Technical efficiency in beef cattle farming in Uruguay: Insights from census data

Livestock farming is the agricultural activity with the greatest individual land-use, but it faces competition from other sectors for land, and is criticized for its environmental footprint. In this global context, Uruguay emerges as an important case study, boasting a long tradition and significance in the beef export sector. Enhancing livestock productivity is imperative to mitigate environmental impacts, and bolster farm competitiveness and food production. This study delves into the technical efficiency of cattle ranches focused on cow-calf production in Uruguay during the 2011 agricultural year, with nationwide and mandatory data coverage. Using data from the 2011 General Agriculture Census we estimate a translog stochastic production frontier model encompassing key inputs (livestock units, grazing area, and labor), along with control variables such as soil suitability and infrastructure improvements. Our findings underscore the potential to augment Uruguay's beef production by an average of 26.4%, harnessing existing resources and technology while improving ranch management. Moreover, variables like the extent of reliance on livestock farming as the primary source of income of the ranch, the use of outsourced services, foreign cattle ownership ratios, and agronomic and veterinary consultation exert noteworthy significant impacts on TE.


Introduction
Livestock farming plays a vital role in supporting the sustenance and economic livelihood of more than 1.3 billion people.By utilizing land unsuitable for traditional crop cultivation, it constitutes the largest single land use, contributing to 17% of the world's total energy intake through food products (1) .Despite these substantial contributions, the livestock sector is increasingly under scrutiny for its environmental impact (2) , and it is also encountering growing competition for land (3) and labor resources.
In a context where projections anticipate ongoing growth in beef demand (4) , the opportunity to enhance livestock productivity becomes clear.This enhancement is essential not only for stimulating economic development but also for mitigating environmental impacts, boosting the competitiveness of cattle farms, increasing overall food production, and fulfilling environmental commitments.
In the global context, Uruguay stands out as a crucial case study due to its longstanding tradition in the global beef export market.Data from the latest agricultural census in 2011 reveal that meat and milk livestock farming served as the primary source of income for 74% of commercial agricultural farms.This sector occupies a vast expanse, encompassing 12.6 million hectares, which constitute 70% of the national territory.
Agrociencia Uruguay 2024;28:e1237 3 Historically, Uruguay's beef production has thrived due to its cost-effective natural field grazing system, providing the country with a unique competitive advantage that endures to this day.However, the beef production growth in Uruguay has not kept pace with other sectors like forestry, agriculture, and dairy (5) .This challenge is further complicated by the fact that, over the past two decades, the evolution of beef production per hectare in Uruguay has exhibited fluctuations without a clear trend (6)(7)(8) (9) .A more comprehensive understanding of livestock farming underscores the importance of investigating the heterogeneity in production at the ranch level, as this is where farmers make the decisions.Various factors unique to each farming operation process, including cattle focus, local weather conditions, management practices, and resource availability, significantly influence beef production.
In Uruguay, a stark contrast exists in the performance of different cattle ranches.The top 10% of ranches produce five times more beef per hectare compared to the bottom 10% (10) (11) .However, these fluctuations in yield alone do not capture the variations in input utilization intensities and other inherent attributes of beef production.Hence, they may not be suitable indicators for comparing the performance of different ranches.To address this issue, the study suggests estimating the farm-level technical efficiency (TE hereafter) as an indicator of the production unit's management capability.
TE is a comparative concept that measures the proportion of actual production observed relative to the maximum potential production attainable, while taking into account factors such as resource availability, input utilization, and available technology.In simpler terms, TE serves as an advanced performance metric, assessing how effectively a production unit transforms inputs into outputs within the constraints of available technology.
Table S1 in the Supplementary material compiles prior research endeavors focused on estimating technical efficiency within beef cattle farming at the farm level, spanning diverse geographic and operational contexts, providing valuable insights into the efficiency of beef cattle farming.Nevertheless, making direct comparisons between these studies is challenging due to variations in the methodologies employed, target populations, and contextual factors.For instance, Trestini (12) used a stochastic production frontier model to evaluate TE using an unbalanced panel of beef cattle farms in Veneto, Italy, reporting an average farm TE of 0.786.Qushim and others (13) delved into scale and technical efficiency in cow-calf farms in the Southeastern United States, employing an input distance function analysis to evaluate economic performance based on gross value of farm production and total principal operator household off-farm income, uncovering an average efficiency of 0.86.Otieno and others (14) estimated TE levels in Kenyan beef cattle production across various systems, including nomads, agro-pastoralists, and ranchers, using a stochastic metafrontier, resulting in an average TE of 0.69.
