Performance assessment of mining operations using

Resources Policy 36 (2011) 159–167

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Performance assessment of mining operations using nonparametric production analysis: A bootstrapping approach in DEA Ioannis E. Tsolas n National Technical University of Athens, School of Applied Mathematics and Physics, 9 Iroon Polytechniou, Zografou Campus, Athens 157 80, Greece

a r t i c l e in f o

abstract

Article history: Received 29 August 2008 Received in revised form 5 October 2010 Accepted 5 October 2010 Available online 27 October 2010

This paper presents a Data Envelopment Analysis (DEA) model combined with bootstrapping to assess performance in mining operations. Since DEA-type indicators based on nonparametric production analysis are simply point estimates without any standard error, we provide a methodology to assess the performance of strip mining operations by means of a DEA bootstrapping approach. This methodology is applied to a sample of fifteen Illinois strip coal mines using publicly available data (Thompson et al., 1995). The applied approach uses a mixed mine environmental performance indicator (MMEPI) that is derived by means of a VRS DEA environmental technology treating overburden as an undesirable output under the weak disposability assumption, and we compare this measure with a traditional output-oriented mine performance indicator (MPI) omitting overburden. Although omitting undesirable output results in biased performance estimates, these findings are based on sample specific results and indicate this bias is not statistically significant. The confidence intervals derived by the bootstrapping of the proposed MMEPI point estimates indicate that significant inefficiency has taken place in the analyzed sample of Illinois strip mines. & 2010 Elsevier Ltd. All rights reserved.

JEL classification: C14 C15 Keywords: Data Envelopment Analysis (DEA) Bootstrapping Coal mining Environmental effects Illinois

Introduction Pursuing sustainable development is becoming increasingly more important for the mining industry and mining firms should be able to measure their progress towards sustainability. Sustainable production processes are needed now more than ever and means for assessing coal producers within an environmental sustainable process is key in terms of subsidies, industry regulations and future policy recommendations and analysis. There is growing recognition of the relationship between energy subsidies and sustainable development. Economic development, social welfare, and environmental protection form the three pillars of sustainable development, but the priority individual governments place on each varies greatly based on various factors such as the stage of development, land use patterns, and political factors. In the least-developed countries, emphasis is usually placed on improving living conditions, though the most developed countries put more emphasis on the environment. The removal or reform of energy subsidies, especially those that encourage fossil fuel consumption, in combination with other policy initiatives, could play a significant role in some countries in steering their development onto a more sustainable path (United Nations Environment Programme and the International Energy Agency, 2001).

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0301-4207/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.resourpol.2010.10.003

Environmental regulations may have differential effects for a firm’s profitability (i.e. adverse effects) versus social welfare (i.e. important benefits concerning the living standards in local communities). In the case of the U.S. mining industry, companies have been forced to retrofit or renovate installations or leave the market. Moreover, increasing operational costs have also affected their international competitiveness, while employment levels have fallen substantially, and local economies have borne part of this cost. Environmental regulations have also brought important benefits such as better air and water quality and reduced health and environmental risks. It should be noted that emphasis is given to the trade-offs (i.e. gains against costs) in environmental policymaking and the difficulties in measuring these trade-offs and in making rationally optimal decisions about the appropriate levels of pollution control and environmental protection (Gana, 1999). In addition to financial and economic considerations, the firm’s decision makers must also take into account environmental and social considerations. Therefore, the traditional measurements of productivity have to be expanded, and efficiency indicators must be added to enterprise management information systems. These indicators should reflect the status of the production system in financial, social, and environmental perspectives (Tolentino, 2000). At the mine level, the contribution to sustainable development can be monitored by aggregate performance indicators (Tsolas and Patmanidou, 2003, 2004). The existing approaches for constructing aggregated performance indicators can be divided into two categories: namely, the indirect and the direct approach. In the

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indirect approach, the key sub-indicators are first identified and are then normalized and integrated into a composite indicator by means of some weighting and aggregating techniques. In the direct approach, an aggregated environmental performance indicator is directly obtained from the observation data set (i.e. quantities of the inputs and outputs of the system studied) using a nonparametric approach called Data Envelopment Analysis (DEA) (Zhou et al., 2007). DEA is an aggregation method in the sense that all relevant information taken into account (i.e. production inputs and outputs, pollutants, financial quantities) is aggregated using self-defined weighting coefficients to produce an aggregate quantity (i.e. indicator), conventionally taken as one for units that are efficient, and less than one for nonefficient units (Tyteca, 1996; Olsthoorn et al., 2001; Berkhout et al., 2001). A further class of performance indicators, the aggregate environmental performance indicators (i.e. indicators used for evaluating the economic and environmental efficiency of a mine in achieving environmental objectives (Tsolas and Patmanidou, 2003, 2004; Tsolas et al., 2007), can be derived by incorporating environmental data into the conventional input/output data set. The environmental performance indicators derived by means of DEA allow studying of the improvement of environmental performance with time comparing a given firm or whole industrial sectors among themselves (see also Tyteca, 1996). This paper proposes a Data Envelopment Analysis (DEA) model for assessing the performance of strip mines also taking into account environmental effects (i.e. undesirable outputs). Moreover, a state-of-the-art technique, the bootstrap (Simar and Wilson, 1998, 2000b) is applied to improve the traditional nonparametric approach in efficiency analysis based on DEA, using DEA environmental modeling principles. The application of the proposed model concerns a sample of fifteen Illinois strip mines. This study complements existing research in three ways: 1. it appears to be the first paper applying DEA on a sample of U.S. strip coal mines for deriving environmental performance indicators; 2. it examines whether omitting undesirable outputs results in biased estimates of conventional technical efficiency indicators; and 3. unlike most of the previous relevant DEA studies in mining, which have lacked estimates of the uncertainties surrounding individual efficiencies, it follows a bootstrapping approach. The rest of the paper is organized as follows: Section 2 presents a survey of the literature related to DEA environmental modeling principles and DEA applications in mining; Section 3 provides the proposed methodology; Section 4 describes the data set used; Section 5 presents the results; and Section 6 draws the conclusions of the paper.

