Abstract Coal mining is one of the highest-risk industries in China. Accident deaths incoal mines attract intense concern every year. This is the first attempt to measure produc-tion efficiency of coal mines with consideration of accident deaths. A combined directionaldistance function and slacks-based model is proposed to assess production and safety effi-ciency across 18 coal-mining provinces in China. Results showed that the average total factorhumanitarian-production efficiency is poor, with nearly half of production potential unex-ploited. Safety efficiency is also low, and half of the deaths would be avoided if all coalenterprises operated at fully efficient levels. The directional contribution analysis pointedout that southern provinces should pay more attention to accident deaths than northern ones,while the importance of reducing accident death in efficiency promotion declined for nearlyall provinces, which creates a tradeoff between safety and efficiency for enterprises and reg-ulators. The results of this study showed that the safety situation of coal mines is not asoptimistic as the official data suggest. Effective prevention mechanisms are urgently neededto prevent disastrous accidents in coal mines in China.
Keywords Total factor humanitarian-production efficiency · Total factor safety efficiency ·Directional distance function · Slacks-based measure · Accident deaths · Coal mining
China is the greatest coal producer in the world, accounting for nearly half of global output(Song andWang 2016). However, China’s coal production conditions are theworst among themain coal producing countries. Gas content is high for numerous coal mines, and in some ofthem, the hydrogeological conditions are complicated. The mine safety record is even worsethan that of other large producers at a similar development stage (Homer 2009). Consideringthat coal is themost important energy source inChina, governments are reluctant to shut downall the high-gasmines, aswell as those at high risk ofwater disaster. Hence, coalmining is stillone of the highest-risk industries in the country. The only way the coal-producing sector canproceed is to invest into safety technologies and management to reduce accidents and deaths.However, focusing on safety necessarily has an influence on production. Some researchersclaim that there is a tradeoff between safety and production in coal mining. Sider (1983)illustrates that declines in productivity can be attributed to changes in safety conditions.
Among the major coal mining countries, China exhibits the lowest level of labor produc-tivity (Tu 2007). This implies that, ceteris paribus, rather than technology and equipment,more workers are involved in the coal production process. With many people working underthese severe conditions, in case of an explosion or a water damage, a lot of casualties willoccur. Every year, China’s government holds a coal safety production work conference. Atthe 2017 conference, the relevant officials mentioned that a total of 249 accidents and 538deaths occurred in 2016. The mortality rate per million tons was 0.156, down by 3.7% fromthe previous year. Therefore, coal mine productivity measurements should take safety con-ditions into account. In this sense, the coal industry should be considered as producing twooutputs: a desirable output, coal; and an undesirable one, accident deaths.
Overall, the number of coal mine accidents in China has dropped dramatically in recentyears. However, there is a great variation in accident and death rates across provinces. Someprovinces have achieved good safety production performances: for example, both Xinjiangand Heilongjiang had only two accidents in 2017. Meanwhile, other provinces experiencedmore accidents: for example, 23 accidents occurred in Inner Mongolia and 18 in Sichuan.This does not necessarily mean that these provinces have had a bad safety performancecompared to their high coal output. If a greater tolerance for accidents can bring aboutmore output, we cannot be sure whether this is efficient or inefficient. To the best of ourknowledge, there is no research examining the efficiency of the Chinese coal mining industryby explicitly considering accidents and deaths. Our main contribution consists in computingsuch efficiency within a formal comprehensive framework.
The methodologies deployed for operations management (OM) research are numerousand include optimization, computational, and simulation models (Choi et al. 2016). Amongthem, data envelopment analysis (DEA), introduced byCharnes andCooper (1962), is widelyused to evaluate the performance of production units, or more strictly, decision-makingunits (DMUs) (Charnes et al. 1978). A wide range of variant models has been developed toaddress specific issues. These DEA model variants differ significantly in radial and orienta-tion properties as well as in economic interpretation. Generally, DEA models are classifiedinto four classes according to whether the improvement is radial or oriented: (1) radial andoriented model, (2) radial and non-oriented model, (3) non-radial and oriented model, and(4) non-radial and non-oriented model. Earlier DEAmodels are mainly radial, which requireadjustments of inputs/outputs to be proportional (radially). However, additional slacks maystill exist with radial models. To utilize information about slacks in identifying efficientDMUs, many non-radial models have been developed, including additive DEA (Charneset al. 1985), slacks-based measures (SBMs) (Tone 2001), and the directional distance func-
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tion (DFF) (Luenberger 1992; Chambers et al. 1996; Chung et al. 1997). In this work, weemploy the DFF approach to measure the production performance of coal mines in China.
This study fills an existing gap in the coal mine productivity literature and contributes tothe methodology of DFF modeling. The specific contributions of this study are threefold.First, accident deaths in coal mines are considered as an undesirable output when measuringthe efficiency of coal production. This consideration will offer fairer benchmarking andcomparisons. Second, a new approach to find a directional vector for the directional distancefunction is proposed. The proposed directional vector can exploit all the slacks of slack-basedmeasure (SBM) models. Third, two indexes, total factor humanitarian-production efficiencyand total factor safety efficiency, are defined based on the new directional distance functionto measure the efficiency of production and safety in Chinese coal mines.
