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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">115</journal-id>
      <journal-id journal-id-type="index">urn:lsid:arphahub.com:pub:32e1b97d-7003-598d-92e7-0ceb44416cc9</journal-id>
      <journal-title-group>
        <journal-title xml:lang="en">BRICS Journal of Economics</journal-title>
        <abbrev-journal-title xml:lang="en">brics-econ</abbrev-journal-title>
      </journal-title-group>
      <issn pub-type="ppub">2712-7702</issn>
      <issn pub-type="epub">2712-7508</issn>
      <publisher>
        <publisher-name>BRICS Journal of Economics</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.3897/brics-econ.7.e172739</article-id>
      <article-id pub-id-type="publisher-id">172739</article-id>
      <article-categories>
        <subj-group subj-group-type="heading">
          <subject>Research Article</subject>
        </subj-group>
        <subj-group subj-group-type="scientific_subject">
          <subject>(E1) General Aggregative Models</subject>
          <subject>(F1) Trade</subject>
          <subject>(F2) International Factor Movements and International Business</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>The Impact of Digital Services Trade on Economic Growth in Developing Economies: A Machine Learning Approach</article-title>
      </title-group>
      <contrib-group content-type="authors">
        <contrib contrib-type="author" corresp="no">
          <name name-style="western">
            <surname>Allamuratov</surname>
            <given-names>Bekzod</given-names>
          </name>
          <uri content-type="orcid">https://orcid.org/0009-0004-8489-4239</uri>
          <xref ref-type="aff" rid="A1">1</xref>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="western">
            <surname>Mowahed</surname>
            <given-names>Shah Mir</given-names>
          </name>
          <email xlink:type="simple">shahmirmowahed785@gmail.com</email>
          <uri content-type="orcid">https://orcid.org/0009-0009-5464-6476</uri>
          <xref ref-type="aff" rid="A1">1</xref>
        </contrib>
      </contrib-group>
      <aff id="A1">
        <label>1</label>
        <addr-line content-type="verbatim">Hunan University, Changsha (China)</addr-line>
        <institution>Hunan University</institution>
        <addr-line content-type="city">Changsha</addr-line>
        <country>China</country>
        <uri content-type="ror">https://ror.org/05htk5m33</uri>
      </aff>
      <author-notes>
        <fn fn-type="corresp">
          <p>Corresponding author: Shah Mir Mowahed (shahmirmowahed785@gmail.com)</p>
        </fn>
        <fn fn-type="edited-by">
          <p>Academic editor: Kapoguzov E.</p>
        </fn>
      </author-notes>
      <pub-date pub-type="collection">
        <year>2026</year>
      </pub-date>
      <pub-date pub-type="epub">
        <day>07</day>
        <month>07</month>
        <year>2026</year>
      </pub-date>
      <volume>7</volume>
      <issue>2</issue>
      <fpage>1</fpage>
      <lpage>34</lpage>
      <uri content-type="arpha" xlink:href="http://openbiodiv.net/A4119C06-F03E-590D-95F8-A3237B45FEF3">A4119C06-F03E-590D-95F8-A3237B45FEF3</uri>
      <history>
        <date date-type="received">
          <day>21</day>
          <month>09</month>
          <year>2025</year>
        </date>
        <date date-type="accepted">
          <day>22</day>
          <month>12</month>
          <year>2025</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>Bekzod Allamuratov, Shah Mir Mowahed</copyright-statement>
        <license license-type="creative-commons-attribution" xlink:href="http://creativecommons.org/licenses/by/4.0/" xlink:type="simple">
          <license-p>This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</license-p>
        </license>
      </permissions>
      <abstract>
        <label>Abs tract</label>
        <p>Digital services trade (<abbrev xlink:title="Digital services trade">DST</abbrev>) has emerged as an important driver for economic growth and development, which has attracted increasing attention from governments, policymakers, scholars, and industry stakeholders. This paper examines the impact of <abbrev xlink:title="Digital services trade">DST</abbrev> on economic growth in 87 developing countries from 2005 to 2023. Using advanced <abbrev xlink:title="machine learning">ML</abbrev> methods, specifically the CrossFit Partialing-out LASSO linear regression (CrossFit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev>), the study shows that the <abbrev xlink:title="Digital services trade">DST</abbrev> has a positive and statistically significant impact on GDP. The robustness of these findings is further validated by Bayesian Model Averaging, Driscoll-Kraay standard error correction, and alternative <abbrev xlink:title="Digital services trade">DST</abbrev> proxy variables. The mechanism analysis reveals that employment and technological innovation serve as important mediators in the relationship between <abbrev xlink:title="Digital services trade">DST</abbrev> and GDP. The heterogeneity analysis indicates that low-income, upper-middle-income and high-income developing economies, as well as countries with strong digital infrastructure, derive greater economic benefits from <abbrev xlink:title="Digital services trade">DST</abbrev> compared to lower-middle-income countries and those with weaker digital infrastructure. Based on these empirical findings, the study proposes policy recommendations aimed at enhancing the developmental benefits associated with <abbrev xlink:title="Digital services trade">DST</abbrev> in developing countries.</p>
      </abstract>
      <kwd-group>
        <label>Keywords</label>
        <kwd>Economic Growth</kwd>
        <kwd>Digital Services Trade</kwd>
        <kwd>Developing Countries</kwd>
        <kwd>Machine Learning Approach.</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>JEL</meta-name>
          <meta-value>F14, O47, C55</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
    <notes>
      <sec sec-type="Citation" id="sec1">
        <title>Citation</title>
        <p>Allamuratov, B., &amp; Mowahed, S. M. (2026). The Impact of Digital Services Trade on Economic Growth in Developing Economies: A Machine Learning Approach. BRICS Journal of Economics, 7(2), 1–34. <ext-link xlink:type="simple" ext-link-type="doi" xlink:href="10.3897/brics-econ.7.e172739">https://doi.org/10.3897/brics-econ.7.e172739</ext-link></p>
      </sec>
    </notes>
  </front>
  <body>
    <sec sec-type="1. Introduction" id="sec2">
      <title>1. Introduction</title>
      <p>Digital economy development is fundamental to economic advancement and significantly impacts productivity, trade and innovation (<xref ref-type="bibr" rid="B33">Mohammed &amp; Yacine, 2025</xref>; <xref ref-type="bibr" rid="B21">Goldfarb &amp; Tucker, 2019</xref>). Digital services trade (<abbrev xlink:title="Digital services trade">DST</abbrev>) is crucial for modern economic policy due to the widespread adoption of ICT, including internet access, broadband, mobile networks, and digital literacy (<xref ref-type="bibr" rid="B39">OECD, 2020</xref>). For developing countries, digitalization of the economy, particularly <abbrev xlink:title="Digital services trade">DST</abbrev>, presents a strategic opportunity to overcome traditional developmental barriers, increase operational efficiency, enhance social inclusion and promote economic growth (<xref ref-type="bibr" rid="B51">UNCTAD, 2021</xref>). Therefore, <abbrev xlink:title="Digital services trade">DST</abbrev> in the form of international trade plays a significant role in economic development. With the advancement of technology, it has become a subject of discussion among policymakers, economists and researchers in various social sciences (<xref ref-type="bibr" rid="B60">Winkler &amp; Satterthwaite, 2017</xref>; Kuhn &amp; Schularick, 2020).</p>
      <p>Recent analysis of global income distribution has revealed a divergent pattern over the past twenty years. <xref ref-type="bibr" rid="B10">Chancel et al. (2022)</xref> found a significant reduction in cross-national inequality, as evidenced by the narrowing gap between the wealthiest 10% and poorest 50% of countries, from 50 to less than 40. This trend towards international convergence, however, was accompanied by a widespread increase in intra-national inequality, as income gaps widened within most individual countries (<xref ref-type="bibr" rid="B10">Chancel et al., 2022</xref>). A significant portion of this reduction in global inequality was brought about by the transfer of knowledge, capital, technology and skills from developed to developing countries through digital trade (<xref ref-type="bibr" rid="B23">Hernandez &amp; Roberts 2018</xref>). In recent years, the trade in digital services has been recognized as a viable alternative to traditional trade. Indeed, <abbrev xlink:title="Digital services trade">DST</abbrev>, driven and reinforced by internet technologies and related activities, plays a key role in global commerce and has seen significant growth since 2010 accounting for over 53% of total services trade (<xref ref-type="bibr" rid="B63">Yeerken &amp; Feng, 2024</xref>). This growing sector of global trade, thanks to networks, innovative technologies, and digitalization, has led to a revolution in the services industry. It is a new form of international trade that uses digital technologies to overcome barriers in the services sector and act as the main driver for economic growth. (<xref ref-type="bibr" rid="B58">Wen et al., 2023</xref>).</p>
      <p>In this new business model, information transfer occurs more rapidly around the world. This development, in turn, enhances the feasibility and likelihood of a worldwide division of labor within various sectors (<xref ref-type="bibr" rid="B48">Sui et al., 2025</xref>). Moreover, since digital services operate automatically, they have accelerated the processes of duplication and customization at no cost, and through delocalization and globalization, they have transformed traditional services from non-tradable to tradable by using advanced communication technologies (<xref ref-type="bibr" rid="B21">Goldfarb &amp; Tucker, 2019</xref>; <xref ref-type="bibr" rid="B30">Ma et al., 2025</xref>). Furthermore, <abbrev xlink:title="Digital services trade">DST</abbrev> has stimulated the development of competitive advantages by compressing costs, time, and distance, thereby improving global workforce specialization and expanding participation in international trade (<xref ref-type="bibr" rid="B68">Zhu &amp; Zhou, 2025</xref>). However, the impact of <abbrev xlink:title="Digital services trade">DST</abbrev> on the economic growth in developing countries requires further empirical study.</p>
      <p>This research empirically examines the contribution of digital services trade to economic growth in developing countries and identifies key factors moderating this relationship.</p>
      <sec sec-type="1.1. Motivation of the Study" id="sec3">
        <title>1.1. Motivation of the Study</title>
        <p>The rapid global expansion of the digital economy has made it a critical driver for contemporary economic progress. A growing body of literature has examined the role of the digital economy, digital trade, and digital services trade (<abbrev xlink:title="Digital services trade">DST</abbrev>) in shaping economic development outcomes. For instance, <xref ref-type="bibr" rid="B12">Cheng and Huang (2022)</xref>, <xref ref-type="bibr" rid="B44">Ren et al. (2022)</xref>, <xref ref-type="bibr" rid="B56">Wang et al. (2022)</xref>, <xref ref-type="bibr" rid="B65">Zhang et al. (2023)</xref>, <xref ref-type="bibr" rid="B64">Zainullin et al. (2024)</xref>, and <xref ref-type="bibr" rid="B52">Wang and Wang (2025)</xref> explored the contribution of digital economy to economic growth and green economic transformation. Similarly, <xref ref-type="bibr" rid="B11">Chen et al. (2025)</xref>, <xref ref-type="bibr" rid="B14">Danish et al. (2023)</xref>, <xref ref-type="bibr" rid="B53">Wang and Rani (2025)</xref>, and <xref ref-type="bibr" rid="B7">Bian and Zhang (2025)</xref> investigated how digital trade contributes to economic expansion and supports sustainable development. The nexus between the digital economy and income inequality was examined by <xref ref-type="bibr" rid="B54">Wang and Shen (2024)</xref>; <xref ref-type="bibr" rid="B34">Mulenga and Mayondi (2022)</xref> and <xref ref-type="bibr" rid="B63">Yeerken and Feng (2024)</xref> analyzed the effects of digital services trade on economic performance and inclusive growth. Empirical findings suggest that <abbrev xlink:title="Digital services trade">DST</abbrev> can help reduce income inequality (<xref ref-type="bibr" rid="B69">Zhu et al., 2022</xref>), enhance learning and competitiveness (<xref ref-type="bibr" rid="B20">Goldberg et al., 2009</xref>), and lower transaction and trade costs (<xref ref-type="bibr" rid="B9">Buckley, 2009</xref>; <xref ref-type="bibr" rid="B24">Humphrey &amp; Schmitz, 2002</xref>). Recent evidence also indicates that <abbrev xlink:title="Digital services trade">DST</abbrev> significantly promotes GDP growth in emerging economies (<xref ref-type="bibr" rid="B63">Yeerken &amp; Feng, 2024</xref>; <xref ref-type="bibr" rid="B34">Mulenga &amp; Mayondi, 2022</xref>), while in OECD countries its impact is often moderated by environmental and regulatory factors (<xref ref-type="bibr" rid="B19">Gao et al., 2024</xref>).</p>
        <p>Despite these advances, empirical research into how the trade in digital services contributes to economic growth remains relatively limited, particularly for developing countries. This gap indicates the need for systematic and comprehensive analysis of the impact of <abbrev xlink:title="Digital services trade">DST</abbrev> on economic performance in such countries. The present study aims to provide robust empirical evidence of how digital service trade contributes to the economic growth of 87 developing economies.</p>
      </sec>
      <sec sec-type="1.2. Contribution of the Study" id="sec4">
        <title>1.2. Contribution of the Study</title>
        <p>The contributions of this research can be summarized as follows:</p>
        <p>First, this study contributes to the existing literature by empirically investigating the impact of <abbrev xlink:title="Digital services trade">DST</abbrev> on economic growth in developing countries - a topic that has received limited scholarly attention to date. Developing countries constitute a substantial and dynamic segment of the global economy, characterized by accelerating digitalization, expanding internet penetration and increasing participation in cross-border digital exchanges. At the same time, these economies are facing structural challenges, such as inadequate digital infrastructure, institutional inefficiencies and regulatory fragmentation, which constrain the full realization of <abbrev xlink:title="Digital services trade">DST</abbrev>’s growth-enhancing potential. By integrating a comprehensive measure of <abbrev xlink:title="Digital services trade">DST</abbrev> into the theoretical framework of cross-border trade, this study offers novel insights into how the expansion of digital services trade influences economic performance in developing contexts.</p>
        <p>Second, the study demonstrates empirically that <abbrev xlink:title="Digital services trade">DST</abbrev> is a significant driver of economic growth in developing countries. It operates through key mechanisms such as generating employment and promoting technological innovation. The analysis reveals that the magnitude of the growth-enhancing effects of <abbrev xlink:title="Digital services trade">DST</abbrev> is conditioned by a number of contextual factors, including the quality of the digital infrastructure, the effectiveness of regulation and the level of human capital. These factors act as critical moderators. This multidimensional framework emphasizes the complex pathways through which the <abbrev xlink:title="Digital services trade">DST</abbrev> influences economic performance. It also shows the importance of the complementary institutional and technical capacities in maximizing the developmental impact of the <abbrev xlink:title="Digital services trade">DST</abbrev>.</p>
        <p>Third, by integrating <abbrev xlink:title="Digital services trade">DST</abbrev> within advanced analytical frameworks, this study provides comprehensive and generalizable empirical evidence that deepens the understanding of the nexus between digital trade and economic growth, thereby enriching the literature on digital trade and international economics. It contributes to theoretical development by linking <abbrev xlink:title="Digital services trade">DST</abbrev> to several strands of economic theory. In particular, <italic>Trade Theory</italic> and <italic>Structural Change Theory</italic> explain the role of trade expansion and sectoral transformation in driving growth; <italic>Endogenous Growth Theory</italic> emphasizes the mediating role of employment through human capital accumulation and knowledge spillovers; and <italic>Schumpeterian Innovation Theory</italic> highlights the contribution of technological innovation to economic development through the mechanism of creative destruction.</p>
