Environmental preservation costs and eco-efficiency in Amazonian agriculture: Application of hyperbolic distance functions

Accepted Manuscript Environmental preservation costs and eco-efficiency in Amazonian agriculture: Application of hyperbolic distance functions

Carlos Rosano Peña, André Luiz Marques Serrano, Paulo Augusto Pettenuzzo de Britto, Víthor Rosa Franco, Patrícia Guarnieri, Karim Marini Thomé PII:

S0959-6526(18)31883-3

DOI:

10.1016/j.jclepro.2018.06.227

Reference:

JCLP 13373

To appear in:

Journal of Cleaner Production

Received Date:

29 March 2017

Accepted Date:

20 June 2018

Please cite this article as: Carlos Rosano Peña, André Luiz Marques Serrano, Paulo Augusto Pettenuzzo de Britto, Víthor Rosa Franco, Patrícia Guarnieri, Karim Marini Thomé, Environmental preservation costs and eco-efficiency in Amazonian agriculture: Application of hyperbolic distance functions, Journal of Cleaner Production (2018), doi: 10.1016/j.jclepro.2018.06.227

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Wordcount: 8,231 words ENVIRONMENTAL PRESERVATION COSTS AND ECO-EFFICIENCY IN AMAZONIAN AGRICULTURE: APPLICATION OF HYPERBOLIC DISTANCE FUNCTIONS Carlos Rosano Peñaa a

Professor at Universidade de Brasília, Faculdade de Administração, Contabilidade, Economia e Gestão de Políticas Públicas, Ala Norte, Campus Universitário Darcy Ribeiro, Asa Norte, 70910900 - Brasília, DF - Brasil André Luiz Marques Serranoa Paulo Augusto Pettenuzzo de Brittoa Víthor Rosa Francob (corresponding author)

b

PhD Student at Universidade de Brasília, Instituto de Psicologia, Instituto Central de Ciências, Ala Sul, Campus Universitário Darcy Ribeiro, Asa Norte, 70910900 Brasília, DF – Brasil [email protected] Patrícia Guarnieria Karim Marini Thoméc c

Professor at Universidade de Brasília, Faculdade de Agronomia e Medicina

Veterinária, Instituto Central de Ciências, Ala Central, Campus Universitário Darcy Ribeiro, Asa Norte, 70910900 - Brasília, DF - Brasil

1

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Abstract This paper studied agricultural eco-efficiency in the Amazon, using hyperbolic distance functions with a stochastic frontier based on the classical variables of the multi-product production function and internalization of two externalities (one positive and one negative). The study allowed the contrast among various specifications of production functions and estimation of the opportunity costs of externalities, marginal rates of substitution and transformation, as well as an index of environmental sustainability and its determinants. The main results of the study indicate that the opportunity cost of preserved areas is between US$ 82.39 and US$ 170.37 per ha/year, and it is possible to increase the desired outputs by 19.5%, simultaneously reducing the degraded areas and inputs by 16.36%, and this only referring to the best practices in the region.

Keywords:

eco-efficiency,

parametric

agriculture, opportunity cost of externality.

hyperbolic

distance

function,

Amazon

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1. Introduction One of the most important events in the last 30 years in Brazil, according to Correa and Schmidt (2014), was the "agricultural revolution", which transformed the country into the world's second largest exporter of food. This happened as a response to the rapid process of industrialization, urbanization and the growth of national and global demand for food products and raw materials. The transformation of subsistence agriculture and monoculture into modern diversified agribusiness has been the result of an improvement in extensive and intensive production methods, strongly fostered by the Brazilian State. The first method consisted in agricultural frontier expansion, especially in Midwestern areas and the Amazon. The second, in turn, was that intensive methods were substantiated with subsidized credit, agricultural extension and public research institutions that allowed the incorporation of the new "green revolution" technologies and, hence, productivity growth. However, these policies favored the economic objective over the proper management of the environment, not considering the potential negative impacts of the modernization model adopted. The persistent threat to key ecosystems is illustrated by data on the Amazon deforestation and on the disorganized expansion of agriculture in this biome (Araujo et al, 2009; Börner et al, 2007). According to data from the Amazon Deforestation Calculation Program (INPE, 2015), it has been estimated that deforestation in the Amazon was 4,848 km2 in 2014, and, since 1988, the accumulated figure is 407,511 km2 (INPE, 2015). This has become a global concern due to evidence of biodiversity loss, pollution and depletion of water resources, soil degradation and, consequently, the growth of greenhouse gas emissions and risks of global climate change (Steinfeld et al, 2006).

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This paper aims to contribute to these issues, showing the possibility of producing more with less environmental impact and less use of resources in the agriculture of the municipalities comprising the Brazilian Amazon biome. With the use of the approaches of hyperbolic functions combined with the Stochastic Frontier Analysis method, elasticity coefficients of marginal rates of substitution and transformation and the shadow prices are estimated. Then, the estimates are used to define useful indicators for the formulation and evaluation of sustainability policies, such as parameters for prizes to reward generators of positive environmental externalities. The application of this method also aims to examine determinants of eco-efficiency and calculate an environmental sustainability index, in compliance with the Pareto optimality, paying attention simultaneously to both the economic and the environmental objectives, based on the best practices in the region. In order to achieve these goals, the paper is divided into five sections, including this introduction. The second section provides a brief theoretical framework. Section three presents the method that summarizes the main concepts of the procedures used to estimate eco-efficiency. Section four describes the variables used. In the fifth section, results are analyzed, particularly those that contribute to the effectiveness of environmental practices, and presents aim to formulate new strategies for sustainable progress consistent with the Brazilian agriculture competitiveness. In the last section, the main conclusions are summarized.

