1.2.1 Energy prices.

Coal, oil, and natural gas are the main fossil fuels that drive China’s economic development, and the combustion of fossil fuels is the main cause of the sharp increase in GHG emissions. Among the three, coal produces the most carbon emissions when burned, followed by oil, both are considered high-carbon energy [13], while natural gas has lowest carbon emissions and is classified as a clean energy. In 2023, China’s energy consumption structure will show an adjustment trend. The proportion of coal consumption will be 55.3%, a decrease of 0.7 percentage points from 2022; the proportion of oil consumption will be 18.3%, an increase of 0.3 percentage points; and the proportion of clean energy consumption will reach 26.4%, an increase of 0.4 percentage points [14]. Coal remains the main source of energy consumption.Energy prices affect carbon prices in two main ways. Firstly, changes in energy prices influence energy demand, and secondly, changes in energy prices triggers substitution effects among energy sources, influencing enterprises’ energy consumption structures. In the case of unchanged production capacity of emission-control enterprises, changes in the energy consumption structure directly affect their carbon emissions, which in turn affects their demand for carbon emission allowances; an increase in the demand for carbon emission allowances prompts a higher carbon price, while a decrease in the demand for carbon emission allowances lowers the carbon price. Rising coal prices result in reduced coal consumption [15], leading to lower CO2 emissions and thereby curbing carbon price increases. Additionally, the relationship between oil prices and carbon prices is complex. Higher oil prices could spur firms to increase coal use, pushing up carbon prices [16]; on the other hand, an increase in oil prices prompts enterprises to increase their use of clean energy, causing carbon prices to fall. [8] found that oil price has an m-shaped nonlinear effect on carbon price through a nonparametric additive regression model. The increase of natural gas price will encourage enterprises to expand the use of low-cost energy sources such as coal and oil, so the natural gas price also has an important impact on the carbon price.

1.2.2 Macroeconomy.

The macroeconomy affects carbon prices in two main ways. First, by influencing the total social demand, the macroeconomy affects the production capacity and energy demand of emission-control enterprises, which further affects the demand of emission-control enterprises and leads to fluctuations in the carbon price. Chevallier utilized a Markov-switching vector autoregressive model to identify a positive correlation between macroeconomic conditions and EU carbon prices [17]. When the macroeconomic environment is robust, overall societal demand grows, enterprises’ energy consumption increases, and carbon emissions rise accordingly, pushing up the need for carbon emission allowances and elevating the cost of carbon. Conversely, in times of recession, the price of carbon decreases. Additionally, the macroeconomy influences public commitment to carbon reduction, thereby affecting carbon prices. The macroeconomic conditions shape public resolve to reduce emissions and, consequently, impact investor behavior.

1.2.3 Development of the electric power industry.

The power industry is currently the only emission-control sector included in the national carbon market. Thus, the overall development of the power industry is closely related to the national carbon market. The development of the power industry has a more direct impact on the production capacity and energy demand of emission-control enterprises than does the macroeconomy. Specifically, the development of the power industry reflects its future trajectory and electricity demand, which influence corporate production planning. This, in turn, shapes industrial energy consumption and ultimately drives carbon price fluctuations through shifts in carbon allowance demand.

1.2.4 Carbon emissions of the electric power industry.

The power industry was the first industry included in the national carbon market, with carbon emissions reaching 4.5 billion tons, accounting for approximately 40% of the national total [18]. Currently, the national carbon market regulates both direct emissions from the thermal power industry and indirect emissions from electricity and heat consumption, making power industry emissions the primary driver of quota demand in the carbon market. The influence of these emissions on carbon prices manifests in two key ways. First, under fixed carbon quotas, the industry’s emissions directly shape enterprises’ demand for carbon allowances, thereby affecting carbon prices. Second, power sector emissions impact policy, technology, and the energy mix. Rising emissions prompt adjustments in carbon quota policies, increasing the total quota allocation. This, in turn, encourages the adoption of low-carbon technologies and boosts clean energy usage, enhancing enterprises’ emission reduction potential and further influencing carbon prices.

