Background of the study

Climate change has amplified the need to change industrial and economic systems, especially in the European Union (EU) region, where historically industrial growth led to economic benefits, but was equally responsible for carbon emissions (Fan and Fang, 2020). Since the inception and subsequent economic integration, the EU region has experienced astonishing industrial development, which has always served as one of several sources of its economic development. This industrial growth has consistently been associated with negative environmental impacts through large volumes of CO₂ and other GHG emissions and impacts on climate change and resource depletion (IEA, 2021). According to the International Energy Agency (IEA), the EU region was responsible for approximately 7.3% of global energy-related CO2 emissions in 2020, primarily due to industrial activities (IEA, 2020). With climate change and environmental decline, reducing greenhouse gas emissions has become a critical component of environmental sustainability (Karimi Alavijeh et al., 2023). The industrial activities continue to produce a high level of CO₂ emissions, particularly within the energy-intensive industries such as steelmaking, cement production, and chemical manufacturing. To meet ambitious climate targets EU has made changes to its industrial policies by enhancing resource efficiency, setting ambitious emission reduction targets, and piloting projects around the Eco-Innovation Partnership (Liu et al., 2018). Against this backdrop, this study seeks to examine the role of Circular Economy (CE) practices in industrial de-carbonization (IDC), while assessing Artificial Intelligence (AI) as moderating role on these effects across EU economies.

New technologies are important factors in economic development and reduction of CO₂ emissions associated with production processes, advancement in technology can alter the pattern of economic development, modify energy systems, and foster the industrial modernization which aids in decreasing carbon intensity (Yu et al., 2023). While restraining the expansion of environmental degradation, AI fostered economic growth through cleaner resource utilization and technological advancement; therefore, AI is viewed as a new driver in the recent technological and industrial transformation (Liu et al., 2022). It is widely accepted that reducing carbon emissions is one of the most impactful measures in addressing climate change. China’s carbon market captures its evolution and importance in emissions reductions through technology innovation, financial legislation and digitalization, emphasizing the need for greater carbon market coverage and increased government intervention for meaningful emissions reductions. (Zhan and Pu, 2025). AI technologies have significantly shifted industries towards adopting CE and functioning at lower carbon intensity levels. AI’s assistance in resource optimization, waste minimization, and recycling facilities enhancement is certainly in line with circularity and sustainability goals (Özsoy, 2023). AI streamlines the implementation of closed-loop supply chains and enhances the efficiency of resource recovery systems, thereby addressing the climate challenges in the adoption of circular economy practices (Pathan et al., 2023).

AI has greatly changed human productivity and AI life in recent years and it is the most considered advanced technology, which is still in the process of development (Acemoglu and Restrepo, 2018). AI has the capability to assist CE practices on the micro and macro levels (Acerbi et al., 2021). Synergizing of AI with CE can be explained through system optimization, system redesign, business model revamping, and ecosystem innovation deregulation (Tutore et al., 2024). The adoption of CE practices, especially in sustainable development, reverse logistics, waste management, supply chain optimization, recycling and manufacturing, is facilitated by the application of AI and machine learning technologies. Computer technology and AI serve as critical drivers of sustainable development, significantly enhancing environmental and economic performance among technology-leading nations (Nazir et al., 2025). The direct impact of AI and rapid integration into renewable energy which enhanced renewable energy production and decreased environmental degradation (Rasheed et al., 2025). Despite increasing attention to sustainability, IDC remains uneven across regions and sectors. AI has the ability to reduce ecological footprints and promote energy transitions by improving energy efficiency and optimizing resource use (Wang et al., 2024). Similarly, digitalization has confirmed measurable reductions in carbon emissions in the quasi-natural experimental contexts, underscoring the importance of technological upgradation for achieving climate goals (Lin, 2024).

The framework of the CE practices suggests minimizing waste and using resources through reuse, recycling, and eco-friendly design. This model provides a systemic approach to lessening the emissions associated with the extraction, production, and disposal of raw materials (Korhonen, 2018). CE has a positive environmental impact by reducing carbon emissions and ecological footprint and increasing load capacity in Belt and Road Initiative Countries (Karimi Alavijeh et al., 2024). CE is gaining more support as a systemic and de-carbonization response framework. However, CE constitutes a route to transformation and could serve as an example of moral licensing (Eickhoff, 2024). Additionally, while some previous studies argued that CE can lead to a positive social and institutional change (Gallardo-Vázquez, 2024), empirical investigation proved that the role of CE and new technologies enhanced IDC. Chauhan et al. (2022) have established a strong conceptual link between digital technologies (AI) and CE practices; they argued that AI and the Internet of Things play a significant role in the transition toward CE. It is essential to establish strategies to reduce carbon emissions that focus on high energy-intensive industries in a social transition from reliance on high-pollution energy systems toward low-pollution ones (Zhang and Chen, 2023).

The contribution of this study is threefold: First, this study pioneers in exploring how CE affects IDC using AI as a moderator within the EU region. Unlike other studies that examined CE and AI separately, using different econometric settings. This study investigates how the two paradigms work together to reduce CO₂ emissions. With the EU’s climate targets in mind, this study fill the gap in the literature by demonstrating how these two powerful paradigms, capable of shaping a large portion of the economy, can be integrated to meet the climate objectives. Second, this study develops new holistic indices of CE and AI, while previous research studies focus on single indicator used for proxy of CE (Recycling waste of municipal waste) used by Varennes et al. (2023) and AI (industrial robot inventory stock) by Wang et al. (2024). The study constructs novel index of CE and AI from eight and five different indicators, respectively, which is mention in Table 1. Finally, the study adopts innovative econometric techniques, PQR-PMG (Panel Quantile regression with Pooled Mean Group (PMG), and Common Correlated Effects (CCE) to examine the moderating effect of AI: how and to what extent AI moderates the relationship between CE and IDC, as well as interdependencies among them. These methods allow for more sophisticated assessments of the effects of CE and AI on industrial d-ecarbonization. PQR-PMG captures differences on different quantiles and examines long-term relationship, while CCE controls for cross-section dependence, slope of heterogeneity and global shocks.

