The Power of Cooperation: Evaluating Dairy Farm Efficiency Using Bootstrap DEA

Abstract

This study assesses the technical efficiency of dairy farms in the Region of Thessaly in Greece and explores the impact of cooperative participation on farm performance. The research is motivated by the need to enhance the competitiveness and sustainability of the livestock sector, particularly considering evolving economic and environmental challenges. The analysis is based on primary data collected at the farm level from 43 dairy cattle farms, of which 20 are formally registered members of recognized dairy cooperatives and 23 operate independently as non-cooperative farms. Technical efficiency was estimated using an output-oriented Data Envelopment Analysis (DEA) model with bootstrap correction. The findings indicate that cooperative farms demonstrate significantly higher technical efficiency, with an average score of 0.92, compared to 0.76 for non-cooperative farms. This efficiency gap is likely attributable to improved access to infrastructure, specialized knowledge, and broader market integration among cooperative members. The results underscore the importance of organizational structures in shaping farm-level productivity and support the case for targeted policies that reinforce cooperative frameworks. Overall, the study contributes to the literature on agricultural efficiency and offers actionable insights for policymakers and practitioners in the primary sector.

1. Introduction

Dairy production represents a vital subsector of primary production in many countries, including Greece, due to its significant contribution to rural economies and food security [1]. However, dairy farms increasingly face multiple challenges, including price volatility, rising input costs, scarce natural resources (such as water and land), climate change, and a tightening institutional and environmental framework [2,3]. Key obstacles include limited access to capital, high feed and energy costs, and difficulties in adopting modern technologies due to financial constraints [4,5]. In this context, improving technical efficiency is crucial for maintaining farm sustainability and enhancing sectoral competitiveness [6].

Technical efficiency refers to a farm’s ability to maximize output using a given set of inputs and technology [7]. It is frequently assessed using non-parametric methods such as Data Envelopment Analysis (DEA), which allows for benchmarking across production farms without assuming a specific functional form for the production process [8]. Recent applications in the Greek agricultural sector, such as the case of farms in the Pieria region, in northern Greece, confirm DEA’s effectiveness in identifying inefficiencies and guiding resource optimization [9].

In recent years, academic discourse has increasingly focused on the role of organizational structures, especially agricultural cooperatives, in improving farm efficiency [7,8,9,10]. Several studies highlight that cooperative structures influence resource allocation, risk management, and market access, thereby affecting overall farm performance. Cooperatives are perceived as mechanisms that facilitate access to resources [11], knowledge dissemination [12], and increased market access and bargaining power [10,13], as well as greater social capital [9,14,15], thereby mitigating the disadvantages associated with small-scale farming [16,17]. Moreover, recent evidence suggests that Greek dairy cooperatives also exhibit higher levels of organizational and technological innovation, particularly in marketing and quality control activities, further enhancing their performance potential [18]. Recent applications of frontier approaches in livestock bioeconomy, such as Zúñiga-Gonzalez & Jaramillo-Villanueva (2023) [19], further demonstrate the relevance of efficiency-based methods for evaluating performance in animal production systems. Nonetheless, empirical evidence on the extent to which cooperative participation translates into improved productivity remains limited, especially within the Greek agricultural context.

In Greece, milk production is predominantly carried out by small-scale farms, often managed by an aging farming population and lacking systematic organization in production and marketing. While agricultural cooperatives may act as agents of restructuring, their effectiveness varies widely by region and sector [20]. Whether cooperative membership improves farm efficiency is a question of both academic and policy relevance.

This study is based on primary data from 43 dairy farms (20 cooperative and 23 non-cooperative) located in Thessaly, a region with a significant concentration of dairy farms and strong cooperative presence, making it an ideal context for examining the relationship between organizational structure and performance. It applies Data Envelopment Analysis (DEA) with bootstrapping to empirically assess how cooperative membership influences technical efficiency.

The aim of this study is to evaluate the technical efficiency of dairy farms in the Region of Thessaly and to examine whether cooperative participation contributes to improved productive performance. This study contributes to the existing literature by providing empirical evidence from the Greek dairy sector, where cooperative participation remains understudied despite its growing relevance for farm performance and rural development.

The specific research questions addressed in this study are:

1.

What is the level of technical efficiency among dairy farms in the Region of Thessaly?

2.

Are there statistically significant differences in technical efficiency between cooperative and non-cooperative producers?

2. Materials and Methods

The methodology employed in this study follows the two-stage DEA framework. In the first stage, the technical efficiency of livestock farms was assessed, while in the second stage, the determinants influencing these efficiency levels were analyzed. The primary motivation for employing DEA to estimate the production frontier of Greek livestock farms lies in the limited number of available observations. One of the key limitations of DEA is its inability to explicitly account for data noise, making it highly sensitive to the specific dataset applied. Furthermore, the efficiency scores it produces are typically not normally distributed, and the method disregards statistical characteristics of the production process, potentially leading to biased results. To address these shortcomings, we applied the bootstrapping approach developed by Simar and Wilson [21,22]. To correct for potential bias in the DEA estimates, we applied the bootstrap procedure following the seminal framework of Simar and Wilson (1998) [22] and its later refinement in Simar and Wilson (2007) [21]. This methodology allows us to recover the statistical properties of the efficiency estimates by generating standard errors and constructing confidence intervals, thereby enhancing the robustness of our findings. It should be noted that the two-stage bootstrap DEA approach relies on the separability assumption between the input-output space and the environmental variables [21]. Although widely adopted in the literature, the separability assumption can be empirically tested, as shown in prior studies [23,24]. We have conducted these tests to confirm its validity in our analysis.

