Changes and Factors Determining the Efficiency of Cattle Farming in the State of Pará, Brazilian Amazon

Abstract

Livestock production in the Brazilian state of Pará, located in the Amazon biome, faces challenges related to sustainable production chains and competitive production systems. Historically, expansion of pastures has led to environmental pressures and low productivity. The objective is to evaluate changes in cattle raising efficiency in the microregions of Pará state and identify the factors contributing to efficient cattle production at the state level. The data analysis techniques used include Data Envelopment Analysis, Malmquist Index, and Tobit Regression. The study found that, on average, there was a marginal improvement in livestock efficiency in Pará over the analyzed years, increasing from 0.75 (75%) in 2006 to 0.76 (76%) in 2017. However, nine out of 17 microregions showed improvement in individual efficiency, while five showed a decline. Non-family agriculture, livestock credit, and land prices were identified as factors that negatively contributed to the activity’s inefficiency, while specialization in soybeans and deforestation were factors that positively contributed to inefficiency. The study suggests that financial support for technological and infrastructure improvements, more rigorous environmental policies, and a more competitive environment can further contribute to improving the efficiency of cattle farming in Pará.

1. Introduction

The continuous growth of the global population has led to an increasingly high demand for food worldwide, thereby elevating the significance of food security and nutrition [1]. Within this context, livestock products assume a pivotal role in meeting these needs, and beef emerges as one of the principal sources of animal protein consumed globally. With the rise in per capita income and the progress of urbanization, significant changes in population consumption patterns can be observed [1]. Notably, in developing countries, consumers are growing more conscious of the potential environmental impacts linked to livestock farming.

Brazil plays a prominent role in global livestock production, being the largest exporter of beef and having the world’s largest commercial herd, with approximately 218.2 million head of cattle [2]. A significant portion of this herd is extensively raised on pasture [3]. Throughout history, the availability of land and the adaptation of cattle breeds to Brazilian climatic conditions have motivated the expansion of the Brazilian cattle herd, consequently causing significant changes in land use [4]. The opening of pasture areas, often preceded by deforestation and the burning of native forests, results in degraded soils and low productivity. This combination of deforestation, low-quality pastures, and the use of pesticides contributes to high greenhouse gas emissions (GHG) [5].

As the availability of land decreases and the pursuit of lower production costs increases, ranchers have been moving to more remote regions of the country, such as the state of Pará, located in the Amazon region. Currently, Pará has the largest cattle herd in the northern region and the third-largest in the country, with approximately 22.4 million head of cattle in 2021 [3]. In the same year, the state was responsible for exporting 26,000 tons of live cattle, becoming the country’s main supplier, along with 81,000 tons of beef, with both products primarily destined for the Asian market [6].

The acceleration of the growth of the livestock industry in the state has been taking place since the end of the 1960s. The implementation of government policies for sector development, such as the establishment of the Superintendence for the Development of the Amazon (SUDAM) in 1966, has led to environmental and social impacts in the region. The development model adopted during this period resulted in deforestation, wildfires, and land conflicts, as deforestation and subsequent establishment of pastures were used to secure land tenure.

With the economic liberalization and change in the exchange rate regime in Brazil in the late 1990s, Pará became one of the leading exporters of commodities [7]. However, from the 2000s, Pará has topped the deforestation ranking in the Legal Amazon [8]. With the accelerated occupation process, areas with greater forest cover were opened up by pioneers who sold valuable forest species, and subsequently, new immigrants occupied the territory and transformed it into areas devoted mainly to the production of commodities, particularly pasture and soybean cultivation [9,10].

The increase in deforestation associated with production expansion and the visibility in the international market prompted the need for the adoption of a different development model. For this, the government has led to a series of environmental policy changes, such as the creation of the Action Plan for the Prevention and Control of Deforestation in the Legal Amazon (PPCDAm) in 2004 [11], the Conditional Credit Policy in 2008 [12], and the legal commitment of the Conduct Adjustment Term (TAC) [13]. The update of the Brazilian Forest Code [14] in 2012, through the location and delimitation of native vegetation areas on rural properties, as well as the consolidation of protected area categories, has also contributed to the containment of deforestation and limited the expansion of extensive activities.

These policies were designed to effectively reduce deforestation [9] and drive changes in land use [15]. They implemented a range of legal instruments to curtail the extensive expansion of economic activities, while simultaneously promoting the sustainable intensification of production systems [16]. The aim of these incentives was to increase productivity in production systems primarily through technological advancements, ensuring the supply of products while limiting the expansion of land areas [17]. Simultaneously, commodity crops, such as grain production, began competing with livestock for available land [17]. Moreover, the rising consumer demand for higher quality products necessitated shorter production cycles, which rely on the nutritional value of animal feed and the herd health management. In other words, there is a need to produce more while using less land and ensuring the production of higher quality products [18,19,20].

In this way, the sustainable development of livestock in the state of Pará was designed to result in less pressure on forest areas. An increase in productivity per area was advocated based on improvements in production systems, that is, an increase in the efficiency of livestock production. Achieving production efficiency is essential for maximizing output and yield while utilizing resources effectively [21,22,23]. It involves striving for optimal economic and productive performance by minimizing costs and maximizing production.

