Neighborhood effects in the Brazilian Amazônia: protected areas
and deforestation
A. Amin∗, J. Choumert†, J-L. Combes∗ , P. Combes-Motel∗ , E.N. Kéré∗ ‡,
J-G. Ongono-Olinga∗ , S. Schwartz∗
September 22, 2016
Abstract
This article analyzes, theoretically and empirically, the interactions between decisions to
deforest and protected areas size in the Brazilian Amazônia. Its aims is to investigate whether
these protected areas are efficient instruments against deforestation. Deforestation decisions are
modelled as a non-cooperative game between municipalities, in which forest cover is a public
good and deforestation allows the production of private goods. A Dynamic Spatial Durbin
Model allows us to assess the direct impact of the different types of protected areas (integral
protected areas, sustainable use areas and indigenous lands) on deforestation and the associated
spillover effects. We theoretically and empirically show that deforestation decisions are strategic
complements. The econometric results differ according to the type of protected area. It is shown
that: i) integral protected areas and indigenous lands allow for reducing deforestation; and ii)
sustainable use areas increase deforestation; and iii) the spillover effects generated by integral
protected areas and indigenous lands help to reduce the deforestation in their vicinity.
Keywords: Protected areas; deforestation; spatial econometrics; Brazil; Amazônia.
JEL Codes: C23, Q24, Q28, Q57.
∗
School of Economics, CERDI, University of Auvergne, 65 Boulevard François Mitterrand 63000 Clermont-Ferrand,
France.
†
Economic Development Initiatives (E.D.I.) P.O. Box 393, Bukoba, Kagera region, Tanzania.
‡
African Development Bank.
1
Abstract
This article analyzes, theoretically and empirically, the interactions between decisions to
deforest and protected areas size in the Brazilian Amazônia. Its aims is to investigate whether
these protected areas are efficient instruments against deforestation. Deforestation decisions are
modelled as a non-cooperative game between municipalities, in which forest cover is a public
good and deforestation allows the production of private goods. A Dynamic Spatial Durbin
Model allows us to assess the direct impact of the different types of protected areas (integral
protected areas, sustainable use areas and indigenous lands) on deforestation and the associated
spillover effects. We theoretically and empirically show that deforestation decisions are strategic
complements. The econometric results differ according to the type of protected area. It is shown
that: i) integral protected areas and indigenous lands allow for reducing deforestation; and ii)
sustainable use areas increase deforestation; and iii) the spillover effects generated by integral
protected areas and indigenous lands help to reduce the deforestation in their vicinity.
Keywords: Protected areas; deforestation; spatial econometrics; Brazil; Amazônia.
JEL Codes: C23, Q24, Q28, Q57.
1
1
Introduction
Deforestation in the Brazilian Amazônia rainforest declined steadily from 2004 to 2010, and
since then, until 2014, it has been about 5,800 square kilometres per year according to INPE.1
Deforestation has experienced an impressive 79% decrease with respect to the 28,000 square kilometers peak in 2004. A range of reasons for the decline of deforestation in Brazil have been put
forward, including the 2008-2009 financial crisis (Nepstad et al. 2009), and the conservation policies
in recent years enforced by the Brazilian authorities which mainly relied on the implementation of
protected areas (Assunção et al. 2012; Hargrave and Kis-Katos 2012; Nolte et al. 2013; Palmer and
di Falco 2012 among others). The surface area of protected areas in the Brazilian Legal Amazônia
doubled between 2000 and 2009, and today amounts to 2 million square kilometres representing
42% of the surface area in the Brazilian Amazônia. This hypothesis is supported by Figure 1 below,
which shows a negative correlation between protected and deforested areas in Brazil.
Effective protected areas are crucial for many reasons in reducing deforestation. Protected areas
support climate change mitigation since they contribute to cutting carbon emissions (Soares-Filho
et al. 2010). Coupling protected areas to other schemes, such as agricultural intensification, is also
attractive because it supports the decoupling of the expansion of soy production from deforestation.
Macedo et al. (2012) showed a similar phenomenon in the southern part of Amazônia (Mato Grosso)
where soy production recently expanded more at the expense of grazing lands than forest lands.
This encouraging effect of protected areas should however be considered in light of the views of
several authors who underline that deforestation rates are relatively higher in Brazil than in other
Latin American countries (Aide et al. 2013). Moreover, the Brazilian Amazônia may suffer from
an "extinction debt" according to which species extinction rates are expected to increase in this
region (Wearn et al. 2012).
1
Instituto Nacional de Pesquisa Espacial - Brazilian National Institute for Space Research, Monitoramento da
floresta Amazônica Brasileira por satélite. Available at http : //www.obt.inpe.br/prodes/ acceded May 2015.
2
Figure 1: Changes in the surface areas of protected areas and deforested areas in the Brazilian
Legal Amazônia (square kilometres). Source: INPE and authors’ calculations. Note that indigenous
lands are not included.
This paper aims to provide new evidence on the link between deforestation in the Brazilian
Amazônia and the protected areas which are the core of environmental policies in this region.
Empirical studies that have examined the impact of protected areas on deforestation have shown
that their ecological characteristics (level of rainfall, slope, and surface temperature) and their
status (belonging or not to indigenous populations, integral versus sustainable use protected area)
have an influence on deforestation (Deininger and Minten 2002, Mertens et al. 2002 and Mertens
et al. 2004).2 The effective impact of protected areas on deforestation is subject to debate because
protected areas are not randomly distributed (Gaston et al. 2008; Gaveau et al. 2009). They
are usually located on land with characteristics that do not favor agricultural expansion, owing
to low soil fertility, slope, poor accessibility, and so forth (Albers and Ferraro, 2006). Neglecting
this location bias could induce an overestimation of the impact of protected areas on deforestation
(Nepstad et al. 2006, Sanchez-Azofeifa et al. 2003, Joppa and Pfaff 2009). The location bias has
2
Contrary to integral protection areas, deforestation can be allowed in sustainable use areas. This classification
of protected areas come from IUCN (Chape et al. 2005).
3
been addressed either with matching methods (Andam et al., 2008, Gaveau et al., 2009, Pfaff et
al., 2009 and Pfaff et al., 2014) or bivariate probit models (Cropper et al. 2001).
We argue that there is another empirical issue in assessing the impact of protected areas. Several
papers draw attention to the indirect land use changes generated by environmental policies. This
thinking is based on displacement or leakage effects induced by land use change (Meyfroidt et al.
2013): agriculture encroaches on grazing lands which are moved towards forests’ frontiers. This
phenomenon might be of crucial importance since it could prevent the mitigation efforts of biofuels
programs (Lapola et al. 2010), as well as the benefits from the voluntary moratoriums of soy
producers on forest conversion (Arima et al. 2011).
