From Policy to Prices: How Carbon Markets Transmit Shocks Across Energy and Labor Systems

Abstract

This paper examines the changing role of emissions trading systems (ETSs) within the macro-financial framework of energy markets, emphasizing price dynamics and systemic spillovers. Utilizing monthly data from seven ETS jurisdictions spanning January 2021 to December 2024 (N = 287 observations after log transformation and first differencing), which includes four auction-based markets (United States, Canada, United Kingdom, South Korea), two secondary markets (China, New Zealand), and a government-set fixed-price scheme (Germany), this research estimates a panel vector autoregression (PVAR) employing a Common Correlated Effects (CCE) model and augments it with machine learning analysis utilizing XGBoost and explainable AI methodologies. The PVAR-CEE reveals numerous unexpected findings related to carbon markets: ETS returns exhibit persistence with an autoregressive coefficient of −0.137 after a four-month lag, while increasing inflation results in rising ETS after the same period. Furthermore, ETSs generate spillover effects in the real economy, as elevated ETSs today forecast a 0.125-point reduction in unemployment one month later and a 0.0173 increase in inflation after two months. Impulse response analysis indicates that exogenous shocks, including Brent oil prices, policy uncertainty, and financial volatility, are swiftly assimilated by ETS pricing, with effects dissipating completely within three to eight months. XGBoost models ascertain that policy uncertainty and Brent oil prices are the most significant predictors of one-month-ahead ETSs, whereas ESG factors are relevant only beyond certain thresholds and in conditions of low policy uncertainty. These findings establish ETS markets as dynamic transmitters of macroeconomic signals, influencing energy management, labor changes, and sustainable finance under carbon pricing frameworks.

1. Introduction

Emissions trading systems (ETSs) have evolved into foundational mechanisms for decarbonization policy, aiming to internalize the externalities of greenhouse gas (GHG) emissions through market-based incentives [1]. Empirical evidence confirms the effectiveness of ETSs in reducing emissions by approximately 2–2.5% per year between 2005 and 2020 [2]. As carbon markets grow in scale, maturity, and complexity, understanding how ETS prices evolve and how they interact with broader economic and financial variables has become a critical area of research for both climate policy and energy management [3,4,5].

The available studies on the main factors affecting the changes in ETS prices are still providing conflicting data. There are still disagreements over energy, finance, policy, social, and economic factors. For example, according to Mo & Wang [6], higher Brent oil prices tend to increase permit demand and carbon costs in businesses and nations that depend on oil for their functioning. But this relationship weakens in areas that are reliant on coal or gas, which suggests that fuel-mix dependence exists between ETS and energy prices [7]. Also, volatility in the stock market can cause fluctuations in the ETS through trading demand [8]. But other studies of the Chinese market show that carbon prices also act as an important factor in determining the rise in stock market volatility [9]. The effect of economic policy uncertainty (EPU) on carbon pricing is also up for debate. Some studies say that EPU spikes can make regional permit prices more volatile [10], while others say that strong local buffers can cancel out these effects when there are credible regulatory regimes in place [11]. Some authors say that ETS has a positive effect on inflation changes in the long run [12], while others say it has almost no effect on the overall Consumer Price Index [12]. There are also different opinions on the effects on the job market, with some saying that investments in green technologies will create net job gains [13] and others saying that transitional job losses will happen in emissions-intensive sectors without targeted support [14]. Finally, higher ESG ratings are often linked to lower carbon intensity and carbon allowances [15]. All these different results show how important it is to have a single system that can handle both linear spillovers and nonlinear, situation-dependent effects.

Despite their growing extent and institutional complexity, ETS markets remain empirically underexplored within system-level economic frameworks. Existing studies tend to model carbon prices as dependent on macroeconomic and policy shocks, offering limited insight into whether and how ETS prices themselves act as transmission channels that influence other sectors [16]. Furthermore, the majority of empirical research is limited to single-country case studies, static modeling frameworks, or low-frequency data, which restricts the comprehension of carbon market responsiveness and subsequent spillover effects. This paper addresses these gaps by focusing on a panel of seven ETS jurisdictions: Germany, the United States, Canada, China, Korea, the United Kingdom, and New Zealand, selected for their economic significance, policy relevance, and availability of high-frequency (monthly) price data [17]. By concentrating on this diverse but tractable group, the study avoids overgeneralization and instead provides detailed insight into the dynamic interdependence between carbon prices and macro-financial variables.

To guide the empirical analysis, the following hypotheses are formulated:

H1:

Shocks to stock market volatility have a statistically significant effect on ETS returns.

H2:

Economic policy uncertainty transmits directly into ETS price dynamics.

H3:

Inflation shocks exert a measurable influence on ETS returns.

H4:

Fluctuations in unemployment have an impact on ETS returns.

H5:

Oil price shocks are reflected in ETS return behavior.

H6:

Changes in global ESG sentiment influence ETS returns.

H7:

Increases in ETS returns generate spillover effects that reduce unemployment.

H8:

ETS returns influence oil prices and financial market volatility, indicating a feedback channel between carbon markets and the broader macro-financial environment.

To this end, this research employs a hybrid methodological approach—a panel vector autoregression (PVAR) model to estimate the dynamic interdependencies between ETS and key macro-financial variables [17]. To capture nonlinearities and interaction effects often masked in parametric models, this paper complements this with a machine learning pipeline (XGBoost), interpreted through explainable AI tools such as SHAP and partial dependence plots [18]. The study focuses on January 2021–December 2024 because this interval aligns with the availability of monthly allowance-price data in all seven jurisdictions and captures a series of systemic shocks such as the post-COVID economic rebound, the 2022 Russia–Ukraine war and energy crisis, and major ETS-design reforms in Europe and China, that together create an informative, high-stress testing ground for carbon-price dynamics.

The contributions are fourfold. First, this study introduces a novel, high-frequency dataset of ETSs across seven different nations with carbon price regimes. Second, both the reactive and proactive functions of ETS pricing within macroeconomic frameworks are assessed, showing their limited predictability but significant transmission effects. Third, nonlinear ESG effects conditioned by the stability of the political environment are presented, offering new insights into the interconnections between sustainability and financial markets. Finally, this article proposes a dual-framework model that integrates econometric and machine learning approaches for predicting green financial transmission processes.

The subsequent sections of this paper are organized as follows. Section 2 examines the literature on ETS design and delineates the conceptual framework that informs the empirical research. Section 3 delineates the dataset and technique, integrating dynamic panel modeling with interpretable machine learning. Section 4 presents the results, while Section 5 analyzes the findings in relation to established theories and policy implications. Section 6 finishes with implications and directions for future research.

2. Literature Review

2.1. Theoretical Background and Global Context of ETS

At its core, ETS has its roots in Pigouvian theory, aiming to internalize the social cost of greenhouse gas emissions through market prices [19,20]. Under emissions trading systems, firms receive or buy a limited number of allowances, creating tradable emission rights. This incentivizes cost-effective abatement by allowing firms with surplus permits to sell them to those facing higher abatement costs [21,22]. In 2005, the European Union launched the first carbon emissions trading scheme (EU ETS) as part of its commitments under the Kyoto Protocol. Since then, the EU ETS has evolved through four major phases, progressively strengthening its design through centralized allocation and the introduction of mechanisms such as the Market Stability Reserve (MSR) [23,24]. Implemented in 2019, the MSR automatically adjusts the supply of carbon allowances based on the total number of allowances in circulation, retiring surplus permits during periods of low demand, and releasing them when needed. This mechanism has helped to mitigate price volatility and maintain the environmental integrity of the system, particularly during crises such as the COVID-19 pandemic [25,26]. The success and scale of the EU ETS catalyzed the global diffusion of emissions trading systems. New Zealand introduced its ETS in 2008, followed by regional initiatives such as California’s cap-and-trade program (2013) and the Regional Greenhouse Gas Initiative in the U.S. Northeast (2009) [27,28]. More recently, China launched the world’s largest ETS in 2021, initially covering the energy sector [29]. However, the diversity of market architectures (from fixed price schemes to secondary markets) continues to shape ETS performance and responsiveness to macroeconomic signals [30,31].

