A Study on the Price Transmission Mechanism of Environmental Benefits for Green Electricity in the Carbon Market and Green Certificate Markets: A Case Study of the East China Power Grid

Abstract

As the global energy transition progresses, green electricity, which is crucial for low-carbon systems, has gained attention. However, the lack of effective market linkages hinders a full understanding of the price transmission effects across green markets. This study uses the Vector Autoregression (VAR) model and Granger causality tests to analyze the price transmission and lag effects between the carbon, green certificate, and China Certified Emission Reduction (CCER) Markets. The findings reveal complex price linkages, offering theoretical insights and policy recommendations for optimizing green electricity markets and environmental rights trading.

1. Introduction

The intensification of global climate change has prompted countries to gradually strengthen the control of greenhouse gas emissions and drive the economic and social transition toward a low-carbon and green transformation. Under the “dual carbon” strategic goals, the development and utilization of green electricity has become an important direction for energy transformation, playing a crucial role in addressing climate change and achieving sustainable development. Green electricity reflects both the energy value of clean energy and additional value in environmental rights [1], which brings new challenges and opportunities for the design and optimization of the energy and electricity market trading system.

In recent years, carbon trading markets and green electricity certificate trading markets have rapidly developed worldwide, and both have gradually become important tools for promoting the marketization of green electricity and enhancing the value of environmental rights. However, there are still many issues regarding the composition of green electricity prices and the transmission mechanisms of price signals in theory and practice. On the one hand, the pricing of green electricity depends not only on its energy value but also on its close relation to environmental rights value. On the other hand, carbon emission allowances (CEAs) [2], China Certified Emission Reductions (CCERs) [3], and Green Electricity Certificates (GECs) [4], as important tools for environmental rights trading, have significant differences in market rules, price composition, and applicable scope, and the mechanisms and effects of their influence on green electricity prices still require further study.

Although the study of the green electricity market has become a hot spot in the energy transition, most of the existing literature focuses on the pricing mechanism of the traditional electricity market and relies on a static regression model that fails to deeply reveal the complex interaction and price transmission mechanism among the green electricity market, carbon market, and green certificate market. Especially in the context of “dual carbon” policy, the lag effect and interdependence between markets have not been fully paid attention to. This study innovatively combines the VAR model and Granger causality test to systematically analyze the dynamic relationship of multiple green environmental rights and interests markets. The VAR model captures the dynamic feedback between markets, while the Granger causality test reveals the causal effect between markets, making up for the shortcomings of traditional static analysis and providing a quantitative analysis framework for multi-market interaction. Through this approach, this paper provides precise theoretical support for policy makers, promotes the coordinated development of green markets, and aims to optimize market mechanisms and provide a scientific basis for the transformation of the low-carbon economy.

2. Domestic and International Research Status

With the accelerated progress of global energy transition and carbon neutrality goals, the green electricity market and environmental rights trading system have become hot research areas. The healthy development of the green electricity market is key to driving the low-carbon energy transition and achieving carbon reduction targets. At the same time, the pricing and trading mechanisms of environmental rights play a core role in the market system [5]. This paper aims to explore the impact of the carbon trading market and the green electricity certificate trading market on the price structure and price signal transmission mechanisms of green electricity. To achieve this, the paper systematically reviews research in related fields from an academic perspective, focusing on the pricing mechanisms of green electricity and the operational mechanisms of the carbon trading and green certificate markets, as well as the interactive relationships and price signal transmission laws between them and green electricity. Through these analyses, the paper aims to provide theoretical support for the scientific pricing of environmental rights value and the optimization of the market system.

2.1. Green Electricity Pricing Mechanism

The pricing mechanism of green electricity has become an important research direction for Chinese scholars in recent years, with research mainly focusing on price composition, policy incentives, and optimization paths. Chinese scholars generally believe that the price of green electricity is composed of both energy value and environmental rights value. Reference [6] points out that with advancements in power generation technology and the expansion of economies of scale, the generation cost of green electricity continues to decrease, while the environmental rights value, reflected through carbon reduction benefits and ecological benefits, significantly influences the price formation. In addition, reference [7] suggests, through an environmental rights value assessment model, that the improvement of carbon pricing mechanisms has significantly increased the share of environmental rights in green electricity prices. However, these studies rely on single quantitative models or static models, which have certain limitations in analyzing the dynamic interaction effects between markets.

The government plays a key role in promoting the marketization of green electricity, and policy incentives are one of the core factors influencing green electricity pricing. Reference [8] indicates that measures such as subsidies, tax incentives, and green certificate trading policies can effectively enhance the market competitiveness of green electricity. For example, in the pilot green electricity market in East China, price subsidies have significantly reduced the user cost of green electricity, boosting market demand. Some Chinese scholars have attempted to construct more scientific pricing mechanisms based on theoretical models and practical experience. The authors of [9] propose a layered pricing strategy based on carbon reduction benefits by incorporating carbon emission factors into green electricity price models, highlighting the importance of environmental rights value in green electricity pricing, However, their analytical approach is overly simplistic, only examining the price formation mechanism from one perspective, while neglecting the long-term effects of multi-market interactions and the impact of policy changes on market mechanisms.

Developed countries, especially in Europe and North America, have established relatively mature green electricity market pricing mechanisms. Reference [10] indicates that price fluctuations in the carbon market are transmitted to the green power market through the power market, significantly enhancing the market competitiveness of renewable energy. The green power premium in the EU is driven primarily by corporate voluntary carbon neutrality demand rather than the direct impact of carbon market prices, which highlights the crucial role of policy design in the coordination of market mechanisms. Reference [11] analyzes the operation mechanisms of the REC markets in India and the United States, finding that mandatory quota policies significantly boost green power demand, while market competition mitigates the impact of REC price fluctuations on market efficiency. Reference [12], which is a study on the European Union Emissions Trading System (EU ETS), points out that market competition is the core driving force for green electricity price formation, with policy incentives playing a supplementary role. In North America, green electricity prices are realized through the market trading of renewable energy credits, reflecting the market value of environmental rights. The efficient utilization of green power relies on advanced energy storage technologies, a field in which international scholars have conducted extensive research.

