Quota allocation of coal overcapacity reduction among provinces in China

Energy Policy 116 (2018) 170–181

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Energy Policy journal homepage: www.elsevier.com/locate/enpol

Quota allocation of coal overcapacity reduction among provinces in China a,⁎

a

Delu Wang , Kaidi Wan , Xuefeng Song a b

T

b

School of Management, China University of Mining and Technology, Xuzhou, Jiangsu 221116, PR China School of Management Science and Industrial Engineering, Nanjing University of Finance and Economics, Nanjing, Jiangsu 210003, PR China

A R T I C L E I N F O

A B S T R A C T

Keywords: Quota allocation Overcapacity reduction Nonlinear programming Coal industry China

Laying down fair and economically viable policies to allocate quotas of coal overcapacity reduction to provinces has drawn great attention from both governments and enterprises. In this study, the production function method and panel variable coefficient model are used to estimate the boundary production function and coal capacities of 25 coal-producing provinces. The results predict that China's coal overcapacity will reach more than 0.803 billion tons by 2020. Then, a quota allocation model of coal overcapacity reduction among the provinces is proposed based on nonlinear programming, with the aim of minimizing the total cost of national overcapacity reduction. The results show that the total cost of national overcapacity reduction based on the optimal allocation scheme is 56.6695 billion yuan less than that based on the government allocation scheme. The Gini coefficient of the optimal allocation scheme is smaller than 0.3, indicating that this plan considers effectiveness and fairness. Furthermore, we calculate the optimal proportions for the provinces to reduce coal overcapacity based on different capacity utilizations and different national coal production control targets. The results show that the optimal proportions for most provinces are approximately the same under different conditions, which means the optimal allocation scheme is robust and efficient.

1. Introduction China is the world's largest producer and consumer of coal. In 2015, it accounted for approximately 47% and 50% of the global total production and consumption, respectively; in addition, coal accounted for 72% of China's energy production and 64% of its energy consumption (Tang and Peng, 2017; Wu and Zhang, 2016; Yuan, 2018). However, since the 2008 global financial crisis, the coal oversupply in China has become increasingly prominent, and the problem of overcapacity has become more serious. Such problems are attributed to the combination of an economic downturn, market failure, system distortion, and energy transformation (Song et al., 2017; Sun et al., 2017; Tang et al., 2018; Wang et al., 2018). The China National Coal Association estimates that, by the end of 2016, China's coal production capacity was 5.7 billion tons, while the actual production was only 3.41 billion tons, a capacity utilization of less than 60%; moreover, under ecological constraints, China's coal production is expected to fall below 3.7 billion tons by 2020. However, it is worth noting that there is still a large number of projects under construction in the coal industry and the tendency for overcapacity is increasing. Without effective measures, China may face economic fluctuations, vicious market competition, serious resource

waste, corporate profit decline, coal price distortion, environmental pollution aggravation, and other problems. Finally, the lack of such measures may also affect the healthy development of the coal industry and even of the whole national economy. Studies show that it is difficult for market forces to make effective adjustments in a short time when the industry has serious overcapacity, so the solution to this problem relies greatly on the central administrative government's control measures (Yang and Wu, 2016). Therefore, in recent years, the Chinese government has implemented a series of measures to solve coal overcapacity.1 In 2016, the National Development and Reform Commission (NDRC) issued the Thirteenth Five-Year Development Plan of Coal Industry, proposed the reduction target of 0.8 billion tons of coal capacity by 2020, and determined the subtasks of 25 provinces. However, in practice, the implementation of relevant policies and measures is not ideal, which brought about higher prices but failed to avoid the recurrence of increasingly worse overcapacity. From a regional perspective, many provinces do not actively participate in the capacity reduction, with some provinces seriously lagging. Many provinces have even adopted the superficial measure of reducing the authorized capacity to fulfill the capacity reduction goal perfunctorily. In addition, many enterprises, including some large state-owned

⁎

Corresponding author. E-mail address: [email protected] (D. Wang). For example, the State Council issued Several Opinions on Restraining Overcapacity and Redundant Construction in Some Industries and Guiding the Healthy Development in 2009, Guidance on Resolving Serious Contradiction of Overcapacity in 2013, and A Suggestion on Restraining Overcapacity and Meeting Anti-poverty and Development Goals in March 2016. 1

https://doi.org/10.1016/j.enpol.2018.02.003 Received 16 November 2017; Received in revised form 28 January 2018; Accepted 2 February 2018 0301-4215/ © 2018 Elsevier Ltd. All rights reserved.

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reduction in China is the high cost of production; especially, the high resettlement cost of surplus workers has seriously hindered the enthusiasm of local governments.2 Therefore, governments at all levels are concerned about formulating an economic viable and equitable allocation scheme of coal overcapacity reduction, and such scheme is a major factor in whether China's coal overcapacity can exit smoothly. In view of this problem, from the perspective of national optimization, we build a quota allocation model of coal overcapacity reduction based on nonlinear programming, determine the minimum total cost of coal overcapacity reduction for the whole country, and propose an optimal allocation scheme of overcapacity reduction quotas for the different provinces.3

enterprises, may oppose controlling measures while seeming supportive of the practice. In April 2016, for example, the NDRC and National Energy Bureau jointly conducted a special inspection of 146 illegal construction of coal mines and found that although some large coal enterprises eliminated small- and medium-sized mines with a capacity of less than 600,000 t, the new coal capacity from their reconstruction or expansion of the main mines through technical transformation is much higher than the capacity reduced. In short, despite the rapid rise in coal prices since July 2016, this price change is unsustainable. From the aspect of supply and demand, there is no fundamental improvement in China's severe coal overcapacity and oversupply. With the decline of China's energy consumption intensity and, especially, the rapid development of renewable and clean energy, it is difficult for coal market demand to have absolute growth space. Therefore, the expanding supply capacity whilst contracting demand clearly indicates the significance of structural reform in China's coal industry (Yuan, 2018). Given the serious impacts of overcapacity on the sustainable development of the coal industry, many motivated researchers in both the academia and industry have focused on coal overcapacity governance and have made great strides in the causes and mechanisms (Dagdeviren, 2016; Wang et al., 2014), measurement methods (Arfa et al., 2017; Ray, 2015), and governance policies (Goh and Effendi, 2017; Wu and Li, 2015; Zhang et al., 2016) of overcapacity. The discussion on the exit strategy of coal overcapacity mainly focused on two aspects: eliminating backward production capacity (Li and Nie, 2017) and resource integration (Cao, 2017). For example, the Thirteenth Five-Year Development Plan of Coal Industry has clearly set the targets of reducing of 0.8 billion of coal capacity and eliminating in 1–3 years mines with a capacity of less than 300,000 t per year, as well as mines with a capacity of less than 150,000 t per year. However, in practice, due to local officials’ GDP-oriented performance evaluation, as well as to employment pressure and other factors, the closure policies for small coal mines have not been effectively implemented in some areas (Jia and Nie, 2017); moreover, some regions with a single economic structure tend to cope with the economic impact of small coal mine closures by expanding the capacity of large coal companies, which weakens the effect of such policy (Andrews-Speed et al., 2005). In addition, the merger and reorganization of coal enterprises has gradually become an important way to reduce coal overcapacity, because such merger and reorganization integrates coal resources and is conducive to enhancing mining technology and financing ability, and controlling the excessive growth of coal capacity (Zhang et al., 2011). Some scholars believe that, under local government intervention, the merger and reorganization is likely to exacerbate the coal overcapacity (Zeng et al., 2016; Zhang et al., 2017). In other words, the Chinese government has implemented a set of measures to solve overcapacity in the coal industry from economic, environmental, technological, safety, and other perspectives. In addition, many scholars have explored the exit strategy for overcapacity. However, studies on quota allocation of coal overcapacity reduction among provinces remain limited, even though quota allocation is a key process of overcapacity governance. It would be insufficient to study the regulation strategy of overcapacity and the realization of the target only from a macroeconomic perspective. This is because China has a vast territory, and there are large differences in the economic development level, coal production conditions, industrial structures, and resource-carrying capacities among provinces (Wang et al., 2017). The economic and social development levels in the eastern region (e.g., Beijing, Shandong, Jiangsu, and other provinces) are significantly higher than those in the central and western regions (e.g., Shanxi, Gansu, the Inner Mongolia Autonomous Region, and other provinces); moreover, compared with the eastern provinces, central and western provinces depend more on the coal industry, having more employees and greater investment in fixed assets in the industry, and these factors determine the costs of coal overcapacity reduction for each province. In fact, the fundamental reason for the slow progress of overcapacity