2.2. Bidirectional Interactions Between ETS and Macro-Financial Variables

Empirical studies highlight several advantages of adopting ETS frameworks: (i) they ensure environmental effectiveness by capping total emissions, (ii) promote cost-effectiveness by market allocation of emission reductions, (iii) generate public revenues when permits are auctioned, and (iv) stimulate low-carbon innovation [16,21,32]. Challenges include over-allocation of allowances, which can reduce carbon prices and mitigation incentives, as was the case in the early phases of the EU ETS [33], as well as market volatility, regulatory uncertainty, and equity concerns regarding the distribution of costs [34,35]. Additionally, there is a risk of carbon leakage, where companies relocate to jurisdictions with more permissive environmental regulations, potentially undermining global efforts to reduce emissions [22].

Empirical studies present a mixed picture of the impact of the Brent crude oil price on EU ETS permit prices: on the one hand, Krokida et al. [36] show that a USD 10 increase in the Brent price increases permit prices by about 5–7 euros per tonne, corresponding to higher marginal abatement costs in oil-intensive sectors. On the other hand, Li et al. [37] show that once coal and gas prices are included in the model, the oil effect disappears, meaning that firms simply switch to cheaper fuels. In addition, Zheng [38] finds, using quantile-VAR, that oil shocks are only important when ETS prices are already low, and Olasehinde-Williams [39] uses E-GARCH to show that ETS volatility can, in turn, amplify oil price volatility.

The Brent oil–ETS link holds in regions or industries where oil is the marginal input, but vanishes when broader fuel competition is modeled, explaining why some studies report strong effects and others none. This research includes oil-price shocks to capture real-world cost pressures that firms face, especially in transport or petrochemical sectors, and to measure how global commodity disruptions translate into carbon-permit demand.

In addition to environmental impacts, the ETS is influenced by macroeconomic cycles, as allowance prices are significantly linked to variations in industrial activity and energy consumption. Consequently, during economic downturns, decreased production leads to lower emissions, which diminishes the demand for allowances and subsequently reduces pricing [40,41]. However, in periods of economic expansion, increased energy production and consumption may raise carbon pricing [42]. These cyclical dynamics are closely linked to unemployment and inflation [43,44]. Unemployment rises during economic recessions when firms reduce production and labor demand, signifying diminished industrial activity and emissions, which consequently lessens the need for carbon allowances. Conversely, inflation, which often escalates during late boom phases, may reduce the real value of ETS and increase investment uncertainty, particularly when energy prices rise alongside carbon taxes [45]. However, Moessner [46] argues that an increase in the price of EU ETS certificates by USD 10 per tonne of CO₂ equivalent leads to an increase of 0.8 percentage points in the inflation of consumer energy prices and an increase of 0.08 percentage points in total inflation. These findings underline the potential of the ETS to contribute to inflationary pressures by increasing energy costs [47]. When considering unemployment, a key concern relates to job reallocation in carbon-intensive sectors, where decarbonization triggers job losses, particularly in fossil fuel extraction, heavy industry, and high-emission transport [48]. At the same time, evidence suggests that climate policy, when combined with proactive support mechanisms, can generate net increases in employment, particularly in sectors related to energy efficiency, renewable energy, and infrastructure [49]. Recent modeling studies emphasize the importance of policy design: redistributing carbon pricing revenues through targeted tax credits or labor market support schemes can improve employment outcomes by stimulating aggregate demand and supporting job creation in lower-emitting industries [50]. This research includes unemployment and inflation to capture the cyclical demand for allowances. Unemployment is a proxy for firms’ production slack, and inflation presents the erosion of the real cost of permits and value of auction revenues.

The volatility of national stock markets significantly impacts carbon prices in emissions trading systems, influencing firms’ behavior and carbon price dynamics. This relationship is confirmed by a study testing Granger causality from stock markets to carbon markets, highlighting that stock price fluctuations can lead to changes in carbon prices, especially in the EU context [51]. Recent studies on China’s carbon trading markets show that carbon price volatility significantly increases stock market volatility, especially in lower-carbon sectors and coastal regions, with the effects remaining stable before and during COVID-19. Even if carbon price changes have limited predictive power, they do lead to contemporaneous volatility spillovers, a point demonstrated by the E-GARCH analysis [9]. Another study complements this by claiming that carbon risk is factored into financial market prices. In this context, it is suggested that investors are increasingly taking the impact of climate change and greenhouse gas emissions into account when making their investment decisions, which could influence market behavior [52]. Notably, ETS price dynamics have the potential to directly impact the volatility of financial markets, as changes in carbon price volatility are significantly influenced by energy and financial market factors, thus suggesting an interactive relationship between carbon, oil, gas, and stock markets [53]. Stock market volatility captures both macro-financial uncertainty and investor sentiment; however, in the EU, it often predicts subsequent carbon-price movements, whereas in China’s pilot schemes, volatility shocks and carbon-price changes occur simultaneously, with little evidence of one leading the other. This heterogeneity reflects differences in market liquidity, regulatory integration, and maturity. This paper includes stock-market volatility as a proxy for macro-financial stress and shifting risk appetites that influence firms’ hedging and allowance-buying behavior.

Economic policy uncertainty (EPU) is another key factor in shaping investors’ expectations about regulatory stability and cap directions; these factors significantly influence price stability in ETS markets [10,54]. Liu et al. [55] investigated the influence of EPU on carbon price volatility in China’s ETS pilot markets, revealing significant regional heterogeneity. The study finds that a 0.01 increase in the EPU growth index leads to a substantial increase in long-term volatility of about 28.8% in Hubei and 5.4% in Beijing, indicating a significant sensitivity of carbon prices to policy uncertainty. The interesting element of the study is that the Guangdong market exhibits an inverse response, with the overall EPU being associated with a reduction in carbon prices. Another study confirms that the EPU amplifies the effects of stock market volatility through the intensification of fluctuations in returns associated with the carbon price. In particular, global EPU leverages a stronger influence than local policy uncertainty, indicating that global signals are more effective in forecasting carbon market volatility [10]. This suggests that carbon price returns can be predicted with a high degree of accuracy when using the global EPU as a leading indicator. In support of this claim, another study finds that growing economic policy uncertainty is driving carbon prices down in both China and the EU, highlighting how uncertainty undermines market trust and disrupts the pricing mechanism in emissions trading schemes [56]. This research incorporates EPU to reflect how uncertainty about regulations and future compliance costs shapes permit-pricing behavior. However, the mixed evidence, showing amplifying and dampening effects, raises an important question: To what extent does policy uncertainty itself drive ETS?

Environment, Social, Governance (ESG) frameworks also shape ETS dynamics, as carbon prices are increasingly integrated into corporate sustainability scores and investment decisions. Companies subject to ETS and aligned to ESG standards often benefit from lower capital costs and increased reputational value, reinforcing the strategic importance of participating in ETS [57]. Studies show that high ESG scores often correlate with lower emissions intensity, lower volatility, and improved resilience to shocks [58,59,60]. Moreover, investor behavior in the context of ESG application has been shown to amplify ETS price responses in stable regulatory environments, while high environmental or public policy uncertainty tends to flatten or reverse these effects [61]. This paper includes the MSCI ESG Leaders Index to capture how firms’ sustainability reputations and related investment flows influence carbon-permit prices. This lets us assess whether higher ESG scores dampen or amplify cost-pass-through effects and pinpoint when additional ESG improvements stop affecting carbon pricing.

2.3. Empirical and Methodological Gaps in ETS Research

While ETS markets have been widely studied, much of the empirical literature remains concentrated on single-country systems (more often: EU ETS and China) [3,22] or relies on theoretical simulation models [62]. Cross-national, high-frequency empirical analyses that assess the dynamic interaction of ETS markets with macro-financial systems remain scarce. This study addresses this gap by integrating monthly multi-jurisdictional ETS data with dynamic panel modeling and explainable machine learning to explore how carbon markets both respond to and transmit macroeconomic signals. Furthermore, many contributions are based on simulation models [63,64] or static econometric frameworks, which do not capture the time feedback loops or nonlinear dependencies that characterize real-world carbon markets.