Furthermore, Gatti and others (15) applied a meta-frontier methodology to assess TE and technology disparities in beef cattle production across distinct regions in Argentina, finding that they could not reject the hypothesis of constant returns to scale but did reject the null hypothesis that the regions shared the same technology.Nwigwe and others (16) measured the TE of nomadic pastoralists, agro-pastoralists, and ranchers in six Nigerian states using a separated stochastic production frontier, finding average TEs of 0.59, 0.69, and 0.83 for the three groups, respectively.Additionally, Qushim and others (17) delved into TEs in U.S. grass-fed beef production through a stochastic input distance function with two outputs (whole farm and grass-fed beef enterprise), revealing average TEs of 0.84 for whole farms and 0.79 for enterprises within the U.S. grass-fed beef sector.Lastly, Martinez-Cillero and others (18) used a latent class stochastic frontier model with an unbalanced panel of Irish farmers to assess TE, focusing on TE in farms classified as specialist cattle producers, and their findings indicate that a single frontier model tends to overestimate technical inefficiency compared to a model that considers technology heterogeneity.
In the Uruguayan context, prior estimations of technical efficiency have relied on private records from ranches associated with technical assistance entities.Lanfranco and Buffa (19) applied the Data Envelopment Analysis technique and revealed that 6 out of the 27 studied companies engaged in beef cattle fattening were efficient.
Similarly, García-Suárez and Lanfranco (20) employed the Data Envelopment Analysis technique to examine beef cattle farms, yielding an average TE of 0.772.Additionally, García-Suárez and others (21) used both a stochastic production frontier with one combined output (equivalent meet) and a stochastic ray frontier with three outputs (beef, sheep-meat and wool), reporting average TE levels of 0.769 and 0.779, respectively.
However, these prior studies, despite their valuable contributions, were limited in their sample coverage, preventing them from providing a comprehensive overview of the TE representative of the entire sector at the national level.This is the primary contribution of our study.To achieve this, we utilize data from the last General Agricultural Census of 2011, which have not been previously utilized for this purpose.
The focus of this article is on ranchers engaged with cow-calf production, primarily involved in cattle grazing, and having more than seven bovine livestock units and over 50 hectares of pasture.Dairy farms and ranches specializing in finishing are intentionally excluded from our target population.As a result, our analysis significantly enhances the accuracy, representativeness, and comprehensiveness of the study, encompassing the entire beef industry in Uruguay with cow-calf production.
While the snapshot presented by the data from the last General Agricultural Census of 2011 may not fully capture the technological landscape of the entire Uruguayan livestock industry, it serves as a valuable point of comparison for cow-calf producers.Moreover, the estimates obtained from this study can be used as a reference point for comparing the data from the upcoming General Agricultural Census 2022, which is currently in progress.
In this study, we aim to address two pivotal research questions: 'How can we comprehensively assess and quantify the technical efficiency (TE) of individual ranches in Uruguay's beef cattle farming sector using census data?', and 'Which variables have a significant impact on TE in Uruguay's beef cattle farming industry?'By addressing these questions, our objective is to provide insights that are pertinent for public policy analysis, offering the potential to inform the design, targeting, monitoring, and evaluation of evidence-based policies within the industry.
We employed a stochastic translog production function approach based on Wang's model (22) to estimate beef production efficiency.This estimation was conducted through cross-sectional data analysis, incorporating three primary inputs: equivalent bovine units, grazing area, and equivalent workers.Additionally, we integrated several control variables into our analysis, including region, on-site infrastructure and improvements, soil suitability for livestock, the proportion of land undergoing forage improvements, and technological orientation.
We also included additional variables to help in interpreting both the expected values and the variance linked to inefficiency.These variables encompass aspects such as the availability of technical assistance in agronomy, veterinary medicine, and accounting; the proportion of cattle owned by third parties; the extent of reliance on livestock farming as the primary source of income, and the utilization of outsourced services.
In our study, we observed a simple average TE of 76.2% among the ranches.When we applied weights to the data by farm size, this average TE increased to 79.1%.Our findings emphasized that factors such as the primary source of income originating from the farm, the utilization of third-party services, the proportion of foreign-owned cattle, and the utilization of agronomic and veterinary technological advice have a significant impact on TE.
This study represents a pioneering effort in utilizing national-level administrative records, including data from the most recent General Agricultural Census and the National Livestock Information System, to estimate TE in Uruguay's beef cattle farming sector.By providing a comprehensive and representative analysis covering the entire beef industry in Uruguay, this research aims to illuminate variations in efficiency at the ranch level, identify significant factors contributing to TE, and offer actionable insights for policy considerations aimed at promoting sustainable development and competitiveness.The findings provide valuable insights for policymaking that align with the nation's economic and environmental objectives, including the goal of reducing emission intensity measured as emissions per gross product (23) .

