The Technical Efficiency of Polish Energy Sector Companies of Different Sizes

Abstract

The energy market in the European Union is dominated by large energy companies. However, the liberalization of this market, the removal of market barriers, and the encouragement of small companies to enter the market are creating new conditions and changing the structure of companies. In addition to large energy companies, a significant number of small entities are also emerging. The aim of this research is to analyze the relationship between the size of energy companies and their technical efficiency. This analysis was carried out for the period 2019–2023. In order to assess the efficiency of the researched energy companies, the Data Envelopment Analysis (DEA) method was employed. The analyzed enterprises were divided into three groups: small (IA), medium (IB), and large (II). The following economic categories were adopted as the division criteria: 1. net sales revenue; 2. operating costs; 3. fixed assets. The findings of our study suggest that small and medium-sized energy companies can exhibit levels of efficiency that are comparable to those of larger enterprises. This result suggests that companies of different sizes can coexist in the energy market. The results obtained are not completely conclusive, as statistically significant differences in technical efficiency (TE) were recorded in 2021 and 2022 but only between small enterprises (IA) and medium-sized enterprises (IB). This study highlights the potential of small energy companies to contribute effectively to Poland’s energy sector and suggests that supporting their development could enhance energy security and market competition. However, many energy companies—regardless of size—exhibited low levels of efficiency, underlining the need for deeper investigation into the sources of inefficiency.

1. Introduction

The global energy industry is struggling with many problems related to the need for an increase in efficiency [1], increasing demand for electricity [2], changes in electricity prices, rising operating costs caused by rising fuel prices (especially volatile gas and coal prices) and CO₂ emission rights, changes in energy policy, the pursuit of decarbonization of the economy [3,4,5,6], and ensuring energy security [7,8,9]. These factors make the economic and financial situation of energy companies more susceptible to the instability of the political and economic environment, causing problems with maintaining an appropriate level of productivity and profitability that would ensure the possibility of stable development [10,11,12,13]. Due to the importance of energy companies in ensuring energy security, the analysis of efficiency is of significance not only to the owners of said companies but also to a range of other stakeholders, including shareholders, potential investors, consumers, politicians, and society at large.

A multitude of factors influences the efficiency of enterprises. In research, attention is paid to the relationship between the size of an enterprise and its efficiency. The issue of the relationship between the efficiency of enterprises and their size is a fundamental problem of the theory of scale economies. The existence of economies of size and/or scale can have broad implications for a given industry. Economies of scale can produce positive effects related to improved economic efficiency but also negative effects [14,15,16]. The phenomenon of economies of scale is not only observed at the level of individual companies but can also lead to changes in the sector and its structure. The increasing advantages of scale or size of companies can lead to pressure for the consolidation of companies, which can have potentially harmful effects on competition and social welfare [17]. Enterprises operating within the energy sector in Poland are distinguished by a high level of concentration. The transformations that have taken place in the Polish electricity generation sector in recent years have resulted in the formation of an oligopolistic market structure [18]. The energy sector is susceptible to concentration, which gives rise to the possibility that energy companies will take advantage of their market position. This market concentration is due to several reasons: a considerable amount of capital is required for investment, high entry barriers, limited possibilities of energy storage and transmission, and an inelastic demand for electricity, which allows for the influence of electricity prices [19]. It should also be noted that the European Union’s climate and energy policy has a clear impact on the energy transition in Member States. It leads to the increased diversification of energy mixes and exerts pressure to reduce market concentration [20]. Consequently, the analysis of the relationship between the size of enterprises and their efficiency is of particular importance for the proper functioning of the electricity market but also allows for the limitation of unfair practices and market failures.

As noted by Kamiński [18], the energy sector in Poland requires continuous assessment from the point of view of the relationship between market power, the degree of concentration, and the efficiency of energy companies. The energy sector consolidation policy, which is periodically adopted by Polish governments, requires thorough analysis and proper assessment. The issue of the efficiency of energy companies is of particular importance from the perspective of final consumers and in the shaping of future energy policy. To the best of our knowledge, there is a distinct lack of analyses of the efficiency of energy companies diversified in terms of their size. The present study aims to address this research gap by examining the relationship between the size of energy companies and their efficiency. This issue is part of the theory of scale economies and is of great importance in the development policy of enterprises. This article aims to fill the gap concerning the impact of the concentration/de-concentration of the energy sector on the efficiency of energy enterprises and additionally aims to present the specificity of the electricity market in Poland for the international reader.

Many different methods are used to analyze the efficiency of companies. These can be both partial efficiency indicators and total factor productivity (TFP) measures. Partial efficiency indicators relate the selected output to a single input. The main advantage of partial efficiency indicators is the ease of calculation and interpretation, but this comes at the cost of the impossibility of a comprehensive assessment using a single indicator [21,22], which makes such interpretation multidimensional. For this reason, one-dimensional indicators are more useful [23]. In this case, both parametric and non-parametric frontier methods can be used. Data Envelopment Analysis (DEA) is one such commonly used method for assessing the efficiency of companies. This method is particularly useful for comparative studies of the efficiency of many objects. It allows their relative evaluation and, in particular, the definition of effective benchmarks for inefficient units. The DEA method is used to assess the efficiency of enterprises in numerous sectors [24,25,26], including the energy sector [27,28,29].

The aim of this article is to analyze the relationship between the size of energy enterprises and their technical efficiency.

2. Literature Review

The economic category of efficiency is employed to evaluate the functioning of economic entities, economic sectors, or the national economy. The prevalence of the concept of “efficiency” in both scientific discourse and economic praxis underscores its significance and importance. An efficiency assessment allows us to identify the strengths and weaknesses of the analyzed units while concomitantly drawing attention to the factors that shape the level of efficiency. The assumption of assessing the efficiency of companies is, among others, the analysis of the relationship between the inputs involved in the production process and the obtained effects [30]. In such a case, the assessment of operational efficiency can be discussed. The measurement of the operational efficiency of a company provides an indication of how well the resources of the organizations concerned are being managed [31,32] and allows for the evaluation of the performance of new technologies [33].

The analysis of the operational efficiency of enterprises is performed using various methods. These methods are most often classified into three broad categories: ratio indicators, parametric methods, and non-parametric methods. A large part of the research on the assessment of the operational efficiency of enterprises employs financial indicators based on the evaluation of the resource-based view, mainly using indicators such as the following: return on total assets (ROA), return on investment (ROI), and return on sales (ROS). An example of such research is the work of Chudy-Laskowska and Rokita [10], where the analysis of factors influencing the efficiency of energy sector companies was carried out using the ROA indicator. In a similar way, a study by Kusz et al. [34] assessed the factors influencing the return on equity (ROE) for agricultural biogas plants. This approach allows for a partial analysis of effectiveness and the identification of weak and strong areas of the company’s functioning. Such an analysis allows for the indication of micro-sources of strategic success or failure. Nevertheless, a financial indicator analysis has the potential to obscure improvements or the lack of improvement in productivity, capacity utilization, and product mix [35]. Therefore, changes in the efficiency assessed in this way can only be the result of changes in the prices of outputs and inputs [36]. Moreover, the construction of indicators in the form of a quotient does not allow for taking into account many dimensions of the enterprise’s activities at once.

