Risk Spillover in the Carbon-Stock System and Sustainability Transition: Empirical Evidence from China’s ETS Pilots and A-Share Emission-Regulated Firms

Abstract

This study employs the TVP-VAR-BK-DY spillover index model to investigate the risk spillover effects between China’s carbon emission trading system (ETS) pilots and A-share listed emission-regulated enterprises. The findings reveal that, due to the nascent stage of China’s carbon market, the overall risk spillover level within the “carbon-stock” system remains low; however, dynamic risk spillovers have shown an upward trend driven by the advancement of ETS pilots. In particular, during compliance periods, enterprises that exceed their emission limits must purchase sufficient allowances on the carbon trading market to avoid high penalties for non-compliance. This creates substantial demand, which drives a rapid increase in the spot prices of carbon allowances, triggering intense short-term price fluctuations and risk spillovers—a pronounced “compliance-driven trading” effect. Frequency domain analysis indicates that long-term shocks have a significantly greater impact on the market than short-term oscillations, reflecting moderate information processing efficiency within the “carbon-stock” system. Directional spillover analysis shows that A-share enterprises initially absorb risks from the carbon market in the short term, but over the long term, they transmit part of these risks back to the carbon market, forming a significant bidirectional risk transmission relationship. Furthermore, heterogeneity analysis reveals marked differences in risk spillover contributions among firms associated with different ETS pilots, as well as between enterprises with polluting behaviors and those with high ESG scores, with the latter contributing considerably higher spillovers to the overall carbon market. These findings offer nuanced insights into the dynamic, structural, and firm-level characteristics of risk spillovers, providing valuable guidance for policymakers and investors to enhance market stability and optimize investment strategies.

1. Introduction

To achieve the “carbon peak and carbon neutrality” (dual carbon) strategic goals and facilitate low-carbon transformation, the Chinese government has continuously refined its low-carbon policies and accelerated the transition toward a green economy. This transition not only addresses climate change mitigation but also serves as a critical pathway to achieving the United Nations Sustainable Development Goals (SDGs), particularly “Climate Action” (SDG13) and “Responsible Consumption and Production” (SDG12). Since 2013, China has implemented carbon emission trading systems (ETS) in multiple regions, culminating in the launch of a national carbon market in 2021. China’s carbon ETS follows a phased pilot approach, with local governments determining participating enterprises based on carbon emissions, thereby providing a structured platform for carbon allowance management and trading. As a pivotal policy instrument for achieving low-carbon targets, ETS compels enterprises to innovate in green technology and reduce emissions while transmitting carbon-related risks into the capital market via market-based mechanisms. This process steers investor attention toward corporate environmental performance and sustainable development, fostering dynamic linkages between the carbon and stock markets—a mechanism that directly contributes to building a global sustainable financial system.

Carbon allowances are the core element in the operation of China’s carbon ETS. A carbon allowance refers to the maximum limit of greenhouse gas emissions allocated to regulated companies by the regulatory authorities based on the total emissions target for a region or industry. The principles for carbon allowance allocation mainly include the following: first, the principle of total control and allocation, which sets the total allowance based on the region or industry’s emission reduction targets and distributes it reasonably among companies; second, the principle of fairness and efficiency, ensuring that companies have a fair competitive environment while incentivizing them to reduce emissions; and third, the principle of dynamic adjustment, which adjusts the allowance allocation plan in a timely manner based on economic development, industry changes, and changes in carbon reduction targets.

Taking the Hubei ETS pilot as an example, since 2014, it has gradually established a relatively complete carbon allowance allocation and trading mechanism. In terms of allowance allocation, the Hubei ETS pilot adopts a combination of historical emission baseline and industry benchmark methods to formulate allocation plans based on the historical emissions of companies and the industry’s emission intensity. To improve market efficiency and incentivize companies to reduce emissions, the Hubei carbon market has introduced an auction mechanism in the allocation of allowances, with part of the allowances allocated through market bidding to ensure reasonable pricing. Lastly, the Hubei carbon market has established an allowance reserve mechanism to cope with market fluctuations and supply-demand imbalances during special events, maintaining market stability. Under the carbon allowance trading system, emission-regulated firms are supervised by specific carbon markets. Due to China’s vast geographic and economic differences, the carbon reduction responsibilities and the demand for carbon allowances from enterprises are influenced by external factors such as climate, environmental conditions, and market scale. Therefore, there are differences in the institutional design, market efficiency, and carbon allowance prices between the ETS pilots and the national carbon market [1,2,3,4]. Nevertheless, the operation of the carbon market has been shown to have a positive impact on corporate R&D investment and green innovation [5], regional emission reduction, and green total factor productivity [6]. Therefore, developing the carbon market and maintaining a stable carbon price are crucial for promoting China’s green economic transformation [7].

As an emerging market, China’s carbon market exhibits both general market characteristics and unique features. One notable characteristic is the volatility of carbon prices [8], which shows long memory and asymmetry [9]. Additionally, significant risk spillovers occur not only among ETS pilots but also between the carbon market and energy and stock markets [10,11]. Notably, the risk spillover between carbon prices and the stock prices of emission-regulated firms exhibits substantial heterogeneity, influenced by industry attributes and firm-specific characteristics.

Companies in high-pollution, high-carbon emission industries experience a more significant positive impact on green innovation output under carbon trading pilot policies [12], thereby affecting their corporate value [13]. Wen et al. [14] further emphasized that stock indices in carbon-intensive industries are more significantly affected by carbon prices. These findings indicate that the intensity of the risk spillover between carbon prices and stock prices of emission-regulated firms varies significantly across industries. From a corporate perspective, this study identifies three important potential factors that influence the risk spillover between carbon prices and the stock prices of emission-regulated firms: the ETS pilot to which the company belongs, whether it is involved in pollution activities, and its Environmental, Social, and Governance (ESG) rating. First, regarding the ETS pilot, once a company is included in a specific carbon market (e.g., China Southern Airlines in the Guangdong ETS pilot), the company can only trade carbon allowances within that market and cannot trade across markets. This restriction directly associates the company with its specific carbon market, with more indirect links to other markets, potentially leading to heterogeneity in risk spillovers within the “carbon-stock” system. Second, in terms of pollution activities, the environmental regulatory costs faced by companies (e.g., environmental protection fees or taxes) are similar to their carbon emission costs. In a market-driven regulatory framework, polluting companies face greater environmental cost pressures, which may significantly influence the risk spillover within the “carbon-stock” system. Finally, from an ESG rating perspective, the carbon trading activities of emission-regulated firms reflect their performance in the “environmental” dimension of the ESG framework. Companies with high ESG ratings are expected to perform better in carbon emission management and actively participate in carbon market trading, thereby attracting more investors and enhancing market competitiveness [15]. In contrast, companies with low ESG ratings may adopt different market strategies, leading to significant differences in risk spillovers within the “carbon-stock” system.

Based on the above analysis, although there has been some research on the risk spillover between carbon markets and stock markets, several key issues remain underexplored. First, existing studies typically use overall or industry stock indices to represent the Chinese stock market [16,17], neglecting the significant scale differences between the carbon and stock markets. These indices include only a limited number of regulated companies, leading to inconclusive empirical findings. Second, while some studies recognize the impact of major policy changes and unexpected events on spillover effects [18,19], they often overlook firm-level heterogeneity in risk transmission. Furthermore, although many studies employ the time-varying parameter vector autoregressive (TVP-VAR) model with the DY spillover index [20], few examine how shocks of different durations affect spillovers from a frequency domain perspective. Therefore, this study aims to answer the following questions: Is the risk spillover between carbon prices and the stock prices of emission-regulated firms more pronounced compared to the overall stock market or industry indices? If so, what are its dynamic and frequency domain characteristics? Does firm-level heterogeneity contribute to variations in risk spillovers?

By addressing these issues, this study offers several key contributions to the understanding of the “carbon-stock” system and its price risk relationship, with a particular focus on the unique dynamics between carbon markets and stock prices of emission-regulated firms. First, it addresses a critical gap in existing research by shifting the focus from aggregate stock indices or industry-wide stock markets to the individual-level “carbon-stock” system. Specifically, it examines the intricate interaction between carbon prices and the stock prices of emission-regulated firms, offering a more granular understanding of the risk spillover mechanisms within the carbon market and the broader stock market. By doing so, the study provides new insights into how fluctuations in carbon prices can uniquely affect individual firms, moving beyond the generalized perspectives typically found in previous research.

Second, the study highlights the heterogeneity of emission-regulated firms in terms of their affiliation with different ETS pilots, pollution behavior, and ESG ratings. By categorizing firms based on these characteristics, the research uncovers significant variations in the intensity and structure of risk spillovers. This distinction reveals the critical role of corporate heterogeneity in shaping risk transmission across markets, thus contributing to the literature on market linkages and risk contagion. The study goes further by examining the potential moderating effects of ESG ratings, which adds a novel dimension to understanding how corporate social responsibility and sustainability practices influence the way firms respond to carbon price fluctuations. This approach provides a deeper understanding of the differential impacts of carbon market volatility on firms based on their regulatory and environmental characteristics.

Third, the paper employs a cutting-edge methodology, utilizing the TVP–VAR model-based BK–DY spillover index, integrated with frequency domain analysis, to dissect the spillover effects into short-term shocks and long-term impacts. This dynamic and frequency-based approach allows for a more nuanced and comprehensive understanding of the persistence of risk spillovers over different time horizons. The ability to differentiate between short-term volatility and long-term systemic risk is critical for both policymakers and investors, as it informs strategic decisions in managing risks related to carbon markets and stock prices. By applying this innovative methodology, the study offers a more precise picture of how shocks in carbon prices influence stock prices of emission-regulated firms and how these effects evolve and persist over time, providing valuable insights into the long-term dynamics and the resilience of firms to carbon market fluctuations.

From a theoretical perspective, this study shifts the focus from broad stock indices and industry markets to emission-regulated firms, exploring their role in the “carbon-stock” system’s price risk relationship. This deepens the academic understanding of the risk spillover between carbon prices and corporate stock prices, laying a theoretical foundation for future research. From a practical perspective, (1) this study provides a framework for investors to strategically allocate assets between ETS pilots and the stock market, helping them identify investment portfolios that match their risk preferences and understand the long-term and short-term characteristics of risks. (2) This study reveals the intrinsic relationship between carbon price fluctuations in ETS pilots and stock price fluctuations of emission-regulated firms, providing scientific evidence for regulatory authorities to develop more effective regulatory frameworks. (3) This study emphasizes the critical role of emission-regulated firms in connecting the carbon market and the stock market, providing empirical evidence for policymakers when compiling corporate lists, promoting the development of a unified carbon market, and expanding market scale.

