Based on the DEA formulation of environmental production technology, we can first simulate maximum potential economic output if the technical inefficiency of each decision-making unit (DMU) is eliminated, considering undesirable output as freely disposable, which is a scenario for unregulated environmental technology (Färe and Grosskopf, 1983; Wang and Feng, 2014; Färe et al., 2016). max y ˜ n s. t. ∑ n = 1 N λ n x i n ≤ x i n     i = 1 , … ,   I ∑ n = 1 N λ n y n ≥ y ˜ n   λ n ≥ 0 ,   n = 1 , … , N (2)

DMUs can freely dispose of their undesirable outputs under the current model specification. The assumption of non-negativity for the intensity variables, λ n , restricts the model to being constant-return-to-scale. It also serves to construct a production frontier through a convex combination of the observed production factors (Brännlund et al., 1998). The sum-up of the optimized desirable output, y ˜ ∗ n , of all the DMUs constitutes the maximum potential desirable output that the environmental production technology can attain (eliminating technical inefficiency) while no emission regulations are posed.

In addition, if we assume null-jointness and weak disposability for desirable and undesirable outputs:

1) For ( x ;   y ,   b ) ∈   P and 0   ≤   θ   ≤   1 , ( x ;   θ y ,   θ b ) ∈   P

2) For ( x ;   y ,   b ) ∈   P and b = 0 , y = 0

Then, we can simulate production activities under emission regulation with command-and-control policies (Färe et al., 2013; Zhang and Zhang, 2018; Yang et al., 2021; Zhao et al., 2022). Considering N decision making units (DMUs) with I inputs, S undesirable outputs, and one desirable output. For each DMU n, the maximum output under command-and-control policies can be expressed as: max y ˜ n   ∑ n = 1 N λ n x i n ≤ x i n     i = 1 , … ,   I ∑ n = 1 N λ n y n ≥ y ˜ n ∑ n = 1 N λ n b s n = b s n s = 1 , … ,   S λ n ≥ 0 , n = 1 , … , N (3)

The equality constraints, ∑ n = 1 N λ n b s n = b s n , on undesirable outputs impose weak disposability.

Under the current specification, each DMU can maximize its desirable output, y n , to an optimal level, y ˜ ∗ n , while maintaining its observed level of undesirable output, b s n . Hence, the model simulates the output losses due to a binding environmental regulation. Here, the desirable output is electricity generation, and CO₂ emission is the sole undesirable output. But the model makes it easy to extend to a case of multiple undesirable outputs. Setting the desirable output as electricity generation excludes monetary value from the specification. Therefore, we do not need to account for the effect of price fluctuation on emission controlling behaviors.

We can further extend the operational model to simulate emission trading. Consider a central regulator that inspects the emissions of all the participating entities. The total emissions from all the entities must comply with the upper limit set by the regulator, while those entities can freely trade their emissions at no transactional cost. We formulate a centralized DEA model as follows to estimate the cost and benefit of participating DMUs in the emission trading scenario: max ∑ n = 1 N y ˜ n s. t. For DMU 1: ∑ n = 1 N λ 1 n x i n ≤ x i 1     i = 1 , … ,   I ∑ n = 1 N λ 1 n y n ≥ y ˜ 1 ∑ n = 1 N λ 1 n b s n = b s 1   s = 1 , … ,   L ∑ n = 1 N λ 1 n b s n = b ˜ s 1   s = L + 1 , … ,   S … For DMU N: ∑ n = 1 N λ N n x i n ≤ x i N     i = 1 , … ,   I ∑ n = 1 N λ N n y n ≥ y ˜ N ∑ n = 1 N λ N n b s n = b s N   s = 1 , … ,   L ∑ n = 1 N λ N n b s n = b ˜ s N   s = L + 1 , … ,   S λ n n ≥ 0 ,   n = 1 , … , N ∑ n = 1 N b ˜ s n ≤ B s ,   s = L + 1 , … , S (4)

In Equation 4, x i n , y n , and b s n are observed values of inputs, desirable outputs, and undesirable outputs, respectively. Some parts of   b s n for s = L + 1 , … ,   S are traded emissions among the participating DMUs, while no emission trading occurs over the other undesirable output ( b s n for s = 1 , … ,   L ). Optimization occurs over λ n n , b ˜ s N , and y ˜ n , to maximize the total desirable output of all the participating DMUs, ∑ n = 1 N y ˜ n . Inputs, x i n , are taken as fixed. b ˜ s N represents the emissions of each power plant after trading, while y ˜ n represents the desirable output. B s = ∑ n = 1 N b s n represents the total emission trading permits that exist in the trading market as regulated by the central regulator. This formulates a traditional cap-and-trade emission trading scheme.