2. Methodology 2.1. Estimation of coal boundary production function based on panel variable coefficient model The production function method is the most widely used method for estimating potential output. Based on the theory of economic growth, this method can reveal the relationship between inputs and outputs for the analysis of the contribution of capital, labor input, and technological progress to output. Moreover, this method requires easily accessible data (Klein and Preston, 1967). Therefore, we select the production function method to measure the potential output of the coal industry in China. The main steps of the estimation are as follows. First, the basic form of the boundary production function is determined, and the concrete form of the production function is estimated using the ordinary least square (OLS) method. Second, the difference between the observed value of the output in the sample interval and the estimated value of the corresponding average production function is calculated, and the concrete form of the boundary production function is obtained by taking the maximum value of the difference and adding it to the constant term of the average production function. Finally, the potential output is calculated according to the concrete form of the boundary production function. Since the data used in this study's empirical analysis are panel data for 25 coal-producing provinces in China from 1986 to 2015, the model form should be set before the regression analysis. In general, the panel data model can be divided into four categories: hybrid, fixed effect, random effect, and variable coefficient models. Due to the obvious heterogeneities in coal resource endowment, economic development level, and technology level among the provinces of China, the invariant coefficient model not only fails to describe the variation of the parameters of explanatory variables over different sections or time, but also affect the validity of the model coefficient estimation. Therefore, it may overestimate or underestimate coal capacity. Hence, we adopt a panel variable coefficient model to estimate the concrete form of the coal production function. In this study, the boundary production function is set as the most widely used Cobb-Douglas production function, and its basic form as 2 The Chinese government has established a 70 billion yuan (RMB) resettlement fund to provide resettlement fees and subsidies to laid-off coal workers. The British Financial Times believes that, although the fund helps alleviate the societal pressure, compared with China's rising cost of living, around 55,000 yuan in laid-off subsidies per capita is obviously on the low side. 3 The main reasons why we discuss quota allocation of overcapacity reduction on a provincial scale are as follows: firstly, since 1980, China's coal industry management system has undergone a series of changes, the current management system can be divided into the four levels known as central, provincial, municipal and county levels, in which the provincial government, as a substantive executive body of policies and regulations, plays the most important role in the process of overcapacity reduction. Secondly, with the large quantity of coal enterprises, the concentration level of China's coal industry is still very poor. In practice, it is hard for the government to allocate reduction quota to each coal enterprise. Thirdly, because the allocation model involves numerous parameters, enterprise-level data is difficult to obtain.

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coal industry are solidified in the coalfield or coal mine (e.g., underground mining, ventilation and transportation systems, and ground production systems), and the main production facilities and equipment, having limited alternative uses, can only be used for coal production. Once the mines are closed, these fixed assets are often difficult to recover and dispose. Therefore, we adopt the fixed asset net loss to characterize the disposal cost of fixed assets incurred during the overcapacity reduction process. The recovery of fixed assets SI is represented as the ratio of the recoverable amount of fixed assets to the stock of fixed assets, where SI = the original value of fixed assets × the estimated net residual value/the average annual balance of fixed assets and (1−SI ) represents the loss rate of fixed assets.

follows:

Y = f (K , L,

A) e−u

=

AK αL β e−u

(1)

where Y stands for output, K represents capital input, L stands for labor input, and α and β represent the output elasticity of capital and labor, respectively. We take the logarithm of both sides of the formula (1) and get

ln Y = ln A + α ln K + β ln L − u

(2)

The boundary production function is

ln Y * = ln A + α ln K + β ln L

(3)

where Y * represents the largest potential output level. We let ln A = δ and E (u) = ε , and formula (2) can be rewritten as (4)

2.2.3. Estimation of overcapacity reduction cost We let capital per capita be ki , where ki = Ki/ Li , and then in-

As E (u − ε ) = 0 , the variable coefficient model of the panel data and the OLS method are used to estimate, and we get

corporate it into the estimated production function Yi = e δi K αi L βi ; then

ln Y = α ln K + β ln L + (δ − ε ) − (u − ε )

∧

∧

∧

∧

ln Yi = αi ln K + βi ln L + (δi − εi ), i = 1, …, n

∧

Formula (5) is the average production function. Based on the property that all the actual output is below the boundary production function, we can further get ∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

∧

ΔKi =

⎡1 − (1 − Ri)1/(αi +βi ) ⎤ (Yi kiβi /e δi )1/(αi +βi ) ⎣ ⎦

ΔLi =

⎡1 − (1 − Ri)1/(αi +βi ) ⎤ (Yi /kiαi e δi )1/(αi +βi ) ⎣ ⎦

∧

(6)

Formula (6) is the value of εi , and we get the value of δi by incorporating it into formula (5). Therefore, the estimated boundary production function is

∧

∧

∧

∧

∧

(8)

∧

(9)

Therefore, we can obtain the labor resettlement cost and disposal cost of fixed asset function of coal overcapacity reduction in each province as follows:

∧

Yi = e δi K αi L βi

∧

∧

β Ki = (Yi ki i / e δi )1/(αi + βi ) and Li = (Yi / kiαi e δi )1/(αi + βi ) . We let the overcapacity reduction proportion in each province be Ri , and we can get

(5)

max   (ln Yi − ln Yi ) = max {ln Yi − [αi ln K + βi ln L + (δi − εi )]}

∧

∧

(7)

Ci (ΔKi ) = (1 − SIi )ΔKi ∧

∧

2.2. Estimation of coal overcapacity reduction cost for provinces

(

∧

∧

β

∧

= (1 − SIi ) ⎡1 − (1 − Ri )1/(αi + βi ) ⎤ Yi ki i / e δi

⎣

According to the production factor theory, the cost of coal capacity reduction mainly includes labor resettlement cost and disposal cost of fixed asset. On one hand, China's coal industry is still a labor-intensive industry,4 and the overcapacity reduction will inevitably cause a massive lay off and consequently, a resettlement problem; on the other hand, production equipment and facilities of coal mines are very special and have limited alternative uses. Moreover, most of the fixed assets are installed in the mines, so it is difficult to dispose and recycle such assets once the mines are shut down. Therefore, in this study, we mainly consider the labor resettlement cost and disposal cost of fixed assets.