Literature review A variety of DEA-based environmental performance indicators that adjust conventional measures of technical efficiency have been proposed in the relevant literature. The development of these indicators might be the result of the worldwide concern on environmental issues and sustainable development, as well as the ability of DEA-based environmental performance models in providing standardized and aggregated environmental performance indicators (Zhou et al., 2008a). DEA is used to model environmental performance at the micro (e.g. Tyteca, 1996, 1997; Hernandez-Sancho et al., 2000; Bevilacqua and Braglia, 2002) and macro level (e.g. Zaim and Taskin, 2000a,b;

¨ et al., 2004; Zofio and Prieto, 2001; Ramanathan, 2002, 2005; Fare Zhou et al., 2006, 2008b). Most studies about the application of DEA to environmental performance measurement follow the concept of radial efficiency measures. Examples of other DEA-type models for measuring environmental efficiency are those of hyperbolic graph measure ¨ et al., 1989), directional distance function (Chung et al., 1997), (Fare slacks-based model (Zhou et al., 2006), and non-radial models (Zhou et al., 2007). For a useful survey of DEA in energy and environmental studies, see Zhou et al. (2008a). DEA-type models that have been introduced for the measurement of ecological efficiency are the extended additive model (Dyckhoff and Allen, 2001), and variants of other radial DEA models based on the assumption of strong disposability of inputs (Korhonen and Luptacik, 2004). In the DEA framework, the approaches for incorporating undesirable outputs in DEA models are classified as indirect and direct (Scheel, 2001). Indirect approaches transform the values of the undesirable outputs by a monotone decreasing function (f) such that the transformed data can be treated as ‘normal’ desirable output. The most acceptable of such transformations for un undesirable output (w) is the so-called additive inverse f(w)¼ w, the translation f(w)¼  w+c, where c is the translation vector, used by Scheel (2001) and Seiford and Zhu (2002), and the multiplicative inverse: f(w)¼1/w used, e.g. by Lovell et al. (1995). For reviews on these transformations, see Scheel (2001) and Liu et al. (2010). Direct approaches use the original undesirable output data in the input or the output side of the DEA. It should be noted that the specific treatment of undesirable outputs as either inputs or outputs has attracted considerable debate in this literature. Some authors (e.g. Dyckhoff and Allen, 2001; Bevilacqua and Braglia, 2002; Tsolas and Manoliadis, 2003; Korhonen and Luptacik, 2004; Tsolas, 2005) treat undesirable output as inputs, because both undesirable outputs and traditional inputs incur costs for firms; moreover, firms generally try to reduce the consumption of inputs and the generation of undesirable outputs. However, other authors have argued that undesirable outputs are outputs and hence should be modeled as such ‘normal’ outputs (Scheel, 2001; Lovell et al., 1995). Daraio and Simar (2005) argue that models based on a one-stage ¨ et al., 1989; Fare ¨ et al., 1994), including approach (see also Fare variables (i.e. factors) that are detrimental (i.e. damaging, unfavorable) to efficiency, can be used if these variables can be considered as free disposal (inputs) and their role on the production process is known a priori. The property of weak disposability of undesirable outputs has been suggested and used by some authors ¨ et al., 1989, 1996; Chung et al., 1997; Tyteca, 1996, 1997; (Fare Zofio and Prieto, 2001; Zhou et al., 2006, 2007) as another alternative for treating the undesirable outputs. Weak disposability generally means it is possible to reduce undesirable outputs by decreasing the level of production activity (Kuosmanen, 2005). However, it should be noted that in some cases, it may be impossible to reduce the undesirable outputs further since a minimal threshold value may be necessary to produce any desirable outputs (Scheel, 2001). In mining, DEA applications concern the measurement of productive efficiency (Byrnes et al., 1984, 1988), the derivation of performance metrics such as: DEA profit ratios for a sample of Illinois strip coal mines (Thompson et al., 1995), Malmquist index for Indian coal mines (Kulshreshtha and Parikh, 2002), and aggregate environmental performance indicators for the South Field lignite mine of Greek Public Power Corporation (GPPC) (Tsolas and Patmanidou, 2003, 2004; Tsolas et al., 2007). Byrnes et al. (1984) applied DEA to a sample of Illinois strip coal mines to disaggregate the technical efficiency into purely technical efficiency, scale efficiency, and input congestion. Byrnes et al.