This study addresses this gap through an original empirical framework that integrates the following:

• High-frequency (monthly) data from seven major ETS jurisdictions (USA, Canada, China, Korea, Germany, UK, and New Zealand), allowing real-time inferences and international comparisons;
• A panel vector autoregression (PVAR) framework that captures bidirectional and dynamic propagation effects;
• A complementary explainable machine learning model (XGBoost with SHAP) to reveal nonlinear interactions, conditional effects, and predictive factors often invisible in traditional econometrics.

However, ETS datasets can be skewed because markets that close or merge are removed (survivorship bias), and because each system’s specific rules (allowance banking limits and borrowing options) affect price movements in different ways. The PVAR–CCE approach captures shared shocks across all markets, reducing bias from missing data, while XGBoost flexibly models the nonlinear effects caused by different compliance-phase designs [65]. This combined framework delivers reliable estimates despite panel gaps and design heterogeneity, and it directly evaluates the hypotheses on two-way macro-financial feedback (H1–H8) and the benefit of blending linear and nonlinear methods for better ETS-return forecasts.

These results offer actionable insights across multiple domains. For policymakers, the demonstration that ETS both absorbs and transmits macroeconomic shocks supports the design of adaptive mechanisms such as stability buffers and price corridors. For market designers, cross-jurisdictional evidence informs debates on linking schemes and calibrating auction rules. Institutional investors and ESG funds benefit from characterization of policy-uncertainty thresholds and nonlinear spillovers, improving climate-aligned allocation strategies.

2.4. Conceptual Framework

Building on the literature review, this research proposes a conceptual framework (Figure 1) that views ETS prices as both reactive indicators and proactive transmitters within a complex macro-financial ecosystem. ETS prices are influenced by external factors such as energy prices, labor market conditions, inflation, ESG developments, financial volatility, and political uncertainty. At the same time, they act as forward-looking signals that influence expectations and decisions related to unemployment, market volatility, and oil prices.

From a theoretical perspective, carbon prices within the ETS exhibit a dual nature. On one side, emissions caps and allocation mechanisms determine the structural supply of allowances and set the foundational pricing environment. On the other side, ETS prices can be impacted by macroeconomic conditions that influence firms’ demand for permits and trading behavior. ETS prices also function as economic signals that affect real-world decisions, where higher carbon prices may prompt firms to accelerate decarbonization investments or adjust labor needs across sectors. This dual-role logic aligns with endogenous expectations theory [66], which asserts that current prices reflect beliefs regarding future policy and influence contemporary behavior, as well as dynamic adaptive policy pathways [67], which emphasizes the informational function of market-based instruments in coordinating private responses to long-term climate objectives.

The conceptual framework identifies five core external factors that guide empirical analysis on ETS (exogenous drivers in Figure 1): (1) Brent oil prices act as an exogenous driver of ETS by influencing industrial production costs and emissions levels, thereby affecting demand for carbon allowances. (2) Among macroeconomic drivers, unemployment reflects industrial contraction and declining emissions, reducing demand for carbon allowances and exerting downward pressure on ETS prices. Inflation, particularly during boom cycles, can undermine the real value of ETS and add investment uncertainty, influencing market expectations and carbon pricing dynamics. (3) Volatility in financial markets frequently indicates risk aversion, diminished liquidity, and speculative activity. In volatile situations, carbon markets may experience heightened price fluctuations as traders react to overarching uncertainty. (4) High Economic Policy Uncertainty reflects ambiguity about future regulations, taxes, or government spending, which can lower investor confidence in carbon pricing mechanisms. Increased EPU raises carbon price volatility due to speculative trading and weakened long-term investment planning. (5) Environment–Social–Governance sentiment reflects both regulatory pressure and investor preferences. Strong ESG momentum can amplify market attention to carbon assets, raising demand for allowances in anticipation of tighter future climate policies or sustainability expectations.

The conceptual framework is also built on the fact that ETS functions as a transmission mechanism that influences three key macro-financial indicators: (1) Higher ETS allowance prices can reduce the expected future demand for oil by making fossil fuels less competitive, which may put downward pressure on oil prices; (2) rapid fluctuations in allowance prices can amplify systemic risk, influence carbon-related asset pricing, and amplify the volatility of the national stock market; and (3) ETS can affect employment by shifting investment and production patterns across sectors.

Because three variables serve both as exogenous drivers for ETS and shock receivers from ETS (unemployment, volatility, and oil prices), the research adopts a VAR framework that allows each series to be endogenous and uses contemporaneous ordering plus four lags to disentangle dynamic interplay.

3. Materials and Methods

3.1. Dataset

This study uses monthly panel data from seven economies spanning the period January 2021 to December 2024. The sample period is determined by the availability of the study’s central independent variable: the emissions trading system price, measured as the monthly settlement or market price of carbon allowances, expressed in national currency per metric ton of CO₂ equivalent (tCO_2e). The data cover seven jurisdictions and were retrieved from the ICAP Allowance Price Explorer, which compiles official auction outcomes, secondary market prices, and institutional metadata. Depending on the jurisdiction, the ETS price reflects different market structures: primary auction settlement prices for the UK, Korea, Canada, and the US; secondary market prices for New Zealand and China; and government-set fixed prices for Germany. A primary market is determined by the direct issuance of emissions allowances by a regulator through scheduled auctions. The auction settlement price reflects the equilibrium clearing price where demand meets supply, and all winning bidders pay the same amount. Most ETS systems operate via primary markets. On the other hand, secondary markets allow firms and intermediaries to trade allowances already in circulation, without government participation. This is why prices are determined by bilateral transactions in these markets and may fluctuate more freely based on market expectations, hedging behavior, and regulatory signals. It should be noted that, for the US and Canada, the underlying ETS price data were only available at a quarterly frequency. To maintain temporal alignment and exploit the full information set, we employed linear interpolation to obtain monthly ETS prices for these two countries. This enabled a uniformity of monthly time series across countries. To ensure cross-country comparability, all ETS prices were converted to euros (EUR) using the official monthly exchange rates corresponding to each national currency.

To further investigate the short-term dynamics of carbon markets across the seven ETS jurisdictions, this paper includes a set of economic, financial, and policy variables commonly associated with carbon market dynamics and volatility transmission. The selection of variables reflects both theoretical expectations and empirical precedent regarding the drivers and transmission channels of ETS price variation (

Table 1. Variable description and their sources.

Variable	Abbrev	Description	Unit	Source
ETS return	ETS	Monthly change in ETS price, capturing short-term dynamics of carbon pricing	EUR per tCO2e	ICAP
Stock market volatility	VOL	Monthly standard deviation of daily stock index returns (domestic)	Standard deviation (unitless)	Yahoo Finance
Policy uncertainty index	EPU	Economic Policy Uncertainty Index (country-specific)	Index	Economic Policy Uncertainty
Consumer Price Index	CPI	National Consumer Price Index—proxy for inflation	Index	OECD/FRED
Unemployment rate	UNEMP	National unemployment rate, % of labor force	Percent (%)	OECD/FRED
Brent oil price	RATE	Brent crude oil price—proxy for global energy shocks	USD per barrel	Investing.com
ESG Leaders Index	ESG	World ESG Leaders Index—proxy for global sustainable investment sentiment	Index	investing.com

).