In this paper, land use decisions are deemed to generate spillover effects and lead to spatial
interactions between municipalities. Several empirical studies have shown that there are strategic interactions between municipalities regarding deforestation decisions. In the Legal Amazônia,
Aguiar et al. (2007), Corrêa de Oliveira and Simões de Almeida (2010), and Igliori (2006) showed
that deforestation decisions are strategic complements. Moreover, in the Peruvian Amazônia, Ewers
and Rodrigues (2008) showed that protected areas could cause leakages in deforestation. Surprisingly, despite the large amount of attention paid to the drivers of deforestation in the Brazilian
Amazônia, no study, to the best of our knowledge, has focused on the municipality cross-border
effects generated by the establishment of protected areas on deforestation. In this paper, we try
to theoretically and empirically fill this gap. First, the theoretical analysis assumes that forest is
a public good but also an input used to produce private goods. The network of protected areas
is analysed taking into account spatial interactions and allows us to establish that deforestation
decisions are strategic complements. An interesting result is that for bordering municipalities the
creation of a protected area in one municipality enables a reduction of deforestation in the other
municipality, even if the latter does not implement protected areas. Second, the empirical analysis
is conducted using a geo-referenced database of land use in the Brazilian Legal Amazônia over the
4
period 2001-2009 at municipal level. The spatial interdependences in deforestation as well as crossborder effects of protected areas are evidenced using a Dynamic Spatial Durbin Model with fixed
effects. Our empirical framework provides evidence of different effects of protected areas according
to their status. Integral protected areas and indigenous lands allow for reductions in deforestation,
sustainable use areas lead to increased deforestation. Moreover the spillover effects generated by
integral protected areas and indigenous lands help to reduce deforestation in the vicinity.
The rest of this article is organized as follows. In Section 2, the theoretical analysis is developed.
In Section 3 the empirical analysis is presented. Concluding remarks are offered in Section 4.
2
Theoretical analysis
To focus on the interdependence between decisions in favor of deforestation and decisions in
favor of the creation of protected areas, we develop a theoretical model. We assume that forest
cover is a public good, and that forest is cut down in order to produce a private good. A municipal
regulator wants to protect the forest localized in his municipality. To do that, he first determines
the optimal surface area of forest and implements it by means of a protected area. He adopts a
non-cooperative strategy with other municipalities. We first present the assumptions of the model
and the benchmark, i.e. the equilibrium without regulation. Then non-cooperative regulation is
presented. Lastly, we present our results.
2.1
Assumptions
We consider two municipalities i, i = 1, 2. In each municipality, we denote by Ti the forest cover before any regulation (with Ti = T−i = T ). We assume a representative consumer in
each municipality. His preferences are represented by the following quasi-linear utility function:
U (xi , gi , g−i , M ) = B(xi ) + [k.J(gi ) + (1 − k)(J(g−i )] + M ∀i = 1, 2, where xi is the private good
5
sold at price p, gi is a local public good (forest cover) and M is the available revenue.3 The parameter k ∈ [1/2, 1] indexes the degree of spillover: k = 1 means that citizens care only about the
public good in their own municipality while k = 1/2 means that they care equally about public
goods in both municipalities (Besley and Coate, 2003). Preferences for the private good and local
public goods are respectively given by the following increasing and concave functions B(xi ) and
J(gi ), where B(xi ) = γxi −
x2i
2
et J(gi ) = βgi −
gi2
2
∀i, with xi < γ and gi < β.
A quantity xi of a final good is produced by a representative firm in i. Producing xi units of the
final good requires xi units of forest cover. The production cost depends on the quantity produced
in Municipality i (xi ) but also on the level of production in another municipality (x−i ). The
more the Municipality −i deforests, the more it is obliged to put in place adequate infrastructure
such as roads. These infrastructures will benefit Municipality i by reducing its isolation and so
its production costs. To isolate this "infrastructure effect" (see Angelsen 2001) we assume that
the marginal cost of production is constant in xi but decreasing in x−i . So the production cost
is such as Ci (xi , x−i ) with Cixi > 0; Cixi xi = 0; Cix−i < 0; Cixi x−i < 0, i = 1, 2. We set
Ci (xi , x−i ) = α.xi .(1 − x−i ) with α < 1.4
2.2
The benchmark: no protected area
We define the benchmark, as the market equilibrium of both municipalities without regulation
to protect forests. We first find the demand for the private good. The representative consumer
maximizes his utility. If R is the revenue before any spending, we have M = R − pxi . We obtain:
Maxxi U (xi , gi , g−i ) = B(xi ) + [k.J(gi ) + (1 − k)(J(g−i )] + R − p.xi .
3
The consumer enjoys the forest due to his preferences towards nature, biodiversity, or recreational activities.
From all these assumptions, we necessarily have xi ∈ [0; T ] and gi = M ax{Ti − xi , 0}. In this article we avoid
total deforestation assuming T > (γ − α)/(1 − α).
4
6
From the first order condition, we find:
B 0 (xi ) = p ∀i = 1, 2.
(1)
The representative consumer can only choose the private good quantity. From Equation (1), this
quantity is such that the marginal benefit from consumption is equal to the good’s price. This
equation gives us the inverse demand function. The consumer cannot decide on the size of the local
public good.
The representative firm maximizes its profit:
Maxxi πi (xi , x−i ) = p.xi − Ci (xi , x−i ).
From the first order condition, we find:
p − Cixi (xi , x−i ) = 0.
If the output price is lower than the marginal cost, the production level is null and indeterminate
if the price is equal to the marginal cost. The supply function can be written in the following way:
xi (p, xj ) =




 0 if p < α.(1 − x−i )
(2)



 [0, γ] otherwise
From Equation (1), we obtain the following market equilibrium, which is always an interior
solution under our assumptions:
B 0 (xi ) − Cixi (xi , x−i ) = 0.
7
(3)
As the quantity produced in one municipality depends on the quantity produced in the other
municipality we find the following best response functions:
xi = f (x−i ) = γ − α.(1 − x−i ) ∀i = 1, 2.
(4)
This quantity decreases with the cost parameter (α) and increases with the benefit parameter
to consume good (γ) and the quantity produced in −i (x−i ), i.e., deforestation in −i. Hence,
production levels, as well as deforestation levels, are strategic complements. Finaly from both
reaction functions given by (4), we find the Nash equilibrium without regulation, x̄i :
x̄i =
γ−α
∀i = 1, 2
1−α
and the size of the forest is Ḡi = T − x̄i ∀i = 1, 2.
Due to several market imperfections, this economy cannot reach the optimum. There is a
consumption externality: when the consumer defines his demand function for the private good, he
does not take into account the fact that his consumption leads to the cutting down of the forest.
There are also cost interdependencies and local public goods.
2.3
A decentralized regulation
A regulator in one municipality decides to provide the local public good, i.e., to regulate logging.
To do so he chooses to implement an integral protected area in which logging will be not allowed.5
The regulator determines the optimal level of the private good and sets the size of the protected
5
In this article we ignore the enforcement costs caused by the establishment of the protected area.