The rest of the paper is organized as follows: Section 2 reviews the relevant literature, Section 3 describes the research methods and data, Section 4 presents the empirical results, Section 5 presents the heterogeneity analysis and Section 6 concludes the study.

2. Literature Review

Similar to the energy market, the carbon market exhibits both commodity and financial attributes, functioning not only as a policy-driven compliance instrument but also as a tradable financial asset with speculative value [21]. This dual nature creates complex linkages with the capital market, which can be understood through both microeconomic firm behavior and macro-level policy and market interactions.

From the business operations perspective, carbon prices directly influence the cost structure and financial health of emission-regulated firms. When carbon prices rise, firms with insufficient allowances face increased marginal abatement costs, leading to higher production expenses, elevated operational risk, and potentially lower profit margins and stock valuations [22]. Conversely, firms with excess allowances can monetize these surpluses, gaining windfall revenues and market-valuation benefits. This creates a compliance-trading-production nexus, where firms continuously adjust their operations, energy portfolios, and allowance trading strategies to align with regulatory requirements and market dynamics [23]. These adjustments impact firms’ cash flows, investor expectations, and ultimately, stock prices. Moreover, the establishment of carbon markets raises the cost of traditional energy sources [24], reshaping firms’ cost-benefit structures and incentivizing technological upgrading or energy substitution [25,26,27]. These structural shifts—often nonlinear and asymmetric across firms and sectors—are gradually priced into the stock market, thereby introducing a long-term structural linkage between carbon and equity markets.

From the price dynamics perspective, fluctuations in the demand for carbon allowances—driven by regulatory stringency, macroeconomic cycles, and sectoral performance—affect both the trend component and volatility regime of carbon prices, which in turn impact the return and risk profile of emission-regulated stocks, reinforcing a bidirectional feedback loop between the two markets.

From the investor perspective, carbon allowances and the equities of emission-regulated firms are increasingly seen as strategic components of environmental investment portfolios. Empirical studies have shown that these firms often exhibit a “carbon premium”, where market participants anticipate potential gains from future carbon efficiency or policy advantages [28]. Investors hold both asset classes to hedge against environmental policy risks and to exploit arbitrage or diversification benefits. Under the framework of the market contagion hypothesis [29], sharp movements in one market (e.g., due to carbon price shocks, regulatory news, or macroeconomic surprises) can induce behavioral overreactions and capital reallocation across asset classes, thereby transmitting risk from the carbon market to equity markets or vice versa.

Furthermore, both carbon and stock markets are deeply embedded in China’s economic fundamentals. Economic expansion leads to increased industrial activity and emissions, elevating the demand for carbon allowances and driving up their price—while simultaneously supporting firm profitability and equity performance [30]. In downturns, shrinking industrial output reduces emissions and allowance demand, but also introduces pessimism and volatility in stock markets. These procyclical movements enhance the systemic correlation and volatility co-movement between the two asset classes, intensifying risk spillovers, especially among firms directly engaged in carbon trading or energy-intensive sectors.

Taken together, these mechanisms suggest that the carbon-stock system operates as a complex adaptive system, where firm-level strategies, investor behavior, regulatory structures, and macroeconomic conditions co-evolve over time. Understanding these dynamics is critical for both policy effectiveness and portfolio risk management [31,32].

Among the earliest and most influential carbon markets globally, the European Union Emissions Trading System (EU ETS) has been extensively examined for its spillover effects with the stock market. Early studies offered conflicting evidence; for instance, Zhu et al. [33] reported that during Phase I, European Union Allowance (EUA) prices significantly negatively affected high-carbon industries, whereas Kumar et al. [34] found no significant relationship. With ongoing development and enhanced market efficiency [35], the linkage has gradually strengthened. Qiu et al. [11] reported a 0.75% short-term linkage between EUA prices and the STOXX600 index—nearly disappearing over the long term. Yang [36] observed an information spillover intensity of 51.4% from EUA prices to global clean energy stock indices, with a net spillover of −5.4%, while Chun et al. [37] noted a net spillover value of 0.51% between EUA prices and renewable energy stocks. Overall, since Phase III, the EU ETS has demonstrated significant price linkages with the stock market, industry markets, and listed companies.

China’s carbon market, with enormous development potential [38], has now surpassed the EU ETS to become the largest globally [39]. As the market expands, studies on the spillover effects between China’s carbon market and the stock market have increased. For instance, Wen et al. [40] found a significant asymmetric relationship between the two markets, whereas Zhang, J. et al. [41] reported relatively low risk spillover between carbon trading pilots in Beijing, Hubei, and Guangdong and the stock market—likely due to the early stage of these systems. Notably, during the 2015 stock market crisis, significant risk spillover from the stock market to the carbon market was observed. While research on industry markets shows substantial spillover effects between carbon prices and sectoral stock indices [42,43,44], studies on the linkage between carbon prices and the stock prices of emission-regulated firms remain limited. Wen et al. [45] indicated that carbon trading pilots enhanced the excess returns of emission-regulated firm stocks but did not deeply examine the price risk linkage between these firms and the carbon market. Although Dong et al. [42] constructed a risk spillover network using the ERGM model, their focus excluded carbon allowance-managed firms and their economic outcomes. Thus, further analysis of the risk spillover network between the carbon market and emission-regulated firms’ stock market is crucial.

Unlike the EU ETS, China operates multiple carbon markets and restarted its China Certified Emission Reduction (CCER) market in Sichuan in 2024. Given the strong economic interconnections among regions and the risk contagion hypothesis [10], studies indicate that carbon trading pilots in different regions are not fully independent and exhibit cross-regional risk contagion. For example, Zhu et al. [46] and Wang et al. [47] documented significant risk spillover among the Hubei, Guangdong, and Shenzhen pilots, with Wang et al. [47] further highlighting that overall market inefficiency and heterogeneity [48] are key drivers of these spillovers. To overcome representativeness limitations in existing research, Guo and Feng [49] and Xiao et al. [28] confirmed notable risk spillover effects after excluding pilots such as Fujian and Sichuan (which only trade CCER). These findings underscore that constructing a comprehensive “carbon-stock” risk spillover network requires considering multiple carbon trading pilots to accurately reflect the overall performance of China’s carbon market.

Researchers have identified several drivers behind the risk spillover between the carbon and stock markets. Wu and Liu [14] developed a green financial system incorporating both the carbon and green bond markets, demonstrating that investor sentiment and climate policy uncertainty significantly affect net spillovers. Similarly, Adekoya and Oliyide [50] found that economic policy uncertainty (EPU) plays a crucial role in spillover effects across financial markets. Moreover, from a heterogeneity perspective, Dong et al. [42] noted that industries differ in their spillover effects, with the energy sector acting as a primary risk transmitter due to high carbon allowance demand. Regarding the linkage mechanism between China’s carbon and stock markets, Razzaq et al. [51] pointed out that under bullish market conditions, the Shenzhen carbon allowance price negatively predicts the overall stock market price, whereas under bearish conditions it exhibits a positive predictive relationship, explaining this phenomenon from the perspective of carbon allowances as a financing tool for enterprises. Wen et al. [40] obtained findings consistent with those of Razzaq et al. [21] in bullish markets, showing that carbon prices are significantly negatively correlated with the overall stock market index; they argued that rising carbon prices indicate reduced production, increased corporate financing costs, and consequent declines in profits and performance, which in turn drive down stock indices. In studies on exogenous shocks, Chen et al. [52] found that on most trading days, both the overall stock market and industry stock markets typically lead the carbon market; however, when the mean return of the carbon market is significantly negative, the leading-lagging relationship reverses. Furthermore, government policy shocks and the US–China trade war can reinforce the leading role of the carbon market for different stock market sectors, whereas the COVID-19 pandemic exerts the opposite effect on the leading-lagging relationship. However, studies exploring the heterogeneity of the “carbon-stock” system from the perspective of corporate characteristics remain limited, which is the central focus of this paper.

In summary, while substantial research has examined the linkage between the “carbon-stock” system and the spillover mechanisms from a corporate behavior perspective, most studies remain focused on the overall market or industry level. The price risk linkage between emission-regulated firms actively engaged in carbon trading and the carbon market is still underexplored. Therefore, this paper focuses on this key group of firms to further investigate their risk linkage characteristics with the carbon market. The core contribution lies in shifting the analytical perspective from the macro market level to the micro corporate level, providing empirical insights into corporate decision-making under the “allowance trading” mechanism and offering a novel perspective for market participants’ risk response strategies.

3. Methods and Data

3.1. Methodology

This study adapts the dynamic BK–DY spillover index proposed by Chatziantoniou et al. [53] based on the Generalized TVP–VAR model to examine the time-varying risk spillover between ETS pilots and A-share listed emission-regulated firms. First, we define a p-order TVP–VAR model as follows:

$${\mathit{x}}_t={\mathsf{\Phi }}_{1t}{\mathit{x}}_{t-1}+{\mathsf{\Phi }}_{2t}{\mathit{x}}_{t-2}+\dots +{\mathsf{\Phi }}_{pt}{\mathit{x}}_{t-p}+{\mathit{ϵ}}_t{\mathit{ϵ}}_t\sim N(\mathbf{0},{\mathbf{\Sigma }}_t)$$

(1)

In this context, ${\mathit{x}}_t$ and ${\mathit{ϵ}}_t$ are N × 1 dimensional time series vectors, while ${\mathbf{\Sigma }}_t$ and ${\Phi }_{it}$ (i = 1, 2, … p) are N × N matrices representing the time-varying variance-covariance matrix and the time-varying VAR coefficients, respectively. After estimating the model using a multivariate Kalman filter, the general expression of the TVP–VAR model is transformed into a Time-Varying Parameter Moving Average (TVP–VMA) model based on the Wold theorem. The time-varying coefficient matrix ${\Psi }_h$ from the TVP–VMA model is extracted and used to compute the Generalized Forecast Error Variance Decomposition (GFEVD). This GFEVD serves as the basis for constructing the spillover network. For H = 1, 2 …, the spillover from variable i to variable j can be expressed as

$${\theta }_{ijt}(H)={\displaystyle \frac{{({\mathsf{\Sigma }}_t)}_{jj}^{-1}{\displaystyle \sum _H^{h=0}}{({({\mathsf{\Psi }}_h{\mathbf{\Sigma }}_t)}_{ijt})}^2}{{\displaystyle \sum _H^{h=0}}{({\mathsf{\Psi }}_h{\mathbf{\Sigma }}_t{\mathsf{\Psi }}_h^{\prime })}_{ii}}}$$