The first explanatory variable is VOL, measured as the standard deviation of daily returns on national equity indices. The source of this variable is Yahoo Finance, and it serves as a proxy for domestic financial uncertainty. It captures fluctuations in investor sentiment and capital market risk that may spill over into carbon markets through portfolio adjustments and speculative trading. The policy uncertainty index (EPU) is sourced from policyuncertainty.com and represents the degree of macroeconomic and regulatory uncertainty in each country. Constructed through frequency analysis of national newspapers, the index reflects investor expectations about economic policymaking and is widely used in studies of financial volatility [68]. Higher levels of EPU may reduce investment in clean technologies, dampen emissions trading activity, or amplify precautionary demand for permits, making it a theoretically grounded predictor of ETS price changes. This research also includes the CPI to control for domestic inflation. Data are obtained from the OECD and the Federal Reserve Economic Data (FRED) repository. General price trends in goods and services are reflected by the CPI, and it helps isolate the real effects of ETS price movements from broader inflationary pressures. The UNEMP captures labor market conditions and is also retrieved from OECD and FRED sources. Expressed as a percentage of the labor force, unemployment is included to assess whether carbon pricing exhibits pro-cyclical or counter-cyclical dynamics in response to labor market shifts. Prior literature suggests that carbon pricing may affect employment through production costs and sectoral reallocation, making this a relevant variable for understanding real economic impacts. As a proxy for global energy shocks, the Brent crude oil price (RATE) is measured as the monthly average price per barrel and is expressed in USD. The series is sourced from Investing.com. Oil prices influence the cost competitiveness of fossil fuels versus cleaner alternatives and are thus expected to interact dynamically with carbon markets. In this framework, Brent prices are treated as an exogenous global signal, influencing all jurisdictions uniformly. Finally, this paper incorporates the MSCI World ESG (ESG) as a proxy for global sustainable investment sentiment. This index tracks the performance of firms with high Environmental, Social, and Governance scores and is retrieved from Investing.com. ESG index values are used to investigate how shifts in sustainability preferences may affect carbon pricing. ESG is particularly relevant in light of growing evidence that investor behavior and institutional norms increasingly influence asset pricing, including that of carbon allowances.

To ensure the temporal stationarity of the series, this research also included the application of standard transformations before estimation. To stabilize variances, all strictly positive series (ETS prices, volatility, ESG scores, Brent crude oil prices, policy uncertainty, inflation, and unemployment) were first log-transformed. We then applied IPS, Maddala–Wu Fisher, and Hadri panel-unit-root tests to each logged series. Any series that remained non-stationary at the 5% level was first-differenced. Further details on the test results and exact transformations are provided in Section 4.2.

Although the dataset used in this study includes a relatively small number of ETS jurisdictions, it reflects a broader empirical reality: ETS price data remain limited in availability and consistency across countries, owing to the varied timelines, structures, and transparency levels of emissions trading schemes. The selected cases, spanning major carbon markets in Europe, North America, and Asia-Pacific, account for a substantial portion of global emissions under formal pricing mechanisms and capture a meaningful diversity of market designs. Focusing on this core group enables a structured analysis of how ETS prices behave across institutional settings and under differing macro-financial conditions. Importantly, these jurisdictions include some of the most mature and economically influential carbon markets, making them particularly relevant for understanding the evolving role of emissions pricing within broader energy systems.

3.2. Methodology

This study employs a dual-modeling strategy that combines dynamic panel econometrics and nonlinear machine learning to analyze the drivers and transmission mechanisms of emissions trading system returns (Figure 2). In the first stage, a panel vector autoregression using a Common Correlated Effects (CCE) model was estimated, which enables the identification of dynamic interdependencies among macro-financial variables within and across jurisdictions [69]. In the second stage, a supervised machine learning model (XGBoost) was deployed, the results of which were interpreted using explainable artificial intelligence tools (SHAP and PDP) to discover nonlinear and interaction effects that may be overlooked by linear systems [70].

3.2.1. Panel Vector Autoregression (PVAR) via Common Correlated Effects (CCE) Estimator

The dynamic structure of monthly ETS is modeled using a PVAR of order p = 4, estimated via the Common Correlated Effects (CCE) approach. This methodology, following Pesaran [71] and Chudik & Pesaran [72], augments the standard panel VAR by including cross-sectional means of all endogenous variables to capture global unobserved common factors and mitigate spurious correlation from purely time-varying regressors.

Let $y_{\left(i,t\right)}\in R^K$ denote a vector of K endogenous variables for jurisdiction i at time t. The PVAR-CCE model is given by

$$y_{i,t}={\sum }_{j=1}^p{A}_j{y}_{i,t-j}+{\gamma \overline{y}}_t+{\epsilon }_{i,t}$$

(1)

where

• $A_j\in R^{K\times K}$ are the coefficient matrices for lag j;
• ${\overline{y}}_t$ is the cross-sectional mean of the endogenous variables at time t;
• ${\epsilon }_{i,t}\sim \mathcal{N}\left(0,{\Sigma }_{\epsilon }\right)$ is a white noise disturbance term.

The vector y_i,t contains

$$y_{i,t}=[{d\_ets}_{i,t}, {l\_vol}_{i,t}, {l\_rate}_{i,t},{l\_esg}_{i,t},{l\_epu}_{i,t},{l\_cpi}_{i,t},{unemp}_{i,t}]\mathrm{T}$$

(2)

Note that l_rate (Brent oil prices) and l_esg (ESG index) are not jurisdiction-specific; they are time-varying but constant across countries. In the CCE framework, including cross-sectional means ensures that global co-movements are robustly accounted for and avoids the pitfalls of weak identification or spurious collinearity that may arise when such variables are entered directly in a fixed-effects model.

Estimation was conducted using the pvarfeols function from the {panelvar} package in R, with cross-sectional means specified as additional exogenous controls [73]. Robust standard errors were applied, and the model passed all residual and stability diagnostics.

Lag selection for the CCE-PVAR model was based on both the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), which indicated an optimal lag order of one (see Appendix A,

Table A1. Lag order selection results (AIC/BIC).

Lags	AIC	BIC
1	−972.79	−687.35
2	−911.74	−494.56
3	−866.10	−317.18
4	−796.66	−115.99

). However, to better account for potential longer-term dynamics and to follow the more conservative specification often used in recent panel VAR literature, we estimated the model with four lags. The main results remain robust if fewer lags are used.

Of note, the CCE estimator is well suited for panels subject to pervasive global shocks and ensures that identification of time-varying global regressors (such as Brent and ESG) is robust to unobserved factor structure. This is especially relevant given the moderate cross-sectional (N = 7) and temporal (T = 41 months) dimensions, where GMM estimators would face well-known limitations due to instrument proliferation, and fixed-effects approaches may inadequately address global co-movement [74,75].

Significant Breusch–Godfrey/Wooldridge and Pesaran CD tests show some indication of cross-sectional dependency and residual serial correlation. Robust standard errors are used to lessen the impact of these problems, which are prevalent in short macro-financial panels. Dynamic stability is confirmed by the fact that all characteristic roots fall inside the unit circle. The persistence of the primary findings is confirmed by robustness testing using different lag durations.

Moreover, impulse response functions (IRFs) were computed from an auxiliary pooled VAR of the key subset {d_ets, l_rate, l_vol, l_epu} using Cholesky decomposition. Confidence bands were generated through bootstrapping (100 replications), and responses were traced over a 12-month horizon.

3.2.2. Nonlinear Learning: XGBoost with SHAP and PDP

To identify potential nonlinearities, threshold effects, and conditional interactions beyond the scope of linear VAR systems, a gradient-boosted tree model (XGBoost) was trained to predict d_ets as a function of the same set of macro-financial features, using R packages {xgboost} and {iml}. All modeling steps were fully reproducible with a fixed random seed.

Prior to modeling, all features were transformed to include a one-period lag to avoid look-ahead bias and ensure causal ordering consistent with the VAR framework. The final dataset excluded rows with missing lag values.

For evaluation, the dataset was divided into an 80% training set and a 20% holdout test set, with the most recent observations reserved for testing to mimic true out-of-sample forecasting. Hyperparameters were set as follows: learning rate (η) = 0.05, maximum tree depth = 4, subsample ratio = 0.9, column subsample ratio = 0.8, and 150 boosting rounds. The loss function minimized by the model is mean squared error, regularized as

$$L\left(\Theta \right)={\sum }_{t=1}^T{\left(y_t-{\overline{y}}_t\right)}^2+{\sum }_{k=1}^K\Omega \left(f_k\right)$$

(3)

where y_t is observed ets, ${\overline{y}}_t$ is the model prediction at time t, and $f_k\in F$ is the k-th regression tree from the ensemble, and the regularization penalty is defined as

$$\Omega \left(f_k\right)=\gamma T_k+\left(1/2\right)\lambda \parallel w_k{\parallel }^2$$

(4)

Here, T_k is the number of terminal nodes (leaves) in tree k, w_k is the vector of leaf weights, and γ and λ are regularization parameters penalizing model complexity and overfitting.

