The Role of Corruption on Deforestation in Amazon Forest

Cassandro Maria Da Veiga Mendes1

Sabino Porto Junior

Federal University of Rio Grande do Sul –Applied Economics (PPGE), Brazil

Abstract

The environment problems related with deforestation has been the main concern of the

government around the world. Due the general concern, the main policies adopted by

the governments and advised by many economist is the use of external regulation, e,g.,

fines to control the problem. We use a simple model of static game theory to analyze the

case of Brazil. Results show that, the inexistence of robust institutions may undermine

the effectiveness of such policies. Our results show that the policies of external control

just have effective outcome, when the agency problem, between the government and the

official, is solved, otherwise, the outcome may be more deforestation.

Key-Words: Illegal Deforestation. Regulation. Corruption. Game Theory

JEL: Q10, Q18, Q23.

1 Corresponding author, contact: cassandromendes@hotmail.com.

2

The Role of Corruption on Deforestation in Amazon Forest

Abstract

The environment problems related with deforestation has been the main concern of the

government around the world. Due the general concern, the main policies adopted by

the governments and advised by many economist is the use of external regulation, e,g.,

fines to control the problem. We use a simple model of static game theory to analyze the

case of Brazil. Results show that, the inexistence of robust institutions may undermine

the effectiveness of such policies. Our results show that the policies of external control

just have effective outcome, when the agency problem, between the government and the

official, is solved, otherwise, the outcome may be more deforestation.

Key-Words: Illegal Deforestation. Regulation. Corruption. Game Theory

JEL: Q10, Q18, Q23.

3

1. Introduction

Deforestation is one of the main environmental problems in countries with great

extensions of rainforest, like Thailand, Malaysia, Indonesia, Congo, Ghana and Brazil,

etc. There is substantial research on various aspects of deforestation, and economic

reasons stand out as primary causes of the problem. Third world countries are the most

at risk of deforestation due to weak or non-existent of institutions (Contreras-

Hermosilla, 2001).

Given the pressing importance on the matter, many countries, among them

African ones, are trying to increase public awareness of the problem, mainly in rural

areas. (Nair e Komero, 2004). In Brazil, illegal deforestation of the Amazon rainforest

is, currently, an debated and talked issue in the national media.

According to a study by Instituto Nacional de Pesquisa Espacial (INPE), the rate

of deforestation decreased in the period 1988-2007. The main culprits of deforestation

are cattle ranchers (60 – 70%), followed by squatters (30 - 40%). Timber extraction and

civil engineering projects are responsible for fewer than 5% of total deforestation.

The economic aspect of the matter inspired endogenous policies that take in

account the profit seeking behavior of the agents, as a way to minimize illegal

deforestation. One of such policy is soil management, which has been considered an

effective way of minimizing deforestation.

The current federal administration plans to decrease deforestation by

introducing more severe penalties and stricter surveillance. However, this policy doesn’t

contemplate the possibility of corruption by the officials. According to Viana (1998)

and Amacher (2006 b)), 80% of the timber extracted from the Amazon forest is illegal.

This fact indicates that, beyond increased surveillance, corrupt practices must be dealt

with, because corruption is possibly one important cause for such high percentage of

illegal deforestation.

4

There are substantial literatures on the economic causes of corruption. The

subject is no longer ignored in the environment economics field, and some research

points corruption as an important determinant in the illegal deforestation. Amacher

(2006 a, 2006 b) assesses the importance of taking corruption into account in fighting

illegal deforestation.2.

Some international studies on deforestation (Pelligrini (2007), Wibowo and

byron (1999), Palo (2002), Amacher (2006), etc, warn about corrupt practices in forest

management and suggest harsher policies (heavier fines, more severe punishment for

those who organize corruption schemes (i.e., landowners)), as a way of curtailing illegal

deforestation. However, the information asymmetry that results of weak institutions

stimulates opportunists behavior (Nair e Kowero, 2004)3. The existence of collusion

undermines the effectiveness of the government policies. That is, in the presence of

information asymmetry, corrupt practices cannot be stopped just by imposing harsher

punishment for corruption.