The study of livestock efficiency in the state of Pará is of utmost importance because it can play a significant role in conserving natural resources and reducing environmental impacts. This efficiency is closely tied to the advancement of professionalism within the livestock sector, incorporating technological advancements and management improvements. The objective of the present study is to evaluate the efficiency of cattle production in the state of Pará in response to recent changes and identify the factors that contribute to efficient production.

To accomplish this, we conducted an analysis of production efficiency for the period between 2006 and 2017, which corresponds to the last two Agricultural Censuses [24,25] that provide periodic insights into the Brazilian agricultural sector. The input variables considered in the analysis include key production factors such as land (pasture), labor (people employed), and capital (representing physical structures within the agricultural establishment). The output variable used to assess efficiency is the revenue generated from bovine production, which includes the value of milk sales and the sale of animals.

This approach enables the differentiation of livestock productivity across micro-regions and the identification of changes in productivity within specific micro-regions over time. It also allows us to determine the factors that have contributed to the increase in livestock productivity in the state. In other words, it helps us identify which micro-regions are efficient and which ones are not, which regions have experienced improvements in efficiency and which ones have not, and ultimately, what factors contribute to the overall efficiency of livestock production in the state of Pará.

2. Materials and Methods

2.1. Study Area

The study area was the state of Pará, located in the Amazon Biome in the Northern region of Brazil, South America, with a territorial extension of approximately 1.24 million km², divided into 6 mesoregions, 22 microregions, and 144 municipalities (Figure 1) [26]. Its population is estimated at 8.7 million people, and it has a population density of about 6.97 habitants/km² [27]. The state is located in the hot equatorial climate zone, with an average air temperature above 18 °C in all months of the year [27]. The microregional approach was chosen to avoid missing values in some variables; thus, the microregions were used as Decision Making Units (DMUs) for efficiency analysis.

2.2. Data Analysis

The analytical methodology used was divided into two phases. The first phase referred to the efficiency determination stage, where the Data Envelopment Analysis (DEA) method and the Malmquist Index were used. Then, the next phase was to analyze the effects of contextual variables on the efficiency of livestock in the most recent period (2017). The analyses were carried out in the statistical software R version 4.1.2, using the “benchmarking” [28] package for DEA and Malmquist Index calculations, and the “AER” [29] package for Tobit regression.

2.2.1. Data Envelopment Analysis (DEA)

To calculate efficiency, we use Data Envelopment Analysis (DEA), a non-parametric method that allows for multiple inputs, multiple outputs, and different production goals, such as increasing production and/or reducing inputs used in production units DMUs [22]. Based on the studies by [21,22] proposed the initial model, called CCR after its creators [22], or CRS, for Constant Returns to Scale. This initial model was developed for DMUs operating with constant returns to scale and similar production scales. Later, ref. [23] proposed a second model, called BCC after its authors [23] or VRS, for Variable Returns to Scale, as it allowed DMUs to operate at different production scales.

In this study, the VRS model with output orientation was used since it was considered that the DMUs operate at different production scales. Additionally, in the presence of factors that cannot be changed in the short term, output orientation is the most appropriate. For the application of DEA, the first condition to be observed concerns the variables considered inputs or outputs, where negative or zero values are not allowed, and these chosen variables must be common to all DMUs [30]. The other condition is actually a consensus on the number of DMUs to be considered in the model, which should be at least three times the number of selected variables [31]. The DEA result varies from 0 to 1 (0 to 100%), and the DMU that presents a score equal to 1 (100%) is considered efficient.

Therefore, the DEA-VRS linear programming model with output orientation is given by:

$$Min h_0={{\displaystyle \sum }}_{i=1}^n{v}_i{x}_{i0}+v$$

(1)

Subject to:

$${\sum }_{j=1}^m{u}_j{y}_{j0}=1$$

(2)

$$-{{\displaystyle \sum }}_{i=1}^n{v}_i{x}_{ik}+{{\displaystyle \sum }}_{i=1}^n{v}_i{x}_{i0}+v \le 0,\forall \kappa$$

(3)

$$u_j\ge 0, u\in \Re$$

$$v_i\ge 0, v\in \Re$$

Being:

▪

h₀ is the efficiency of the DMU under analysis;

▪

v_i is the weight calculated for input i, i = 1, …, n;

▪

u_j is the weight calculated for the product j, j = 1, …, n;

▪

x_i0 is the amount of input i for the DMU under analysis;

▪

y_i0 is the quantity of product j for the DMU under analysis;

▪

v is the numerator scale return variable;

▪

κ is the number of the DMU under analysis;

▪

n is the number of inputs;

▪

m is the number of products.