International scholars focus on quantifying and making environmental rights value explicit. The authors of [13] construct a price model based on carbon factors and find that the proportion of environmental rights in green electricity prices significantly increases with the development of the carbon trading market. In Europe, environmental rights value is directly linked to carbon market prices, enabling the market to effectively price emission reduction benefits. Unlike China, the European and American regions more frequently use dynamic analysis models to explore green electricity pricing mechanisms. Reference [14] reveals, through a VAR model and Granger causality test, the dynamic price interconnection between the carbon trading market, green certificate market, and green electricity market, indicating that price formation is influenced by complex interactions between markets. However, international studies often overlook China’s unique policy environment and regional market differences, lacking in-depth analysis tailored to the specific conditions of the Chinese market.

Foreign research also focuses on pricing differences among different types of green electricity. Reference [15] points out that different types of renewable energy (such as wind and solar power) exhibit significant differences in pricing mechanisms due to variations in production costs and market acceptance. This differentiated strategy helps improve market efficiency.

2.2. The Operational Mechanisms of the Carbon Trading and Green Certificate Markets

The carbon trading market and the green certificate market, as two major platforms for environmental rights trading, exhibit significant differences in certification standards, trading mechanisms, and market participants. In-depth research and understanding of their operational mechanisms are crucial for analyzing their roles in the transmission of green electricity price signals. Both markets play a key role in promoting the low-carbon energy transition and enhancing the marketization of renewable energy, serving as important supports for achieving green development and sustainable energy goals.

The research focus of the carbon trading market’s operational mechanism lies in total cap control, quota allocation, market price formation, and the impact of policy drivers on the market. In China, scholars primarily explore the regional differences in the carbon market and the rationality of the quota allocation mechanism. Reference [16] points out that total cap control and quota allocation are central to the operation of the carbon market and that the supply–demand relationship of quotas and policy adjustments have a significant impact on market price fluctuations. Additionally, reference [17] studies the regional operational efficiency of China’s carbon market, finding that the carbon market efficiency in the developed eastern regions is significantly higher than that in the central and western regions, reflecting the important influence of regional policies and market maturity on the carbon trading market. Internationally, the European Union Emissions Trading System (EU ETS), as the largest and most mature carbon market in the world, has attracted considerable attention regarding its operational mechanisms. Reference [18] analyzes the EU ETS quota allocation and price formation mechanisms, pointing out that the scarcity of quotas and market liquidity are key factors influencing carbon price fluctuations. Further research, in [19], reveals the positive role of carbon market price signals in promoting renewable energy investment and driving energy structure transformation.

Research on the green certificate market focuses on policy design, price formation mechanisms, and its interconnection with the renewable energy market. Domestically, ref. [20] proposes that the operational mechanism of the green certificate market mainly includes the participation mechanism of power generation enterprises, the price formation mechanism of green certificates, and the linkage effects between green certificates and the power market. Research shows that green certificate prices are influenced by a combination of policy subsidies, market demand, and renewable energy consumption targets, with a relatively low level of marketization. International research tends to focus on the price formation and operational efficiency of the green certificate market. Reference [21] analyzes the market mechanisms of renewable energy certificates (RECs) in the United States and India, finding that the price of green certificates is closely related to policy stability, market competition, and the cost of renewable energy generation. In Europe, reference [22] conducts a multi-country case study, pointing out that the operational efficiency of the green certificate market is significantly affected by policy transparency and the stability of market design.

As shown in

Table 1. Comparison of carbon market policy and green electricity market mechanism.

Region	Market Participants	Carbon Market Mechanism	Carbon Offset Mechanism	Pricing Mechanism	Green Electricity Market Mechanism	Price Transmission Relationship Between Markets
European Union (EU ETS)	Power, industry, and aviation	Auction-based quota allocation	Carbon credits are not allowed to offset surrender quotas	Carbon quota prices are determined by market supply and demand, with significant price volatility	Voluntary market transactions; green certificate prices are determined by market supply and demand; physical electricity and green certificates are traded separately	The carbon market and the green electricity market are relatively independent. Carbon prices mainly drive emission reduction costs, while green electricity premiums are more driven by corporate voluntary carbon neutrality and demand, with weaker transmission
California, USA (CCTP)	Power, cement, steel, etc.	A combination of auction and free allocation	Carbon offsetting is allowed (such as forestry carbon sinks), accounting for 8%	Carbon quota prices are determined by market supply and demand, with significant price volatility	Green electricity prices are determined by market supply and demand. Some states have subsidies or tax incentives	State-level RPS (Renewable Portfolio Standard) promotes green certificate demand. The impact of carbon prices on green electricity prices is relatively small
China (GBC)	Power (with plans to gradually include steel, building materials, aviation, and eight other major industries in the future)	Mainly free allocation, gradually introducing auction mechanisms	CCER can be used to offset carbon emission quotas, with a maximum offset ratio of 5%	Carbon quota prices are determined by a combination of government guidance and market bidding, with relatively lower prices	Certificate-electricity separation or certificate-electricity integration trading; only one transaction is allowed, and prices are determined by bilateral negotiation, listing trading, or centralized bidding	In the initial stage of the carbon market, only the power industry is included. There is potential competition between green certificates and CCER. If policies clearly define mutual recognition rules (such as allowing green certificates to offset quotas), the transmission effect will be significantly enhanced

, there are obvious differences in carbon market policies in different regions, resulting in a very complicated price transmission mechanism in the green electricity market. Because of its mature and dynamic carbon pricing system, the European Union is weakly linked to the green electricity market. In contrast, California’s carbon market is relatively stable, and carbon market prices have a moderate impact on the green electricity market. China’s carbon market currently has a limited impact on the green electricity market due to its early stage, but the impact is expected to increase gradually as the market matures. This comparison emphasizes that in the process of promoting the transition to a low-carbon economy, the coordination of carbon market and green power policies is crucial, and the policy docking between the two should be optimized to improve market efficiency and the transmission effect of price signals.