Model robustness and performance were assessed via time-series (rolling-origin) cross-validation on the training data, using an expanding window and one-step-ahead prediction, with mean cross-validated RMSE reported. Out-of-sample RMSE was computed on the test set and compared with a linear regression benchmark using the same features and lag structure.

Predictor attribution and interpretability were obtained through (i) global feature importance, based on mean squared error (MSE) loss reduction; (ii) partial dependence plots (PDPs), which isolate the marginal impact of ESG scores across their empirical distribution; and (iii) SHAP (SHapley Additive exPlanations) values, capturing local and global variable contributions and revealing interaction effects, especially between ESG and EPU [76,77]. This dual-model strategy enables robust triangulation of insights: while the PVAR identifies statistically significant dynamic interactions and structural spillovers, the machine learning framework uncovers nonlinearities, saturation effects, and conditional dependencies that would otherwise remain hidden.

4. Results

4.1. Evolution and Design of ETS Markets

To contextualize the empirical analysis, the research begins by examining the evolution of emissions trading system prices from January 2021 to December 2024, using log-transformed prices disaggregated by country and market design. Figure 3 presents these trajectories across seven jurisdictions: Canada, China, Germany, Korea, New Zealand, the UK, and the US, grouped by ETS type: auction-based, fixed-price, or secondary market.

A general upward trend in ETS prices is evident in most jurisdictions, consistent with the global tightening of carbon market regulations during this period. However, the pace and volatility of this increase differ substantially by market design.

Germany, the only fixed-price system shown, exhibits a stepwise, non-volatile trajectory, characteristic of administratively set carbon prices. The distinct jumps in price levels reflect scheduled adjustments to the carbon tax floor rather than market forces. In contrast, auction-based systems, which include Canada, the UK, the US, and Korea, show more pronounced fluctuations. These markets exhibit cyclical patterns, local peaks and troughs, and higher amplitudes in price changes, indicating responsiveness to broader macroeconomic and policy conditions. A noteworthy pattern emerges when comparing Canada and the US. Despite separate national schemes, their permit-price trajectories are virtually identical, with a Pearson correlation of r = 0.9996 (p < 0.001) on monthly log-transformed ETS prices. Both markets peak around mid-2023 before partially reverting, reflecting shared economic shocks, regional policy coordination, and aligned cap-tightening schedules. China, which operates a secondary market, displays a pattern of low but volatile ETS prices, with substantial short-run variability around a relatively stable mean. This behavior reflects thin trading volumes, evolving institutional frameworks, and limited inter-sectoral linkages during the early phases of China’s carbon market development. New Zealand’s ETS, also operating on a secondary market, shows a mid-period surge followed by a decline, linked to changing policy expectations or market corrections.

In sum, auction-based ETS markets demonstrate greater price flexibility and sensitivity to external shocks, while fixed-price systems like Germany provide stability and administrative control. Secondary markets, exemplified by China and New Zealand, show less directional clarity but high short-term volatility.

Figure 4 compares the volatility of ETS returns—measured as the standard deviation of monthly log price differences—across three distinct market designs: auction-based, fixed-price, and secondary markets.

As expected, the fixed-price system (represented solely by Germany) exhibits the lowest level of volatility, with a flat, singular value reflecting its administratively managed price path. While not zero, the observed fluctuations stem from scheduled adjustments or indirect policy effects rather than market trading dynamics.

In contrast, auction-based markets show the greatest dispersion in volatility, as reflected by a wide interquartile range and the presence of an outlier. This variability suggests that price movements in these systems are highly sensitive to market liquidity, regulatory expectations, and investor sentiment. While some auction-based systems maintain moderate volatility, others, such as those facing policy shocks, experience significant fluctuations.

Interestingly, out of the three market types, auction-based ETS markets exhibit the highest average volatility, but with more dispersion than secondary markets. This is in line with the sharp price fluctuations and cyclical trends seen in a number of auction-based systems in Figure 3, which demonstrate increased susceptibility to investor sentiment, market liquidity, and regulatory expectations. On the other hand, secondary markets, although also showing moderately high volatility, are characterized by less dispersion, which is likely due to changing institutional frameworks, low trading depth, and changing market infrastructure.

4.2. Pre-Estimation Diagnostics

Before estimating the panel vector autoregressive model, a comprehensive set of diagnostics was performed to assess the statistical adequacy and structural stability of the data. These pre-tests address key concerns common in macro-panel settings involving financial and environmental time series: non-stationarity, cross-sectional dependence, and dynamic misspecification.

To begin with, cross-sectional dependence was observed, assessed using Pesaran’s CD test applied to all panel variables. In all cases, the null hypothesis of cross-sectional independence is strongly rejected, indicating significant residual correlation across countries. This result is consistent with the shared exposure of ETS markets to global economic conditions, energy prices, and policy cycles. The presence of cross-sectional dependence supports the use of system-wide estimators and motivates robust inference procedures.

To assess stationarity, three complementary panel unit root tests—the Im–Pesaran–Shin (IPS) test, the ADF-Fisher test (Maddala–Wu), and the Hadri test—were applied (

Table 2. Unit root test results.

Variable	IPS Stat	IPS p	MW Stat	MW p	Hadri Stat	Hadri p
ETS	−1.50	0.13	5.2	0.74	15	0
VOL	−8.58	0	114.38	0	4.83	0
RATE	−1.70	0.09	10.5	0.13	12.5	0
EPU	−6.54	0	83.4	0	11.1	0
CPI	−4.63	0	62.86	0	49.81	0
UNEMP	−1.38	0.08	47.43	0	23.24	0
ESG	2.19	0.99	2.79	0.99	35.59	0

Source: Authors’ estimations in R.

). Across all specifications, results consistently indicate that only three variables, including log ETS prices (ETS), oil price proxies (RATE), and ESG scores (ESG), are non-stationary in levels but stationary in first differences. Note, however, that RATE and ESG are time-series shared across countries; their panel stationarity reflects time dynamics only, not cross-sectional behavior. This finding justifies differencing key series and supports the use of d_ETS (first difference of log ETS prices) as the main dependent variable. Importantly, this difference-stationarity aligns with prior empirical work suggesting that carbon pricing mechanisms behave as integrated processes influenced by persistent shocks rather than reverting to a fixed mean.

The Breusch–Pagan test for heteroskedasticity reveals mild to moderate variance heterogeneity across countries, particularly in variables related to volatility. While fixed-effects estimation accommodates level heterogeneity, this result underscores the need for robust standard errors, which are used throughout the PVAR estimation.

Lastly, the Wooldridge test for serial correlation (pbgtest) identifies first-order autocorrelation in several series, especially in ETS and volatility, reinforcing the need for a lag structure of at least two periods. This choice balances model parsimony with capturing dynamic persistence in the panel.

Together, these diagnostic results justify a demeaned PVAR specification with robust inference, a stationary transformed series, and a two-lag structure. These pre-estimation checks form a critical empirical foundation for the validity of the model results that follow.

4.3. Dynamic Estimation of ETS Drivers and Transmission Effects

First,

Table 3. Descriptive statistics for panel variables *.