The limitations of an indicator analysis prompted the exploration of alternative methodologies for evaluating the efficiency of enterprises. The most commonly used methodologies in efficiency studies are frontier approaches [31]. There are two approaches in this area: parametric and non-parametric. Of these two groups of methods, the Data Envelopment Analysis (DEA) method is often used to assess the effectiveness of organizational units [37,38,39,40]. The DEA is a non-parametric method for the assessment of the relative effectiveness of the decision-making units (DMUs) [41,42]. The DEA method, first introduced by Charnes et al. [43], is distinguished by its flexibility and simplicity; the method does not necessitate a substantial sample size or any preliminary specification of a functional form for the production technology. The DEA method makes comparisons between functionally similar entities and is capable of deriving a relative efficiency score. This score can then be used to make comparisons between decision-making units (DMUs) [44]. Another advantage of this method is that it can easily incorporate multiple inputs and outputs [45,46,47,48]. The DEA method first establishes an “efficient frontier”, formed by a set of decision-making units (DMUs) that exhibit best practices. Then, the efficiency level is assigned to other non-frontier units according to their distances to the efficient frontier. The basic idea has since generated a wide range of variations in measuring efficiency. The frontier technology with DEA is constructed as a piecewise function over the data. In terms of the context or industry under investigation, the estimation of DEA models can be conducted with either input or output orientation, following either constant or variable returns to scale (CRS or VRS) [46,47,48,49]. Traditional DEA models treat decision-making units (DMUs) as “black boxes” that convert inputs into outputs, without considering the internal structure of the transformation process. However, certain DEA extensions, known as Network DEA (NDEA), recognize that the overall system comprises multiple interconnected subprocesses (or sub-DMUs), with internal links representing intermediate products produced and consumed within the system. These models enable a more detailed level of analysis and enhance the discriminatory power of efficiency assessments [50,51,52,53,54]. The Network DEA model enables a more detailed assessment of the performance of decision-making units (DMUs) by incorporating the internal structure of the production process. As a result, it can offer process-specific insights to independently improve efficiency within individual subsystems. This model is also used in the energy sector [55].

The DEA method is widely used to assess efficiency in the energy sector [56,57,58]. Table 1 presents examples of how the DEA method can be used in sample efficiency studies in the energy sector. In order to assess the efficiency of the energy sector, studies were conducted using a diverse set of input and output data. These included macroeconomic, microeconomic, environmental and social data, taking into account negative effects.

The question of why some companies perform better than others is a central subject in analyzing many business disciplines. The answers to this question are varied and point to a multitude of factors that determine the efficiency of enterprises. One explanation for this problem is provided by the theory of economies of scale. The relationship between the size of a firm and its efficiency is theoretically supported by the economies of scale concept, and the justification for this has been evident in many previous works [74,75,76], but it is also a current issue today [77,78]. The benefits associated with scale economies mainly concern the benefits associated with reducing unit production costs and increasing market share [79]. Large-scale production has led to the standardization of products, which in turn reduces logistic costs. Larger companies have greater bargaining power in the market but are also characterized by a greater ability to obtain external financing. Attention is drawn to the fact that large companies are usually more capable of conducting a lot of R&D and producing many innovations, financing research and development initiatives. This makes them more flexible, risk-resistant, adaptable, and more able to benefit from spillovers than their rivals [80,81]. Large companies can also benefit from better management and bigger market share, stronger bargaining power, stronger competitive power, and more opportunities to work in the fields that require high capital rates, which gives them the ability to obtain greater economic benefits than in smaller companies [77,82]. Although large companies can benefit from economies of scale, there is a certain risk. It is related to the lower flexibility of large companies in terms of quick adaptation to changing macroeconomic and political conditions. In addition, centralized production in some economic sectors may generate greater negative externalities (e.g., related to negative impact on the natural environment) than distributed production. In such cases, the benefits achieved by large companies may be smaller than the negative externalities [83].

There are also studies that show a weak, negative, or insignificant relationship between company size and its efficiency. For example, Niresh and Velnampy [84] did not find any relationship between the size of the firm and its profitability. Similarly, in the studies by Abeyrathna and Priyadarshana [85], no statistically significant relationship was found between the size of the firm and its efficiency. In turn, in the studies by Kartikasari and Merianti [86] a negative relationship was found between the size of the firm and its efficiency. In larger, more authoritarian organizations, there may be a loss of efficiency [87]. Research by Diaz and Sanchez [88] indicates that small and medium-sized firms tend to be less inefficient than the large firms. The greater efficiency of small and medium-sized companies in these studies is explained by the complexity of larger companies in organization and managerial control. Also, the less efficient small firms will exit the market under economic difficulties more easily than large firms will. In addition to the positive, negative, and neutral relationships between firm size and efficiency, the literature also shows relationships in the form of a “U” curve [89,90]. In such a situation, the most effective are the smallest and largest companies.

At the same time, the literature on the subject emphasizes that the benefits of scale economies do not directly require increasing the scale of production or condemning small enterprises to low efficiency. Production at any scale can be as efficient as possible. The scale of production must be compatible with the production technology. The utilization of a specific production technology in large-scale manufacturing facilities does not guarantee its applicability to small enterprises [91,92]. The scale curve (the long run average cost curve of the firm) is also a result of given prices of production factors, which are factors that are assumed to be in perfectly elastic supply, so that their prices are not affected by scale. This introduction of factor prices makes it clear that, at each scale, the least-cost combination of factors is sought, which allows for high efficiency [91]. This means that both small and large enterprises can be effective, which is confirmed, for example, by the research of Marques Serrano et al. [93]. However, the growth of the scale of production is limited, which results from the physical nature of the world. The lack of a limit to the growth of the scale of production would lead to a universal monopolization of the market. But, in practice, there are many offsetting influences that limit the size of firms [94]. These include external barriers related to market entry barriers, the changing and complex business environment, legal, tax, and financial barriers resulting from state policy, and internal constraints resulting from the weakness of the enterprise, including primarily resource shortages or competence limitations [95].

Previous studies show ambiguous results and a variable impact of company size on its efficiency. This points to the need for a continued analysis of this issue.