2.3. The Interactions and Price Signal Transmission Between the Carbon Trading, Green Certificate, and Green Electricity Markets

The carbon trading market, green certificate market, and green electricity market are three crucial market mechanisms that promote the transition to a low-carbon economy and drive the development of renewable energy. The interaction and price signal transmission mechanisms between these markets are currently hot topics in academic research. Through the linkage between these markets, resource allocation can be optimized, market efficiency enhanced, and ultimately energy transition and carbon reduction goals achieved.

Research on the interaction between the carbon trading market and the green electricity market mainly focuses on the transmission mechanism of carbon price to green electricity prices and their synergistic effects. Domestic studies indicate that carbon market prices can influence green electricity market prices through policy guidance and market linkage mechanisms, significantly impacting the market competitiveness of renewable energy. The authors of [23] investigate the transmission effect of carbon market quota prices on green electricity prices in China, finding that an increase in carbon prices can raise green electricity prices by driving up demand for green electricity, thereby advancing the marketization process of renewable energy. Based on the system dynamics model, ref. [24] introduced the formation mechanism of green certificate price, and further analyzed the impact of green certificate trading on the marginal cost of coal and green electricity in the power market. However, the presets of the quota system in this report are quite different from the current policies.

Internationally, more attention is given to the long-term effects of the synergy between the carbon market and the green electricity market. Reference [25] uses dynamic modeling to analyze the synergistic effects between the EU carbon market and the green electricity market, concluding that carbon market price signals are transmitted to the green electricity market through the electricity market, thereby promoting investment and development in renewable energy. Reference [26] points out that the volatility of carbon market prices not only affects green electricity prices but can also accelerate the low-carbon energy transition by altering the relative competitiveness of renewable energy generation costs.

The price linkage between the green certificate market and the green electricity market is mainly reflected in the mandatory quota mechanism driven by policies. Reference [27] states that there is a significant positive correlation between green certificate prices and green electricity prices, especially under the implementation of mandatory renewable energy consumption policies. An increase in green certificate prices can significantly drive the growth of demand in the green electricity market. Reference [28] further reveals that the price feedback effect from the green electricity market plays an important role in stabilizing green certificate prices. The synergistic fluctuation mechanism between the two helps improve market efficiency and enhance the absorption capacity of renewable energy. The authors of [29] conduct an in-depth analysis of the interaction between China’s green certificate market and green electricity market, showing that fluctuations in green certificate prices have a significant driving effect on green electricity market demand. In particular, under stricter quota policies, the linkage between green certificate prices and green electricity prices becomes even tighter.

The price signal transmission mechanism is key to understanding the interaction between different markets. The theory of price signal transmission emphasizes that information between markets is conveyed through price changes, affecting resource allocation and market behavior. Reference [30] establishes an interactive SD model to simulate and analyze the price interactions and investment behaviors between China’s CET, TGC, and electricity markets, providing references and insights for low-carbon policy design and energy market construction. Reference [31] uses game theory to analyze the synergistic effects of electricity trading, carbon emission trading, and the green certificate market, revealing the optimization of power generation companies’ strategic behavior through multi-mechanism linkage. The research shows that policy coordination can significantly promote the development of clean energy and carbon reduction, achieving a balance between environmental and economic benefits. Reference [32] summarizes the experience of the joint operation of carbon–electricity markets abroad and analyzes the interactive influence mechanisms and coordinated development directions of the electricity–carbon-certificate market in China, offering suggestions for the connection mechanisms of the green electricity environmental value between markets.

Table 2. Comparison between relevant studies and this paper.

Papers	Research Method	Dataset	Research Content	Research Limitation
[33,34]	Game model	Data on China’s electricity market and carbon market	The interaction between carbon market and green electricity market is studied.	The complexity of the behavior of market participants and the incomplete competition of the market are not fully considered and are also mainly based on static analysis.
[35,36]	Regression model and static analysis	Relevant data of China’s carbon emission trading market and green certificate market	The price fluctuation and mutual influence of carbon market and green certificate market are analyzed.	The research is mainly based on static analysis and does not deeply explore the dynamic changes of market mechanism, ignoring the delay effect and lag factors in the market.
[37,38,39,40]	System dynamics model	Carbon market, electricity market, and green certificate market transaction data	The coupling mechanism of electricity market, carbon market, and green certificate market is analyzed, and the complex interaction between the markets is simulated by a model.	The system dynamics model relies on a large number of assumptions and parameter settings, and it is easy to ignore the influence of some market factors.
This paper	VAR model + Granger causality test	Carbon markets, green certificates, and green electricity data 2021–2024	The complex interaction and price transfer mechanism of green electricity market, carbon market, and green certificate market are revealed, including lag effect and causality.	The VAR model cannot capture causality directly and relies on lag selection. In order to make up for the deficiency, this paper discusses the causality between variables through Granger causality test.

lists a number of studies on the correlation analysis of green markets and compares them with this paper. The superiority of the research method in this paper can be clearly seen from the table. The combination method of the VAR model and Granger causality test can not only discern the dynamic relationship between green markets but also identify the causal relationship.