It should be noted that Equation 4 models the maximum gains that any cap-and-trade programs can reap, i.e., a perfect market where trading is allowed without any barriers or transaction costs. It mimics the condition in which an overall emission cap is enforced by the central regulator while no cap is set for market participants. This market design can, therefore, be interpreted as emission trading with auctioning in the market. Efficient bargaining is achieved under the current model specification, where each entity can attain an efficient level of emission allowance (Cramton and Kerr, 2002).

A common practice in emission trading or cap-and-trade programs is the free allocation of a portion of emission allowances to individual trading entities in the emission trading market, which existed in the initial phase of ETS to lower political barriers for its implementation (Helm, 2010). However, to regulate the overall emission cap, emission trading is often implemented in parallel to command-and-control regulation. In this scenario, binding caps are often set for each regulating entity, usually at a ratio of its historical emissions. Based on the emission trading model, we can further extend the integration of emission trading and command-and-control as follows: max ∑ n = 1 N y ˜ n s. t.   For DMU 1: ∑ n = 1 N λ 1 n x i n ≤ x i 1     i = 1 , … ,   I ∑ n = 1 N λ 1 n y n ≥ y ˜ 1 ∑ n = 1 N λ 1 n b s n = b s 1   s = 1 , … ,   L ∑ n = 1 N λ 1 n b s n = b ˜ s 1   s = L + 1 , … ,   S b ˜ s 1 ≤ b ′ ˜ s 1 … For DMU N:   ∑ n = 1 N λ N n x i n ≤ x i N     i = 1 , … ,   I ∑ n = 1 N λ N n y n ≥ y ˜ N ∑ n = 1 N λ N n b s n = b s N   s = 1 , … ,   L ∑ n = 1 N λ N n b s n = b ˜ s N   s = L + 1 , … ,   S b ˜ s N ≤ b ′ ˜ s N λ n n ≥ 0 ,   n = 1 , … , N ∑ n = 1 N b ˜ s n ≤ B s ,   s = L + 1 , … , S (5)

The model features a variation of the emission trading model by Färe et al. (2013). First, a common practice is that market regulators may retain a certain percentage of the total emission allowance for the purpose of market stabilization (Park and Hong, 2014). Hence, the total amount of cap emissions, ∑ n = 1 N b ' s n ˜ , could be different from the total tradeable emissions, B s , which simulates the condition when the trading market regulator retains some of the permits from trading. The effect of the total amount of cap emissions on potential gains from emission allocation can also be investigated. Further, in Equation 5, we introduce b ' s n ˜ as an exogenous variable that determines the additional command-and-control emission cap of each DMU through the constraint, b ˜ s N ≤ b ' s N ˜ . This constraint mimics the command-and-control constraint, where binding caps are assigned to individual participating entities. Overall, the current model setting simulates the maximum potential gains and the minimum cost when emission trading and command-and-control policy are simultaneously implemented.

Again, due to the fact that the current work considered only CO₂ emissions, no additional constraints were posed to DMUs on other undesirable outputs. But the model can be easily extended to a case where data for multiple undesirable outputs is available. Furthermore, the model can also be easily generalized to an inter-temporal and inter-spatial model, similar to the case of Färe et al. (2013), which simulates an emission trading scheme where borrowing and banking are allowed (Boemare and Quirion, 2002). We leave it to future research.

Korea announced its national CO₂ emission abatement target in 2008, which aimed at cutting 30% of CO₂ emissions by 2020 compared to a business-as-usual scenario. Therefore, in 2010, a presidential decree ratified the target and established the TMS, a command-and-control policy setting that was initiated in 2011 and formally began to operate in 2012, which directly enforced firms’ compliance with emission reduction targets (Park and Hong, 2014). Major energy producers were all included in TMS. Following the enactment of TMS, there was the promulgation of the Act on the Allocation and Trading of Greenhouse Gas Emission Allowances (ETS Act) in 2012, which began its trading in 2015, 3 years after TMS. The two regulatory schemes operate in parallel but cover mostly different categories of entities. The ETS act covers the major emitters of CO₂, while TMS complements it with smaller but still relatively large (or medium-sized) emitters as well as public organizations that cannot be easily workable in ETS. Nonetheless, there are still chances for any DMU to overlap in this parallel system. For example, the company may participate in ETS as a major player, while one of the facilities of the company may be located under TMS. From the managerial perspective, therefore, strategic consideration may happen in these overlapping cases, and all the other companies may consider this kind of by-passing way between ETS and TMS, resulting in the integrated, yet parallel governance of the emission management policies. The Korean government may consider the TMS as a complementary mechanism to support higher abatement of ETS, but in reality, it allows the participating companies in ETS to enter the TMS. Nonetheless, TMS has a different condition as an additional target of energy consumption, which is not in the ETS, resulting in a very complicated, yet complex alleyway between these two measures.

