Assessing regional environmental efficiency in China with distinguishing weak and strong disposability of undesirable outputs

Accepted Manuscript Assessing regional environmental efficiency in China with distinguishing weak and strong disposability of undesirable outputs

Sheng-Ren Piao, Jian Li, Ching-Jung Ting PII:

S0959-6526(19)31294-6

DOI:

10.1016/j.jclepro.2019.04.207

Reference:

JCLP 16563

To appear in:

Journal of Cleaner Production

Received Date:

13 February 2017

Accepted Date:

18 April 2019

Please cite this article as: Sheng-Ren Piao, Jian Li, Ching-Jung Ting, Assessing regional environmental efficiency in China with distinguishing weak and strong disposability of undesirable outputs, Journal of Cleaner Production (2019), doi: 10.1016/j.jclepro.2019.04.207

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ACCEPTED MANUSCRIPT

[Title Page] Assessing regional environmental efficiency in China with distinguishing weak and strong disposability of undesirable outputs Sheng-Ren Piao1,* , Jian Li1, Ching-Jung Ting2 1School

of Management, Tianjin University of Technology, Tianjin

300384, China. E-mail address: [email protected]. 2Department

of Industrial Engineering and Management, Yuan Ze

University, Taiwan 32003.

Correspondence information: Sheng-Ren Piao, School of Management, Tianjin University of Technology, No. 391, binshui west road, TianJin, [email protected], 86-15022179273.

ACCEPTED MANUSCRIPT Assessing regional environmental efficiency in China with distinguishing weak and strong disposability of undesirable outputs Sheng-Ren Piao1,*, Jian Li1, Ching-Jung Ting2 Abstract: China has developed a remarkable economic growth in the past 30 years by accompanying with undesirable outputs. The assumptions of weak and strong of undesirable outputs have become the focus discussion in data envelopment analysis (DEA) models. To have a comprehensive environmental efficiency measurement, this paper proposes three DEA models considering weak disposability, strong disposability and distinguishing weak and strong disposability of undesirable outputs, respectively. We further combine with the Malmquist-Luenberger productivity index to assess the environmental efficiency and the dynamic change trend of 30 provinces in China from 2005-2014. The results show that distinguishing technical features of undesirable outputs makes a significant difference to final environmental efficiency score at different regions. The environmental efficiency of the whole nation, however, does not show any increasing trend during the ten years. Enhancing environmental efficiency of central and west area is an urgent task for Chinese government. The change trend of Malmquist-Luenberger productivity index and technological change shows a similar shape. Technical progress is the main driving force to enhance the environmental efficiency. Relevant suggestions are presented for improving the regional environmental efficiency in China in the future. Keywords: Regional environmental efficiency; Undesirable outputs; Strong and weak disposability; DEA model; Malmquist-Luenberger index; China

1. Introduction Since the implementation of reform and opening up, China’s economic development has made remarkable achievements and become the world’s second largest economy (Wu et al., 2015). According to National Bureau of Statistics, China's gross domestic product (GDP) in 2015 is about 67.7 trillion yuan, 185 times higher than that in 1978. However, the rapid economic growth is accompanied with the high energy consumption and high pollution emissions (Zhang et al., 2015). Based on figures provided by the World Bank, China has become the largest energy consuming country and is the biggest emitter of carbon dioxide (World Bank, 2013). Balancing economic and environmental development has become an important task for the Chinese government. In order to improve energy and environmental efficiency, Chinese government has proposed to construct a resource-saving and environment-friendly society and promised to reduce the amount of CO2 produced per unit of GDP by 40%-45% over the period of 2005-2020 (Zhang et al., 2013). Furthermore, President Xi has announced new targets to peak CO2 emissions around 2030 (US White House Press, 2014). Therefore, it is important to coordinate the development of economy and environment in China. “Environmental efficiency”, which is an instrument for analyzing the impact of economic level on environment, was first put forward by the Global Governance and Sustainable Economic Development Forum in 1992 (Song et al., 2013). The measurement of environmental efficiency can provide quantitative environmental information for the policy makers. Hence, it is necessary to measure and improve regional environmental efficiency in China. It is important to find a suitable method to assess environmental performance. The material flow analysis (MFA) approach (Čuček et al., 2012; Wang et al., 2016), the stochastic frontier analysis (SFA) approach (Reinhard et al., 2000; Hattori et al., 2002; Lin et al., 2014) and the data envelopment analysis (DEA) approach (Taskin et al., 2001; Song et al., 2012; Sueyoshi et al., 2013) are generally used in environmental efficiency measurement. With regard of MFA, it is usually limited by the availability of data. SFA is a parametric approach 1School

of Management, Tianjin University of Technology, Tianjin 300384, China. E-mail address: [email protected]. 2Department of Industrial Engineering and Management, Yuan Ze University, Taiwan 32003. 1