Existing research reveals the operational mechanisms of the carbon market and the green certificate market and their impact on green electricity market prices. However, most methods rely on univariate regression models and lack a systematic analysis of multi-market interactions, with especially little research on the lag effects of price transmission. Research on China’s green electricity pricing mechanism is more policy-driven, with a low level of marketization and insufficient analysis of dynamic price changes and multi-market interactions. On the other hand, international research focuses on marketization, emphasizing the explicitness of environmental rights and dynamic interactions between multiple markets, but lacks in-depth exploration of China’s unique policy context and regional market characteristics. To address these issues, this paper uses a VAR model to quantitatively analyze the price interaction relationships between China’s green electricity, green certificates, carbon emission allowances, and CCERs, constructing a matrix for environmental rights price signal transmission relationships. Granger causality tests are used to validate the influence relationships between markets. This research not only helps improve the price formation mechanism of the green electricity market but also provides theoretical support and practical guidance for optimizing the environmental rights market system.

3. Analysis of the Impact of the Carbon Market and Green Certificate Market on Green Electricity Prices

At present, the environmental value of China’s green power is usually measured by the difference between the green power transaction price and the benchmark electricity price, while the carbon emission quota (CEA), China Certified Emission Reduction (CCER), and Green Power Certificate (GEC) also provide environmental value [41]. Studying the mechanisms of value transfer between these markets is crucial to understanding their impact on the price of green electricity.

Based on the VAR model, this paper analyzes the dynamic price relationship and interaction mechanism of the carbon market, the green certificate market, and the green electricity market. Research shows that these market prices are highly correlated, may influence each other through multiple feedback mechanisms, and are influenced by external factors. The unstructured approach of the VAR model, without presupposing causality, reveals complex dynamic interactions between markets by analyzing lag terms, which makes the VAR model particularly suitable for research scenarios lacking theoretical causal inference.

3.1. Methodology

This study uses the Vector Autoregression (VAR) model to analyze the dynamic price relationships and interaction mechanisms between the carbon market, green certificate market, and green electricity market. The specific research methodology and process are shown in Figure 1, which clearly and comprehensively presents the research process of this paper. The research logic in the figure will then be explained in detail. Based on publicly available data from the China Green Electricity Certificate Trading Platform, Shanghai Environmental Energy Exchange, and regional green electricity markets, a time series dataset covering green certificate prices, carbon emission allowance (CEA) prices, China Certified Emission Reduction (CCER) prices, and green electricity environmental rights value is constructed. Unit root tests and differencing are applied to ensure the stationarity of the series. The optimal lag length of the VAR model is determined using the Akaike Information Criterion (AIC) and Hannan–Quinn Information Criterion (HQ). By constructing the model and conducting the analysis, the coefficient matrix of different lag lengths of the VAR model is estimated using Ordinary Least Squares (OLS). The comprehensive dynamic relationship matrix is obtained by summing and normalizing the variable relationships. The stability of the model is tested using eigenvalue tests, and Granger causality tests are performed to reveal the price linkage mechanism, lag effects, and contribution to price fluctuations between different markets, providing empirical support for the optimization of the green market synergy mechanism.

3.2. Data Analysis

Market price data for carbon emission allowances, CCER, green certificates, and green electricity are collected in time series. To facilitate the analysis of the relationships among them, the environmental rights value is used as the trading object. The green electricity premium is taken to represent the price of the green electricity environmental rights value. The green certificate price and the green electricity premium are then converted into carbon reduction prices (CNY/ton) using the East China Power Grid carbon emission factor (0.5992 t CO²/MWh). Descriptive statistics are then generated using the environmental rights value price data from each green market, which can visually display the characteristics and distribution of the price data.

Figure 2 is a line chart depicting the collected data on the environmental value and prices of green certificates and green electricity. The data primarily come from the China Green Power Certificate Trading Platform and the green electricity transaction data published by the State Grid.

Figure 3 is a discount chart comparing the prices of green certificates and green electricity environmental value after being converted into emission reduction prices using the carbon emission factor, with carbon market price data. The carbon market price data mainly comes from the Shanghai Environmental and Energy Exchange’s carbon emission trading platform.

Table 3. Descriptive statistics table of green market price data.

Variable Name	Maximum	Minimum	Mean	Standard Deviation	Median	Variance	Kurtosis	Skewness	Coefficient of Variation (CV)
Green Certificate	228.638	12.65	72.88	47.368	76.769	2243.694	3.178	1.362	0.65
Carbon Emission Rights	98.83	23	67.966	18.186	60	330.73	−0.082	−0.151	0.268
CCER	86.94	10	49.712	22.349	39	499.494	−1.145	0.446	0.45
Green Electricity Environmental Value	147.079	30.424	94.412	25.063	89.736	628.172	1.472	−0.246	0.265

was obtained through descriptive statistical analysis. There are outliers in the current data that need to be analyzed and processed for the more prominent data indicators. According to the 3-sigma outlier detection criterion, the outliers in the data will be replaced with the median of the dataset, and a new dataset will be generated for further analysis.

3.3. Correlation Analysis

Before establishing the VAR model, it is necessary to conduct a stationarity test on each time series variable. If all time series are stationary, the VAR model can be established; otherwise, the resulting vector autoregressive model would be a spurious regression.

Before establishing the VAR model, it is necessary to perform the Augmented Dickey–Fuller (ADF) unit root test on each time series variable to ensure that the time series is stationary; otherwise, the resulting model may be a spurious regression model. The ADF unit root test results in

Table 4. ADF test results.

Variable	T (Statistic)	P (p-Value)	Critical Values
			1%	5%	10%
Green Certificate	−0.728	0.839	−3.724	−2.986	−2.633
Carbon Emission Rights	−2.396	0.143	−3.711	−2.981	−2.63
CCER	1.083	0.995 *	−3.809	−3.022	−2.651
Green Electricity Environmental Value	−3.292	0.015 **	−3.833	−3.031	−2.656

Note: **, * represent significance levels of 5% and 10%, respectively.

show that the data for green electricity environmental value can reject the null hypothesis of a unit root, indicating that the time series is stationary. However, for the other data, the p-values are higher than the 10% significance level, meaning that the null hypothesis of a unit root cannot be rejected and the time series is non-stationary. After applying differencing, the carbon emission rights and green electricity environmental value became stationary, with p-values less than 0.05. The time series data for green certificates and CCER remained non-stationary, but after second-order differencing, the data show stationarity.

