Factors Inﬂuencing Technical Efﬁciency in the EU Dairy Farms

: This paper aims to analyse the technical efﬁciency (TE) of dairy farms and ﬁnd its determinants. To accomplish this problem, the Stochastic Frontier Analysis was applied. The data were obtained from the Farm Accountancy Data Network database for dairy farms (TF15-45—Specialist dairying) for 2004–2019. Dairy farms were divided into four clusters according to their physical size (number of livestock units per farm) and economic size (standard output per farm). The largest farms by physical and economic size are located in Denmark and Cyprus. The smallest, in comparison, are in Bulgaria, Croatia, Latvia, Lithuania, Austria, Poland, Romania, and Slovenia. Farms in the EU are relatively technically efﬁcient, i.e., they use their resources efﬁciently to produce maximum output (production). However, they have the potential to achieve better economic results and be more competitive, as the size of farms’ is not fully optimised. The abolition of the milk quota can be considered a factor in improving technical efﬁciency, as the indicator is higher after the abolition. New and old member states have almost comparable technical efﬁciency levels (the p -value of the t -test is 0.463), with old members having slightly higher level TE. Subsidies have contradictory effects on TE. Farm efﬁciency with higher subsidies per cow is higher for farms with € 51–100/cow. However, as subsidies increase, TE decreases. Only the group of farms with the highest subsidies has a higher TE. More diversiﬁed farms are more technically efﬁcient than specialised farms. Milk yield did not inﬂuence the analysed indicator. The analysis results can serve the stakeholders as a tool for modelling future agricultural policy, as the European farms are very heterogenous and show different conditions and economic outcomes.


Introduction
The dairy sector is associated with a particular degree of uncertainty. In livestock, diseases in animal husbandry, perishability of the product, product prices and feed prices play a role and influence productivity positively and negatively [1]. The dairy sector is affected by structural changes, including the geographical relocation of milk production or the introduction of an intensive production system. These changes may affect farm efficiency, farm profitability, or the sector's sustainability in traditional milk-producing areas [2].
EU milk production is important in a global context. EU countries are the secondlargest milk producers in the world (after India). The EU is also one of the largest milk exporters, together with New Zealand and the United States. In 2020, milk production in the EU increased. The largest importer is China. In the following years, EU production is expected to grow, but at a slower rate than the global average; the herd is expected to decrease but milk yields are expected to increase. The dairy sector has been relatively stable during the pandemic, but some structural changes may have long-term implications [3]. The role of competitiveness in the dairy market has become significant. The main EU milk production countries are Germany, France, the Netherlands, Poland, and Italy, that account for more than 66% of the total EU milk production in 2019 [4]. data from the other three member states were removed from the dataset. The production function estimation includes an output variable and several input variables-capital, labour, land, and material. The output variable is expressed by cow's milk production per farm (€/farm). All variables in financial units (euros) were deflated by the corresponding price index to correct the values for inflation. The labour variable is represented by the annual work unit (AWU). The land variable is the total utilised agricultural land used by farm. The capital variable is expressed by the depreciation of fixed assets plus contract work. The material variable is represented by the cost of feed for grazing livestock. The next step of the study was to analyse the relationship among TE and various indicators such as the number of cows (in LU) per farm, subsidies for milk production, milk yield in kg, farm specialisation expressed by the share of dairy cows (LU) in total LU and by the share of milk production in total output.

Cluster Analysis
The first step of the study was to apply cluster analysis to aggregate European countries according to their homogeneity in terms of different physical and economic size. Cluster analysis involves different methods and algorithms to group the observations (in our case, the member states). For the objective of this work, the hierarchical Ward's method was used. Unlike the other methods that measure the distance directly, Ward's method analyses the variance of clusters. Ward's method is considered the most appropriate method for quantitative variables [32].
The clusters were formed based on the indicators of physical size, expressed by the livestock unit per farm, and the indicator of economic size, expressed by the standard output per farm. Both indicators were calculated for the farm of TF14-45 Specialist dairying, according to the FADN grouping. The data refer to the year 2016, the last available year for the required grouping level.