ACCEPTED MANUSCRIPT and is suitable only for one-output scenarios that hypothesizes a functional form and use the data to econometrically estimate the parameters of that function using the entire set of decision making units (DMUs). However, it is not appropriate to evaluate environmental efficiency using a single factor (Wang et al., 2011). In addition, incorrect results may be obtained due to using an incorrect form of production function (Dyson and Shale, 2010; Kuosmanen and Kortelainen, 2012). By contrast, DEA is a non-parametric approach that considers multiple inputs and outputs of DMUs (Zhu, 2004; Zhou et al., 2008; Saen, 2005; Cooper et al., 2007; Cook et al., 2009). Additionally, DEA method does not require a pre-set function hypothesis between inputs and outputs and can avoid man-made subjective weighting (Seiford and Thrall, 1990). For the effectivity of determining the optimal production front and ranking the DMUs of DEA mothed, it has been widely used in efficiency assessment benchmarking of school (Charnes et al., 1994), hospital (Prior, 2006; Du et al., 2014; Mitropoulos et al., 2014), firms (Mahdiloo et al., 2012), bank branches (Schaffnit et al., 1997), and so on. Therefore, DEA is the main method in this paper for measuring regional environmental performance. The concept of weak and strong disposability was first specified by Färe et al. (1989). Strong disposability implies that a decision maker unit (DMU) disposes an undesirable output at no cost, while weak disposability assumes diversion of inputs from the production of good output. Since then, both desirable and undesirable outputs are discussed in weak and strong disposability. Many studies applied DEA to evaluate environmental efficiency for China considering undesirable outputs. Hu and Wang (2006) first used DEA model to measure total-factor energy efficiency of regions in China. Later, many articles used slack-based measure (SBM) model to evaluate the regional environmental efficiency in China considering both desirable and undesirable outputs (Li and Hu, 2012; Zhang and Choi, 2013; Li et al., 2013; Huang et al., 2014, Guo et al., 2016; Tao et al., 2016; Chen and Jia, 2017; Zhang et al., 2017; Xiao et al., 2018; Yang et al., 2018). Also, some scholars focused on industrial energy efficiency of areas (Shi et al., 2010; Wu et al., 2012; Chang and Zhang et al., 2013; Jiang and Folmer et al., 2016). To our knowledge, most relative studies just applied the DEA models to measure regional environmental efficiency with assuming a uniform disposability for all undesirable outputs. In reality, various undesirable outputs often present different technical characteristic. Only limited research modeled undesirable outputs as outputs, assuming a weak disposability for undesirable outputs (Yang and Pollitt, 2010). It is needed to distinguish different disposability of undesirable outputs for assessing regional environmental efficiency objectively. Therefore, DEA models with distinguishing different disposability of undesirable outputs, as combined the Malmquist-Luenberger productivity index, are proposed to assess environmental efficiency of 30 provinces in mainland China from 2004-2012. The remainder of the paper is organized as follows. Section 2 reviews the literature related to efficiency measurement with weak and strong disposability of undesirable outputs. Section 3 describes method and model that used in this paper. Section 4 outlines the data set. Section 5 is the empirical results and analysis. Section 6 shows conclusions.

2. Literature Review With the emergence of environmental problems, more and more scholars begin to pay attention to the disposability of undesirable outputs (Chung et al., 1997; Scheel, 2001; Bevilacqua and Braglia, 2002; Seiford and Zhu, 2002; Korhonen and Luptacik, 2004). In the relevant papers, undesirable outputs have been discussed in the environmental efficiency measurement mainly in two different ways. One view treats outputs as inputs, the justification based on desirable and undesirable outputs are positively correlated (Cropper, 1992; Tyteca, 1996, 1997; Dyson, 2001; Seiford and Joe, 2002). However, this kind of assumption does not reflect the real production activities well. The other view recognizes undesirable outputs as outputs, assuming it has weak disposability. For instance, Färe et al. (1989) proposed to distinguish weak and strong disposability between desirable and undesirable outputs. Later, Ball et al. (1994) improved the assessment method of traditional total factor productivity by deal with the disposability of undesirable outputs. Since then, this topic was fiercely debated between Hailu and Färe, their focus is the operation of undesirable outputs in practice (Hailu 2

ACCEPTED MANUSCRIPT and Veeman, 2001, 2003; Färe et al., 2003). Motivated by previous studies, Kuosmanen et al. (2005, 2009, 2011) pointed out the limitation of traditional weak disposal technology which was advocated by Färe, and they optimized the production technology set. Furthermore, Yang and Pollitt (2007, 2010) distinguished disposability features among undesirable outputs in Chinese coal-fired power plants. Some scholars also discussed the effect of different dispositional assumptions on efficiency considering materials balance condition (Dakpo et al., 2016; Kenneth, 2016; Førsund, 2018; Wang et al., 2018). Recently, disposability of undesirable outputs has been applied in different aspects, e.g., congestion (Sueyoshi et al., 2012), random data (Wu et al., 2013), pollution inputs (Ray et al., 2016), and others. Regarding the research on environmental efficiency evaluation in China, Li and Hu (2012) computed the ecological total-factor energy efficiency in 30 regions between 2005 and 2009 through SBM model with undesirable outputs. Wang et al. (2012) utilized several DEA-based models to evaluate the total-factor energy and emission performance of China’s 30 regions with in a joint production frame-work of considering desirable and undesirable outputs as well as separated energy and non-energy inputs. Zhang and Choi (2013) evaluated China's regional economies during 2001-2010 using a SBM model with three undesirable outputs and suggested that the government should consider regional differences when making environmental policy. Li et al. (2013) constructed the Super-SBM model under undesirable outputs to measure regional environmental efficiency in China, and then tested influential factors of China’s environmental efficiency between 1991-2001 by means of the Tobit regression model. Huang et al. (2014) proposed a comprehensive DEA model combining benchmark technology, undesirable output, super efficiency and SBM to investigate the dynamics of regional eco-efficiency in China from 2000 to 2010. Wang et al. (2014) illustrated China's regional energy efficiency from both static and dynamic perspectives based on China's provincial panel data for the period of 2001-2010 by using the global DEA model. Chen and Song (2015) et al. calculated environmental efficiency in 30 provinces of China during the period 2001-2010 by employing DEA model and conducted a hypothesis analysis to the results. They found that the environmental efficiency in China was low from 2001 to 2010. Wang and Feng (2015) measured China’s energy, environmental, and economic efficiency by using a method based on global data envelopment analysis, and verified that energy and environmental efficiency had gradually improved in recent years. Guo et al. (2016) utilized a modified SBM model measure the performance of energy saving and emission reduction for mainland China's provincial-level regions. Tao et al. (2016) constructed a non-separable input/output SBM model to measure China’s provincial green economic efficiency during1995-2012. Chen and Jia (2017) used SBM model considering undesirable outputs to evaluate the environmental efficiencies of China's industry using data from 2008 to 2012. Zhang et al. (2017) used a Super-SBM model with undesirable outputs, as combined with the Malmquist productivity index, to measure the low-carbon economy efficiency (LCEE) and the dynamic low-carbon economy efficiency (DLCEE) of 30 provinces in mainland China from 2005 to 2012. He et al. (2018) evaluated the environmental efficiency of major socioeconomic sectors, including agriculture, power, industry, residential and transportation, at the province level in China in 2010 based on a slack-based measure DEA model with nonseparable bad output and weights determined by the coefficient of variation method. Yang and Zhang (2018) developed an extended data envelopment analysis model to investigate the dynamic trends of regional eco-efficiency in China from 2003 to 2014, and the result showed that the eastern and northern regions have experienced the greatest advances in both resource and environmental efficiency. Yang et al. (2018) proposed an epsilon-based measure DEA approach to measure the regional ecological energy efficiency for 30 regions in China during 2007-2015 and found that China's ecological energy efficiency was relatively low and regional differences were significant. Xiao et al. (2018) used a super-efficiency SBM model with undesirable outputs to evaluate the energy-environmental efficiency of 31 sectors in China. Yang et al. (2018) analyzed energy efficiency of China by using a super efficiency SBM model with undesirable outputs, the results showed that China’s overall energy efficiency had decreased while taking the undesirable outputs into consideration. 3