I.E. Tsolas / Resources Policy 36 (2011) 159–167

(1988) compared the abilities of DEA and statistical regression to shed light on the union/non-union productivity differentials using two samples of U.S. surface coal mines. Thompson et al. (1995) reformulated the data set of Byrnes et al. (1984) and applied DEA to derive profit ratios. Kulshreshtha and Parikh (2002) used DEA to derive a Malmquist index for decomposing total factor productivity growth in Indian coal mines into technical advancements (i.e. the improvement of production possibilities through the employment of new technology) and efficiency improvement components (i.e. more complete use of readily available resources). DEAbased aggregate environmental performance indicators for the South Field lignite mine of GPPC provided by Tsolas and Patmanidou (2003, 2004) and Tsolas et al. (2007), where inputs are judged against desirable and undesirable output. When using DEA, an alternative occurs in the identification of inefficiency: The efficiency analysis can have an input or an output orientation. The input-oriented (i.e. saving) efficiency reflects the ability of a DMU to contract inputs given a set of outputs, and the output-oriented (i.e. augmenting) efficiency reflects the ability of a DMU to augment outputs given a set of inputs. The main objective of this paper is to assess the environmental efficiency of a sample of Illinois strip mines from a technological perspective, where output is judged against both inputs and undesirable output. We assess output and inputs via traditional output (i.e. coal produced) and inputs (i.e. labor, capital), respectively, and undesirable output through overburden removal. An extension of this paper is that it includes an undesirable output (overburden) under the weak disposability assumption. Moreover, in order to perform inference for the proposed performance measures, a state-of-the-art technique is applied: the bootstrap. We propose an output-oriented DEA model based on previous relevant DEA studies and the possible ways to treat mining environmental effects. From a managerial perspective, this is a sensible manner by which to model performance since a mine manager may be first concerned about how to increase desirable output and second about how to concurrently decrease undesirable output for a given vector of inputs. This output-oriented analysis can be used to examine whether omitting undesirable outputs results in biased estimates of conventional technical efficiency estimates. The mine performance indicators that consider both desirable and undesirable outputs are referred to in this article as mixed mine environmental performance indicators (MMEPIs). These indicators are compared with traditional output-oriented performance indicators that consider only desirable output (we refer to these measures as (desirable) output-oriented mine performance indicators (MPIs)).

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inputs. For more about DEA, see Norman and Stoker (1991), Charnes et al. (1994), and Thanassoulis (2001). DEA is based on the typical procedure: 1. 2. 3. 4.

selection of inputs and outputs; selection of DEA model; derivation of relative efficiency scores; and bootstrapping the derived relative efficiency scores in order to investigate the sampling properties of DEA estimators and to calculate confidence intervals.

Nonparametric production analysis with undesirable outputs using DEA modeling The nonparametric production analysis originated from the work by Afriat (1972), Hanoch and Rothschild (1972), and Varian (1984). In this analysis, firms are assumed to behave according to a model of optimizing behavior (e.g. profit maximization or cost minimization). Next, tests are performing to determine whether the data are consistent with optimization and, if so, an empirical production set is produced. By contrast, DEA allows for nonoptimizing behavior or inefficiency, and it focuses on estimating the degree of relative efficiency (Cherchye, 2003). Using the nonparametric production analysis with undesirable outputs, aggregate performance indicators (i.e. environmental efficiency indicators) can be constructed by comparing the assessed production units under alternative assumptions on disposability of undesirable outputs (Taskin and Zaim, 2001; see also Kuosmanen, 2005). To describe the theoretical background of the model used here, suppose we observe a sample of k¼1,y,K production units (i.e. mines), each of which uses inputs x A RNþ to produce desirable J outputs y A RM þ and undesirable outputs w A R þ . As a matter of k notation, let xn be the quantity of input n used by unit k and let ykm and wkj be the quantity of desirable output m and undesirable output j produced by unit k, respectively. These data can be placed into data matrixes Y, a K  M matrix of desirable output levels, whose k, ith element is ykm ; W, a K  J matrix of undesirable output levels whose k, ith element is wkj ; and X, a K  N matrix of input levels whose k, ith element is xkn . Assuming the production process satisfies strong disposability of desirable outputs and inputs and weak disposability of undesirable outputs, the variable returns to scale (VRS) environmental output set P(x) can be constructed from observed data by means of (Zhou et al., 2008b): PðxÞ ¼ fðy,wÞ : zY Z ay, zW ¼ aw, zX r x, zeT ¼ 1, a Z 1, z A RKþ g T