(2)

$${\tilde{\theta }}_{ijt}(H)={\displaystyle \frac{{\theta }_{ijt}(H)}{{\displaystyle \sum _N^{k=1}}{\theta }_{ijt}(H)}}$$

(3)

where when H = 1, 2, …, ${\theta }_{ijt}(H)$ represents the contribution of the j-th variable to the forecast error variance of the i-th variable. Since the row sums of ${\tilde{\theta }}_{ijt}(H)$ do not equal 1, normalization is necessary to obtain ${\tilde{\theta }}_{ijt}$, leading to the following equations: ${\displaystyle \sum _{i=1}^N{\tilde{\theta }}_{ijt}(H)}=1$ and ${\displaystyle \sum _{j=1}^N{\displaystyle \sum _{i=1}^N{\tilde{\theta }}_{ijt}(H)}}=N$. At this point, the connectedness of the spillover network can be estimated, starting with the Net Pairwise Directional Connectedness (NPDC), defined as:

$$NPD{C}_{ijt}(H)={\tilde{\theta }}_{ijt}(H)-{\tilde{\theta }}_{jit}(H)$$

(4)

If $NPD{C}_{ijt}(H)>0$, it indicates that the influence of variable i on variable j is greater, and vice versa. Subsequently, Equations (8) and (9) measure the directional spillover from variable i to all other variables j, and the directional spillover into variable i from all other variables j, respectively:

$$T{O}_{it}(H)=\sum _N^{i=1,i\ne j}{\tilde{\theta }}_{jit}(H)$$

(5)

$$FRO{M}_{it}(H)=\sum _N^{j=1,i\ne j}{\tilde{\theta }}_{ijt}(H)$$

(6)

$T{O}_{it}(H)$ measures the total spillover effect of variable i on all other variables in the network, while $FRO{M}_{it}(H)$ measures the total spillover effect received by variable i from all other variables in the network. Subtracting Equation (9) from Equation (8) yields the Net Spillover Index (NET), which is generally interpreted as the overall impact of variable i on the network:

$$NE{T}_{it}(H)=T{O}_{it}(H)-FRO{M}_{it}(H)$$

(7)

Finally, the Total Spillover Index (TSI) measures the overall interconnectedness among assets within the network, reflecting the system-wide net influence of risk spillovers.

$$TS{I}_t(H)=N^{-1}\sum _N^{i=1}T{O}_{it}(H)=N^{-1}\sum _N^{i=1}FRO{M}_{it}(H)$$

(8)

The TSI indicates the average impact of a shock from one variable on all other variables. A higher TSI value signifies greater connectedness or risk spillover levels within the “Carbon-Stock” system, and vice versa. The above methods focus on estimating the spillover network connectedness from a time-domain perspective. Next, based on the spectral decomposition method by Stiassny [54], the connectedness of the spillover network will be estimated from a frequency-domain perspective. First, consider the frequency response function:

$$\Psi (e^{-i\omega })=\sum _{\infty }^{h=0}{e}^{-i\omega h}{\Psi }_h$$

(9)

where $i=\sqrt{-1}$ and $\omega$ denotes the frequency to continue with the spectral density of $x_t$ at frequency $\omega$ which can be defined as a Fourier transformation of the TVP-VMA (∞)

$$\begin{array}{c}{S}_x(\omega )={\displaystyle \sum _{\infty }^{h=-\infty }}E({\mathit{x}}_t{\mathit{x}}_{t-h}^{\prime })e^{-i\omega h}=\Psi (e^{-i\omega h}){\mathsf{\Sigma }}_t{\Psi }^{\prime }(e^{+i\omega h})\end{array}$$

(10)

The frequency GFEVD is the combination of the spectral density and the GFEVD. As in the time domain case we need to normalize the frequency GFEVD which can be formulated as follows,

$${\theta }_{ijt}(\omega )={\displaystyle \frac{{({\mathsf{\Sigma }}_t)}_{jj}^{-1}|{\displaystyle \sum _{\infty }^{h=0}}{(\Psi (e^{-i\omega h}){\mathbf{\Sigma }}_t)}_{ijt}{|}^2}{{\displaystyle \sum _{\infty }^{h=0}}{(\Psi (e^{-i\omega h}){\mathbf{\Sigma }}_t\Psi (e^{i\omega h}))}_{ii}}}$$

(11)

$${\tilde{\theta }}_{ijt}(\omega )={\displaystyle \frac{{\theta }_{ijt}(\omega )}{{\displaystyle \sum _N^{k=1}}{\theta }_{ijt}(\omega )}}$$

(12)

where ${\tilde{\theta }}_{ijt}(\omega )$ represents the portion of the spectrum of the ith variable at a given frequency $\omega$ that can be attributed to a shock in the jth variable. It can be interpreted as a within-frequency indicator.

To assess short-term and long-term connectedness rather than connectedness at a single frequency, we aggregate all frequencies within a specific range, $\begin{array}{c}d=(a,b):a,b\in (-\pi ,\pi ),a<b\end{array}$:

$${\tilde{\theta }}_{ijt}(d)=\underset{a}{\overset{b}{{\displaystyle \int }}}{\tilde{\theta }}_{ijt}(\omega )d\omega$$

(13)

Based on this, the spillover network connectedness can be calculated, which is interpreted in the same way as in Diebold and Yılmaz (2012, 2014) [55,56]. In this case, it refers to frequency connectedness, specifically the spillover effects within a certain frequency range d:

$$NPD{C}_{ijt}(d)={\tilde{\theta }}_{ijt}(d)-{\tilde{\theta }}_{jit}(d)$$

(14)

$$T{O}_{it}(d)=\sum _N^{i=1,i\ne j}{\tilde{\theta }}_{jit}(d)$$

(15)

$$FRO{M}_{it}(d)=\sum _N^{i=1,i\ne j}{\tilde{\theta }}_{ijt}(d)$$

(16)

$$NE{T}_{it}(d)=T{O}_{it}(d)-FRO{M}_{it}(d)$$

(17)

$$\begin{array}{c}TS{I}_t(d)=N^{-1}{\displaystyle \sum _N^{i=1}}T{O}_{it}(d)=N^{-1}{\displaystyle \sum _N^{i=1}}FRO{M}_{it}(d)\end{array}$$

(18)

All measurement methods provide information on specific ranges rather than overall impact. Following the approach of Barunik and Krehlik [57], overall frequency connectedness measures are obtained by weighting the contributions of each frequency band relative to the entire system, where the weight $\mathsf{\Gamma }(d)$ is defined as $\mathsf{\Gamma }(d)={\displaystyle \sum _N^{i,j=1}}{\tilde{\theta }}_{ijt}(d)/N$.

$${\widetilde{NPDC}}_{ijt}(d)=\mathsf{\Gamma }(d)\cdot NPD{C}_{ijt}(d)$$

(19)

$$\widetilde{TO}it(d)=\mathsf{\Gamma }(d)\cdot T{O}_{it}(d)$$

(20)

$${\widetilde{FROM}}_{it}(d)=\mathsf{\Gamma }(d)\cdot FRO{M}_{it}(d)$$

(21)

$${\widetilde{NET}}_{it}(d)=\mathsf{\Gamma }(d)\cdot NE{T}_{it}(d)$$

(22)

Finally, this paper presents the relationship between frequency domain connectedness measures and time domain connectedness measures:

$$NPD{C}_{ijt}(H)=\sum _{d}NPD{C}_{ijt}(d)$$

(23)

$$T{O}_{it}(H)=\sum _{d}T{O}_{it}(d)$$

(24)

$$FRO{M}_{it}(H)=\sum _{d}FRO{M}_{it}(d)$$

(25)

$$NE{T}_{it}(H)=\sum _{d}NE{T}_{it}(d)$$

(26)

$$TS{I}_t(H)=\sum _{d}TS{I}_t(d)$$

(27)

3.2. Data

This study uses daily data to analyze the risk spillover relationship between the Chinese carbon market and the stock market from 5 May 2014 to 31 December 2022, ensuring the completeness, availability, and consistency of the data. As mentioned earlier, China currently has nine carbon markets, including eight carbon trading pilot projects and the national carbon market. However, through data sorting and analysis, it was found that only five carbon trading pilots—Beijing (BJ), Shanghai (SH), Hubei (HB), Shenzhen (SZ), and Guangdong (GD)—had relatively complete and less missing data during the selected sample period. Based on data availability and completeness, and referring to Wu and Qin [58], this study uses the carbon emission quota closing prices of these five carbon trading pilots to represent the overall performance of the Chinese carbon market. The carbon trading pilots of Fujian, Chongqing, and Tianjin, as well as the national carbon market, were excluded due to severe data deficiencies. Additionally, since the Sichuan carbon trading pilot only trades CCER, its carbon price data was also excluded.

To more intuitively demonstrate the representativeness of the carbon trading pilots,

Table 1. Cumulative Trading Statistics of Carbon Trading Pilot Programs as of 2023.

	Primary Market		Secondary Market
	Trading Volume (10,000 tons)	Trading Amount (100 million yuan)	Trading Volume (10,000 tons)	Trading Amount (100 million yuan)
HB	1469.32	4.31	37,039.24	91.44
GD	2271.83	9.91	19,581.29	48.61
SZ	654.84	3.32	11,271.28	24.19
BJ	246.11	2.7	5062.47	13.52
SH	78.08	0.32	4933.90	8.78
TJ	664.64	1.48	2979.91	7.60
FJ	10.00	---	3032.82	7.00
CQ	1159.27	3.36	4425.22	6.16
SC	0.00	0.00	0.00	0.00

presents the cumulative trading volume and transaction value of carbon allowances across various regional pilots as disclosed by the Hubei carbon trading pilot as of December 2023. As clearly shown in Table 1, the four excluded carbon trading pilots—Tianjin (TJ), Fujian (FJ), Chongqing (CQ), and Sichuan (SC)—exhibit significantly lower cumulative trading volumes and transaction values in the secondary market compared to the other carbon trading pilots selected for this study. Additionally, based on the data collected, the number of effective trading days during the sample period for TJ, FJ, and CQ were 833, 796, and 749 days, respectively, which is also substantially fewer than those of the other carbon trading pilots included in this study. In summary, the five carbon trading pilots selected in this study effectively represent the overall operation of China’s carbon market.

For the Beijing carbon trading pilot, due to the lack of closing price data, the average transaction price was used as a substitute. These five carbon trading pilots are the most mature and have the highest market participation, thus providing a more comprehensive reflection of the overall operation of the Chinese carbon market. The daily price data for the above pilots is sourced from the WIND database.