Data sources
In this study, we have integrated data from Uruguay's most recent General Agricultural Census (CGA, for its Spanish acronym) with records from the National Livestock Information System (SNIG, for its Spanish acronym), which is Uruguay's livestock traceability system.The CGA (24) , although it is based on data from 2011, offers a comprehensive overview of all agricultural ranches in the country.On the other hand, the SNIG is mandatory for all livestock owners and tracks the temporal and spatial dynamics of various species, including bovine, ovine, swine, equine, and goat.This system combines annual stock declarations (as of June 30) with all associated changes in livestock ownership or location.
By merging these datasets at the farm level (10) , we define a farm as the unit of analysis in the census data.Then, a farm is represented by an aggregation of plots unified by shared production factors and management.This combined dataset enables us to measure production and performance on a granular, farm-by-farm basis across the country.While the agricultural year data from the 2011 census may appear out of date, it remains as an invaluable benchmark, offering insights into the intricacies and changes within the livestock sector.

Method
To measure technical efficiency (TE), we used the output increasing oriented indicator proposed by Farrel (25) , contrasting the observed output of a farm with the potential output of a fully efficient farm using the same inputs and technology.
The Stochastic Production Frontier (SPF) approach can be viewed as a generalization of the classical production model.In this approach, the efficiency of resources is considered as an empirical constraint to be tested, rather than an a priori assumption of neoclassical production theory (26) .For recent literature on this topic, refer to Kumbhakar and others (27)(28) (29) , and Sickles and Zelenyuk (26) .
Let   represent the output of production unit ,   an input vector of dimension K, and (  ; ) the production function.We introduce   as a non-negative error following the distribution  + (  ,    ), and   a symmetric normal error.While   accounts for elements such as measurement error, specification issues, and random variability in the production process,   represents technical inefficiency that reduces the observed output level relative to its potential.
The SPF for cross-sectional data can be expressed as: To estimate this equation parametrically, it is necessary to specify (  ; ), which we assume to be a translog functional form due to its flexibility (27) : The functional form described facilitates the derivation of product input elasticities and accommodates nonconstant returns to scale.Specifically, when all coefficients tied to second-degree terms (  ) are zero, the Cobb-Douglas function emerges as a subset.It's worth noting that the translog and Cobb-Douglas functions can be conceptualized as the second and first-order Taylor series approximations of a broader production function, respectively (27) .
Additionally, it is necessary to assume the distribution of the technical inefficiency term (  ), which, by definition, can only take positive values.The model developed by Wang (22) assumes that there is a set of exogenous variables Z that affects the mean and the variance of technical inefficiency, and it is assumed to be positive truncated normal:   ~+ (  ′ , (  ′ )) Wang's model encompasses several specific cases.These include the Half Normal (30) and Truncated Normal (31) (TN) specifications, which do not incorporate contextual variables.There are also variations such as the Kumbhakar, Ghosh and McGuckin (32) (KGM) model, which parameterizes the distribution mean of inefficiency with exogenous variables, and the Caudill and Ford (33) (CF) model, which parameterized the variance.
Additionally, we include control variables in the production frontier to account for variations in technological orientation among livestock ranches, natural soil suitability, the utilization of forage enhancements, and spatial production disparities.Therefore, the equation to be estimated, which includes a vector of control variables   with a vector of coefficients   , is as follows: To estimate the likelihood of the model, it is assumed that the distribution of the random variables   and   is independent, conditional on (  ,   ).The estimation of all the model parameters is carried out in a single stage using the maximum likelihood method.In a second stage, the estimation of TE is derived, using the conditional distribution of   |  : Implicitly, the model assumes exogeneity of all inputs, which implies the absence of unobservable producerlevel heterogeneity that could account for variations in input utilization.
To test the hypotheses on the model restrictions, the likelihood ratio test is employed, expressed as ), where ( 0 ) and (  ) represent the likelihood under the null and alternative hypothesis, respectively.The LR statistic asymptotically follows a chi-square distribution with J degrees of freedom.
Finally, to explore the heterogeneity in TE across farms, we employed a tree-based algorithm to group the farms (34) .This approach allows for a flexible modeling of the relationship between TE and a set of explanatory variables without imposing restrictive assumptions about the functional form.Specifically, we employed a Conditional Inference Tree (35) (CTREE) regression for this purpose.Tree-type models iteratively divide the explanatory variable space, optimizing the dependent variable (TE).The CTREE determines the significance of each partition based on the strength of the association between the explanatory variable and the target variable, using non-parametric tests to test all possible associations.It is important to note that these results are exploratory and should not be interpreted causally (36) .