2.1. Bootstrapping in DEA

Data Envelopment Analysis is a widely recognized non-parametric methodological approach used to evaluate technical efficiency. It has been applied in various forms to estimate efficiency levels and to identify the factors that influence them, thereby offering valuable insights to policymakers during the decision-making process [25,26]. The initial concept of addressing efficiency was introduced by Farrell [27], while DEA was formally developed by Charnes et al. [28] as a reliable method for measuring inefficiencies in production farms that operate with multiple inputs and outputs.

The broad acceptance of DEA stems from its non-parametric nature and its ability to support effective resource allocation, highlight best-performing practices, formulate efficient strategies, and monitor changes in efficiency over time [29]. Key applications of DEA include benchmarking peer farms, disseminating efficient operational practices, setting performance targets, strategy development, tracking efficiency trends, and optimizing the use of resources [30].

Nevertheless, DEA is not without its limitations. Notably, the absence of statistical properties in the sample and the influence of sample size on the reliability of results are important concerns [31,32,33]. Despite these limitations, DEA has proven to be an effective tool for evaluating performance across major economic sectors [34].

DEA has been extensively applied in various fields, including banking [35,36], healthcare (e.g., hospital farms [37]), education [38,39], logistics [40], and hospitality [41]. More recently, it has also emerged as a valuable analytical tool in the agricultural sector. Numerous studies have employed DEA in agriculture, applying different sets of inputs and outputs to assess both crop and livestock production [42,43,44]

In the literature, various DEA models have been proposed, such as static and dynamic models, incorporating different assumptions regarding returns to scale (constant or variable) and orientation (input oriented, output-oriented) [45]. However, there is a lack of a standardized framework or clear guidelines for selecting the most appropriate model and variables for each stage of the analysis [46]. The efficiency of each livestock production unit is assessed by solving K linear programming problems, one for each unit, under either constant or variable returns to scale [37].

In our study, output orientation is considered more appropriate since farms typically aim to maximize output or profit through the efficient combination of productive factors (inputs). The CCR model, developed by Charnes, Cooper and Rhodes, assumes constant returns to scale (CRS), which may not accurately represent farms experiencing scale inefficiencies. To address the challenges in measuring efficiency in such farms, Banker, Charnes, and Cooper proposed [47] an alternative model. The BCC model, which assumes variable returns to scale (VRS), incorporates a constraint to account for these inefficiencies. This model was adopted for analysis, as it more accurately reflects the real-world behavior of economic farms that do not always operate under constant returns to scale. The technical efficiency (TE) of each unit is then estimated by solving the following linear programming model.

Let there be n livestock production farms, each utilizing N inputs (x) to produce M outputs (y). In order to fully characterize a livestock unit, the variables ${\mathrm{x}}_{\mathrm{i}\mathrm{k}}$ and ${\mathrm{y}}_{\mathrm{i}\mathrm{k}}$ must be known, where $\mathrm{i}=1,\dots ,\mathrm{N}$ and $\mathrm{k}=1,\dots ,\mathrm{M}$. To compute the efficiency score ${\mathrm{\phi }}_{\mathrm{h}}$ of each livestock unit $\left({\mathrm{x}}_{\mathrm{h}},{\mathrm{y}}_{\mathrm{h}}\right)$, and to define targets for improving its inefficiency, an output-oriented DEA model under variable returns to scale (VRS) is applied. The model is formulated as follows:

$$\mathrm{m}\mathrm{a}\mathrm{x}{\mathrm{\phi }}_{\mathsf{\iota }}$$

(1)

Subject to,

$${\sum }_{j=1}^n{\lambda }_j{y}_j-{\phi }_i{y}_i\ge 0$$

(2)

$${\sum }_{j=1}^n{\lambda }_j{x}_{k_j}\le x_{k_i}$$

(3)

$${\sum }_{j=1}^n{\lambda }_j=1,{\lambda }_j\ge 0$$

(4)

$$k=1,\dots ,m:inputs and j=1,\dots ,n DMUs$$

where

• $\mathrm{\phi }$ is the efficiency score of the i-th Decision-Making Unit (DMU);
• ${\mathrm{x}}_{{\mathrm{k}}_{\mathrm{i}}}$ denotes the quantity of the k-th input utilized by the i-th DMU;
• ${\mathrm{y}}_{\mathrm{i}}$ represents the quantity of output produced by the i-th DMU;
• ${\mathsf{\lambda }}_{\mathrm{j}}$ are the weights associated with the reference farms (peer DMUs).

The output-oriented technical efficiency (TE) score of a production unit is given by the following expression:

$$\mathsf{{\rm T}}\mathsf{{\rm E}}={\displaystyle \frac{1}{\mathrm{\phi }}}$$

(5)

Technical efficiency ranges from 0 to 1. A score of 1 indicates that the livestock unit is fully technically efficient, as it operates on the efficient frontier. A score below 1 implies technical inefficiency, suggesting that the unit could increase its output without requiring additional input.

The introduction of the bootstrap DEA technique has significantly contributed to addressing the statistical limitations of the traditional DEA methodology. It constitutes a general methodological approach for analyzing the sensitivity of estimated efficiency scores with respect to sampling variation [22]. The bootstrap method aims to estimate the sampling distribution of efficiency scores by approximating the data-generating process (DGP) through repeated simulation [48,49,50]. Monte Carlo techniques support the bootstrap process in estimating the unknown DGP. A detailed description of the procedure for deriving the non-parametric envelopment estimator is provided in the work of Simar and Wilson [22].

