Let Y be the value of the estimated mean efficiency for each study, and let se (Y) be the value of its standard deviation. Then, regarding the random-effects model, and for the sake of estimate the overall efficiency, the weights were given by 
, being the between-study variance, 
. Thus, the pooled efficiency was given by 
, and 
Therefore, firstly, it was necessary to estimate , which was based on the value of the Cochran’s Q statistics. And then the heterogeneity measures were initially calculated.
Heterogeneity was analyzed with the Cochran’s Q statistics and the value I2 of Higgins [43, 44].
For the computation of Q, it was assigned a weight for each value of Y. This weight was 
. And then the value of Q was given by 
.
The value I2 of Higgins was then estimated with 
, being Q the Cochran’s Q, and df = n – 1 the degrees of freedom, where n was the number of studies. The estimate of the between-
study variance, , was given by . In addition to the heterogeneity test, a meta-regression was needed for an accurate identification of the sources of heterogeneity.
Forest plot
In each Forest Plot (FIGS. 1, 2 and 3), each horizontal entry describes the results from a single study. The study number, the efficiency estimate (“te” column), the standard deviation (“sd” column) and the weight assigned to the study were also reported. The length of the horizontal line represents the 95 % confidence interval (CI) for the efficiency for the individual study.
In the plots, the center of the circle marks the efficiency estimate for the study, and the area of such circle was proportional to the weight assigned to such study. The vertical dashed line in these pictures indicates the overall efficiency for the studies included in each specific group.
Meta-regression
Meta-regression aims to investigate whether heterogeneity among results of multiple studies was related to specific characteristics of the studies. With this purpose, a regression model was estimated where the variable of interest was the TE of each study Yi, and the explanatory variables were the factors which could influence the lack of homogeneity of the studies.
These are: sample size, temporal aspects, applied method, orientation approach, zone, and PS. All these explanatory variables were categorical except sample size. Temporal Aspect factor includes a coded variable which considers Cross Sectional Approach and omits Panel Data.
About Orientation Approach, Output orientation was omitted; about Zone the omitted value was Europe group; and, finally, regarding PS, the omitted value was Dairy System.
Meta-regression model differs from general lineal models usually applied, mainly because it estimates with methods which utilize not only the value of the variable of interest (Yi), but also its standard deviation (Yi).
The proportion of the between-study variance explained by the covariates (adjusted R-squared) was 
, where 
and 
were the estimates of the between-study variance in models with and without the covariates, respectively.
Once has been estimated, the estimated coefficients, 
, j = 1, …, k, were obtained by a weighted least-squares regression of Y on X with the weights . The estimate of the variance-covariance matrix of coefficients is 
, where 
. A statistical test for evidence of effect of a particular covariate was available via a Wald test using the statistic 
, j = 1, …, k. If the value of this statistic was not significantly different from 0, then the corresponding variable does not generate heterogeneity in the MA. After the identification of the heterogeneity sources with the MR, a MA was carried out for each homogeneous group.
Therefore, separate MA was developed for the orientation groups: output and input oriented. And also for the three diverse groups regarding the PS: dairy cattle, beef cattle, and the rest. The specific software for MA included in the Stata package [68] has been used for applying the methodology [62].
RESULTS AND DISCUSSION
Efficiency and its characteristic parameters on the basis of the published studies
The efficiency levels of the PS with ruminants have been obtained firstly from the results and conclusions reported by the 58 published studies and this paper was also a survey of them.
TABLE II shows the main characteristics of the 58 studies included in the MA, with the corresponding Forest Plot shown in FIGS. 1, 2 and 3.
The mean value of the efficiency indexes estimated was 77.24 % with standard deviation of 11.48, and all the estimates lie between the values 50.10 and 99.23.
On the other hand, it was also observed a great variability of the sample size of the different studies selected.
This variability lies from studies with a sample size of 21 decision making units to studies with a sample size of 3,351 units. The mean of decision making units considered in the studies selected was 285.69 units with a standard deviation of 512.59 units.