Empirical strategy
The target population of this article comprises ranchers with cow-calf production, with a minimum production scale (more than 50 grazing hectares and 7 livestock units), and a specific focus in cattle grazing.To reduce the heterogeneity of production systems, we have excluded the following categories: dairy farms, ranches specialized in sheep production, cattle breeders, feedlots, and ranches specialized in fattening.These exclusions are intended to simplify the complexity of beef farming and approximate it through a production function focused on a single composite product.This simplification aids in mapping inputs to products and modeling the technology.
After defining our target population and assessing the quality of the livestock census forms (see the appendix in the Supplementary materials for details), our sample comprises 5,057 farms, collectively managing more than 3.7 million hectares of land and 3 million animals.
In this analysis, we have included farms owned by corporations.This inclusion requires the exclusion of certain explanatory variables for technical efficiency that are only available for farms owned by individuals (e.g., age, sex, educational level, residing on the farm).
The variables used to model beef production are based on previous studies (see Table S1) and the available information in our database.The chosen output variable to characterize beef cattle farming is the production of live cattle meat in the livestock year 2011/2012 (in kg).The computation of meat production at the livestock farm level is based on the net difference between sales and purchases, accounting for inventory changes due to events such as births, deaths, and category changes resulting from animal growth.Sales are categorized into two primary types: the sale of fattened cattle intended for slaughter, and the exchange of lean cattle among producers.The details to compute beef production are described in Aguirre (9) .
The inputs of production encompass the products and services employed in the beef cattle production process, including materials, labor, and capital.These inputs must satisfy specific criteria: they should be essential, show a positive monotonic relationship with the output, and be divisible.The inputs considered in the analysis are: (1) bovine animals measured in bovine livestock units (BLU); (2) LAND area devoted to beef cattle production; (3) total LABOR force in the farm, calculated as the sum of permanent workers plus the number of hired daily laborers in the year divided by 250 (total work days in a year).
In Uruguay, a BLU represents the energy requirements of a cow of 380 kg of live weight in maintenance.An equivalence system is widely used, assigning different categories of cattle a coefficient that weighs their relative consumption compared to that of the standard BLU.
To address the heterogeneity in livestock farming, the production function includes a set of control variables: (1) forage production capacity, represented by the natural productivity of soil for cattle production using the CONEAT index, and the proportion of area with forage improvements; (2) technological orientation, distinguishing between cattle ranchers or mixed operations, and those engaged in cow-calf or complete cycle production; (3) ranch infrastructure, encompassing amenities such as electricity, water reservoirs, rainwater tanks, private vehicles, cattle weighing chutes, and cattle scales; and (4) geographical factors, captured by 18 dummy variables representing each region (department in Uruguay), excluding Montevideo.
The CONEAT index was developed by the Uruguayan government to measure the production capacity of land in terms of meat and wool and the land units that comprise it.The index is used for fiscal purposes, has an average value of 100 at the national level, and ranges from 0 (land not suitable for livestock) to a maximum of 250.
All the variables used in this study are expressed in physical units rather than monetary values.This approach enables us to account for price fluctuations, eliminating the need for substantial assumptions about resource prices or opportunity costs.