8
area. To this end, he maximizes the surplus in the economy:
Maxxi S(xi , xj ) = B(xi ) + [k.J(gi ) + (1 − k)(J(g−i ))]
−k.J(T ) − Ci (xi , x−i )
(5)
subject to Gi = Ti − xi ≥ 0.
The first order condition is:
B 0 (xi ) − Cixi (xi , x−i ) − k.J 0 (gi ) = 0.
(6)
Compared to Equation (3), the regulator internalizes the negative externality, taking into account
the third term in (6). As the optimal level of the private good depends on the quantity produced
in municipality j, we also find a reaction function:
xi = f (x−i ) =
γ − α.(1 − x−i ) − k.[β − T ]
.
1+k
(7)
As in the benchmark, this quantity increases with (γ) and (x−i ) and it decreases with (α), and also
now with preferences for forest (β), especially in Municipality i (k). The equilibrium depends on
the policy in Municipality −i. The regulator −i can choose to regulate logging or remain "laissez
faire." We assume that both regulators make their decision simultaneously. In this case, the results
are given by Nash equilibria.
9
2.3.1
The Nash symmetric equilibrium
If each municipality implements a protected area, both regulators behave as Equation (7). The
quantities at the Nash symmetric equilibrium are the following:
xns
i =
γ − α − k.[β − T ]
∀i = 1, 2
1−α+k
(8)
ns
and the sizes of the protected area (AP ) are AP ns = Gns
i = T − xi .
2.3.2
The Nash asymmetric equilibrium
At the Nash asymmetric equilibrium, Municipality 1 chooses to regulate the market, whereas
Municipality 2 does not. The equilibrium is obtained from reaction functions given by Equations
(4) and (7). Th results are given by:
(γ − α)(1 + α) − k.[β − T ]
(1 − α)(1 + α) + k
k.[(γ − α) + (1 − α)(B − T )]
= xna
i +
(1 − α)(1 + α) + k
xna
=
1
xna
2
na
na
na
and AP1na = Gna
1 = T − x1 and G2 = T − x2 .
2.4
Results
We begin by comparing the "laissez faire" equilibrium and the Nash symmetric equilibrium. We
find:
xns
i < x̄i , i = 1, 2..
Introducing the Nash asymmetric equilibrium, we obtain the following comparisons:
na
xna
1 < x2
10
and:
xns
< xna
1
1 < x̄1
xns
< xna
2
2 < x̄2
Under the symmetric non-cooperative equilibrium, the regulators internalize the negative externality which comes from consumption in each municipality. They take as a given the "spillover
effect" which comes from local public goods as well as the "cost effect" i.e. the impact of the
production level in i (−i) on the production cost in −i (i). If both municipalities internalize the
negative externality we find that production levels are lower than levels without regulation.
Establishing a protected area only in Municipality 1 leads to an increase of the production cost
in Municipality 2. Hence, the firm located in Municipality 2 has to decrease its production level.
Since this municipality does not implement a protected area, it bears the "cost effect." Finally,
quantities at the Nash asymmetric equilibrium are higher than quantities at the symmetric ones in
both municipalities but lower than the "laissez faire" quantities. Therefore, establishing a protected
area only in one municipality leads to preservation of forest in another municipality even if the latter
does not regulate. Asymmetric regulation is better than no regulation for forest preservation.
Under symmetric or asymmetric equilibrium, the size of the protected area negatively depends
on the level of deforestation in the other municipality. This result seems counterintuitive. However,
the more the production in Municipality −i, the less the production cost in Municipality i. Hence
the traditional trade-off between marginal social benefit and marginal social cost given by Equation
(6) balances toward production and so reduces the size of the protected area.
11
In this section, we have highlighted, theoretically, the mechanism leading to the setting of
the size of a protected area.6 It mainly depends on the firms’ production costs, on preferences for
forest, and on the relationship between municipalities. The following section will empirically analyze
several interactions between municipalities, as far as deforestation and protected area creation are
concerned. From this theoretical model, we will empirically test the following propositions:
Proposition 1. Deforestation decisions are strategic complements.
Proposition 2. Creating a protected area in a municipality reduces deforestation in this municipality.
Proposition 3. Creating a protected area in Municipality i (−i) reduces deforestation in Municpality −i (i).
3
Empirical analysis
We first present a study of the Brazilian Legal Amazônia area and then the econometric back-
ground. After developing our empirical results we pay attention to the effect of control variables.
3.1
The Brazilian Legal Amazônia study area
Data on forest cover and protected areas in the Brazilian Legal Amazônia are available for
the period 2001 - 2009 from the PRODES System of the Instituto Nacional de Pesquisa Espacial
- INPE (National institute space research center).7 A surface is considered as deforested if it is
converted from forest to non-forest land between year t and year t+1. The deforestation variable
corresponds to the area deforested each year during the period. Figure 2 depicts the familiar arc
6
We note that decentralized regulation cannot reach the optimum because cost and local public good interdependencies between municipalities are not internalized. In this case, a centralized regulator would implement protected
areas for both municipalities. This question is beyond the scope of this article.
7
Legal Amazônia is an administrative division of the Brazilian territory created in 1953 for regional policy purposes.
With a geographic area of 5 million sq. km located in the northwestern part of the country, it includes the states of
Rondonia, Acre, Amazonas, Roraima, Para, Amapa, Tocantins, Mato Grosso, and parts of Maranhão and Goias (a
very small part in the latter).
12
of deforestation (Fearnside 2005; Alves 2002) in the Brazilian Amazônia with notably high rates of
deforestation along the southern and eastern edges. Deforestation appears to spread northward.
Figure 2: Deforestation rates in the municipalities of Brazilian Legal Amazônia between 2001 and
2009 as a % of 2001 forest surface area. Source: INPE, authors’ calculations.
Brazil has recently invested in the creation of protected areas in Amazônia, in particular, via
the Amazônia Region Protected Areas Project (ARPA). The objective of this project is to create a
mosaic of protected areas around productive landscapes to maintain the ecological integrity of the
area over the long term. According to INPE, protected areas currently represent more than 44%
of the Brazilian Amazônia (Pfaff et al. 2014).
Under Brazilian law No. 9.985/ 2000, the creation of a protected area must be based on
a technical study that takes into account the forest cover, biodiversity, presence of indigenous
peoples, property rights and the pressure on forest resources. A consultation with the residents of
the municipalities is organized. Its aim is to define the degree of protection of protected areas. As
part of this process, the decision to create protected areas is generally taken by the federal state.
13
But municipalities can influence the size of protected areas and the degree of protection. They can
also create their own protected areas.
