How to determine the optimal fine in court?

Game theoretical and empirical analysis[1]

January 2004

Sandra ROUSSEAU and Carole Billiet

Centre for Economic Studies

K.U.Leuven

Naamsestraat 69

B-3000 Leuven

Belgium

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

I. INTRODUCTION

II. GAME THEORETICAL ANALYSIS

1.Set-up of the game

2.Decision on the fine by the judge

3.Decision of the firm and the Public Prosecutor

3.1 Decision of the Public Prosecutor

3.2 Decision of the firm

3.3 Equilibrium

4.Discussion of the results

III. EMPIRICAL ANALYSIS

1.Determinants of the fine level

2.Background to the case study

3.Description of variables and data

4.Expected results

5.Estimation method

6.Results

6.1 First instance

6.2 Court of Appeal

7.Discussion of the results

IV. CONCLUSION

REFERENCES

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 orders[2]) 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.

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.

First the firm causes an extra discharge of some pollutant. These emissions lead to environmental harm . 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, 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.

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 the judge finds the defendant not guilty and with probability 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:

with , and . An innocent firm is exonerated with probability . This upper limit is not necessarily equal to one since we allow for procedural errors. The probability that a guilty firm 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:

with hfithe estimate of the harm presented by the firm, ha the estimate of the harm presented by the prosecution, , and .

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:

with csequal 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:

Therefore, in order for the firm to make the right decision, we need:

or

The optimal fine pronounced by the judge, based on his estimate of the harm , is:

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 decreases.

In order to optimise deterrence the following condition has to be fulfilled:

This gives:

or

It is optimal for the Public Prosecutor to spend resources on prosecution until the estimate 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 as an approximation of hi. This gives:

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:

or

The first order condition is:

This first order condition determines the optimal amount 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 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 and defence is defined by the following set of equations:

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.

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.