When calculating descriptive statistics for the output and input variables (Table S2 and Table S3 in the Supplementary material), we observe significant heterogeneity in terms of the range of variation, the interquartile range (p75-p25), and the coefficient of variation (S.D/Mean).For example, the coefficient of variation is 1.61 for bovine meat, 1.49 for bovine livestock units, 1.58 for land area, and 0.88 for labor.As expected, there is a strong linear correlation between meat production (output) and the inputs.The Pearson correlation coefficient for bovine meat with bovine livestock units is 0.948, with land area it is 0.899, and with the number of workers it is 0.741.

The beef production model
This section presents the results of the models for the 5,057 livestock farms in the sample that meet our study universe's definition.The estimations were performed using the sfcross package in the STATA software (37) .
The Wang translog specification allows us to test hypotheses by comparing it with alternative models as special cases (see Table S4 in the Supplementary material).Firstly, we reject the hypothesis ( 01 ) that the Cobb-Douglas functional form is preferred over the translog alternative (pv < 0.1%).We also reject the hypothesis of the absence of technical inefficiency ( 05 ).Next, we contrast whether the Wang model is preferred over the alternative without explanatory variables for inefficiency (Wang vs. TN), with explanatory variables parameterized only at the mean (Wang vs. KGM), and with explanatory variables parameterized only at the variance (Wang vs. CF).All three alternatives are rejected (pv < 0.1%).Therefore, from now on, we will provide a detailed discussion of the results of the Wang translog specification.
Figure 1 displays the 95% confidence intervals (CI) for the input-output elasticities, evaluated at the mean values of the inputs.A 1% increment in BLU, LAND, and LABOUR leads to an average increase in meat production of 0.789%, 0.164%, and 0.03% respectively, all statistically significant at the 5% level.The response of elasticity is not uniform across the inputs' support (Figure 2): BLU's impact increases up to 400 and then levels off; LAND's effect declines until 500 and then stabilizes at a value beneath the average elasticity; LABOUR's influence shows no significant deviation from the mean value throughout the observed range.The study reveals an average return to scale of 0.983, which is statistically indistinguishable from 1 (p-value of 0.142), indicating constant returns to scale.A closer look at the entire input range (Figure 3) reveals no substantial deviations from this scale elasticity at the mean value.The only exception is a marginally higher return to scale for smaller-sized farms in BLU. Figure 4 shows the partial effect of the control variables.The CONEAT index variable is statistically significant (p-value < 0.1%), and, when considering the other variables, a 10-point increase in the CONEAT index is expected to result in a 1% increase in meat production.Ranches without improvements over natural fields produce, on average, 3.2% less meat compared to those with improvements.Additionally, for each 1% expansion in the area of improved land, a corresponding 0.2% growth in meat production is expected (p-value < 0.1%).When examining livestock composition, ranches specialized in cattle farming exhibit 5.6% higher production compared to mixed ranches (p-value < 0.1%).Meanwhile, ranches oriented towards cow-calf production do not present significant differences when compared to those following a complete cycle of livestock farming (p-value = 0.384).
Infrastructure-wise, we observe significant variations: producers equipped with livestock scales and cattle handling facilities yield 7.2% and 4.4% more meat production, respectively (p-value < 0.1% and p-value = 0.035), while factors such as the absence of electricity (p-value = 0.340), vehicle presence (p-value = 0.306), and the existence of a rainwater tank (p-value = 0.934) or a stock pond (p-value = 0.326) do not yield statistically significant differences.Lastly, geographical variations also impact production.Beef output in Canelones region exceeds that in Rivera (omitted category) by 23.6% after accounting for input usage and other variables (Figure 5).These discrepancies point to structural variations among different production regions not captured by the inputs and control variables in the model.In future research, it may be beneficial to explore the possibility of modeling spatial production variations by employing precise georeferencing data for each property, thereby achieving a better control over spatially unobservable heterogeneity.Note: In each final node of the tree, the mean TE value, the numbers of observation (n), and the mean square error (MSE) are presented.