        <p>Lastly, previous studies have mostly used traditional econometric methods, which can be subject to methodological issues such as multicollinearity, endogeneity and overfitting of models, all of which can undermine the accuracy and reliability of empirical findings, especially when analyzing large datasets. To more effectively capture complex interactions between variables, this study uses advanced machine learning methods, including the Double-Selection LASSO linear regression (<abbrev xlink:title="Double-Selection LASSO linear regression">DSLR</abbrev>), Partialing-Out LASSO Linear Regression (<abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev>) and Cross-fit Partialing-Out LASSO Linear Regression (Cross-fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev>). These approaches improve model accuracy, reduce overfitting and effectively handle high-dimensional data, thus providing a more rigorous and reliable empirical analysis of the factors that influence economic growth.</p>
        <p>The study is divided into six main sections. The first section introduces the topic, followed by a literature review in the second section. The third section describes the theoretical framework and model development. The fourth section contains data and explains the empirical estimation strategy. The fifth section presents the findings of the study, and the sixth section draws conclusions and discusses research implications.</p>
      </sec>
    </sec>
    <sec sec-type="2. Literature Review and Theoretical Framework" id="sec5">
      <title>2. Literature Review and Theoretical Framework</title>
      <sec sec-type="2.1. Literature Review" id="sec6">
        <title>2.1. Literature Review</title>
        <p>The concept of digital trade is widely discussed in the economic literature, covering various aspects such as sharing economy, digital economy, digital transformation and interaction economy. Although the digitalization of the economy is generally recognized as inevitable, it is not fully reflected in national accounting systems (<xref ref-type="bibr" rid="B27">Katz &amp; Koutroumpis, 2013</xref>; <xref ref-type="bibr" rid="B40">OECD, 2024</xref>). This is largely because the national accounts continue to focus on tangible products, blurring the distinction between trade in public services and trade in digital services, despite the rapid expansion of the latter in recent decades (<xref ref-type="bibr" rid="B25">IMF, 2023</xref>). In today’s world, the internet has significantly transformed global economic activity. It has eliminated the importance of geographical distance and strengthened connections between people and businesses at an unprecedented speed and scale. While the economy of the 20th century was primarily driven by the flow of physical goods, today’s economy is increasingly centered around the exchange of intangible goods, specifically the flow of digital services (<xref ref-type="bibr" rid="B36">Neil &amp; Yeung, 2019</xref>).</p>
        <p>A growing body of empirical literature has examined the economic implications of trade in digital services, though most studies have focused on developed economies and left developing countries relatively unexplored. For example, Zhang et al. (2021) investigated the impact of digital services trade on economic growth across 30 Chinese provinces during the period 2015–2019. Their findings indicate that technologically advanced digital infrastructure, sectoral digital industry development and regional factor productivity proxied by R&amp;D expenditure all have a positive and significant impact on economic growth. Similarly, <xref ref-type="bibr" rid="B55">Wang and Choi (2018)</xref> examined the relationship between the digital economy and economic growth in the BRICS countries using data spanning 2000–2016. They concluded that the digital economy positively influenced economic growth in these emerging economies and pointed out that the BRICS nations needed to invest substantially in digital trade infrastructure and Internet facilities in order to maximize the benefits of digitalization. In parallel, <xref ref-type="bibr" rid="B46">Simon and Pingfang (2021)</xref> assessed the impact of the digital economy on international trade and economic growth across 53 African countries between 2000 and 2018. Their findings suggest that the digital economy has a positive and significant impact on both trade and growth. This leads the authors to recommend investing heavily in digital technologies as a way to accelerate Africa’s economic development.</p>
        <p>Further empirical contributions reinforce these findings. <xref ref-type="bibr" rid="B2">Bakry et al. (2023)</xref> and <xref ref-type="bibr" rid="B37">Niebel (2018)</xref> examined the relationship between the digital economy, ICT development and economic growth in Jordan and other emerging economies. Both studies found that the digital economy and adoption of ICTs have a positive impact on economic growth, emphasizing the importance of policies that improve digital infrastructure and promote digital literacy. In addition to this, <xref ref-type="bibr" rid="B32">Maune (2019)</xref> explored the role of digital services trade in African economies and found that although trade in digital services promotes economic growth, it also reduces the volume of exports of goods. This suggests a complex reallocation effect on trade structures. Additional evidence from India shows that digital services trade has a significant impact on both economic growth and the current account balance. Digital services imports, however, tend to hinder growth in developed countries (<xref ref-type="bibr" rid="B50">Thomas, 2018</xref>). Extending the scope of this literature, <xref ref-type="bibr" rid="B41">Pan et al. (2022)</xref> revealed that the digital economy contributed positively and significantly to total factor productivity in China. However, their analysis emphasizes that the extent of this effect depends on the level of digital infrastructure development. This indicates that infrastructure remains a crucial prerequisite for realizing the economic benefits of digitalization.</p>
        <p>Taken together, these studies establish a consistent empirical foundation suggesting that digital services trade and the broader digital economy positively influence economic growth. However, much of this evidence is derived from developed economies or from a limited set of emerging markets, leaving the dynamics in developing economies underexplored. The existing literature reveals important heterogeneities across countries and regions, particularly regarding the role of infrastructure, the structure of goods versus services trade and the differential impacts between advanced and developing economies. This gap underscores the need for more comprehensive, cross-country analyses of developing economies. Addressing this gap, this study examines the impact of trade in digital services on GDP growth in 87 developing countries, thereby contributing to a relatively under-developed area of literature.</p>
      </sec>
      <sec sec-type="2.2. Theoretical Framework" id="sec7">
        <title>2.2. Theoretical Framework</title>
        <p>Digital trade can be conceptually grounded in the New Trade Theory (<abbrev xlink:title="New Trade Theory">NTT</abbrev>), which provides a framework for understanding international trade in the context of technological disruption and rapidly evolving global data flows (<xref ref-type="bibr" rid="B15">Dirk &amp; Michael, 2012</xref>). Unlike traditional trade theories that emphasize comparative advantage, <abbrev xlink:title="New Trade Theory">NTT</abbrev> highlights the role of digital trade in helping market participants to operate under monopoly competition, paying particular attention to scale economies, product differentiation and innovation-led trade. The fragmentation of international trade, characterized by the cross-border dispersal of production and service activities, reduces trade costs and improves resource allocation efficiency (<xref ref-type="bibr" rid="B22">Helpman &amp; Krugman, 1985</xref>). There is a key difference between traditional trade in services and digital trade, which uses digital technologies to provide services with minimal dependence on physical distance. <abbrev xlink:title="Digital services trade">DST</abbrev> not only expands trade but also facilitates technological diffusion, enhancing firm productivity and fostering innovation. From a growth perspective, total factor productivity (<abbrev xlink:title="total factor productivity">TFP</abbrev>) within the augmented Solow growth model is expected to increase alongside the expansion of the digital economy and digital infrastructure (Zhang et al., 2021; <xref ref-type="bibr" rid="B50">Thomas, 2018</xref>; <xref ref-type="bibr" rid="B41">Pan et al., 2022</xref>). The model’s incorporation of human capital and technology provides a theoretical foundation for linking digital transformation to long-term growth (<xref ref-type="bibr" rid="B31">Mankiw et al, 1992</xref>).</p>
        <p>Furthermore, <abbrev xlink:title="Digital services trade">DST</abbrev> impacts GDP both directly and indirectly. Directly, it contributes to economic output by expanding the scope and efficiency of service delivery. Indirectly, <abbrev xlink:title="Digital services trade">DST</abbrev> mediates growth through employment (<abbrev xlink:title="employment">EMP</abbrev>) and technological innovation (<abbrev xlink:title="technological innovation">TI</abbrev>). Increased digital trade generates labor demand in both skilled and supporting sectors, raising household incomes and consumption. Simultaneously, participation in <abbrev xlink:title="Digital services trade">DST</abbrev> encourages companies to adopt advanced technologies and continuously innovate, enhancing productivity and supporting long-term economic growth. By integrating <abbrev xlink:title="New Trade Theory">NTT</abbrev> with the augmented Solow growth framework, this study conceptualizes <abbrev xlink:title="Digital services trade">DST</abbrev> as a critical driver for GDP growth in developing countries, operating through multiple channels that combine trade expansion, human capital utilization, and technological advancement. The definition of the growth model can be found in <xref ref-type="bibr" rid="B47">Solow (1957)</xref> and <xref ref-type="bibr" rid="B31">Mankiw et al. (1992)</xref>.</p>
        <p><mml:math id="M1"><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mi>α</mml:mi></mml:msubsup><mml:mo>⋅</mml:mo><mml:msubsup><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mi>β</mml:mi></mml:msubsup><mml:mo>⋅</mml:mo><mml:msubsup><mml:mi>L</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mi>θ</mml:mi></mml:msubsup></mml:math>	(1)</p>
        <p>where <italic>Yt</italic> is GDP over time (<italic>t</italic>) in response to physical capital (<italic>K</italic>), human capital (<italic>H</italic>), labor (<italic>L</italic>), and technology (<italic>A</italic>) over time <italic>t</italic> and country <italic>i</italic>. It is necessary to note that <italic>L</italic> and <italic>H</italic> are not the same. While human capital refers to the skills acquired through education, training, and experience, labor implies the abilities that people naturally possess (Mankiw et al, 1992).</p>
        <p>In contemporary economies, <abbrev xlink:title="Digital services trade">DST</abbrev> enhances productivity by improving information flows, reducing transaction costs and enabling innovation (<xref ref-type="bibr" rid="B37">Niebel, 2018</xref>). So <abbrev xlink:title="Digital services trade">DST</abbrev> can be modeled as a determinant of <abbrev xlink:title="total factor productivity">TFP</abbrev>, making <italic>A<sub>t</sub></italic> a function of <abbrev xlink:title="Digital services trade">DST</abbrev>:</p>
        <p><mml:math id="M2"><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>A</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:msub><mml:mi>δ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>L</mml:mi><mml:mi>n</mml:mi><mml:mi>D</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mtext>it </mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:msup></mml:math>	(2)</p>
        <p>By substituting <italic>A<sub>it</sub></italic> from Eq. (2) into Eq. (1) and taking the natural logarithm of both sides, the growth model can be expressed as a function of <abbrev xlink:title="Digital services trade">DST</abbrev> as follows:</p>
        <p><mml:math id="M3"><mml:mi>Ln</mml:mi><mml:msub><mml:mi>Y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>Ln</mml:mi><mml:msub><mml:mi>A</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mi>Ln</mml:mi><mml:mi>D</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>Ln</mml:mi><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mi>α</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:mi>Ln</mml:mi><mml:msubsup><mml:mi>H</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mi>β</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:mi>Ln</mml:mi><mml:msubsup><mml:mi>L</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mi>θ</mml:mi></mml:msubsup></mml:math>	(3)</p>
        <p>Next, by incorporating control variables (<italic>X<sub>it</sub></italic>) as well as country (μ<italic><sub>i</sub></italic>) and time (π<sub><italic>t</italic></sub>) fixed effects, the baseline model can be formulated as follows:</p>
        <p><mml:math id="M4"><mml:mi>LnGDP</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:msub><mml:mi>LnDST</mml:mi><mml:mrow><mml:mi>it</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mi>Ln</mml:mi><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>μ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>π</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ε</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math>	(4)</p>
        <p>where <italic>LnGDP<sub>it</sub></italic> = <italic>LnY</italic>, δ<sub>0</sub> = <italic>LnA</italic><sub>0</sub> is the constant term, δ<sub>1</sub> is the slope coefficient for <abbrev xlink:title="Digital services trade">DST</abbrev>, and δ<sub><italic>k</italic></sub> shows the impact of all control variables of Eq. (4), respectively.</p>
        <p>Finally, by taking the partial derivative of <italic>LnGDP</italic> with respect to <italic>LnDST</italic>, the marginal effect of <abbrev xlink:title="Digital services trade">DST</abbrev> on economic growth can be derived as follows:</p>
        <p><mml:math id="M5"><mml:munder><mml:mrow><mml:munder><mml:mrow><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>D</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mfrac><mml:mrow><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>D</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>⏟</mml:mo></mml:munder></mml:mrow><mml:mrow><mml:mtext>Change in unit </mml:mtext></mml:mrow></mml:munder><mml:mtext> or </mml:mtext><mml:munder><mml:mrow><mml:munder><mml:mrow><mml:mfrac><mml:mrow><mml:mi>∂</mml:mi><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi>∂</mml:mi><mml:mi>D</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>D</mml:mi><mml:mi>S</mml:mi><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>⏟</mml:mo></mml:munder></mml:mrow><mml:mrow><mml:mtext>Change in \% </mml:mtext></mml:mrow></mml:munder></mml:math>	(5)</p>
        <p>Building upon the theoretical foundations discussed above, this study formulates the following research hypotheses:</p>
        <p><bold><italic>H<sub>1</sub></italic></bold>: Digital Service Trade (<abbrev xlink:title="Digital services trade">DST</abbrev>) has a significant positive impact on economic growth in developing countries.</p>
        <p><bold><italic>H<sub>2</sub></italic></bold>: Employment and technological innovation mediate the relationship between <abbrev xlink:title="Digital services trade">DST</abbrev> and economic growth.</p>
        <p><bold><italic>H<sub>3</sub></italic></bold>: Digital infrastructure, human capital, and regulatory quality moderate the relationship between <abbrev xlink:title="Digital services trade">DST</abbrev> and economic growth.</p>
      </sec>
    </sec>
    <sec sec-type="3. Data and Methodology" id="sec8">
      <title>3. Data and Methodology</title>
      <sec sec-type="3.1. Data and Variables" id="sec9">
        <title>3.1. Data and Variables</title>
        <p>This study employs panel data spanning the period 2005–2023 for 87 developing economies. All variables are obtained from reliable international sources, specifically the World Development Indicators (<abbrev xlink:title="World Development Indicators">WDI</abbrev>) and <abbrev xlink:title="United Nations Conference on Trade and Development">UNCTAD</abbrev> databases. For analytical clarity, the selected variables are categorized as follows:</p>
        <p><bold><italic>Explained variables</italic></bold>: In this paper, per capita GDP is employed as the primary dependent variable, as it is widely recognized as a reliable indicator of economic performance. This approach is consistent with prior studies, including <xref ref-type="bibr" rid="B63">Yeerken and Feng (2024)</xref> and <xref ref-type="bibr" rid="B34">Mulenga and Mayondi (2022)</xref>, which similarly utilize per capita GDP to capture variations in economic outcomes.</p>
        <p><bold><italic>Core explanatory variable</italic></bold>: Digital services trade (<abbrev xlink:title="Digital services trade">DST</abbrev>) encompassing both digital services exports and imports refers to the delivery of services through digital channels. The United Nations Conference on Trade and Development (<abbrev xlink:title="United Nations Conference on Trade and Development">UNCTAD</abbrev>) employs a primary product classification system to identify services that can be transmitted online across borders, thereby distinguishing between digital and non-digital service transactions. Using statistical data and computational methods, <abbrev xlink:title="United Nations Conference on Trade and Development">UNCTAD</abbrev> has further estimated the overall volume of digital services trade across countries. Building on the frameworks established by <xref ref-type="bibr" rid="B63">Yeerken and Feng (2024)</xref>, and <xref ref-type="bibr" rid="B34">Mulenga and Mayondi (2022)</xref>, this study adopts <abbrev xlink:title="Digital services trade">DST</abbrev> delivery indicators as the primary explanatory variable to evaluate the extent of digital services trade development in a country.</p>