2. Theoretical framework Currently, public strategies have begun to pay attention to environmental sustainability issues of the agricultural sector in the Amazon biome to ensure regional

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economic development without compromising the needs of future generations (Sierra and Russman, 2006 and Börner et al, 2010). This characterizes the challenge of developing policies for sustainable agriculture in the region, which has required that researchers present feasible answers to the following questions: Are the economic efficiency goals of agribusiness compatible with the balance and limitations of natural resources? What are the costs of degradation and environmental protection in the sector? How can the agriculture be eco-efficient? Numerous theoretical and empirical studies have looked into problems of efficiency and evaluation of environmental impacts (Tyteca, 1996; Bravo-Ureta et al., 2007; Darku et al., 2013; Lampe et al, 2015; Caiado et al., 2017). Indeed, due to the complexity of the issue, various, non-hierarchized, methods have incorporated the environmental impacts in the efficiency analysis. One of these methods follows the theory of production, the distance functions of Shephard (1953) and the concept of ecoefficiency. This methodology, developed by Färe et al. (1989), allows the estimation of eco-efficiency indices and the economic value of externalities, without using data about market prices. For this, both non-parametric and parametric methods can be used, each presenting singular advantages and disadvantages. One of the most prominent non-parametric methods for estimating efficiency and eco-efficiency is Data Envelopment Analysis (DEA), which can be complemented for longitudinal analysis with the Malmquist Productivity Index (MPI; Gomes, 2008). This method can be used to easily model multi-product technologies and the internalization of externalities associated with the production process. Representing the technology by means of non-parametric distance functions, this method does not need to previously define a stochastic production function nor a specific type of distribution (behavior) of

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the unknown border deviations, being free of the possible flaws resulting from these definitions. On the other hand, this method, for being deterministic, ignores the random perturbations of the productivity process (Simar & Wilson, 2004). This method was used by several authors and has been presenting interesting results. It is possible to cite the work of Ball et al. (1998), which assessed the dynamics of American agriculture incorporating environmental impact with the Malmquist Productivity Index; and the research by Picazo-Tadeo et al. (2011), which evaluated the eco-efficiency of agriculture in Spanish regions using DEA with directional distance functions. Among works employing non-parametric methods in Brazilian agriculture, it is worth mentioning Padrão et al.

(2012), who compared the technical and

environmental efficiency of agricultural production in the Amazon and estimated the opportunity cost of the Forest Code using the DEA model; as well as Rosano-Peña et al. (2014) evaluated the eco-efficiency and sustainability of Brazilian state agriculture using directional distance functions with DEA; and finally Campos et al. (2014), who studied the economic and environmental performance of dairy farmers in Minas Gerais using the DEA model. The parametric method use for also estimating efficiency is the Stochastic Frontier Analysis (SFA) model (Lampe & Hilgers, 2015). This model brought an advance when compared to the previous models of deterministic frontiers, given that it makes it possible to rule out stochastic processes that have an impact at the efficiency frontier, hence, SFA. To use the model, first it is necessary to choose a parametric distance function that expresses the functional relationship between the products (desired and undesired) and inputs, to represent the production possibility frontier (PPF). Next, SFA decomposes the deviation from the frontier into its stochastic noise

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and technical inefficiency components. This was the steps followed by Coelli and Perlman (1999), Cuesta et al (2009), Cuesta and Zofio (2005), Färe et al (1993), Lovell et al (1994), and others. Several papers analyzing eco-efficiency in the agricultural sector with parametric methods can be found, begin worth the mention Reinhard, Lovell and Thijssen (1999), who introduced an environmental impact residue as input to measure the environmental efficiency of a set of Dutch dairy farms; Areal et al. (2012), who estimated the environmental efficiency of British dairy farms, including environmental outputs in the analysis; and O'Donnell (2012), who complemented this technique with Bayesian methods to analyze the dynamics of American agricultural productivity. In addition, there are works that estimate parametric distance functions with mathematical (deterministic) programming techniques, such as the work of Färe et al. (2006) estimating the costs of pollutant opportunities and eco-efficiency indices of agriculture in the United States. Nevertheless, the use of these techniques to study ecoefficiency and shadow price of externalities in Brazilian agriculture is still incipient.

3. Method The definition of eco-efficiency presupposes knowledge of the production technology sector studied (Basset-Mens et al, 2009). Nevertheless, as the technology results from the continuous incorporation of scientific innovations and individual management experiences into production processes, its status at any given moment is unknown (Lauwers, 2009). Being unknown, it is common to describe it using the set of inputs, which, after being combined and processed, produce a vector of new goods and services (outputs), in a given period (Lauwers, 2009).

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Therefore, technology, which represents the set of possible combination of inputs and outputs, is represented by the production possibilities set T= {(x, y, b): x can produce y, b ∧ x≥ 0, y≥ 0, b ≥ 0} Where:

x   n = the set of inputs used; y   p and b   q = the set of desirable

output and undesirable outputs respectively, for each Decision Making Unit (DMU) i observed (Färe et al, 1989). To attain applicability, the axioms applied to T determine a non-negative multidimensional space Rp+q+n formed by the technological frontier and the coordinate axes (Färe et al, 1985), i.e., T= {(x,b,y): y ≤ 𝑓(x, b), x, b, y ≥ 0} Here f(x,b) represents the maximum desirable outputs and the sign ≤ warns about the possibility of strong disposability associated to the technological possibility of producing a smaller number of y, with the same inputs and polluting by-products, or requiring a greater amount of x and b for a certain level of production. Hence, there arises a definition of eco-efficiency as the ability of a company or economy (DMU) to produce a given amount of a product with the least set of inputs and simultaneously lower environmental impact. The optimal eco-efficiency associated with a set of inputs is reached at the T frontier, in the Pareto optimal, when there is no other production process or combination of processes that can produce the same level of output, using smaller amounts of inputs with lower environmental impact. One of the most promising techniques to model T and estimate the multidimensional efficiency measurements is the Shephard (1953) distance function. It arises as an alternative to classical methods of the index numbers and the production functions, and its resulting functions of cost, revenue and profit. The distance function

