EU carbon pricing and clean energy markets: evidence from cross-quantilogram and multivariate time-varying quantile regression

Abstract

Understanding how regionally determined carbon-pricing signals are transmitted into globally traded clean energy equities is increasingly important as climate policy and financial markets become more integrated. Yet, evidence remains limited on whether these linkages are nonlinear, state-dependent, and heterogeneous across clean energy technologies. This study examines how movements in European Union Emissions Trading System (EU-ETS) futures, a regional carbon market and policy-linked price signal, are reflected in the returns of ten globally listed clean energy subsectors using daily data from 19 October 2010 to 6 July 2024. Using disaggregated NASDAQ OMX Clean Energy subsector indices, the analysis captures how carbon-pricing information originating in the EU is incorporated into globally integrated equity markets. The study combines the Cross-Quantilogram (CQ) and Multivariate Time-Varying Quantile Regression (MTVQR) frameworks to examine directional predictability and conditional impacts, while controlling for financial uncertainty (VIX) and oil-market conditions (Brent crude oil prices). The CQ results show that EU-ETS futures contain significant predictive information for clean energy returns, with nonlinear, asymmetric dependence concentrated on the tails of the distribution. The MTVQR results further show that the conditional impact of carbon-pricing signals varies across market states and technologies. More mature subsectors, such as solar, wind, and smart grid, respond more strongly in weak and normal markets, while capital-intensive and enabling technologies, including biofuels, geothermal, storage, and fuel cells, exhibit stronger upper-tail or nonlinear responses. The findings highlight EU carbon pricing as a forward-looking transition-risk signal with implications for climate policy, portfolio allocation, and transition-risk management.

Introduction

As the global push for decarbonization accelerates, carbon pricing has taken centre stage as a policy lever to drive low-carbon investments and align market behaviour with environmental goals. At the forefront of this shift is the European Union Emissions Trading System (EU-ETS), the world’s most established carbon market, designed to internalise the environmental cost of carbon emissions and provide a dynamic price signal that shapes investment expectations [1, 2]. At the same time, clean energy markets have gained strategic importance as drivers of sustainable growth, innovation, and climate resilience. These markets are inherently global, comprising firms listed across multiple regions, and are increasingly influenced by major carbon pricing regimes such as the EU-ETS, which serves as a benchmark policy signal in international climate finance [3, 4].

Despite this convergence of emissions pricing and clean energy finance, their dynamic interplay remains insufficiently understood, especially under conditions of market stress and policy uncertainty. Earlier studies often relied on linear or mean-based models that overlook how carbon prices interact with different segments of the clean energy market across the return distribution (e.g., [5, 6]). More recent research has begun to address these limitations by employing nonlinear and distribution-sensitive approaches, including quantile-based models, wavelet techniques, and related methods capable of capturing asymmetric dependencies between carbon and energy markets [7–10]. However, even within this growing nonlinear literature, important gaps remain. In particular, relatively little attention has been paid to how EU carbon price shocks propagate across the full joint distribution of globally listed clean energy returns at the subsector level, or to how these relationships evolve across different market regimes using high-frequency data. As geopolitical disruptions, inflationary pressures, and climate policy reforms increasingly affect both carbon and clean energy markets, developing empirical frameworks to capture these tail-dependent, state-contingent transmission mechanisms has become both timely and critical.

Understanding how carbon pricing shapes the behaviour of clean energy markets carries implications that extend well beyond academic debate. Within the EU, the carbon market has become one of the principal channels through which climate policy is reflected in financial decision-making. Prices in the EU-ETS increasingly influence expectations about the pace and credibility of decarbonization, thereby shaping how investors assess risk and value firms operating in low-carbon industries across global financial markets. When signals from carbon prices are transmitted unevenly across clean energy subsectors, the resulting investment responses may diverge from climate policy objectives. In such circumstances, capital may flow disproportionately toward certain technologies, while others essential to the broader energy transition remain underfinanced. These dynamics are particularly important in financial markets where regulatory expectations, technological change, and investor sentiment interact in complex ways. A clearer understanding of how carbon price movements influence different segments of the global clean energy market, therefore, has direct relevance for the design of effective climate policy and for the management of transition-related financial risks. For policymakers, it provides insight into how the EU-ETS can better support long-term decarbonization objectives. For investors and financial regulators, it offers evidence that may improve the assessment of transition risk and guide capital allocation in an increasingly carbon-constrained economy.

Despite the central role of the EU-ETS in Europe’s climate transition, little is known about how carbon price fluctuations are transmitted to specific global clean energy subsectors across different market regimes. Existing studies have made important progress in documenting nonlinear and asymmetric relationships between carbon and energy markets. However, many still rely on aggregate clean energy indices, single-dimensional quantile approaches, or frameworks that do not jointly examine directional predictability and dependence across the distribution. This lack of high-resolution evidence limits policymakers’, investors’, and regulators’ ability to accurately assess transition risks, anticipate market adjustments, and design effective climate–finance instruments. Accordingly, this study asks: How are movements in carbon prices, as proxied by EU-ETS futures, reflected in global clean energy subsector returns? In particular, we explore whether the direction and intensity of this influence vary across bullish, normal, and bearish market states, and how this relationship unfolds over time. Our analysis relies on daily data from 19 October 2010 to 6 July 2024, capturing high-frequency interactions between EU carbon futures and disaggregated clean energy equity indices across ten subsectors from the NASDAQ OMX Clean Energy family, which represents globally listed firms.

To address these gaps, the primary objective of this study is to examine the nonlinear, asymmetric, and quantile-dependent effects of EU-ETS carbon price changes on returns in global clean energy subsectors. Using advanced distribution-sensitive methods, we seek to uncover tail-risk behaviour, lagged dependence, and subsectoral heterogeneity that traditional models overlook. To achieve this, we employ two advanced econometric tools. First, the Cross-Quantilogram (CQ) framework [11] enables us to detect directional dependence across quantiles and time lags, uncovering how shocks in carbon prices predict clean energy returns. Second, the Multivariate Time-Varying Quantile Regression (MTVQR) framework extends this analysis by estimating the conditional impact of EU-ETS returns on clean energy subsector returns across quantiles, while controlling for financial uncertainty and oil market conditions.

Empirically, the study finds that EU carbon pricing is strongly associated with asymmetric and state-dependent movements in global clean energy market returns, with the strength and direction of this effect varying across market conditions and subsectors. Using high-frequency data and quantile-based methods, the results show that extreme movements in carbon prices, both upward and downward, are associated with stronger responses in clean energy markets than moderate changes. These responses are not uniform: subsectors such as solar, storage, and renewable fuels are more sensitive to rising carbon prices, while others, especially those with higher capital intensity, are more vulnerable during downturns. The evidence also reveals lagged and state-dependent transmission, suggesting that, in a predictive sense, clean energy investors respond differently to prevailing regulatory signals and the risk environment. Collectively, the findings underscore the nonlinear and tail-risk nature of the relationship between emissions pricing and green asset performance in globally integrated financial markets.

This study builds on an earlier work on European transition climate risk in clean energy financial markets [12] but advances the analysis in several important ways. The earlier study examined how a composite European transition-risk indicator is priced across international clean energy subsectors and documented asymmetric and nonlinear dependence between transition-risk signals and clean energy returns, using CQ and wavelet cross-quantile correlation techniques. While those findings established that transition-related shocks are reflected in the performance of clean energy assets, the analysis did not isolate the specific market mechanism by which climate policy signals are transmitted to these financial markets, nor did it provide a direct link between observable policy instruments and asset-pricing outcomes.

The present study addresses this limitation by focusing directly on EU-ETS futures as the observable, policy-linked price signal through which climate policy expectations are conveyed. This shift allows the analysis to move beyond identifying general transition-risk pricing toward examining a more specific transmission mechanism: how changes in carbon price signals are reflected in the valuation of clean energy assets and are consistent with changes in investor expectations and perceived transition costs. In this context, the observed nonlinear and state-dependent relationships are not merely statistical features but also reflect variations in the strength and credibility of carbon pricing signals, allowance market conditions, and investor responses across different market environments.