Methods Data Envelopment Analysis DEA is a nonparametric approach developed by Charnes et al. (1978) as a technique to assess the performance of a set of different entities (i.e. production units, firms, etc.) called decision-making units (DMUs) which operate under similar conditions employing the same inputs and producing the same outputs. DEA derives a unit-free consolidated performance metric formed as a ratio of aggregated outputs to aggregated inputs. The measurement of efficiency by means of a nonparametric approach dates back to Farrell (1957), who introduced the concept of the best practice frontier that delineates the technological limits of what a DMU can achieve with a given level of resources. DEA identifies the relative ‘best practices’ (i.e. efficient DMUs) and establishes an efficient frontier using data of the observation set of DMU outputs and

ð1Þ

where e is a row vector consisting of ones, and z is a K  1 intensity vector that serves to construct convex combinations of the observed inputs and outputs, forming a feasible polytope with ¨ facets connecting the best practice observed points (see also Fare et al., 1989, 1996). Eq. (1) constructs a reference technology from the observed inputs and desirable and undesirable outputs relative to which the efficiency of each production unit can be calculated. Under VRS environmental technology Eq. (1), in line with Zhou et al. (2008b), we use the following fractional programming model for deriving a mixed mine environmental performance indicator (MMEPI; i.e. a desirable/undesirable output-oriented mine performance measure), considering the simultaneous adjustments of desirable and undesirable outputs max

y l

s:t: K X k¼1

0

zk ykm Z y aykm , m ¼ 1,. . .,M

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K X k¼1 K X k¼1 K X

0

zk xkn r xkn , n ¼ 1,. . .,N 0

zk wkj ¼ l awkj , j ¼ 1,. . .,J zk ¼ 1

k¼1

a Z 1, y Z1, l r 1, zk Z 0, k ¼ 1,. . .,K

ð2Þ

In the mathematical programming model (2), the removal of the adjusting parameter a would have no influence on its optimal objective value (see Zhou et al., 2008b for details); the existence of a may bring great inconvenience in solving Eq. (2) because this problem will have infinite optimal solutions. We therefore substitute programming model (2) by the following model: max

y l

s:t: K X k¼1 K X k¼1 K X k¼1 K X

0

zk ykm Z yykm , 0 zk xkn r xkn ,

m ¼ 1,. . .,M

zk ykm Z yyku m, zk xkn rxku n,

zk wkj ¼ lwkj ,

m ¼ 1,. . .,M n ¼ 1,. . .,N

zk ¼ 1

k¼1 k

k ¼ 1,. . .,K

ð5Þ

j ¼ 1,. . .,J Bootstrapping the DEA aggregate performance indicators

k

z ¼ 1, ð3Þ

Since Eq. (3) is a non-linear programming model, we follow the procedure described by Zhou et al. (2008b) to transfer it into its equivalent linear programming model. Dividing both sides of each constraint in model (3) by l and letting b ¼1/l, Wb ¼ j and zk b ¼ zuk (k¼1,y, K), we then obtain the following linear programming model: maxj j,zu

k¼1 K X

s:t: K X

z Z 0, 0

y Z1, l r1,z Z 0, k ¼ 1,. . .,K

k¼1 K X

y,z

k¼1 K X

n ¼ 1,. . .,N

k

k¼1 K X

maxy

k¼1 K X

k¼1

s:t: K X

If j* ¼1, we may say the mine under evaluation is at its most environmental scale size. If j*41, this indicates the mine under evaluation does not operate at its most environmental scale size. If a mine has a larger j* than another mine, we may conclude the former has a worse environmental performance under the VRS DEA environmental technology. In the above model (4), mines are deemed efficient (i.e. the solution value j* ¼1) if they are lying on the frontier of the production set; otherwise (i.e. j* 41), they are inefficient and should increase the levels of outputs. In case we omit the undesirable outputs from the analysis, the (desirable) output-oriented mine performance indicator (MPI) turns to the reciprocal of conventional VRS output-oriented technical efficiency that stems from the solution of the following linear programming model:

zuk ykm Z jyku m,

m ¼ 1,:::,M

zuk xkn r bxku n,

n ¼ 1,:::,N

zuk wkj ¼ wku j ,

j ¼ 1,:::,J

zuk ¼ b

k¼1

The DEA aggregate performance indicators derived from model (4) measure performance relative to an estimate of the true and unobservable production frontier and provide point estimates of performance. Since estimates of the frontier are based on finite samples, DEA measures based on these estimates are subject to sampling variation of the frontier. To address this problem, we assume a data Generating Process (DGP) wherein DMUs randomly deviate from the underlying true frontier, and these random deviations from the frontier are measured by the distance function. In DGP, the DEA scores calculated from the original data are used to form a large number (say B) of pseudo data sets. Each pseudo data set is similar to the original data set in the sense that both follow the same distributions of inefficiency, and this assures the levels of performance presented by the bootstrapping results are within the realm of observed behavior. Using the B pseudo data sets, the DEA scores can be calculated and the empirical distribution for the efficiency measures can be constructed from the B efficiency scores. Simar and Wilson (1998, 2000a, 2000b) outline a smooth bootstrap procedure to investigate the sampling properties of DEA estimators and evaluate the robustness of DEA point estimates by construction of confidence intervals. The algorithm for the bootstrap of the MMEPIs is based on Simar and Wilson’s (2000b) methodology1:

b Z1, zuk Z 0,

k ¼ 1,:::,K

ð4Þ

For each observation, k0 the solution value j* (i.e. the aggregate performance indicator value) will be the proportional scaling of the desirable output required to project the observed point onto the best practice frontier. That projected point will be determined as a weighted average (convex combination) of the ‘closest’ best practice frontier points, where the ‘weights’ will be the solution values of the z0 k’s. These are determined separately for each observation.

(i) Calculate the original DEA performance indicators ^ ðk ¼ 1,:::,KÞ by solving the linear programming problem (4). f k ^ ,:::, f ^ . (ii) Let fkb ,:::, fkb , b ¼ 1,:::,B be a sample generated from f 1 K (iii) Smooth the sampled values using the following equation: 

f~ k ¼ ffkb þ hek if fkb þ hek Z 1 or 2fkb hek if fkb þ hek o 1g ð6Þ

1 For the output oriented bootstrapping algorithm of Simar and Wilson (2000b), see also Walden (2006).

I.E. Tsolas / Resources Policy 36 (2011) 159–167

where h is a smoothing parameter and e is a randomly drawn error term. For the estimation of h, this study maximizes a likelihood cross-referencing function using methods developed by Ferris and Voelker (2002), see also Walden (2006). (iv) Calculate the final value f* by adjusting the smoothed sample value using the following equation: 

fk ¼ B þ

f~ k B

ð7Þ

2

^ f Þ1=2 ð1 þ h2 =s

where B¼

K 1X f , k k ¼ 1 kb

b ¼ 1,. . .,B

ð8Þ

and

s^ 2f ¼

K 1X ^ 2 ^ f ðf kÞ kk¼1 k

ð9Þ

^ ^ . where fk is the mean value of f k ^ =f . (v) Adjust the original outputs using the ratio f k k (vi) Resolve the model (4) using the adjusted outputs to obtain  f^ kb ,b ¼ 1,:::,B. (vii) Compute estimated confidence intervals for the performance indicators. The procedure described by Simar and Wilson (2000b) for constructing confidence intervals is as follows: The bias of the original estimate is calculated using the following equation: ^ ^ Þ ¼ B1 biasð f k

B X





^ ¼ f f ^ f^ kb f k k k

ð10Þ

163

Data The proposed DEA model is employed using data cited in Byrnes et al. (1984) and Thompson et al. (1995) for a sample of fifteen Illinois strip mines. Byrnes et al. (1984) modeled fifteen Illinois strip mines by means of DEA using operational data of 1978; tons of coal used as output and in the input side of DEA were used variables to proxy capital (dragline capacity, power-shovel capacity, wheelexcavator capacity), labor (man days), and seam characteristics (thickness of first seam mined, reciprocal of depth to first seam mined, thickness of second seam mined, reciprocal of depth to second-seam mined). Part of the data set of Byrnes et al. (1984) was reformulated by Thompson et al. (1995) in order to aggregate the three capacity equipment variables into one single input (expressed in constant 1990 dollars) to reflect total capital and to consolidate the above four separated mine characteristics into one single input, in accordance with the strip ratio as used in practice, to reflect mine quality. Thompson et al. (1995) used on other relevant studies to convert the three capacity inputs into dollars and summed to obtain one capital input. Moreover, for each mine in the sample, the strip ratio (in tons of overburden per ton of coal) was measured by the Illinois Department of Energy and Natural Resources (State Geological Survey Division). They used the inverse of strip ratio instead of the four mine characteristic inputs (thickness of first seam mined, reciprocal of depth to first-seam mined, thickness of second seam mined, reciprocal of depth to second-seam mined) cited in Byrnes et al. (1984). For more on the transformation of data, see Thompson et al. (1995). Table 1 reports the descriptive statistics of the four variables used.

b¼1

A bias corrected estimator of the true value of fk can then be computed using the following equation: ^

^ B1 ^ ¼ 2f f k k

B X





^ ¼ 2f ^ f f k kb k

ð11Þ

b¼1

It should be noted that the bias correction should not be used unless the ratio r as it stems from the following is well above unity: r¼

1 ^ ^ ÞÞ2 =s ^ 2j ðbiasB ðf k 3

ð12Þ

Using the pseudo estimates, it is possible to find b^ a , a^ a such ^  f ^ r aa Þ ¼ 1a. Finding b^ a , a^ a means sorting the that Prðba r f k k  ^ ^ values fkb fk in ascending order and then deleting 100 a/2% of the rows from both ends of the list and setting b^ a ,a^ a to the endpoints values of the list with a^ a r b^ a . The 1a^ a % confidence interval is then ^ þ a^ a r f r f ^ þ b^ a . given by the interval f k k k

