How to determine the optimal fine in court?
Game theoretical and empirical analysis1
January 2004
Sandra ROUSSEAU and Carole Billiet
Centre for Economic Studies
K.U.Leuven
Naamsestraat 69
B-3000 Leuven
Belgium
Sandra.Rousseau@econ.kuleuven.ac.be
Carole.Billiet@econ.kuleuven.ac.be
Abstract
The importance of monitoring and enforcement for the effectiveness of environmental regulation is obvious.
Studying the level of penal fines is a first step in the analysis of which sanctions violators encounter. Our main
objective is to find out which factors determine the type and the stringency of the sanctions. First we perform a
game theoretical analysis to determine the optimal fine set by a judge in a court case. The decisions on how
much to spend on defence and prosecution by the firm and the public prosecutor respectively are influenced by
the optimal fine set by the court. The fine that optimises deterrence will include the damage caused and the extra
costs to society caused by the trial. Secondly we perform an analysis of the level of the fines pronounced by the
Court of Appeal in Gent (Belgium) during the period 1990-2000. Using a regression analysis we aim to confirm
the optimality results obtained in the theoretical analysis. Moreover we also find that it is not plausible to work
with a fixed fine independent of the size of the violation when modelling enforcement issues. Further the results
show that the violator’s compliance history influences the level of the fine. Violators with a criminal record have
a significantly higher probability of receiving a higher penalty. And finally, the fact that declining industries are
being treated more leniently than others is quite intriguing.
Keywords: Monitoring and enforcement / Fines / Environmental Law
We would like to acknowledge the financial support of the SSTC research program PODO II – contract nr.
CP/01/111 (Law & Economics and the Enforcement of Environmental Law). We would also like to thank Ellen
Moons for her useful suggestions.
1
I. INTRODUCTION ............................................................................................................................... 3
II. GAME THEORETICAL ANALYSIS ............................................................................................... 4
1.
Set-up of the game ....................................................................................................................... 4
2.
Decision on the fine by the judge ................................................................................................ 6
3.
Decision of the firm and the Public Prosecutor ........................................................................... 7
3.1 Decision of the Public Prosecutor ............................................................................................. 7
3.2 Decision of the firm ................................................................................................................... 8
3.3 Equilibrium................................................................................................................................ 9
4.
Discussion of the results .............................................................................................................. 9
III. EMPIRICAL ANALYSIS ................................................................................................................. 9
1.
Determinants of the fine level ..................................................................................................... 9
2.
Background to the case study .................................................................................................... 10
3.
Description of variables and data .............................................................................................. 11
4.
Expected results......................................................................................................................... 13
5.
Estimation method..................................................................................................................... 14
6.
Results ....................................................................................................................................... 15
6.1 First instance............................................................................................................................ 15
6.2 Court of Appeal ....................................................................................................................... 17
7.
Discussion of the results ............................................................................................................ 18
IV. CONCLUSION ............................................................................................................................... 20
REFERENCES ...................................................................................................................................... 21
2
I. INTRODUCTION
The importance of monitoring and enforcement for the effectiveness of environmental
regulation is obvious. Without a proper monitoring and enforcement policy environmental
legislation remains an empty chest. An essential decision factor for firms deciding on
compliance is the sanction they can expect if they get caught. Studying the level of penal fines
is an important step in the analysis of which sanctions violators encounter.
First we turn to the existing literature for some related papers. Kilgour et al. (1992) develop
and analyse simple game theoretic models of inspection and enforcement processes. They
compare systems using administrative instruments (namely, irrevocable control orders2) to
those relying on court termination of guilt and punishment. P’ng (1983) develops a model of
strategic behaviour in litigation, which reveals how information is exploited and how the
litigants' strategies are interdependent. The model derives conditions on the parameters under
which suit is filed, the action is settled and the action is tried. Although the court trial is
incorporated in these models, it is not explicitly analysed. The outcome of the court game is
pre-determined. The decision moment in these models falls before the actual verdict. In our
model we start the analysis after the decision to go to court has been taken. The defendant and
the Public Prosecutor have therefore decided not to settle.
Daughety and Reinganum (1994) model both the settlement and litigation process, allowing
for incomplete information about the level of damages (incurred by the plaintiff) on the part
of both the defendant and the court, and use the model to examine the effect of making
settlement demands admissible as evidence in court (currently inadmissible) should a case
proceed to trial. This model is closely related to our model. However, the authors consider
damages paid by the defendant to the plaintiff. We deviate in two respects from this formula.
We allow for punitive sanctions and we do not assume that damages are paid to the victim.
The revenues from fines go directly to the federal government. Andreoni (1991) shows that
