Unified analysis of the technical efficiency of sugar production in Mexico

Abstract

In Mexico, sugarcane is an important crop because it is the primary input for sugar production and impacts employment generation in 15 states and 272 municipalities. This study aimed to estimate the technical efficiency of sugar mills of the 2022-2023 harvest in the production of standard sugar. The methodology used was the stochastic nonparametric envelopment of data (StoNED) analysis, which unifies the approaches of data envelopment analysis and stochastic frontier analysis. The results showed the existence of heterogeneity in the relative technical efficiency of sugar production across the mills. Five groups of mills were identified: a) ten mills with optimal efficiency; b) 25 mills with high relative efficiency; c) four mills at the threshold of high relative efficiency; d) five mills with potential for improvement; and e) a mill in a critical situation due to its high technical inefficiency (26%), which was El Carmen. The average efficiency of agribusiness was 96%. It is concluded that there is a regularity in the behavior of the El Carmen and El Mante mills as two decision-making units, which, given their high inefficiency in the production of standard sugar, due to causes attributable to their management and production practices, could stop operating temporarily or permanently.

Keywords

data envelopment analysis, resource and input management, stochastic frontier, technical inefficiency.

Introduction

Sugarcane in Mexico is essential because it is the input of the primary sweetener used in the country, which is cane sugar, which has a 77.54% share of the Mexican sweetener market demand ( Santillán et al ., 2017 ; CONADESUCA, 2025 ) and impacts employment generation in 15 states and 272 municipalities ( CONADESUCA, 2024 ).

In the 2023-2024 harvest, 271 303 direct jobs were generated in 49 mills in the field and factory links of the sugarcane mills ( CNIAA, 2024 ). In 2023, sugarcane generated 5.7% of the total value of cyclical and perennial crop production (SIAP, 2025).

In recent decades, multidimensional efficiency analysis methodologies, in which multiple inputs and multiple outputs are considered simultaneously, have been gaining prominence ( Johnson and Kuosmanen, 2011 ). The two methodologies that have been most developed are data envelopment analysis (DEA) and stochastic frontier analysis (SFA). DEA has been applied in a multitude of areas, including agriculture.

Aldaz and Millán (2003) compared the nonparametric methodologies of the Malmquist index and the DEA to quantify agricultural efficiency in the European Union for the 1985-2000 period and concluded that the evaluation of efficiency with slightly different approaches to the same methodology is significantly affected.

Santiago et al . (2021) applied the DEA analysis in their variant of the Malmquist index to a balanced sugarcane panel dataset comprising 50 sugar mills that operated during the 2006-2007-2015-2016 harvest period. Their results showed that the San Miguel del Naranjo mill had falls of -10.4% in productivity, with setbacks in technical efficiency (-10.2%) and technology (-0.3%), and that, for the study period, 20 mills had negative productivity, and in 30 mills, this indicator improved.

Valdivia et al . (2022) analyzed the efficiency and nature of returns to scale for sugar mills that milled in the 2010-2011 harvest. The results showed that 23 mills operated at their optimal scale, nine mills at total efficiency, but with pure inefficiency and scale inefficiency, and a third group operated with total inefficiency, pure inefficiency, and scale inefficiency, and that 23 mills operated with constant returns to scale, 29 with increasing returns to scale, and only two mills with decreasing returns to scale. The main conclusion indicates that the 29 mills with increasing returns to scale could improve their performance if they expanded their size, since production and factor productivity would increase more than proportionally.

The stochastic frontier methodology has been applied very limitedly in Mexico and in agriculture, except for Ortega et al . (2025) ; Sandoval et al . (2025) . Authors such as Ortega et al . (2023) analyzed the technical efficiency of sugarcane in Mexico using the stochastic production frontier, based on data from the 2019 National Agricultural Survey ( INEGI, 2020 ). Their main result was that, at the sugarcane production unit level, the average technical efficiency was only 47%, with a range of variation from 15% to 71%, which means an opportunity to improve technical efficiency at the production unit level.

Stochastic production frontier analysis is one of the two methods used to estimate the inefficiency of units of analysis; the other is data envelopment analysis, which estimates the efficiency of decision-making units in a nonparametric and deterministic way. However, the rapid advancement and development of new techniques in the field of technical, allocative, and economic efficiency now allows us to estimate this efficiency indicator by unifying the two approaches in what has been called stochastic nonparametric envelopment of data (StoNED) analysis ( Andor and Hesse, 2014 ; Kuosmanen et al ., 2015 ).

In this context, the objective of this research is to estimate the technical efficiency of the mills in the production of the standard sugar of the sugarcane agribusiness in order to determine which were the decision-making units with the best performance in terms of technical efficiency during the milling of the 2022-2023 harvest of the sugarcane agribusiness in Mexico.

Materials and methods

In the analysis, the primary sources of information were the statistical report on sugarcane agribusiness of the National Union of Sugarcane Growers ( UNC-CNPR, 2024 ) and the Mexican sugar manual of the CNIAA (2024) . The variables used in the research are described in Table 1 .