The paper proceeds as follows: Sect. 2 presents the literature review, introducing mineefficiency studies applying DEA and the methodology of DFF models. Section 3 illustratesthe proposed DFF model, while Sect. 4 applies this approach to evaluate coal productionefficiency. Finally, conclusions as well as policy implications from this study are outlined inSect. 5.
2 Literature review
Although DEA is widely used to evaluate efficiency in various fields, such as thermal power,environmental impacts, etc., there are limited studies measuring coal or other mines’ produc-tive efficiency. Byrnes et al. (1984) employed the DEA method on a sample of Illinois stripmines and found that inefficiency primarily arises from deviations from optimal scales ofproduction. Byrnes et al. (1988) compared two competing methods, DEA and econometrictechniques, using a sample of US surface coal mines. The results showed that the formeris preferable to the latter when conducting composition analysis. Kulshreshtha and Parikh(2002) investigated Indian coal mines from 1985 to 1997; their DEA analysis showed thatthe productive efficiency of opencast mining is not higher than that of underground mining.Tsolas (2011) combined a bootstrapping approach with DEA to evaluate the environmentalperformance of Illinois strip mines and found significant inefficiency in the analyzed sample.Geissler et al. (2015) measured the performance of major global corporations engaged inphosphate rock mining with DEA methods, which showed that larger firms are not moreefficient than smaller ones. Wang et al. (2015) assessed the performance of Indian min-ing and metal companies using hybrid DEA and found that three companies, namely, theNational Mineral Development Corporation, Hindalco Industries Limited, and Coal India,always maintained the highest rankings. Besides DEA-based works, Choi (2015) built a for-mal optimization model to study the sustainable management of mining operations, in whichthe accidents followed a Poisson distribution. The results showed that the risk aversion ofthe mining company did not affect the choice of the accident reduction technology. In theexisting literature, to the best of our knowledge, only the study by Fang et al. (2009) con-sidered Chinese coal mines. Specifically, the authors compared Chinese and US coal mines’technical efficiency performance based on DEA, and found that the former is much lowerthan the latter in all indicators, including total technical efficiency, pure technical, and scaleefficiency.
Traditional radial DEA models, such as the CCR and BCC models, only seek maximiza-tion of output or minimization of inputs and cannot address undesirable outputs directly.To this aim, this study employs a directional distance function model, originally proposedby Luenberger (1992). Chung et al. (1997), Färe and Grosskopf (2006), and Färe et al.
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(2007) extended DFF models to deal with the problem of undesirable outputs. Their mod-els are widely used in environmental efficiency assessments involving pollution emissions.Recent examples include Lozano and Gutiérrez (2008), Kumar and Managi (2010), Wanget al. (2016), Song et al. (2016), Wu et al. (2017), and Shen et al. (2017). There are alsosome applications that consider accidents and safety breaches as undesirable outputs, mostlyfocusing on the transport industry, such as Weber and Weber (2004), Yu and Fan (2006), andPal and Mitra (2016).
Choosing a direction is the first step when using the directional distance function. Thiscan be done in many ways, as the existing literature shows. Following Chung et al. (1997),Lozano and Gutiérrez (2008) and Kumar and Managi (2010) took the observation of eachDMU as the directional vector. Weber and Weber (2004) adopted a unit move g � (1, 1) asthe vector direction, as per Färe and Grosskopf (2006). Wang et al. (2016) seemed to choosethe observation as the directional vector, but did not use it when DMUs move to the frontier.Shen et al. (2017) employed the aggregate input–output observation as the directional vectorfor all DMUs. In practice, different directional vectors will lead to different efficiency scores,and the vector choice is closely associatedwith the efficiency results. Although the directionalvector proposed byChung et al. (1997) is popular in the existing literature, it is not determinedby a definite rule, but is rather arbitrary. Many researchers claimed that using an observationas a direction would result in an overestimation of the efficiency value, as slacks would notbe considered (Fukuyama andWeber 2009; Zhou et al. 2013). To address this problem,Wanget al. (2016) further suggested the use of a non-radial DDF. To distinguish it from the non-radial DFF approach, they treated traditional DFF as the radial variant. However, due to thelack of selection of a direction vector, the non-radial DDF is no longer a direction distancefunction as defined by Chambers et al. (1996).