In Brazil, the application of DEA in livestock systems began in the 1990s with the work developed by [32] to evaluate the efficiency of 241 dairy farms in the state of Minas Gerais. Subsequently, other studies were developed in the same vein, such as [33], who evaluated the efficiency of livestock systems in the Mato Grosso Pantanal after technological incorporation, and [34], applying it to evaluate efficiency in the modal phase of livestock production in Brazil. In the Amazon, studies applying DEA are still scarce, but recent. A study evaluated the efficiency of dairy farming in 39 properties in the state of Acre [35]. Another analyzed the effects of agricultural efficiency on deforestation in the Legal Amazon [36]. A study applied DEA to evaluate the eco-efficiency of agricultural activity in the municipalities of the Legal Amazon using data from the Agricultural Census [37].

Table 1. Variables and data source used in the DEA model.

Variables	Class	Data Source
Number of establishments with cattle 1 (n)	Input	Agricultural Census [24,25]
Number of people employed in cattle 2 (n)	Input	Agricultural Census [24,25]
Area with pasture in establishments with cattle 3 (ha)	Input	Agricultural Census [24,25]
Value of the sale of cattle and milk in establishments (1000 reais)	Output	Agricultural Census [24,25]

Note: ¹ establishments where the main economic activity is livestock; ² people, over 14 years old, who declare to work in the livestock activity in the establishments; ³ pasture area of establishments with cattle.

presents the variables used in the DEA VRS model with output orientation and their respective sources. One limitation in the choice of variables was the availability of data for the activity of cattle breeding. Therefore, only variables available for this filter were used, and the calculated efficiency is a reliable performance measure only for this specific activity.

DEA is a deterministic methodology that is highly sensitive to the presence of outliers. To obtain more reliable efficiency estimates, [38] suggested using the super-efficiency model to filter observations with gross data errors (outliers) and remove them. This method removes the constraint of values equal to or less than 1, allowing DMUs to obtain scores greater than 1. In this study, DMUs presenting super-efficiency greater than 2 [39] were considered outliers and removed from the sample studied.

Table 2. Descriptive summary of the inputs and output of the microregions of the state of Pará.

Before Removing Outliers	n	Interval			Mean ± SD			CV (%)
Reference year: 2006
Number of establishments (1000 units.)	21	0.07	-	8.51	3.00	±	2.71	90.55
People employed (1000 units.)	21	0.24	-	22.74	8.80	±	7.51	85.31
Pasture area (1000 ha.)	21	17.51	-	1635.71	443.89	±	450.33	101.45
Financial income (1000 reais) 1	21	7.13	-	740.70	212.76	±	229.21	107.73
Reference year: 2017
Number of establishments (1000 units.)	21	0.05	-	12.71	4.65	±	4.01	86.09
People employed (1000 units.)	21	0.14	-	30.90	11.41	±	10.29	90.18
Pasture area (1000 ha.)	21	0.49	-	2.380.62	583.20	±	659.30	113.05
Financial income (1000 reais) 1	21	0,81	-	1485.13	466.31	±	469.49	100.68
After removing outliers	n	Interval			Mean ± SD			CV (%)
Reference year: 2006
Number of establishments (1000 units.)	17	0.15	-	8.51	3.65	±	2.60	71.30
People employed (1000 units.)	17	0.53	-	22.74	10.70	±	7.10	66.41
Pasture area (1000 ha.)	17	17.56	-	1.635.71	537.43	±	452.03	84.11
Financial income (1000 reais) 1	17	16.29	-	740.70	258.87	±	231.96	89.60
Reference year: 2017
Number of establishments (1000 units.)	17	0.23	-	12.71	5.66	±	3.79	66.98
People employed (1000 units.)	17	0.47	-	30.90	13.93	±	9.85	70.75
Pasture area (1000 ha.)	17	11.59	-	2380.62	717.40	±	665.49	92.76
Financial income (1000 reais) 1	17	21.14	-	1485.13	558.69	±	475.24	85.06

Note: ¹ Values deflated according to the General Price Index—Internal Availability (IGP-DI) provided by Getulio Vargas Foundation [40] for October 2021.

presents the descriptive summary of the variables used as inputs and outputs in the DEA model for microregions in the state of Pará. The displayed information includes the range of values (Interval), the mean ± the standard deviation (SD), and the coefficient of variation (CV). Before the super-efficiency analysis, one microregion in Pará did not have values for some variables used in the DEA model, so it was removed, and the super-efficiency model was initiated with 21 microregions. As a result of the super-efficiency analysis, four microregions had values greater than 2, which significantly shifted the efficiency frontier.

These microregions were identified as outliers and considered super-efficient. They operated on small scales, a result that can be justified considering the nature of the data, which are census data where the smaller the number of informants for a particular variable, the more the data are de-identified, a procedure adopted by [41] that omits the data by using the character ‘X’ to protect the confidentiality of informants in small samples. The microregions identified as super-efficient have a low share of the cattle herd and are characterized by low technological levels. Therefore, the super-efficiency analysis was useful in removing an unrepresentative sample for livestock activity among the microregions of the state of Pará.

