</xref>) note that additional income streams, such as rental income and dividends, can be generated through wealth. The reasoning outlined previously aligns with the Asset-Based Welfare Theory, which emphasises that asset accumulation is essential for long-term well-being and economic security (Bryant, Spies-Butcher &#x0026; Stebbing <xref ref-type="bibr" rid="CIT0004">2024</xref>; Johnson &#x0026; Sherraden <xref ref-type="bibr" rid="CIT0018">1992</xref>; Sherraden <xref ref-type="bibr" rid="CIT0028">1991</xref>; Steele <xref ref-type="bibr" rid="CIT0035">2020</xref>; Walks <xref ref-type="bibr" rid="CIT0040">2016</xref>). This is particularly relevant when examining the relationship between the characteristics of household heads and the wealth they accumulate. In addition, this study draws on stratification theory, especially in the context of systemic and structural inequalities in South Africa. Factors such as educational attainment, race, gender and ethnicity of household heads are considered either barriers or catalysts to wealth accumulation among South African households (Pfeffer &#x0026; Waitkus <xref ref-type="bibr" rid="CIT0026">2021</xref>; Spilerman <xref ref-type="bibr" rid="CIT0034">2000</xref>).</p>
<p>Therefore, understanding this phenomenon is crucial for policymakers and academics alike. Besides, some studies aim to understand the dynamics of wealth inequality, while others focus on detecting its determinants, among other things. This study aligns with the latter perspective as it seeks to shed light on the relationships between household heads&#x2019; characteristics and household wealth.</p>
<p>The importance of scholarly attention to this issue is clear, as public policies designed to improve people&#x2019;s lives should be grounded in sound scientific evidence. Before proceeding, it is worth pointing out that wealth in general remains a central issue in South Africa, both in public discourse and academic research. This is largely because of the persistently high levels of inequality in the country, despite the implementation of progressive public policies by the democratic government since 1994. The empirical analysis in this study aims to contribute to this ongoing debate by exploring whether the characteristics of household heads serve as determinants of household wealth in South Africa.</p>
<p>Another noticeable feature in the literature is the deficiency of studies that focus on developing countries, in particular when it comes to the employ of micro-level data (e.g. individuals and households) as opposed to studies that focus on the developed world. This is because of the scarcity of reliable data and other related challenges, such as the complexities involved in measuring wealth itself. For example, Chatterjee et al. (<xref ref-type="bibr" rid="CIT0009">2022</xref>) discuss some limitations of the wealth data in the NIDS.</p>
<p>Regarding the NIDS, it must be noted that some studies (Chelwa et al. <xref ref-type="bibr" rid="CIT0010">2024</xref>; Daniels &#x0026; Khan <xref ref-type="bibr" rid="CIT0011">2019</xref>) offer a counter-argument to the view expressed by Chatterjee et al. (<xref ref-type="bibr" rid="CIT0009">2022</xref>), specifically highlighting steps taken in Wave 5 of the NIDS to improve the data. These works have concluded that the wealth variable(s) in Wave 5 of the NIDS is suitable for cross-sectional analysis. For example, Branson et al. (<xref ref-type="bibr" rid="CIT0003">2024</xref>) and Chelwa et al. (<xref ref-type="bibr" rid="CIT0010">2024</xref>) have used Wave 5 of the NIDS to assess wealth in South Africa at the micro-level.</p>
<p>Despite this positive development regarding micro-level data and empirical application in South Africa, two important methodological aspects still merit mentioning. Initially, the issue of NIDS data clustering has been overlooked in previous studies. It should be noted that individuals&#x2019; or households&#x2019; characteristics in the NIDS are nested within districts, which plausibly makes these observations exhibit dependency within districts. Therefore, traditional single-level econometric techniques used in previous empirical studies may not be suitable for the NIDS data. On the contrary, multilevel or fixed-effects modelling can be a suitable alternative.</p>
<p>While there is an ongoing debate in the social sciences literature regarding the suitability of multilevel versus fixed-effects and other modelling techniques for clustered data, as summarised in Huang (<xref ref-type="bibr" rid="CIT0016">2016</xref>) and Oshchepkov and Shirokanova (<xref ref-type="bibr" rid="CIT0025">2022</xref>), this study sets aside that important discussion for another time and instead opts for multilevel modelling guided by the second research question. In other words, by adopting a multilevel modelling approach, this study does not treat the issue of clustering in the NIDS data as just a nuisance, as is the case in studies that employ fixed effects and other prominent modelling techniques in economics. Furthermore, as Mulamba (<xref ref-type="bibr" rid="CIT0022">2022</xref>) argues, multilevel modelling involves accounting for district-level clustering by dividing the variance of the disturbance term into two random components: a group-specific (i.e. district) random effects component and an error term applicable to all observations. This approach is crucial for addressing the second research question posed in this study, as further discussed in the methodology section.</p>
<p>Moreover, consistent with the argument presented by Bond-Smith et al. (<xref ref-type="bibr" rid="CIT0002">2024</xref>), multilevel modelling in spatial economics implicitly recognises the influence of location &#x2013; such as districts &#x2013; on the relationships under study. This suggests that location- or district-specific factors can influence the economic phenomena under investigation. For instance, a cultural norm that promotes or hinders wealth accumulation might be prevalent in certain districts or regions, while it may be absent in others. From a multilevel modelling point of view, one does not necessarily need to observe these district-specific factors. Instead, the group random effects component of the model takes care of that, as is discussed further in the methodology section of this study.</p>
<p>The preceding discussion highlights the importance of understanding or gaining insight into location-specific factors for public policy-formulation purposes. While the approach taken is a step in the right direction, it should be pointed out, however, that the exploration of all dimensions of location-specific factors is beyond the scope of the present article. Further investigation therefore is warranted.</p>
<p>Moreover, the application of conventional multilevel modelling (or any other single-level regression, for that matter) assumes that independent variables are related to the dependent variable solely through its location parameter, typically the mean. This also means that the outcome (dependent) variable is affected by the predictors in a similar manner, both in terms of magnitude and direction, across the entire distribution. In addition, this assumption seems inappropriate, particularly when studying a phenomenon such as household wealth in South Africa, where wealth or income inequality is well established (Chatterjee et al. <xref ref-type="bibr" rid="CIT0009">2022</xref>; Fortuin, Grebe &#x0026; Makoni <xref ref-type="bibr" rid="CIT0012">2022</xref>; Leibbrandt &#x0026; Diaz Pabon <xref ref-type="bibr" rid="CIT0020">2021</xref>; Wittenberg <xref ref-type="bibr" rid="CIT0041">2017</xref>). This reflects the fact that the influence of household heads&#x2019; characteristics may vary across different levels of wealth distribution. For example, the association at a given <italic>wealth rank, i</italic>, may differ in sign, size and significance from that at <italic>wealth rank j</italic>, because of heterogeneity in the household wealth distribution and many other factors. Thus, rather than merely applying a traditional multilevel modelling approach, it is important to incorporate both multilevel and quantile regression aspects as a more comprehensive, quantitative approach.</p>
