An Analysis of the Eco-Efficiency of the Agricultural Industry in the Brazilian Amazon Biome

Abstract

The exponential growth of the agricultural industry in the Amazon region has brought about notable economic advancements. However, this growth has substantially cost the region’s ecosystems, manifesting in increased deforestation and biodiversity degradation within the Amazon forest. This article is dedicated to assessing the eco-efficiency of agricultural production in Amazon Biome municipalities. It places particular emphasis on identifying critical determinants through the utilization of the classic Data Envelopment Analysis (DEA) model for efficiency computation, super-efficiency models for distinctive characterization, bootstrap computational techniques for robust resampling, and the Malmquist index for calculating annual eco-efficiency indices of each Decision-Making Unit (DMU). An exploration of the correlation between efficiency and meteorological attributes of the municipalities is conducted. The findings of this study reveal the following significant points: Eco-efficient municipalities within the Amazon Biome can serve as benchmarks for other DMUs striving to attain optimal input–output levels, most municipalities in the Amazon Biome operate close to the productive frontier due to the prevalent technology employed in their agricultural activities, the nature of the technological frontier’s return suggests that small and large DMUs possess eco-efficiency potential, and the current dataset does not yield conclusive evidence regarding a direct correlation between the variables. Leveraging this information, strategic pathways can be formulated to drive economic development in tandem with the sustainability of Amazon Biome municipalities. These strategies promise to foster social, economic, and environmental benefits for the populace while providing valuable insights to inform future research within this thematic domain.

1. Introduction

The issue of sustainable development became significantly relevant after the publication of the Club of Rome’s report, “The Limits to Growth” [1]. The report warned that the planet could not support continued economic growth without exceeding the Earth’s carrying capacity due to the increasing pressure on energy and natural resources, pollution, and climate change. This prompted the United Nations to establish conferences and commissions worldwide to study and discuss sustainable development and develop commitments and solutions.

Thus, in the Brundtland Report published by the United Nations World Commission on Environment and Development entitled “Our Common Future” [2], the definition of sustainable development emerged based on the concept of the “triple bottom line” of sustainability. The three dimensions are outlined as follows. (i) The economic dimension refers to the traditional search for profit and financial value creation. It involves assessing an organization’s ability to be financially healthy. (ii) According to the social dimension, a production unit must consider its impact on society and the communities in which it operates. This can include corporate social responsibility; the quality of relations with employees, customers, and suppliers; and contributions to social development. (iii) According to the environmental dimension, an organization assesses its environmental impact and contribution to long-term sustainability. This involves issues such as reducing greenhouse gas emissions, managing natural resources efficiently, minimizing waste, and adopting sustainable practices and products, meaning that an organization’s success should not only be measured by its financial performance but also by how it contributes to people’s well-being and the preservation of the environment.

Since its inception, the concept of sustainable development has been adopted in the theoretical literature. It is practiced by companies and countries seeking a balance between financial prosperity, social responsibility, and environmental preservation. From this perspective, we can highlight the study by Heyder and Theuvsen [3], where the authors developed a survey of 170 companies in the agricultural industry of small and large multinational corporations in Germany related to social and environmental dimensions. In addition, other studies have proposed the construction of multidimensional sustainability indicators to evaluate the performance of the agricultural industry’s production system. Some of them can be highlighted, such as [4,5,6,7].

Moving in this direction, the 26th Conference of Nations on Climate Change, which took place in Glasgow, Scotland, referred to the conservation of forests. During this conference, according to the United Nations website (https://news.un.org/en/story/2021/11/1104642 (accessed on 24 June 2024), 110 countries that are home to 85% of the world’s forests signed a declaration committing to halt and reverse deforestation by 2030. This declaration was an essential step towards the preservation of the environment. However, the most challenging task lies in achieving this regional and local commitment without compromising the sustainable development and resilience to climate change of families who live and work in forests. They are producers with limited resources to maintain and improve productivity and competitiveness. They are marginalized from primary social services and impacted by the independence of adult children who give up and migrate to the urban environment or are fragmenting family property [8].

As a result, introducing ever stricter environmental protection regulations has caused great concern due to their social effects. This situation is no different in the Brazilian Amazon rain forest, where decision-makers face two challenges. This is due to the need to make communities more productive and efficient to offer more products of higher quality and competitive prices and, thus, to be able to face direct competition with agriculture on an industrial scale [9]. The second challenge arises from the evidence that agricultural intensification and expansion in forest areas can generate irreversible environmental damage that economic benefits may not offset [6].

Removing native primary vegetation cover is known to compromise the ecosystem services of flora and fauna, which are also at risk of degradation. In addition, deforestation causes erosion, a reduction in soil nutrients, and an increase in greenhouse gas (GHG) emissions, which interfere with rainfall and the planet’s temperature. This creates a vicious cycle, as changes in temperature and rainfall patterns can harm agricultural activity itself [8,10]. There is also the fact that increased territorial expansion and human exploitation of the environment are increasingly depleting native forests. Climate change is known to cause direct effects, such as changes in soil moisture and temperature regimes. However, these changes also cause what Butterbach-Bahl and Dannenmann [11] call indirect effects, such as an increase in carbon dioxide (CO₂) in the atmosphere and soil dethatching (N₂).

In the Amazon Biome, this phenomenon is no different, making the issue of deforestation one of the main problems facing Brazil [12]. There are several consequences of deforestation in the Amazon. Among these consequences, we can see decreases in rainfall (220 to 640 mm/year) and evaporation (164 to 500 mm/year) and a slight increase in temperature (0 °C to 3 °C) [6,13,14,15,16]. From these observations, it can be inferred that the impact on the biome is significant, causing changes in other regions and biomes across the planet, such as a decrease in precipitation, an increase in temperature, and even a decrease in the efficiency of local agriculture [17]. Therefore, a rapid change is needed in how these natural resources are used and preserved [18].

Another factor causing deforestation in the Amazon is mechanized farming, which promotes burning [19]. The typical fires that cause deforestation are called high-frequency fires. These fires have contributed to more than 40% of the fires detected in recent years, while on the Bolivian border and in the states of Mato Grosso, Pará, and Rondônia, this figure is as high as 84% [19]. However, it is interesting to review how the agricultural industry operates and how it would be possible to improve the use of resources without failing to produce what is needed more efficiently. For this reason, it is impossible to think of reducing production to protect the environment. Instead, it is necessary to think of ways to develop production sustainably by introducing new technologies and improving planting methods.

This means that production must be performed in a way that does not harm the environment and consumes as few resources as possible. For this reason, one of the keywords in this research is efficiency. By efficiency, we mean production that delivers the maximum output level while spending as few resources as possible [20], thereby reaching the optimum point between the ratio of input and output within the production frontier. In this way, it is expected to produce as much food as possible, consuming as few environmental resources and emitting as little CO₂ as possible. DEA is used to assess efficiency.