2.2.2. Malmquist Index

To verify temporal changes in efficiency, the Malmquist Index was used. Initially applied by [42] and subsequently used in conjunction with DEA by [43], the Malmquist Index measures the change in productivity of a DMU between two distinct time periods (t and t + 1), decomposing it into two factors: the frontier-shift effect and the catch-up effect [43].

The Malmquist Index with output orientation is represented by the following equation:

$$Malmquis{t}_0= \left(\frac{D_o^t\left(x^{t+1},y^{t+1}\right)}{D_o^t\left(x^t,y^t\right)}\right)\times {\left[\left(\frac{D_o^t\left(x^{t+1},y^{t+1}\right)}{D_o^t\left(x^t,y^t\right)}\right)\left(\frac{D_o^{t+1}\left(x^{t+1},y^{t+1}\right)}{D_o^{t+1}\left(x^t,y^t\right)}\right)\right]}^{\frac{1}{2}}$$

(4)

where:

$$Frontier-shif{t}_o={\left[\left(\frac{D_o^t\left(x^{t+1},y^{t+1}\right)}{D_o^t\left(x^t,y^t\right)}\right)\left(\frac{D_o^{t+1}\left(x^{t+1},y^{t+1}\right)}{D_o^{t+1}\left(x^t,y^t\right)}\right)\right]}^{\frac{1}{2}}$$

(5)

$$Catch-u{p}_0=\left(\frac{D_o^t\left(x^{t+1},y^{t+1}\right)}{D_o^t\left(x^t,y^t\right)}\right)$$

(6)

Being:

▪

$Malmquis{t}_0$ is the change in productivity of DMU 0;

▪

$Frontier-shif{t}_o$ is the frontier-shift effect of DMU 0;

▪

$Catch-u{p}_0$ is the DMU 0 catch-up effect;

▪

$D_o^t\left(x^{t+1},y^{t+1}\right)$ is the distance from DMU 0 in period t + 1 relative to the boundary of base period t;

▪

$D_o^t\left(x^t, y^t\right)$ is the distance from DMU 0 in base period t relative to the boundary of base period t;

▪

$D_o^{t+1}\left(x^{t+1},y^{t+1}\right)$ is the distance from DMU 0 in period t + 1 relative to the boundary of period t + 1;

▪

$D_o^{t+1}\left(x^t,y^t\right)$ is the distance from DMU 0 in base period t relative to the boundary of period t + 1.

Regarding the decomposition of the Malmquist Index, the frontier-shift effect represents the shift of the frontier or the improvement of the group’s performance, while the catch-up effect represents the improvement of the individual performance of the DMU. The result of the Malmquist Index and the frontier-shift and catch-up effects can be greater than 1, indicating an increase or progress; equal to 1, indicating the absence of change; or less than 1, indicating a decrease or regression.

2.2.3. Tobit Regression

To investigate the relationship between efficiency and contextual factors, the Tobit regression was used. The Tobit regression was initially proposed by [44] and is used when the dependent variable assumes censored values, as in the case of DEA scores, which have limits between 0 and 1. The regression is obtained using Maximum Likelihood Estimation (MLE), which consists of estimating the unknown parameters so that the likelihood function is maximized. As contextual variables or determining factors, the variables presented in

Table 3. Variables and data source used in the Tobit Regression.

Variables	Concept	Data Source
Technical assistance	Proportion of livestock establishments that receive technical assistance in relation to the total number of livestock establishments.	2017 Agricultural Census [25]
Producer Experience	Proportion of livestock producers under the age of 55 in relation to the total number of livestock producers.	2017 Agricultural Census [25]
Non—Family farming	Proportion of livestock establishments that are classified as non-family farming in relation to the total number of livestock establishments.	2017 Agricultural Census [25]
Specialization in soybean	Locational Quotient of the value of soybean production in relation to the value of agricultural production	2017 Agricultural Census [25]
Livestock credit	Average value of livestock rural credit operations from 2015 to 2017	Rural Credit Data Matrix [45]
Deforestation	Deforested area in the period from 2015 to 2017.	PRODES Project [8]
Land price	Average land price in the year 2017.	Value per hectare/city/year [46]

were used.

The technical assistance, producer experience, and non-family farming refer to the proportion of livestock establishments with the desired characteristic. The Location Quotient (LQ) is used to verify specialization in soybean production, which is calculated from a mathematical relationship that represents the degree of importance of a sector in relation to a reference economy, as used by [47]. The LQ does not have a unit because it is a mathematical relationship of importance, that is, the ratio between two economic structures Thus, the LQ was:

$$\mathrm{LQ}=\frac{\left({\mathrm{VP}}_{ij}/{\mathrm{VP}}_j\right)}{\left({\mathrm{VP}}_{iA}/{\mathrm{VP}}_A\right)}$$

(7)

Being:

▪

VP_ij: the value of soybean production in microregion j;

▪

VP_j: the value of agricultural production in the microregion j;

▪

VP_iA: the value of soybean production in the state of Pará;

▪

VP_A: the value of agricultural production in the state of Pará.

