Circular Economy Energy Transitions and Sustainable 2 Growth in BRICS Economies: Distributional Heterogeneity 3 and the Energy Rebound Effect

1. Introduction

The transition to a circular economy (CE) represents a fundamental shift from linear "take-make-dispose" models toward regenerative systems that decouple economic growth from resource consumption [1,2]. As the BRICS economies—Brazil, China, India, South Africa, Egypt, and Indonesia—collectively represent approximately 3.4 billion people and over 30% of global GDP, understanding the macroeconomic implications of CE energy transitions has become critically important for both national policymakers and international climate governance. These economies span the spectrum from mature renewable systems (Brazil) to early-stage transitions (Egypt and South Africa), providing rich variation for examining heterogeneous effects [3,4].

Despite growing scholarly attention, the empirical literature on the CE–growth nexus remains fragmented and inconclusive. Several studies document positive long-run relationships between renewable energy consumption and economic growth [5,6], while others report negative or insignificant effects depending on country-specific conditions and methodological approaches [7,8]. This ambiguity stems in part from methodological limitations: most existing studies rely on mean-based estimators, such as pooled OLS or standard panel ARDL, that yield a single average coefficient and potentially mask substantial heterogeneity across countries at different stages of development. As recent research emphasizes, macroeconomic variables rarely behave symmetrically and linearly across the distribution of outcomes [9,10]—yet conventional estimators implicitly assume they do.

The energy rebound effect—whereby efficiency improvements stimulate additional demand that partially or fully offsets the initial savings—remains inadequately tested in BRICS contexts. While theoretical and empirical evidence from advanced and emerging economies suggests rebound effects ranging from 20% to 60% [11,12], systematic evidence from diverse BRICS economies remains scarce. This gap is particularly significant given that these economies are at varying stages of energy transition, from mature renewable systems (Brazil) to early-stage transitions (Egypt and South Africa) [13,14].

Several critical gaps therefore remain in the BRICS-specific literature. First, most studies rely on mean-based estimators that obscure how CE effects vary across the growth distribution. Second, rebound effects in BRICS economies have rarely been quantified directly, and where they have been inferred—for example, from sign reversals in wavelet-decomposed coefficients [15], the magnitude remains unknown. Third, cross-sectional dependence is often ignored in BRICS panel studies despite evident global spillovers [16,17]. Fourth, Egypt and Indonesia, as new BRICS members, have received limited attention. Fifth, no study has integrated MMQR with fixed effects and direct rebound quantification in a unified framework.

This study addresses these gaps through four contributions. First, methodologically, we employ Method of Moments Quantile Regression (MMQR) as the primary estimator [11], with fixed effects as a robustness check and with formal diagnostics for cross-sectional dependence [18,19] and panel integration order [20]. This allows us to capture distributional heterogeneity across the growth distribution—a dimension neglected in prior work, including recent wavelet-based studies [21,22]. Second, substantively, we provide quantile-based evidence showing that CE energy transition effects vary significantly across the growth distribution, a pattern masked by mean-based estimators. Third, we provide a direct estimate of the energy rebound effect for the BRICS panel following the empirical approach of Sorrell [23] and Frondel [24], updated with recent panel methodologies [25,26]. The estimated rebound effect is 25.68%, implying net savings of 74.32% from energy efficiency improvements. Fourth, we offer differentiated policy recommendations tailored to low-, middle-, and high-growth economies, moving beyond one-size-fits-all prescriptions [27,28].

Based on these gaps and the theoretical mechanisms reviewed in Section 2, we test eight hypotheses. H1: renewable energy share affects growth heterogeneously across quantiles. H2: energy intensity positively affects growth at specific quantiles. H3: gross capital formation is a robust driver of growth across the distribution. H4: trade openness promotes growth. H5: FDI promotes growth across quantiles. H6: urbanization negatively affects growth. H7: domestic credit negatively affects growth. H8: energy efficiency improvements yield net savings, consistent with a partial rebound effect.

The remainder of the paper is organized as follows. Section 2 reviews the theoretical and empirical literature. Section 3 describes the data, variables, and methodology. Section 4 presents empirical results. Section 5 discusses the findings and policy implications. Section 6 concludes and identifies directions for future research.

2. Literature Review

2.1. Circular Economy, Energy Transition, and Economic Growth

The circular economy (CE) has emerged as a transformative policy framework aimed at decoupling economic prosperity from raw material consumption and environmental degradation [1,2]. By promoting resource efficiency, waste reduction, and renewable energy deployment, CE principles offer a pathway toward sustainable development that aligns with multiple Sustainable Development Goals (SDGs), particularly SDG 7 (Affordable and Clean Energy), SDG 8 (Decent Work and Economic Growth), SDG 9 (Industry, Innovation, and Infrastructure), SDG 12 (Responsible Consumption and Production), and SDG 13 (Climate Action) [3,4].

The Ellen MacArthur Foundation [28] codified the circular economy as "an industrial economy that aims to depend on renewable energy and eliminate waste through meticulous design," emphasizing that the CE generates no waste, in contrast to the linear "take-make-dispose" model. The World Bank [29] defines it as "a new and comprehensive economic model aimed at reducing pollution and waste, extending product life cycles, and enhancing the sharing and redeployment of physical and natural assets." More recent scholarship has refined these definitions, emphasizing that the circular economy is not merely a waste management strategy but a systemic transformation of production and consumption systems [30,31].

At the macroeconomic level, CE transitions operate through multiple channels. Ghisellini et al. [32] identify three key mechanisms: (i) reduced marginal energy production costs as renewable capacity matures; (ii) decreased fossil-fuel import dependence; and (iii) technological spillovers from clean energy R&D that raise total factor productivity. Stahel [33] emphasizes the role of resource productivity gains, arguing that extending product life cycles and recirculating materials reduces the energy and material intensity of economic output. More recently, De Pascale et al. [34] provide a systematic review of 61 CE indicators, highlighting the multidimensional nature of CE transitions and the need for comprehensive measurement frameworks.

The energy dimension of CE transitions—particularly renewable energy deployment and energy efficiency improvements—has received the most empirical attention. A growing body of literature examines the renewable energy–growth nexus. Inglesi-Lotz [5] finds that renewable energy consumption positively affects economic growth, particularly in countries with higher renewable shares. Vural [6] confirms this relationship for Sub-Saharan African countries, while Khan et al. [7] demonstrate that energy transitions contribute to environmental sustainability in OECD countries. However, the sign and magnitude of effects vary considerably across studies, time periods, and country groupings. Kahia [8] find mixed results for MENA countries, while Shahzad [9] reports that renewable energy transition effects depend on country-specific conditions and technological capacity.

Using Pooled Mean Group (PMG) estimation across 24 African countries, Nathaniel and Khan [35] document a significantly positive long-run renewable–growth effect alongside an insignificant short-run coefficient—a pattern that aligns with the theoretical expectation of short-run adjustment costs giving way to long-run structural dividends. Similarly, Raihan [36] confirms positive long-run renewable–growth linkages for ASEAN economies, while Amin [26] identifies green technological advancements as key drivers of carbon emission reduction in BRICS economies.

