Ecological Economics 84 (2012) 23–36

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Ecological Economics

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Analysis

The dynamics of land-use in Brazilian Amazon

Mário Jorge Mendonça a, Paulo R.A. Loureiro b,⁎, Adolfo Sachsida a

a IPEA – Instituto de Pesquisa Econômica Aplicada, Brazilb University of Brasilia (UnB), Brazil

⁎ Corresponding author.E-mail addresses: mario.mendonca@ipea.gov.br (M.J

pauloloureiro@unb.br (P.R.A. Loureiro), sachsida@hotm

0921-8009/$ – see front matter © 2012 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.ecolecon.2012.08.014

a b s t r a c t

a r t i c l e i n f o

Article history:Received 11 September 2011Received in revised form 29 May 2012Accepted 21 August 2012Available online 15 October 2012

JEL classification:Q24Q34Q56C33C38

Keywords:Brazilian AmazonVector autoregressivePanel dataSpatial autocorrelationImpulse response functionsVariance Decomposition

This paper studies the dynamics of land-use in the Brazilian Amazon using a structural vector autoregressive(SVAR)model. A fixed effect panel data specification is used to control for the heterogeneity in the data. Mean-while, spatial autocorrelation is also diagnosed by a statistical methodology that allows us to split themodel insubsamples (clusters) of more homogenous municipalities. The clustering analysis shows that there are threeclusters whose land-use patterns are strongly different in an economical point of view. The first cluster iden-tifies municipalities dedicated to logging, natural resources exploitation and slash-and-burn cultures; the sec-ond cluster shows a more diversified agriculture; while the third cluster presents very developed intensiveagriculture municipalities.Another contribution of this article relies on the assessment of contemporaneous causal relation among dis-tinct land-uses areas. This new approach allows us to evaluate the dynamics relations arisen from unexpectedinnovations in the process of soil occupation. The impulse response functions (IRF) and the forecast errorvariance decompositions (FEVD) generate the following results: (1) in the opposition direction of previousstudies, we find that the demand for cropping does not require to clear new areas of forest.; (2) contraryto previous studies we do not find indication that cattle ranching is the primary driver of deforestation;(3) the impact of a shock of pasture land on itself is virtually null at the initial stages, but increases overtime, not requiring to clear extra areas of forest land but rather competing with crop land; (4) it seemsthat if not for all the Amazon Basin, at least in one cluster, cattle ranching and cropping could be competitiveactivities; and (5) we find out that in the long run pasture innovation is responsible for the major percent ofthe forecast error concern all land uses. It probably means that the destiny of distinct categories of land, incluster one, is endogenously determine by activities connected to cattle.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Over the last decades the international community began to payattention to the risks associated with the deforestation in the Brazil-ian Amazon. The impacts on global carbon cycle, regional climatechange and the loss of biodiversity are among the main consequencesof extensive land-use change processes in this region. A correct un-derstanding of the dynamics of land-use in the Brazilian Amazon isan important step toward a better comprehension of this issue.

Several articles addressed the underlying processes which driveland-use changes in the Amazon (Caldas et al., 2010; Ludewigset al., 2009; Vosti et al., 2003); inter alia]. One of the main difficultiesof land-use studies lies in the fact that relevant economic and naturalprocesses are fundamentally defined (and face constraints) at a finegeographic scale. This calls for an effort to bridge methodologicalgaps within a triangle of three approaches: classical economic approach(e.g. Angelsen, 1996), agent-based models (e.g. Soares-Filho et al.,

. Mendonça),ail.com (A. Sachsida).

rights reserved.

2006) and econometric modelling [(Pfaff, 1999; Reis and Blanco,1997; Reis and Guzmán, 1994), inter allia]. Each of these approacheshas advantages and drawbacks relative to their respective researchobjectives. Here,we focus on the econometric approach. Thismethodol-ogy, applied to land-use, has been criticized for its lack of economicconsistency (in comparison to sector or general equilibrium models),but it has definitively the advantage to unveil the most out of existingdata when the primary research issue is to describe land-use dynamicsin the whole Amazonian perimeter, including non-optimal successionof uses from a strict economic standpoint.

Econometric and statistical methods have been used to determinethe dynamics features between succeeding anthropogenic land-use se-quence, like, e.g., cropland, pastures, and regeneration,which constitutea typical pattern of successive land-uses following land clearing. Indeed,in order to seek for deforestation drivers, it is important to know up towhat extent, in past deforestation trends, cropland or pastures uses aremore or less keen to immediately be followed by deforestation. Suchtrends may also differ in different “frontier patterns”, for example theeastern versus southwestern frontiers of the Amazonian Basin.

In one of the first attempts to determine a succession profile forthe whole Amazon, Andersen et al. (2002, 1997) estimated a reduced

24 M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

form vector autoregressive (VAR) model involving the municipalitiesof Brazilian Amazon over the period 1970 through 1995. Concerningthe use of this model to formulate environmental policies someremarks need be stated. A first difficulty lies in the fact that spatialheterogeneity among cross-section units (municipalities) has to betaken into account in order to contemplate the geographic, environ-mental and economic diversity among those different units and theeffect of their mutual interactions. A second difficulty is related tothe fact that land-use census data in the Brazilian Amazon are onlyavailable in a few 5-years time steps.

The environment in the Amazon is subject to very strong dynamicforces that are capable to change the patterns of land-use even in amoderately short time periods of five years, that is, the period inwhich the data are collected. Furthermore, Andersen et al. model isa reduced form VAR and not a structural model, which implies thatthe contemporaneous relationships among distinct land-uses occur-ring during a given time period are not correctly treated. In thiscase, the model fails to adequately estimate the dynamics that derivesfrom contemporaneous causal orders of land-use change. In otherwords, such an approach is not adequate to uncover stylized factson the short-run impacts of the identified exogenous sources in theland-use process. For instance, an exogenous demand shock on agri-cultural product or meat prices generates both a current and sub-sequent effect on soil occupation. In the same way a technologicalshock, or demographic shock, can induce a new unexpected evolutionof land-use. That is, the proper understanding of this kind of “diffu-sion processes” in Amazonian land-occupation can be improved byusing a model that captures the structural relations among differentland-uses.

In this paper we adopt the structural VAR (SVAR) model withpanel data methodology to assess impacts of the identified exogenoussources. We expand and refine previous works to tackle these meth-odological issues. First, we take into account the heterogeneity amongland units using the panel data1 model (Arellano, 2003; Baltagi, 1995;Hsiao, 1995), mixing information concerning variation among indi-vidual units with variations taking place over time. Second, in thestructural VAR literature, the contemporaneous relationship is iden-tified on the basis of prior information supported by a-theoreticalconsiderations. Notwithstanding, another distinctive feature of thisarticle is the employment of Directed Acyclic Graphs (DAGs) to assessthe contemporaneous causal order of the SVAR. Using the selectedorderings to identify the SVAR models we obtained their impulse re-sponse functions (IRFs) and the forecast error variance decomposi-tions (FEVD) (Enders, 1995; Hamilton, 1993). The IR functions allowmodeling the dynamics of distinct land-uses derived from an unex-pected shock on the occupation of the Amazon Basin. Finally, becausethe object of this study is clearly the spatial process that results fromthe complex interplay of many phenomena occurring in a muchextended spatial domain, it is obviously a spatial phenomenon andwe may expect spatial autocorrelation to be present in the data. Themethodology developed here aims to diagnose the severity of thisproblem. Then, in a second step, we can re-estimate the model onsubsamples of more homogenous groups of municipalities. Moreover,this methodology allows us to propose a comprehensive interpreta-tion of the meaning of the clusters in an economic point of view.

The article is organized as follows. Besides this introduction,Section 2 presents the methodology used to analysis the dynamicsof land-use in the Brazilian Amazon. The dataset is described inSection 3. The econometric results are presented in Sections 4 and 5.In Section 4 we present many partial, but important results derivedfrom estimation, spatial analysis and the identification procedure

1 Important sources of variation may be left out if the data is only pooled in a single(temporal or spatial) dimension, and more precise parameter estimates can beobtained in panel approaches that explore the variability present in the data bothacross counties and within counties over time.

undertaken by our methodology. In Section 5 we present the cluster-ing, and the Impulse Response Functions. The concluding remarksare stated in Section 6.