For livestock credit and deforested area, the average and the sum of three years, respectively, was used to account for investments and impacts of production with greater precision. All variables were linearized by applying the natural logarithm, except for the LQ, which was transformed into a dummy variable assuming a value of 1 when the LQ was greater than or equal to 1, and a value of 0 when the LQ was less than 1. The descriptive statistics of contextual variables are presented in

Table 4. Descriptive summary of the variables used in the Tobit Regression.

Variables	n	Interval			Mean ± SD			CV (%)
Technical assistance	17	0.04	-	0.22	0.12	±	0.07	55.56
Producer Experience	17	0.64	-	0.77	0.69	±	0.03	4.86
Non-Family farming	17	0.19	-	0.43	0.27	±	0.07	25.57
Specialization in soybean	17	0.00	-	4.00	0.70	±	1.31	186.79
Livestock credit (1000 reais) 1	17	1.12	-	312.37	118.07	±	105.82	89.63
Deforestation (km2)	17	6.80	-	2394.20	419.27	±	609.79	145.44
Land price (1000 reais/ha) 1	17	0.63	-	2.96	1.26	±	0.60	47.48

Note: ¹ Values deflated according to the General Price Index—Internal Availability (IGP-DI) provided by Getulio Vargas Foundation [40] for October 2021.

.

Thus, the Tobit regression model used with the variables after their respective transformations was:

$$\begin{array}{cc}\hfill \ln \left(1/eff17\right)={\beta }_0& +{\beta }_1\ln \left(Technical assistance\right)+{\beta }_{2}ln\left(Producer Experience\right)\hfill \\ & +{\beta }_{3}ln\left(Non-Family farming\right)+{\beta }_4\left(Specialization in soybean\right)\hfill \\ & +{\beta }_{5}ln\left(Livestock credit\right)+{\beta }_{6}ln\left(Deforestation\right)\hfill \\ & +{\beta }_{7}ln\left(Land prince\right)\hfill \end{array}$$

(8)

Being:

▪

$ln\left(1/eff17\right)$ is the natural logarithm of the inverse of the efficiency score in the year 2017, that is, the natural logarithm of the inefficiency score;

▪

β indicates the parameters or coefficients to be estimated;

▪

$ln\left(X\right)$ is the natural logarithm of each contextual variable, except the dummy variable used for soybean specialization.

The Tobit model has been validated through various measures and statistical tests. The adjusted Pseudo R² was used to assess the quality of model fit, providing a measure of how much variability is explained by the independent variables [48]. The Log likelihood was calculated to determine the overall adequacy of the model in terms of maximizing the likelihood function [48]. The Wald statistics far was employed to test the statistical significance of the estimated coefficients, enabling the determination of whether the independent variables have a significant effect on the dependent variable [48,49]. The Shapiro–Wilk test was applied to check the normality of residuals, ensuring that the assumptions of the model are being met [49]. Additionally, the Variance Inflation Factor (VIF) was computed to detect the presence of multicollinearity among the independent variables, avoiding collinearity issues that could compromise the interpretation of the results [49]. These measures and tests provided a comprehensive and rigorous validation of the Tobit model, enabling a reliable analysis of the data.

3. Results

3.1. Efficiency Analysis between 2006 and 2017

In this session, the efficiency results of in 2006 and 2017 are presented, using the DEA-Malmquist method.

Table 5. Efficiency scores of the DEA VRS model with output orientation, of the microregions of the state of Pará, in the years 2006 and 2017.

Microregion	Mesoregion	2006	2017
Almeirim	Baixo Amazonas	0.6055	0.6839
Altamira	Southwest of Pará	0.5265	0.7487
Arari	Marajó	1	0.5518
Bragantina	Northeast of Pará	0.7319	0.9970
Conceição do Araguaia	Southeast of Pará	0.6917	0.4960
Guamá	Northeast of Pará	0.6179	0.6336
Itaituba	Southwest of Pará	0.4180	0.5516
Marabá	Southeast of Pará	0.8904	0.9215
Óbidos	Baixo Amazonas	0.4424	0.4596
Paragominas	Southeast Pará	0.8165	0.7219
Parauapebas	Southeast of Pará	1	1
Redenção	Southeast of Pará	1	1
Salgado	Northeast of Pará	1	1
Santarém	Baixo Amazonas	0.6522	0.4714
São Félix do Xingu	Southeast of Pará	0.9250	1.0000
Tomé-Açu	Northeast of Pará	0.8856	0.7915
Tucuruí	Southeast of Pará	0.5703	0.8217
Frequency
Efficient (value = 1)		4	5
Inefficient (value < 1)		13	12
Minimum		0.4180	0.4596
Mean		0.7514	0.7559
SD		0.2034	0.2047
CV (%)		27.07	27.08

shows the efficiency scores for each year. The average efficiency scores for both periods were very close, with 0.75 (75%) and 0.76 (76%) in 2006 and 2017, respectively. That is, with the same level of inputs, revenue could be increased by 25% and 24%. In 2006, only four microregions had efficiency scores of 1: Arari, Parauapebas, Redenção, and Salgado. In 2017, there were five efficient microregions: Bragantina, Parauapebas, Redenção, Salgado, and São Félix do Xingu. These microregions are considered to be hubs of livestock production in the state, except for Arari and Salgado, which have smaller production scales.