Robustness test
Finally, to ensure the reliability and robustness of our results, we conducted some additional tests.Initially, we ran the model while excluding outliers.Among the 5,057 farms included in our analysis, only eleven were identified as outliers.While we have not presented the specific results in this section, it is important to note that the outcomes of these tests were consistent with the main findings we have discussed earlier in the study.
As part of our robustness checks, we conducted a second test.In this test, we adjusted the inconsistency filter related to the information reported in stock versus recorded cattle movements.The greater the level of inconsistency, the less credible the data become, and this, by definition, affects the estimated value of meat production (9) .Initially, we used a tolerance range of -5% to 5% for discrepancies, but in this test we have expanded the range to -25% to 25% of the herd.This relaxation of the filter criteria resulted in an increase in the number of farms meeting the filters, growing from the initial 5,057 to more than 8,075 ranches.
It is important to note that even with this adjustment, the results remained qualitatively consistent across various aspects, including input-output elasticities, returns to scale, and the influence of explanatory variables on efficiency.However, the notable change was a decrease in the average efficiency rate, which dropped to 70.9%.This makes sense, especially considering that we are adding more than 3,000 ranches.

Discussion
In a context where projections anticipate ongoing growth in global beef demand, increasing livestock productivity represents a significant opportunity for rural development in Uruguay.This enhancement is essential for stimulating economic development, boosting the competitiveness of cattle farms, and ensuring food security.Moreover, enhancing livestock productivity is crucial for meeting the goals associated with sovereign bonds indexed to environmental sustainability indicators (23) .
Through this study, our objective is to contribute to the expanding field of research concerning TE in beef cattle farming.We specifically concentrate on one of the three primary avenues for enhancing productivity over time, which is TE.The other two pathways involve technological advancements and productivity improvements resulting from changes in scale.Gaining a thorough understanding of these efficiency aspects is of utmost importance, as it can provide essential guidance for the development, targeting, monitoring, and assessment of evidencebased policy measures.
In this paper, we present novel estimates of the production function and TE in Uruguayan beef cattle farming.Our analysis is based on comprehensive data derived from the national census and administrative records for individual farms across the country.We find that the average TE stands at 76.2%.This result is consistent with previous studies conducted in Uruguay, such as García-Suárez, Pérez-Quesada, and Molina (21) , who reported an efficiency level of 76.9%, and García-Suárez and Lanfranco (20) , who found a TE of 72.3%.
The overall average TE masks significant variations, as the most efficient farm in the top decile achieves 89.5% efficiency, which stands in stark contrast to the bottom 10% with only 56.2% efficiency.This substantial difference results in a remarkable 59.2% increase in efficiency when moving from the lowest to the highest decile (by TE).
When we account for farm size by weighting the data for bovine livestock units (BLU), the TE average increases to 79.1%, compared to an unadjusted mean of 76.2%.This adjustment highlights the frequent lower efficiency found in smaller farms.With this 79.1% efficiency level, there is the potential to produce an additional 26% of beef using the existing resources and technology, implying a significant opportunity for productivity improvement.
Our analysis of TE disparities aligns with previous Uruguayan researches, which also emphasized significant production variations across farms based on administrative records (8)(10)(39) (40) .However, our findings indicate a reduction in these variations, likely attributed to the consideration of heterogeneity in inputs, infrastructure, technology, and advisory services.