This method consists of non-parametric mathematics that, using linear programming algorithms, can compare entities that carry out similar processes of transforming inputs into outputs to define an efficiency index between them in which the most efficient compared entity receives an index value equal to 1. The others receive a score below one proportional to how much less efficient they are. As a traditional technique, DEA is being popularized and has gained a lot of relevance, especially in research and academic circles. DEA is the only way to evaluate the efficiency of a transformation process by considering multiple inputs and outputs without having to transform these components into a single value, such as financial value.

In this study, we intend to address issues related to agricultural production in the municipalities of the Brazilian Amazon Biome. Our aim is to measure the eco-efficiency of municipalities belonging to the Amazon Biome, taking into account agricultural production and environmental preservation variables. To describe eco-efficient municipalities and, thus, provide a strategic vision for critical (inefficient) municipalities of how agriculture in the Amazon Biome can achieve more efficient production with minimal environmental impact and use of resources, using bootstrap computer models. We mapped the Brazilian municipalities considered to be outliers given the latest Brazilian agricultural census of 2017 and evaluated the eco-efficiency trend of the municipalities during the period from 2006 to 2017 using the Malmquist Index technique.

The application of Data Envelopment Analysis (DEA) to evaluate agriculture has been a consolidated practice in the literature [21,22,23,24,25]. However, most studies focus on China and continents such as Europe [26], where they seek to propose alternatives to make agriculture more efficient [27]. Few studies have focused on Brazil, since comparative analysis is carried out considering more than one region or municipality [28] or other regions of the Brazilian territory. On the other hand, it is interesting to have a view on a national scale. However, there has been little focus on trying to understand the relationship between inputs and outputs in one of the world’s main environmental reserves (the Amazon); conducting eco-efficiency analysis using bootstrap and computational methods, as well as the Malmquist index to calculate eco-efficiency over time; identifying the dynamics of efficiency in the agricultural sector; and considering data from the period from 2006 to 2017 [29].

The remainder of this article is organized as follows. In Section 2, we present a theoretical discussion about the main concepts involved in data envelopment analysis. Section 3 presents the materials and methods used to carry out the research, describes in detail the mathematical models for calculating eco-efficiency using bootstrap computational methods, as well as the approach using the super efficiency to detect anomalous data, and the application of the Malmquist Index. Then, Section 4 presents a discussion of the main results obtained in this research. Finally, the article ends with Section 5, concisely describing the main results found by the research, as well as its contributions to the literature.

2. Theoretical Framework

Efficiency is a concept based on economics, mathematics, and operational research to reach an optimum point between the ratio of inputs to be transformed (x) and the outputs generated (y), given a technological set (T) so that $T=\left\{\right(x,y\left)\right|x$ can produce $y\}$ in a concept of production possibilities (CPP), whose properties are described by Färe [30]. In this way, eco-efficiency represents the factors involving economic, social, and environmental issues that form a tripod to make up the inputs and outputs of the production process. The inputs, (x) represent the ecological costs necessary to generate the desirable products (y) [31]. In theory, there is a minimization of inputs (x) and a maximization of outputs (y). Nonetheless, this relationship is not generalized for cases of desirable inputs, such as preserved areas, and undesirable outputs, such as CO₂ emissions; this relationship is inverted, given a technological set ($T=\left\{\right(x,y\left)\right|x$) can produce $1/y\}$.

The DMUs (Decision-Making Units)—Inefficient DMUs are inserted within the CPP, formed by linear segment combinations of efficient DMUs that include a convex figure. However, they do not present optimal performance between the ratio of inputs and outputs [32]. The upper part of the frontier segment represents the $\left(T^{\delta }\right)$ of the CPP, formed by a negative space ($R^{p+q}$) and structured by the x and y $\epsilon$ $\left(R^q\right)$ of the DMUs. From this discussion, the concept of eco-efficiency emerges. It is achieved when the set of n DMUs (decision-making units) that form the production frontier, composed of x and y, present the lowest possible quantity of inputs (related to the environmental cost of the process) and the highest possible amount of outputs (related to the impact that activities can have on the environment).

This distance between the inefficient point and the benchmarks made up of the frontier of efficient DMUs is called the Euclidean distance. Therefore, to achieve technical efficiency, it can be input-oriented (when inputs are minimized, without changing the level of outputs) and output-oriented (when outputs are maximized, without changing the status of inputs) [32], where the inverse of technical efficiency is the radial efficiency described in [31]. Thus, the DEA model is a mathematical model that, by receiving the input and output variables of a process, can define how efficient the entity carrying it out is [33].

To do this, the model uses several entities that carry out the same transformation process to, in a comparative analysis, find the limit of efficiency and how each of these entities (DMUs) is classified with respect to this limit. With enough DMUs, creating a scatter plot with all these DMUs distributed along the Y-axis, representing the outputs that a given DMU produces, is possible. The X-axis is the axis that quantifies the inputs that this DMU needs to consume to reach this production level. Thus, Figure 1 is a graphic example in which DMUs A, B, C, D, and E are considered benchmarks of excellence, i.e., those that have achieved technical efficiency [32].

Still analyzing the graph in Figure 1, it can be seen how much more $DM{U}_E$ would need to produce to achieve technical efficiency and how much less it should consume—or even a combination of the two. In this context, the efficiency frontier is then generated by drawing a line between the points where it is positioned on the graph. The DEA model can calculate an efficiency index given the distance from the end to the line, and it is up to the researcher to indicate in which direction the line size should be measured. Next, the model can be oriented towards input, i.e., how much less a given $DM{U}_i$ could consume to maintain the output production level.

In this way, all the DMUs are compared, and each is given an efficiency index with the symbol $\theta$. This efficiency index ranges from 0 to 1, with 1 being the maximum, corresponding to the achievement of technical efficiency. By multiplying $\theta$ by the inputs of a given ($DM{U}_i$), we obtain the ideal amount of inputs for it to achieve technical efficiency. To calculate $\theta$, a set of n observations is needed, considering $S_n=\{x_i,y_{i}toi=\{1,\dots n\}\}$. With this set, it is possible to estimate the efficiency frontier and the efficiency index ($\widehat{\theta }$) for each DMU after solving a series of mathematical inequalities. The model determines the technological level (T) using an estimator (${\widehat{T}}_{CRS}$); with this estimator ($X_i$, $Y_i$), for each $DM{U}_i$, we can calculate the efficiency index by solving the following mathematical problem.

$${\widehat{\theta }}_i{(x_i,y_i)}_{OI-CRS}=max\left\{{\widehat{\theta }}_i\right|{\widehat{\theta }}_i(y_i\le Y\lambda ,x_i\ge X\lambda ),\lambda \in {\mathbb{R}}_{+}^n\}$$

(1)

where $X=[X_i,\dots ,X_n]$ and $Y=[Y_i,\dots ,Y_n]$ are the matrices representing the sets of inputs and outputs of the n observed DMUs; $X_i$ and $Y_i$ represent the vectors of inputs consumed and outputs produced by a given $DM{U}_i$, respectively; and $\lambda =[{\lambda }_1,\dots ,{\lambda }_n]$ are the combinations of inputs and outputs that make it possible to achieve the most excellent efficiency.