1.3.1 Trading volume.

Under the carbon market mechanism, the government determines the total carbon emission quota at the start of a new compliance cycle and distributes it to emission-control enterprises, which are required to fulfill their quota obligations within the cycle. Variations in the trading volume of carbon emission quotas reflect both the demand for allowances among enterprises and stimulate competition within the carbon market. Given the fixed total quota, fluctuations in trading volume influence the decisions of emission-control enterprises and investors, thereby driving carbon price volatility. It is worth noting that trading activity tends to surge with the end of the compliance period, leading to a subsequent increase in carbon market prices.

1.3.2 Foreign carbon prices.

Europe’s industrial development peaked earlier than that of other regions, leading to an awareness of the importance of environmental protection in advance and proactive actions on carbon emissions reduction. The EU Emissions Trading System, established in 2005, is now a relatively mature carbon market, whereas China did not establish a relatively unified national carbon market until 2021, so there is a long road ahead. The EU carbon market serves as a guide and model for China’s carbon market. Relevant Chinese scholars and experts draw on the relatively mature and stable practices of the EU carbon market to better stabilize China’s carbon market, improve its pricing mechanism, and manage risks. The carbon emission reduction tasks are jointly determined by the United Nations committee and the governments of various countries, and participating countries strictly limit China’s carbon emissions to meet reduction goals, thereby affecting carbon prices in China. Thus, foreign carbon prices affect the fluctuations in domestic carbon prices.

2.1.1 VEC model.

The Vector Autoregression (VAR) model, introduced by Christopher Sims in 1980, is a widely employed econometric model. It primarily aims to elucidate how temporal variations in a set of variables are influenced by both their own past values and those of other variables within a time series context. Here, Y_t represents a K-dimensional vector of endogenous variables, p denotes the lag order, A signifies the coefficient matrix to be estimated, C is a constant vector, ε_t is a K-dimensional vector of random disturbances, and T indicates the sample size. The VAR(p) model is expressed as follows:

The VEC model is a constrained VAR model, which adds a cointegration constraint to the VAR model. This means that the variables can be nonstationary, but they must have a cointegration relationship. The general cointegration regression is expressed as follows:

where α and β are both n × r matrices. α is a short-term parameter and serves as the weight of the equilibrium error correction term, reflecting the adjustment speed of the model from a nonequilibrium state to a long-term equilibrium state. β is a long-term parameter and is a matrix that consists of cointegration vectors. The error term ε_t (t = 1, 2, …, k) in each equation is assumed to be stationary. A cointegration system can be represented in multiple ways, with the error correction model being a frequently employed approach to address such issues.

where ecm_t-1 denotes the error correction term, capturing the long-term equilibrium relationship.

2.1.2 Impulse response.

The VAR model captures the aggregate influence among variables, focusing solely on their static impact within the model without analyzing the specific extent of influence one variable exerts on others. However, Impulse Response Functions (IRFs) depict how endogenous variables react to an error shock. Specifically, this method involves observing the responses of other variables by applying a one-time impulse (unit shock) to a particular variable. IRF describes the impact on the current and future values of endogenous variables after applying a standard deviation-level shock to the random error term.

Suppose we consider a system containing k variables, where the i-th variable is denoted as y_i. The VAR(p) model of this system is given as:

where c is a constant vector, A₁, A₂, …, A_p are k × k coefficient matrices representing the lagged effect of each variable, and ε_t is a k-dimensional error term. IRF describes the response of other variables y_i (i ≠ j) when the value of the j-th variable y_j is increased by one unit at time t = 0. IRF is expressed as follows:

where IRF_ji(h) represents the impact of the j-th variable on the i-th variable, and h denotes the number of time lag periods. IRF clearly represents the extent to which an impulse shock to the j-th variable y_j at the current time (t = 0) affects the i-th variable over the subsequent h periods.