Table 1 Variables, symbols, sources and website link.
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The remainder of the paper is organized as follows: Section 2 presents a theoretical background, literature review and research gap, Section 3 describes the data collection and econometric methods, Section 4 presents the empirical results, and long-term relationships between the variables. Finally, Section 5 summarizes the key conclusions, policy implications, and future direction.

Theoretical background and literature review

The study is grounded in industrial ecology, sustainable development, and innovation diffusion theory, which provide the foundation for examining the relationship between CE, AI, and IDC in the EU region. Industrial ecology theory explores how efficient use of renewable resources, some waste reduction, recycling of resources, and atmospheric pollution mitigation provide pathway to less environmental degradation and climate change (Wiprächtiger et al., 2023). Building on industrial ecology theory, CE captures a system change from a linear model to a circular model to improve sustainable production and consumption. Artificial intelligence is based on innovation diffusion theory, which speaks to the adoption of new technologies that simultaneously improve resource efficiency, automate supply chains, and reduce emissions through predictive analytics and machine learning (Cainelli et al., 2020). Similarly, sustainable development theory provides a lens to understand the integration of CE and AI as a viable pathway to long-term ecological and economic outcomes, linking eco-IDC to innovation-based sustainability.

The transition from the traditional linear economic model to CE model represents a paradigm shift towards an economically mature system that prioritizes the recycling of waste into resources and the use of renewable inputs. This model is fundamentally concerned with sustainable resource and energy flows, ecosystem preservation, and the maximization of efficiency, constituting a systemic solution for global resource challenges (Hong Nham and Ha, 2022). Recognizing its potential, the European Commission formalized this approach through its Circular Economy Action Plan (CEAP), which seeks to integrate CE principles into policy to address not only product design and waste management but also broader goals of mitigating biodiversity loss and fostering resilient economies (Fetting, 2020). CE is a new approach to the economy that differs from the linear model, which emphasizes and simplifies the process into “take, make, and dispose” (Figge, 2022). CE indicators such as policy and regulatory support, waste reduction and zero waste goals, and recycling and upcycling have significantly reduced carbon emission in China, these results highlight the need to develop tailored policy frameworks and financial subsidy to improve and implement CE practices in order to reduce carbon emissions (Xiao, 2025). CE practices can mitigate greenhouse gas emissions from industry, waste management, energy use, building construction, and transportation by dealing directly with carbon emissions and contributing to climate change mitigation (Yang et al., 2023). The role of enhancing CE practices decreases the carbon emission in 285 Chinese cities and emphasizes to implement CE practices where it is effective for specific places to support Net-Zero goals (Niu et al., 2025).

CE practices are a critical driver for IDC; empirical evidence from previous studies suggests that CE practices, particularly in material-intensive sectors like construction and manufacturing, could reduce global emissions by up to 39% by 2050 (Kirchherr et al., 2019). Circular economy practices exert a statistically significant contribution to reducing carbon emissions and alleviating carbon emission intensity in China (Li and Hu, 2024). Transitioning to a CE is linked to substantial reductions in CO2 emissions, with ambitious CE scenarios projected to decrease emissions by a median of 24.6% by 2030 compared to business-as-usual, while also supporting economic growth and job creation (Hailemariam and Erdiaw-Kwasie, 2022).

Circular economy alone may have a positive effect and increase carbon emissions, while the interaction of CE with strong institutions exerts a significant negative effect on carbon emissions and enhances environmental quality (Mawutor et al., 2025). Employing causality analysis on a broader panel of 24 EU members uncovered complex, bidirectional causal relationships between CO2 emissions and indicators of CE, their finding indicates that CE indicators mitigates carbon emissions in long-run but insignificant in short-run due to infancy of CE in EU region (Pao and Chen, 2022). Moreover, a recent study of EU-23 countries using data from 2010 to 2020 revealed that CE practices have negative significant effect on carbon footprint, an increase in circularity practices reduced carbon footprints (Chen et al., 2024). Although some research regarding the CE practices has advanced significantly, primarily in developed countries, where carbon reductions and resource efficiency associated with CE practices, which reduced carbon emission (Kumar et al., 2024) and its scarce in developing countries (Afshari et al., 2024). CE practices are key in mitigating resource dependency, leading to lower carbon emissions to achieve Net-Zero goals. As industries move away from resource-intensive production models, they can synthesize CE practices (Baldassarre, 2025). These CE practices mitigate carbon footprint associated with production and consumption while build supply chain resilience by lowering exposure to resource scarcity and price volatility (Barreiro and Lozano, 2020).

Artificial intelligence (AI) has a positive and substantial effect on renewable energy production in the long-term under symmetric and asymmetric framework, result also highlight the country specific investigation in Austria, Germany, and New Zealand have both positive and negative effect of AI improve clean energy in short-run which enhance the environmental quality (Rasheed et al., 2024a). Within the energy sector, AI is important for optimizing the efficiency of smart grids, leading to more accurate demand predictions, and aiding renewable sources, such as solar and wind, in local and power system-wide integration into the generation portfolio, by directly increasing de-carbonization of energy sources (Rolnick et al., 2022; Zhang and Chen, 2023).