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is reciprocal to the Farrell (1957) technical efficiency, and eliminates the use of prices (shadow and/or market) of the variables involved, as well as the aggregation of products into a single value, through the construction of a monetary indicator. This introduces the advantage of describing the multiple output-input technology and discards the efficient behavior assumption of all analyzed units. Distance functions can be basically described in three equivalent ways: oriented to products, oriented to inputs, and oriented concurrently to inputs and outputs. The first two ways have been widely reported in the literature, but do not include the undesired and desired outputs asymmetrically. These ways only model the undesired outputs as input to be minimized, or as output variables with inverted or negative values to be maximized using the oriented radial measurements of Farrell (Zhou et al, 2008). The third, called hyperbolic, finds the optimal expansion of production and simultaneous reduction of inputs and undesired outputs. The hyperbolic distance function is so called due to the hyperbolic way in which it should approach the efficient frontier. Formally, it is written as: Dh(x, y, b)= Min {ρ: (xρ, y/ρ, bρ) Є T} Where: 0 < ρ ≤ 1 is the expansion of the desired output vector and the reduction of inputs and undesired outputs at the same time, to become part of the T efficient subset. Thus, if the assessed unit is eco-efficient and is on the environmental technology frontier ρ= 1 and Dh(x, y, b)= 1; otherwise (ρ <1) will be eco-inefficient, but can improve its performance using ρ. By way of illustration, if ρ is equal 0.8, then the desired output can be increased by 25% (1/0.8= 1.25), whereas the inputs and undesired outputs may be reduced by 20% (0.2= 1 to 0.8) simultaneously.

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This function has another property. It is non-increasing in inputs and undesired outputs and non-decreasing in outputs and it is homogeneous of degree -1, 1, -1, 1. In other words, if the set of inputs and undesired outputs is reduced by a given proportion and the set of outputs is increased by the same proportion, then the function increases by that same proportion. The distance hyperbolic functions used in this paper employed SFA, proposed independently by Aigner et al (1977) and Meeusen and Broeck (1977), to represent the T frontier. As mentioned previously, this parametric method starts by choosing an ideal functional form that, according to Coelli et al. (2005), should be: i) flexible, ii) linear in the parameters, iii) bearer of the main desired characteristics of the production technology, and iv) easy to compute. Seeking to meet these recommendations, most of the recent papers use logarithmic transcendental functions - translog, introduced by Christensen et al. (1971). Having selected the translog functional form, the hyperbolic distance function model follows Cuesta et al. (2009), and is expressed for the assumption of multiples output and inputs as an additive combination of log-transformed inputs and outputs. By Young's theorem, the second-order crusader parameters are estimated, assuming that 𝛼𝑝𝑠 = 𝛼𝑠𝑝

; 𝛽𝑛𝑙 = 𝛽𝑙𝑛 and 𝜏𝑞𝑟 = 𝜏𝑟𝑞.

The second-order parameters

𝜗, 𝜑

and 𝜔 designate the relation of non-separability

between each input-output pair, and the null test of their values can be used to evaluate the separability. The calculation of this function requires the use of restrictions based on Euler's theorem and linear homogeneity. The first, equation (2), is formed by the elasticity of the distance function, based on the change of each variable, equivalent to

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the partial derivatives of each, so that equation (2) may take the logarithmic specification. 𝑃

∂ln (𝐷ℎ𝑖)

𝑁

∂ln (𝐷ℎ𝑖)

𝑄

(

∂ln (𝐷ℎ𝑖)

∑ ∂ln (𝑦 ) ∑ ∂ln (𝑥 ) ∑ ∂ln (𝑏 ) = 1 𝑝

𝑝=1

∂ln (𝐷ℎ𝑖) ∂ln (𝑦𝑝)

∂ln (𝐷ℎ𝑖) ∂ln (𝑏𝑞)

∂ln (𝐷ℎ𝑖) ∂ln (𝑥𝑛)

‒

= 𝜏𝑞 +

= 𝛽𝑛 +

∑

𝑛

𝑛=1

𝑃

= 𝛼𝑝 +

‒

𝑄

𝛼𝑝𝑠ln (𝑦𝑠) +

∑

𝑞

𝑞=1

𝑵

∑𝜗

𝜑𝑝𝑞ln (𝑏𝑞) +

𝑠=1

𝑞=1

𝑛=1

𝑄

𝑃

𝑵

∑𝜏

𝑞𝑟ln

(𝑏𝑟) +

∑𝜑

𝑝𝑞ln

𝑛=1

𝑁

𝑃

𝑸

𝑙

𝑙=1

𝑛𝑞ln

𝑞𝑛ln

𝑝=1

(

∀ (𝑝 = 1, 2, ..𝑃)

(𝑥𝑛)

(

∀ (𝑞 = 1, 2, ..𝑄)

(3)

∑𝜔

(𝑦𝑝) +

(𝑥𝑛)

(2) 𝑞𝑛ln

𝑝=1

∑𝛽 ln (𝑥 ) + ∑𝜗

𝑝𝑛ln

∑𝜔

(𝑦𝑝) +

𝑟=1

𝑛𝑙

(1)

(𝑏𝑞)

𝑞=1

(

∀ (𝑛 = 1, 2, ..𝑁)

(4)

The elasticity derived from the translog distance function can be seen as not constant (such as the Cobb-Douglas), but, depending on the complementarity or substitutability between factors, expressed by the sign of the crossed parameters of the second order and on the existence of increasing or decreasing returns to the factors considered, expressed by the sign of the square parameters of the second order. Besides that, for the linear homogeneity, it is necessary that (1) satisfies the following restrictions: 𝑃

𝑄

𝑁

(

∑𝛼 ‒ ∑𝜏 ‒ ∑𝛽 = 1; 𝑝

𝑝=1

𝑃

𝑞

𝑟=1

𝑃

𝑝𝑠

𝑝𝑞

𝑝=1

𝑵

∑

𝑛=1

(5)

∑

𝑛𝑝 = 0 ,∀

(

𝑝 = 1, 2, .., 𝑃

𝑝=1

𝑵

𝜗𝑝𝑛 ‒

𝑙=1

𝑃

∑𝛼 ‒ ∑ 𝜑 ‒ ∑ 𝜗 𝑠=1

𝑛

(6)

𝑁

𝜔𝑞𝑛 ‒

𝑛=1

∑𝛽

𝑛𝑙 = 0,

𝑙=1

(

∀ 𝑛 = 1, 2, ..,𝑁

(7)