uniformly maximal penalties may actually encourage crime rather than deter it if the judicial
system is built on the "reasonable doubt test". He finds that optimal fines should rise with the
severity of the infraction, that is, the penalty should ‘fit the crime’. Polinsky and Shavell
(1998) have made an extensive economic analysis of the optimal level of punitive damages.
We will make use of their insights in order to obtain optimal deterrence by setting fines.
2
A control order may contain a variety of specific provisions, including limiting or stopping the discharge of a
contaminant. It may be issued to the operator of a facility believed to be in violation of the Environmental
Protection Act of Ontario (Canada). The control order can be appealable or irrevocable.
3
Our main objective is to find out which factors determine the type and the stringency of fines.
First we perform a game theoretical analysis to determine the optimal fine set by a judge in a
court case. We identify the different players and their objective function. We distinguish three
parties: the judge, the accused firm and the Public Prosecutor. The decisions on how much to
spend on defence and prosecution by the firm and the Public Prosecutor respectively are
influenced by the optimal fine set by the court. The fine that optimises deterrence will take
into account the damage caused and the extra costs to government caused by the trial.
Secondly, we take a look at the reality and we perform an analysis of the fine level
pronounced by the Court of Appeal in Gent (Belgium) during the period 1990-2000. Using a
regression analysis we aim to confirm the optimality results obtained in the theoretical
analysis. Moreover, we are able to answer three questions. Firstly, is it plausible to work with
a fixed fine independent of the size of the violation when modelling enforcement issues? This
is an assumption which is often encountered in the literature and which is debated quite often.
We find that working with a fixed fine is highly unrealistic. The level of the fine should
depend on the size of the violation. Secondly, does the compliance history of the violator
influence the level of the fine? Following the literature on state-dependent enforcement,
which started with Landsberger and Meilijson (1982), the optimal enforcement scheme should
depend on the defendant’s violation record. Our results suggest that the compliance history is
taken into account when the level of the firm is determined. And thirdly, are firms from
contracting industries punished more leniently? This influence of firm characteristics is often
encountered in the empirical literature (see, for example, Deily and Gray (1991)). We find
evidence that judges take the financial burden of the sanction into account when they decide
on the level of the fine. After all, the hurt caused by a 100 € fine to a poorer firm can be equal
to the hurt caused by a 1000 € fine to a wealthier firm.
In the following section we present the game theoretical analysis. In section three we give the
results of our empirical study and in section four we conclude.
II. GAME THEORETICAL ANALYSIS
1. Set-up of the game
Looking at the players in a courtroom, we distinguish three parties: the judge, the Public
Prosecutor and the defendant. We assume the defendant is a firm and not a person. Each of
these players has actions to take and decisions to make.
4
First the firm causes an extra discharge of some pollutant. These emissions lead to
environmental harm hi   h, h  . The harm is distributed uniformly. The firm receives a
certain benefit bi from this extra discharge – e.g. it did not have to invest in abatement or it
did not have to pay for disposal. For reasons of simplicity we assume that private and social
benefits are equal. We work in a strict liability framework. The cause of the discharge
therefore does not matter.
The violating firm now faces a lawsuit with a certain probability (hi)3. This probability
depends, among others, on the size of the environmental damage or the seriousness of the
violation. Moreover, the probability of a lawsuit depends on the probability of detection of the
harm and also on the fact whether the firm can be linked to the damage or not. Especially this
last part is often difficult to prove. Remember that, if a firm faces trial, this implies that it has
refused to comply at an earlier stage of the enforcement process. It chose to ignore warnings
and Notices of Violation. When offered the choice by the prosecution, the firm also did not
settle. Another important assumption is the fact that the defendant is not necessarily the real
wrongdoer. Measurement errors, uncertainties or stochastic pollution processes can cause an
innocent firm to stand to trial.
Once it is fixed that the case goes to trial, the defendant and the Public Prosecution decide
simultaneously on the funds they want to spend on, respectively, defence (Bfi) and attack (Ba).
The more the defendant wants to spend on legal representation, experts and/or tests, the lower
the estimate of the damage caused and therefore the lower the fine. The firm takes the
decision in order to minimise its expected costs. The more the Public Prosecutor spends on
experts and/or tests, the higher the estimate and the better the proof of the damage caused. We
assume that the Public Prosecutor wants to optimise deterrence. After all, the Public
Prosecutor cannot change the harm caused but it can try to deter potential future violators.
With a certain probability ˆi , depending on Ba, Bfi and hi, the firm is acquitted. For guilty
firms this probability of acquittal represents procedural errors, the capability of the lawyers
and the steadfastness of defence and prosecution.
In a final stage the judge decides on the level of the fine taking into account the decisions
made by the firm and the Public Prosecutor. We assume that the judge first decides on the
question of guilt and next chooses the optimal fine in order to optimise deterrence.
In the following sections we solve the problem by backward induction.
3
In the remainder of the text we use  instead of (hi) in order to simplify notation.
5
2. Decision on the fine by the judge
As we mentioned before the judge first decides whether the defendant is guilty or innocent.
With probability ˆi the judge finds the defendant not guilty and with probability 1  ˆi the
firm is considered to be responsible for the environmental damage caused. This probability of
acquittal is based on the testimony presented by the defendant and the prosecution and is
defined as:
ˆi  B fi , Ba , hi   
if hi  0
  i  B fi , Ba 
with  i  B fi , Ba    ,   ,
if hi  0
di
di
 0 . An innocent firm  hi  0 is exonerated with
 0 and
dBa
dB fi
probability  . This upper limit is not necessarily equal to one since we allow for procedural
errors. The probability that a guilty firm  hi  0 is convicted depends on the resources spent
by the defendant and the prosecution.
We find that the judge’s estimate of the harm caused by the defendant equals:
hˆi  B fi , Ba , hi   0