        <p><bold><italic>Control variables</italic></bold>: Drawing on prior research, including <xref ref-type="bibr" rid="B63">Yeerken and Feng (2024)</xref>, and <xref ref-type="bibr" rid="B34">Mulenga and Mayondi (2022)</xref>, this study incorporates a set of control variables, namely goods imports (<abbrev xlink:title="goods imports">GIM</abbrev>), goods exports (<abbrev xlink:title="goods exports ,">GEX</abbrev>), trade openness (<abbrev xlink:title="trade openness">TO</abbrev>), structural change (<abbrev xlink:title="structural change">SCH</abbrev>), and population (<abbrev xlink:title="population">POP</abbrev>). These variables are widely recognized as significant determinants of GDP growth dynamics and are therefore included as essential control factors in the present analysis.</p>
        <p><bold><italic>Mediating variables</italic></bold>: In this study, the level of employment (<italic><abbrev xlink:title="employment">EMP</abbrev></italic>) and technological innovation (<italic><abbrev xlink:title="technological innovation">TI</abbrev></italic>) are used as the main mediating variables, with data obtained from the World Development Indicators (<abbrev xlink:title="World Development Indicators">WDI</abbrev>). Yeerken and Feng in their 2024 paper also use these factors as mediators. The impact of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on <italic>GDP</italic> can be mediated through <italic><abbrev xlink:title="employment">EMP</abbrev></italic> and <italic><abbrev xlink:title="technological innovation">TI</abbrev>.</italic> By fostering the expansion of the digital industry, it generates new job opportunities, which increase household income and stimulate aggregate demand. This, in turn, supports economic growth. It also facilitates cross-border knowledge transfer and encourages firms to adopt advanced technologies, which increases productivity and competitiveness. These channels illustrate how the <abbrev xlink:title="employment">EMP</abbrev> and <abbrev xlink:title="technological innovation">TI</abbrev> work together to help <abbrev xlink:title="Digital services trade">DST</abbrev> translate into higher GDP.</p>
        <p><bold><italic>Moderating Variables</italic></bold>: The Digital Infrastructure Index (<abbrev xlink:title="Digital Infrastructure Index">DII</abbrev>) is constructed by combining three key indicators of digital connectivity and technological capability: internet users (% of the population), mobile broadband subscriptions (per 100 people), and secure internet servers (per million people). These elements together determine a country’s ability to support and promote digital trade. Human capital of the right quality, as measured by the average number of years of schooling among adults aged 15 and older, is essential for improving digital skills, fostering innovation and effectively using digital technologies. Regulatory quality (<abbrev xlink:title="Regulatory quality">REQ</abbrev>), represented by the Regulatory Quality Estimate from the Worldwide Governance Indicators, reflects the capacity of governments to design and implement sound policies that foster digital trade and economic growth.</p>
        <p>Table <xref ref-type="table" rid="T1">1</xref> gives a detailed overview of the selected variables; Fig. <xref ref-type="fig" rid="F1">1</xref> depicts the annual trends of <italic>GDP</italic> and <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> across 87 developing economies from 2005 to 2023. The figure indicates that <italic>GDP</italic> experienced a decline during certain periods (2020), whereas <italic>LnDST</italic>  peaked in 2021, likely reflecting the accelerated reliance on digital services during the COVID-19 pandemic.</p>
        <fig id="F1">
          <object-id content-type="doi">10.3897/brics-econ.7.e172739.fig1</object-id>
          <object-id content-type="arpha">C5D60F80-CC10-51AE-BC1C-5B81F3851032</object-id>
          <label>Fig. 1.</label>
          <caption>
            <p>Annual rise of <italic>LnGDP</italic> and <italic>LnDST</italic> for 87 developing countries from 2005 to 2023.</p>
          </caption>
          <graphic xlink:href="brics-econ-07-001-g001.jpg" id="oo_1710249.jpg">
            <uri content-type="original_file">https://binary.pensoft.net/fig/1710249</uri>
          </graphic>
        </fig>
        <table-wrap id="T1" position="float" orientation="portrait">
          <label>Table 1.</label>
          <caption>
            <p>Variables Descriptions and Data Sources</p>
          </caption>
          <table>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>Variable</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Role</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Description</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Sources</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">GDP</td>
                <td rowspan="1" colspan="1">Dep. V.</td>
                <td rowspan="1" colspan="1">GDP per capita (constant 2015 US$)</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="Digital services trade">DST</abbrev>
                </td>
                <td rowspan="1" colspan="1">Core Ind. V.</td>
                <td rowspan="1" colspan="1">Digital Services Export + Digital Services Import (BoP, current US$)</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="United Nations Conference on Trade and Development">UNCTAD</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="goods imports">GIM</abbrev>
                </td>
                <td rowspan="5" colspan="1">Control V.</td>
                <td rowspan="1" colspan="1">Goods exports (BoP, current US$)</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="goods exports ,">GEX</abbrev>
                </td>
                <td rowspan="1" colspan="1">Goods imports (BoP, current US$)</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="trade openness">TO</abbrev>
                </td>
                <td rowspan="1" colspan="1">Trade (% of GDP)</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="structural change">SCH</abbrev>
                </td>
                <td rowspan="1" colspan="1">Industry (including construction), value added (constant 2015 US$)</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="population">POP</abbrev>
                </td>
                <td rowspan="1" colspan="1">Population, total</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="employment">EMP</abbrev>
                </td>
                <td rowspan="2" colspan="1">Mediating V.</td>
                <td rowspan="1" colspan="1">The proportion of the employed population to the total labor force</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="technological innovation">TI</abbrev>
                </td>
                <td rowspan="1" colspan="1">Patent applications, Residents and non-residents</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="Digital Infrastructure Index">DII</abbrev>
                </td>
                <td rowspan="3" colspan="1">Moderating V.</td>
                <td rowspan="1" colspan="1">Digital Infrastructure Index (<abbrev xlink:title="Digital Infrastructure Index">DII</abbrev>) constructed by combining Internet users (% of population), Mobile broadband subscriptions (per 100 people), and Secure Internet servers (per 1 million people)</td>
                <td rowspan="1" colspan="1">Authors’ calculation</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="human capital">HC</abbrev>
                </td>
                <td rowspan="1" colspan="1">Mean years of education among adults (aged 15+)</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="Regulatory quality">REQ</abbrev>
                </td>
                <td rowspan="1" colspan="1">Regulatory Quality: Estimate</td>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="World Development Indicators">WDI</abbrev>
                </td>
              </tr>
            </tbody>
          </table>
          <table-wrap-foot>
            <fn>
              <p><italic>Notes</italic>: This table provides detailed information about four categories of variables, including the main dependent variable (GDP), core independent variable (<abbrev xlink:title="Digital services trade">DST</abbrev>), control variables (<abbrev xlink:title="goods imports">GIM</abbrev>, <abbrev xlink:title="goods exports ,">GEX</abbrev>, <abbrev xlink:title="trade openness">TO</abbrev>, <abbrev xlink:title="structural change">SCH</abbrev>, and <abbrev xlink:title="population">POP</abbrev>), mediating variables (<abbrev xlink:title="employment">EMP</abbrev> and <abbrev xlink:title="technological innovation">TI</abbrev>, and moderating variables.</p>
            </fn>
          </table-wrap-foot>
        </table-wrap>
        <p>Table <xref ref-type="table" rid="T2">2</xref> presents the descriptive statistics and correlation coefficients for the variables included in this study. As reported in Panel A, <italic><abbrev xlink:title="structural change">SCH</abbrev></italic> records the highest mean value, whereas <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> exhibits the lowest. In terms of dispersion, <italic><abbrev xlink:title="goods exports ,">GEX</abbrev></italic> shows the highest standard deviation, while <italic><abbrev xlink:title="trade openness">TO</abbrev></italic> demonstrates the lowest, reflecting notable differences in variability across the variables. Panel B reports the correlation coefficients, where <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> and <italic>GDP</italic> display a modest positive correlation of 4.3%. Among the control variables, <italic><abbrev xlink:title="structural change">SCH</abbrev></italic> exhibits the strongest positive association with <italic>GDP</italic>, whereas <italic><abbrev xlink:title="population">POP</abbrev></italic> shows the strongest negative correlation. These preliminary observations indicate that structural change may exert a more substantial influence on <italic>GDP</italic> growth, and the relatively modest correlation between <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> and <italic>GDP</italic> suggests that the effects of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> may operate indirectly through mediating mechanisms such as <italic><abbrev xlink:title="employment">EMP</abbrev></italic> and <italic><abbrev xlink:title="technological innovation">TI</abbrev></italic> or be conditioned by moderating factors such as <italic><abbrev xlink:title="Digital Infrastructure Index">DII</abbrev></italic>, <italic><abbrev xlink:title="human capital">HC</abbrev></italic>, and <italic><abbrev xlink:title="Regulatory quality">REQ</abbrev>.</italic></p>
        <table-wrap id="T2" position="float" orientation="portrait">
          <label>Table 2.</label>
          <caption>
            <p>Descriptive Statistics and Correlation Analysis<bold/></p>
          </caption>
          <table>
            <tbody>
              <tr>
                <td rowspan="1" colspan="8"><bold>Panel A: Descriptive Statistics Results</bold>.</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>Statistics</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnDST</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGIM</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGEX</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnTO</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnSCH</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnPOP</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Mean</td>
                <td rowspan="1" colspan="1">3.560</td>
                <td rowspan="1" colspan="1">1.258</td>
                <td rowspan="1" colspan="1">10.018</td>
                <td rowspan="1" colspan="1">9.875</td>
                <td rowspan="1" colspan="1">1.809</td>
                <td rowspan="1" colspan="1">10.042</td>
                <td rowspan="1" colspan="1">6.963</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Max</td>
                <td rowspan="1" colspan="1">4.866</td>
                <td rowspan="1" colspan="1">5.333</td>
                <td rowspan="1" colspan="1">12.428</td>
                <td rowspan="1" colspan="1">12.525</td>
                <td rowspan="1" colspan="1">2.641</td>
                <td rowspan="1" colspan="1">12.828</td>
                <td rowspan="1" colspan="1">9.155</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Min</td>
                <td rowspan="1" colspan="1">2.486</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">6.983</td>
                <td rowspan="1" colspan="1">5.161</td>
                <td rowspan="1" colspan="1">0.344</td>
                <td rowspan="1" colspan="1">6.412</td>
                <td rowspan="1" colspan="1">3.996</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Std. D.</td>
                <td rowspan="1" colspan="1">0.503</td>
                <td rowspan="1" colspan="1">0.598</td>
                <td rowspan="1" colspan="1">0.887</td>
                <td rowspan="1" colspan="1">1.118</td>
                <td rowspan="1" colspan="1">0.236</td>
                <td rowspan="1" colspan="1">1.017</td>
                <td rowspan="1" colspan="1">0.918</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Obs.</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="8"><bold>Panel B: Correlation Coefficients Results</bold>.</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>Variables</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnDST</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGIM</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGEX</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnTO</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnSCH</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnPOP</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGDP</td>
                <td rowspan="1" colspan="1">1.000</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnDST</td>
                <td rowspan="1" colspan="1">0.043</td>
                <td rowspan="1" colspan="1">1.000</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGIM</td>
                <td rowspan="1" colspan="1">0.335</td>
                <td rowspan="1" colspan="1">0.100</td>
                <td rowspan="1" colspan="1">1.000</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGEX</td>
                <td rowspan="1" colspan="1">0.355</td>
                <td rowspan="1" colspan="1">0.100</td>
                <td rowspan="1" colspan="1">0.954</td>
                <td rowspan="1" colspan="1">1.000</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnTO</td>
                <td rowspan="1" colspan="1">0.086</td>
                <td rowspan="1" colspan="1">-0.097</td>
                <td rowspan="1" colspan="1">-0.075</td>
                <td rowspan="1" colspan="1">-0.034</td>
                <td rowspan="1" colspan="1">1.000</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnSCH</td>
                <td rowspan="1" colspan="1">0.371</td>
                <td rowspan="1" colspan="1">0.097</td>
                <td rowspan="1" colspan="1">0.829</td>
                <td rowspan="1" colspan="1">0.785</td>
                <td rowspan="1" colspan="1">-0.246</td>
                <td rowspan="1" colspan="1">1.000</td>
                <td rowspan="1" colspan="1"/>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnPOP</td>
                <td rowspan="1" colspan="1">-0.081</td>
                <td rowspan="1" colspan="1">0.028</td>
                <td rowspan="1" colspan="1">0.740</td>
                <td rowspan="1" colspan="1">0.692</td>
                <td rowspan="1" colspan="1">-0.211</td>
                <td rowspan="1" colspan="1">0.666</td>
                <td rowspan="1" colspan="1">1.000</td>
              </tr>
            </tbody>
          </table>
          <table-wrap-foot>
            <fn>
              <p><italic>Notes</italic>: This table presents descriptive statistics of the variables, including mean, max, min, standard deviation (Std. D), the number of observations in Panel A, and the correlation analysis between the response variable (<italic>LnDST</italic>, <italic>LnGIM</italic>, <italic>LnGEM</italic>, <italic>LnTO</italic>, <italic>LnSCH</italic>, and <italic>LnPOP</italic>) in Panel B.</p>
            </fn>
          </table-wrap-foot>
        </table-wrap>
      </sec>
      <sec sec-type="3.2. Estimation Strategy" id="sec10">
        <title>3.2. Estimation Strategy</title>
        <sec sec-type="3.2.1. Panel Data Prerequisite Tests" id="sec11">
          <title>3.2.1. Panel Data Prerequisite Tests</title>
          <p>Before proceeding with the <abbrev xlink:title="machine learning">ML</abbrev> (machine learning) estimations, a series of preliminary diagnostic tests were performed to examine the characteristics and statistical properties of the dataset. The outcomes of these tests informed the selection of the most appropriate econometric techniques to reliably estimate the impact of the explanatory variables on the dependent variable, GDP. In panel data analysis, common econometric challenges such as cross-sectional dependence (<abbrev xlink:title="cross-sectional dependence">CSD</abbrev>) and slope heterogeneity (<abbrev xlink:title="slope heterogeneity">SH</abbrev>) often arise. Neglecting these issues may lead to model misspecification and biased or inconsistent results. To address potential cross-sectional dependence, this study employed the Lagrange Multiplier (<abbrev xlink:title="Lagrange Multiplier">LM</abbrev>) test developed by <xref ref-type="bibr" rid="B8">Breusch and Pagan (1980)</xref> and the bias-corrected scaled <abbrev xlink:title="Lagrange Multiplier">LM</abbrev> test (SLM<sub>BC</sub>) proposed by <xref ref-type="bibr" rid="B3">Baltagi et al. (2012)</xref>.</p>