In doing so, the study complements recent nonlinear contributions by combining the CQ approach with MTVQR, thereby enabling a more explicit examination of directional predictability and dependence in the joint distribution of carbon price changes and clean energy returns. Importantly, the analysis is framed around how EU-ETS price movements are transmitted through globally integrated financial markets and reflected in the performance of globally listed clean energy subsectors. By disaggregating the clean energy market into technology-specific segments, the study further shows that this transmission is not uniform. Differences across subsectors can be linked to variations in technological exposure, capital intensity, and sensitivity to policy-driven transition risk, which shape firms’ responses to changes in carbon pricing signals. Using EU-ETS futures alongside high-frequency data, this framework provides more direct evidence of how carbon pricing operates as a transmission channel from EU climate policy to global clean-energy financial markets. In contrast to the earlier study, which captured transition risk in aggregate, the present analysis identifies a clearer economic pathway by which policy signals are formed, interpreted, and incorporated into asset prices. It shows that this process varies systematically across market states and across clean energy technologies.

The remainder of the paper is organised as follows: Sect. "Theoretical framework and literature review" presents a review of relevant literature. Sect. "Methodology and data" outlines the data and methodology. Sect. "Empirical results" reports the empirical findings. Sect. "Conclusion and policy insights" concludes with key insights and policy implications.

Theoretical framework and literature review

Theoretical framework

This study is grounded in a multidisciplinary framework that combines environmental economics, financial market theory, and the economics of policy-driven technological change to explain how carbon pricing signals are transmitted to clean energy markets. At its core are the Polluter Pays Principle (PPP) and the Porter Hypothesis, which provide the economic rationale for emissions pricing mechanisms such as the EU-ETS. These are complemented by insights from financial economics, particularly the Efficient Market Hypothesis (EMH), while also recognising the role of information frictions, heterogeneous expectations, and nonlinear investor behaviour in shaping market outcomes.

The PPP establishes that agents responsible for environmental damage should bear the associated social costs, thereby internalising negative externalities into market decisions [13, 14]. In the EU-ETS, this principle is integrated through a cap-and-trade system that assigns a market price to carbon emissions. This price signal alters relative costs across technologies, discouraging carbon-intensive production while improving the economic viability of low-carbon alternatives. From this perspective, carbon pricing serves as a fundamental driver of structural change in energy systems.

The Porter Hypothesis [15] extends this reasoning by suggesting that well-designed environmental regulation can stimulate innovation and enhance long-term competitiveness. In the context of emissions trading, carbon pricing not only penalises emissions but also encourages firms to invest in cleaner technologies, thereby facilitating the expansion of clean energy sectors. However, the strength and timing of this response depend critically on the credibility and persistence of policy signals, as well as on firms’ expectations about future regulatory conditions.

While these principles explain why carbon pricing should influence clean energy markets, they do not imply a uniform response across all market conditions. From a financial market perspective, the EMH posits that asset prices promptly incorporate available information, including policy signals. In practice, however, the transmission of carbon pricing to asset prices is shaped by information asymmetry, differences in investor beliefs, and changing risk perceptions [16, 17]. These factors introduce nonlinearities into the adjustment process, particularly during periods of heightened uncertainty or market stress. This provides a theoretical basis for expecting differences across the distribution of returns. Investors do not react identically in all market states. In adverse conditions, attention shifts toward downside risk, policy credibility, and business model resilience, leading to greater sensitivity to signals that affect future regulatory or financing conditions. In more favourable market environments, investors may place greater weight on growth opportunities and technological potential, amplifying the impact of positive policy signals. As a result, the influence of carbon pricing is likely to vary across bearish, normal, and bullish states, giving rise to quantile-dependent relationships between carbon prices and clean energy returns.

The global nature of clean energy firms further strengthens this transmission mechanism. Although the EU-ETS is a regional policy instrument, its pricing signals are interpreted and transmitted through globally integrated financial markets. The economic influence of EU carbon pricing on globally listed clean energy equities can be understood through three interrelated transmission channels. The first is the multinational corporate exposure channel. Many firms included in global clean energy indices are multinational, with operations, sales, supply chains, financing arrangements, or strategic market exposure tied to Europe. Since the European Union remains one of the largest markets for renewable energy deployment and climate-related investment, changes in EU carbon prices can alter expected demand for low-carbon technologies [18, 19], shift competitive dynamics between clean and fossil-fuel technologies, and affect expected future profitability for globally operating clean energy firms. Through this mechanism, EU carbon-pricing signals affect firm valuation through expected earnings and growth prospects.

The second is the global carbon-pricing expectations channel. As the world’s largest and most mature emissions trading system, the EU-ETS serves as an international benchmark for climate-policy credibility and regulatory direction [20, 21]. Investors often interpret changes in EU-ETS prices as signals regarding the future tightening, expansion, or convergence of carbon-pricing mechanisms in other jurisdictions. In this sense, EU carbon prices contain informational value beyond Europe, influencing expectations about the future global regulatory environment. This expectation-based mechanism can affect the valuation of clean energy firms worldwide by shaping beliefs about future carbon constraints, market incentives, and low-carbon investment opportunities. The third is the portfolio reallocation and transition-risk channel. Carbon prices function as forward-looking indicators of transition risk, affecting how investors allocate capital between carbon-intensive and low-carbon assets [7, 22]. Rising carbon prices may strengthen expectations of regulatory tightening and increase the relative attractiveness of clean energy firms, thereby encouraging capital inflows into renewable energy assets. Conversely, falling carbon prices may weaken perceptions of policy commitment or delay transition expectations, reducing capital allocation toward clean energy sectors. This mechanism is consistent with financial theories of risk repricing, where investors continuously update asset valuations in response to evolving policy and market signals.

Within this framework, the concept of causality is best understood as predictive economic transmission rather than direct regulatory causation. EU-ETS prices contain forward-looking information about climate-policy stringency, expected compliance costs, technological competitiveness, and the future pace of decarbonization. Investors incorporate this information into their expectations regarding the profitability and risk profile of clean energy firms. As these expectations evolve, past movements in carbon prices inform future clean energy returns through expectation formation, capital reallocation, and earnings revisions. Importantly, this predictive transmission mechanism is not constant but varies across market states and over time, reflecting differences in investor behaviour, policy credibility, and macro-financial conditions.

Given these theoretical considerations, the use of quantile-based methods is well justified. Traditional mean-based models impose a uniform relationship across the distribution and may obscure important asymmetries and tail dynamics. In contrast, quantile-based approaches allow for the examination of how carbon pricing signals are associated with different parts of the return distribution, capturing both extreme downside and upside responses. The CQ framework enables the analysis of directional dependence across quantiles and time horizons. At the same time, the MTVQR approach provides a more detailed assessment of how the conditional effect of EU-ETS returns varies across clean-energy return quantiles, after accounting for broader financial uncertainty and oil-market conditions. Overall, this framework highlights that the relationship between EU carbon pricing and clean energy markets is inherently nonlinear, state-dependent, and driven by expectation formation within a globally integrated financial system. Quantile-dependent effects, therefore, arise naturally from the interaction between policy signals, investor behaviour, and market conditions, providing a coherent theoretical foundation for the empirical analysis that follows.

Literature review

Carbon pricing as a policy signal

Guided by the theoretical framework in Sect. "Theoretical framework", the empirical literature may be understood as examining carbon pricing through two related channels. First, as a policy signal that alters expected transition costs and the relative attractiveness of low-carbon technologies, and second, as a market-state signal whose informational content and valuation effects intensify under stress, optimism, and heightened investor attention. The literature on carbon pricing and clean energy markets has gradually moved from a focus on average effects and market efficiency toward one that recognises asymmetry, tail dependence, and state-contingent transmission. This shift aligns closely with the theoretical framework of this study. At a broad level, existing contributions can be grouped into two complementary perspectives. The first treats carbon prices as a policy signal consistent with the Polluter Pays Principle (PPP) and the Porter Hypothesis, where emissions pricing changes relative production costs, shapes expectations about future regulation, and affects the competitiveness of low-carbon technologies. The second view of carbon prices as a market-state signal reflecting changing investor sentiment, transition risk, and information frictions is more closely aligned with financial-market theories of heterogeneous expectations and nonlinear price adjustment.