On the other hand, the model can also be output-oriented. In this orientation, the focus is on understanding how much more a given $DM{U}_i$ could produce. Therefore, the technical efficiency index, in this case, ranges from 1 for greater efficiency to infinity and is represented by the Greek letter $\varphi$. However, if we calculate $1/\varphi$, we also obtain an index from 0 to 1. The same $DM{U}_i$ should receive similar efficiency indices, regardless of whether the orientation is towards inputs or outputs. As with input-oriented DEA, product-oriented DEA also allows you to calculate how much $DM{U}_i$ should produce to be technically efficient by multiplying $\varphi$ by the DMU’s outputs. Using the same principles for input-oriented DEA, we would have the following formula for output-oriented DEA:

$${\widehat{\varphi }}_i{(x_i,y_i)}_{OO-CRS}=min\left\{{\widehat{\varphi }}_i\right|{\widehat{\varphi }}_i(y_i\le Y\lambda ,x_i\ge X\lambda ),\lambda \in {\mathbb{R}}_{+}^n\}$$

(2)

In addition to orientation, the DEA model can vary in analyzing DMU efficiencies. Charnes et al. [34] developed the first model that did not consider the variation in efficiency that scale can provide. They then created a DEA model called CRS for constant return to scale.

However, there are cases where the return to scale is not constant. For example, producing the maximum batch of a machine in industry is more efficient than producing half that batch. This is because, simultaneously, people and machines can be used for both scenarios, while the former produces twice as much as the latter. In this case, it is unfeasible for the industry in the second scenario to improve its efficiency without increasing its production scale, since it cannot use half a machine to reduce its inputs.

To solve this problem, Banker et al. [33] created the variable return to scale (VRS) model, which calculates the maximum efficiency of each $DM{U}_i$, taking into account the DMU’s level of production scale. Hence, in the previous example, the company could be technically efficient in both scenarios, since the first and second machines could operate on the efficiency frontiers of their scales. The concept of allocative efficiency was created for DMUs that are technically efficient and at the optimal scale. Allocatively efficient DMUs are DMUs that manage to produce more efficiently than all others DMUs, operating the ideal scale for the production process. They also tend to have the highest profit among all their peers [32,35,36,37].

Thus, eco-efficiency is achieved when a DMU obtains the highest possible level of desired outputs with a given level of inputs and environmental impact or requires the lowest possible amount of inputs and environmental costs to produce a given number of outputs. Its measurement results are obtained by calculating the Euclidean distance that separates each DMU from the border formed by the benchmarks. Thus, it is possible to define the following two measures of technical efficiency: (i) Farrell’s technical efficiency oriented to maximize outputs with a given input level (${\theta }_0$) and (ii) Farrell’s technical efficiency aimed at minimizing the inputs with a given level of products (${\theta }_I$). According to [32], technical efficiencies are inverse to [31] radial efficiency.

The evolution of the model is described in Figure 2.

3. Materials and Methods

3.1. Detection and Outliers Using Super-Efficiency

The DEA model calculates its indices based on a comparative analysis between peers. However, it has some limitations when there is a considerable range of productive units to be analyzed, making it necessary to use additional models to support the CRS, configuring the case of the super-efficiency model [35,36]. Thus, outliers can generate super-efficient DMUs. This means that these DMUs are far removed from the other DMUs and cause a distortion in the efficiency frontier. This method calculates each DMU’s impact on the model to determine whether it is an atypical case, and the greater the effect, the more atypical the unit of measurement—DMU.

To perform this calculation, the model removes a particular DMU and recalculates the efficiency of the other DMUs. The volume of the initial data set created by the distribution of the efficiencies generated by the model is calculated. After removing $DM{U}_i$, the volume is calculated and compared with the initial volume. Therefore, the closer to 0, the more significant the impact that $DM{U}_i$ will have on the total volume in the data set, which means that it is an outlier [40]. This process is repeated for all DMUs and must be performed again after removing each outlier, since one outlier can mask the existence of another.

The researcher must decide how many DMUs should be drawn from the database they are working with. Despite that, studies such as [41] suggest approximately 10%.

3.2. Stochastic DEA Model—Bootstrap

A significant criticism of DEA models is their deterministic nature, since they consider past events and do not account for stochastic effects. It would, therefore, be relevant to use statistical models in conjunction with DEA to validate hypotheses, confidence intervals, and correlation analyses. With this improvement, we can have more confidence in the efficiency results and correlation with exogenous variables.

For these two reasons, the bootstrap method is used in this research. The concept of bootstrapping arises from the studies reported in [38], based on which Simar and Wilson [39] applied the DEA stochastic model to a data generation process (DMP). Bootstrapping is a statistical technique for manipulating sampling to create a probability distribution of a dependent variable from a single sample, which is necessary when the nature of the data in the original model is not exhaustively known. The data generation process is described in four steps as follows:

• The efficiency (${\theta }_i$) of the original sample is calculated for each $DM{U}_i$, where $(i=1,2,\dots ,n)$ considering $(x_i,y_i)$, considering that it is a linear programming problem (LPP) as described in the Equations (1) and (2), depending on the type of orientation to be adopted.
• A new distribution is created, generated by simulated samples (${x^{*}}_i=[{x^{*}}_1,{x^{*}}_2,\dots ,{x^{*}}_n]$) based on the original sample ($x_i=[x_1,x_2,\dots ,x_n]$) of the same size, so ${x^{*}}_i=x_i\frac{{\theta }_i}{{{\theta }^{*}}_i}$. Then, the efficiency scores are calculated for each generated $DM{U}_i$, and each value is stored, resulting in a set of estimates (${{\widehat{\theta }}^{*}}_{b,i}$).

  $${{\widehat{\theta }}^{*}}_{b,i}=min\left\{{\theta }_i\right|{\theta }_i(y_i\le Y\lambda ,x_i\ge X\lambda ),\lambda \in {\mathbb{R}}_{+}^n\}$$

  (3)
• The observations are replaced B times (for the estimate to be significant, usually $B\ge 1000$) with simulated comments that respect the rules of the original sample with $(B=1,2,\dots ,b)$, and the calculations are repeated on top of each simulation. In this way, it is possible to understand how the values of the dependent variable or the estimator (${\theta }^{*}$) respond to variation in the sample. To estimate the standard error, the $D_p$ error of the replications is used.

  $$D_p\left({\theta }^{*}\right)=\sqrt{\frac{{\sum }_{b=1}^B({\theta }_b^{*}-{\overline{\theta }}^{*})}{B-1}}$$

  (4)
• With that, the confidence limits are calculated, having their intervals determined by the default mode with $\alpha =95\%$ for each estimate, with $\{{\widehat{\theta }}_{i,b}^{*},b=1,\dots ,B\}$, making the results even more robust and reliable [39].

3.3. Calculation of the Return to Scale Test

The choice of which model to use to calculate efficiency is not an arbitrary one because pre-adopting a model without investigating the nature of the behavior of the Constant Return on Scale or Variable Return on Scale (CRS or VRS) of the technological frontier $\left(T\right)$ can cause the result to be biased. This is because, in the case of a model with constant returns to scale, it is not taken into account that certain DMUs that are close in terms of efficiency may have particularities, so total efficiency is calculated. It is analyzed that not every DMU considered efficient in the VRS model will be regarded as efficient in the CRS model [42].