To deal with these problems, two mechanisms are frequently used. The first one is basedon economic principles, such as profit maximization, cost minimization, or achieving Nashequilibrium, etc. Zofio et al. (2013) proposed choosing a directional vector so that inefficientfirms can be projected to the profit maximization frontier, where information on prices isknown. Lee and Johnson (2015) identified a Nash equilibrium of an imperfectly competitivemarket when prices are endogenous; then, an improved direction toward such equilibriumwas offered. The second mechanism entails obtaining a direction along which some specificgoal, not cost minimization or profit maximization, can be achieved. Baek and Lee (2009)adopted a least-distance measure model to obtain the nearest benchmark, highlighting thatmoving along the proposed direction to the production frontier is the easiest way to improveefficiency. Färe et al. (2013, 2015) proposed a technique to find an endogenous directionvector for an inefficient DMU, along which its projection can exploit the slacks. Arabi et al.(2015) adopted the same strategy, where slacks or improvement potentials are computedthrough a DEA model. A simultaneous equation is then solved to get the final directionvector. Daraio and Simar (2016) provided a direction selection method that can accountfor the heterogeneity of DMUs and their contextual factors. Recently, the issue of directiondetermination has attracted increasing concern. In this respect, Wang et al. (2017) provideda comprehensive literature review.
Summarizing, the existing studies of coal production efficiency mainly applied traditionalCCR and BCC models without considering accident deaths. As an undesirable output, acci-dent deaths play a key role in equitable efficiency evaluations and comparisons. In this study,we try to fill these gaps and measure the productive efficiency of Chinese coal mines usinga DFF model, which provides an easy way to treat an undesirable output. In addition, mostprevious studies adopted value indicators such as earnings per share, operating revenue,
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and profit before tax. To avoid the influence of price fluctuations, here we employ a purelyquantitative indicator, that is, the amount of coal output.
3 Methodology
3.1 Undesirable outputs and the directional distance function
Let x be the input vector and y be the output vector. Thus, a multi-output technology with anundesirable output b can be expressed as follows:
T � {(x, y, b) : x can produce (y, b)} . (1)
Assume T satisfies certain axiomatic properties of the production theory, that is, inactivity isalways possible, finite inputs can only produce finite outputs, and inputs are freely disposable.This setting allows us to examine the considered technology within an axiomatic framework(Färe and Grosskopf 2006).
Two further axioms associatedwith undesirable outputs need be satisfied (Färe et al. 2007):
(x, y, b) ∈ T (x) and 0 ≤ θ ≤ 1 imply (x, θy, θb) ∈ T (x). (2)
(2) means that if x produces the output combination (y, b), then we can decrease such outputcombination by a certain proportion θ , which is known as weak disposability. According tothis principle, reducing undesirable outputs only is unfeasible. Note that if a single desirableoutput is involved, this proportion is not needed, or, reducing the desirable output costlesslyis feasible.
(x, y, b) ∈ T (x) and b � 0 imply y � 0 (3)
This means that if we produce a desirable output, then the bad output also has to be produced,which is called null-jointness. If we want to eliminate the undesirable output totally, the onlyway is to stop production.
Many methods can be used to integrate the assumptions in (2) and (3) into the representa-tion of a technology. In what follows, we use a nonparametric approach to express technologyT . Assume there are k � 1, . . . , K observations, and each observation has m � 1, . . . , Mdesirable outputs, j � 1, . . . , J undesirable outputs, and n � 1, . . . , N inputs. The technol-ogy T can be described as follows:
T �
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨
⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
(ym, b j , xn) :K∑
k�1zk ykm ≥ ym, m � 1, . . . , M,
K∑
k�1zkbk j � b j , j � 1, . . . , J,
K∑
k�1zk xkn ≤ xn, n � 1, . . . , N
(4)
It can be proved that (4) satisfies weak disposability and null-jointness (Färe and Grosskopf2006). Once the technology T is obtained, several DEA variants can be presented basedon it, such as the SBM models, the DDF models, etc. The DDF, first defined by Chamberset al. (1996) as an extension of Luenberger (1992), is a DEA method for calculating theinefficiency scores along a chosen direction. Obviously, the DDF does not require that inputscontract and outputs expand in the same proportion, thus categorizing it as a non-radial DEA
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model. Chung et al. (1997) employed this method to measure productivity while consideringundesirable outputs, with an approach closely linked to our work. Themain idea is to increasedesirable outputs and decrease undesirable outputs under a series of axiomatic assumptions,such as joint weak disposability of desirable outputs and undesirable outputs. For observation0, the DDF model by Chung et al. (1997) is as follows:
D(x0n, b0 j , y0m
) � maxβ
s.t.K∑
k�1zk ykm ≥ y0m + βy0m, m � 1, . . . , M,
K∑
k�1zkbk j � b0 j − βb0 j , j � 1, . . . , J,
K∑
k�1zk xkn ≤ x0n − βx0n, n � 1, . . . , N
(5)
where the chosen directional vector is the observation (x0, b0, y0), with the advantage of theunit invariant. Nonetheless, according to Fukuyama and Weber (2009), this may result inefficiency overestimation.