          <p><mml:math id="M6"><mml:mi>L</mml:mi><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>B</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>T</mml:mi><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:msubsup><mml:mrow><mml:mover><mml:mi>ρ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:math>	(6)</p>
          <p><mml:math id="M7"><mml:mi>S</mml:mi><mml:mi>L</mml:mi><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>B</mml:mi><mml:mi>C</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mi>N</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:msqrt><mml:mrow><mml:mo>(</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mrow><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:msubsup><mml:mrow><mml:mover><mml:mi>ρ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mfrac><mml:mi>N</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>(</mml:mo><mml:mi>T</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:math>	(7)</p>
          <p>The term <mml:math id="M8"><mml:msubsup><mml:mrow><mml:mover><mml:mi>ρ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:math> in Eqs (6) and (7) represents the estimated pairwise correlation of the regression residuals. <xref ref-type="bibr" rid="B8">Breusch and Pagan (1980)</xref> demonstrated that, under the null hypothesis of no cross-sectional dependence, the <abbrev xlink:title="Lagrange Multiplier">LM</abbrev><sub>BP</sub> test statistic follows an asymptotic chi-squared (<italic>X<sup>2</sup></italic>) distribution. To examine the stationarity properties of the panel data, this study employed the Cross-Sectionally Augmented Im, Pesaran, and Shin (<abbrev xlink:title="Cross-Sectionally Augmented Im, Pesaran, and Shin">CIPS</abbrev>) test and the Cross-Sectionally Augmented Dickey–Fuller (<abbrev xlink:title="Cross-Sectionally Augmented Dickey–Fuller">CADF</abbrev>) test. These approaches, proposed by <xref ref-type="bibr" rid="B42">Pesaran (2007)</xref>, are specifically designed to account for both <abbrev xlink:title="cross-sectional dependence">CSD</abbrev> and <abbrev xlink:title="slope heterogeneity">SH</abbrev> within the data — limitations that traditional panel unit root tests typically overlook. Consequently, the <abbrev xlink:title="Cross-Sectionally Augmented Im, Pesaran, and Shin">CIPS</abbrev> and <abbrev xlink:title="Cross-Sectionally Augmented Dickey–Fuller">CADF</abbrev> tests provide more robust and reliable assessments of unit roots in the presence of interdependencies across cross-sectional units. The corresponding test statistics for <abbrev xlink:title="Cross-Sectionally Augmented Dickey–Fuller">CADF</abbrev> and <abbrev xlink:title="Cross-Sectionally Augmented Im, Pesaran, and Shin">CIPS</abbrev> are presented in Eqs (8) and (9), respectively.</p>
          <p><mml:math id="M9"><mml:mi>Δ</mml:mi><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>α</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>β</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mrow><mml:mover><mml:mi>y</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>λ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mi>Δ</mml:mi><mml:msub><mml:mrow><mml:mover><mml:mi>y</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ε</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math>	(8)</p>
          <p><mml:math id="M10"><mml:mi>C</mml:mi><mml:mi>I</mml:mi><mml:mrow><mml:mover><mml:mrow><mml:mi>P</mml:mi><mml:mi>S</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mi>C</mml:mi><mml:mi>A</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>F</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math>	(9)</p>
          <p>The panel cointegration test developed by <xref ref-type="bibr" rid="B59">Westerlund (2007)</xref> was used to examine whether there is a long-term cointegrated relationship between <abbrev xlink:title="Digital services trade">DST</abbrev> and GDP growth. This methodology offers several advantages over traditional approaches as it accounts for <abbrev xlink:title="cross-sectional dependence">CSD</abbrev>, accommodates <abbrev xlink:title="slope heterogeneity">SH</abbrev>, and allows for variables with different integration orders. Moreover, the Westerlund test produces reliable results even in moderate-sized samples and is computationally more efficient than residual-based cointegration techniques (<xref ref-type="bibr" rid="B6">Bhattacharya et al., 2018</xref>). The mathematical formulations of the Westerlund test are presented as follows:</p>
          <p><mml:math id="M11"><mml:msub><mml:mi>G</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mfrac><mml:msub><mml:mrow><mml:mover><mml:mi>ϑ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>E</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mover><mml:mi>ϑ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:math>	(10)</p>
          <p><mml:math id="M12"><mml:msub><mml:mi>G</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:munderover><mml:mfrac><mml:mrow><mml:mi>T</mml:mi><mml:msub><mml:mrow><mml:mover><mml:mi>ϑ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mover><mml:mi>ϑ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:math>	(11)</p>
          <p><mml:math id="M13"><mml:msub><mml:mi>P</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mover><mml:mi>ϑ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>S</mml:mi><mml:mi>E</mml:mi><mml:mo>(</mml:mo><mml:mrow><mml:mover><mml:mi>ϑ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:math>	(12)</p>
          <p><mml:math id="M14"><mml:msub><mml:mi>P</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>T</mml:mi><mml:mrow><mml:mover><mml:mi>ϑ</mml:mi><mml:mo>^</mml:mo></mml:mover></mml:mrow></mml:math>	(13)</p>
          <p>In Eqs (10) and (11), the group tests (G<sub>t</sub> and G<sub>a</sub>) evaluate the null hypothesis of no cointegration for each cross-sectional unit individually, thereby assessing whether a cointegrating relationship exists within the model at the unit level. In contrast, the panel tests (P<sub>t</sub> and P<sub>a</sub>) presented in Eqs (12) and (13) examine the null hypothesis that there is no cointegration between all the units in the panel, to determine whether at least one unit exhibits a long-term cointegrated relationship.</p>
        </sec>
        <sec sec-type="3.2.2. Long-run estimation using LASSO’s inferential models" id="sec12">
          <title>3.2.2. Long-run estimation using LASSO’s inferential models</title>
          <p>While preliminary diagnostic tests reveal the statistical properties of the panel data, they do not estimate the marginal effects of explanatory variables on GDP. To address this, the study employs several LASSO-based inferential methods, including Double-Selection LASSO (<abbrev xlink:title="Double-Selection LASSO linear regression">DSLR</abbrev>), Partialing-Out LASSO (<abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev>), Cross-Fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev>, and Partialing-Out Instrumental Variable LASSO (<abbrev xlink:title="Partialing-Out Instrumental Variable LASSO">POIVLR</abbrev>), which are well-suited for high-dimensional datasets, allowing for robust causal inference under multicollinearity, sparsity and potential endogeneity.</p>
          <p>The <abbrev xlink:title="Double-Selection LASSO linear regression">DSLR</abbrev> model (<xref ref-type="bibr" rid="B5">Belloni et al., 2014</xref>) identifies the key predictors of GDP while controlling for weaker covariates that may influence outcomes. It is expressed as:</p>
          <p><mml:math id="M15"><mml:mi>E</mml:mi><mml:mo>[</mml:mo><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:mi>P</mml:mi><mml:mo>∣</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mo>]</mml:mo><mml:mo>=</mml:mo><mml:mi>ψ</mml:mi><mml:msup><mml:mi>α</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>ϕ</mml:mi><mml:msup><mml:mi>θ</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup></mml:math>	(14)</p>
          <p>where ψ denotes the primary covariates selected through LASSO or Elastic Net, and φ represents secondary drivers.</p>
          <p>The <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> approach (<xref ref-type="bibr" rid="B13">Chernozhukov et al., 2015</xref>; <xref ref-type="bibr" rid="B4">Belloni et al., 2012</xref>) enhances inferential precision by “partialing out” control variables, allowing the direct causal effect of <abbrev xlink:title="Digital services trade">DST</abbrev> to be isolated:</p>
          <p><mml:math id="M16"><mml:mi>E</mml:mi><mml:mo>[</mml:mo><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:mi>P</mml:mi><mml:mo>∣</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mo>]</mml:mo><mml:mo>=</mml:mo><mml:mi>d</mml:mi><mml:msup><mml:mi>α</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>X</mml:mi><mml:msup><mml:mi>θ</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup></mml:math>	(15)</p>
          <p>where <italic>d</italic> is the main covariate of interest and <italic>X</italic> contains selected control variables.</p>
          <p>The Cross-Fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> model further improves robustness by applying sample splitting and cross-fitting, which mitigates model selection errors and accommodates a larger set of covariates while maintaining sparsity:</p>
          <p><mml:math id="M17"><mml:mi>E</mml:mi><mml:mo>[</mml:mo><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:mi>P</mml:mi><mml:mo>∣</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mo>]</mml:mo><mml:mo>=</mml:mo><mml:mi>d</mml:mi><mml:msup><mml:mi>α</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>X</mml:mi><mml:msup><mml:mi>θ</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup></mml:math>	(16)</p>
          <p>Here, <italic>d</italic> is a limited set of covariates of interest, <italic>X</italic> contains potentially high-dimensional controls, and represents additional coefficients obtained through cross-fitting.</p>
          <p>Finally, the <abbrev xlink:title="Partialing-Out Instrumental Variable LASSO">POIVLR</abbrev> model addresses endogeneity in key covariates by incorporating exogenous instrumental variables (IVs), formalized as:</p>
          <p><mml:math id="M18"><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mi>H</mml:mi><mml:msubsup><mml:mi>α</mml:mi><mml:mi>d</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>N</mml:mi><mml:msubsup><mml:mi>α</mml:mi><mml:mi>f</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:mi>X</mml:mi><mml:msup><mml:mi>θ</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msup><mml:mo>+</mml:mo><mml:mi>ε</mml:mi></mml:math>	(17)</p>
          <p>where <italic>H</italic> includes endogenous variables of interest, <italic>N</italic> contains exogenous covariates, and <italic>X</italic> represents additional controls.</p>
          <p>To validate the results obtained from the LASSO inferential models, this study employs the Bayesian Model Averaging (<abbrev xlink:title="Bayesian Model Averaging">BMA</abbrev>) method as a robustness check. <abbrev xlink:title="Bayesian Model Averaging">BMA</abbrev> provides a systematic framework for estimating multiple plausible models by weighting them according to their posterior probabilities, thus accounting for model uncertainty. This approach ensures that inferences are not overly dependent on a single model specification. The mathematical formulation of <abbrev xlink:title="Bayesian Model Averaging">BMA</abbrev> can be expressed as follows:</p>
          <p><mml:math id="M19"><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>∣</mml:mo><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:mi>P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>h</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msup><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:msup></mml:mrow></mml:munderover><mml:msub><mml:mi>l</mml:mi><mml:mrow><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:mi>P</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mi>P</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:math>	(18)</p>
          <p>where <italic>l<sub>GDP</sub></italic>(<italic>M<sub>j</sub></italic>) denotes the marginal likelihood of the data under model <italic>M<sub>j</sub></italic> , obtained by integrating the likelihood over the parameter space with respect to the model-specific prior (<italic>l<sub>FPER</sub></italic>(<italic>M<sub>j</sub></italic>) = ∫<italic>p</italic> (GDP|α, β<italic><sub>j</sub></italic>, σ, <italic>M<sub>j</sub></italic>) <italic>p</italic> (α, β<sub><italic>j</italic></sub>, σ, <italic>M<sub>j</sub></italic>) <italic>d</italic>α<italic>d</italic>β<italic><sub>j</sub> d</italic>σ). The denominator ensures that the posterior probabilities sum to one over the space of all 2<sup><italic>k</italic></sup> possible models (<xref ref-type="bibr" rid="B57">Wang et al., 2024</xref>; <xref ref-type="bibr" rid="B16">Espoir. D. K. et al., 2024</xref>; and <xref ref-type="bibr" rid="B1">Aller et al., 2021</xref>).</p>
          <p>The research design is visually summarized in two key figures. Figure <xref ref-type="fig" rid="F2">2</xref> outlines the sequential steps of the empirical analysis, from initial screening to the heterogeneity analysis. Complementing this, Figure <xref ref-type="fig" rid="F3">3</xref> presents the conceptual framework, illustrating the hypothesized relationships between the core independent and dependent variables, mechanisms and control variables under investigation.</p>
          <fig id="F2">
            <object-id content-type="doi">10.3897/brics-econ.7.e172739.fig2</object-id>
            <object-id content-type="arpha">8C0ABE75-D71F-5C89-9449-32FF0E98B6A7</object-id>
            <label>Fig. 2.</label>
            <caption>
              <p>Empirical Analysis Steps of the Study.</p>
            </caption>
            <graphic xlink:href="brics-econ-07-001-g002.jpg" id="oo_1710250.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1710250</uri>
            </graphic>
          </fig>
          <fig id="F3">
            <object-id content-type="doi">10.3897/brics-econ.7.e172739.fig3</object-id>
            <object-id content-type="arpha">6F4D8292-FAC0-5E91-91C4-6ED608FFDEA9</object-id>
            <label>Fig. 3.</label>
            <caption>
              <p>Conceptual Framework of the Study.</p>
            </caption>
            <graphic xlink:href="brics-econ-07-001-g003.jpg" id="oo_1710251.jpg">
              <uri content-type="original_file">https://binary.pensoft.net/fig/1710251</uri>
            </graphic>
          </fig>
        </sec>
      </sec>
    </sec>
    <sec sec-type="4. Empirical results" id="sec13">
      <title>4. Empirical results</title>
      <sec sec-type="4.1. Prerequisite tests results" id="sec14">
        <title>4.1. Prerequisite tests results</title>
        <p>Before applying the advanced machine learning techniques, we first assessed several preliminary statistical tests, including cross-sectional dependence (<abbrev xlink:title="cross-sectional dependence">CSD</abbrev>) among the variables, stationarity tests, cointegration tests, and machine learning regularization. Table <xref ref-type="table" rid="T3">3</xref> presents cross-sectional dependency (<abbrev xlink:title="cross-sectional dependence">CSD</abbrev>) and panel unit root tests, focusing on various economic variables. The <abbrev xlink:title="cross-sectional dependence">CSD</abbrev> tests, as indicated by the BP<sub><abbrev xlink:title="Lagrange Multiplier">LM</abbrev></sub> and PS<sub><abbrev xlink:title="Lagrange Multiplier">LM</abbrev></sub> statistics, reveal a strong dependency among the variables, with significant values across the board, particularly for <italic>GDP</italic> (4.9E+4) and <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> (1.5E+4), suggesting a high degree of correlation among the cross-sectional units in the dataset. The Pesaran-CD test also supports this dependency.</p>
        <table-wrap id="T3" position="float" orientation="portrait">
          <label>Table 3.</label>
          <caption>
            <p><abbrev xlink:title="cross-sectional dependence">CSD</abbrev> and Unit Root Tests</p>
          </caption>
          <table>
            <tbody>
              <tr>
                <td rowspan="3" colspan="1">
                  <bold>Variables</bold>
                </td>
                <td rowspan="1" colspan="3">
                  <bold><abbrev xlink:title="cross-sectional dependence">CSD</abbrev> Tests</bold>
                </td>
                <td rowspan="1" colspan="4">
                  <bold>Unit Root Tests</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="2" colspan="1">
                  <bold>BP<sub><abbrev xlink:title="Lagrange Multiplier">LM</abbrev></sub></bold>
                </td>
                <td rowspan="2" colspan="1">
                  <bold>PS<sub><abbrev xlink:title="Lagrange Multiplier">LM</abbrev></sub></bold>
                </td>
                <td rowspan="2" colspan="1">
                  <bold>Pesaran-CD</bold>
                </td>
                <td rowspan="1" colspan="2">
                  <bold>
                    <abbrev xlink:title="Cross-Sectionally Augmented Dickey–Fuller">CADF</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="2">