Three types of protected areas have been defined in Brazil - integral protection areas, sustainable
use areas, and indigenous lands. Integral protection areas, which represented 19% of the protected
surface area in 2009, prioritize preservation of biodiversity. In these protected areas, no production
activity is allowed. They can be classified in the most restrictive categories of the International
Union for Conservation of Nature (IUCN) classification (categories I, II and III). Sustainable use
areas which accounted for 32% of the protected surface area allow a "sustainable use" of resources
(equivalent to categories IV, V, and VI of the IUCN classification). Indigenous lands are devoted
to the protection of the living space of indigenous peoples. These areas have no equivalent in
the IUCN classification. Figure 3 shows the boundaries of the protected areas in 2009. A rough
comparison of Figure 2 and Figure 3 shows that protected areas are found more in northern Legal
Amazônia than in the area of the arc of deforestation.
In this study, neighborhood effects are investigated at the municipal level. In line with several
studies (e.g. Andrade de Sá et al. 2013), we aggregate the municipal data into the 248 Minimum
Comparable Areas (MCAs) located in the Brazilian Legal Amazônia.8 Socio-economic data on
MCAs (GDP per capita, number of cattle per sq. km., and population density) are available from
the Instituto Brasileiro de Geografia e Estatistica - IBGE (Brazilian agency for statistical and
geographical information). The description and sources of data used are summarized in Table A.1
of the Appendix.
8
Using MCA data allows comparison (because the number and size of municipalities may change through time).
The list of MCAs is available from the Brazilian Institute of Applied Economic Research (IPEA - Instituto de Pesquisa
Econômica Aplicada).
14
Figure 3: Spatial distribution of protected areas by type in 2009. Source : INPE, authors’
calculations.
3.2
The Econometric setting
The Spatial Durbin Model (SDM) allows identification of global spillovers, i.e. endogenous
interactions with feedback effects.9 The SDM has the advantage of producing unbiased estimates
even if the underlying data generator process is a Spatial Autoregressive Model (SAR) or Spatial
Error Model (SEM) (Elhorst 2010b). Moreover, we take advantage of the panel data structure for
the 2001 to 2009 period and therefore estimate a Dynamic Spatial Durbin Model (DSDM). Indeed,
according to several studies (e.g. Andrade de Sá et al. 2013; Wendland et al. 2015), taking into
account the temporal dimension helps to better identify the determinants of land-use changes.
Estimating the impact of protected areas on deforestation raises econometric issues pertaining
to reverse causality and unobserved factors. Potential reverse causality is suggested by studies
9
LeSage (2014) distinguishes between global and local spillovers. Global spillovers arise if spatial spillovers concern
the neighbors of municipality i, but also the neighbors of its neighbors, and so on. Local spillovers imply only
interactions with neighbors and not higher-order neighbors.
15
which have drawn attention to the effectiveness of protected areas in curbing deforestation (among
others Albers and Ferraro 2006; Nelson and Chomitz 2011; Pfaff et al. 2009; Pfaff et al. 2014).
To address the reverse causality problem, we take the time lagged values of protected areas as
explanatory variables instead of their current values.10 Regressing the error term on the explanatory variables allows for the verification of the effectiveness of this procedure while simultaneously
checking for the absence of correlation between unobserved time varying variables and protected
areas. Fixed effects take the unobserved heterogeneity specific to each MCA into account. This
also allows to control for for location bias of protected areas, whose determinants do not vary over
time.
The model to be estimated is written as follows:
Defit = αDefi(t−1) + ρW Defit + β1 P Ai(t−1) + β2 W P Ai(t−1) + β3 Xit + β4 W Xit + µi + it
(9)
where t=2001, ... , 2009 and i=1, ... , 248. W is the inverse distance matrix that is applicable
in the case of global spillovers because it allows all MCAs to be connected together. It gives
more weight to the nearest neighbors. We normalize this matrix by dividing each element by
the sum of the line. Defit represents the deforested surface area of land observed in MCA i at
time t, W Def is the vector of the spatially lagged dependent variable. ρ measures the spatial
autocorrelation. P Ai(t−1) is the surface area of protected areas in MCA i at time t − 1 and β1
measures the effect of protected areas on deforestation in the MCA i. W P Ai(t−1) is the vector
of the spatially lagged variable of protected areas, and β2 measures its effect on deforestation in
10
This endogeneity would ideally be addressed while running the Instrumental Variables and Generalized Method of
Moments (IV/GMM). It is however difficult, if not impossible, to derive Maximum Likelihood (ML) or Bayesian estimators of models with spatial dependence and additional endogenous explanatory variables (Elhorst, 2014). Moreover,
the use of IV/GMM to estimate a SDM is less effective than ordinary least squares unless the number of observations
is greater than 500,000 (Pace et al. 2012). Since the second order spatially lagged explanatory variables in a SDM
are weak instruments, they do not properly identify the spatial autocorrelation coefficient.
16
neighboring municipalities. X is the matrix of exogenous explanatory variables and vector β3 the
associated parameters. W X is the matrix of the spatially lagged exogenous explanatory variables ,
and β4 is the vector of associated parameters. This matrix contains the following control variables:
GDP per capita, population density, livestock per sq. km., the level of rainfall and forest area at
the initial period. µi represents the fixed effects associates with each MCA and it the error term.
We apply the maximum likelihood method estimator developed by Elhorst (2010a) and Lee and
Yu (2010) and implemented in Stata by Hughes and Mortari (2013).
3.3
Empirical results
We first justify the choice of the model used and we then consider the pattern of spatial autocorrelation. Finally, we present our results, i.e. the effects of protected areas on deforestation.
3.3.1
Specification and Robustness Tests
In order to confirm the choice of the DSDM, the Dynamic Spatial Autoregressive Model (DSAR)
is tested against the DSDM. This amounts to testing the joint nullity of all coefficients of spatially
lagged independent variables. The null hypothesis (β2 = β4 = 0) is rejected by the χ2 test at
the 1% level and therefore the DSDM is the preferred specification. Following Elhorst (2014), the
equalities (β2 = −ρβ1 ) and (β4 = −ρβ3 ) are also tested and rejected, which comforts the DSDM
with respect to the SEM specification (Spatial Error Model). A Hausman test is carried out to
confirm that fixed effects are statistically required. The χ2 statistic rejects the null hypothesis
of independence between errors and explanatory variables, and therefore favors fixed rather than
random effects. All the specification tests are presented at the bottom of the tables B.1 and B.3 in
the Appendix.
Regressing the error terms of our specifications on the explanatory variables validates the hypothesis of no correlation between the error term and explanatory variables and therefore the
17
effectiveness of our procedure in controlling for endogeneity. These results are presented in the
tables B.2 and B.5 in the Appendix.
Lastly, the robustness of our results is tested in two ways. First, we proceed by the gradual
inclusion of explanatory variables. Marginal effects are presented in Table 1 and estimated coefficients in Table B.1 in the Appendix. Second, the impact of each type of protected area on
deforestation with all the control variables is evaluated independently. Estimated coefficients and
marginal effects are presented in tables B.3 and B.4 respectively. Our results are robust to these
robustness checks.
