2.1 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 CGA²⁴, 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 level¹⁰, 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 While the agricultural year data from the 2011 census may appear out of date, it remains as an invaluable benchmark, offering insights into the intricacies and changes within the livestock sector.

2.2 Method

To measure technical efficiency (TE), we used the output increasing oriented indicator proposed by Farrel²⁵, 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 theory²⁶. For recent literature on this topic, refer to Kumbhakar and others ^{_27)(28) 29}, and Sickles and Zelenyuk²⁶.

Let 70. Y 71. 𝑖 72. represent the output of production unit 𝑖, 73. 𝑋 74. 𝑖 75. an input vector of dimension K, and 76. 𝑓(𝑋 77. 𝑖 78. ;𝛽) the production function. We introduce 79. 𝑢 80. 𝑖 81. as a non-negative error following the distribution 82. 𝐅 83. + 84. ( 85. 𝛍 86. 𝐮 87. , 88. 𝛔 89. 𝐮 90. 𝟐 91. ), and 92. 𝑣 93. 𝑖 94. a symmetric normal error. While 95. 𝑣 96. 𝑖 97. accounts for elements such as measurement error, specification issues, and random variability in the production process, 98. 𝑢 99. 𝑖 100. 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 f(Xi _; β), which we assume to be a translog functional form due to its flexibility²⁷:

The functional form described facilitates the derivation of product input elasticities and accommodates non-constant returns to scale. Specifically, when all coefficients tied to second-degree terms ( 110. 𝛽 111. 𝒋𝒔 112. ) 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, respectively²⁷.

Additionally, it is necessary to assume the distribution of the technical inefficiency term ( 114. 𝑢 115. 𝑖 116. ), which, by definition, can only take positive values. The model developed by Wang²² 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 Normal³⁰ and Truncated Normal³¹ (TN) specifications, which do not incorporate contextual variables. There are also variations such as the Kumbhakar, Ghosh and McGuckin³² (KGM) model, which parameterizes the distribution mean of inefficiency with exogenous variables, and the Caudill and Ford³³ (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 122. 𝑪 123. 𝒊 124. with a vector of coefficients 125. 𝜃 126. 𝑻 127. , is as follows:

To estimate the likelihood of the model, it is assumed that the distribution of the random variables 132. 𝑢 133. 𝑖 134. and 135. 𝑣 136. 𝑖 137. is independent, conditional on ( 138. 𝑋 139. 𝑖 140. , 141. 𝑍 142. 𝑖 143. ). 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 144. 𝑢 145. 𝑖 146. | 147. 𝑣 148. 𝑖 149. :

Implicitly, the model assumes exogeneity of all inputs, which implies the absence of unobservable producer-level 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 L(H_o) and L(H _A ) 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 farms³⁴. 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 Tree³⁵ (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 causally³⁶.

2.3 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 Aguirre⁹.

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.

Table 1: Definition of variables 

The ratio of area with improvements represents the proportion of the soil that has enhancements over natural grass, allowing for greater forage capacity, and therefore, the potential to feed more cattle. The greater the proportion of improved area, the higher the expected forage capacity, and, consequently, a greater potential to sustain more livestock.

Lastly, a set of explanatory variables Z is introduced to consider factors that potentially affect efficiency. While these variables do not influence the production possibilities frontier, they can impact the distance between the evaluated farm and the frontier. The explanatory variables consist of: (1) the utilization of services and technical assistance (agronomic, veterinary, and accounting); (2) the type of land tenure; (3) the type of ownership of the ranch; (4) the proportion of livestock owned by others, and (5) the importance of beef production in the family's income.

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.

3.1 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 software³⁷.

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 ( 192. 𝐻 193. 01 194. ) 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 ( 195. 𝐻 196. 05 197. ). 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.

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) 

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.

Figure 2: 95% confidence intervals for input-output elasticities across the inputs’ support 

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 3: 95% confidence intervals for return to scale across the inputs’ support 

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.

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

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.

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

3.2 Technical efficiency

When computing technical efficiency, we analyze the data in two distinct ways: weighting it by the size of the ranches in livestock units and treating all farms with equal weight (as shown in Figure 6). These two approaches yield two different indicators: the simple average efficiency of the farms in our sample, which is relevant for assessing the heterogeneity within our dataset, and a weighted average that provides a more representative measure of the state of the livestock sector in Uruguay.

Figure 6: 95% density estimates of TE, and TE weighted by bovine livestock units 

When using the weighted sample by size, it is observed that the average TE level increases from 76.2% to 79.1%, and the dispersion narrows (Table 2). This is evident as the p90/p10 ratio decreases from 59.2% to 41.2%.

Table 3 presents the Pearson bivariate correlation coefficients between the estimated TE and the variables included in the model. TE shows a positive correlation with the output and all inputs, which may be influenced by the farm's size (we will come back to this point later).

