Understanding DEA Efficiency Results in Energy Technologies: The Role of Non-Discretionary Inputs and Undesirable Outputs

Abstract

Data Envelopment Analysis (DEA) is widely applied to evaluate technological efficiency in the energy sector, yet its results are often difficult to interpret, particularly when extended model specifications are used. This study investigates how alternative treatments of environmental conditions and undesirable outputs influence efficiency measurement in energy technologies. Four DEA specifications are compared: the classical CCR model, a model incorporating non-discretionary inputs (CCR-ND), a model including undesirable outputs (CCR-B), and a combined specification (CCR-ND-B). The empirical analysis is based on data describing coal gasification technologies and is supplemented with controlled hypothetical cases designed to isolate the effects of environmental parameters. The results show that incorporating non-discretionary inputs and undesirable outputs does not necessarily reduce efficiency scores but reshapes the geometry of the production possibility set and modifies the structure of benchmark technologies. The findings highlight the importance of careful classification of inputs and outputs and emphasize that DEA results should be interpreted in relation to the underlying modeling assumptions. Comparing alternative model specifications improves transparency and helps avoid treating DEA as a “black box”, supporting more informed efficiency assessment in energy technology analysis.

1. Introduction

In recent decades, Data Envelopment Analysis (DEA) has become a widely applied tool for assessing technical efficiency in sectors characterized by complex production structures, including the energy sector. The method allows for the simultaneous analysis of multiple inputs and outputs without assuming a specific functional form of production, making it particularly suitable for evaluating heterogeneous technologies—from conventional thermal power plants to renewable energy sources (RES). At the same time, in the era of energy transition, increasing environmental constraints, and diverse geographical conditions, the assessment of technological efficiency has evolved from a purely analytical instrument into a strategic tool for sectoral development planning.

The foundations of modern technical efficiency analysis date back to the seminal work of Farrell [1], who proposed the first non-parametric approach to measuring efficiency based on the distance of observations from the production possibility frontier. Farrell introduced the concepts of technical and allocative efficiency, thereby establishing the basis for methods that do not require prior knowledge of the production function. Building on this foundation, Charnes, Cooper, and Rhodes [2] formulated the CCR model, the first complete DEA model. This model assumed constant returns to scale (CRS) and relied on linear programming to determine the relative efficiency of decision-making units (DMUs).

A subsequent breakthrough occurred with the work of Banker, Charnes, and Cooper [3], who extended DEA by incorporating the assumption of variable returns to scale (VRS), thus creating the BCC model. This development enabled the decomposition of technical efficiency into pure technical efficiency and scale efficiency, significantly increasing the flexibility of the method. In the following decades, numerous DEA variants were developed, including additive models [4], Tone’s non-radial Slacks-Based Measure (SBM) [5], the Range Adjusted Measure (RAM) model [6], and the Directional Distance Function (DDF) approach [7], all aiming to capture efficiency more precisely in complex production systems.

In these analyses, it is increasingly emphasized that DMUs operate under conditions beyond their full control—such as location, climate, quality of natural resources, or regulatory environment. Classical DEA models assume that all inputs and outputs are fully discretionary, meaning that they can be freely increased or decreased in the optimization process. In practice, however, many variables are non-discretionary—they remain outside managerial control while simultaneously influencing production outcomes and emission levels. Banker and Morey [8] already demonstrated that failing to account for such variables may lead to unfair comparisons across units and, consequently, biased conclusions regarding technical efficiency.

Two opposing perspectives have emerged in the literature. On the one hand, incorporating non-discretionary variables is viewed as a correction mechanism that enhances realism and eliminates biases arising from exogenous factors [9,10,11]. On the other hand, researchers such as Ruggiero [12] and Khezrimotlagh and Zhu [13] argue that improper inclusion of non-discretionary variables—through incorrect classification or excessive efficiency adjustment—may distort the production possibility set and undermine DEA’s ability to identify best practices. Importantly, this concern also applies to discretionary variables: their inappropriate specification may distort results and, more critically, lead to incorrect interpretation.

The importance of these issues in the energy and environmental domain is well documented in the DEA literature, where model selection, disposability assumptions, and the treatment of environmental variables are recognized as central methodological concerns [14]. For example, wind power plants operate under heterogeneous wind regimes, while biomass installations depend on local feedstock availability and subsidy policies. In such settings, classical DEA may penalize units for factors beyond their control, thereby violating the principle of fair comparison. Conversely, excessive compensation through unjustified relaxation of non-discretionary variables may artificially inflate efficiency scores.

In response to these challenges, recent research has developed alternative approaches to modeling disposability. Khezrimotlagh [13] proposes the introduction of the no free disposability condition, which better reflects technological constraints in emission-generating processes. Mehdiloo and Podinovski [11] introduce the concept of Selective Strong/Weak Disposability, allowing for differentiated treatment of groups of variables. Meanwhile, Tone’s [5] Slacks-Based Measure (SBM) model and its recent extensions [15,16,17] enable efficiency evaluation in the presence of undesirable outputs, such as CO₂ emissions. A common feature of these approaches is the pursuit of greater realism in frontier construction while preserving the objectivity of comparisons. At the same time, it should be emphasized that transparency and interpretability remain key requirements in efficiency analysis. From a practical perspective, the development of DEA-based approaches should aim at identifying methodological solutions that combine analytical adequacy with conceptual simplicity, allowing users to obtain reliable efficiency assessments while maintaining clarity of interpretation and ease of application. Consequently, although these approaches increase the realism of DEA, they also make the interpretation of performance results more dependent on the modeling assumptions adopted. This issue is reflected in the long-standing debate between data-transformation approaches and explicit environmental technology formulations, which shows that alternative treatments of undesirable outputs imply different assumptions about the production process and may lead to different efficiency interpretations [18,19,20].