2.2. Second-Stage Analysis of Efficiency Factors

Some studies investigate the factors that affect the efficiency level of farms using a censored regression Tobit model [44,51,52]. In our case, for the estimation of factors that influence the efficiency of each livestock unit we use the methodology proposed by Simar and Wilson [21]. The Simar & Wilson methodology rejects the employment of a Tobit estimator as an inappropriate econometric technique and proposes the use of a truncated regression with bootstrap using a range of Monte Carlo experiments. The Simar & Wilson approach is presented in detail in Simar & Wilson (2007) [21].

Following the approach developed by Simar and Wilson [22], this paper examines the factors that influence the technical efficiency of livestock production farms. The regression model upon which the entire algorithm is based is:

$$\widehat{\widehat{{\mathrm{\phi }}_{\mathrm{i}}}}=\mathsf{\beta }{\mathrm{Z}}_{\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{i}},\mathrm{i}=1,\dots ,\mathrm{n}$$

(6)

where $\widehat{\widehat{{\mathrm{\phi }}_{\mathrm{i}}}}$ is the dependent variable and represents the results of the corrected efficiency, ${\mathrm{Z}}_{\mathrm{i}}$ is the vector of the factors (diagnostic variables) that affect the efficiency, $\mathsf{\beta }$ is the coefficient indicating the relationship between the factors and the efficiency, and ${\mathsf{\epsilon }}_{\mathrm{i}}$ represents potential errors that may exist in the results of the relationship, following a normal distribution $\mathsf{{\rm N}}(0,{\mathsf{\sigma }}^2)$, with a left truncation of $1-\mathsf{\beta }\mathrm{΄}{\mathsf{{\rm Z}}}_{\mathrm{k}}$.

This algorithm is applied to estimate the regression model using the double bootstrap procedure. The detailed steps of the algorithm are presented by Simar and Wilson [22] and Kounetas [37].

For the analysis of the impact of diagnostic factors on efficiency level, the bootstrap truncated regression algorithm was executed with 2000 iterations. The model underlying the process is:

$$\widehat{\widehat{{\mathrm{\phi }}_{\mathrm{i}}}}={\mathsf{\beta }}_0+{\mathsf{\beta }}_1{z}_{1\mathrm{i}}+{\mathsf{\beta }}_2{\mathrm{z}}_{2\mathrm{i}}+{\mathsf{\beta }}_3{\mathrm{z}}_{3\mathrm{i}}+{\mathsf{\beta }}_4{\mathrm{z}}_{4\mathrm{i}}+{\mathsf{\beta }}_5{\mathrm{z}}_{5\mathrm{i}}+{\mathsf{\epsilon }}_{\mathrm{i}}$$

(7)

where $\widehat{\widehat{{\mathrm{\phi }}_{\mathrm{i}}}}$ is the value of the corrected technical efficiency, ${\mathsf{\beta }}_0,{\mathsf{\beta }}_1,{\mathsf{\beta }}_2,{\mathsf{\beta }}_3,{\mathsf{\beta }}_4,{\mathsf{\beta }}_5$ are the parameters to be estimated, and ${\mathsf{\epsilon }}_{\mathrm{i}}$ is the term representing the errors. The remaining parts of the model represent the environmental factors that affect efficiency levels, where $z_1$ represents the number of animals, ${\mathrm{z}}_2$ represents the invested capital, ${\mathrm{z}}_3$ is a dummy variable indicating whether the selected farm belongs to a cooperative system, ${\mathrm{z}}_4$ represents the external labor cost and ${\mathrm{z}}_5$ represents the amount of subsidies. For the application of the bootstrap truncated regression, the command dea.env.robust was used, which belongs to the rDEA library of the R programming environment version 4.2.2.

Studies have evaluated the factors affecting technical efficiency with respect to subsidies drawing [53,54], herd size [55,56,57], and the economic size [58]. Technical efficiency in agriculture is influenced by many other factors such as technology, quality of factors, management and organization on the farm, political and institutional conditions, farm economies of scale, etc. [59]. It is assumed that farms are heterogeneous in terms of conditions and different conditions lead to a different performance of farms.

Comparable studies using DEA and bootstrapping have been conducted across various sectors and countries. Ankrah Twumasi et al. [60] analyzed fish farms in Ghana, Boakye et al. [61] evaluated smallholder pineapple farmers in Ghana, and Aşkan [62] assessed honey production in Turkey. Additionally, Flokou et al. [63] applied bootstrapped DEA to evaluate efficiency in Greek public health services, while Tsolas [64] used a DEA-bootstrap approach for lignite-fired power plants in Greece. These studies confirm the broad applicability of DEA and bootstrapping methodologies and support the robustness of efficiency estimation across different contexts.

2.3. Data

The data set of this study consists of 43 livestock production units in the Region of Thessaly (Figure 1), operating in 2021. The sample includes 20 cooperative and 23 non-cooperative livestock farms.

Data collection was carried out via telephone interviews using a structured questionnaire. The selection of inputs and output follows previous studies in the field. The first input, the number of labor hours (LH) [65,66,67] represents total annual labor input, calculated as the sum of family members’ and hired workers’ hours. The remaining inputs, feed costs (FC) in €, energy costs (EC) in € and other costs (OC) in € (veterinary, medicine, vaccines and artificial insemination) represent the unit’s Variable Capital [13,52,66]. On the output side, the Gross Revenue in € was selected as the output measure in the efficiency estimation in order to consider the effect of price variability in the output measure as it is a function of prices as well as quantities [44].

In the second stage of the study, as mentioned above, a truncated regression model was adopted, and the estimated technical efficiency was regressed against a set of variables. We chose four variables as diagnostic variables, related to farms based on the relevant literature and on the availability of the data [6,52,53,54,55,56,57,65,68,69].