with probability ˆi
h fi  B fi   ha  Ba 
2
with probability 1  ˆi
with hfi the estimate of the harm presented by the firm, ha the estimate of the harm presented
by the prosecution, h fi , ha   h, h  , h'fi  0 and ha'  0 .
Next the judge wants optimal deterrence of potential environmental violations. He only
allows for discharges if the social benefits bi from this act exceed the social costs. In order
words, we want the internalisation of external costs by firms. Firms should discharge only if:
bi  hi    cs  Ba*  B*fi 
with cs equal to the costs of the trial for society. Examples of these costs are the wage of the
judge, infrastructure needed, administration and opportunity costs.
Firms, however, decide to discharge if their benefit exceeds the expected trial costs plus the
expected fine:
bi    B*fi  1  ˆi  Fi 
Therefore, in order for the firm to make the right decision, we need:
  B*fi  1  ˆi  Fi   hi    cs  Ba*  B*fi 
or
Fi 
hi
c  Ba*
 s
 1  ˆi  1  ˆi 
6
The optimal fine Fi * pronounced by the judge, based on his estimate of the harm hˆi , is:
Fi *
0

if hˆi  0
hˆi
c  Ba*
 s
if hˆi  0
 1  ˆi  1  ˆi 
We find that the optimal fine for a violator depends on the harm caused, weighted by the
probability of being punished and on the costs caused to society (court costs and prosecution
costs) weighted by the probability of being fined once the defendant stands to trial. This is
consistent with existing literature (Polinsky and Shavell, 1998 and Cohen, 1987).
3. Decision of the firm and the Public Prosecutor
When it is certain that the case will go to court, both the firm and the prosecutor have to
decide how much effort they will devote to this lawsuit. We do not consider the parties’
strategic decisions taken before the case actually came to trial. Furthermore we assume that
there can be false positives. Some firms that are brought to court are innocent.
The firm has to decide on the amount of resources it will spend on defending itself. This
defence decision is taken simultaneously with the Public Prosecutor’s decision on how much
to spend on prosecution. Subsequently, we discuss each party in turn.
3.1 Decision of the Public Prosecutor
We look at the decision made by the Public Prosecutor. Remember that this decision is taken
simultaneously with the firm’s defence assessment. The Public Prosecutor cannot influence
the environmental quality since the harm has already been done. However, he can make sure
that potential violators, including the current defendant, are deterred from causing future
environmental damage. We assume, therefore, that the prosecution wants to optimise
deterrence. Contrary to the judge’s behaviour, the public prosecutor does not have to decide
about the culpability of the defendant. Obviously, since the firm is prosecuted, the defendant
is assumed to be guilty.
Remember that the more the Public Prosecutor spends, the higher the estimate of the harm
caused since he will have more and better test results. He will also have more relevant expert
witnesses. Generally spoken the quality of the prosecution will increase. Moreover, the
probability of acquittal ˆi  B fi , Ba , hi  decreases.
In order to optimise deterrence the following condition has to be fulfilled:
7
  B*fi  1  ˆi  Fi   hi    cs  Ba  B*fi 

This gives:  1  ˆi  B , Ba 
or
*
fi
hˆi 


hˆi  B*fi , Ba 
cs  Ba


*
  1  ˆi  B fi , Ba 
1  ˆi  B*fi , Ba 


 
h fi  B*fi   ha  Ba* 
2


  hi    cs  Ba 


 hi
It is optimal for the Public Prosecutor to spend resources on prosecution until the estimate hˆi
of the environmental harm by the judge equals the actual damage hi caused. However, since
the actual harm is unknown, the prosecution will use its estimate ha  Ba  as an approximation
of hi. This gives:
h fi  B*fi   ha  Ba* 
The Public Prosecutor decides to spend money on prosecution until his estimate of the harm caused
equals the firm’s estimate.
3.2 Decision of the firm
We turn to the decision made by the defendant. The firm’s defence costs may include hiring a
lawyer, consulting experts and gathering test results. The more funds they spend on defence,
the lower the estimate of the harm they will present to the court.
The accused firm minimises its expected costs associated with the trial:
min 1  ˆi  Fi  B fi
B fi
or
min
h fi  B fi   ha  Ba* 
2
B fi
 cs  Ba*  B fi
The first order condition is:
dh fi

dB fi

dha  Ba* 
dB fi
2
dBa*

1
dB fi
This first order condition determines the optimal amount B*fi to spend on defence when the
firm is charged with an environmental violation. We obtain the familiar result that the
marginal cost of an extra unit spent on defence should equal the marginal benefit acquired
through it. This benefit consists of a decrease in the fine payment by the firm. Remark that the
8
optimal decision of the firm is independent of whether it is responsible or not for the
environmental damage.
3.3 Equilibrium
The Nash equilibrium that determines the optimal amount of resources committed to
prosecution Ba* and defence B*fi is defined by the following set of equations:
h fi  B*fi   ha  Ba* 