Results We first derive point estimates of the MMEPIs and MPIs for each mine of the sample using models (4) and (5), respectively. The estimated MMEPIs and MPIs for each mine and the bias that can be obtained from the difference between MMEPIs and MPIs are presented in Table 2. Mines with positive bias numbers are overestimated under the MPIs, whereas mines with negative bias numbers are underestimated under the MPIs. In order to define whether omitting undesirable output results in biased performance estimates, the Mann–Whitney U test was conducted. The null hypothesis is that MMEPIs and MPIs have the same population of relative frequency distributions. The Mann– Whitney U is 104.5 (p-value¼0.75), and the null hypothesis is not rejected at a 5% level. Therefore, although omitting undesirable output results in biased performance estimates, this bias is not statistically significant. This finding is based on sample specific results, so we will proceed with the desirable/undesirable output

Table 1 Illinois coal mining data. Descriptive statistics.

Min Max Mean SD

Labor (thousand man days)a

Capital (mil $)a

Output (thousand tons)a

Overburden (thousand tons)b

20.70 98.50 50.86 23.56

15.47 113.25 46.05 25.60

396.00 3 264.00 1 335.36 9 84.56

3618.04 22 373.90 9 745.48 5 089.86

SD: Standard deviation. Number of observations ¼15 a Source: International Journal of Production Economics, 39, Thompson, R.G., Dharmapala, P.S. and Thrall, R.M., Linked-cone DEA profit ratios and technical efficiency with application to Illinois coal mines. 99–115, Copyright (1995), Elsevier. b Own calculations based on Thompson et al. (1995).

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analysis to assess the mines of the sample by means of the proposed MMEPI bootstrapping estimates. An innovation of this paper is to provide a statistical interpretation to the original MMEPI estimates, and in order to bound them with a confidence interval, we apply the bootstrapping algorithm presented in Section 3. We use the original MMEPI estimator in constructing the confidence interval of the true aggregate performance indicator. The bootstrapping algorithm accounts for the possibility that the mines that really define the efficient frontier have been left out from the sample, but it does not account for possible measurement errors in the observation set. As a result, the bootstrapping results that are bounded with confidence intervals will be lower than or equal to the point estimates. Table 3 shows the bias-corrected MMEPI estimates, the estimated variance across bootstrap replications for each observation, the ratio rk, and the estimated 95% confidence

Table 2 MMEPI and MPI point estimates and the magnitude of bias by mine when undesirable output is not considered. Mine identifier

MMEPI

MPI

Bias

M-1 M-2 M-3 M-4 M-5 M-6 M-7 M-8 M-9 M-10 M-11 M-12 M-13 M-14 M-15 Min Max Mean SD

1.2900 1.7800 1.0000 1.6300 1.2400 2.0200 2.7500 1.0000 1.4000 2.6700 5.8500 1.0000 1.0000 1.0000 1.0000 1.0000 5.8500 1.7753 1.2735

1.0000 1.0000 1.0000 1.1700 1.2400 1.5400 2.2300 1.1400 1.7000 2.6200 3.5000 1.0000 1.0000 1.9100 1.0000 1.0000 3.5000 1.5367 0.7456

0.2900 0.7800 0.0000 0.4600 0.0000 0.4800 0.5200  0.1400  0.3000 0.0500 2.3500 0.0000 0.0000  0.9100 0.0000  0.9100 2.3500 0.2387 0.7078

SD: Standard deviation.

bounds and their respective widths. Results were produced using B ¼2000 bootstrap replications with the aid of routines developed in GAMS; the DEA/CPLEX solver was used to derive the mine performance indicators. This study uses MATLAB programs publicly available at the website of NOOA Fisheries: Office of Science and Technology (2009) to calculate h (see also Walden, 2006). Table 3 also reveals the estimated biases are negative, as expected. We clearly notice the upward bias in the original estimates. The width of the confidence intervals ranges for the MMEPI estimates from 0.3557 (¼ 1.4109 1.0552; mine Number 3) to 1.6932 ( ¼7.7378 6.0446; mine Number 11) with an average of 0.6559 (Table 3). It suggests the mines might be more inefficient than revealed by the MMEPI point estimates alone. For example, the mean MMEPI of the sample showed the mines could, on average, attain the same level of inputs and undesirable output by increasing their desirable output by 77.53 ( ¼1.7753 1)% (Table 2). However, the confidence intervals suggest that, on average, output could be increased by between 84.85 (¼ 1.8485 1) and 150.45 ( ¼2.5045  1)% with an average of 114.24% (¼ 2.1424 1) (Tables 3 and 4). It is quite obvious the bias-correction estimate has to be done for all the mines since we make an estimation in four dimensions (two inputs and two outputs, i.e. one desirable output and one undesirable output) and we use only fifteen observations. In DEA applications, a suggested rule of thumb to achieve a reasonable level of discrimination among DMUs evaluated is that the practitioner needs the number of units to be greater or equal to max{mxs, 3(m+s)}, where mxs is the product and m+s is the sum of the number of inputs and number of outputs, respectively (Cooper et al., 2000). Due to low number of observations, we cannot derive definitive answers on the performance of mines and the bootstrapping approach is useful in this case to point out that we have little information, and for the confidence intervals on the estimated efficiency scores are quite large. Table 4 reports the descriptive statistics for the original MMEPIs, the corresponding bias-corrected MMEPI estimates, and the estimated 95% confidence bounds. The mines of the sample have an average bias-corrected estimate of 2.1424. Of fifteen mines in ^ k ¼ 1). The the data set, six appear ostensibly efficient (i.e. j remaining nine mines have MMEPI point estimates ranging from 1.2400 to 5.8500 with an average of 2.2922. In fact, among all the observations, lower bounds for the estimated 95% confidence