The majority of the microregions were considered inefficient in both years. In 2006, 13 microregions were classified as inefficient, while in 2017, this number decreased to 12. The minimum efficiency values were very close, being 0.42 (42%) in 2006, for the Itaituba microregion in the Southwest of Pará, and 0.46 (46%) in 2017, for the Arari microregion, located in the Baixo Amazonas mesoregion.

To verify changes in productivity and their decomposition,

Table 6. Malmquist Index, frontier-shift effect, and catch-up effect of DMUs between the years 2006–2017.

Microregion	Mesoregion	Frontier-Shift	Catch-Up	Malmquist
Almeirim	Baixo Amazonas	1.4369	1.1296	1.6231
Altamira	Southwest of Pará	1.7735	1.4222	2.5223
Arari	Marajó	1.4081	0.5518	0.7770
Bragantina	Northeast of Pará	1.6703	1.3623	2.2753
Conceição do Araguaia	Southeast of Pará	1.5899	0.7170	1.1400
Guamá	Northeast of Pará	1.6385	1.0255	1.6803
Itaituba	Southwest of Pará	1.7044	1.3197	2.2492
Marabá	Southeast of Pará	1.6625	1.0350	1.7206
Óbidos	Baixo Amazonas	1.6550	1.0391	1.7197
Paragominas	Southeast of Pará	1.6671	0.8841	1.4738
Parauapebas	Southeast of Pará	1.7129	1	1.7129
Redenção	Southeast of Pará	1.6380	1	1.6380
Salgado	Northeast of Pará	1	1	1
Santarém	Baixo Amazonas	1.6424	0.7227	1.1870
São Félix do Xingu	Southeast of Pará	1.8620	1.0811	2.0129
Tomé-Açu	Northeast of Pará	1.5905	0.8938	1.4215
Tucuruí	Southeast of Pará	1.6288	1.4408	2.3468
Frequency
Increased (value > 1)		16	9	15
Without changes (value = 1)		1	3	1
Decreased (value < 1)		0	5	1
Minimum		1.0000	0.5518	0.7770
Maximum		1.8620	1.4408	2.5223
Mean		1.6048	1.0367	1.6765
SD		0.1092	0.2490	0.4752
CV (%)		11.74	24.02	29.35

presents results for the Malmquist index, frontier-shift effect, and catch-up effect. Total productivity increased in 15 microregions, meaning that they had a Malmquist index greater than 1. One microregion (Arari) experienced a reduction in productivity, while another (Salgado) maintained the same level. The greatest progress in terms of Malmquist was achieved by Altamira (2.52), followed by Tucuruí (2.35) and Bragantina (2.28), indicating productivity gains in the Southwest, Southeast, and Northeast of Pará, respectively. All microregions in the Baixo Amazonas also had a Malmquist index greater than 1. Thus, of the five mesoregions in Pará, there were productivity gains in the livestock sector in four, revealing an overall improvement in the sector in the state of Pará.

Regarding the decomposition of the Malmquist index, the frontier-shift effect increased in 16 microregions, with Salgado being the only one to present a value equal to 1, remaining at the base of the frontier. The increase in frontier displacement is in line with the Malmquist indices found. On the other hand, the results for the catch-up effect presented greater differences. A total of nine microregions had values greater than 1, representing gains in efficiency. Another five microregions had values lower than 1, indicating a loss of efficiency, and three others obtained values equal to 1, that is, they maintained efficiency. Therefore, although there was a general improvement in the state’s productivity, only 9 out of 17 microregions had efficiency gains, responsible for 61.4% of the state’s livestock.

3.2. Determining Factors of Efficiency

In this section, we present the results of the Tobit regression analysis that examined the influence of contextual variables on recent inefficiencies in livestock farming (2017). The estimated coefficients of the Tobit regression are presented in

Table 7. Tobit regression of cattle ranching inefficiency scores in 2017.

Variable	Coefficient	Std. Error	z-Value	p-Value	VIF
(Intercept)	3.1471	0.9377	3.3560	0.0008	-
Technical assistance	0.0466 ns	0.1594	0.2920	0.7699	5.4653
Producer Experience	0.4749 ns	1.0103	0.4700	0.6383	3.3843
Non-Family farming	−0.9360 ***	0.3045	−3.0740	0.0021	1.4463
Specialization in soybean	0.3473 ***	0.1195	2.9060	0.0037	1.4301
Livestock credit	−0.1078 **	0.0479	−2.2510	0.0244	4.1855
Deforestation	0.1041 *	0.0548	1.8990	0.0576	4.6231
Land price	−0.5002 ***	0.1785	−2.8020	0.0051	2.8398
Log (scale)	−1.8679 ***	0.2000	−9.3380	0.0000	-
Pseudo R2	0.9146
Pseudo Adjusted R2	0.8482
Log-likelihood	3.869 ***			0.0000
Wald-statistic	40.860 ***			0.0000
Shapiro–Wilk test	0.9321			0.2356

Note: (ns) not significant; (*) significance at 10% probability; (**) significance at 5% probability.; (***) significance at 1% probability; Log(scale) is the estimated standard error of the regression; Log-likelihood is the Likelihood Function.