However, these studies share a common limitation: they rely on mean-based estimators that produce a single average coefficient, potentially masking substantial heterogeneity across countries at different stages of development. As recent research emphasizes, macroeconomic variables rarely behave symmetrically and linearly across the distribution of outcomes [10,11], yet conventional estimators implicitly assume they do.

2.2. The Energy Rebound Effect: Theory and Evidence

The macroeconomic rebound effect—first documented by William Stanley Jevons [37] describes the phenomenon whereby efficiency improvements lower the cost of energy services, stimulating additional demand that partially or fully offsets the initial savings. Jevons observed that improvements in steam engine coal efficiency led to more, not less, aggregate coal consumption: lower unit costs made coal-powered production economically attractive at scales that had previously been unprofitable.

The modern rebound effect literature distinguishes between direct, indirect, and economy-wide rebounds [12,22]:

• Direct Rebound: Consumers Increase Use of the Same Energy Service Due to Lower Cost
• Indirect Rebound: Savings from Efficiency Are Spent on Other Energy-Intensive Goods and Services
• Economy-Wide Rebound: Efficiency Gains Stimulate Additional Economic Activity, Increasing Total Energy Demand

Saunders [38] worked out the conditions under which "backfire" (rebound exceeding 100%) is theoretically possible in a neoclassical production framework. More recent theoretical developments have extended this framework to incorporate behavioral responses and macroeconomic feedbacks [12,14].

Empirically, the magnitude of rebound effects varies considerably across contexts. Sorrell [22] estimates UK economy-wide rebound at 26–56%; Roy [39] documents significant rebound in India (approximately 35%); Turner [40] finds backfire conditions in Chinese manufacturing; and Chen [13] estimate a 35% rebound in residential electricity consumption in the European Union. More recent studies have extended this evidence base. Brockway et al. [12] provide a comprehensive review of economy-wide rebound effects, concluding that rebound is generally between 10% and 60% depending on methodological approach and country context. Wei et al. [14] review empirical evidence on rebound effects in China, finding that rebound is generally higher in the residential sector than in the industrial sector.

In emerging market contexts, the magnitude of rebound effects is theoretically ambiguous. On one hand, income constraints may limit consumption responses, yielding lower rebound [41]. On the other hand, rapidly industrializing economies may exhibit higher rebound as efficiency gains enable expansion of energy-intensive activities [14]. Di Domenico [42] develop a macro-evolutionary input–output model highlighting that circular economy practices, while reducing resource depletion, can simultaneously lead to energy rebound effects. Dong [24] examins the impact of renewable energy on CO₂ emissions across different income levels, finding that the effect varies significantly by development stage.

Importantly, the rebound effect has been primarily inferred rather than directly quantified in recent CE–growth studies. Esmail and Yousef [20] infer the existence of a rebound effect from the sign reversal of the energy intensity coefficient across frequency bands—from negative in the short run to positive in the long run. However, as they acknowledge, "we present this sign reversal as a directional signature of the Jevons mechanism rather than claim a definitive multi-frequency Jevons Rebound Effect." This highlights the need for direct quantification of the rebound effect in emerging markets—a gap this study addresses.

2.3. Time-Horizon vs. Distributional Heterogeneity: A Critical Distinction

Recent methodological innovations have addressed key limitations of traditional panel estimators, with a notable distinction between two types of heterogeneity: time-horizon heterogeneity and distributional heterogeneity.

2.3.1. Time-Horizon Heterogeneity: The Wavelet Approach

Wavelet analysis, introduced to economics by Ramsey and Lampart [43] and extended to energy economics by Aguiar-Conraria [44] and Jammazi and Aloui [45], decomposes a time series into components at distinct frequency scales without losing temporal localization. Applied at Level 2 with the Daubechies (db2) filter, the decomposition yields three orthogonal components: D1 (short run, 2–4 years), D2 (medium run, 4–8 years), and A2 (long run, 8+ years).

However, this approach has several limitations. First, the wavelet decomposition relies on a relatively short time series (T = 19), which the authors themselves acknowledge "provides D2 and A2 components with much lower signal-to-noise ratios than the original series." They note that "extending the panel to T ≥ 26 (achievable by 2031) would support Level-3 decomposition with much sharper frequency separation." Second, the core CE variables—renewable energy share and energy intensity—fail to achieve statistical significance under conservative Wild Cluster Bootstrap inference, leading the authors to characterize their findings as merely "suggestive" and "directional." Third, the wavelet approach examines only time-horizon heterogeneity, neglecting the question of whether CE effects differ across the growth distribution.

2.3.2. Distributional Heterogeneity: The Quantile Regression Approach

The Method of Moments Quantile Regression (MMQR), developed by Machado and Silva [11], offers a fundamentally different lens for examining heterogeneity. Rather than decomposing time into frequency bands, MMQR estimates effects at different points of the conditional distribution of the dependent variable (in this case, economic growth). This allows researchers to ask: do CE energy transitions affect low-growth economies differently from high-growth economies [10,21]?

This distinction is critical for several reasons. First, mean-based estimators—including standard panel fixed effects and wavelet decompositions—produce a single average coefficient that may be statistically insignificant or substantively misleading if effects vary across the growth distribution. A variable may have a positive effect for middle-growth economies but a negative effect for high-growth economies, or vice versa. Mean-based estimators would average these opposing effects, potentially producing an insignificant or directionally misleading coefficient [10,46].

Second, the theoretical mechanisms underlying CE–growth dynamics may differ systematically across growth levels. For low-growth economies, structural factors beyond the energy transition (institutional quality, political stability, commodity dependence) may be the primary determinants of growth [47]. For middle-growth economies, energy efficiency improvements may yield the greatest growth dividends as industrial expansion proceeds. For high-growth economies, rapid renewable energy deployment may impose significant adjustment costs, suppressing growth in the short to medium term [15,16].

Third, distributional heterogeneity has direct policy implications. Differentiated policy strategies are needed for low-, middle-, and high-growth economies—a nuance entirely lost in mean-based estimators [26,27].

2.4. Methodological Advances: MMQR

MMQR, developed by Machado and Silva [11], allows individual influences to affect the entire distribution rather than only shifting means, enabling the identification of conditional heterogeneous covariance effects. The estimator is particularly applicable when panel data models include endogenous explanatory variables and individual effects [21]. Three properties make it suitable for the present study. First, it does not require assumptions about the distribution of the error term. Second, it produces robust estimates in the presence of outliers and nonlinear relationships. Third, unlike Canay's [54] two-step quantile estimator, MMQR permits individual fixed effects to vary across quantiles rather than being restricted to location shifts. This last property is essential for a heterogeneous panel such as the BRICS, where country-specific structural characteristics—resource endowments, institutional quality, and industrial composition—plausibly shape how CE transitions affect growth at different points of the conditional growth distribution [47].

2.5. BRICS-Specific Evidence, Research Gaps, and Hypotheses

Studies specifically examining the CE–growth nexus in BRICS economies have emerged in recent years. Amin et al. [26] identify green technological advancements and resource yields as key drivers of carbon emission reduction, explicitly linking these outcomes to achieving the SDGs. Yadav et al. [27] demonstrate that renewable energy investment impacts on emissions reduction in BRICS countries are significantly amplified by green finance mechanisms and effective governance. Makhdum [47] study China and find that institutional quality, natural resource management, renewable energy deployment, and financial development collectively contribute to reducing environmental footprint without hindering growth.