The heterogeneous effects of AI on carbon emissions across 66 countries from 1993 to 2019 using quantile regression and panel smooth transition regression methodology. Their finding reveal that AI decreases carbon emissions in high-emission and high-income economies (Zong et al., 2024). In Asian developing economies, the integration of AI robotics and technological advancement into the current industrial structure could decrease the carbon footprint and enhance environmental quality (Rasheed et al., 2024b). Trade globalization has a dual role, harming ecological quality in nations with lower environmental health but improving it in the most sustainable nations. The study also finds an inverted U-shaped connection between economic growth and the load capacity factor (Ahmed et al., 2025). Trade openness has a negative association with carbon footprint, which increases environmental degradation in the top ten high‐per‐capita high‐income countries (Australia, Belgium, Denmark, Germany, France, Luxembourg, Singapore, Norway, Sweden, and the United States) (Rasheed et al., 2024c). Utilizing the MMQR approach in 14 EU countries, economic growth increases carbon emissions and decreases environmental quality at all quantiles (Karimi Alavijeh et al., 2023). Economic growth has a U-shaped relationship with carbon emission in Canada; while economic growth initially increases carbon emission, it then contributes to environmental quality improvements at higher levels of income (Ali et al., 2025). Research and development investment have significant contribution in overall spillover reduction in carbon emission in 58 global countries (Mamkhezri and Khezri, 2024), R&D also reduce carbon emission in 19 OECD countries (Koçak et al., 2019). Figure 1 shows the conceptual framework.

Fig. 1
Fig. 1
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Conceptual Framework.

Htpotheses

H1: Circular economy has positive significant relationship with industrial de-carbonization

H2: Artificial intelligence has positive significant relationship with industrial de-carbonization.

H3: Artificial intelligence positively moderate the relationship between circular economy and industrial de-carbonization.

Research gap

While previous studies have provided interesting contributions to understanding CE practices and AI for sustainable development, the majority have taken an approach to CE and AI separately (Niu et al., 2025; Wu and Zhou, 2025) without a joint assessment of their interaction on IDC, particularly in the context of the EU. Furthermore, the existing literature mainly focuses on individual indicators, for instance, recycling rates (Varennes et al., 2023) for CE or industrial robot stock (Wang et al., 2024) for AI, and overlooks the multidimensional complexity of CE and AI together, along with their interrelated effects. This study contructs novel indices of CE and AI from eight and five indicators which in mention in Table 1 through novel econometric appraoch called time-specific heterogeneous factor analysis (TSHFA) developed by Ul-Durar et al. (2025). Thirdly, and most importantly the advanced econometric methodology PQR-PMG and CCE approach, which handles the heterogeneity, cross-sectional dependency, stationarity problem and analyse the quantile-specific effect. Addressing these gaps, this study offers more convincing evidence towards meeting the EU objectives around climate change by taking both CE and AI as complementary systems.

Data collection and methodology

Variable definition and data collection

The study collected panel data from 27 EU countries spanning the period from 2000 to 2023. The data were collected from different sources, such as WDI (https://data.worldbank.org/) and Eurostat (https://ec.europa.eu/eurostat). This study used IDC as the dependent variable, CE as an independent variable, and AI as a moderator between CE and IDC. Trade openness, R&D and economic growth are control variables. Circular economy is measured by constructing index from eight different variables (consumer footprint, circular material use rate, generation of municipal waste per capita, patent related to recycling and secondary raw material, recycling rate of municipal waste, recycling waste of packaging waste, trade in recycling raw material) and AI is also measured by constructing index from five variables (human resource in science and technology, information computer technology in gross added value, internet use by individual, level of internet access house hold, R&D expenditure of ICT sector) through a novel econometric technique called TSHFA developed by (Ul-Durar et al., 2025). IDC is measured by carbon emission metric tons GDP per capita, and Trade openness, R&D and economic growth are measured by Trade (% of GDP), GDP in constant US dollars of 2021 and percentage of GDP, respectively. This study aims to explore the effect of CE on IDC, while AI acts as a moderator between CE and IDC in the EU region. All acronyms and variable abbreviations used in this study are summarized in Table 2.

Table 2 Abbreviation.
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Econometric model

This study has three main questions that we examine using a battery of tests. First, what is the direct effect of CE on industrial de-carbonization in EU countries. Second, what is the direct effect of AI on industrial de-carbonization? Third, how does AI moderate the positive effect of the CE on industrial decarbonization?

In doing that, this study applied an advanced econometric model, PQR with Pooled Mean Group(PQR-PMG) following the recent studies of (Işık et al., 2024; Lamarche, 2010; Pesaran et al., 1999) to capture the quantile-specific effect of circular economy and AI on IDC and also used PQR with Common Correlated Effect (PQR-CCE) following the recent studies of (Harding et al., 2020; Chudik and Pesaran, 2015; Shiyun and Qiankun, 2022, Pesaran, 2006; Chudik and Pesaran 2015). This approach enables us to obtain quantile-specific heterogeneous effects while controlling for cross-sectional dependence and interactive unobservables to ensure more robust estimates. These extended method follows the literature of (Işık et al., 2024; Mehmood and Kaewsaeng-on, 2024; Lamarche, 2010; Galvao, 2011) and (Harding et al., 2020; Chudik and Pesaran, 2015: Shiyun and Qiankun, 2022), which represents a novel integration that allows us to assess quantile-specific effects while also capturing long-run relationship estimates. This is especially suitable for cross-country panels where countries have common long-term equilibrium relationships but differ in their adjustment paths. The econometric equation is given below:

$$\begin{array}{l}{{\rm{IDC}}}_{{\rm{\tau }}{\rm{it}}}\,=\,{{\rm{\alpha }}}_{\tau 0}+{{\rm{\alpha }}}_{\tau 1}{{\rm{CE}}}_{{\rm{it}}}+{\alpha }_{\tau 2}{{\rm{AI}}}_{{\rm{it}}}+{{\rm{\alpha }}}_{\tau 3}{{\rm{CE}}}^{* }{\rm{AI}}+{{{\rm{\alpha }}}_{\tau 4}{\rm{EG}}}_{{\rm{it}}}\\\qquad\qquad\,\,+\,{\alpha }_{\tau 5}{{\rm{R\& D}}}_{{\rm{it}}}+{{\rm{\alpha }}}_{\tau 6}{{\rm{TOP}}}_{{\rm{it}}}+{\varepsilon }_{{\rm{it}}}\end{array}$$
(1)

where IDCτit, CEit, AIit, EGit, TOPit, R&Dit indicate IDC, CE, AI, economic growth, and research and development of country i at time t. CE*AI are the interaction terms of CE and AI, whereas εit is the error term. Additionally, the moderating effect of AI used as a moderator is integrated in this study to enrich the value of the study. Table 1 exhibits the variables, symbols, sources, and website link.

Time-specific heterogeneous factor analysis

This study applied a novel method termed TSHFA, developed by Ul-Durar et al. (2025), to develop two different indices, namely the CE and AI. TSHFA is an advanced econometric and statistical model designed to analyse panel data; it is superior to cross-sectional heterogeneous factor analysis. In cross-section, the probability of non-stationarity increases as the number of years increases. TSHFA uses the time dimension and assumes stationarity over extended years, which increases the reliability of parameter estimates. This makes it a stronger and more credible option for longitudinal data. TSHFA is particularly favorable when the panel data exhibit temporal homogeneity because it assumes that several parameters remain stable over time. TSHFA also incorporates homogeneous factors as heterogeneous factors, allowing any influence of individual variables to vary over time instead of staying constant. These time-varying dynamics provide a more effective method of modeling change over time in the relationships among variables. TSHFA effectively captures time-varying factors while accounting for the fundamental structural nature of the data (Kakar and Wang, et al., 2024).

Cross-sectional dependence and slope of homogeneity

The first empirical estimating step is evaluating slope of heterogeneity and CSD among EU countries. Trade, investment flows, and policy coordination make EU economies highly interdependent. This interdependence has potential unintended consequences that violate the consistency and efficiency of the panel data estimators. In order to provide a preliminary understanding and insight into the possibility of CSD, the study employed the Pesaran CD test of Pesaran (2007), and Friedman (1937) to assess the existence of CSD in the panel data. The different CSD test equations are given below:

$${\rm{Friedman}}{\rm{\mbox{'}}}{\rm{s}}\,{\chi }^{2}{\rm{statistic}}:\left({\rm{T}}-1\right)\left[\frac{2}{N}\mathop{\sum }\limits_{i=1}^{N-1}\mathop{\sum }\limits_{j=i+1}^{N}{\hat{r}}_{{ij}}+1\right]\to {\chi }^{2}(T-1)$$
(2)
$${\rm{Pesaran}}{\rm{\mbox{'}}}{\rm{s\; statistic}}:\sqrt{\frac{2T}{N(N-1)}}\left(\mathop{\sum }\limits_{i=1}^{N-1}\mathop{\sum }\limits_{j=i+1}^{N}{\hat{\rho }}_{{ij}}\right)\to N(0,1)$$
(3)

where SE(Q), \({\hat{r}}_{{ij}}\), and \({\hat{\rho }}_{{ij}}\) are the standard error of the Q distribution, rank coefficient estimates, and correlation coefficient estimates, respectively. The null hypotheses of cross-sectional dependency are identical for all three tests. In addition to economic interdependence, there is a large amount of structural diversity within the EU countries with respect to industrial growth, energy security, economic development, as well as green human capital and policy frameworks. The study also employed the Pesaran and Yamagata (2008) slope of homogeneity test to examine variations in slope coefficients among nations. The following equations describe the process for conducting the test.

$${\Delta }_{{SH}}={\left(N\right)}^{1/2}{\left(2K\right)}^{1/2}\left(\frac{1}{{\rm{N}}}{\rm{S}}-{\rm{K}}\right)$$
(4)
$${\varDelta }_{{\rm{A}}{SH}}={\left(N\right)}^{1/2}\left(\frac{2K(T-k-1)}{{\rm{T}}+1}\right)1/2\left(\frac{1}{{\rm{N}}}{\rm{S}}-{\rm{K}}\right)$$
(5)

Panel unit root test

CSD methods determine a suitable unit root test for detection and long-term behaviour. If the EU region dataset exhibits heterogeneity and the CSD problem, then it is essential to conduct second-generation unit root test because it is capable of accounting for these factors: first-generation unit root tests, such as ADF, PP, and LLC, cannot handle heterogeneity and CSD. Thus, this study applied CIPS and CADF unit root tests to assess the stationarity properties of the variables. These tests are more suitable for checking data stationarity, having heterogeneity and cross-sectional problems. Equation for the cross-sectional Augmented IPS is given below:

$${\varDelta y}_{t}=\alpha +{\beta }_{t}+{\gamma y}_{t-1}+{D}_{1}{\delta t}_{t}+{D}_{2}{\delta }_{t}^{2}+{nt}_{{\rm{t}}}$$
(6)

where Δytis the variable of the first difference of y at time t-1. This equation includes an intercept (α), a time trend (βt), an autoregressive term (γyt−1), cross-sectional augmentation terms (D1 δt and D2 δ2t), and an error term (nt).