ACCEPTED MANUSCRIPT Among those aforementioned studies, Yang and Pollitt’s (2010) study seems to be the only one that distinguishes weak and strong disposability among undesirable outputs in Chinese coal-fired power plants, but their research is based on the assumption of constant returns to scale in a production model. For further extend his research, based on the assumption of variable return to scale, this paper uses DEA model to measure the regional environmental efficiency considering weak and strong disposability according to technical features of undesirable outputs.

3. Methods 3.1 The concept of weak and strong disposability As mentioned previously, Färe et al. (1989) discussed the weak and strong disposability on undesirable outputs and made a pioneering work. Following the Färe’s research, assuming that all the decision-making units to invest resources to produce a product, while emissions out of a pollutant. We use an input vector x in order to produce a vector y  y d , y u . As shown in Fig. 1, assume there are 3 observed producers use equal input vector to produce out vectors labelled A, B, C. If the undesirable outputs can be free disposal, the output set P S x  is the region OEBCD. If the undesirable outputs can be weak disposal, the output set P w x  is the region OABCD. The difference between the two production sets is OABE. Where OE line segment is not feasible, which implies the production is not feasible if the pollution is zero.





P w x  Weak disposability PPS P S x  Strong disposability PPS

yD

E

'

B

P x  A S

P w x 

C

O

D

yU

Fig. 1. Weak and strong disposability of undesirable outputs. In Yang et al. (2010)’s research, giving a certain level of desirable outputs, the purpose of this production process is making both the input and the expected output less. Fig. 2 presents the input and undesirable outputs curve under different disposability assumptions. Is and Iw represent the frontier under strong and weak disposability assumptions, respectively. IR represents the real efficiency frontier. Under different disposability, the production frontier appears in different position (Pollit, 1995). Further, their study (2010) supposes the real efficiency production frontier IR is between the strong and weak extremes. In a DEA model, a DMU’s efficiency is often assessed by the relative distance to the best practice frontier. For DMU A, the real production efficiency is between OB/OA and OC/OA.

4

ACCEPTED MANUSCRIPT

Undesirable outputs

yu / y d

IS

IW

IR

A

C B

Inputs

O

x / yd

Fig.2. Inputs–undesirable outputs curves under different disposability assumptions. (Source: Yang et al., 2010) 3.2 DEA model Consider a production process that has n DMUs, each uses m inputs to produce p desirable outputs and q desirable outputs. Let us assume DMUj represents the jth DMU, j  J = {1, …, n}. x j  x1 j ,  xmj   Rm denotes the consumption of input i by DMU j. Similarly

y dj  ( y1dj ,, y dpj )T  R p and y uj  ( y1uj , , yqju )T  R q state the production of desirable and undesirable output p, q by DMU j, respectively. P(x) denotes the production possibility set. Let T  x, y d , y u : x  Rn , y d  Rp , y u  Rq be the empirical production possibility set.







There is at least a group set meeting input x can produce ( y d , y u ) . Define P(x) is a set of outputs and satisfies properties of closed, convex and bounded, and at the same time limited inputs can produce limited outputs. In addition, this paper considers the properties of outputs as follows: (i) Null-joint: (yd, yu)  P(x) and y u  0 then y d  0 . If an output ( y d , y u ) is feasible and there are no undesirable outputs produced, then under null joint only zero desirable output can be produced. (ii) Strong (Free) disposability: which requires that if (yd, yu)  P(x) and (yd’, yu)  (yd, yu) then (yd’, yu)  P(x). (iii) Weak disposability: In contrast to strong disposability, (yd, yu)  P(x), 0    1 then d (y , yu)  P(x). It means that a production process can reduce undesirable outputs by scaling down of the activity level proportionally. Where the multiplier  interpreted as reduction factor scaling of production process. The assumption of variable returns of scale is used in this paper. We consider the strong disposability of inputs and desirable outputs and distinguish different disposability of undesirable outputs. Consider a certain level of desirable output, the DMU will reduce the inputs and undesirable outputs. 1) Model 1 Model 1 was proposed by Färe et al. (1989). Consider the weak disposability of all undesirable outputs. Production technology set is as follows:





T w  x, y d , y u : y d  Y d  , y u  Y u  , x  X ,   R Then the model for technical efficiency evaluation is as follows:

F j  ( X , Y d , Y u )  min[  eT (s d  s  )]

5



ACCEPTED MANUSCRIPT Y d  s d  y dj Y u  y uj X  s   x j

s.t .

n

 j 1

j

(1)

 1

 j， s  , s d  0;( j  1,2, , N )   0

Here,  represents the objective function value.  is the proportion when reconstructing n

an efficiency DMU relative to the DMUj0. Additional convexity

 j 1

j

 1 means that VRS

（ variable returns to scale） technology, sd and s- are the slack variables.  is non-Archimedean element defined to be very small positive number. 2) Model 2 Model 2 is in contrast to model 1, considering the strong disposability of all undesirable outputs (Korhonen et al., 2004). Production technology set is as follows:





T S  x, y d , y u : y d  Y d  , y u  Y u  , x  X ,   R



Then the model for technical efficiency evaluation is as follows:

F j  (X,Y d ,Y u )  min[θ  εeT (s d  s u  s  )]

Y d  s d  y dj Y u  s u  y uj X  s   x j s.t .

n

 j 1

j

(2)

 1

 j , s , s , s  0;( j  1,2, , N ) d



u

  0 u

Where s are the slack variables of undesirable outputs considering strong disposability. 3) Model 3 For different undesirable output Model 3 distinguishes the strong and weak disposability (Yang and Pollitt, 2010). Production technology set is as follows:





T S&W  x, y d , y wu , y su : y d  Y d  , y wu  Ywu  , y su  Ysu  , x  X ,   R



Then the model for technical efficiency evaluation is as follows: u

F j  (X,Y d ,Yw ,Ysu )  min[θ  εeT (s d  s u  s  )]

Y d  s d  y dj Ywu  y wju s.t .