Figure 1. Forest Plot of the dairy cattle production system, Efficiencies, weights and overall efficiency
Figure 2. Forest Plot of the beef cattle production systemS, Efficiencies, weights and overall efficiency
Figure 3. Forest Plot of the small ruminants, dUAL purpose cattle and mix production systemS, Efficiencies, weights and overall efficiency
Efficiency in dairy production systems
The mean value of the efficiency reported by the considered studies dealing with milk (dairy cattle) is 80.8 % with a minimum of 57.7 % and a maximum of 96 %. The management strategies and best-practices concerning health, feed and animal reproduction show positive influence on efficiency [23, 25, 31, 59, 75]. Farmer’s decisions of analyzing forage and cereal fodder, in feeding portions for milk cows were relevant for the efficiency [4, 5, 39]. In milk farms of Wisconsin, the intensification of the systems improves the TE [18], and the farmers on the efficiency frontier had a relatively higher milk production, milk production per cow, and land surface [24, 66]. In addition, Álvarez-Pinilla and del Corral [2] have found that the intensive livestock farms were more efficient and productive than the extensive ones, in South America the least efficient farms were operating at a sub-optimal size [16]. Others studied the effect of the quota system and subsidy [49, 50].
Other papers considered the environmental impact. They concluded that the firms, with a more efficient use of the inputs, reduce their greenhouse gas emissions for each liter of milk [3, 65]. On the other hand, Mukherjee et al. [60] deduced that the global warming could increase the heat stress of the animals, and the milk production was affected.
Hansson et al. [40] analyzed with logistic regression the effects of mastitis prevention measures. Their results show that taking actions, as contact a vet and perform hygiene general test routines, led every firm to increase significantly its probability to be totally efficient. In addition, Barnes et al. [10] concluded that the farmers must try to reduce the laminitis below the 10% level for an efficient use of the resources. Studies showed that several farmers characteristics as agriculture training, household labor, farm management experience, study group participation, the help of advisers as important information sources, and accounting control, aid considerably for improving the farm TE [17, 19, 21, 37, 69]. Hazneci and Ceyhan [41] proposed new strategies such as providing better agricultural extension services and farmer training programs to increase the educational level of farmers, and providing farmers with the opportunity of accessing loan to enhance their technical efficiency.
The research of Hansson [38] in dairy cattle systems in Sweden deduced that greater farms were technically better regarding the use of their inputs. The management of the herd influences the quality of the produced milk, and quality improvements lead to quantity reduction. In Turkey, the results illustrate that animals with high genetic quality must be numbered in the herds [1, 42, 47].
Efficiency in beef production systems
The mean value of the reported efficiency of the beef cattle studies was 76.59 %, the minimum value was 53.44 % and the maximum 99.23 %.
Under the approach of input saving, several farms in Sweden and Brazil were analysed. As a result, the most efficient farms were farms which involve all the actions of breeding, rearing and fattening livestock [52]. Castillo-Quero [20] deals with the farms in Spanish pasture. It concludes that intensification, measured by stocking density and mechanization index, influences the efficiency. Similar results were proposed in feedlot systems, where in a smaller area of the field could lead to a better TE [36].
Gatti et al. [35], in beef systems cattle in Argentina, compared different areas of La Pampa, grouping them on the basis of partial productivity indexes. They pointed out significantly differences in efficiency among these areas, mainly due to several characteristics as the existence of electric lighting, artificial insemination, contribution of technical advisers, and supplementary food. A similar approach was applied in Kenya by Otieno et al. [61], regarding pastoralism systems, agrarian grazing and ranches. They found out differences of efficiency due to native breeds, mating control, specialization, age, and presence farmer. Mlote [55] in Tanzania pointed out the socio-economic determinants of the respondents’ technical efficiency were age, education, experience, extension services and ethnicity.