⎦

∧ i

∧

)1/(α +β ) i

(10)

Ci (ΔL) = (CIi p1i + CRi p2i + CDi p3i )ΔLi =   (CIi p1i + CRi p2i + CDi p3i ) ⎡1 ⎢ ⎣ ∧

∧

∧

∧

∧

∧

∧

− (1 − Ri )1/(αi + βi ) ⎤ (Yi / kiαi e δi )1/(αi + βi ) ⎥ ⎦

(11)

where p1i , p2i , and p3i represent the ratio of the internal retired, diverted, and fired workers, respectively, to the total workers needed to be resettled in the process of overcapacity reduction.

2.2.1. Labor resettlement cost In the process of overcapacity reduction of coal enterprises, there are mainly three kinds of resettlement methods of surplus workers, namely internal retirement, reassigning, and dismissal. According to The opinions on how to properly arrange workers’ resettlement in the process of solving problem of overcapacity of steel and coal industry, released by Human Resources Social Security Department, National Development and Reform Commission and five other departments in April 2016, and the distribution plan of coal mine workers released by coal production provinces, we develop the estimation method of coal mine workers’ resettlement cost, as shown in Table 1.

2.3. Nonlinear programming model for quota allocation of coal overcapacity reduction Due to the imbalance between coal resource distribution and economic development in China, there are also significant differences between coal production and consumption in each region. Therefore, the NDRC and National Energy Bureau jointly issued the Thirteenth FiveYear Development Plan of Coal Industry in December 2016. On one hand, the overall coal overcapacity reduction target in 2020 is proposed to solve the excessive coal capacity. On the other hand, the minimum coal outputs in the northeast, eastern, central, and western regions are determined to ensure the regional coal market demand and optimize the layout of coal development. As a result, restricted by both the national overall coal overcapacity reduction target and the minimum coal output in each region, we need to select the appropriate plan for quota allocation to achieve the goal of the lowest cost at the national level. This nonlinear programming model can be expressed as follows:

2.2.2. Disposal cost of fixed assets Due to the particularity of coal production, most of the assets of the 4 In 2012, for example, the coal output in the United States was 1 billion tons, and industry workers totaled about 100,000 people. In the same year, China's coal output was 3.65 billion tons, and industry workers totaled about 5.25 million people. That is to say, China's coal output is 3.6 times of that of the United States, but the number of its industry workers is 52.5 times of that of the United States.

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Table 1 Labor resettlement and corresponding cost estimation methods. Resettlement method

Basic meaning

Cost structure

Estimation formula

Internal retirement

Refers to facilitating the retirement of workers who have not yet reached the legal retirement age but have met a certain condition, and who then leave work after the approval of relevant department.

Mainly includes living expenses, social insurance premiums, and housing accumulation funds during the internal retirement.

CIi represents the per capita resettlement cost of retired workers, S1i

Reassigning

Refers to diverting surplus workers to storage mines within the enterprise and non-coal industries, diverting surplus workers to other companies by establishing resettlement service companies, or guiding employees to start their own businesses.

Mainly includes living expenses, social insurance premiums, housing accumulation funds, and training expenses during the post-waiting or startup period.

CRi = (Smi a2i + b2i S2i SR2i + S1i λ ) t2i CRi represents the per capita resettlement cost of diverted workers, Smi represents the minimum wage in various provinces and cities (unit: yuan/year/person), a2i represents the ratio of living expenses of diverted worked to minimum wage, SR2i represents the sum of the payment ratio of social security and housing accumulation fund, λ represents the ratio of the training fee to the average salary of coal industry workers, and t2i represents the average years of post-waiting (unit: year).

Dismissal

Refers to the termination of the labor contract according to law.

The one-time economic compensation that the enterprise pays to worker.

CDi =

Min TC =

∑

CIi = (S1i a1i + S2i b1i SR1i ) t1i represents the average salary of coal industry workers (unit: yuan/ year/person), a1i represents the ratio of living expenses of retired workers to average wages of employees in the industry, S2i represents the average salary of workers in urban areas (unit: yuan/year/person), b1i represents the ratio of the base pay to the average salary of workers in urban areas, SR1i represents the sum of the payment ratio of social security and housing accumulation funds, and t1i represents the payment years during the internal retirement (unit: year).

S1i t 12 3i

CDi represents the per capita resettlement cost of fired workers, and t3i represents the average working years of fired workers.

[Ci (ΔK ) + Ci (ΔL)]

2.4. Distribution equity evaluation model

[(1 − SIi )ΔKi + (CIi p1i + CRi p2i + CDi p3i )ΔLi ]

We use the Gini coefficient to measure the regional fairness of the quota allocation scheme of coal overcapacity reduction based on cost minimization. The Gini coefficient, which is a common index used to measure the gap in income distribution, was first proposed by Italian economist Gini according to the Lorentz curve in 1922. Generally, a Gini coefficient with a value of less than 0.2 indicates an absolute average income, a value between 0.2 and 0.3 indicates an average income, a value between 0.3 and 0.4 indicates a relatively reasonable income distribution, a value between 0.4 and 0.5 indicates a gap in income distribution, and a value of more than 0.5 indicates a wide gap in income distribution (i.e., between the rich and the poor). We use the trapezoidal area method to estimate the Gini coefficient. Calculation formula is as follows:

i

=

∑ i

1

=

∑ i

∧ ∧ ⎧ ∧ ∧ 1 β ⎞ ⎛ ⎡ ⎪ ∧ ∧ ⎤ Yi k i (αi + βi ) i ( ) α + β (1 − SIi ) ⎢1 − (1 − Ri ) i i ⎥ ⎜ ∧ ⎟ ⎨ ⎜ δ ⎟ ⎢ ⎥ ⎣ ⎦⎝ e i ⎠ ⎪ ⎩

⎡ + (CIi p1i + CRi p2i + CDi p3i ) ⎢1 ⎢ ⎣ 1

− (1 −

⎧∑ ⎪ i ⎪ ⎪∑ ⎪ ⎪ i ⎪ s. t . = ∑ ⎨ i ⎪ ⎪∑ ⎪ i ⎪ ⎪∑ ⎪ ⎩ i

1

∧ ⎞ (α∧i + βi ) ⎫ ⎪ ⎜ ∧ ∧⎟ ⎬ ⎜ αi δi ⎟ ⎥ ⎪ ⎦ ⎝ ki e ⎠ ⎭

∧ ∧ ⎤⎛ Ri ) (αi + βi ) ⎥

∧

Yi

n

∧

Yi Ri = TCR

Gini coefficient = =1 −

i = 1, …, 25

∑ (Xi − Xi −1)(Yi + Yi −1) i=1

∧

(13)

where Xi stands for the cumulative percent of reference factor, Yi stands for the cumulative percent of amount or cost of overcapacity reduction. Xi − 1 and Yi − 1 are seen as 0 when i = 1.