Table 3 MMEPI bootstrapping estimates. Mine identifier

Bias

Bias corrected

Variance

rk

Lower bound

Upper bound

Bound width

M-1 M-2 M-3 M-4 M-5 M-6 M-7 M-8 M-9 M-10 M-11 M-12 M-13 M-14 M-15 Min Max Mean SD

 0.1716  0.2424  0.2448  0.2868  0.2258  0.4063  0.4217  0.3239  0.2940  0.4826  0.8934  0.3786  0.3821  0.3806  0.3708  0.8934  0.1716  0.3670 0.1686

1.4616 2.0224 1.2448 1.9168 1.4658 2.4263 3.1717 1.3239 1.694 3.1526 6.7434 1.3786 1.3821 1.3806 1.3708 1.2448 6.7434 2.1424 1.4225

0.0085 0.0165 0.0083 0.0164 0.0100 0.0282 0.0416 0.0162 0.0137 0.0412 0.1928 0.0387 0.0380 0.0364 0.0375 0.0083 0.1928 0.0363 0.0452

135.8549 71.9409 289.9649 101.9411 169.9521 69.1949 34.2531 133.2510 153.5084 45.7361 7.1574 31.9020 33.7028 36.4430 32.5908 7.1574 289.9649 89.8262 75.5574

1.6782 2.3165 1.4109 2.1902 1.6675 2.7508 3.6261 1.5187 1.9225 3.5714 7.7378 1.7978 1.7962 1.7929 1.7894 1.4109 7.7378 2.5045 1.6011

1.3178 1.8203 1.0552 1.6982 1.2881 2.1152 2.8456 1.0604 1.4589 2.7931 6.0446 1.0524 1.0567 1.0601 1.0615 1.0524 6.0446 1.8485 1.3117

0.3604 0.4962 0.3557 0.4920 0.3794 0.6356 0.7805 0.4583 0.4636 0.7783 1.6932 0.7454 0.7395 0.7328 0.7279 0.3557 1.6932 0.6559 0.3290

SD: Standard deviation.

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Conclusions

Table 4 Descriptive statistics of original MMEPIs and bootstrapping estimates. Min

Max

Mean

SD

Panel A: efficient and inefficient mines MMEPI point estimates 1.0000 Bias corrected 1.2448 Lower bound 1.4109 Upper bound 1.0524 Bound width 0.3557

5.8500 6.7434 7.7378 6.0446 1.6932

1.7753 2.1424 2.5045 1.8485 0.6559

1.2735 1.4225 1.6011 1.3117 0.3290

Panel B: efficient mines Bias corrected Lower bound Upper bound Bound width

1.2448 1.4109 1.0524 0.3557

1.3821 1.7978 1.0615 0.7454

1.3468 1.6843 1.0577 0.6266

0.0546 0.1734 0.0035 0.1733

Panel C: inefficient mines MMEPI point estimates Bias corrected Lower bound Upper bound Bound width

1.2400 1.4616 1.6675 1.2881 0.3604

5.8500 6.7434 7.7378 6.0446 1.6932

2.2922 2.6727 3.0512 2.3758 0.6755

1.4445 1.6578 1.9043 1.4931 0.4118

MMEPI bootstrapping efficiency estimates

SD: Standard deviation.

7.0000 6.0000 5.0000 4.0000 3.0000

BC

LB

UP

2.0000

M-11

M-7

M-6

M-10

M-2

M-4

M-9

M-5

M-1

M-13

M-14

M-15

M-12

M-8

1.0000 M-3

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Mines Fig. 1. Comparison of the bias-corrected MMEPI estimates (BC) and the estimated 95% confidence bounds, i.e. lower (LB) and upper bounds (UB). Mines are presented in descending order of BC. Mine identifiers are as in Tables 3 and 4.