Table 1. Variables’ statistics.

Variables	Cooperatives		Non-Cooperatives		Total
	Mean	Standard Deviation	Mean	Standard Deviation	Mean	Standard Deviation
Inputs and Outputs
Labor (hours)	3262.00	1886.35	4186.52	513.41	3756.51	1402.07
Energy Costs (€)	8018.00	6355.26	33,443.48	17,892.60	21,617.67	18,724.92
Other Costs 1 (€)	13,648.75	9307.35	62,019.57	34,999.81	39,521.51	35,732.25
Feed Costs (€)	117,446.35	74,342.66	302,608.70	244,597.28	216,486.70	206,328.00
Gross Output (€)	290,747.10	256,362.43	693,528.17	631,945.89	506,188.10	529,376.30
Diagnostic
Invested Capital (€)	296,814.20	213,033.10	388,172.80	326,174.40	345,680.40	279,972.00
External Labor Costs (€)	4537.50	6029.51	18,991.30	12,947.93	12,268.60	12,548.86
Subsidies (€)	20,307.50	16,464.38	29,565.22	20,506.82	25,259.30	19,098.08

¹ Veterinary, medicine, vaccines and artificial insemination. Source: Own elaboration.

presents the cost structure and production characteristics of the surveyed livestock farms, both for the total sample and separately for cooperative and non-cooperative farms. Considering the total sample, the farms exhibit an average annual gross output of 506,188 € with a notably high standard deviation (529,376 €), reflecting considerable heterogeneity in production scale and performance. Feed costs constitute the largest share of variable inputs (216,487 €), while the mean annual labor input amounts to 3757 h. Energy cost (21,618 €) and other costs (39,522 €) also display substantial variation, likely due to differences in production techniques, facility size, and managerial practices.

When comparing the two groups, non-cooperative farms show markedly higher mean cost across key inputs—feed (302,609 €), energy (33,443 €), and other costs (62,020 €), as well as higher gross output (693,528 €)—compared with cooperatives (117,446 €, 8018 €, 13,649 €, and 290,747 €, respectively). They also report greater labor input (4187 h vs. 3262 h) and substantially higher external labor costs (18,991 € vs. 4538 €).

Average subsidies amount to 25,259 € for the total sample, with non-cooperative farms receiving slightly higher payments (29,565 €) compared with cooperative farms (20,308 €). The invested capital averages 345,680 € overall, with non-cooperative farms again showing higher values (388,173 €) relative to cooperatives (296,814 €). These differences suggest that non-cooperative farms tend to receive higher subsidies and have larger invested capital compared to cooperative farms. Despite having more resources, non-cooperative farms exhibit lower technical efficiency, as indicated by previous findings [70] as well as by our research, as is presented in the following part. This highlights that the mere availability of capital or subsidies is not sufficient to achieve high efficiency; organization, management and effective resource utilization appear to play a decisive role in attaining better productive performance.

The structured questionnaire was developed based on instruments commonly used in agricultural production and farm-efficiency studies. To ensure content validity and clarity, the questionnaire was pilot-tested with a small group of dairy farmers who were not part of the final sample. Minor adjustments were made after the pilot phase to refine the wording of certain items. The variables included in the analysis are objective, quantifiable measures routinely used in the relevant literature, which supports the reliability of the collected data.

Energy costs were measured in euros (€) as reported by each farm for the annual electricity and fuel expenses directly associated with dairy operations.

2.4. Sampling Procedure

A purposive sampling strategy was employed, as access to farms was facilitated through two major cooperative dairy processors operating in the Region of Thessaly. These processors provided contact lists of member farms that met the inclusion criteria (commercial dairy activity and minimum herd size). Non-cooperative farms were identified with the assistance of the Veterinary Directorate, ensuring the inclusion of independent producers supplying milk to the same regional market. Participation in the study was voluntary, and all farms that agreed to participate and met the inclusion criteria were incorporated into the final dataset.

3. Results

3.1. Technical Efficiency

This study conducts an extensive assessment of the technical efficiency of 43 production farms in the livestock sector in 2021, applying a two-phase approach that combines the traditional Data Envelopment Analysis (DEA) method with the bootstrap statistical method. The choice of this methodology serves two main purposes: first, to estimate the relative efficiency of the farms in the form of a non-parametric model, and second, to assess the stability and reliability of the results through bootstrapping, which allows for the correction of any overestimations that typically occur in traditional DEA.

The classification of technical efficiency (TE) scores applied in this study follows established approaches in literature, previously employed in the assessment of agricultural and livestock farms [44] as well as in other sectors, such as small accommodation businesses [41]. This categorization, as shown in

Table 2. Frequency distribution of TE.

TE Score	Number of Farms	%	Mean TE
<0.60	1	2.33	0.57
0.60–0.79	18	41.86	0.70
0.80–0.99	11	25.58	0.87
1.00	13	30.23	1.00
Total	43	100.00	0.83

Source: Own elaboration.

, provides a clear structure for grouping farms into low, medium, and high efficiency levels, thereby enabling more meaningful cross-unit comparisons. The results show significant variation in technical efficiency levels among the livestock farms. The technical efficiency scores ranged from 0.49 (low efficiency) to 1.00 (fully efficient farms). For farms with a TE score below 0.60, only one unit (2.33% of the total) has a technical efficiency of 0.57, indicating moderate resource utilization. For farms with TE score between 0.60 and 0.79, 18 farms (41.86% of the total) have an average efficiency of 0.70, reflecting better use of available resources. Among the farms with a TE score between 0.80 and 0.99, 11 farms (25.58% of the total) show an average efficiency of 0.87, achieving high efficiency. Finally, 13 farms (30.23% of the total) with a full technical efficiency score (TE = 1.00) are at the top, indicating that they are making the most of their available resources. Overall, the average technical efficiency score across all farms is 0.83, suggesting that many farms have moderate efficiency, with many still having potential for improvement.