3.3.2
Pattern of spatial autocorrelation
The spatial autocorrelation coefficient of deforestation, ρ, is positive and significantly different
from zero. This result is consistent with Proposition 1 which posits that deforestation decisions are
strategic complements. This result is also in line with previous studies (Andrade de Sá et al., 2015;
Aguiar et al., 2007; Corrêa de Oliveira and Simões de Almeida, 2010; and Igliori, 2006). According
to Lesage and Pace (2009) in the presence of spatial interactions, the impact of the explanatory
variables on the dependent variable can be broken down into direct and indirect effects. The direct
effect of protected areas on deforestation measures the impact of a change in the surface area of
protected areas in MCA i on deforestation in MCA i. The indirect effect measures the impact
of a change in the surface area of protected areas in i on deforestation in all other MCAs. Put
differently, indirect effects are global spillovers because they arise in all MCAs, and not just in
neighboring MCAs. However, indirect effects pertain more to MCA i’s vicinity because it decreases
with the distance between MCA i which created the protected area and other MCAs.
18
Table 1: Marginal effects of protected areas on deforestation by introducing explanatory variables
gradually
Direct
Forest
(1)
Def
(2)
Def
(3)
Def
(4)
Def
(5)
Def
(6)
Def
(7)
Def
(8)
Def
0.0618***
(0.0037)
0.0591***
(0.0041)
-0.0776***
(0.0235)
0.0607***
(0.0041)
-0.0920***
(0.0230)
0.1161***
(0.0249)
0.0610***
(0.0042)
-0.0715***
(0.0229)
0.1429***
(0.0257)
-0.0573*
(0.0298)
0.0609***
(0.0041)
-0.0721***
(0.0256)
0.1420***
(0.0256)
-0.0568*
(0.0290)
-1.0517
(4.5718)
0.0610***
(0.0043)
-0.0713***
(0.0259)
0.1423***
(0.0253)
-0.0563*
(0.0301)
-1.0964
(4.4867)
-0.0813
(0.4444)
0.0597***
(0.0040)
-0.0692***
(0.0238)
0.1365***
(0.0249)
-0.0606**
(0.0296)
-0.4379
(4.5236)
-0.0852
(0.4428)
0.1745***
(0.0479)
0.0602***
(0.0040)
-0.0646***
(0.0234)
0.1358***
(0.0254)
-0.0645**
(0.0283)
-0.0600
(4.6281)
-0.0737
(0.4409)
0.1766***
(0.0479)
0.0202
(4.5750)
-0.0662**
(0.0295)
-0.1709***
(0.0369)
-1.8027***
(0.3670)
-0.1476***
(0.0356)
-1.8000***
(0.3848)
0.1229
(0.2318)
-0.1559***
(0.0351)
-1.3516***
(0.3642)
0.3763
(0.2408)
-0.6911**
(0.2722)
-0.1676***
(0.0400)
-1.3868***
(0.4061)
0.3451
(0.2421)
-0.6705**
(0.2898)
-11.0040
(15.6351)
-0.1658***
(0.0335)
-1.3757***
(0.3714)
0.3556
(0.2389)
-0.6520**
(0.2815)
-13.7072
(17.5542)
0.2935
(1.2732)
-0.1923***
(0.0384)
-1.3012***
(0.3955)
0.2862
(0.2249)
-0.7443**
(0.3037)
-8.7010
(18.7840)
0.5633
(1.1232)
-0.2321***
(0.0624)
-0.1940***
(0.0410)
-1.1993***
(0.3171)
0.2339
(0.2291)
-0.7832**
(0.3094)
-19.0514
(15.6707)
1.1641
(1.0150)
-0.2536***
(0.0653)
61.2021**
(24.1239)
-0.0044
(0.0287)
-0.1118***
(0.0364)
-1.8803***
(0.3743)
-0.0868**
(0.0349)
-1.8919***
(0.3919)
0.2390
(0.2427)
-0.0949***
(0.0342)
-1.4231***
(0.3688)
0.5192**
(0.2508)
-0.7484***
(0.2835)
-0.1067***
(0.0393)
-1.4589***
(0.4188)
0.4871*
(0.2520)
-0.7274**
(0.2983)
-12.0557
(15.4603)
-0.1048***
(0.0331)
-1.4471***
(0.3843)
0.4978**
(0.2476)
-0.7083**
(0.2952)
-14.8036
(16.5280)
0.2122
(1.2480)
-0.1326***
(0.0370)
-1.3704***
(0.4044)
0.4226*
(0.2318)
-0.8048**
(0.3148)
-9.1388
(18.3506)
0.4781
(1.0882)
-0.0576**
(0.0281)
-0.1338***
(0.0396)
-1.2639***
(0.3242)
0.3697
(0.2386)
-0.8477***
(0.3158)
-19.1114
(15.5832)
1.0904
(0.9491)
-0.0770**
(0.0352)
61.2223***
(23.7093)
Integral
Sustainable
Indigenous
GDP
Pop_dens
Rainfall
Cattle
Indirect
Forest
Integral
Sustainable
Indigenous
GDP
Pop_dens
Rainfall
Cattle
Total
Forest
Integral
Sustainable
Indigenous
GDP
Pop_dens
Rainfall
Cattle
Standard errors in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01
3.3.3
Effect of protected areas on deforestation
The effect of protected areas on deforestation can also be investigated by calcuting elasticities
as follows:
εP A = M arg_Ef f ect ∗
19
PA
Def
(10)
where P A the average area of protected areas and and Def the average area of deforestation„ and
M arg_Ef f ect are the marginal effects of PA ( ∂Def
∂P A ) as presented in column (8) of Table 1. The
results are summarized in Table 2.
Table 2: Summary of the impact of protected areas on deforestation: marginal effects and elasticity.
Marginal effect
Direct
Indigenous
Sustainable
Integral
Indirect
Indigenous
Sustainable
Integral
Total
Indigenous
Sustainable
Integral
-0.0065 **
(0.0028)
0.0136 ***
(0.0025)
-0.0065 ***
(0.0023)
-0.0783 **
(0.0309)
0.0234
(0.0229)
-0.1199 ***
(0.0343)
-0.0848 ***
(0.0316)
0.037
(0.0239)
-0.1264 ***
(0.0324)
Elasticity
Increase of protected
areas by 10% (sq. km.)
Impact on
deforestation (sq. km.)
-0.0826
115.731
-0.7523
0.0886
59.355
0.8072
-0.0596
83.593
-0.543
-0.9953
115.731
-9.0618
0.1525
59.355
1.3889
-1.1009
83.593
-10.0228
-1.078
115.731
-9.814
0.2412
59.355
2.1961
-1.1606
83.593
-10.566
Standard errors in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01
The impact in terms of avoided deforestation is low in absolute terms because the surface areas
of protected areas are much bigger than deforestation areas. In 2009 there were over 1,000,000 sq.
km. of protected areas against less than 7,000 sq. km. of cleared forest. Moreover, protected areas
located on sites with low clearing threat will have no or a very small effect on deforestation.