The null hypothesis ($H_0$) considers the model to be constant (CRS), given consistent returns to scale, and the alternative hypothesis ($H_1$) believes the model to be variable (VRS), given variable returns to scale. By design, the efficiency calculated by the constant model is always lower than the efficiency calculated by the variable model, so ${\theta }_{i,CRS}\le {\theta }_{i,VRS}$; therefore, the estimator (S) is calculated by the ratio of the sum of ${\theta }_{i,CRS}$ and ${\theta }_{i,VRS}$.

$$S=\frac{{\sum }_{i=1}^n{\theta }_{i,CRS}}{{\sum }_{i=1}^n{\theta }_{i,VRS}}\le 1$$

(5)

With an estimator value of $S=1$, $H_0$ is considered to hold, although this value is hardly reached. Therefore, when the estimator S is close to 1, the model to be considered is CRS. In $H_a$, the estimator (S) is significantly less than 1, so VRS is the model considered. To state whether it is significantly smaller, the critical value ($C_{\alpha }$) is obtained with a significance level of $\alpha =5\%$, so $S\le C_{\alpha }$. Given that the natural distribution of the original sample is not exhaustively known, bootstrapping is applied with the boot.sw98 package inside the R environment to calculate the efficiencies (${\theta }_{i,CRS}$ and ${\theta }_{i,VRS}$) according to the resampling method to obtain the estimated value of S [43]. In this way, a decision is made between $H_0$ and $H_a$ based on the result of Equation (5).

3.4. Malmquist Index Model

To clarify this question, the Malmquist Index was developed, named after Sten Malmquist [44]. To calculate the efficiency gain in period T compared to period $T-X$, the technical efficiency frontiers must first be calculated using DEA for the DMUs in both periods. When comparing DMU efficiencies over time, two variables can be measured, namely the slope of the efficiency frontier, which would mean that there is a new technology enabling DMUs to be more efficient—a phenomenon is known as the frontier shift effect; and the catch-up effect, or pairing, which is when a given $DM{U}_i$ has decreased its distance to the efficient frontier. The Malmquist Index is the multiplication of these two variables.

The two scenarios are presented in Figure 3. A frontier shift can be seen in the efficiency frontier created by DMUs A, B, and C, representing the efficiency frontier in period $T+1$, since it is closer to the Y-axis and further away from the X-axis. The decrease can be seen in the pairing effect in the distance from $DM{U}_M$ to the efficiency frontier for the period it is in. In period T, $DM{U}_M$ was at a distance of X from the border, while in period $T+1$, it was at a distance of $0.7_X$.

The matching effect, or catch-up, is the result of continuous improvements in production processes, using the same technology. Therefore, the comparison of technical efficiency between two periods can be defined as follows:

$${\displaystyle \frac{{\theta }_k^t(x_k^t,y_k^t)}{{\theta }_k^{t-1}(x_k^{t-1},y_k^{t-1})}}$$

(6)

where:

${\theta }_k^t(x_k^t,y_k^t)$ = $DM{U}_K$ is technical efficiency in a given period (t);

${\theta }_k^{t-1}(x_k^{t-1},y_k^{t-1})$ = $DM{U}_K$ is technical efficiency in a given period of t + 1.

Frontier shift can be calculated according to the following formula:

$$\sqrt{{\displaystyle \frac{{\theta }_k^{t-1}(x_k^{t-1},y_k^{t-1})}{{\theta }_k^t(x_k^{t-1},y_k^{t-1})}}{\displaystyle \frac{{\theta }_k^{t-1}(x_k^t,y_k^t)}{{\theta }_k^t(x_k^t,y_k^t)}}}$$

(7)

Therefore, multiplying Equation (6) by Equation (7) and passing the second term of the expression (7) into the square root, the word is transformed into the product of the pairing by the frontier shift. Consequently, a result less than 1 means an improvement in the DMU’s technical efficiency index, and an effect greater than 1 implies a worsening in the DMU’s technical efficiency index. Therefore, the same can be said for the Malmquist Index, calculated with constant returns to scale ($Mo$) as follows:

$$Mo={\displaystyle \frac{{\theta }_k^t(x_k^t,y_k^t)}{{\theta }_k^{t-1}(x_k^{t-1},y_k^{t-1})}}·\sqrt{{\displaystyle \frac{{\theta }_k^{t-1}(x_k^{t-1},y_k^{t-1})}{{\theta }_k^t(x_k^{t-1},y_k^{t-1})}}{\displaystyle \frac{{\theta }_k^{t-1}(x_k^t,y_k^t)}{{\theta }_k^t(x_k^t,y_k^t)}}}$$

(8)

3.5. Database

To assess the agricultural eco-efficiency of the municipalities that make up the Amazon Biome, a set of variables available in the 2006 and 2016 Agricultural Censuses was adopted, and a time series was generated using linear regression to fill in all the missing years. The sector’s classic inputs and outputs were considered, plus one positive and one negative externality.

To calculate the municipalities’ operational efficiencies of agricultural production, the variables used as inputs were people engaged in agricultural work, hectares dedicated to rural production, and hectares preserved, the latter being a desirable input. The selected outputs were the value of agricultural production in thousands of BRL and CO₂ emissions as an undesirable output. All these variables were at the municipality level. As a general rule, the following classic inputs and outputs were used in the modeling:

• $X_1$—People engaged in agricultural industry;
• $X_2$—Hectares dedicated to agricultural production;
• $X_3$—Preserved hectares;
• $Y_1$—Value of agricultural production in thousands of BRL;
• $Y_2$—CO₂ emissions with an undesirable output;
• $Z_1$—Average temperature;
• $Z_2$—Precipitation.

The area variables (hectares dedicated to production and hectares preserved), as well as the production value and people employed, come from the official Brazilian Institute of Geography and Statistics (IBGE) (https://www.ibge.gov.br/estatisticas/economicas/agricultura-e-pecuaria/9827-censo-agropecuario.html (accessed on 24 June 2024)) databases according to the censuses carried out in 2006 and 2017. For the years for which there is no official census information by the municipality, a simulation was performed using the estimated growth in annual production in the state according to CONAB (https://www.conab.gov.br/ (accessed on 24 June 2024)) (National Supply Company) year-on-year, combined with an estimate of how much each municipality should have as a share (in %) within each state, using an arithmetic progression calculation between the municipalities’ claims in 2006 and the municipalities’ claims in 2017. All the consolidated data and results found by this research are available and can be consulted on figshare (https://doi.org/10.6084/m9.figshare.25958827 (accessed on 24 June 2024)).

4. Results and Discussions

4.1. Analysis Variables

Figure 4 and Figure 5 show the area dedicated to agricultural activities in each municipality as a percentage of total municipal area in 2006 and 2017, respectively. The municipalities with a more proportional area dedicated to agriculture are along the eastern and southern borders of the Amazon Forest. From 2006 to 2017, the increase in agricultural area occurred mostly in the municipalities that already had strong agricultural activities.