As shown in

Table 5. Second-order differencing ADF test results.

Variable	T (Statistic)	P (p-Value)	Critical Values
			1%	5%	10%
Green Certificate	−2.8818	0.0475 **	−3.964	−3.085	−2.682
Carbon Emission Rights	−4.0709	0.0011 ***	−3.809	−3.022	−2.651
CCER	−2.037	0.0474 **	−3.964	−3.085	−2.682
Green Electricity Environmental Value	−2.8733	0.0485 **	−3.833	−3.031	−2.656

Note: ***, **, represent significance levels of 1% and 5%, respectively.

, the p-values corresponding to the test statistics of each dataset are less than 0.05, indicating that the time series data have become stationary after second-order differencing and can be directly used to establish the VAR model.

In the VAR model, each variable is represented as a lag of all the variables in the system. This method allows us to analyze the correlations between variables and understand their short-term dynamics by examining how these prices respond to market price shocks. For the four variables in the green market—carbon emission rights price, CCER price, green certificate price, and green electricity price—the following VAR model can be constructed:

$${\mathrm{Y}}_{\mathrm{t}}=\mathrm{c}+{\sum }_{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{A}}_{\mathrm{i}}{\mathrm{Y}}_{\mathrm{t}-\mathrm{i}}+{\mathsf{ϵ}}_{\mathrm{t}}$$

(1)

where

${\mathrm{Y}}_{\mathrm{t}}$ is the vector composed of the prices of different green markets arranged by time, specifically ${\mathrm{Y}}_{\mathrm{t}}={\left[{\mathrm{P}}_{\mathrm{C},\mathrm{t}},{\mathrm{P}}_{\mathrm{C}\mathrm{C}\mathrm{E}\mathrm{R},\mathrm{t}},{\mathrm{P}}_{\mathrm{G}\mathrm{E}\mathrm{C},\mathrm{t}},{\mathrm{P}}_{\mathrm{G}\mathrm{E},\mathrm{t}}\right]}^{\mathrm{T}}$.

$\mathrm{c}$ is a constant vector, representing the intercept of the model.

${\mathrm{A}}_{\mathrm{i}}$ is the coefficient matrix of the k-th lag, representing the lagged effect of each variable on itself and other variables.

$\mathrm{p}$ is the optimal lag order, determined by information criteria.

${\mathsf{ϵ}}_{\mathrm{t}}$ is the error term vector, assumed to be white noise.

When using the Vector Autoregressive (VAR) model for time series analysis of data, selecting the appropriate lag order is crucial, as it directly affects the model’s predictive ability and the robustness of parameter estimates.

By comparing the statistical criteria for different lag orders in

Table 6. Comparison of different lag orders.

Lag Order	Log L	AIC	SC	HQ	FPE
0	−475.66	24.179	24.371	24.236	31,681,256,194.491
1	−399.396	20.91	21.877 *	21.188	1,228,540,973.541
2	−363.402	20.601	22.356	21.087	1,012,511,536.871 *
3	−331.227	20.584	23.137	21.261	1,461,698,948.426
4	−289.62	19.746 *	23.103	20.59 *	2,009,909,138.106

Note: * Indicates that the lag order is the optimal choice under the corresponding criteria.

, the suitability of each lag order can be systematically evaluated. According to the information criteria in the table, a lag order of 4 is the optimal model choice, as it has the smallest values for both the AIC and HQ criteria, and both are marked with an asterisk (*). This indicates that, when balancing model complexity and overall fit, the VAR model with a lag order of 4 is the best model.

Based on the selected lag order, an extended data matrix is constructed, including the lagged values of each variable as explanatory variables. Ordinary Least Squares (OLS) are then applied to estimate the parameters in the VAR model, which represent the impact of the independent variables on the dependent variables.

Table 7. VAR model parameter estimation results.

Variable	Coefficient	Standard Error	t-Statistic	p-Value
Constant	−0.2399	0.1088	−2.205	0.027 *
L1. Green Certificate	1.7132	0.4534	3.778	0.000 *
L1. Green Electricity Environmental Value	−1.6404	0.3020	−5.432	0.000 *
L1. Carbon Emission Rights	0.2810	0.3904	0.720	0.472
L1. CCER	0.4353	0.4003	1.088	0.277
L2. Green Certificate	1.1394	0.6257	1.821	0.069
L2. Green Electricity Environmental Value	0.1583	0.5119	0.309	0.757
L2. Carbon Emission Rights	0.5939	0.3493	1.700	0.089
L2. CCER	0.8000	0.5220	1.533	0.125
L3. Green Certificate	1.0091	0.4835	2.087	0.037 *
L3. Green Electricity Environmental Value	0.0676	0.4301	0.157	0.875
L3. Carbon Emission Rights	0.8914	0.3148	2.832	0.005 *
L3. CCER	0.4601	0.5003	0.920	0.358
L4. Green Certificate	−0.1406	0.2078	−0.677	0.499
L4. Green Electricity Environmental Value	0.7676	0.3553	2.161	0.031 *
L4. Carbon Emission Rights	0.8113	0.4392	1.847	0.065
L4. CCER	1.0120	0.6071	1.667	0.096

Note: * Indicates that the estimated value of the coefficient is statistically significant.

shows the estimated parameters for the green electricity environmental value in the VAR model.

In Table 7, L1 represents a lag of one period. In time series analysis, a lag refers to the value of a variable at the previous time point. The data in this study are collected monthly, so L1. Green Certificate refers to the green certificate price data from one month ago. This equation includes the first to fourth lag terms of the green electricity environmental value itself, as well as the other three variables (green certificate, carbon emission rights, and CCER). The coefficient of each term represents the magnitude of the impact of that lag term on the green electricity environmental value, while the p-value is used to determine whether this impact is statistically significant.