. The model fit was considered satisfactory based on the Log-likelihood and Wald test values, which showed significant values at a 5% probability level. The Shapiro–Wilk test indicates the normality of the residuals. The Pseudo R² supports the indication of a good fit of the model to the observed data. The values for the VIF were less than 10, indicating the absence of critical multicollinearity among the predictor variables [49].

The interpretation of the β coefficient in Tobit regression is not as straightforward as in linear regression, as potential changes in contextual variables not only affect the mean of the dependent variable within the observed limit, but also the probability of the variable being within this limit [48]. However, the results indicate the influence of five contextual variables on efficiency: non-family agriculture, specialization in soybean production, livestock credit, deforestation, and land price.

Non-family agriculture, livestock credit, and land price had negative effects on livestock inefficiency in the analyzed microregions, indicating a positive relationship with livestock efficiency. On the other hand, deforestation and specialization in soybean production had positive coefficients with the inefficiency of the microregions, indicating a negative influence on livestock efficiency.

The variables that were not influential are technical assistance and producer experience. One limitation regarding the non-significant variables is that they are only available in aggregated form, that is, for livestock farming in general, not specifically for cattle farming, which may contribute to inconclusive relationships with other variables specific to cattle farming. The average coverage of technical assistance in the microregions was 12%, indicating still low access to the service, limiting the impact on economic performance.

4. Discussion

4.1. Efficiency Factors: Non-Family Agriculture, Livestock Credit, and Land Price

In Brazil, a family farmer is defined as an individual who meets the following criteria simultaneously: (1) owns an area of up to four fiscal modules, regardless of ownership type; (2) uses at least 50% of the family workforce in production and income generation; (3) generates at least 50% of their family income from their establishment or enterprise; and (4) has strictly family management of the establishment or enterprise [50].

The positive association between non-family farming and efficiency in Brazil can be attributed to factors such as land productivity and management capacity. Studies have shown that the relationship between efficiency and land size can be represented by a “U” curve, indicating that extreme property sizes are generally less efficient, while sizes closer to the average adopt more efficient production practices [51,52]. In addition, research has demonstrated that the intensification of livestock production has a non-linear relationship with the demand for productive land. Initially, as ranches become more intensive, the demand for recently cleared land increases, but this trend decreases with further intensification [53].

Non-family farms have been shown to be more adept at implementing resource efficient practices to make the land more productive, which can help mitigate the impact of agricultural expansion on the environment. The reasons for this relate to the security of property rights, facilitating access to credit and markets [54]. This is not a desired consequence of the development of the activity, since it represents the concentration of land and income.

Land price had a positive effect on efficiency. Historically, land prices have been positively and negatively associated with livestock activity. According to [55], land prices are formed with the development of economic activities, so increased credit not only finances the economic development of these locations, but also signals the existence of a potentially more intensified production model. The activity, in an extensive production model, besides its low production costs, was used to secure land ownership [56,57]. Factors such as years in the area, agricultural production area, and housing values increase land prices, while distance from the city and forested area decrease the values [56].

The efficient microregions in 2017 Parauapebas, Redenção, and São Félix do Xingu are located in the Southeast of Pará, a region considered a consolidated pioneer front [58] and with higher technological levels in 2006 [59] and 2017 [60]. The technological level in these studies is given by an index constructed from variables referring to technological innovations and socioeconomic, institutional, and environmental aspects [59,60]. In 2017, Arari ceased to be an efficient microregion of small scale, and Bragantina, along with Salgado, occupied these positions, both belonging to Northeast of Pará. In these areas, livestock farming is still predominantly developed in traditional extensive systems [61].

The effect of credit on cattle farming in the state was studied and according to the authors [62], from 1999 to 2015, every 10% increase in credit supply resulted in a 4.85% increase in cattle herds, ceteris paribus. In Pará, especially in the municipalities of Southeast of Pará, which are part of Brazil’s high resource collection cluster, investments are mainly directed towards the acquisition, rearing, and fattening of cattle, as well as pastures, machinery, and tractors [61]. The positive effects of rural credit were also observed [20], where it was found that rural credit policies contributed to the increase in the herd in Pará from 1995 to 2019, facilitating the acquisition of animals for reproduction, investment in pasture, management, and the implementation and recovery of intensive systems.

However, as infrastructure improvements are implemented in a region, as well as the advancement of other land uses, the tendency is for land prices to rise [55,57]. Consequently, this rise in prices tends to reduce the advantages of extensive livestock farming as a convenient system due to the difficulty of expanding production through area expansion [56,57], a factor that can lead systems that operate under this model to move to areas considered new agricultural frontiers or even stimulate intensification as a way to remain competitive.

The negative association of non-family farming, livestock credit and land prince with inefficiency may indicate that more technologically and entrepreneurially advanced microregions are efficient, contributing to better results.

