The Efficiency of China’s Carbon Trading Schemes: A Tale of Seven Pilot Markets

Abstract

This study evaluates the efficiency of China’s seven emission trading schemes (ETS) piloted in 2013. We evaluate seven pilots’ overall technical and scale efficiencies and temporal dynamics during 2014–2023. We use a bootstrap correction data envelopment analysis (bootstrap-DEA), which guarantees a more accurate efficiency estimation than the traditional DEA model. The results show that the average overall (pure technical) efficiency of the seven pilot markets increased from 0.612 (0.844) in 2014 to 0.898 (0.990) in 2023. Furthermore, we document that seven ETS pilots differ remarkably in efficiency and transaction price, whilst all have shortages. Specifically, the small-scale market transaction is the main constraint effect on the average scale efficiency of the ETS. This study provides concrete recommendations for policy makers to consummate institutional designs to improve ETS efficiency.

1. Introduction

Extreme climate events caused by global warming [1] have become challenging risks threatening the Earth’s natural ecosystem [2], human survival [3], and global political and economic stability [4]. The main reason for global warming is the relentless growth of greenhouse gases (hereafter GHG), especially carbon dioxide emissions [5]. The international community has formulated and adopted the United Nations Framework Convention on Climate Change (UNFCCC), the Kyoto Protocol and the Paris Agreement to cope with climate change [6]. The emissions trading system (hereafter ETS) is one of the policies proposed by the Kyoto Protocol and a supplementary provision of UNFCCC. Moreover, the signatory parties of the Paris Agreement determine their emissions targets as nationally determined contributions for coping with climate change, thereby laying a foundation for promoting national carbon transactions [7].

ETS is a policy tool for reducing GHG emissions by market-oriented means adopted in the European Union, the United States, China, Canada, Japan, Korea, New Zealand, and other countries or districts [4]. Based on ETS, CO2 emissions are transformed into a tradable commodity, and their external cost is internalized [8]. Theoretically, carbon trading can maximize the profits of enterprises with different marginal emissions-reduction costs while minimizing society’s emissions-reduction costs [9]. The ETS has the following advantages. (1) It contributes to the potential GDP growth or the recovery of GDP losses [10]. (2) The government can promote energy saving, emissions reduction, and the development of a low-carbon economy through the ETS [11,12]. (3) It results in more cost savings than the command control policy, strengthens the economy and has the potential for emissions reduction [13]. (4) The ETS provides a capital bonus for sustainable development and stimulates environmental and ecological governance [14].

As the largest carbon emitter, China released a notice on carrying out the emissions trading pilot work in October 2011 to achieve the emissions reduction goal. Beijing, Tianjin, Shanghai, Guangdong, Shenzhen, Hubei, and Chongqing were selected as areas for the ETS pilots [15]. Figure 1 shows the distribution and concentration of the average transaction prices of the seven pilot ETS markets between 2014 and 2023. The yellow color highlights regions where the average transaction prices are relatively higher, particularly emphasizing the areas surrounding the price. We can observe that the price span of the carbon market in Beijing is the largest, with the lowest (highest) price of 24.0 (149.64) yuan, ranging mainly from 40 to 64 yuan. On the contrary, the Tianjin ETS has the smallest price span of 7.0–50.1 yuan, with prices ranging from 22 to 30 yuan. Overall, Figure 1 indicates significantly different prices among pilot carbon markets. The desirable carbon price should equal the minimum marginal emission reduction cost for achieving the emissions-reduction target. Therefore, the incorrect carbon price caused by an imperfect quota system will affect the participation and commitment of enterprises in the ETS, thus affecting market efficiency [16].

Given the above backdrop, this study evaluates the efficiencies of seven Chinese ETS pilots from 2014 to 2023. We employ an improved data envelopment analysis (hereafter DEA) model: bootstrap-DEA. The specific operating shortboards of ETS efficiency are identified by decomposing the overall efficiency into pure technical and scale efficiency. The research outcomes provide novel empirical evidence which can help consummate China’s pilot ETS and establish the national ETS.

The contributions of this study lie in the following two aspects. First, the decomposition of average efficiency into pure technical and scale efficiency sheds new light on the key influencing factors on the efficiency of seven ETF pilots. Second, in terms of research methods, bootstrap-DEA combining the bootstrap sampling technique with the DEA model offers a solution to the limitations of the traditional DEA model, such as sample sensitivity and overestimation of efficiency [17].

The rest of this paper is organized as follows: Section 2 presents a literature review. Section 3 introduces the research methods and data. Section 4 provides the empirical results. Section 5 concludes this study and offers concrete policy suggestions.

2. Literature Review

A growing body of literature has focused on China’s pilot ETS. Ref. [18] summarized the development status of China’s seven pilot carbon markets. They compared the characteristics of ETS, e.g., the coverage range, initial quota, monitoring, reporting and verification. Ref. [19] pointed out that 23.7% of the total emissions-reduction cost in the carbon markets could be reduced, and the suitable emissions trading scheme might have different cost-saving effects across provinces. Meanwhile, some studies focused on disclosing problems in China’s pilot ETS. For example, ref. [20] noted an imperfect supervision system and the need for a unified market regulatory organization. Ref. [21] evaluated the maturity of the seven pilot markets through the fuzzy analytical hierarchy process and identified the constraint factors of a well-performing ETS. Ref. [22] verified that the overall maturity of China’s carbon market is low using the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method.

Some pieces of literature focused on a specific pilot ETS in China. Ref. [23] investigated the institutional background and the supervision framework of Shenzhen pilot ETS. Ref. [24] qualitatively explored the flaws of Shanghai pilot ETS mechanism designs and proposed countermeasures for quota allocation, carbon information disclosure and risk management. Ref. [25] studied the pros and cons of Hubei’s ETS design, including the upper limit, the quota, the transaction mechanism and the compliance factors. Ref. [26] simulated the initial allocation of Shanghai’s carbon ETS based on the Shapley value to explore the fair quota allocation mechanism.