The method used to estimate the technical efficiency (or inefficiency) of decision-making units (DMU) is a nonparametric method that combines convex nonparametric least squares (CNLS) with the stochastic nonparametric envelopment of data (StoNED) ( Kuosmanen et al ., 2015 ).

In the first stage, we work with the CNLS model, in which the convex production frontier is estimated by solving the optimization problem m i n α i , β i , ε i ∑ i = 1 n ϵ i 2 subject to the constraints: 1) adjustment restrictions for each D M U i : y i = α i + β i ' x i - ϵ i 2). Convexity constraints for all pairs of units ( i , j ) that guarantee that the production frontier is convex: α i + β i ' x j ≤ α i + β j ' x j 3). Monotonicity constraints that guarantee that the increase in any input does not result in a reduction in output since the coefficients are non-negative: β i ≥ 0 , where n= is the total number of decision-making units or units of analysis; α i = is the intercept for the D M U i ; β i = is the vector of coefficients or slopes that is the marginal contribution of each output in the D M U i ; ε i = is the compound error term (statistical noise and technical inefficiency) for the D M U i ; y i = is the output observed of the D M U i ; x i = is the vector of inputs of the D M U i ; β i ' x i = is the scalar product of the coefficients and inputs (linear impact of the inputs on the output).

Once the CNLS residues have been estimated in the first stage, they are used in the second phase, in which they are decomposed into ε i = v i - u i . Where: v i ~ N ( 0 , σ v 2 ) , and the error that represents the technical inefficiency u i ; in this paper, it is assumed that it is distributed asymmetrically by means of a half-normal distribution and u i ≥ 0 . Estimation of the parameters requires estimating the variance of statistical noise ( σ v 2 ) and the variance of inefficiency ( σ u 2 ) by maximum likelihood (MLE), maximizing: L σ v 2 , = ∑ i = 1 n f ε i σ v 2 , σ u 2 , where f ( • ) = is the joint density function of v i - u i . The expected value of the error representing the inefficiency u i , conditional of statistical noise ε i , is estimated using the so-called predictor of Jondrow et al . (1982) , which is: E u i ε o = σ λ 1 - λ 2 φ z i 1 - Φ z 0 - z i . Where: φ ( • ) and Φ ( • ) correspond to the density function and the cumulative distribution of a standard normal distribution, respectively and the expression λ = σ u σ v represents the ratio of inefficiency over statistical noise; σ = σ v 2 + σ u 2 is the joint standard deviation, and z i = ε i λ σ is a standardized auxiliary variable.

To make the CNLS-StoNED model operational, the multiplicative form of the compound error was assumed, which results in the expression for the calculation of u i being now ε i = ln ⁡ y i - ln ⁡ f ( x i ) . This also makes it easier to interpret u i because technical inefficiency will now be a percentage of the output. An advantage of the CNLS-StoNED approach is that it allows us to discriminate causes that are merely random and beyond the control of the respective decision-making unit or the particular administrator. The estimation of the empirical model was carried out using the Benchmarking package of the R 4.2.3 program, developed by Bogetoft and Otto (2025) . Finally, it is necessary to note that the definition of the ranges of values of the efficiency scores in which the sugar mills were grouped was based on Cooper et al . (1984).

Results and discussion

The relevant descriptive statistics of the variables of the estimated model, which correspond to cross-sectional data from 47 sugar mills out of the 49 that operated in the 2022-2023 harvest, are presented in Table 2 .

Based on the estimated model results, it is possible to distinguish five groups of mills according to their technical efficiency, estimated using the CNLS-StoNED approach. In the first, there are 10 sugar mills with optimal technical efficiency (100%) located along the observed efficiency frontier. These mills are Alianza Popular, Atencingo, Central Casasano, Central Progreso, El Molino, Emiliano Zapata, Plan de San Luis Potosí, La Fe Pujiltic, Quesería and Tamazula.

In a second group, there are 25 sugar mills, which were called mills of high relative technical efficiency or quasi-efficient mills, whose efficiency score range extends from 90.4% to 97.97%. At the lower limit of this group is the Motzorongo mill with an efficiency of 90.4% and an inefficiency of 9.6% attributable exclusively to causes of management of resources, inputs, and practices under the control of said DMU and not to merely random causes that are beyond the control of the mill, such as excessive rainfall or droughts, among others.

This is the key difference of the method used in this research, the stochastic nonparametric envelopment of data (StoNED) analysis and the data envelopment analysis (DEA), where all the technical inefficiency is attributed exclusively to the management of the production unit in question, since this method does not include a statistical error that reflects the inefficiency attributable only to random factors beyond the control of the managers of the respective mill. At the upper limit is the Plan de Ayala mill with a technical inefficiency of 2.1%, so it is at the threshold of efficient mills with optimal performance. This group of mills is shown in Table 3 .