Bhattacharya et al. [15] examine the effect of renewable energy consumption on economic growth across 38 countries, including BRICS economies, finding that renewable energy positively affects growth but the effect varies across income levels. Wang et al. [16] analyze energy consumption per capita across 186 countries, finding that urbanization and economic growth are key drivers, while energy prices exert a negative effect.

More recently, Uche et al. [48] examine dynamic interactions of green innovations, green transitions, and ecological load capacity factor in BRICS economies, finding that green innovations and transitions contribute to environmental sustainability. Shahzad et al. [9] provide evidence that technological innovations and renewable energy transition matter for environmental sustainability in emerging economies, but the effects are conditional on institutional quality and absorptive capacity.

Several critical gaps nevertheless remain in the BRICS-specific literature. First, most studies rely on mean-based estimators that obscure how CE effects vary across the growth distribution. Second, testing and direct quantification of rebound effects in BRICS economies remain limited. Third, BRICS panel studies often ignore cross-sectional dependence despite evident global spillovers [17,18]. Fourth, Egypt and Indonesia—new BRICS members—have received limited attention. Fifth, no study has integrated MMQR with fixed effects and direct rebound quantification in a unified framework.

Based on these gaps, we test the following hypotheses:

H1 

: Renewable energy share affects economic growth heterogeneously across the growth distribution.

H2 

: Energy intensity positively affects growth at specific quantiles of the growth distribution.

H3 

: Gross capital formation is a robust positive driver of growth across all quantiles.

H4 

: Trade openness promotes economic growth.

H5 

: FDI promotes economic growth across all quantiles.

H6 

: Urbanization negatively affects economic growth.

H7 

: Domestic credit negatively affects economic growth.

H8 

: Energy efficiency improvements yield net energy savings, consistent with a partial rebound effect.

2.6. Control Variables: Theoretical Rationale

Based on the theoretical and empirical literature, we include five control variables. Their rationale is summarized in Table 1.

3. Materials and Methods

3.1. Data and Variables

The sample comprises six BRICS emerging economies—Brazil, China, India, South Africa, Egypt, and Indonesia—observed annually from 2000 to 2025. This yields a balanced panel of N = 150 country-year observations (6 countries × 25 years). The selection is deliberate for four reasons: (i) all six are current BRICS members, with Egypt acceding on 1 January 2025 and Indonesia on 6 January 2025; (ii) the panel spans three continents (Asia, Africa, and Latin America); (iii) it covers the full spectrum of energy transition stages, from mature renewable systems (Brazil) to early-stage transitions (Egypt and South Africa); and (iv) complete data coverage exists for all variables across the study window.

Russia is excluded from the sample. Two considerations motivate this decision. First, key energy and financial variables for Russia are unavailable or unreliable in the World Bank WDI and IEA databases for the post-2022 period following the imposition of international sanctions. Second, the structural break introduced by the 2022 conflict creates a discontinuity that cannot be accommodated by the estimation framework without distorting the panel-wide estimates. Excluding Russia allows a balanced panel with consistent measurement, at the cost of reduced coverage of the original BRICS-5.

The variables, definitions, units, and sources are summarized in Table 2.

3.2. Estimation Strategy

The empirical strategy proceeds in four phases: preliminary diagnostics, MMQR estimation, fixed effects robustness, and rebound effect estimation.

3.2.1. Phase 1: Preliminary Diagnostics

Four diagnostic tests are conducted before estimation:

• Cross-sectional dependence (Pesaran CD test) [17]. In a panel of major economies with substantial trade and financial linkages, unobserved common shocks—global commodity prices, financial cycles, climate policy shocks—can induce cross-sectional dependence, which biases first-generation panel estimators. A statistically significant CD statistic justifies second-generation methods that account for common factors.
• Slope homogeneity (Pesaran–Yamagata test) [54]. This test determines whether the slope coefficients can be pooled across countries. Rejection of homogeneity supports heterogeneous-coefficient estimators such as MMQR.
• Panel unit root (CIPS test) [55]. The CIPS test is a second-generation panel unit root test robust to cross-sectional dependence. It determines the order of integration of each series, which informs the choice between level and first-differenced specifications.
• Panel cointegration (Westerlund test) [56]. If the variables are integrated of order one, this test establishes whether a long-run equilibrium relationship exists among them, which in turn justifies estimation in levels rather than differences.

3.2.2. Phase 2: Method of Moments Quantile Regression (MMQR)

Following Machado and Silva [11], we employ MMQR as the primary estimator. Three properties motivate its selection.

First, unlike mean-based estimators—including standard panel fixed effects and wavelet decompositions—MMQR estimates effects at different points of the conditional distribution of GDP growth, capturing distributional heterogeneity that would otherwise be masked by averaging. This matters because a variable may have a positive effect for middle-growth economies and a negative effect for high-growth economies; mean-based estimators would average these opposing effects into an insignificant or directionally misleading coefficient [10,21].

Second, MMQR permits individual fixed effects to influence the entire distribution rather than only shifting the mean. This is particularly important for heterogeneous panels such as the BRICS, where country-specific structural characteristics—resource endowments, institutional quality, industrial composition—plausibly shape how CE transitions affect growth at different points of the growth distribution [47].

Third, MMQR produces estimates robust to outliers and nonlinear relationships without requiring assumptions about the distribution of the error term. It accommodates individual effects that vary across the distribution, thereby mitigating bias from time-invariant unobserved heterogeneity [11].

The estimated model is specified as:

Yit=αi+Xitβ+(δi+Zitγ)Uit

(1)

where Yit is GDP growth, Xit is the vector of independent variables, αirepresents individual fixed effects, and Uit is the error term. The conditional quantile function is:

QY(τ∣Xit)=(αi+δiq(τ))+Xitβ+Zitγq(τ)

(2)

We estimate effects at the 10th, 25th, 50th, 75th, and 90th quantiles of the growth distribution. The MMQR approach is advantageous because it (a) allows individual effects to affect the entire distribution, (b) handles endogenous explanatory variables, and (c) produces robust estimates even in the presence of outliers and nonlinear relationships.

3.2.3. Phase 3: Fixed Effects Model — Robustness Check

To validate the MMQR findings, we employ a fixed effects (FE) panel regression as a robustness check. The FE model controls for unobserved country-specific heterogeneity that is time-invariant, such as institutional quality, geographic characteristics, and cultural factors. The model is specified as:

Y_it=α_i+β1RE_it+β2EI_it+γ′Z_it+ϵ_it

(3)

where α_i represents country fixed effects, RE_it is renewable energy share, EI_it is energy intensity, Zit is the vector of control variables, and ϵit is the idiosyncratic error term. Standard errors are clustered at the country level to account for heteroskedasticity and serial correlation.

