SPATIAL CONVERGENCE OF THE GROSS VALUE OF PRODUCTION OF FIREWOOD IN THE MESOREGIONS OF THE BRAZILIAN NORTHEAST VALOR BRUTO DE PRODUÇÃO LENHA

– This paper analyzed the process of convergence in the gross value of wood production in mesoregions of Northeast Brazil, in the period of 1994 and 2013. The object of study was the Gross Value of Production (GVP) of firewood per km 2 of the mesoregions of the Northeast of Brazil. In the methodology the Absolute Convergence Model was applied and estimated through the classical model and spatial models. In the spatial approach we used the Spatial Autoregressive Model (SAR) and the Spatial Error Model (SEM). From the results obtained, the following conclusions were reached: The mesoregions of the Northeast of Brazil had an average fall of 3.94% a.a. of the GVP/km 2 of native wood for the period 1994 to 2013. Considering the classical linear regression model, convergence was verified and also the presence of spatial dependence for GVP/km 2 of firewood. In order to correct the spatial dependence, the SAR and SEM Models were adequate and according to Akaike’s Information Criterion and used the rook matrix the SEM was configured the best model. This study showed the importance of the involvement of the spatial question in the models, either by the overlap of information of the GVP and in the development of public policies that positively affect the neighborhood.


INTRODUCTION
Firewood is the oldest of all energy sources. The growth of cities spurred an increase in energy demand and promoted exploration in response to the limited regeneration capacity of the forest, which resulted in a short age of firewood in some regions (Uhlig, 2008).
In tropical regions, firewood costs little and requires no processing before use. In Brazil, 8.1% of the internal energy demand comes from forest resources (firewood and vegetable charcoal). Firewood is of considerable importance in the Brazilian energy matrix, and there has been a shortage of native firewood supply in some regions in Brazil. This may be due to decreasing vegetable exploration; the consequences are price increases and the need for reforestation. The most intensive use of firewood as an energy source is concentrated in the South, Southeast and Northeast of Brazil (IEA, 2006a,b, Brito andDeglise, 1991).
In Brazil, in 2013, the production of firewood reached 86.35 million m3. Of this total, 64.15% of the wood was from planted forests (silviculture) and 35.86% from native forest (vegetal extractivism). The main woodproducing regions for that year were the South (42.85%), the Northeast (21.82%), the Southeast (17.61%), the Midwest (10.84%) and the North (6.87%). Within these regions there is a discrepancy in proportion as to its origin, in the South and Southeast 90% of the supply of firewood comes from forestry, while more than 90% of the wood from the North and Northeast comes from the vegetal extractivism. The gross value of production (VBP) of wood from the Brazilian vegetable extractivism reached R$ 670.41 million and the Northeast corresponded to 43.80%, inserted in the caatinga biome (IBGE, 2018).
In the Northeast, firewood production matches demand. The producers decrease production when there are no buyers at suitable prices. The volume and the geographical distribution of firewood supply depend on buyers being willing to pay prices that interest the producers. This current supply pattern leads to the following risk: the concentration of production near consumer poles may promote degradation from the super-exploration of firewood (Riegelhaupt and Pareyn, 2010).
The Brazilian Northeast represents 18% of the national territory. It has about 2.5 million rural establishments, or 50% of Brazil. The semiarid Biome represents 10% of the Brazilian area and corresponds 39% of the rural population. Around 1.5 million rural settlements are located in the semiarid region, which 72% of them do not have definitive ownership of the land, reflecting the rate of deforestation and firewood production (Medeiros et al., 2012a). In the economic literature, there is an abundance of studies that test the convergence hypothesis of gross domestic product (GDP) or income, whether between nations or between regions of a country. The classic models of economic growth predict that if the free mobility condition of the production factors is satisfied, the per capita income of the different regions of a country will equalize. In neoclassic theory, this occurs because of the existence of decreasing marginal returns in the use of production factors (Ferreira, 1995).
These models consider that if the economies encompass similar technologies and preferences, poorer economies will have a higher growth rate for the GDP compared to richer economies. Therefore, the development distance between the economies will be reduced (Spohr and Freitas, 2011). To accommodate the need of using firewood with forest conservation, public policy must be aimed at effective management programs (Medeiros, 2010). It is important to understand the spatial distribution of firewood production in the Northeast, as well as how this production relates between regions, to identify a possible spatial dependence.
Spatial dependence or spatial autocorrelation is defined as the presence of positive or negative correlation of the distance between points and the similarity of the values measured for a certain variable to a degree greater than expected by chance. When the values are not statistically independent, they are said to be auto correlated. This violates one of the assumptions of traditional tests: the independence of the sample data (Legendre, 1993). Spatial econometric models incorporate the spatial dependence problem in the data, which improves the predicting power of the models. Spatial econometrics is a field in econometrics composed of techniques that address the inherent dependencies on space: spatial interrelations and spatial structure (Anselin, 2002). Spatial econometric results provide better information for decision support.
In Brazil, there are few papers dealing with the convergence of spatial income in the agrarian sciences. We highlight: Almeida et al. (2008) that dealt with the absolute convergence for the Brazilian average agricultural productivity, controlling the spatial effects and; (Aiher et al., 2016) analyzed the evolution of agricultural productivity in the microregions of Brazilian southern in the period of 1996 and 2006. However, there are no studies in the forestry sector that address the convergence of their production.
In view of the above, it is important to deal with the spatial effects of the convergence of the gross value of wood production, mainly in the Brazilian Northeast. Thus, this article analyzed the process of spatial convergence of the gross value of wood production in mesoregions of the Brazilian Northeast, in the period of 1994 and 2013.