3. Materials and Methods

This study covered 51 energy sector companies operating in Poland. Data for the analysis were obtained from financial statements published by the analyzed companies. Companies that had published full financial reports for the years 2019–2023 were selected for this study. Data come from the EMIS database [96]. The analysis covered 5 years, from 2019 to 2023. This study selected companies from the energy sector based on the following criteria: their core operational activity was electricity generation; complete financial data were available for the years 2019–2023; their financial statements were free of errors; they did not report negative equity; they demonstrated a diversified scale of production; and their data were consistent across the examined years. Although the sample does not represent the entire population, it was designed to ensure structural and functional diversity within the energy sector, enabling an exploratory and comparative analysis of efficiency. Due to the aim of this work, the surveyed companies were divided into groups depending on their size. The following economic categories were adopted as the division criteria: 1. net sales revenue: this criterion indicates the market power of the company; 2. operating costs; 3. fixed assets. Criteria 2 and 3 indicate the size of the enterprise resulting from its resources, which refer to resource-based theories of competitive advantage [97,98]. Net sales revenue is defined as the revenue generated by the company’s operations prior to the deduction of expenses. This variable is extensively applied in many studies related to technical efficiency [1,73,99]. We used fixed assets to represent the amount of all tangible assets owned by a company. The value of fixed assets is often used in studies of the efficiency of energy companies [59,100,101]. This study used this variable as an economic resource employed to generate revenues in the energy business. Operating costs are also often used in the study of the efficiency of energy companies and determine the generated sales revenues [73,102,103,104]. Due to the lack of information on the number of employees in the surveyed enterprises, the criteria for dividing enterprises into small, medium, and large were not applied in accordance with the recommendations of the Commission of the European Communities [105]. The criteria for dividing companies adopted by us (net sales revenue, operating costs, fixed assets) are frequently utilized as indicators to characterize the size of companies [106]. Financial indicators of companies seem to be better indicators for assessing the size of companies than the level of employment. The level of employment is characterized by greater rigidity than the value of assets and sales. In particular, the level of sales is the most flexible measure of the size of the company. The level of employment is the least flexible, and its changes occur with a significant delay [107].

One of the agglomeration methods—Ward’s method—was used to divide enterprises into homogeneous clusters. First, the data were standardized. The range transformation method was used to standardize x_ij, the jth evaluation indicator of the ith decision-making unit. The selected indicators are all positive, so the standardization equation is

(1)$s_{ij}={\displaystyle \frac{x_{ij}-min\left(x_{ij}\right)}{max\left(x_{ij}\right)-min\left(x_{ij}\right)}}$

The procedure of grouping enterprises was conducted in two stages. In the first stage, two groups of enterprises were obtained (Appendix A, Figure A1; Group I—small enterprises, consisting of 48 enterprises, and Group II—large enterprises, consisting of 3 enterprises). The basic characteristics of the groups of enterprises thus distinguished are presented in Table 2. The division of the surveyed enterprises into two groups differing in size reflects the structure of the energy enterprise market in Poland.

However, the substantial size of the small energy enterprise group prompted us to further divide the companies into more homogeneous groups. This will allow for a more in-depth analysis of the impact of the size of energy companies on their efficiency. In the second stage of the procedure, the 48 small enterprises were divided into groups once more using the Ward’s method with Euclidean distance. This procedure was preceded by the re-standardization of indicators, utilizing Formula 1. Consequently, this division resulted in the identification of two distinct subgroups within the group of small enterprises (Appendix A, Figure A2; Group IA—small enterprises, consisting of 42 enterprises, and Group IB—medium enterprises, consisting of 6 enterprises). Ultimately, three groups of companies were obtained. Table 3 presents basic statistics regarding the analyzed variables for the analyzed enterprises, divided into three groups in the second step. Compared to the division of enterprises in the first step, in the second step, two groups, IA and IB, were obtained (Table 3), which were characterized by lower variability of the analyzed economic categories than in the first step (Table 2).

In order to assess the efficiency of the researched energy companies, the Data Envelopment Analysis (DEA) method was employed. The DEA model can be classified as either input- or output-oriented. Furthermore, DEA models can be categorized according to the type of returns to scale. In this regard, the following models can be distinguished: the CCR model, proposed by Charnes et al. [43], which provides for constant returns to scale; and the BCC model, which provides for a variable return to scale [108]. The DEA model allows the identification of the frontier efficiency function (Figure 1). DMUs are considered to be technically efficient if they are on the efficiency curve (their efficiency index is 1). DMU 2 and DMU 3 are in the CCR efficiency curve (with constant returns to scale), maximizing the output/input ratio, whereas DMUs 1, 2, 3, and 4 are in the BCC efficiency curve (with variable returns to scale). DMU 5 and DMU 6 are outside the efficiency curve, lie below the efficient frontier, and are technically inefficient (their efficiency index is less than 1).

Primary form of DEA model (2) assumes definition of decision-making units (DMUs), and efficiency rate is understood as a maximization of a quotient of measured outcomes to measured inputs under condition that such rates will be less or equal to 1 for each DMU. The DEA makes it possible to identify the most efficient objects and, on this basis, to determine the production possibilities frontier. This frontier serves as a reference point for evaluating the efficiency of the remaining objects and also suggests ways to improve their technical efficiency (TE). TE is calculated according to the following formula [49,90]:

(2)${TE}_j={\displaystyle \frac{\sum _{r=1}^l{\mu }_r{y}_{rj}}{\sum _{i=1}^k{\gamma }_i{x}_{ij}}}$

Subject to

(3)${\displaystyle \frac{\sum _{r=1}^l{\mu }_r{y}_{rj}}{\sum _{i=1}^k{\gamma }_i{x}_{ij}}}\le 1 \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{a}\mathrm{l}\mathrm{l} i=1,2 \dots ,n$

(4)${\mu }_r\ge 0, {\gamma }_i\ge 0 \mathrm{for} \mathrm{all} r=1, \dots ,l;i=1, \dots ,k$

where

j—Index of the evaluated DMU, j = 1, …, n;

l—Number of outputs;

k—Number of inputs;

y_rj—Amount of output r for DMU j;

x_ij—Amount of input i for DMU j;

µ_r—Weight assigned to output r;

γ_i—Weight assigned to input i.

The analysis of technical efficiency of energy companies using the DEA method was conducted with the following input and output variables:

Inputs:

x₁—Operating costs (PLN 1000);

x₂—The value of fixed assets (PLN 1000),

Outputs:

y₁—Sales revenue (PLN 1000).

The adopted variables are often used to analyze the efficiency of energy companies [99,100,109]. An input-oriented model with constant returns to scale (CCR model) was used to analyze technical efficiency. This model allows for determining a potential input reduction without any alteration in the output. The DEA model with constant returns to scale (CRS) and input orientation assumes constant returns to scale, meaning that an increase in inputs results in a proportional increase in outputs. In the case of energy companies operating within a uniform macroeconomic environment shaped by legal and regulatory frameworks, and where production technologies are largely similar, the application of the DEA model with constant returns to scale (CRSs) is well justified. Moreover, the choice of an input-oriented approach is based on the fact that energy companies have significantly greater control over their inputs (e.g., operating costs, capital assets) than over their outputs (e.g., sales revenue), which are often influenced by external market forces, regulatory constraints, and demand-side conditions. The input-oriented model focuses on identifying potential reductions in resource consumption without decreasing output levels, which is highly relevant for improving cost efficiency and operational performance in the energy sector. The calculations were performed using the DEAP (Data Envelopment Analysis Program) software (DEAP Version 2.1) [110].