Ysu  s u  y sju X  s   x j n

 j 1

j

 1

 j , s d , ssu , s   0;( j  1,2, , N )   0 u w

Where Y

depicts the undesirable outputs considering weak disposability. 6

(3)

ACCEPTED MANUSCRIPT 3.3 Malmquist-Luenberger index model The above three models is static analyses of environmental efficiency, and the Malmquist Index model can describe the dynamic changes in environmental total factor productivity of China’s regions from two periods. The Malmquist Index model was proposed in 1953 in order to analyze changes in consumption in different periods (Malmquist, 1953). This model was developed by Färe et al. (1994). Later, Chung et al. (1997) applied directional distance function to the Malmquist index and proposed the Malmquist-Luenberger index in consideration of undesired outputs. This study follows Chung et al. (1997) and uses directional distance function to measure Malmquist-Luenberger index. The output-oriented Malmquist-Luenberger index was defined as follows:









1

 t+1  t  2 1+ D0  xt , y t ,u t ; y t ,-u t  1+ D0  xt , y t ,u t ; y t ,-u t    1 MLt+  t+1 t+1 t+1 t+1 t+1 t+1   t t+1 t+1 t+1 t+1 t+1  (4) t =  1+ D0  x , y ,u ; y ,-u    1+ D0  x , y ,u ; y ,-u     t t t t t t Here D0  x , y ,u ; y ,-u  denotes the level of technology at current period by the  t+1 technology of period t, D0  x t+1 , y t+1 ,u t+1 ; y t+1 ,-u t+1  denotes the level of technology at  t+1 current period by the technology of period t + 1, D0  x t , y t ,u t ; y t ,-u t  denotes the level of  t technology at t period by the technology of period t + 1, D0  x t+1 , y t+1 ,u t+1 ; y t+1 ,-u t+1  1 denotes the level of technology at t + 1 period by the technology of period t. MLt+ denotes t







the overall level of productivity. If M-L is greater than 1, it means that the productivity level of the DMU has increased from t to t + 1.On the contrary, if M-L is less than 1, it means that the productivity level of the DMU has fallen down from t to t + 1. If M-L index is greater than 1, it means that the productivity level of the DMU has increased from t to t + 1.On the contrary, if M-L index is less than 1, it means that the productivity level of the DMU has fallen down from t to t+1. Malmquist-Luenberger index can be further decomposed into the technical efficiency change index (MLEFFCH) and the technical progress index (MLTECH) as follows: 1 t+1 (5) MLt+  MLTECH tt+1 t = MLEFFCH t Here, MLEFFCH denotes the catch-up effect on technology of DMU. MLTECH measures the improvement of the overall technical level of the industry in which DMU is located.

4. Data and descriptive statistics In this paper, the DMUs are 30 regions in China. Tibet is not included because of lack of relevant data. The 30 regions are divided into three major areas by taking the standard of National Bureau of Statistics of China. The east area covers 11 regions including 3 municipalities (Beijing, Tianjin, and Shanghai) and 8 coastal provinces (Hebei, Liaoning, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan). The central area is constituted by 8 regions which are Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei and Hunan. The west are consists of 11 regions including Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shanxi, Gansu, Qinghai, Ningxia and Xinjiang. According to the actual production process and relevant literature (Wang et al., 2012; Bian and Feng, 2010; Choi et al., 2012), each region consumes four inputs, labor, water, energy and capital to produce one desirable output, Gross Domestic Product (GDP) and four undesirable outputs, CO2 , SO2, waste water and waste solid. This paper selects the data from 2005 to 2014 for regional environmental efficiency evaluation. Primary data can be obtained from China Energy Statistical Yearbook and China Statistical Yearbook. A detailed description of indicators and data is as follows: (i) Labor input: Using number of employment in three industries as an input instead of number of workers. The number of employees of each province at the end of a year is 7

ACCEPTED MANUSCRIPT considered as labor input, and the data is collected from the China Statistic Yearbook (2006– 2015). (ii) Water input: Total water consumption includes domestic water and industrial water. (iii) Energy input: Energy consumption is the main indicator of energy utility of regions, which includes coal, oil and natural gas and so on. (iv) Capital stock: The data cannot be directly obtained from the Statistical Yearbook, and the capital stock data are estimated by using the perpetual inventory method, which is expressed by Shan (2008). (6) K it  K it  1(1   it )  I it Where Kit is the capital stock for ith region in the year t, Ki,t-1 is the capital stock of previous year. Iit is the capital formation in year t and it denotes the capital depreciation rate in the year t and assumed to be 10.96% in all provinces. In this paper all the monetary variables are converted into 2005 constant prices. The capital stock data is from China Statistical Yearbook 2016 (NBSC, 2016). (v) Desirable output: GDP of each region is selected as the indicator for desirable output. (vi) Undesirable output: Although seasonal factors have a certain effect on undesirable outputs, but this paper selects the annual data to carry out the research due to the availability of data. The data of SO2, waste water and solid wastes can be obtained from the Statistical Yearbook. Regarding the CO2 emissions, we follow previous research (Wang and Wei, 2014; Wang et al., 2016) to compute the emission generated from energy consumption. The methods used for calculating CO2 emissions are from the article (IPCC, 2006). CO2 emissions can be estimated using the following equation: EC 