 dh fi dha  Ba* 


dB fi
 dB fi
dBa*


1

2

dB
fi

4. Discussion of the results
This game theoretical analysis provides us with an answer to the question what the optimal
level of a fine pronounced in court can be. This optimal fine level depends crucially on the
harm caused by the violation, the costs to society and the probability that the guilty party will
be punished. Next we want to compare this result to what happens in reality.
III. EMPIRICAL ANALYSIS
In this part we aim to empirically answer some questions. Firstly, we want to check whether
the theoretical model we derive is a realistic one. Secondly, we examine whether it is
plausible to work with a fixed fine independent of the size of the violation when modelling
enforcement issues. Further we observe the fining practice. We investigate the influence of
the violator’s compliance history on the level of the fine. Looking at the other legal factors,
we expect to see a strong influence of the fine level pronounced in first instance on that
pronounced by the Court of Appeal. More specifically this would imply that variables that
were significant in first instance, have a second additional influence on the level of the fine if
they are also significant in the ‘appeal’ specification. And finally, we want to investigate
whether some industries are being treated more leniently than others.
1. Determinants of the fine level
In general in the literature we can distinguish four groups of determinants that influence
penalties: environmental, legal, firm and political factors.
9
Environmental factors consist of, among others, the size of the damage, the size of the
violation and the environment in which the discharge took place. In a legal setting the size of
the violation is often measured in terms of the damage caused to environment or public
health. The size of the violation is often difficult to measure. Therefore, one often encounters
a legal classification of crimes according to their seriousness and impact.
Among the legal factors that influence the penalty level we find, among others, the state of
mind of the violator, the compliance history, the type of legislation that was violated and the
offences and penalties specified in that legislation. Moreover, violators who broke the law on
purpose, especially to realise financial benefits, will face higher penalties than those who just
had an accidental discharge.
Firm characteristics have received little attention in the theoretical literature. However, in the
empirical literature several characteristics seem relevant; such as the location of the firm, the
firm’s size or the industry.
Political factors include, among others, the program of ruling political parties or the form of
government in the country under consideration. Studies that take these factors into account
are, for example, Kleit et al. (1998) and Helland (2001). However, in this paper we do not
consider this last set of factors since the political climate in Belgium has not changed
profoundly in the last decade.
2. Background to the case study
Our empirical exercise uses the jurisprudence of the Court of Appeal in Gent (Belgium) for
the period 1990-2000 concerning (a) discharge permits (Law on Surface Waters 1971) and (b)
environmental permits (the discharge permit was included in the environmental permit due to
the Decree on Environmental Permits 1985). In most cases charges were also filed for other
violations. If these additional charges concerned violations of environmental regulations, they
were included in the analysis. This is the reason why we also include data on the Labour
Safety Law (ARAB 1946; includes a.o. an environmental permit). Sentences determined in
the previously described regulation can be found in Table 1.
The data only include prosecutions of persons. The Law on Legal responsibility of Legal
Bodies 1999 was only relevant towards the end of the research period, as it came into force on
2 July 1999. We include 38 cases with 53 fines levied.
10
ARAB 1946 (since 1974)
Labour Safety Law
Wet 1971 Oppervlaktewateren
Law on Surface Water
Milieuvergunningsdecreet 1985
Environmental Permit Decree
Imprisonment
8 days – 1 month
Penalty
1.25 – 1250 EURO4
8 days – 6 month
0.65 – 125 EURO
8 days – 1 year
2.50 – 2500 EURO
Table 1: Overview of sentences
3. Description of variables and data
The dependant variable is the level of the fine levied following an environmental violation.
We discuss the fine pronounced in first instance as well as that in appeal. We immediately
take the Belgian legal correction factor (‘opdeciemen’) into account since the corrected fine is
the amount with which the convicted party is confronted. We distinguish three groups of
factors that determine the sanctioning of environmental crimes: environmental, legal and firm
characteristics. For an overview and definition of these variables see Table 2.
The environmental characteristics are represented by the variables DURATION and
SERIOUS. Through the variable DURATION we measure the duration of the violation. Some
criminal offences (such as the absence of an appropriate permit) could last a long time while
others (such as an accidental point discharge) were non-recurrent. The dummy SERIOUS
indicates whether the environmental violation caused serious damage to the ecology and/or
lead to sizeable nuisance for the surrounding community.
The legal influences we take into account are the costs for the Public Prosecutor in first
instance (PPFIRST) and in appeal (PPAPPEAL). We also include a measure of the court costs
(COURT). The variable TP indicates whether there are third parties involved in the case.
Moreover we take the type of violated legislation into consideration. We distinguish four
types of legislation: Labour Safety Law (LSL), Environmental Permits Decree (EPD) and
Law on Surface Waters (LSW). The variables count the number of violations of one type of
legislation. Further we also measure the influence of the compliance history through the
variable RECORD. This 0/1-variable shows whether the accused already had a criminal
record or not. We also include the variable PRISON, which indicates whether next to the fine
there was also a prison sentence pronounced. Finally, we also include the variable INTENT
that counts the number of aggravating circumstances mentioned against the defendant. It
4
We decided to convert all sums from Belgian Franks to Euros to improve the ease of exposition. We have
approximated the amounts. The conversion rate for BEF in Euro is 40.3399 BEF = 1 Euro. These amounts do not
include the Belgian legal correction factor (‘opdeciemen’) since this factor changes over the years.
11
measures the intent of the wrongdoer. When we examine the fines pronounced in the Court of
Appeal, we also include the fine specified in first instance (FIFINE) in the analysis.
Variables
Dependent variable
Description
FINES
Fine pronounced in first instance or in appeal
Independent variables
DURATION
SERIOUS (0/1)
PPFIRST
PPAPPEAL
COURT
LSW
EPD
LSL
OTHER
TP (0/1)
RECORD (0/1)
PRISON (0/1)
INTENT
FIFINE
GROW (0/1)
STEADY (0/1)
DECLINE (0/1)
PRE94 (0/1)
Duration of violation (in months)
= 1 if serious damage or nuisance was caused
Costs for Public Prosecutor caused by court case in first instance
Costs for Public Prosecutor caused by appeal
Court costs caused by trial
Charges within scope of Law on Surface Waters
Charges within scope of Environmental Permit Decree
Charges within scope of Labour Safety Law (ARAB) 1946