In summary, in terms of the research content of China’s ETS, many studies investigated the development status and problems of China’s overall carbon market or a pilot carbon trading market. A few studies have begun to pay attention to the efficiency of the carbon trading system. For instance, Ref. [27] evaluated the efficiency of China’s carbon market during the 2015–2017 period by using the DEA method. Ref. [28] established the efficient market model of China’s ETS based on the fair game model. They found that China’s ETS had reached weak form efficiency but failed to reach semi-strong and strong form efficiency. Ref. [10] identified the reasons for the low efficiency of China’s ETS by taking full consideration of four determinant factors: carbon price, trading volume, market liquidity, and information transparency. The authors argued that the underlying reasons might be the lack of supportive institutional arrangements for ETS, insufficient market preparation, and system design defects. Ref. [29] studied seven pilots’ comprehensive service capability and market efficiency in ETS markets using factor analysis, the AHP (Analytical Hierarchy Process) and the DEA methods. They confirmed the presence of significant differences in comprehensive serviceability among the seven pilot ETS markets.

In terms of the research methodology in the existing studies, the evaluation of carbon market efficiency mainly includes the variance ratio test [30], multi-fractal detrended analysis [31], the fair game model [28], detrended fluctuation analysis (DFA) [32] and the entropy weight–TOPSIS evaluation method [33]. Ref. [31] found that China’s ETS has low efficiency, which positively (negatively) correlated with short-term (long-term) market activity. Ref. [28] reported weak form efficiency using the efficient market model for China’s ETS. Ref. [32] found that, on the one hand, the efficiency of China’s pilot ETS was generally low and, thus, challenging for the market to play a price discovery function. On the other hand, when investors were active in trading, they tended to be concentrated near the delivery period. In contrast, the market activity was lower on the regular trading day and performed poorly. Ref. [33] showed that the differences in transaction mechanism design among seven Chinese ETS pilots caused a significant difference in their operational efficiency.

DEA outperforms game theory, regression analysis, and other analysis methods in evaluating a multi-dimensional input and output structure system, whilst the carbon trading market is a complex multi-agent and multi-variable system. Ref. [34] assessed the operation efficiency of the ETS by employing the DEA model. They showed that the operation of the ETS markets in Shenzhen, Hubei and Tianjin was efficient. In contrast, the efficiency of the ETS markets in Shanghai, Beijing, Guangdong and Chongqing was low. More recently, Ref. [27] used the DEA model and found that the average efficiency of China’s seven pilot ETS markets increased yearly.

Although many studies on China’s ETS have been conducted, the following deficiencies must be addressed. (1) Regarding research content, most studies investigate either the effect of ETS’ on carbon emissions or the development and existing problems of the ETS but need to pay more attention to the operation efficiency of the carbon market. (2) As for the studies on the efficiency of the ETS, the research methods merit further improvement. Specifically, the ETS has characteristics of multi-agent and multi-variable. Thus, more than traditional methods such as game theory or regression analysis are needed to achieve practical carbon market analysis. (3) Few scholars have employed the traditional DEA method to measure the efficiency of the ETS. However, due to sample sensitivity, vulnerability to extreme values, and deviated estimation of small samples [17], the estimated efficiency value is prone to be higher than the actual value in assessing the efficiency of ETS. This work corrects the above-listed issues associated with the traditional DEA method using the bootstrap-DEA model for a more accurate and authentic carbon market efficiency estimation.

3. Analysis of Empirical Results

3.1. Data Analysis on Output Indicators

Trading volume affects market efficiency and is an essential indicator for measuring the carbon market scale.

Table A1. Raw data on input–output indicators.

Year	Carbon Market	Input—Total Quota (Billion Tonnes)	Input—Number of Verifying Institutions (Number)	Input—Number of Emission Control Enterprises	Output—Total Volume Traded (Tonnes)	Output—Carbon Price Stability (%)
2014	Beijing	0.50	19	543	1,069,605	32.21
2014	Tianjin	1.60	3	114	1,011,340	33.10
2014	Shanghai	1.60	10	191	1,666,724	20.00
2014	Guangdong	4.08	16	184	1,055,542	56.45
2014	Shenzhen	0.33	21	635	1,816,381	54.53
2014	Hubei	3.24	3	138	7,001,171	8.38
2014	Chongqing	1.16	10	240	145,000	0.00
2015	Beijing	0.47	19	973	1,243,046	26.40
2015	Tianjin	1.60	4	112	975,713	14.34
2015	Shanghai	0.53	10	191	1,476,108	25.80
2015	Guangdong	3.70	16	186	6,756,520	20.11
2015	Shenzhen	0.30	21	634	4,326,048	29.42
2015	Hubei	3.24	3	138	14,731,100	8.11
2015	Chongqing	1.06	11	237	132,099	13.60
2016	Beijing	0.47	19	947	2,426,412	31.60
2016	Tianjin	1.60	4	112	367,796	16.20
2016	Shanghai	1.55	10	368	3,867,071	23.01
2016	Guangdong	3.70	16	218	22,232,995	10.88
2016	Shenzhen	0.30	21	824	10,643,885	27.20
2016	Hubei	3.24	3	166	11,722,793	13.63
2016	Chongqing	1.06	11	254	459,846	44.24
2017	Beijing	0.50	28	943	2,323,443	29.24
2017	Tianjin	1.60	4	109	1,162,370	5.04
2017	Shanghai	1.56	9	381	2,368,328	14.60
2017	Guangdong	4.22	31	246	16,573,388	7.85
2017	Shenzhen	0.30	23	787	5,245,930	11.98
2017	Hubei	2.57	8	344	12,488,892	7.89
2017	Chongqing	1.30	11	254	7,436,603	18.99
2018	Beijing	0.50	35	903	3,214,335	44.28
2018	Tianjin	1.60	8	107	1,875,205	0.00
2018	Shanghai	1.58	9	381	2,665,961	14.79
2018	Guangdong	4.22	35	249	26,860,458	9.07
2018	Shenzhen	0.30	23	794	12,657,462	22.00
2018	Hubei	2.56	8	344	8,607,490	18.64
2018	Chongqing	1.00	11	197	269,445	29.69
2019	Beijing	0.45	27	843	3,013,700	39.08
2019	Tianjin	1.50	8	125	43,400	22.70
2019	Shanghai	1.50	9	313	2,683,300	20.47
2019	Guangdong	4.65	21	242	12,250,600	22.86
2019	Shenzhen	0.29	22	721	784,900	32.34
2019	Hubei	2.40	8	373	4,022,300	22.00
2019	Chongqing	1.17	11	187	112,800	36.32
2020	Beijing	0.50	26	859	1,150,600	40.38
2020	Tianjin	1.60	8	216	5,202,700	12.00
2020	Shanghai	1.58	12	314	2,147,200	21.33
2020	Guangdong	4.65	31	243	19,488,600	18.83
2020	Shenzhen	0.29	22	687	1,239,200	39.08
2020	Hubei	2.70	8	332	14,216,200	18.70
2020	Chongqing	1.30	11	187	219,700	33.71
2021	Beijing	0.50	25	886	1,870,700	83.26
2021	Tianjin	1.60	8	192	4,948,700	13.10
2021	Shanghai	1.05	10	323	1,380,000	8.91
2021	Guangdong	4.65	41	178	26,835,400	18.81
2021	Shenzhen	0.30	25	750	5,992,900	35.32
2021	Hubei	1.66	8	339	3,852,900	18.60
2021	Chongqing	1.30	11	308	1,147,200	19.59
2022	Beijing	0.50	25	909	1,752,800	107.49
2022	Tianjin	0.75	8	145	5,143,600	13.76
2022	Shanghai	1.09	11	378	1,648,400	21.24
2022	Guangdong	2.66	34	200	14,609,100	24.10
2022	Shenzhen	0.25	14	684	5,080,700	61.90
2022	Hubei	1.82	8	343	5,733,500	24.20
2022	Chongqing	1.45	11	308	759,100	20.20
2023	Beijing	0.50	29	1126	3,016,212	89.81
2023	Tianjin	1.20	10	218	6,145,784	8.49
2023	Shanghai	1.30	11	433	2,109,692	15.31
2023	Guangdong	4.02	41	268	27,226,192	12.46
2023	Shenzhen	0.27	20	906	6,120,611	42.47
2023	Hubei	1.63	10	440	5,441,108	25.49
2023	Chongqing	1.39	11	336	1,032,182	31.96