Variable	Mean	Std. Dev.	Min	Max	Skew	Kurtosis	Description
ETS	0.00	0.08	−0.34	0.41	0.39	4.02	First-diff log ETS price
VOL	4.14	1.87	−1.04	6.57	−1.52	1.20	Log equity index volatility
EPU	5.32	0.61	4.32	7.00	0.71	−0.36	Log economic policy uncertainty (national)
CPI	4.82	0.14	4.61	5.09	0.20	−1.14	Log Consumer Price Index
UNEMP	1.39	0.25	0.92	1.96	0.18	−0.93	Log unemployment rate

* Source: Authors’ estimations in R. Note: N = 7 jurisdictions, T = 21 months.

summarizes the key panel variables included in the PVAR estimation. ETS returns (d_ets) are centered around zero with occasional large deviations and excess kurtosis, consistent with shock-driven dynamics. l_vol, capturing national vol, shows substantial dispersion, consistent with episodes of market stress. l_epu, l_cpi, and unemp also display meaningful cross-country and temporal variation. Notably, globally invariant variables, such as RATE (d_rate) and the ESG (d_esg), were excluded from the table, as they are time series shared identically across countries and do not contribute to cross-sectional statistics. These are instead interpreted as time series shocks shared across the panel, treated accordingly in model specifications.

To analyze the interactions between ETS, domestic macro-financial variables, and global shocks, a Common Correlated Effects (CCE) panel VAR was estimated with four lags and robust standard errors. The model includes as endogenous variables: ETS, volatility, policy uncertainty, inflation, and unemployment. The global Brent price and MSCI ESG index are included as exogenous variables, and the cross-sectional means of all endogenous variables are incorporated to account for unobserved global shocks and spillovers.

Table 4. CCE-PVAR coefficient estimates (full system).

Variable	D_ETS	VOL	EPU	CPI	UNEMP
lag1_d_ets	0.0490 (0.0634)	0.0613 (0.2132)	−0.0520 (0.1825)	−0.0059 (0.0077)	−0.1207 *** (0.0346)
lag1_vol	0.0216 (0.0182)	0.1544 * (0.0613)	0.0314 (0.0524)	−0.0017 (0.0022)	−0.0123 (0.0099)
lag1_epu	0.0116 (0.0223)	−0.1426 (0.0749)	0.1728 ** (0.0641)	0.0028 (0.0027)	0.0151 (0.0121)
lag1_cpi	0.1864 (0.5738)	0.1679 (1.9296)	−0.4317 (1.6513)	0.9709 *** (0.0701)	0.1922 (0.3131)
lag1_unemp	−0.0583 (0.1283)	0.8118 (0.4315)	0.5283 (0.3692)	0.0109 (0.0157)	0.5058 *** (0.0700)
lag2_d_ets	−0.0385 (0.0658)	0.0882 (0.2213)	0.0381 (0.1894)	0.0173 * (0.0080)	0.0424 (0.0359)
lag2_vol	−0.0236 (0.0189)	−0.0828 (0.0635)	0.0046 (0.0543)	−0.0028 (0.0023)	0.0069 (0.0103)
lag2_epu	0.0032 (0.0227)	0.0061 (0.0764)	0.0877 (0.0654)	−0.0029 (0.0028)	0.0075 (0.0124)
lag2_cpi	0.0116 (0.6591)	1.2570 (2.2163)	−0.3730 (1.8967)	−0.0963 (0.0805)	−0.5707 (0.3596)
lag2_unemp	0.0175 (0.1439)	0.1073 (0.4841)	−0.1985 (0.4143)	−0.0008 (0.0176)	0.1096 (0.0786)
lag3_d_ets	−0.0993 (0.0650)	0.1720 (0.2186)	−0.1507 (0.1870)	−0.0069 (0.0079)	−0.0425 (0.0355)
lag3_vol	−0.0242 (0.0183)	0.0259 (0.0616)	−0.0009 (0.0527)	0.0020 (0.0022)	0.0035 (0.0100)
lag3_epu	0.0163 (0.0226)	0.0987 (0.0760)	0.0165 (0.0650)	0.0021 (0.0028)	0.0008 (0.0123)
lag3_cpi	−0.4192 (0.4780)	−0.1216 (1.6076)	0.2953 (1.3757)	0.0247 (0.0584)	0.2555 (0.2609)
lag3_unemp	−0.1015 (0.1413)	−0.5186 (0.4751)	−0.5563 (0.4066)	−0.0097 (0.0173)	0.1078 (0.0771)
lag4_d_ets	−0.1375 * (0.0638)	−0.0732 (0.2147)	−0.1214 (0.1837)	0.0001 (0.0078)	−0.0449 (0.0348)
lag4_vol	−0.0273 (0.0184)	0.0224 (0.0618)	−0.0447 (0.0528)	0.0002 (0.0022)	−0.0099 (0.0100)
lag4_epu	0.0105 (0.0221)	0.0148 (0.0742)	0.0500 (0.0635)	0.0026 (0.0027)	0.0124 (0.0120)
lag4_cpi	0.7408 * (0.3542)	−1.2105 (1.1913)	−0.1746 (1.0195)	−0.0411 (0.0433)	0.3625 (0.1933)
lag4_unemp	−0.0135 (0.1194)	−0.3069 (0.4014)	0.2246 (0.3435)	0.0091 (0.0146)	0.0313 (0.0651)
d_ets.mean	0.9366 *** (0.1571)	0.3273 (0.5284)	0.0609 (0.4522)	−0.0003 (0.0192)	−0.1529 (0.0857)
vol.mean	0.0046 (0.0310)	0.9910 *** (0.1044)	−0.0420 (0.0893)	−0.0008 (0.0038)	−0.0081 (0.0169)
epu.mean	0.0148 (0.0502)	0.0121 (0.1687)	1.0041 *** (0.1443)	−0.0006 (0.0061)	0.0068 (0.0274)
cpi.mean	−0.6871 (0.4000)	−0.3919 (1.3451)	0.4772 (1.1511)	0.1532 ** (0.0489)	−0.1390 (0.2183)
unemp.mean	0.1062 (0.1692)	0.1350 (0.5690)	0.3624 (0.4870)	−0.0291 (0.0207)	0.3599 *** (0.0923)
d_rate	−0.0033 (0.0774)	0.0154 (0.2602)	0.1651 (0.2227)	0.0044 (0.0095)	−0.0257 (0.0422)
d_esg	−0.0131 (0.1189)	−0.1193 (0.3997)	0.1249 (0.3421)	−0.0053 (0.0145)	−0.0045 (0.0649)

Note: Robust standard errors in parentheses. Stars denote significance: *** p < 0.001; ** p < 0.01; * p < 0.05. Authors’ estimations in R.

summarizes selected coefficient estimates for the ETS equation.

As demonstrated by the highly substantial effect of the cross-sectional mean of ETS (d_ets.mean; coefficient 0.936, SE 0.156, ** p < 0.001), the estimation findings show that robust global co-movement predominantly shapes ETS. This indicates how well the sample’s carbon markets are integrated and synchronized. None of the global variables, such as Brent price (d_rate) or ESG index (d_esg), exert a statistically significant direct effect on ETS after controlling for global common factors and cross-sectional dependence. Similarly, among the domestic controls, neither volatility, EPU, nor unemployment displays a significant contemporaneous or lagged effect on ETS, apart from a positive fourth lag for inflation (lag4_cpi; coefficient 0.7408, SE 0.3542, p < 0.05) and a weak negative fourth lag (lag4_d_ets; coefficient −0.1375, SE 0.063, p < 0.05), suggesting only a limited persistence in ETS dynamics.

Regarding the influence of ETS on other variables, a robust and highly significant negative effect is detected in the unemployment equation: the first lag of ETS is associated with a decrease in unemployment (coefficient −0.1207, SE 0.034, ** p < 0.001). This suggests that improvements in the carbon market are associated with a future reduction in unemployment, implying that a functioning ETS could have beneficial macroeconomic spillovers. Additionally, the second lag of ETS exhibits a small but significant positive effect on inflation, with a coefficient of 0.0173 (SE 0.0080, p < 0.05), indicating that past carbon-price gains modestly impact consumer-price dynamics.

Model diagnostics reveal some evidence of residual serial correlation and cross-sectional dependence, as indicated by significant test statistics in the Breusch–Godfrey/Wooldridge and Pesaran CD tests. Such results are not unusual in macro-financial panels of limited size and scope. Particularly, a notable spike at lag 12 is characteristic of annual cycles in emissions trading and compliance reporting, as documented in the literature [23,78]. Thus, to mitigate the impact of these issues, robust standard errors were employed for all coefficient estimates. Additional robustness checks, including model re-estimation with two, three, and four lags, confirm that the main findings are stable across specifications, and all characteristic roots remain inside the unit circle, confirming system stability.