Charges within other laws
= 1 if third parties are involved in the law suit
= 1 if the defendant has a legal history
= 1 if there was a prison sentence on top of the fine
State of mind of defendant (number of negative aspects)
Fine pronounced in first instance
= 1 if the defendant works in a growing industry
= 1 if the defendant works in a stagnating industry
= 1 if the defendant works in a declining industry
= 1 if the case started in first instance before 1994
Table 2: Definition of the variables
Moreover, we also include the sector in which the defendant works in the analysis. We
distinguish several sectors: agriculture, building industry, food industry, sand extraction, scrap
yards, furniture industry and some others. We divided the industries into three groups:
growing (GROW), stagnating (STEADY) and declining (DECLINE) industries. This division
depends on the evolution of the industry’s current ratio, solvency ratio and the return on total
assets5. If two or more of these measures increased from 1995 to 1999, the industry is said to
be growing. If none of the measures increased, the industry was marked as declining. Further
we also observe when the case first started. This is summarized in the variable PRE94 that
represents whether the trial in first instance started before or after 1994. We use this variable
to search for a time trend in our data.
We perform two estimations: one for the verdict in first instance and one for the appeal. The
selection of the independent variables was slightly different in both cases. A description of the
selected variables can be found in Table 3.
5
These data were obtained from AMADEUS a Pan European financial database.
12
Min
FINES =FINE/1000
0
FINE
0
DURATION 0.03
SERIOUS
0
PPFIRST
0
PPAPPEAL
COURT
0
LSW
0
EPD
0
LSL
0
OTHER
0
TP
0
RECORD
0
PRISON
0
INTENT
0
FIFINE
GROW
0
STEADY
0
DECLINE
0
PRE94
0
Number of
observations N
First instance
Max
Mean
12.4
12 394.7
159
1
2 205.2
24.8
3
5
1
3
1
1
1
1
1
1
1
1
51
3.097
3 096.725
15.868
0.608
71.837
17.255
0.353
1.314
0.078
0.510
0.235
0.039
0.235
0.667
0.314
0.255
0.431
0.275
Exp.
sign
+
+
+
+
+
+
?
+
+
+
+
+
0
-
Min
0
0
0.03
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
52
Max
Appeal
Mean
44.6
44 620.8
136
1
97.1
24.8
3
5
1
3
1
1
1
1
99.2
1
1
1
1
5.079
5 078.957
13.116
0.596
48.988
21.214
0.365
1.289
0.077
0.481
0.231
0.039
0.269
0.673
5.087
0.346
0.231
0.423
0.289
Exp.
sign
+
+
+
+
+
+
?
+
+
+
+
+
+
0
-
Table 3: Descriptive statistics and expected signs
4. Expected results
We now discuss briefly the expected signs of the different variables (see Table 3).
When we look at the duration of the violation, we can assume that longer violations (which
are usually more serious) will be punished more severely. We therefore expect the coefficient
of DURATION to be positive. We also anticipate a positive coefficient for the variable
SERIOUS, which indicates if there was serious damage or nuisance caused by the violation.
According to existing models, e.g. Polinsky and Shavell (1992), the optimal fine is higher if
the enforcement costs are higher. Therefore we expect the variables PPFIRST, PPAPPEAL
and COURT to show a positive sign.
Looking at the variables that represent the violated legislation, we take the maximum
allowable sentences (see Table 1) into account. We find that penalties pronounced for
violating the Law on Surface Waters (LSW) cannot be higher than 125 Euro, times the legal
correction factor, while those pronounced for violating the Environmental Permit Decree
(EPD) can amount to 2500 Euro, times the legal correction factor. Therefore we expect a
positive sign for EPD and LSL.
13
Further we consider the impact of having third parties represented at the trial. We assume that
the coefficient of TP will be positive. The presence of third parties, after all, implies that the
violation was potentially damaging to other persons.
Next we can expect that a violator with a criminal record will be more heavily punished
(Polinsky and Rubinfeld, 1991). Therefore, we expect the variable RECORD to have a
positive sign. We can also assume that the variable INTENT will show a positive sign. It is
logical to punish the deliberate violator more stringently than the accidental violator. We also
investigate how the simultaneous punishment with a prison sentence, influences the level of
the fine. Since executing a prison sentence is more expensive to society than levying a fine,
we assume that a prison sentence will only be used if the fine is already at its legal maximum.
Therefore, we assume that the sign of PRISON is positive.
Moreover, we assume that the fine in appeal will be higher if the fine (represented by the
variable FIFINE) in first instance was higher. FIFINE has therefore a positive expected sign.
Next we consider the industry variables GROW, STEADY and DECLINE. The enforcer is
assumed to take the defendant’s ability-to-pay into account when deciding on the level of the
fine. The focus is on the hurt caused rather than on the nominal level of the sanction. Firms
from less prosperous industries will, therefore, face less stringent penalties than wealthier
ones. Previous economic research has established that regulations favour struggling industries
and slower-growing regions (Deily and Gray, 1991). The regulator is thought to be sensitive
to the potential political costs of the trade-off between pollution control and employment.
This strand of the literature, therefore, deems it likely that the regulator’s enforcement
decisions are influenced by this political trade-off. However, we think that these political
considerations have only token impact on the judge’s sanctioning decision compared to the
influence of the defendant’s ability-to-pay. In conclusion, we expect the sign of GROW to be
positive and that of DECLINE to be negative.
For the variable that represents the time trend (PRE94), we expect a negative sign.
Environmental awareness has increased considerably during the nineties. The explosive
growth of environmental legislation since mid nineties confirms this. It is reasonable to
assume that this development has resulted in a more stringent enforcement of infractions.
5. Estimation method
We estimate the penalty function via the Ordinary Least Squares method (OLS). The linear
regression model equals:
14
Y  b0  b X  
(1)
with Y the dependent variable, b0 the constant, X the vector of independent variables, b the
regression coefficients and  the error term. The variables we include in our two models can
found in Table 2. We used the statistical program LIMDEP for our estimations.
6. Results
As mentioned before we estimate two separate models: the penalty function for the first
instance and that for the appeal. We discuss in turn the results for both models.
6.1 First instance
Firstly we notice that the assumption of normality of the error terms is not rejected by the
standard tests. Secondly it became immediately clear that we experienced problems with
heteroskedasticity. Therefore, we use White or heteroskedasticity-consistent standard errors.
The results of this modified estimation can be found in Table 4. It is clear that, for a crosssection model, we obtain a high R²-value. Our model explains 64 % of the variances of the
fines pronounced by the courts of first instance. We now discuss the three groups of
determinants we distinguished: environmental, legal and industry factors.
The influence of environmental factors on the level of the fine was measured through the