                  <bold>
                    <abbrev xlink:title="Cross-Sectionally Augmented Im, Pesaran, and Shin">CIPS</abbrev>
                  </bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>Level</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>1<sup>st</sup> Diff</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Level</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>1<sup>st</sup> Diff</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGDP</td>
                <td rowspan="1" colspan="1">4.9E+4<sup>***</sup></td>
                <td rowspan="1" colspan="1">451.56<sup>***</sup></td>
                <td rowspan="1" colspan="1">136.59<sup>***</sup></td>
                <td rowspan="1" colspan="1">-1.825</td>
                <td rowspan="1" colspan="1">-2.825<sup>***</sup></td>
                <td rowspan="1" colspan="1">-1.525</td>
                <td rowspan="1" colspan="1">-2.698<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnDST</td>
                <td rowspan="1" colspan="1">1.5E+4<sup>***</sup></td>
                <td rowspan="1" colspan="1">104.76<sup>***</sup></td>
                <td rowspan="1" colspan="1">11.81<sup>***</sup></td>
                <td rowspan="1" colspan="1">-2.047</td>
                <td rowspan="1" colspan="1">-4.007<sup>***</sup></td>
                <td rowspan="1" colspan="1">-1.390</td>
                <td rowspan="1" colspan="1">-3.772<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGIM</td>
                <td rowspan="1" colspan="1">4.5E+4<sup>***</sup></td>
                <td rowspan="1" colspan="1">413.88<sup>***</sup></td>
                <td rowspan="1" colspan="1">181.96<sup>***</sup></td>
                <td rowspan="1" colspan="1">-1.562</td>
                <td rowspan="1" colspan="1">2.728<sup>***</sup></td>
                <td rowspan="1" colspan="1">-1.448</td>
                <td rowspan="1" colspan="1">-2.459<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGEX</td>
                <td rowspan="1" colspan="1">3.6E+4<sup>***</sup></td>
                <td rowspan="1" colspan="1">319.91<sup>***</sup></td>
                <td rowspan="1" colspan="1">156.53<sup>***</sup></td>
                <td rowspan="1" colspan="1">-1.869</td>
                <td rowspan="1" colspan="1">-2.954<sup>***</sup></td>
                <td rowspan="1" colspan="1">-1.603</td>
                <td rowspan="1" colspan="1">-2.758<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnTO</td>
                <td rowspan="1" colspan="1">1.6E+4<sup>***</sup></td>
                <td rowspan="1" colspan="1">116.72<sup>***</sup></td>
                <td rowspan="1" colspan="1">44.54<sup>***</sup></td>
                <td rowspan="1" colspan="1">-1.119</td>
                <td rowspan="1" colspan="1">-2.813<sup>***</sup></td>
                <td rowspan="1" colspan="1">-0.997</td>
                <td rowspan="1" colspan="1">-2.482<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnSCH</td>
                <td rowspan="1" colspan="1">3.6E+4<sup>***</sup></td>
                <td rowspan="1" colspan="1">325.29<sup>***</sup></td>
                <td rowspan="1" colspan="1">100.47<sup>***</sup></td>
                <td rowspan="1" colspan="1">-2.795<sup>***</sup></td>
                <td rowspan="1" colspan="1">-3.487<sup>***</sup></td>
                <td rowspan="1" colspan="1">-2.124<sup>**</sup></td>
                <td rowspan="1" colspan="1">-3.401<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnPOP</td>
                <td rowspan="1" colspan="1">8.6E+4<sup>***</sup></td>
                <td rowspan="1" colspan="1">826.62<sup>***</sup></td>
                <td rowspan="1" colspan="1">270.19<sup>***</sup></td>
                <td rowspan="1" colspan="1">-1.611</td>
                <td rowspan="1" colspan="1">-2.489<sup>**</sup></td>
                <td rowspan="1" colspan="1">-2.013<sup>*</sup></td>
                <td rowspan="1" colspan="1">-1.780</td>
              </tr>
            </tbody>
          </table>
          <table-wrap-foot>
            <fn>
              <p><italic>Note</italic>: Standard errors in parentheses. * p &lt; 0.1, ** p &lt; 0.05, *** p &lt; 0.01.</p>
            </fn>
          </table-wrap-foot>
        </table-wrap>
        <p>In the unit root analysis, the <abbrev xlink:title="Cross-Sectionally Augmented Dickey–Fuller">CADF</abbrev> and <abbrev xlink:title="Cross-Sectionally Augmented Im, Pesaran, and Shin">CIPS</abbrev> tests are used to assess stationarity. Most variables, including <italic>GDP</italic> and <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic>, <italic><abbrev xlink:title="goods imports">GIM</abbrev></italic>, <italic><abbrev xlink:title="goods exports ,">GEX</abbrev></italic> and <italic><abbrev xlink:title="trade openness">TO</abbrev></italic>, display non-stationarity at the level, with negative test statistics that do not exceed critical values. However, upon first differencing, all variables become stationary. This analysis suggests that while the variables exhibit cross-sectional dependence, they require differencing to achieve stationarity, a prerequisite for reliable econometric modeling.</p>
        <p>In Table <xref ref-type="table" rid="T4">4</xref>, the Westerlund cointegration test is employed to examine the presence of long-run equilibrium relationships between the dependent and independent variables. The results of the <italic>G<sub>t</sub></italic>, <italic>P<sub>t</sub></italic>, and <italic>P<sub>a</sub></italic> statistics confirm a significant long-term association among the variables, whereas the <italic>G<sub>a</sub></italic> statistic does not provide sufficient evidence to support the existence of a long-run effect of <abbrev xlink:title="Digital services trade">DST</abbrev> on GDP growth.</p>
        <table-wrap id="T4" position="float" orientation="portrait">
          <label>Table 4.</label>
          <caption>
            <p>Westerlund Cointegration Analysis</p>
          </caption>
          <table>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1"><bold>Statistic</bold>s</td>
                <td rowspan="1" colspan="1">
                  <bold>Value</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Z-value</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Robust P-value</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Gt</td>
                <td rowspan="1" colspan="1">-2.127<sup>***</sup></td>
                <td rowspan="1" colspan="1">-4.053</td>
                <td rowspan="1" colspan="1">0.000</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Ga</td>
                <td rowspan="1" colspan="1">9.967</td>
                <td rowspan="1" colspan="1">28.321</td>
                <td rowspan="1" colspan="1">1.000</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Pt</td>
                <td rowspan="1" colspan="1">-14.978<sup>*</sup></td>
                <td rowspan="1" colspan="1">-1.430</td>
                <td rowspan="1" colspan="1">0.076</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Pa</td>
                <td rowspan="1" colspan="1">-9.209<sup>***</sup></td>
                <td rowspan="1" colspan="1">-7.782</td>
                <td rowspan="1" colspan="1">0.000</td>
              </tr>
            </tbody>
          </table>
          <table-wrap-foot>
            <fn>
              <p><italic>Note</italic>: Standard errors in parentheses. * p &lt; 0.1, ** p &lt; 0.05, *** p &lt; 0.01.</p>
            </fn>
          </table-wrap-foot>
        </table-wrap>
        <p>Table <xref ref-type="table" rid="T5">5</xref> presents the variable selection procedure and lists all selected variables based on the Standard LASSO, Adaptive LASSO and ElasticNet LASSO estimators. The optimal alpha values indicate the level of regularization used by each model. The Standard LASSO uses the weakest regularization, the Adaptive LASSO applies moderate regularization, and the Elastic-Net LASSO employs the strongest regularization. Despite the differences in alpha, all models yield similar predictive performance, with Mean Squared Errors (<abbrev xlink:title="Mean Squared Errors">MSE</abbrev>) around 0.057. However, Adaptive LASSO emerges as the best model, striking a balance between effective regularization and minimal prediction error, evidenced by its lowest <abbrev xlink:title="Mean Squared Errors">MSE</abbrev> and more refined variable selection through adaptive weighting.</p>
        <table-wrap id="T5" position="float" orientation="portrait">
          <label>Table 5.</label>
          <caption>
            <p>Variables Selection Procedure</p>
          </caption>
          <table>
            <tbody>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>Variables</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Standard LASSO</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Adaptive LASSO</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>Elastic-Net Estimator</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnDST</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGIM</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGEX</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnTO</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">м</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnSCH</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnPOP</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
                <td rowspan="1" colspan="1">P</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Optimal α</td>
                <td rowspan="1" colspan="1">0.0041</td>
                <td rowspan="1" colspan="1">0.0126</td>
                <td rowspan="1" colspan="1">0.0157</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <abbrev xlink:title="Mean Squared Errors">MSE</abbrev>
                </td>
                <td rowspan="1" colspan="1">0.0578</td>
                <td rowspan="1" colspan="1">0.0574</td>
                <td rowspan="1" colspan="1">0.0577</td>
              </tr>
            </tbody>
          </table>
          <table-wrap-foot>
            <fn>
              <p><italic>Note</italic>: This table lists all selected drivers of LnDST; the notation ‘√ ‘shows the identified explanatory variable based on the Standard, ElasticNet and Adaptive LASSOs approaches.</p>
            </fn>
          </table-wrap-foot>
        </table-wrap>
        <p>Figs <xref ref-type="fig" rid="F4">4</xref>, <xref ref-type="fig" rid="F5">5</xref>, <xref ref-type="fig" rid="F6">6</xref> illustrate the coefficient path plots and cross-validation plots for the Standard, Adaptive, and ElasticNet LASSOs, respectively. The coefficients path plots display the variability of each variable’s coefficient in response to changes in the regularization factors, showing how coefficients approach zero as the optimal lambda increases. The cross-validation plots highlight model performance across different values of the regularization factors, with the lowest <abbrev xlink:title="Mean Squared Errors">MSE</abbrev> (green line) and the best lambda (red dashed line), clearly marked. Similarly, other dashed lines represent the individual cross-validation folds.</p>
        <fig id="F4">
          <object-id content-type="doi">10.3897/brics-econ.7.e172739.fig4</object-id>
          <object-id content-type="arpha">D03A078C-B7EF-5618-92F5-9D6BB7E6159D</object-id>
          <label>Fig. 4.</label>
          <caption>
            <p>The coefficient path plots (left) and the Cross-validation plot (right) based on the Standard LASSO algorithm.</p>
          </caption>
          <graphic xlink:href="brics-econ-07-001-g004.jpg" id="oo_1710252.jpg">
            <uri content-type="original_file">https://binary.pensoft.net/fig/1710252</uri>
          </graphic>
        </fig>
        <fig id="F5">
          <object-id content-type="doi">10.3897/brics-econ.7.e172739.fig5</object-id>
          <object-id content-type="arpha">C0BBA1E8-7152-526F-8351-F88FC3543465</object-id>
          <label>Fig. 5.</label>
          <caption>
            <p>The coefficient path plots (left) and the Cross-validation plot (right) based on the Adaptive LASSO algorithm.</p>
          </caption>
          <graphic xlink:href="brics-econ-07-001-g005.jpg" id="oo_1710253.jpg">
            <uri content-type="original_file">https://binary.pensoft.net/fig/1710253</uri>
          </graphic>
        </fig>
        <fig id="F6">
          <object-id content-type="doi">10.3897/brics-econ.7.e172739.fig6</object-id>
          <object-id content-type="arpha">623BC634-7065-5913-8418-3363D9BB7293</object-id>
          <label>Fig. 6.</label>
          <caption>
            <p>The coefficient path plots (left) and the Cross-validation plot (right) based on the ElasticNet LASSO algorithm.</p>
          </caption>
          <graphic xlink:href="brics-econ-07-001-g006.jpg" id="oo_1710254.jpg">
            <uri content-type="original_file">https://binary.pensoft.net/fig/1710254</uri>
          </graphic>
        </fig>
      </sec>
      <sec sec-type="4.2. Long-run estimation results" id="sec15">
        <title>4.2. Long-run estimation results</title>
        <p>After conducting preliminary panel data analysis and applying LASSO regularization techniques to variable selection, this study uses inferential LASSO-based machine learning methods — namely <abbrev xlink:title="Double-Selection LASSO linear regression">DSLR</abbrev>, <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev>, and Cross-fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> — to estimate the long-run impact of <abbrev xlink:title="Digital services trade">DST</abbrev> on GDP. The results are reported in Table <xref ref-type="table" rid="T6">6</xref>. Columns (1), (3), and (5) present the impact of <abbrev xlink:title="Digital services trade">DST</abbrev> on GDP without including control variables, whereas Columns (2), (4), and (6) display the results after accounting for control variables. Among these approaches, the Cross-fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> model stand outs, as it is built on a robust LASSO framework and shows superior performance in capturing temporal dynamics and minimizing model selection bias. The results reveal that all selected variables exert a statistically significant influence on GDP in developing economies. Specifically, holding other factors constant, a 1% increase in <abbrev xlink:title="Digital services trade">DST</abbrev> leads to an estimated 0.034% increase in GDP.</p>
        <table-wrap id="T6" position="float" orientation="portrait">
          <label>Table 6.</label>
          <caption>
            <p>Long-run estimation using <abbrev xlink:title="Double-Selection LASSO linear regression">DSLR</abbrev>, <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev>, and Cross-fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev></p>
          </caption>
          <table>
            <tbody>
              <tr>
                <td rowspan="3" colspan="1">
                  <bold>Variables</bold>
                </td>
                <td rowspan="1" colspan="2">
                  <bold><abbrev xlink:title="Double-Selection LASSO linear regression">DSLR</abbrev> Method</bold>
                </td>
                <td rowspan="1" colspan="2">
                  <bold><abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> Method</bold>
                </td>
                <td rowspan="1" colspan="2">
                  <bold>Cross-fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> Method</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>(1)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(2)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(3)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(4)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(5)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(6)</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnDST</td>
                <td rowspan="1" colspan="1">0.026<sup>***</sup></td>
                <td rowspan="1" colspan="1">0.033<sup>***</sup></td>
                <td rowspan="1" colspan="1">0.020<sup>***</sup></td>
                <td rowspan="1" colspan="1">0.035<sup>***</sup></td>
                <td rowspan="1" colspan="1">0.031<sup>**</sup></td>
                <td rowspan="1" colspan="1">0.034<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.006)</td>
                <td rowspan="1" colspan="1">(0.013)</td>
                <td rowspan="1" colspan="1">(0.005)</td>
                <td rowspan="1" colspan="1">(0.013)</td>
                <td rowspan="1" colspan="1">(0.014)</td>
                <td rowspan="1" colspan="1">(0.012)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGIM</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">0.351<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">0.347<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">0.346<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.042)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.040)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.041)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnGEX</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">0.148<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">0.148<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">0.149<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.016)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.016)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.017)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnTO</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">-0.175<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">-0.172<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">-0.171<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.042)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.040)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.043)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnPOP</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">-0.590<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">-0.589<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">-0.587<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.036)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.035)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.036)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnSCH</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">0.160<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">0.162<sup>***</sup></td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">0.159<sup>***</sup></td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.017)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.017)</td>