Stochastic Frontier Analysis (SFA)
The first step in calculating technical efficiency is to estimate the production function. The SFA was chosen for estimation because it is the most appropriate approach under agricultural sector conditions. The production function can be written and estimated as follows [10]: where y i is the production (output), x i represents the production factors (inputs), β are the estimated parameters, v i is the error term, and u i is the technical inefficiency. There are two models that can be estimated under SFA-the fixed-effects model and the random-effects model. In the fixed-effects model, the inefficiency term is assumed to be fixed and correlated with the regressors. In contrast to the fixed-effects model, the inefficiency term u i in the random-effects model is randomly distributed with constant mean and constant variance, and is expected to be uncorrelated with the regressors and the error term v it .
Greene [33] discussed that the proposed random-effects model has serious flaws. The most important one is that the inefficiency is the same in time. For long time-series data, this is an undesirable assumption. To avoid these limitations, Greene [33] proposed a "true" random Effects model that can be formulated as follows: where w i is the random firm specific effect and v it and u it are the symmetric and onesided components. Following Färe [34], to estimate a production function in transcendental logarithmic (translogarithmic) form, we used the factors of production land, labour, capital, material, and a time variable. The translogarithmic production function can be written as follows: +0.5β MM ln(M)ln(M) + 0.5α TT TT + β PK ln(P)ln(K) + β PL ln(P)ln(L) + β PM ln(P)ln(M) where y is the output variable; A depicts the total factor productivity; α and β are the estimated parameters (coefficients), their subscripts represent the relevant input variable; input variables: p, land; K, capital; L, labour; M, material; T is the time variable representing technical change; v it is the error term, and u it is the technical inefficiency term.
The true random effects (TRE) model described above was used to estimate the production function [34].
Once the production function has been estimated, the technical efficiency (TE) can be calculated. An index for TE can be defined as the ratio between the observed output (y) and the maximum realisable output (y*): Since y ≤ y*, the index TE is restricted to a value between 0 and 1; TE reaches 1 when a farm produces the maximum possible output (i.e., y = y*), with the given inputs. According to the theory of production efficiency, a farm can operate below the frontier due to technical inefficiency [35]. Jondrow [36] proposed to calculate TE for the half-normal distribution of the inefficiency term from the error term ε i as the expected value of −u i conditional on ε i : represent the standard normal density and Φ(·) the standard normal cumulative density functions.
Coelli et al. [10] discussed that the best estimator for the model is the maximum likelihood (ML) method, while the other estimators (ordinary least squares (OLS) and corrected ordinary least squares (COLS)) could provide biased estimates. However, Schmidt [37] pointed out the possibility of SFA providing biased estimates due to measurement error. M-estimators, which are considered robust regression estimators, can avoid the problems of data imperfections and ignore outliers [38]. Forty-eight robust M-estimators were presented by de Menezes et al. [39]; it is likely that these estimators can be used to avoid problems of SFA.

Linear Regression Model
A linear regression model was estimated to analyse the relationship between TE and the indicators. The model attempts to fit a linear equation to the given data. A linear regression model can be written in the form Y = a + bX, where X is the explanatory variable (in our case, an indicator), and Y is the dependent variable (in our case TE).
All variables used for empirical analysis are represented in Table 1. Share of dairy cows on total LU H5 Share of milk production on total output

Results
The section on results is divided into several parts. The first part describes the leading milk producers in the EU. Other parts are devoted to the analysis of technical efficiency analysis in relation to selected criteria that may influence efficiency.