<p>Against this background, this study employs a linear quantile multilevel modelling approach (LQMM) to analyse the NIDS data in order to answer the two questions posed. Besides the fact of NIDS data clustering and the suitability of the research methods discussed precedingly, the quest for understanding the relationship between household headship and wealth is not limited to one group of countries. For instance, Vo and Ho (<xref ref-type="bibr" rid="CIT0038">2023</xref>), Vo et al. (<xref ref-type="bibr" rid="CIT0039">2023</xref>) and Wittenberg (<xref ref-type="bibr" rid="CIT0041">2017</xref>) are but a few of the researchers investigating this relationship in developing as well as in developed country contexts. One reason for focusing on household headship is that some of its selected characteristics may hide important societal norms that can explain the phenomenon of household wealth accumulation in South Africa.</p>
<p>Thus, it is not surprising that this study focuses on household headship in South Africa, given the country&#x2019;s historical context. The exclusion of the Black majority and women from access to economic opportunities can be attributed to the establishment and enforcement of the apartheid regime in South Africa, which may still have lingering effects in the present era. As a result, it is plausible that female-headed households may face greater challenges in wealth accumulation than their male-headed counterparts.</p>
<p>Based on the above-stated, this study hypothesises that women (or any other previously or currently disadvantaged groups) may have begun accumulating wealth under less favourable conditions because of historical exclusion. Similarly, ethnicity or race plays a role, as non-black African-headed households may benefit from historical privileges to which black African-headed households did not have access. Thus, the focus of this study is on these household heads&#x2019; characteristics: gender, ethnicity, education, age and marital status.</p>
<p>The structure of this study is as follows. The article begins with an introduction to the study, outlining the problem, main questions, objectives and significance. This is followed by a discussion of the previous studies on the topic and how they are related to this study. Next, the article describes the study&#x2019;s methodology and data. The discussion of the main results and findings follows, concluding with recommendations..</p>
</sec>
<sec id="s0002">
<title>Literature review</title>
<p>This section discusses previous studies on the subject matter. Some aspects of these studies were already introduced earlier (e.g. the issue of methodology), so the focus here is on exploring additional aspects not yet covered. In this respect, research in South Africa focuses predominantly on income rather than wealth, particularly when it comes to micro-level analysis. However, there is a strand of literature that focuses on some aspects of wealth in South Africa. For instance, studies focusing on understanding wealth inequality and distribution have concluded that, even in post-apartheid South Africa, the country continues to experience high levels of wealth inequality (Chatterjee <xref ref-type="bibr" rid="CIT0007">2019</xref>; Chatterjee et al. <xref ref-type="bibr" rid="CIT0008">2020</xref>, <xref ref-type="bibr" rid="CIT0009">2022</xref>).</p>
<p>Other studies have focused on gender and race (ethnicity) to examine individual wealth gaps in South Africa (Casale &#x0026; Oyenubi <xref ref-type="bibr" rid="CIT0006">2024</xref>; Chelwa et al. <xref ref-type="bibr" rid="CIT0010">2024</xref>). The study conducted by Casale and Oyenubi (<xref ref-type="bibr" rid="CIT0006">2024</xref>) argues that understanding wealth at the individual level is crucial, as household-level aggregation can obscure important differences given that household members are not necessarily homogeneous. These findings confirm the existence of gender-based wealth disparities. Chelwa et al. (<xref ref-type="bibr" rid="CIT0010">2024</xref>) compared racial wealth gaps in the United States of America (USA) and South Africa, given the similarities in their histories of discriminatory policies that prevented certain segments of the population in both countries from owning property and fully participating in the economy or led to the dispossession of their assets. These authors conclude that the Black-White wealth gap pattern in South Africa is similar to that in the USA and explain that these gaps exist at different levels of education and age of individuals.</p>
<p>As discussed in the introduction, wealth data discrepancies and measurement challenges at the micro-level have been prominent in earlier studies focusing on South Africa. Notably, the wealth data from NIDS, particularly in Wave 5, is reliable (Chelwa et al. <xref ref-type="bibr" rid="CIT0010">2024</xref>; Daniels &#x0026; Khan <xref ref-type="bibr" rid="CIT0011">2019</xref>). However, despite the availability of this rich micro-level data, no study has yet investigated the relationships between household wealth and the characteristics of household heads in South Africa. The suggestion made by Casale and Oyenubi (<xref ref-type="bibr" rid="CIT0006">2024</xref>) to assess individual wealth rather than household wealth is valid. Nevertheless, this idea presents challenges when considering the economic well-being of individuals. This notion of economic well-being should be understood within the context of the household, which is a functional unit, where members share the benefits of wealth, irrespective of who owns specific assets such as income or housing, as well as the effects of debts within the household.</p>
<p>Based on the preceding, one should note that focusing solely on individuals presents a risk of overlooking the critical aspect of household economic well-being and may lead to the assumption that resources are not pooled among household members living together. In addition to using households as the unit of analysis, this study incorporates individual wealth, as outlined in Casale and Oyenubi (<xref ref-type="bibr" rid="CIT0006">2024</xref>), by including an independent variable called &#x2018;Working Household Members&#x2019;. This variable represents the number of household members who reported being employed or self-employed, and it is assumed that these members have the economic ability to possess wealth (discussed further in Section 3.3).</p>
<p>While there is a scarcity of studies examining the relationship between household wealth and headship in South Africa, a few related studies focus on this topic in other developing countries (Jin &#x0026; Xie <xref ref-type="bibr" rid="CIT0017">2017</xref>; Vo &#x0026; Ho <xref ref-type="bibr" rid="CIT0038">2023</xref>; Vo, Vo &#x0026; Ho <xref ref-type="bibr" rid="CIT0039">2023</xref>). This study builds on their findings to address the gap in research specific to South Africa. In addition, as mentioned in the introduction, the methodology used here offers a unique contribution, particularly in modelling hierarchical (clustered) data such as that from the NIDS.</p>
</sec>
<sec id="s0003">
<title>Research design</title>
<p>As already discussed in the introductory section, an LQMM approach is adopted in this study to answer the two research questions. This section outlines the reasoning behind the chosen econometric modelling approach, the estimation process employed and the data utilised for analysis.</p>
<sec id="s20004">
<title>Rationale for adopting linear quantile multilevel modelling approach</title>
<p>There are two main reasons for utilising the LQMM approach in this study. Firstly, the NIDS data &#x2013; the sole data source for this study &#x2013; provides socioeconomic characteristics of households and individuals nested within district municipalities and provinces in South Africa. This hierarchy structure in the data requires careful attention to the assumption of independence in the distribution of error terms, which is typically presumed in single-level models. Simply assuming independence, or addressing it through a robust estimation, is equivalent to throwing away valuable insights to conform to econometric modelling for single-level models. Instead, the model specification must account for the hierarchical nature of the data by incorporating the group- (i.e., district-) level random effects, as is the case with multilevel or mixed effects modelling.</p>