From a policy-signal perspective, earlier studies have mainly examined whether carbon-pricing mechanisms, such as the EU-ETS, influence investment incentives, emissions reductions, and firm behaviour. Ellerman and Buchner [23], Martin et al. [24], and Bredin and Parsons [1] show that carbon pricing is not merely a regulatory instrument but a market-based mechanism that shapes expectations about future production costs and the competitiveness of low-carbon technologies. This strand of literature establishes the economic relevance of carbon pricing but focuses mainly on real-sector outcomes or average effects, leaving open the question of how carbon-pricing signals are transmitted into clean energy asset valuations.

Carbon pricing and financial market transmission

A second strand of literature moves more directly into financial market analysis by examining the links among carbon prices, energy assets, and equity markets. Bredin and Muckley [20], Creti et al. [21], and Creti et al. [25] show that carbon prices are linked to broader dynamics in energy and stock markets, with important implications for asset pricing and volatility transmission. These studies are important because they establish carbon pricing as a financial variable with informational value for investors, rather than simply an environmental policy instrument. This perspective is strengthened by Chevallier [2] and Reboredo [3], who argue that carbon-market signals increasingly influence clean-energy asset pricing through expectation formation and portfolio reallocation.

Climate policy uncertainty and clean energy markets

A related and increasingly important strand of literature examines climate policy uncertainty (CPU) as a broader policy-based transmission mechanism. Although distinct from carbon pricing, CPU captures uncertainty surrounding the direction, credibility, and consistency of climate policy, which can shape energy investment decisions in similar ways. Syed et al. [26] show that climate policy uncertainty significantly reduces renewable energy consumption in the United States, mainly because uncertainty delays investment decisions and weakens policy credibility. Their findings highlight that policy-related climate signals do not automatically encourage renewable-energy development,rather, their effects depend on how economic agents interpret policy stability and long-term transition commitment.

Similarly, Hashmi et al. [27] show that climate policy uncertainty has a nonlinear, quantile-dependent effect on energy efficiency, with stronger effects emerging at higher quantiles. This suggests that climate-related policy signals become more economically relevant under stronger market conditions or when adjustment pressures intensify. These contributions are important to the present study because they reinforce the idea that climate policy signals are inherently state-dependent and should be analysed beyond average effects. More importantly, they provide a useful conceptual bridge: while the CPU captures uncertainty around policy direction, carbon prices represent the market-based realisation of those policy expectations. In that sense, EU-ETS futures provide a more direct and tradable signal of climate-policy credibility and transition costs.

Nonlinear and quantile-based evidence

Beyond the policy-signal channel, recent literature increasingly emphasises the nonlinear and state-dependent nature of the relationship between carbon markets and clean energy assets. Traditional linear models often impose a constant relationship across the distribution and may therefore miss important asymmetries. This has led to the growing use of quantile-based approaches. Sim and Zhou [28] introduce the quantile-on-quantile framework to capture dependence across distributions, while later studies, such as Han et al. [11], show that tail dependence often contains stronger predictive content than average dependence. In the context of climate finance and energy markets, these methods have become particularly valuable because they enable analysis of dependence under different market conditions, including periods of extreme upside or downside movements.

Despite these advances, most of the existing literature treats clean energy as a broad aggregate category, overlooking important technological heterogeneity across subsectors. This remains an important limitation because clean energy technologies differ significantly in their capital intensity, maturity, subsidy dependence, commercialisation risk, and market integration. Solar and wind technologies, for example, are relatively mature and directly exposed to carbon-pricing incentives through their substitution relationship with fossil-fuel generation. By contrast, storage, fuel-cell, geothermal, and biofuel technologies involve longer investment horizons, higher capital requirements, and greater commercialisation uncertainty, which may alter how carbon-pricing signals are incorporated into valuations.

To synthesise the literature and clarify the position of the present study, Table 1 classifies prior work along two dimensions: methodological orientation and distributional focus. The first dimension is linear/mean-based versus nonlinear/distribution-sensitive approaches. The second focuses on average-effect studies versus tail- or state-dependent-effect studies. This classification brings out a clear shift in the literature toward nonlinear and tail-sensitive methods, but also shows that an important niche remains underexplored: studies that combine advanced quantile-based tools to see how an explicit carbon-policy signal (EU-ETS futures) predicts and transmits across the full joint distribution of returns for globally listed clean energy subsectors.

Table 1.

Conceptual positioning of the literature on carbon pricing and clean energy markets

Distributional focus / methodological orientation	Linear / mean-based approaches	Nonlinear / distribution-sensitive approaches
Average-effect focus	Early foundational studies examining the average effects of carbon pricing on emissions, firm behaviour, and energy markets. These include Ellerman and Buchner [23], Martin et al. [24], and Bredin and Parsons [1], which focus on mean relationships and aggregate impacts	Studies that examine nonlinear average effects or regime shifts without detailed tail analysis, such as Wang and Zhao [8] and Su et al. [29], allow for time variation and some asymmetry but do not fully explore tail dependencies
Tail / state-dependent focus	Limited studies acknowledge market stress or crisis episodes but rely on linear or mean-based methods (e.g., Aatola et al. [30] and Reboredo [31], which discuss instability but lack full distributional modelling	Recent advances employing quantile regressions, copulas, wavelet coherence, and dual-quantile causality frameworks, including Dutta et al. [7], Zhao et al. [10], and Akadiri and Olasehinde-Williams [32]. These capture asymmetric, tail-dependent, and state-contingent relationships. This study extends this strand by combining the CQ and QQGC methods, focusing on EU-ETS futures and technology-specific subsectors

Research gap

Despite the growing literature on carbon markets, climate policy uncertainty, and clean energy finance, several important gaps remain. First, most existing studies treat clean energy as an aggregate market, overlooking substantial heterogeneity across technologies. This is important because clean energy subsectors differ in maturity, capital intensity, subsidy dependence, commercialisation risk, and transition sensitivity, all of which shape how carbon-pricing signals are incorporated into asset valuations. Aggregate analysis may therefore conceal important technology-specific responses. Second, existing studies largely examine carbon-pricing effects within domestic or regional market settings, implicitly treating the impact of carbon policy as geographically contained. However, this assumption is increasingly difficult to sustain in globally integrated financial markets. Although the EU-ETS is a regional climate policy instrument, its price signals carry broader informational value regarding climate policy credibility, expected transition costs, and future regulatory ambition. These signals can shape investor expectations and capital allocation decisions far beyond Europe, influencing the valuation of globally listed clean energy firms through cross-border portfolio flows and internationally connected equity markets. Yet this regional-to-global transmission mechanism remains largely unexplored in the literature.

Third, while the climate policy uncertainty literature has improved understanding of how policy-related climate signals affect renewable energy and energy efficiency, much less is known about how observable carbon-pricing signals, rather than policy uncertainty itself, affect clean energy asset pricing. This distinction matters because climate policy uncertainty captures uncertainty surrounding future policy direction, whereas carbon prices represent the realised market valuation of those expectations. EU-ETS futures, therefore, provide a more direct and tradable signal of policy credibility and expected transition costs. Fourth, much of the existing evidence relies on average-effect models that assume constant relationships across market conditions. This is restrictive because the economic effect of carbon-pricing signals is unlikely to be constant. Investor responses to carbon-price movements are shaped by market sentiment, financing conditions, and policy credibility, all of which vary across market states. Quantile-based evidence suggests that these effects are often concentrated in the tails of the distribution, yet this nonlinear, state-dependent transmission remains underexplored, particularly at the clean energy subsector level.