For n decision-making units (DMUs), each using k = 2 inputs to produce l = 1 output, the data on inputs and output can be represented as a matrix of size n × (k + l) [111]:

(5)$D=\left[\begin{array}{ccc}{x}_{11}& x_{12}& y_{11}\\ x_{21}& x_{22}& y_{21}\\ ⋮& ⋮& ⋮\\ x_{n1}& x_{n2}& y_{n1}\end{array}\right]\in R^{n\times 3}$

where x_i1 and x_i2 denote the operating costs and fixed assets of unit i, and y_i1 denotes the sales revenue of unit i.

The technical efficiency of a specific decision-making unit DMU_N where 1 ≤ N ≤ n is determined by solving the following linear programming model [111]:

$\underset{\theta ,\lambda }{min} \theta$

subject to

(6)${\sum }_{i=1}^n{\lambda }_i{y}_{i1}\ge y_{N1}(\mathrm{the} \mathrm{outputs} \mathrm{remain} \mathrm{at} \mathrm{a} \mathrm{constant} \mathrm{level})$

${\sum }_{i=1}^n{\lambda }_i{x}_{i1}\le \theta x_{N1}$

(7)${\sum }_{i=1}^n{\lambda }_i{x}_{i2}\le \theta x_{N2}(\mathrm{the} \mathrm{inputs} \mathrm{are} \mathrm{proportionally} \mathrm{reduced})$

${\lambda }_i\ge 0 \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{a}\mathrm{l}\mathrm{l} i=1, \dots , n$

A DMU is considered technically efficient if the optimal solution satisfies

${\lambda }_i=0 \mathrm{for} i\ne N, {\lambda }_N=1, \theta =1$

If $\theta$ = 1, the DMU is considered effective, a value of 1 indicating a point on the frontier and hence a technically efficient DMU. In contrast, the value 1 − $\theta$ illustrates how much the inputs can be diminished without a corresponding output reduction [112].

The Malmquist index was employed to evaluate the year-on-year changes in total factor productivity (TFPCH) in analysis of energy companies over the period 2019–2023. The Malmquist index is defined using distance functions. The employment of distance functions facilitates the description of a multi-input, multi-output production technology, obviating the necessity for the specification of a behavioral objective (e.g., cost minimization or profit maximization) [98]. The concept of Malmquist productivity index was first introduced by Malmquist [113] and has further been developed by several authors [114,115]. It is an index representing total factor productivity growth of a DMU, in that it reflects progress or regress in efficiency along with progress or regress of the frontier technology over time under the multiple inputs and multiple output framework [116]. The Malmquist index (total factor productivity change—TFPCH) for decision-making unit A, which characterizes the change in total factor productivity (TFPCH) level between period t and t + 1, is determined by the following formula [115]:

(8)$M{I}_{t,t+1}(A)=\underset{\mathrm{E}\mathrm{F}\mathrm{F}\mathrm{C}\mathrm{H}}{\underbrace{{\displaystyle \frac{E^{t+1}\left(A_{t+1}\right)}{E^t\left(A_t\right)}}}}\underset{\mathrm{T}\mathrm{E}\mathrm{C}\mathrm{H}\mathrm{C}\mathrm{H}}{\underbrace{\sqrt{{\displaystyle \frac{E^t\left(A_t\right)}{E^{t+1}\left(A_t\right)}}\cdot {\displaystyle \frac{E^t\left(A_{t+1}\right)}{E^{t+1}\left(A_{t+1}\right)}}}}}$

where EFFCH—changes in technical efficiency; TECHCH—technological change; $E^{t+1}\left(A_{t+1}\right)$—technical efficiency of the entity for data for the t + 1 period and technology in period t + 1; $E^t\left(A_t\right)$—technical efficiency of the entity for data for the t period and technology in period t; $E^t\left(A_{t+1}\right)$—technical efficiency of the entity for data for the t period and technology in period t + 1; and $E^{t+1}\left(A_t\right)$—technical efficiency of the entity for data for the t + 1 period and technology in period t.

The efficiency change (EFFCH) is equivalent to the ratio of the technical efficiency in period t + 1 to the technical efficiency in period t, which will be higher than 1 if there was an increase in efficiency. The ratio EFFCH measures the change in relative efficiency (i.e., the change in how far observed production is from maximum potential production) between years t and t + 1. The ratio TECHCH is the geometric mean of the shift in technology between the two periods, evaluated at t + 1 and also at t. It is an indicator of the distance covered by the efficient frontier from one period to another and thus a measure of technological improvement between the periods. The TECHCH index can be less than, equal to, or greater than one, indicating that technological practices are deteriorating, remaining unchanged, or improving, respectively. Similarly, if the Malmquist index value is less than, equal to, or greater than one, it means that TFPCH is decreasing, remaining unchanged, or increasing, respectively [98,117]. In order to extract the Malmquist productivity indices, the same set of variables was employed as in the case of analyzing the efficiency of energy companies using the DEA method.

Given that the DEA approach is non-parametric, i.e., it does not make any a priori assumptions about the distribution of the variables, and the non-parametric Kruskal–Wallis test was implemented for the purpose of conducting the statistical analysis [118]. The advantages of this test are that it does not require the assumption of a normal distribution or equal variances across groups, is less sensitive to extreme values, and performs well even when group sizes are small or unequal—situations where parametric tests may not be reliable. Post hoc analysis for Kruskal–Wallis ANOVA was performed by using a multiple comparison test. The Wilcoxon test was used to assess the non-randomness of changes in selected variables over time. All statistical calculations were performed using STATISTICA 13.3 PL (StatSoft, Krakow, Poland) software.

4. Results

4.1. Technical Efficiency of the Analized Energy Companies

Table 4 presents the results of the assessment of the technical efficiency of the surveyed energy companies for individual years of the analyzed period. In the event of the obtained value of the technical efficiency scores being equal to one, it is assumed that the given DMU is characterized by the maximum level of efficiency and is on the frontier of the efficiency function defined by the DEA model. Whereas all other less-efficient DMUs are scored somewhere between zero and one. In the analyzed enterprises, efficiency indicators were at a low level (total enterprises: minimum average value: 0.135 in 2019; maximum average value: 0.162 in 2022; minimum median: 0.065 in 2020; and maximum median: 0.102 in 2022). This indicates a large efficiency gap in the analyzed enterprises and a large variation in the technical efficiency scores between enterprises (coefficient of variation: from 133.39% to 175.47%).