Research in Brazil on deforestation is concerned mainly with dealing with

squatters and ranchers and with improving soil management techniques4. Information

asymmetry almost always breeds corruption and conduces to results different from the

ones intended. So, one policy of closer surveillance and harsher punishment to squatters

and ranchers may not result in less deforestation, because surveillance and dispensing

fines are not directly controlled by the central government (i.e., the high rank officials),

but by low rank, low salaries officials. So, assuming the existence of information

asymmetry between government and low rank officials appears an agency problem. In

such a situation, fraud is a possible equilibrium outcome, leading to illegal

deforestation.

This paper puts in question the partial results of the policy of increased

surveillance and heavier penalties for squatters, ranchers, lumber producers and others

2 Várious works like: Contreras-Hermosilha (2001), (2003), Pelligrini (2007), Wibowo and Byron (1999), Palo (2002), McAllister (2005), Kowero and Nair (2004), analyze the role of corruption in stimulating deforestation. 3 Existence of information asymmetry and the resulting corrupt practices persuaded some researchers that heavier penalties and closer surveillance are the most effective policies. In this paper game theory is used to show that heavier penalties not necessarily decrease the rate of deforestation. On the contrary, it is shown that, due to information asymmetry, these harsher policies could lead to increased deforestation. 4 These matters are relevant in fighting illegal deforestation. Nevertheless, this paper intends to show that corruption is an issue that cannot be neglected.

5

activities that implies in illegal deforestation. The central point of this paper, (a point

neglected in other papers), is the possibility of collusion between the landowner and the

IBAMA official. This collusion, besides eliminating the effects of penalties on the

landowners also guarantees that, under certain conditions, the penalties for corrupt

officials (i.e., the ones with inspection duties) may not result in less illegal

deforestation. This possibility is contrary to the mainstream international research on

corruption. Imposing penalties is a necessary but not sufficient condition to eliminate

collusion. The central result of this paper is that, when there is information asymmetry,

heavier penalties for the landowner may result in more illegal deforestation.

Beyond this introduction the papers is structured in the following way: the next

sub-sections presents some highlights about the linkage between the forest sector and

corruption, the following one we will present the model used here. The second section

presents the conclusion of the paper.

1.1 Corruption and the Forest sector

The linkage between corruption and the Forest sector is not a new issue, the

international researches has claimed that the government have to incorporate such

element in any policy adopted, e.g., see Damania (2002); Pellegrini and Gerlagh (2006);

Amacher (2006); Transparency International (2002), (2007).

Despite the well known influence of corruption in the forest sector, the way that

they are co-related still little known, (Tranparency International, 2007). The existence of

such phenomenon can undermine all the policies i.e., external policies, to avoid the

illegal logging, Damania (2002)5.

Pellegrini (2006b), through a cross-section approach, found that between

democracy and corruption, the first is the most important to control the Forest.

Moreover, the democracy doesn’t have statistic influence on the environment controls.

Welsch (2004) analyzed the influence of corruption and Per capita GDP in the

pollution levels. He found that there is a monotonic positive relationship between

pollution and corruption, and negative influences of the Per capita GDP on the pollution 5 The problem of corruption in the forest sector is also responsible for great tax revenue evasion. The Liberian government loose each year many millions of dollars due this kind of problem (Transparency International (2007).

6

There is an international consensus that corruption has an important role in

illegal logging. However, this reality has not been given much attention by Brazilian

researches and government. There is so many works spending a great effort in

empirical/econometric analysis, while theoretical questions are disregarded. The

announced policies from the government only strikes those directly related with illegal

logging, i.e., farmers, etc. there no internal mechanism design to avoid the problem of

agency. Thus, given the private interest of the involved agents, the outcome of any

policy may be totally different. The inexistence of an internal surveillance mechanism

allows presence of an environment of collusion and corruption. At this point, it seems

that is important to analyses such peculiarity of the illegal deforestation in Amazon

forest. In this context, game theory seems to be a powerful tool to model these

interactions and incentives.

Our work introduces several new ideas about how corruption may influence the

illegal deforestation level in Brazil. The use of the game theory is not a new one, but its

application, for the case of Brazil, is. The present paper intends to fill some theoretical

gaps left by previous studies, thus, we intend to make a zoom in about the process of

illegal deforestation in Amazon forest. For this purpose, we present a game theoretical

model of corruption and incentives with many modifications in relation with empirical

works. The paper also analyses the influences of external policies, used by the Brazilian

government, in the level of illegal deforestation. We used many environment scenarios

to analyze the direct and indirect ways that corruption may influence the effectiveness

of the government policies.