2. Methodology

2.1. Overview

The need for a specific methodology to deal with the contempora-neous relationship existing among distinct land-uses was soon per-ceived by many authors. For example, Aguiar et al. (2007) exploredthe heterogeneous pattern of human occupation in Brazilian Amazonto run spatial regression models. They divide the sample in fourpatitions: the whole Amazon; the Densely Populated Arch (southernand eastern parts of the Amazon); Central Amazon; and OccidentalAmazon. In the same way, Aldrich et al. (2006) share the sampleaccording to the following (1) the land-use dynamics of smallholderhouseholds, (2) the formation of pasture by large-scale ranchers,and (3) structural processes of land aggregation by ranchers. Thesame rationality applies to the work of Morana et al. (2000) whichexamines the role of soil fertility and land-use history on the ratesof forest successional regrowth in five regions of the Amazon Basin:Bragantina Region, Tomé Açú Region, Altamira Region, and MarajóRegion.

Andersen et al. (1997, 2002) and Weinhold (1999) estimated amodel of land-use using a vector autoregressive (VAR) specificationon the municipalities of Brazilian Amazon. This model is given bythe system of Eq. (1):2

cropit ¼ α1Dclearit þ α2cropit−1 þ α3pastureit−1 þ α4f allowit−1 þ ε1itpastureit ¼ β1Dclearit þ β2cropit−1 þ β3pastureit−1 þ β4f allowit−1 þ ε2itf allowit ¼ γ1Dclearit þ γ2cropit−1 þ γ3pastureit−1 þ γ4f allowit−1 þ ε3it

ð1Þ

The indexes i and tare associated, respectively, to each municipal-ity and each time period. Our point here is to reformulate this modelin order to contemplate some interesting issues about land-use in theBrazilian Amazon. The first issue is how to identify the contempora-neous causal order underlying the land-use process. Any model thatdoes not take this point into account is inappropriate in a policy per-spective concerning land-use in the Amazon. The second issue is thatequation system (1) does not deal explicitly with the heterogeneity inclimate, soil quality, etc among the municipalities of the BrazilianAmazon. As a third issue, we question the possibility to analyze ade-quately deforestation in this dynamic framework. Finally, consideringthat the land-use change is a spatial phenomenon the treatment ofspatial autocorrelation in the data is an open issue.

In this paper, these questions are tackled in the following way. Thetwo first problems are treated simultaneously using an econometricmodel that contemplates spatial heterogeneity among countiesand contemporaneous causal order in the same framework. This isperformed in a structural vector autoregressive (SVAR) with paneldata specification. In order to model deforestation we include to sys-tem (1) an extra endogenous variable associated explicitly to defores-tation and hereafter designated by forest.3 Finally, considering thedifficulty to incorporate directly spatial autocorrelation in a SVARmodel with a panel structure, we chose a more progressive routewhere in a first step we carefully study the spatial correlation in theresiduals after a first estimation step. Indeed, the literature either im-plements SVAR panel models (Canova and Ciccarelli, 2009) or spatial

2 Here clearit=cropit+pastureit+ fallowit and Dclearit=clearit clearit1.3 This variable is associated to natural land and considers both natural forest and

natural pasture. More comments about the variables used in this research appear inSection 4.

7 The matrix A0 cannot have, together, a number of free parameters bigger than thenumber of free parameters in the symmetric matrix Σ. If n is the number of endoge-nous variables of the model then, to satisfy the order condition for identification ofA0, it is necessary that the number of free parameters to be estimated in A0be no biggerthan n(n−1)/2. When n is smaller than n(n−1)/2 the model is over-identified. Thereexists no simple general condition for local identification of the parameters of A. How-ever, as has been shown by Rothenberg (1971), a necessary and sufficient condition forlocal identification of any regular point in Rn is that the determinant of the informationmatrix be different from zero. In practice, evaluations of the determinant of the infor-mation matrix at some points, randomly chosen in the parameter space, is enough toestablish the identification of a model.

8 Demiralp and Hoover (2003) evaluate the PC algorithm employed by TETRAD in a

25M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

SVAR models (Di Giacinto, 2003). The direct estimation of the modelwith a spatial component would require further theoretical develop-ments. Thus we rely on spatial autocorrelation diagnosis tests andpropose to split the sample into homogeneous sub-samples forre-estimation with the idea to lower spatial autocorrelation.

2.2. VAR analysis: Reduced x Structural Form and Identification

Considering that natural forest can be seen as another category ofland-use, the endogenous variables of our model can be representedby the following vector (y1it, y2it, y3it, y4it)=(cropit, pastureit, fallowit,forestit). Under this notation we propose to use the following modelto formalize the dynamics of land-use in Brazilian Amazon:

1 a12 a13 a14a21 1 a23 a24a31 a32 1 a34a41 a42 a43 1

0BB@1CCA

y1ity2ity3ity4it

0BB@1CCA

¼c1c2c3c4

0BB@1CCAþ

b11 b12 b13 b14b21 b22 b23 b24b31 b32 b33 b34b41 b42 b43 b44

0BB@1CCA

y1it−1y2it−1y3it−1y4i−1t

0BB@1CCAþ

ε1itε2itε3itε4it

0BB@1CCA

ð2Þ

The spatial heterogeneity present in the data of can be accountedfor using panel data methods to estimate the model. According to thepanel data analysis literature (Baltagi, 1995; Hsiao, 1995), for eachequation j the disturbance εjit for i=1, …, N, t=1, …, T and j=1, …, J4

in Eq. (2) can be broken down into two stochastic components, suchthat, εjit=αji+ηjit. Here αji is a stochastic term specific to theobservations and denoted the fixed effect. The term αji is introduced tomodel the spatial heterogeneity likely to be present among themunicipalities. The term ηjit is the noise with expected value equal tozero and variance E η2jit

� �¼ σ jη

2.Taking Yt=(y1it, y2it, y3it, y4it)′, Yt−1=(y1it−1, y2it−1, y3it−1, y4it−1)′

and εt=(ε1it, ε2it, ε3it, ε4it)′ system (2) can be rewritten in matrix form:

A0Yt ¼ cþ A1Yt−1 þ εt ð3Þ

System (3) is called the structural vector autoregressive5 (SVAR)where Yt=(y1it, y2it, y3it, y4it)′ is the vector of endogenous variables.If we assume that A0 is invertible then Eq. (3) has a reduced formVAR expression given by:

Yt ¼ bþ B1Yt−1 þ ut ð4Þ

with u~N(0,Σ) where u is the reduced form of disturbance covariancematrix and it is also assumed that ε~(0,Ω), with Ω a diagonal matrix.The relationship between structural form and reduced form is based onthe following identities, providing A0 is invertible, b=A0

−1c,B1=A0−1A1,

ut=A0−1εt and:

Σ ¼ A−10 E εtε

;tð Þ A−1

0 Þ′ ¼ A−10 Ω A−1

0 Þ′��

ð5Þ

Note that this representation does not allow the identification ofthe effects of exogenous independent shocks onto the variables;since reduced form residuals are contemporaneously correlated (theΣ matrix is not diagonal).6 That is, the reduced form residuals utcanbe interpreted as the result of linear combinations of exogenousshocks that are not contemporaneously (in the same instant oftime) correlated. In evaluations of the model (and economic policies)

4 In our case it is clear that J=4.5 For a concise reference on SVAR see Hamilton (1993). Enders (1995) provides a

more intuitive treatment.6 These shocks are primitive and exogenous forces, with no common causes, that af-

fect the variables of the model.

it only makes sense to measure exogenous independent shocks.Therefore, it is necessary to present the model in another formwhere the residuals are not contemporaneously correlated.

Thus, without additional restrictions on A0 we cannot recover thestructural form from the reduced form because Σ does not haveenough estimated coefficients to identify an unrestricted A0 matrix.Therefore, we need to set up restrictions in order to identify and esti-mate A0.7 This procedure is named identification. It is possible to esti-mate the reduced form parametersb, B1 and Σ consistently, but exceptfor forecasting Yt given Yt−1, these matrices are not the parameters ofinterest.

Spirtes et al. (1993, 2000) [hereafter SGS] and Pearl and Verma(1991) claimed that it is possible to make causal inferences basedon associations observed in non-experimental data without previousknowledge. These restrictions follow from directed acyclic graphs(DAGs) estimated by the TETRAD software developed by SGS usingas input the covariance matrix of the reduced form disturbances.Moreover, if the causal relations can be represented by DAGs,SGS have shown that under some weak conditions – the MarkovCondition and distribution of random variables “faithful” to the causalgraph – there exist methods for identification of causal relations thatare asymptotically (in sample size) correct.8 The results of SGS arediscussed in several articles.9 In other words, this methodology en-ables us to “read” from the data the contemporaneous relationshipsexisting among distinct land-uses in the Amazon.