Fifth, prior research on European transition climate risk in clean energy financial markets [12] established that broad transition-risk signals are asymmetrically priced across clean energy subsectors. However, that analysis relied on a composite transition-risk measure and therefore could not isolate the specific market mechanism through which climate-policy expectations are transmitted into asset prices. By focusing directly on EU-ETS futures, the present study addresses this limitation by identifying a clearer and more observable transmission channel through which carbon-pricing signals influence investor expectations, perceived transition costs, and clean energy valuations.

Against this background, the study makes four contributions. First, it provides subsector-level evidence on how carbon-pricing signals affect clean energy asset pricing, moving beyond aggregate market analysis. Second, it explains how a regional carbon-pricing mechanism feeds into globally integrated clean-energy financial markets, showing that EU climate-policy signals have financial effects beyond their immediate regulatory boundaries. Third, by focusing directly on EU-ETS futures, it identifies a clearer market-based transmission channel than broader policy uncertainty or composite transition-risk measures. Fourth, by combining the Cross-Quantilogram (CQ) and Multivariate Time-Varying Quantile Regression (MTVQR) frameworks, it captures nonlinear, asymmetric, and state-dependent dependence while accounting for broader financial uncertainty and oil-market conditions. Together, these contributions provide a more precise understanding of how carbon-pricing signals are formed, transmitted, and incorporated into global clean energy valuations.

Methodology and data

Methodology

Understanding the intricate dynamics between carbon emissions pricing and clean energy market behaviour in global financial markets influenced by EU carbon pricing requires econometric tools capable of uncovering complex, asymmetric, and distributionally varying relationships. Standard linear models fall short of capturing the nonlinear dependencies and tail-driven dynamics that characterise financial markets. In this study, we adopt two complementary quantile-based approaches, CQ and MTVQR, to analyse how EU emissions pricing is linked to returns in global clean energy markets represented by internationally listed firms. While the CQ method reveals directional predictability across conditional quantiles and multiple lags, the MTVQR framework estimates the conditional impact of EU-ETS returns on clean energy subsector returns across market states, while controlling for financial uncertainty and oil market conditions. Together, these methods provide a more complete assessment of carbon-pricing transmission by combining dependence mapping with multivariate conditional-effect estimation.

Cross-quantilogram (CQ) approach

Unlike conventional correlation metrics that primarily capture average linear relationships, the CQ approach is particularly well-suited for analysing carbon pricing dynamics in financial markets, as it detects nuanced and asymmetric dependencies across different parts of the distribution [33, 34]. This feature is critical in the context of the EU’s climate transition policies, where abrupt carbon pricing shifts, often triggered by regulatory announcements or energy market shocks, can prompt disproportionate financial responses. Assuming stationarity, the CQ framework examines how the quantiles of carbon price movements relate to those of sector-specific financial indices across various lags. The resulting CQ matrices are visualised using heatmaps, which illustrate how dependence varies across market states. Colour gradients reflect both the strength and direction of the relationship, highlighting how globally listed clean energy markets respond differently to carbon pricing shocks under normal versus turbulent conditions. This makes CQ an essential tool for uncovering hidden channels of risk transmission arising from EU carbon pricing within globally integrated financial markets.

The CQ approach evaluates serial dependence between two events: and for an arbitrary pair of , where the is the α j-th conditional quantile of series . This allows us to investigate directional predictability at specific quantile levels. As established by Han et al. [11], the CQ is defined as the correlation between two quantile-hit processes:

1

Here, is the quantile-overshoot indicator function., where 1{·} denotes the indicator function.

The CQ may be calculated for two different quantile levels, , where α 1 is the carbon price and α 2 is the global clean energy subsector return series. The current iteration of the CQ is specified thus:

2

To establish the statistical significance of , a Ljung-Box style test is employed as described in Han et al. [11]. The test statistic is given as:

3

The null hypothesis for every lag implies no directional quantile dependence, whereas rejection suggests at least one lag exhibits significant dependency.

Multivariate time-varying quantile regression (MTVQR) approach

Although the CQ approach discussed in the preceding subsection establishes the existence, direction, and persistence of quantile dependence between EU carbon pricing and clean energy subsector returns, it is bivariate. It does not account for the effects of other relevant market-wide factors. The response of clean energy assets to carbon-pricing signals is often impacted by broader uncertainty conditions and fluctuations in conventional energy markets. Ignoring these factors may thus distort the actual transmission effect of carbon pricing. To deal with the potential distortionary effect of omitted variable bias, we complement the CQ analysis with the Multivariate Time-Varying Quantile Regression (MTVQR) framework.

The MTVQR approach extends the standard quantile regression model of Koenker and Bassett [35] by incorporating the rolling-window analysis and integrating additional regressors into the conditional quantile analysis [36]. This multivariate extension allows us to test the effect of EU-ETS returns on clean energy subsector returns across different periods and market states, while controlling for broader market uncertainty and energy price dynamics. Specifically, we include the CBOE volatility index (VIX) as a control for global financial market uncertainty. Financial uncertainty, as measured by the VIX, influences investors’ risk appetite and portfolio allocation decisions, particularly in climate-sensitive sectors. Brent crude oil price is also included as a control for conventional energy market conditions. This is because energy prices affect the relative competitiveness of clean energy technologies, as changes in fossil fuel prices influence substitution incentives between dirty and clean energy sources. Controlling for these factors enables us to isolate the net effect of EU carbon-pricing signals on clean energy market returns.

The MTVQR model for each clean energy subsector is specified as:

4

where Y denotes each clean energy subsector return series (GRNAM, GRNBIO, GRNDO, GRNFUEL, GRNGEO, GRNSOLAR, GRNWIND, GRNMAN, GRNSTOR, QGRD). represents the i-th rolling window. refers to the j-th conditional quantile (0 < Q < 1). The term is the time- and quantile-specific intercept. Finally, the coefficients, , , measure the time-varying quantile effects of EU carbon pricing, financial market uncertainty, and oil price movements, respectively.

Data

To investigate the dynamic links between European carbon pricing and the performance of clean energy sectors, we utilise daily data from 19 October 2010 through 6 July 2024. Our focus is on the interplay between the EU carbon price (as reflected in EU-ETS futures) and clean energy stock indices that represent various subsectors of the industry.

The EU-ETS

The EU-ETS is the world’s largest and most established carbon market and represents the central instrument of the EU’s climate policy framework. It operates as a cap-and-trade system in which a limit is placed on total greenhouse gas emissions from covered sectors, and firms can trade emission allowances depending on their compliance needs. By placing a price on carbon, the EU-ETS creates a market-based mechanism that incentivises emissions reductions and promotes investment in low-carbon technologies [2, 37, 38]. Since its introduction in 2005, the EU-ETS has undergone several phases and structural reforms aimed at improving its efficiency and credibility. Early phases were characterised by an excess supply of allowances and relatively low carbon prices, which weakened the policy signal [23, 39]. More recent reforms, particularly the introduction of the Market Stability Reserve (MSR) and tighter emission caps under Phase III and Phase IV, have contributed to a more robust and responsive pricing system. As a result, carbon prices have become more informative, reflecting changes in regulatory expectations, energy market conditions, and macroeconomic activity [40].

Importantly, while the EU-ETS is a regional policy mechanism, its influence extends beyond the EU [39]. Carbon prices under the EU-ETS are widely viewed as a benchmark indicator of climate policy ambition and transition risk [38]. Consequently, fluctuations in EU-ETS prices are closely monitored by global investors and are increasingly incorporated into asset pricing, risk assessment, and portfolio allocation decisions. This makes the EU-ETS not only a compliance tool for regulated firms but also a key signal in globally integrated financial markets, particularly for sectors exposed to the low-carbon transition. We therefore proxy for carbon pricing in the EU using prices from the EU-ETS futures contracts. This futures price reflects the market cost of carbon allowances in the EU’s cap-and-trade system and serves as a benchmark for carbon prices.