From an analysis of the differences in technical efficiency between the selected groups of enterprises, it can be seen that enterprises from Group II (large) are characterized by a higher level of technical efficiency than enterprises from Group IA (small) and IB (medium) (Table 4). These differences are related to mean values. In the case of technical efficiency expressed by the median, the large enterprises achieve worse results than the other two groups of enterprises. To determine the differences in the technical efficiency of enterprises from the distinguished groups, the Kruskal–Wallis test was used. The Kruskal–Wallis test confirmed a statistically significant impact of enterprise size on technical efficiency in 2020 and 2021 (appropriately p = 0.011; p = 0.027). In the remaining years, no statistically significant impact of enterprise size on their efficiency was found. To determine which groups of surveyed companies differ statistically significantly from each other, the Kruskal–Wallis post hoc test was used. In 2020, statistically significant differences in the technical efficiency scores were identified between the IA (small) and IB (medium) groups (p = 0.012), and the same relationships were found in 2021 (p = 0.028) (Table 5). The technical efficiency of Group IA (small) enterprises in 2020 and 2021 was statistically significantly higher than that of Group IB (medium) enterprises.

Significant variations in the technical efficiency of the analyzed companies are confirmed by the distribution of enterprises according to their efficiency levels. Table 6 includes information on the number of DMUs that present inefficient or less-efficient practices and the number of DMUs that present the best efficient practices. The analysis of the distribution of enterprises depending on the level of the technical efficiency scores indicates a significant share in all groups of enterprises with the lowest technical efficiency (less than 0.1). Among the analyzed DMUs, only two achieved a technical efficiency score of 1 (θ = 1) in 2019, while, in the remaining years, this number increased to three DMUs. The predominant share was held by DMUs with very low technical efficiency scores (less than 0.1 and in the range 0.1 ≤ TE < 0.3). The best situation was observed in 2022, where the technical efficiency score was the highest (average 0.162, median 0.102), and the proportion of DMUs in the range of less than 0.1 was at its lowest during the specified period (48.08%). This could be related to the higher level of energy prices on the market (Figure 2 and Figure 3) and the resulting improvement in macroeconomic conditions. However, in the following year, 2023, despite high energy prices, the share of companies with a low level of technical efficiency (less than 0.1) was high and significantly higher than in 2022. The reasons for this situation can be found in changes in the value of revenues and costs. In 2023, the value of operating costs increased more (by 40%) than the value of net sales (by 34.5%) (Table 7). The year 2022 was more favorable in this respect, as the rate of growth of net sales revenues was slightly higher (47.5%) than the rate of growth of operating costs (46.6%).

These results indicate that enterprise size is not the primary factor determining efficiency. The statistically significant differences in technical efficiency recorded in 2020 and 2021 apply only to small (IA) and medium-sized enterprises (IB). There were no statistically significant differences in technical efficiency between the group of large enterprises (II) and the other two groups. In the same macroeconomic environment conditions in which the analyzed enterprises operate, sources of efficiency and inefficiency should be sought in the internal conditions of enterprises. These sources can be related to the applied production technologies, management, organization, resources of enterprises, or the method of energy production.

4.2. Changes in Total Factor Productivity (Malmquist Index) of Analyzed Energy Companies

Table 8 presents an assessment of changes in the level of efficiency of the energy companies under study, employing the Malmquist index (TFPCH) with its decomposition into two components: technical efficiency change (EFFCH) and technological change (TECHCH). This evaluation was conducted by undertaking a comparative analysis between the period t + 1 and the preceding period t. In each of the years analyzed, an increase in total factor productivity (TFPCH) was recorded. In the last year analyzed (2023/2022), a slight increase in the Malmquist index (TFPCH) was recorded (on average by 5.1%), but, in the case of the median, it was a decrease by 4%. By decomposing TFPCH into two components, EFFCH and TECHCH, one can assess the change in technical efficiency and the change in the technological possibilities frontier (technological progress) [117]. In the compared years of 2020/2019 and 2021/2020, the increase in the Malmquist index resulted from both the improvement of technical efficiency (EFFCH), i.e., the shift in DMUs towards the production possibilities frontier set by the reference unit, and technological progress (TECHCH), i.e., the shift in the production function. In 2022/2021, there was a clear increase in technical efficiency (EFFCH) and a significant decrease in technological capabilities (TECHCH). The next period of 2023/2022 is, in turn, an increase in technological capabilities (TECHCH) and a decrease in technical efficiency (EFFCH). Similar relationships for the entire set of enterprises occur in individual groups of enterprises, both small and large. Table 9 presents the results of the Wilcoxon test for comparisons between the analyzed periods. This analysis shows that statistically significant differences were observed for the total set of companies only when comparing the Malmquist index (TFPCH) between 2023 and 2022 (p = 0.046; significance level p < 0.05). Statistically significant differences in the Malmquist index (TFPCH) were also found for Group IA (small companies) during the same period (p = 0.024). In Group IB (medium-sized companies), significant differences were observed only in 2020 compared to 2019. The lack of statistically significant differences in the Malmquist index (TFPCH) in other periods may suggest that the analyzed companies did not improve their efficiency over time.

5. Discussion

Effectively operating companies in the energy sector are able to develop and compete in the energy market. The efficiency of these companies is also important from the point of view of the energy security of the society of a given country [121]. The activities of energy companies are associated with their specificity. On the one hand, these companies strive to achieve economic goals, and, on the other hand, they also perform an important social function. Therefore, the analysis of the factors that determine the efficiency of such companies is not only an important issue from a scientific point of view, but it is also important for political decision-makers and society. In addition, companies supplying electricity are treated as companies of strategic importance for the economy [122,123]. Energy policy in many European countries is conducted in a way that naturally favors the stable growth of enterprises rather than maximizing effects in the short term [124].

Among the factors determining efficiency, attention is paid to the size of enterprises. The greater efficiency of larger enterprises results from the scale effect. In our research, statistically significant differences in technical efficiency were found only between small and medium enterprises and only in two of the five analyzed years. In the remaining cases, no statistically significant effect of the size of enterprises on their technical efficiency was found. This finding suggests that the size of an energy company is not a determining factor in the efficiency of its operations. In addition, the results of our research also suggest that small energy companies can be characterized by technical efficiency at the level of large companies. This finding is important from the point of view of the possibility of dispersing the infrastructure responsible for electricity production without losses in the efficiency of its production. Similarly, in the studies of Iovino and Migliaccio [125], it was found that small enterprises can achieve financial results at the level of large energy companies. Similarly, in a study by Kusz et al. [59], it was found that small agricultural biogas plants can be as efficient as large agricultural biogas plants. Also, in a study by Rheynaldi et al. [126], no statistically significant impact of the size of energy companies operating in Indonesia on financial indicators was found. The results of Thakur et al. [127] indicate a negative relationship between the size of energy companies and their efficiency. In turn, research by Shun-xian [89] on the relation of scale of plants and technical efficiency presents a “U” curve. Our research also partly indicates the possibility of a U-shaped relationship between technical efficiency and the size of enterprises. This applies to the years 2020 and 2021, where small enterprises were characterized by technical efficiency statistically higher than medium enterprises. In research conducted by Fachrudin and Ihsan [128], they showed that firm size has a positive effect on stock returns of the largest users of energy production of oil, gas, and coal, but this effect is not significant. Similarly, in research conducted by Chen [129], Bai and Song [130], and Steinbrunner [131], a positive influence of the size of energy companies on their efficiency was demonstrated. Also, in a study by Coto-Millán et al. [132], they showed that size is a significant variable, as large companies achieve higher levels of technical efficiency. The findings of this research demonstrate a diverse impact of the magnitude of energy companies on their efficiency or an absence of a statistically significant relationship. This finding suggests the necessity for a more comprehensive investigation into the factors that influence the efficiency of energy companies. These factors may be both exogenous and endogenous.