If we consider all lag orders, the VAR model for the green electricity environmental value can be written as:

$${\mathrm{P}}_{\mathrm{GE},\mathrm{t}}=\mathsf{\alpha }+{\sum }_{\mathrm{i}=1}^{\mathrm{p}}{\sum }_{\mathrm{j}=1}^4{{\mathrm{A}}_{\mathrm{i}\mathrm{j}}\mathrm{P}}_{\mathrm{j},\mathrm{t}-\mathrm{i}}+{\mathsf{ϵ}}_{\mathrm{t}}$$

(2)

where

${\mathrm{P}}_{\mathrm{GE},\mathrm{t}}$ represents the green electricity environmental value variable at time t.

$\mathsf{\alpha }=-$0.2399 is the constant term, representing the baseline value when all explanatory variables are zero.

$\mathrm{P}$ is the lag order, with the maximum lag order taken as 4 in this case.

${\mathrm{A}}_{\mathrm{i}\mathrm{j}}$ is the coefficient matrix, where i denotes the lag order and j denotes the variable index (1 represents P_GEC, 2 represents P_GE, 3 represents P_C, and 4 represents P_CCER).

${\mathrm{P}}_{\mathrm{j},\mathrm{t}-\mathrm{i}}$ represents the value of the j-th variable at time t.

${\mathsf{ϵ}}_{\mathrm{t}}$ is the error term vector, assumed to be white noise.

The system matrix ${\mathrm{A}}_{\mathrm{i}\mathrm{j}}$ is as follows:

$${\mathrm{A}}_{\mathrm{i}\mathrm{j}}=\left[\begin{array}{cccc}1.7132& -1.6404& 0.2810& 0.4353\\ 1.1394& 0.1583& 0.5939& 0.8000\\ 1.0091& 0.0676& 0.8914& 0.4601\\ -0.1406& 0.7676& 0.8113& 1.0120\end{array}\right]$$

(3)

The calculation of the lag matrix ${\mathrm{A}}_{\mathrm{i}\mathrm{j}}$ is the core step of the VAR model, directly used for analyzing the dynamic relationships between variables.

The form of the VAR model can be written as:

$$\mathrm{Y}=\mathrm{X}\mathsf{\beta }+\mathsf{ϵ}$$

(4)

where

$\mathrm{Y}$ is the target vector at the current time, with dimensions $\mathrm{T}\times \mathrm{n}$ (T is the sample size, and n is the number of variables).

$\mathrm{X}$ is the lagged variable matrix, with dimensions $\mathrm{T}\times \left(\mathrm{n}\mathrm{i}+1\right)$, containing both the current and lagged variables.

$\mathsf{\beta }$ is the estimated coefficient matrix, with dimensions $\left(\mathrm{n}\mathrm{i}+1\right)\times \mathrm{n}$.

$\mathsf{ϵ}$ is the residual vector, with dimensions $\mathrm{T}\times \mathrm{n}$.

The structure of $\mathsf{\beta }$ is:

$$\mathsf{\beta }=\left[\begin{array}{c}\mathrm{c}\\ {\mathrm{A}}_1\\ {\mathrm{A}}_2\\ ⋮\\ {\mathrm{A}}_{\mathrm{p}}\end{array}\right]$$

(5)

where ${\mathrm{A}}_{\mathrm{k}}$ is the lag matrix for the k-th lag, describing the dynamic effect of the variable at time t-k on the current variable.

3.4. Calculation of Lag Coefficient Matrix

To estimate $\mathsf{\beta }$, the lag coefficient matrix is found by minimizing the sum of squared forecast errors $\mathsf{ϵ}$:

$$\underset{\mathsf{\beta }}{\mathsf{ϵ}=\mathrm{m}\mathrm{i}\mathrm{n}}{‖\mathrm{Y}-\mathrm{X}\mathsf{\beta }‖}^2$$

(6)

The coefficient matrix is estimated by Ordinary Least Squares (OLS):

$$\widehat{\mathsf{\beta }}={\left({\mathrm{X}}^{\mathrm{T}}\mathrm{X}\right)}^{-1}{\mathrm{X}}^{\mathrm{T}}\mathrm{Y}$$

(7)

The estimation results for $\mathsf{\beta }$ include the constant term $\mathsf{\alpha }$ and the coefficient matrices for lags 1 to p $\left({\mathrm{A}}_1,{\mathrm{A}}_2,\dots ,{\mathrm{A}}_{\mathrm{p}}\right)$.

The coefficient matrix ${\mathrm{A}}_{\mathrm{k}}$ is given by:

$${\mathrm{A}}_{\mathrm{k}}=\left\{{\mathsf{\beta }}_{\mathrm{i}\mathrm{j}}\right|\mathrm{i}\in \left[\left(\mathrm{k}-1\right)\mathrm{n}+1,\mathrm{k}\mathrm{n}\right],\mathrm{j}\in \left[1,\mathrm{n}\right]\}$$

(8)

where ${\mathrm{A}}_{\mathrm{k}}\left(\mathrm{i},\mathrm{j}\right)$ represents the i-th variable in the k-th lag and ${\mathsf{\beta }}_{\mathrm{i}\mathrm{j}}$ represents the coefficient of the j-th variable in the whole lag matrix $\mathsf{\beta }$.

For the VAR model with four time lags and p = 4, the coefficient matrices for lags 1, 2, 3, and 4, extracted from the model fitting, are shown in

Table 8. VAR model coefficients.