<p>As discussed throughout this study, the multilevel modelling approach allows for determining whether latent district-wide factors are important to explain household wealth under investigation through the multilevel modelling approach. In addition, this approach is essential for highlighting the between-district variation in household wealth in South Africa. Gaining these insights is valuable for policy formulation, as designing a one-size-fits-all public policy may not be effective when clear differences between districts are evident.</p>
<p>Secondly, besides the independent assumption, generally applied econometric models often require the error term to have a constant variance. One common approach in empirical research is to transform the dependent variable to meet this requirement. However, similar to the previous point, there are cases in which the non-constant variance of the error term provides valuable insights into the economic phenomenon being studied. As this study examines household wealth to determine its relationship with household heads&#x2019; characteristics, it is unreasonable, and also not sound, to assume, <italic>a priori</italic>, that these characteristics may influence household wealth in the same way in both magnitude and direction across districts in South Africa. In other words, this study assumes that the impact of household heads&#x2019; characteristics on wealth varies between less wealthy households and wealthy ones. This <italic>a priori</italic> assumption is based on the already established literature on inequality in South Africa (Chatterjee et al. <xref ref-type="bibr" rid="CIT0009">2022</xref>; Fortuin et al. <xref ref-type="bibr" rid="CIT0012">2022</xref>; Leibbrandt &#x0026; Diaz Pabon <xref ref-type="bibr" rid="CIT0020">2021</xref>; Shifa et al. <xref ref-type="bibr" rid="CIT0029">2023</xref>). Therefore, the quantile econometric approach is relevant for answering the research questions.</p>
<p>For the reasons discussed precedingly, this study combines mixed effects and quantile model dimensions, leading to the adoption of the LQMM modelling approach to address the research questions. In summary, the application of LQMM, as discussed previously, offers a distinct advantage in examining how household heads&#x2019; characteristics influence various points along the household wealth distribution, particularly when accounting for hierarchically structured data. Unlike standard mixed-effects regression, which estimates effects only at the mean of household wealth, and conventional quantile regression, which overlooks within-district correlations and inter-district heterogeneity, the LQMM approach provides robust, quantile-specific estimates. Moreover, this method yields a richer understanding of the heterogeneity across the household wealth distribution while effectively addressing unobserved district-level effects. The following section outlines the strategy used to implement the LQMM approach.</p>
</sec>
<sec id="s20005">
<title>Model specification and estimation procedure</title>
<p>The nesting of households within districts indicates that the NIDS data contain two levels of information: households at level one and districts at level two. For model specification, households are indexed by, <italic>i</italic>(<italic>i</italic> = 1,&#x2026;<italic>M</italic>), while districts are represented by <italic>j</italic>(<italic>j</italic> = 1,&#x2026;<italic>N</italic>). Districts refer to the 8 metropolitan and 44 district municipalities as demarcated in 2011 (since 2001, municipal boundaries in South Africa have been re-demarcated by the Municipal Demarcation Board every 5 years to align with the local government election cycle), while 5413 out of 13 719 households with complete information are retained for analysis. The specification and estimation of the LQMM models follow a two-step procedure, as discussed next.</p>
<sec id="s30006">
<title>Specification of null linear quantile multilevel modelling approach models</title>
<p>For a given quantile <italic>&#x03C4;</italic>, the following <xref ref-type="disp-formula" rid="FD1">Equation 1</xref> represents the null or unconditional LQMM model:</p>
<disp-formula id="FD1"><alternatives><mml:math display="block" id="M1"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>u</mml:mi><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mi>u</mml:mi><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>~</mml:mo><mml:mi>N</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>u</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>~</mml:mo><mml:mi>N</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>u</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-e001.tif"/></alternatives><label>[Eqn 1]</label></disp-formula>
<p>where <italic>y</italic><sub>ij</sub> is <italic>household i&#x2019;s wealth</italic> in <italic>district j, &#x03B1;</italic><sup>(</sup><italic><sup>&#x03C4;</sup></italic><sup>)</sup> is the grand mean of household wealth at quantile <italic>&#x03C4;</italic>, <inline-formula id="I1"><alternatives><mml:math display="inline" id="MI1"><mml:mrow><mml:msubsup><mml:mi>u</mml:mi><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>r</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i001.tif"/></alternatives></inline-formula> is the random effect for <italic>district j</italic> at quantile <italic>&#x03C4;</italic> that is assumed to be normally independent and identical and <inline-formula id="I2"><alternatives><mml:math display="inline" id="MI2"><mml:mrow><mml:msubsup><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i002.tif"/></alternatives></inline-formula> is the error term at quantile <italic>&#x03C4;</italic> that is assumed to be independent, identical and follows a normal distribution with zero means and a constant variance.</p>
<p><xref ref-type="disp-formula" rid="FD1">Equation 1</xref> is referred to as unconditional LQMM because it does not link the dependent variable to any predictor. Its purpose is to assess whether the data at hand are suitable for a multilevel modelling specification. In addition, <xref ref-type="disp-formula" rid="FD1">Equation 1</xref> has two components, fixed and random effects, which need explanation. The fixed-effects component is represented by <inline-formula id="I3"><alternatives><mml:math display="inline" id="MI3"><mml:mrow><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mn>0</mml:mn><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i003.tif"/></alternatives></inline-formula>, which is the grand mean that applies to any household, regardless of the district in which it is located. In other words, it represents the overall intercept of <xref ref-type="disp-formula" rid="FD1">Equation 1</xref> at quantile (<italic>&#x03C4;</italic>). In contrast, the random effect component, denoted by <inline-formula id="I4"><alternatives><mml:math display="inline" id="MI4"><mml:mrow><mml:msubsup><mml:mi>u</mml:mi><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i004.tif"/></alternatives></inline-formula>, is the district-specific intercept at quantile (<italic>&#x03C4;</italic>). Essentially, <inline-formula id="I5"><alternatives><mml:math display="inline" id="MI5"><mml:mrow><mml:msubsup><mml:mi>u</mml:mi><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i005.tif"/></alternatives></inline-formula> captures the variability in household wealth across districts while also reflecting the level of homogeneity within each district.</p>