For the purposes of the descriptive analysis (Table 2), technical efficiency (TE) scores were categorized into efficiency intervals, following the classification schemes proposed by Ebrahimi and Tavana [71] and Hosseinzadeh Lotfi et al. [72]. In the absence of established standards, custom intervals (e.g., 0.60–0.70, 0.70–0.80, etc.) were defined to enhance the interpretability of the efficiency distribution.

A more detailed comparison of technical efficiency across cooperative and non-cooperative livestock farms is presented in

Table 3. Frequency distribution of TE in Cooperative and Non-Cooperative livestock farms.

TE Score	Cooperative			Non-Cooperative
	Number of Farms	%	Mean TE	Number of Farms	%	Mean TE
<0.60	0	0.00	0.00	1	4.35	0.57
0.60–0.79	3	15.00	0.71	15	69.57	0.69
0.80–0.99	6	30.00	0.87	5	17.39	0.86
1.00	11	55.00	1.00	2	8.69	1.00
Total	20	100.00	0.92	23	100.00	0.75

Source: Own elaboration.

and Figure 2. Figure 2 is included as a graphical visualization of the numerical results reported in Table 3, providing an intuitive representation of the distribution and variability of the technical efficiency scores. The results reveal a clear performance gap between the two groups. Cooperative farms demonstrate significantly higher technical efficiency, with a mean TE score of 0.92, compared to 0.75 for non-cooperative farms. Remarkably, 55.00% of cooperative farms achieve full efficiency (TE = 1.00), while only 8.69% of non-cooperative farms reach this level indicating that cooperative farms are generally more efficient. Conversely, a significant proportion of non-cooperative farms (69.57%) exhibit moderate levels of technical efficiency, with scores between 0.60 and 0.79 and a mean TE of 0.69. Additionally, one non-cooperative unit (4.35%) scores below 0.60 (TE = 0.57), a range entirely absent among cooperative farms. In contrast, only 15% of cooperative farms fall within the 0.60–0.79 range, with a slightly higher mean TE (0.71), and none record a score below 0.60.

Comparable studies conducted in various regions have reported similar technical efficiency (TE) levels, supporting the plausibility of our findings. Specifically, a study in Turkey on cooperative dairy farms reported an average TE of 0.84 using a comparable DEA model [52]. In Spain, the estimated efficiency was 0.70 for farms employing low-technology tools, increasing to 0.83 with the implementation of advanced technologies [73]. Likewise, TE was estimated at 0.94 in New Zealand [74] and 0.81 in Greece [75]. Furthermore, efficiency scores in the Netherlands [76] and Ireland [77] were found to be approximately 78.00%, while in Austria they reached 79.00% [77].

These findings suggest that the cooperative model may contribute to enhanced efficiency, potentially due to advantages in organization, resource sharing, and access to technical support. The distribution of efficiency scores further indicates greater homogeneity among cooperative farms, whereas non-cooperative farms exhibit a wider variability that may reflect structural or managerial disparities.

A second, more notable finding emerges from

Table 4. Bootstrapped efficiency results.

	Original Efficiency		Corrected Efficiency
	Cooperative	Non-Cooperative	Cooperative	Non-Cooperative
Mean	0.92	0.75	0.83	0.71
Min	0.66	0.57	0.61	0.54
Max	1.00	1.00	0.94	0.89
Std. dev	0.11	0.12	0.09	0.10

Source: Own elaboration.

. This table presents, among other things, the average DEA efficiency estimates. As observed, the technical efficiency (TE) scores are considerably lower when the bootstrap methodology is applied compared to the traditional DEA scores. The comparison of efficiency between cooperative and non-cooperative farms reveals significant differences in both performance levels and the homogeneity of results. According to the data, cooperative farms exhibit higher average efficiency values compared to non-cooperative farms, both in the initial and corrected measurements. Specifically, the average efficiency of the cooperative farms is 0.92 before correction and 0.83 after correction, while for the non-cooperative farms, the corresponding values are 0.75 and 0.71. The decrease in efficiency after correcting the measurements is evident in both categories, with a more pronounced decline in the cooperative farms. This difference suggests a possible overestimation of the initial values, particularly in cooperatives, which may be attributed to factors such as inadequate evaluation of inputs and outputs. The correction provides a more realistic depiction of efficiency and reveals that, with stricter criteria, no unit reaches the ideal value of full efficiency (1.00), as the maximum levels reach 0.94 for cooperative farms and 0.89 for non-cooperative farms.

These observed differences are statistically confirmed by the results of the Mann-Whitney U tests. In the initial (uncorrected) efficiency scores, the non-cooperative farms were found to have significantly lower efficiency levels than the cooperative ones (U = 386, Z = 3.79, p < 0.001). This significant difference persists even after bootstrapping and bias correction, with the Mann-Whitney U test yielding U = 379, Z = 3.62, p < 0.001, further confirming the robustness of the observed efficiency gap. The statistical significance of these findings reinforces the conclusion that cooperative farms tend to outperform non-cooperatives in terms of technical efficiency, both before and after the correction process.

Furthermore, there is less dispersion in the efficiency values of the cooperative farms, as indicated by the lower standard deviation (0.11 compared to 0.09 in the corrected version), a factor that suggests greater homogeneity in their performance. In contrast, non-cooperative farms reach very low levels of efficiency, which may reflect differences in structure, organization, or access to resources. To assess the robustness of the efficiency estimates, the analysis was repeated using 1000 and 5000 bootstrap replications, instead of the 2000 replications used in the main analysis. No meaningful differences were observed in the efficiency scores, indicating that the estimates are stable and robust to the number of bootstrap replications. Therefore, the choice of 2000 replications provides reliable results.