Figure 6 and Figure 7 present the protected area as a percentage of the total municipal area in 2006 and 2017, respectively. Two characteristics of these maps need attention. (i) The majority of the municipalities have a very low percentage of protected area (see the number of municipalities in each group—numbers in brackets in the map caption). (ii) The municipalities with more protected area are the same as those with high agricultural area. These contradictory results come from the definition of the protected area variable in the censuses, as it represents protected areas on farms, not including Indigenous reservation areas, (environment) conservation units, and other public areas (with no private owners). Hence, the municipalities with known intact forests (in the center-west of the Amazon Forest area) are shown with a low percentage of protected area because they have very small areas of private farms. For this study, however, the definition of the protected area variable considering only the area on farms is adequate, since it is derived from farmers’ decisions on how much of an area to allocate for agriculture and environmental protection.

The data regarding CO₂ emissions were downloaded from the official site of Greenhouse Gas Emission and Removal Estimation Systems (SEEG) (https://plataforma.seeg.eco.br/total_emission (accessed on 24 June 2024)). This variable is measured in tons of carbon dioxide emitted by the agribusiness and property transformation but with an annual uninterrupted update since 2000. After that, an official database was collected from INMETRO using all the automatic measuring agencies in each state for every hour of every day to analyze the relation between the production efficiency index and the recorded weather. Then, the average temperature for each year in each state was calculated, and these values were used for each municipality that composes the Brazilian Biome.

4.2. Removing the Outliers

Next, given super-efficient DMUs, the Bogetoft and Otto [40] method was applied. The model is based on the assumption that a super-efficient DMU, considered to be an outlier, masks an efficient DMU, so looping is applied to recalculate the efficiencies with an input orientation and remove the super-efficient DMUs until there are no more super-efficient DMUs. To achieve this, there is a pause criterion in the process of eliminating outliers given by ${\displaystyle \frac{V_f}{V}}$, with a value of less than 0.7, where a DMU could produce 70% of what it has and still be considered a technically efficient DMU. The sdea() function predefined in the “Benchmarking” package was used for the calculation. Given the deaR model, the efficiencies of DMUs with an output and input orientation were calculated using the processes in the RVE box.

The looping removal model is applied again each year. Each year should have a few DMUs considered super-efficient, creating a list of all the super-efficient DMUs to be removed from all the years, i.e., from the entire database. We used $0.7$ for the efficiency index, since 150 DMUs would be removed from the sample with this parameter, which is no more than 30% of the database used in [41]. To compare the time windows, data processing is needed to give continuity to the efficiency gain, where the frontier shift index for year T is multiplied by the index for year $T-1$; then, the index for the year $T+1$ is multiplied by the product of the two previous indices in an accumulative manner. Using the efficiency index of the years, a cross base is created with the annual meteorological information, and the multivariate linear regression of the floor is analyzed, with the meteorological data being the independent variable and the efficiency of the year as the dependent variable.

Another technique is to create cut-off ranges by estimating DEA with super-efficiency. Figure 8 shows the municipalities considered outliers and super-efficient in 2017 that were excluded from the Malmquist Index analysis below.

The data cloud technique was used because it is robust for identifying outliers. In summary, the volume of the combined matrix of inputs and outputs is observed, where a significant reduction in this volume following the removal of a DMU indicates that this unit is an outlier. As can be seen in Figure 8, most of these DMUs are in undeveloped areas in Amapá and Amazonas states and some very urbanized municipalities (but small in total area) in Pará, Maranhão, and Tocantins states (sast of the map).

Totaling the number of outliers found by the cloud technique, 95 DMUs were removed, which represents around 16.99% of the total. This shows that the model adopted based on the super-efficiency cloud technique was more effective at detecting outliers compared to that reported in [29], which identified around 4.5% of outliers, most of which were in Pará, while the cloud technique brought in many outliers from the states of Amazonas and Amapá.

4.3. Scale Return Test

The result found for the critical value was $C_{\alpha }$ = 0.3854, and the estimated value was 0.9605, which is higher than the critical value ($C_{\alpha }$). With these results, there was no statistical evidence to reject the null hypothesis, accepting that the best model for this problem is the CRS (constant return to scale). The conclusion, therefore, must be that scale has no direct influence on the efficiency of agricultural production in the municipalities of the biome included in this study, so small, medium, and large producers can all become eco-efficient, reaching the technological frontier.

What, at first, may be a controversial result considering the analysis of studies that used all Brazilian municipalities as a sample, compared to previous studies carried out in the same region (Amazon), they also pointed out that the result of the scale test is constant [29], confirming the null hypothesis. When analyzing the productivity of an agricultural unit, the main determining variables are soil, climate, and the technologies used. Whether the production unit is larger or smaller is not affected by soil and climate. What determine these conditions are geography and the location of these units. As for technology, a team with greater production power could have more resources to invest in machinery. However, as the object of this study is entire municipalities, this effect is diluted among the various production units within each municipality and is therefore regressed to an average.

4.4. Eco-Efficiency of Municipalities the Amazon Biome

First, it is essential to analyze the current scenario of the agricultural industry in the Amazon to measure potential gains and even map out action plans to capture these gains. The results shown in

Table 1. Summary of data regarding the efficiency of municipalities.

Min.	First Q	Median	Mean	Third Q	Max.
1.000	1.015	1.051	1.099	1.123	1.975

were achieved using DEA for inputs with constant returns to scale. Thus, it is possible to see that, on average, DMUs should produce 9.9% more than they did in 2017 to become efficient. In addition, it is also possible to see that the worst DMU should have approximately twice as much, or 197.5% of what it produces.

These results show how current agricultural industry practice, on average, has become more sustainable, since most DMUs are close to technical efficiency, given that, in the first quartile, DMUs would only need to produce 1.5% more to achieve efficiency and, in the third quartile, this figure increases to 12.3%. Few municipalities would need to improve their production significantly to achieve technical efficiency, so only 25% of municipalities would need to increase production by more than 12.3%.

Figure 9 shows the results of CRS efficiency by municipality in 2017. The following geographical concentrations of the most efficient DMUs can be seen: (i) one group along the southern border in the state of Mato Grosso, where highly technical soybean and corn plantations are the main agricultural activities; (ii) one group in the state of Amapá (north of the map), where farming activities are lacking; and (iii) one group in the west of the state of Amazonas (west of the map), where farming activities are scarce. On the other hand, less efficient DMUs are located in the southeast of Pará state, where farmers focus on raising beef cattle, and in Rondônia state (southwest of the map), where agricultural activities are spread across several crops. These results provide insights on how to achieve eco-efficiency for agriculture in the region, as discussed later.

Table 2. Variables of efficient municipalities, inputs, and outputs.