<p>It must be pointed out that, while <inline-formula id="I6"><alternatives><mml:math display="inline" id="MI6"><mml:mrow><mml:msubsup><mml:mi>u</mml:mi><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i006.tif"/></alternatives></inline-formula>is essential in the specification of <xref ref-type="disp-formula" rid="FD1">Equation 1</xref>, it is rather its variance, <inline-formula id="I7"><alternatives><mml:math display="inline" id="MI7"><mml:mrow><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>u</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i007.tif"/></alternatives></inline-formula>, which conveys useful information for the analysis, as discussed next. This is because this variance together with<inline-formula id="I8"><alternatives><mml:math display="inline" id="MI8"><mml:mrow><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>&#x03B5;</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i008.tif"/></alternatives></inline-formula> is key in determining the suitability of LQMM. The introduction of the random-effect component in <xref ref-type="disp-formula" rid="FD1">Equation 1</xref> can be understood as breaking the variance of <italic>y</italic><sub>ij</sub> into two components:<inline-formula id="I9"><alternatives><mml:math display="inline" id="MI9"><mml:mrow><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>u</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i009.tif"/></alternatives></inline-formula>, representing the within-district variation, and <inline-formula id="I10"><alternatives><mml:math display="inline" id="MI10"><mml:mrow><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>&#x03B5;</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i010.tif"/></alternatives></inline-formula>, representing the between-district variation. Therefore, the total variance of <italic>y</italic><sub>ij</sub> is equal to that shown in <xref ref-type="disp-formula" rid="FD2">Equation 2</xref> as follows:</p>
<disp-formula id="FD2"><alternatives><mml:math display="block" id="M2"><mml:mrow><mml:mi>V</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>u</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>&#x03B5;</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:math><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-e002.tif"/></alternatives><label>[Eqn 2]</label></disp-formula>
<p>Against the above-discussed background, the suitability of LQMM for the data is confirmed only if the proportion of between-district variation is high. This suggests that one must first calculate the interclass coefficient (ICC) shown in <xref ref-type="disp-formula" rid="FD3">Equation 3</xref>. A higher ICC is an indication that there is a higher dependence of the dependent variable (household wealth) within districts. The challenge remains in determining what constitutes a higher ICC. This study, however, uses the conventional threshold of an ICC that should be equal to or greater than 0.05 to determine whether LQMM is suitable for the data (Heck, Thomas &#x0026; Tabata <xref ref-type="bibr" rid="CIT0015">2014</xref>):</p>
<disp-formula id="FD3"><alternatives><mml:math display="block" id="M3"><mml:mrow><mml:mi>I</mml:mi><mml:mi>C</mml:mi><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mover accent="true"><mml:mi>&#x03C3;</mml:mi><mml:mo>&#x005E;</mml:mo></mml:mover><mml:mi>u</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mover accent="true"><mml:mi>&#x03C3;</mml:mi><mml:mo>&#x005E;</mml:mo></mml:mover><mml:mi>u</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mover accent="true"><mml:mi>&#x03C3;</mml:mi><mml:mo>&#x005E;</mml:mo></mml:mover><mml:mi>&#x03B5;</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mfrac></mml:mrow></mml:math><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-e003.tif"/></alternatives><label>[Eqn 3]</label></disp-formula>
</sec>
<sec id="s30007">
<title>Specification of random-intercept linear quantile multilevel modelling approach models</title>
<p>The second step depends on the outcome of the first step. If the ICC statistic confirms that the LQMM approach is more suitable than single-level quantile models, then random-intercept or random-slope LQMM models can be estimated. For brevity, only one type of random effect is considered in this study, namely the random-intercept LQMM models, in which only the intercept is allowed to vary across districts. <xref ref-type="disp-formula" rid="FD4">Equation 4</xref> represents the specification of a random-intercept LQMM model at quantile (<italic>&#x03C4;</italic>):</p>
<disp-formula id="FD4"><alternatives><mml:math display="block" id="M4"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>&#x03B1;</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:msubsup><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>K</mml:mi></mml:msubsup><mml:mrow><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mi>k</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo>&#x00AF;</mml:mo></mml:mover><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msubsup><mml:mi>u</mml:mi><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mi>u</mml:mi><mml:mi>j</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>~</mml:mo><mml:mi>N</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>u</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mi>&#x03B5;</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>~</mml:mo><mml:mi>N</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msubsup><mml:mi>&#x03C3;</mml:mi><mml:mi>&#x03B5;</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-e004.tif"/></alternatives><label>[Eqn 4]</label></disp-formula>
<p>All symbols in <xref ref-type="disp-formula" rid="FD4">Equation 4</xref> are consistent with those in <xref ref-type="disp-formula" rid="FD1">Equation 1</xref>, except that the independent variables, which include both the variables of interest, and the control variables related to <italic>household i</italic> in <italic>district j</italic>, are represented as deviations from their respective district averages. This method aligns with the existing literature on mixed-effects modelling, as elaborated further in Mulamba (<xref ref-type="bibr" rid="CIT0022">2022</xref>). It should be pointed out that these deviations are derived using a centring within a cluster (CWC) approach. For binary independent variables, the CWC is applied according to the procedure described by Sommet and Morselli (<xref ref-type="bibr" rid="CIT0031">2017</xref>). The slopes of these dummy variables, treated as deviations, should be interpreted as the average effect of being in the target group on the household wealth within clusters (Yaremych, Preacher &#x0026; Hedeker <xref ref-type="bibr" rid="CIT0042">2021</xref>). Moreover, the term <inline-formula id="I111"><alternatives><mml:math display="inline" id="MI11"><mml:mrow><mml:msubsup><mml:mi>&#x03B2;</mml:mi><mml:mi>k</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x03C4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-i011.tif"/></alternatives></inline-formula> represents the coefficient of the <italic>k</italic>-th independent variable (in deviation) at quantile <italic>&#x03C4;</italic>.</p>
<p>Like <xref ref-type="disp-formula" rid="FD1">Equation 1</xref>, <xref ref-type="disp-formula" rid="FD4">Equation 4</xref> comprises two components, fixed effects and random effects. Coefficients of the fixed-effects component are interpreted as in traditional single-level quantile models. <xref ref-type="disp-formula" rid="FD1">Equations 1</xref> and <xref ref-type="disp-formula" rid="FD4">4</xref> are estimated following the approach proposed by Geraci (<xref ref-type="bibr" rid="CIT0013">2014</xref>) and Geraci and Bottai (<xref ref-type="bibr" rid="CIT0014">2014</xref>) for Q0.25, Q0.5, Q0.75 and Q0.85.</p>
</sec>
</sec>
<sec id="s20008">
<title>Data</title>
<p>The description of the variables used to estimate the LQMM models, as discussed in Section 3.2, is presented in <xref ref-type="table" rid="T0001">Table 1</xref>. All variables were sourced from Wave 5 of the NIDS (Southern Africa Labour and Development Research Institute <xref ref-type="bibr" rid="CIT0033">2018</xref>). To carry out the LQMM analysis, households and their respective heads were considered a level 1 observation, while districts were taken as information for level 2. Although provinces represent the highest hierarchy in the NIDS data, they are not considered for modelling in this study because of their relatively small size (i.e., there are only nine provinces in South Africa).</p>
<table-wrap id="T0001">
<label>TABLE 1</label>
<caption><p>Data description.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th valign="top" align="left">Variables</th>
<th valign="top" align="left">Descriptions</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Household wealth</td>
<td align="left">Household net worth. It is equal to total household assets minus total household debts.</td>
</tr>
<tr>
<td align="left">Age</td>
<td align="left">Number of years of the household head at the time of the interview.</td>
</tr>
<tr>
<td align="left">Gender</td>
<td align="left">Gender of the household head. It is equal to 1 if the household head is male and zero otherwise.</td>
</tr>
<tr>