                <td rowspan="1" colspan="1"/>
                <td rowspan="1" colspan="1">(0.017)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Country FE</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Time FE</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Wald <italic>X<sup>2</sup></italic></td>
                <td rowspan="1" colspan="1">14.38</td>
                <td rowspan="1" colspan="1">1038.78</td>
                <td rowspan="1" colspan="1">14.01</td>
                <td rowspan="1" colspan="1">979.47</td>
                <td rowspan="1" colspan="1">4.93</td>
                <td rowspan="1" colspan="1">1000.15</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Prob. <italic>X<sup>2</sup></italic></td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">N</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
                <td rowspan="1" colspan="1">1653</td>
              </tr>
            </tbody>
          </table>
          <table-wrap-foot>
            <fn>
              <p><italic>Note</italic>: Standard errors in parentheses. * p &lt; 0.1, ** p &lt; 0.05, *** p &lt; 0.01.</p>
            </fn>
          </table-wrap-foot>
        </table-wrap>
        <p>The positive and significant effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on <italic>GDP</italic> growth seems both theoretically sound and practically justified. According to the economic concept of comparative advantage, countries benefit from expertise in efficient production; the growth of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> is considered a form of efficient production (<xref ref-type="bibr" rid="B67">Zhou &amp; Dahal, 2024</xref>; <xref ref-type="bibr" rid="B49">Tetteh, 2024</xref>). Similarly, the theory of endogenous growth emphasizes that the development of technology and knowledge leads to economic growth (<xref ref-type="bibr" rid="B22">Helpman &amp; Krugman, 1985</xref>; <xref ref-type="bibr" rid="B17">Etro, 2023</xref>). Besides, the diffusion of technology helps to boost productivity, allowing local firms to operate with higher industrial added value (<xref ref-type="bibr" rid="B38">Nucci et al., 2023</xref>; <xref ref-type="bibr" rid="B18">Foster &amp; He, 2022</xref>).</p>
        <p>Moreover, the impacts of <italic><abbrev xlink:title="goods imports">GIM</abbrev></italic> and <italic><abbrev xlink:title="goods exports ,">GEX</abbrev></italic> on <italic>GDP</italic> are also positive, indicating that higher trade volumes contribute to <italic>GDP</italic> growth. <italic><abbrev xlink:title="population">POP</abbrev></italic> presents a negative coefficient of -0.586, meaning diminishing returns to <italic>GDP</italic> growth with larger populations, which may complicate resource management. The <italic><abbrev xlink:title="structural change">SCH</abbrev></italic> has a coefficient of 0.159, indicating that structural change plays a significant positive role in this relationship at the 1% significance level.</p>
      </sec>
      <sec sec-type="4.3. Robustness checks and endogeneity analyses" id="sec16">
        <title>4.3. Robustness checks and endogeneity analyses</title>
        <sec sec-type="4.3.1. Robustness checks" id="sec17">
          <title>4.3.1. Robustness checks</title>
          <p>To ensure the validity of long-run estimates, we assessed the impact of <abbrev xlink:title="Digital services trade">DST</abbrev> on GDP using Bayesian model averaging (<abbrev xlink:title="Bayesian Model Averaging">BMA</abbrev>) and Driscoll-Kraay methods instead of econometric techniques, and substituted <abbrev xlink:title="Digital services trade">DST</abbrev> with its main proxies, including digital services imports (<abbrev xlink:title="digital services imports">DSIM</abbrev>), digital services exports (<abbrev xlink:title="digital services exports">DSEX</abbrev>) and ICT.</p>
          <p>In Panel A of Table <xref ref-type="table" rid="T7">7</xref>, the <abbrev xlink:title="Bayesian Model Averaging">BMA</abbrev> results in Column (1) and the Driscoll-Kraay results in Column (2) confirm the positive and significant effect of <abbrev xlink:title="Digital services trade">DST</abbrev> on GDP in developing countries, validating the reliability of the <abbrev xlink:title="Double-Selection LASSO linear regression">DSLR</abbrev>, <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> and Cross-fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> machine learning outcomes presented in Table <xref ref-type="table" rid="T6">6</xref>. Similarly, as shown in Columns (3)–(5), <abbrev xlink:title="digital services imports">DSIM</abbrev>, <abbrev xlink:title="digital services exports">DSEX</abbrev>, and ICT collectively contribute to GDP growth in developing countries through complementary channels. <abbrev xlink:title="digital services imports">DSIM</abbrev> facilitates technology transfer, enhances productivity, and improves business efficiency by providing access to advanced software, cloud services and data-driven tools. <abbrev xlink:title="digital services exports">DSEX</abbrev>, while often limited in scale, can still support economic activity by generating foreign exchange earnings, promoting innovation, and integrating firms into global value chains, even if its direct impact on GDP is modest or statistically insignificant. The role of ICT is indeed crucial as it improves communication, lowers transaction costs, supports structural transformation and enables both the import and export of digital services. Together, these findings further verify the consistency and robustness of the <abbrev xlink:title="Digital services trade">DST</abbrev>–GDP relationship in the context of developing economies.</p>
          <table-wrap id="T7" position="float" orientation="portrait">
            <label>Table 7.</label>
            <caption>
              <p>Robustness check and endogeneity analysis</p>
            </caption>
            <table>
              <tbody>
                <tr>
                  <td rowspan="1" colspan="9">
                    <bold>Panel A: Robustness checks using alternative estimation techniques and proxies of <abbrev xlink:title="Digital services trade">DST</abbrev></bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="3" colspan="1">
                    <bold>Variables</bold>
                  </td>
                  <td rowspan="1" colspan="4">
                    <bold>Changing the estimation techniques to <abbrev xlink:title="Bayesian Model Averaging">BMA</abbrev> and D–K</bold>
                  </td>
                  <td rowspan="1" colspan="4">
                    <bold>Changing the main explanatory variable to <abbrev xlink:title="digital services imports">DSIM</abbrev>, <abbrev xlink:title="digital services exports">DSEX</abbrev>, and ICT</bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">
                    <bold>(1)</bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>(2)</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>(3)</bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>(4)</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>(5)</bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>LnGDP</bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnDST</td>
                  <td rowspan="1" colspan="2">0.026<sup>**</sup> (0.010)</td>
                  <td rowspan="1" colspan="2">0.026<sup>**</sup> (0.011)</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnDSIM</td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1">0.018<sup>**</sup> (0.006)</td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnDSEX</td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2">0.009 (0.007)</td>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnICT</td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1">0.015<sup>**</sup> (0.007)</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Controls</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Country FE</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Time FE</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Wald <italic>X<sup>2</sup></italic></td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="2">2612.230</td>
                  <td rowspan="1" colspan="1">250.700</td>
                  <td rowspan="1" colspan="2">233.490</td>
                  <td rowspan="1" colspan="1">236.630</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Prob. <italic>X<sup>2</sup></italic></td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="2">0.000</td>
                  <td rowspan="1" colspan="1">0.000</td>
                  <td rowspan="1" colspan="2">0.000</td>
                  <td rowspan="1" colspan="1">0.000</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">R<sup>2</sup></td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="2">0.621</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">N</td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="2">1653</td>
                  <td rowspan="1" colspan="1">1653</td>
                  <td rowspan="1" colspan="2">1653</td>
                  <td rowspan="1" colspan="1">1653</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="9">
                    <bold>Panel B: Edogeneity analysis using internal <abbrev xlink:title="instrumental variable">IV</abbrev> (<italic><abbrev xlink:title="Digital services trade">DST</abbrev><sub>t</sub></italic><sub>– 2</sub>, <italic><abbrev xlink:title="Digital services trade">DST</abbrev><sub>t</sub></italic><sub>– 3</sub>) and external <abbrev xlink:title="instrumental variable">IV</abbrev> (<italic>IUR<sub>t</sub></italic><sub>– 1</sub>)*PRFTL)</bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="3" colspan="2">
                    <bold>Variables</bold>
                  </td>
                  <td rowspan="1" colspan="3">
                    <bold>Lewbel Method (<italic><abbrev xlink:title="Digital services trade">DST</abbrev><sub>t</sub></italic><sub>– 2</sub>, <italic><abbrev xlink:title="Digital services trade">DST</abbrev><sub>t</sub></italic><sub>– 3</sub>)</bold>
                  </td>
                  <td rowspan="1" colspan="4">
                    <bold>
                      <abbrev xlink:title="conventional two-stage least squares">2SLS-IV</abbrev>
                    </bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">
                    <bold>
                      <abbrev xlink:title="Partialing-Out Instrumental Variable LASSO">POIVLR</abbrev>
                    </bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>Cross-fit <abbrev xlink:title="Partialing-Out Instrumental Variable LASSO">POIVLR</abbrev></bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>1<sup>st</sup> Stage <abbrev xlink:title="instrumental variable">IV</abbrev> Result</bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>2<sup>nd</sup> Stage <abbrev xlink:title="instrumental variable">IV</abbrev> Result</bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>LnDST</bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>LnGDP</bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">LnDST</td>
                  <td rowspan="1" colspan="2">0.029<sup>**</sup> (0.014)</td>
                  <td rowspan="1" colspan="1">0.029<sup>**</sup> (0.013)</td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="2">0.012<sup>**</sup> (0.005)</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">IUR<sub>t-1</sub>*PRFTL</td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2">0.038<sup>***</sup> (0.007)</td>
                  <td rowspan="1" colspan="2"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">Controls</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">Country FE</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">Time FE</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">KP <abbrev xlink:title="Lagrange Multiplier">LM</abbrev> Test</td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2">24.500</td>
                  <td rowspan="1" colspan="2">24.499</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">CD Wald F</td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2">34.190</td>
                  <td rowspan="1" colspan="2">34.193</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">Wald <italic>X<sup>2</sup></italic></td>
                  <td rowspan="1" colspan="2">1138.640</td>
                  <td rowspan="1" colspan="1">1031.630</td>
                  <td rowspan="1" colspan="2">27.110</td>
                  <td rowspan="1" colspan="2">51.800</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">Prob. <italic>X<sup>2</sup></italic></td>
                  <td rowspan="1" colspan="2">0.000</td>
                  <td rowspan="1" colspan="1">0.000</td>
                  <td rowspan="1" colspan="2">0.000</td>
                  <td rowspan="1" colspan="2">0.000</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">R<sup>2</sup></td>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="2">0.967</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="2">N</td>
                  <td rowspan="1" colspan="2">1479</td>
                  <td rowspan="1" colspan="1">1392</td>
                  <td rowspan="1" colspan="2">1652</td>
                  <td rowspan="1" colspan="2">1652</td>
                </tr>
              </tbody>
            </table>
            <table-wrap-foot>
              <fn>
                <p><italic>Note</italic>: Standard errors in parentheses. * p &lt; 0.1, ** p &lt; 0.05, *** p &lt; 0.01. In Panel B, KP <abbrev xlink:title="Lagrange Multiplier">LM</abbrev> Test and CD Wald F stand for Kleibergen-Paap rk <abbrev xlink:title="Lagrange Multiplier">LM</abbrev> and Cragg-Donald Wald F statistics.</p>
              </fn>
            </table-wrap-foot>
          </table-wrap>
        </sec>
        <sec sec-type="4.3.2. Endogeneity analysis" id="sec18">
          <title>4.3.2. Endogeneity analysis</title>
          <p>To address potential endogeneity concerns in the primary model, this study employs instrumental variable (<abbrev xlink:title="instrumental variable">IV</abbrev>) approaches, specifically the methods proposed by <xref ref-type="bibr" rid="B29">Lewbel (2012)</xref> and conventional two-stage least squares (<abbrev xlink:title="conventional two-stage least squares">2SLS-IV</abbrev>). In accordance with Lewbel’s framework, internally generated IVs are constructed using the two-period (<italic><abbrev xlink:title="Digital services trade">DST</abbrev><sub>t</sub></italic><sub>– 2</sub>) and three-period (<italic><abbrev xlink:title="Digital services trade">DST</abbrev><sub>t</sub></italic><sub>– 3</sub>) lags of the <abbrev xlink:title="Digital services trade">DST</abbrev> variable. These instruments are then used within the <abbrev xlink:title="Partialing-Out Instrumental Variable LASSO">POIVLR</abbrev> and Cross-fit <abbrev xlink:title="Partialing-Out Instrumental Variable LASSO">POIVLR</abbrev> models, respectively, to conduct rigorous endogeneity analysis. The results, presented in Panel B of Table <xref ref-type="table" rid="T7">7</xref>, exhibit strong consistency with the baseline estimates reported in Table <xref ref-type="table" rid="T6">6</xref>, thereby reinforcing the robustness of the findings and confirming that the estimated relationship between <abbrev xlink:title="Digital services trade">DST</abbrev> and GDP is not influenced by endogeneity bias.</p>
          <p>Additionally, following <xref ref-type="bibr" rid="B43">Qu and Fan (2024)</xref>, in this study, the <abbrev xlink:title="instrumental variable">IV</abbrev> is constructed as the one-period lag of Internet user rates (<italic>IUR<sub>t</sub></italic><sub>–1</sub>) multiplied by the fixed telephone line penetration rate in 1984 (<italic>PRFTL</italic>). This <abbrev xlink:title="instrumental variable">IV</abbrev> captures exogenous variation in digital infrastructure that plausibly affects a country’s capacity to engage in <abbrev xlink:title="Digital services trade">DST</abbrev> but is unlikely to have a direct effect on current GDP.</p>
          <p>The results of the <abbrev xlink:title="conventional two-stage least squares">2SLS-IV</abbrev> analysis, also reported in Panel B of Table <xref ref-type="table" rid="T7">7</xref>, indicate that the <italic>IUR<sub>t</sub></italic><sub>–1</sub> * <italic>PRFTL</italic> positively, significantly and directly affects the <abbrev xlink:title="Digital services trade">DST</abbrev>, indirectly affects GDP, as demonstrated by the 1<sup>st</sup> and 2<sup>nd</sup> stages outcomes. The KP <abbrev xlink:title="Lagrange Multiplier">LM</abbrev> Test and CD Wald F statistics in all specifications considerably exceed the Stock–Yogo weak identification test critical values at the 10% significance level, thus rejecting the null hypothesis of weak instruments and confirming their strong statistical relevance. Furthermore, the KP <abbrev xlink:title="Lagrange Multiplier">LM</abbrev> test results show a significant rejection of the null hypothesis of under-identification at the 1% significance level, providing robust evidence that the selected <abbrev xlink:title="instrumental variable">IV</abbrev> is valid and properly identified.</p>