Main Milk Producers in the EU
The first part of the paper identifies leading milk producers in the EU using cluster analysis. Dairy farms were classified into four groups according to their physical (PS) and economic size (ES).
The first group consists of the largest farms with more than 217 LU/farm and more than 700 thousand €/farm ( Figure 1). Only two countries belong to this group-Denmark and Cyprus (according to the FADN methodology, they belong to the economic size class XI, i.e., large farms). The second-largest group of farms includes Belgium, Czechia, Estonia, Luxembourg, the Netherlands, Sweden, and the United Kingdom. These farms have 130-241 LU/farm and 301-498 thousand €/farm (economic class IX, middle-sized farms). Smaller farms represent the third group with 46-129 LU/farm and standard output of 86-236 thous. €/farm (economic size VII and VIII, i.e., middle-sized farms). These are mainly western EU countries and some eastern countries. Germany, Ireland, Greece, Spain, France, Hungary, Malta, Portugal, Slovakia, and Finland belong to the third group. The smallest farms are represented by the countries located mainly in the east and south-east of the European continent and having 4-21 LU/farm with a standard output of 6-68 thousand €/farm (economic size III-VII, i.e., mainly small farms). This group is represented by Bulgaria, Croatia, Latvia, Lithuania, Austria, Poland, Romania, and Slovenia.
The level of technical efficiency was calculated below. There are no significant differences between the TE of a given cluster (p-value is higher than 0.600). However, it is observed that TE is slightly higher in the member states with a larger size of farms in the sector.

Technical Efficiency of EU Dairy Farms
All the estimated first-order parameters of the production factors are significant at the 1% level of significance, based on the z-test ( Table 2). The assumption of monotonicity and quasiconcavity was satisfied in the case of all production factors, since the values of the production factors in the dataset were normalised by their geometric mean, the estimated parameters of the production factors can be interpreted as production elasticities. All the production elasticities had a positive sign, which is consistent with economic theory. The production elasticity showed the change in total output when the value of production Agriculture 2021, 11, 1114 6 of 14 increased by 1%. The factor of production labour (0.302) and capital (0.322) had the highest elasticities. This means that total output changed by 0.3% when labour or capital increased by 1%.

Technical Efficiency of EU Dairy Farms
All the estimated first-order parameters of the production factors are significant at the 1% level of significance, based on the z-test ( Table 2). The assumption of monotonicity and quasiconcavity was satisfied in the case of all production factors, since the values of the production factors in the dataset were normalised by their geometric mean, the estimated parameters of the production factors can be interpreted as production elasticities. All the production elasticities had a positive sign, which is consistent with economic theory. The production elasticity showed the change in total output when the value of production increased by 1%. The factor of production labour (0.302) and capital (0.322) had the highest elasticities. This means that total output changed by 0.3% when labour or capital increased by 1%.   In comparison, the land and material variables had lower elasticity. The parameter λ (lambda) represents the ratio between the variance of the inefficiency term u it and the error term v it . The significant parameter indicates the presence and the significance of technical inefficiency in the variation in residuals. The return to scale for European milk farms is increasing (1.147), which means that the scale of farms is not fully optimal and could be increased to achieve better economic results.
The calculated TE in the different EU member states is shown in Figure 2. The average technical efficiency in the EU is 0.900, which means that European dairy farms are relatively efficient. The average technical efficiency of the EU-13 member states (0.897) is lower than the EU-15 average (0.903), although the difference is not significant according to the t-test Among the EU-15 countries, the highest technical efficiency is achieved by Austria, Finland, and the Netherlands. Finland and the Netherlands belong to the second large cluster. Austria, on the other hand, belongs to a cluster with small farms. The lowest efficiency among the EU-15 countries was found in Italy and the United Kingdom. Among the EU-13 countries, Poland and the Czech Republic achieved the best efficiency. Poland reached very good results with TE equal to 0.921 compared to the most efficient EU-15 countries, although it belongs to the last cluster with a small economic size.
(lambda) represents the ratio between the variance of the inefficiency term uit and the error term vit. The significant parameter indicates the presence and the significance of technical inefficiency in the variation in residuals. The return to scale for European milk farms is increasing (1.147), which means that the scale of farms is not fully optimal and could be increased to achieve better economic results.
The calculated TE in the different EU member states is shown in Figure 2. The average technical efficiency in the EU is 0.900, which means that European dairy farms are relatively efficient. The average technical efficiency of the EU-13 member states (0.897) is lower than the EU-15 average (0.903), although the difference is not significant according to the t-test (p-value 0.463). The technical efficiency of the old and new member states is comparable. Among the EU-15 countries, the highest technical efficiency is achieved by Austria, Finland, and the Netherlands. Finland and the Netherlands belong to the second large cluster. Austria, on the other hand, belongs to a cluster with small farms. The lowest efficiency among the EU-15 countries was found in Italy and the United Kingdom. Among the EU-13 countries, Poland and the Czech Republic achieved the best efficiency. Poland reached very good results with TE equal to 0.921 compared to the most efficient EU-15 countries, although it belongs to the last cluster with a small economic size. The development of TE showed an increasing linear trend (as shown in Figure 3). The largest decrease in TE was observed in 2009, the year of the financial crisis. The EU-15 and the EU-13 member states showed a very similar development. However, the fluctuations of the development curve were more pronounced in the EU-13. The TE was higher after the abolition of milk quotas (after April 2015). According to Čechura et al. [13], the main driver of productivity growth is the scale effect, which could be strengthened after the abolition of milk quotas, positively impacting farms. The development of TE showed an increasing linear trend (as shown in Figure 3). The largest decrease in TE was observed in 2009, the year of the financial crisis. The EU-15 and the EU-13 member states showed a very similar development. However, the fluctuations of the development curve were more pronounced in the EU-13. The TE was higher after the abolition of milk quotas (after April 2015). According toČechura et al. [13], the main driver of productivity growth is the scale effect, which could be strengthened after the abolition of milk quotas, positively impacting farms.