		Input			Output
		Input		Desirable Input	Output	Undesirable Output
ID	Municipality	Production Hectares ${\mathbf{10}}^{\mathbf{3}}$	Employed People (${\mathbf{10}}^{\mathbf{3}}$)	Preserved Hectares ${\mathbf{10}}^{\mathbf{2}}$	Revenue BRL ${\mathbf{10}}^{\mathbf{3}}$	CO2 Emissions Tons ${\mathbf{10}}^{\mathbf{3}}$
2109601	Rosário	1	16.46	3	3	7
1300060	Amaturá	6	25.15	50	9	3
1600154	Pedra Branca do Amapari	33	20.43	289	16	6
1600279	Laranjal do Jari	30	11.99	259	14	13
5105101	Juara	1522	54.69	8461	226	2016
2101350	Bacurituba	1	7.69	3	0	22
5107248	Santa Carmem	234	9.30	1136	464	190
1301308	Codajás	70	38.78	610	22	9
1302108	Japurá	3	12.56	20	3	4
1302801	Maraã	4	26.26	15	17	5
1303205	Novo Airão	8	17.40	65	5	3
1303700	Santo Antônio do Içá	3	33.29	24	6	4
1304062	Tabatinga	3	87.79	12	13	2
1304203	Tefé	21	117.49	155	65	8
1500305	Afuá	134	121.28	1201	92	37
1503002	Faro	6	3.33	43	1	30
1503101	Gurupá	57	52.83	523	27	18
1507961	Terra Alta	2	3.45	9	2	6
2106755	Miranda do Norte	20	3.04	18	1	18
5106224	Nova Mutum	766	47.29	2.630	1957	233
5106307	Paranatinga	1300	46.75	5.268	827	263
5107156	Reserva do Cabaçal	105	6.08	657	0	34
5107925	Sorriso	828	49.37	2011	2812	432
5108907	Nova Maringá	612	14.74	3966	515	297
1200708	Xapuri	494	55.20	3758	19	435
1300409	Barcelos	8	27.47	52	23	4
1300839	Caapiranga	4	6.20	26	5	6
1303536	Presidente Figueiredo	197	76.92	1642	64	33
1500701	Anajás	163	29.00	1323	20	19
1504000	Limoeiro do Ajuru	37	141.21	317	51	13
2104909	Guimarães	1	24.50	2	2	7
2111201	São José de Ribamar	1	27.06	2	1	4
5101407	Aripuanã	1112	55.18	7085	33	1012
5102702	Canarana	790	26.23	4107	756	246
5107065	Querência	834	57.70	3813	1546	551
1300102	Anori	22	29.31	186	15	3
5105259	Lucas do Rio Verde	316	26.05	828	1111	55

shows that the variables relating to inputs and outputs between the municipalities have heterogeneous values, coinciding with the type of return to scale identified in the CRS model, where small and large producers can both be considered eco-efficient, even though they have different levels of resources and results. This is the case of Juara, which has proportionally higher values for inputs and outputs compared to the municipality of Rosário, but both are considered eco-efficient.

Table 3. Efficient municipalities.

ID		DEA	ID		DEA	ID		DEA
IBGE	Municipality	Index CRS Output	IBGE	Municipality	Index CRS Output	IBGE	Municipality	Index CRS Output
2109601	Rosário	1	1304203	Tefé	1	1300839	Caapiranga	1
1300060	Amaturá	1	1500305	Afuá	1	1303536	Presidente Figueiredo	1
1600154	Pedra Branca do Amapari	1	1503002	Faro	1	1500701	Anajás	1
1600279	Laranjal do Jari	1	1503101	Gurupá	1	1504000	Limoeiro do Ajuru	1
5105101	Juara	1	1507961	Terra Alta	1	2104909	Guimarães	1
2101350	Bacurituba	1	2106755	Miranda do Norte	1	2111201	São José de Ribamar	1
5107248	Santa Carmem	1	5106224	Nova Mutum	1	5101407	Aripuanã	1
1301308	Codajás	1	5106307	Paranatinga	1	5102702	Canarana	1
1302108	Japurá	1	5107156	Reserva do Cabaçal	1	5107065	Querência	1
1302801	Maraã	1	5107925	Sorriso	1	1300102	Anori	1
1303205	Novo Airão	1	5108907	Nova Maringá	1	5105259	Lucas do Rio Verde	1
1303700	Santo Antônio do Içá	1	1200708	Xapuri	1
1304062	Tabatinga	1	1300409	Barcelos	1

lists all the municipalities considered efficient, i.e., they have an eco-efficiency index equal to 1, totaling 37 eco-efficient municipalities. This represents 6.22% of the initial 595 municipalities, a low figure at first. Still, considering that most of the municipalities are close to the production frontier, it can be concluded that the DMUs considered efficient do have an optimum level of total efficiency.

Municipalities such as Novo Airão (AM) and Presidente Figueiredo (AM) have also been considered efficient in studies considering different variables [29], which demonstrates the excellent management of these municipalities. As DEA investigates direct relationships between the inputs and outputs of processes, the choice of variables has a strong impact on the DMUs that will be considered efficient, so there may be divergences, even if the analysis is carried out in the same region but considers different variables. For example, the DMUs of Marabá, Cáceres, Vila Bela da Santíssima Trindade, São Félix do Xingu, Novo Repartimento, Santa Maria das Barreiras, Porto Velho, Água Azul do Norte, and Cumaru do Norte had already been designated as inefficient, and Rosano-Peña et al. [29] pointed out that Santa L. do Paruá (MA), Garrafão do Norte (PA), Anajatuba (MA), Governador Nunes F. (MA), and were also Itapecuru Mirim (MA) were also inefficient DMUs.

The results of eco-efficiency also indicate that the global average was $0.920$, but on average, when compared between the states, the values tend to diverge. The state with the highest average was Amazonas, unlike the results reported in [29], where the state with the best performance was Amapá, with a score of $0.720$, in contrast to the results found in this study of $0.984$, followed by Acre ($0.937$), Roraima ($0.939$), Mato Grosso ($0.884$), Amazonas ($0.978$), Pará ($0.905$), Tocantins ($0.945$), Maranhão ($0.962$), and Rondônia ($0.835$). There was a $26.83\%$ difference between the scores, demonstrating that the detection of a greater number of outliers had a significant impact on the results.

4.5. Evolution of Eco-Efficiency Using the Malmquist Index

The Malmquist index was calculated for series from 2006 to 2017 (link: https://doi.org/10.6084/m9.figshare.25958827 (accessed on 24 June 2024)). Using the Malmquist function, the frontier shift, pairing effect, and Malmquist index are calculated for each municipality. To calculate the frontier effect for the year, a geometric mean of all the frontier shift indices for all the DMUs in the corresponding year is used. The first year is discarded, since the calculation is made by comparing efficiency in years T and $T-1$. To solve the problem, the data for 2006 is repeated, simulating 2005, where 2006 has a frontier displacement index equal to 1. Figure 10 shows the aggregated index (2006–2017).