duration of the violation (DURATION) and the presence of serious damage (SERIOUS). The
variable DURATION is significant (5 % level) and negative. This does not match our
expectations. The longer a violation continues, the lower the fine will be. If the time in
violation increases with a month, the fine will decrease with approximately 21 Euro.
However, the coefficient of SERIOUS is significant (5 % level) and positive. This result
corresponds with our intuition that more serious crime should be punished more severely.
The legal influences included in the analysis are the costs for the Public Prosecutor of going
to court in the first instance (PPFIRST) and the court costs (COURT). The variable PPFIRST
is not significant in our analysis. The variable COURT, however, is positive and significant at
the 1% level. Further we see that the variable TP, which indicates the presence of third
parties, is not significant. Moreover, we take the type of violated legislation into account
(LSL, EPD and LSW). Here we distinguish differences in the sanctioning of Labour Safety
Law (LSL – significant on 1 % level), the Environmental Permit Decree (EPD – significant
on 1% level) and the Law on Surface Waters (LSW - significant at 5 % level) compared with
15
other legislation. In these three instances the fine will be higher if these particular laws are
violated.
(Constant)
DURATION
SERIOUS
PPFIRST
COURT
TP
INTENT
PRISON
RECORD
LSL
EPD
LSW
DECLINE
PRE94
R² = 0.644
Adj. R² = 0.520
F-stat = 5.16
N = 51
***
**
**
***
***
***
***
***
**
**
Coefficient
-4.747
-0.021
1.740
-0.00062
0.207
1.156
-0.490
3.545
5.344
3.700
1.265
1.258
-0.152
2.041
t-ratio
-3.153
-2.188
2.064
-1.079
5.537
1.273
-1.428
3.909
2.938
2.855
2.898
2.428
-0.165
2.110
p-value (sign.)
0.0032
0.0351
0.0461
0.2874
0.0000
0.2111
0.1618
0.0004
0.0057
0.0070
0.0063
0.0202
0.8699
0.0417
Dependent variable: FINES = FINE/1000
* = significant on 10% level
** = significant on 5% level
*** = significant on 1% level
Table 4: Estimation results for first instance
The variable RECORD, measuring the influence of the defendant’s compliance history, is
significant on the 1 % level and positive. The presence of a criminal record increases the fine
with approximately 5300 Euro. The variable PRISON, indicating whether there was a prison
sentence pronounced, is also significant in our model (1 % level). The sign of PRISON is
positive. We can explain this result as follows: a prison sentence is costly to society and will
only be imposed when the fine for the case is already maximal. The variable representing the
number of aggravating circumstances mentioned during trial (INTENT) was not significant.
Firm factors include the sector in which the defendant works. We included the variable
DECLINE, which indicated whether the industry was declining or not, in our analysis. This
variable was not significant.
The variable PRE94 was positive and significant at the 5 % level. This result is contrary to
our intuition. It implies that cases that went to court before 1994 were punished more harshly.
We expected to find the reverse since environmental awareness has increased noticeably
during the nineties. A possible explanation for our result can be found in the type of cases that
went to court. We have reason to belief that in the past only very deliberate and seriously
damaging violations were brought to court. By the end of the nineties this trend would then be
weakened.
16
6.2 Court of Appeal
Again we notice that the assumption of normality of the standard errors was not rejected and
we experienced heteroskedasticity. Therefore, we decided to use White or heteroskedasticityconsistent standard errors. The results of the estimation can be found in Table 5. The R²-value
of this estimation is quite high. We could explain more than 83 percent of the variance in the
dependent variable. We discuss the three groups of determinants of fines for environmental
crimes: environmental, legal and firm factors.
The influence of environmental factors in the level of the fine is measured through the
duration of the violation (DURATION) and the significance of the damage caused
(SERIOUS). The variable DURATION was not significant. However, the variable SERIOUS
was positive and significant at the 10 % level. A serious violator, who appeals to the verdict,
will most likely be punished even more severely. If the impact of the violation involved
significant damage or nuisance to the neighbourhood, the fine will increase with
approximately 2200 Euro.
(Constant)
FIFINE
DURATION
SERIOUS
PPAPPEAL
COURT
TP
INTENT
PRISON
RECORD
LSL
EPD
LSW
DECLINE
PRE94
***
*
***
*
**
*
*
*
R² = 0.831
Adj. R² = 0.768
F-stat = 13.03
N = 52
Coefficient
t-ratio
p-value (sign.)
1.383
0.681
0.5001
0.423
20.460
0.0000
-0.028
-1.280
0.2084
2.260
1.854
0.0717
0.0022
0.141
0.8888
-0.018
-0.284
0.7783
4.588
2.932
0.0058
0.871
1.794
0.0809
3.985
2.554
0.0149
1.387
0.505
0.6165
-1.879
-1.169
0.2499
-0.246
-0.348
0.7297
-0.882
-1.922
0.0623
-2.813
-1.975
0.0558
-2.447
-1.854
0.0717
Dependent variable: FINES = FINE/1000
* = significant on 10% level
** = significant on 5% level
*** = significant on 1% level
Table 5: Estimation results for appeal
Among the legal influence we include we find the costs for the Public Prosecutor of going the
trial in the Court of Appeal (PPAPPEAL) and the court costs (COURT). Both variables are
not significant. However, the variable TP, which represents the presence of third parties, is
positive and significant at the 1 % level. If third parties are present, the fine after the appeal
17
will be approximately 4600 Euro higher. Moreover, we take the legislation that was violated
into account (LSL, EPD and LSW). In this model only the coefficient of the Law on Surface
Waters of 1971 (LSW) is significant at the 10 % level. The fine after an appeal will be lower
if this type of legislation is violated. The explanation for this result can be found by looking at
the maximum fine (125 Euro) allowed by the LSW (Table 1). This maximum is at least ten
times smaller than the maximum fine allowed by the other two regulations.
Next we also measure the influence of the defendant’s compliance history through the
variable RECORD. This variable turns out to be insignificant in appeal. The variable
INTENT representing the number of aggravating circumstances is now in contrast to the first
estimation results significant at the 10 % level. The sign of the coefficient was positive as
expected. The variable PRISON, indicating whether there was a prison sentence pronounced,
is again positive and significant in our model (5 % level). A very important explanatory
variable is without a doubt the fine that was imposed in first instance (FIFINE). The size of
this fine is directly and positively related to one pronounced in appeal.
The sector dummy represents the firm characteristics. The variable DECLINE is now
negative and significant at the 10 % level. This implies that defendants, who work in a
declining industry, can expect a lower sanction in appeal. The fine would be approximately
2800 Euro lower than for firms from a growing or stagnating industry.
The variable PRE94 is again significant at the 10 % level. However, this time the sign of the
coefficient is negative and in line with our intuition. The result implies that the fines
pronounced at the court of appeal were more stringent at the end of the nineties than at the
beginning.
7. Discussion of the results
We obtain results that are more or less in line with our expectations.