<td align="left">Marital status</td>
<td align="left">Marital status of the household head. It is equal to 1 if the head is formally married or living together with a partner.</td>
</tr>
<tr>
<td align="left">Education</td>
<td align="left">A binary variable that indicates whether the household head has completed secondary school or equivalent. It is equal to 1 if the head has completed school and zero otherwise.</td>
</tr>
<tr>
<td align="left">Ethnicity</td>
<td align="left">A binary variable that indicates the predominant race in the household. It is equal to 1 if the predominant race is black African and zero otherwise.</td>
</tr>
<tr>
<td align="left">Working household members</td>
<td align="left">Number of residents in the household who received wages from employment in the last month before the interview or are self-employed.</td>
</tr>
<tr>
<td align="left">Residence</td>
<td align="left">A binary variable that indicates whether the household&#x2019;s dwelling is located in an urban or non-urban area. It is equal to 1 if the dwelling is in an urban area and zero otherwise.</td>
</tr>
<tr>
<td align="left">Size</td>
<td align="left">Number of household residents.</td>
</tr>
<tr>
<td align="left">Gender&#x002A;education</td>
<td align="left">A binary variable that captures the interaction between gender and education level of the household head. It is equal to 1 if the household head is a male and has completed secondary school and zero otherwise.</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="TFN0001"><label>&#x002A;</label><p>, indicates the interaction between gender and education.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>In addition, some of the binary variables presented in <xref ref-type="table" rid="T0001">Table 1</xref> were originally categorical in the source data. For computational purposes, these variables were recoded into binary format. Because of space constraints, it is not feasible to provide a detailed explanation of the binary coding process within the manuscript. However, it is acknowledged that this transformation may introduce certain limitations, particularly in relation to the disaggregated groups represented by the original categorical variables.</p>
<p>The independent variables, particularly those of primary interest, were selected deliberately to address the research questions posed in this study. Moreover, these variables, including the control variables, are consistent with the existing literature. Some of them were derived from raw data across three NIDS datasets, namely &#x2018;hhderived_w5_anon_v1.00&#x2019;, &#x2018;householdroster_w5_anon_v1.0.0&#x2019; and &#x2018;hhquestionnaire_w5_anon_v1.0.0&#x2019;. In addition, NIDS data related to education, ethnicity (race) and household residential typology (&#x2018;Residence&#x2019;) contained more than two categories. To facilitate a straightforward interpretation of the estimated parameters, binary variables were created by collapsing these categories into two (an R script on data wrangling, written by the author, is available on request).</p>
<p>The dependent variable, &#x2018;Household wealth&#x2019;, is defined as the net worth of household assets minus household debts, as provided in the dataset (Brophy et al. <xref ref-type="bibr" rid="CIT0005">2018</xref>). Although earlier waves of NIDS faced some criticism regarding the wealth-related variables (Chatterjee et al. <xref ref-type="bibr" rid="CIT0009">2022</xref>), as noted in the introduction, other studies have argued that the data on wealth in Wave 5, which were used for analysis in this study, have seen significant improvement (Chelwa et al. <xref ref-type="bibr" rid="CIT0010">2024</xref>; Daniels &#x0026; Khan <xref ref-type="bibr" rid="CIT0011">2019</xref>).</p>
<p>As this study aimed to investigate the relationships between household wealth and certain characteristics of household heads, the following independent variables (listed in <xref ref-type="table" rid="T0001">Table 1</xref>) are variables of interest: &#x2018;Age&#x2019;, &#x2018;Gender&#x2019;, &#x2018;Marital Status&#x2019;, &#x2018;Education&#x2019; and the interaction between gender and education (&#x2018;Gender&#x002A;Education&#x2019;).</p>
<p>In this context, one might intuitively expect the following relationships. Firstly, households with older heads may be associated with higher wealth levels than those with younger heads. This may be attributed to the fact that wealth tends to accumulate over time, and older heads are presumed to have achieved greater stability in employment or in their careers, enabling their households to accumulate more wealth.</p>
<p>Secondly, considering South Africa&#x2019;s historical context, where certain segments of the population, including women, were excluded from economic opportunities, it is reasonable to expect that female-headed households may accumulate less wealth than male-headed households. Although the variable &#x2018;Ethnicity&#x2019; pertains to the entire household, the same logic applies, as predominantly black African households have historically faced greater economic challenges than other groups. As a result, one would expect a negative relationship between black African households and household wealth.</p>
<p>Thirdly, married household heads often have access to multiple income sources if their spouse also earns, which can enable these households to accumulate more wealth compared to those with unmarried heads. For example, the US Census Bureau reported that the median wealth of households led by married heads was consistently higher across all age groups than that of households with unmarried heads (Sullivan, Hays &#x0026; Bennett <xref ref-type="bibr" rid="CIT0036">2023</xref>).</p>
<p>Fourthly, the relationship between education and household wealth is well established in the literature. For example, one study suggests that the educational attainment of the household head plays a significant role in wealth accumulation (Vo et al. <xref ref-type="bibr" rid="CIT0039">2023</xref>). This may be explained by the fact that education is closely linked to employability and earnings, which enable households to accumulate wealth. Consequently, it is reasonable to expect that households headed by individuals with at least a secondary education qualification will have more wealth compared to those with no formal education.</p>
<p>Fifthly, the inclusion of the interaction term &#x2018;Gender&#x002A;Education&#x2019; aims to evaluate the combined effect of these characteristics on household wealth, consistent with findings from an existing study in the literature (Vo et al. <xref ref-type="bibr" rid="CIT0039">2023</xref>). This variable introduces an important nuance, as it allows for an assessment of whether education serves as an equaliser in addressing gender disparities in wealth accumulation.</p>
<p>In addition to the above-discussed five key independent variables, this study adds four control variables, as outlined in <xref ref-type="table" rid="T0001">Table 1</xref>: &#x2018;Ethnicity&#x2019;, &#x2018;Working Household Members&#x2019;, &#x2018;Residence&#x2019; and &#x2018;Size&#x2019;. The expected relationship between &#x2018;Ethnicity&#x2019; and household wealth has already been addressed in the preceding paragraphs. Regarding &#x2018;Working Household Members&#x2019;, a positive relationship with household wealth is intuitively expected. As the number of working members in a household increase, so do the earnings, thereby enhancing the household&#x2019;s capacity to accumulate wealth.</p>
<p>Moreover, in the context of South Africa, where well-paid jobs are concentrated in urban areas, and owning significant assets such as land in rural regions is challenging because of communal land ownership, urban households are expected to have an advantage in wealth accumulation over their rural counterparts. Household size is also presumed to be linked to wealth although this relationship is not straightforward. While some studies have explored this connection (Vo et al. <xref ref-type="bibr" rid="CIT0039">2023</xref>; Vo &#x0026; Ho <xref ref-type="bibr" rid="CIT0038">2023</xref>), this study contends that the direction of the relationship remains unclear. For instance, based on the findings of a related study conducted by Van Winkle and Monden (<xref ref-type="bibr" rid="CIT0037">2022</xref>), one can conclude that it is not just the size of the household but also its composition, which influences wealth accumulation. Although household composition is an important topic for debate, it will not be explored further here. As a result, the expected relationship between household size and wealth in this study could be either positive or negative.</p>