3.2 Finding a direction based on SBM
To overcome the overestimation problem, we suggested an approach to find a directionfor the DDF based on SBM. Bogetoft and Otto (2011) argued that it is natural to select adirection in accordance with the opportunity of improvement. If there are more improvementopportunities in a certain input/output factor than in others, then the direction should leanmore toward this input/output factor than toward others. The SBMmethod proposed by Tone(2001) can provide us with such improvement opportunities, which represent slacks, whilecalculating efficiency. We intend to combine the SBM and the DDF models to get a novelmodel, which we call the DDF–SBM model. As a first step, we solve an SBM model withundesirable output for the specific observation 0:
ρ∗ � min1− 1
N
∑Nn�1
sxnx0n
1+ 1M+J
(∑M
m�1sym
y0m+∑J
j�1
sbjb0 j
)
s.t.K∑
k�1zk ykm � y0m + sym, m � 1, . . . , M,
K∑
k�1zkbk j � b0 j − sbj , j � 1, . . . , J,
K∑
k�1zk xkn � x0n − sxn , n � 1, . . . , N
(6)
Through (6), the efficiencymeasure ρ∗ and the slacks vector s � (sym, sbj , sxn ) can be obtained,
the latter being useful for calculating the direction in the next step.Suppose the direction vector to be found is g0 � (gy0m, gb0 j , g
x0n). If g0 is known, the
objective value β∗ can be calculated from the following the DDF model:
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β∗ � maxβ
s.t.K∑
k�1zk ykm ≥ y0m + βgy0m, m � 1, . . . , M,
K∑
k�1zkbk j � b0m − βgb0m, j � 1, . . . , J,
K∑
k�1zk xkn ≤ x0m − βgx0n, n � 1, . . . , N
(7)
Nonetheless, g0 is unknown in our case. To obtain the direction vector, we set up thefollowing system of simultaneous equations to make the direction reflect the improvementopportunity:
where the known variables include sym , sbj , and sxn , while the unknown variables include theefficiency measure β and the M + J + N + 1 components of the direction vector g0 However,we only have M + J + N equations, which is not enough to obtain a unique solution. Weimpose exogenous constraints on the system of Eq. (8), following Färe et al. (2013):
∑
m∈E
(gy0m
/ykm
)+
∑
j∈F
(gb0 j
/bkj
)+
∑
n∈G
(gx0n
/xkn
) � M ′ + J ′ + N ′ (9)
where E � {m|sym > 0}, F � { j |sbj > 0}, and G � {n|sxn > 0}, respectively. M ′, J ′, and N ′are the numbers of elements in E , F , andG, respectively. In the above system of simultaneousequations, sub-simultaneous equations in (8) determine the direction of the direction vector,while Eq. (9) is associated with its length. In fact, the length is as important as the directionin measuring the efficiency of a DMU. According to the translation property suggested byFäre and Grosskopf (2006), the DDF is homogeneous of degree −1 in the direction vector,which states that, if the length of the directional vector is multiplied by a factor, then theDDF is multiplied by a power of −1 of this factor. Equation (9) ensures that the length ofthe direction vector is constrained by the length of the observation. Some other DDFs cansatisfy (9), such as the one in Chung et al. (1997).
Moreover, the following situation should not be ignored. If E , F , and G are all emptysets for a DMU, then this DMU lies on the frontier, and the direction vector can be assignedany value. According to elementary algebra, the simultaneous Eqs. (8) and (9) can easilybe verified as yielding a unique solution. Thus, we can find an efficiency measure β ′ and adirection g′
0 to exploit the improvement opportunity calculated from the slacks. Since thedirectional vector is selected according to the results of the SBM model, the present modelcan be called the DDF–SBM model.
3.3 Further discussion of the DDF–SBM model
As we have seen above, the efficiency measure β ′ is not actually calculated using the DDFmodel, but through a combination of the SBM model and simultaneous equations. The fol-lowing proposition shows that using the DDF model (7) along this direction provides thesame efficiency measure.
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Table 1 Properties comparison across different models
Unit invariance Overestimationproblem
Reflection of improvementopportunity
Färe et al. (2013) × × √Chung et al. (1997)
√ √ ×SBM–DDF
√ × √
Proposition 1 The objective value β∗ obtained from the DDF model (7) along the directionvector g′
0 is equal to the efficiency measure β ′ obtained from the simultaneous equationsystem consisting of (8) and (9).
Proof Suppose β∗ � β ′, then either β∗ > β ′ or β∗ < β ′ holds. If β∗ > β ′, we multiplythe direction vector g′
0 by β∗ to get the excess value and the short value, which can act asfeasible slacks in the SBM model, but are bigger than s � (sym, sbj , s
xn ). This means that
s � (sym, sbj , sxn ) is not the optimal solution of the SBMmodel. If β∗ < β ′, then β ′ is feasible
for the DDF model (7) because s � (sym, sbj , sxn ) is the optimal solution (also a feasible
solution) for the SBM model (6). This implies that β∗ is not the optimal value of the DDF(7).