7

E i 1

i

 CEFi 

7

E i 1

i

 12

 CC i  H i  Oi  44

(7)

where EC represents CO2 emissions from fossil fuels. Ei is regional consumption of fossil fuel i. CEFi denotes the coefficient of carbon emissions from fossil fuel i. CCi signifies carbon content of fossil fuel i. Hi represents the heat equivalent of fossil fuel i, Oi is the carbon oxidation factor of fossil fuel i and the number (44/12) is the molecular weight ratio of CO2 to C. The CO2 emission factor of major carbonaceous fuel type in China, as shown in Table 1.The descriptive statistics of regions are shown in Table 2 and a Pearson correlation test is used between inputs and outputs variables in Table 3. Table 1 Coefficients of carbon emissions and folded standard coal of different energy Fuels Coal Coke Kerosene Petrol Diesel Fuel oil Natural gas CCa 27.28 29.41 19.60 18.90 20.17 21.09 15.32 Ha 178.24 284.35 447.50 448.00 433.30 401.90 0.38 O(%) 92.30 92.80 98.60 98.00 98.20 98.50 99.00 Source: Wu et al. (2016). a Note: CC and H are expressed in units of tons carbon/trillion Joules and trillion Joules/104 tons(m3), respectively. Table 2 Descriptive statistics of research sample Variable Employment （ten thousand persons） Annual water consumption (billion cubic metres) Inputs Capital stock （one hundred-million RMB） Energy consumption （ten thousand tce）

Year 2005 2010 2014 2005 2010 2014 2005 2010 2014 2005 2010 2014 8

Max 5662.41 6041.60 6606.50 519.72 552.19 591.29 29390.94 84750.36 172185.74 24161.95 34807.77 36510.99

Min 267.62 294.10 317.33 23.09 22.49 24.09 1026.34 3362.05 9583.35 822.20 1358.51 1819.93

Mean 2262.90 2555.32 2735.49 186.66 199.56 202.146 9468.15 30697.15 66076.97 8781.93 12983.65 14664.86

Std. dev. 1484.13 1672.31 1774.73 131.22 138.70 146.08 7897.67 20536.32 40897.88 5561.12 8035.03 8392.46

ACCEPTED MANUSCRIPT Desirable output

GDP （one hundred-million RMB） CO2（ten thousand tons） SO2（ten thousand tons）

Undesirab le outputs

Waste water produced(billion cubic metres) Solid wastes produced （ten thousand tons）

2005 2010 2014 2005 2010 2014 2005 2010 2014 2005 2010 2014 2005 2010 2014

22557.37 46013.06 67809.85 19718.86 30483.55 34923.93 200.20 153.78 159.02 63.84 72.30 90.51 16279.00 31688.00 41927.59

543.32 1350.43 2303.32 334.41 1039.46 1463.71 2.20 2.881 3.26 1.94 2.26 2.30 127.00 212.00 515.42

6632.64 14551.15 22780.95 6892.75 10037.55 11449.68 84.97 72.82546 65.80 17.47 20.56 22.05 4481.40 8031.00 10841.23

5342.92 11118.84 16527.77 4832.39 6825.59 7749.11 50.15 40.46 37.88 13.92 16.01 17.57 3541.97 6524.24 9397.90

Table 2 presets that the mean GDP of 2014 is 4.08 times as many as that of 2005 ,which demonstrates that economic of 30 regions have greatly increased from 2005 to 2014. Meanwhile, the amount of CO2 emission, waste water and solid wastes in 2014 are 1.66, 1.37 and 2.71 times over the amount in 2005 and the emission of SO2 is 0.77 times than that of 2005 ,which reveals that the amount of CO2, waste water and solid wastes are rising gradually and the emission of SO2 is showing a downward trend. The energy and annual water consumption are increasing sharply during the period of 2005-2014, which indicates that Chinese government should take measures to tackle this problem. Table 3 Pearson Correlation Coefficient between Input and Output Variable Variable

capital stock

capital stock

1.000

labour

0.962**

1.000

Annual water

0.872**

0.963

1.000

Energy

0.917**

0.985**

0.976**

1.000

GDP

0.987**

0.989**

0.933**

0.966**

1.000

CO2

0.926**

0.988**

0.977**

0.998**

0.973**

1.000

SO2

-0.931**

-0.967*

-0.915**

-0.939*

-0.951*

-0.933*

1.000

Waste water

0.641*

0.618*

0.652*

0.564

0.650*

0.600*

-0.597*

labour

Annual water

Energy

GDP

Solid 0.929** 0.970** 0.951** 0.979** 0.971** wastes Note: **The parameter is significantly important at 1% level. *The parameter is significantly important at 5% level.

9

CO2

0.988**

SO2

-0.895* *

Waste water

Solid wastes

1.000 0.625*

1.000

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Fig. 3. Scatter plots of GDP, CO2 ,waste water, solid waste and SO2

Table 3 shows that CO2, waste water and solid wastes have positive correlation with the variables of inputs at 0.01 level. SO2 emissions have a negative correlation with other variables at 0.05 level. As shown in Fig. 3, we further analyze the relationship between GDP and CO2, waste water and solid waste again between GDP and SO2. With the increase of GDP, CO2, waste water and solid waste emissions show an increasing trend, while SO2 emissions present downward trend. In the above analysis, it is effective to reduce SO2 emissions through employing the desulphurization equipment, however, in reality CO2, waste water and solid waste cannot be abated by dramatic changes through current techniques. The conclusion is similar to the results in Yang and Pollit (2010). So it is appropriate to assume weak disposability with CO2 and solid waste and strong disposability with SO2 and waste water. It is the emphasis in this paper, while previous studies paid little attention to the technical differences among undesirable outputs in region environmental efficiency measurement.

5. Empirical Results and Discussion 5.1 Analysis of regional environmental efficiency based on the three models Based on the three models in section 3.2 and analysis of section 4, the uniform weak disposability and strong disposability assumption are used in model 1 and model 2, respectively. In model 3, weak disposability assumption is used for CO2 and solid waste and strong disposability assumption is applied for SO2 and waste water. The calculation of the three models is obtained by MATLAB programs, as shown in Table 4. Table 4 Summary statistics of regional environmental efficiency scores Model 1 Model 2 Model 3 Mean 0.999 0.918 0.982 Max 1.000 1.000 1.000 2005 Min 0.971 0.741 0.822 Std. dev. 0.005 0.083 0.062 Mean 1.000 0.906 0.970 2006 Max 1.000 1.000 1.000 Year

10

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2007

2008

2009

2010

2011

2012

2013

2014

Min Std. dev. Mean Max Min Std. dev. Mean Max Min Std. dev. Mean Max Min Std. dev. Mean Max Min Std. dev. Mean Max Min Std. dev. Mean Max Min Std. dev. Mean Max Min Std. dev. Mean Max Min Std. dev.