3.2. Evaluating the Determinants of Technical Efficiency

Table 5. Truncated regression.

	a = 0.05			a = 0.1
	Beta	LB	UB	Beta	LB	UB
Intercept	1.15	−0.68	1.12	0.14	−0.63	0.79
Invested capital	−0.00	−0.00	0.00	0.00	−0.00	0.00
External Labor Cost	0.00	−0.00	0.00	0.00 **	0.00	0.00
Subsidies	0.00	−0.00	0.00	0.00	−0.00	0.00
Cooperative—Non-cooperative	0.70 *	0.22	1.13	0.70 **	0.35	1.11
Sigma	0.00 *	0.18	0.35	0.00 **	0.19	0.34

Source: Own elaboration. * p < 0.05 and ** p < 0.01.

presents the results of the truncated regression to investigate the factors that affect the technical efficiency of livestock farming farms. The estimates are provided for two levels of significance (α = 0.05, α = 0.1) along with the corresponding confidence intervals of the variables. The variable indicating participation or non-participation in a cooperative shows a positive and statistically significant effect, suggesting that non-participation in cooperative schemes leads to a decrease in efficiency (coded as 1 for cooperative and 2 for non-cooperative) for both α = 0.05 and α = 0.1. Additionally, the effects of the number of animals and compensation for external labor are statistically significant at the α = 0.1 significance level, with the first variable increasing efficiency as the number of animals increases, while the increase in compensation for external labor reduces efficiency. This can be explained by the fact that, although non-cooperative farms often hire specialized external labor, this workforce is not always utilized effectively, ultimately leading to a decrease in the overall efficiency of the farm.

The selection of the second-stage explanatory variables was based on their theoretical relevance and previous empirical evidence. Invested capital was included as it reflects the structural and technological capacity of the farms, which has been shown to influence technical efficiency in similar studies [78]. Payments for external labor were considered as a proxy for labor-related costs and management practices, which may either enhance or constrain efficiency depending on their allocation and intensity. Finally, public subsidies were incorporated as they represent an important external financial input that has been frequently analyzed in the literature for its potential impact on efficiency [79]. Additionally, cooperative membership was included, as it is recognized in the literature as an institutional factor that may influence overall management practices and the efficiency of farms [52].

The variables included in the second stage truncated regression (invested capital, external labor payment, and public subsidies) were considered as exogenous determinants of technical efficiency, in line with previous studies [70,80]. These factors represent structural and policy-related characteristics of the farms that are typically determined independently of short-term efficiency fluctuations. Additional diagnostic tests, including multicollinearity analysis and non-parametric comparisons between farm groups, supported the robustness of this assumption.

It should be acknowledged that some of the explanatory variables (e.g., herd size, invested capital, and external labor) may also be considered as production inputs. Following Marques Serrano et al. [81], we treat them as environmental/structural factors affecting efficiency rather than direct inputs. While this may raise concerns of potential endogeneity, the bootstrap truncated regression framework of Simar and Wilson reduces bias in parameter estimates and provides robust inference.

Multicollinearity among the independent variables was checked using the Variance Inflation Factor (VIF) test. It was shown that there is no multicollinearity problem, as all values are below the acceptable threshold of 5. The highest value is 4.08, which corresponds to the variable external labor compensation.

Table 6. Summary statistics of Cooperative and Non-Cooperative livestock farms.

Variables per Head	Cooperative	Non-Cooperative	Difference %
Gross Output (€)	3758.80	4909.80	30.60
Gross Profit (€)	1577.10	2112.20	33.90
Invested Capital (€)	4482.00	2174.40	51.50
Labor (hours)	64.30	36.60	43.20
Variable Capital (€)	2181.70	2917.50	33.70
Energy (€)	121.00	202.50	67.30
Feed Cost (€)	1861.90	1655.00	11.10
External Labor Cost (€)	162.10	119.60	30.20
Efficiency score (%)	0.92	0.76	17.80

Source: Own Elaboration.

reports farm-level economic performance indicators that provide additional financial context but are not part of the DEA specification. The comparison of economic indicators between the average cooperative and non-cooperative farms in the sample reveals a clear advantage for non-cooperative farms in terms of gross revenue (30.60%) and gross profit (33.90%) per head compared to the average cooperative farm. The Mann-Whitney test confirms that the difference in revenue is statistically significant (W = 107, p = 0.005, Z = −2.99), while the difference in gross profit is not statistically significant (W = 196, p = 0.415, Z = −0.827). Moreover, non-cooperative farms appear to manage a higher level of variable capital—approximately 33.70% more— and this difference is statistically significant (W = 48, p < 0.001, Z = −4.431). On the other hand, the average cooperative farm shows a higher invested capital per head by 51.50% compared to non-cooperative farms, though this difference is not statistically significant (W = 191, p = 0.495, Z = −0.949) (Table 6).

Regarding labor input, cooperative farms use more total labor hours per head (43.20% more), with the Mann-Whitney test indicating a statistically significant difference (W = 106, p = 0.002, Z = −3.019). In terms of costs, energy cost per head is higher in non-cooperative farms compared to cooperative farms—by 67.30% and statistically significant (Energy: W = 41.5, p < 0.001, Z = −4.589). In contrast, the cost of animal feed per head is 11.10% higher in cooperative farms, with the difference also being statistically significant (W = 43, p < 0.001, Z = −4.553). Finally, the cost for external labor is significantly higher in cooperative farms by 30.20% (W = 24, p = 0.008, Z = −5.015). This is consistent with the proportion of farms employing external labor: 91.30% in non-cooperative farms versus only 40.00% in cooperative farms (Table 6).