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𝑄

𝑄

𝑸

∑ 𝜑 ‒ ∑𝜏 ‒ ∑ 𝜔 𝑝𝑞

𝑞=1

12

𝑞𝑛 =

𝑞𝑟

𝑟=1

(

0, ∀ 𝑞 = 1,2,.., 𝑄

𝑞=1

(8)

Due all the restrictions, the distance function for the translog model used in the present study can be simply represented as: ∗

∗

∗

𝑙𝑛(𝑦𝑗𝑖) = 𝑇𝐿(𝑦 𝑖 , 𝑏 𝑖 , 𝑥 𝑖 , 𝛼, 𝜏, 𝛽,𝜗, 𝜑,𝜔) + 𝑣𝑖 ‒ 𝑢𝑖

(9)

In this new form, the parametric distance hyperbolic function is made up of two components, one systematic (ui) and the other random (vi). The first is the eco-efficient frontier and the second, the random error, which, in turn, can be justified as follows. The random component, vi, represents factors related to statistical noise, including uncertainties, favorable and unfavorable events beyond the control of the DMU, such as weather, pests, topography, strikes and luck, in addition to measurement errors and the implications of the combination of variables not specified in the production function, which alone are irrelevant. These random errors are assumed independent and identically distributed (iid) following a normal distribution with a zero mean and 2

constant variance 𝜎𝑣. The systematic component, ui, represents factors controlled by managers and, therefore, represents the individual inefficiency of the DMUs. For example, decisions taken by the company that may result in a lower level of output relative to the potential expressed by the frontier. These are independent from vi and represent non-negative random variable, which can follow a normal distribution truncated at zero (Coelli et al, 1998), half-normal (Aigner et al, 1977), exponential (Meusen and Broeck, 1977), gamma (Greene, 1997), or others. According to Coelli et al (1998), there is not a priori justification for the selection of any of these forms of distribution.

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As in other papers, in the present research another model was used, the method of Battese and Coelli (1995), assuming for ui a normal truncated distribution, with zero as the lower limit, mean zi𝛿 and variance

2

𝜎𝑢.

Thus, ui= zi 𝛿 + 𝑤𝑖, where zi is a vector of

explanatory variables associated with technical inefficiency, 𝛿 are the parameters to be estimated and wi is the random error of ui, following a truncated normal distribution with a zero mean and variance

2

𝜎𝑢 ,

such that wi

≥

- zi 𝛿. To simultaneously calculate the

parameters of the stochastic frontier and the effects of inefficiency, Battese and Coelli (1995) proposed the method of maximum likelihood. This is due to the fact that the distribution of the composite error (e=u+v) should be negatively asymmetric with a non-zero average, which prevents the use of traditional regression models (Ordinary Least Squares) in the estimation of the stochastic frontier. The deduction of the maximum likelihood function is presented in Battese and Coelli (1993), and its respective parameters, as well as the efficiency indexes, can be calculated using an iterative optimization procedure programmed in the Frontier 4.1 software (Coelli, 1996). The maximum likelihood function is expressed in terms of the variance parameters:

2

2

2

𝜎 = 𝜎𝑣 + 𝜎𝑢

and 1. When 𝛾 is zero,

𝜎𝑢 = 0

and

and/or

2

2

𝛾 = 𝜎𝑢 𝜎 𝜎𝑣

, where the parameter

𝛾

must lie between 0

tends to infinity, all border deviations are known 2

to be due to statistical noise v and e~𝑁(0,𝜎 ). On the other hand, when

𝛾=1,

inefficiency

is the main source of the deviation from the border. In turn, the inefficiency of each DMU is estimated by:

𝐸𝑇𝑖=

𝑦𝑗𝑖 𝐸

𝑦𝑗𝑖

∗

=

∗

∗

exp[𝑇𝐿(𝑦 𝑖 , 𝑏 𝑖 , 𝑥 𝑖 , 𝛼, 𝜏, 𝛽,𝜗, 𝜑,𝜔) + 𝑣𝑖 ‒ 𝑢𝑖] ∗

∗

∗

exp[𝑇𝐿(𝑦 𝑖 , 𝑏 𝑖 , 𝑥 𝑖 , 𝛼, 𝜏, 𝛽,𝜗, 𝜑,𝜔) + 𝑣𝑖] 𝛿 ‒ 𝑊𝑖)=Dhi

= exp(-ui)= exp(-zi

(10)

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Therefore, it is worth noting that, after calculating the parameters of the translog hyperbolic distance function with the maximum likelihood method, it is possible to compute the partial elasticity of each of the desired outputs for any input. These specific elasticities for each DMU are obtained using the following formulations: ∂ln 𝐷0

∂𝑦𝑝

∂ln 𝑥𝑛

𝑦𝑝

∂ln 𝐷0 ∂ln 𝑦𝑝

=

∂𝑥𝑛

=

∗

∗

∗

∗

∗

∗

∗

∗

∗

∗

∗

∗

∗

∗

𝛽 𝑛 + 𝛽𝑛𝑛ln 𝑥𝑛 + 𝛽12ln 𝑥2 + 𝜗𝑛1ln 𝑦1 + 𝜗𝑛2ln 𝑦2 + 𝜔1𝑛ln 𝑏1 + 𝜔2𝑛ln 𝑏2 𝛼 𝑝 + 𝛼𝑝𝑝ln 𝑦𝑝 + 𝛼12ln 𝑦2 + 𝜗1𝑝ln 𝑥1 + 𝜗2𝑝ln 𝑥2 + 𝜑1𝑝ln 𝑏1 + 𝜑1𝑝ln 𝑏2

(11)

𝑥𝑛

However, there is another procedure to facilitate these calculations: the transformation of data so as to allow direct interpretation of the of the first-order translog parameters (𝛼𝑝, 𝜏𝑞, 𝛽𝑛) as the elasticities evaluated at the sample means. This procedure is simply the normalization of the original data by dividing each input and each output by its geometric mean. The use of this procedure has an advantage the possibility of estimating five parameters (Färe et al, 1993). The first is the scale elasticity, which, in conditions of constant returns to scale, should be equal to 0.5, and different of 0.5, otherwise. The second is the partial elasticity of each desired output with respect to any input, which shows how an output is marginally influenced by changes in an input. The third is the marginal rate of technical substitution, which expresses the slope of the multidimensional isoquant in a certain direction. The fourth is the marginal rate of transformation, which expresses how many units of a product would not be manufactured with the same inputs, with an additional amount of another product. Finally, the fifth is the opportunity cost of production yp relative to an undesired output bq, which allows estimation of the relationship between the shadow prices of bq and yp. Finally, the normalization of all inputs and outputs—with each variable being divided by its geometric mean—facilitates the understanding of the parameters of the