Yi (1 − Ri ) ≥ A1 i = 1, …, 3 ∧

Yi (1 − Ri ) ≥ A2 i = 1, …, 5

3. Data

∧

Yi (1 − Ri ) ≥ A3 i = 1, …, 6

China's abundant coal resources are distributed across all provinces except Shanghai, albeit very unevenly. China's coal resources are concentrated in northern China, in the area between Da Hinggan Mountains-Taihang Mountains and Helan Mountains, accounting for about 50% of the national coal resources and more than 55% of the coal resources in all of northern China. The region's geography includes all or most of Inner Mongolia and the Shanxi, Shaanxi, Ningxia, Gansu, and Henna provinces, which have a total of more than 1000 × 108 t of coal resources. In southern China, the coal are mainly distributed in the Guizhou, Yunnan, and Sichuan provinces, which have a total of 3525.74 × 108 t of coal resources, accounting for 91.470% of the coal resources in all of southern China; the proven reserves also account for more than 90% of that the reserves in all of southern China. Currently, there are 25 coal-producing provinces, namely Liaoning (LN), Jilin (JL)

∧

Yi (1 − Ri ) ≥ A 4 i = 1, …, 11 (12)

where TC represents the national total cost of coal overcapacity reduction; Ri , the decision variable, represents the coal overcapacity reduction proportion of province i ; TCR represents the national total amount of coal overcapacity reduction; and A1, A2 , A3 and A 4 represent the minimum coal output in the northeast, eastern, central, and western regions, respectively. By solving the planning model above, we can obtain the optimal allocation plan of coal overcapacity reduction in the provinces and determine the minimum cost of overcapacity reduction nationwide.

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Fig. 1. Location and output of the 25 coal-producing provinces in China in 2015.

Strengthening the Management of Laid-off Workers of State-owned Enterprises and the Construction of Reemployment Service Centers, the Notice on Adjusting the Insurance Rate of Industrial Injury, Reducing Social Insurance Rate and Birth Insurance Rate, and the Economic Compensation for Breach and Termination of Labor Contract released by the Ministry of Human Resources and Social Security, we set a1i = 0.6, b1i = 0.7, SR1i = 0.38, t1i = 5, a2i = 0.7 , SR2i = 0.4 , λ = 0.015, t2i = 3, and t3i = 12 . According to the Notice on Stopping and Correcting Illegal Procedures in Early Retirement of Enterprise Employees released by the Ministry of Human Resources and Social Security, and the resettlement schemes of surplus workers and the average age of employees in the coal industry issued by each province, the proportion of internal retired, diverted, and fired workers to the total number of resettled workers ( p1i , p2i , and p3i , respectively) can be determined. To determine the total overcapacity reduction in China, we first calculate the coal capacity of each province in 2015 using the estimated border production function of the coal industry. According to the new capacity of the provinces from 2016 to 2020, we can obtain the coal capacity of each province and the total coal capacity for 2020.5 The data of the new capacity are from the China coal resources website (http://www.sxcoal.com). Then, according to the requirements of coal output within 3.9 billion tons in 2020 and the existing literature, we set 78–82% as the reasonable capacity utilization rate range of the coal industry (in this study, capacity utilization is set as 80%). In addition, we can calculate the reasonable coal capacity Yr in China for 2020, where Yr = the coal output demand/reasonable capacity utilization rate

and Heilongjiang in northeast China; Beijing (BJ), Hebei (HB), Jiangsu (JS), Fujian (FJ), and Shandong (SD) in eastern China; Shanxi (SX), Anhui (AH), Jiangxi (JX), Henan (HN), Hubei (HUB), and Hunan (HUN) in central China; and Inner Mongolia (IM), Qinghai (QH), Ningxia (NX), Xinjiang (XJ), Guangxi (GX), Chongqing (CQ), Sichuan (CQ), Guizhou (GZ), Yunnan (YN), and Shaanxi (SHX) and Gansu (GS) in western China. The location and coal output of the 25 provinces in 2015 are shown in Fig. 1. To estimate the relative parameters of the coal boundary production function, this study selects data from 1986 to 2015 as the sample interval. The output Y is measured by raw coal output (unit: 10,000 t), the capital input K is measured by the average balance of the fixed asset net value of the coal industry, and the labor input L is measured by the average number of employees in the coal industry. Since the average balance of the fixed asset net value in statistical yearbooks is just the book value, we deflate it with the fixed asset investment price index of each province (in constant prices for 1985). The data for these indicators are from the China Industrial Economic Statistics Yearbook (1986–2016). In the estimation of the disposal cost of fixed assets in the process of overcapacity reduction in the provinces, the data for the average annual balance of the fixed asset original and net values of the coal industry are from the 2016 provincial statistical yearbook. According to the Notice on the Follow-up Management of the Canceled Enterprise Income Tax Approval Project issued by the State Administration of Taxation, the estimated net residual value of fixed assets is set as 3%. In the estimation of the labor resettlement cost in the process of overcapacity reduction in the provinces, the data for the average wage of coal industry employees are from the 2016 China Labor Statistics Yearbook, the data for the average salary of town workers are from the 2016 China Statistical Yearbook, and the data for the minimum wage are from the official website of the Ministry of Human Resources and Social Security (http://www.mohrss.gov.cn). According to the Notice on

5 The Suggestion on Restraining Coal Overcapacity and Meeting Anti-poverty and Development Goals issued by the State Council in February 2016 pointed out that, from 2016 to 2020, the government will stop the examination and approval of new coal mine projects, technical innovation of new capacity projects, and authorized capacity increase projects, as well as and implement measures of reduction and replacement if absolutely necessary. Thus, during 2016–2020, the new national coal capacity mainly comes from new and ongoing projects that have received government.

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= 3.9/0.8 = 4.875 billion tons. Further, we can calculate the total coal capacity in China for 2020. In the same way, according to the lowest coal output in four areas mentioned in the Thirteenth Five-Year Development Plan of Coal Industry, we can get the corresponding regional coal capacity constraints ( A1, A2 , A3 and A 4 ).

above, δi can be determined as listed on the fifth column, Table 2. The goodness of fit, R2 , is 0.993 as a whole, which is considerably acceptable. All the provincial coefficients of the regression pass the statistical test, which also indicate the credibility of this model. Utilizing the boundary production function that we estimated, we can calculate the coal capacity of the provinces in 2015 (the maximum potential output). The results can be obtained when estimating the capacity in 2020 if the new capacity in 2016–2020 is added (results are shown in columns 6 and 7 in Table 2). It can be predicted that China's coal capacity will add up to 5.6780 billion tons in 2020. The rational capacity enough to meet all market demands is only 4.8750 billion tons, and thus, overcapacity amounts to 0.803 billion tons. These results show the seriousness of the coal overcapacity and calls for immediate actions to tackle the problem. Meanwhile, the results are in accordance with the for overcapacity reduction established by the State Council in April 2016, which verify the reasonableness and effectiveness of this study's boundary production function.