2.3. Spatial Autocorrelation

In order to assess spatial autocorrelation directly in system (3)some new elements must be introduced in our analysis. A standardchoice is to include in the mean process a spatial autoregressive com-ponent that takes the spatial locations into account. This can be doneby the use of a contiguity or neighborhood matrix W=(wij) with wij

representing the neighborhood between the sites i and j, such thatwij≠0 if the sites i and j are neighbors, and wij=0 otherwise. Thisspatial weight matrix is a square matrix representing the spatial con-text. It encodes the neighborhood relationship among the spatialunits. The literature on this subject is vast, we shall only retain herethat the neighborhood relationships chosen by the analyst maychange the results.10 In this sense Eq. (3) may be rewritten in the fol-lowing way:

A0Yt ¼ cþΦW1Yt þ A1Yt−1 þ α þ ηtηt ¼ ΨW2ηt þ υt

ð6Þ

where Φ=(ϕij) and Ψ=(ψij) are matrices and υt~(0,I).

Monte Carlo study and conclude that it is an effective tool for the selection the contem-poraneous causal order of SVARs.

9 Swanson and Granger (1997) were the first to apply graphical models to identifycontemporaneous causal order of a SVAR, although they restrict the admissible struc-tures to causal chains. Bessler and Lee (2002) use error correction and DAGs to studyboth lagged and contemporaneous relations in late 19th and early 20th century U.S.data.10 See Anselin et al. (1988) for a detailed discussion.

26 M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

In this study we assume that Φ=0 which means that we focusour attention in random spatial effect or spatial correlation inerrors. The development of a spatial SVAR panel data model inEq. (6) is left for further research. We implement here the spatialanalysis as a non stationarity and we propose to split the sampleto estimate separate models. In doing so we expect to capture theland-use dynamics in homogeneous areas. The spatial autocorrela-tion analysis is conducted on the mean residuals of the model, thatis, the arithmetic mean of the reduced form VAR model residuals,11

because we are mainly interested in the splitting of the sampleover the whole period.

The methodology is implemented in four steps. First, spatial auto-correlation in the mean residuals of the model is tested by the Moranscatterplot (Anselin, 1988). We check two distinct contiguity struc-tures (see below) to assess the stability of the results. That is, if theresults are coherent for those different neighborhood structures weassume enough confidence to proceed. Second, the residuals are spa-tially smoothed meaning that current values are replaced by the aver-age of the neighbors conditional on the neighborhood structure.Third, a principal component analysis (PCA) on the smoothed resid-uals is conducted. This method is motivated in Benali and Escoffier(1990) who name it “Local Principal Component Analysis” as a wayto extract the systematic spatial features present in the data by localsmoothing and dimension reduction.12 As a byproduct, this tends toproduce spatially connected clusters which is a desirable propertyof clusters for spatial data. Fourth, from the LPCA results we computeby clustering homogenous areas to split the model for re-estimation.

Because one may have some difficulty to grasp all the differentsteps of the analysis we present a summary of the methodology weused in this paper. It can be described in the following way

a) In the first step we estimate the reduced form VAR for unrestrictedsample;

b) With the residuals of VAR we analyse spatial autocorrelationthroughout themethod described in Section 2.3. Based on this anal-ysis the sub-samples of homogeneous areas (clusters) are selected;

c) Next we re-estimate the VAR on selected sub-samples. In this stepthe structural VAR is recovered using the DAGs method to identifythe contemporaneous causal orders; and

d) Finally, the impulse response functions are computed.

3. Dataset

The main source of the data available for this study comes fromBrazilian National Agriculture Census elaborated by the Brazilian In-stitute for Geography and Statistics (IBGE) which is usually conductedevery five years. Others original data sources used are the Industrialand Commercial Census that were also elaborated by the IBGE forthe same periods. The data were collected for the following years1970, 1975, 1980, 1985 and 1995 at the municipality level. The datawere cleaned, harmonized and merged with data of other sourcesby the Institute for Applied Economic Research (IPEA) managed bythe team of IPEADATA.13 The original database includes data on eco-nomic, demographic, ecological and agriculture variables.

In the Brazilian Amazon Basin a county can be subjected to ongo-ing change in its size mainly during the expansion of the agriculturalfrontier in Amazon. This fact obstructs the comparison betweenperiods at county level. That is why the concept of Minimum Compa-rable Area (MCA) 14 was introduced, which is the smallest stable

11 Formal tests on the whole residuals are left to posterior work.12 Note that in their original paper, these authors develop the dual of this analysiswhich consists in substracting from the original data the average of the neighbors. Thismethod is not discussed here.13 http://www.ipeadata.gov.br.14 For further details about the concept of MCA see Reis et al. (2007).

spatial unity during these five censuses that accommodates thechanging county boundaries over the panel. The aggregation ofcounties in the later census years, in order to match the county areain 1970, is greatest in the more recently populated and sub-dividedregions found in the legal Amazon.

The agricultural censuses group all land into private land and publicland. Private land is stratified into eight categories according to agricul-tural use. These are (i) annual crops, (ii) perennial crops, (iii) plantedforest, (iv) planted pasture, (v) short fallow and (vi) long falloware classified in cleared land, while (vii) natural forest and natural pas-ture are considered non-cleared land. A small category of private non-usable land (rivers, mountains, etc.) is also considered non-clearedland. Finally, all land that is not claimed by anyone is considered publicland and by definition non-cleared.

Based on these definitions the dependent variables used in ourland-use model fall into one of the following four categories: cropland(crop), pasture (pasture), fallow (fallow) and natural land (forest).Cropland covers annual crops, perennial crops and planted forest.Pasture is planted pasture only. Fallow land includes short fallow,long fallow and non-usable land like roads, dams, etc. Natural landconsiders natural forest and natural pasture.

4. Econometric Results

4.1. Regression Analysis

We propose in this section a consistent method to estimate the re-duced form VAR with panel data (4). Before derivation of the estima-tor, we must introduce notations to accommodate the data sample.The observations related to each equation j can be represented inthe following way. For j=1, …, J, yj=(yj11, …, yj1T, …, yjN1, …, yjNT)′where yj is aNT×1 vector of dependent variables associated to equationj. Let αj=(αj1, …, αjN)′ the N×1 vector of individual effects and NT×1the vector of noise given by ηj=(ηj11, …, ηj1T, …, ηjN1, …, ηjNT)′. Weassume that individual effects are fixed. In this sense the individualeffect can be included into the set of parameters. Thus the error covari-ance matrix is defined so that E εjε′j

� � ¼ Ωjj ¼ σ jη2INT .

Some additional notations is needed in order to write the data

into a compact system of equations. Then let y ¼ y′1;…; y′j;…; y′JÞ′�

be a JTN×1 vector of the endogenous variables, Z is the JTN× JMmatrix of the lagged variables such that:

Z ¼ IM⊗X ¼X 0 … 00 X … 0… … … 00 0 … X

0BB@1CCA

where ⊗ is the Kronecker product. Note that in the standard VAR,each equation j has the same set X of explanatory variables, and theJ equations of the reduced form VAR (Eq. (3)) can be written:15

y ¼ Zβ þ η̃ ð7Þ

whereβ=(β1,…,βJ)′ is the vector of parameterswhileβj=(β1j,…,βMj)′

is the set of parameters of equation j and η̃ ¼ η̃1;…;η̃J� �

′is the JTN×1

vector of stochastic disturbances. The set of equations in Eq. (7) can beseen as seemingly unrelated regressions (SUR) system. In this way, onecan estimate each equation separately. Particularly, here this model is

15 The tilde is used over the disturbance term to indicate that it is not a primitiveshock. In this notation the order between variables and parameters was changed re-garding the notation used in (3). It was done to ease the calculus and does affect theresult.

27M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

estimated by GMM (Arellano, 2003; Arellano and Bond, 1991; Blundelland Bond, 2002).16

4.2. Spatial Analysis

4.2.1. Autocorrelation testsThe residuals of the model estimated in the preceding section are

analyzed as follows. First, the mean residuals over the all periods arecomputed. Second, these mean residuals are further centered andstandardized. In short, the residuals are transformed into:

�esi ¼�ei−��e i

σ �ei

ð8Þ

with “s” standing for “standardized.” This transformation is per-formed on each of the four equations of the SVAR, that is residualsof the crop, pasture, fallow and forest equations, in that order. Inother words, the present analysis does not use the NJ-K observationsof the estimated model but the mean of the residual vector on the Nspatial units: the 257 AMCs of the Amazon Basin.