        </sec>
      </sec>
      <sec sec-type="4.4. Mediation and Moderation Analyses" id="sec19">
        <title>4.4. Mediation and Moderation Analyses</title>
        <sec sec-type="4.4.1. Mediation analysis" id="sec20">
          <title>4.4.1. Mediation analysis</title>
          <p>Given that the results of long-term estimation and robustness checks have confirmed the significant and positive effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on <italic>GDP</italic> growth, this study employs a three-step mediation analysis using the <italic><abbrev xlink:title="employment">EMP</abbrev></italic> and <italic><abbrev xlink:title="technological innovation">TI</abbrev></italic> as mediating factors. The choice of these two variables as channels that can mediate the effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on GDP is rooted in the fact that <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> leads to the creation of job opportunities, higher employment rates for workers, increased income levels and ultimately improved <italic>GDP</italic> performance. Additionally, the expansion of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> facilitates the introduction of advanced technologies and products from developed countries to developing countries. This flow of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> provides an opportunity for developing nations to advance <italic><abbrev xlink:title="technological innovation">TI</abbrev></italic>, which in turn improves efficiency and productivity in economic sectors that are the sources of <italic>GDP</italic> growth. Therefore, the mediating role of <italic><abbrev xlink:title="employment">EMP</abbrev></italic> and <italic><abbrev xlink:title="technological innovation">TI</abbrev></italic> in the link to the effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on <italic>GDP</italic> is formulated as follows:</p>
          <p><mml:math id="M20"><mml:msub><mml:mi>Med</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>φ</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>φ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:msub><mml:mi>LnDST</mml:mi><mml:mrow><mml:mi>it</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>ϕ</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mi>i</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>μ</mml:mi><mml:mi>t</mml:mi><mml:mrow><mml:mi>′</mml:mi></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msub><mml:mi>ε</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math>	(19)</p>
          <p><mml:math id="M21"><mml:mi>LnGDP</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>LnDST</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>M</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ψ</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>δ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>μ</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ε</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:math>	(20)</p>
          <p><mml:math id="M22"><mml:mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"><mml:mtr><mml:mtd><mml:mi>Ln</mml:mi><mml:mi>G</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>φ</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ϑ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>φ</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>LnDST</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>+</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msub><mml:mi>ψ</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msub><mml:mi>ϑ</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>ϕ</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>τ</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ε</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math>	(21)</p>
          <p>where <italic>Med<sub>it</sub></italic> represents our mediating variables such as <italic>LnEMP</italic> and <italic>LnTI</italic>. ϑ<sub>1</sub> shows the direct effect, ϑ<sub>2</sub>ϕ<sub>1</sub> presents the indirect effect and ϑ<sub>1</sub> + ϑ<sub>2</sub>ϕ<sub>1</sub> indicates the total effect of the <abbrev xlink:title="Digital services trade">DST</abbrev> on economic growth.</p>
          <p>The results of the mediation analysis are presented in Table <xref ref-type="table" rid="T8">8</xref>. Column (1) denotes the total effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on <italic>GDP</italic>, while column (2) presents the effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on <italic><abbrev xlink:title="employment">EMP</abbrev>.</italic> Column (3) illustrates the simultaneous impact of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> and <italic><abbrev xlink:title="employment">EMP</abbrev></italic> on <italic>GDP</italic>, which is statistically significant and positive, indicating that <italic><abbrev xlink:title="employment">EMP</abbrev></italic> positively and partially mediates the effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on <italic>GDP.</italic> More specifically, <italic><abbrev xlink:title="employment">EMP</abbrev></italic> mediates 13.26% of the total effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on <italic>GDP.</italic> Similarly, column (4) shows that <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> positively and significantly improves <italic><abbrev xlink:title="technological innovation">TI</abbrev></italic>, and the simultaneous positive and significant effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> and <italic><abbrev xlink:title="technological innovation">TI</abbrev></italic> on <italic>GDP</italic> in column (5) reflects the fact that <italic>LnTI</italic> positively and partially mediates 31.36% of the total effect of <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> on <italic>GDP</italic> in the case of developing economies.</p>
          <table-wrap id="T8" position="float" orientation="portrait">
            <label>Table 8.</label>
            <caption>
              <p>Mechanism analysis results</p>
            </caption>
            <table>
              <tbody>
                <tr>
                  <td rowspan="3" colspan="1">
                    <bold>Variables</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>Baseline Results</bold>
                  </td>
                  <td rowspan="1" colspan="5">
                    <bold>Mediating role of <abbrev xlink:title="employment">EMP</abbrev> and <abbrev xlink:title="technological innovation">TI</abbrev></bold>
                  </td>
                  <td rowspan="1" colspan="3">
                    <bold>Moderating role of <abbrev xlink:title="Digital Infrastructure Index">DII</abbrev>, <abbrev xlink:title="human capital">HC</abbrev> and <abbrev xlink:title="Regulatory quality">REQ</abbrev></bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">
                    <bold>(1)</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>(2)</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>(3)</bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>(4)</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>(5)</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>(6)</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>(7)</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>(8)</bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>LnEMP</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="2">
                    <bold>LnTI</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>LnGDP</bold>
                  </td>
                  <td rowspan="1" colspan="1">
                    <bold>LnGDP</bold>
                  </td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnDST</td>
                  <td rowspan="1" colspan="1">0.034<sup>***</sup> (0.012)</td>
                  <td rowspan="1" colspan="1">0.027<sup>*</sup> (0.015)</td>
                  <td rowspan="1" colspan="2">0.029<sup>**</sup> (0.012)</td>
                  <td rowspan="1" colspan="1">0.124<sup>***</sup> (0.023)</td>
                  <td rowspan="1" colspan="1">0.025<sup>**</sup> (0.012)</td>
                  <td rowspan="1" colspan="1">0.022<sup>***</sup> (0.007)</td>
                  <td rowspan="1" colspan="1">0.018<sup>**</sup> (0.007)</td>
                  <td rowspan="1" colspan="1">0.031<sup>***</sup> (0.008)</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnEMP</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2">0.167<sup>***</sup> (0.018)</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnTI</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1">0.086<sup>***</sup> (0.009)</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnDII</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1">0.217<sup>***</sup> (0.051)</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnHC</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1">0.507<sup>***</sup> (0.114)</td>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnREQ</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1">0.052<sup>**</sup> (0.021)</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnDST*LnDII</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1">0.012<sup>*</sup> (0.007)</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnDST*LnHC</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1">0.017<sup>*</sup> (0.009)</td>
                  <td rowspan="1" colspan="1"/>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">LnDST*LnREQ</td>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="2"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1"/>
                  <td rowspan="1" colspan="1">0.001 (0.003)</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Controls</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Country FE</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Year FE</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="2">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                  <td rowspan="1" colspan="1">YES</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Wald <italic>X<sup>2</sup></italic> Prob. <italic>X<sup>2</sup></italic></td>
                  <td rowspan="1" colspan="1">1000.15 0.000</td>
                  <td rowspan="1" colspan="1">348.84 0.000</td>
                  <td rowspan="1" colspan="2">1724.43 0.000</td>
                  <td rowspan="1" colspan="1">682.54 0.000</td>
                  <td rowspan="1" colspan="1">2005.38 0.000</td>
                  <td rowspan="1" colspan="1">996.31 0.000</td>
                  <td rowspan="1" colspan="1">1025.23 0.000</td>
                  <td rowspan="1" colspan="1">986.32 0.000</td>
                </tr>
                <tr>
                  <td rowspan="1" colspan="1">Obs.</td>
                  <td rowspan="1" colspan="1">1653</td>
                  <td rowspan="1" colspan="1">1653</td>
                  <td rowspan="1" colspan="2">1653</td>
                  <td rowspan="1" colspan="1">1653</td>
                  <td rowspan="1" colspan="1">1653</td>
                  <td rowspan="1" colspan="1">1653</td>
                  <td rowspan="1" colspan="1">1653</td>
                  <td rowspan="1" colspan="1">1653</td>
                </tr>
              </tbody>
            </table>
            <table-wrap-foot>
              <fn>
                <p><italic>Notes</italic>: Standard errors in parentheses. * p &lt; 0.1, ** p &lt; 0.05, *** p &lt; 0.01.</p>
              </fn>
            </table-wrap-foot>
          </table-wrap>
          <p>The findings of our mediation analysis are consistent with economic theories. For example, classical economic theory posits that increased trade, particularly digital trade, leads to higher demand for labor and more job opportunities. In turn, increased employment can lead to higher household spending, which then contributes to economic growth. In turn, the labor market serves as a conduit through which the benefits of trade and economic growth are realized. In a similar analysis, endogenous growth theories suggest that trade in digital services stimulates investment growth, which in turn improves the level of technology and innovation in a country. Therefore, as companies become more involved in digital services, they strive to adopt more efficient technologies to ensure their survival in competitive markets by offering new goods and services. The findings in this section of the paper are consistent with studies by Zhang et al. (2021), <xref ref-type="bibr" rid="B46">Simon and Pingfang (2021)</xref>, and <xref ref-type="bibr" rid="B63">Yeerken and Feng (2024)</xref>.</p>
        </sec>
        <sec sec-type="4.4.2. Moderating analysis" id="sec21">
          <title>4.4.2. Moderating analysis</title>
          <p>To empirically analyze the moderating role of digital infrastructure (<italic><abbrev xlink:title="Digital Infrastructure Index">DII</abbrev></italic>), human capital (<italic><abbrev xlink:title="human capital">HC</abbrev></italic>), and regulatory quality (<italic><abbrev xlink:title="Regulatory quality">REQ</abbrev></italic>), the study estimates the following econometric model:</p>
          <p><mml:math id="M23"><mml:mtable displaystyle="true" columnspacing="1em" rowspacing="3pt"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>LnGDP</mml:mi><mml:mrow><mml:mi>it</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>ξ</mml:mi><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ξ</mml:mi><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>Ln</mml:mi><mml:msub><mml:mi>DST</mml:mi><mml:mrow><mml:mi>it</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ξ</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mi>Mod</mml:mi><mml:mrow><mml:mi>it</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ξ</mml:mi><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:msubsup><mml:mi>LnDST</mml:mi><mml:mrow><mml:mi>it</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msubsup><mml:msub><mml:mi>Mod</mml:mi><mml:mrow><mml:mi>it</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>+</mml:mo><mml:msub><mml:mi>η</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:msub><mml:mi>X</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ζ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>v</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>ε</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:math>	(22)</p>
          <p>where <italic>Mod<sub>it</sub></italic> represents our moderating variables such as <italic>LnDII</italic> and <italic>LnHC</italic>, and <italic>LnREQ</italic>. ξ<sub>1</sub> shows the direct effect, ξ<sub>2</sub> presents the direct effect of moderating factors, and ξ<sub>3</sub> indicates the indirect effect of the <abbrev xlink:title="Digital services trade">DST</abbrev> on the economic growth through the moderating variables.</p>
          <p>The moderating analysis results in Columns (6) and (7) of Table <xref ref-type="table" rid="T8">8</xref> reveal that <italic><abbrev xlink:title="Digital Infrastructure Index">DII</abbrev></italic> and <italic><abbrev xlink:title="human capital">HC</abbrev></italic> exert a positive and significant moderating effect on the relationship between <italic><abbrev xlink:title="Digital services trade">DST</abbrev></italic> and <italic>GDP</italic>, indicating that economies with stronger digital infrastructure and higher levels of human capital are better positioned to translate digital trade expansion into economic growth. <italic><abbrev xlink:title="Regulatory quality">REQ</abbrev></italic> also moderates this relationship positively but insignificantly, suggesting that while sound regulatory frameworks contribute to improving the growth effects of digital trade, their impact remains limited, potentially due to institutional inefficiencies or uneven enforcement across countries.</p>
        </sec>
      </sec>
      <sec sec-type="4.5. Heterogeneity Analysis" id="sec22">
        <title>4.5. Heterogeneity Analysis</title>
        <p>Table <xref ref-type="table" rid="T9">9</xref> presents the results of the heterogeneity analysis based on income levels, digital infrastructure, and regulatory quality, offering insights into how the impact of <abbrev xlink:title="Digital services trade">DST</abbrev> on GDP varies across different country groups. Specifically, Columns (1), (3) and (4) show that low-income (<abbrev xlink:title="low-income">LI</abbrev>), upper-middle-income (<abbrev xlink:title="upper-middle-income">UMI</abbrev>), and high-income (<abbrev xlink:title="high-income">HI</abbrev>) countries exhibit positive and statistically significant coefficients of 0.017, 0.017, and 0.095, respectively. These findings indicate that higher levels of <abbrev xlink:title="Digital services trade">DST</abbrev> are positively associated with GDP growth in these economies. In contrast, the results in Column (2) reveal that lower-middle-income (<abbrev xlink:title="lower-middle-income">LMI</abbrev>) countries experience a negative but statistically insignificant relationship between <abbrev xlink:title="Digital services trade">DST</abbrev> and GDP.</p>
        <table-wrap id="T9" position="float" orientation="portrait">
          <label>Table 9.</label>
          <caption>
            <p>Heterogeneity analysis results</p>
          </caption>
          <table>
            <tbody>
              <tr>
                <td rowspan="4" colspan="1">