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translog distance functions. With this normalization, the first-order coefficients acquire the significance of the elasticity of the distance function in relation to the changes of each of the variables at the point of the data averages. Second, the linear homogeneity constraints, expressed in equations (5) to (8), were used to calculate the value of the first-order parameter of the product used in the normalization (y1) of the distance function (9). In this research, three models of hyperbolic distance functions were statistically evaluated to check which one showed the best fit to the data. The models were: 1. Translog hyperbolic function with the effects of inefficiency and without the separability restriction:

1 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ 2 ∗ ∗ ‒ ln 𝑦1i = 𝛼0 + 𝛼 ln 𝑦 2i + 𝛼3𝑙𝑛 𝑦 3i + 𝛼4𝑙𝑛 𝑦 4i + 𝜏1ln 𝑏 1i + 𝛽1ln 𝑥 1i + 𝛽2ln 𝑥 2i + 𝛽3ln 𝑥 3i + 𝛽4ln 𝑥 4i + 𝛼22(ln 𝑦 2i ) + 𝛼23 ln 𝑦 2i ln 𝑦 3i + 2 2 ( 1 1 ∗ 2 ∗ ∗ ∗ ∗ ∗ ∗ ∗ 2 ∗ ∗ ∗ ∗ 𝛽 [ln 𝑥 1i ] + 𝛽12ln 𝑥 1i ln 𝑥 2i + 𝛽13ln 𝑥 1i ln 𝑥 3i + 𝛽14ln 𝑥 1i ln 𝑥 4i + 𝛽22[ln 𝑥 2i ] + 𝛽23ln 𝑥 2i ln 𝑥 3i + 𝛽24ln 𝑥 2i ln 𝑥 4i 2 11 2 + 1 1 ∗ 2 ∗ ∗ ∗ 2 ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ 𝛽 [ln 𝑥 3i ] + 𝛽34ln 𝑥 3i ln 𝑥 4i + 𝛽44[ln 𝑥 4i ] + 𝜗21ln 𝑦 2i ln 𝑥 1i + 𝜗22ln 𝑦 2i ln 𝑥 2i + 𝜗23ln 𝑦 2i ln 𝑥 3i + 𝜗24ln 𝑦 2i ln 𝑥 4i + 𝜗31ln 𝑦 3i ln 𝑥 1i + 𝜗32ln 𝑦 2 33 2 (12)

( )

( )

( )

9

𝑢𝑖 =

∑𝛿 𝐷

(

𝑧 𝑧𝑖 + 𝛿10𝐹1𝑖 + 𝛿11𝐹2𝑖 + 𝛿12𝐹3𝑖 + 𝛿13𝐹4𝑖 + 𝛿14𝐹5𝑖 + 𝛿15𝐹6𝑖 + 𝑤𝑖𝑖

𝑧=1

where the dummies were: D1 – Rondônia, D2 – Acre, D3 – Amazonas, D4 – Roraima, D5 Pará, D6 - Amapá, D7 - Tocantins, D8 - Maranhão, and D9 - Mato Grosso. 2. Translog hyperbolic function with the effects of inefficiency and separability between inputs and outputs (STLE). This model is equivalent to TLE, although it demands that the input-output parameters (𝜗, 𝜑 e 𝜔) be null. 3. Cobb-Douglas hyperbolic function with the effects of inefficiency (CDE). This model requires the invalidity of all second-order parameters, expressed as:

( ∗)

( ∗)

( ∗)

∗

∗

∗

∗

∗

‒ ln (𝑦1𝑖) = 𝛼0 + 𝛼 ln 𝑦 2i + 𝛼3𝑙𝑛 𝑦 3i + 𝛼4𝑙𝑛 𝑦 4i + 𝜏1ln 𝑏 1i + 𝛽1ln 𝑥 1i + 𝛽2ln 𝑥 2i + 𝛽3ln 𝑥 3i + 𝛽4ln 𝑥 4i + 𝑣𝑖 ‒ 𝑢𝑖 2

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(13) For quantifying the differences between the models, the generalized likelihood ratio test (LR Test) was used. The LR Test uses the calculation of the logarithm of the likelihood function at the highest point (LLF) of two models, with and without restriction, i.e. LLF (H0) and LLF (H1), where H0 and H1 are the null and alternative hypotheses, respectively. Therefore, if the restriction (H0) is true, the values of LLF(H0) and LLF(H1) should be close. This approach is defined by: LR=-2 [LLF(H0)- LLF(H1)], that is asymptotically distributed as chi-squared

2

𝜒𝑔,

with g degrees of freedom,

equivalent to the number of restrictions imposed on the model (Kode & Palm, 1986). 3.1 Object and variables of the research The production processes evaluated on this research are the farming and ranching activities in the 528 municipalities that make up the Amazon biome. This biome is the largest in Brazil (see Figures 1 and 2) and is characterized by a great biodiversity, integrated by the Amazon Rainforest and the catchment area of the Amazon River. According to the website of the Brazilian Forest Institute (2017), this biome covers 4.1 million km2, equivalent to 49.9% of Brazilian territory. With 21 million inhabitants, it occupies the whole states of Acre, Amapá, Amazonas, Pará, Rondônia and significant part of Roraima (99%), Mato Grosso (54%), Maranhão (34%) and Tocantins (9%).