Figure 7 illustrates the relationship between TE and meat production per hectare, which is the standard performance measure for ranches. We have plotted a local regression between these two variables, revealing a nonlinear positive relationship. The Pearson correlation coefficient between the variables at the level is 0.6174, and in ranks (Spearman) it is 0.713. Notably, there seems to be a cutoff point at 80 kg/ha; for values lower than this, the Pearson correlation is 0.7364, whereas for values greater than 80 kg/ha, it drops to 0.3779.

Table 3: Pearson's correlation 

Note: values with * are statistically significant at 1%. Output and inputs are presented in level form to facilitate the interpretation.

Figure 7: Scatter plot TE and beef/ha 

To assess the influence of the explanatory variables on efficiency, we compute the average partial effect of each variable on the expected value and variance of technical inefficiency (as shown in Table 4). Standard errors are estimated using bootstrapping with 1000 iterations, following the methodology outlined by Kumbhakar and others²⁷.

Table 4: Average partial effect (APE) of explanatory variables on expectation and variance of inefficiency  

Note: standard errors of APE on E(u) and V(u) estimated by bootstrap with 1000 repetitions (*** pv<0.01; **pv<0.05: * pv<0.1). Categorical variable tenure and ownership type have as omitted category owner and individual ownership, respectively.

The variables that significantly affect the expected value of TE at the 1% level are: the ratio of foreign cattle (11.4%), possession of technical agronomic assistance (-6.8%), veterinary services (-5.7%), the main income sourced from the farm (-4.8%), and contracted services to external parties (-3.9%). Conversely, factors such as the ratio of foreign cattle (7.3%), the presence of technical agronomic assistance (-4.3%) and veterinary services (-3.7%), primary income being farm-related (-3.1%), and third-party hired services (-2.5%) are significantly related to the variance of the TE score. The variable accounting for technical assistance is not statistically significant at the 10% level.

This implies that, for example, ranches with agronomic technical assistance have an average level of technical inefficiency that is 6.8% lower than those without agronomic advice. Additionally, the variance of technical inefficiency for ranches with agronomic assistance is 4.3% lower than for those without such assistance.

When analyzing the data based on the types of land tenure, which include tenant, tenant-owner, and other forms (with the 100% owner category as the reference), we observe statistically significant lower levels (-7.3%) and variance (-4.8%) of inefficiency in other forms of tenure. This category encompasses various arrangements such as grazing for 11 months exclusively, sharecropping, occupants, and other similar forms.

Finally, when exploring the impact of the type of ownership, which includes corporate ownership with and without contracts (with individual ownership as the reference category), we discovered that farms owned by corporate ownership tend to have lower efficiency levels. Specifically, corporate ownership without contracts or successions exhibit a level and variance of technical inefficiency that are 25% and 16.5% lower than those owned by natural persons.

3.3 Descriptive analysis by TE deciles

As part of our exploratory analysis, we categorized ranches into ten equal-sized groups (deciles) based on their technical efficiency (TE), sorting them from lowest to highest TE. This categorization allowed us to describe the composition of these groups (Table 5, 6, 7 and 8). It is worth noting that given the multiple hypothesis tests conducted, we applied a Bonferroni correction³⁸. The correction involves dividing the significance level (5%) by the number of comparisons, which in this case is 45 (representing combinations of 2 out of 10 groups). This correction helps to control for the increased risk of making a Type I error due to multiple testing.

An increasing relationship between TE and meat production per hectare is observed, corroborating the results commented above. However, it is important to note that not all the groups show statistically significant differences.

There is a positive association between TE and the size of the farm (measured in livestock units or grazing area), but there is no clear relationship between TE and the CONEAT index or the level of soil intensification.

Concerning the sheep-to-cattle ratio and the proportion of foreign-owned animals within the ranches, they are negatively associated with TE. In contrast, TE shows a positive association with the availability of technical advice (including agronomic, veterinary, or accounting assistance), infrastructure resources, and access to hired services. Additionally, the relationship between the ratio of bovine livestock units (BLU) per hectare and TE follows an inverted U-shaped pattern.

Remarkably, the decile associated with the lowest TE also exhibits a cattle mortality rate of 6.4%, which is over twice the overall average of 2.6%.

3.4 Descriptive analysis using regression trees

Figure 8 depicts the regression tree, dividing livestock ranches based on the average TE. The tree effectively segments ranches into 10 end nodes, reflecting the heterogeneity of the results, with average technical efficiency groups spanning from 61% to 86.5%.

The algorithm starts the segmentation process by assessing whether there is a cattle weighing scale present. The presence of such a scale suggests more precise herd management, indicating better overall farm management or TE.

Lower levels of TE are found in groups that lack technical assistance, and are distinguished by either a low ratio of livestock units to surface area (below 0.368) or a high percentage of third-party-owned livestock (above 53%). The presence of agronomic and veterinary technical advisory services divides the farms, with higher levels of efficiency observed in those ranches that utilize these services.

Figure 8: CTREE for TE. 

3.5 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 production⁹. 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.