4. Results and discussion 4.1. Quota allocation of coal overcapacity reduction 4.1.1. Estimation of provincial coal overcapacity The panel contains both cross-section and time-series data. An unsteady time-series may result in the problem of spurious regression, which calls for a stationarity test. The common unit root tests for the panel data include the Augmented Dickey-Fuller, Levin, and PhillipsPerron tests. In this study, conclusions can be accepted only if two out of the three test results are identical with each other. In the condition of the non-difference method, only the original value of fixed assets of the coal industry is non-stationary time-series. When the first-order difference applied, the logarithms of all variables are proven stable. At the cost of data loss, non-stationary time-series data can be transformed into stable data using to the difference method. A better way is to run a cointegration test. If the data are cointegrated, their linear combination may be found to be stable and good for dynamic panel estimation. A common cointegration test is the Kao test, which was developed based on the Engle-Grander test and is free of the lag phase. In this study, the t value of Kao test is − 8.566, with a company probability of 0.000, which sheds light on the cointegration relationship between the outcome and income of the coal industry. As a result, dynamic panel estimation can be directly used. Taking into consideration the contemporaneous correlation and heteroscedasticity of the data, we apply cross-section seemingly unrelated regression (SUR) and white cross-section methods to calculate the coefficient covariance to overcome the problem of coefficient covariance and contemporaneous correlation. The elastic coefficient of assets and labor force are shown in Table 2. Following the steps stated

4.1.2. Optimal allocation proportion With the analysis using the above model, an optimal allocation plan of coal overcapacity reduction is developed, composed of the ratio of the national total for each province. Fig. 2 shows the quantity and optimal proportion of each province's coal overcapacity reduction. It is easy to conclude that the three provinces with the highest proposition are SX, IM, and SHX, with 17.296%, 13.676%, and 9.237% respectively, while the three provinces with the least proposition are QH, FJ, and GX with 0.606%, 0.604%, and 0.540%, respectively. The five provinces with the highest proportions (SX, IM, SHX, GZ, and SD) account for 55.478% of the total proportion. Under the cost-minimum principle, a few provinces take the major task of coal overcapacity reduction. Based on the assumptions of the model and the cost function, provinces with a lower cost of reduction contribute a greater proportion. Meanwhile, provinces with stronger increasing return to scales have a lower marginal cost of reduction at the beginning but suffer a sharply increasing rate, which restricts their potential. In this case, when

Table 2 Estimate of Boundary Production Function of coal-producing provinces and calculation results of capacity (Units: 10,000 t). Province

LN JL HLJ BJ HB JS FJ SD SX AH JX HN HUB HUN IM GX CQ SC GZ YN SHX GS QH NX XJ

∧

∧

∧

∧

αi

βi

δi − εi

δi

0.145 (2.100)** 0.460 (5.075)*** 0.629 (3.628)*** − 0.882 (− 4.197)*** 0.786 (3.090)*** 0.068 (2.398)** 0.118 (1.904)* 0.075 (1.852)* 0.410(10.725)*** 0.518(11.303)*** 0.454 (5.466)*** 0.089 (1.943)* 0.573 (3.843)*** 0.358 (4.005)*** 0.559 (6.213)*** 0.202 (2.352)** 0.186 (3.998)*** 0.178 (3.230)*** 0.348 (3.101)*** 0.100(5.7215)*** 0.403 (5.998)*** 0.589 (8.159)*** 0.712 (4.748)*** 0.568(16.806)*** 0.544 (9.017)***

0.877 (4.494)*** 1.732 (3.574)*** 0.397 (3.087)*** 1.696 (5.851)*** 1.886 (2.617) ** 1.019 (4.200)*** 1.298(18.755)*** 0.944 (5.861)*** 0.627 (3.125)*** 0.718 (4.361)*** 1.143 (4.853)*** 2.575(12.781)*** 0.504 (2.048)** 1.662(16.835)*** 1.304 (6.510)*** 0.853 (2.242)** 1.053(15.285)*** 1.408(29.642)*** 0.704 (1.748)* 0.979(14.524)*** 1.810 (9.096)*** 0.471 (2.848)*** 0.720 (2.549)*** 0.604 (2.310)*** 1.109 (4.900)***

5.006–8.996@ (− 3.189)*** − 8.865 to 8.996@ (− 3.189)*** 3.860–8.996@ (− 3.189)*** 8.108–8.996@ (− 3.189)** − 17.134 to 8.996@ (− 3.189)** 3.717–8.996@ (− 3.189)** 0.707–8.996@ (− 3.189)** 4.602–8.996@ (− 3.189)** 7.503–8.996@ (− 3.189)*** 4.045–8.996@ (− 3.189)*** 0.584–8.996@ (− 3.189)*** − 13.935 to 8.996@ (− 3.189)*** 6.472–8.996@ (− 3 .189)*** − 4.670 to 8.996@ (− 3.189)*** − 7.365 to 8.996@ (− 3.189)*** 2.192–8.996@ (− 3.189)*** − 0.454 to 8.996@ (− 3.189)*** − 4.802 to 8.996@ (− 3.189)*** 2.480–8.996@ (− 3.189)*** 2.993–8.996@ (− 3.189)*** − 11.110 to 8.996@ (− 3.189)*** 1.385–8.996@ (− 3.189)*** − 1.427 to 8.996@ (− 3.189)*** 0.225–8.996@ (− 3.189)*** − 4.019 to 8.996@(− 3.189)***

− − − − − − − − − − − − − − − − − − − − − − − − −

3.827 17.598 4.929 0.205 25.491 4.743 7.761 3.892 4.003 7.507 10.772 25.481 4.836 16.115 13.382 3.890 6.661 11.000 3.601 3.051 17.152 4.764 7.251 5.787 10.190

Capacity in 2015

Capacity in 2020

6083.994 4283.090 8891.674 493.191 11,444.331 2084.233 1619.230 15,948.871 117,279.751 14,909.991 3098.974 14,700.709 1324.072 4374.373 132,574.005 759.710 3590.015 6404.460 22,696.244 5296.952 84,334.517 6700.177 2528.726 13,516.140 19,103.802

6293.994 4484.090 10,954.674 520.000 11,624.331 2084.233 1730.230 16,803.871 142,059.751 15,699.991 3218.974 19,575.709 2260.072 4464.373 134,754.005 1014.710 4135.015 7394.460 27,623.244 6825.952 85,371.517 9797.177 2669.726 14,656.140 31,778.802

Notes: (1) *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively, and the numbers in parentheses indicate t-test values. (2) The test results are R2 = 0.993, F = 4341.196, and DW = 2.619.