2.3.1 Stationarity test.

To avoid spurious regression, a stationarity test was performed on the data. The augmented Dickey‒Fuller (ADF) test was used to test the stationarity of each variable. These variables usually do not increase or decrease over time, and thus do not have significant time trends or intercept terms. Thus, when the ADF test was conducted, no time trends or intercept terms were added. The test outcomes are presented in Table 2. The P-values for the original series of all variables exceed 0.05, indicating that the original series are non-stationary. Following first-order differencing, the results reveal that all series achieve stationarity. Consequently, all series are first-order integrated, meeting the necessary condition for the cointegration test.

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Table 2. Results of stationarity test of variables.

https://doi.org/10.1371/journal.pone.0333788.t002

2.3.2 Determination of the optimal lag order.

To establish a suitable VAR or VEC model, determining the optimal lag order is essential. In this research, the optimal lag order was identified using the LR, AIC, SC, HQ, and FPE criterion. As shown in the results in Table 3, the optimal lag order selected is 1 by SC, 2 by HQ, and 3 by both AIC and FPE. Thus, the lag order of 3, chosen by more criteria, was selected as the optimal lag order.

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Table 3. Results of the optimal lag order.

https://doi.org/10.1371/journal.pone.0333788.t003

2.3.3 Cointegration test.

The cointegration test assesses whether a long-term stable equilibrium exists among variables. Even if individual variables are nonstationary, identifying such an equilibrium allows for the establishment of a VEC model. Common cointegration tests include the Engle-Granger test and the Johansen test. Due to its effectiveness in analyzing multiple variables, the Johansen test was utilized in this study. The results, displayed in Tables 4 and 5, show that under the null hypothesis of no cointegration, the trace statistic is 231.0067, exceeding the critical value of 197.3709 at the 5% significance level, with a P-value below 0.05. Consequently, the null hypothesis is rejected, indicating the presence of at least one cointegration relationship. Under the null hypothesis of at most one cointegration relationship, the trace statistic of 140.8083 is less than the critical value of 159.5297, leading to the acceptance of the null hypothesis and suggesting the existence of at most one cointegration relationship. The maximum eigenvalue test yields consistent results, confirming one cointegration relationship, which signifies a long-term equilibrium between the national carbon price and the variables.

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Table 4. Results of the Johansen cointegration test(a).

https://doi.org/10.1371/journal.pone.0333788.t004

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Table 5. Results of the Johansen cointegration test(b).

https://doi.org/10.1371/journal.pone.0333788.t005

The normalized cointegration equation is as follows:

From the cointegration equation, it can be seen that under the long-term equilibrium relationship, when other variables are constant, a 1% increase in coal price decreases the national carbon price by 1.448%; when other variables are constant, a 1% increase in Power 300 index increases the national carbon price by 1.195%; when other variables are constant, a 1% increase in power industry carbon emissions increase by 1%, the national carbon price decreases by 0.757%; when other variables are held constant, a 1% increase in the EU carbon price decreases the national carbon price by 0.368%; when other variables are held constant, a 1% increase in the price of natural gas increases the national carbon price by 0.336%; when other variables are held constant, a 1% increase in the price of oil increases the national carbon price by 0.465; and when other variables are held constant, a 1% increase in turnover increases the national carbon price increases by 0.063%. The negative elasticity coefficient of EU carbon prices may reflect the policy competition effect under the fragmentation of global carbon markets: When the EU strengthened emission reduction by raising the carbon price, the national carbon market was still in the early stage of establishment, following the strategy of seeking progress while maintaining stability, and the institutional system was still in the process of continuous improvement, so the level of the carbon price was still maintained at a relatively low state in order to achieve a balance between environmental protection and industrial development. This dynamic relationship may change as the national carbon market matures and international climate policy coordination deepens. The elasticity coefficient of carbon emissions from the power industry is negative, which may be due to the fact that in the long-term process, the increase in carbon emissions from the power industry has prompted enterprises to enhance their low-carbon emission reduction technology level and increase the space for carbon emission reduction, and the demand for carbon emission rights from enterprises has decreased, while the government has also increased the supply of carbon emission rights, which has led to the reduction of carbon price for enterprises. The standard errors and t-statistics of the coefficients of the cointegration equation and VEC model are shown in Table 6.