3.3. Rebound Effects Specification

To quantify the energy rebound effect—the extent to which energy efficiency improvements are offset by increased consumption—we employ a fixed effects panel regression following the empirical approach of Sorrell [22], Frondel Peters, and Vance [23], and Brockway et al. [12]. The specification is:

ln(EnergyConsumption_it)=α_i+λ_t+β₁ln(EnergyIntensity_it)+β₂ln(GDPpc_it)+γ′Z_it+ϵ_it

(4)

The coefficient on energy intensity (β₁) represents the elasticity of energy consumption with respect to energy intensity. A coefficient of 0 would indicate full rebound (no net savings), while a coefficient of 1 would indicate zero rebound (full savings realized). The rebound effect is calculated as (1−β1)×100%.

Figure 1. Methodological Framework.

Figure 1. Methodological Framework.

4. Results

Table 3 presents the descriptive statistics for all variables used in the analysis. The average GDP growth rate is 4.71%, indicating the dynamic nature of BRICS economies during the study period (2000–2025). Renewable energy share averages 24.91% but exhibits substantial variation (ranging from 1.64% to 89.50%), reflecting the diverse stages of energy transitions across the sample. Energy intensity averages 5.40 MJ/USD, highlighting significant differences in energy efficiency across countries. Gross capital formation averages 26.41% of GDP, while trade openness averages 44.16%. The relatively high standard deviations for renewable energy share, urbanization, and domestic credit suggest considerable heterogeneity across countries and over time, justifying our quantile-based approach.

Figure 2. Effectively highlights the substantial cross-country heterogeneity that motivates the paper’s distribution-sensitive approach. Brazil is a clear outlier in renewable energy share (around 80%), reflecting its mature renewable system, while South Africa has the lowest renewable share (near 2%) and, together with China, the highest energy intensity (around 8 MJ/USD). Growth performance also differs sharply: China, India, and Indonesia average above 5% GDP growth, whereas Brazil and South Africa average only about 2–2.5%. FDI is relatively similar across countries, with Brazil slightly higher, and trade openness is highest in South Africa and lowest in Brazil. These patterns confirm that the six BRICS economies occupy different positions along the energy-transition and growth spectra. They also provide descriptive support for the study’s central argument: mean-based estimators can mask distributional heterogeneity, whereas the MMQR approach can reveal how circular economy energy transition effects differ between low-growth and high-growth economies. The figure therefore reinforces the case for differentiated, rather than one-size-fits-all, policy prescriptions.

Table 4. Correlation Matrix.

Variable	(1)	(2)	(3)	(4)	(5)		(6)	(7)	(8)
(1) GDP Growth	1.000
(2) Renewable Share	-0.219	1.000
(3) Energy Intensity	0.319	-0.329	1.000
(4) Gross Capital	0.639	-0.183	0.312	1.000
(5) Trade Openness	0.227	-0.654	0.374	0.061	1.000
(6) FDI	0.177	0.252	0.020	-0.024	-0.016		1.000
(7) Urbanization	-0.480	0.780	-0.159	-0.471	-0.427		0.215	1.000
(8) Domestic Credit	0.071	-0.159	0.700	0.290	0.165		-0.018	0.167	1.000

Source: done by authors.

Table 4. Correlation Matrix.

Variable	(1)	(2)	(3)	(4)	(5)		(6)	(7)	(8)
(1) GDP Growth	1.000
(2) Renewable Share	-0.219	1.000
(3) Energy Intensity	0.319	-0.329	1.000
(4) Gross Capital	0.639	-0.183	0.312	1.000
(5) Trade Openness	0.227	-0.654	0.374	0.061	1.000
(6) FDI	0.177	0.252	0.020	-0.024	-0.016		1.000
(7) Urbanization	-0.480	0.780	-0.159	-0.471	-0.427		0.215	1.000
(8) Domestic Credit	0.071	-0.159	0.700	0.290	0.165		-0.018	0.167	1.000

Source: done by authors.

The correlation matrix reveals several notable relationships. GDP growth exhibits a strong positive correlation with gross capital formation (r = 0.639), confirming the importance of investment as a driver of economic growth.

GDP growth is also positively correlated with energy intensity (r = 0.319) and trade openness (r = 0.227). Conversely, GDP growth shows a

Negative correlation with urbanization (r = -0.480), reflecting the fact that countries with lower initial urbanization levels (e.g., China, India) experienced higher growth rates. Renewable energy share exhibits a strong positive correlation with urbanization (r = 0.780) and a negative correlation with trade openness (r = -0.654) and energy intensity (r = -0.329). Energy intensity shows a strong positive correlation with domestic credit (r = 0.700).

Figure 3 presents a visual representation of the correlation matrix. The plot confirms the strong positive correlation between GDP growth and gross capital formation (r = 0.639), and the negative correlation between GDP growth and urbanization (r = -0.480). Renewable energy share shows a strong positive correlation with urbanization (r = 0.780) and a negative correlation with trade openness (r = -0.654). The visual representation highlights these patterns clearly.

The Pesaran Cross-Sectional Dependence (CD) test results indicate significant cross-sectional dependence for GDP growth, energy intensity, gross capital formation, and urbanization (p < 0.01), suggesting that global shocks simultaneously affect these variables across BRICS economies. Renewable energy share and FDI show no evidence of cross-sectional dependence (p > 0.10). Trade openness shows weak evidence of cross-sectional dependence (p = 0.089). The presence of cross-sectional dependence for key variables justifies the use of second-generation panel methods that account for cross-sectional dependence.

The panel unit root test results, based on the Augmented Dickey-Fuller (ADF) test, reveal a mixed integration order. Only FDI is found to be stationary at level [I(0)] with a p-value of 0.010, indicating that FDI reverts to its mean over time. All other variables—GDP growth, renewable energy share, energy intensity, gross capital formation, trade openness, urbanization, and domestic credit—are non-stationary at level [I(1)], meaning they require first differencing to achieve stationarity. This mixed integration order (I(0) and I(1)) confirms that ARDL-based methods, which can accommodate variables with different integration orders, are appropriate for estimation [7,18]. The non-stationarity of GDP growth is noteworthy, suggesting that growth dynamics in BRICS economies are persistent and subject to structural changes.

Table 5 presents the Method of Moments Quantile Regression (MMQR) results across five growth quantiles [11]. The results reveal significant heterogeneity in the effects of circular economy variables across the growth distribution.

Renewable Energy Share: Renewable energy share shows a positive and statistically significant effect at the 50th quantile (coefficient = 0.042, p < 0.01), 75th quantile (coefficient = 0.042, p < 0.05), and 90th quantile (coefficient = 0.049, p < 0.05). However, the effect is not significant at the 10th and 25th quantiles. This suggests that renewable energy deployment yields growth dividends for economies with above-average growth rates (50th–90th percentiles), while the effect is less pronounced for low-growth economies. This finding is consistent with the "green transition cost hypothesis" where economies with slower growth may face higher adjustment costs, while faster-growing economies benefit from renewable energy dividends [9,15].

Energy Intensity: Energy intensity exhibits a positive and highly significant effect at the 50th quantile (coefficient = 0.341, p < 0.01), 75th quantile (coefficient = 0.419, p < 0.01), and 90th quantile (coefficient = 0.551, p < 0.01). The coefficient increases from 0.125 at Q25 to 0.551 at Q90, indicating that the effect becomes stronger at higher growth levels. This suggests that energy efficiency improvements yield the greatest growth dividends for economies with above-average growth rates [24,41]. At Q90, a 1% increase in energy intensity is associated with a 0.55 percentage point increase in GDP growth. This counterintuitive finding may reflect the fact that rapidly growing economies require more energy-intensive production, and the positive effect of economic activity outweighs the negative effect of inefficiency.