The municipalities that improved most in the period are in the state of Mato Grosso (South of the map)m where highly technical soybean and corn plantations became the main activity. Municipalities where eco-efficiency worsened are in the southeast of Pará state, a region where the raising of beef cattle increased considerably, and in Rondônia state (west of Mato Grosso state), where agriculture with several crops increased. Although a great increase in the value of agricultural production was observed in these DMUs, it was accompanied by a large increase in emissions. Another important result from the Malmquist analysis is that DMUs that are very eco-efficient but have very small agricultural production achieved minimal progress in the period.

4.6. Optimizing Variables to Identify Potential Improvement

In absolute terms, as the chosen orientation is towards output, the possible impact on each variable ($Y_1$ and $Y_2$) is analyzed if all the municipalities converge towards efficiency. The values are described in

Table 4. Potential production gains.

Variable	Value
Revenue	3,195,002,000 (R$)
CO2 emission	25,849,560,000 (ton)

, where the CO₂ emission variable represents reduction or savings, generating ecological gains, while the production value represents the increase needed to turn inefficient DMUs into efficient ones. BRL is the Brazilian currency; USD 1.00 = BRL 4.90 in August 2023.

Due to the way data envelopment analysis is calculated, the efficiency index is applied equally to all variables, so if the index is 1.5, the municipality should produce 50% more of all products. Therefore, the ranking of the cities in relative values will remain static, regardless of the variable being analyzed. However, this ranking can change in nominal values. With this in mind,

Table 5. Worst municipalities analyzed by simulation.

IBGE Index	Municipality	DEA Index CRS Output	IBGE Index	Municipality	DEA Index CRS Output
1504208	Marabá	1.975094	5102504	Cáceres	1.626327
5105507	Vila Bela da Santíssima Trindade	1.883153	1507300	São Félix do Xingu	1.601048
1505064	Novo Repartimento	1.781707	1506583	Santa Maria das Barreiras	1.573696
1100205	Porto Velho	1.703062	1500347	Água Azul do Norte	1.537795
1502764	Cumaru do Norte	1.694544

lists the least efficient municipalities.

Although it does not have the worst efficiency index, the municipality with the most significant potential for gains in production value is São Félix do Araguai, totaling of BRL 182 million, and the municipality with the most potential for savings in CO₂ emissions is São Félix do Xingu, which could save approximately 1.7 billion tons, as can be seen in

Table 6. Municipalities with the greatest potential in terms of production value and CO₂ emission savings.

Variable	Municipality	Potential
Revenue	São Félix do Araguai	183,353,000.00 (BRL)
CO2 emissions	São Félix do Xingu	−1,683,912,000.00 (tons)

.

It is also possible to measure the impact of efficiency gains on input savings. However, it is important to remember that you shouldn’t look at outputs and inputs simultaneously, since the profits from these two perspectives are mutually exclusive. The results for savings in production hectares and people employed, as well as the potential for increasing the area preserved, can be found in

Table 7. Economic potential.

Variable	Value
Employed people	242,438 (un)
Production area	13,916,750 (ha)
Preserved area	6,248,745 (ha)

.

The municipality with the most significant potential for gain, São Félix do Xingu, is presented in

Table 8. São Félix do Xingu’ economic opportunity.

Variable	Quantity
Employed people	8455 (un)
Production area	924,292 (ha)
Preserved area	578,568 (ha)

, along with the values needed to improve each variable to achieve efficiency.

For the statistical modeling part, a linear regression study was carried out. The efficiency index of the municipalities was chosen as a dependent variable. The independent variables, or predictors, were the meteorological characteristics, volume of precipitation, average temperature, average humidity, and standard deviation of temperature over the months. The study sought to simulate the different seasons and capture the impact of this natural phenomenon and the various crops that can be planted depending on the season. It is also interesting to understand production and efficiency by state.

Table 9. Summary of states.

		Input			Output
		Input		Desirable Input	Output	Undesirable Output
State	Efficiency Index	Production Hectares 103	Employed People (103)	Preserved Hectares 102	Revenue BRL 103	CO2 Emission Tons 103
AC	1.069	4233	126,514	2544	442	5870
AM	1.023	3733	307,201	2150	1294	3102
AP	1.017	1501	30,732	871	226	822
MA	1.041	4652	293,574	862	865	7794
MT	1.140	38,164	283,069	15,349	26,914	45,209
PA	1.111	27,637	951,857	10,338	6036	42,360
RO	1.203	9220	270,812	2319	1582	28,552
RR	1.067	2636	67,070	1181	395	1792
TO	1.059	2867	51,596	669	211	4170

presents the values achieved for each of the variables analyzed in 2017, as well as the state’s total efficiency index, calculated as the geometric mean of the efficiencies of the municipalities in each state.

Still analyzing Table 9, it can be seen that the state with the highest efficiency is Amapá, with an index of 1.017, followed by Amazonas, which obtained a result of 1.02. The state with the worst recorded efficiency was Rondônia. Despite being the state with the third-highest financial value of production, the amount of CO₂ emitted and the number of hectares used for production were much higher than ideal. It is also interesting to understand production and efficiency by state. Table 9 presents the values achieved for each of the variables analyzed in 2017, as well as the states’ total efficiency indices, calculated as the geometric mean of the efficiencies of the municipalities in each state.

The ideal consumption quantities per state are presented in

Table 10. Ideal consumption by state.

State	Production Hectares ${10}^3$	Employed People (${10}^3$)	Preserved Hectares ${10}^2$
AC	3903	117,526	2738
AM	3521	297,925	2263
AP	1467	29,940	888
MA	4232	280,095	964
MT	32,929	241,189	17,856
PA	22,309	845,996	12,830
RO	7313	216,768	3007
RR	2402	62,525	1261
TO	2651	48,023	725

. If the states reach these values, production remains constant, with the values in the “Revenue” and “CO₂ Emissions” columns shown in Table 9.

Therefore, Table 10 represents the ideal level of consumption while maintaining the quantity produced. By comparing these tables, it is possible to calculate the number of inputs that could be saved or boosted in the case of the desirable input of preserved area. The state of Rondônia, for example, could use approximately two million hectares and fifty-four thousand fewer people to maintain its production level and still increase the preserved area by about seventy thousand hectares.

On the other hand, the states could increase production. In this scenario, the states’ consumption would maintain the same values in the “Production Hectares”, “Employed People”, and “Preserved Hectares” columns of Table 10.

The ideal production values, maintaining current consumption, can be found in

Table 11. Ideal production by state.

State	Revenue BRL ${10}^3$	CO2 Emissions Tons ${10}^3$
AC	470.2961	5292.594
AM	1334.37	2834.646
AP	231.9256	795.1486
MA	950.0968	7111.449
MT	28,795	37,305.74
PA	6792.038	32,472.07
RO	1923.489	22,531.48
RR	435.6717	1644.752
TO	226.3446	3834.731

. Rondônia, which is the state with the worst eco-efficiency index in the Amazon Biome, would need to increase the value of production by BRL 341 thousand and reduce CO₂ emissions by approximately6000 to reach the production frontier given by the DMUs in the northern region.

Table 12. Consumption reduction potential per quartile.