Recent studies have also shown that the way environmental variables are incorporated into DEA may substantially affect both model behaviour and the interpretation of efficiency results. Sueyoshi and Goto [21] developed environmental DEA frameworks in which desirable and undesirable outputs are jointly evaluated, emphasizing that environmental assessment requires a different treatment of production technology than standard efficiency analysis. Pishgar-Komleh et al. [22] compared alternative methods of incorporating undesirable outputs in an LCA + DEA setting and showed that different modelling choices may lead to different efficiency scores and target values. More recently, Lin and Xu [23] demonstrated that the joint inclusion of non-discretionary inputs and undesirable outputs may fundamentally affect the feasible set and technical properties of DEA models. Taken together, these studies indicate that environmental variables are not merely supplementary factors in DEA, but structural elements shaping both the measurement and interpretation of efficiency.

Despite extensive research on DEA models with environmental variables, limited attention has been devoted to systematically comparing how alternative modeling assumptions affect efficiency interpretation in energy technology analysis. In particular, existing studies tend to focus on methodological extensions or empirical applications, while less emphasis is placed on how different modeling assumptions influence the geometry of the production possibility set, the structure of benchmark technologies, and the resulting efficiency rankings. As a consequence, DEA is often applied as a “black box”, where changes in model specification are not fully reflected in the interpretation of results. This creates a gap between methodological developments and their practical use in energy technology assessment.

This paper addresses this gap by comparing alternative DEA model specifications within a unified CCR-based framework applied to energy technologies. The main objective of the study is to show how the inclusion of non-discretionary inputs and undesirable outputs affects the interpretation of DEA results, rather than merely the numerical values of efficiency scores. In particular, the study examines how these modelling assumptions influence the position of units relative to the efficiency frontier, the composition of benchmark technologies, and the conclusions drawn about technological efficiency under alternative specifications of environmental variables.

The contribution of the study is threefold. First, it compares four CCR-based specifications in a consistent analytical setting, which makes it possible to isolate the effect of environmental modelling assumptions from other DEA design choices. Second, it demonstrates that incorporating non-discretionary inputs and undesirable outputs changes not only efficiency scores, but also the underlying benchmark structure and the discriminatory power of the model. Third, it provides an interpretative perspective relevant for energy technology assessment by showing that efficiency changes observed after extending the DEA specification should not automatically be interpreted as improvements in technological capability, but may reflect altered comparison rules resulting from contextual and environmental constraints. The analysis is positioned in relation to recent methodological developments from 2022 to 2025, integrating classical DEA models with environmental assessment approaches [24,25,26].

2. Materials and Methods

In the framework of DEA, inputs are generally understood as all resources whose use is expected to be minimized for a given level of outputs. In this sense, both non-discretionary inputs and undesirable outputs may be interpreted as factors whose reduction is desirable from the perspective of efficiency assessment. However, to distinguish these categories more precisely, the DEA literature introduces additional constraints that modify the representation of the production technology and the construction of the production possibility set (PPS) [27].

Two main modelling approaches are typically applied: (1) In the first approach, used for non-discretionary inputs, the common production technology assumes that all comparable DMUs operate under identical levels of these inputs or at levels not exceeding those observed for the evaluated unit. (2) In the second approach, used for undesirable outputs, the production technology requires that the compared units achieve the same level of these measures as the evaluated DMU [28,29].

Consequently, although both non-discretionary inputs and undesirable outputs may be interpreted as variables whose reduction is desirable, their inclusion in DEA models affects the geometry of the production technology in different ways. Evaluating how these alternative modelling assumptions influence the efficiency assessment of energy technologies constitutes the main objective of this study.

Accordingly, the empirical design of the study is not intended to provide a broad statistical generalization across the energy sector, but to isolate the interpretative consequences of alternative DEA specifications under controlled conditions. The methodological logic of the study is therefore comparative rather than predictive: the same set of technologies, the same basic input-output structure, and the same radial framework are maintained across all model variants so that any observed differences can be attributed to the treatment of non-discretionary inputs and undesirable outputs.

2.1. Experimental Design

The experimental design was constructed as a controlled specification comparison. Rather than testing alternative datasets or alternative DEA families simultaneously, the analysis keeps the core modelling structure constant and varies only the treatment of environmental variables. This design makes it possible to identify how changes in specification affect the interpretation of efficiency results without confounding these effects with changes in returns to scale assumptions, orientation, or non-radial measurement. To achieve this objective, four DEA model specifications were compared:

• CCR model—the baseline model assuming that all inputs are discretionary and that only desirable outputs are produced.
• CCR-ND model—an extended model incorporating non-discretionary inputs.
• CCR-B model—a model incorporating undesirable outputs.
• CCR-ND-B model—a comprehensive specification including both non-discretionary inputs and undesirable outputs.