in Appendix A shows that various pilot ETS trading volumes have fluctuated slightly. Furthermore, they showed an overall upward trend, indicating that the development of China’s ETS has been tortuous since its establishment, but the broad market scale is expanding. Furthermore, Table A1 suggests that the trading volumes of various ETS markets varied greatly. For instance, Guangdong’s ETS quota trading volumes were relatively high, reaching 27.2 million tons in 2023. On the contrary, the trading volumes of carbon emissions in Chongqing and Beijing were relatively low, i.e., only 1.03 and 3.02 million tons in 2023, respectively.

Price stability is an essential indicator for measuring market stability and reflects market risk. Specifically, if the price stability is strong, the market is stable, and the market risk is low; otherwise, the market is unstable, and the market risk is high. Figure 2 shows that in 2023, the price stability of the Beijing ETS was the highest, reaching 89.8%, reflecting the emissions reduction cost of the emissions-control enterprises in the Beijing pilot carbon market. This result indicates that Beijing’s ETS in 2023 was stable and had a small risk. Meanwhile, the price stability of Tianjin’s carbon market was the lowest, i.e., only 8.49%. Such findings suggest that the price signal was seriously distorted, and the ability to reflect the emissions reduction cost through price was weak in Tianjin’s pilot ETS.

3.2. Empirical Results and Discussion

According to the input–output indicators outlined in Section 3.2, this study calculates the traditional DEA efficiency and the DEA efficiency value adjusted by the bootstrap method. First, the overall efficiency is calculated using the CCR model. Next, pure technical efficiency is obtained using the BCC model. Finally, the scale efficiency is obtained by dividing overall efficiency by pure technical efficiency.

3.2.1. Comparative Analysis of Efficiency between Traditional DEA and Bootstrap DEA

Figure 3 shows from top to bottom: the technical efficiency using the CCR model (CCR_TE), the technical efficiency modified by the Bootstrap method (CCR_TE_Bootstrap), the technical efficiency based on the BBC model (BBC_TE), and the technical efficiency modified by Bootstrap (BBC_TE_Bootstrap). The horizontal axis represents the average efficiency value distribution of China’s seven pilot ETS markets. The vertical axis denotes the probability of the distribution of the efficiency values.

Figure 3 and

Table 1. Technical efficiency (TE) and pure technical efficiency (PTE) values of pilot ETS markets under the CCR and BCC models in 2014–2023.

Model	Year	Traditional DEA	Bootstrap DEA
CCR-TE	2014	0.749	0.612
	2015	0.799	0.749
	2016	0.749	0.635
	2017	0.994	0.986
	2018	0.849	0.718
	2019	0.950	0.991
	2020	0.930	0.930
	2021	0.832	0.832
	2022	0.819	0.819
	2023	0.898	0.898
	Average	0.857	0.817
BCC-PTE	2014	0.926	0.844
	2015	0.940	0.874
	2016	0.970	0.935
	2017	0.999	0.999
	2018	0.967	0.921
	2019	0.960	1.000
	2020	0.966	0.966
	2021	1.000	1.000
	2022	0.917	0.917
	2023	0.990	0.990
	Average	0.964	0.945

show that the average DEA efficiency values under the CCR and BCC model adjusted by the Bootstrap method are smaller than those by the traditional DEA in 2014–2023. This finding can be attributed to the ability of the sample’s distribution based on the bootstrap method to simulate the original sample estimator’s distribution and correct the efficiency value’s deviation. Therefore, as expected, the results confirm that the traditional DEA model tends to overestimate the efficiency of the pilot carbon trading markets. In contrast, the DEA efficiency value modified by Bootstrap is more consistent with the actual market efficiency than that of the traditional DEA model.

3.2.2. Efficiency Analysis of Pilot ETS Markets under the CCR and BCC Models

Table 2. The efficiencies of various pilot ETS adjusted by bootstrapping.