1.2. The Static Game Models with Imperfect Information

We follow the same approach of Mendes (2009), and we suppose n the model,

that there are three players: the landowner, the government official and the government.

A proportion ϒ of the number of officials is composed of corrupt individuals. Let T be

the size of the forest which belongs to the representative landowner, where it the lower

bound is and st the upper bound. The landowner is allowed to clear the forest up to the

limit mt , which is a number between the lower and upper bounds. If the landowner

surpasses the upper limit, he receives a fine ( )δ . Surveillance is not done directly by

the government, but by a hired official. After the area is inspected, the hired official

7

reports to the government possible occurrence of illegal deforestation. At the end of the

period, the official earns a salary ( )w , not contingent on his reports6. The official net

gain, when he investigate the agent, is salary menus the effort applied. The

landowner can choose whether to clear the forest up to the allowed limit or to go

beyond the limit and risks to be fined. That is, there are two states of nature: when the

landowner clears more forest than he is allowed to ( )imt t> and when the landowner

respects the limit ( )imt t≤ 7. The real state of nature is not known by the government,

because the official may decide to not report illegal deforestation8. If all officials are

honest ( 0)ϒ = , then the reports received by the government precisely inform whether

the landowner cleared more forest than he was allowed to. If the honesty of officials is

questionable, the government has just a probability distribution over the real state of

nature. One aim of this paper is to find out whether the proposed relationship involving

the players incentive the collusion.

The actual relationship between the three players is: there is the landowner, L ,

who can choose to illegally clear the forest, ID , or not NID . The landowner may be

inspected, I , (or not NI) ,by the official, F , with probability q. If an investigation

takes place, the official finds out whether illegal deforestation occurred, mit t> , or not,

imt t≤ . The government, G , receives the report, but doesn’t know, for sure, the actual

state of nature. It just has a probability distribution of the real state of nature.

Given the relationship involving the three players, it is possible to ascertain the

effects of collusion between the landowner and the corrupt official. The analysis is

made by means of simultaneous games between the landowner and the IBAMA official.

6 The salary of the official is not contingent on government revenue from fines on landowners that cleared Forest beyond the upper limit. 7 Under a policy of giving fines which magnitude is not correlated to the magnitude of the damage done (illegal deforestation), the following result is trivial:

: such that : , ; ,j i jm st t t t t j i i jδ +∀ ∈ℜ ∀ > ⇒ = ∀ > ∈ � , where the index represents the degree of

deforestation (the greater the index, the bigger the amount of deforestation). Since the penalty is fixed and known, the dominant strategy for the landowner is to clear all his land. That is, this policy brings about the possibility of total deforestation. 8 We assume that the official has the means to appraise the real state of nature when inspecting a landowner’s lot.

8

Type of Equilibriums in the simultaneous game

In the game between landowner and official, let the compact set { }1 2,is s s= , be

the actions space for each player. There is a pay-off function for each player, suitable

for the strategy adopted in response to the one adopted by the other player. For clearer

explanation, the game played is a simultaneous one. The strategies set for each player,

are:

1

2 i

s colludes

s not collude

== =

We follow the same approach of Mendes (2010), thus, the landowner’s profit,

( , )p vπ is a function of the prices level p and of output ν 9. Sales depend directly on

the deforested area t , where { },i mt t t∈ and ( )tν λ= . It is assumed that: 0 0t ttλ λ> ∧ = .

In the special case that the coefficient equals the unity, the landowner’s profit is ( , )p tπ .

The official’s pay-off is given by the salary w earned in the end of the game.

To make feasible the game, is necessary to analyze the case of illegal

deforestation, that is, when imt t> 10. When illegal deforestation takes place, the

landowner can allure the official by proposing collusion. The official may agree to

collude or not11. If the official accepts, he has a pay-off given by ( )mw w t t+ ∆ > , (Case

D below) where ( )mw t t∆ > represents the bribe paid by the landowner. The

landowner’s pay-off, in this case, is given by ( , ) ( , )mp t p t tπ π ε+∆ > − (Case A below)

where ( , )mp t tπ∆ > represents the earnings from clearing the forest beyond the allowed

area, and ε represents the fine due to the official, ( , )mp t tπ +∆ > ∈ℜ and ε +∈ℜ 12, is