In the stock market aspect, this study collected the list of emission-regulated firms from the CSMAR database between 2014 and 2022, selecting A-share listed companies in the Hubei, Guangdong, Shenzhen, Beijing, and Shanghai carbon trading pilot areas for analysis. As the largest stock market in China, the A-share market reflects the macroeconomic conditions of the country. The sample of A-share emission-regulated firms was processed as follows: (1) financial and insurance firms were excluded; (2) all firms marked as ST or *ST were excluded. The final sample includes 172 firms, and their specific names and daily closing price data are detailed in Supplementary Material. Since the TVP–VAR model can accommodate a limited number of variables, this study created a composite variable called StockAll, which reflects the price changes of all A-share emission-regulated firms. This variable is calculated by averaging the daily closing prices of all selected firms, following the method outlined by DeMiguel et al. [59]. Detailed information about the data processing is provided in the Supplementary Material. The study collected all publicly available data and made every effort to ensure that no emission-regulated firms in the five carbon trading pilots were overlooked.

In the heterogeneity analysis, A-share emission-regulated firms are classified along three dimensions: carbon trading pilot affiliation, pollution behavior, and ESG rating level. First, firms are classified based on their participation in carbon trading pilots, with five categories representing Hubei (StockHB), Guangdong (StockGD), Shenzhen (StockSZ), Beijing (StockBJ), and Shanghai (StockSH). This classification is based on differences in the policy implementation and market maturity of these carbon trading regions, which are representative in China’s carbon market. Therefore, this classification helps to reveal the impact of regional differences in carbon markets on carbon price fluctuations. Second, pollution behavior is classified using environmental expense and tax data from the CSMAR database, assessing pollutant emissions (such as air, water, solid waste, noise) and industry characteristics. Firms are divided into a pollution behavior group (StockP, i.e., “polluting stocks”) and a non-pollution behavior group (StockC, i.e., “clean stocks”). This classification combines the tax standards for pollutant emissions in environmental tax and fee policies with the industry’s characteristics, ensuring objectivity. Finally, ESG ratings are classified based on composite rating data from the WIND database, with the median ESG score calculated annually. Firms below the median are categorized as low ESG (StockLESG), and those equal to or above the median are categorized as high ESG (StockHESG). The core purpose of this classification is to ensure that annual changes in corporate ESG performance are dynamically reflected, to better study the differences in how stocks of firms with different attributes react to carbon price fluctuations, and to further explore the micro-level dynamics of the specific group of “emission-regulated firms.”

Due to some carbon trading pilots experiencing zero transaction volumes or trading suspensions during the sample period, missing values appeared in the return series. Since zero transaction volumes and trading suspensions themselves convey market information, missing values are filled with zeros in this study. Given that the focus of this study is on risk spillover, market risk is proxied by the volatility of the variable. First, the logarithmic differences of the daily price series are taken to obtain the return series, expressed as percentages. Second, considering that the GARCH model and RV model are difficult to adapt to the return series of carbon trading pilots to estimate volatility [49], this study follows Forsberg and Ghysels [16] and Zheng et al. [60], using the absolute values of the return series to characterize volatility. Overall,

Table 2. Definition, construction, and data sources of variables.

Variable	Definition	Construction Method	Data Source
HB	Hubei carbon trading pilot carbon allowance	Daily closing price (or average transaction price if missing)	WIND Database
GD	Guangdong carbon trading pilot carbon allowance	Daily closing price	WIND Database
SZ	Shenzhen carbon trading pilot carbon allowance	Daily closing price	WIND Database
BJ	Shanghai carbon trading pilot carbon allowance	Daily closing price	WIND Database
SH	Beijing carbon trading pilot carbon allowance	Average transaction price (due to lack of closing price data)	WIND Database
StockAll	Composite index of all A-share emission-regulated firms	Equal-weighted average of daily closing prices (DeMiguel et al., 2009) [59]	CSMAR Database (stock prices)
StockHB	Stocks of emission-regulated firms in Hubei carbon trading pilot	Average daily closing price of firms registered in Hubei	CSMAR Database
StockGD	Stocks of emission-regulated firms in Guangdong carbon trading pilot	Average daily closing price of firms registered in Guangdong	CSMAR Database
StockSZ	Stocks of emission-regulated firms in Shenzhen carbon trading pilot	Average daily closing price of firms registered in Shenzhen	CSMAR Database
StockBJ	Stocks of emission-regulated firms in Beijing carbon trading pilot	Average daily closing price of firms registered in Beijing	CSMAR Database
StockSH	Stocks of emission-regulated firms in Shanghai carbon trading pilot	Average daily closing price of firms registered in Shanghai	CSMAR Database
StockP	Polluting stocks (high environmental expense/tax firms)	Firms with significant pollution behavior based on environmental expense data	CSMAR (environmental tax data)
StockC	Clean stocks (low environmental expense/tax firms)	Firms with minimal pollution behavior	CSMAR (environmental tax data)
StockLESG	Low-ESG-rated emission-regulated firms	Firms with ESG scores below annual industry median	WIND (ESG ratings)
StockHESG	High-ESG-rated emission-regulated firms	Firms with ESG scores equal to or above annual industry median	WIND (ESG ratings)

presents the definitions, calculation methods, and sources of all variables.

Figure 1 illustrates the trends in the daily price series and daily return series for all variables. Overall, the price trends of different ETS pilot markets exhibit significant variations. The prices of HB and BJ show a continuous upward trend throughout the sample period, while GD prices follow a “decline–stabilization–increase” pattern. SZ prices experience a consistent decline before 2022, followed by a sharp increase, whereas SH prices remain stable before 2022 and then rise substantially. These differences indicate that ETS pilots are at different stages of market development and are influenced by distinct policy factors.

Regarding returns, the volatility patterns of different ETS pilot markets vary significantly. SZ exhibits extreme fluctuations from February to June 2019 and from October 2021 to March 2022, with return swings nearing ±200%, indicating substantial price risk. BJ returns display a “volatility clustering” pattern, while SH returns remain largely stable with occasional significant fluctuations. This suggests that different ETS pilot markets have distinct price formation mechanisms and levels of market maturity, with some being more susceptible to short-term trading behaviors or policy-driven impacts.

In contrast, the stock prices of A-share listed emission-regulated firms demonstrate greater consistency. All stock variables reach a peak around June 2015 and a trough near January 2019. Moreover, the return fluctuations of all stocks remain within a relatively stable range of −10% to 7%, reflecting a more structured market behavior. This indicates that, despite the diverse volatility patterns of the carbon market, the stock prices of emission-regulated firms are primarily driven by common market factors, suggesting that fluctuations in carbon allowance prices may influence their valuations.

Table 3. Descriptive statistical results of variables.

Obs = 2108	Mean	Max	Min	Std. Dev.	Skew	Kurt	J-B	ADF	PP
	Panel A: Volatility (%)
HB	1.736	19.721	0	2.261	2.249	6.086	5040.955 ***	−9.234 ***	−1433.019 ***
GD	2.43	23.985	0	3.024	1.544	1.979	1184.195 ***	−8.926 ***	−1853.324 ***
SZ	14.787	247.948	0	29.965	4.432	22.276	50,591.883 ***	−7.542 ***	−1707.008 ***
BJ	3.379	46.962	0	5.913	2.149	4.319	3269.003 ***	−9.786 ***	−1682.987 ***
SH	2.139	92.846	0	4.73	7.648	112.937	1,143,053.971 ***	−10.632 ***	−2145.079 ***
StockAll	1.26	9.174	0	1.269	2.327	7.528	6896.557 ***	−6.939 ***	−2707.331 ***
StockHB	1.341	9.666	0	1.271	2.117	6.626	5443.775 ***	−7.8 ***	−2621.265 ***
StockGD	1.543	10.573	0	1.76	2.426	7.405	6899.96 ***	−6.982 ***	−2256.69 ***
StockSZ	1.396	9.216	0	1.341	1.986	5.545	4095.28 ***	−7.002 ***	−2716.859 ***
StockBJ	1.407	9.462	0	1.357	1.897	4.583	3115.845 ***	−7.602 ***	−2529.304 ***
StockSH	1.228	10.46	0.001	1.431	3.089	12.517	17,151.352 ***	−6.567 ***	−2068.422 ***
StockP	1.297	10.532	0.002	1.301	2.326	7.957	7478.623 ***	−7.222 ***	−2610.125 ***
StockC	1.287	9.193	0	1.285	2.251	7.044	6152 ***	−6.854 ***	−2686.743 ***
StockLESG	1.281	9.674	0.002	1.299	2.215	6.671	5645.462 ***	−7.002 ***	−2644.37 ***
StockHESG	1.298	9.69	0.001	1.304	2.344	7.811	7306.54 ***	−6.869 ***	−2708.379 ***
	Panel B: Volatility based on Box–Cox transformation (%)
HB	−0.127	3.004	−3.874	1.332	−0.448	−0.087	71.182 ***	−8.458 ***	−1705.061 ***
GD	0.272	3.137	−4.42	1.278	−0.472	0.123	79.758 ***	−9.092 ***	−2044.018 ***
SZ	1.584	4.627	−4.671	1.278	−0.411	0.516	83.177 ***	−6.519 ***	−1725.428 ***
BJ	0.426	3.339	−5.376	1.243	−0.325	1.528	243.454 ***	−8.82 ***	−1780.585 ***
SH	0.261	4.087	−4.484	1.125	−0.435	2.286	527.37 ***	−9.684 ***	−2087.715 ***
StockAll	−0.263	2.245	−5.999	1.141	−0.935	1.749	577.55 ***	−8.041 ***	−2622.364 ***
StockHB	−0.157	2.412	−5.777	1.107	−0.843	1.265	391.378 ***	−8.761 ***	−2498.889 ***
StockGD	−0.062	2.451	−6.187	1.161	−0.707	1.235	310.658 ***	−8.012 ***	−2296.988 ***
StockSZ	−0.158	2.305	−6.168	1.166	−0.943	1.496	510.834 ***	−8.002 ***	−2444.155 ***
StockBJ	−0.142	2.339	−6.127	1.146	−0.92	1.754	569.718 ***	−8.116 ***	−2396.558 ***
StockSH	−0.325	2.491	−5.843	1.159	−0.655	1.147	267.365 ***	−7.516 ***	−2398.263 ***
StockP	−0.238	2.514	−5.261	1.172	−0.869	1.286	411.927 ***	−8.393 ***	−2466.856 ***
StockC	−0.242	2.279	−6.364	1.148	−0.922	1.639	536.407 ***	−7.957 ***	−2552.916 ***
StockLESG	−0.251	2.362	−5.588	1.142	−0.757	1.026	294.768 ***	−8.261 ***	−2541.728 ***
StockHESG	−0.235	2.35	−6.242	1.157	−0.952	1.852	621.529 ***	−7.959 ***	−2545.835 ***

Note: *** indicate significance at the 1% level.

presents the descriptive statistics for the volatility series of all variables, each comprising 2108 observations. As shown in Panel A, among the ETS pilots, the average volatility for all variables, except for SZ, ranges from 1% to 4%, with standard deviations between 1% and 6%. Notably, the average volatility and standard deviation for SZ are significantly higher, at 14.787% and 29.965%, respectively, indicating substantial price risk within the Shenzhen ETS pilot. In the stock market, all variables exhibit relatively low standard deviations of volatility, with StockGD having the highest at 1.76%. Conversely, the variable with the lowest standard deviation in the ETS pilots is Guangdong (GD) at 2.261%, still exceeding the standard deviation of StockGD, suggesting that the price risk in ETS pilots surpasses that of A-share listed emission-regulated firms.