Reflection on the results obtained from our own research stating the lack of a clear impact of the size of energy companies on their technical efficiency or the indication that small companies can achieve technical efficiency at a similar level to large companies provides useful policy implications. Iovino and Migliaccio [125] draw attention to this in their research, indicating that the analysis of the impact of the size of enterprises on their efficiency is important from the point of view of future investors. It allows for making the right choices and indicates the possibilities of investing in smaller firms. Thanks to this, it is possible to limit the investment risk. The possibility of developing small energy companies is also important from the point of view of energy security. The dispersion of energy infrastructure facilities is a factor that increases energy security. This issue also falls within the aspect of the energy market structure. In practice, electricity markets are oligopoly markets with imperfect competition [133]. In general, centralized markets are less flexible. The possibility of developing small businesses in the energy market will allow an increase in competition, the priority of liberalization of the energy sector, a broader choice among different suppliers, a reduction in prices, and an improvement in service quality. However, there may be certain barriers to the operation of small, local energy companies. According to Fuentes González et al. [134], small local energy companies may have problems with profitability and be characterized by high reliance on long-term debt. Implementing development investments can be difficult as a result. They also draw attention to the importance of small energy enterprises not only in the context of energy security but also the benefits associated with the operation of small and medium-sized enterprises (SMEs) for the development of the national economy, the local economy, and the importance of the latter in socially relevant issues as important as employment, innovation, and the standard of living [134,135].

6. Conclusions

Energy sectors have been traditionally characterized by large companies, but liberalizations allowed smaller firms to enter electricity markets [131]. Despite institutional and structural changes in the energy market in the European Union and the liberalizations of this market, the European electricity generation industry is still highly concentrated [136]. It is therefore particularly pertinent to consider the relationship between companies’ performance and firm size in the energy sector, as these policies have reallocated resources from larger to smaller firms [131]. Changing the operating conditions of energy companies requires attention to their consequences. The approach we used, based on the DEA method, allowed us to use widely available financial data to assess the technical efficiency of the energy companies studied. The advantage of this approach is the possibility of a relatively simple assessment of the efficiency of energy companies in different spatial and temporal systems.

The findings of our study suggest that

Small and medium-sized energy companies can exhibit levels of efficiency that are comparable to those of larger enterprises. This finding indicates that entities of varying sizes can coexist within the energy market. A prerequisite for such coexistence is the utilization of appropriate production technology that is adapted to the planned scale of production. Analysis of the relationship between energy production technology and enterprise efficiency requires further detailed research.

The surveyed enterprises exhibited low technical efficiency (TE) levels, with a significant proportion recording TE scores below 0.3. This suggests considerable potential for improving technical efficiency across many enterprises and highlights the need to identify the underlying causes of inefficiency. Addressing this issue poses a challenge for enterprise managers and represents a crucial aspect in shaping energy policy mechanisms and tools.

The best results for both technical efficiency (TE) and the Malmquist index were recorded in 2022. This may have resulted from favorable macroeconomic conditions, particularly the sharp increase in energy prices. Consequently, the surveyed companies experienced a more dynamic growth in sales revenues than in operating costs. This underscores the significant role of macroeconomic conditions in shaping the efficiency of energy companies.

The conducted research is particularly important from the point of view of the policy of development of the energy sector, its liberalization, removing market barriers, and encouraging small energy companies to enter the market. The conducted research shows that, in Poland, small energy companies can conduct business with a similar level of technical efficiency as large energy companies. It is also important for policymakers that the development of small energy companies can be supported in the policy of development of the energy sector. This research also shows that a large percentage of energy companies are characterized by a low level of technical efficiency. Further research should pay attention to the causes of this inefficiency. Understanding these causes will allow for the development of methods of counteracting and will protect against the relocation of resources (e.g., in the form of public aid) to less productive enterprises. This will protect the market from the tendency to conserve the industry structure by keeping less efficient energy firms in the market. In addition, a large share of companies with low technical efficiency is a threat to the country’s energy security.

Future research should focus on the marginal effects of firm size. The marginal effects of firm size diminish when enterprises grow in size. While smaller enterprises benefit from larger productivity rises given learning processes, the impact on larger firms is smaller, as exploiting returns to scale becomes more difficult, and agency problems and other frictions eat up larger parts of the benefits from larger companies [131]. In addition, future research should also pay attention to the relationship between the method of energy production and the efficiency of enterprises. This is particularly important in the context of the development policy of obtaining energy from different sources and assessing the efficiency of such investment projects.

Research limitations include the use of a limited number of variables in the analysis of technical efficiency and the limited sample size. This is due to data availability. The present study concentrated on corporate internal performance variables in the form of economic categories whilst eschewing the consideration of macroeconomic factors or other risk investment factors. Moreover, this study did not take into account technological conditions or energy production methods. This requires in-depth analysis. The inclusion of macroeconomic factors, economic risk factors, and energy production technologies in future studies will provide a more comprehensive picture of the research findings.

Author Contributions

Conceptualization, B.K. (Bożena Kusz), D.K., O.J., M.J., B.K. (Bartosz Kozicki), and S.T.; methodology, B.K. (Bożena Kusz) and D.K.; software, B.K. (Bożena Kusz) and D.K.; validation, B.K. (Bożena Kusz), D.K., O.J., and M.J.; formal analysis, B.K. (Bożena Kusz), D.K., O.J., M.J., B.K. (Bartosz Kozicki), and S.T.; investigation, B.K. (Bożena Kusz), D.K., O.J., and M.J.; resources, B.K. (Bożena Kusz); data curation, B.K. (Bożena Kusz) and D.K.; writing—original draft preparation, B.K. (Bożena Kusz), D.K., O.J., M.J., B.K. (Bartosz Kozicki), and S.T.; writing—review and editing, B.K. (Bożena Kusz), D.K., O.J., M.J., B.K. (Bartosz Kozicki), and S.T.; visualization, B.K. (Bożena Kusz); supervision, B.K. (Bożena Kusz); project administration, B.K. (Bożena Kusz) and D.K.; funding acquisition, B.K. (Bartosz Kozicki), B.K. (Bożena Kusz), D.K., O.J., M.J., and S.T. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in this study are included in this article, and further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:

BCC-DEA	Banker, Charnes, and Cooper model of Data Envelopment Analysis
CRSs	Constant returns to scale
DEA	Data Envelopment Analysis
DEA-CCR	Data Envelopment Analysis—Charnes, Cooper, Rhodes model
DESA	Data envelopment scenario analysis
DMU	Decision-making units
EFFCH	Changes in technical efficiency
EMIS	Emerging Markets Information Service
ROA	Return on total assets
ROE	Return on equity
ROI	Return on investment
ROS	Return on sales
SBM-DEA	Slacks-based measure DEA
SE-DEA	Superefficiency data envelopment analysis
TE	Technical efficiency
TECHCH	Technological change
TFP	Total factor productivity
TFPCH	Total factor productivity change
VRS	Variable returns to scale

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1 CCR efficiency curve and BCC efficiency curve. Sources: Own study based on the study of [26].