4.2.2. Spatial weightsThe spatial weight matrix is the square N by Nmatrix representing

the spatial context. In this context we intend to test several neighbor-hood schemes to check the stability of our computations. Note that inthe literature it is generally admitted that the analyst may test severalneighborhood matrices and retain the most stable or meaningfulresults. This is why we use two common neighborhood structuresto compute our tests.

The most common way to introduce spatial weights is the conti-guity matrix, which is defined by the presence of a common frontierbetween two spatial units. We have thenwij=1 if i and j share a com-mon border, zero if not. The second form of neighborhood retainedhere is the k-nearest neighbors matrix, (with k=4 and k=8). Oneeasily sees that contiguity is a symmetric relation, but not nearestneighbors. Consequently, the contiguity matrix is symmetric but notthe k-nearest neighbors matrix. The row sums are the degrees ofthe incidence matrix of the graph associated to the neighborhood re-lation; in the contiguity case, the degree is variable but in thek-nearest neighbors case it is constant and equal to k. Symmetry isa desirable property in spatial analysis but generally it is lost via nor-malization. Effectively, it is often more practical to standardize theneighborhood matrices, and this is done by dividing each row bythe degree, that is, the number of neighbors.

4.2.3. Moran testThe Moran spatial autocorrelation coefficient is defined as the

ratio of the local autocovariances to the total variance of the series:

I ¼ nS

� � ∑wij xi−�xð Þ xj−�x� �

xi−�xð Þ2

0@ 1A ð9Þ

In other words it is the ratio of the covariance between neighborsto the variance of the whole series (complete graph): it is the fractionof total variance accounted by spatial neighborhood relationship. Forthe neighbors the normalization constant is S=∑∑ijwi,j, i. e., thetotal number of links in the neighborhood matrix. The computation

16 This formulation, however, forgets the dependence bewteen the variable throughthe error component caused by the non-diagonal form of the error covariance matrix.Although not pursued here it may be possible to improve the efficiency by jointly esti-mating. Optimal joint GMM estimates would take into account the moment conditionsof all the equations (Arellano, 2003-page 120).

and visualization of the statistic can be greatly enhanced by theMoran scatterplot where the Moran I statistic is computed on thestandardized residuals. From Eq. (8), let us call zi=ei

S; given a rowstandardized neighborhood matrix W, then each row sums to one,and as there are exactly N rows, S=n, thus the first term of Eq. (8)is equal to one, to give in matrix form:

I ¼tzWztzz

!ð10Þ

Then Moran I statistic can be easily expressed as a regression coef-ficient, as one can verify that if we pose: y=Wz, and noting that thedenominator of (10) may be written as (tzz)−1, we obtain:

I ¼ tzz� �−1tzy ð11Þ

This offers an easy way to compute Moran I, which is simply theslope coefficient of the regression Eq. (11) on the variable Wz, thatis, one simply regresses y=Wz on z without a constant. The depen-dent is the spatially smoothed variable Wz and the independent isthe original (standardized) variable. The standardization allows aclear interpretation of the regression graphs (see below). This phe-nomenon is easily understood in this context as Anselin et al. (2003)puts it: he quotes deforestation studies as an exemplary case for spa-tial autocorrelation left in the residuals of an econometric modelbecause of non observed variables.

4.2.4. Spatial autocorrelation analysisThe spatial correlation coefficients are summed up in Table 1 by

contiguity structure. The computations were performed as explainedin Section 2.5, Eqs. (3) and (4). Thus, neighborhood matrices are rowstandardized so that direct estimation by regression is possible. Com-putations where performed in GEODA (Anselin et al., 2006) andGRETL for comparison purposes and also because of a minor technicalproblem.17

Spatial autocorrelation is present and significant for most vari-ables. For example, considering the contiguity neighborhood, it islower for the crop equation (~0.07); but quite higher for the threeother variables: forest (~0.27), pasture (~0.30) and fallow (~0.31)which is the highest of all four spatial autocorrelation coefficientscomputed for both software application and neighborhood structure.The magnitudes of these autocorrelation coefficients may seem mod-est, but because they relate to residuals estimates, they are in factrather high. We can expect these to decrease for both neighborhoodstructures (higher order of contiguity and number of near neighbors).

There are slight differences between neighborhood structures, butthe conclusions are convergent between the two software implemen-tations except for the crop residuals which are not significant underthe 4 and 8 nearest neighbors in GRETL. These differences are due tothe different implementations of the permutation tests between thesoftwares. According to GEODA, all neighborhood structures show sig-nificant spatial autocorrelation of the mean residuals for all equationsbut not in the case of GRETL. However, the orders of magnitude of thecomputed coefficients are identical between software implementationsat least up to the second decimal place and often to higher places.

There is thus a relatively good stability of the estimates amongneighborhood structures and softwares, because the magnitude of

17 In the first version of this paper we could not use GEODA to compute the Moran I'sfor the contiguity matrix because GEODA could not built properly the matrix becauseof defects in the shapefile of the Amazon Basin. These has now been corrected andthe full results presented here.

Table 1Moran coefficients by contiguity structure.

Neighborhood matrix Variable GRETL GEODA

Moran I Bootstrapp-value for t

Moran I Bootstrapp-value for t

First order Crop 0.066 0.023⁎⁎ 0.066 0.007⁎⁎⁎

Pasture 0.303 0.000⁎⁎⁎ 0.303 0.002⁎⁎⁎

Fallow 0.306 0.000⁎⁎⁎ 0.307 0.001⁎⁎⁎

Forest 0.266 0.000⁎⁎⁎ 0.266 0.003⁎⁎⁎

4NN Crop 0.035 0.153 0.035 0.020⁎⁎

Pasture 0.124 0.000⁎⁎⁎ 0.124 0.004⁎⁎⁎

Fallow 0.239 0.000⁎⁎⁎ 0.239 0.001⁎⁎⁎

Forest 0.123 0.000⁎⁎⁎ 0.123 0.006⁎⁎⁎

8NN Crop 0.026 0.113 0.026 0.030⁎⁎

Pasture 0.102 0.000⁎⁎⁎ 0.102 0.001⁎⁎⁎

Fallow 0.239 0.000⁎⁎⁎ 0.239 0.001⁎⁎⁎

Forest 0.063 0.003⁎⁎⁎ 0.063 0.014⁎⁎

All tests performed with 999 permutations.⁎⁎ Significant at 5%.

⁎⁎⁎ Significant at 1% or less.

28 M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

the computed coefficients leads to a similar ordering of spatial auto-correlation present in the residuals. Both for contiguity, and nearestneighbors, the crop is the lowest followed by forest, then pastureand fallow which is always highest.

The magnitude of the autocorrelation coefficients for the nearestneighbors matrices decreases slowly for all variables except for fallow.This may be explained by the increasing smoothing effect induced bythe growing number of neighbors which lower the difference to theaverage at each location and thus the Moran I. However, this effectdoes not seem to affect the fallow equation mean residuals. For thisvariable, it appears that spatial autocorrelation may be both strongerthan for the other variables (at a given distance or contiguity order)but also that it may be felt up farther away.18

To sum up, there is significant autocorrelation for all residuals,with fairly robust conclusions. The fallow equation residuals showthe highest and strongest spatial autocorrelation among the fourseries, this may indicate that the SVAR specification may lack ex-planatory power for this variable, but seem better for the othersvariables.

4.2.5. Clustering analysisThis step allows splitting the panel of MCAs in the Amazon Basin

as a way to reduce spatial autocorrelation that may be present inthe residuals. The same spatially smoothed data are used to performthe PCA on the 4 vectors of spatially smoothed residuals. The smoothedmean residuals are defined by:

�es�i ¼ 1ki∑iej W�esi ð11Þ

which is technically the same as variable y=Wz above. That is, thestared (spatially smoothed) residuals are the average of the neighbor-ing residuals. The computations are done on the non symmetrick-nearest neighbors, with k=4.8 and for the order one contiguity ma-trix. The results for k=8 do not differ from those relative to k=4, sothey are not presented here at this stage. The reader shall note thatthe splitted samples are exactly the same for both these orders ofneighborhood.

From the 4 vectors, the first two principal components explain85 % of the variability in the data. Now on we apply the k-means algo-rithm on the two first principal components. Three clusters are found

18 We note this fact for further investigation.

to be optimal. The clusters are depicted on Map 1 below. Table 3 inAppendix 3 gives the bootstrapped Moran I computations for clusterI and II of this map. Here cluster I is composed of 156 municipalitiesand cluster II 75 municipalities. The 26 municipalities cluster is notincluded while it could not be estimated because of an insufficientnumber of degrees of freedom.