The first commitment period of the ETS system is designated to begin on 1 January 2015 (Oh et al., 2016). For the initial allowance allocation, 100% of the previous year’s emissions were retained as the total allowance, with an additional 3% of the total allowances being set aside as a reserve for market stabilization. For the second allowance period between 2018 and 2020, 97% of the allowance was freely allocated to each entity, with a 3% abatement target to be tradable in the ETS market. ETS entered the third stage in 2021, with 90% of the free allowance and a 10% abatement target to be tradable in the market. In the year 2021, the initial year of the third stage, the participating entities in ETS will be 684, with a total allowance of 2.9 billion CO₂. Among those abatement targets, 18.2 million tons are allocated as tradable allowances, implying that 10.8 million tons, or 62.8% of total allowances, are reserved for the government. As a parallel measure, the entities under TMS comprise 403 members in the private sector and 837 entities in the public sector in the year 2021.

From the year 2011 till the year 2015, we collected and used only data for coal-fired power plants in Korea. This data fits the homogeneity assumption of environmental production technology. Therefore, there is no need to consider heterogeneity in the modelling of the production technology. The sample period includes the first year of no regulation, the three following consecutive years of command and control regulation, and the latest year of emission trading. In total, 258 observations were collected. The observations consist of two inputs (unit capacity in kW and energy usage in kcal), one desirable output (net electricity generation in MWh), and one undesirable output (CO₂ emissions in tons). The data was obtained from Statistics of Electric Power in Korea (2016). CO₂ emissions were calculated using IPCC emission factors, provided by Zhang and Choi (2013). Table 1 reports descriptive statistics for inputs and outputs in the study period.

Figure 1 shows the cumulative desirable output—electricity generation—of all the coal fired power plants in each year under different environmental regulation scenarios. Depending on the regulatory strategy of the scenarios, the implications of the results vary.

If no environmental regulations were posed (Korea in 2011), Equation 2 calculates the maximum potential output each coal power plant can attain under current input constraints. Thus, its difference with the base case represents the maximum electricity production of Korean coal-fired power plants if technical inefficiency is eliminated. The difference between Equation 3 and 2 is the opportunity cost each power plant may bear to implement CAC regulation on their emissions and restrict them to the observed level. The difference between equation 4 and 2 is the potential costs and benefits an emission trading system brings about for these power plants. While the difference between Equation 5 and 2 is the potential cost of additional CAC regulation combined with the ETS.

If environmental regulation has already been forced on those coal-fired power plants (Korea from 2012 to 2014), the difference between Equation 3 and 2 implies potential gains from rescinding current environmental regulations. The cost and benefit of rescinding existing regulations can be substantially different from implementing a new regulation (Evans et al., 2021). When rescinding an existing regulation, compliance costs have already sunk. No immediate benefit will be paid to entities that comply. Besides, upon the elimination of a regulation, market conditions and technologies have already changed. Previously profitable operational conditions may not be viable at the time of rescinding the regulation. The difference between Equation 4 and 3 is the maximum potential economic benefit the whole trading system can reap by mobilizing productive factors in these environmentally regulated power plants. And the difference between Equation 5 and 3 is the gains the trading system as a whole can reap with additional binding on the emission cap of each power plant.

Furthermore, if an ETS has already been implemented (Korea in 2015), the difference between Equation 4 and 3 explains the foregone benefits of emission trading. The foregone benefits, different from the potential benefits in a no emission trading setting, explain potentially existing transactional barriers, e.g., transaction costs rendered by collecting information, bargaining and deciding, and monitoring and enforcement, that prohibit a competitive market from exerting its full power to maximize factor allocation efficiency (Stavins, 1995). The difference between Equation 5 and 4 represents potential costs—the emission abatement costs and market efficiency losses—with the overlap of command-and-control regulation and emission trading.

As shown in Figure 1, the potential output increase from eliminating technical inefficiency in power plant operations is on average 7.434% (no regulation case). Upon implementing command-and-control CO₂ emission regulation, an increase in technical inefficiency can be seen in 2012 (9.548%), which is largely due to the curtailment of existing coal-fired power plants to meet the CO₂ emission target (201.8 TWh of electricity generation in 2011 versus 199.3 TWh of electricity generation in 2012). While the sudden increase (9.706%) of technical inefficiency from 2013 to 2014 is due to the installation of a new megawatt-scale power generation unit.