The classical CCR model is formulated as follows [27]:

$$E_j=\min {\theta }_j$$

(1)

p.o.

$${\displaystyle \sum _{k=1}^K}{e}_{qk}{\lambda }_{kj}\le {\theta }_j{e}_{qj}, q=\mathrm{1,2},\dots ,Q,$$

(2)

$${\displaystyle \sum _{k=1}^K}{g}_{rk}{\lambda }_{kj}\ge g_{rj}, r=\mathrm{1,2},\dots ,R,$$

(3)

$${\lambda }_{kj}\ge 0, k=\mathrm{1,2},\dots ,K$$

(4)

where

• q—index of the q-th discretionary input;
• r—index of the r-th output;
• k—index of the k-th unit (DMU);
• j—index of the j-th unit (DMU);
• ${\lambda }_{kj}$—decision variable, with weight assigned to unit k from the standpoint of unit j;
• $e_j={\left[e_{qj}\right]}_{q=1,\dots ,Q}$—discretionary-input vector of unit j;
• $g_j={\left[g_{rj}\right]}_{r=1,\dots ,R}$—vector of desirable outputs produced by unit j;
• ${\theta }_j$—input-scaling factor for unit j;
• $E_j$—efficiency score of unit j.

This formulation corresponds to a linear production technology exhibiting constant returns to scale and strong disposability of inputs and outputs.

In the CCR-ND model, inputs are divided into discretionary and non-discretionary categories. Non-discretionary inputs represent environmental conditions beyond managerial control:

• Discretionary inputs ($e_q$)—controllable by the DMU and are still described by the following equation:

$${\displaystyle \sum _{k=1}^K}{e}_{qk}{\lambda }_{kj}\le {\theta }_j{e}_{qj}, q=\mathrm{1,2},\dots ,Q,$$

(5)

• Non-discretionary inputs ($x_n$)—parameters beyond managerial control but influencing efficiency are subject to the following restrictions:

$${\displaystyle \sum _{k=1}^K}{x}_{nk}{\lambda }_{kj}\le x_{nj}, n=\mathrm{1,2},\dots ,N,$$

(6)

To incorporate undesirable outputs (CCR-B), an additional constraint is introduced linking the undesirable outputs of the evaluated unit to the benchmark technology:

$${\displaystyle \sum _{k=1}^K}{b}_{fk}{\lambda }_{kj}=b_{fj}, f=\mathrm{1,2},\dots ,F,$$

(7)

where $b_p$ represents undesirable outputs such as emissions or waste. This formulation imposes equality between the undesirable outputs of the evaluated unit and those generated by the reference technology, ensuring that units are compared under the same level of environmental burden [30].

The most comprehensive specification combines both extensions (CCR-ND-B). This specification simultaneously accounts for environmental operating conditions (non-discretionary inputs) and environmental externalities (undesirable outputs). The final CCR-ND-B model is formulated as follows:

$$E_j=\min {\theta }_j$$

(8)

p.o.

$${\displaystyle \sum _{k=1}^K}{e}_{qk}{\lambda }_{kj}\le {\theta }_j{e}_{qj}, q=\mathrm{1,2},\dots ,Q,$$

(9)

$${\displaystyle \sum _{k=1}^K}{x}_{nk}{\lambda }_{kj}\le x_{nj}, n=\mathrm{1,2},\dots ,N,$$

(10)

$${\displaystyle \sum _{k=1}^K}{g}_{rk}{\lambda }_{kj}\ge g_{rj}, r=\mathrm{1,2},\dots ,R,$$

(11)

$${\displaystyle \sum _{k=1}^K}{b}_{fk}{\lambda }_{kj}=b_{fj}, f=\mathrm{1,2},\dots ,F,$$

(12)

$${\lambda }_{kj}\ge 0, k=\mathrm{1,2},\dots ,K$$

(13)

All models are input-oriented, meaning that efficiency is evaluated by minimizing inputs while maintaining at least the observed level of outputs. This orientation is appropriate for technological analyses in sectors where output levels are largely determined by demand conditions, while input usage can be adjusted through managerial or technological decisions. All four models were applied to the same set of DMUs and identical input-output variables. Consequently, any differences in efficiency scores arise exclusively from whether environmental variables and undesirable outputs are included or excluded in the model specification.

The CCR model was selected as the baseline specification in order to ensure a consistent analytical framework for comparing alternative treatments of environmental variables. The use of a single model structure allows isolating the impact of non-discretionary inputs and undesirable outputs on efficiency scores and benchmark construction. More advanced DEA models, such as BCC or SBM, introduce additional assumptions (e.g., variable returns to scale or non-radial measures), which could confound the interpretation of results. For this reason, the analysis focuses on CCR-based specifications.

To assess the stability of efficiency rankings across alternative DEA model specifications, rank-based correlation measures were applied. Spearman’s rank correlation coefficient was calculated for each pair of model variants (CCR, CCR-ND, CCR-B, and CCR-ND-B). These measures allow the evaluation of the degree of agreement between rankings generated by different model specifications without assuming any particular distribution of efficiency scores.

2.2. Empirical Data and Variable Structure

The dataset consists of 40 technological units representing different coal gasification process variants (

Table 1. Summary statistics of input and output variables (based on [31]).

No.	Parameter	Unit	Mean	SD	Min	Max
Economic and Financial Parameters
1	Operating costs	M€	134	40	31	207
2	Total capital investment	M€	741	367	115	1693
3	E_RADR 1	%	15.4	2.5	10.9	22.1
4	Revenue	M€	130	60	22	288
Technical Parameters
1	Effective operating time	days	322	14	292	344
2	Internal energy consumption	MWh	40	24	2	81
Environmental Parameters
1	Water consumption	m3	3.6	1.9	0.4	8.1
2	CO2 emissions to the atmosphere	Mg	99	104	1	331

¹ Effective Risk-Adjusted Discount Rate.