9 For example, the landowner who engages in logging has a profit that is a function of the price of the cubic meter and the quantity of timber extracted from the forest. For the sake of simplicity, production costs (capital and labor) are considered as zero. 10 When there was not illegal deforestation, landowner and official have no reason to collude. So the situation of interest is the players´ behavior in the event of illegal deforestation. 11 Any one of the players can propose collusion. That is, once the official finds out about the illicit act, he may offer a collusion agreement to the landowner. 12 Collusion makes possible to landowner and official to split the fine due to the government. Bargaining power is considered the same to both parties. It will be seen how shifts in the bargaining power of the parties do not affect illegal deforestation. The possibility of collusion is profitable to the landowner if

(.) (.)π ε π δ∆ − > ∆ − .

9

easy to see that ( , )mp t tπ ε∆ > = . However, if the official choose to collude but the

landowner not, his pay-off will be just his salary (Case C below), in this case the pay-

off for the landowner would be ( , ) ( , )mp t p t tπ π δ+ ∆ > − (Case B below) where δ is

the fine imposed, to the landowner, by the government,

0 ( , ) , mp t tε π δ δ +< ≤ ∆ > < ∈ℜ ≤ ∞ 13. In the event of illegal deforestation and the

official is not willing to take the bribe, his pay-off depends of the strategies of the

landowner: if the landowner decided to collude, he can receive w α+ (Case C´´ Below)

where w represent the salary and α represent external or internal incentives received

by the official, in this case the landowner would receive ( , ) ( , )mp t p t tπ π δ+ ∆ > − (case

B below). However, if the landowner didn’t collude he receive just w i θ− + (case C´

below) where i represent the net cost of effort (exogenous determinate), and θ represent

the internal gains due the decision for not colluding, i.e., moral issues (see Carrillo

(2000), he uses the same approach in a different modeling)14, in this case the landowner

would receive ( , ) ( , )mp t p t tπ π δ κ+∆ > − − where κ represent the landowner social

cost for the media national communication on the matter15. The following chart shows

the normal representation of the game.

13 In the event of illegal deforestation, the fine is split between landowner and official. The landowner’s amount enters in (.)π∆ . The fine for illegal deforestation is defined as xδ ε= + ., where x represents

the part not deductible from the landowner’s profit i.e., 0xδ ε> ∀ ≠ . Thus, for the same bargaining

power, ( , )mx w p t t= ∆ > . The condition that the fine be limited, postulated by other researchers, is not necessary. In fact, this paper shows that, in the presence of information asymmetry, even heavy fines ( )δ →∞ cannot promote a first best solution. On the contrary, such policies may bring worse outcomes

for society. 14 In the present model we suppose that when the landowner is available for colluding, and the official is not, the latter can receive an internal or external benefit for his behavior. The internal gain represents his moral well-being for not got in a corrupt process. The external incentives can represent promotion in his job. 15 Is a fact that when IBAMA officials found any illegal deforestation related with any enterprise (landowner), they are widely exposed through the media communication about. These national communications impose a moral cost to the enterprise. In our model, these costs are presented by k. Thus, there is a difference in this case with the one when the landowner opted to collude (Case B), in the latter, the landowner opted to collude and we suppose that in such case the landowner cannot be exposed to the media, thus he is just fined directly.

10

The game in its normal form is:16

Official

Landowner

Collude Not collude

Collude D, A C, B

Not collude C’’, B C’, B’

Where: ( , ) ( , )mA p t p t tπ π ε= +∆ > −

( , ) ( , )mB p t p t tπ π δ= + ∆ > −

C w=

´´C w α= +

( )mD w w t t= + ∆ >

' ( , ) ( , )mB p t p t tπ π δ κ= + ∆ > − −

'C w i θ= − +

The analysis of the strategies shows that there is a dominant strategy to both

players. That is, the equilibrium is reached through dominant strategies. To reach this

equilibrium, we need some assumption: (.)w α∆ > ; i θ> ; δ ε> .

16 The components of the pay-offs represented in the game are: the right side represent the official pay-off and the left side represent the landowner pay-off.