Analysis of Factors Affecting Technical Efficiency
The following hypothesis were formulated and tested to analyse the relationship between TE and different indicators (Table 3). Table 3. The hypothesis testing of the relationship between indicators of milk production of the EU

Analysis of Factors Affecting Technical Efficiency
The following hypothesis were formulated and tested to analyse the relationship between TE and different indicators (Table 3). For each relationship, the linear regression model was estimated. The parameter (linear regression coefficient) represents the significance of the relationship, i.e., whether the chosen indicator has an impact on TE. Three of the five relationships tested proved to be significant. These relationships are analysed in more detail below. Two relationships were not demonstrated.

Relationship between Technical Efficiency and Number of Cows
The analysis revealed significant differences in technical efficiency among farms in relation to the number of cows (herd size). Most farms in the EU have on average 11-100 cows. The fewest farms have more than 200 cows (mainly Germany and Slovakia) or less than ten cows (mainly Bulgaria, Croatia, Lithuania, Poland, and Romania). The highest TE was observed in the group of farms with less than 50 cows (Figure 4). The group of farms with the highest TE (11-50 cows) is the most numerous. As the herd size increases (up to 200 cows) TE is decreases. However, the average TE of farms with more than 200 cows is 0.8522, which is higher than the TE of the previous two groups. Large farms with more than 200 cows achieve very good efficiency.
Agriculture 2021, 11, x FOR PEER REVIEW 9 of 15 TE was observed in the group of farms with less than 50 cows (Figure 4). The group of farms with the highest TE (11-50 cows) is the most numerous. As the herd size increases (up to 200 cows) TE is decreases. However, the average TE of farms with more than 200 cows is 0.8522, which is higher than the TE of the previous two groups. Large farms with more than 200 cows achieve very good efficiency.