TheDDF–SBMmodel is able tomaintain unit invariance, which is an advantage comparedwith the model of Färe et al. (2013). Two factors contribute toward this desirable property.First, the unit of the directional vector is identical to that of the corresponding input oroutput, which makes the measure independent of unit, according to Simar and Vanhems(2012). Second, the constraint imposed on the directional vector (9) is adopted according tothe relative value, not the absolute value, making it immune to unit changes. Table 1 comparesthe properties of the SBM–DDF model with those of other related models.
3.4 Performance measure and directional contribution
Similarly to the literature focused on environment impacts, such as Li and Hu (2012), inthis study a total factor humanitarian-production efficiency (TFHPE) is defined, reflectingnot only general inputs or outputs, but also undesirable outputs, that is, coal mine accidentdeaths. β∗ in (7) measures the distance to the frontier and provides a basis for inefficiencyindex. The higher β∗, the lower the efficiency. Thus, as an efficiency index, TFHPE is definedas follows:
T FH PE � 1/(1 + β∗) (10)
To reflect the safety situation of coal mine exclusively, we define a total factor safetyefficiency (TFSE) as well, which can be measured as the ratio of target deaths to total deaths:
T FSE � Target deaths
Actual deaths� Actual deaths − slack of deaths
Actual deaths(11)
Based on the work by Asmild et al. (2016), the directional contribution is defined as apolar angle in p hyperspherical coordinates. Let d � (d1, . . . , dp) be the direction vector; adirectional contribution of given dimension i can be defined as:
θ � arccos(di
/‖d‖) , where ‖d‖ �√
d21 + · · · + d2p (12)
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Table 2 Descriptive statistics forthe input and output variables
Variables Mean SD CV Min Max
Inputs
Labor 1.184 1.773 1.497 0.021 12.373
Assets 2.330 2.020 0.867 0.218 9.967
Outputs
Coal 1.728 2.339 1.353 0.061 10.419
Deaths 3.436 4.207 1.224 0.200 36.000
SD denotes standard deviation,while CV stands for coefficient ofvariation
A small polar angle for the dimension i means that this dimension makes a great con-tribution in choosing the direction, which prompts the DMU to pay more attention to theadjustment factor i . As seen in (8), each slack is proportional to the corresponding compo-nent of the direction vector. Slacks play different roles in constructing the direction. Thus,the bigger the slack, the higher the effect it has in determining the direction and the smallerthe polar angle. Actually, it is reasonable that the slacks from the SBM model determinethe direction vector. Greater slack implies more significant improvement opportunities; moreeffort should be then made in this direction to catch up with competitors as soon as possible.
4 Empirical study
4.1 Data and sources
In this section, we used province-level data from 2007 to 2014 in mainland China.Considering that not every province has abundant coal resources, we only focused on18 provinces, namely: Hebei, Shanxi, Neimenggu, Liaoning, Jilin, Heilongjiang, Anhui,Jiangxi, Henan, Hubei, Hunan, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu,and Xinjiang. The number of deaths occurred in these provinces is 4432, account-ing for 97.9% of all deaths over the observation period. Moreover, some provincessuch as Shandong, Fujian, Ningxia, and Guangxi, are excluded for the lack of acci-dent deaths. The number deaths reported for these provinces is only 49, that is, 1% oftotal deaths. In practice, details about China’s coal mine deaths are hard to collect andcan only be obtained through the Internet. Even the selected provinces contained miss-ing data in some years. Therefore, we deal with an unbalanced panel dataset. China’sIndustrial Enterprises Statistical Yearbooks provide most input data (capital and labor)for the coal sector at the provincial level. Capital input is measured by total assets(hundred billion yuan), comprising fixed and liquid assets. Labor input is measuredby annual average employment (hundred thousand persons), where the data for 2012and 2013 are missing. To complement these data, we first collected the national aver-age employment in the coal sector in each year, and then allocated this populationacross provinces according to the proportions of 2012 and 2013. The desirable out-put is the coal production amount for each province (hundred million tons), which isretrieved from China Energy Statistics Yearbooks. The undesirable output is representedby accident deaths (in tens of persons) in each province, reflecting safety productionconditions. The data was collected from web documents of the state administration forproduction safety supervision and management. The descriptive statistics are reported inTable 2.
Fig. 1 Scatter points and average of annual TFHPE for 18 main coal-producing provinces
4.2 Efficiency calculation results
The TFHPE for 18 main coal-producing provinces calculated by the DDF–SBMmethod arepresented in Fig. 1. According to TFHPE, there is no obvious evidence that coal mines pro-gressed dramatically in production efficiency; instead, production efficiency has a downwardtrend over time. The average TFHPE across sample provinces is 0.717 in 2014, much lowerthan in 2007, 0.851. Actually, the average TFHPE dropped year by year before 2014, with adecrease rate of 4% per year. Looking at the number of efficient provinces, nine provinceswere on the practice frontier in 2007. Over time, the number of efficient provinces decreaseduntil 2013, when noDMUwas on the practice frontier. In 2014, the average TFHPE of sampleprovinces began to reverse its sliding trend with a positive growth rate of 7.9% and threeprovinces stood on the practice frontier again. However, TFHPE in 2014 was still lower thanthe level in 2011. The average of all observable sample provinces within these 8 years was0.7516, meaning that 42.86% of production potential remains unexploited in Chinese coalmines, according to (10).