Figure 2 The average price of electricity for a household consumer and the trend line (PLN/kWh). Sources: Own study based on the study of [119].

Figure 3 The average sale price of electricity on the competitive market and the trend line (PLN/MWh). Sources: Own study based on the study of [120].

Table 1

Efficiency studies focused on the assessment of the energy sector using a DEA-based approach.

Authors	Methods	Units	Inputs	Outputs
Borozan and Starcevic [1]	Bootstrap DEA	28 EU energycompanies	Total assetNumber of employees Gross investment	Revenues GHG emissions
Chai et al. [11]	SBM–DEA model (the efficiency evaluation, including positive and negative output)	17 companies in China’s thermal power sector	Employment (persons)Clean energy installed Capacity (10,000 kWh)Coal power installed Capacity (10,000 kWh)	Total power generationSulfur dioxide emissionsNOx emissionsSoot emissions
Kusz et al. [59]	DEA-CCRMalmquist index	43 agricultural biogas plants	Raw materials and consumables usedEmployee benefit expense The value of fixed assets	Total operating revenue
Ślusarz et al. [60]	DEA-CCR	16 voivodeships	Consumption of biogas Consumption of biomass	Total production of heat from biogas and biomass
Agrell and Bogetoft [61]	DEA model withextensions Malmquist index	310 and 253 heat plants and combined heat and power plants	Primary energy input from different sourcesSecondary heat input from different sourcesTotal carbon dioxide CO2 emissionExpenditures for operation, maintenance, administration, and meteringExpenditures for primary and secondary energyExpenditure for primary fuel	Net delivered thermal energyDelivered electric energyNumber of subscribed connection points of the distribution systemRevenue from sales of electricityLength of distribution network
Athanassopoulos et al. [62]	DESA model	Micro-scenario planning at the level of individual production plants	FuelControllable costsCapital expenditure	Energy producedAvailabilityAccidentsEmissions of pollution
Maradin et al. [29]	DEA-CCR	47 offshore wind energy companies	Tangible fixed assetsCash and cash equivalentCurrent assets	EBIT (earnings before interest and taxes)
Ratner and Ratner [63]	Input-oriented DEA-CCRMalmquist index	24 electric generating companies—first stage11 power plants—second stage	Atmospheric emissionsSolid wasteFreshwater consumption	Generated electricity
Arcos-Vargas et al. [64]	Input-oriented CCR-DEA and VRS-DEA	102 small-scale electricity distributors	Remunerationassets	Distributed energyPoints of supplyAmount of energy not supply
Blázquez-Gómez and Grifell-Tatjé [65]	DEA-CCR	8 electricity distributors	High-voltage distribution networks Medium-voltage distribution networks Low-voltage distribution networksTransformation capacity of the substations for high-to-highvoltage, high-to-medium voltage, in addition to medium-to-low transformation facilities	Number of consumers supplied by each distributorHigh and medium-voltage electricity suppliedLow-voltage electricity supplied
Liu et al. [66]	DEA Malmquist index	8 energy companies	Liability/asset ratioSolvency current ratioAverage inventory turnoverTotal asset turnover	Operating income to paid-in capitalProfit before tax to paid-in capitalNet profit to salesEarnings per share
Ueasin and Wongchai [67]	SE-DEA (superefficiency data envelopment)	8 energy companies	Liability/asset ratioSolvency current ratioAverage inventory turnoverTotal asset turnover	Operating income to Paid-in capitalProfit before tax to paid-in capitalNet profit to salesEarnings per share
Kim and Jo [68]	DEA-CCR	51 electricity companies	Number of employeesinstalled capacity	RevenueProfitElectricity
Rączka [69]	DEA-BCC	41 heat plants	Labor, fuel and pollution	Heat production
Chen and Song [70]	Three-stage DEA	315 renewable energy businesses	The total number of technical professionals employed annuallyThe total R&D investment	Number of patents granted to the company each yearIncrease in intangible assets
Yilmaz [71]	DEA-CCR	10 wind power plants	Number of wind turbinesInvestment costDistance from the grid	Electricity productionDaily production time
Curtis [72]	DEA-CCR	12 wind farms	Total assets	RevenuesEBIT
Zhang et al. [73]	Three-stage DEA	30 companies engaged in hydrogen energy	The number of employeesThe main business costThe fixed assets	The main business incomeThe net profit

Table 2

Economic categories in the analyzed enterprises in individual clusters (averages for 2019–2023, PLN 1000)—first step.

Statistics	Total	Group I (Small)	Group II (Large)
Net sales revenue
Mean	2590.41	361.90	38,989.45
Median	50.51	48.66	29,127.80
Coefficient of variation (%)	381.70	223.86	49.22
Operating costs
Mean	2120.60	295.31	31,933.74
Median	29.23	24.99	33,716.74
Coefficient of variation (%)	455.36	251.54	96.50
Fixed assets
Mean	2370.54	298.40	36,215.50
Median	95.25	91.90	29,439.23
Coefficient of variation (%)	409.75	201.80	66.14

Source: Own study.

Table 3

Economic categories in the analyzed enterprises in individual clusters (averages for 2019–2023, PLN 1000)—second step.

Statistics	Total	Group IA (Small)	Group IB (Medium)	Group II (Large)
Number of DMU	51	42	6	3
	Net sales revenue
Mean	2590.41	85.0	234.6	38,989.45
Median	50.51	43.6	202.9	29,127.80
Coefficient of variation (%)	381.70	170.24	36.66	49.22
	Operating costs
Mean	2120.60	44.4	209.3	31,933.74
Median	29.23	19.6	174.3	33,716.74
Coefficient of variation (%)	455.36	158.16	43.64	96.50
	Fixed assets
Mean	2370.54	107.9	166.3	36,215.50
Median	95.25	87.0	151.2	29,439.23
Coefficient of variation (%)	409.75	104.89	54.63	66.14

Source: Own study.

Table 4

Technical efficiency (TE) scores of the analyzed energy companies and results of the Kruskal–Wallis test for the period 2019–2023.