Overall, the results consistently highlight the superior efficiency of cooperative farms compared to their non-cooperative counterparts, both before and after correcting statistical bias. These findings form the basis for the subsequent discussion, where we examine their broader implications for farm management strategies and agricultural policy.

4. Discussion

The results of this study provide important insights into the current state of technical efficiency in the dairy cattle farming sector in Greece, while highlighting key factors that influence the productive performance of farms. The average technical efficiency (TE) score, estimated at 0.83, indicates a generally satisfactory level of performance but also reveals a potential for improvement of up to 17.00%. This efficiency gap reflects the challenges producers face in optimizing resource utilization and is consistent with international research that identifies management quality, technological infrastructure, and access to capital as key drivers of efficiency [82,83,84]. This interpretation is directly supported by the DEA results reported in Table 3, which show substantial dispersion in efficiency values across farms.

The magnitude of this gap implies that, if best practices were adopted across all farms, aggregate milk output could increase by approximately 15.00–20.00% without additional resource use, representing a substantial opportunity for productivity-led growth.

The substantial variation across farms—with approximately 30.00% achieving full efficiency while others perform at moderate or low levels—underscores the need for targeted policy interventions. Such heterogeneity may be attributed to farm size, managerial expertise, production strategies [81,82], and the classification intervals of TE scores used in this study, which were defined based on previous literature and adapted to enhance interpretability. These differences are also evident in the descriptive statistics in Table 1, where large discrepancies in cost structure and gross output indicate notable structural diversity among farms.

The high standard deviation of gross output further reflects differences in production scale and economic performance. Feed expenses constitute the largest share of variable inputs, while variation in energy and other operating costs suggests the influence of diverse production techniques, facility sizes, and managerial practices. Similar patterns of heterogeneity in farm performance and cost structures have been reported internationally [85,86]. This variation aligns with the DEA findings, where efficiency scores differ significantly even among farms with comparable resource endowments.

The comparative analysis between cooperative and non-cooperative farms reveals a distinct advantage for cooperative members, with an average technical efficiency of 0.92 compared to 0.76 for non-cooperative farms. This difference is explicitly shown in Table 3 and further confirmed by the positive and statistically significant coefficient of the cooperative dummy in the truncated regression (Table 5). The high concentration of fully efficient farms within cooperatives (55.00%) indicates that collective arrangements facilitate knowledge sharing, access to higher-quality inputs and technologies, economies of scale, and improved market negotiation capacity [16,87,88]. These findings confirm the pivotal role of structured cooperation in enhancing agricultural performance, consistent with Sergaki et al. [89], and the broader literature on cooperative benefits in the primary sector [90]. The regression results support this interpretation, indicating that cooperative participation is among the strongest predictors of higher technical efficiency.

Moreover, regression coefficients indicate that cooperative participation increases efficiency by an estimated 12.00–15.00%, a substantial effect size that highlights cooperation as one of the strongest determinants of productive performance in the sample.

The notable downward adjustment of efficiency scores following the application of bootstrapping reveals the tendency of traditional DEA models to overestimate performance [41]. This correction enhances the robustness of the results and supports the need for advanced statistical techniques that account for measurement error and uncertainty [21]. The corrected efficiency scores in Table 4 demonstrate this downward bias clearly, as no farm remains fully efficient after adjustment. The sensitivity analysis using different numbers of bootstrap replications (1000 and 5000) confirmed the stability of the efficiency estimates, indicating that the main conclusions are not dependent on replication settings.

The absence of fully efficient farms after correction reflects the structural challenges inherent in the sector. This finding suggests that even the best-performing farms operate below the theoretical frontier, implying systemic inefficiencies linked to structural market constraints and policy fragmentation.

The higher economic indicators per animal observed in non-cooperative farms—such as gross output and profit per head—should not be directly interpreted as indicators of greater technical efficiency. Technical efficiency reflects the ability of a farm to maximize output relative to input used, whereas revenue and profit are often influenced by external market factors, such as price fluctuations or niche marketing strategies. Non-cooperative farms may benefit temporarily from such market conditions without improving their production efficiency. This finding aligns with studies showing that the availability of capital or subsidies alone does not guarantee higher efficiency unless accompanied by effective organizational and managerial practices [70,91]. The truncated regression results (Table 5) also show that subsidies and invested capital do not have a statistically significant effect on efficiency, reinforcing this conclusion.

The statistically significant positive effects of cooperative participation and herd size on efficiency reaffirm the importance of collaboration and scale economies. A plausible mechanism behind the positive association between herd size and technical efficiency is the presence of scale-related advantages in livestock production. Larger herds allow for the dilution of fixed costs (e.g., equipment, housing, veterinary services), more efficient use of feeding and milking technologies, and improved labor specialization. Additionally, larger farms tend to have stronger bargaining power in input markets and greater ability to adopt modern management tools, all of which contribute to higher productive efficiency. These mechanisms are widely acknowledged in the efficiency literature and are consistent with our empirical findings. Conversely, the negative association between external labor costs and efficiency may reflect issues related to high labor expenses or suboptimal workforce management [92,93]. This interpretation is supported by the negative and statistically significant coefficient on external labor costs in Table 4, which confirms that farms relying more heavily on hired labor tend to have lower efficiency scores. These results indicate that cooperative farms tend to employ external labor per animal more strategically and in a more structured manner, mitigating potential negative effects on efficiency. In contrast, non-cooperative farms rely on external labor more frequently and under less coordinated conditions, which contributes to reduced performance. Similar findings have been reported by Latruffe et al. [69], who emphasized that labor organization and human resource management significantly influence efficiency outcomes in livestock farms. Thus, the evidence from our second-stage regression is fully consistent with this literature, highlighting the role of structured labor management as a key determinant of efficiency.