In a third group, it was possible to place four sugar mills that can be characterized as mills whose efficiency score ranged between 89.2% and 89.7%; that is, they are mills that are on the threshold of being considered high-efficiency or quasi-efficient mills. This group is shown in Table 4 .

In a fourth group, there are five mills, which, following Cooper et al . (1984), have been called mills with potential for improvement in their technical efficiency. However, their situation already reflects a certain degree of critical status, so it is advisable to improve production practices and the management of resources and inputs over which these economic units have control. As mentioned, their technical inefficiency is attributed to the productive practices, management, administration, and social relations between sugarcane suppliers and sugar industrialists, which are not purely random events, such as climatic factors and others that are totally beyond the control of these decision-making units. This group of sugar mills consists of those presented in Table 5 .

In a fifth group, although with only one mill, is the El Carmen sugar mill, whose performance, in terms of technical efficiency, places it in a critical situation. Its technical inefficiency reached 26% in the study harvest, as determined with the methodology used, and as mentioned, technical inefficiency is attributable to causes within the decision-making unit itself.

Finally, the average relative technical efficiency of the 47 mills considered in the research was 94%. This number can be considered as an average for sugarcane agribusiness in Mexico, so it can be asserted that the national agribusiness is a sector with high relative technical efficiency. Nevertheless, the 6% inefficiency is due to causes not attributable to merely random phenomena, such as climate, but to the management capacity and productive practices of the resources and inputs of the decision-making units of said agribusiness.

To discuss the results of this research, no similar study was found, to the best of our knowledge, that used the CNLS-StoNED methodology in agriculture or sugarcane at the sugar mill level. Some studies have applied either data envelopment analysis or the stochastic frontier separately. Sandoval et al . (2025) applied stochastic frontier analysis to evaluate the agroindustrial yield or sucrose per hectare of sugar mills and found that, of the 37 sugar mills studied, two of them were the ones with the highest technical inefficiency of agroindustrial yield: El Mante with an inefficiency of 11.4% and El Carmen with a technical inefficiency of 15.1%.

Although El Mante had a technical inefficiency of 10.8% in the present research, in the work by Sandoval et al . (2025) , who applied the stochastic frontier exclusively, it had a technical inefficiency of 15.1%. As observed, the StoNED methodology allowed us to estimate a lower inefficiency score attributable to the productive and management practices of said mill; in essence, its situation is worrying and could lead to it ceasing operations either temporarily or permanently. The same reasoning applies to the case of the El Carmen sugar mill.

Ortega et al . (2023) also applied the stochastic frontier approach to estimate the technical efficiency of the sugarcane industry using data from the 2019 National Agricultural Survey ( INEGI, 2020 ) and found that the average score of the sugarcane industry for that indicator was 47%, varying in a range from 15% to 71%. This level of efficiency contrasts with the agribusiness average of 96% estimated by Sandoval et al . (2025) .

Nonetheless, it should be noted that the work of Ortega et al . (2023) was based on information from the 2019 National Agricultural Survey (INEGI), so the estimate of the efficiency index included more than thirteen variables and refers to decision-making units at the level of agricultural production units rather than at the level of sugar mills.

Escobedo et al . (2019) , using data from the 2015-2015 harvest, calculated the technical efficiency of the 50 sugar mills that operated in that harvest using the data envelopment analysis and found that the average efficiency of the agribusiness was 89% when they did not consider the mechanization of the cane harvest, and it rose to 96.5% when they considered the mechanization of the cutting and collection of cane. In this study, it was found that the four mills with the lowest technical efficiency were El Carmen, San José de Abajo, El Refugio and El Mante, whose relative technical efficiency is 69%, 69.8%, 75% and 76.4%, respectively.

As can be seen, El Carmen and El Mante have been two mills that, in the studies reviewed, using data envelopment analysis, the stochastic frontier or StoNED, which unifies both methodologies, have shown poor performance in terms of their technical efficiency.

Conclusions

The analysis was based on the use of the Stochastic Nonparametric Envelopment of Data (StoNED) approach, which represents the unification of two previously distinct approaches: data envelopment analysis and stochastic frontier analysis.

The methodological integration allows us to consider during the analysis both the nonparametric and axiomatic characteristics of the data envelopment analysis, which is helpful to handle multiple inputs and multiple outputs without assuming a specific functional form and the capacity of the stochastic frontier analysis to model the statistical noise of the production processes, which yields a robust evaluation of technical efficiency.

The findings of this research have revealed significant variation in the levels of technical efficiency across the mills that make up the Mexican sugarcane agribusiness. This made it possible to identify groups of mills ranging from those with optimal efficiency, reaching 100%, to others that show high relative efficiency, mills on the threshold of achieving this high efficiency, and finally, mills with clear potential for improvement.

In this context, the El Mante and El Carmen mills are a particularly notable case, since both have shown a tendency to exhibit persistent technical inefficiency compared to the rest of the mills analyzed, as shown by previous studies on technical efficiency as in this work.