Integral protection areas either negatively impact on deforestation in the MCA (direct effect)
or in all other MCAs (indirect effect). A 10% increase (83.5 sq. km.) in integral protection
areas reduces deforestation by 0.59% (0.543 sq. km) in the MCA and by 11.0% (10.02 sq. km.)
in all other MCAs. These results support the idea that integral protection areas do not lead to
deforestation leakage in MCAs vicinities. Rather, they create synergies between initiatives against
deforestation since indirect effects are stronger than direct ones. The total effect of a 10% increase
in integral protection areas is estimated at 11.6% (10.56 sq. km).
20
In addition, we show that a 10% increase (115.7 sq. km.) in the indigenous lands of MCA i
reduces deforestation by 0.826 % (0.7523 sq. km.) in MCA i. This result is consistent with those
obtained by Pfaff et al. (2011) and Ricketts et al. (2010). In addition, our study provides evidence
that a 10% increase in indigenous lands helps to reduce deforestation in other MCAs by 9.954%
0
1,000
2,000
3,000
(9.062 sq. km.). This direct effect is reinforced by an indirect one.
Q1
Q2
Q3
Sustainable
Indigenous
Q4
Integral
Figure 4: Average surface area of protected areas by deforestation quartile. Source : INPE,
authors’ calculations.
Hence, Proposition 2 and Proposition 3 derived from the theoretical analysis hold for integral
protected areas and indigenous land. However it is not the case for sustainable use areas. Our
empirical results show that the direct effect of sustainable use areas on deforestation is positive. A
10% increase in the surface area of sustainable use areas (59.355 sq. km) results in a 0.886% (0.807
sq. km) increase in deforestation. This result may contradict the Pfaff et al. (2014) findings in the
state of Acre. We argue here that though sustainable use protected areas are effective in the state of
Acre, it is not necessarily the case for the Legal Amazônia states as a whole. The rationale behind
this is that the sustainable use areas of the state of Acre are more located on sites with a high
21
clearing threat than the state of Acre integral protected areas, as measured by contemporaneous
deforestation rates. Figure 4 suggests that, on average, sustainable use protected areas are more
often found in the MCAs which are experiencing low deforestation rates (first quartile, Figure 4)
while integral protected areas and indigenous lands are located in the MCAs with high deforestation
rates (second and third quartiles). Indirect effects as well as the total effect of more sustainable
use protected areas are found to be non-significant in the Brazilian Legal Amazônia.
3.4
Control variables
We also investigate the effect of control variables. The time lag coefficient of deforestation is
significant and positive, which means that deforestation is characterized by an inertia phenomenon.
This result may be explained by the fact that it is hard to get rid of deforestation incentives (e.g.
those introduced by for instance, transportation infrastructures which ease additional land clearing).
The positive direct effect of initial forest stocks is more than offset by negative indirect effects which
result in a significantly negative total effect of initial stocks of forests. Indeed, the forest area at the
initial period (Forest) allows us to take into account the effect of scarcity or abundance of forest.
A low level of forest stock may reveal scarcity and then have a negative effect on deforestation.
While a high level of forest stock at the initial period will increase deforestation. However, a
large forest area throughout the neighborhood tends to discourage deforestation. A large forest in
the vicinity means that the forest has been little exploited in the past, and therefore the lack of
necessary infrastructure for the forest’s operation. This is the case for example of Amazona’s State
municipalities.
Rainfall has a negative (total) effect on deforestation while cattle density has a positive (total)
effect. These findings may be related to the effect of agricultural profitability on deforestation. The
effect of rainfall is in line with Nelson and Chomitz (2011) who emphasized that deforestation is
lower in locations that are not suitable for agriculture i.e. characterized by heavy rainfall. On the
22
contrary, the positive effect of cattle density on deforestation illustrates how profitable conditions
for agro-pastoral activities are detrimental to forests. This effect is driven by indirect effects which
provide evidence that an increase in cattle ranching in MCA i signals profitable conditions for
agriculture in neighboring municipalities and gives an impetus to land clearing. Then we witness a
cattle production displacement which leads to an increase in deforestation in often distant counties
(Arima et al. 2011). This positive effect of cattle ranching on deforestation reinforces the conclusion
of Bowman et al. (2012) in favor of reforming agricultural policies that still promote deforestation
in the Brazilian Amazônia.
The expected impact of population density on deforestation is ambiguous: first it can fuel the
demand for arable lands but, it can also favor the demand for forest products (Cropper and Griffiths,
1994). We find that population density is not significant (for a similar result: Pfaff: 1999). Moreover
the GDP per capita does not have a significant effect on deforestation. A potential colinearity with
other deforestation determinants could explain this result.
4
Concluding remarks
In this article we theoretically and empirically investigate the existence of spatial interactions
between deforestation and the surfaces areas of the designated protected areas. The aim of this work
was to investigate if protected areas (integral protected areas, sustainable use areas and indegenous
lands) are effective in terms of preventing deforestation in the Brazilian Amazônia.
Our methodological contribution to theory is the modeling of the impact of protected areas
and the spillover effects that result using a noncooperative game between municipalities, in which
forest cover is a public good and deforestation allows the production of private goods. Empirically,
we analyze these effects using a Dynamic Spatial Durbin Model. We also consider empirically the
nature of the protected areas: integral protected areas, sustainable use areas, and indigenous lands.
23
We theoretically and empirically show that deforestation decisions are strategic complements. We
show that the integral protection areas are effective not only in reducing deforestation in the MCA,
but also in all other MCAs. Our empirical estimations demonstrate that indigenous lands contribute
to the reduction of deforestation in the MCA and in its vicinity. We show that, for an increase
in the surface area of protected areas of 10%, the avoided deforestation is estimated at 10.56 sq.
km. for integral protected areas and 9.81 sq. km for indigenous lands. Hence, our empirical results
corroborate our theoretical predictions. On the contrary, sustainable use areas contribute to an
increase in deforestation in the MCA.
Information about the nature of these cross-border effects can improve the design of policies
aimed at fighting against deforestation and biodiversity depletion. Our results are not very optimistic about preventing deforestation in Brazil because integral protection areas only account for
19% of total protected areas while sustainable use areas account for 32%. But we can be happy
about the existence of indigenous areas because, although their main purpose is not to prevent
deforestation, they contribute a lot to the prevention of deforestation.
In this article, we do not distinguish between forest cover degradation and deforestation. Taking into account these different factors would enable us to obtain more precise results about the
effectiveness of the protected areas. Finally, our study does not address empirically a crucial issue
that is related to a potential dilemma between environmental objectives (biodiversity preservation)
and development objectives (poverty alleviation).11
11
See, e.g., Combes Motel et al., 2014.