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Figure 1. Brazilian biomes

17

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Figure 2. States and municipalities of the Amazon Biome

To assess the agricultural eco-efficiency of the 528 municipalities that make up the Amazon biome, we adopted a set of variables available in the 2006 Agricultural Census (IBGE, 2010): the classic inputs and outputs of the sector, plus a positive externality and one negative. As in most cases (Gomes, 2008 and Kazim, 2015), the classic inputs used in the modeling were: x1i - Labor used in properties located in municipality i, in terms of numbers of people;

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x2i - Capital estimated by depreciation, 10% of the value of the fixed assets of properties located in municipality i, measured in US$ 470.00 (at prices of 2006); x3i - Total area used for cultivation and pasture in the rural establishments in municipality i, measured in hectares; x4i – Other running costs (fertilizers, electricity, fuel, animal feed, etc.) incurred by the rural establishments of municipality i, measured in US$ 470.00; Whereas the classical outputs involve the following: y1i - Desired output - Total Revenue from agricultural product sales of the rural establishments in municipality i, in US$ 470.00; y2i - Desired output - Total Revenue from sales of livestock products and derivatives of the rural establishments in municipality i, in US$ 470.00; y3i - Desired product - Other revenues earned by the rural establishments in municipality i, in US$ 470.00; y4i - Environmentally desired output - natural forest areas and forests preserved in the rural establishments of municipality i, in hectares. This includes the Permanent Preservation Areas and Legal Reserve that the properties must conserve and can only be used with the aim of preservation, that is, without any commercial purpose. According to the New Brazilian Forest Code, Law No. 12,651/12, these areas situated in the Amazon biome must occupy at least 80% of the property (Brasil, 2012). b1 - Environmentally undesired output - areas of degraded land on the property, in hectares (does not consider abandoned land, whether degraded or not).

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The output definitions above, in line with the preceding discussion, include two variables that allow the capture of the positive (y4) and negative (b1) effects of the externalities. Finally, the model chosen requires the explanatory variables of eco-inefficiency. Fifteen were selected. The first nine determinants must capture the fixed effects of the nine states. Despite the homogeneity of the agricultural production processes, it is known that there are differences among the states studied: different logistic supports, the scale of local markets, oversight levels and support from public authorities, among others, which may elucidate the different levels of eco-efficiency. To control these effects, dummies (𝐷𝑧) were included, wherein each variable takes the value of 1 in the municipality of the corresponding state, and zero otherwise. In addition, there was a choice of six 2006 agricultural census variables, which, according to Bravo-Ureta and Pinheiro (1993), can induce eco-efficient behavior in municipality i: F1i - % children (under 14 years old) employed in establishments; F2i - % establishments that received technical guidance; F3i - % of establishments that use burning as an agricultural practice; F4i - % establishments that received funding; F5i - % of the people who run establishments with high school and graduate educational levels; F6i - % of establishments classified as family farms.

4. Results and Discussion Results of the research are presented, divided into three subsections. First, three alternative specifications are compared, in order to select the function that best fits the

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data, i.e., the most suitable model, in this case, to estimate the eco-efficiency. Secondly, parameters of the best model are analyzed. Finally, the determinants of eco-efficiency are described, as well as the performance index of the municipalities studied. 4.1 Test of the best function to fit the data In Table 1, the LR Tests to evaluate the models are shown. Firstly, the three tests 2

2

for H0= 𝛾 = 𝜎𝑢 𝜎 =0 indicate that the application method of stochastic frontier with inefficiency effects on the selected models, is statistically valid. Thus, the specification of this method produces better estimates than the traditional reviews of the production function with the method of ordinary least squares (OLS) in the absence of inefficiency effects. Secondly, the test that compares models 1 and 2 is presented in Table 1. The null hypothesis (the separability) is tested: 𝜗𝑛𝑝 = 𝜑𝑝1 = 𝜔𝑛1 = 0 for all n=1, 2, 3, 4 and p=1, 2, 3, 4. The test refutes the separability. Finally, Models 1 and 3 are confronted. As shown in Table 1, the last test does not confirm the null hypothesis, accepting the alternative (the parameters are different from zero), and indicating, in this case, that there are non-constant effects of substitution and complementation between inputs and outputs. Therefore, among the three models, the first (TLE) is the one that best fits the data, providing evidence that the use of simple functional forms to analyze production processes with multiple inputs and outputs can be problematic. Similar results were found by Constantin P. et al. (2009) in their research in which they applied CobbDouglas, Translog Stochastic Production Function to estimate the inefficiency over time (2001-2006) in the main grain crops in Brazil. TABLE 1. Results of the likelihood ratio tests to evaluate the models Model and H0 Model 1 H0= 𝛾=0 Model 2 H0= 𝛾=0 Model 3 H0= 𝛾=0

LR Test= -2(LLF0-LLF1) -2(-269.61-(-235.61))=68.01 -2(269.61-(-258.74))=21.74 -2(-396.95-(-359.34))=75.21

Critical Value χ20,05 3.84 3.84 3.84

Decision H0 rejected H0 rejected H0 rejected

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Model 1 vs. Model2 H0= 𝜗np=𝜔qn = 𝜑𝑞𝑝 =0 Model 1 vs. Model3 H0= 𝜗np=𝜔qn = 𝜑pq=αpp=βnn=τqq =0

22

-2(-269.74-(-235.61))=46.27

30.14

H0 rejected

-2(-359-(-235.61))=247.47

51.00

H0 rejected

Once Model 1 (TLE) is chosen, the next step is to evaluate the sign and the statistical significance of the parameters of this specification. The analysis is limited to the first-order coefficients, since the normalization of variables is sufficient to achieve the objectives of this study. According to the properties of the hyperbolic distance function, it is expected that the desired output parameters are negative, and the parameters of the undesired outputs and inputs remain positive. 4.2 Parameter estimation for the best model Table 2 shows the estimates of the parameters of the TLE model, where the parameters of outputs, representing the elasticity of the distance function are seen to have the appropriate signs and t-student significance levels (p<0.05). Therefore, the reduction in land degradation, or the increase in desired outputs, should reduce the distance from the eco-efficiency frontier. However, it is noteworthy that, among all these outputs, y1 (agricultural products) has the largest impact on the eco-efficiency variable, followed by livestock products (y2) and natural areas set aside for preservation (y4). The environmentally undesired output b1 has the least effect on eco-efficiency. According to formulation (21), the ratio of these parameters, side by side, can be interpreted as the opportunity cost or the ratio of the shadow prices of a DMU with average eco-efficient behavior. Thus, the quotient -α1/α2=-2.07 implies that, in ecoefficient municipalities, the value of cultivation is approximately twice that of livestock. This is corroborated by several studies that highlight the low rate of return with livestock in the region, and explain its persistence due to the liquidity of the activity, the