The clean energy indices

To capture the performance of clean energy markets, this study employs a set of clean energy indices from the NASDAQ OMX Clean Edge family. These indices track the equity performance of firms involved in various segments of the clean energy industry, including solar, wind, fuel cells, energy storage, biofuels, and related technologies. Importantly, the indices comprise globally listed companies, reflecting the international nature of clean energy production, innovation, and investment [41]. The use of subsector-specific indices enables more granular analysis of clean energy markets. Distinct cost structures, regulatory exposure, and stages of technological maturity characterise different technologies. As a result, the response of clean energy firms to policy signals, including carbon pricing, is likely to vary across subsectors.

These indices provide a market-based representation of how investors value clean energy technologies under evolving economic and policy conditions. Because the underlying firms operate across multiple regions, their performance reflects not only domestic policy environments but also global demand conditions, technological competitiveness, and international capital flows [12]. This global composition is particularly important in the context of this study, as it enables examination of how EU carbon pricing signals are transmitted beyond regional boundaries and incorporated into the valuation of clean energy assets worldwide. According to the index provider, the NASDAQ OMX Clean Energy indices can be grouped into four broad categories (as summarised in Table 2 of our study) covering a total of 10 distinct clean energy subsector markets. These indices represent globally listed clean energy firms, enabling analysis of how EU carbon pricing signals are transmitted across international financial markets.

Table 2.

NASDAQ OMX clean energy index

Category	Index	Symbol	Description
Advanced materials	NASDAQ OMX ADVANCED MATERIALS	GRNAM	Includes companies that manufacture components supporting renewable energy advancement or reducing reliance on fossil fuels
Bio/clean fuels	NASDAQ OMX BIO/CLEAN FUELS INDEX	GRNBIO	Includes firms producing biofuels as alternatives to traditional petroleum-based transport fuels
Renewable energy	NASDAQ OMX DEVELOPER/OPERATOR	GRNDO	Encompasses firms that develop and manage projects powered by renewable sources such as solar and wind
	NASDAQ OMX FUEL CELL	GRNFUEL	Covers energy providers utilizing fuel cell technology to generate electricity
	NASDAQ OMX GEOTHERMAL	GRNGEO	Represents firms focused on geothermal-based energy generation
	NASDAQ OMX SOLAR	GRNSOLAR	Tracks companies engaged in the production of solar-based electricity
	NASDAQ OMX WIND	GRNWIND	Covers firms involved in harnessing wind energy for power generation
Energy efficiency	NASDAQ OMX ENERGY MANAGEMENT	GRNMAN	Focuses on firms offering technologies to enhance energy efficiency, including control systems and high-efficiency motors
	NASDAQ OMX ENERGY STORAGE	GRNSTOR	Includes businesses developing battery technologies and other energy storage innovations
	NASDAQ OMX SMART GRID	QGRD	Tracks companies improving grid efficiency and smart capabilities through innovative modernization technologies

The availability of data on clean energy indices determines our sample period. The NASDAQ OMX Clean Energy indices began trading in October 2010, so we start our analysis on 19 October 2010, which is the earliest date for which all series are available. We include daily observations up to mid-2024 (in line with the latest data, approximately through July 2024), yielding a rich time series of daily returns. All price series (for carbon and each clean energy subsector index) are converted into daily log returns. This transformation to returns mitigates issues of nonstationarity and differing units, allowing us to interpret the connectedness in terms of percentage price changes. All data used for empirical analyses were obtained from Investing.com.

The summary statistics in Table 3 provide important insights into the distributional and time-series properties of EU-ETS futures and clean energy subsector returns. On average, all clean energy subsector return series have a mean of zero, which is typical for daily financial returns, whereas the EU-ETS series has a small positive mean. Variance is notably higher in the EU-ETS series, indicating greater volatility than in the clean energy subsectors. Most of the series are negatively skewed, implying a tendency toward more extreme negative returns, except GRNGEO and GRNFUEL, which display slight positive skewness. Excess kurtosis values are significantly different from zero for all series, suggesting fat tails and deviations from normality, a result reinforced by the highly significant Jarque–Bera statistics. The Elliot-Rothenberg-Stock (ERS) test results confirm stationarity across all return series, with all test statistics significant at the 1% level. Furthermore, the Ljung-Box Q(10) and Q²(10) tests detect significant autocorrelation and volatility clustering in the return and squared return series, respectively. These findings collectively validate the need for models that accommodate non-normality and serial dependence in assessing the link between carbon pricing and clean energy markets. Additional information on the data trends is also visualised in Fig. 1.

Table 3.

Statistical properties of variables

	EU ETS	GRNDO	QGRD	GRNSTOR	GRNMAN	GRNWIND	GRNSOLAR	GRNGEO	GRNFUEL	GRNBIO	GRNAM
Mean	0.016	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000
Variance	1.154	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.001	0.000	0.000
Skewness	-1.041a	-1.239a	-0.770a	-0.221a	-0.342a	-0.327a	-0.384a	0.374a	0.374a	-0.780a	-0.429a
Ex. Kurtosis	22.090a	22.738a	12.143a	3.149a	8.797a	4.301a	5.512a	12.262a	4.788a	10.474a	5.782a
JB	72,141.876a	76,795.043a	21,992.793a	1484.221a	11,427.844a	2778.470a	4547.070a	22,154.530a	3447.298a	16,460.089a	5015.939a
ERS	-21.041a	-8.675a	-5.968a	-25.459a	-23.560a	-24.760a	-17.560a	-23.866a	-26.090a	-10.866a	-24.998a

(1) Ex. Kurtosis, JB, and ERS denote the statistics for excess kurtosis, the Jarque–Bera test for normality, and the stationarity test of Elliot et al. [46], respectively. (2) ^a denotes statistical significance at 1%

Fig. 1.

Trends of EU-ETS and clean energy markets returns series

Empirical results

Nonlinear dependence

Before applying the CQ and MTVQR frameworks, both designed to capture nonlinear, asymmetric, and quantile-dependent dynamics, it is essential to evaluate whether the underlying data exhibit characteristics that justify their use. In this context, the Brock–Dechert–Scheinkman (BDS) test is employed as a diagnostic tool to assess whether the return series for EU carbon futures and clean energy subsectors deviate from the standard assumption of independently and identically distributed (i.i.d.) behaviour.

The results of the BDS test, presented in Table 4, reveal strong and consistent rejection of the i.i.d. null hypothesis at the 1% significance level across all series and embedding dimensions (2–6). This suggests the presence of complex, nonlinear dependencies in the data, precisely the type of structure that traditional linear models are ill-equipped to handle. These findings provide empirical validation for the methodological choice to employ CQ and MTVQR, which are better suited to detecting directional predictability and tail-dependent co-movements between carbon pricing and clean energy markets. By confirming the data’s nonlinearity, the BDS test strengthens the case for analysing these relationships within a quantile-based framework.

Table 4.

BDS test results

Variables	Dimensions
	2nd	3rd	4th	5th	6th
EU ETS	0.067a	0.141a	0.201a	0.245a	0.276a
GRNAM	0.010a	0.024a	0.033a	0.039a	0.040a
GRNBIO	0.015a	0.033a	0.049a	0.058a	0.064a
GRNDO	0.017a	0.036a	0.049a	0.056a	0.059a
GRNMAN	0.017a	0.036a	0.050a	0.059a	0.063a
GRNSTOR	0.013a	0.031a	0.044a	0.052a	0.054a
GRNFUEL	0.016a	0.034a	0.046a	0.053a	0.055a
GRNGEO	0.025a	0.050a	0.066a	0.073a	0.075a
GRNSOLAR	0.013a	0.027a	0.037a	0.043a	0.045a
GRNWIND	0.012a	0.025a	0.033a	0.038a	0.040a
QGRD	0.015a	0.034a	0.048a	0.055a	0.058a

(1) ^a denotes statistical significance at 1%

Nonlinear unit root test

Given the nonlinear dynamics observed in the return series, confirmed through the BDS test results, this study departs from conventional linear unit root testing and instead applies the nonlinear unit root test based on the Exponential Smooth Transition Autoregressive (ESTAR) model developed by Kapetanios et al. [42]. This approach is particularly appropriate for the current analysis, as it can detect subtle forms of nonstationarity and nonlinear mean-reverting behaviour that standard linear tests may overlook. The ESTAR framework is well-suited to modelling smooth transitions and regime shifts, which are likely to arise in markets influenced by evolving climate policy signals and sectoral responses.