Additionally, except for GD, the kurtosis values of volatility for all other variables are greater than 3, indicating a leptokurtic distribution characteristic. The Jarque–Bera test strongly rejects the null hypothesis that all variables follow a normal distribution. However, the assumption of normality in VAR models during GVD analysis [61] may result in skewness and kurtosis in the original data, affecting the robustness of the estimation results. To address this, this paper follows Guo and Feng [49] by applying the Box–Cox transformation [62] to the volatility data, thereby approximating its distribution to a normal distribution. Panel B of Table 1 presents the descriptive statistics for each variable after the Box–Cox transformation, showing a significant reduction in the J-B statistic. Finally, a unit root test was conducted, with results from both the augmented Dickey–Fuller and Phillips–Perron tests indicating that the volatility series of all variables are stationary at the 1% significance level.

4. Empirical Results

This section presents the empirical results and discusses the issues encountered during the analysis. The results are based on an empirical framework integrating the methods of Diebold and Yılmaz [55,56], Koop and Korobilis [63], Barunik and Krehlik [57], and Antonakakis et al. [20]. It is important to emphasize again that the results in this section are derived from the TVP–VAR model, from which the generalized forecast error variance decompositions (GFEVDs) used to calculate the spillover indices are extracted.

This study calculates the spillover indices for low-frequency and high-frequency intervals, corresponding to short-term and long-term levels, respectively. According to the research of Meng et al. [64] and Chatziantoniou et al. [53], when the high-frequency interval dominates the “carbon-stock” system connectivity, it indicates that the related markets can process information quickly, with shock transmission mainly occurring as short-term events (i.e., events that occurred 1 to 5 days ago). This suggests that long-term impacts (i.e., events that occurred 6 to 100 days ago) are insufficient to outweigh the current market developments influencing the connectivity of the “carbon-stock” system. In contrast, when the low-frequency interval dominates the network connectivity, this may reflect recent structural changes that gradually emerge over time.

In this section, the optimal lag order was selected based on the Akaike Information Criterion (AIC), Hannan–Quinn (HQ), Schwarz Criterion (SC), and Final Prediction Error (FPE) criteria, leading to the establishment of a VAR(5) model. Following the study by Chatziantoniou et al. [53], the forecast period is set to 100 periods, with the frequency intervals defined as one to five periods (i.e., 1–5 days) for the short-term decomposition, and more than five periods (i.e., 6–100 days) for the long-term decomposition of the TSI.

4.1. Total Spillover Analysis

When exploring the risk spillover between the “Carbon-Stock” system, the focus is primarily on static risk spillover (see

Table 4. Static spillovers.

	HB	GD	SZ	BJ	SH	StockAll	FROM
HB	85.85(51.67)[34.18]	3.20(1.23)[1.97]	3.99(1.35)[2.65]	2.52(1.37)[1.15]	2.34(1.25)[1.09]	2.11(1.23)[0.87]	14.15(6.42)[7.73]
GD	3.28(1.08)[2.20]	84.36(46.44)[37.92]	3.05(1.16)[1.89]	3.19(1.21)[1.97]	2.82(1.42)[1.40]	3.30(1.41)[1.89]	15.64(6.29)[9.35]
SZ	2.24(0.93)[1.31]	3.40(0.89)[2.51]	84.50(44.30)[40.20]	3.22(1.05)[2.17]	2.63(0.95)[1.68]	4.02(1.06)[2.96]	15.50(4.88)[10.63]
BJ	2.23(1.12)[1.11]	3.12(1.39)[1.73]	2.51(1.17)[1.34]	85.71(52.07)[33.64]	3.03(1.37)[1.66]	3.39(1.23)[2.16]	14.29(6.28)[8.00]
SH	2.18(1.33)[0.85]	3.31(1.43)[1.88]	2.82(1.12)[1.70]	4.13(2.03)[2.10]	84.76(54.55)[30.20]	2.80(1.38)[1.42]	15.24(7.29)[7.95]
StockAll	2.10(1.32)[0.79]	3.21(1.56)[1.65]	2.63(1.68)[0.95]	2.82(2.07)[0.75]	2.19(1.39)[0.80]	87.05(63.07)[23.98]	12.95(8.01)[4.94]
TO	12.03(5.78)[6.25]	16.24(6.49)[9.75]	15.01(6.48)[8.53]	15.87(7.73)[8.15]	13.01(6.37)[6.64]	15.61(6.32)[9.30]	TSI
NET	−2.12(−0.64)[−1.48]	0.60(0.20)[0.40]	−0.49(1.60)[−2.09]	1.58(1.44)[0.14]	−2.23(−0.91)[−1.32]	2.66(−1.69)[4.35]	14.63(6.53)[8.10]

Note: The results are based on a TVP–VAR model with a lag order of five and a GFEVD with a forecast horizon of 100. The “FROM” column represents directional spillover values received, while the “TO” column indicates directional spillover values transmitted. The “NET” column reflects the net directional spillover value, which is the difference between directional “TO” spillovers and directional “FROM” spillovers. The “TSI” is used to measure the degree of spillover within the “Carbon-Stock” system. The values in parentheses () and square brackets [] represent short-term and long-term frequency connectivity measures, respectively (Barunik and Krehlik, 2018) [57], while all other values correspond to the respective temporal connectivity measures (Diebold and Yılmaz, 2012) [55].

) and dynamic risk spillover (see Figure 2). The results in Table 4 indicate that the TSI of the “Carbon-Stock” system is 14.63%, suggesting that 14.63% of the forecast error variance in this system can be attributed to interactions within the spillover network, while the remaining 85.37% is explained by the specific components of individual variables. In contrast, the study by Dong et al. [42] indicates that 96.57% of the forecast error variance in the system composed of the entire carbon market and the overall stock market arises from the specific components of the variables. This suggests that, compared to the former, the risk spillover within the “Carbon-Stock” system, composed of the whole carbon market and emission-regulated firm samples, is more significant.

On the other hand, Figure 2 illustrates the dynamic risk spillover of the “Carbon-Stock” system during the sample period, with the TSI showing a characteristic of persistent fluctuations. This may reflect both the internal dynamic risk spillovers within the “Carbon-Stock” system and the impacts of external events. Furthermore, the TSI displays an upward trend, which may be linked to the development of ETS pilots, the inclusion of more A-share listed companies in these pilots, and increased trading activity of emission-regulated firms in the carbon market. This has led to a gradual enhancement of the connectivity of the “Carbon-Stock” system over the sample period.

The period from June 2014 to December 2016 marked the initial ascent phase of the TSI. During this stage, China’s carbon market transitioned from pilot construction to substantive operation, with seven regional carbon markets successively launching trading activities. The refinement of allowance allocation and verification mechanisms significantly boosted participation among emission-regulated firms. However, due to insufficient corporate awareness and immature market mechanisms, carbon price fluctuations remained limited, keeping the TSI at relatively low levels (below 10%). The signing of the Paris Agreement in December 2015 emerged as a critical inflection point, as this international commitment reinforced domestic policy expectations for carbon markets. This development strengthened the linkage between A-share new energy sectors (such as photovoltaics and wind power) and carbon allowance prices. Despite the systemic turbulence caused by the 2015 stock market crash, the TSI failed to break significantly above 10%, reflecting the carbon market’s limited capacity to absorb systemic risks due to its narrow pilot scope and indicating that the “Carbon-Stock” system connectivity remained in its embryonic stage.

From January 2017 to June 2021, the TSI entered a relatively stable plateau, fluctuating between 10% and 20%. The release of the National Carbon Market Construction Plan in December 2017 marked a pivotal shift from pilot experiences to nationwide market development, prompting emission-regulated firms to accelerate adjustments in carbon asset allocation strategies and driving a rebound in the TSI from lower levels. However, the U.S.–China trade war from 2018 to 2019 triggered significant stock volatility in export-dependent industries (such as steel and chemicals), while the fragmented nature of carbon market pilots prevented synchronized reactions, thereby constraining further TSI growth. The outbreak of COVID-19 in early 2020 led to a temporary decline in the TSI as production halts sharply reduced carbon allowance demand. However, the announcement of the “dual-carbon” targets in September 2020 unleashed policy-driven momentum, spurring simultaneous surges in new energy stocks and carbon prices. By the end of 2020, the TSI surpassed 20%, underscoring the decisive role of policy signals in enhancing the connectivity of the “Carbon-Stock” system.

The period from July 2021 to December 2022 witnessed a leap in the TSI following the official launch of the national carbon market. During the first compliance cycle in December 2021, concentrated allowance trading by emission-regulated firms, coupled with stringent restrictions on high-energy-consuming industries under the September 2021 Dual-Control Policy on Energy Consumption, led to divergent market reactions: stocks in sectors like steel and cement declined due to capacity constraints, while carbon prices rose amid allowance scarcity. This volatility resonance propelled the TSI to its sample-period peak. The Russia–Ukraine conflict in 2022 further extended the duration of elevated TSI levels, as energy security concerns exacerbated divergence between traditional energy (e.g., coal) and new energy sectors in the A-share market. Meanwhile, expectations of industry expansion in the national carbon market strengthened its linkage with equities. This phase demonstrated that the maturation of the national carbon market, combined with high-intensity policy interventions (e.g., energy consumption controls), amplified risk transmission channels within the “Carbon-Stock” system, driving a pronounced cyclical upward trend in the TSI.