MATERIALS AND METHODS
The data used were the Gross Value of Production (GVP) of firewood from vegetal extraction in the mesoregions of the Brazilian Northeast between 1994 and 2013.The data were acquired from the Automatic Recovery System (Sistema de Recuperação Automática -SIDRA) of the Brazilian Institute of Geography and Statistics (Instituto Brasileiro de Geografia e Estatística-IBGE). The values were corrected by the General Price Index -Internal Availability (Índice Geral de Preços -Disponibilidade Interna -IGP-DI) (2012 Base = 100). After normalization (monetary correction), the GVPs of each mesoregion were divided by the area (km 2 ) obtained from IBGE. This ensured that the area of the territory did not influence the results. Therefore, the index per area indicated the GVP/km 2 of the firewood in the extraction.
The Solow model (1956;1957) was one of the precursors in this type of analysis. The convergence can be measured in two ways: -convergence and âconvergence. The first type refers to the dispersion values of a variable. The second type is related to the speed of convergence. The parameter -convergence is classified as absolute or conditional. The absolute case occurs when the economies converge to the same steady state, whereas the conditional case occurs when the economies converge to their own steady states (Barro and Sala-I-Martin, 1991). The absolute convergence is realized performed by regression of the GVP growth rate in relation to the logarithm of the initial per capita income. The according with Almeida et al. (2008) Note that  is the spatial lag coefficient, and because >0, the presence of positive spatial autocorrelation is indicated. If  is negative, there is absolute convergence; i.e., the mesoregions with larger GVP of firewood have lower growth rates.
Spatial econometrics models address potential problems originating from the existence of spatial effects in the regression analysis. The spatial dependence, one of these effects, appears as a consequence of autocorrelation in explanatory (Wx) and dependent (Wy) variables or in the error term (Wu) (Schumacher, 2013). For the spatial dependency models, was realized according to Baumont (2004), the following:

1.Estimation of the classical model of linear regression by Method of Ordinary Least Squares (OLS);
In the classic linear regression model, the dependent variable was the natural logarithm of the GVP of firewood per area in the year 2013 in relation to the year 1994: 1n[(GVP 2013 /km 2 )/(GVP 1994 /km 2 )]. The independent variable was the natural logarithm of the GVP of firewood per area in 1994: 1n(GVP 1994 /km 2 ). To test the presence of spatial dependence, the following matrices were used: contiguity ("queen" and "rook" conventions) and number of nearest neighbors (1, 2, 3, 4 and 5 neighbors).
2.Testing of residuals of the spatial autocorrelation model, using Moran's I for a set of matrices W; Moran's I test is a test used to investigate the presence of the spatial autocorrelation (spatial dependence) of the regression residuals. In Cliff and Ord (1973), Moran's I test is expressed as: where, e = y X*, where * is the ordinary least squares (OLS) estimator for , and S 0 =  i  j w ij , representing a normalization factor.
3.Selection of the spatial weight matrix that originated the largest value in Moran's I test and that has statistical significance;