Similarly, the CADF test is expressed as:

$$\Delta {X}_{{it}}={\gamma }_{{it}}+{\theta }_{{it}-1}+{\delta }_{i}T+\mathop{\sum }\limits_{j=1}^{n}{\gamma }_{{it}-j}+{\varepsilon }_{{it}}$$
(7)

In this model, Xit is the variable under study, T and γ represent time trends and intercepts, respectively, and εit is the error term. The study used the Akaike Information Criterion to find the ideal lag length, which guarantees a thorough analysis of stationarity.

Co-integration test

Once the selected panel variables are confirmed to be integrated of order one, I (1), the panel co-integration test is employed to investigate the presence of a long-run equilibrium relationship among them. The study employed the Pedroni (2004) panel co-integration test, which is the most common test for heterogeneous panels. Pedroni’s co-integration test considers both within-dimension tests (refer to panel tests) and between-dimension tests (refer to group tests) statistics, and it allows for cross-sectional heterogeneous short-run dynamics and fixed effects. Along with the Pedroni test, this study will also apply the Westerlund and Edgerton (2008) error-correction-based co-integration test to further explore the long-run equilibrium association among variables for EU countries. Deviating from residual-based methods, the Westerlund test examines co-integration directly via the error-correction term at the panel levels. This framework provides greater robustness to cross-sectional dependence and offers improved performance over traditional tests like those of Pedroni and Kao (Zafar et al. 2019). The following are the equations used for (Pedroni, 2004) and Westerlund and Edgerton (2008) for the existence of a long-term relationship:

$${Y}_{{it}}={\propto }_{i}+{\delta }_{{it}}+{X}_{{it}}{\beta }_{i}+{\varepsilon }_{{it}}$$
(8)
$${Y}_{{it}}={\rho }_{i}{\vartheta }_{t}+{\alpha }_{i}\left({Y}_{{it}-1}-\pi {X}_{{it}-1}\right)+\mathop{\sum }\limits_{j=1}^{{P}_{i}}{\sigma }_{{it}}{Y}_{{it}-1}+\mathop{\sum }\limits_{j=0}^{{P}_{i}}{\tau }_{{it}}{X}_{{it}-1}+{\mu }_{{it}}$$
(9)

Results and discussion

Descriptive statistics

Table 3 provides descriptive statistics of the variables under study. These statistics provide an overview of the mean, median and standard deviation of the sample. Furthermore, it also shows skewness and kurtosis and the Shapiro-Wilk test value for normality. The above table shows the statistics of IDC, CE, AI, economic growth, research and development and trade openness. The mean values of IDC and TOP are higher than median; the standard deviation of IDC is higher than both mean and median (SD = 10.2958), while the standard deviation of TOP is lower than mean and median (SD = 58.998). IDC is right-skewed distribution with high variability while TOP mild right-skewed distribution with very low variability (SK = 2.0022, 1.7351), the high kurtosis values for IDC (6.5624) and TOP (7.3507), signify heavy tails, though normality is rejected (p < 0.05).

Table 3 Descriptive statistics.
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Conversely, the mean and median of CE and AI is almost zero and standard deviation is higher than mean and median (SD = 0.9522, 0.9714) which shows symmetric distribution and exhibits both moderate variabilities, though normality is rejected by shapiro-wilk (p < 0.05). GDP and R&D have almost same mean and median and standard deviation (SD = 4.0731) of GDP is higher than mean and median while standard deviation (SD = 0.9040) of R&D is lower than mean and median, though the normality is rejected. The Skewness of CE, AI an R&D is positive while GDP is negative (SK = 1.0467, 0.1776, 0.7269, −0.1309). On the other hand, kurtosis of CE and GDP is greater than 3 which indicates platykurtosis behavior while AI and R&D have less than 3 which indicates leptokurtic behavior. Figure 2 shows IDC across EU Countries. The yellow region shows high industrial de-carbonization countries; the brown color region shows median industrial de-carbonization countries, and the red color region shows low industrial de-carbonization countries.

Fig. 2
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Industrial decarbonization.

Time-specific heterogeneous factor analysis

This study employed TSHFA, an advanced econometric technique to develop two novel indices CE and AI. TSHFA is optimally designed to analyse panel datasets, allowing for the shifting dynamics and multi-directional relationships between variables over time. Time-specific heterogeneous factor analysis is an advanced econometric and statistical methodology used for identifying latent common factors in panel data, while explicitly addressing heterogeneity across cross-sections and time. TSHFA diminishes the assumptions of homogeneity and stationarity used in traditional factor analysis or principal component analysis by allowing factor loadings and relationships to vary over time. This makes it especially useful for developing indices from panel datasets that may experience structural changes, country-specific shocks, or technological changes. The CE index is constructed from 7 variables and AI index from 5 variables that capture fundamental aspects of CE and AI were used. Figures 3 and 4 show KMO (Kaiser-Meyer-Olkin) test results for factor analysis, the results show that KMO values vary between 0.0 and 0.8, values closer to 1 represent strong sampling adequacy which implies all the variables of CE and AI are useful for factor analysis. Figure 5 depicts the year-wise comparison of the CE index for the years 2000 to 2023. The changes in the graph demonstrate a change in value of CE over a period of time, which indicates positive or negative change in resource use efficiency, waste management, and sustainability. The graph also shows the progressive changes in the CE index efforts throughout the years in the given period. As shown in Fig. 6, the year-by-year pattern of the AI is reflected in the 2000 to 2023 timeframe. Changes in the graph reflect the trend of innovation forecasts, technology adoption, and R&D investment in computer technology, establishing whether AI is on a positive, neutral or negative trajectory in a period of time. This clarifies the processes associated with AI with respect to the precision of timeframes and its future impacts.