11

Typology of the Equilibrium: Mixed Strategies Equilibrium17

The engagement of the individuals in the collusion process, demands several

worries about the behavior of the other player, that is, nobody has the conviction about

the strategy that the other player will adopt. So, the best way to analyze such kind of

situation is to analyze the mixed strategies in the game played between both, i.e.,

landowner and IBAMA official. In such way, the new static form is presented in the

following way:

Official

Landowner

Collude (q) Not collude (1-q)

Collude (p) D, A C, B

Not collude (1-p) C’’, B C’, B’

Where p represent the probability that the Official will opt to collude, in the

same sense, q represent the probability that the Landowner will collude. Given the

structure we can define a p=p* such that the Landowner is indifferent between the both

choices, or q=q* such that the Official in indifferent between both choices. To calculate

such probabilities we can analyze the expected gain, from each player point of view, in

each case.

The case of pure strategies equilibrium is just a particular case (degenerate one)

of mixture equilibrium. To analyze the relationship between the two agents we must

introduce the expected gain from each strategy.

17 The consequence of the pure strategies equilibrium is well defined in Mendes (2009). Nevertheless, the pure strategies equilibrium is just a degenerate case of the mixed strategies equilibrium.

12

Mixed Strategies Equilibrium

The Problem for the Official

The expected gain for the colluding or not, for the official, depends of the

strategies adopted by the landowner. The expected gain for colluding is:

( ) ( ) [ ](.) 1w w q w q E C+ ∆ + − → (1)

And for not colluding, is:

( ) ( ) ( ) [ ]1w q w i q E NCα θ+ + − + − → (2)

The official is indifferent between colluding or not if [ ] [ ]E C E NC=

Solving the official problem we find that, the probability of collusion from the

landowner point of view, is:

( ) ( )

*(.)

iq

i wθ

α θ−

=+ − ∆ +

Note that, as a probability we must have: [ ]* 0,1q ∈ thus, we must have:

( ) ( )(.)i wα θ+ > ∆ + or ( ) ( )(.)i wθ α− > ∆ − .

The Problem for the landowner

The expected gain for the colluding or not, for the landowner, depends of the

strategies adopted by the official. The expected gain for colluding is:

( ) ( )( ) [ ](.) (.) (.) (.) 1p p E Cπ π ε π π δ+ ∆ − + + ∆ − − → (3)

And for not colluding, is:

( ) ( )( ) [ ](.) (.) (.) (.) 1p p E NCπ π δ π π δ κ+ ∆ − + + ∆ − − − → (4)

The official is indifferent between colluding or not if [ ] [ ]E C E NC=

Solving the landowner problem we find that, the probability of collusion from the

official point of view, is:

13

( )

*pκ

ε κ δ=

+ −

According with the results, we can see that the condition for existence of equilibrium in

this relationship, we must have the following conditions satisfied:

For the Official:

( ) ( )

( )( ) ( )

(.),

(.) (.)

wii w i w

θ αθα θ α θ

− +∆− + − ∆ + + − ∆ +

And

( ) ( ),

κ ε δε κ δ ε κ δ

− + − + −

For the landowner.

Given the set of probabilities, the landowner and the official are indifferent if

these probabilities are considered. Thus, we can use the static comparative to analyze

the effect of some policies in the probabilities kept for each player.

Mixed Strategies Equilibrium and “ex-post” collusion: effects on illegal

deforestation

To analyze the effect of the policies adopted by the government, for the case of

mixed strategies equilibrium, we can use the static comparative. On the earlier section,

we obtained the following probabilities:

The probabilities that the landowner will collude (being corrupt), is:

( ) ( )*

(.)i

qi w

θα θ

−=

+ − ∆ +

The probably that official will collude (being corruptible), is:

( )*p

κε κ δ

=+ −

14

Thus, we have the following results:

( ) ( ) 2

*0

(.) (.)

q iw i w

θ

α θ

∂ −= >

∂∆ + − ∆ +

That is, the increase of bribe increase the incentive for the landowner to opted to

collude because he knows that more corrupt gain more available the official will be for

corrupt behavior.

( ) ( ) 2

*0

(.)

q i

i w

θα α θ

∂ −= <

∂ + − ∆ +

More internal incentives, e.g., promotion, can be an important tool to avoid the

problem. As we can see, the partial derivates indicates that more incentives will reduce

the probability of the landowner to collude. Thus, this kind of policies cannot be

neglected by the government.

( ) ( ) 2

* (.)0

(.)

q wi i w

α

α θ

∂ −∆= <

∂ + − ∆ +

The net effort implemented can be another important issue for the decision

adopted by the landowner, because this variable can be determinant for the official

decision about the strategy of collusion.