). It includes economic, technical, and environmental variables. The data are based on technical and economic parameters reported in the monograph Coal gasification—conditions, effectiveness and perspectives for development [31], but have been transformed and anonymized for research purposes, so that they do not reproduce the original values or allow identification of specific technologies. The dataset is used as a controlled analytical framework to examine the effects of DEA model specification and is not intended to represent a comprehensive statistical sample of industrial technologies.

In the baseline CCR model, all input variables were treated as discretionary. These include operating costs, total capital investment, internal energy consumption, and water consumption. Operating costs and capital investment represent short- and long-term economic commitments, while internal energy consumption and water consumption reflect operational and technological efficiency. Under this specification, all inputs are assumed to be controllable by the decision-making units.

In the CCR-ND model, one variable was classified as non-discretionary input: E_RADR (Effective Risk-Adjusted Discount Rate). E_RADR represents external financial risk conditions related to capital costs and investment environment and was therefore considered exogenous to managerial control.

In the CCR-B model, CO₂ emissions were modeled explicitly as an undesirable output, reflecting the environmental burden generated by the production process. In this formulation, undesirable outputs are linked to the reference technology through equality constraints, ensuring that the evaluated unit is compared with technologies generating the same level of environmental externalities.

Finally, the CCR-ND-B model combines both extensions by simultaneously incorporating non-discretionary inputs and undesirable outputs. In this specification, E_RADR is treated as a non-discretionary input while CO₂ emissions are modeled as an undesirable output.

For all model specifications, the output variables were revenue and effective operating time. Revenue captures economic performance and market viability, whereas effective operating time reflects process reliability and operational utilization.

To analyze the influence of environmental variables under extreme conditions, two hypothetical units were introduced. Units A and B (

Table 2. Characteristics of hypothetical Units A and B.

No.	Parameter	Unit	Units A	Units B
1	Operating costs	M€	134	134
2	Total capital investment	M€	741	741
3	E_RADR 1	%	10.9	22.1
4	Revenue	M€	130	130
1	Effective operating time	days	322	322
2	Internal energy consumption	MWh	40	40
1	Water consumption	m3	3.6	3.6
2	CO2 emissions to the atmosphere	Mg	99	331

¹ Effective Risk-Adjusted Discount Rate.

) were designed to achieve output levels close to the sample mean and to exhibit comparable performance with respect to discretionary inputs. The only differences between the units concern environmental parameters. Unit A represents a case with favorable environmental conditions, characterized by low values of non-discretionary inputs and undesirable outputs. In contrast, Unit B represents unfavorable environmental conditions with high levels of these variables. This contrast design enables a clearer identification of how alternative model specifications affect efficiency classification. The purpose of this assumption is not predictive validation, but rather a structural analysis (contrast cases) of the behavior of the DEA model under alternative specifications.

It should be emphasized that the distinction between discretionary and non-discretionary variables, as well as the treatment of undesirable outputs, ultimately reflects modeling assumptions regarding managerial control, technological rigidity, and environmental constraints. The experimental framework of this study was designed to examine how these alternative assumptions influence efficiency scores and rankings.

All DEA models were implemented in Python 3.12 using a custom code based on linear programming. The optimization problems were solved using the linprog function from the SciPy 1.16 library with the HiGHS solver.

3. Results

The efficiency results obtained for Units A and B using four model specifications are presented in

Table 3. Efficiency index for units A and B.

Model	Unit A	Unit B
CCR	0.59	0.59
CCR-ND	1.00	0.59
CCR-B	0.70	0.60
CCR-ND-B	1.00	0.60

and

Table 4. Set of weights λ for unit A and B.

DMU	CCR	CCR	CCR-ND	CCR-ND	CCR-B	CCR-B	CCR-ND-B	CCR-ND-B
	Unit A	Unit B	Unit A	Unit B	Unit A	Unit B	Unit A	Unit B
11	-	-	-	-	0.45	0.04	-	0.04
23	-	-	-	-	0.32	-	-	-
27	1.26	1.26	-	1.24	0.13	1.15	-	1.15
31	0.05	0.05	-	0.05	0.07	0.05	-	0.05
Unit A	-	-	1.00	-	-	-	1.00	-
Unit B	-	-	-	-	-	-	-	-

.

In the classical CCR specification, both Unit A and Unit B obtain identical efficiency scores of 0.59. This result indicates that, under the assumption that all inputs are discretionary and no undesirable outputs are explicitly modeled, both units are evaluated relative to the same reference technology and require a proportional reduction in inputs of approximately 41% to reach the efficient frontier.

Introducing non-discretionary inputs in the CCR-ND model leads to a substantial change in the efficiency assessment of Unit A. Its efficiency score increases to 1.00, indicating that once exogenous operating conditions are taken into account, Unit A becomes fully efficient relative to the observed technology. In contrast, the efficiency score of Unit B remains unchanged at 0.59. This result does not imply that non-discretionary variables have no influence on the efficiency assessment. Rather, it reflects the different external operating conditions under which the two units function. Unit A operates with a relatively low level of non-discretionary inputs and therefore functions under comparatively favorable external conditions. By contrast, Unit B is characterized by a high level of non-discretionary inputs and thus operates under less advantageous environmental constraints.