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Fig. 2. Optimal allocation of national capacity reduction in coal-producing provinces.

degree of egalitarianism compared with the optimal model allocation scheme. In terms of the total cost of coal overcapacity reduction in China, the costs based on the government allocation scheme are much higher than the costs based on the optimal model allocation scheme, which means that the optimal model allocation scheme can save 15.05% on costs. Specifically, the optimal model allocation scheme saves 35.6471 billion yuan on the disposal cost of fixed assets and 21.0224 billion yuan in labor resettlement costs. The reason for the difference is that, compared with the government scheme, under the optimal scheme, the provinces with an increasing amount of overcapacity reduction are mainly QH, GS, YN, SX, and IM, and most of these provinces are in the less developed western region with relatively low wages, so the cost of worker resettlement is lower. Moreover, most mining areas of QH, GS, and YN and some mining areas of SX and IM have complex mining conditions and relatively backward equipment. Therefore, the cost of fixed asset disposal in the process of overcapacity reduction is lower too. Thus, increasing the amount of coal overcapacity reduction in these provinces not only help reduce the cost of overcapacity reduction, but also meet the basic principles of the state to eliminate backward production capacity and optimize coal production structure. China should significantly emphasize the human aspect in its process of coal overcapacity reduction. The seamless diversion and proper resettlement of workers are the prerequisites to implementing reduction smoothly and are the key factors of social stability and harmonious development. At present, the basic reason for the lag in the resettlement of surplus workers is the huge funding gap. Therefore, we further compare the differences in labor resettlement cost between the two schemes, and the results are shown in Figs. 3 and 4. According to Table 3, the total cost of labor resettlement is 117.910 billion yuan and 138.932 billion yuan under the optimal model allocation and the government allocation schemes, respectively, which means that the optimal model allocation scheme can save 15.13% on labor resettlement cost. According to and Fig. 3, from the horizontal perspective, under the optimal model allocation scheme, there are only two provinces (SX and SD) with a resettlement cost of more than 10 billion yuan and eight provinces with a cost between 5 billion and 10 billion yuan. The costs of those 10 provinces account for 71.76% of the country's total resettlement cost; according to Fig. 4, under the government allocation scheme, there are five provinces with a resettlement cost of more than 10 billion yuan and five provinces with a cost between 5 billion and 10 billion yuan. Thus, compared with the government allocation scheme, under the optimal model allocation scheme, not only is the cost of labor resettlement significantly lower, the number of provinces with a higher cost is also fewer. The provinces with a higher cost of labor resettlement are also the provinces with a high coal capacity and a large amount of coal overcapacity reduction. Therefore, lowering the cost of resettlement in these provinces will

provinces share the same conditions but face increasing returns to scale, the task of coal overcapacity reduction is first arranged in provinces with greater increasing returns to scale until these provinces no longer have that potential and the advantages of cost of reduction. For example, although HUB and HUN do not significantly differ in terms of resettlement cost per capita, HUN's returns to scale are twice that of HUB. Thus, although HUN's coal capacity is twice that of HUB, HUN's overcapacity deduction is only 30% greater than that of HUB. Other things being equal, the capacity potential of the provinces with lower returns to scale (BJ, SD, LN, HLJ, and SX) is greater. In contrast, the capacity potential of the provinces with stronger returns to scale (HB, HN, SHX, JL, etc.) is lower. The marginal cost of overcapacity reduction is directly correlated with the proportion of reduction. With the same proportion, provinces with a large production reduce a greater amount of overcapacity. For example, as HUB's coal capacity is 1.23 times greater than that of GX, HUB bears a larger portion of the overcapacity reduction than GX, approximately 2.19 times as much. In addition, SX province has the largest coal production, followed by IM, SHX, XJ, GZ, and HN, and thus, bear the biggest portions of coal overcapacity reduction, with the exception of XJ. 4.2. Comparison between optimal model quota allocation scheme and government quota allocation scheme To determine the validity and rationality of the optimal model quota allocation scheme, we compare and analyze the scheme above and the government preliminary scheme based on cost effectiveness and distributive equity. 4.2.1. Comparison of overcapacity reduction cost In 2016, the NDRC established the preliminary task of coal overcapacity reduction in 25 coal-producing provinces. Based on this task, we can examine the cost of overcapacity reduction in each province under those two schemes. The results in Table 3 shows that, according to the government scheme, the provinces with the largest amount of overcapacity reduction are SX, GZ, and SD, and the provinces with the smallest amount are BJ, GZ, and QH. The five provinces with the largest amount of overcapacity reduction account for 47.163% of the country's total amount of overcapacity reduction, which is lower than the corresponding amount based on optimal model quota allocation scheme. In further comparing the standard deviation of the amount of overcapacity reduction and of the overcapacity reduction proportion in each province under those two schemes, we find that the standard deviations (2710.140 and 0.034, respectively) based on the government allocation scheme are much smaller than the standard deviations (3386.830 and 0.042, respectively) based on the optimal model allocation scheme. The results show that the government allocation scheme has a certain 176

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Table 3 Comparison of overcapacity reduction cost under the government and optimal schemes (Units: tons and hundred million yuan). Province

LN JL HLJ BJ HB JS FJ SD SX AH JX HN HUB HUN IM GX CQ SC GZ YN SHX GS QH NX XJ Country

Optimal model quota allocation scheme

Government quota allocation scheme

Capacity reduction amount

Capacity reduction proportion

Total cost

Asset disposal cost

Labor resettlement cost

Capacity reduction amount

Capacity reduction proportion

Total cost

Asset disposal cost

Labor resettlement cost

2208.796 2391.010 2132.952 520.000 3881.988 891.727 485.185 5733.765 13,887.821 2356.006 1468.485 4878.812 950.021 1237.725 10,949.622 433.863 1769.381 2417.144 6557.518 2587.800 7417.020 1830.846 486.912 842.162 1978.479 80,295

35.094% 53.322% 19.471% 100% 33.395% 42.784% 28.042% 34.122% 9.776% 15.006% 45.620% 24.923% 42.035% 27.724% 8.126% 42.757% 42.790% 32.689% 23.739% 37.911% 8.688% 18.687% 18.238% 5.746% 6.226% 14.142%

118.787 103.055 114.936 30.576 208.408 53.359 28.287 350.150 633.447 105.967 59.324 203.260 42.486 51.936 322.801 12.843 50.193 67.289 195.811 76.349 217.492 54.724 14.192 25.214 58.738 3199.625

68.782 47.705 61.816 4.521 113.266 33.437 9.375 240.454 437.650 68.558 32.314 124.054 21.235 27.080 265.631 6.120 22.872 30.752 103.143 42.367 159.515 31.087 8.951 14.851 44.995 2020.529

50.005 55.351 53.119 26.055 95.142 19.923 18.913 109.696 195.797 37.410 27.010 79.207 21.251 24.856 57.170 6.723 27.321 36.538 92.668 33.983 57.977 23.637 5.240 10.363 13.742 1179.096

3040 2733 2567 520 5103 1182 600 6460 11,400 3258 1868 6314 800 1500 6143 473 2300 3303 7414 2178 4706 1000 276 1119 3743 80,000

48.300% 60.949% 23.433% 100. % 43.899% 56.711% 34.677% 38.444% 8.025% 20.752% 58.031% 32.254% 35.397% 33.599% 4.559% 46.614% 55.623% 44.669% 26.840% 31.908% 5.512% 10.207% 10.338% 7.635% 11.778% 14.090%

163.806 122.434 138.405 30.576 287.338 71.354 35.428 394.716 598.522 169.405 89.649 310.688 40.649 73.246 238.127 17.676 83.600 119.254 281.441 81.716 179.031 38.096 10.239 43.010 147.917 3766.320

94.849 56.675 74.439 4.521 156.163 44.713 11.741 271.058 420.181 111.621 50.000 193.485 20.852 39.152 200.924 9.087 41.230 58.974 158.744 48.351 136.385 23.031 6.809 26.876 117.139 2377.000

68.957 65.759 63.966 26.055 131.175 26.641 23.687 123.658 178.342 57.785 39.649 117.203 19.798 34.093 37.202 8.588 42.370 60.281 122.697 33.365 42.645 15.065 3.429 16.133 30.778 1389.320

Fig. 3. Labor resettlement costs of provinces based on the optimal model quota allocation scheme.