Fig. 3
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KMO test result of circular economy.

Fig. 4
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KMO test result of artificial intelligence.

Fig. 5
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Year-wise comparison of circular economy index-I.

Fig. 6
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Year-wise comparison of artificial intelligence index-II.

Figures 7 and 8 provide results of the Bartlett test for different time intervals, which provide evidence of the sphericity of the data that were utilized for constructing the CE and AI index. The values shown above the bars in Figs. 7 and 8 correspond to the graphical illustration of the Bartlett test for all time intervals, which proves the construction of the indices to facilitate robust verification of the processes. Figures 9 and 10 provide the scree plot for the overall index, which reveals the ideal number of indices which could be generated from the variable set. The line is on a significant decrease from 2 to 3, which suggests that it is best to construct index from different variables. Figures 11 and 12 present the temporal changes in the CE and AI factor loadings of different indicators. This makes it easier to understand how the CE and AI factor loading scores changed over time. This is the new feature of this heteroskedastic factor analysis method and evolving patterns reveal how the significance of each variable shifts over time, are features of method called time heterogeneous factor analysis. The chart captures changes in the CE performance alongside AI adoption, providing deeper multidimensional insights into the interconnected trends.

Fig. 7
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The Index-I of circular economy year-specific Bartlett test result.

Fig. 8
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Index-II of artificial intelligence year-specific Bartlett test result.

Fig. 9
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Scree plot of Circular Economy Index-I.

Fig. 10
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Scree plot of Artificial Intelligence Index-II.

Fig. 11
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Factor loadings of the CE-Index overtime.

Fig. 12
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Factor loadings of the AI-Index overtime.

Panel unit test: CIPS and CADF

Upon confirming the presence of CSD in the dataset, the subsequent step is to assess the stationarity of the data. The CSD results validate the presence of cross-sectional dependence in the dataset. The second-generation unit root tests (CIPS and CADF) were employed due to the inadequacy of first-generation unit root tests in addressing cross-sectional dependency and heterogeneity. Table 4 display the results of the second-generation unit root test (CIPS and CADF). The cross-sectional IPS result reveals that nearly all variables are stationarity at the first difference level except GDP which is stationary at the level, indicating a mixed order of integration. CADF validates that all variables are stationary at the first difference level. The results of CIPS and CADF should assurance the credibility and dependability of subsequent econometric procedures like co-integrative or causative examinations.

Table 4 Panel unit root test.
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Co-integration test

Table 5 display the results of panel co-integration tests from Westerlund and Edgerton (2008) and Pedroni (2004) to validate the long-term equilibrium relationship among the variables. The Pedroni test results reveal that: The Modified Phillips–Perron t-statistic is highly significant (6.0354, p = 0.000), strongly suggesting the rejection of the null hypothesis of no co-integration, the Phillips-Perron t-statistic (−12.371, p = 0.000) and ADF t-statistic (−10.514, p = 0.000) are also significant at conventional levels, indicating stronger evidence for co-integration when considered independently. The substantial Westerlund test statistic (p < 0.05) provides evidence of co-integration, enabling the interpretation of long-run coefficients from the PQR-PMG and PQR-CCE models. The results indicate the presence of co-integration among the variables.

Table 5 Co-integration and Westerlund.
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Correlation matrix

Table 6 illustrates the correlation matrix among industrial de-carbonization, CE, AI, economic growth, R&D and trade openness. All variables exhibit a positive link with industrial de-carbonization, with the exception of economic growth and trade openness, which demonstrates a negative correlation. The lack of significant correlations, all under 0.5, indicates the absence of serious multi-collinearity problems, hence validating the inclusion of these variables in the study. Table 6 also display the result of variance inflation factor (VIF) which shows that VIF value is less than 5 (mean VIF = 1.24) it means there is no multi-collinearity exists among the study variables.

Table 6 Correlation matrix and VIF Test.
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Cross-sectional dependence test

Table 7 presents two varieties of cross-sectional dependence (CSD) tests to evaluate CSD within the panel data set of EU countries. The two categories of CSD tests are Pesaran (2004) and Friedman (1937); the outcomes of these tests provide compelling evidence for the existence of CSD. The Pesaran (2004) test yielded a statistically significant result (9.761, p = 0.000) at the 1% level, so affirming the rejection of the null hypothesis and providing robust evidence for the presence of CSD. The Friedman (1937) test statistic yielded also to reject the null hypothesis of independence (86.007, p = 0.000), indicating strong evidence cross-section dependence. The results are indicative, relying on the substantial findings of Pesaran and Friedman, which demonstrate that the dataset exhibits cross-sectional dependence. Table 7 additionally display the results of the slope of heterogeneity, confirming that the values of ΔSH and adjΔSH provide substantial evidence of heterogeneity within the panel data set. The p-value is markedly significant and substantiates the rejection of the null hypothesis.