The fact that both units obtain the same efficiency score in the classical CCR model indicates that these environmental differences are not captured when the assumed inputs are discretionary. In other words, when the surrounding conditions are ignored, both technologies appear equally efficient, as they transform the same level of inputs into identical outputs. In the context of electricity generation technologies, this would correspond to two production technologies that achieve the same output levels from identical inputs when the influence of the external environment is disregarded. However, once non-discretionary inputs representing external operating conditions are incorporated into the model, the interpretation of the results changes. The unit operating under less favorable conditions (Unit B) maintains its original efficiency score, while the unit operating under more favorable environmental conditions (Unit A) becomes fully efficient. From the perspective of strict technological efficiency, such a result may appear counterintuitive. If two technologies transform inputs into outputs with identical performance, yet one operates under more challenging environmental conditions, it could be argued that the latter demonstrates greater technological robustness. Consequently, the efficiency improvement observed for Unit A in the CCR-ND specification should primarily be interpreted as reflecting the preferential external conditions under which it operates, rather than a superior technological capability.

When undesirable outputs are incorporated in the CCR-B model, the efficiency scores change differently. Unit A obtains an efficiency value of 0.70, while Unit B reaches 0.60. The inclusion of undesirable outputs modifies the structure of the production technology by accounting for environmental burdens associated with production processes. This change is reflected in the modification of the intensity variables (λ), as shown in Table 4, indicating that the benchmark technology used for comparison has changed. It is important to note that the specification used in this model imposes a strict equality condition linking the undesirable outputs of the evaluated unit with those generated by the reference technology. Interestingly, both units experience an increase in efficiency relative to the classical CCR model, despite the fact that Unit A generates several times fewer undesirable outputs than Unit B while maintaining identical levels of the remaining variables. This outcome illustrates that the incorporation of undesirable outputs primarily modifies the feasible technology set rather than simply rewarding environmentally cleaner technologies.

The most comprehensive specification, CCR-ND-B, simultaneously accounts for both non-discretionary inputs and undesirable outputs. Under this model, Unit A again becomes fully efficient with a score of 1.00, while Unit B reaches an efficiency value of 0.60. The results therefore reflect the combined influence of the two mechanisms described above: the adjustment of efficiency scores resulting from the explicit consideration of non-discretionary operating conditions and the modification of the production technology associated with the incorporation of undesirable outputs.

The reference sets identified through the intensity variables (λ) are reported in Table 4. In the classical CCR model, both units are benchmarked against the same composite reference technology formed primarily by Units 27 and 31. This indicates that these units represent the best observed combination of inputs and outputs within the sample under the basic DEA assumptions. In the CCR-ND specification, the benchmark structure changes for Unit A as it becomes fully efficient. In this case, the empirical technology of Unit A itself becomes part of the efficient frontier, and therefore, no external reference units are required for its evaluation. For Unit B, the reference structure remains largely unchanged. When undesirable outputs are incorporated (CCR-B), the composition of the reference set expands. In addition to Units 27 and 31, Units 11 and 23 also appear in the benchmark structure. This reflects the fact that once environmental burdens are considered, the definition of best-practice technology changes and additional units contribute to constructing the efficient frontier. The CCR-ND-B model preserves this extended benchmark structure while simultaneously accounting for non-discretionary factors. In this specification, Unit A remains efficient and therefore serves as its own reference point, while Unit B continues to be evaluated relative to a composite benchmark dominated by Units 27 and 31, with minor contributions from other units.

To examine whether the observed patterns hold more generally,

Table 5. Efficiency scores across DEA models and corresponding environmental variables.

DMU	CCR	CCR-ND	CCR-B	CCR-ND-B	E_RADR 1 [%]	CO2 Emissions [Mg]
1	0.59	0.97	0.66	1.00	11.7%	182
2	0.44	0.50	0.54	0.56	13.9%	18
3	0.55	1.00	0.59	1.00	10.9%	204
4	0.42	0.45	0.51	0.51	14.3%	20
5	1.00	1.00	1.00	1.00	11.4%	24
6	0.87	0.88	1.00	1.00	13.7%	7
7	1.00	1.00	1.00	1.00	11.4%	105
8	0.87	0.88	1.00	1.00	14.4%	10
9	0.50	0.60	0.54	0.65	13.0%	164
10	0.77	0.99	0.85	1.00	13.1%	184
11	0.87	1.00	1.00	1.00	13.1%	105
12	0.40	0.40	0.51	0.51	15.1%	17
13	0.69	0.73	0.88	0.91	16.0%	20
14	0.77	0.87	1.00	1.00	15.5%	6
15	0.48	0.55	0.51	0.58	13.6%	171
16	0.66	0.89	0.71	0.93	13.0%	192
17	0.78	0.94	0.90	0.94	13.1%	118
18	0.38	0.38	0.46	0.46	15.1%	17
19	0.55	0.56	0.72	0.72	16.8%	20
20	0.69	0.78	1.00	1.00	15.1%	6
21	0.68	0.88	0.76	0.91	13.5%	182
22	0.56	0.64	0.74	0.77	15.3%	18
23	1.00	1.00	1.00	1.00	15.2%	14
24	0.97	0.97	1.00	1.00	17.2%	1
25	1.00	1.00	1.00	1.00	17.2%	281
26	0.99	0.99	1.00	1.00	19.4%	31
27	1.00	1.00	1.00	1.00	17.2%	276
28	0.99	0.99	1.00	1.00	22.2%	31
29	0.42	0.45	0.46	0.46	15.1%	183
30	0.51	0.60	0.59	0.61	15.3%	161
31	1.00	1.00	1.00	1.00	15.7%	158
32	0.43	0.44	0.55	0.55	17.5%	28
33	0.26	0.26	0.39	0.39	20.1%	13
34	0.79	0.85	1.00	1.00	17.8%	13
35	0.58	0.63	0.62	0.65	18.4%	301
36	0.80	1.00	1.00	1.00	15.1%	331
37	0.61	0.76	0.65	1.00	15.1%	291
38	0.29	0.29	0.37	0.37	17.5%	19
39	0.46	0.46	0.59	0.59	17.3%	15
40	0.85	0.85	1.00	1.00	19.8%	14
Unit A	0.59	1.00	0.70	1.00	10.9%	99
Unit B	0.59	0.59	0.60	0.60	22.1%	331