Efficiency in small ruminant, DP cattle, and mixed production systems
The mean value of efficiency reported in the studies of these livestock PS is 68.18 %. The minimum value was 50.10 % and the maximum is 83 %.
Most of these small-ruminant systems were characterized by a high dependency from the pastureland, and from the restricted access to suitable resources and production methods. These were significant structural limitations, nevertheless, the ovine and goat production was still a matter of the greatest importance to economic, environmental and social issues in Mediterranean Countries [28].
In several Countries, as Syria and Greece, the traditional systems have been studied by Shomo et al. [64]. These systems have been classified on the basis of livestock and people movements, and regarding the use of natural resources. The sedentary PS was the most efficient, and the migratory one the less efficient. The main reasons of inefficiency were a high abortion rate, low fertility, high lamb mortality, and the long distances to water sources and markets. Other results indicated that the European Union subsidies have a significant impact in the technical efficiency of farms with low levels of efficiency and small size. In ovine farms in Chios, Greece, it has been observed that big size farms are positively correlated with technical efficiency. These results showed that the farms could be associated in order to achieve an optimal size and increase their production. The estimation of the scale efficiency shows that scale economies could be profitable for productivity [46, 53, 70]. Arzubi et al. [6] concludes that the specialized systems in ovine-wool and ovine-meat production have more technical and economic efficiency than the mixed systems.
The efficient and sustainable managements were compared in the region of Villuercas-Ibores (Spain). It was observed that the big farms devoted to both sheep and goat flocks, and which were not in the Protected Designation of Origin, were the most sustainable and, in several issues, the most efficient [54]. In addition, they deduce that, for improving the competitiveness of the less efficient farms, supplementary food and an increasing of the production capacity of the sheep were required. This conclusion coincides with the results of the research of Morantes [56], Morantes et al. [57] and Toro-Mujica et al. [72] where the ovine production in Castilla-La Mancha (Spain) was studied, and the management and productivity levels were related. As a result, if the functions of organization, planning, direction and control were well performed in the farm, the farm was more efficient. Regarding this result, it is also possible to mention the paper of Gaspar et al. [34], who pointed out that the economic results in the ovine farms in the Spanish pastureland were connected with the labour management of the owners of the farms.
Urdaneta et al. [73] deal with DP cattle in Venezuela. Their results showed different efficiencies among agro-economic zones, and that the supplementary food has a determinate effect in these livestock, and Peña [63] pointed out the managerial performance of farmers. Gamarra [32] studied DP cattle in Colombia. The use of organic fertilizers and insecticides (ha), and the livestock density (animals/ha) were factors which affect efficiency.
A crucial aspect in mixed systems was the definition of the outputs. The high heterogeneity of the produced outputs helps the different authors to unify the measure units with monetary or weight units [27, 29]. The papers of Hussein [45] and Beshir et al. [12] coincide with the conclusion that the implementation of new technologies was a determinate factor in the efficiency of these systems.
Gaspar et al. [33], in their research of the farms of the Spanish pasture, study the effect of the funding coming from the Common Agricultural Policy (CAP) of the European Union. The farms with pigs (Sus scrofa domesticus) were the most efficient. It has been suggested that several modification in the livestock density should be performed, in order to use suitably the natural resources to achieve better efficiency levels in the farms of the pasture.
Efficiency with meta-analysis
The total efficiency mean was 77.24, which does not take into account the accuracy of the computation of the different estimates.
The overall efficiency, found out by the MA of all the 58 studies, is 81.85 with a 95 % CI defined by the extremes 79.23 and 84.48. The Forest Plot of the whole sample was not presented due to space reasons and because it would provide redundant information (FIGS. 1, 2 and 3). These three pictures, respectively, illustrate the Forest Plots of the separate MA for the three groups of PS considered: dairy cattle, beef cattle, and mixed group. The information of each study does not changed and it keeps invariant when the study was taken into an overall sample or into a specific group of studies MA. For instance, the information of the study number 1 shown in FIG. 1 (dairy firms MA) was just the same of the information of such study number 1 in an overall sample MA.