(a) Overall Efficiency
Year	Pilot ETS
	Beijing	Guangdong	Hubei	Shanghai	Shenzhen	Tianjin	Chongqing
2014	0.685	0.175	0.758	0.865	0.759	0.250	0.792
2015	0.888	0.660	0.825	0.868	0.829	0.852	0.321
2016	0.890	0.787	0.786	0.401	0.747	0.044	0.792
2017	0.991	0.991	0.992	0.954	0.992	0.992	0.992
2018	0.655	0.812	0.861	0.847	0.807	0.842	0.205
2019	1.000	1.000	1.000	1.000	1.000	0.935	1.000
2020	0.839	1.000	1.000	0.674	1.000	1.000	1.000
2021	1.000	1.000	0.843	0.350	1.000	0.956	0.674
2022	1.000	1.000	0.693	0.488	1.000	1.000	0.554
2023	1.000	0.998	0.876	0.486	1.000	0.924	1.000
Average	0.895	0.842	0.863	0.693	0.913	0.780	0.733
(b) Pure Technical Efficiency
Year	Pilot ETS
	Beijing	Guangdong	Hubei	Shanghai	Shenzhen	Tianjin	Chongqing
2014	0.952	0.468	0.890	0.943	0.873	0.877	0.908
2015	0.933	0.948	0.906	0.908	0.909	0.910	0.605
2016	0.984	0.956	0.958	0.778	0.958	0.959	0.955
2017	0.999	0.999	0.999	0.995	0.999	0.999	0.999
2018	0.753	0.953	0.951	0.950	0.946	0.946	0.947
2019	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2020	1.000	1.000	1.000	0.762	1.000	1.000	1.000
2021	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2022	1.000	1.000	1.000	0.705	1.000	1.000	0.716
2023	1.000	1.000	1.000	0.932	1.000	1.000	1.000
Average	0.962	0.932	0.970	0.897	0.969	0.969	0.913
(c) Scale Efficiency
Year	Pilot ETS
	Beijing	Guangdong	Hubei	Shanghai	Shenzhen	Tianjin	Chongqing
2014	0.719	0.373	0.851	0.917	0.870	0.285	0.872
2015	0.952	0.696	0.911	0.956	0.912	0.937	0.530
2016	0.905	0.824	0.821	0.515	0.780	0.046	0.829
2017	0.992	0.992	0.993	0.959	0.993	0.993	0.992
2018	0.870	0.852	0.905	0.891	0.852	0.890	0.216
2019	1.000	1.000	1.000	1.000	1.000	0.935	1.000
2020	0.839	1.000	1.000	0.884	1.000	1.000	1.000
2021	1.000	1.000	0.843	0.350	1.000	0.956	0.674
2022	1.000	1.000	0.693	0.692	1.000	1.000	0.774
2023	1.000	0.998	0.876	0.522	1.000	0.924	1.000
Average	0.928	0.874	0.889	0.769	0.941	0.797	0.789

presents the annual overall (a), pure technical (b) and scale efficiency values (c) adjusted by the bootstrap method for each of the seven carbon market pilots. These efficiency values offer insights into the performance of the carbon markets. The efficiency value usually ranges from 0 to 1, where 1 represents complete efficiency, which means that the evaluated unit has reached the optimal level of resource utilization and the maximum output level. 0 means complete inefficiency, which means that the assessed unit cannot reach the level of the reference unit through any resource allocation. The closer the efficiency value is to 1, the more efficient the unit is; the closer the efficiency value is to 0, the less efficient the unit is. Overall efficiency represents the combined measure of technical and scale efficiency, while pure technical efficiency focuses solely on technical efficiency. On the other hand, scale efficiency indicates the overall efficiency ratio to pure technical efficiency.

We can observe that during the 2014–2023 period, carbon markets’ overall efficiencies were smaller than their respective pure technical efficiencies. Due to that, the scale efficiency values (ratio of overall to pure technical efficiency) of all of China’s pilot ETS were less than one during the entire sample period, signifying suboptimal scale utilization. The total quota of China’s pilot ETS is up to 11.360 billion tons during the sample period, while the total trading volume is only 0.406 billion tons, according to Table A1 in Appendix A. This phenomenon may be due to a lack of continuity in government policies, leading to low emissions reduction awareness among enterprises, a stagnant carbon trading market, low market liquidity, and an insufficient scale of the carbon market.

Table 2 also highlights that before 2019, the overall scale and pure technical efficiency values adjusted by Bootstrap in the pilot ETS peaked in 2017. However, in 2018, the efficiency of various carbon markets declined, particularly with Chongqing’s overall efficiency plummeting to 20.5%. From Table 3, the ETS’s overall and pure technical efficiency in 2018 decreased by 27.15% and 7.76%, respectively. These results can be mainly attributed to the rapid decline of the price stability of most carbon markets in 2018. Except for the slight increase in price stability in Chongqing, the price stability of the remaining six pilot areas decreased significantly. The average price stability of the seven pilots’ ETS decreased from 60.59% in 2017 to 27.99% in 2018, reaching 53.81% monthly (see Table A1 in Appendix A).

Despite these fluctuations, from 2019 to 2023, various carbon markets’ overall efficiency and pure technical efficiency began to exhibit high stability, with many carbon markets maintaining or approaching perfect efficiency. The carbon trading practices in Beijing, Shenzhen, and Chongqing intermittently achieved perfect efficiency, reflecting the gradual improvement in the operational mechanisms of China’s carbon emission trading system and the increased awareness of enterprise participation in carbon trading. Furthermore, the sustained pure technical efficiency value of 1 in several cities demonstrates the robustness and progress of the carbon markets in terms of technological advancement.

3.2.3. Comparative Analysis of Seven Pilot ETS Markets’ Efficiencies

In this section, we analyze the operating efficiency of China’s pilot ETS markets. Figure 4 and Figure 5 are the graphical equivalents of the numerical results presented in Table 3. Specifically, Figure 4 and Figure 5 displays the average (annual) efficiency values for each of the seven ETS pilots. The results presented in Table 2, as well as Figure 4 and Figure 5, show the following. During the sample period, the Shenzhen ETS consistently demonstrated high levels of efficiency compared to the other pilot ETS markets. For instance, it had an average overall efficiency of 0.913 (see Figure 4), ranking first among the seven pilot markets. Moreover, the overall efficiency of the Shenzhen ETS was subject to relatively minor fluctuations (from the lowest of 0.747 in 2016 to perfect efficiency in 2019 and beyond) whilst remaining high during the sample period. The average pure technical and scale efficiencies were also high, i.e., 0.969 and 0.941, respectively. Furthermore, pure technical efficiency increased yearly from 2014 to 2017 and remained perfect after 2019. Compared to most other pilots, the scale efficiency of Shenzhen was more stable, indicating that the efficiency of the Shenzhen ETS was not as greatly affected by changes in the market size.