Quartile	Production Hectares ${10}^3$	Employed People (${10}^3$)	Preserved Hectares ${10}^2$
1	−26	−2374	14
2	−428	−15,480	200
3	−1584	−45,162	651
4	−11,879	−179,423	5384

shows an analysis of the number of inputs that could be saved. In the fourth quartile, since it is the quartile with the worst DMUs, there would have to be a reduction of eleven million hectares and one hundred and seventy-nine thousand people, as well as an increase of five hundred and eighty-four thousand hectares preserved to reach the level of efficiency, provided that the level of production remains constant.

As for

Table 13. Ideal production per quartile.

Quartile	Revenue BRL ${10}^3$	CO2 Emissions Tons ${10}^3$
1	20.00	−19.06
2	251.65	−388.72
3	627.22	−2305.30
4	2296.13	−23,136.49

, how much more could the municipalities produce to reach the maximum possible production for each quartile? Again, in quartile four, the value of production would have to increase by approximately BRL two million, CO₂ emissions would have ot be reduced by about twenty-three thousand tons, assuming that inputs remain constant, i.e., do not change.

By summarizing the efficiency quartiles, it is also possible to measure the results divided into efficiency groups. This summary can be found in

Table 14. Quartile summary.

		Input			Output
		Input		Desirable Input	Output	Undesirable Output
Quartil	Efficiency Index	Production Hectares ${\mathbf{10}}^{\mathbf{3}}$	Employed People (${\mathbf{10}}^{\mathbf{3}}$)	Preserved Hectares ${\mathbf{10}}^{\mathbf{2}}$	Revenue BRL ${\mathbf{10}}^{\mathbf{3}}$	CO2 Emissions Tons ${\mathbf{10}}^{\mathbf{3}}$
1	1.005	12,763	463,090	6704	13,174	8163
2	1.031	13,374	539,044	6133	8420	11,606
3	1.085	19,919	578,013	7546	7686	27,829
4	1.265	48,586	802,278	15,900	8684	92,074

. Between quartile 1 and quartiles 2 and 3, there is no significant difference between the determined eco-efficiency indices of 1.005, 1.031, and 1.085, respectively, at which point the hypothesis that, on average, there is no considerable distance between the eco-efficient and inefficient DMUs is, once again, confirmed. This can also be seen in the difference between the first quartile and the fourth quartile, where the eco-efficiency index values are 1.005 and 1.265, respectively, and there is no considerable discrepancy between these indices.

Various combinations of independent variables were investigated to find the best predictive model for the average annual efficiency index. The most assertive model with static significance, defined by the p-value test, used average dry bulb temperature, average dew-point temperature, average relative humidity, annual rainfall volume, and the standard deviation of temperature over the months.

The model calculated using these variables to predict the efficiency index achieved a p value of 0.0007 and an R2 of 0.9721. The figures presented by the model are encouraging. However, a closer look at the statistics reveals that this relationship may not be one of cause and effect. Efficiency has increased steadily over the years without showing much variation or volatility in this growth, which tends to be explained by advancing technology crop growth linked to the agricultural industry. At the same time, with respect to the analyzed climate phenomena, it can be said that the world is undergoing a gradual process of global warming. As such, the correlation may result from two phenomena showing the same trend.

4.7. Impact of Climate Variables on Eco-Efficiency Indices

It is essential to understand the influences of climate variables ($Z_1,Z_2$) on the eco-efficiency of municipalities, as they can represent gains or losses in efficiency over time. All regions of the planet are subject to climate variations caused by factors such as global warming and increases in periods of rain and drought, as well as natural phenomena such as El Niño, which, when they occur, can significantly reduced the productive capacity of areas dedicated to the agricultural sector, generating reductions in essential inputs for the world economy. Therefore, it is understood that correlations between meteorological characteristics and productive efficiency can enable the development of alternative technologies to better prepare producers to face the above phenomena. However, it was not possible to prove a direct correlation between the variables. Even if the numbers were good and passed statistical tests, it was impossible to rule out the hypothesis that made them a coincidence. Although this hypothesis cannot be ruled out, there are studies that have been able to prove this relationship between eco-efficiency indices and climate factors, providing vital information for the environmental decision-making process, such as the work of Rosano-Peña et al, who concluded that the changes caused by the decrease in rainfall and the increase in temperature would have a positive impact on the mountainous region of the TMCF in Mexico, specifically in an area located in the Sierra Madre Oriental between 2016 and 2017.

Finally, we emphasize challenges related to the availability of data to obtain longer periods to determine relevant inputs and outputs, as well as the lack of open access to data for other non-agricultural contexts, such as industry and business. The research fulfilled its guidelines and achieved results relevant to its data structure, providing indicators of social, environmental, and economic development. According to [45], this balance between the search for economic and social development, aligned with the appropriate use of natural resources, arouses interest in studies focused on the area to promote a set of actions that have social and environmental impacts due to the updates that have occurred in recent years in agribusiness, which have led the country in the search for sustainable development.

4.8. Implications

The contributions of this study regarding theoretical implications are represented by the use of the DEA super-efficiency, bootstrap, and Malmquist Index methods to measure the efficiency of the Amazon Biome in the period from 2006 to 2017. The super-efficiency model was used to remove outliers. Many studies do not consider the removal of outliers when calculating the efficiency of models that use DEA [21,24,25,36,46]. Failing to address outliers can lead to biased results, as the DEA model is highly sensitive to this type of variable. An approach based on bootstrap computational models was used to calculate the efficiencies of municipalities in 2017, which also makes the results more robust. This is because the DEA model does not naturally make use of parametric models, resulting in the resampling provided by bootstrapping to create confidence intervals. It uses the Malmquist model to provide a systematic analysis of the development of agricultural eco-efficiency in the Amazon Biome.

The study’s practical implications show that measuring efficiency in the agricultural sector of municipalities in the Amazon Biome in Brazil can help in proposing public policies and strategic planning for decision makers such as farmers, business people, governors, mayors, and the federal government. This can contribute to greater economic and sustainable development in the region, improve residents’ quality of life, and respect the biodiversity and environmental wealth of this important area. This study also identifies potential improvements for inefficient municipalities and highlights which municipalities are efficient, providing models that can be used to improve the management of these areas.

5. Conclusions

The results point to an essential interpretation that most municipalities are already operating at a satisfactory level of efficiency, given the technological level available; around 7.17% of the municipalities are already working at an eco-efficient scale.

The production frontier of the municipalities results in a technological behavior of constant returns to scale (CRS), which is a relevant result for understanding factors that involve inequality between producers in municipalities because, given the results of the model, small, medium, and large producers can all be eco-efficient (total efficiency), given the CRS frontier within the Amazon Biome. Hence, these differences occur regardless of the production level, so there will be inefficient and efficient small, medium, and large producers.

We also recommend redoing the DEA modeling with different groups of municipalities, separating them by state or region rather than comparing all the municipalities with each other. In addition, comparing the results with those obtained in other areas of the country and even other countries makes sense. Adding input or output variables to the survey would also enrich the analysis. This would allow a larger volume of data and different situations to be tested.