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For the choice of the best spatial model, the following procedure was used (Almeida, 2012): a.Estimation of the Classical Linear Regression Model (MCRL) model for OLS without any spatial lag b.Testing of residuals by a diffuse spatial autocorrelation test with Moran's I c.If there is no evidence of spatial autocorrelation, one must use the model estimated by OLS. If there is spatial dependence, the next step is taken; d.Estimation of the spatial models; Two types of spatial econometrics modeling were performed: Spatial Autoregressive Model (SAR) and Spatial Error Model (SEM). The maximum likelihood method was used. For Anselin et al. (2000), the SAR can be represented by: y =Wy + X+, where, y = matrix of dependent variables; Wy = spatially lagging dependent variable;  = intensity of interdependencies among sample observations of the endogenous variable; X= matrix of independent variables; = estimated regression coefficients; and  = the error term distributed with zero mean and constant variance.
For Almeida (2012), in the SAR model, the estimation of the parameters by the ordinary least squares (OLS) method can create a bias leading to inconsistency. The importance of the estimation by maximum likelihood is in the asymptotic properties: consistency, efficiency and normality (Arbia, 2006). Rêgo and Pena (2012) show that the SEM is expressed by: y=X+W, where, W = errors with spatial effect;  = refers to random errors with zero mean and variance   ; and  = the autoregressive coefficient.
Note that the null hypothesis for the absence of autocorrelation is that .
The model chosen was the one that satisfied two conditions: not having evidence of spatial autocorrelation in its residuals and presenting the lowest Akaike information criterion (AIC).

RESULTS
3.1. Analysis of the growth of the gross value of production of firewood Table 1 presents the real GVP per area (GVP/km²) of firewood from extraction in the mesoregions in the Brazilian Northeast for the years of 1994 and 2013 (IGP-DI 2012 Base =100). Table 2 presents the classic linear regression model via ordinary least squares (OLS) for the matrices of closest neighbors and of contiguity ("queen" and "rook"). Table 3 shows the estimation of the econometric SAR and SEM models.  (Table 1), the Brazilian Northeast (1,554,291,744 km²) exhibited a decrease of 3.94% average annual (a.a.) in the GVP/km² of firewood. This reduce was largely verified in the states of Bahia, Maranhão and Ceará, and is associated with the substitution of firewood for other energy sources in the local production process, as well as the decrease in the supply of wood from forest suppression through expansion and occupation of urban and agricultural settlements.

Convergence of the gross value of production of firewood
However, some mesoregions showed a growth in firewood supply, mainly in the mesoregions of the States of Pernambuco (Sertão Pernambucano, São Francisco in Pernambuco), Paraíba (Borborema), Piauí (Southeastern Piauí) and Maranhão (Southern Maranhão). In Silva (2008Silva ( -2009, this can be explained by the municipalities that compose the plaster complexin Chapada do Araripe, where the consumption of firewood reaches 30,000 m³ per month, resulting in deforestation of approximately 25 ha/day. The growing demand for firewood by the plaster complex justifies the tendency to use firewood because of its low cost. The use of firewood in the calcination process in the plaster pole of Araripe reduces the cost by approximately 80.44%. Silva (2008Silva ( -2009 showed the use of native firewood an excellent opportunity cost, which must be practiced in a sustainable manner, as opposed to the substitution of other energy sources, for example, natural gas, electricity, etc. According Table 1, in 1994, the largest GVP/km 2 of firewood in Northeast Brazil were in mesoregions of the States of Ceará (Metropolitan Fortaleza, Northern Maranhão) and Rio Grande do Norte (Center Rio Grande do Norte, Western Rio Grande do Norte). In 2013, they were in the mesoregions of the Spatial convergence of the gross...