We can also analyze the effect of the penalties, δ, (those announced by IBAMA)

when the principal (Brazilian Government through the IBAMA) don’t get an internal

process of auditing about the reports from the officials incharged with the surveillance.

Since:

(.)w α∆ >

we have:

15

* (.). 0

(.)q q w

wδ δ++

∂ ∂ ∂∆= >

∂ ∂∆ 123123

The present results show the dramatic situation about the effectiveness of the

policies adopted by the Brazilian Government. We summarize this finding through the

following proposition:

Proposition-1:(Crowding-out proposition): Ceteris Paribus, an increase of the penalty

for landowners engaging in illegal deforestation,δ , engenders greater incentives for

collusion, increasing illegal deforestation.

Proof: (cited above).

Based on the regulation theory, the Brazilian Government has applied higher

fines to avoid the problem. However, the static comparative shows that more penalties

increase the landowner probability in colluding. Thus, the regulation theory has not

been adequately adopted by the government, and the economists have forgotten how the

incentives between the all three-party are important for the effective outcome.

We can also use the static comparative to analyze the effect some variables on

the probability of collusion from the official point of view.

The probability that the official will be collude is given by:

( )

*pκ

ε κ δ=

+ −

Thus, using trivial calculus we find that:

( ) 2

*0

p ε δκ ε κ δ

∂ −= <

∂ + −

The more are the cost for media exposition, more risk the landowner will incurs. Thus,

an increase in this cost will make the landowner less likely to commit corrupt behavior.

The interesting question, is how the official will behave when changes the

parameters of the policies used by the government. The results show that:

16

( ) 2

*0

p kδ ε κ δ

∂= >

∂ + −

Proposition-2:(Crowding-out Proposition 2): Ceteris Paribus, an increase of the

penalty for landowners engaging in illegal deforestation,δ , engenders greater

incentives for collusion, from the Official point of view, increasing illegal deforestation.

Proof: (cited above).

The results show that the policies of more penalties more the official will want

to collude, because more penalties means more bribe paid by the landowner. This

results show that the increasing penalties can make more profitable the corrupt behavior

from the official point of view. This result can be more easily obtained when we analyze

the influence of the bribe paid and probability of colluding. As we stressed earlier,

xδ ε= + that is ( )fε δ= and so, 1( )fδ ε−= , really speaking, we get δ λε= , where

(1,sup( )λ + ∈ ℜ < ∞ so we have (do not forget that (.)wε = ∆ ):

( ) 1

*( )

kp

ε κ δ ε−= + −

Such that: {{

*. 0

p p δε δ ε

+ +

∂ ∂ ∂= >

∂ ∂ ∂

Because: ( )

( ) 2

1*0

1

p κ λε λ ε κ

− −∂= >

∂ − +

Thus, the probability to be corrupted increases as the bribe paid increase. We use this

approach and we make endogenous the determination of the bribe paid. This result,

again, shows that the policies adopted by the governments may backfire the ex-ante

expected outcome.

Equilibrium Strategies and the Influences of Surveillance by the Government:

Mixed Equilibrium

We can analyze the influences of the surveillance used by the government to

avoid the problems of corrupt behavior. To analyze this policy, we suppose that,

17

initially, the agents are indifferent between two possibilities, namely: illegal

deforestation or not:

( ) ( ) ( )( ) ( ) [ ](.) 1 (.) 1w w w w F q w q E Cβ β+ ∆ − + + ∆ − + − → (5)

( ) ( ) ( ) [ ]1w q w i q E NCα θ+ + − + − → (6)

The term F that represents the fines for corrupt behavior, and the term β , that

represent the probability that the official will be investigated. Solving for the

indifference level we obtain the following outcome:

( )

( ) ( )*

(.)

i Fq

i w

β θα θ− +

=+ − ∆ +

For the landowner the problem will be:

( ) ( )( )( ) ( ) ( ) [ ](.) (.) (.) (.) 1 (.) (.) 1p p E Cπ π ε φ β π π ε β π π δ+ ∆ − − + + ∆ − − + + ∆ − − →

(10)

When he opts to collude, and:

( ) ( )( ) [ ](.) (.) (.) (.) 1p p E NCπ π δ π π δ κ+ ∆ − + + ∆ − − − → (7)

Otherwise. The indifferent condition, implies that the two expected gain will be the

same. Solving for this condition we find that:

( )

*k

pk ε φβ δ

=+ + −

Where φ represent the fine paid by the landowner when the official is investigated.