The TFSE calculated by using (11) for 18 main coal-producing provinces is presentedin Fig. 2. Similarly to the TFHPE, no significant improvement signs in coal mine safetyefficiency emerge. Compared with TFHPE, TFSE is more dispersed and more disorderedalong the time axis. The average TFSE in 2008 was 0.582, the highest value during these8 years. The lowest average TFSE was 0.404 in 2010. Both the beginning and end values fellbetween above two numbers, implying that the overall coal mine safety efficiency fluctuated
Fig. 2 Scatter points and average of TFSE for 18 main coal-producing provinces
between 2007 and 2014. The average TFSE for 18 provinces over 8 years was 0.504; in otherwords, half of the deaths could be avoided if safety management achieved full efficiency.Therefore, safety efficiency in Chinese coal mines was low, and the situation has deterioratedover recent years. Nevertheless, some DMUs exhibited a TFSE of 1 every year. Thus, it ispossible for the inefficient DMUs to improve their safety situation through learning frombenchmarking DMUs.
Figure 3 presents the TFHPE and TFSE for 18 provinces using a Tukey Boxplot, whichis clearer in showing the provincial differences. Here, the median is considered to repre-sent the efficiency scores of 8 years. Jiangxi, Hunan, and Neimenggu are the top three interms of median TFHPE, meaning that they are the most efficient provinces in humanitarianproduction. Specifically, Neimenggu’s median and first quintile are both 1, implying thatmore than a half of TFHPE scores are equal to 1. Hunan stands on the efficient frontierthree times, in 2007, 2008, and 2014, which makes it relatively efficient. Jiangxi has onlyone score of 1, in 2011, but it did not perform too badly in other years, with most scoresaround 0.8 or 0.9. TFHPE scores for Hebei, Henan, and Liaoning are low. These are big,high-population provinces in northern China, where the low cost of labor perhaps worsenshumanitarian production performance. Regarding safety efficiency (TFSE), most provinceshave a more decentralized distribution of scores, such as Heilongjiang, Henan, Jilin, Sichuan,and Xinjiang, implying that their safety production fluctuates at a great extent throughoutthese years.
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.2 .4 .6 .8 1
TFHPPI
Yunnan
Xinjiang
Sichuan
Shanxi
Shaanxi
Neimenggu
Liaoning
Jilin
Jiangxi
Hunan
Hubei
Henan
Heilongjiang
Hebei
Guizhou
Gansu
Chongqing
Anhui
0 .2 .4 .6 .8 1
TFSE
Yunnan
Xinjiang
Sichuan
Shanxi
Shaanxi
Neimenggu
Liaoning
Jilin
Jiangxi
Hunan
Hubei
Henan
Heilongjiang
Hebei
Guizhou
Gansu
Chongqing
Anhui
Fig. 3 Technology efficiency and safety efficiency by provinces
4.3 Directional contribution calculation
Directional contribution can be used to determine the degree of importance of specific factorsin performance improvement. We primarily consider mine accident deaths and then detecttheir role in the humanitarian-production performance index. The directional contributionresults are shown in Table 3. The missing values indicate either lack of data, or full TFHPE,not having potential to exploit and thus not needing a directional vector or directional con-tribution. In Table 3, the line of the Qinling Mountains to Huaihe River is used to divide thewhole country into North and South to further survey the geographical character of the direc-tional contribution. For each province, the average value of the directional contribution iscalculated. As per the above definition, the directional contribution is determined by the polarangle. A large angle can be interpreted as a low correlation between this specific dimensionand the overall directional vector. Therefore, an increasing directional contribution impliesa decreasing correlation between accident deaths and the directional vector. The differencebetween North and South China is big. The directional contribution in the North is generallyhigher than that in the South. In North China, only two out of eight provinces’ average direc-tional contributions are less than 0.5, Jilin and Shaanxi. The latter extends across North andSouth. In contrast, in South China, most average directional contributions are less than 0.5,except for Anhui and Sichuan. Anhui is also across North and South. Therefore, to promotethe TFHPE, improving safety conditions is more important for southern provinces than fornorthern ones. It is important tomention that there aremanydirectional contributions of 1.571.This is the greatest value in Table 3, mostly occurring in the North. Because 1.571 � π/2,there is an angle of 90° between the directional vector and the deaths component. In thesecases, the slacks for accident deaths have no effect in determining the directional vector.