The average overall efficiency of the Beijing ETS was 0.895, ranking second among the pilot markets. Generally, the average overall efficiency of the Beijing carbon market increased yearly between 2014 and 2017 and remained at complete efficiency from 2019 to 2023. The Beijing ETS pilot’s average pure technical and scale efficiencies were also high, accounting for 0.962 and 0.928, respectively. As for the annual pure technical efficiency values, these followed a similar (although less volatile) trend as overall yearly efficiencies. Specifically, pure technical efficiency achieved near-perfect efficiency in 2017 but declined by 24.6% in 2018 and maintained at one after 2019. Moving on to the scale efficiency, it was unstable and followed a rising–declining–rising–declining (zigzag) trend but did not fluctuate considerably. Moreover, the scale efficiency remained high, indicating that the Beijing ETS’s operation mechanism and scale setting were well-designed. Pure technical efficiency was the primary factor determining the overall efficiency of the Beijing ETS.

The average overall efficiency of the Hubei ETS was 0.863, ranking it third among the pilot markets. Generally, the overall efficiency of the Hubei carbon market during the sample period was unstable, showing a jigsaw trend. We can observe that the decline in 2022 of 17.8% (to a value of 0.693) in the overall efficiency was the most pronounced. Hubei ETS market’s average pure technical and scale efficiencies were high, i.e., 0.97 and 0.889, respectively. Pure technical efficiency was the highest (lowest) from 2019 to 2023 (2014) at the complete level and decreased slightly by 4.8% in 2018. Furthermore, the time trend of scale efficiency was almost identical to overall efficiency, fluctuating and declining in 2022 to the lowest value of 0.693. This observation, in turn, indicates that the overall efficiency of the Hubei ETS was mainly affected by scale efficiency.

The average overall efficiency of the Guangdong ETS was 0.842, placing it fourth among the seven markets. The annual overall efficiency increased massively between 2014 and 2017 by a staggering 466.3%, from a meagre value of 0.175 to a maximum of 0.991. Although it decreased by 18.1% in 2018, the overall efficiency was maintained at a complete efficiency level in 2019 and after that. In addition, the average pure technical and scale efficiencies were also relatively high, i.e., 0.932 and 0.874, respectively. Furthermore, all three types of efficiencies followed a similar pattern over the sample period, increasing significantly from 2014 to 2017 but decreasing slightly in 2018 and remaining at a perfect level after 2019. Overall, we can conclude that the efficiency of the Guangdong ETS was significantly influenced by scale efficiency.

The average overall efficiency of the Tianjin ETS was low, i.e., 0.780, ranking fifth. Moreover, the annual fluctuations in overall efficiency from 2014 to 2018 were the most significant, indicating this period was the most volatile within the sample timeframe. Specifically, the overall efficiency in 2014 was only 0.250 and increased to 0.852 in 2015. Then, the overall efficiency decreased (increased) to 0.044 (0.992) in 2016 (2017), then declined again in 2018 by 15.1% to 0.842. Post-2019, the overall efficiency of Tianjin ETS has remained relatively stable, consistently maintaining levels above 0.92. On the contrary, the pure technical efficiency of the Tianjin ETS remained relatively stable, ranging between 0.877 (2014) and 1 (2019 and beyond). Finally, the annual scale efficiency of Tianjin ETS fluctuated the most before 2019 but stabilized at the highest level after that, following a virtually identical pattern as the overall efficiency. Summing up, similar to the pilot ETS in Hubei and Guangdong, the overall efficiency of the Tianjin ETS was primarily affected by the scale efficiency.

The performance of the Chongqing ETS during the 2014–2023 period was poor, and its average overall efficiency was equal to 0.733, ranking sixth. Moreover, the annual overall efficiency of the Chongqing carbon market showed significant volatility during each of the sampled years. For instance, in 2015 (2016), the overall efficiency decreased (increased) by 59.5% (146.7%), while it decreased significantly again in 2018, 2021 and 2022 (by 79.3%,32.6% and 17.8%, respectively). The pure technical efficiency was high, i.e., 0.913, while the scale efficiency was low, i.e., only 0.789, in the stage of scale increase. The changing trend of pure technical efficiency was the same as that of the overall efficiency of the Chongqing ETS before 2019, significantly decreasing by 33.4% in 2015 and slightly decreasing by 5.2% in 2018. Post-2019, except for minor fluctuations in specific years, the pure technical efficiency generally maintained perfect efficiency. The scale and overall efficiencies have the same changing trend, i.e., decreasing notably by 39.2%, 78.2% and 32.6% in 2015, 2018 and 2021, respectively. Thus, the overall efficiency of the Chongqing ETS was greatly affected by scale efficiency.

The performance of the Shanghai ETS was the worst, with an average overall efficiency of only 0.693. The overall yearly efficiency of the Shanghai carbon market was stable in 2014–2015, 2017–2019 and 2021–2023. However, it fluctuated considerably from 2015 to 2017 and 2019 to 2021. Specifically, the overall efficiency decreased (increased) by 53.9% (137.9%) in 2016 (2017) from 0.868 to 0.401 (from 0.401 to 0.954). From 2019 to 2021, the overall efficiency dropped significantly from complete efficiency to 0.35, with an average annual decrease of 40.3%. The average pure technical (scale) efficiency of the Shanghai ETS was 0.897 (0.769). The pure technical efficiency fluctuated less than the average and scale efficiencies and remained high during the sample period, reaching minimum and maximum values of 0.705 and 1 in 2022 and 2021, respectively. On the contrary, the scale efficiency was volatile and followed a similar pattern as the overall efficiency. Specifically, it decreased significantly by 46.2% (from a value of 0.956 to 0.515) in 2016, reaching the same level as in 2015 (0.959) in the following year, thus increasing by 86.2%. Between 2019 and 2021, the scale efficiency rapidly declined from 1 to 0.35, with an average annual decrease of 36%, and slightly decreased by 24.6% in 2023. The scale efficiency played a critical role in changes documented in the overall efficiency of the Shanghai ETS.