Gross Capital Formation: Gross capital formation shows a positive and highly significant effect across all quantiles (p < 0.01 at Q25–Q90; p < 0.05 at Q10). The coefficient ranges from 0.104 to 0.205, indicating that a 1 percentage point increase in gross capital formation as a share of GDP is associated with approximately 0.10–0.21 percentage point increase in GDP growth. This confirms that gross capital formation is the most robust and consistent driver of growth across the entire growth distribution, aligning with the manufacturing-led development model [53,57].

FDI: FDI exhibits a positive and highly significant effect across all quantiles (p < 0.01 at Q25–Q75; p < 0.05 at Q10 and Q90). The coefficient remains relatively stable around 0.344–0.451, indicating that a 1 percentage point increase in FDI as a share of GDP is associated with approximately 0.34–0.45 percentage point increase in GDP growth. This finding is consistent with the literature emphasizing the role of FDI in providing capital, technology transfer, and knowledge spillovers [27,47,58].

Urbanization: Urbanization shows a negative and statistically significant effect at Q25 (coefficient = -0.096, p < 0.05), Q50 (coefficient = -0.095, p < 0.01), Q75 (coefficient = -0.088, p < 0.01), and Q90 (coefficient = -0.097, p < 0.05). The effect is not significant at Q10 (coefficient = -0.050). This suggests that rapid urbanization may impose transitional costs on growth, reflecting challenges associated with urban infrastructure deficits, housing shortages, congestion, and environmental degradation [16,51].

However, the coefficient is relatively small, indicating that the effect is modest.

Figure 4. MMQR Coefficient Plot.

Figure 4. MMQR Coefficient Plot.

Trade Openness and Domestic Credit: Trade openness shows positive but statistically insignificant coefficients across most quantiles (ranging from -0.010 to 0.071).

While the effect is positive at most quantiles, the lack of statistical significance suggests that trade integration does not have a robust effect on growth in this sample [9,49]. Domestic credit shows small negative coefficients that are not statistically significant across all quantiles (ranging from -0.025 to -0.001), which may reflect the "too much finance" phenomenon where excessive financial development can crowd out productive investment [59].

Table 6 presents the MMQR results with standard errors in parentheses. The standard errors are bootstrapped with 200 replications to ensure robust inference [23]. The results confirm the statistical significance of key variables at specific quantiles. Renewable energy share, energy intensity, gross capital formation, FDI, and urbanization show significant effects at middle to high quantiles, while trade openness and domestic credit are not statistically significant.

Table 6. Panel Unit Root Test Results (ADF).

Variable	p-value	Result	Integration Order
GDP Growth	0.3534	Non-Stationary	I(1)
Renewable Energy Share	0.5979	Non-Stationary	I(1)
Energy Intensity	0.4353	Non-Stationary	I(1)
Gross Capital Formation	0.5293	Non-Stationary	I(1)
Trade Openness	0.3765	Non-Stationary	I(1)
FDI	0.0100	Stationary	I(0)
Urbanization	0.7892	Non-Stationary	I(1)
Domestic Credit	0.4677	Non-Stationary	I(1)

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

Table 6. Panel Unit Root Test Results (ADF).

Variable	p-value	Result	Integration Order
GDP Growth	0.3534	Non-Stationary	I(1)
Renewable Energy Share	0.5979	Non-Stationary	I(1)
Energy Intensity	0.4353	Non-Stationary	I(1)
Gross Capital Formation	0.5293	Non-Stationary	I(1)
Trade Openness	0.3765	Non-Stationary	I(1)
FDI	0.0100	Stationary	I(0)
Urbanization	0.7892	Non-Stationary	I(1)
Domestic Credit	0.4677	Non-Stationary	I(1)

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

Table 7. MMQR Estimation Results.

Variable	Q10	Q25	Q50	Q75	Q90
Renewable Energy Share	-0.011	0.033	0.042***	0.042**	0.049**
Energy Intensity	0.418	0.125	0.341***	0.419***	0.551***
Gross Capital Formation	0.205**	0.153***	0.132***	0.104***	0.118***
Trade Openness	0.071	0.031	0.014	0.009	-0.010
FDI	0.451**	0.378***	0.364***	0.344***	0.445**
Urbanization	-0.050	-0.096**	-0.095***	-0.088***	-0.097**
Domestic Credit	-0.025	-0.001	-0.005	-0.007	-0.005

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

Table 7. MMQR Estimation Results.

Variable	Q10	Q25	Q50	Q75	Q90
Renewable Energy Share	-0.011	0.033	0.042***	0.042**	0.049**
Energy Intensity	0.418	0.125	0.341***	0.419***	0.551***
Gross Capital Formation	0.205**	0.153***	0.132***	0.104***	0.118***
Trade Openness	0.071	0.031	0.014	0.009	-0.010
FDI	0.451**	0.378***	0.364***	0.344***	0.445**
Urbanization	-0.050	-0.096**	-0.095***	-0.088***	-0.097**
Domestic Credit	-0.025	-0.001	-0.005	-0.007	-0.005

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

Table 8. MMQR Results with Standard Errors.

Variable	Q10	Q25	Q50	Q75	Q90
Renewable Energy Share
Coefficient	-0.011	0.033	0.042***	0.042**	0.049**
Std. Error	(0.057)	(0.023)	(0.014)	(0.017)	(0.021)
Energy Intensity
Coefficient	0.418	0.125	0.341***	0.419***	0.551***
Std. Error	(0.379)	(0.231)	(0.111)	(0.101)	(0.195)
Gross Capital Formation
Coefficient	0.205**	0.153***	0.132***	0.104***	0.118***
Std. Error	(0.101)	(0.028)	(0.016)	(0.025)	(0.037)
Trade Openness
Coefficient	0.071	0.031	0.014	0.009	-0.010
Std. Error	(0.060)	(0.030)	(0.017)	(0.020)	(0.037)
FDI
Coefficient	0.451**	0.378***	0.364***	0.344***	0.445**
Std. Error	(0.184)	(0.080)	(0.069)	(0.107)	(0.181)
Urbanization
Coefficient	-0.050	-0.096**	-0.095***	-0.088***	-0.097**
Std. Error	(0.100)	(0.038)	(0.020)	(0.030)	(0.040)
Domestic Credit
Coefficient	-0.025	-0.001	-0.005	-0.007	-0.005
Std. Error	(0.023)	(0.014)	(0.005)	(0.006)	(0.013)

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

Table 8. MMQR Results with Standard Errors.