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Tabl
e3Directio
nalcon
tributionun
dertheDDF–
SBM
mod
el
2007
2008
2009
2010
2011
2012
2013
2014
Regional-
average
North
China
Hebei
0.63
60.34
71.57
11.50
11.51
71.34
91.15
3
Shanxi
0.04
60.60
40.82
41.48
31.44
10.88
0
Neimengg
u0.05
30.06
81.55
40.55
8
Liaon
ing
0.11
40.31
30.45
90.65
10.64
30.70
81.37
10.60
8
Jilin
0.01
90.03
20
0.01
11.57
11.02
30.44
3
Heilong
jiang
1.05
91.57
11.07
30.17
90.46
50.42
90.31
70.72
8
Henan
0.30
70.61
30.52
91.55
41.57
11.56
01.02
2
Shaanx
i0
0.03
00.08
80.41
11.15
31.04
40.58
90.47
4
SouthChina
Anh
ui1.57
11.57
11.57
11.48
41.54
91.54
9
Jiangx
i0.02
10.03
90
0.02
70
0.02
40.90
50.14
5
Hub
ei0.10
50
0.03
50.00
40.00
40
0.05
20.10
40.03
8
Hun
an0
0.00
60.00
50
00.00
2
Cho
ngqing
0.00
50.08
70.14
40.03
50.17
90.56
11.13
60.55
30.33
8
Sichuan
00.03
50.11
91.57
10.76
20.92
70.56
9
Guizhou
0.00
90.00
10.04
00.02
40.06
30.39
10.45
80.80
50.22
4
Yun
nan
00
00.03
20.04
00.07
70.83
10.14
0
Gansu
0.00
50.06
00.04
80.37
50.24
81.17
10.31
8
Xinjia
ng0
00
00
0.10
50.01
7
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00.51
1.52
2.53
3.54
4.55
Labo
ur p
rodu
ctiv
ity
TFHPPI
Fig. 4 Scatter points of labor productivity and TFHPE
For nearly all provinces, the directional contribution of mine accident deaths shows anupward trend from 2007 to 2014, except for Heilongjiang, Anhui, Hubei, and Hunan. Notethat although coal safety efficiency shown in Fig. 2 has not improved significantly, the rolethat accident deaths play in determining the directional vector declines constantly. This alsomeans that safety management is not as important as before in promoting TFHPE. In fact,these two indicators are measuring different contents. It is not surprising that one provincewith low safety efficiency does not take safety management as a priority, because otherinput/output factors may have lower performances and draw more attention. From (11),TFSE is only associated with actual deaths and their corresponding slacks. However, as per(12), the directional contribution of accident deaths depends on the ratio of deaths slacks toother factor slacks.
4.4 The comparison between total factor and single-factor efficiency indicators
In practice, the labor productivity index is used frequently to measure the efficiency of coalproduction. We calculate the ratio of coal output to labor employed for each province andcompare it with our TFHPE in Fig. 4. It can be seen that there is a roughly positive correla-tion between the two indexes, meaning that labor productivity can partly reflect productionefficiency, and that our method is robust to some degree. There are observations with incon-sistencies between the two indexes, as some observations with high labor productivity have alow TFHPE score. Xinjiang’s coal output per capita was 2.5 thousand tons in 2012, which ishigher than 93% of all observations. Looking at the humanitarian-production performance,Xinjiang performs quite badly in 2012, with a score below 95% of all observations. Thecontradiction stems from the different factors considered in each method. The DDF–SBMmodel takes four factors into account, whereas the general labor productivity method onlyconsiders labor and output. If assets instead of labor are considered, we can compare assetproductivity with TFHPE in Fig. 5. Here, a more significant positive correlation can be found.
4.5 Results discussion
As the largest coal producer, China contributes to nearly half of the global output. How-ever, due to poor working conditions, such output is accompanied by a large number ofaccidents and deaths, which we define as an undesirable output. When evaluating coalmines’ productivity, it is necessary to take this undesirable output into account. This study
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0
1
2
3
4
5
6
7
asse
t pro
duct
ivity
TFHPPI
Fig. 5 Scatter points of asset productivity and TFHPE
explicitly considered it by proposing a DDF–SBM model to assess coal mine productionconditions in China. The results show no significant progress in production efficiencyin China, which may be attributed to the structure of the coal market. Over the period2007–2014, the coal price remained at a relatively high level in the country with somefluctuations: for example, the price of Datong mixed coal was above 500 yuan per tonover these years. During this period, China’s other economic sectors, such as construc-tion, automobile manufacturing, and other durable consumer goods, maintained prosperity,which pushed up coal prices. In this situation, China’s coal companies could achieve prof-its without technological investment. Many small companies with poor technology andequipment can survive, and big companies with advanced technology do not have a compet-itive advantage, resulting in a lower concentration of China’s coal industry as compared toUSA, Russia, and India. A dependence on the market rather than on technological progresscould be an explanation for the empirical finding of technology stagnation in China’s coalmines.