	Green Certificate	Carbon Emission Rights	CCER	Green Electricity Environmental Value
L1. Green Certificate	0.0795	0.0019	−0.0415	0.4403
L1. Carbon Emission Rights	0.5112	−0.5884	0.6386	0.6470
L1. CCER	0.1119	0.0123	−0.8840	0.3217
L1. Green Electricity Environmental Value	−4.3648	−0.2348	0.1662	−1.6404
L2. Green Certificate	0.3856	0.1868	−0.4829	0.2928
L2. Carbon Emission Rights	1.4427	0.1692	1.3065	1.3676
L2. CCER	1.9611	0.0972	−0.7505	0.5912
L2. Green Electricity Environmental Value	−2.1222	−0.4324	1.1673	0.1583
L3. Green Certificate	0.9133	0.1399	−0.5680	0.2593
L3. Carbon Emission Rights	2.9814	0.0059	1.8557	2.0524
L3. CCER	1.9171	0.2114	−0.4502	0.3400
L3. Green Electricity Environmental Value	−1.6027	0.1940	0.2328	0.0676
L4. Green Certificate	0.0913	0.0616	−0.1521	−0.0361
L4. Carbon Emission Rights	5.4118	−0.4292	−0.1952	1.8680
L4. CCER	3.0084	0.0261	0.1276	0.7478
L4. Green Electricity Environmental Value	1.6656	0.2344	−1.0439	0.7675

.

The coefficient matrices of each lagged variable are combined to obtain a comprehensive dynamic relationship matrix, which is then normalized to process the relationships, as shown in the formula below:

$${\mathrm{R}}_{\mathrm{i}\mathrm{j}}=\mathrm{L}{1}_{\mathrm{i}\mathrm{j}}+\mathrm{L}{2}_{\mathrm{i}\mathrm{j}}+\mathrm{L}{3}_{\mathrm{i}\mathrm{j}}+\mathrm{L}{4}_{\mathrm{i}\mathrm{j}}$$

(9)

$${\mathrm{R}}_{\mathrm{i}\mathrm{j}}^{\mathrm{normalized}}={\displaystyle \frac{{\mathrm{R}}_{\mathrm{i}\mathrm{j}}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\left|{\mathrm{R}}_{\mathrm{i}\mathrm{j}}\right|}}$$

(10)

Table 9. Overall dynamic relationship coefficient matrix.

	Green Certificate	Carbon Emission Rights	CCER	Green Electricity Environmental Value
CCER	0.2773	0.1908	−0.2669	0.2097
Carbon Emission Rights	0.4099	−0.4632	0.4919	0.6222
Green Electricity Environmental Value	−0.2545	−0.1313	0.0713	−0.0678
Green Certificate	0.0582	0.2146	−0.1698	0.1003

is the calculated overall price signal transmission relationship matrix.

This matrix represents the normalized dynamic relationships between the four market prices: green certificates, carbon emission rights, CCER, and green electricity environmental value. Each value in the matrix indicates the relative influence between variables, and the normalized values make comparisons easier. In the matrix structure, rows represent the affected variables (dependent variables) and columns represent the influencing variables (independent variables). Each value reflects the standardized total impact of one variable’s dynamic lag effect on another variable.

Positive values indicate a positive dynamic impact (price increases of the independent variable promote the dependent variable), while negative values indicate a negative dynamic impact (price increases of the independent variable suppress the dependent variable).

From the coefficient matrix, it is evident that there are complex dynamic linkages between the green certificate, carbon emission rights, CCER, and green electricity environmental value markets. Each market plays a different role in price fluctuations and generates significant interactive effects. The impact of green certificate prices on other markets is relatively weak, but to some extent, through both positive and negative interactive effects, it forms a dynamic linkage with the carbon emission rights and green electricity markets. Carbon emission rights play a significant central role in price transmission, especially in contributing to the green electricity environmental value. The CCER market has a relatively balanced positive promotion effect across markets, particularly in promoting price transmission in the green certificate market. The green electricity environmental value has a smaller reverse effect on other market prices and shows some suppressive effects, indicating that its price fluctuations are more driven by external factors.

In the Vector Autoregressive (VAR) model, stability is one of the key assumptions to ensure the validity of the model. The stability of the model requires that the forecast results of the time series are reliable and that the coefficients of the model remain stable over time without exhibiting sharp fluctuations. To verify the stability of the VAR model, the eigenvalue test method is commonly used. The core of this test is to analyze whether the eigenvalues of the model lie within the unit circle. If all the eigenvalues lie within the unit circle, it indicates that the model is stable, meaning that the impact effects of the variables will gradually diminish over time.

Figure 4 shows the AR root plot of the VAR model. Since all the eigenvalue points lie within the unit circle, it can be concluded that the VAR system is stable. The model can then be further analyzed through impulse response analysis and variance decomposition to observe the underlying relationships.

4. Granger Causality Test

The Granger causality test is a statistical hypothesis testing method used to determine whether one time series can predict another time series. Specifically, if the past values of time series X can significantly predict the future values of time series Y, while the past values of Y cannot, then we can say that X Granger-causes Y. The key to this method lies in the lagged values of the time series, i.e., past data points.

Before performing the Granger causality test, it is necessary to ensure that the time series data are stationary. As the data have already been made stationary through differencing before constructing the VAR model, the Granger causality test can be conducted.

The Granger causality test results using the price data of green certificates and green electricity environmental value as variables are shown in

Table 10. Granger causality test results (1).

Lag Order (Lag)	AIC	F-Test	p-Value	Chi-Square Test Chi2	p-Value	Likelihood Ratio Test Chi2	p-Value	F Test for Parameters	p-Value
1	14.015	0.2845	0.5989	0.3217	0.5706	0.3197	0.5718	0.2845	0.5989
2	13.242	0.2277	0.7984	0.5691	0.7523	0.5628	0.7547	0.2277	0.7984
3	13.602	0.1646	0.9187	0.6973	0.8738	0.6874	0.8762	0.1646	0.9187
4	13.657	0.6821	0.6158	4.4826	0.3446	4.0954	0.3933	0.6821	0.6158
5	13.204	0.9540	0.0485	9.5402	0.0894	7.9248	0.1604	0.9540	0.0485

.