Relationship between Technical Efficiency and Subsidies per Cow in Dairy Farming
Technical efficiency was assessed with respect to subsidy dairying, which includes all subsidies for dairy products. Most farms in the dataset in the EU have subsidies per cow of less than 50 EUR/cow. Bulgaria, Lithuania, Poland, and Romania have the lowest subsidies. The lowest TE belongs to farms with subsidies for dairy products of 201-300 EUR/cow ( Figure 5). From subsidies of 201-300 EUR/cow, the technical efficiency increases with a higher subsidy amount. This means that farms with more than 300 EUR/cow have the highest technical efficiency. These farms are mostly located in Finland and Sweden. The dairy sector in these countries is the most productive in terms of milk yield, where it is at or above nine thousand kg/cow.

Relationship between Technical Efficiency and Subsidies per Cow in Dairy Farming
Technical efficiency was assessed with respect to subsidy dairying, which includes all subsidies for dairy products. Most farms in the dataset in the EU have subsidies per cow of less than 50 EUR/cow. Bulgaria, Lithuania, Poland, and Romania have the lowest subsidies.
The lowest TE belongs to farms with subsidies for dairy products of 201-300 EUR/cow ( Figure 5). From subsidies of 201-300 EUR/cow, the technical efficiency increases with a higher subsidy amount. This means that farms with more than 300 EUR/cow have the highest technical efficiency. These farms are mostly located in Finland and Sweden. The dairy sector in these countries is the most productive in terms of milk yield, where it is at or above nine thousand kg/cow.

Relationship between Technical Efficiency and the Proportion of Dairy Cows (in LU) in the Total LU
The share of dairy cows (in LU) in the total LU represents the specialisation of dairy farms. The higher the proportion of dairy cows (LU) in the total LU, the more specialized the farm is in milk production. TE increases as specialisation decreases and farm diversification increases (as shown in Figure 6). Assuming that the farm focuses only on milk production (dairy cows), the technical efficiency is the lowest. If the share of dairy cows (in LU) in the total LU is more than 70%, the technical efficiency is low.

Relationship between Technical Efficiency and the Proportion of Dairy Cows (in LU) in the Total LU
The share of dairy cows (in LU) in the total LU represents the specialisation of dairy farms. The higher the proportion of dairy cows (LU) in the total LU, the more specialized the farm is in milk production. TE increases as specialisation decreases and farm diversification increases (as shown in Figure 6). Assuming that the farm focuses only on milk production (dairy cows), the technical efficiency is the lowest. If the share of dairy cows (in LU) in the total LU is more than 70%, the technical efficiency is low.

Relationship between Technical Efficiency and the Proportion of Dairy Cows (in LU) in the Total LU
The share of dairy cows (in LU) in the total LU represents the specialisation of dairy farms. The higher the proportion of dairy cows (LU) in the total LU, the more specialized the farm is in milk production. TE increases as specialisation decreases and farm diversification increases (as shown in Figure 6). Assuming that the farm focuses only on milk production (dairy cows), the technical efficiency is the lowest. If the share of dairy cows (in LU) in the total LU is more than 70%, the technical efficiency is low.