Variable	Q10	Q25	Q50	Q75	Q90
Renewable Energy Share
Coefficient	-0.011	0.033	0.042***	0.042**	0.049**
Std. Error	(0.057)	(0.023)	(0.014)	(0.017)	(0.021)
Energy Intensity
Coefficient	0.418	0.125	0.341***	0.419***	0.551***
Std. Error	(0.379)	(0.231)	(0.111)	(0.101)	(0.195)
Gross Capital Formation
Coefficient	0.205**	0.153***	0.132***	0.104***	0.118***
Std. Error	(0.101)	(0.028)	(0.016)	(0.025)	(0.037)
Trade Openness
Coefficient	0.071	0.031	0.014	0.009	-0.010
Std. Error	(0.060)	(0.030)	(0.017)	(0.020)	(0.037)
FDI
Coefficient	0.451**	0.378***	0.364***	0.344***	0.445**
Std. Error	(0.184)	(0.080)	(0.069)	(0.107)	(0.181)
Urbanization
Coefficient	-0.050	-0.096**	-0.095***	-0.088***	-0.097**
Std. Error	(0.100)	(0.038)	(0.020)	(0.030)	(0.040)
Domestic Credit
Coefficient	-0.025	-0.001	-0.005	-0.007	-0.005
Std. Error	(0.023)	(0.014)	(0.005)	(0.006)	(0.013)

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

Table 9. Fixed Effects Model (Robustness Check).

Variable	Coefficient	Std. Error	p-value	Significance
Renewable Energy Share	-0.0182	0.0626	0.7713
Energy Intensity	-0.0284	0.5273	0.9571
Gross Capital Formation	0.2351	0.0594	0.0001	***
Trade Openness	0.0533	0.0228	0.0209	*
FDI	0.1747	0.1278	0.1738
Urbanization	-0.2176	0.1699	0.2025
Domestic Credit	-0.0185	0.0170	0.2784
R² (within)		0.392
F-statistic		3.424 (p < 0.01)

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

Table 9. Fixed Effects Model (Robustness Check).

Variable	Coefficient	Std. Error	p-value	Significance
Renewable Energy Share	-0.0182	0.0626	0.7713
Energy Intensity	-0.0284	0.5273	0.9571
Gross Capital Formation	0.2351	0.0594	0.0001	***
Trade Openness	0.0533	0.0228	0.0209	*
FDI	0.1747	0.1278	0.1738
Urbanization	-0.2176	0.1699	0.2025
Domestic Credit	-0.0185	0.0170	0.2784
R² (within)		0.392
F-statistic		3.424 (p < 0.01)

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

The fixed effects model serves as a robustness check for the MMQR results. The results confirm that gross capital formation is the most robust driver of growth (coefficient = 0.235, p < 0.01), consistent with the MMQR findings. Trade openness also shows a positive and significant effect (coefficient = 0.053, p < 0.05). However, renewable energy share and energy intensity are not statistically significant in the fixed effects model, highlighting the importance of the quantile-based approach in revealing heterogeneous effects that are masked by mean-based estimators. The model explains approximately 39% of the within-country variation in GDP growth.

Table 10. VIF Multicollinearity Test.

Variable	VIF	Interpretation
Urbanization	9.286	Moderate concern
Renewable Energy Share	7.707	Moderate concern
Domestic Credit	4.492	Acceptable
Gross Capital Formation	2.886	Acceptable
Energy Intensity	2.596	Acceptable
Trade Openness	2.026	Acceptable
FDI	1.128	Acceptable

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

Table 10. VIF Multicollinearity Test.

Variable	VIF	Interpretation
Urbanization	9.286	Moderate concern
Renewable Energy Share	7.707	Moderate concern
Domestic Credit	4.492	Acceptable
Gross Capital Formation	2.886	Acceptable
Energy Intensity	2.596	Acceptable
Trade Openness	2.026	Acceptable
FDI	1.128	Acceptable

Note: *** p < 0.01, ** p < 0.05, * p < 0.10*.

The Variance Inflation Factor (VIF) test results indicate moderate multicollinearity concerns for urbanization (VIF = 9.286) and renewable energy share (VIF = 7.707). This is expected given the strong correlation between these two variables (r = 0.780). However, these values remain below the critical threshold of 10, suggesting that multicollinearity does not severely compromise the estimation. All other variables show VIF values below 5, confirming that multicollinearity does not pose a significant issue for our estimation.

To examine whether energy efficiency improvements in BRICS economies are partially offset by increased consumption—a phenomenon known as the rebound effect—we estimate the elasticity of energy consumption with respect to energy intensity. Following the empirical approach of Sorrell [22], we specify a fixed effects panel model where energy consumption is regressed on energy intensity, GDP per capita, trade openness, urbanization, FDI, and domestic credit. The coefficient on energy intensity (β) allows us to calculate the rebound effect as (1 - β) × 100%. A coefficient of 1 indicates zero rebound (full energy savings), while a coefficient of 0 indicates full rebound (no net savings.

Table 11. Rebound Effects Estimation Results.

Variable	Coefficient	Std. Error	p-value	Significance
Energy Intensity (ln)	0.7432	0.1976	0.0003	***
GDP per capita (ln)	0.0248	0.0259	0.3387
Trade Openness	-0.0084	0.0021	0.0001	***
Urbanization	-0.0224	0.0117	0.0569	**
FDI	-0.0049	0.0109	0.6503
Domestic Credit	-0.0012	0.0015	0.4389
Implied rebound effect	25.68%
Implied net savings	74.32%

Notes: *** p < 0.01, ** p < 0.05, * p < 0.10. The rebound effect is computed as (1 − β₁) × 100%, where β₁ is the coefficient on ln (Energy Intensity). A coefficient of 1 implies zero rebound; a coefficient of 0 implies full rebound.

Table 11. Rebound Effects Estimation Results.

Variable	Coefficient	Std. Error	p-value	Significance
Energy Intensity (ln)	0.7432	0.1976	0.0003	***
GDP per capita (ln)	0.0248	0.0259	0.3387
Trade Openness	-0.0084	0.0021	0.0001	***
Urbanization	-0.0224	0.0117	0.0569	**
FDI	-0.0049	0.0109	0.6503
Domestic Credit	-0.0012	0.0015	0.4389
Implied rebound effect	25.68%
Implied net savings	74.32%

Notes: *** p < 0.01, ** p < 0.05, * p < 0.10. The rebound effect is computed as (1 − β₁) × 100%, where β₁ is the coefficient on ln (Energy Intensity). A coefficient of 1 implies zero rebound; a coefficient of 0 implies full rebound.

The rebound effects estimation reveals a partial rebound effect of approximately 25.68%. This means that for every 1% improvement in energy intensity (i.e., energy efficiency), energy consumption decreases by 0.743%, implying that 25.68% of efficiency gains are offset by increased consumption, while 74.32% represent net savings. This partial rebound effect is lower than estimates from advanced economies (26–67%) and consistent with the lower rebound observed in emerging markets due to income constraints.

Figure 5 presents the energy rebound effect in BRICS economies. The results show that approximately 25.68% of energy efficiency gains are offset by increased consumption (rebound effect), while 74.32% represent net savings. This partial rebound effect is lower than estimates from advanced economies (26–67%, Sorrell, [22,23], and consistent with the lower rebound observed in emerging markets due to income constraints [12,14,39]

Table 12. Summary of Hypothesis Testing.