Statistics	Total	Groups			p-Value
		IA (Small)	IB (Medium)	II (Large)
2019
Mean	0.135	0.134	0.039	0.347
Median	0.076	0.087	0.031	0.024	0.052
Coefficient of variation (%)	169.01	156.01	45.29	162.73
2020
Mean	0.137	0.137	0.032	0.353
Median	0.065	0.084	0.032	0.030	0.011
Coefficient of variation (%)	175.04	163.68	15.56	158.96
2021
Mean	0.134	0.133	0.034	0.352
Median	0.074	0.085	0.033	0.030	0.027
Coefficient of variation (%)	175.47	164.06	21.38	159.19
2022
Mean	0.162	0.160	0.071	0.369
Median	0.102	0.124	0.062	0.056	0.082
Coefficient of variation (%)	133.39	122.02	24.26	148.09
2023
Mean	0.138	0.128	0.091	0.365
Median	0.072	0.072	0.073	0.050	0.750
Coefficient of variation (%)	161.08	157.61	57.66	150.88

Source: Own study.

Table 5

The p-value for the multiple comparisons of the variable: technical efficiency (TE) scores for the period 2020–2021 (Kruskal–Wallis test).

Groups	IA (Small)	IB (Medium)	II (Large)
	2020
IA (small)		0.012	0.817
IB (medium)	0.012		1
II (large)	0.817	1
	2021
IA (small)		0.028	1
IB (medium)	0.028		1
II (large)	1	1

Source: Own study.

Table 6

Distribution of technical efficiency scores (TEs) in energy companies.

Characteristics	Total	Group IA (Small)	Group IB (Medium)	Group II (Large)
	2019
Efficient DMUs (number of units)	2	1	0	1
Efficiency scores (% of units)
Less than 0.1	67.31	62.79	100.0	66.67
0.1 ≤ TE < 0.3	23.08	27.91		-
0.3 ≤ TE < 0.5	1.92	2.33		-
0.5 ≤ TE < 0.7	1.92	2.33		-
0.7 ≤ TE < 0.9	-	-		-
0.9 ≤ TE < 1	1.92	2.33		-
TE = 1	3.85	2.33		33.33
	2020
Efficient DMUs (number of units)	3	2	0	1
Efficiency scores (% of units)
Less than 0.1	73.08	69.77	100.0	66.67
0.1 ≤ TE < 0.3	19.23	23.26		-
0.3 ≤ TE < 0.5	-	-		-
0.5 ≤ TE < 0.7	-	-		-
0.7 ≤ TE < 0.9	1.92	2.33		-
0.9 ≤ TE < 1	-	-		-
TE = 1	5.77	4.65		33.33
	2021
Efficient DMUs (number of units)	3	2	0	1
Efficiency scores (% of units)
Less than 0.1	73.08	69.77	100.0	66.67
0.1 ≤ TE < 0.3	19.23	23.26		-
0.3 ≤ TE < 0.5	-	-		-
0.5 ≤ TE < 0.7	1.92	2.33		-
0.7 ≤ TE < 0.9	-	-		-
0.9 ≤ TE < 1	-	-		-
TE = 1	5.77	4.65		33.33
	2022
Efficient DMUs (number of units)	3	2	0	1
Efficiency scores (% of units)
Less than 0.1	48.08	41.86	83.33	66.67
0.1 ≤ TE < 0.3	44.23	51.16	16.67	-
0.3 ≤ TE < 0.5	1.92	2.33		-
0.5 ≤ TE < 0.7	-	-		-
0.7 ≤ TE < 0.9	-	-		-
0.9 ≤ TE < 1	-	-		-
TE = 1	5.77	4.65		33.33
	2023
Efficient DMUs (number of units)	3	2	0	1
Efficiency scores (% of units)
Less than 0.1	76.92	76.74	83.33	66.67
0.1 ≤ TE < 0.3	15.38	16.28	16.77	-
0.3 ≤ TE < 0.5	1.92	2.33		-
0.5 ≤ TE < 0.7	-	-		-
0.7 ≤ TE < 0.9	-	-		-
0.9 ≤ TE < 1	-	-		-
TE = 1	5.77	4.65		33.33

Source: Own study.

Table 7

Growth index of the analyzed variables (previous year = 1.00).

Characteristics	2020	2021	2022	2023
Net sales revenue	1.175	1.121	1.475	1.345
Operating costs	0.986	1.125	1.466	1.400

Source: Own study.

Table 8

Malmquist index (from year to year; previous year = 1).

Statistics	Total			Group IA (Small)			Group IB (Medium)			Group II (Large)
	effch	techch	tfpch	effch	techch	tfpch	effch	techch	tfpch	effch	techch	tfpch
2020
Mean	1.071	1.074	1.137	1.08	1.091	1.163	0.911	0.965	0.867	1.274	1.051	1.301
Median	1.003	1.031	1.023	0.993	1.039	1.036	1.013	0.913	0.925	1.279	0.914	1.325
Coefficient of variation (%)	46.18	23.44	46.39	41.12	24.37	48.68	24.40	11.94	19.74	21.35	22.61	9.41
2021
Mean	1.011	1.069	1.082	1.001	1.074	1.084	1.049	1.015	1.065	0.982	1.105	1.087
Median	0.988	1.063	1.030	0.962	1.081	1.026	1.048	1.007	1.053	0.988	1.005	0.993
Coefficient of variation (%)	21.72	7.24	23.31	23.82	6.76	25.21	6.90	1.88	7.93	2.15	15.63	17.34
2022
Mean	1.663	0.721	1.162	1.606	0.736	1.156	2.109	0.575	1.223	1.582	0.801	1.122
Median	1.617	0.723	1.068	1.530	0.757	1.067	1.913	0.549	1.078	1.855	0.552	1.044
Coefficient of variation (%)	32.21	21.12	30.35	33.32	16.73	31.89	18.30	10.33	27.40	31.88	53.79	13.58
2023
Mean	0.861	1.232	1.051	0.786	1.248	0.976	1.365	1.175	1.600	0.920	1.115	1.030
Median	0.785	1.221	0.960	0.740	1.277	0.936	1.068	1.158	1.165	0.891	1.070	0.954
Coefficient of variation (%)	56.94	9.99	57.66	49.49	9.69	52.07	66.39	10.11	67.22	7.625	7.89	15.73

Source: Own study.

Table 9

The p-value of the Wilcoxon test for comparisons of the indicator: total factor productivity change (Malmquist index) in the analyzed period (from period to period, period t + 1 to t).

Period	Total	Group IA (Small)	Group IB (Medium)	Group II (Large)
2021 to 2020	0.670	0.871	0.046	0.109
2022 to 2021	0.259	0.378	0.600	0.285
2023 to 2022	0.046	0.024	0.601	0.109

Source: Own study.

Appendix A

Figure A1 Cluster dendrograms—first step.

Figure A2 Cluster dendrograms—second step.

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