Discussion
According to the results, only two hypotheses were rejected (H3: the level of milk yield has a significant influence on technical efficiency; H5: influence of the share of milk production on total output). No significant impact on efficiency was found. Provided study confirmed hypothesis H1: the number of cows on the farm has a significant influence on technical efficiency; H2: the level of subsidies per LU has a significant influence on technical efficiency, H4: the specialisation of the farm (share of dairy cows in total Lu) has a significant influence on technical efficiency. Significant impact was found.
Clustering considering physical and economic size showed the heterogeneity of dairy farms in the EU. Several studies have also demonstrated the heterogeneity of different countries and regions in terms of the dairy production sector. Poczta [40] used FADN data to classify dairy farms into five groups in terms of farm characteristics. The authors conclude that the most productive farms are medium and large farms, characterised by high specialisation, high production scale, and intensive production process. These farms are less dependent on subsidies from CAP [40].
In recent years, traditional dairy production has reduced the number of cows [2]. Efficiency is considered as the essential factor that can help dairy farms to survive [41]. Our results show that the return to scale of European dairy farmers is increasing. The scale of farms is not fully optimal and could be increased to achieve better financial results. The existence of increasing returns to scale in dairy production was also confirmed by Žáková Kroupová [26] orČechura [14]. Žáková Kroupová [26] found that decreasing returns to scale are only in Romania, Hungary, Finland, Estonia, and Spain.
The average technical efficiency of the old (EU-15) and new member states (EU-13) is comparable. The efficiency of the EU-13 (0.897) was lower than the average of the EU-15 (0.903). Moreover, some new member states with a small economic size achieved very good efficiency compared to the most efficient countries of the EU-15. In contrast, Žáková Kroupová [26] calculated the EU-15 average to be 0.9445 and significant differences with the EU-13. In their opinion, the changes in the EU-15 are a harbinger of the development in the EU-13. Other studies have proved that dairy farms' technical efficiency varies among states (even in relation to new or old member states). According toČechura [14], there are differences in milk productivity in the EU (at NUTS 2 (regional) level). Productivity is highest in the north-west of the EU, i.e., in the old member states. Only the Czech Republic, Slovakia, and Hungary have achieved sufficient total factor productivity growth to catch up with the more competitive EU-15 member states [14]. The accession of new member states has been associated with side effects for both old and new states. The study also pointed out the lack of studies dealing with the productivity of the new and old member states. Data from the FADN of 24 EU countries up to 2011 were analysed. The highest productivity was found in the old member states. Irz and Jansik [15] analysed the productivity in selected countries in 1995-2010 and found differences and the stable position of older EU member states. The efficiency of dairy farms may also vary from region to region. The Norwegian study of Alem [16] also analysed the technical efficiency of dairy farms from a regional perspective. The results indicate minor regional differences in efficiency and input use. These results can be used for region-specific agricultural policies. Farms from different regions have different production possibilities, use different equipment or technologies. Other differences such as soil quality, temperature, and rainfall can also be expected [16,17]. Regional differences have also been noted by Batha et al. [18].
The TE is higher after the abolition of milk quotas (after April 2015). Some studies addressed the efficiency of dairy in the context of the abolition of quotas. For example, some studies [11] examined the technical efficiency and the change in total factor productivity of dairy farms in the EU. They identified the best-performing countries in relation to quota regimes using Data Envelopment Analysis (DEA) applied to 22 EU countries over the period 2004-2012. The results showed that there is a little scope for improving efficiency through technical input. The evaluation of total factor productivity shows that dairy farms in the EU have suffered a decline in productivity. Areal [12] analysed technical efficiency in relation to milk quotas. The way farmers use the milk quota market is associated with farm efficiency. According toČechura [13], the main driver of productivity growth is the scale effect, which was strengthened after the abolition of milk quotas and positively impacted farms. They also found a positive effect on productivity after the abolition of milk quotas, as also shown in our study The paper also analysed the relationship between TE and various indicators. The study found no significant effect of milk yield on technical efficiency. The absence of the relationship can be explained by the fact that the output "cow's milk and milk products" in the dataset includes buffalo's milk. The yield of buffaloes is lower than the yield of cows. This is especially relevant for Italy, where the production of buffalo milk has a long tradition. Špička and Smutka [20] came to almost the same results. They found higher milk yields in efficient regions, but the difference was not statistically significant. According to Wilczynski [42], the efficiency of farms increases with a higher milk yield.
Despite the varieties of dairy cow breeds existing in the world and in Europe, the Holstein/Friesian breed with high milk yield is the most prevalent and is becoming a very important breed in the EU in recent years The other breeds include the Normande, the Montbéliarde, the Swiss Brown, the Jersey, the Simmental, and the Ayrshire but these are not so widespread, and the production of milk of these breeds is not so significant [43]. Friesian/Holstein is the most expanded in main milk-producing countries such as Germany, France, Italy, the Netherlands, Belgium, United Kingdom, and Spain [44].
In assessing technical efficiency, several determinants were considered that may affect the level of efficiency. One of them was subsidy per cow. Latruffe [45] analysed the effect of subsidies on TE of dairy farms. The authors considered the following payments: direct payments for areas planted with specific crops and for heads of specific livestock; decoupled subsidies introduced in 2005 (namely the Single Farm Payments); and subsidies provided to farms located in less-favoured areas. They concluded that subsidies had a positive effect in two European countries, while in other countries, subsidies tended to be negative, or the significant effect could not be demonstrated on TE. Our study showed that subsidies significantly affect efficiency, especially when the dairy farm receives more than 300 EUR/cow. The effect of subsidies on farm performance is also an interesting topic for policymakers [46]. It can be concluded that subsidies in the EU have helped dairy farms to achieve better efficiency. The highest is the subsidy per cow, and the highest is the technical efficiency. Some studies evaluate the impact of Common Agricultural Policy on efficiency [46]. Their study showed that a higher level of coupling in farm support negatively affects efficiency. Farmers are less motivated to be efficient because they depend on a higher level of subsidies. Minviel and Latruffe [47] or Marzec and Pisulewksi [48] also found a negative relationship between farm technical efficiency and subsidies. Lakner [19] studied the impact of agricultural subsidies and regional factors that may affect technical efficiency on dairy farms. The results showed that agri-environmental payments did not affect efficiency. Farms with investment subsidies had lower efficiency. Špička and Smutka [20] found that rural development subsidies are significantly higher in inefficient regions.
The results show significant differences in the technical efficiency of farms with respect to herd size. Farms with less than 50 farms and more than 200 cows achieved the highest efficiency. These results can also be related to capital costs, which may be lower on large farms. More efficient farms tend to have more cows and can take advantage of scale [49]. The positive relationship between herd size and efficiency was also confirmed by Demircan [50]. According to Batha et al. [18], technical efficiency increases with an increasing number of cattle. Priyanka et al. [21] showed that technical efficiency was high for all herd size categories. Kovács and Szücs [22] found that farms keeping more than 501 dairy cows were more efficient.
Technical efficiency increases with decreasing specialisation and increasing farm diversification. If the proportion of dairy cows (in LU) in the total number LU is more than 70%, technical efficiency is low. According to Špička and Smutka [20], different livestock intensity was found, but diversification of activities is not a driver of higher efficiency. On the opposite, the ratio of the total number of dairy cows to the total number of cattle is an important factor that positively influences efficiency [23].