<p><xref ref-type="table" rid="T0002">Table 2</xref> presents descriptive statistics for continuous variables, while <xref ref-type="table" rid="T0003">Table 3</xref> summarises information on categorical variables. For modelling purposes, all four continuous variables were log transformed. However, as the raw dependent variable, &#x2018;Household wealth&#x2019;, contains negative values &#x2013; indicating that household debts exceed the value of their assets &#x2013; a constant of one was added to each observation, followed by subtracting all values by the minimum before applying the logarithmic transformation. This procedure ensured that all values of &#x2018;Household wealth&#x2019; were positive while preserving the relative differences in the data. It is important to note that, although this transformation is necessary from a computational standpoint, it may affect the distributional accuracy because of the arbitrary choice of the constant. Therefore, to ensure the results are robust and reliable, two other constants in addition to one (1), respectively, 0.5 and 2, were alternatively used for logarithmic transformations.</p>
<table-wrap id="T0002">
<label>TABLE 2</label>
<caption><p>Summary statistics of continuous variables used in linear quantile multilevel modelling approach, National Income Dynamics Study Wave 5.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th valign="top" align="left" rowspan="2">Statistic</th>
<th valign="top" align="center" colspan="4">Variables<hr/></th>
</tr>
<tr>
<th valign="top" align="center">Household wealth</th>
<th valign="top" align="center">Age (years)</th>
<th valign="top" align="center">Working household members (No.)</th>
<th valign="top" align="center">Size</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left">Weighted mean</td>
<td align="center">R1 100 118</td>
<td align="center">45</td>
<td align="center">1</td>
<td align="center">3</td>
</tr>
<tr>
<td align="left">Q0.25</td>
<td align="center">R31 409</td>
<td align="center">35</td>
<td align="center">0</td>
<td align="center">2</td>
</tr>
<tr>
<td align="left">Q0.5</td>
<td align="center">R111 309</td>
<td align="center">46</td>
<td align="center">1</td>
<td align="center">4</td>
</tr>
<tr>
<td align="left">Q0.75</td>
<td align="center">R451 921</td>
<td align="center">57</td>
<td align="center">2</td>
<td align="center">5</td>
</tr>
<tr>
<td align="left">Minimum</td>
<td align="center">R -1 387 035</td>
<td align="center">18</td>
<td align="center">0</td>
<td align="center">1</td>
</tr>
<tr>
<td align="left">Maximum</td>
<td align="center">R350 103 808</td>
<td align="center">92</td>
<td align="center">9</td>
<td align="center">26</td>
</tr>
<tr>
<td align="left">Weighted standard deviation</td>
<td align="center">R7 395 613</td>
<td align="center">13</td>
<td align="center">1</td>
<td align="center">2</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T0003">
<label>TABLE 3</label>
<caption><p>Summary of categorical variables used in linear quantile multilevel modelling approach, National Income Dynamics Study Wave 5.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th valign="top" align="left">Variables</th>
<th valign="top" align="left">Category</th>
<th valign="top" align="center">Proportion</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" rowspan="2" valign="top">Gender</td>
<td align="left">Male</td>
<td align="center">0.58</td>
</tr>
<tr>
<td align="left">Female</td>
<td align="center">0.42</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Marital status</td>
<td align="left">Married</td>
<td align="center">0.77</td>
</tr>
<tr>
<td align="left">Not married</td>
<td align="center">0.23</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Education</td>
<td align="left">Secondary school completed</td>
<td align="center">0.35</td>
</tr>
<tr>
<td align="left">Secondary school not completed</td>
<td align="center">0.65</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Ethnicity</td>
<td align="left">Black African</td>
<td align="center">0.71</td>
</tr>
<tr>
<td align="left">Non-black African</td>
<td align="center">0.29</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Residence</td>
<td align="left">Urban</td>
<td align="center">0.63</td>
</tr>
<tr>
<td align="left">Non-urban</td>
<td align="center">0.37</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Gender<xref ref-type="table-fn" rid="TFN0002">&#x002A;</xref>education</td>
<td align="left">Male and completed secondary school</td>
<td align="center">0.22</td>
</tr>
<tr>
<td align="left">Otherwise (e.g. female and completed or male and secondary school not completed)</td>
<td align="center">0.78</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn id="TFN0002"><label>&#x002A;</label><p>, indicates the interaction between gender and education.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>These transformed variables were then used in regression analyses, and the results were compared with the main findings presented in <xref ref-type="table" rid="T0004">Table 4</xref>. This sensitivity check confirmed the robustness of the transformation.</p>
<table-wrap id="T0004">
<label>TABLE 4</label>
<caption><p>Random-intercept linear quantile multilevel modelling approach estimates.</p></caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th valign="top" align="left" rowspan="2">Parameter</th>
<th valign="top" align="center" colspan="4">Model<hr/></th>
</tr>
<tr>
<th valign="top" align="center"><italic>&#x03C4;</italic> = 0.25</th>
<th valign="top" align="center"><italic>&#x03C4;</italic> = 0.50</th>
<th valign="top" align="center"><italic>&#x03C4;</italic> = 0.75</th>
<th valign="top" align="center"><italic>&#x03C4;</italic> = 0.85</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" rowspan="2" valign="top">Intercept</td>
<td align="center">6.259<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">6.259<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">6.253<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">6.367<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Age</td>
<td align="center">0.373<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">0.373<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">0.371<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">0.420<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Gender</td>
<td align="center">0.0009</td>
<td align="center">0.0009</td>
<td align="center">0.011<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">&#x2212;0.011</td>
</tr>
<tr>
<td align="center">(0.837)</td>
<td align="center">(0.789)</td>
<td align="center">(0.009)</td>
<td align="center">(0.557)</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Marital status</td>
<td align="center">0.012<xref ref-type="table-fn" rid="TFN0003">&#x002A;</xref></td>
<td align="center">0.012<xref ref-type="table-fn" rid="TFN0003">&#x002A;</xref></td>
<td align="center">0.016<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;</xref></td>
<td align="center">0.014</td>
</tr>
<tr>
<td align="center">(0.079)</td>
<td align="center">(0.084)</td>
<td align="center">(0.012)</td>
<td align="center">(0.514)</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Education</td>
<td align="center">0.095<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">0.095<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">0.093<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">0.129<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.001)</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Ethnicity</td>
<td align="center">&#x2212;0.117<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">&#x2212;0.117<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">&#x2212;0.131<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">&#x2212;0.159<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Working household members</td>