The results, presented in Table 5, indicate that the null hypothesis of a unit root is rejected for all return series at their levels. These outcomes suggest that the EU-ETS returns and the clean energy subsector returns are stationary despite nonlinear adjustment processes. The analysis utilises the Schwarz Information Criterion (SIC) to determine the lag structure. Alternative selection methods, such as the Akaike Information Criterion (AIC) and general-to-specific procedures (at 5% and 10% levels), yield similar results and are thus not reported. This confirmation of stationarity under nonlinear conditions is crucial for the validity of the subsequent empirical strategy. Both the CQ and MTVQR techniques rely on stationary series to accurately capture tail-dependent, distribution-sensitive, and asymmetric relationships between EU carbon pricing and clean energy market performance. The nonlinear ESTAR test thus provides a robust foundation for the quantile-based modelling framework adopted in this study.

Table 5.

ESTAR unit root test results

NBR
Criteria	Test. Stat	P-value	1% CV	5% CV	10% CV
EU-ETS	-8.650a	0.000	-3.478	-2.930	-2.652
GRNAM	-23.196a	0.000	-3.481	-2.934	-2.655
GRNBIO	-22.394a	0.000	-3.481	-2.934	-2.655
GRNDO	-19.617a	0.000	-3.481	-2.934	-2.655
GRNMAN	-17.043a	0.000	-3.481	-2.934	-2.655
GRNSTOR	-21.819a	0.000	-3.481	-2.934	-2.655
GRNFUEL	-19.009a	0.000	-3.481	-2.934	-2.655
GRNGEO	-15.610a	0.000	-3.481	-2.934	-2.655
GRNSOLAR	-20.000a	0.000	-3.481	-2.934	-2.655
GRNWIND	-15.932a	0.000	-3.481	-2.934	-2.655
QGRD	-16.596a	0.000	-3.481	-2.934	-2.655

(1) ^a denotes statistical significance at 1%

Correlation analysis

Before moving into advanced quantile-based techniques such as the CQ and MTVQR, it is important to establish a preliminary understanding of the linear dependence structure among the variables of interest. A simple Pearson correlation analysis provides a foundational perspective on how EU carbon prices and clean energy subsector returns co-move on average. While correlation does not imply causation or account for nonlinear or tail-dependent dynamics, it serves as a valuable diagnostic to identify general patterns of association and to inform expectations about potential transmission channels between carbon pricing and different segments of the clean energy market.

As shown in the correlation matrix, the linear association between EU-ETS returns and clean energy returns is generally weak but positive and statistically significant at conventional levels. The highest correlation with EU-ETS returns is observed in GRNMAN, followed by moderate associations with GRNAM and GRNSTOR. These results suggest that some subsectors may be more responsive to carbon-pricing signals than others, though the relatively low magnitudes highlight the limitations of linear measures. In contrast, interdependencies among clean energy subsectors themselves are much stronger, highlighting shared exposures to technological and policy drivers. These insights validate the next step of the analysis, which employs nonlinear and distribution-sensitive tools to capture more complex, asymmetric relationships that linear correlations may obscure Fig. 2.

Fig. 2.

Correlation matrix

Cross-quantilogram results

To assess the dynamic and distributional dependence between the EU-ETS and global clean energy subsectors, we apply the CQ approach across multiple temporal lags, specifically at daily (1-day), weekly (5-day), and monthly (22-day) intervals. These lag structures are selected to capture the heterogeneous speed at which carbon price signals are incorporated into financial markets. The 1-day lag reflects immediate market reactions and short-term trading behaviour, in which new information on carbon pricing is rapidly incorporated into clean energy equities. The 5-day lag approximates a weekly adjustment horizon, capturing short-run portfolio rebalancing and the response of institutional investors who update positions based on evolving market and policy signals. The 22-day lag represents a monthly horizon, allowing assessment of more persistent adjustments driven by medium-term expectations, regulatory developments, and capital allocation decisions. These horizons provide a comprehensive framework for examining how EU carbon pricing signals propagate through global clean energy markets over different time scales, from high-frequency reactions to more gradual, expectation-driven adjustments.

The results are generated as heatmaps, with colour intensity indicating the strength and direction of the dependence: red for positive dependence and blue for negative dependence. This enables a comprehensive examination of the lead-lag structures between carbon pricing and clean energy markets, offering insights into whether and how past variations in carbon pricing, proxied by EU-ETS returns, can predict clean energy sector performance over different investment horizons. While the detailed heatmaps are presented (Figs. 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12) for specific subsectors (GRNAM, GRNBIO, GRNDO, GRNFUEL, GRNGEO, GRNSOLAR, GRNWIND, GRNMAN, GRNSTOR, QGRD), a generalizable and consistent pattern emerges across the broader clean energy spectrum. Specifically, when EU-ETS returns fall in the lower quantiles (e.g., 0.05 to 0.25), indicative of declining carbon prices, a negative dependence (blue patches) is typically observed with higher quantiles of clean energy returns, and a positive dependence (red patches) is often observed with their lower quantiles. On the other hand, when EU-ETS returns are in the upper quantiles (e.g., 0.75–0.95), reflecting rising carbon prices, the reverse pattern prevails. Positive dependence (red hues) with higher clean energy quantiles and negative dependence (blue hues) with lower ones. These asymmetric dependencies underscore the risk-return asymmetry that characterises climate-sensitive sectors and suggest that carbon market signals are priced heterogeneously across the clean energy return distribution.

Fig. 3.

Cross-quantilogram (EU-ETS → GRNDO)

Fig. 4.

Cross-quantilogram (EU-ETS → QGRD)

Fig. 5.

Cross-quantilogram (EU-ETS → GRNSTOR)

Fig. 6.

Cross-quantilogram (EU-ETS → GRNMAN)

Fig. 7.

Cross-quantilogram (EU-ETS → GRNWIND)

Fig. 8.

Cross-quantilogram (EU-ETS → GRNSOLAR)

Fig. 9.

Cross-quantilogram (EU-ETS → GRNGEO)

Fig. 10.

Cross-quantilogram (EU-ETS → GRNFUEL)

Fig. 11.

Cross-quantilogram (EU-ETS → GRNBIO)

Fig. 12.

Cross-quantilogram (EU-ETS → GRNAM)

Notably, these dependence structures exhibit strong temporal consistency across lags. At short (1-day), medium (5-day), and longer-term (22-day) intervals, the same directional patterns of association generally hold, albeit with some amplification or attenuation in intensity. This temporal persistence suggests that markets do not fully adjust to carbon price signals immediately; instead, they react over a range of horizons, possibly reflecting staggered portfolio rebalancing or institutional information diffusion processes.

From a statistical standpoint, the CQ methodology robustly identifies significant tail dependencies that are otherwise undetectable using linear or mean-based techniques. These dependencies are asymmetric and vary across both the conditional quantiles of the EU-ETS and the clean energy subsectors [32, 43]. Economically, the results suggest that carbon pricing dynamics serve as a transition-risk indicator, exhibiting a nonlinear, quantile-specific association with the performance of clean energy firms. When carbon prices decline, potentially signalling weaker climate policy expectations or increased regulatory uncertainty, the predictive patterns are consistent with a reallocation away from more sensitive or high-performing clean energy segments, which is reflected in weaker performance in the upper quantiles. Simultaneously, lower-performing firms may benefit from lower transition expectations, as reflected in positive movements in their lower-quantile returns. When carbon prices rise, however, signalling strengthened climate action and more binding emission caps, the results are consistent with capital flowing toward mid- to high-performing clean energy firms, particularly those well-positioned to benefit from carbon abatement opportunities. Moreover, our results provide new insights by showing that the strength and direction of dependence are not only quantile- and sector-specific but also temporally robust across different horizons. This offers a richer understanding than commonly used linear models, which often miss tail effects and asymmetric transmission.