A more complex picture of the carbon–finance relationship is presented by these findings. ETS carries forward-looking information that influences labor market outcomes, even while macro variables cannot readily forecast them. Therefore, the overall framework implies that carbon pricing serves as both a source of macroeconomic signals and a tool for policy.

4.4. Impulse Response Analysis

To examine the dynamics of the transmission of external shocks to carbon markets, impulse response functions (IRFs) were calculated from a reduced-form VAR model, with ETS as the response variable.

Figure 5 presents the IRFs, each accompanied by 95% bootstrapped confidence intervals. The sequence of variables in the VAR model, which establishes the Cholesky decomposition for impulse response analysis, was configured as follows: d_ETS, VOL, EPU, CPI, UNEMP, d_RATE, and d_ESG. This ordering follows standard economic reasoning, placing more exogenous and slower-moving variables (such as oil prices and ESG indicators) after more endogenous or market-responsive variables (such as returns and volatility). All impulse response functions are based on this identification.

According to the IRFs, the effects of global shocks on ETS are typically brief and transient, with responses declining to zero in around six to ten periods. The response magnitude remains moderate, and the confidence intervals reveal significant uncertainty, reflecting both market volatility and the panel’s restricted temporal scope.

The results indicate that a positive shock to Brent crude prices elicits a minor response in ETS, peaking within the initial two periods; however, the effect rapidly diminishes and becomes statistically insignificant after the third period. This pattern indicates that energy price signals are swiftly integrated into carbon markets but fail to provide enduring effects. Moreover, the response of ETS to an EPU shock is again short-lived, reverting to zero within six periods. This indicates that policy-related uncertainty occasionally prompts immediate but unsustained adjustments in ETS pricing. Furthermore, an exogenous increase in global market volatility produces a negative, short-term effect on ets, with the largest decline seen in the first five periods after the shock. The response gradually returns toward zero after period eight, consistent with the view that surges in global risk aversion temporarily suppress carbon market performance. Finally, a positive innovation in the ESG index yields a brief, positive impulse in ETS, peaking after four months and then fading. While the effect is not statistically significant throughout (as indicated by the wide confidence bands), the direction aligns with expectations that global sustainability sentiment can momentarily buoy carbon prices.

The IRF results corroborate the CCE-PVAR estimation findings: global shocks, whether economic, financial, or sustainability-related, are swiftly conveyed to carbon markets; nevertheless, their impact is generally ephemeral and accompanied by considerable uncertainty. These patterns underscore the integration of ETS markets with global influences and the difficulties in discerning enduring effects amid significant common causes and turbulent dynamics.

4.5. Machine Learning Evidence on ETS Determinants

To complement the parametric insights from the PVAR model, a machine learning-based analysis using gradient-boosted trees (XGBoost) and explainable AI (XAI) techniques was implemented to further investigate the determinants of ETS. This approach allows for exploring nonlinearities and conditional interactions that may not be fully captured by linear dynamic models.

The same macro-financial predictors used in the PVAR—rate, vol, ESG, EPU, CPI, andUNEMP—are used to train the XGBoost model to maintain methodological consistency and prevent look-ahead bias. All predictors are lagged by one period, such that ETS at time t are forecast using only information available up to time t − 1.

Time-series (rolling-origin) cross-validation is employed on the training set to assess model robustness, yielding a mean RMSE of 0.070. A linear regression benchmark (RMSE = 0.0783) fitted to the identical set of lagged predictors was outperformed by the holdout test set’s out-of-sample RMSE of 0.0712. These findings support the model’s strong prediction accuracy and consistent performance across several data folds.

Interpretability is facilitated through state-of-the-art XAI tools. Figure 6 presents the model’s global feature importance based on mean squared error reduction.

The machine learning model’s results suggest that CPI and Brent are the best predictors of ETS. Both have comparable significance in terms of average SHAP values, and the change in ESG index comes in after. UNEMP exhibits the minimal predictive impact on ETS under this framework. This sequence corresponds with the IRF analysis, which demonstrated that fluctuations in oil prices and the ESG index had a favorable short-term impact on ETS.

In addition to global feature attribution, the marginal impacts of ESG performance on ETS were investigated through a partial dependence plot (PDP).

Figure 7 illustrates the average predicted impact of l_esg on d_ets. It illustrates a nonlinear, non-monotonic relationship between lagged ESG scores and predicted ETS. For ESG scores below approximately 5.05, the marginal effect on ETS is close to zero or slightly negative, suggesting limited market response at low ESG levels. When ESG scores rise from about 5.05 to 5.18, predicted returns increase sharply, indicating a threshold where moderate ESG improvements are strongly rewarded. In the range between 5.18 and 5.22, the effect plateaus or even slightly declines, reflecting a possible saturation zone where additional ESG progress yields diminishing returns. However, for ESG scores above 5.22, the marginal effect becomes positive once again, with predicted returns rising as ESG scores reach their highest observed values. This pattern suggests that the market may distinguish between moderate, plateau, and exceptional ESG performance, with incremental improvements valued most at both the transition from low to moderate and from high to very high ESG compliance. Such a piecewise nonlinear pattern highlights the complexity of ESG pricing and investor learning, consistent with both threshold and informational exhaustion hypotheses, but also points to renewed differentiation at very high ESG levels.

To examine how ESG effects depend on the policy environment, Figure 8 presents a SHAP interaction plot between ESG scores and economic EPU. Each point represents a prediction for a given observation, colored by the corresponding lagged EPU value (with blue indicating low uncertainty and red high uncertainty). The results reveal a non-monotonic relationship: when EPU is low (bluer points), ESG scores are associated with a strong positive contribution to ETS. In contrast, under high uncertainty (redder points), the ESG effect diminishes or reverses, indicating that the value of ESG information is conditional on macro-predictability.

This context dependence reinforces the idea that investors reward ESG alignment more reliably in stable environments, whereas under heightened uncertainty, ESG signals are either discounted or crowded out by more urgent risk factors. These findings suggest that ESG-linked pricing is not structurally dominant but rather situationally salient, which is an insight not captured by the PVAR framework.

Lastly, Figure 9 summarizes the average marginal contribution of each variable on ETS return forecasts by revisiting the global feature importance using SHAP values. According to the global XGBoost attribution, EPU and Brent oil prices (RATE) continue to be the most prominent features, with inflation (CPI) coming in second. Even when fully preserved as time-series inputs, ESG scores rank among the least significant predictors. This further supports the fact that ESG ratings have a limited direct predictive potential.

Altogether, the machine learning results offer converging evidence with the PVAR estimates while unveiling additional conditional structures that deserve further structural modeling. Importantly, while PVAR offers limited leverage on globally invariant variables such as oil prices, the machine learning model that is unconstrained by panel structure still finds oil prices to have predictive value. This reinforces the view that, although ETSs react to oil price shocks in the short term (as shown by IRFs), carbon and fossil fuel markets may not be tightly coupled in a forward-looking or structural sense.

5. Discussion

This study set out to evaluate how ETSs are shaped by and respond to macroeconomic, energy, and sustainability-related shocks, and whether ETS prices themselves transmit effects into broader economic systems. Using a dual-method framework, panel VAR, and machine learning technique, the theoretical expectations outlined in the conceptual model, along with the eight hypotheses, were tested. This section discusses the empirical findings considering prior literature and addresses where these results align with or challenge existing theories.

The PVAR model and explainable ML analysis both indicate that ETS are difficult to predict with high accuracy, confirming findings by Xu et al. [79] and Jang et al. [80], who note high volatility and weak forecasting power in carbon prices. When analyzing ETS as a reactive indicator, the results offer partial confirmation. Consistent with prior literature, it was expected that ETS would be driven by labor market conditions, inflation, oil prices, volatility, policy uncertainty, and ESG scores. However, the PVAR model demonstrates that inflation is the sole variable that predicts ETS, by a four-month lag, confirming the H3 hypothesis. A surge in inflation takes time to ripple through the economy and into the carbon market, which is why its strongest effect on ETS prices is about four months later. Rising inflation prompts central banks to raise interest rates. In doing so, they cool industrial production over a few months, leading firms to then expect lower future emissions and demand fewer allowances. Moreover, higher energy and commodity costs discourage investment in low-carbon technologies, but traders only adjust prices once they have observed a few months of actual activity declines. This discovery is consistent with the concept of supply-side rigidity in carbon markets during periods of economic downturn [81].