<td align="center">0.049<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">0.049<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">0.047<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">0.090<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.000)</td>
<td align="center">(0.011)</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Residence</td>
<td align="center">0.010</td>
<td align="center">0.010</td>
<td align="center">0.021<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;</xref></td>
<td align="center">0.026</td>
</tr>
<tr>
<td align="center">(0.283)</td>
<td align="center">(0.329)</td>
<td align="center">(0.031)</td>
<td align="center">(0.359)</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Size</td>
<td align="center">&#x2212;0.028<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;</xref></td>
<td align="center">&#x2212;0.027<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;</xref></td>
<td align="center">&#x2212;0.046<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
<td align="center">&#x2212;0.074<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;&#x002A;</xref></td>
</tr>
<tr>
<td align="center">(0.025)</td>
<td align="center">(0.017)</td>
<td align="center">(0.000)</td>
<td align="center">(0.003)</td>
</tr>
<tr>
<td align="left" rowspan="2" valign="top">Gender<xref ref-type="table-fn" rid="TFN0003">&#x002A;</xref>education</td>
<td align="center">0.020</td>
<td align="center">0.020</td>
<td align="center">0.033<xref ref-type="table-fn" rid="TFN0004">&#x002A;&#x002A;</xref></td>
<td align="center">0.042</td>
</tr>
<tr>
<td align="center">(0.194)</td>
<td align="center">(0.103)</td>
<td align="center">(0.030)</td>
<td align="center">(0.314)</td>
</tr>
<tr>
<td align="left">Variance of random effects</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">0.8881</td>
</tr>
<tr>
<td align="left">Variance of residuals</td>
<td align="center">0.053</td>
<td align="center">0.024</td>
<td align="center">0.051</td>
<td align="center">0.09</td>
</tr>
<tr>
<td align="left">Log-likelihood</td>
<td align="center">1 416 835</td>
<td align="center">3 266 398</td>
<td align="center">1289</td>
<td align="center">268.4</td>
</tr>
<tr>
<td align="left">AIC</td>
<td align="center">&#x2212;2 833 646</td>
<td align="center">&#x2212;6 521 917</td>
<td align="center">&#x2212;2554</td>
<td align="center">&#x2212;498.9</td>
</tr>
<tr>
<td align="left">ICC for null LQMM</td>
<td align="center">0.93</td>
<td align="center">0.97</td>
<td align="center">0.93</td>
<td align="center">0.49</td>
</tr>
<tr>
<td align="left">Number of observations (households)</td>
<td align="center">5413</td>
<td align="center">5413</td>
<td align="center">5413</td>
<td align="center">5413</td>
</tr>
<tr>
<td align="left">Number of groups (districts)</td>
<td align="center">52</td>
<td align="center">52</td>
<td align="center">52</td>
<td align="center">52</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn><p>AIC, Akaike Information Criterion; ICC, interclass coefficient; LQMM, linear quantile multilevel modelling approach.</p></fn>
<fn id="TFN0003"><label>&#x002A;</label><p>, indicates the interaction between gender and education.</p></fn>
<fn id="TFN0004"><label>&#x002A;&#x002A; and &#x002A;&#x002A;&#x002A;</label><p>, mean the coefficient is statistically significant at 1&#x0025;, 5&#x0025; and 10&#x0025;, respectively.</p></fn>
</table-wrap-foot>
</table-wrap>
<p>Moreover, the data in <xref ref-type="table" rid="T0002">Table 2</xref> highlight significant disparities in South Africa concerning household wealth, the number of working household members and household size. Based on the available data, the calculated Gini coefficient for household wealth is 0.83. This is unsurprising, as inequality is deeply entrenched in South Africa. <xref ref-type="fig" rid="F0001">Figure 1</xref> illustrates the same information, depicting the inequalities in household wealth. Because the mean of household wealth is way above its median (Q0.5), this suggests that wealth in South Africa is highly concentrated among a small group at the top. This finding is also confirmed in <xref ref-type="fig" rid="F0001">Figure 1</xref>.</p>
<fig id="F0001">
<label>FIGURE 1</label>
<caption><p>Lorenz curve of household wealth.</p></caption>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JEF-18-1056-g001.tif"/>
</fig>
<p>There are a few key points to note in <xref ref-type="table" rid="T0003">Table 3</xref>. It is surprising that, even after 30 years of democracy, only 35&#x0025; of household heads in South Africa have attained at least a secondary education. This has significant implications for wealth accumulation, as the lack of adequate education limits individuals&#x2019; access to better opportunities, hence wealth creation. There are more married household heads, and more households are located in urban than rural areas in South Africa.</p>
</sec>
<sec id="s20009">
<title>Ethical considerations</title>
<p>This article followed all ethical standards for research without direct contact with human or animal subjects.</p>
</sec>
</sec>
<sec id="s0010">
<title>Results and discussion</title>
<p>Following the stepwise estimation approach outlined in Section 3.2, two regressions were estimated at each of the four selected quantiles: a null LQMM and a corresponding random-intercept LQMM, totalling eight regressions. However, because of space constraints, only the LQMM estimates at Q0.25, Q0.50, Q0.75 and Q0.85, along with the ICCs for the null LQMM models, are presented in <xref ref-type="table" rid="T0004">Table 4</xref>. Including ICCs is essential, as they are applied to assess whether the LQMM approach is more suitable than single-level quantile regression at each predetermined quantile.</p>
<p>It can be seen that the reported ICCs in <xref ref-type="table" rid="T0004">Table 4</xref> exceed the conventional threshold of 0.05, indicating that 93&#x0025;, 97&#x0025;, 93&#x0025; and 49&#x0025; of the variation in household wealth at Q0.25, Q0.50, Q0.75 and Q0.85, respectively, are explained by district-specific latent factors. This confirms that the LQMM approach is more appropriate for the data.</p>
<p>Given the various LQMM estimates presented in <xref ref-type="table" rid="T0004">Table 4</xref>, this study adopts a straightforward approach to assess each coefficient in terms of the three Ss: significance, sign and size, to facilitate interpretation. In this context, a few main observations arise. Before delving into the discussion of the results, it is important to again highlight the rationale for applying the LQMM in this study. The primary motivation was to account for within-district clustering while also capturing the distributional variation in &#x2018;Household wealth&#x2019;. A key advantage of this approach is its ability to provide a nuanced understanding of how predictors influence different points of the conditional distribution, beyond the mean.</p>
<p>However, it must be acknowledged that the LQMM, particularly as implemented using the R package proposed by Geraci (<xref ref-type="bibr" rid="CIT0013">2014</xref>), does not inherently address potential endogeneity arising from omitted variables, measurement error or simultaneity. Although within-district centring of predictors helps mitigate group-level confounding and enhances interpretability, it does not fully resolve endogeneity concerns. Therefore, while the estimates presented in <xref ref-type="table" rid="T0004">Table 4</xref> offer valuable insights into heterogeneous effects across quantiles, they should be interpreted with caution in light of possible endogeneity.</p>
<p>Firstly, the random-intercept LQMM models at Q0.25 and Q0.5 show similar coefficient patterns based on the three Ss, indicating that the effects of independent variables on household wealth are comparable for both less wealthy households and those at median wealth levels in South Africa.</p>
<p>Secondly, overall, the estimates at Q0.75 and Q0.85 quantiles are not comparable to each other, nor to those at Q0.25 and Q0.5, based on the three Ss. For example, the coefficient for &#x2018;Age&#x2019; is significantly larger at Q0.85, while &#x2018;Gender&#x2019; is only significant at Q0.75. This suggests that, above the median value, household wealth in South Africa is influenced differently, offering valuable insights for a more differentiated approach to public policy design or intervention. It is also worth noting that, for statistically significant LQMM estimates, <xref ref-type="table" rid="T0004">Table 4</xref> reports larger coefficient magnitudes. This implies that changes in household heads&#x2019; characteristics have a greater impact on wealth for wealthier households in South Africa.</p>