Multivariate time-varying quantile regression (MTVQR) results

The MTVQR results provide a more robust multivariate assessment of the carbon-pricing channel because they estimate the EU-ETS effect after accounting for broader market uncertainty (VIX) and oil-market conditions (Brent). Figures 13, 14, 15, 16, 17, 18, 19, 20, 21 and 22 show that the effect of EU-ETS on clean energy returns differs across subsectors, market conditions, and time. The average slope patterns show that this effect is rarely constant across the return distribution. Instead, most subsectors display either gradual changes or clear nonlinear shifts across quantiles. This shows that EU carbon-pricing signals are not absorbed in the same way across clean energy stocks, but are interpreted differently depending on whether market conditions are weak, stable, or strong.

Fig. 13.

MTVQR (EU-ETS → GRNDO|VIX, BRENT)

Fig. 14.

MTVQR (EU-ETS → QGRD|VIX, BRENT)

Fig. 15.

MTVQR (EU-ETS → GRNSTOR|VIX, BRENT)

Fig. 16.

MTVQR (EU-ETS → GRNMAN|VIX, BRENT)

Fig. 17.

MTVQR (EU-ETS → GRNWIND|VIX, BRENT)

Fig. 18.

MTVQR (EU-ETS → GRNSOLAR|VIX, BRENT)

Fig. 19.

MTVQR (EU-ETS → GRNGEO|VIX, BRENT)

Fig. 20.

MTVQR (EU-ETS → GRNFUEL|VIX, BRENT)

Fig. 21.

MTVQR (EU-ETS → GRNBIO|VIX, BRENT)

Fig. 22.

MTVQR (EU-ETS → GRNAM|VIX, BRENT)

A first and dominant group includes renewable developers/operators (GRNDO), smart-grid firms (QGRD), energy-management firms (GRNMAN), wind-energy firms (GRNWIND), solar-energy firms (GRNSOLAR), and advanced-material firms (GRNAM). These subsectors show a broadly similar pattern: the EU-ETS effect is positive at the lower-to-middle quantiles but turns negative at the upper quantiles. This suggests that carbon-pricing signals are most supportive when these sectors are under pressure or performing at normal levels. The economic logic is simple: higher carbon prices raise the cost of fossil-fuel energy, making renewable technologies and efficiency solutions more attractive. In weaker markets, investors interpret rising carbon prices as a sign of stronger climate policy and stronger future demand, which supports valuations. But when these sectors are already performing strongly, much of that benefit may already be reflected in stock prices. At that point, additional carbon-price increases can raise concerns about higher project costs, financing pressures, and valuation risks. This reversal is stronger in solar (GRNSOLAR) and wind (GRNWIND), where expansion depends heavily on policy support and capital-intensive investment, whereas the decline is milder in smart-grid (QGRD) and energy-management (GRNMAN) firms, as their revenues depend more on infrastructure upgrades and efficiency improvements.

A second group consists of biofuel firms (GRNBIO) and geothermal firms (GRNGEO), both of which show a negative-to-positive pattern across the quantiles. This means that carbon-pricing signals have weaker or negative effects when markets are weak, but stronger positive effects when market conditions improve. The economic intuition is that both biofuel and geothermal investments are long-term and highly capital-intensive, making investors more cautious in weak market conditions. In these states, higher carbon prices may not be enough to offset concerns about project costs, long payback periods, and technology risks. However, when market conditions strengthen and investor confidence improves, rising carbon prices reinforce the long-run profitability of these technologies by enhancing their competitiveness relative to fossil fuels. This explains why the positive effects become stronger in the upper quantiles.

The third group includes energy-storage firms (GRNSTOR) and fuel-cell firms (GRNFUEL), which show more mixed and nonlinear responses. These subsectors do not move in one clear direction across market states because of their strategic role in supporting the broader clean-energy transition. Storage technologies are critical for balancing intermittent renewable supply, while fuel-cell technologies support industrial decarbonization and energy diversification. Their value becomes more visible during market extremes. In weaker markets, higher carbon prices strengthen expectations of future renewable expansion, increasing the expected need for storage and fuel-cell systems. In stronger markets, the same carbon-pricing signals reinforce expectations of faster transition and wider technology adoption. Their weaker middle-quantile effects suggest that in normal market conditions, investors remain cautious and focus more on commercialisation risks, capital intensity, and uncertain profitability.

Overall, the MTVQR results reveal a clear economic divide across clean energy subsectors. More mature and commercially established sectors, such as solar, wind, smart grid, energy management, renewable developers, and advanced materials, benefit most from carbon-pricing signals when markets are weak or stable, but less when optimism is already high. By contrast, more specialised and capital-intensive technologies, such as biofuels and geothermal, benefit more when market confidence strengthens, while strategic enabling technologies, such as storage and fuel cells, respond most strongly during market extremes. These findings strengthen the CQ evidence by showing that EU carbon-pricing signals remain an important and independent driver of clean energy returns even after controlling for uncertainty and oil-market conditions, but their effect depends strongly on market conditions and the economic structure of each clean-energy technology.

Discussion of findings

The findings from the CQ and MTVQR analyses provide a consistent picture of how EU carbon-pricing signals are transmitted into global clean energy equity markets. The results show that this transmission is not linear or uniform. Instead, it is asymmetric, state-dependent, and varies considerably across clean energy technologies. While the CQ framework establishes the existence and direction of quantile dependence across different market states and time horizons, the MTVQR results strengthen this evidence by showing that these relationships remain robust even after controlling for broader financial uncertainty and oil-market conditions. This is important because it suggests that the observed dependence is not simply a reflection of broader market movements but rather captures an independent carbon-pricing channel operating through investor expectations and transition-risk repricing. The combined evidence supports the view that EU-ETS prices function as a forward-looking policy signal that shapes how global investors value clean energy assets [2–4].

A key result from both approaches is that the influence of carbon-pricing signals differs sharply across market states. For a large group of more established clean energy subsectors, including solar (GRNSOLAR), wind (GRNWIND), renewable developers/operators (GRNDO), smart-grid firms (QGRD), energy-management firms (GRNMAN), and advanced materials (GRNAM), higher carbon prices are associated with stronger returns in weak and normal market conditions, but weaker or negative effects when market conditions are already strong. This pattern reflects the economic role of carbon pricing in improving the competitiveness of low-carbon technologies relative to fossil fuels. In weaker market conditions, rising carbon prices strengthen expectations of tighter climate policy and stronger future clean-energy demand, supporting valuations. This is consistent with the Porter Hypothesis, which argues that environmental regulation can stimulate innovation and strengthen long-run competitiveness [15]. However, when these sectors are already performing strongly, much of this policy benefit appears to have been priced in. At that stage, further increases in carbon prices can shift investor attention toward project costs, financing burdens, and valuation risks. This helps explain why the positive effect weakens or reverses at the upper tail, consistent with financial repricing mechanisms under the Efficient Market Hypothesis.

A different pattern emerges for biofuels (GRNBIO) and geothermal (GRNGEO). For these subsectors, the effect of EU carbon pricing is weaker or negative in lower market states but becomes increasingly positive as market conditions strengthen. This suggests that these technologies require a stronger investment environment before the benefits of carbon pricing are fully reflected in valuations. Both sectors are characterised by high capital intensity, longer development cycles, and greater uncertainty around commercial scaling. In weak markets, investors may remain cautious despite stronger carbon-pricing signals. But when market confidence improves, carbon pricing strengthens the economic case for these technologies by enhancing their long-run competitiveness relative to fossil fuels. This interpretation is consistent with the idea that policy credibility and long-term carbon constraints influence investment incentives more strongly when financing conditions improve [1].