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relative simplicity of the extensive production processes, the low level of capital investment, as well as deforestation (Rivero, 2009). The ratio of the coefficients of the preserved area and agricultural production (α4/α1=-0.17549) indicates that a hectare of preserved land is worth US$ 82.39 (at prices of 2006) in terms of the value of the agricultural products per hectare per year. In terms of livestock revenue, the relative shadow price is US$ 170.34 per hectare per year (α4/α2), whose greatest magnitude reflects the fact that livestock is less productive than cultivation. The estimated opportunity costs show the losses that farmers in the eco-efficient municipalities incur in restricting their choices of land use when they decide to increase the area of permanent preservation and legal reserve. In other words, they indicate that the payments, from these annual yields per hectare, begin to create interest in the farmers to voluntarily maintain the preserved areas. Therefore, these values represent a valuable aid to political decision-making: on the one hand, they show the economic impact on revenue of legislation that increases the preserved areas; on the other, they can be used to define the minimum premiums to reward generators of positive environmental externalities arising from preservation as a worthwhile strategy. Thus, the values are similar to the annual payments for environmental services (PSA) for preservation projects involving legal reserves with springs and water courses. These pay on average a minimum of US$ 36.15 per hectare and a maximum of US$149.76. The estimate of these values is made considering the opportunity cost calculated solely by the weighted average of the profitability of the productive areas (MMA, 2011). Therefore, it is believed that the values mentioned in this study are more consistent and robust.

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The same reasoning applies to the negative externality b1. As formulation (22), the quotient of the parameters of degraded areas (b1) and agricultural income y1, τ1/α1=0.025 is US$ 11.76 per hectare annually. In terms of livestock revenue, τ1/α2=-0.0517 corresponds to US$ 24.31 per hectare. These values indicate the shadow prices of degraded areas and point out the marginal revenue that each eco-efficient municipality has to give up to reduce an additional unit of degraded area. The present value of this annual flow (at 6% for 20 years) represents at least US$ 248.82. It is interesting to note that the cost found is below the recovery costs of degraded areas in this biome and higher than the price of land for example in the state of Pará. According to Townsend et al. (2009), this value can reach US$ 1056.34/ha and in accordance with Brito and Cardoso (2015), land values practiced in 2011 by Instituto de Terras do Pará averaged US$ 152.58/ha with a minimum and a maximum of 110 and 522 respectively. This, coupled with low land regularization and state oversight, explains the increasing rates of abandoned degraded land.

TABLE 2. Parameters of the production frontier for Model 1 (TLE) estimated by the maximum likelihood method Coefficient

α0 α1 α2 α3 α4 τ1 β1 β2 β3 β4 α22 α23 α24

0.43 -1.13 -0.55 -0.05 -0.20 0.03 0.08 0.08 0.31 0.43 -0.09 0.01 0.02

Standard Error 0.05

t –ratio 8.58*

Coefficient ϑ21 ϑ22

0.02 0.01 0.02 0.01 0.03 0.03 0.03 0.03 0.01 0.01 0.01

-31.87* -3.52* -10.91* 3.90* 2.46* 3.06* 10.36* 12.30* -7.71* 1.72* 2.24*

ϑ23 ϑ24 ϑ31 ϑ32 ϑ42 ϑ43 ϑ44

ω11 ω12 ω13 ω14

0.03 0.01 -0.02 0.01 0.01 0.00 0.00 -0.01 -0.01 0.01 0.01 -0.01 0.00

Standard Error 0.02 0.00 0.01 0.01 0.01 0.01 0.01 0.02 0.00 0.01 0.00 0.00 0.01

t-ratio 1.62** 1.93* -1.09 0.65 1.17 -0.13 0.09 -0.64 -1.61** 2.10* 1.13 -2.90* 0.23

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φ21 α33 α34 φ 31 α44 φ 41 τ11 β11 β12 β13 β14 β22 β23 β24 β33 β34 β44

0.00 0.00 -0.38 δ1 -0.42 0.94 -0.45 -0.01 0.01 -0.98 δ2 -1.39 0.76 -1.82* -0.02 0.01 -2.27* δ3 0.29 0.50 0.58 0.00 0.00 1.03 δ4 0.50 0.53 0.95 -0.08 0.05 -1.54 δ5 -0.28 0.64 -0.45 -0.07 0.03 -2.31* δ6 -0.68 1.83 -0.37 0.00 0.03 -0.03 δ7 0.30 0.57 0.52 0.07 0.03 1.97* δ8 0.82 0.46 1.77* -0.07 0.03 -2.92* δ9 -0.63 1.20 -0.53 0.03 0.02 1.39 δ10 1.32 0.93 1.42 0.07 0.03 2.17* δ11 0.43 0.51 0.84 0.09 0.02 3.95* δ12 0.21 0.15 1.33 -0.06 0.03 -2.10* δ13 -2.24 1.24 -1.80* -0.08 0.04 -1.96** δ14 -0.26 0.60 -0.43 -0.03 0.02 -1.18 δ15 -0.06 0.25 -0.22 2 -0.01 0.01 -0.57 σ 0.18 0.02 7.95* -0.02 0.02 -1.64** γ 0.32 0.12 2.70* Log Likelihood Function -235.61 Mean Efficiency 0.84 Note: Estimates obtained using the software Frontier 4.1. The * are parameters significant at 5%, and ** are parameters significant at 10%.