Heterogeneity was also analyzed with the Q-Cochran test. The Cochran’s Q was 67.74 with P = 0.156. Another heterogeneity measures were given by I2, with a value of 15.86, and τ², which is equal to 11.83. Therefore, for better understanding the heterogeneity reasons, a MR analysis was applied. To perform the MR, the variable to be explained was the efficiency (with its standard deviation S.D.), and the explanatory variables were the sources of heterogeneity.
The MR results were condensed in TABLE III with τ² equal to 20.01. These results show that two explanatory orientation (O) and PS variables were significant, in addition to the constant, with a significance level of α < 0.05. As regards O, the value of the coefficient of the explanatory variable was 8.85 with positive sign. It suggests that the efficiency of the input oriented studies was around 8.85 % larger than the output oriented studies (default category).
Regarding PA, it was significant the coefficient of the set of mix PS. This mix PS group comprises small ruminants, DP and mix. These PS showed an efficiency level around 13.38 % lower than the efficiency levels of dairy cattle PS (default category). The MR results proved that O and PS were sources of heterogeneity, additional separate MA of the different groups were performed.
Firstly, the overall efficiency of the groups studied separately by their PS (i.e., dairy firms, beef firms and mixed group firms) was estimated with the corresponding MA. The results of these additional MA were depicted by the Forest Plots (FIGS. 1, 2 and 3).
The overall efficiency for the dairy cattle PS was 82.54 (FIG. 1), in the beef PS 83.39 (FIG. 2) and in the mixed group was 70.27 (FIG. 3). These values lie, respectively, in the 95 % CI defined by the limits 79.34 and 85.73 (dairy cattle, FIG. 1), 74.77 and 92.00 (beef cattle, FIG. 2), and 59.99 and 80.55 (mix group, FIG. 3).
Finally, the overall efficiency of the groups studied separately by their orientation was also estimated with their corresponding additional MA. These two additional MA performed separately by O confirm the previous results provided by the MR. The overall estimated efficiency in output oriented studies (76.39, lying in a 95 % CI with limits 71.35 and 81.44) was lower than the overall efficiency of input oriented studies (84.9, lying in a 95 % CI with limits 82.52 and 87.44).
As a result of the performed MA of the whole sample, the overall efficiency of the sector was estimated to be 81.85 % with a 95 per cent CI with limits 79.23 and 84.48. This overall efficiency level was large, but it also means that improvement strategies could be implemented to enhance efficiency between 15.5 and 21 % in some of the two directions: increasing production or decreasing resource consumption. Besides, by comparing the overall efficiency estimated by the MA (81.85), with the sample arithmetic mean (77.24), it could be concluded that this methodology was quite suitable. In fact, the consideration of the accuracy of the efficiency estimates of the different studies leads to modify the overall efficiency estimate, avoiding incorrect and misleading conclusions. The output O studies had lower efficiency than input orientation studies. These results agree with the results obtained by Bravo-Ureta et al. [73].
Improving measures could be taken to achieve better efficiency levels, and these actions must be based on the factors which influence efficiency. These relevant factors pointed out by the varied published papers regarding the different PS are similar.
CONCLUSIONS
The systematic survey conducted has been useful for identifying the determinant factors of the efficiency of the PS analyzed. In addition, it has been the basis for performing a MA. MA and MR provide a well-founded and supported comparison among PS. As a result of this comparison, it was concluded that small ruminant PS were less efficient than dairy or cattle PS.
In summary, the most relevant and crucial aspects to be considered in order to improve efficiency levels in PS with ruminants were the following: management training and more attention must be paid to livestock, particularly looking after their management, health and well-being. It also entails intensifying new technologies usage to achieve the required levels of sustainability.
Acknowledgements
Corresponding author research is partially supported by Spanish Government Research Project MTM 2017-84150-P.
BIBLIOGRAPHIC REFERENCES