Traditionally, China has adopted the death rate per million tons as a measure of safetyefficiency. In 2016, the mortality rate per million tons was 0.156, down by 3.7% with respectto the previous year. In 2007, the corresponding figure was 1.49 per million tons. This indi-cator shows that China has made great progress in dealing with mine accidents. However,the death rate per million tons is a macro performance index and cannot reflect practical safemanagement levels. Recently, benchmarking analysis is used by more and more regulationauthorities (Farsi et al. 2005, 2006; Choi 2016). If this idea is accepted, a huge improve-ment potential could be found. From 2007 to 2014, the safety efficiency of Chinese coalmines remained at a very low level, about 0.5, meaning that half of the deaths could beavoided in China. For example, in 2014 a total of 931 coal workers died, and the averagesafety efficiency was about 0.54. In this case, at least 425 workers could have been savedif all inefficient enterprises had promoted their safety management level to the benchmarklevel. Overall, China’s coal safety situation is not as optimistic as indicated by the trend indeath rate per million tons, and coal mine companies’ safety management has a long way togo.
Nevertheless, as the directional contribution analysis shows, it becomes increasinglydifficult to raise the TFHPE by only reducing accident deaths over time. Adjusting otherfactors, such as reducing labor or assets and expanding coal output, is increasingly effec-tive in promoting production efficiency. This will involve a tradeoff between safety and
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efficiency. Does the coal company or the regulator need to continue highlight safety asbefore? Life is an unalienable right for all human beings. Safe production is the mostdirect reflection of respect for the right to life. With improvements in social civilization,securing safe production is also becoming an increasingly important task for China’s gov-ernment. In implementing coal mine supervision policies, safe production should be stressedand strengthened. When safety and other issues conflict, safety issues must be given thepriority. For coal mine enterprises, safety inputs cannot be ignored in order to improve effi-ciency.
5 Concluding remarks
This study represents the first assessment of the total factor humanitarian-production effi-ciency and safety efficiency of coal mines in China to include the consideration of accidentdeaths. The study proposed a DDF variant, called the DDF–SBMmodel, and proposed a newapproach to selecting the directional vector that exploits the slacks of the SBM model. Thenew model overcomes overestimation problems and maintains the unit-invariance property.With this model, the production and safety efficiency of coal mines across 18 provinces wereexplored, together with the directional distribution of accident deaths. The empirical resultsindicated that Chinese coal mines have poor total factor humanitarian-production efficiencywith a downward trend, and nearly half of the production potential remained unexploited overthese years. Similarly to the total factor production efficiency, coal mines’ safety efficiencyis also low in China without any sign of improvement. If all the coal mines operate at fullyefficient levels in safety management, half of the accident deaths can be avoided, which isequal to the lives of 425 workers in 2014. Directional contributions of accident deaths werecalculated to explore their role in determining the directional vector. These values showed thatsouthern provinces should pay more attention to accident deaths than northern ones, whilethe role that accident deaths play declined constantly for nearly all provinces. As time passes,the other input/output factors become more important in promoting total factor efficiency,which brings a tradeoff between safety and efficiency.
This study showed that the real safety situation is not as optimistic as the official datareleased indicate. Disastrous accidents in coal mines often happen even today. In fact, miningfor coal is still relatively dangerous work in China. There is a long way to go to improve coalmine enterprises’ safety management. Specifically, the following recommendations shouldbe considered by relevant government and coal companies.
The number one priority is to establish effective prevention mechanisms. Gas, waterdamage, and fire are major disasters in Chinese coal mines, the deaths from which cover ashare of more than 90%. More in detail, old state-owned and small mines present relativelyworse safety conditions, and are thus more vulnerable to accidents. The prevention of suchaccidents is a top priority to decrease the number of deaths. In this respect, local governmentsand regulators should identify the key potential disasters by inspecting the actual conditionsof each mine to formulate targeted measures.
Moreover, it is urgent to establish long lasting and effective fund input mechanisms forcoal mine safety. On the one hand, the government should increase the investments in coalmine safety, and the fund management ought to be strengthened furtherly. On the otherhand, it is necessary to support and supervise coal companies towards more investmentsin safety facilities and equipment. Local governments should also supervise and urge themines that are prone to accidents to upgrade. Then, the ones still failing to meet the safety
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requirement should be promptly shut down. In particular, with the perspective of cutting theexcess capacity in the coal industry, coal mines with poor safety conditions should limit theirproduction.
Finally, strengthening safety training and education of coal mines employees must notbe neglected. Mining should not be regarded as a simple and unskilled work. Vocationalqualification systems are needed to guarantee employees’ safety technical quality. In addi-tion, Chinese mine enterprises should develop exchanges with mine companies in developedcountries, in order to acquire their experience and the lessons learned.
Acknowledgements We would like to show our appreciation for the support of the Humanities and SocialScience Research of the Ministry of Education Youth Project of China (No. 16YJCZH155), the Program forNew Century Excellent Talents in University (No. NCET-12-0595), National Natural Science Foundation ofChina (No. 71171001), Key Foundation of Natural Science for Colleges and Universities in Anhui, China(No. KJ2011A001), Soft Science Foundation of Anhui, China (No. 12020503063), and Key Foundation ofNational Research in Statistics of China (No. 2011LZ023), Humanities and Social Science Research Projectof Education Department in Liaoning, China (No. LN2017QN001).
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