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Fig. 4. Labor resettlement costs of the provinces based on the government quota allocation scheme.

Fig. 5. Lorentz curves based on capacity reduction per capita.

Fig. 6. Lorentz curves based on capacity reduction cost per capita.

undoubtedly help reduce personnel resistance in the process of overcapacity reduction, and finally, ensures the work of overcapacity reduction advances smoothly nationwide.

0.227 and 0.245 under the government and optimal model allocation schemes, respectively. Similarly, based on the capacity reduction per capita, the Gini coefficients are 0.181 and 0.196 under the government and optimal model allocation schemes, respectively. Although the optimal model quota allocation scheme, which has the goal of determining the minimum cost nationwide, has lost some equity, its Gini coefficient is still less than 0.3 (relative average) and 0.2 (absolute average). Therefore, in general, the study's quota allocation scheme of coal overcapacity reduction is fair and rational.

4.2.2. Comparison of results for distribution equity In this study, taking the capacity reduction per capita and cost for capacity reduction per capita as the order basis of the Lorentz curve, and taking the cumulative percentage of employees and of capacity reduction (or cumulative percentage of cost for capacity reduction) as the horizontal and vertical coordinates, respectively, we get the Lorentz curve of the optimal model and government allocation schemes. The results are shown in Figs. 5 and 6. We use the trapezoidal area method to estimate the Gini coefficient. Based on the capacity reduction per capita, the Gini coefficients are

4.3. Scenario analysis In the previous analysis, we set China's coal production control target as 3.9 billion tons by 2020 and set the reasonable capacity 178

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Table 4 Coal overcapacity reduction in different scenarios based on the quota allocation scheme. Province

Capacity utilization rate scenarios (total coal output = 3.9 billion tons) 78%

LN JL HLJ BJ HB JS FJ SD SX AH JX HN HUB HUN IM GX CQ SC GZ YN SHX GS QH NX XJ Country

Total coal output scenarios (capacity utilization rate = 80%) 82%

3.7 billion tons

4.1billion tons

Capacity reduction amount

Distribution proportion

Capacity reduction amount

Distribution proportion

Capacity reduction amount

Distribution proportion

Capacity reduction amount

Distribution proportion

2071.107 2388.363 1888.673 520.000 3871.239 878.855 481.499 5216.200 9859.194 2277.222 1463.218 4852.352 929.678 1230.539 9401.004 365.456 1697.650 2339.089 3970.257 2246.387 6593.866 976.951 444.862 290.127 1541.252 67,795.041

3.055% 3.523% 2.786% 0.767% 5.710% 1.296% 0.710% 7.694% 14.543% 3.359% 2.158% 7.157% 1.371% 1.815% 13.867% 0.539% 2.504% 3.450% 5.856% 3.313% 9.726% 1.441% 0.656% 0.428% 2.273% 100%

2339.261 2393.598 2365.752 520.000 3892.653 904.379 488.837 6225.089 17,716.782 2432.767 1473.632 4904.697 969.656 1244.751 12,500.916 495.893 1839.985 2495.088 8892.931 2908.117 8243.198 2612.579 528.754 1380.449 2415.520 92,185.285

2.538% 2.597% 2.566% 0.564% 4.223% 0.981% 0.530% 6.753% 19.219% 2.639% 1.599% 5.320% 1.052% 1.350% 13.561% 0.538% 1.996% 2.707% 9.647% 3.155% 8.942% 2.834% 0.574% 1.497% 2.620% 100%

2482.512 2396.537 2622.940 520.000 3904.955 918.826 493.042 6765.585 21,934.696 2519.573 1479.469 4934.096 991.643 1252.727 14,306.369 560.615 1920.588 2585.490 11,317.858 3255.074 9206.785 3436.913 577.093 1988.687 2922.968 105,295.041

2.358% 2.276% 2.491% 0.494% 3.709% 0.873% 0.468% 6.425% 20.832% 2.393% 1.405% 4.686% 0.942% 1.190% 13.587% 0.532% 1.824% 2.455% 10.749% 3.091% 8.744% 3.264% 0.548% 1.889% 2.776% 100%

1932.876 2385.787 1644.864 520.000 3860.926 866.398 477.959 4697.638 5574.494 2200.304 1458.087 4826.620 909.628 1223.549 7879.104 291.321 1625.933 2262.147 1154.957 1888.661 5786.449 60.557 403.265 252.856 1110.661 55,295.041

3.496% 4.315% 2.975% 0.940% 6.982% 1.567% 0.864% 8.496% 10.081% 3.979% 2.637% 8.729% 1.645% 2.213% 14.249% 0.527% 2.940% 4.091% 2.089% 3.416% 10.465% 0.110% 0.729% 0.457% 2.009% 100%

82% utilization rate scenarios and 3.7 billion tons and 4.1 billion tons total coal output scenarios. The quota allocation scheme of coal overcapacity reduction under different scenarios is shown in Table 4, and the optimal allocation proportions of coal capacity reduction of each province under the different scenarios are shown in Figs. 7 and 8. Obviously, the lower the capacity utilization ratio of the coal industry, the higher the total coal output and the smaller the total overcapacity reduction nationwide. Otherwise, the total overcapacity reduction will be larger. Fig. 7 shows that, with a capacity utilization rate of the coal industry, capacity reduction of SX, GZ, and GS accounts for a growing proportion of the country's total capacity reduction, while the capacity reduction of HN, HB, and JL accounts for a decreasing proportion of the country's total capacity reduction; in other provinces, the change in capacity reduction proportion is not obvious under different capacity utilization rate

utilization rate as 80%. In fact, China's coal production target differs according to the various existing studies and reports (Han et al., 2016). For example, according to the forecasts of Liu et al. (2017), China's coal production will reach around 4.1 billion tons by 2020; however, according to China's Thirteenth Five-Year Coal Control Project Report released in 2015 by China's coal consumption control and policy research group, under ecological resource constraints, China's coal production will be controlled to within 3.7 billion tons by 2020. Moreover, with regard to the standard reasonable capacity utilization rate, Western countries generally believe that the reasonable capacity utilization rate of an industry is 78–82% (Kou et al., 2017). Capacity utilization rate over 90% indicates insufficient production capacity, while lower than 79% indicates excess capacity. Therefore, we set the national coal output control target of 3.9 billion tons and the capacity utilization rate of 80% as the benchmark scenario. Based on this, we conduct 78% and

Fig. 7. Optimal allocation of national capacity reduction under different scenarios for capacity utilization rate.

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Fig. 8. Optimal allocation of national capacity reduction under different scenarios for total coal output.