1.000 0.005 0.988 1.000 0.850 0.036 0.982 1.000 0.800 0.054 0.981 1.000 0.798 0.055 0.983 1.000 0.807 0.052 0.983 1.000 0.789 0.051 0.980 1.000 0.779 0.055 0.970 1.000 0.765 0.066 0.967 1.000 0.793 0.069

0.766 0.090 0.890 1.000 0.728 0.099 0.875 1.000 0.694 0.110 0.857 1.000 0.662 0.115 0.858 1.000 0.649 0.118 0.849 1.000 0.626 0.126 0.830 1.000 0.611 0.137 0.809 1.000 0.560 0.156 0.797 1.000 0.557 0.162

0.788 0.124 0.958 1.000 0.766 0.172 0.944 1.000 0.703 0.235 0.935 1.000 0.707 0.242 0.949 1.000 0.715 0.225 0.951 1.000 0.716 0.250 0.942 1.000 0.719 0.287 0.934 1.000 0.710 0.332 0.936 1.000 0.730 0.319

According to the results of Table 4, the comparison of regional environmental efficiency scores is presented in Fig. 4, which illustrates the differences of regional environmental efficiency over 2005-2014 based on three models: Model 1 ≥ Model 3 ≥ Model 2. The value of environmental efficiency calculated by Model 1 is largest, and Model 2 produces the least value, while Model 3 produces the middle number. This indicates that distinguishing technical feature of different undesirable outputs affects the regional environmental efficiency measurement significantly.

11

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Fig. 4. Difference of environmental efficiency based on three models For the purpose of verifying whether environmental efficiency value based on the three models are significantly different, we use Wilcoxon-Mann-Whitney test to test the hypothesis of no difference in any two groups of efficiency score of three models. The results of the Wilcoxon-Mann-Whitney test are presented in Table 5. We can reject the null hypothesis at the 0.1% and 1% level based on the results. That means different assumptions of disposability have a significant influence on the regional environmental efficiency assessment. Models Model1 Model 2

Table 5 Wilcoxon-Mann-Whitney test statistics. Model 1 Model 2 0.000*** 0.000 -

Model 3 0.001** 0.000***

Note: ***The parameter is significantly important at 0.1%. **The parameter is significantly important at 1% level.

Table 6 shows that 30 regions in China have the 22, 7 and 17 efficient DMUs for model 1, model 2 and model 3, respectively. In model l, it cannot effectively distinguish between decision making units. According to the three models above, the environmental efficiency score of Beijing, Tianjin, Shanghai, Shandong, Guangdong, Hainan and Qinghai are relatively effective than other regions for the three models, while those of Fujian, Jilin, Heilongjiang, Anhui, Hubei, Hunan, Guangxi and Gansu are less than 1. Jiangsu, Zhejiang, Shanxi, Jiangxi, Henan, Inner Mongolia, Chongqing, Guizhou, Shaanxi and Ningxia has the same value of environmental efficiency according to Model 1 and Model 3, and its efficiency score of Model 1 is 1. In models 1 to 3, Hubei, Anhui and Yunnan have the lowest environmental efficiency score of 0.847, 0.672 and 0.758, respectively. Therefore, it indicates that different disposability has potential impacts on different regions. It is necessary to design suitable measurement model when making environmental regulation policy. Table 6 Results of regional environmental efficiency evaluation DMU Model 1 Model 2 Model 3 Beijing 1.000 1.000 1.000 Tianjin 1.000 1.000 1.000 Hebei 1.000 0.848 0.886 Shanghai 1.000 1.000 1.000 Liaoning 1.000 0.839 0.934 12

ACCEPTED MANUSCRIPT Jiangsu Zhejiang Fujian Shandong Guangdong Hainan Mean of east areaa Shanxi Jilin Heilongjiang Anhui Jiangxi Henan Hubei Hunan Mean of central area Inner Mongolia Guangxi Chongqing Sichuan Guizhou Yunnan Shaanxi Gansu Qinghai Ningxia Xinjiang Mean of west area Average

1.000 1.000 0.970 1.000 1.000 1.000 0.997 1.000 0.866 0.957 0.997 1.000 1.000 0.847 0.902 0.946 1.000 0.966 1.000 1.000 1.000 1.000 1.000 0.994 1.000 1.000 1.000 0.996 0.983

0.990 0.980 0.841 1.000 1.000 1.000 0.954 0.800 0.743 0.869 0.672 0.750 0.810 0.779 0.811 0.779 0.998 0.754 0.706 0.730 0.791 0.715 0.793 0.849 1.000 0.968 0.739 0.822 0.859

1.000 1.000 0.899 1.000 1.000 1.000 0.974 1.000 0.779 0.891 0.765 1.000 1.000 0.811 0.882 0.891 1.000 0.960 1.000 0.971 1.000 0.758 1.000 0.982 1.000 1.000 0.986 0.969 0.950

aThe

30 regions are divided into three larger regions: East area, central area and west area based on geographical location