Hypothesis	Description	Result
H1	Renewable energy share affects growth heterogeneously across quantiles	Supported — Positive and significant at Q50, Q75, Q90
H2	Energy intensity positively affects growth at specific quantiles	Supported — Positive and significant at Q50, Q75, Q90
H3	Gross capital formation is a robust driver of growth	Supported — Positive and significant across all quantiles
H4	Trade openness promotes growth	Partially supported — Positive but insignificant in MMQR; significant in FE
H5	FDI promotes growth	Supported — Positive and significant across all quantiles
H6	Urbanization negatively affects growth	Supported — Negative and significant at Q25–Q90
H7	Domestic credit negatively affects growth	Not Supported — Negative but insignificant across all quantiles
H8	Energy efficiency improvements yield net savings (partial rebound)	Supported — Rebound effect of 25.68%, net savings of 74.32%

Table 12. Summary of Hypothesis Testing.

Hypothesis	Description	Result
H1	Renewable energy share affects growth heterogeneously across quantiles	Supported — Positive and significant at Q50, Q75, Q90
H2	Energy intensity positively affects growth at specific quantiles	Supported — Positive and significant at Q50, Q75, Q90
H3	Gross capital formation is a robust driver of growth	Supported — Positive and significant across all quantiles
H4	Trade openness promotes growth	Partially supported — Positive but insignificant in MMQR; significant in FE
H5	FDI promotes growth	Supported — Positive and significant across all quantiles
H6	Urbanization negatively affects growth	Supported — Negative and significant at Q25–Q90
H7	Domestic credit negatively affects growth	Not Supported — Negative but insignificant across all quantiles
H8	Energy efficiency improvements yield net savings (partial rebound)	Supported — Rebound effect of 25.68%, net savings of 74.32%

5. Discussion

The MMQR estimates reveal three broad patterns. First, gross capital formation and FDI are the most robust and statistically significant drivers of growth across the entire growth distribution, confirming the importance of investment and foreign capital as structural engines of economic expansion in BRICS economies. Second, renewable energy share and energy intensity exhibit positive and significant effects at middle-to-high quantiles, suggesting that energy transition policies yield the greatest growth dividends for economies with above-average growth rates. Third, urbanization shows a negative and significant effect at middle-to-high quantiles, indicating transitional costs associated with rapid urban growth. In addition, the rebound-effect estimate indicates that roughly one quarter of energy efficiency gains are offset by increased consumption. Each of these findings is discussed in turn.

5.1. Distributional Heterogeneity in CE–Growth Effects

The MMQR results show that CE variables affect growth differently across quantiles. Energy intensity, renewable energy share, gross capital formation, and FDI are most significant at middle-to-high quantiles (50th–90th percentiles). This finding underscores the importance of considering distributional heterogeneity in policy design, since one-size-fits-all policies may be ineffective or even counterproductive [10,11].

The finding that renewable energy share positively affects growth only at middle-to-high quantiles (Q50–Q90) suggests that renewable energy deployment yields growth dividends primarily for economies with above-average growth rates. This aligns with the "green transition cost hypothesis," under which slower-growing economies face higher adjustment costs—capital reallocation, grid integration, and fossil-fuel sector disruption—that suppress contemporaneous output [9,15]. For low-growth economies, the insignificant effect suggests that structural factors beyond the energy transition (institutional quality, political stability, commodity dependence) may be the primary determinants of growth [47].

The energy intensity finding is particularly noteworthy. The positive and significant effect at Q50–Q90, with the coefficient rising from 0.341 at Q50 to 0.551 at Q90, suggests that energy-intensive production remains closely tied to growth in faster-growing BRICS economies. The positive effect of expanding economic activity evidently outweighs the negative effect of inefficiency [24,41]. This does not imply that energy efficiency is unimportant; rather, it implies that policymakers should pursue "green growth" strategies that decouple growth from resource consumption rather than simply reducing energy intensity in isolation.

These results contrast with the wavelet-based study by Esmail and Yousef [20] in one important respect: while their core CE variables failed to achieve statistical significance under conservative Wild Cluster Bootstrap inference, we find significant effects at specific quantiles. This indicates that the effects were not absent but rather averaged out in mean-based specifications. The contrast highlights the value of distribution-sensitive estimation.

5.2. Gross Capital Formation and FDI as Robust Drivers

Gross capital formation emerges as the most robust and consistent driver of growth across the entire distribution, with positive and significant effects at all quantiles (p < 0.01 at Q25–Q90; p < 0.10 at Q10). The coefficient ranges from 0.104 to 0.205, indicating that a 1 percentage point increase in gross capital formation as a share of GDP is associated with approximately a 0.10–0.21 percentage point increase in GDP growth. This aligns with the manufacturing-led development model [30] and with the literature emphasizing investment as a structural driver of growth [53].

FDI also emerges as a robust driver across all quantiles, with a relatively stable coefficient in the range 0.344–0.451. A 1 percentage point increase in FDI as a share of GDP is associated with approximately a 0.34–0.45 percentage point increase in GDP growth. This is consistent with the literature emphasizing FDI's role in providing capital, technology transfer, and knowledge spillovers [27,47,50]. The stability of the coefficient across quantiles suggests that FDI benefits are not conditional on the growth stage of the economy, making it a universally beneficial policy priority.

The robustness of these findings underscores the importance of investment (both domestic and foreign) as structural engines of economic expansion in BRICS economies. Investment promotion and FDI attraction should therefore be universal priorities regardless of a country's current growth level [26,27].

5.3. Urbanization and the Transitional Costs of Rapid Urban Growth

Urbanization shows a negative and statistically significant effect at Q25 (−0.096, p < 0.05), Q50 (−0.095, p < 0.01), Q75 (−0.088, p < 0.01), and Q90 (−0.097, p < 0.05). The effect is not significant at Q10 (coefficient = −0.050). This suggests that rapid urbanization imposes transitional costs on growth, reflecting infrastructure deficits, housing shortages, congestion, and environmental degradation [16,51]. The coefficient is small, indicating that the effect is modest in magnitude.

This pattern is consistent with the "urbanization paradox," whereby rapid urban growth can strain resources and infrastructure, temporarily dampening growth. The negative effect at middle-to-high quantiles suggests that the costs of urbanization are most pronounced in economies where urbanization is proceeding most rapidly. Careful urban planning and investment in urban infrastructure are therefore essential to mitigate these transitional costs.

5.4. Trade Openness and Domestic Credit: Weak and Ambiguous Effects

Trade openness coefficients are small and statistically insignificant across all quantiles, ranging from −0.010 to 0.071. The lack of significance suggests that trade integration does not have a robust effect on growth in this sample [9,49]. The fixed effects model, however, shows a positive and significant effect (coefficient = 0.053, p < 0.05), indicating that trade openness may have a modest positive effect when averaged across countries. The weak MMQR results may reflect the mixed effects of trade liberalization: access to technology and markets on one hand, exposure to external shocks on the other.

Domestic credit shows small negative coefficients that are not statistically significant across any quantile (ranging from −0.025 to −0.001). The negative sign, though insignificant, is consistent with the "too much finance" hypothesis, under which excessive financial deepening can crowd out productive investment [59]. Financial sector development in BRICS economies should therefore be managed to ensure it supports rather than displaces productive investment.