Table 7 Pesaran and Friedman test.
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Panel quantile regression-PMG results

Table 8 exhibits the PQR-PMG long-run estimates at different quantiles. The results shows the long-run effect of CE, AI and the moderation effect of AI between CE and IDC across different quantiles in EU region. The results indicates that when there is a 1% increase in the CE in the EU region, the estimates associated with CE went from 0.93 at the 25th quantile to 9.1 at the 90th, suggesting that CE practices contribute a greater impact to IDC in EU countries with higher level of IDC and as we move toward the upper quantiles the size of the effect gets bigger. The positive effects of CE, AI, and particularly the interaction (CE*AI) are quite strong at the higher quantiles (75th and 90th), highlighting that in more advanced or more carbon-intensive regions, CE and AI provide greater support to improve IDC. This trend indicates that countries which are already in decreasing carbon emission experience higher marginal benefits from these technologies and strategies. One possible reason: these countries have the advanced sustainable infrastructure, technological maturity, a skilled workforce, and a regulatory environment to effectively absorb and implement CE practices and AI technologies. Thus, the efficiency improvements and emission reductions that these technologies may realize would be further pronounced in these contexts. The results align with the results of (Hailemariam and Erdiaw‐Kwasie, 2022) present strong empirical evidence that CE growth plays a significant role in improving environmental quality through the reduction of CO₂ emissions. Similarly, Bressanelli (2025) also support our finding that how manufacturing companies adopt CE practices to decrease carbon emission and is widely varied and depends on the systematic change across a number of industrial areas. He employed a pragmatic tool for measuring industrial circular practices first, and then links to actual reductions in carbon footprints, knowing that CE implementation generates variable benefits attributed to varying levels of CE practices.

Table 8 Long-run Quantile Wise-estimates (PQR-PMG).
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AI exhibits strong positive effect on IDC at all quantiles and is even larger at higher quantile levels, underscoring the pivotal role of AI in enhancing IDC and increase the environmental quality. The result of AI on IDC aligns with the result of (Zhong et al., 2024), AI can reduce carbon emission and confirms the importance of industrial and demographic structures in promoting carbon emission reduction. The interaction of AI with CE practices (CE*AI) has strong positive impacts at all quantiles and grows towards the upper quantiles (values vary from 0.49 to 3.59). This suggests that AI alone significantly enhance IDC while also moderate the relationship between the CE practices and IDC in EU region. The results of the joint effect of CE*AI align with the findings of (Zhang et al., 2025), quantifiable emission reduction effects arising from the integration of these approaches particularly in leading decarbonizing economies. These findings are in line with earlier studies which pointed to the relevance of the implementation of the CE paradigm and Artificial intelligence towards sustainable development.

Conversely, TOP (Trade Openness) has a persistent negative effect at all quantiles. This suggests that 1% increase in TOP causes the decrease in IDC, this is likely a function of structural trade. The negative impact of limited value-added type exports and structural trade difficulties is indicated and supported by recent evidence of trade vulnerabilities in recent scenarios open economies. This dynamic is particularly relevant in the EU’s complex industrial supply chains, where openness can simultaneously drive economic benefits and environmental challenges. The result is similar with the finding of (Derindag et al., 2023). Conversely, R&D exerts a substantial and positive influence, at lower signifying that technology investment is essential for facilitating advancements in de-carbonization. However, at median becomes negative and at higher quantiles 75th, indicating diminishing returns, possible inefficiencies and rebound effects when technological advancements result in increased emission. This result is similar to that of (Mamkhezri and Khezri, 2024). GDP is insignificant at all quantiles. This could be an indication of saturation effect, where ongoing economic growth in high-income countries is not producing proportional improvements to the environment. This insignificant results of economic growth are similar to those of (Abd El-Aal, 2024), which empirically shows that economic growth exhibits insignificant with carbon emission in high-income countries.

Having examined the effects of these variables, the question arises: how can these factors be effectively leveraged to enhance IDC? To address this, the study provides dynamic factor loadings in Figs. 10 and 11. The magnitude of these factor loadings reflects the relative contribution of each variable to the overall outcome. Notably, CE and AI emerge as critical drivers, particularly at higher quantiles, emphasizing their potential to drive transformative change. The coefficient in the overall model is both significant and positively correlated, pointing to a baseline improvement in the IDC. This implies that the model captures an inherent underlying effect, reinforcing the reliability and strength of the findings.