5.2 Static Analysis In this section, the trend of environmental efficiency is analyzed in eastern, central and western China during the time of 2005-2014. Fig.5 shows that the overall value of environmental efficiency in China initiates a downward trend, and the environmental efficiency score are significant differences among eastern, central and western China. The environmental efficiency under model 3 is analyzed emphatically. The specific analysis is as follows: (i) The mean value of environmental efficiency in Eastern China is 0.974 during the period of 2005-2014, which is far greater than central. During the studied period, Beijing, Tianjin, Shanghai, Jiangsu, Zhejiang, Shandong, Guangdong and Hainan have always been the benchmark for lying on the environmental efficiency frontier. Liaoning almost gains an efficiency value above 0.900, closer to the frontier. Hebei has the lowest efficiency score 0.886, Through further analysis, Hebei's carbon dioxide and sulfur dioxide emissions are significantly higher than other regions. From the perspective of disposability, sulfur emissions in Hebei have a greater impact on environmental efficiency than carbon emissions, which implies there is room for improvement of sulfur dioxide emissions in Hebei. (ii) In central area, the mean value of environmental efficiency is 0.891 lower than that of national level. Shanxi, Jiangxi and Henan obtain the highest score 1.000. Heilongjiang, Hubei and Hunan gain an efficiency score between 0.800-0.900. Jilin and Anhui have efficiency score between 0.750-0.800. Anhui has the lowest environmental efficiency among the western regions. Through further analysis of the original data, we find that the central region's inputs and undesired outputs are all higher than the eastern and western regions, 13

ACCEPTED MANUSCRIPT indicating not only it has the pressure on economic development but also environment problems and it needs to adjust the economic structure and reduce the energy consumption. (iii) The west area gains the second highest mean environmental efficiency score 0.969, which is lower than east and higher than central area. Inner Mongolia, Chongqing, Guizhou, Shaanxi, Qinghai and Ningxia have been lying on the environmental efficiency frontier. The efficiency score of Guangxi, Sichuan, Gansu and Xinjiang are just around 0.950-1.000. Yunnan is considered having lowest efficiency score at 0.758. An analysis of the undesirable outputs structure in Yunnan shows that the solid waste emissions in Yunnan are higher than the average, while the other undesirable outputs are all lower than the average, so the solid waste has more impact on the environmental efficiency of Yunnan, and Yunnan should take more measures to control the solid waste. For the western region, in order to narrow the gap with eastern region, government should increase investment of environmental technological innovation and bring more talents to west area.

Fig. 5. Comparison of environmental efficiency score in three areas 5.3 Dynamic environmental performance analysis DEA Model described in three models above is mainly for static analysis. In order to grasp the change trend of regional environmental efficiency, we also estimate Malmquist-Luenberger (M-L) index according to equations (4)-(5) over the time of 2005-2014. Based on previous results, we compute the M-L index by MATLAB2015a software with considering the strong and weak disposability of undesirable outputs. The M-L indexes for three models are shown in Table 7. Table 7 Difference of M-L index based on weak and strong disposability from 2005 to 2014 Year Weak Strong Weak and Strong M-L EFFCH TECH M-L EFFCH TECH M-L EFFCH TECH 2005-2006 0.9633 0.9841 0.9779 0.9558 0.9769 0.9780 0.9632 0.9837 0.9786 2006-2007 1.0357 0.9672 1.0772 0.9949 0.9628 1.0330 1.0320 0.9660 1.0735 2007-2008 1.0172 0.9819 1.0358 1.0111 0.9827 1.0287 1.0186 0.9847 1.0346 2008-2009 0.9289 0.9856 0.9447 0.9456 0.9701 0.9743 0.9253 0.9903 0.9370 2009-2010 1.0487 0.9754 1.0740 1.0205 0.9836 1.0375 1.0361 0.9724 1.0638 2010-2011 1.1517 1.0247 1.1209 1.0534 0.9879 1.0604 1.0858 1.0194 1.0679 2011-2012 0.9760 0.9384 1.0434 0.9785 0.9591 1.0199 0.9653 0.9448 1.0281 2012-2013 0.9831 0.9640 1.0246 0.9884 0.9802 1.0082 0.9920 0.9692 1.0280 2013-2014 1.0083 0.9957 1.0125 1.0093 0.9955 1.0138 1.0162 0.9963 1.0194 14

ACCEPTED MANUSCRIPT Mean

1.0126

0.9797

1.0346

0.9953

0.9776

1.0171

1.0038

0.9808

1.0257

According to the results of Table 7, the mean ordering of M-L index during the study period is as follows: Weak ≥ Weak and Strong ≥ Strong. We believe that it is more consistent with the actual situation to distinguish between strong and weak disposability, so M-L index under strong and weak disposability is applied for dynamic analysis. From the view of time series data, in its entirety, the M-L index of regional environmental efficiency is greater than 1.000. The M-L index of 2006-2007, 2007-2008, 2009-2010, 2010-2011, 2014-2014 are greater than 1.000, and that of the rest of years are smaller than 1. Among them, the M-L index in period of 2010-2011 improves 8.58%, being the highest score. Furthermore, the mean value of technical progress index is higher than 1.000, and the mean of technical change index is smaller than 1.000. It indicates that the technical progress plays positive effects on environmental efficiency, while environmental efficiency improvement is mainly driven by technological improvement. The M-L index based on weak and strong disposability for each region is shown in Table 8. From Table 8, among 30 provinces of China, the total factor productivity indexes of 11 provinces are above the national average, while the indexes of the other 19 provinces are under the national average. The top five provinces are Jiangsu, Zhejing, Inner Mongolia, Jiangxi, Shanghai. The last five are: Tianjin, Hainan, Hebei, Heilongjiang, Guizhou. Sub-region， environment efficiency improvement of eastern region is mainly caused by technological progress change, it shows that eastern region has utilized the convenience brought by technical progress to complete industrial upgrading. It is necessary to expand the scale of industry and improve environmental efficiency through agglomeration effect. In the central region, the input factors can be further reduced based on the output angle, and the central region should improve its management level and reduce the consumption of energy. In the western region, the total factor environmental efficiency is also mainly affected by technical progress, the MLEFFCH index of western region is higher than eastern region, meaning that the scale economy of the western region played a certain role during the study period. In order to narrow the gap with the eastern region, the western region should invest more in technological innovation and introduce advanced management technology. Table 8 The mean M-L index and decomposition of regional environmental efficiency DMU M-L index MLEFFCH MLTECH Beijing 1.0124 0.9556 1.0595 Tianjin 0.9444 0.9568 0.9870 Hebei 0.9221 0.9558 0.9647 Shanghai 1.0589 0.9616 1.1012 Liaoning 1.0286 0.9990 1.0296 Jiangsu 1.2023 0.9610 1.2511 Zhejiang 1.1962 0.9625 1.2428 Fujian 0.9647 0.9579 1.0071 Shandong 0.9707 0.9695 1.0012 Guangdong 0.9532 0.9511 1.0022 Hainan 0.9249 0.9501 0.9734 Mean of east area 1.0161 0.9619 1.0563 Shanxi 0.9722 0.9970 0.9751 Jilin 0.9815 0.9500 1.0332 Heilongjiang 0.9221 0.9630 0.9576 Anhui 0.9915 0.9770 1.0148 Jiangxi 1.0790 1.0343 1.0433 Henan 1.0179 1.0102 1.0076 Hubei 0.9839 0.9825 1.0015 Hunan 0.9640 0.9713 0.9924 Mean of central area 0.9888 0.9857 1.0032 15