The biggest clusters (156 and 75 municipalities) encompassesmost of the Amazon basin where the average spatially smoothedresiduals tend to be low for crop and high for fallow and the reversefor the second cluster. Thus we have two compact clusters with fewisolated sites. The clustering appears satisfactory on the spatial con-nectedness point of view. However, the third cluster has only a fewmunicipalities (26) and this may pose a problem in re-estimation ofthe full model on this cluster. At least, it is reassuring to find compactclusters of contiguous municipalities. As noted above, the clusteringwith 8-neighbors lead to the same partition. This is not surprisingas in this case the smoothing is stronger because each residual isreplaced by the mean of its 8 nearest neighbors instead of 4. Thesame remarks apply to the results of the PCA: it does not changemuch between the two smoothings.

The clustering analysis on the residuals of panel VAR identifiesthree homogeneous areas for the counties of Brazilian Amazon. Thisfinding points out the existence of specific and different patternsof land-use dynamics for different “frontiers” (Smith et al., 1997).For instance, some authors advocate that because it precedes othersactivities slash-and-burn agriculture is identified as the cause ofdeforestation even though it can be also considered as an instrumentfor cattle rising. This practice has commonly been used by smallfarmers, as they burn a piece of forest and grow annual crop forabout three years until the soil becomes useless. In contrast toslash-and-burn farming in forest areas, crop production in “cerrado”is dominated by technically advanced large-scale agriculture orientedtowards soybean production, and is also an obvious cause of defores-tation in the state of Mato Grosso for instance. Fearnside (2006) cor-roborates this view pointing out that the drivers are by no means thesame for all the sites of the Amazon.

South-western Amazonian Basin, the two factors (bovine meatproduction and crop production) may coincide, while in the easternpart of the Amazonian Basin, the pasture factormight be predominant.Apart from ideological and theoretical divergences, the intellectualbattle about the process behind land-use dynamics in the Amazon isnot supported by empirical evidence. In fact there is no clear explana-tion about the actors and forces that drive land-use in Brazilian Ama-zon. This why we restrict the use of prior theoretical restrictions inorder to identify the matrix of contemporaneous relationship A0.

4.3. Identification

4.3.1. The identification problemStructural inference and policy analysis employing VAR model

require differentiating between correlation and causation, an issueknown as “the identification problem.” The practice in the literaturehas been the use of identifying assumptions based on “economictheory” or institutional knowledge to sort out the contemporaneouslinks among the variables in order to allow correlations to be inter-preted causally. Given an exogenous impact on a certain category ofland, it dictates the subsequent constraints by which the mechanismof land-use takes place during the period of five years after this exog-enous shock. In short, it detects how the other categories of land-usereact given a primary impulse on a certain type of land-use. In thispaper it can be associated to the drivers or prime forcers of the soiloccupation in this region.

For example, credit and fiscal subsidies to the agriculture jointlywith the expansion of the road network pushed the agricultural fron-tier in the northwestern part of the Amazon Basin while the coloniza-tion programs aided to fix people in the interior. Strong incentives

Map 1. Clustering on the first two principal components.

29M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

were created to clear land for pasture. In fact, the growth of cattleherds has consistently been cited as one of the primary factors behindthe land clearing in Amazon. Regarding the problem of the identifica-tion this analysis implies that the subsequent effect of an enlargementof the area of pasture has a contemporaneous effect on the otherland-uses, most likely on forest land where new areas are requiredto be opened. Notwithstanding we need to check if it really happen.

4.3.2. The identification using DAGsBased on the results of the spatial autocorrelation analysis we

re-estimate the reduced form VAR using the data related only forthe biggest cluster (156MCAs) becausewe doubt that the other clustershave enough information to warrant the computations of the results.Applying TETRAD at the 0.5% significance level19 on the estimated dis-turbance covariance matrix Σ̂ and assuming that the variables selectedfor the model are causally sufficient,20 we obtain what is known as apattern.21 The pattern is a graphical representation of the set of obser-vationally equivalent DAGs containing the contemporaneous causalordering of the variables.

19 The significance level cannot be interpreted as the probability of type I error for thepattern output, but merely as a parameter of the search. Based on simulation tests withrandom DAGs, SGS suggests setting the significance level at 20% for sample size smallerthan 100; at 10% for sample size between 100 and 300; and at 0.5% (or smaller) forlarger samples. Here we followed their suggestion. However, slight changes in the sig-nificance level can produce large variations in TETRAD's output.20 A set of variables V is said to be causally sufficient if every common cause of anytwo or more variables in V is in V. TETRAD has a bias towards excluding causal relationspresent in the data, to overcome this problem it is suggested that a 20% significancelevel be used.21 A pattern is a partially oriented DAG, where the directed edges represent arrowsthat are common to every member in the class, while the undirected edges are directedone way in some DAGs and another way in others. Undirected edges ( — ) mean thatthere is causality in one of the two directions but not on both, while double orientededges (↔) mean causality on both directions.

The DGAs detected four valid representations of the contempora-neous causal ordering. In accordance with this pattern three of thecontemporaneous causal ordering display causality in one directionwhile one indicates causal ordering exists but it does not allow toknow which one is the true.22 In this case we produced the IRFs ofboth identifications separately. Fortunately we did not note any rel-evant difference between them.23 The relations derived from DGAsenter in matrix A0 as restrictions that will help to identify the con-temporaneous relationships.24 The Fig. 1 shows the matrix A0 identi-fied using the causal ordering obtained from DGAs.25 In this matrixone observes seven identified conditions represented by zeros. Be-cause more the VAR has four variables the matrix A0 requires sixconditions for identification. Hence this matrix is over-identified.26

5. Analysis of empirical results

5.1. An economic Interpretation of the Partition in Three Clusters

Given a partition built by a clustering on the mean residuals ofthe unrestricted VAR model, i.e. the estimates on the whole sampleof 257 Amazon municipalities27 we would like to know the most

22 The DAGs display the following pattern: pastures → crops, fallow → crops, forest →crops and pasture — forest.23 The results can be obtained under request.24 In Appendix Appendix 1 we show how to apply the causal ordering obtained byDGAs to identify matrix A0.25 We assume that pasture affects forest contemporaneous but the reverse is not true.26 See footnote 9.27 The data form a panel consisting in the 257 municipalities of Legal Amazon for thespace domain and 5 dates in the time domain. The dates are separated by about fiveyears which where years of censuses. Let us stress that the partitions where built fromthe mean residuals of the SVAR model estimated on all the panel, thus the partitionsare generated on 257 mean residuals.

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

100

0100

0010

1

A42forest

fallow

past

A14A13A12crops

forestfallowpastcrops

A0

Fig. 1. Causal Relations indicated by DAGs.

30 M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

salient features of the partitions. In this aim, we use the notion of“valeurs-test” proposed in the French school of Exploratory DataAnalysis. A “valeur-test” is the equivalent of a t-stat computed onthe means of the clusters, provided that these variables are exter-nal to the computations Lebart et al. (1995)). It is then a test ofsignificance of the difference of means in the clusters to the meanon the whole sample; the test is done in the context of samplingwithout replacement. In this work we consider a variable mean in acluster to significantly differ from the population mean if thevaleur-test is greater than 2.0 in absolute value. This means that a var-iable for which a “test-score” is greater than 2.0 conveys significantinformation on the feature pertaining to the given variable in thecluster. The usual and natural interpretation of these statisticscarries over: a negative score indicates a significantly inferior meanin the cluster and conversely for a positive value.

We computed different statistics for each separate year of censusand also from all the years. This gives an interesting perspectiveabout the evolution of the clusters characteristics through time: thepartitions are fixed (fixed zoning) but test-scores may vary at differ-ent dates. This would allow to sort out effects that may be presentin the long run (30 years) from effects that are felt differently intime or more from more recent times.