4. Research Methods and Data

4.1. Research Methods

4.1.1. The DEA Method

DEA is an effective method for evaluating the multi-index input–output system [35]. The technique aims to assess the relative efficiency of decision-making units (hereafter DMUs) with multi-input and multi-output by solving mathematical programming problems. DEA’s most significant advantage is that it does not need to set the assumption about the DMU’s efficiency distribution [27]. For each DMU, the constant returns to scale (hereafter CCR) DEA model can be written as follows:

$$\begin{array}{l}\max {\displaystyle \frac{{\displaystyle \sum _{r=1}^q{u}_r{y}_{rk}}}{{\displaystyle \sum _{i=1}^m{v}_i{x}_{ik}}}}\\ s.t.{\displaystyle \frac{{\displaystyle \sum _{r=1}^q{u}_r{y}_{rk}}}{{\displaystyle \sum _{i=1}^m{v}_i{x}_{ik}}}}\le 1\\ v\ge 0;u\ge 0\\ i=1,2,\cdots ,m;r=1,2,\cdots q;j=1,2,\cdots ,n\end{array}$$

(1)

where $x_{ik}$ ($y_{rk}$) refers to the ith input (rth output) variable of the decision-making unit $DM{U}_k$ and $v_i$ ($u_r$) represents its input (output) weight. To calculate the efficiency value of the DMU, $v_i$ and $u_r$ must be determined to maximize its efficiency, and the constraint conditions must be set to make the efficiency value of each DMU less than 1.

In the CCR model, it is assumed that the return to scale of production technology remains constant. However, many DMUs need to be in the optimal scale production state. Therefore, ref. [36] extended the CCR model to the BCC model by adding the constraint conditions for the variable return to scale. By doing this, they made the production scale in the projection point at the same level as the production scale of the DMU to be evaluated, thus excluding the influence of scale efficiency on technical efficiency under variable returns to scale. The specific model as per Equation (2), where $\theta$ refers to the efficiency of the variable return to scale of the DMU, is as follows:

$$\begin{array}{l}\min \theta \\ \mathrm{s}.\mathrm{t}. {\displaystyle \sum _{j=1}^n{\lambda }_j{x}_{ij}}\le \theta x_{ik}\\ \hspace{1em}\hspace{1em}{\displaystyle \sum _{j=1}^n{\lambda }_j{\mathrm{y}}_{rj}}\ge y_{rk}\\ \hspace{1em}\hspace{1em}{\displaystyle \sum _{j=1}^n{\lambda }_j=1}\\ \hspace{1em}\hspace{1em}\lambda \ge 0\\ \hspace{1em}\hspace{1em}i=1,2,\cdots ,m;r=1,2,\cdots ,q;j=1,2,\cdots ,n\end{array}$$

(2)

4.1.2. The Bootstrap-DEA Method

Although DEA has some advantages that cannot be compared by the parameter estimation method, it is also susceptible to sample sensitivity, vulnerability to outliers, and estimation deviation for small-size samples [17]. Therefore, ref. [37] introduced the bootstrap method in the DEA model. The combined approach does not need to set the function of the input and output variables in advance. Moreover, the bootstrap-DEA method is suitable for evaluating the efficiency of a DMU with a multi-dimensional input–output structure. Furthermore, the bootstrap approach is used to infer the empirical distribution of the DEA estimator by producing many simulated samples by repeated sampling.

Considering the sensitivity of the efficiency value to sample change, the confidence interval of the efficiency value is set, making the estimated value highly consistent with the actual value under a relatively loose condition. Therefore, the defects of the traditional DEA method are addressed, whilst the basis for judging the stability of the efficiency value is provided. The bootstrap-DEA method’s estimation process is presented in steps 1 to 5, Equations (3) to (5) below, and outlined in Figure 6.

• Assuming the original sample data in which each decision-making unit $DM{U}_k$ input and output ($X_k,Y_k$), $k=1,\cdots ,n,$ the DEA method is adopted to calculate the efficiency value (${\stackrel{\wedge }{\theta }}_k$).
• Assuming the efficiency values of n decision-making units (${\stackrel{\wedge }{\theta }}_k$), $k=1,\cdots ,n,$ the bootstrap method is adopted to obtain random efficiency values ${\theta }_{1b}^{*},\cdots ,{\theta }_{nb}^{*},$ where b refers to the number of iterations using the bootstrap method.
• In the next step, we calculate the simulated sample ($X_{\mathrm{kb}}^{*},Y_k$), $k=1,\cdots ,n,$ where $X_{\mathrm{kb}}^{*}=\left({\displaystyle \frac{{\stackrel{\wedge }{\theta }}_k}{{\theta }_{nb}^{*}}}\right)\ast X_k, k=1,\cdots ,n$.
• We adopt the DEA method for each simulated sample to calculate the efficiency value: $\stackrel{\wedge }{{\theta }_{kb}^{*}},k=1,\cdots ,n.$
• Steps 2 to 4 are repeated B times to produce a series of efficiency values:
• $\left\{\stackrel{\Lambda }{{\theta }_{kb}^{*}},k=\mathrm{1,2},\cdots ,n;b=\mathrm{1,2},\cdots ,B\right\}$.

Given that the DEA method may cause estimation bias in the case of a few samples, a smooth bootstrap distribution can simulate the distribution of the original sample estimator to correct the estimation deviation of DEA, as shown below.

$$\begin{array}{l}Bias\left(\stackrel{\wedge }{{\theta }_k}\right)=E\left(\stackrel{\wedge }{{\theta }_k}\right)-\stackrel{\wedge }{{\theta }_k},\\ \stackrel{\wedge }{Bias}\left(\stackrel{\wedge }{{\theta }_k}\right)=B^{-1}{\displaystyle \sum _{b=1}^B\stackrel{\wedge }{({\theta }_{kb}^{*}}})-\stackrel{\wedge }{{\theta }_k}.\end{array}$$

(3)

Accordingly, the efficiency value can be computed as in Equation (4) after modifying the bootstrap-DEA deviation.

$$\widetilde{{\theta }_{\mathrm{k}}}={\stackrel{\wedge }{\theta }}_k-\stackrel{\wedge }{Bias}({\stackrel{\wedge }{\theta }}_k)=2{\stackrel{\wedge }{\theta }}_k-B^{-1}{\displaystyle \sum _{b=1}^B\stackrel{\wedge }{{\theta }_{kb}^{*}}}$$

(4)