ACCEPTED MANUSCRIPT Inner Mongolia 1.1051 1.0319 1.0709 Guangxi 0.9640 0.9563 1.0080 Chongqing 0.9882 0.9591 1.0303 Sichuan 0.9932 0.9663 1.0279 Guizhou 0.9088 0.9703 0.9366 Yunnan 0.9660 0.9732 0.9926 Shanxi 1.0672 1.0320 1.0341 Gansu 0.9994 1.0443 0.9571 Qinghai 0.9980 0.9818 1.0165 Ningxia 1.0440 1.0322 1.0115 Xinjiang 1.0486 1.0089 1.0393 Mean of west area 1.0073 0.9960 1.0113 Furthermore, the relationship between M-L index, MLEFFCH index and MLTECH index is analyzed in accordance with the eastern, central, western area and whole nation.

Fig. 6. Comparison of three areas in a) M-L index, b) MLEFFCH index, and c) MLTECH index. As can be seen from Fig. 6, the change trend of M-L index and technological progress change shows a similar shape change. In terms of time series, M-L index of eastern region in the 2005-2006, 2006-2007, 2007-2008, 2009-2010, 2013-2014 are greater than 1.000, The year 2008 is an important time node. Because the Beijing Olympic Games put forward the slogan of "green Olympics", the M-L index of the eastern region is higher under the constraint of the policy. After 2008, M-L index in the eastern region decreases, but with the increase of environmental protection, it begins to be raised again. The M-L index in the central region fluctuates greatly from 2010 to 2011, but shows an overall upward trend. The change of M-L index in the western region is relatively stable. During the whole evaluation periods, the average score of MEFFCH is 0.9808, meaning it does not play a positive role in enhancing environmental efficiency. Regions should change the mode of economic so as to make the reasonable inputs and effective management..

6. Conclusion DEA efficiency measures with considering the weak disposability of undesirable outputs have gained popularity in environmental efficiency assessment in recent years. Most studies assume a unified disposability for undesirable outputs and the environmental DEA technology exhibits CRS. However, undesirable outputs may have different technology feature and variant returns to scale are likely to be observed in actual situations. This paper applies the 16

ACCEPTED MANUSCRIPT three DEA models to measure environmental efficiency of 30 regions in mainland China with considering the different disposability of undesirable outputs. Combined the M-L index model, the change of technical efficiency and technical progress are computed for all consecutive two-year periods. After that, we make a static and dynamic analysis for three areas of China. The conclusions as below: (i) The regional environmental efficiency score is significantly influenced when distinguishing different assumption of disposability for undesirable outputs. It indicates that ignoring the technical characteristics of undesirable outputs may result in biased efficiency scores. The assumption of weak disposability of undesirable outputs gains higher efficiency score than that of assumption of strong disposability. To embody fairness and rationality, the government should design appropriate evaluation method, and give full consideration to technical characteristic of undesirable outputs. (ii) According to a comparative analysis, there are significant differences in environmental efficiency score among east, central and west areas of China. The central region has the lowest environmental efficiency. The environmental efficiency results show that China's economy and ecological environment development is not harmonious. Chinese government should do more to improve regional environmental efficiency. (iii) Both technical progress and technical efficiency can influence environmental efficiency, while technological progress is the main force of enhancing environmental efficiency. Technical efficiency is a weak hindrance to the improvement of regional environmental efficiency. The conclusion has important significance at the policy level. (1) DEA model with considering the different disposability of undesirable outputs and M-L index can measure the regional environmental efficiency effectively. Regional government may build a set of related evaluation system as a basis for environmental performance evaluation. The disposability of undesirable outputs can reflect the sensitivity of the region to undesired output. For example, when Hebei and Yunnan formulate undesired output reduction strategies, they should focus on the actual situation. The urgent task of Hebei is to control the amount of sulfur dioxide emitted, while Yunnan need to control solid waste emissions. (2) When making environmental control policy, we should give more objective evaluation for regional environmental efficiency level and take a full account the difference of economic development and energy consumption avoiding the phenomenon of “one-size-fits-all”. Although the eastern area's environmental efficiency is relatively high, for example, Beijing, Tianjin, Shanghai, Jiangsu, Zhejiang, Shandong, Guangdong and Hainan are the benchmark for lying on the environmental efficiency frontier during the studied period, this situation has a close connection with geographical position and preferential policies behind environmental pollution control. In the process of economic development, the east areas can attract more foreign capital and advanced technology, so they have much money to curb environmental pollution. But Hebei, Liaoning and Fujian in this area have relative low environmental efficiency. They should adjust the industrial structure, promote industrial upgrading and eliminate backward production capacity. Furthermore, it is necessary to adjust the mode of economic growth and industrial structure in the central region. While for the western area, most of regions in that have the low level of economic development and are lack of talents. The government should implement more supporting policies for their environmental development. (3) Technological progress should be considered the main way to improve environmental efficiency in the middle and western areas. However, improving the technology in a short period is difficult. So, mid-western area should strengthen the industrial structure adjustment and environmental management level.

Acknowledgements This research was supported by the Chinese National Social Science Foundation (NO.15BGL211) and the ministry of education the ministry of education philosophy and social sciences research project for major project (NO.15JZD021). The authors would like to 17

ACCEPTED MANUSCRIPT thank the editor and two anonymous reviewers for their valuable comments and suggestions on earlier version of our manuscript.

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