Panel quantile regression-CCE results

Table 9 shows the CCE heterogeneous effect at different quantile. The CCE results reveal heterogeneous effects of the CE, artificial intelligence (AI) and interaction term (CE*AI) across the 25th, 50th, 75th, and 90th quantiles. The effect of CE, AI and their interaction (CE*AI) are not the same at different points of the conditional distribution of the IDC in EU region. At lower quantile 25th CE and AI have positive and significant effects, although the sizes are small which implies that countries that are relatively early in the process of de-carbonization can receive some positive benefits, but the benefits are not large. At median quantile 50th CE is slightly high and AI is insignificant and mostly the interaction CE*AI drive the IDC. This suggests that using CE and AI in combination, in the median quantile the use of these strategies is more powerful than using either CE or AI alone. The positive effects of CE, AI, and particularly the interaction (CE*AI) are quite strong at the higher quantiles (75th and 90th), highlighting that the more advanced or more carbon-intensive regions, CE and AI provide greater support for IDC. In essence, the heterogeneous effect underscores that CE and AI are not uniformly influential; instead, their effectiveness strengthens in high-emission, while their standalone effects are weaker at the lower and middle quantiles. The results of heterogeneous effect of CE aligned with the finding of (Wang et al., 2023) who studied the heterogeneous of CE on carbon emission in top 7 carbon emission countries, they indicate that CE have positive association with carbon emission in designated countries. These results of heterogeneous effect of AI are similar to the findings of (Zhong J et al., 2024), investigated the heterogeneous effect of AI on carbon emission in 66 global economies, they present that AI effect varies across different regions its effect increases in places with older population. Trade openness (TOP) shows the negative significant effect at all quantiles. This negative effect is stronger at upper quantiles which means that greater TOP associated with higher carbon intensity specially in countries with higher carbon emission. Conversely, R&D exerts a substantial and positive influence, at lower signifying that technology investment is essential for facilitating advancements in de-carbonization. However, at median becomes negative and at higher quantiles 75th, indicating diminishing returns, possible inefficiencies and rebound effects when technological advancements result in increased emission. GDP is insignificant at all quantiles. This could be an indication of saturation effect, where ongoing economic growth in high-income countries is not producing proportional improvements to the environment. These findings highlight that CE and AI adoption are the primary drivers of IDC, trade openness continually hinders de-carbonization, whereas R&D funding is most efficacious at initial stages but diminishes in efficacy as economies progress up the distribution. These results confirm the steady and remarkable impacts of CE, AI, and CE*AI at higher quantiles most especially in having positive. Figure 13 shows that CE, Artificial Intelligence (AI), and their interaction (CE*AI) are increasingly strong positive effects in regard to higher quantiles, emphasizing that they are more responsible for improvement in a region with higher levels de-carbonization., Gross Domestic Product (GDP) showed mixed effects, it was positive in PQR-PMG but predominantly negative in PQR-CCE but insignificant. Research and Development (R&D) has mixed effect, being positive at the lower quantiles, then turning negative in between quantiles, then being of benefit at the top quantile’s lows, this suggests that R&D may have differing effectiveness depending on the level of development of a society. Trade Openness (TOP) showed negative effects consistently, even worsening at higher quantiles, this suggests a potential environmental cost of being open to trade. Both CE, AI and the interaction of both, you can conclude that CE, AI, and CE*AI are responsible for sustainable improvement, while GDP, R&D, and TOP have relatively more complicated or adverse effects in respective contexts.

Table 9 Long-term Quantile-wise estimates (PQR-CCE).
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Fig. 13
Fig. 13
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Quantile wise graph.

Conclusion, policy implication and future direction

Conclusion

This study advances existing knowledge being the first to jointly analyse the effects of CE, artificial intelligence, and the moderating role of artificial intelligence in EU countries. The purpose of the study to analyse the quantile-wise long-term and heterogeneous effect of CE, artificial intelligence as a moderator, trade openness, R&D and economic growth on IDC through advanced econometric PQR-PMG and PQR-CCE approach. The study collected data of 27 EU countries spanning period from 2000 to 2023. Before proceeding, the model first the study adopts different diagnostic tests, such as the second-generation unit root test and Cointegration, to determine whether Cointegration there is exist a long-run relationship or not, and the order of stationarity at which the data is stationary at what level, Cross-sectional dependency whether there exist CSD or not. The results of PQR-PMG and PQR-CCE approach indicate that CE were found to have the most positive effect at all quantiles and notably with stronger effects at higher levels of IDC, while artificial intelligence (AI) also has a positive effect on IDC. When AI increases, the IDC also increases at all quantiles.

The moderation effect of AI on the relationship between CE and IDC is positive. This suggest that AI increase the positive effect of CE practices on IDC in EU countries. The CE and AI effect have been persistently positive throughout the quantiles which implies that CE, AI and their interaction is needed in order to achieve optimal goal. The interaction term (CE*AI) also validates these findings, indicating that AI is a source of significant synergies when utilized with CE practices, especially in the upper quantiles where the interaction is the most pronounced. Trade openness (TOP) was found to have negative impact at all quantiles. The negative impact of limited value-added type exports and structural trade difficulties is indicated and supported by recent evidence of trade vulnerabilities in recent scenarios open economies. Research and Development (R&D) has found to be beneficial on lower quantiles while harmful on higher quantiles. This suggests that there must be efforts in targeted and contextual specific level for R&D investments to be efficient. Economic growth shows insignificant results in almost all the quantiles. In particular, the study emphasizes the need to foster CE approaches, intensify investment and other proactive measures in CE models due to their positive effect on the economy. The combination of artificial intelligence and advanced technologies with the CE to increase their combined impact and increase IDC. Reassess Trade Policies reduce the negative consequences resulting from greater trade openness having policies that support trade and sustainability goals. Improve direct attention to particular and contextual R&D approaches where positive impacts are guaranteed.

Policy implication

Policy makers should focus on investment in CE infrastructure, recycling, and reuse systems and more efforts toward the CE should be prioritized alongside the integration of AI technologies to optimize their distinct advantages and adoption in circular supply chains should be created. Moreover, certain trade policies are required to shift toward enhancing sustainability while reducing harmful effects. Flexible context-specific R&D policies ought to be shaped, so that maximal value can be achieved, especially where value add is greater. By tailoring these essential back drivers and focusing on more the more socio economically vulnerable regions, policy strategies become more effective toward the desired sustainable and inclusive impacts on environmental quality.

Future direction

Future studies should expand the analysis outside the EU to compare results across developing and developed countries. Differences in sectoral heterogeneity can be studied since AI and CE may function differently in energy intensive sectors versus technology-intensive sectors. Also, future studies may incorporate factors such as institutional quality, regulatory institutions and green finance. Examining the dynamics of new policies, specifically policy shocks will inform us of unintended consequences of regional plans with big data available in quasi-experiments.