Furthermore, the confidence interval with an $\alpha$ confidence level is calculated as follows:

$$\begin{array}{c}\mathrm{Pr}\left(-{\stackrel{\wedge }{b}}_{\alpha }\le {\stackrel{\wedge }{\theta }}_{kb}^{*}-{\stackrel{\wedge }{\theta }}_k\le -{\stackrel{\wedge }{\mathrm{a}}}_{\alpha }\right)=1-\alpha ,\\ \mathrm{Pr}\left(-{\stackrel{\wedge }{b}}_{\alpha }\le {\stackrel{\wedge }{\theta }}_k-{\theta }_k\le -{\stackrel{\wedge }{\mathrm{a}}}_{\alpha }\right)\approx 1-\alpha ,\\ {\stackrel{\wedge }{\theta }}_k+{\stackrel{\wedge }{\mathrm{a}}}_{\alpha }\le {\theta }_k\le {\stackrel{\wedge }{\theta }}_k+{\stackrel{\wedge }{b}}_{\alpha }.\end{array}$$

(5)

The traditional DEA method has two basic models: the CCR model, based on constant returns to scale and the BCC model, based on variable returns to scale. [37] showed that when the actual research problem is based on constant returns to scale, the estimators ($\stackrel{\wedge }{{\theta }^{CCR}}$ and $\stackrel{\wedge }{{\theta }^{BBC}}$) calculated by using the CCR and BCC models are consistent. However, if the actual research problem is based on variable returns to scale, $\stackrel{\wedge }{{\theta }^{BBC}}$ ($\stackrel{\wedge }{{\theta }^{CCR}}$) is consistent (inconsistent). Therefore, we calculate the efficiency based on the BCC model to reduce the deviation of the calculation results caused by improper model selection. Furthermore, the bootstrap method proposed by [37] is adopted to correct the deviation of the efficiency score.

4.2. Index Selection and Data Sources

Following the relevant studies, we employ the three most popular input indicators shown in Table 3.

Table 3. Description of input–output indicators.

Indicators		Definitions	Literature
Input indicators	Total quota (x1)	Annual carbon emission limit of all emission-control enterprises in the pilot area	[34,38,39,40,41]
	Number of emissions-control enterprises (x2)	Number of enterprises keeping an agreement on carbon emission in the pilot area	[22,42,43]
	Third-party verification institutions (x3)	Number of institutions for monitoring and verifying the carbon emission behavior of emission-control enterprises and providing relevant services	[27,43,44,45]
Output indicators	Total trading volume (y1)	The annual cumulative trading volume of carbon emission quota	[29,46,47,48,49,50]
	Stability of carbon price (y2)	For measuring the stability of carbon trading price near the weighted average price	[10,51,52,53]

Table 3. Description of input–output indicators.

Indicators		Definitions	Literature
Input indicators	Total quota (x1)	Annual carbon emission limit of all emission-control enterprises in the pilot area	[34,38,39,40,41]
	Number of emissions-control enterprises (x2)	Number of enterprises keeping an agreement on carbon emission in the pilot area	[22,42,43]
	Third-party verification institutions (x3)	Number of institutions for monitoring and verifying the carbon emission behavior of emission-control enterprises and providing relevant services	[27,43,44,45]
Output indicators	Total trading volume (y1)	The annual cumulative trading volume of carbon emission quota	[29,46,47,48,49,50]
	Stability of carbon price (y2)	For measuring the stability of carbon trading price near the weighted average price	[10,51,52,53]

The total quota (x₁) indicator refers to the annual total carbon emissions quota determined by the pilot provinces and cities according to the GHG emissions control objectives and the national/provincial industrial policies. It reflects the depth of the market and its coverage. If the coverage is broad, it is conducive to improving carbon price efficiency and limiting the environmental arbitrage space of high-emission enterprises [54]. Therefore, the total quota (x₁) is the basis of the supply–demand relationship in the ETS, which determines the carbon price and trading volume to a certain extent. It is an essential input variable affecting the operation of the carbon market [41].

The number of emission control enterprises (x₂) refers to the number of units agreeing on carbon emissions in the pilot ETS. Including x₂ incorporated into the carbon trading system reflects the breadth of the carbon financial market, ensuring sufficient buyers and sellers and the effectiveness of the carbon emissions trading price [54]. Consequently, broader coverage of emissions control by multiple enterprises leads to increased liquidity of high-quality, low-carbon resources across various industries, strengthens the effectiveness of the ETS, and amplifies the emissions reduction potential of the carbon market.

The number of verification institutions (x₃) captures the institutions designated or entrusted by relevant governmental departments to monitor and verify the carbon emissions information of carbon emissions control enterprises and provide appropriate services [27]. Therefore, x₃ is an essential prerequisite for the authority of carbon prices [54], which ensures the efficiency of the ETS and helps promote the discovery of the value of carbon emissions trading rights and the transparency of market information disclosure.

The total trading scale represents market activity. If the activity is high (low), the trading scale is large (small). The trading scale in the market has two categories: total trading volume (y₁) and trading amount. As highlighted in previous research, the total trading volume is a crucial indicator for determining market trends and direction [53].

The stability of carbon pricing is a vital monitoring indicator of ETS efficiency, with a relatively stable price being essential for a large-scale trading operation. The volatility indicators commonly used are calculated from different transaction prices using statistical methods, allowing horizontal comparisons with other markets. However, China’s ETS is partly active and inactive, while some markets have nearly no trading. If price volatility is used as an indicator, then a quiet market demonstrates stronger stability, while an active market shows weaker stability. Comparing the two does not hold much significance. Therefore, referring to the practice of [46], a price stability indicator (y₂) based on the weighted average price is used in this study (see

Table A2. Weighted carbon prices of China’s pilot ETS markets in 2014–2023 (Unit: RMB/ton).