¹ Effective Risk-Adjusted Discount Rate.

presents the efficiency scores for all units under the four model specifications together with the corresponding levels of non-discretionary inputs (E_RADR) and undesirable outputs (CO₂ emissions). This combined presentation allows for a direct comparison between environmental conditions and efficiency rankings. The results show that the inclusion of non-discretionary inputs does not reduce efficiency scores for any unit. Instead, in several cases, efficiency scores increase when exogenous operating conditions are explicitly incorporated. The introduction of undesirable outputs leads to a systematic increase in the number of efficient units. As shown in

Table 6. Percentage of fully effective DMUs.

CCR	CCR-ND	CCR-B	CCR-ND-B
14.3%	23.8%	40.5%	52.4%

, the proportion of fully efficient DMUs increases from 14.3% in the classical CCR model to 40.5% in the CCR-B model, and further to 52.4% in the combined CCR-ND-B specification. This outcome reflects the modification of the production possibility set once environmental performance indicators are incorporated into the model.

The rank correlation analysis (

Table 7. Spearman’s rank-order correlation between DEA model specifications.

Variable	CCR	CCR-ND	CCR-B	CCR-ND-B
CCR	1.00	0.86	0.95	0.86
CCR-ND	0.86	1.00	0.78	0.88
CCR-B	0.95	0.78	1.00	0.88
CCR-ND-B	0.86	0.88	0.88	1.00

) indicates a high level of agreement between the efficiency rankings generated by different DEA specifications. Spearman correlation coefficients range between approximately 0.78 and 0.95. These results suggest that although the efficiency scores change across model variants, the relative ordering of technologies remains largely stable. The highest similarity is observed between the CCR and CCR-B models, whereas the lowest correlation occurs between the CCR-ND and CCR-B specifications.

Overall, the results demonstrate that model specification has a significant impact on the efficiency assessment in DEA. Accounting for non-discretionary inputs and undesirable outputs modifies both the position of individual units relative to the frontier and the composition of the reference technology. In the analyzed case, the inclusion of these additional elements generally leads to higher efficiency scores for a large proportion of units. While this reflects a more comprehensive representation of the production environment, it simultaneously reduces the discriminatory power of the model by increasing the number of units classified as fully efficient. As a consequence, the resulting ranking of units becomes less transparent. Moreover, the interpretation of inefficiency for the remaining non-efficient units becomes more complex, as the sources of inefficiency are more difficult to attribute to specific technological or environmental factors

The results of this study should be interpreted in light of the limitations of the dataset. The analysis is based on a relatively small and sector-specific sample of coal gasification technologies derived from a single source. Therefore, the findings should not be interpreted as representative of the entire energy sector, but rather as an illustration of how DEA model specification affects efficiency assessment under controlled and relatively homogeneous conditions. The use of a homogeneous dataset is intentional, as it allows isolating the impact of model specification without introducing additional variability related to technological heterogeneity. While the empirical results are dataset-specific, the methodological insights are transferable to other contexts in which environmental variables play a significant role in efficiency analysis.

4. Discussion

The empirical results indicate that DEA specification affects not only the magnitude of efficiency scores, but also the logic according to which technologies are compared. In the analyzed setting, changes in model specification alter the reference technology, modify the geometry of the production possibility set, and reshape the interpretation of what counts as inefficiency. For this reason, the differences observed between CCR, CCR-ND, CCR-B, and CCR-ND-B should not be read simply as measurement refinements, but as shifts in the comparison rule embedded in the model. The interpretation of such results becomes particularly complex when environmental variables represent fundamentally different types of external conditions.

These findings should be interpreted in relation to the structure of the dataset used in the study. The analysis is based on a relatively homogeneous sample of 40 coal gasification technology variants derived from a single source, supplemented by two hypothetical contrast cases designed to isolate the effects of environmental variables. This controlled empirical setting reduces interference from broad technological heterogeneity and makes it possible to observe more clearly how alternative DEA specifications affect efficiency scores, benchmark composition, and rank stability.

Consider, for example, an energy technology whose market performance depends on factors such as the average annual ambient temperature in a given region and the level of market risk associated with the investment environment. Both variables may plausibly be treated as non-discretionary inputs because they are largely beyond the control of the decision-making unit. However, their interpretation differs substantially. If ambient temperature is considered a non-discretionary input, a technology operating under more adverse climatic conditions but producing the same outputs with identical discretionary inputs could be interpreted as technologically superior because it achieves the same results despite harsher environmental conditions. In contrast, market risk represents an economic characteristic of the investment environment. A technology operating under lower market risk would typically be preferred not because it is technologically superior, but because it offers more favorable financial conditions. In the standard DEA formulation with non-discretionary inputs, however, the model implicitly treats both variables in a similar way: units operating under more favorable external conditions—such as lower market risk or milder temperatures—may obtain higher efficiency scores even if their technological performance is identical to that of units operating under more adverse conditions. This example illustrates that the interpretation of efficiency scores depends critically on how external variables are conceptualized within the model. The observed changes in efficiency scores after introducing non-discretionary variables are consistent with the findings of Ruggiero [12], who showed that environmental factors may bias DEA results when not properly accounted for. However, the results of this study suggest a broader interpretation of this phenomenon. Rather than acting solely as a bias-correction mechanism, the inclusion of non-discretionary inputs modifies the structure of the production possibility set and, consequently, the interpretation of efficiency itself. In particular, the differences observed between the CCR and CCR-ND models indicate that a portion of the inefficiency measured in the baseline specification reflects external operating conditions rather than purely technological performance. This mechanism is also visible in the hypothetical contrast cases. In the baseline CCR model, both Units A and B obtain the same efficiency score of 0.59, whereas after introducing non-discretionary inputs, Unit A becomes fully efficient (1.00) while Unit B remains at 0.59. In causal terms, this change does not reflect an improvement in technological capability itself, but a change in the comparison rule: once exogenous operating conditions are embedded in the model, part of the inefficiency measured in the baseline specification is reclassified as contextual rather than technological.