<p>Thirdly, turning now to the independent variable of interest, the household head&#x2019;s age and education level consistently explain household wealth, regardless of the household&#x2019;s wealth status. Notably, the relationships between these two characteristics and household wealth are both positive, as expected. While LQMM modelling was not applied in some studies, it is worth noting that these findings are consistent with previous research (Vo &#x0026; Ho <xref ref-type="bibr" rid="CIT0038">2023</xref>; Vo et al. <xref ref-type="bibr" rid="CIT0039">2023</xref>). Specifically, the results for age show that a 1&#x0025; increase in the household head&#x2019;s age is associated with a 0.37&#x0025;, 0.37&#x0025;, 0.37&#x0025; and 0.42&#x0025; increase in household wealth, on average, at Q0.25, Q0.5, Q0.75 and Q0.85, respectively, all other factors being held constant within a cluster. Regarding education, the results imply that the effects of a household head having completed at least secondary education on the logarithm of household wealth are 0.095, 0.095, 0.093 and 0.123 at Q0.25, Q0.5, Q0.75 and Q0.85, respectively.</p>
<p>The marital status of the household head positively explains household wealth only at quantiles lower than Q0.85. As discussed in Section 3, one possible explanation for this positive relationship is that married couples benefit from combining their sources of income, thereby accumulating more wealth than households with unmarried heads. However, this does not apply to wealthier households, as the coefficient for &#x2018;Marital status&#x2019; at Q0.85 is not statistically significant.</p>
<p>In addition, the relationships between &#x2018;Gender&#x2019; and &#x2018;Gender&#x002A;Education&#x2019; with &#x2018;Household Wealth&#x2019; remain unconfirmed, except at Q0.75, where a positive association is observed in both cases. These results indicate that a male-headed household is linked to an increase of 0.011 logarithms in household wealth, while a male-headed household whose head has completed at least secondary education corresponds to an increase of 0.033 logarithms in household wealth within South African districts at Q0.75, holding all else constant. Although this trend is only significant at Q0.75, it highlights existing disparities in South Africa, particularly based on gender. As discussed in Section 3.3, it is evident that female-headed households encounter challenges in wealth accumulation, especially if the head lacks secondary education.</p>
<p>Fourthly, all control variables except for &#x2018;Residence&#x2019; explain household wealth at all quantiles, as shown in <xref ref-type="table" rid="T0004">Table 4</xref>. As anticipated, there is a negative impact on household wealth levels within districts when a household is predominantly black African, as indicated by all four LQMM models. This suggests that ethnicity is an additional dimension contributing to wealth disparities in South Africa. One possible explanation, as argued in this study, is the public policies of exclusion implemented by the apartheid regime, the lingering effects of which continue to disadvantage the black African majority in the country to accumulate wealth, as opposed to other races.</p>
<p>Moreover, &#x2018;Household wealth&#x2019; is positively associated with &#x2018;Working Household Members&#x2019;, indicating that households with a relatively high number of working household members can accumulate more wealth than those with fewer working household members. This suggests that having more working household members provides the household with multiple sources of income, positioning it to accumulate wealth, as discussed in Section 3.3. In contrast, the number of household members represented by &#x2018;Size&#x2019;, regardless of their employment status, is negatively related to the level of household wealth.</p>
<p>After discussing the LQMM estimates, it is now time to assess whether the analysis conducted addresses the research questions posed. Regarding the first question, except for less wealthy households and those at the median level (Q0.25 and Q0.50), household wealth is generally affected by some household heads&#x2019; characteristics in terms of magnitude. For the second question, the reported ICCs reveal significant differences in the variability of household wealth distribution within districts compared to between districts. Therefore, through the application of the LQMM modelling approach, this study has attempted to answer the research questions.</p>
</sec>
<sec id="s0011">
<title>Conclusion</title>
<p>This study used the LQMM modelling approach to examine whether household heads&#x2019; characteristics are associated with household wealth across South African districts and to explore differences in the variability of household wealth within and between districts. Rich data from Wave 5 of NIDS was utilised for this purpose. After implementing a rigorous estimation procedure, the analysis confirmed that certain household characteristics are indeed related to household wealth, as expected. In addition, it was found that these relationships vary in magnitude between wealthier and less wealthy households, and significant differences in wealth variability were observed within and between districts in South Africa.</p>
<p>The findings of this study highlight the need for targeted policies to promote household wealth accumulation in South Africa. For example, the Reconstruction and Development Programme&#x2019;s (RDP) housing initiative should be strengthened and localised at the district level. In the long run, such a programme can enable households to accumulate wealth, as homeownership represents a significant asset that can also serve as collateral for acquiring other types of assets. Similarly, education policies and instruments, such as the National Student Financial Aid Scheme (NSFAS),<xref ref-type="fn" rid="FN0001"><sup>1</sup></xref> require reinforcement, given this study&#x2019;s evidence that a household head&#x2019;s educational attainment is closely linked to household wealth accumulation. Land redistribution also remains crucial, not only for agricultural development but also as a key pathway for asset accumulation among previously disadvantaged households and communities.<xref ref-type="fn" rid="FN0002"><sup>2</sup></xref></p>
</sec>
</body>
<back>
<ack>
<title>Acknowledgements</title>
<sec id="s20012" sec-type="COI-statement">
<title>Competing interests</title>
<p>The author declares that he has no financial or personal relationships that may have inappropriately influenced him in writing this article.</p>
</sec>
<sec id="s20013">
<title>Author&#x2019;s contribution</title>
<p>K.C.M. is the sole author of this research article.</p>
</sec>
<sec id="s20014" sec-type="data-availability">
<title>Data availability</title>
<p>The data that support the findings of this study are available from the corresponding author, K.C.M. upon reasonable request.</p>
</sec>
<sec id="s20015">
<title>Disclaimer</title>
<p>The views and opinions expressed in this article are those of the author and are the product of professional research. The article does not necessarily reflect the official policy or position of any affiliated institution, funder or agency of the author or that of the publisher. The author is responsible for this article&#x2019;s results, findings and content.</p>
</sec>
</ack>
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<fn-group>
<fn><p><bold>How to cite this article:</bold> Mulamba, K.C., 2025, &#x2018;Linking wealth and household head traits via quantile multilevel models in South Africa&#x2019;, <italic>Journal of Economic and Financial Sciences</italic> 18(1), a1056. <ext-link ext-link-type="uri" xlink:href="https://doi.org/10.4102/jef.v18i1.1056">https://doi.org/10.4102/jef.v18i1.1056</ext-link></p></fn>
<fn id="FN0001"><label>1</label><p>NSFAS.</p></fn>
<fn id="FN0002"><label>2</label><p>Land redistribution for agricultural development | South African Government.</p></fn>
</fn-group>
</back>
</article>