Finding that the variable SERIOUS is both in first instance and in appeal significant and
positive is quite reassuring. The impact of this variable, supported by the positive sign for
DURATION at the first instance, shows that in the studied environmental jurisdiction the
seriousness of the violation is taken into account. Moreover, this indicates that is not a
realistic research assumption to work with a fine independent of the harm caused by
incompliance.

Looking at the legal factors, we would first like to mention the large influence of the level
of the fine pronounced in first instance on that pronounced by the Court of Appeal
18
(variable FIFINE). More specifically this variable implies that variables that were
significant in first instance, have a second additional influence on the level of the fine if
they are also significant in the ‘appeal’ specification. This cumulative aspect is very clear
for the variable SERIOUS.
Considering the regulation that was violated, the results for the Labour Safety Law 1946
(LSL), the Environmental Permit Decree 1985 (EPD) and the Law on Surface Waters
(LSW) are noteworthy. At the first instance breaches of this laws are sanctioned more
severely than violations of other regulation. However, at the appeal stage, we find that the
violations of the Law on Surface Waters are treated more mildly. As mentioned before,
we can find the rationale behind this result when we look at the maximal allowable fines
by the different legislations (Table 1). In appeal the judge seems to be restricted by the
maximum fine for breaches of the Law on Surface Waters. This indicates the need to
incorporate higher allowable fines in legislation.
It was also interesting to see the positive influence of third parties on the level of the fine.
This implies that the sanction is influenced by the harm caused to other people. This is
contrary to a recent legislative trend. The Belgian regulator now focuses on improving or
maintaining environmental quality instead of protecting public health. However, our
results show that, in practice, public health considerations still have a central role to play
in the sanctioning decision.
Considering the variables related to the defendant, we find that the influence of a criminal
record (variable RECORD) is really important while the influence of the defendant’s state
of mind (variable INTENT) is smaller. Obviously the objective fact of the absence or
presence of a criminal record provides the judge with a trustworthy signal of the civil
responsibility of the violator. The less objective variable INTENT was only significant in
the appeal case. We can now raise the question whether it is more difficult to objectively
measure the intentions and the profit seeking behaviour of firms. Therefore less monetary
consequences are associated with the variable INTENT. This topic could certainly benefit
from additional research.