We then compare the difference between the no regulation scenario and with the command-and-control scenario. In 2011, no CO₂ emission regulations were posed to Korean coal-fired power plants, and thus the difference between these two models represents the potential cost of implementing emission regulations. The potential cost in 2011 is estimated to be only 0.969% at the time of implementing CAC (TMS). However, as the TMS regulation was implemented in 2012, the potential benefit of rescinding the policy was raised to 4.386% of total electricity generation, revealing that the emission regulation policy presents a major hurdle to power plants’ production activities. However, the potential benefit of rolling back emission regulation shrank to 0.757% in 2014, suggesting that power plants rapidly reflected the command-and-control regulation and substantially improved their environmental technology to comply with the emission standard, such that the negative effect of emission regulation was alleviated. Furthermore, the potential benefits of rescinding emission regulation are the lowest in 2015, suggesting that emission trading has effectively lowered the overall cost of compliance.

In addition, we can see that emission trading has the potential to increase output by 0.990% on average in those power plants during the TMS regulation period (2012–2014). However, most of the promised benefits have not materialized. In 2015, the ETS was implemented in Korea. Yet, the potential output under the emission-trading model (emission trading with no trading friction) is still 0.861% higher than the command-and-control model. The persistent gap between the command-and-control model and the emission-trading model suggests that little or no efficiency increase is achieved through the first-year of emission trading at least. In contrast, over 85% of the promised efficiency increase by emission trading has not been realized. Färe et al. (2013) suggest that the gap—the foregone benefit in the emission trading scheme—represents the upper limit of transaction costs involved in emission trading, which impedes participating entities from sufficient trades in the allowance market to reach an efficient status. The results indicate that the transaction cost in the Korean emission trading market is on a non-negligible scale. Efforts must be made to alleviate this huge cost so it boosts the potential of emission trading more effectively.

Furthermore, the integration of command-and-control and emission trading requires a cap that restrains plants’ emissions at their observed levels. In this way, we can distinguish the effect of binding emission caps on the foregone emission trading benefit, which can be accounted for as a regulatory cost when integrating command-and-control and emission trading. Our results show that electricity generation under the integrated model in 2015 was about 224.5 TWh, compared to 224.6 TWh for the emission trading model and 222.7 TWh for the command-and-control model. Command-and-control regulation deviates emission trading from its efficient level, accounting for only 5.567% of the total unrealized gains under emission trading in 2015.

Another concern is marginal abatement cost under different emission regulation schemes. The marginal abatement cost could dictate the policy-making over emission mitigation (Wu and Ma, 2018). Besides, marginal abatement cost curves is a widely accepted tool to characterize the overall cost if a certain level of abatement is to be achieved (Kesicki and Strachan, 2011). Figure 2 presents the marginal abatement cost curve—abatement cost denominated by electricity generation losses under different levels of binding emission cap setting—for Korean coal power. Interestingly, electricity output reduction does not linearly respond to a tighter emission cap, indicating a diminishing rate of increase in the marginal abatement costs at a certain point. The marginal cost of reducing the first 1% of emissions (cap from 100 to 99%) under the emission trading and cap mechanism is 0.098% of electricity generation decreased; while the last 1% of emissions reduction (cap from 2 to 1%) costs as much as 2.18% of electricity generation. If policymakers were to regulate emissions levels with the current level (the 2015 level) of electricity generation (minimizing undesirable output while keeping the current desirable output), an emission cap and trading scheme could cut about 46% of CO₂ emissions.

This distributional effect of an emission regulation policy is also of paramount importance to policy makers. A progressive emission regulation policy would prevail and is politically more tenable, since it delivers the good to the larger (Eskeland and Jimenez, 1992). Figure 3 presents the distribution of output gains (or losses) by power plants from emission trading. Detailed results are shown in Appendix Supplementary Table A1. In the emission trading scenario, Korean coal-fired power plants could, in total, increase electricity output by 1.934 TWh of potential electricity output without increasing CO₂ emissions. All the participating units will at least be better off in the emission trading scenario. Five power plants reap a dominant share of the total gains. They will increase their electricity output by 1.333 TWh in the emission trading scenario compared with the command-and-control scenario, equivalent to 68.9% of the total benefit from ET.

Upon integrating CAC with ET, those that reap the dominant gains of ET tend not to be affected by additional CAC. But there are another 15 power plants whose welfare will be disproportionately affected. In total, these 15 power plants generated 71.95 TWh of electricity in 2015 (equivalent to 38.9% of total electricity generation). In the emission trading scenario, their total gains are 0.108 TWh, which is barely 8.10% of the total gains from emission trading. In the CAC + ET scenario, their potential gains are reduced to zero. This is due to the fact that the CAC restricts their strategies to response to emission mitigation compliance. In the emission trading scenario, they may buy residual emission allowances left by those efficient producers so that they can expand their production capacity. Under the ET + CAC scenario, fewer emission allowances will be available in the market due to the restriction of CAC. Those efficient producers will retain their additional un-used allowances. Finally, those less efficient producers acquire a smaller number of allowances, thus bearing the cost of CAC. Therefore, the implementation of ET + CAC may result in disproportionately high costs for a part of the market due to the invalidation of abatement cost equalization by CAC.