Conclusions
The paper aimed to evaluate the technical efficiency of dairy farms in the EU using stochastic frontier analysis and to analyse the impact of different factors on technical efficiency.
The first part of the paper dealt with the clustering of EU dairy farms according to their physical and economic size. It was confirmed that there are differences among farms.
Analysis of technical efficiency has shown an increasing return to scale in EU dairy farms. There is potential to achieve better economic results by increasing the size of farms. The EU dairy sector has the opportunity to develop and increase its competitiveness. Technical efficiency between EU-15 and EU-13 is comparable and is not influenced by physical or economic size.
The amount of milk yield did not affect efficiency. The reason is probably the presence of buffalo' milk with lower yields than cow milk. After the abolition of the milk quota, dairy farms achieved higher efficiency. As herd size increases, TE decreases. However, the average TE of farms with more than 200 cows is higher than TE in other groups. When dairy farms are specialised, they achieve lower efficiency. In this case, diversification helps to obtain better efficiency. Subsidies are a major determinant limiting technical efficiency. Farms with subsidies of more than 300 Eur/cow were the most efficient.
In summary, small and large, highly diversified farms play a crucial role in milk production in the EU. They have a higher level of technical efficiency with an advantageous production potential. The analysis results should help to understand the relationship between the efficiency of EU dairy farms and find factors limiting competitiveness. The analysis can serve as supporting material for stakeholders in policy settings.