4.3 Understanding the determinants of eco-efficiency and the performance of the municipalities Upon analysis of the parameters of the outputs, the inputs are seen to have the appropriate signs and significance levels. Therefore, any increase in input should increase the distance from the eco-efficiency frontier. However, it is observed that of all the inputs, the x4 (other inputs) has the biggest impact on the eco-efficiency, followed by land (x3) and labor (x1), with weight almost equal to capital (x2). With these parameters, one can deduce the types of economies of scale, and the marginal rates of replacement techniques at the midpoint of the data as formulations (18 and 20), respectively. Table 2 shows the values of

𝛽1, 𝛽2, 𝛽3 𝛽4

and τ1, whose sum is

greater than 0.5, indicating the presence of decreasing returns to scale. This means that an increase in all inputs by 1% in the Amazon region should cause a proportionally lower increase in production, in this case 0.93%. In other words, there is an oversizing

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of production in the municipalities as a whole at the midpoint, and a reduction in the production scale should reduce the scale inefficiencies. As regard to the marginal rates of technical substitution, it indicates the amount by which the quantity of one input has to be reduced when one extra unit of another input is used, so that output remains constant. This information is also important to define strategies for more sustainable production. For example, it is convenient to know by how much to reduce the land factor by replacing it with lower impact factors in ecoinefficiency (capital and labor) without changing the level of production. The TMgST land-capital = β3/β2 = 4.06 suggests the exchange of one hectare of land for the additional investment of BRL 4,059.24, and the TMgST land-labor = β3/β1=3.77 indicates that, in order to give up a hectare of land, about 4 additional laborers are needed. Therefore, one can maintain or expand the Amazon agriculture with less area, without further deforestation. Another set of parameters studied is related to explanatory eco-efficiency variables (δ), also recorded in Table 2. In general, a negative parameter indicates that the variable increases the eco-efficiency, and vice versa. Regarding the Brazilian states dummies, the estimated coefficients show that the characteristics which most favor ecoefficiency are in Acre State (𝛿2), while the least favorable ones are in Maranhão (𝛿8),. For the other six variables included, three have a negative sign, indicating a contribution to eco-efficiency. Thus, it is expected that public policies can induce increased funding in areas that are not deforested δ13, in the education of managers δ14 and the weight of family farming δ15, in order to strengthen environmental sustainability. On the other hand, the positive signs of δ10 and δ12 (child labor and burning) indicate that stricter supervision and punishment regarding these adversities

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would have similar effects. However, the negative sign of technical guidance δ11 was unexpected, and deserves further consideration. Moreover, it is necessary to stress that this is only a denotation, since the variables δ2, δ8 and δ13 are significantly different from zero. In Table 2, it is also noted that σ2 and γ are statistically significant. In the 2

2

estimated model, 𝛾 = 𝜎𝑢 𝜎 = 0,32, which implies 32% of the frontier deviation is explained by eco inefficiency. To conclude this section, it seems relevant to highlight that the estimated ecoefficiency indexes show how far the inefficient units are from the frontier. The overall average for the municipalities studied is 0.8364. Hence, it can be concluded that the eco-inefficient municipalities, as a whole, can increase the average production of the desired outputs (including preserved areas) by 19.5%=1/0.8364 and, simultaneously reduce degraded areas and inputs by 16.36% (1-0.8364), only adopting already known practices. The distribution of the indexes is shown in Figure 3. Note that 70% of the assessed municipalities have an eco-efficiency index over 0.81, and the remaining 30% (138 of the 528 municipalities) have lower rates. The lowest level is observed in the municipality of Guimarães, in Maranhão, and the largest in Acrelândia, in Acre. Acre has the highest mean eco-efficiency, with a score of 0.9644, followed by Mato Grosso (0.9489), Amapá (0.9382), Rondônia (0.9302), Pará (0.9185), Tocantins (0.826), Amazon (0.7709), Roraima (0.6775) and Maranhão (0.6014).

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Figure 3. Distribution of estimated eco-efficiency indexes.

Source: Results

5. Conclusions By proposing the use of parametric hyperbolic distance functions with the internalization of negative and positive externalities, this paper fills an important gap regarding evaluation of the Brazilian agriculture eco-efficiency, especially in the Amazon area. SFA with hyperbolic distance functions is a methodology that allows the contrast of various specifications of the production functions, estimating the costs of production opportunities without market prices, the marginal rates of inputs and outputs substitution, as well as an environmental sustainability index and its determinants. The main results of this study are summarized in the following set of recommendations for sustainable development of the Amazonian agriculture: 1. Stimulating cultivation instead of livestock. The evidence shows that cultivation has a greater positive impact on eco-efficiency. The estimates showed that, on average, cultivation is two times more productive than cattle ranching, and hence

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induce less deforestation. This strategy can be vital to the success in recent years on reducing deforestation in the Amazon. 2.

Adopting mechanisms to encourage environmental protection in the form of compensation proportional to the area preserved, whose values can take as reference the estimated opportunity costs: between US$ 82.39 and US$ 170.37 per hectare/year, depending on the type of production (livestock or cultivation).

3. Urging the adoption of land-saving technologies. The marginal rates of substitution indicate that it is possible to replace a hectare of land with four additional units of labor or capital investments of US$ 1905.75 per property. 4. Investigating why the general specifics of Acre are the most conducive to ecoefficiency, while those in Maranhão are the least favorable. 5. Using tighter financing mechanisms to articulate the previous set of recommendations in areas that are not deforested. They proved to be statistically significant in reducing eco-inefficiency. 6. Analyzing the production processes of the best municipal practices to define improvement targets in eco-inefficient municipalities. The results of this paper show that this strategy could increase total production by 19.5% and simultaneously reduce degraded areas and inputs by 16.36% on average. Finally, it is worth noting that there is great potential for discovering patterns in data with extensions of the methods used in the present study. Therefore, for future studies, it is suggested that a temporal dimension is introduced in the model, which will create a dynamic model to study other important issues for the sustainability of Brazilian agriculture, such as productivity improvements and the nature of the temporal

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trajectory, whether showing fluctuations or not, and even tendencies to converge or diverge.

Funding: This research was supported by the Fundação de Apoio a Pesquisa of the Federal District.

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ACCEPTED MANUSCRIPT 

Productivity growth in Amazon is not eco-efficient oriented;



Hyperbolic distance functions can be used to measure eco-efficiency;

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It is possible to decrease degraded areas and inputs by at least 16.36%;

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Acre is the most eco-efficient state, while Maranhão is the most eco-inefficient.