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Table 6. Normalized cointegration equation and VEC model.

https://doi.org/10.1371/journal.pone.0333788.t006

2.3.4 Establishment of the VEC model.

The cointegration test only describes whether there is a long-term equilibrium between the variables and cannot reflect the short-term adjustment between the variables, so in order to further explore the relationship between long-term equilibrium and short-term adjustment, a VEC model is established. The estimation formula of D(LNCEA) in the VEC model is as follows:

The negative adjustment coefficient aligns with the corrective mechanism of the VEC model. The absolute value of the adjustment coefficient is 0.046, which indicates that when deviating from the equilibrium state, there will be an adjustment strength of 0.046 to pull the national carbon price back to equilibrium. The adjustment coefficient is small because the national carbon market was established not long ago, and the relevant mechanisms remain incomplete, and unable to quickly and effectively transmit information or price fluctuations from other markets.

A stability test of the VEC model was performed to examine its validity. The results in Fig 2 show that all points (positions of the unit roots) are inside the circle, indicating that the model is stable.

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Fig 2. AR root test results of the VEC model.

https://doi.org/10.1371/journal.pone.0333788.g002

2.3.5 Impulse response.

The impulse response refers to the process by which the dependent variable, namely the national carbon price, is affected when a standard deviation shock is applied to the explanatory variables, including the duration of action and the impact path. A total of 20 periods was selected, and the data were all daily data. Thus, 20 periods represent 20 days. The short-term impact was studied, and the results are shown in Fig 3, in which the horizontal axis represents the lag period, and the vertical axis indicates the effect of the shock on the national carbon price.

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Fig 3. Impulse response results.

https://doi.org/10.1371/journal.pone.0333788.g003

1. (1). National carbon price. The findings indicate that the national carbon price is positively impacted by its own historical price levels, with the greatest impact level occurring in the first period, starting to fluctuate after the second period, and stabilizing around the 12th period.
2. (2). Trading volume. Trading volume positively impacts the national carbon price, with a long lag effect, starting at zero in the first period and gradually increasing until stabilizing after the 18th period. The rise in trading volume intensifies competition within the carbon market, thereby driving up the national carbon price.
3. (3). Carbon emissions from the power industry. The carbon emissions from the power industry have a short-term positive effect on the national carbon price, starting at zero in the first period, gradually increasing, then decreasing after the third period, and stabilizing from the 15th period onward. This is contrary to the result under the long-term situation in the cointegration equation. The primary reason for this discrepancy lies in the short-term dynamics: rising carbon emissions from the power industry directly indicate heightened emissions by enterprises, thereby increasing their need for carbon allowances and pushing the national carbon price upward. Thus, power industry emissions have a short-term positive effect on the national carbon price. Conversely, in the long term, increased emissions from the power sector prompt policy adjustments, such as higher total carbon quotas. This also spurs enterprises to adopt low-carbon technologies and increase clean energy consumption, thereby expanding their potential for emission reduction and ultimately lowering the national carbon price. This long-term effect is opposite to the short-term direct impact of power industry emissions on the national carbon price.
4. (4). EU carbon price. EU carbon price negatively impacts the national carbon price, beginning with no impact in the initial period, gradually rising in the second period, showing slight fluctuations between the third and fourth periods, and stabilizing from the 16th period onward. The negative impact of EU carbon prices may stem from policy competition in global carbon markets. When the EU strengthened emission reduction by raising the carbon price, the national carbon market was still in the early stage of establishment, following the strategy of seeking progress while maintaining stability, and the institutional system was still in the process of continuous improvement, so the level of the carbon price was still maintained at a relatively low state in order to achieve a balance between environmental protection and industrial development.
5. (5). Energy prices. Among energy price indicators, coal price negatively impacts the national carbon price (consistent with the results of [24]), starting at zero in the first period, showing positive growth in the second period but with nearly no impact, and beginning to show negative growth after the third period. An increase in coal prices prompts enterprises to switch to alternative energy sources. Given coal’s high carbon emissions, such substitution reduces overall emissions, thereby lowering the national carbon price. Conversely, oil prices positively influence the national carbon price (consistent with the results of [25,26]). Specifically, oil price fluctuations show a brief negative impact in the third period but stabilize and turn positive from the fourth period onward. The impact of the natural gas price on the national carbon price is roughly similar to that of the oil price, but the positive impact of natural gas is slightly smaller. When the oil price increases, the rigid demand of enterprises for oil leads to an increase in the cost of reducing carbon emissions for the enterprise, which is passed on to the carbon price, resulting in a higher carbon price.. When natural gas prices rise, substituting with other energy sources results in higher carbon emissions compared to natural gas, thereby increasing the expense of emission reduction. In contrast, the continued use of natural gas has a long-term price advantage and aligns with the low-carbon policy direction.
6. (6). CSI 300 Index. The CSI 300 Index positively impacts the national carbon price, but its influence is small, almost approaching zero.
7. (7). The EL 300 Index positively impacts the national carbon price, with a significant influence that starts at zero in the first period and gradually increases until it stabilizes around the tenth period. The power industry is more tightly connected to the carbon trading market compared to the macroeconomy. As a result, its development has a more pronounced effect on the national carbon price. The positive growth in both factors enhances corporate production capacity, driving up carbon emissions and subsequently the national carbon price.