4.2. Inefficiency Factors: Deforestation and Specialization in Soybean

Considering the positive effect of livestock credit on efficiency, the negative effect of deforestation on efficiency was a desired outcome after the implementation of the Conditional Credit Policy [12], as a way to reduce deforestation in the Legal Amazon region, since deforestation is associated with the horizontal expansion of activity. In turn, soybean specialization has been analyzed through studies that have shown that the advance of soybean production in the country has greater impacts on family and traditional livestock farmers, who perceive the activity negatively due to the unavailability of land and environmental impacts, as opposed to a group of livestock farmers with a more business-oriented perspective who see the activity within their supply chain, being important for the economic development of the regions [63,64,65,66].

The relationship between deforestation and family farming has also been studied in the context of the last few decades. It has been observed that there has been a shift in the profile of deforestation in the Amazon, with increasing rates of small-scale deforestation (forest degradation associated with small sequential clearings) due to the diversification of productive activities related to family farming [67]. According to a study [68], there has been a significant reduction in the number of new, large forest clearing areas (>50 ha) in the Amazon over time (46%), while the number of new, small forest clearing areas (<1 ha) increased by 34% between 2001–2007 and 2008–2014. Thus, deforestation in Pará is associated with productive activities and land occupation processes, such as extensive livestock, family farming, land grabbing, road construction, and the recent expansion of mechanized grain agriculture, particularly soybeans [69,70].

The microregion that experienced the most efficiency gain was Tucuruí. The installation of Federally Inspected Slaughterhouses (FIS) in Tucuruí and Redenção promoted greater productivity through genetic improvement and encouraged local producers to sell animals, semen, and embryos [60,71]. It is worth noting the efficiency gain in Altamira and São Felix do Xingu, neighboring microregions that have been marked by numerous territorial conflicts involving livestock farming [72]. The increase in efficiency also corroborates with another study that found an association between these microregions and indicators of transition to more sustainable practices [60].

Of the microregions studied, three were identified as specialized in soybean production: Conceição do Araguaia, Paragominas, and Santarém. Conceição do Araguaia was the entry point for soybean production in the state in the 1990s and is currently the main center for the grain in the state, with production expanding from this microregion to adjacent regions [73]. In Paragominas, soybean production has been occurring in degraded pasture areas near highways due to the ease of product transportation [69,74,75]. In Santarém, the installation of multinational ports from 2003, together with infrastructure works, has promoted rapid growth in soybean production in the region [76]. These microregions lost efficiency over the years analyzed, indicating competition between activities.

In the microregions that have lost efficiency Conceição do Araguaia, Paragominas, Santarém, and Tomé-Açu, are microregions with high and growing levels of specialization in grain production [77,78]. One of the factors that has contributed most to the specialization of soybean production in these regions is the logistical ease of transporting the production and the increasing competitiveness of highly technician production in other regions. Many livestock farmers who migrated to the Pará territory purchased large areas of pastureland for conversion to grain crops, especially soybeans [76,77,78].

5. Conclusions

The average efficiency of livestock production in the state experienced a modest increase of only 1% between 2006 and 2017. Nevertheless, it is important to highlight significant variations among the microregions. Out of the analyzed micro-regions, nine showed an increase in productivity over the years, while five experienced a decrease, and three did not show significant changes. This indicates that despite the productivity increase in some micro-regions, the lack of change or decrease in others may have an impact on the overall performance of the livestock sector in the state.

In light of this, it became necessary to investigate the factors that contributed to these variations and seek strategies to improve efficiency in the microregions facing productivity challenges. The study found that variables such as non-family agriculture, livestock credit, and land price have a positive effect on efficiency, while deforestation and soy specialization have a negative effect. The efficient microregions distance themselves from deforestation and may discourage the substitution of pasture areas with soy, thus remaining competitive. It is important to note that as the competitiveness of the production environment grows, efficiency gains are necessary to ensure the competitiveness of livestock production in the region.

The results of this study were intended to guide public policies and business practices aimed at promoting sustainable development in the region. The government can design guidelines to address the specific challenges faced by the livestock production sector. This may include providing conditional financial incentives to promote the adoption of advanced agricultural technologies, infrastructure improvements, and efficient production practices. In addition, indispensably, strengthening environmental policies, as they help mitigate the environmental impacts associated with livestock production and promote restrictions that lead to the need for increased productivity, thus increasing the efficiency of production systems.

The study also contributes to decision making for entrepreneurs by presenting the competitive environment and how it relates to the required levels of intensification. The relationship between non-family producers and efficiency reinforces this reality, as in a more competitive environment, entrepreneurial producers who can make necessary adaptations and operate at scale prevail. The advancement of soybean crops, for example, currently poses a threat to livestock farmers who cannot intensify production sufficiently to cover the opportunity cost of land in certain micro-regions.

Furthermore, the study paves the way for new research that can deepen knowledge about the relationship between productive efficiency, sustainable development, and environmental conservation in agricultural hubs in the state of Pará and in the Amazon.