This distinction has an important methodological implication. Non-discretionary inputs do not form a conceptually uniform category: some of them represent adverse operating conditions, whereas others represent advantageous contextual circumstances. As a result, the effect of introducing ND variables cannot be interpreted mechanically as a fairness correction. Instead, it depends on the economic meaning of the variable and on whether the model effectively rewards resilience under adverse conditions or embeds contextual privilege into the efficiency frontier. This interpretation is consistent with recent methodological work emphasizing that non-discretionary inputs and undesirable outputs are not marginal additions to DEA models, but factors that reshape the feasible comparison space. Lin and Xu [23] show this in a more advanced super-efficiency setting, where the joint inclusion of ND inputs and undesirable outputs changes not only the evaluation result but also the technical properties of the model itself. The present study complements that literature by showing that even in a simple CCR-based radial framework, these variables materially affect the meaning of efficiency scores and benchmark relations. This reinforces the view that the inclusion of environmental variables changes not only the measured outcome, but also the analytical meaning of the comparison.

A related interpretative issue arises in the treatment of undesirable outputs. Consider the classic example of CO₂ emissions in electricity generation. When emissions are modeled as undesirable outputs through equality constraints, the DEA model effectively compares each technology with units characterized by a similar emission level. In the case of coal-based energy technologies with and without carbon capture and storage (CCS), technologies without CCS will therefore be benchmarked primarily against other high-emission technologies. In extreme situations, if a particular unit exhibits exceptionally high emissions relative to the rest of the sample, it may effectively become its own benchmark. Within the DEA framework, this situation implies that the unit appears fully efficient despite exhibiting poor environmental performance. Consequently, the treatment of undesirable outputs may alter the structure of the feasible technology set in ways that influence both efficiency scores and their interpretation.

This effect is consistent with the theoretical framework proposed by Podinovski [11]. However, the results of this study highlight the practical implications of this theoretical insight. In particular, undesirable outputs cannot be treated under the assumption of strong disposability, as their reduction typically requires additional inputs or technological adjustments. As a consequence, incorporating undesirable outputs alters not only the feasible production set, but also the composition of benchmark technologies. This is reflected in the observed shifts in efficiency scores and reference sets, indicating that changes in model specification affect the underlying structure of comparisons rather than simply adjusting efficiency levels. This result is in line with earlier environmental DEA studies showing that undesirable outputs require a distinct analytical treatment. Sueyoshi and Goto [21] emphasized that environmental assessment cannot be reduced to standard efficiency analysis once desirable and undesirable outputs are jointly considered. Similarly, Pishgar-Komleh et al. [22] demonstrated that different methods of incorporating undesirable outputs may lead not only to different efficiency scores but also to different practical target implications. Against this background, the present results suggest that the treatment of undesirable outputs in DEA should be understood as a structural modelling choice that changes both the feasible benchmark set and the substantive meaning of the resulting comparison. The benchmark results illustrate this effect directly. In the baseline CCR model, both hypothetical units are referenced mainly against Units 27 and 31, whereas after incorporating undesirable outputs, the reference structure expands to include Units 11 and 23; once non-discretionary inputs are additionally introduced, Unit A becomes fully efficient and serves as its own reference point. This confirms that model extensions do not merely reposition units relative to a fixed frontier, but redefine the peer group against which performance is judged. In this respect, the present findings are consistent with earlier environmental DEA studies showing that different treatments of undesirable outputs may generate different frontiers and different efficiency interpretations. At the same time, the present study differs from most of this literature in emphasis: rather than proposing a new DEA formulation, it focuses on clarifying the interpretative consequences of specification changes within one unified CCR-based framework. In the context of energy technologies, these issues are particularly relevant because production processes are strongly influenced by environmental constraints, regulatory conditions, and technological characteristics such as emission intensity. The classification of variables as discretionary inputs, non-discretionary inputs, or undesirable outputs is therefore not purely technical but reflects conceptual assumptions about managerial control and the technological flexibility of the analysis. For example, emission levels may be partially controllable through technological investment but may also depend on process design and regulatory requirements. Misclassification of such variables may therefore lead either to masking genuine technological inefficiencies or to artificially inflating efficiency by embedding structural advantages into the frontier.