2.3.6 Variance decomposition.

Variance decomposition and impulse response analysis offer complementary perspectives on the same phenomenon. Impulse response analysis measures the reaction of an economic variable to impulses from another variable, whereas variance decomposition quantifies the contribution of each structural shock to the variance of other variables, highlighting the differences in the magnitude of their impacts. To ensure consistency in the research, the number of periods analyzed is set to 20, matching the impulse response analysis. The variance decomposition results for each variable’s impact on the carbon price are shown in Table 7. The findings reveal that the variance of the prediction error of the national carbon price is predominantly influenced by its own historical price fluctuations. Although this influence diminishes over time, it still accounts for more than 85% of the explanatory power. The impact of trading volume on the national carbon price starts at zero in the first period, gradually increases, and reaches an explanatory level of 11% by the 20th period. The effects of coal price, EL 300 Index, EU carbon price, natural gas price, and crude oil price on the national carbon price are initially zero but grow slightly over time, though their contributions remain minimal. The CSI 300 Index’s impact on the national carbon price starts at zero, fluctuates in the subsequent periods, and eventually stabilizes with a negligible contribution, almost zero. Likewise, the impact of carbon emissions from the power industry begins at zero, increases gradually, starts to decline in the sixth period, and stabilizes around the 15th period.

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Table 7. Variance decomposition results.

https://doi.org/10.1371/journal.pone.0333788.t007

During the 18th period, the contributions of various factors to the carbon price fluctuations stabilize. We conducted analysis and research based on the stabilized contribution rate of each factor. In the 18th period, various influencing factors in the national carbon market are ranked by contribution as follows: own historical prices > trading volume > EL 300 Index > EU carbon price > coal price > oil price > natural gas price > carbon emissions from the power industry > CSI 300 Index. The carbon emissions of power industry had a limited impact on the national carbon price, mainly because of their limited ability to rapidly influence the wider carbon market in the short term. More specifically, the emissions from regulated enterprises directly affect their demand for carbon allowances, while the broader industry’s impact on the carbon market exhibits a significant lag. Additionally, the CSI 300 Index has an insignificant effect on the national carbon price, as the power industry’s development more directly impacts the carbon market than the macroeconomy does. These variance decomposition findings align with the impulse response results, further validating the effectiveness of the VEC model.