Additionally, as shown in Figure 2, the TSI exhibits a clear “rise-fall” cyclical fluctuation around June each year, except for 2014 and 2020. Analyzing the carbon emission quota verification and compliance timelines of ETS pilots reveals that from March to April each year, regulated firms typically verify and declare their actual carbon emissions from the previous year, while June to July is the compliance period for ETS pilots. To avoid high penalties for non-compliance, firms need to purchase sufficient carbon quotas in the carbon market during this period, significantly increasing demand for carbon quotas and enhancing trading activity. This demand leads to dramatic fluctuations in carbon prices, while A-share listed emission-regulated firms experience cash flow volatility from buying or selling carbon quotas, exacerbating their stock price fluctuations. As a result, TSI values rise significantly during the compliance period and quickly drop after it ends. This phenomenon indicates the existence of a “compliance-driven trading” effect in China’s carbon market, where trading activities of regulated firms are primarily concentrated during the compliance period. However, in 2014, as the early stage of China’s carbon market, trading volumes in ETS pilots were severely insufficient, failing to demonstrate a significant “compliance-driven trading” effect. As for June 2020, the continuous rise in TSI is closely related to the impact of the COVID-19 pandemic. On one hand, the pandemic disrupted the production and operational activities of regulated firms, inhibiting the emergence of the “compliance-driven trading” effect. On the other hand, as Chinese enterprises gradually overcame the pandemic’s effects and accelerated their resumption of work and production, the connectivity of the “Carbon-Stock” system gradually recovered, leading to a rebound in TSI.

Finally, regarding frequency band, the results in Table 4 indicate that the TSI of the “Carbon-Stock” system consists of short-term shocks (i.e., shock transmission) and long-term effects, with the short-term value (6.53%) slightly lower than the long-term value (8.10%). Figure 2 shows that the short-term TSI value stabilizes after a period of increase, fluctuating around 7.5%, suggesting that since August 2016, the system’s capacity to reflect information in the short term has stabilized. On the other hand, the long-term TSI value undergoes an initial rising phase, a stabilization period, and a subsequent rising phase, with August 2016 and July 2020 serving as dividing points. During both the rising and subsequent rising phases, the long-term value is significantly higher than the short-term value, indicating that the “Carbon-Stock” system reacts more slowly to short-term shocks compared to long-term effects. While the system’s information processing speed remains stable, its capacity to respond to short-term shocks has diminished. During the stabilization period, there is no significant difference between the long-term and short-term values, suggesting an improved capacity for the “Carbon-Stock” system to reflect information. This indicates that when China’s carbon market is undergoing rapid development or recovery, the long-term effects on the connectivity of the “Carbon- -Stock” system rise sharply, leading to a reduced capacity to respond to short-term shocks.

The dominance of long-term effects is closely tied to the unique policy-technology dual-driver mechanism inherent in carbon markets. Theoretically, corporate investments in emission-reduction technologies influence long-term carbon price trends through two channels: (1) technological innovation reduces marginal abatement costs, enabling firms to generate tradable surplus allowances through excess emission reductions, thereby enhancing market supply elasticity; and (2) the sunk-cost effect of low-carbon technology adoption prompts firms to form long-term carbon price expectations, which in turn stabilize short-term price fluctuations through allowance banking strategies. On the policy front, two critical milestones—the release of the national carbon market construction plan in August 2016 and the announcement of the “dual-carbon” targets in July 2020—triggered adaptive adjustments by emission-regulated firms toward medium- to long-term carbon constraint policies. These adjustments included 5-year technology investment plans and intertemporal allowance trading strategies, behavioral patterns rooted in policy expectations that inherently exhibit low-frequency characteristics. In contrast, short-term shocks (such as concentrated trading during compliance periods or energy price volatility) primarily affect liquidity. Given the limited participation of financial institutions and the scarcity of derivative instruments in China’s carbon market, shallow market depth weakens short-term price discovery, further reinforcing the predominance of long-term effects.

4.2. Analysis of Net Directional Spillovers

Next, this study focuses on the net risk spillover of each variable within the spillover network, particularly the net volatility spillovers. First, Table 4 presents the static net volatility spillover across all variables. In the “Carbon-Stock” system, the primary net spillover recipients are Hubei (−2.12%) and Shanghai (−2.23%). This can be attributed to the central role of the Hubei ETS pilot among the ETS pilots and the pivotal economic position of Shanghai in China. According to public data, as of 21 June 2024, the cumulative trading volume of the Hubei ETS pilot reached 403 million tons of CO₂, accounting for 42.9% of the total trading volume across China’s ETS pilots, with a cumulative transaction value of 9.806 billion RMB, representing 41.7% of the national total, both ranking first in the country. Additionally, Wuhan’s carbon registration center undertakes key functions, including registration, recording, and settlement for the National Carbon Market. The Shanghai ETS pilot, located in China’s most financially developed city and key financial hub, enables it to absorb a large amount of information from other markets within the “Carbon-Stock” system. Consequently, the Hubei and Shanghai ETS pilots act as central nodes in the spillover network, fully absorbing net volatility spillovers from other variables. Conversely, the main net volatility spillover contributor in the “Carbon-Stock” system is StockAll (2.66%), indicating that the stock prices of A-share listed emission-regulated firms exhibit significant risk spillovers to the overall carbon market within the spillover network.

In terms of frequency band, the net spillover (NET) values for all variables, except for BJ, are predominantly influenced by long-term values, indicating that the static net volatility spillover structure of these variables aligns with the overall static spillover structure of the “Carbon-Stock” system. This system exhibits moderate information processing speed but slower response speed to information. In contrast, the NET value for BJ comprises a short-term value of 1.44% and a long-term value of 0.14%, demonstrating that the Beijing ETS pilot responds very quickly to information and carbon price fluctuations. This phenomenon may be related to Beijing’s unique status as the capital of China, where the ETS pilot must swiftly address carbon price volatility and serve as a model for the development of other ETS pilots. Notably, the NET value for StockAll consists of a short-term value of −1.69% and a long-term value of 4.35%, indicating a significant bidirectional risk spillover between A-share listed emission-regulated firms and the overall carbon market. This further illustrates that while the stock prices of these firms are influenced by carbon price fluctuations in the short term, the long-term demand for carbon quotas changes due to measures such as energy substitution and the development of low-carbon technologies, resulting in sustained impacts on carbon prices over the long term.

Figure 3 illustrates the dynamic changes in net volatility spillovers within the spillover network. Firstly, except for BJ, the NET values of all variables are closer to their long-term values, aligning with the characteristics of static net volatility spillovers. Secondly, the dynamic NET values of all variables show significant fluctuations over time, oscillating around zero, indicating that these variables frequently switch between being net spillover transmitters and receivers. However, there is some asymmetry in the NET value fluctuations, leading to notable net inflows or outflows in the static spillover. For instance, HB’s absolute NET value when positive is significantly lower than when negative, while StockAll exhibits the opposite pattern. Overall, this further confirms the existence of significant, dynamic, two-way risk spillovers between A-share listed emission-regulated firms and the broader carbon market. In summary, the spillover network of the “Carbon-Stock” system exhibits pronounced dynamic characteristics, with the risk spillover levels of various variables demonstrating complex fluctuation patterns over time.

4.3. Analysis of Net Pairwise Spillovers

By analyzing the relationships between A-share listed emission-regulated firms and various ETS pilots, this study further investigates the directional spillover characteristics of the spillover network.

Table 5. Static net pairwise spillovers.

	HB	GD	SZ	BJ	SH	StockAll
HB	0.00(0.00)[0.00]	−0.08(0.15)[−0.23]	1.75(0.42)[1.34]	0.29(0.25)[0.04]	0.16(−0.08)[0.24]	0.01(−0.09)[0.08]
GD	0.08(−0.15)[0.23]	0.00(0.00)[0.00]	−0.35(0.27)[−0.62]	0.07(−0.18)[0.24]	−0.49(−0.01)[−0.48]	0.09(−0.15)[0.24]
SZ	−1.75(−0.42)[−1.34]	0.35(−0.27)[0.62]	0.00(0.00)[0.00]	0.71(−0.12)[0.83]	−0.19(−0.17)[−0.02]	1.39(−0.62)[2.01]
BJ	−0.29(−0.25)[−0.04]	−0.07(0.18)[−0.24]	−0.71(0.12)[−0.83]	0.00(0.00)[0.00]	−1.10(−0.66)[−0.44]	0.57(−0.84)[1.41]
SH	−0.16(0.08)[−0.24]	0.49(0.01)[0.48]	0.19(0.17)[0.02]	1.10(0.66)[0.44]	0.00(0.00)[0.00]	0.61(−0.01)[0.62]
StockAll	−0.01(0.09)[−0.08]	−0.09(0.15)[−0.24]	−1.39(0.62)[−2.01]	−0.57(0.84)[−1.41]	−0.61(0.01)[−0.62]	0.00(0.00)[0.00]

Note: This table describes the NPDC of each variable. Taking the element “0.08(−0.15)[0.23]” in the first column of the second row as an example, it represents the NPDC from StockAll to BJ, with the total-term, short-term, and long-term measures being “−0.08”, “−0.15”, and “0.23”, respectively.

presents the static NPDC results, revealing significant risk spillovers among different regional ETS pilots. Notably, the absolute NPDC value between the Hubei ETS pilot and the Shenzhen ETS pilot is 1.75%, the highest in the spillover network, indicating a strong connection between these two carbon markets. This strong linkage may be due to carbon price fluctuations in the Shenzhen ETS pilot influencing the Hubei ETS pilot. Additionally, a notable risk spillover exists between the Shanghai and Beijing ETS pilots, with an absolute NPDC value of 1.1%, reflecting the close political and economic ties between Shanghai and Beijing.

For A-share listed emission-regulated firms, the NPDC values of StockAll concerning HB, GD, SZ, SH, and BJ are all positive. The short-term NPDC values are negative, while the long-term values are all positive, aligning with the net spillover analysis results. Figure 4 illustrates the dynamic NPDC of StockAll relative to HB, GD, SZ, SH, and BJ. The NPDC values of StockAll for HB, GD, SZ, and SH are closer to the short-term values, whereas the NPDC value for BJ aligns more with the long-term value. Furthermore, the NPDC values of StockAll for HB, GD, SZ, SH, and BJ fluctuate around zero, confirming significant, dynamic two-way risk spillovers between A-share listed emission-regulated firms and the overall carbon market.

Significant events in the stock market during the sample period caused notable fluctuations in the NPDC values of StockAll concerning HB, GD, SZ, SH, and BJ. First, the introduction of the circuit breaker mechanism in the A-share market in 2016 exacerbated market panic, leading to “cross-market risk transmission” under the “Herding Effect”, which caused varying degrees of risk spillover or inflow between StockAll and HB, GD, SZ, SH, and BJ. Second, the outbreak of the China–US trade war in 2018 intensified risks to China’s economic fundamentals, leading to increased risk spillover between StockAll and HB, GD, BJ, and SH, heightening systemic risk in the “Carbon-Stock” system. Third, the registration system reform in the A-share market in 2019 resulted in slight fluctuations in the NPDC values of StockAll concerning HB, GD, SZ, SH, and BJ, indicating that the reform had not yet significantly benefited the market. Fourth, the COVID-19 global pandemic in early 2020 caused ongoing fluctuations in the NPDC values of StockAll for HB, GD, SZ, SH, and BJ. Fifth, the outbreak of the Russia–Ukraine war in early 2022 resulted in dramatic fluctuations in the NPDC values of StockAll concerning BJ and SH. Interestingly, the “stock market crash” in China in 2015 did not significantly impact the NPDC values, only slightly affecting the risk spillover from SH to StockAll, likely due to the incomplete construction of regional ETS pilots at that time, which limited the connectivity of the “Carbon-Stock” system. Overall, since 2016, the risk spillover between ETS pilots and A-share listed emission-regulated firms has demonstrated strong sensitivity to major events.