The t-scores on the illustrative attributes are used to describe themost interesting features of the clusters in each of the two partitions.To ease the exposition, the different attributes have been regroupedunder the different topics: Demography, Agricultural Economy, Gen-eral Economy, Education, Infrastructure, Natural Environment andLand-Use. The complete table is reported in Appendix 3. The readeris warned that not all variables may be present for all the years, wereport and comment statistics for separate years on the available vari-ables; note that some attributes are present on all years. For eachpartition a t-score was computed on all the attributes and every clus-ter in the partition. The number of municipalities of each clusteris indicated as a number in parentheses under the cluster number.The t-scores have been computed on a set of 39 variables in thepanel database, on all the years. In those computations, means andstandard errors were computed using total population as a weightingvariable.28

It is interesting to present a brief description of the clusters bytopic and then compare the two partitions and comment thoseresults. In accordance with the table of t-scores in Appendix 3the demographic topic t-scores show that population and con-sequently dwellings are significantly higher than the averagein group 1, lower and group 2, and not significantly differentfrom the average in group 3. Thus, the biggest cluster of 156 mu-nicipalities has a higher population, while the second is signifi-cantly less populated. We shall see below that this is also true

28 More detailed results by year are available from the authors.

for the size of municipalities. For this we would have to computet-scores for the shares of dwellings with sanitation and electriclighting per group.

The agricultural economy profile of t-scores shows that, in clus-ter one, even as we have seen average population is higher thancluster two, agricultural investment is the lowest, while it is stilllower than the average in cluster two and far higher in clusterthree. The same is true for bovine livestock, total irrigated landarea and number of tractors. On the contrary, labor force in the ag-ricultural sector is higher than the average in cluster one, lower incluster two and insignificant in cluster three. The value of woodproduction differs only in cluster two, and the average rentalvalue of land is higher in the municipalities of cluster one, lowerin those of cluster two, and not different from the average in clus-ter three. However, the volume of commercialized wood is themost significantly different from the average in cluster one, witha t-score of +27.31, lowest in cluster two (−8.75), and signif-icantly under the average in cluster 3. However, the averagewood production potential (cubic meters per hectare) is essentiallythe same in clusters one and two and it is far above the average.Thus, it is quite clear that municipalities of cluster one are largelydevoted to logging production, having a higher population andtotal employment in the agricultural sector, while those of clustertwo have a more diversified agriculture that is less reliant on log-ging: these have even a larger than average surface of irrigatedland while being less populated on the average but still retaininga similar logging potential. Finally, the average purchase price oflive beef is significantly higher than average in cluster one, andlower in cluster two.

The general economy profile of the clusters shows significant dif-ferences: higher share of wages in group one, lower in group 2; signif-icantly lower average wages in group one, average in group threeand far higher in group 3; lower industrial wages in group two butnot significantly different from the Amazon mean in groups 1 and 3;Interestingly, a very significantly lower share of government/Bancodo Brasil financing in cluster 1 but both higher in clusters 2 and 3and the lowest SUDAM financing for cluster one, lower than averagein group 2 and of course, significantly higher in group 3. These dif-ferences in economic profile illustrate differences of economicstructures.

Consider now the education and infrastructure profiles. Surpris-ingly, the share of persons with five years of schooling is far abovethe Amazon average in group 1, and significantly lower in group 2;the same is observed with the average number of years of educa-tion in the population. On the paved roads length, cluster oneshows no difference to the average, but significantly less unpavedroads, and both lower for cluster two. There are slight differencesin infrastructure between clusters one and two, and cluster threehas significantly higher level of infrastructure. The contrast is thegreatest between cluster one and three: the average areas of mu-nicipalities is roughly the same in both of them, but infrastructuresare far more developed in cluster three than one, and the leastdeveloped in cluster two, but with respectively far smaller munic-ipalities than the average. It seems now clear the contrast in infra-structure level between group 1 and 2 has its roots in a developmentlag. We have roughly equal municipalities, far more populated thanaverage in cluster one but with much less infrastructure than ingroup 3.

On the natural environment side, the highest carbon and nitrogencontent of the soil, the area deforested is in cluster three (as in the par-tition in two classes), however, in clusters one and two it is still signif-icantly under the average. In other words, cluster three appears as agroup of municipalities where deforestation is largely done, and stillunderway in the first two. The only difference in profile is the impor-tance of water masses in the cluster one (t-score of 11.25 vs. −8.25and −2.87 for group 2 and 3 respectively). This finding mitigates

30 It can be seen in Section 3 the interval of time dimension of the sample is not con-stant. The data were collected for the following years 1970, 1975, 1980, 1985 and 1995.31 The Appendix Appendix 4 shows the graphic of IRFs for time horizon of 75 years.

31M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

our preceding conclusions about infrastructure lag above: in fact, it ispossible that the lack in roads in cluster one is not caused by underde-velopment but rather is explained by a greater reliance on river com-munications.29

In the land-use picture, the surface dedicated to agriculture is thelowest in group 1, then group 2 (roughly twice higher), and far higherin group 3. This is an important finding, because it contrasts the factthat while municipalities in group 2 are by far the smallest relativeto the Amazon Basin, they do not have the smallest areas dedicatedto agriculture, and largely so. This would reinforce the perception ofa specialization of group 1 in logging. But, while in group two, all sur-face are lower than average, in group one, the permanent plowingsurfaces are significantly higher than average: there is obviouslyculture in these municipalities, and let us say it, these are the pioneerfronts and largely dedicated to logging and natural resourcesexploitation.

These remarks finally allow us to describe the groups:

Group 1 the pioneer fronts; dedicated to logging and naturalresources exploitation;

Group 2 the margins; older pioneer fronts that have grown a morediversified agriculture;

Group 3 the oldest, most developed agriculture intensive intechnology.

5.2. Analysis of IRFs for the Biggest Cluster (156 MCAs)

In this section we use the selected causal ordering obtained byDAGs to identify the structural model on the biggest cluster of 156MCA in order to build up the impulse response functions (IRFs)(Enders, 1995; Hamilton, 1993). This procedure allows assessingthe dynamic effect on different types of land-use that derived froman unexpected innovation in a specific land-use. It can be used toevaluate the impacts on areas of pasture, fallow and forest due toan unexpected event on crop land, for instance. The dynamic effectincludes not only the contemporaneous responses but also thefuture effects.

Before to introduce the analysis of IRFs, we would like posesome preliminaries comments. Firstly, an important point refersto the fact that economic analysis can be indirectly performed bymeans of the proper interpretation of the innovation shock. The in-novation shock refers to the response of the model that is not relat-ed to the movement of the endogenous variables. Second, althoughthe IRFs cannot be confused with “drivers” (factors that affect thenet benefits of the various land-use types), the “drivers” whetherthey do exist are implicitly included the IRFs and determine thedynamic of it. As a matter of fact, they can be included as an exog-enous variable if one knows how to identify them. The “transitionmatrix” approach employed focuses strongly on land-use timepaths, even to the point that information is not included on“drivers.” Third, the land-use-following-land-use patterns aredescribed as causal, in the sense that if an exogenous shock wereto promote pasture the estimated transition matrix implies a timepath of implications. For instance, an unexpected expansion ofcredit and subsidies implemented by a government policy aimedat promoting agricultural activities can be seen as an innovationon the variable crop. Unexpected movements of price can be alsoincorporated in this analysis like, for example, a rise in the priceof timber may cause a growth of deforestation. In the same sense,an elevation of the price of meat derived from a demand shockcan be linked in the current context like a shock on pasture land.

29 We have no way to check this hypothesis with the available data; this would re-quire further data on rivers in each municipalities from the IPEA DESMAT dataset.

Fourthly, the interpretation of IRFs must be connected to the eco-nomic environment related to the cluster 1 and not all BrazilianAmazon. Finally, it cannot be discarded the occurrence of structuralbreak, i.e. the parameters of the model the can change over time.For instance, if land being in one use really does very dependablyit can increase the probability of a certain next land use. For exam-ple, inevitable biophysical linkages such as cows compressing soiland thereby limiting crop potential immediately afterward becauseit reduce nutrients. The introduction of new technique that im-proves the productivity of the soil can mitigate the effect of ashock in the land of pasture or crop on the dynamic of land use.These are all examples of inevitable shifts in constraints. In sum-mary, it could be that our model suffers from structural break inlong run, but this kind of caveat concern not only for this modelbut also for the majority of studies that applied this kind of analy-sis. But the problem of structural break cannot be checked andtreated properly because the temporal dimension of our data isvery short (five years).