24
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31
Appendix
A
Description and sources of data
Table A.1: Variables, definitions, and descriptive statistics
Variables
Def
Integral
Sustainable
Indigenous
Forest
GDP
Pop_dens
Cattle
Rainfall
Description
deforested area (sq. km.)
protected areas (sq. km.)
protected areas (sq. km.)
Indigenous lands (sq. km.)
forest area in sq. km. at start date of
the estimation (2000 or 2004 depending on
estimation)
GDP per capita (Constant 2000 R$)
density of the total population per sq. km.
number of head of cattle (beef-cattle) per
sq. km.
rainfall of municipality (millimeter per
year)
32
Sources
Prodes
UNEP-Prodes
UNEP-Prodes
UNEP-Prodes
Prodes
Mean
91.00
835.9
593.5
1157
13203
Std. Dev.
424.6
4489
3643
5411
37312
IBGE
IBGE
IBGE
3.021
41.4
3.876
3.430
192.4
6.305
CRU TS 3.2 University East Anglia 2012
2101
607.2
B
Empirical Results
33
Table B.1: Estimation results of the impact of protected areas on deforestation by introducing
explanatory variables gradually
(1)
Def
Main
L.Def
Forest
(2)
Def
(3)
Def
(4)
Def
(5)
Def
(6)
Def
(7)
Def
(8)
Def
0.2202***
(0.0158)
0.0632***
(0.0036)
0.2038***
(0.0161)
0.0628***
(0.0039)
-0.0376*
(0.0204)
0.1999***
(0.0160)
0.0638***
(0.0039)
-0.0525**
(0.0206)
0.1133***
(0.0239)
0.2014***
(0.0160)
0.0642***
(0.0039)
-0.0426**
(0.0208)
0.1342***
(0.0251)
-0.0469*
(0.0279)
0.2006***
(0.0160)
0.0644***
(0.0039)
-0.0423**
(0.0208)
0.1342***
(0.0251)
-0.0470*
(0.0279)
-1.7403
(4.6001)
0.2008***
(0.0160)
0.0643***
(0.0040)
-0.0423**
(0.0208)
0.1342***
(0.0251)
-0.0470*
(0.0279)
-1.7267
(4.6002)
-0.0900
(0.4242)
0.2012***
(0.0160)
0.0636***
(0.0040)
-0.0421**
(0.0208)
0.1300***
(0.0250)
-0.0493*
(0.0278)
-1.1781
(4.5887)
-0.1002
(0.4229)
0.1818***
(0.0501)
0.1987***
(0.0160)
0.0641***
(0.0040)
-0.0402*
(0.0208)
0.1306***
(0.0250)
-0.0525*
(0.0279)
-0.6061
(4.6528)
-0.1012
(0.4222)
0.1845***
(0.0500)
-0.6285
(4.9529)
-0.0653***
(0.0156)
-0.1255***
(0.0192)
-1.0598***
(0.1824)
-0.1166***
(0.0206)
-1.0931***
(0.1878)
0.0281
(0.1279)
-0.1225***
(0.0209)
-0.7970***
(0.2148)
0.1663
(0.1381)
-0.3896**
(0.1719)
-0.1259***
(0.0214)
-0.7942***
(0.2148)
0.1627
(0.1382)
-0.3898**
(0.1719)
-5.7497
(10.9626)
-0.1252***
(0.0216)
-0.7939***
(0.2148)
0.1642
(0.1383)
-0.3883**
(0.1720)
-6.1140
(11.0743)
0.2297
(0.7449)
-0.1411***
(0.0221)
-0.7680***
(0.2144)
0.1202
(0.1384)
-0.4174**
(0.1722)
-3.9095
(11.0715)
0.5589
(0.7698)
-0.2204***
(0.0581)
-0.1445***
(0.0221)
-0.7318***
(0.2154)
0.1076
(0.1383)
-0.4624***
(0.1733)
-8.3457
(11.2217)
0.6541
(0.7693)
-0.2282***
(0.0581)
37.7457***
(14.0012)
0.4579***
(0.0612)
27379***
(781.7)
0.4078***
(0.0638)
26897***
(766.4)
0.4145***
(0.0635)
26583***
(757.7)
0.4150***
(0.0634)
26471***
(754.5)
0.4132***
(0.0635)
26463***
(754.2)
0.4134***
(0.0635)
26462***
(754.2)
0.4021***
(0.0641)
26289***
(748.9)
0.3883***
(0.0648)
26205***
(746.1)
1984
25715
-12849
1984
25683
-12828.9255
1984
25671
-12817
1984
25673
-12813
1984
25682
-12813
1984
25692
-12813
1984
25687
-12805
1984
25689.8270
-12801
821.68
0.0000
2332.68
0.0000
600.48
0.0000
7503.84
0.0000
1681.69
0.0000
1036.62
0.0000
963.55
0.0000
1356.02
0.0000
46.71
0.0000
47.45
0.0000
48.07
0.0000
48.17
0.0000
61.96
0.0000
69.50
0.0000
41.33
0.0000
41.80
0.0000
41.88
0.0000
53.19
0.0000
60.73
0.0000
Integral
Sustainable
Indigenous
GDP
Pop_dens
Rainfall
Cattle
Wx
Forest
Integral
Sustainable
Indigenous
GDP
Pop_dens
Rainfall
Cattle
rho
sigma2_e
Observations
AIC
Log lik.