Note that we suppose that when the surveillance is done by the government, he discover

the real state of nature. In this case both players are penalized, i.e., the official and the

landowner, thus in this case the landowner receives two penalizations.

With these two results, we can analyze the static comparative when changes the

parameters of government policies, namely: , β φ .

18

( ) ( )( ) ( ) 2

(.)*0

(.)

F i wq

i w

α θβ α θ

− + − ∆ + ∂ = <∂ + − ∆ +

( ) ( )( ) ( ) 2

(.)*0

(.)

i wqF i w

β α θ

α θ

− + − ∆ + ∂ = <∂ + − ∆ +

The results show that, there is a positive effect of the policy of surveillance in

the probability that the landowner will want to collude. More surveillance will increase

the expected loss for engaging in the illegal activity, and these new environment will

lower the incentives for colluding (from the landowner point of view).

The condition of indifference for landowner implies that:

( )*

kp

k ε φβ δ=

+ + −

Thus:

( ) 2

*0

p k

k

βφ ε φβ δ

∂ −= <

∂ + + −

The probability that the official will commit fraud depends on the fines paid by

the landowner, when he engaged in the corrupt dealing. Increasing the latter, we will

have a decrease of the first one. This result means that the policy of surveillance can be

an important tool to avoid the problem. Using the same approach, we can see the

influence of the probability of surveillance. Results have shown that:

[ ] [ ]1

lim * sup * 0,1p pβ→

= ∈

That is: ( ) 2

*0

p kF

kβ ε φβ δ

∂ −= <

∂ + + −

Thus, the policy of internal surveillance and fines can be an important tool to avoid the

problem of illegal deforestation, i.e., to avoid the agency problem. However, as

expressed in Greezy and Rustichini (1998), the fines can be adopted as price from both

players. So more fines, from engaging in illegal behavior, will be incorporated in the

19

pay-offs by the agents. Thus, the effectiveness of such policies can be mined if we have

a wealth effect bigger than the price or cost effect.

The Substitution Effect and the Crowing out effect (Wealth

Effect)

The important issue to answer is the effect of both policies, i.e., fines from

engaging in illegal deforestation, surveillance and fines from engaging in corrupt

behavior. A nave analysis would defend that these policies, jointly, would mitigate the

problem of illegal deforestation in Amazon forest. Using simple calculus we can find

the answer. Ceteris paribus, we can define the probability to collude, from the Official

point of view, as:

( ),p f φβ δ=

Thus using the derivate approximation, we find that:

( )

{( )

{( ), ( ),

( )

f fp

φβ δ φβ δφ δ

φβ δ +++−+−

∂ ∂∆ = ∆ + ∆

∂ ∂142431424314424431442443

If , ( )1 2 0δ δ δ∆ = − >

Where, we can define the first part as a substitution effect and the second part as a

wealth effect or crowding out effect.

The substitution effect represents the change in the official behavior due the

existence of internal surveillance in IBAMA, i.e., more surveillance means more

expected loss. Thus, more surveillance or more fines (for corrupt behavior) represents

more expected cost. This substitution effect makes agents willing to avoid being corrupt

official, i.e., in the case of illegal deforestation he would report the truth to the principal.

The first effect would attract fewer officials for corrupt behavior, and thus making more

costly the illegal deforestation, from the landowner point of view - this result would

imply in less illegal deforestation.

However, the policies adopted by the government would use the fines, δ , in a

landowner point of view, for illegal deforestation. As we see, in presence of such

20

policies, the landowner can offer a bribe to the official, that is, increasing the fines more

available rent would be the official to be corrupt, i.e., 1

(.)w ε δλ

∆ = = .

Thus, increasing the fines would increase the will to be corrupt, from the official

point of view, this result we call the crowding out effect (wealth effect) that can

undermine all the policies adopted by the government, this effect is represented by the

second part in the total derivate. The net effect of the policies depends of the weight of

each effect.