The IRFs are showed in Fig. 2. This figure must be viewed like amatrix in which each graph represents the effect of a shock of theland-use of column j on the land-use of row i. Again one musthave on mind that our analysis concern the region defined by clus-ter one more related to the pioneer fronts; dedicated to logging,natural resources exploitation and slash-and-burn cultures as weposed above. On the other words, the analysis could not be correctfor the clusters 2 and 3 that we identify by the methodology weapplied in Section 4.2. Another point is that because the time fre-quency of our sample is about five years the time length of inter-val of IRFs is about the same duration.30 Then the time horizon ofthe IRFs is around sixty years.31

We start the analysis of IRFs checking the consequences of ashock on crops. In this case there exists an immediate effect on for-est land. One can still see that there is lag effect on fallow and pas-ture about six periods after. The new demand for croppingrequires to open new areas of forest and maybe due to the poorquality of Amazon's soil, crop land will be transformed in in pastureland only the in long run or left as fallow. It is interesting to noticethat both responses on pasture and fallow use land occur in longterm what is in connection with happens in fact. This processcould also be in accordance to the analysis that appears in Smithet al. (1997) and can be considered a necessary outcome for theslash-and-burn agriculture, a common practice in the Amazon.32

This cluster as it can be seen in Section 4 is associated to a less devel-oped agriculture. Differently, one can figure out a situation in whichthese results is enshrining the net effect of arbitrary time paths ofthe many factors that affect land cover in this region. Perhaps thepast driver time paths led crops to follow pasture while the futuresof these drivers' paths might yield the opposite sequence. In thiscase it is more dependably the case of thinking about profit maximi-zation in land use than to say just that pasture follows forest in longterm. For instance, high slope discourages agriculture. In terms ofmaking room for drivers one can pose that "drivers" vary overtime, e.g. slope differences could privilege different land covers. Tobe honest, we do not think in this way. Remembering that our

As one can be seen the results remain unchanged.32 The cycle of slash-and burn agriculture can be briefly described in the followingway. In the first place, it begins with deforestation targeting the implementation of ag-ricultural activities involving many perennials crops. In the following stage, when thesoil fertility declines, the site is used as pasture land. The cycle finishes when the soilis entirely exhausted and pasture area is converted into fallow land.

Fig. 2. Impulse response functions (horizon: 60 years).

32 M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

analysis is constraint to cluster 1, we think that is more acceptablethat in long run the soil will reduce the productivity for crop andcattle will take place. Then in order to preserve and reduce the fu-ture impacts on the environment conservation policy is necessary.Each policy must be design concern specific site.

We adopt the hypothesis that the “drivers” which determines thedynamic of land use must be specific and associated to each cluster.Therefore, the drivers of cluster are distinct from the other clusters.Based on this proposition and using the results of Section 5.1, it is sen-sible to adopt the hypothesis that logging and natural resourceexploitation are the main drivers for this region.

Differently from the previous studies, in this cluster we do not findstrong evidence that an unexpected positive shock in cattle ranchingoccurs at the expense of deforestation. Checking the last graphic ofsecond column of the Fig. 2, the contemporaneous effect of this inno-vation is positive although subsequently it changes to be negative, butin long run the effect becomes is positive. One must have on mindthat the interpretation of this result must be constraint to cluster 1.This cluster as it can be seen in Section 4 is associated to a less devel-oped agriculture as we already said. In this sense it can be indicatethat the absolute level of the share of output in cattle has been highfor a long time and remains. This is in accordance with the WorldBank's environment policies (for instance, the World Bank Low

Carbon plan) for Brazilian Amazon to have a major emphasis on re-ducing cattle area.

As a matter of fact, it can be seen that the area of forest grows inthe future (Fig. 2, graph at row 4, column 2). As we expected theeffect on the area of fallow in response to the impulse on pastureland occurs fundamentally many periods after the shock (graph atrow 3, column 2). The figure also shows that the impact of a shockon pasture land on itself is almost null initially but augments sub-stantially over time (graph at row 2, column 2); it do not requireextra areas of forest land to clear but rather competes with cropland (compare, graphs at row 1 and 2, column 2). In this sense pas-ture affects crops not only in the current period but also in the longerterm while this long run impact appears considerably stronger thanits contemporaneous counterpart. Our results suggest evidence that,at least in this cluster, if not for all the Amazon Basin, that cattleranching and cropping could be competitive activities.

A very related concept to impulse response is the forecast errorvariance decompositions (FEVD) (Enders, 1995; Hamilton, 1993). Ituses the variance decompositionmethod to break down the varianceof the forecast error of h-step for into components that can be attrib-uted to each innovation of the endogenous variables. In otherwords, the forecast error variance is decomposed into componentsaccounted for by the innovations in the different variables of the

Table 2Forecast error decomposition of the crop/pasture/fallow/forest system.

Proportions of the forecast error variance hperiods ahead accounted by innovations in:

Forecast errorin

Forecast Crop Pasture Fallow Forest

horizon (years) % % % %

Crop 5 100,00 0,00 0,00 0,0010 91.60 1.20 6.95 0.2320 92.11 0.65 7.00 0.2350 64.49 29.07 6.26 0.1675 21.16 73.46 5.33 0.04

Pasture 5 1.32 98.679 0,00 0,0010 11.30 84.46 4.21 0.0320 16.71 78.31 4.94 0.0350 18.62 76.08 5.28 0.0375 18.64 76.05 5.28 0.03

Fallow 5 5.47 2,63 91.90 0.0010 12.77 2.14 84.85 0.2320 14.43 4.64 80.69 0.2350 18.43 62.26 19.61 0.0775 18.63 75.68 5,66 0.03

Forest 5 0.24 0.29 3.16 96.3110 46.71 0.15 11.52 41.6220 50.94 0.17 11.32 37.5750 48.31 7.46 10.78 33.4575 24.15 63.34 6.30 6.21

33M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

system. If a shock on X, εX explains none of the forecast error varianceof Ywe can say that Y sequence is exogenous. In such a circumstance,the Y sequence evolves independently of εX. Differently, if εX shockscould explain certain proportion of the forecast error of Y, so thatthis variable would be partially endogenous. The FEVD of the fourvariables appears in Table 2. The message of this table can be under-stood in this way. For instance, at h=10 years about 91.60% of theforecast error of crop is accounted for by own innovation and about6.95% in fallow innovation.

Looking the results more carefully, one can notice some interest-ing points. As it was expected in applied research using structuralVAR, at the beginning of the horizon a variable accounts almost allits forecast error while smaller percent in long run. In the case ofcrop, the importance of pasture for account the forecast error is grow-ing over time. In the long run the situation change and just 21.16% ofthe forecast error of crop is due to by own innovation and about73.46% is due to innovation in pasture. Fallow and forest innovationdo not display important account to explain forecast error of cropfor all horizon. Considering now pasture, the relevance of crop inno-vation for account the forecast error increases over time reachingaround 20.00% in sixty years. Other point that requires some com-mentary is the evolution of FEDV for forest innovation. Here for theshort horizon, a large percent of forecast error of this variable is ac-count for crop innovation during long horizon. For instance, betweenten and fifty years it remains stable around 50.00%. But the influenceof pasture shock dominates afterwards and, at the end of sixty yearscrop innovation is in charge of 63.34% of the proportion of forecasterror. Finally, one can notice that in the long term pasture innovationis responsible for the major percent of the forecast error concern allvariables. It probably means that the destiny of distinct categories ofland concern in the cluster one is endogenously determine by activi-ties connected to cattle.

Finally, because we assume that logging and natural resourceexploitation are the main drivers in this cluster. Therefore, thepath of urbanization follows from it and not the contrary. In otherwords, logging determines urbanization. Take this viewpoint intoaccount it is more acceptable to imagine that is a “big phenome-non” of longstanding and ongoing urbanization is not the major

problem by itself, instead it comes as a consequence from anotherphenomenon. Because our database is restricted we do not under-take further investigation in this direction. But any public policytargeting to investigate how to preserve environment and futuredevelopment in Brazilian Amazon must take this point intoconsideration.

6. Concluding Remarks

This paper studies the dynamics of land-use in the BrazilianAmazon using a structural vector autoregressive (SVAR) model. Theheterogeneity in the data is controlled by the mean of fixed effectpanel data approach. This method takes into account the specific fea-tures (like geographic, environmental, and economic diversity) pres-ent among the different sites. Considering that the land-use is alsodetermined by the interaction of the counties among themselves,possible spatial autocorrelation in the data must be taken into ac-count. In this scenario, spatial autocorrelation is diagnosed by a statis-tical methodology which split the model in sub-samples of morehomogenous municipalities. After that, we re-estimate the modelinside the more homogeneous subsamples (clusters). In doing so,cluster analysis shows that there are three clusters whose land-usepatterns are strongly different. Furthermore, the illustrative attributesare used to describe the most interesting features in each cluster. Ina general sense, we can infer that cluster 1 identifies the pioneerfronts; dedicated to logging, natural resources exploitation andslash-and-burn cultures. Cluster 2 has grown on a more diversifiedagriculture. And cluster 3 presents most developed, intensive agricul-ture oriented municipalities.