Hausman test
χ2 statistic
p-value
Test DSDM vs DSAR: β2 = β4 = 0
χ2 statistic
p-value
17.58
0.0000
48.68
0.0000
Test DSDM vs SEM: β2 = −ρ ∗ β1 or β4 = −ρ ∗ β3
χ2 statistic
p-value
6.46
0.0110
40.28
0.0000
40.17
0.0000
Standard errors in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01
34
Table B.2: Regression of error terms of tables B.1 on the explanatory variable
Forest
(1)
errora1
-0.0001
(0.0030)
(2)
errora2
-0.0001
(0.0033)
-0.0000
(0.0208)
(3)
errora3
-0.0001
(0.0034)
-0.0000
(0.0209)
0.0001
(0.0253)
(4)
errora4
-0.0001
(0.0034)
-0.0001
(0.0211)
0.0001
(0.0263)
0.0002
(0.0283)
(5)
errora5
-0.0001
(0.0034)
-0.0001
(0.0211)
0.0001
(0.0263)
0.0002
(0.0283)
0.0274
(4.3401)
(6)
errora6
-0.0001
(0.0034)
-0.0001
(0.0211)
0.0001
(0.0264)
0.0002
(0.0283)
0.0265
(4.3464)
0.0014
(0.3909)
(7)
errora7
-0.0000
(0.0034)
-0.0001
(0.0211)
0.0001
(0.0263)
0.0002
(0.0282)
0.0238
(4.3365)
0.0013
(0.3932)
0.0001
(0.0158)
1.0689
(39.6580)
1984
0.7929
(45.0092)
1984
0.7386
(45.4315)
1984
0.6973
(46.0980)
1984
0.5810
(48.7321)
1984
0.5273
(51.2485)
1984
0.3063
(60.4554)
1984
Integral
Sustainable
Indigenous
GDP
Pop_dens
Rainfall
Cattle
Constant
Observations
Standard errors in parentheses; * p < 0.10, ** p < 0.05, *** p < 0.01
35
(8)
errora8
-0.0000
(0.0034)
-0.0001
(0.0211)
0.0001
(0.0263)
0.0002
(0.0282)
0.0220
(4.3741)
0.0013
(0.3927)
0.0001
(0.0158)
0.0092
(4.9281)
0.2470
(62.8017)
1984
Table B.3: Test of the impact of protected areas independently on deforestation
L.Def
Integral
(1)
Def
0.2011***
(0.0161)
-0.0371*
(0.0205)
(2)
Def
0.2164***
(0.0157)
Sustainable
0.0905***
(0.0238)
Indigenous
GDP
Pop_dens
Forest
Rainfall
Cattle
Wx
Integral
-0.2783
(4.6886)
-0.1023
(0.4255)
0.0622***
(0.0039)
0.1900***
(0.0502)
-2.9443
(4.9610)
-0.8385
(4.7098)
-0.1098
(0.4275)
0.0655***
(0.0036)
0.1784***
(0.0506)
-2.8051
(4.9581)
-0.2638**
(0.1258)
Indigenous
Pop_dens
Forest
Rainfall
Cattle
rho
sigma2_e
Observations
AIC
Log lik.
-0.0416
(0.0264)
-0.3648
(4.7031)
-0.0878
(0.4268)
0.0642***
(0.0036)
0.2010***
(0.0504)
-0.9616
(4.9677)
-1.0802***
(0.1819)
Sustainable
GDP
(3)
Def
0.2125***
(0.0157)
-8.4947
(11.3048)
0.6398
(0.7754)
-0.1408***
(0.0200)
-0.2304***
(0.0580)
36.1491**
(14.0476)
0.3838***
(0.0650)
26626***
(758.0)
1984
25700
-12817
-9.4607
(11.3587)
0.7614
(0.7787)
-0.0952***
(0.0198)
-0.2192***
(0.0587)
36.9481***
(14.1276)
0.4366***
(0.0625)
26872***
(766.5)
1984
25725
-12829
-0.6376***
(0.1401)
-9.8423
(11.3389)
0.7031
(0.7775)
-0.1369***
(0.0201)
-0.2521***
(0.0584)
41.5257***
(14.1137)
0.4060***
(0.0639)
26788***
(763.2)
1984
25715
-12824
1610.51
0.0000
1816.82
0.0000
957.58
0.0000
Hausman test
χ2 statistic
p-value
Test DSDM vs DSAR: β2 = β4 = 0
χ2 statistic
p-value
70.73
0.0000
37.38
0.0000
63.46
0.0000
Test DSDM vs SEM: β2 = −ρ ∗ β1 or β4 = −ρ ∗ β3
χ2 statistic
p-value
58.91
0.0000
24.93
0.0004
49.24
0.0000
Standard errors in parentheses; * p < 0.10, ** p < 0.05,
*** p < 0.01
36
Table B.4: Marginal effects of regressions in Table B.3
(1)
Def
Direct
Integral
(2)
Def
-0.0735***
(0.0230)
Sustainable
0.0814***
(0.0267)
Indigenous
GDP
Pop_dens
Forest
Rainfall
Cattle
Indirect
Integral
-0.2165
(5.1312)
-0.0601
(0.4538)
0.0583***
(0.0036)
0.1950***
(0.0473)
-0.8853
(4.9403)
-0.8801
(5.1538)
-0.0597
(0.4558)
0.0628***
(0.0033)
0.1831***
(0.0476)
-0.5060
(4.9224)
-0.3928
(0.2432)
Indigenous
Pop_dens
Forest
Rainfall
Cattle
Total
Integral
-14.1454
(15.3314)
0.8432
(0.9871)
-0.1857***
(0.0347)
-0.2586***
(0.0587)
51.9377**
(20.6304)
-17.5180
(16.7141)
1.1133
(1.0769)
-0.1173***
(0.0357)
-0.2536***
(0.0615)
58.0486**
(22.8566)
-0.3114
(0.2519)
Indigenous
Pop_dens
Forest
Rainfall
Cattle
-1.0683***
(0.2623)
-16.9090
(15.8926)
0.9819
(1.0255)
-0.1831***
(0.0360)
-0.2891***
(0.0603)
63.8156***
(21.7882)
-1.7872***
(0.3372)
Sustainable
GDP
-0.0653**
(0.0283)
-0.3750
(5.1461)
-0.0418
(0.4551)
0.0602***
(0.0034)
0.2051***
(0.0475)
1.4129
(4.9381)
-1.7137***
(0.3306)
Sustainable
GDP
(3)
Def
-14.3619
(15.3772)
0.7831
(0.9913)
-0.1274***
(0.0343)
-0.0636**
(0.0289)
51.0523**
(20.2904)
-18.3981
(16.8857)
1.0535
(1.0911)
-0.0545
(0.0354)
-0.0705**
(0.0320)
57.5425**
(22.6726)
-1.1336***
(0.2653)
-17.2840
(15.9882)
0.9401
(1.0331)
-0.1229***
(0.0358)
-0.0840***
(0.0306)
65.2285***
(21.5638)
Standard errors in parentheses; * p < 0.10, ** p < 0.05,
*** p < 0.01
37
Table B.5: Regression of error terms of tables B.3 on the explanatory variables
GDP
Pop_dens
Forest
Rainfall
Cattle
Integral
(1)
error1
0.0220
(4.4059)
0.0013
(0.3957)
-0.0001
(0.0033)
0.0001
(0.0159)
0.0108
(4.9520)
-0.0000
(0.0208)
(2)
error2
0.0323
(4.4251)
0.0019
(0.3973)
-0.0001
(0.0031)
0.0001
(0.0160)
0.0152
(4.9616)
Sustainable
0.0002
(0.0253)
Indigenous
Constant
Observations
AIC
BIC
Log lik.
(3)
error3
0.0262
(4.4185)
0.0015
(0.3968)
-0.0001
(0.0031)
0.0001
(0.0160)
0.0109
(4.9691)
0.3187
(62.5241)
1984
25624.2803
25663.4304
-12805.1401
0.3254
(60.2647)
1984
25640.9702
25680.1203
-12813.4851
Standard errors in parentheses
* p < 0.10, ** p < 0.05, *** p < 0.01
38
0.0002
(0.0269)
0.2790
(60.4978)
1984
25635.5888
25674.7389
-12810.7944