The response is even more nonlinear for energy storage (GRNSTOR) and fuel cells (GRNFUEL). These subsectors occupy a strategic position in the energy transition because they support system flexibility, energy diversification, and industrial decarbonization. Their stronger tail dependence suggests that carbon-pricing signals matter most during market extremes. In weak markets, higher carbon prices strengthen expectations of future renewable expansion, increasing the strategic value of storage and fuel-cell systems. In strong markets, the same carbon-pricing signals reinforce expectations of faster transition and wider technology adoption. This explains why their responses are concentrated around market extremes rather than normal market states. This nonlinear response reflects broader transition-risk repricing, where investors update expectations more aggressively under conditions of stress or accelerated transition [7, 22]. These differences across subsectors reveal an important economic divide. More mature clean energy technologies respond more immediately to carbon-pricing signals because their business models are already closely tied to renewable deployment and policy support. By contrast, more specialised and capital-intensive technologies require stronger market confidence before investors fully price in their long-term benefits. This helps explain why the transmission of carbon-pricing signals is not uniform across the clean energy market and supports the view that technological maturity and capital structure shape the speed and strength of policy transmission.

More broadly, the results support interpreting EU carbon pricing as a transition-risk signal rather than simply a compliance-cost indicator [7, 22]. Changes in EU-ETS prices affect investor expectations about policy credibility, future carbon constraints, and the pace of decarbonization. These expectations shape capital allocation decisions across clean energy technologies, but the strength of that effect depends on market conditions and technology-specific investment dynamics. The concentration of dependence in the tails of the distribution also highlights that carbon-pricing effects are strongest during periods of market stress or rapid market adjustment, reinforcing the importance of quantile-based approaches for capturing these nonlinear dynamics.

Overall, the findings suggest that EU carbon pricing increasingly functions as an international benchmark for climate-policy credibility, with effects that extend well beyond Europe through globally integrated financial markets. What matters is not simply the level of carbon prices, but how investors interpret those price signals under different market conditions and how they shape capital flows across clean energy technologies. This highlights the broader role of carbon pricing in influencing not only emissions reductions, but also the direction and pace of clean-energy investment worldwide [3, 4].

Conclusion and policy insights

Conclusion

This study investigates the asymmetric and quantile-dependent relationship between European carbon emissions pricing, proxied by EU-ETS futures, and the performance of clean energy markets, utilising the CQ and MTVQR methods. These methods enable a comprehensive assessment of nonlinear, distribution-sensitive, and state-dependent interactions, particularly during extreme market conditions. Relying on daily data spanning from October 2010 to July 2024, we examine the interconnectedness between EU-ETS carbon futures and sector-specific clean energy stock indices from the NASDAQ OMX Clean Energy family. Our findings provide compelling evidence that emissions pricing is strongly associated with clean energy subsector returns, with the strength and direction of this relationship varying across quantiles, market conditions, and subsectors.

The CQ analysis uncovers significant directional dependence across different parts of the joint distribution, indicating a time-varying predictive transmission channel between carbon pricing and clean energy investments. The results show that extreme changes in carbon prices, both upward and downward, contain stronger predictive information for clean energy returns than moderate fluctuations. This pattern is especially pronounced in subsectors with stronger exposure to policy signals and technological deployment, such as solar, wind, and renewable developers. The MTVQR results strengthen this evidence by showing that the conditional impact of EU-ETS returns remains significant even after accounting for broader financial uncertainty and oil-market conditions. More importantly, the results reveal substantial heterogeneity across subsectors, reflecting differences in technological maturity, capital intensity, financing requirements, and transition-function roles.

Overall, the findings suggest that EU carbon pricing increasingly functions as a forward-looking transition-risk signal, with financial relevance extending beyond Europe through globally integrated capital markets. The results further show that the transmission of carbon-pricing signals into clean energy asset valuations depends not only on market conditions but also on the economic structure and transition role of each clean energy technology.

Policy insights

The findings of this study indicate that the policy relevance of carbon pricing extends beyond the conventional view that higher and more stable carbon prices uniformly support clean energy investment. Instead, EU-ETS price movements are associated with differentiated effects across global clean energy subsectors, market conditions, and return states. This suggests that carbon pricing operates as a state-dependent policy signal reflected through globally integrated financial markets rather than being confined to European economic stabilisation.

The first implication concerns the design of carbon market stabilisation mechanisms. The results show that extreme movements in EU-ETS prices have disproportionately strong predictive and valuation effects on global clean energy subsectors, particularly during periods of market stress or heightened optimism. This implies that the policy challenge is not only the level of carbon prices but also the stability of the signal they generate. Large price swings can alter market expectations and amplify financial volatility across clean energy sectors. Mechanisms such as the Market Stability Reserve should therefore be assessed not only in terms of emissions control but also for their role in stabilising climate-policy signals and supporting long-term investment planning.

A second implication is that carbon pricing alone may not generate balanced investment incentives across all clean energy technologies. The results reveal substantial heterogeneity across subsectors, with mature technologies such as solar, wind, and renewable developers responding differently from more capital-intensive or enabling technologies such as geothermal, storage, and fuel cells. This implies that while carbon pricing may accelerate investment in commercially established technologies, it may be less sufficient for technologies with longer commercialisation horizons or higher financing barriers. Policymakers should therefore complement carbon pricing with targeted support mechanisms to ensure broader technological diversification within the energy transition.

A third implication relates to the management of transition risk in financial markets. The concentration of dependence in the tails of the distribution suggests that carbon-pricing signals become most influential during periods of financial stress or rapid market adjustment. This has important implications for financial regulators and central banks. Climate stress-testing frameworks should incorporate carbon-price shocks into transition-risk assessment, particularly for portfolios with significant exposure to clean-energy assets.

A fourth implication arises from the regional-to-global transmission of EU-ETS signals. Although the EU-ETS is a regional climate-policy instrument, the findings show that its price signals are incorporated into the valuation of globally listed clean energy firms through internationally integrated financial markets. This means that changes in EU carbon-pricing conditions can generate financial spillovers beyond Europe by shaping expectations about climate-policy credibility, future transition costs, and regulatory tightening. For policymakers, this implies that the effects of regional carbon-pricing reforms are not geographically contained. Policy changes within the EU can influence clean energy financing conditions, investment incentives, and asset valuations across global markets. This strengthens the case for greater international coordination in carbon-pricing design and clearer long-term policy communication, since the credibility of regional carbon markets increasingly carries global financial consequences.

Finally, the findings highlight the importance of differentiated investment strategies. Since carbon-pricing signals are transmitted unevenly across clean energy subsectors, investors should avoid treating clean energy as a homogeneous asset class. Instead, portfolio strategies should account for differences in technological maturity, capital intensity, and market-state sensitivity to improve resilience under changing climate-policy conditions.

Future studies

Future studies could expand this research by incorporating other green financial instruments, such as green bonds, sustainability-linked derivatives, or renewable energy ETFs, to evaluate whether EU emissions pricing affects broader sustainable finance markets. Comparative analyses across different emissions trading schemes, including China’s ETS and California’s cap-and-trade system, could shed light on how institutional contexts shape market reactions. In addition, future work could explore alternative carbon market proxies, such as EUA spot prices, auction volumes, or allowance market stress indicators, to assess whether the transmission of carbon pricing signals to clean energy markets remains consistent across different representations of the carbon market. Employing intraday data may uncover microstructural market responses to carbon shocks, especially during policy announcements or carbon auctions. Additionally, incorporating investor sentiment, ESG disclosure quality, or climate risk perceptions could illuminate the behavioural drivers behind the observed asymmetric responses. Finally, advanced models, such as machine learning and time-varying copulas, may offer deeper insights into evolving nonlinear dependencies and regime shifts under extreme market conditions.

Author contributions

SSA: Writing – review & editing, Writing – original draft, Supervision, Project administration. GO: Conceptualisation; Software, Methodology, Resources, Data curation.

Funding

The authors did not receive any funding for this study.

Data availability

Data will be made available upon request.

Declarations

Ethics approval and consent to participate

The Authors mentioned in the manuscript have agreed to authorship, read and approved the manuscript, and provided consent for submission and publication.

Competing interests

The authors declare no competing interests.