Despite higher labor expenses per animal in cooperative farms, their structured labor management minimizes inefficiencies. In non-cooperative farms, excessive or uncoordinated use of external labor appears to be a key factor in lower efficiency levels. The lack of statistically significant effects from capital investments and subsidies further suggests that efficiency is primarily driven by how resources are managed rather than by their mere availability [12,79,94]. This finding highlights that policy tools emphasizing management training, farm advisory systems, and cooperative governance reform may yield higher returns than direct financial transfers.

Taken together, the findings emphasize both the constraints and opportunities for the Greek dairy sector. Strengthening cooperative structures, improving human resource management, and integrating performance evaluation tools represent key strategies for enhancing sustainability and competitiveness. The application of resampling methods such as bootstrapping should be considered best practice for rigorous efficiency evaluation and policy-oriented research. In addition, the integration of efficiency metrics into national agricultural policy frameworks (e.g., under the EU’s CAP performance monitoring system) could improve the alignment of subsidies with measurable productivity outcomes, promoting evidence-based decision-making in the sector.

Beyond the empirical findings, this study makes several theoretical and practical contributions. From a theoretical perspective, it extends existing efficiency research by applying a combined DEA–bootstrap–truncated regression framework to examine the role of cooperative participation in a livestock production system characterized by small-scale units and structural fragmentation. Although cooperatives have been widely discussed in organizational and rural development literature, quantitative evidence on their measurable effect on production efficiency—especially in Mediterranean and Balkan agricultural systems—remains scarce. By demonstrating that cooperative membership has a statistically robust and economically meaningful impact on technical efficiency, this study contributes to a more nuanced understanding of how organizational arrangements shape production frontiers. Moreover, the identification of herd size and labor management as key mechanisms reinforces existing theories on scale economies and human capital in agriculture while providing empirical validation within an underexplored context.

Practically, the results carry significant implications for policy and farm-level decision-making. First, the strong performance of cooperative farms suggests that strengthening cooperative governance, improving member services, and enhancing market coordination could be effective strategies for raising sector-wide productivity. Second, the negative association between external labor cost and efficiency underscores the need for targeted training programs, advisory services, and professionalization of labor management on dairy farms. Third, the finding that subsidies and invested capital do not necessarily translate into higher efficiency indicates that policy frameworks—such as the EU CAP—should prioritize management-oriented interventions, performance-based conditionalities, and digital advisory tools rather than focusing solely on financial transfers. For cooperative managers, the results highlight the importance of structured training, shared infrastructure, and coordinated technology adoption. For non-cooperative farms, the evidence suggests that joining well-governed cooperative structures may enhance technical performance and resilience. Overall, the study provides actionable insights for improving both the economic viability and the long-term sustainability of dairy farming in Greece and comparable agricultural systems.

5. Limitations and Directions for Future Research

Despite the strengths of this study, several limitations should be acknowledged. First, the analysis is based on a relatively small sample of dairy farms (n = 43), which reflects the challenges of accessing primary farm-level data in Greece but nonetheless limits the statistical generalizability of the results. Future research would benefit from expanding the sample size across additional regions to capture a broader spectrum of production systems.

Second, the sampling strategy was purposive rather than random, due to the need for mediated access through cooperative processors and official veterinary services. Although this approach ensured the inclusion of both cooperative and non-cooperative farms, it may introduce selection bias. Randomized sampling procedures or stratified sampling frameworks could help strengthen representativeness in future studies.

Third, the DEA method, while widely used, remains sensitive to outliers and measurement noise. The incorporation of bootstrapping improves bias correction, but alternative frontier methods—such as Stochastic Frontier Analysis (SFA) or Bayesian DEA—could be employed in future work to triangulate results and improve robustness.

Fourth, the study relies on cross-sectional data from a single production year, which does not allow for the assessment of dynamic efficiency changes over time. Longitudinal datasets would enable the analysis of productivity trends, technology adoption trajectories, and the long-term impact of cooperative participation.

Finally, the model does not incorporate multi-output dimensions such as milk quality, animal welfare indicators, or environmental performance. Future research could adopt a multi-output or multi-criteria framework to capture the multidimensional nature of dairy farm efficiency.

6. Conclusions

This study evaluated the technical efficiency of dairy farms in the Region of Thessaly using a bootstrapped DEA approach and demonstrated substantial efficiency variation across farms. Cooperative farms consistently outperformed non-cooperative ones, as evidenced by both the DEA scores and the truncated regression results, highlighting the role of structured collaboration, access to shared resources, and more organized management practices in improving performance. The results further indicate that neither higher capital investment nor larger subsidy amounts translate into improved efficiency, underscoring that managerial quality and the effectiveness of resource allocation are more decisive than input quantity. These results provide a sound empirical basis for designing targeted policy measures aimed at improving resource use efficiency in the dairy sector.

From a policy perspective, the findings suggest that strengthening cooperative participation, improving managerial skills, and fostering more structured labor organization could substantially enhance productivity in the dairy sector. The bootstrapped DEA framework proved to be a useful tool for providing reliable efficiency estimates and can support evidence-based decision-making. Overall, the study contributes empirical insight into how organizational structures shape farm performance and offers practical guidance for promoting a more competitive and sustainable dairy sector.