                  <bold>Variables</bold>
                </td>
                <td rowspan="1" colspan="4">
                  <bold>Income Levels</bold>
                </td>
                <td rowspan="1" colspan="2">
                  <bold>Digital infrastructure level</bold>
                </td>
                <td rowspan="1" colspan="2">
                  <bold>Regulatory quality level</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="low-income">LI</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="lower-middle-income">LMI</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="upper-middle-income">UMI</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="high-income">HI</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="high digital infrastructure levels">HDIL</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>
                    <abbrev xlink:title="low digital infrastructure levels">LDIL</abbrev>
                  </bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>HRQL</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LRQL</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>(1)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(2)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(3)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(4)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(5)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(6)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(7)</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>(8)</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
                <td rowspan="1" colspan="1">
                  <bold>LnGDP</bold>
                </td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">LnDST</td>
                <td rowspan="1" colspan="1">0.017<sup>**</sup> (0.007)</td>
                <td rowspan="1" colspan="1">-0.001 (0.005)</td>
                <td rowspan="1" colspan="1">0.017<sup>*</sup> (0.009)</td>
                <td rowspan="1" colspan="1">0.095<sup>***</sup> (0.033)</td>
                <td rowspan="1" colspan="1">0.049<sup>**</sup> (0.020)</td>
                <td rowspan="1" colspan="1">0.008 (0.020)</td>
                <td rowspan="1" colspan="1">0.004 (0.013)</td>
                <td rowspan="1" colspan="1">0.008 (0.018)</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Controls</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Country FE</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Year FE</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
                <td rowspan="1" colspan="1">YES</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Wald <italic>X<sup>2</sup></italic></td>
                <td rowspan="1" colspan="1">352.85</td>
                <td rowspan="1" colspan="1">605.21</td>
                <td rowspan="1" colspan="1">483.77</td>
                <td rowspan="1" colspan="1">118.47</td>
                <td rowspan="1" colspan="1">587.43</td>
                <td rowspan="1" colspan="1">206.52</td>
                <td rowspan="1" colspan="1">332.75</td>
                <td rowspan="1" colspan="1">326.33</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">Prob. <italic>X<sup>2</sup></italic></td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
                <td rowspan="1" colspan="1">0.000</td>
              </tr>
              <tr>
                <td rowspan="1" colspan="1">N</td>
                <td rowspan="1" colspan="1">228</td>
                <td rowspan="1" colspan="1">836</td>
                <td rowspan="1" colspan="1">551</td>
                <td rowspan="1" colspan="1">38</td>
                <td rowspan="1" colspan="1">833</td>
                <td rowspan="1" colspan="1">820</td>
                <td rowspan="1" colspan="1">832</td>
                <td rowspan="1" colspan="1">821</td>
              </tr>
            </tbody>
          </table>
          <table-wrap-foot>
            <fn>
              <p><italic>Notes</italic>: Standard errors in parentheses. * p &lt; 0.1, ** p &lt; 0.05, *** p &lt; 0.01.</p>
            </fn>
          </table-wrap-foot>
        </table-wrap>
        <p>Furthermore, as reported in Column (5), <abbrev xlink:title="Digital services trade">DST</abbrev> exerts a positive and statistically significant effect on GDP growth in countries with high digital infrastructure levels (<abbrev xlink:title="high digital infrastructure levels">HDIL</abbrev>). However, the effects of <abbrev xlink:title="Digital services trade">DST</abbrev> on GDP in countries with low digital infrastructure levels (<abbrev xlink:title="low digital infrastructure levels">LDIL</abbrev>), as well as in those with high or low regulatory quality, remain positive but statistically insignificant. These findings highlight the critical role of digital infrastructure in enhancing the economic benefits of <abbrev xlink:title="Digital services trade">DST</abbrev> adoption across different development contexts.</p>
      </sec>
      <sec sec-type="4.6. Discussion" id="sec23">
        <title>4.6. Discussion</title>
        <p>The empirical findings of this study provide robust evidence that <abbrev xlink:title="Digital services trade">DST</abbrev> exerts a positive and significant impact on GDP growth across 87 developing economies, corroborating both theoretical and practical expectations (<xref ref-type="bibr" rid="B19">Gao et al., 2024</xref>; <xref ref-type="bibr" rid="B61">Xiong &amp; Luo, 2023</xref>). Using advanced <abbrev xlink:title="machine learning">ML</abbrev> techniques, particularly the Cross-fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> model, we find that a 1% increase in <abbrev xlink:title="Digital services trade">DST</abbrev> is associated with a 0.034% increase in GDP, highlighting the economic relevance of <abbrev xlink:title="Digital services trade">DST</abbrev> as a driver of economic performance. This result supports <bold><italic>H<sub>1</sub></italic></bold> and aligns with previous empirical studies, including those by <xref ref-type="bibr" rid="B63">Yeerken &amp; Feng (2024)</xref>, <xref ref-type="bibr" rid="B34">Mulenga &amp; Mayondi (2022)</xref>, <xref ref-type="bibr" rid="B19">Gao et al. (2024)</xref> and <xref ref-type="bibr" rid="B61">Xiong &amp; Luo (2023)</xref>. Additionally, the positive effect of <abbrev xlink:title="Digital services trade">DST</abbrev> is consistent with classical economic theory, which emphasizes gains from comparative advantage and production efficiency (<xref ref-type="bibr" rid="B67">Zhou &amp; Dahal, 2024</xref>; <xref ref-type="bibr" rid="B49">Tetteh, 2024</xref>). It is also in line with endogenous growth theory, which highlights the importance of technological advancement and knowledge diffusion in fostering long-run economic expansion (<xref ref-type="bibr" rid="B22">Helpman &amp; Krugman, 1985</xref>; <xref ref-type="bibr" rid="B17">Etro, 2023</xref>; <xref ref-type="bibr" rid="B38">Nucci et al., 2023</xref>; <xref ref-type="bibr" rid="B18">Foster &amp; He, 2022</xref>).</p>
        <p>The mechanism analysis further underscores the mediating roles of employment and technological innovation in translating <abbrev xlink:title="Digital services trade">DST</abbrev> into economic growth. Consistent with the empirical evidence of <xref ref-type="bibr" rid="B63">Yeerken &amp; Feng (2024)</xref>, <xref ref-type="bibr" rid="B26">Jin &amp; Lu (2024)</xref>, and <xref ref-type="bibr" rid="B35">Ndubuisi et al. (2021)</xref>, increased participation in digital trade creates additional labor demand and employment opportunities, raising household income and consumer spending. At the same time, engagement with digital services encourages companies to adopt advanced technology and pursue continuous innovation. This enhances productivity and supports sustainable economic growth (<xref ref-type="bibr" rid="B58">Wen et al., 2023</xref>). These findings confirm <bold><italic>H<sub>2</sub></italic></bold> and align with the theoretical framework that identifies labor-market dynamics and technological development as critical transmission channels through which the benefits of <abbrev xlink:title="Digital services trade">DST</abbrev> materialize (Zhang et al., 2021; <xref ref-type="bibr" rid="B46">Simon &amp; Pingfang, 2021</xref>).</p>
        <p>The endogeneity analysis, which uses lagged forms of <abbrev xlink:title="Digital services trade">DST</abbrev> and the interaction between the one-period lag of Internet-user rates and the penetration rate of fixed telephone lines in 1984 as instrumental variables, demonstrates that the main findings are not affected by endogeneity concerns. The results of the <abbrev xlink:title="Partialing-Out Instrumental Variable LASSO">POIVLR</abbrev>, Cross-fit <abbrev xlink:title="Partialing-Out Instrumental Variable LASSO">POIVLR</abbrev>, and 2SLS models consistently confirm the validity of the <abbrev xlink:title="instrumental variable">IV</abbrev> strategy. The 2SLS estimates further support <bold><italic>H<sub>3</sub></italic></bold>, which is in line with <xref ref-type="bibr" rid="B45">Rodriguez-Crespo et al. (2019)</xref>, who also found a positive and significant relationship between Internet use and trade in both developing and developed economies.</p>
        <p>The heterogeneity analysis reveals that the impact of <abbrev xlink:title="Digital services trade">DST</abbrev> on GDP is contingent upon countries’ income levels, digital-infrastructure readiness and regulatory-quality conditions. The income-based heterogeneity results show that low-income and upper-middle-income economies experience modest positive effects, whereas high-income developing countries benefit the most from <abbrev xlink:title="Digital services trade">DST</abbrev>. Conversely, lower-middle-income countries display no statistically significant effect, suggesting potential barriers to harnessing digital trade, such as limited digital infrastructure, skill shortages, or regulatory constraints. The heterogeneity analysis based on digital infrastructure and regulatory quality further indicates that only economies with high levels of digital infrastructure experience positive and significant effects of <abbrev xlink:title="Digital services trade">DST</abbrev> on GDP. In contrast, countries with low digital infrastructure, as well as those with both high and low regulatory quality, do not exhibit significant effects. Collectively, these findings suggest that the capacity to benefit from digital trade is determined by structural factors, including digital readiness, institutional quality and the broader enabling environment.</p>
        <p>Finally, the results highlight the reinforcing roles of traditional trade and structural transformation in shaping GDP outcomes. Goods exports (<abbrev xlink:title="goods exports ,">GEX</abbrev>) and goods imports (<abbrev xlink:title="goods imports">GIM</abbrev>) both contribute positively to economic growth, while structural change (<abbrev xlink:title="structural change">SCH</abbrev>) emerges as a significant driver, suggesting that broader economic transformation complements the growth-enhancing effects of digital trade. The negative association between population (<abbrev xlink:title="population">POP</abbrev>) and GDP may reflect diminishing returns in more populous countries, underscoring the need for effective resource allocation and targeted policies to maximize the benefits of digitalization.</p>
      </sec>
    </sec>
    <sec sec-type="5. Conclusion, policy recommendation and limitations" id="sec24">
      <title>5. Conclusion, policy recommendation and limitations</title>
      <sec sec-type="5.1. Conclusion" id="sec25">
        <title>5.1. Conclusion</title>
        <p>This study examines the role of <abbrev xlink:title="Digital services trade">DST</abbrev> in fostering economic growth across 87 developing economies from 2005 to 2023. Using state-of-the-art <abbrev xlink:title="machine learning">ML</abbrev> techniques, including the Cross-fit <abbrev xlink:title="Partialing-Out LASSO Linear Regression">POLR</abbrev> model, the findings consistently demonstrate that <abbrev xlink:title="Digital services trade">DST</abbrev> exerts a positive and statistically significant impact on GDP. These results reinforce theoretical expectations from both classical and endogenous growth frameworks, underscoring the importance of digitalization, technological advancement and knowledge diffusion as engines of economic expansion.</p>
        <p>The mechanism analysis further reveals that employment generation and technological innovation serve as key channels through which <abbrev xlink:title="Digital services trade">DST</abbrev> contributes to economic performance. Digital engagement enhances labor market opportunities and encourages firms to adopt advanced technologies, which improve productivity and support growth. These findings highlight the critical role of human capital development and innovation systems in translating digital trade participation into tangible economic gains. Additionally, the endogeneity analysis demonstrates that the main findings are not affected by endogeneity concerns.</p>
        <p>Heterogeneity analyses show that the benefits of <abbrev xlink:title="Digital services trade">DST</abbrev> are not uniform across countries but depend heavily on structural characteristics such as income level, digital infrastructure and regulatory quality. High-income developing economies and those with advanced digital infrastructure enjoy the strongest gains, while lower-middle-income countries and those with weak infrastructure benefit less. This underscores the necessity of targeted policy interventions aimed at strengthening digital connectivity, improving regulatory environments and enhancing digital readiness to ensure more inclusive participation in the digital economy.</p>
        <p>Traditional trade flows and structural transformations continue to play a reinforcing role in shaping economic outcomes. This suggests that digital trade can complement, rather than replace, broader development strategies. The negative association observed between population size and GDP highlights the importance of effective resource allocation and policies that allow economies to benefit from demographic trends.</p>
      </sec>
      <sec sec-type="5.2. Policy Recommendation" id="sec26">
        <title>5.2. Policy Recommendation</title>
        <p>The findings of this study, indicate that, first, developing countries should officially recognize digital services trade (<abbrev xlink:title="Digital services trade">DST</abbrev>) as a strategic driver for economic growth. This can be achieved through the establishment of dedicated agencies to monitor <abbrev xlink:title="Digital services trade">DST</abbrev> expansion. These agencies should provide targeted incentives, such as tax breaks for digital service providers. They should also set clear, measurable goals for <abbrev xlink:title="Digital services trade">DST</abbrev>’s contribution to the GDP. Second, based on the results of the mechanism analysis, policymakers should consider investing in the development of digital skills for the workforce, vocational training, and research and development of digital services in order to improve productivity, labor market outcomes and innovation at the firm level. Third, according to the heterogeneity analysis results, governments should prioritize expanding broadband networks, modernizing customs procedures, promoting digital literacy and implementing regulatory reforms to balance foreign investment and domestic protections. These measures will enhance countries’ capacity to participate effectively in digital trade and reduce structural barriers that limit growth potential in lower-income or lower-infrastructure economies. Finally, in line with the moderation analysis, policymakers should prioritize investments in nationwide broadband expansion, ICT infrastructure and digital connectivity to strengthen the technological backbone of the economy. Simultaneously, targeted programs aiming to improve digital literacy, vocational training and higher education in the field of ICT and related areas can build a human capital that is capable of fully exploiting digital trade opportunities.</p>
      </sec>
      <sec sec-type="5.3. Limitations" id="sec27">
        <title>5.3. Limitations</title>
        <p>This study is not without its limitations. First, the availability of the underlying data may pose challenges, as the accuracy and representativeness of the databases used can affect the validity of the empirical results. Second, although the analysis identified significant associations between key variables, the observational nature of the study limited the ability to make definitive causal inferences. Third, the findings of this study may be context-dependent, and caution should be exercised when attempting to generalize the results to other geographic regions or economic contexts, given potential differences in structural, institutional and developmental factors. Finally, the measurement of digital trade (<abbrev xlink:title="Digital services trade">DST</abbrev>) relies exclusively on <abbrev xlink:title="United Nations Conference on Trade and Development">UNCTAD</abbrev>’s BoP-based aggregates, which, in line with concerns raised by the OECD–WTO–IMF Handbook on Measuring Digital Trade (2023), may conflate digitally delivered services with digitally enabled but non-digital services. This measurement constraint introduces the risk of classification error, which could affect the accuracy of the estimated relationship between <abbrev xlink:title="Digital services trade">DST</abbrev> and GDP.</p>
      </sec>
    </sec>
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