intervals range from 1.4109 to 7.7378; upper bounds range from 1.0524 to 6.0446. Mines originally identified as being on the frontier may, in fact, lie well below it. For example, mine numbers 3, 8, 12, 13, 14, and 15 with a MMEPI of 1 (point estimates) have an average bias-corrected estimates of 1.3468 and average lower and upper confidence bounds of 1.6843 and 1.0577, respectively. Moreover, it is evident that on the bias-corrected estimates, no one mine scores 1, indicating the mines that really define the frontier are not included in the sample. The ranking of ostensibly efficient mines by MMEPI might be also different than originally estimated, see also Fig. 1. The average width of the confidence intervals is 0.6266. The widest intervals correspond to mine Numbers 11 (1.6932) and 7 (0.7805). Mine Numbers 3 (0.3557) and 1 (0.3604) have the smallest confidence intervals at 95%. Due to the upward bias in the original estimates and the bootstrap correction in the confidence intervals, the original estimates lie for every mine outside, albeit close to the upper bound of the confidence interval. However, the bias-corrected estimates lie for every observation inside the confidence intervals.

This paper assesses the performance of a sample of U.S. coal strip mines by means of DEA VRS environmental technology to take also into account the undesirable outputs (i.e. overburden). Three main reasons motivated the analysis: the absence of prior DEA research on the assessment of U.S. strip coal mines for deriving environmental performance indicators; the importance to investigate whether omitting undesirable outputs results in biased estimates of conventional technical efficiency indicators; and the lack of estimates of uncertainties surrounding mine performance indicator point estimates in the relevant studies. Coal mining and overburden are used as desirable and undesirable output, respectively. As inputs, we use labor miner days and capital (1990 constant dollars of investment in equipment). We proposed the use of an MMEPI derived by means of a VRS DEA environmental technology, treating overburden as an undesirable output under the weak disposability assumption, and we compare this proposed measure with a traditional output-oriented MPI omitting overburden. Our sample specific results suggest the omission of undesirable output (overburden) results in bias estimates (obtained from the difference between MMEPIs and MPIs) that are not statistically significant. Moreover, including undesirable output the mines in the sample are considerable more inefficient than revealed by the initial point estimates of MMEPI. The results derived by the bootstrapping algorithm indicate that inefficiency in the sense of the proposed MMEPI has taken place in the mines of the sample analyzed here. We view the statistical properties of the DEA estimates as some of the most important findings from this paper. Since DEA-type indicators are simply point estimates without any standard error, we have presented a methodology that can be used to assess mine performance by means of DEA aggregate performance indicators whose statistical properties can be assessed via the bootstrapping approach. Among the DEA applications in modeling mine performance, the bootstrapping approach in DEA shows its superiority over DEA models that do not address the uncertainty surrounding DEA point estimates. Because the DEA bootstrapping model used here provides bias-corrected and confidence intervals for the point estimates, it is more preferable. This paper not only contributes to the research methodology regarding how to incorporate undesirable outputs into a bootstrapping in DEA assessment in the strip mine production setting, but it also entails various policy and managerial implications. To evaluate the performance of strip coal mines, it is necessary to consider not only traditional inputs and outputs, but also the overburden. The use of bootstrapping in DEA can provide meaningful information on building an efficient industry and may endanger the selection of correct regulation policy. Against the increasing environmental concern, it seems reasonable to give some priority to those mines that are operating more efficiently. The presented DEA model might be preferred in cases where a performance appraisal of a group of mines is demanded due to the increasing concern among policymakers for the environmental effects of the coal mining industry. The derived performance indicators can be used to pinpoint mines that suffer the least inefficiency, and priority efforts should be devoted to increase the performance of these mines. Although this study is based on a sample of Illinois strip coal mines, it has policy implications of a much wider scope, as the variables identified are likely to be relevant to coal mines in other states and other countries. Understanding the variables underlying mine, industry, and economic abilities to compete is of great importance in designing policies that promote sustainability (i.e. the rational use of the natural environment as well as economic growth.)

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Thus, the development of a model as part of a benchmarking study of a sample of mines’ or mining firms’ abilities to compete is essential to develop a long-term environmental policy for the mining industry. An important policy implication of this research is that a country needs to integrate environmental and industrial policies if its economy is to follow an environmentally sensitive pattern of development in reviewing environmental regulations in the mining industry. The DEA model proposed in this paper provides such an option; it not only incorporates environmental impact data to conventional input (desirable)/output data but also treats overburden as undesirable output in line with the regulated mine production setting. Moreover, the model has been improved further via the consideration of variable returns to scale and inference, combining DEA with computational statistics methods such bootstrapping, in line with the research stream that has lately been established. The outcomes of the model deal with bias in (a) not incorporating environmental impact data into the analysis and (b) uncertainty dealing with the sample selection. These outcomes are deemed essential and are based upon design an industrial and/or national environmental policy. This paper suggests that the concept of mine environmental performance can be made operational by means of a bootstrap-DEA model, but it is also essential from the part of regulators and/or governments to set measurable policy targets and design policy mechanisms that support implementation. Finally, as a contribution to sustainable development in mining, the model-building procedure represents an advance over previous models, such as those guided by the point estimate principle without inference.

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