As the number of lag periods increases, the model’s fit gradually improves, with the AIC value being the smallest at a lag of 5. For lags 1 to 4, the p-values of all tests (including the F-test and Chi-Square test) are greater than 0.05, failing to indicate a significant impact of green certificate prices on green electricity prices. However, at a lag of 5, the p-values for the F-test and the parameter F-test are both below 0.05, indicating a significant causal relationship between green certificate prices and the green electricity environmental value prices.

The Granger causality test results using the price data of carbon emission rights and green electricity environmental value as variables are shown in

Table 11. Granger causality test results (2).

Lag Order (Lag)	AIC	F-Test	p-Value	Chi-Square Test Chi2	p-Value	Likelihood Ratio Test Chi2	p-Value	F Test for Parameters	p-Value
1	9.548	0.0332	0.8571	0.0375	0.8465	0.0375	0.8465	0.0332	0.8571
2	9.563	0.3205	0.7295	0.8012	0.6699	0.7886	0.6741	0.3205	0.7295
3	9.832	0.5535	0.6527	2.3444	0.5041	2.2368	0.5247	0.5535	0.6527
4	9.483	1.3951	0.2861	9.1676	0.0570	7.7157	0.1026	1.3951	0.2861
5	9.310	1.5501	0.2526	15.5014	0.0084	11.7334	0.0386	1.5501	0.2526

.

Table 11 analyzes the relationship between carbon emission rights and green electricity environmental value prices at different lag periods. As the number of lags increases, the model’s fit gradually improves, with the AIC value being the lowest at a lag of 5. For lags 1 to 3, the p-values of various tests (including the F-test and Chi-Square test) are all greater than 0.05, failing to significantly demonstrate the impact of carbon emission rights prices on green electricity environmental value prices. At lag 4, the p-value of the Chi-Square test is close to 0.05, indicating a potential causal relationship, but it is still not significant. At lag 5, the p-values of both the Chi-Square test and Likelihood Ratio test are significantly below 0.05, indicating that changes in carbon emission rights prices have a significant impact on green electricity environmental value prices and show a strong causal relationship.

The Granger causality test results using the price data of CCER and green electricity environmental value as variables are shown in

Table 12. Granger causality test results (3).

Lag Order (Lag)	AIC	F-Test	p-Value	Chi-Square Test Chi2	p-Value	Likelihood Ratio Test Chi2	p-Value	F Test for Parameters	p-Value
1	12.278	0.0123	0.9127	0.0139	0.9061	0.0139	0.9062	0.0123	0.9127
2	12.289	2.1888	0.1382	5.4721	0.0648	4.9484	0.0842	2.1888	0.1382
3	12.457	1.0335	0.4028	4.3772	0.2235	4.0208	0.2592	1.0335	0.4028
4	12.371	0.8507	0.5165	5.5901	0.2319	5.0040	0.2869	0.8507	0.5165
5	12.086	1.2385	0.3551	12.3847	0.0299	9.8245	0.0804	1.2385	0.3551

.

Table 12 analyzes the relationship between CCER and green electricity environmental value prices at different lag periods. As the number of lags increases, the model’s fit improves, with the AIC value being the lowest at a lag of 5. The tests for lags 1, 3, and 4 all show that CCER prices have a significant impact on green electricity environmental value prices, while the correlation is weaker at lag 2. Overall, historical changes in CCER prices significantly affect green electricity environmental value prices, particularly at lag 5, reflecting the lagged characteristics of market price transmission.

5. Conclusions and Policy Implications

5.1. Conclusions

The analysis of the VAR model’s dynamic relationship matrix reveals the price transmission mechanisms among the green certificates, carbon emission rights, CCER, and green electricity environmental value markets. The carbon emission rights market plays a central role, significantly influencing green electricity environmental value. The CCER market also facilitates price transmission but with a weaker impact. The green certificate market has less influence, though interactions exist. Green electricity environmental value exhibits a weaker, negative effect on the other markets, indicating its passive role, driven by price fluctuations in other markets. Granger causality tests show significant lag effects, with price changes in the carbon and CCER markets impacting the green electricity environmental value after a delay. These findings highlight that market changes take time to manifest, emphasizing the delayed nature of price transmission in green markets.

It should be further explained that external factors such as renewable energy investment policies, fuel price fluctuations, and electricity market reforms will also have a profound impact on the market price of green electricity. These external factors are ignored in this paper, and how they affect the pricing mechanism will be further explored in future studies to build more complex green electricity price models.

5.2. Policy Implications

To enhance the price signal transmission of green electricity markets and optimize the structure of environmental rights markets, this paper proposes the following policy recommendations:

Strengthen the Core Role of the Carbon Market. Policymakers should optimize carbon emission quota allocation, enhance market transparency, and improve liquidity to stabilize carbon market prices, ensuring accurate price signal transmission to guide green electricity pricing.

Optimize the CCER Market. Expand market participation, increase liquidity, and strengthen project certification and supervision to boost the CCER market’s influence on green certificate and green electricity markets.

Promote Marketization of the Green Certificate Market. Refine the green certificate price formation mechanism, encourage active participation from power producers, and strengthen linkage with electricity markets to enhance market efficiency.

Improve Transparency and Participation in the Green Electricity Market. Increase market transparency to help stakeholders better predict policy changes, and encourage diverse market players (e.g., consumers, investors, and environmental organizations) to engage in green electricity trading. Expanding participation and diversity will promote market health and resource allocation efficiency.

Foster Cross-Sector Policy Coordination. Address price transmission lags by creating unified green market development plans and linkage mechanisms. Strengthen cross-departmental collaboration, promote information sharing, and ensure that market mechanisms complement each other to improve overall efficiency and accelerate the adoption of green electricity.

By implementing these measures, the green electricity market’s price signal transmission can be enhanced, the environmental rights market structure optimized, and progress made toward global carbon neutrality and green economic transformation.