States of Ceará (Southern Ceará), Pernambuco (Sertão Pernambucano), Rio Grande do Norte (Western Rio
Grande do Norte) and Bahia (Center Northern Bahia). Silveira (2007) showed that these regions are related to the production of ceramics, given that, together with Piauí and Maranhão, they stand out as ceramic producers in the Northeast.
The GVP/km 2 retractions of native firewood from the Northeast are associated with its exacerbated consumption, performed during previous periods, as

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energy source for ceramics, lime kilns, cheese factories, bakeries, flour mills, brick kilns, coal plants, manufacturing units of homemade cookies, confectioneries, stills, mills, mining, roasting industries, textile industries, margarine and soap industries, etc. Thus, there was an uncontrolled use of native vegetation due to the lack of a sustainable management plan for rural establishments and environmental agencies oversight, generating problems of market equilibrium; Besides favoring the phenomenon of desertification in the Brazilian semiarid biome (Riegelhaupt and Pareyn, 2010;Medeiros et al., 2012a,b) The growth of GVP/km 2 of native wood in northeastern Brazilian mesoregions, mainly regarding the Sertão in Pernambuco, is related to the Local Productive Arrangement (LPA) of the Polo Gesseiro do Araripe, which corresponds to 94% of the national production of plaster. In 2008, the plaster production was approximately 4.2 million tons, which demanded approximately 2.94 million stere meters (stm) of firewood. Together with other productive sectors, the demand for firewood as an energy source exceeded 4 million stm (Silva, 2008(Silva, -2009).
These poles of development with their respective LPA, linked by the demand for native wood, contribute to reduce the inequalities of wood production according to their availability of forest exploration.
For the mesoregions of the State of Sergipe, the drop in the annual average growth of the GVP/km 2 of firewood can be explained by the absence of plantations of forest species with rapid growth and lack of licensing projects at environmental agencies for management of the caatinga. In addition, the demand for firewood, mainly from the ceramics sector, promotes an imbalance between supply and demand of this resource in the State of Sergipe (Aragão et al., 2008).