Another distinctive contribution of this article is to assess the con-temporaneous causal order that exist among different land-uses. Thisallows the evaluation of the succession dynamics that derive from un-expected innovations in the process of soil occupation, by means ofimpulse response functions (IRFs). Concerning the IRF analysis, themain findings are the following: (1) in cluster one, cattle ranchingand agriculture are competitive activities; (2) we did not find anyevidence pointing out that cattle ranching is a primary cause of defor-estation; (3) a growth on crop land, due to an unexpected rise on theprice of agricultural products, reduces the area of forest in the longrun; and (4) since we adopt the hypothesis that logging and naturalresource exploitation are the main drivers for cluster one, these activ-ities determines urbanization. Therefore it is more acceptable toimagine that a “big phenomenon” of longstanding and ongoingurbanization is not the major problem by itself, instead it comes asa consequence from another phenomenon. In this way, any publicpolicy targeting to investigate how to preserve environment andfuture development in Brazilian Amazon must take this point intoconsideration.

Appendix 1. DAGS and the Identification of Structural Form VAR

The SGS procedures allow us to establish the conditional inde-pendence relations that are equivalent to determining whose coef-ficients of matrix A0 are equal to zero. The framework developed bySGS does not rule out the possibility of finding alternative sets ofconditional independence relations for a given data set. In thiscase we arrive at a set of matrices A0 that are observationallyequivalent. It may be the case that the found conditional indepen-dence relations are not enough to allow for the identification of thematrices. In this case, additional restrictions are needed in order toidentify the model. Next we show how DAGs can be used to imposerestrictions that allows identification of Structural VARS (SVARs).In the example below we assume that the VAR has four endoge-nous variables.

34 M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

The relationship between reduced form and structural form resid-uals is given by the following equation:

νt ¼ I−A0½ �νt þ εt

where:

νt column vector, with dimension 4x1, with reduced formVAR residuals at period t;

εt column vector, with dimension 4x1, with structural formVAR residual at period t;

A0 full rank matrix with the relationship between the twotypes of residuals.

The above equations form a system of linear equations, whereeach variable (reduced form residual) is a linear function of itsdirect causes and an error term (structural residual), with errorterms independent of each other. If the graph G that representsthe model has no cycles (is a DAG) then the variables are generatedby a Markovian model. Therefore, the model satisfy the propertythat guarantees the compatibility between its distribution func-tion and graph G.33 Because conditional independence implieszero partial correlation, Proposition 2 translates into a graphicaltest for identifying the partial correlations that must vanish in themodel.34 Therefore, Eq. (3) can be structured according to a DAGG, and the partial correlation coefficient ρV1V2.V3 vanishes when-ever the vertices corresponding to the variables in V3 d-separatevertex V1 from vertex V2 in G.

We present below an example of the relationship between a DAG(the graph below), Eq. (3) and the coefficients that are considereddifferent from zero in A0

35:

Fig. A.1.

Robins et al. (2003) [RSSW] use classicalmethods to analyze carefullythe asymptotic properties36 of the SGS methodology. They show that inaddition to being asymptotically consistent, the procedures are

33 For a sketch of the proof see Pearl (2000).34 The partial correlation coefficient of X and Y, controlling for Z is given byρXY :Z ¼ ρXY−ρXZρYZð Þ= 1−ρXZð Þ1=2 1−ρYZð Þ1=2.35 εi is the structural error term of equation i (i=1,2,3,4).36 There are a variety of senses of asymptotic reliability in statistical inference, amongwhich the most commonly discussed classical notions are pointwise consistency anduniform consistency. A pointwise consistent test is guaranteed to avoid incorrect deci-sion if the sample size can be increased indefinitely. However, pointwise consistency isonly a guarantee about what happens in the limit, not at any finite sample size.Pointwise consistency is compatible with there being at each sample size, some valueof the parameter such that the probability of the estimator being far from the true val-ue is high. A stronger form of consistency, uniform consistency, guarantees that it ispossible to bind the decisions' error rates with a finite number of observations.

pointwise consistent, but not uniform consistent. Furthermore, theyalso show that there exists no causality test, based on associations ofnon-experimental data under the Markov and faithfulnessassumptions, which is uniform consistent. Therefore, for any finite sam-ple, it is impossible to guarantee that the results of the SGS causality tests(or any other causality test) will converge to the asymptotic results.

Appendix 2. Clustering Analysis Using Bootstrapped Moran IComputations

The following table gives the bootstrapped Moran I computationsfor cluster 1 and 2 of Map 1. Here cluster 1 is composed of 156 munic-ipalities and cluster 2 of 75 municipalities. The 26 municipalities clus-ter is not included as the model could not be estimated because ofinsufficient degrees of freedom. All the computations were performedin GRETL because GEODA is lacking functionalities to select subsam-ples and compute associated stats.

Here we present for comparison both final results for the truncat-ed matrices and the correctly re-indexed matrix but only for thenearest neighbors structure. To be more precise, it is not possibleto re-index the contiguity because when a neighbor is in anothergroup, there are no new neighbors to replace it. This is why theborder effect must be stronger, and subsequently the bias for thecontiguity neighborhood. Table 3 presents the results for both com-putations of neighborhood, this allows to compare results and inter-estingly provide a qualitative assessment of border effects biases.

Zone 1 spatial autocorrelation is not significant for the 4NN, exceptfor the fallow residuals. We know from initial computationson the whole model that fallow residuals display the stron-gest spatial autocorrelation, here it is significant at 5 % butlargely reduced. For the 8NN, spatial autocorrelation is signif-icant for crop and pasture. Note that it is negative for cropwhich is an interesting result meaning crop residuals valuesare significantly dissimilar at farther distance. Note that itis the only variable for which we find negative spatial auto-correlation. Then, both pasture and forest residuals do notdisplay any significant spatial autocorrelation in the residualsof zone 1.

Zone 2 At the 4NN we find the same results as for zone 1: significantspatial autocorrelation for fallow residuals. At the 8NN thepicture is quite different, as we see significant autocorrelationfor crop, pasture and forest residuals. The comparison of theresults for truncated and correct neighborhood matricesshow differences in values that are substantial for zone 2(large differences) but smaller for zone 2. Also, the computedvalues for zone 1 at 8NN are nearly the same but significancelevels differ strongly. These findings point to substantialbiases due the boundary (border) effects and open interestingfurther research on this subject.

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Table 3Moran test and bootstrap p-values for clusters I and II.

Neighborhood structure Variables Moran I test sample

Trucated matrices Correct matrices

Zone 1 Zone 2 Zone 1 Zone 2

Moran I Bootstrappvaluefor t

Moran I Bootstrappvaluefor t

Moran I Bootstrappvaluefor t

Moran I Bootstrappvaluefor t

First Order Contiguity CROP −0.091 0.072⁎ 0.176 0.004⁎⁎⁎ NAPASTURE 0.256 0.003⁎⁎⁎ 0.638 0.000⁎⁎⁎

FALLOW −0.010 0.842 0.088 0.120FOREST 0.062 0.219 0.252 0.001⁎⁎⁎

4NN CROP −0.007 0.691 0.186 0.005⁎⁎⁎ −0.004 0.802 0.219 0.120PASTURE 0.023 0.243 0.259 0.000⁎⁎⁎ 0.019 0.310 0.388 0.233FALLOW 0.032 0.089⁎ 0.058 0.203 0.064 0.041⁎⁎ 0.095 0.048⁎⁎

FOREST 0.058 0.131 0.173 0.000⁎⁎⁎ 0.016 0.617 0.221 0.1258NN CROP −0.044 0.006⁎⁎⁎ 0.120 0.005⁎⁎⁎ −0.044 0.011⁎⁎ 0.004 0.004⁎⁎⁎

PASTURE 0.025 0.144 0.201 0.000⁎⁎⁎ 0.026 0.118 0.000 0.000⁎⁎⁎

FALLOW 0.020 0.221 0.067 0.055⁎ 0.051 0.014⁎⁎ 0.049 0.243FOREST 0.031 0.281 0.132 0.001 0.025 0.388 0.000 0.002⁎⁎⁎

All tests performed with 999 permutations; NA: Not Applicable.⁎ Significant at 10%.

⁎⁎ Significant at 5 %.⁎⁎⁎ Significant at 1 %.

Appendix 4

Appendix 3

35M.J. Mendonça et al. / Ecological Economics 84 (2012) 23–36

Impulse Response Functions (Horizon: 75 years)

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