5. Conclusions and Implications

relatively fair. Thus, the proposed optimal model allocation scheme has the advantages of economic viability and fairness. Moreover, considering the non-uniqueness of the capacity utilization rate and the uncertainty of future coal market demand, we also calculate the optimal distribution ratios of coal overcapacity reduction under the different capacity utilization rates and control targets of nationwide coal output. In general, most provinces have the same proportion of capacity reduction allocation under the different scenarios, indicating that the distribution scheme based on the optimal model allocation scheme is robust.

5.1. Conclusions

5.2. Policy implications

An economically viable and fair quota allocation scheme of coal overcapacity reduction is of great significance for reducing the pressure on local governments and for accelerating the supply-side structural reform. In this study, we use the production function method to estimate the boundary production function of the coal industry in 25 coalproducing provinces and estimate their coal production capacity in 2020. The results show that, under the control goal for total coal output proposed by the Chinese government, the coal overcapacity situation will be more serious, with the national coal overcapacity expected to reach 0.803 billion tons by 2020. Meanwhile, the results are in accordance with the goals for overcapacity reduction established by the State Council, which verifies the reasonableness and effectiveness of the study's boundary production function and coal capacity estimation results. Considering the pressure on the government to provide support funds for overcapacity reduction, we set obtaining the minimum cost of overcapacity reduction as the goal and the total nationwide overcapacity reduction and regional lowest amount of coal output as the constraints. We thereby build a quota allocation model based on nonlinear programming. Through the proposed method, we develop a quota allocation plan of coal overcapacity reduction, which determines the optimal distribution ratios of the different provinces to the total nationwide overcapacity reduction. There are some differences between the optimal allocation scheme and the government scheme (i.e., that tentatively identified by NDRC). To test the rationality of the optimal model allocation scheme, it is analyzed and compared together with the government allocation scheme in terms of cost and fairness. The results show that the total cost of national overcapacity reduction based on the optimal model allocation scheme is 56.6695 billion yuan less than that based on the government allocation scheme, composed of 35.6471 billion yuan of disposal cost of fixed assets and 21.0224 billion yuan of resettlement cost of redundant staff. Meanwhile, the fairness analysis shows that, despite the different indexes, the Gini coefficients of these two allocation schemes are always in the same range and smaller than 0.3, which is

First, the international emission reduction trend and China's environmental pollution have brought great pressure to China's energy transformation. As the main body of China's energy structure, the coal industry is bound to become the focus and key to success of China's energy revolution, and the reduction of coal proportion is an inevitable trend. In addition, the transformation of other industries, especially the transformation of the power system, has further reduced the total coal demand (Yuan et al., 2016). However, coal overcapacity reduction is a complex form system engineering and suffers from numerous problems in the process of advancing, such as how to compress active capacity, resettle staff, raise funds, and dispose assets and liabilities. Essentially, behind these difficulties are the interests of different stakeholders. Therefore, formulating a fair and economically viable quota allocation scheme for coal overcapacity reduction is important to implement energy supply-side reform smoothly in China. When allocating the coal overcapacity reduction amounts to the various provinces, the government should consider discrepancies in costs between the various provinces at the time of meeting the targets for nationwide overcapacity reduction and the needs of coal market. As much as possible, a capacity reduction allocation with fairness and economic viability should be adopted. Second, while the optimal model allocation saves significantly on the disposal cost of fixed assets compared to the government allocation scheme, this cost still reaches up to 200 billion yuan, which will cause significant losses in assets and severely impact companies’ enthusiasm in the overcapacity reduction. Hence, on one hand, to encourage “zombie” enterprises to take the initiative to reduce production capacity, the government should provide them indirect compensation through financing support, financial assistance, and tax preference. On the other hand, to reduce the disposal cost of fixed assets in the process of overcapacity reduction, the government should focus on building a coal industry property rights trading system where the government formulates trading rules and the market operates under the trading procedures. Meanwhile, the legal supervision system should be

conditions. As can be seen from Fig. 8, with a higher the total coal output, the proportion of capacity reduction of HN, HB, JL, and SD increases, while the proportion of capacity reduction of SX, GZ, and GS decreases gradually; in the other provinces, the change in capacity reduce proportion is not obvious under different control targets for total coal output. In general, most provinces have the same proportion of capacity reduction allocation in different scenarios, indicating that the distribution based on the optimal model allocation scheme is robust.

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perfected and the subject of property rights transaction and transaction behavior should be regulated through legislation. The government should give the market full responsibility for the resource allocation optimization in the function of optimizing resource allocation and remove barriers generated by the disposal cost of fixed assets. Finally, like the disposal cost of fixed assets, the surplus worker resettlement cost based on the optimal model allocation scheme is high at over 117.9 billion yuan. However, the special funds for worker resettlement set up by the State Council to reduce coal overcapacity is only 70 billion yuan, indicating a deficiency of 47.9 billion yuan. Thus, it is not enough to rely on the government's financial support to solve the resettlement problem. On one hand, solving the problem requires the government to consider actual staffing costs and local financial status comprehensively and distribute special funds overall, meaning that it is not sufficient to provide financial support simply according to the amount of overcapacity reduction and the number of workers to be resettled. On the other hand, the local governments should establish reemployment innovation and development funds. They should first distribute the funds from the government and then absorb social capital through increasing leverages. Also, supporting the diversion of workers through start-ups and re-employment as the primary standard, the local governments should implement a microcredit financing support policy to diverted workers who want to become entrepreneurs and establish their own small or micro-service enterprises, which in turn can absorb other diverted workers.

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5.3. Outlook While this research provides results that can serve as valuable references for allocating coal overcapacity reduction amounts to different provinces, it also has some limitations. It considers only the principle of the country's minimum total cost of overcapacity reduction, and no other factors, such as the financial ability of the different provinces, competitiveness of the coal industry, and sustainable livelihood capacity of the miners. Provinces with a lower overcapacity reduction cost bear more of the overcapacity reduction allocation, which would be unacceptable if they also bear all costs themselves. Moreover, the large number of laid-off workers and such workers’ resettlement resulting from the overcapacity reduction will put pressure on the society. Therefore, the interests of different stakeholders need to be considered, and quota allocation strategies of coal overcapacity reduction based on multiple targets and constraints should be explored in future research. Acknowledgments

Delu Wang is a professor at School of Management, China University of Mining and Technology. He received his Ph.D. from China University of Mining and Technology. His publications have appeared in journals such as Energy Policy, Journal of Forecasting, Journal of Cleaner Production, Expert Systems, Journal of Family Business Strategy, etc. His research interests include energy policy and sustainable development.

This research is supported by the National Natural Science Foundation of China (No. 71573252) and the Fundamental Research Funds for the Central Universities (No. 2017XKQY085). Declaration of interest

Kaidi Wan is a master candidate at School of Management, China University of Mining and Technology. She has co-authored articles in major journals in energy economics. Her research focuses on energy policy.

None.

Xuefeng Song is a professor at School of Management Science and Industrial Engineering, Nanjing University of Finance and Economics. He is now the President of Nanjing University of Finance and Economics. His publications have appeared in journals such as Energy Policy, Journal of Organizational Behavior Management, Journal of Forecasting, International Journal of Global Energy Issues, Journal of Management Sciences in China, Journal of Systems Engineering, etc. His research focuses on energy economics.

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