The interesting outcome, in this approach, is that decreasing the penalties and

increasing the expected cost for corrupt behavior, would decrease the incentive for

corrupt behavior. Using derivate approximation we find that:

{ {( , ) ( , )f f

pφ δ φ δ

φ δφ δ −+

+−−−

∂ ∂∆ = ∆ + ∆

∂ ∂14243142431424314243

If ( )1 2 0δ δ δ∆ = − <

In this case, both, the substitution and crowding out effect has negative signal,

meaning that the incentive to collude in lower, meaning more cost for illegal

deforestation from the landowner point of view.

Using the same approach we can test the separate effect of surveillance, penalty,

and the bribe amount.

( , , )p f φ ε β=

Thus, { { {( , , ) ( , , ) ( , , )f f f

pφ ε β φ ε β φ ε β

φ ε βφ ε β++ +

+− −+− −

∂ ∂ ∂∆ = ∆ + ∆ + ∆

∂ ∂ ∂1424314243 1424314424431442443 1442443

Again, we cannot see the net effect of such policies because we have effects with

different signal. In the present case, the part in the middle is the wealth effect, and the

others the substitution effect, because they imply in lower probability to engage in

corrupt behavior.

21

The following charts shows the outcomes of each policies adopted by the government.

Figure- 1: Summary of the effects of the government policies for Mixed

Strategies Equilibrium

Policy Effect

Situation:

η∆ , τ∆

( ( ))mw t t∆ ∆ >

Landowner’s

strategy

(probability

q)

Official’s

strategy

(probability

p)

Illegal

deforestation

Mixed Strategies

Increase “δ ”,

and 0β = .

( ( ))mw t t +∆ ∆ > ∈ℜ increase increase Increases

0τ∆ = , 0φ∆ =

Increase “δ ”,

and ( )0,1β β= ∈

(.) (.).

f fF

Fβ δ

β δ∂ ∂

∆ > ∆∂ ∂

(.) (.).

f fF

βφ δβ δ∂ ∂

∆ > ∆∂ ∂

increase increase Increases

(.) (.).

f fF

Fβ δ

β δ∂ ∂

∆ < ∆∂ ∂

(.) (.).

f fF

βφ δβ δ∂ ∂

∆ < ∆∂ ∂

decrease decrease Decreases

Increase “ω ”,

and δ δ += ∈ℜ .

*β β> , decrease decrease Decreases

*β β< increase increase Increases

22

δ −∆ ∈ℜ

and

β +∆ ∈ℜ

(.). 0

(.)0

f

f

ββ

δδ

∂∆ <

∂∂

∆ <∂

decrease decrease Decreases

0δ∆ = and

0β∆ =

α +∆ ∈ℜ

κ +∆ ∈ℜ

decrease decrease Decrease

Source: Author’s elaboration.

The chart shows that in the event that official and landowner agree to collude,

the policies implemented by the government may be ineffective.

The situation investigated in this paper, shows that the interactions of each

player, creates an incentive to frauds, thus rendering ineffective the policies adopted by

Brazilian government on fighting illegal deforestation in Amazon forest. A new

regulatory framework must be implemented in order to dissuade officials and landowner

from colluding.

2. Conclusion

The agency problem in the relationship between the government and the IBAMA official has widely neglected by theorist and analyst. Such problem can be an important variable in determination the success or not of the government’s policies.

Even thought, many cases of corruption of IBAMA official has been denounced in the media, between a bunch of empirical work on the matter, none of them have incorporates the problem of corruption. Thus, this is the first works that focus in the problem of corruption as leading variable for illegal deforestation.

Using a theoretical approach, static game, we analyzed how the actual relationship between the IBAMA official and the government, can be an important variable for illegal deforestation.

Generally speaking, our model suggests that the actual relationship between the official and the landowner can promote collusion strategy for both player. The gain for the game is greater when they collude than otherwise. In the present context the external regulation policies adopted by the government is useless, that is, corruption can mine all the effort from the government to avoid the problem of illegal deforestation.

23

The result seems somewhat paradoxical when the government uses the policies of heavier fines. In the present context more fines can induce more illegal deforestation.

The fines and penalties is incorporate in the payoff as a price, and thus, cannot mitigate the illegal deforestation if the profitability of the illegal activity still worthy.

The present work defends that all the relationship between the three players must be changed to avoid the problem of corruption. The researchers must change their perception about the problem, and see that corruption can be the main seed under all the process of illegal deforestation in Amazon forest begins.

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