Conversely, macro-financial variables such as unemployment, oil prices, market volatility, ESG, and EPU did not present statistically significant predictive effects on ETS in the PVAR-CCE, given the country sample and high-frequency period analyzed. Based on PVAR-CCE results, we reject the Hypotheses H1, H2, H4, H5, and H6, and this contrasts with prior research, which has consistently documented strong connections between macroeconomic indicators and carbon-market dynamics [39,45]. However, the machine learning framework (XGBoost with SHAP) shows some other interesting and more specific, conditional relationships that the linear PVAR fails to capture. ESG scores emerge as significant predictors of ETS, confirming H6 and displaying a nonlinear saturation pattern consistent with investor learning mechanisms, as proposed by Engle et al. [82]. A novel contribution of this study is the discovery that the influence of ESG on ETSs is conditional on economic policy uncertainty. SHAP and PDP plots reveal strong nonlinear interactions, whereby ESG factors become more influential when EPU is low. Moreover, to further explore the muted coefficients for policy uncertainty and ESG, we conducted a sensitivity analysis by introducing the interaction between policy uncertainty and ESG (demeaned_d_esg × demeaned_epu) in the CCE-PVAR framework. The detailed estimation outcomes are reported in Appendix A,

Table A2. Sensitivity analysis: CCE-PVAR with policy uncertainty × ESG interaction term.

Dependent Variable	Demeaned_D_ETS	Demeaned_VOL	Demeaned_EPU	Demeaned_CPI	Demeaned_UNEMP	Demeaned_D_ESG
demeaned_esg_epu	0.0321 (0.1834)	0.2129 (0.6201)	0.1913 * (0.0009)	−0.0068 (0.0226)	0.0035 (0.0952)	0.0000 (0.0000)

Note: Table reports coefficients of the ESG×EPU interaction term from CCE-PVAR estimation. Standard errors in parentheses. Only the policy uncertainty equation (demeaned_EPU) displays a statistically significant effect for the interaction (* meaning that p < 0.001). Complete estimation results are available upon request.

. The interaction term is statistically significant only in the policy uncertainty equation, while it remains insignificant in the other system equations. The overall results for policy uncertainty and ESG themselves remain consistent with our main findings. Thus, when policies are unpredictable, even the greenest companies stock up on extra permits to guard against possible policy changes, driving up demand and prices. But when policy is stable, good ESG performance more clearly means lower emissions, leading firms to buy fewer allowances, and prices ease. This finding advances the discussion on ESG–carbon linkages by showing that market participants’ valuation of sustainability signals depends not only on corporate disclosure but also on macro-policy predictability.

The role of oil prices is nuanced. Although neither the PVAR nor the machine learning model identifies them as strong predictors of ETSs, impulse response functions reveal a short-term negative reaction to oil price shocks, while global feature importance ranked Brent oil prices as the second most influential predictor of ETSs. This suggests that ETS markets are sensitive to energy cost shocks in the short run (so H5 holds in the short run), but oil prices do not serve as persistent drivers of ETS dynamics, supporting the findings of Soliman and Nasir [83].

The paper provides more robust support for the second pillar of the framework, which views ETSs as transmitters of macroeconomic influence. While the original hypotheses (H7 and H8) envisioned that ETSs would significantly affect oil prices, stock market volatility, and unemployment, the evidence only partially confirms this. ETSs present consistent transmission effects on labor markets and inflation, whereas no meaningful spillover into financial market volatility or oil prices is observed via the PVAR model (H8 is rejected). Specifically, lagged ETS exerts downward pressure on the labor market specifications. This means that rising ETSs are associated with reduced rates of unemployment in the short run, supporting H7 and highlighting labor reallocation effects and investment responses in low-carbon sectors. This finding reinforces the argument of Bowen & Kuralbayeva [84] that well-designed carbon pricing can generate positive employment outcomes under supportive policy environments.

Supporting the findings of Moessner [46] and Santabárbara & Suárez-Varela [47], PVAR-CCE results state that a one-unit rise in ETS prices two months earlier raises inflation by 0.0173, indicating a short-run inflationary pass-through. This implies that higher carbon prices signal greater future cost burdens, leading firms to push up their output and energy expenses onto consumer prices, thus reinforcing upward inflation pressure.

These findings contribute to filling a major gap in the empirical literature: the lack of high-frequency, multi-country analyses that integrate ETS markets within macro-financial modeling frameworks. While earlier studies have focused predominantly on the EU ETS or China’s pilot systems, this approach expands the analytical lens to include seven diverse jurisdictions and applies a hybrid methodology that is both dynamic and non-parametric. The convergence of results from the PVAR and ML models, despite methodological differences, provides robust cross-validation and highlights the value of integrating econometric rigor with machine learning interpretability.

6. Conclusions

This study contributes to the growing empirical literature on carbon markets by examining the dynamic drivers and transmission effects of ETSs across seven jurisdictions with diverse policy architectures. Unlike prior ETS research that uses either linear VAR or opaque machine learning alone, the hybrid framework marries the two: the CCE-PVAR maps out structural, bidirectional shock transmissions, while XGBoost + SHAP detects nonlinear thresholds and interactions. This approach enhances ETS research by increasing forecast precision and providing meaningful policy insights, identifying regime-dependent tipping points that conventional methods fail to expose.

In the PVAR-CCE model, inflation proves to be the most important and statistically significant predictor of ETS returns, amplifying the effect of supply-side rigidity and meaning that ETSs cannot release extra permits to offset demand shocks, accentuating price persistence and making inflation’s impact on carbon costs even more pronounced during downturns. One of the study’s most innovative findings is related to the ESG effects, which manifest solely within specific policy uncertainty frameworks, as demonstrated by the SHAP-based interaction analysis.

Going further, ETS markets, while relatively insulated from short-term financial volatility, exert forward influence on unemployment. This suggests an evolving role for ETS prices as active transmission channels within the energy–economy nexus. ESG-related influences also emerge as nonlinear and context-dependent, with their pricing relevance varying based on the level of policy uncertainty.

Several limitations merit attention. First, the analysis is constrained by data availability: high-frequency, cross-national ETS price series remain rare, limiting both sample breadth and statistical power. Second, the study does not undertake formal structural identification (e.g., sign restrictions or structural VARs), which limits causal interpretation. Third, while machine learning models add interpretive value, they remain sensitive to hyperparameter selection and lack formal inferential structure. Finally, the price of Brent crude oil is the study’s only proxy for shocks in the global energy market. Brent is often seen as the main benchmark for energy pricing around the world, although it may not take into consideration the effects of other energy price shocks, such as those involving coal or natural gas.

Future research should extend this dual framework to incorporate structural identification strategies, explore interactions at the sectoral or firm level, integrate a broader set of energy market indicators, and evaluate the predictive power of additional policy instruments or climate risk disclosures. As carbon markets expand and deepen, understanding their integration with macro-financial systems will be essential—not only for climate finance but for macroeconomic stability and sustainable policy design.

These findings have several policy implications. The long-run influence of ETS prices on unemployment highlights the need for proactive labor market planning in carbon-intensive sectors, especially as carbon prices rise or fluctuate. Policymakers could consider aligning ETS delivery mechanisms with broader macroeconomic conditions to mitigate unintended employment effects. In addition, the context-dependent role of ESG signals underlines the importance of reducing regulatory uncertainty and improving transparency to ensure consistent market responses. Stakeholders, including regulators, firms, and trade union organizations, should coordinate their efforts to anticipate and adapt to the transmission effects revealed in this study, supporting a more resilient and equitable low-carbon transition.