Convergence of the gross value of production of firewood
According Table 2 and equation 6, it was observed that the coefficient of the constant, as well as the independent variable ln (GVP 1994 /km²), presented values with negative signs. The p-values of the independent variable were significant at 5%. y = -1,5712 -0,4543(GVP 1994 /km 2 ) +  Despite the observation of divergence in a large number of the mesoregions, the negative sign of the independent variable indicates absolute convergence. Some mesoregions with low values of GVP/km 2 of firewood are growing at rates higher than mesoregions with higher GVPs/km 2 . The global convergence of the GVP/km 2 of firewood is associated with the availability of vegetation, the intensification of forest exploitation and the increase of agricultural and urban expansion. The mesoregions with the highest values of GVP/km 2 of firewood were highly explored, reducing the availability of these forest resources and decreasing firewood production. With the development of sustainable management practices for the forest in the Caatinga, mesoregions in the states of Pernambuco, Paraíba and Piauí were found promising for firewood production. Some municipalities in these mesoregions present a strong demand for firewood.
This sustainable production of firewood in the semiarid region will attenuate the inequalities of the regional production that infers in the convergence of production, according to the model presented (Table 2 and equation 6). The public policy guidelines have been providing affirmative actions for the development of sectors that use firewood with energy source. One of those is the program to combat desertification, linked to the Ministry of Environment, which uses strategies for the sustainable use of biodiversity of the caatinga through. One example is the Sustainable Industrial Production Center (CEPIS), which focuses on optimizing processes, energy efficiency and promoting economic and environmental sustainability for industries in the Northeast region, making it easier to enter the world market. They train, mainly, ceramic companies and rural proprietors to the economic efficiency of the forest resources through the management of industrial processes and the plans of forest management in the caatinga.
The residual test for the model (Residual P-value) indicated the presence of spatial autocorrelation (Table 2). Therefore, the GVP/km 2 of firewood of a certain mesoregion is associated with others mesoregion(s). The spatial dependence observed for the GVP/km 2 of firewood is connected to the differences of availability of the vegetation among the mesoregions. The politicaladministrative geographical boundaries are different from the native vegetation areas, and the forest exploration of an area may end up being recorded in another area, which creates measurement errors. This result suggests that the classic linear regression model is not appropriate for econometric estimations, which demand models with spatial correlations.
In this context, adopted public policies can produce spatial overflow effects on wood production, not only in the target area of the policy itself, but also in its neighborhood. This shows the relevance of estimation strategies that consider the spatial correction of the model.
The Moran's I test by the Baumont (2004) criterion showed that the highest value came from the rook contiguity matrix (2.7617) and queen type (2.7303), respectively. Thus, for the estimation strategies of the spatial models, these two matrices were used.
According to Table 3, the SAR model, considering the queen weights matrix, it was verified that both the coefficient of the constant and of the independent variable ln(GVP 1994 /km²) had negative signs and statistically significant at 5%. The result of the explanatory variable indicates that mesoregions of the Brazilian northeast with lower GVP/km 2 of firewood are growing at higher rates than the mesoregions with higher GVP/ km 2 . In other words, there is a tendency for convergence GVP/km 2 of firewood.
The SAR model solved the spatial dependence problem, since the value obtained for the residual test (residual p-value) was not significant for rook and queen spatial weight matrices. The coefficient of the explanatory variable was negative and statistically significant. This indicates the occurrence of convergence GVP/km 2 of firewood in the mesoregions of Northeast Brazil.
In the SEM model, considering the queen matrix, the values of the coefficients of the constant and ln(GVP 1994 /km²) variables were -1.610105 and -0.4610661, respectively and were statistically significant. Compared to the SAR model, the SEM model also exhibited convergence. The p-value for the variables was significant at 5%: constant (0.00000) and ln (GVP 1994 )(0.00356). The residual p-value for the SEM model did not indicate statistical significance for the spatial dependence and was higher (0.313000) than the SAR model of the queen matrix. The AIC value (121.065) was lower than that observed in the SAR (122.774) model; therefore, the SEM model was observed to be better than the SAR model.
The SEM model estimated for the contiguity matrix of type rook converged with the following coefficients for the variables: constant (-1.649592) and ln (GVP 1994 / km²) (-0.4910877). The p-values of the constant and dependent variables indicated statistical significance at 5%: 0.00000 and 0.00177, respectively.

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The strategy used to estimate spatial models solved the problem of spatial dependence because the value obtained in the residual test (residual p-value) was not significant for the presence of spatial autocorrelation. Despite the SAR model (considering the rook matrix) also solving the spatial dependence problem, the SEM model exhibited a higher residual p-value (0.302). Also noteworthy is that the value of the AIC (120.893) was smaller than that verified by the SAR model (122.932). Thus, the SEM model is better than the SAR model.

5.CONCLUSION
From the analyses performed, the following conclusions were determined: -The mesoregions of the Brazilian Northeast had an average fall of 3.94% a.a. of the (GVP / km 2 )of native firewood, for the period 1994 to 2013. The main mesoregions of the Northeast with the highest average annual growth of firewood and (GVP / Km 2 ) were: Southern Maranhão, Southwestern Piauí, Borborema, São Francisco in Pernambuco and Sertão in Pernambuco; -Among the matrices analyzed, queen and rook showed higher values for Moran's I Test, and the SAR and SEM models solved the problem of spatial dependence. According to AIC the SEM Model was better; -This study showed the importance of spatial involvement in the econometric models of the effects of space overflows, that is, by overlapping information from the GVP and in the development of public policies that positively affect the neighborhood; -The lack of information or non-existence of the firewood VBP in the municipalities of the Brazilian Northeast impairs the accuracy of the results obtained, not providing elements for a better orientation in public policies; -The limitation of this study (absolute convergence) is to use the data itself to explain convergence. For future work, other variables and methods should be used to consider regional differences; -The research should be continued through the methodology of conditional convergence, cross section data and panel data. These methods can also consider and correct spatial heterogeneity due to differences in geographic units in order to obtain more efficient results.