The input-output elasticities and returns to scale exhibit positive values consistent with theoretical expectations.However, these values vary across ranches.Farms with fewer than 400 BLU show a more pronounced response in meat production to changes in animal allocation.Additionally, findings suggest that returns to scale may not be constant, particularly exceeding the mean value for farms with fewer than 100 BLU.
Indeed, given the significance of fixed costs in influencing economies of scale, it would be valuable for future research to compute scale elasticity while considering a stochastic net income function.Furthermore, delving into economic modeling of ranch decisions that incorporates factors like opportunity costs and risks could be a pertinent direction for upcoming studies.
Interpreting the results of our study requires caution due to the cross-sectional nature of the data and the assumption of input exogeneity.In the TE literature, there are two approaches to endogenize input use: using a statistical model with instrumental variables or employing an economic model based on a structural framework (26) .Nevertheless, in our case involving cross-sectional census data, the task of identifying appropriate instrumental variables or accurately specifying the objective function which producers would intend to optimize remains a challenging endeavor.
Shifting our attention to another critical aspect, climate plays a significant role in beef cattle farming, particularly in pasture growth.Uruguay benefits from low-altitude relief, a temperate climate, and evenly distributed rainfall throughout the year, although there are notable annual variations.However, quantifying the influence of climate through specific variables can be challenging.In our technical efficiency model, we typically controlled the farm's geographical region.Future research could enhance this analysis by georeferencing farms and utilizing satellite imagery to more accurately assess conditions such as soil moisture, forage quality, and production levels.
Another limitation of our study is the reliance on data from a single snapshot in time, considering the inherent inertia of beef farming due to long-term biological cycles.The development of dynamic models for beef production represents an important avenue for future research.This challenge is further complicated by the frequency of available data, as the response of variables is likely to vary across different time periods or windows.Furthermore, having access to panel data would allow the use of less restrictive models and improved control for unobservable heterogeneity, providing a more nuanced understanding of the factors influencing production efficiency.
As expected, variables related to improved animal management practices, such as weighing scales, cattle chutes, and technological guidance, exhibit a positive correlation with efficiency.While causality remains uncertain, this association highlights a meaningful connection between technical advice and efficiency, even after accounting for input levels, regional differences, and technology.
Finally, evaluating technical efficiency at the individual livestock farm level provides a deeper understanding of farm management practices.This fine-grained perspective facilitates direct comparisons among diverse production units, thereby yielding more precise insights into the efficacy of livestock-related programs and policies.This granularity is especially pertinent since technical efficiency serves as a superior outcome variable for evaluating the effects of interventions on the livestock population, offering a more targeted and meaningful measure for evaluating success and identifying areas for improvement.

Figure 1 .
Figure 1.95% confidence intervals for input-output elasticities and returns to scale, all evaluated at the mean value (BLU=497, LAND=722, LABOUR=2.79)

Figure 2 .
Figure 2. 95% confidence intervals for input-output elasticities across the inputs' support

Figure 3 .
Figure 3. 95% confidence intervals for return to scale across the inputs' support

Figure 4 .
Figure 4.The 95% confidence intervals for partial effect of the control variables in the production function

Figure 5 .
Figure 5. 95% confidence intervals of the partial effect of the farm department on the production function