Based on the comprehensive analysis above, this section concludes with the following main findings: First, there is a significant two-way risk spillover between China’s carbon market and A-share listed emission-regulated firms, with the level of risk spillover in the “Carbon-Stock” system gradually increasing as the carbon market develops. Second, the “Carbon-Stock” system exhibits a moderate speed of information processing, but the long-term impacts of information shocks are greater than those of short-term shocks, indicating a generally low response level of the system to information. Finally, in the short term, fluctuations in carbon prices affect the production and operations of A-share listed emission-regulated firms, causing them to absorb risk spillover from the overall carbon market; however, with long-term adjustments in their demand for carbon quotas, these firms ultimately contribute to risk spillover to the whole carbon market.

4.4. Robustness Tests

Considering that variations in lag terms and forecast horizons may impact the original results, this study performs a robustness check by adjusting the number of lags in the TVP–VAR model and modifying the forecast horizon. The lags are set to 3, 4, 6, and 7, while the forecast horizon is adjusted to 50, 75, 100, 125, and 150 days. For clarity,

Table 6. Sensitivity of volatility spillover to the forecast horizon and VAR lags.

		Forecast Horizon = 50 Days	Forecast Horizon = 75 Days	Forecast Horizon = 100 Days	Forecast Horizon = 125 Days	Forecast Horizon = 150 Days
P = 3	Net risk spillover of StockAll	2.29(−1.18)[3.46]	2.29(−1.22)[3.51]	2.29(−1.20)[3.49]	2.29(−1.23)[3.51]	2.29(−1.21)[3.50]
	TSI	11.24(4.70)[6.54]	11.24(4.50)[6.74]	11.24(4.59)[6.65]	11.24(4.49)[6.75]	11.24(4.55)[6.69]
P = 4	Net risk spillover of StockAll	2.65(−1.37)[4.02]	2.65(−1.38)[4.04]	2.65(−1.38)[4.03]	2.65(−1.38)[4.04]	2.65(−1.38)[4.03]
	TSI	13.06(5.69)[7.37]	13.06(5.49)[7.57]	13.06(5.58)[7.48]	13.06(5.48)[7.58]	13.06(5.54)[7.52]
P = 6	Net risk spillover of StockAll	3.60(−2.08)[5.68]	3.62(−2.12)[5.75]	3.63(−2.11)[5.74]	3.63(−2.13)[5.76]	3.63(−2.12)[5.75]
	TSI	16.20(7.75)[8.45]	16.24(7.53)[8.71]	16.24(7.63)[8.62]	16.24(7.52)[8.72]	16.24(7.59)[8.66]
P = 7	Net risk spillover of StockAll	3.90(−2.45)[6.35]	3.93(−2.51)[6.44]	3.94(−2.50)[6.43]	3.94(−2.52)[6.45]	3.94(−2.50)[6.44]
	TSI	17.67(8.86)[8.81]	17.75(8.60)[9.15]	17.77(8.71)[9.06]	17.77(8.59)[9.18]	17.78(8.67)[9.11]

presents the net volatility spillover of StockAll and the TSI of the “Carbon-market” system under these different conditions. It is observed that an increase in the number of lags leads to higher NET and TSI values for StockAll, while variations in the forecast horizon have a negligible effect on the estimated results. This suggests that longer lags contribute to more significant spillover effects, consistent with findings from existing research (Guo and Feng, 2021) [49]. Nonetheless, the changes in the NET and TSI values of StockAll remain within acceptable limits, highlighting the importance of selecting appropriate lag periods for the accuracy of the TVP–VAR model’s estimates. Although the short-term and long-term values fluctuate with changes in the forecast horizon, these variations do not significantly alter the spillover effect estimates. In summary, the estimation results of this study are relatively robust.

To address potential distortions caused by extreme values in carbon trading pilot markets—particularly in cases such as SZ, where carbon quota prices exhibited abnormal volatility (with maximum returns approaching 200%)—this study applies a 1% winsorization to the main variables. As shown in

Table 7. Estimation results after 1% winsorization of the main variables.

	HB	GD	SZ	BJ	SH	StockAll	FROM
HB	85.72(51.46)[34.26]	3.21(1.21)[2.00]	3.95(1.34)[2.61]	2.63(1.42)[1.21]	2.34(1.27)[1.07]	2.14(1.29)[0.86]	14.28(6.53)[7.75]
GD	3.24(1.07)[2.17]	84.28(46.29)[37.99]	3.01(1.13)[1.88]	3.20(1.16)[2.04]	2.84(1.44)[1.40]	3.42(1.43)[1.99]	15.72(6.24)[9.49]
SZ	2.19(0.90)[1.29]	3.42(0.89)[2.53]	84.36(43.72)[40.64]	3.24(1.02)[2.22]	2.68(1.00)[1.69]	4.11(1.07)[3.04]	15.64(4.88)[10.76]
BJ	2.29(1.15)[1.14]	3.16(1.36)[1.79]	2.56(1.17)[1.39]	85.44(51.61)[33.83]	3.13(1.39)[1.74]	3.42(1.24)[2.19]	14.56(6.31)[8.25]
SH	2.21(1.34)[0.88]	3.34(1.45)[1.89]	2.77(1.15)[1.61]	4.21(2.05)[2.16]	84.63(53.85)[30.78]	2.84(1.37)[1.47]	15.37(7.36)[8.01]
StockAll	2.16(1.35)[0.81]	3.23(1.59)[1.64]	2.72(1.76)[0.96]	2.75(1.98)[0.77]	2.17(1.37)[0.80]	86.96(62.85)[24.11]	13.04(8.06)[4.98]
TO	12.09(5.79)[6.29]	16.37(6.52)[9.86]	15.01(6.56)[8.46]	16.03(7.63)[8.40]	13.17(6.47)[6.70]	15.94(6.40)[9.54]	TCI
NET	−2.19(−0.73)[−1.46]	0.65(0.28)[0.37]	−0.63(1.68)[−2.31]	1.47(1.32)[0.15]	−2.20(−0.88)[−1.32]	2.90(−1.66)[4.56]	14.77(6.56)[8.21]

, the post-winsorization estimates remain highly consistent with the pre-winsorization results, indicating that outliers exert minimal influence on the findings. This robustness check further supports the reliability of our empirical analysis.

5. Heterogeneity Analysis

The previous section presented the core findings of this study, highlighting a significant bidirectional risk spillover between A-share listed emission-regulated firms and the overall carbon market. Further analysis revealed distinct differences among the A-share listed emission-regulated firms that comprise the variable StockAll. Firstly, these firms belong to specific ETS pilots, establishing direct connections with the corresponding pilots. Secondly, some firms engage in polluting activities and are obligated to pay environmental fees or taxes, while others do not exhibit such behaviors. Lastly, there are variations in ESG ratings among these firms, with some receiving higher ratings than others. This section aims to explore whether these characteristics influence the risk spillover within the “Carbon-Stock” system and, if so, through what mechanisms these characteristics impact risk spillover. To address these questions, this study employs the AIC, HQ, SC, and FPE criteria, establishing a VAR(3) model with a forecasting horizon of 100 days based on heterogeneity analysis.

5.1. The Impact of A-Share Listed Emission-Regulated Firms Belonging to Different ETS Pilots on Risk Spillover

This paper presents the NPDC values and total NPDC (Total) values of A-share listed emission-regulated firms based on specific ETS pilot classifications in

Table 8. The NPDC values and Total values of A-share listed emission-regulated firms for each ETS pilot—based on the classification of ETS pilots to which the A-share listed emission-regulated firms sample belongs.

	StockHB	StockGD	StockSZ	StockBJ	StockSH
HB	0.44(0.11)[0.34]	0.30(0.09)[0.19]	0.55(0.15)[0.40]	1.00(0.14)[0.85]	0.57(0.01)[0.55]
GD	0.36(−0.02)[0.37]	0.17(0.21)[−0.05]	1.17(0.27)[0.90]	0.88(0.16)[0.72]	0.84(0.10)[0.74]
SZ	0.22(−0.36)[0.59]	0.33(−0.13)[0.46]	0.66(−0.05)[0.72]	0.60(−0.38)[0.97]	1.33(0.06)[1.27]
BJ	−0.05(−0.36)[0.31]	0.63(−0.08)[0.70]	0.28(−0.36)[0.65]	0.45(−0.33)[0.78]	0.15(−0.36)[0.51]
SH	0.35(0.25)[0.09]	0.25(0.22)[0.04]	1.07(0.52)[0.55]	0.68(0.50)[0.18]	0.08(0.19)[−0.12]
Total	1.32(−0.38)[1.70]	1.68(0.31)[1.34]	3.73(0.53)[3.22]	3.61(0.09)[3.50]	2.97(0.00)[2.95]

. The results indicate that the Total values for all A-share listed emission-regulated firms concerning each ETS pilot are greater than 0, with StockSZ showing the highest Total value at 3.73%. This can be attributed to the significant price risk in the Shenzhen ETS pilot, which exacerbates the stock price risk of A-share listed emission-regulated firms, leading to spillover effects on other ETS pilots. In contrast, StockHB has the lowest Total value at 1.32%. This lower spillover level may be due to the Hubei ETS pilot’s central role in China’s ETS, where higher market activity and trading reduce the short-term risk spillover for firms in this pilot.

Additionally, StockGD has a relatively low total value at 1.68%, likely because the Guangdong ETS pilot does not include companies listed in Shenzhen. As Shenzhen is the most economically developed city in Guangdong Province, its listed companies typically account for over 50% of the province’s total. Furthermore, the Supplementary Material indicates that the sample size of A-share emission-regulated firms in StockSZ is significantly higher than in StockGD, suggesting that the Shenzhen ETS pilot has diverted substantial attention from listed companies within the Guangdong ETS pilot, thereby diminishing the impact of Guangdong-listed firms on ETS carbon prices. Simultaneously, StockBJ (3.61%) and StockSH (2.97%) exhibit moderate total values, reflecting the economic and political significance of Beijing and Shanghai. In summary, when A-share listed emission-regulated firms are affiliated with different regional ETS pilots, there are significant differences in their risk spillover to the overall carbon market.