Pilot ETS	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Beijing	59.50	46.63	48.77	50.06	57.95	78.76	87.09	60.95	96.42	113.26
Tianjin	20.23	14.30	11.33	8.90	12.12	13.66	22.53	27.26	33.85	32.54
Shanghai	34.87	25.41	8.41	34.87	36.54	40.46	39.98	40.89	56.21	62.87
Guangdong	53.27	16.37	12.45	13.57	12.45	16.13	17.34	16.77	23.47	31.44
Shenzhen	62.55	38.15	26.45	27.91	23.46	13.30	23.45	11.61	36.72	59.38
Hubei	23.79	24.99	17.67	14.63	22.91	21.42	15.47	22.74	30.72	29.49
Chongqing	30.74	17.74	7.96	2.25	4.36	9.74	26.46	30.63	38.35	35.10

in Appendix A). Specifically, we calculate the weighted average price per year ($P^{\prime }={\displaystyle \frac{\sum P_{\mathrm{ij}}{Q}_{\mathrm{ij}}}{\sum Q_{ij}}}$), where P_ij (Q_ij) refers to the trading price (volume) on the Jth day of the ith year. Taking $P^{\prime }$ as the centre, (−10%, 10%) as the price fluctuation diameter and the ratio of the trading volume in this interval to the total trading volume, price stability indicator y₂ $\in$ (0,1) is obtained. A small value of y₂ indicates low and unstable trading volume around the weighted average price, while a higher value suggests price stability.

This paper focuses on the seven pilot ETS markets in China, which were established in Beijing, Shenzhen, Shanghai, Tianjin, Guangdong, Hubei, and Chongqing. According to the requirements for data integrity, the selected sample interval is 2014–2023. Among the data indicators, the specific data about the total trading volume and the trading price are sourced from the Wind financial database. Total quota, the number of verification institutions, and the number of emission-control enterprises come from China’s Carbon Market Report and open data published by China’s carbon emission and trading network supplemented by multiple independent manual searches and cross-verification to ensure the completeness of data sources.

5. Conclusions and Policy Recommendations

This study uses the bootstrap-DEA method to evaluate the efficiency of China’s seven pilot ETS markets from 2014 to 2023. It proposes a multi-input and output indicator evaluation system by selecting the total quota, the number of emission-control enterprises, and third-party verification institutions (annual total trading volume and carbon price stability) as input (output) indicators. This study has the following main findings.

From the temporal dynamic perspective, the overall efficiency of China’s seven pilot ETS markets increased between 2014 and 2017. However, the pure technical and scale efficiencies fluctuated frequently during the same period. Additionally, the fluctuations in the carbon price of China’s ETS can be attributed to fluctuating pure technical efficiency, which affects the supply and demand dynamics, and fluctuations in scale efficiency, which influence market participants’ behavior and their willingness to buy or sell carbon allowances. Furthermore, it is worth noting that the carbon price in an ETS plays a crucial role in signaling the value of emissions reductions and incentivizing long-term investments. The lack of a clear market price signal within the ETS hinders enterprises’ ability to make long-term emissions reduction investments and undermines the market’s sustainable development. In 2018, the scarcity of quotas was enhanced due to the promotion of the unified national ETS [55]. Accordingly, the price stability of most ETS markets decreased rapidly, and the carbon price fluctuated wildly, resulting in increased trading risk and reduced market activity. Thus, the overall efficiency, pure technical efficiency, and scale efficiency of various ETS markets declined slightly in 2018. From 2019 to 2023, with the establishment of the unified national ETS, the requirement for the operation mechanism of the ETS increased. Consequently, most pilot ETS markets’ overall efficiency, pure technical efficiency and scale efficiency have progressively converged towards sustained levels of complete efficiency. On this basis, each pilot ETS should establish and perfect a unified trading mechanism to ensure the stable and sustainable development of the carbon market and strive to integrate with the national carbon trading market.

From the horizontal comparison perspective, some differences can be observed across the seven pilot ETS markets. Specifically, the average overall efficiency was distributed in the relatively wide range of 0.693–0.913. The average trading prices of the ETS markets also varied greatly. The average price in Beijing was mainly 45–90 yuan/ton, while that in Chongqing was only 0–30 yuan/ton (see Figure 1), possibly because of the different economic development levels and industrial structures of emissions-control enterprises in various regions. The apparent price differences could also relate to the regions’ inconsistent regulatory policies and ETS mechanisms. Consequently, the local governments where the pilot ETS markets are located should consider strengthening legal supervision and allocate carbon resources according to the local economic development and industrial structure. Meanwhile, the decision-makers should also support the publicity of the carbon trading policy and invest in workforce and material resources to strengthen the operational quality of the ETS to improve enterprises’ emissions reduction awareness and trading enthusiasm.

Regarding the influencing factors of the ETS efficiency, except for the Beijing ETS market, low-scale efficiency appears to be the main reason for the low overall efficiency. Thus, low-scale efficiency is a common problem faced by China’s ETS markets and mainly manifests in the low trading volume and amount. This, in turn, leads to worrying inactive market transactions and low market activity. Consequently, the ETS cannot fully exert its emissions reduction effect. In China’s ETS, the insufficient market scale can be primarily attributed to the excessive total quota [56], which directly impacts the enthusiasm of enterprises and subsequently affects the operational efficiency of the market.

Enterprises’ initial annual carbon emissions quotas are approved based on the historical emissions level in the seven pilot markets of China. However, the historical emissions method is relatively primitive, and the data is rough [57]. As a result, the quotas allocated based on this method may not accurately reflect the actual emission levels of industries [58]. Except for Shenzhen and Beijing, the total trading volume of the pilot ETS markets in China failed to reach 5% of the full quota. The total trading volume in the Chongqing ETS is only 0.93%. The other one is the ETS policy’s insufficient continuity [59], which leads to unclear market expectations of trading enterprises. The operation mechanism and trading rules in various pilot ETS markets are adjusted frequently, resulting in insufficient awareness of emission reduction and a lack of market trading power [60]. Centralized transaction only occurs near the performance period, while the trading volume is low on regular trading days. Thus, the liquidity of the ETS is extremely low, and the market trading is highly inactive.

Based on the research findings, the following policy recommendations are proposed to improve the efficiency of China’s ETS market. First, it is essential to improve the relevant laws and regulations on the carbon trading market, strengthen the legal supervision and ensure policy stability for the market to form a stable policy expectation. Second, ETS market designs should scientifically allocate carbon emission rights and refine the total volume determination and allocation method to promote the expansion of the trading volume and amount. Third, the adequacy and transparency of the supervision and information disclosure systems should be improved. To address the low market scale, it is recommended that various pilot ETS markets further consider and determine the total volume and allocation methods. By appropriately reducing the quota amount and actively promoting the growth of total trading volume and transaction amounts, the market scale can be expanded, improving operational efficiency. Additionally, attention should be given to policy continuity and unity, providing a clear market expectation for enterprises.