The fact that the variable DECLINE turns out to be significant and negative in the appeal
case supports the idea that the violator’s ability-to-pay plays an important role in the
sanctioning decision. The hurt caused by the fine is more important than the nominal level
of the penalty. It is also possible that, to a lesser extent, environmental considerations are
weighted against socio-economic aspects, such as employment.
19

Furthermore, the analysis of the variable PRE94 gives us an ambiguous signal. In both
cases we find a time trend. However, the trend is negative in first instance and positive in
appeal. This mixed result does not allow us to draw an explicit conclusion.
This legislative study provides us with some suggestions for the legal practice; at least for those
situations where, after a conviction in first instance, the parties contemplate to go in appeal. Even if
the maximum fine in appeal is much smaller than the one in first instance, the level of the average fine
in appeal is higher than that in first instance. The question of the appropriateness of going in appeal
certainly arises.
IV. CONCLUSION
We have studied the level of penal fines in both a game theoretical and empirical way. The
penal fine is an important enforcement instrument for environmental regulations. The game
theoretical analysis provides us with an answer to the question what the optimal level of a fine
pronounced in court can be. This optimal fine level depends crucially on the harm caused by
the violation, the costs to the government and the probability that the guilty party will be
punished. Subsequently we compare this result to what happens in reality.
In our empirical analysis we were not able to examine the influence of the probability that the
guilty party will be punished on the level of the fine due to lack of data. However we are able
to empirically answer some other questions. Firstly, we find that the theoretical model we
derive is a realistic one. The different independent variables that represent the factors that
determine the optimal fine level turn out significantly in our empirical exercise. Secondly, we
find that it is not plausible to work with a fixed fine independent of the size of the violation
when modelling enforcement issues. Nevertheless this is an assumption often used in
theoretical models. In our sample the seriousness of the violation influences the fine level.
Further we can also make some observations regarding the fining practice. The results show
that the violator’s compliance history influences the level of the fine. Violators with a
criminal record have a significantly higher probability of receiving a higher penalty.
Obviously, the objective fact of the absence or presence of a criminal record provides the
judge with a trustworthy signal of the civil responsibility of the violator. Looking at the other
legal factors, the large influence of the fine level pronounced in first instance on that
pronounced by the Court of Appeal is instantly noticeable. More specifically, this implies that
variables, which were significant in first instance, have a second additional influence on the
level of the fine if they are also significant in the ‘appeal’ specification. And finally, we
20
observe that industries in difficulties are treated more leniently due to other financial, or even
political, considerations.
Finally, we would like to say that our sample size is relatively small. This is an important
caveat when discussing our results. Moreover, it would be interesting to correct for the sample
selection bias (Heckman, 1979). However, we lack the necessary data to do this.
REFERENCES
Andreoni, J. (1991). Reasonable doubt and the optimal magnitude of fines: should the penalty
fit the crime? RAND Journal of Economics, vol. 22[3], p.385-395.
Cohen, M.A. (1987). Optimal enforcement strategy to prevent oil spills: an application of a
principal-agent model with moral hazard. Journal of Law and Economics, vol. 30, p. 23-51.
Daughety, A.F. and Reinganum, J.F. (1994). Keeping society in the dark: on the admissibility
of pretrial negotiations as evidence in court. Working paper.
Deily, M.E. and Gray, W.B. (1991). Enforcement of pollution regulations in a declining
industry. Journal of Environmental Economics and Management, vol. 21, p.260-274.
Heckman, J.J. (1979). Sample selection bias as a specification error. Econometrica, vol.
47(1), p.153-161.
Helland, E. (2001). Prosecutorial discretion at the EPA: some evidence on litigation strategy.
Journal of Regulatory Economics, vol. 19(3), p. 271-294.
Kilgour, D.M., Fang, L., and Hipel, K.W. (1992). Game-theoretic analyses of enforcement of
environmental laws and regulations. Water Resources Bulletin, vol. 28[1], p.141-153.
Kleit, A.N., Pierce, M.A. and Hill, R.C. (1998). Environmental protection, agency
motivations and rent extraction: the regulation of water pollution in Louisiana. Journal of
Regulatory Economics, vol. 13, p. 121-137
Landsberger, M. and Meilijson, I. (1982). Incentive generating state dependent penalty
system. Journal of Public Economics, vol. 19, p.333-352.
P'ng, I.P.L.(1983). Strategic behavior in suit, settlement and trial. Bell Journal of Economics,
vol.14, p.539-550.
Polinsky, A.M. and Rubinfeld, D.L. (1991). A model of optimal fines for repeat offenders.
Journal of Public Economics, vol. 46, p. 291-306
Polinsky, A.M. and Shavell, S. (1992). Enforcement costs and the optimal magnitude and
probability of fines. Journal of Law and Economics, vol. 35, p. 133-148
Polinsky, A.M. and Shavell, S. (1998). Punitive Damages: An Economic Analysis. Harvard
Law Review.
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