Notably, except for the Hubei ETS pilot, the NPDC values for other ETS pilots and their corresponding A-share emission-regulated firms did not reach maximum levels. For instance, the highest absolute NPDC value for StockHB is associated with HB (0.44%), while StockGD’s highest NPDC absolute value comes from BJ (0.63%). This indicates that A-share emission-regulated firms in each ETS pilot tend to spill more price risk to other pilots, resulting in more pronounced reactions in the carbon prices of other ETS pilots when stock prices of A-share emission-regulated firms in a specific pilot fluctuate.

5.2. The Impact of Polluting Behavior of A-Share Listed Emission-Regulated Firms on Risk Spillover

The results in

Table 9. The NPDC values and Total NPDC values of A-share listed emission-regulated firms for each ETS pilot—classified based on whether the A-share listed emission-regulated firms exhibit polluting behavior.

	StockP	StockC
HB	0.33(0.17)[0.17]	0.17(−0.13)[0.30]
GD	0.12(0.11)[0.01]	0.37(0.07)[0.30]
SZ	0.88(−0.30)[1.17]	1.47(−0.14)[1.61]
BJ	0.16(−0.39)[0.55]	0.57(−0.33)[0.90]
SH	0.41(0.25)[0.17]	0.96(0.38)[0.58]
Total	1.90(−0.16)[2.07]	3.54(−0.15)[3.69]

indicate that the Total value for StockP is 1.90% (with a short-term value of −0.16% and a long-term value of 2.07%), while the Total value for StockC is 3.54% (with a short-term value of −0.15% and a long-term value of 3.69%). Thus, A-share listed emission-regulated firms without polluting behavior exhibit significantly higher risk spillover to the entire carbon market compared to those with polluting behavior. Based on this empirical finding, the following potential explanations are proposed.

In China, companies incur environmental taxes or fees due to polluting activities, leading to higher pollution-related costs. Although all emission-regulated firms in the ETS pilots aim to reduce carbon emissions through green technological innovation, those with polluting behavior tend to focus on developing low-cost, low-quality, and shorter-term green utility model patents for low-carbon, energy-saving, and alternative energy technologies, influenced by carbon emission costs [24,38]. Furthermore, these companies face an “exclusion effect” within the ETS pilots, where the costs associated with carbon emissions may hinder their green innovation efforts, compelling them to rely more on reducing production activities to meet annual emission targets [65].

In the short term, A-share listed emission-regulated firms with polluting behavior absorb more risk spillover from the overall carbon market than those without such behavior. Conversely, in the long term, non-polluting firms in the ETS pilots accumulate high-quality green innovation technologies, which decreases their overall demand for carbon allowances. This allows them to profit more actively from carbon trading, leading to their stock prices being significantly more influenced by carbon price fluctuations than those of firms with polluting behavior. In summary, non-polluting firms demonstrate a higher net spillover effect on carbon price fluctuations in the long run compared to their polluting counterparts.

5.3. The Impact of ESG Ratings of A-Share Listed Emission-Regulated Firms on Risk Spillover

The results in

Table 10. The NPDC values and Total NPDC values of A-share listed emission-regulated firms for each ETS pilot—classified based on the ESG scores of the A-share listed emission-regulated firms.

	StockLESG	StockHESG
HB	0.26(0.10)[0.15]	0.12(−0.16)[0.27]
GD	0.09(0.12)[−0.02]	0.08(−0.03)[0.11]
SZ	0.95(0.10)[0.85]	1.24(−0.14)[1.38]
BJ	0.46(−0.28)[0.73]	0.82(−0.25)[1.07]
SH	1.07(0.29)[0.78]	0.83(0.35)[0.49]
Total	2.83(0.33)[2.49]	3.09(−0.23)[3.32]

indicate that the Total value for StockLESG is 2.83%, significantly lower than that of StockHESG. In terms of frequency band, StockLESG exhibits a short-term risk spillover of 0.33%, while StockHESG shows a short-term risk inflow of −0.23%. Furthermore, the long-term Total value for StockLESG (2.49%) is notably lower than that of StockHESG (3.32%). This suggests that the stock prices of firms with lower ESG ratings are less responsive to carbon price fluctuations compared to those with higher ESG ratings.

In light of this, the following potential explanations are proposed. According to Li, H. et al. [66], publicly listed companies in the same region experience peer pressure regarding ESG ratings, and there is a negative correlation between stock returns and ESG scores. Thus, in the short term, companies with low ESG scores are more actively involved in carbon trading to mitigate the adverse effects of low ESG ratings on stock returns, demonstrating risk spillover to the overall carbon market. However, in the long term, due to a lack of environmental awareness among corporate executives [67,68], these firms invest less in low-carbon initiatives [10], leading to diminished efforts to reduce carbon emissions through green technological innovation. Instead, they tend to meet emission reduction targets through carbon trading or production cuts, ultimately resulting in a lower long-term impact on the overall carbon market.

Conversely, companies with high ESG scores effectively manage ESG issues, cultivate a positive corporate culture, and achieve long-term environmental strategic goals [69]. These companies are committed to maintaining strong carbon emission management through continuous participation in carbon trading, thus exerting a sustained influence in the carbon market. In summary, compared to companies with low ESG scores, those with high ESG scores have a lower short-term impact on the overall carbon market but significantly greater long-term influence.

6. Conclusions and Recommendations

This study conducts an in-depth analysis of the risk spillover between China’s five carbon emission trading pilot markets and A-share listed enterprises regulated by carbon emission policies, yielding several important conclusions: (1) There are significant risk spillover effects in the “carbon-stock” system, highlighting the interaction between compliance-driven carbon trading activities and the stock market. Enterprises increase trading intensity to fulfill their obligations under the Emissions Trading System (ETS), which exacerbates short-term market volatility and transmits risks between interconnected carbon and stock markets. This feedback loop indicates that policy frameworks play a critical role in managing systemic risks during the advancement of carbon trading pilots. Moreover, the upward trend in dynamic risk spillovers aligns with the increasing linkage between the carbon and stock markets, suggesting that market participants are becoming more responsive to shared economic fundamentals and shocks. These results reflect the systemic interdependence of financial markets and environmental regulation and provide valuable insights for constructing a resilient and sustainable financial system aligned with climate objectives. (2) Frequency-domain analysis further reveals the adaptability of the “carbon-stock” system to shocks over different time spans and its uneven responses. Although the system demonstrates high efficiency in processing long-term information, it reacts sluggishly to short-term shocks, reflecting structural constraints in the trading mechanisms and liquidity of the carbon market. Over time, the stability of information processing speed may reflect market learning and strategic adjustments by participants. It is noteworthy that A-share enterprises, especially those with high ESG ratings or no polluting behaviors, exert a long-term influence on systemic risks, enhancing the risk connectivity between regulated enterprises and ETS pilots. This finding emphasizes the importance of firm characteristics, such as ESG strategies and market influence, in shaping risk transmission patterns, and reinforces the need to integrate sustainability metrics into risk assessment frameworks.

The empirical results of this study have significant practical implications for investors and policymakers in the context of sustainability transitions: (1) For environmental investors, this research highlights the potential of holding carbon assets alongside stocks of A-share enterprises regulated by emissions policies as a diversification strategy to mitigate risks and reduce the impact of volatility in any single market. Based on the frequency-domain analysis, investors should adjust their portfolio allocations according to both short-term and long-term sustainability objectives. Specifically, they can increase exposure to carbon assets during periods of low volatility and reduce exposure during high-volatility periods, balancing risk between carbon and stock assets. Additionally, investors should focus on stocks that show less sensitivity to carbon price fluctuations, particularly in times of volatility, to stabilize their portfolios and enhance resilience. (2) For policymakers in carbon markets, the findings underscore the importance of understanding risk spillover mechanisms and their implications for market design. Policymakers could introduce circuit breakers to limit extreme carbon price fluctuations in high-volatility markets, thus mitigating systemic risks. Temporary price range mechanisms could be implemented for markets with significant short-term volatility to provide stability and confidence. Furthermore, in less active ETS pilots, policymakers could reduce transaction costs for A-share regulated enterprises to encourage participation and attract more environmental investors. However, such measures should be carefully calibrated to avoid exacerbating market volatility caused by excessive trading activity. (3) For stock market regulators, optimizing market mechanisms to improve stability and attractiveness is essential. Regulatory measures should be differentiated based on firm characteristics, especially regarding their environmental impact. For example, incentives could be provided to highly polluting and low ESG-rated enterprises to encourage their participation in carbon markets, driving them towards greener business practices. At the same time, stronger regulations should be applied to firms with high ESG ratings or no polluting behaviors, as they may disproportionately influence market volatility and risk transmission. These differentiated policy approaches will contribute to building a sustainable financial infrastructure that promotes environmental accountability, fosters green innovation, and supports broader climate-resilient economic systems.

This study has several limitations that warrant consideration in future research. First, the study only examines five carbon emission trading pilot markets, excluding other pilot markets and the national carbon market. This selective sample may affect the generalizability of the conclusions, and future studies should expand the sample to include a broader range of pilot markets or even the national carbon market to improve representativeness. Second, the proxy for volatility used in this study, the absolute value of daily returns, may overlook extreme volatility and nonlinear features, such as jump risks, especially in high-frequency data. While the simplicity and consistency of this approach have advantages, future research could adopt more sophisticated volatility measures, such as realized volatility, high-frequency volatility measures, or jump detection methods to address these limitations and provide a more comprehensive analysis of market volatility. Third, the classification of polluting and non-polluting enterprises is based on environmental tax and fee data, which could introduce some subjective bias, as the threshold for classifying enterprises is not explicitly stated. Furthermore, the ESG rating grouping is based on the annual median without accounting for dynamic changes or industry-specific differences. Future research should explore ways to improve these classifications by accounting for regional enforcement differences and industry-specific characteristics. Additionally, a more dynamic approach to ESG ratings could be implemented to capture changes over time and address industry heterogeneity. Fourth, while this study identifies the compliance-driven trading effect as a key mechanism, it does not provide an in-depth analysis of how companies concentrate their trading quotas during compliance periods, which could lead to short-term volatility and risk spillovers. Future studies could focus on the specific mechanisms of this effect by examining case studies and the actual behavior of firms in compliance periods. Lastly, the study does not explore the potential interactions between international carbon markets or cross-border trading, which could also influence China’s carbon market. Future research could extend the analysis to a more global perspective by considering the impact of international carbon market dynamics and their potential spillovers into the domestic market.