Another important implication concerns the interpretability of efficiency rankings. The results indicate that extending the model by incorporating environmental variables tends to increase the number of units classified as efficient: the share of fully efficient DMUs rises from 14.3% in the classical CCR model to 23.8% in CCR-ND, 40.5% in CCR-B, and 52.4% in CCR-ND-B. While this may improve comparability under heterogeneous contextual conditions, it simultaneously reduces the discriminatory power of the model and makes the interpretation of inefficiency more difficult. At the same time, the Spearman rank correlations remain relatively high, ranging from 0.78 to 0.95, which suggests that model extensions modify efficiency levels and benchmark structures more strongly than the overall ordinal structure of the ranking. In practical benchmarking applications, this creates a trade-off between representational realism and ranking sharpness: the model becomes more context-sensitive, but less able to distinguish clearly between technological leaders and followers. The increase in the number of fully efficient units observed in the extended models is consistent with the general DEA literature, which indicates that adding constraints related to environmental variables reduces the discriminatory power of the model [32].

From a methodological perspective, the results suggest that the choice of DEA specification should depend on the objective of the analysis. When the goal is to compare technologies operating under heterogeneous environmental conditions, models incorporating non-discretionary inputs and undesirable outputs may provide a more realistic representation of the production process. However, when the primary objective is technological benchmarking and the identification of internal inefficiencies, the classical CCR specification may offer clearer diagnostic insights. In energy technology analysis, it may therefore be useful to apply multiple model specifications simultaneously. The joint use of CCR, CCR-ND, CCR-B, and CCR-ND-B models allows researchers to distinguish between technological capability, environmental performance, and contextual operating conditions, thereby reducing the risk of misinterpreting efficiency rankings.

At the same time, the results should be interpreted with caution. As noted by Ruggiero [12], when non-discretionary variables are correlated with efficiency, standard DEA models may not fully disentangle environmental effects from true technological inefficiency, which may lead to systematic bias in efficiency estimates. Therefore, while the extended models improve the interpretation of efficiency, they may still be affected by underlying methodological limitations. Recent studies also highlight that incorporating undesirable outputs and environmental variables introduces additional methodological challenges, including feasibility issues and model sensitivity [23]. Furthermore, alternative non-radial approaches, such as SBM or BAM models, have been proposed to better capture non-proportional adjustments in such contexts [33]. However, the present results demonstrate that even within a radial framework, the treatment of environmental variables remains a key determinant of efficiency outcomes. Overall, the present findings are consistent with the DEA literature in showing that the treatment of non-discretionary inputs and undesirable outputs materially affects efficiency assessment and benchmark relations. At the same time, the specific contribution of this study lies not in proposing a new DEA formulation, but in clarifying how alternative specifications alter the interpretation of results within one controlled CCR-based framework.

5. Conclusions

This study compared four CCR-based DEA specifications in order to examine how different treatments of environmental variables influence the interpretation of technological efficiency results. In the analyzed dataset, the share of fully efficient units increased from 14.3% in the classical CCR model to 23.8% in CCR-ND, 40.5% in CCR-B, and 52.4% in CCR-ND-B, indicating a substantial reduction in the discriminatory power of the model once environmental variables were incorporated. At the same time, rank-order similarity remained relatively high, with Spearman correlation coefficients ranging from 0.78 to 0.95, which suggests that model extensions modified efficiency levels and benchmark structures more strongly than the overall ordering of units. The contrast between the hypothetical Units A and B further illustrates this mechanism: both units scored 0.59 in the baseline CCR model, whereas Unit A became fully efficient in CCR-ND and CCR-ND-B, while Unit B remained at 0.59 and 0.60, respectively. These results confirm that DEA specification changes not only the magnitude of efficiency scores but also the logic of comparison embedded in the model.

The findings indicate that lower levels of non-discretionary inputs may lead to higher efficiency scores, not because of superior technological capability, but because they reflect more favorable external conditions. For this reason, the interpretation of efficiency changes depends critically on the economic and technological meaning of the variables classified in this category. A related effect occurs when undesirable outputs are incorporated into the model. Their inclusion modifies the feasible benchmark set and may increase efficiency scores for some technologies even when environmental burdens remain relatively high. This shows that the treatment of undesirable outputs in DEA should be understood as a structural modelling assumption rather than a purely technical choice.

From a practical perspective, the choice of DEA specification should be aligned with the objective of the analysis. The classical CCR model is more suitable for technological benchmarking and the identification of internal inefficiencies, as it provides stronger discriminatory power and clearer differentiation between units. In contrast, models incorporating non-discretionary inputs and undesirable outputs (CCR-ND and CCR-ND-B) are more appropriate when the aim is to account for external operating conditions and environmental constraints. However, these extensions tend to increase the number of units classified as efficient, thereby reducing the discriminatory power of the model and making rankings less transparent. Therefore, the selection of the model should reflect the intended interpretation of efficiency rather than relying on a single specification.

At the same time, the present study should be interpreted within the limits of its design. The analysis does not aim to identify a universally superior DEA specification, nor to provide a representative ranking for the whole energy sector. Instead, it offers a controlled methodological comparison showing how alternative assumptions regarding non-discretionary inputs and undesirable outputs affect the meaning of DEA results within a controlled empirical setting.

Future research should extend this comparison to broader and more heterogeneous datasets and to more advanced DEA formulations, including non-radial, slack-based, and directional models. Such studies would help determine which effects observed here are specific to the CCR-based framework and which reflect more general properties of environmental DEA. Such systematic investigations are essential for establishing transparent and consistent principles for interpreting DEA results. From a practical perspective, efficiency assessment can only serve as a reliable decision-support tool if the measurement process is clearly understood and its underlying assumptions are explicitly recognized. Therefore, improving the transparency and interpretability of DEA models remains an important direction for future methodological research, particularly in applications involving complex production systems such as energy technologies.