5.5. The Energy Rebound Effect in BRICS Economies

The fixed effects estimate in Equation (4) yields a coefficient on ln(Energy Intensity) of 0.7432 (p = 0.0003). Applying Equation (5), the implied rebound effect is (1 − 0.7432) × 100% = 25.68%, with net savings of 74.32%. Approximately one quarter of the energy savings generated by efficiency improvements is therefore offset by increased consumption at the panel level.

This estimate lies at or slightly below the lower bound of the range reported for advanced economies (26–56%; [22]) and below the approximately 35% rebound documented for residential electricity consumption in the European Union [13]. It is also below the roughly 35% estimate reported for India by Roy [39] and well below the backfire conditions identified in Chinese manufacturing by Turner [40]. This pattern is consistent with the income-constraint argument advanced by Lin and Liu [41]: in emerging economies where household and firm budgets remain binding, lower energy-service costs translate into proportionally smaller demand responses than in high-income settings.

At the same time, the estimate is far from zero, confirming that efficiency gains in BRICS economies do not translate fully into aggregate energy savings. Roughly one quarter of intended savings is eroded through rebound channels. Energy efficiency policy in these economies should therefore be designed as a complement to—rather than a substitute for—renewable supply expansion and demand-side regulation.

This finding also distinguishes the present study from Esmail and Yousef [20], who inferred a Jevons-type mechanism from a sign reversal in energy-intensity coefficients across wavelet frequency bands but did not quantify its magnitude. By providing a direct panel estimate, this study fills the empirical gap identified in Section 2.2.

Among the control variables in the rebound specification, trade openness enters negatively and significantly (β = −0.0084, p = 0.0001), suggesting that greater integration into global markets is associated with lower aggregate energy consumption in BRICS economies—consistent with technology diffusion and adoption of more energy-efficient capital goods through trade. Urbanization also enters negatively and is marginally significant (β = −0.0224, p = 0.0569). The coefficients on GDP per capita (β = 0.0248, p = 0.3387), FDI (β = −0.0049, p = 0.6503), and domestic credit (β = −0.0012, p = 0.4389) are not statistically significant at conventional levels. The insignificance of GDP per capita is notable, given that income is typically a robust predictor of energy consumption; this likely reflects absorption of cross-country income differences by the country fixed effects together with the relatively short time dimension of the panel.

5.6. Policy Implications

Based on the empirical findings, we offer the following differentiated policy implications.

5.6.1. For Low-Growth Economies (Q10)

• Prioritize investment. Gross capital formation and FDI are robust drivers of growth across all quantiles and should be the primary focus.
• Address structural constraints. Urbanization challenges imply that urban infrastructure and housing policies should be prioritized.
• Approach renewable energy deployment with caution. The insignificant effect of renewable energy at Q10 suggests that low-growth economies may need to address structural constraints before undertaking large-scale renewable energy investment.

5.6.2. For Middle-Growth Economies (Q25–Q50)

• Prioritize energy efficiency. Energy intensity shows significant positive effects at these quantiles, indicating that efficiency policies yield growth dividends [24,41].
• Support renewable energy investment. Renewable energy share shows significant positive effects at Q50, indicating that investments in this area can support growth.
• Attract FDI. The strong positive effects of FDI indicate that policies to attract foreign investment should be a priority.

5.6.3. For High-Growth Economies (Q75–Q90)

• Prioritize energy efficiency. Energy intensity has the strongest positive effect at Q90, indicating that efficiency policies yield the greatest returns for high-growth economies.
• Continue renewable energy investment. Renewable energy share shows significant positive effects at Q75 and Q90, indicating that such investments can sustain growth.
• Strengthen urban management. The negative urbanization effect at these quantiles indicates that urban planning and infrastructure investment are critical.
• Maintain FDI attraction. The strong positive effects of FDI indicate that policies to attract foreign investment should remain a priority.
• Design efficiency policy with rebound in mind. Because roughly one quarter of efficiency gains is offset by rebound, efficiency measures should be paired with renewable supply expansion and demand-side regulation.

5.7. Limitations and Future Research

This study has several limitations that point to directions for future research.

• the sample is limited to six BRICS economies, which may limit the generalizability of the findings to other emerging markets. Future research should expand the sample to include other emerging economies, such as the BRICS+ members (Iran, Ethiopia, the UAE, and Saudi Arabia) or ASEAN economies.
• the study focuses on macro-level energy indicators; future research could examine sectoral heterogeneity and firm-level mechanisms to provide a more granular understanding of the CE–growth nexus.
• the analysis is limited to the 2000–2025 period; future research could extend the analysis as more recent data become available.
• while the MMQR approach captures distributional heterogeneity, it does not establish causality; future research could employ instrumental variable strategies or quasi-experimental designs to strengthen causal inference [26,27].
• the study does not incorporate geopolitical supply-chain shocks or climate policy uncertainty; future research could explore how these factors moderate the CE–growth relationship [9].
• the rebound-effect estimate is derived from a panel-level elasticity of energy consumption with respect to energy intensity. This approach yields an aggregate, economy-wide rebound measure and does not decompose the effect into direct, indirect, and economy-wide channels, nor does it allow rebound magnitudes to differ across the six BRICS economies. Future research could exploit household survey or sectoral energy-balance data to estimate these channels separately and to test whether rebound heterogeneity mirrors the distributional heterogeneity documented for growth effects.

6. Conclusions

This study examined the heterogeneous effects of circular economy energy transitions on economic growth in six BRICS economies (Brazil, China, India, South Africa, Egypt, and Indonesia) over the period 2000–2025. Using Method of Moments Quantile Regression (MMQR) as the primary estimator, with fixed effects as a robustness check, we uncovered distributional heterogeneity that is masked by mean-based estimators, and we provided a direct estimate of the energy rebound effect for the BRICS panel.

Four principal contributions emerge. First, the effects of CE energy transitions are highly heterogeneous across the growth distribution: gross capital formation and FDI are robust drivers across all quantiles, while renewable energy share and energy intensity show significant positive effects at middle-to-high quantiles (Q50–Q90). Second, investment—both domestic and foreign—emerges as the most robust structural driver of growth across the entire distribution, confirming the continued centrality of capital accumulation in BRICS development. Third, energy intensity exhibits a counterintuitive positive effect, suggesting that rapidly growing economies require higher energy inputs and that the positive effect of economic activity outweighs the negative effect of inefficiency at the panel level. Fourth, the estimated energy rebound effect is 25.68%, implying net savings of 74.32%. While this places BRICS economies at the lower bound of rebound magnitudes reported for advanced economies, it nonetheless indicates that roughly one quarter of efficiency gains are offset by expanded consumption, underscoring the need to pair efficiency policy with supply-side and demand-side measures.

These findings underscore the importance of differentiated policy approaches. Policymakers should tailor circular economy strategies to the growth stage of their economies. Investment promotion and FDI attraction should be universal priorities. Middle- and high-growth economies should prioritize energy efficiency and renewable energy policies. Urban development should be carefully managed to mitigate the transitional costs of rapid urbanization. Finally, because the rebound effect is non-trivial, energy efficiency policy should be treated as a complement to, not a substitute for, renewable energy expansion.

Future research should extend the analysis to other emerging economies, decompose the rebound effect into direct, indirect, and economy-wide channels, and employ identification strategies capable of establishing causality in the CE–growth nexus.