# Simultaneous Decision Making of Juries: Evidence From the Paris Labor Court

Claudine Desrieux, Romain Espinosa, Michael Visser

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Claudine Desrieux, Romain Espinosa, Michael Visser. Simultaneous Decision Making of Juries: Evidence From the Paris Labor Court: CRED Working paper, n° 2022-05. 2022. hal-04104190

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CRED WORKING PAPER N° 2022-05

Simultaneous Decision Making of Juries:
Evidence From the Paris Labor Court

November 17, 2022

CLAUDINE DESRIEUX* ROMAIN ESPINOSA† AND MICHAEL VISSER‡

<footnote>*CRED, University of Paris 2</footnote>

<footnote>†CIRED (CNRS) and CRED, University of Paris 2</footnote>

<footnote>‡ENSAE-CREST and CRED, University of Paris 2</footnote>
Simultaneous Decision Making of Juries:
Evidence from the Paris Labor Court*

Claudine Desrieux†

Romain Espinosa‡

Michael Visser§

November 17, 2022

Abstract

This paper analyzes the decisions made by juries at the Paris Labor Court. These juries (made up of two judges representing workers' unions and two representing employers' federations) decide how much money defendants (employers) should pay to plaintiffs (employees). Multiple cases are typically examined during a court session, and the jury then decides simultaneously how each plaintiff is to be compensated after all cases have been heard. We exploit the quasi-random assignment of cases and juries to sessions and estimate simultaneous Tobit models, accounting thereby for the mass at zero of the awarded amount and the simultaneous nature of the decision process. The awarded amount is not affected by the (average) amount awarded to other plaintiffs, suggesting that in this respect a simultaneous decision process is preferable to a sequential one (wherein decisions have been shown to be affected by path dependency). Furthermore, the awarded amount is significantly higher when one or both employee representatives are left-wing orientated, or if the jury is headed by a judge from a workers' union. Finally, plaintiffs get less money when they are examined in sessions containing relatively many cases.

Keywords: Labor dispute; simultaneous judicial decision-making

JEL classification: J52; K31

<footnote>*We thank the GIP Ministère de la Justice and ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047 for financial support. We are also grateful to Joshua Teitelbaum, seminar participants at the University of Paris 2 and the 39th EALE conference, for helpful remarks, and to Isabelle Lapeyronnie for her explanations of the practical aspects of the Paris Labor Court.</footnote>

<footnote>†CRED, University of Paris 2. Email: claudine.desrieux@u-paris2.fr.</footnote>

<footnote>‡CIRED (CNRS) and CRED, University of Paris 2. Email: romain.espinosa@cnrs.fr.</footnote>

<footnote>§ENSAE-CREST and CRED, University of Paris 2. Email: michael.visser@ensae.fr.</footnote>
# 1 Introduction

Judges often have to hear multiple cases during a given court session. They are required to examine the different cases in their caseload within a short span of time (e.g., during a day or an afternoon), and pronounce judicial verdicts on each of them. Are these decisions influenced by the exposure to other cases within a caseload? A recent empirical literature (Chen et al. (2016), Leibovitch (2016), Bindler and Hjalmarsson (2019)) provides some evidence of interrelationships across case outcomes in judicial decision making. These studies investigate courts where decisions are made “sequentially”: the different cases are evaluated one after the other, and a verdict is pronounced on each case right after its examination is finished (i.e., before the next one is brought to court). This so-called path dependency (the fact that past decisions affect the current decision) is clearly a highly undesirable phenomenon, especially when court outcomes have far-reaching consequences (for example death sentences, or asylum decisions in immigration courts). In this paper, we investigate whether caseload exposure plays a role when judicial decisions are made “simultaneously”. In such a procedure a judge also hears all cases of a given session one after the other, but makes a decision on each of them only at the end, i.e., after the last case of the session has been heard.<fnref n="1" /> The objective is thus to test for the presence of the analogue of path dependency, namely simultaneity in decision making. Our data come from the Paris Labor Court.

While the differences between these two procedures have drawn no attention in studies on judicial decision-making (nor are there any papers on simultaneous court decisions), they have been explored in other contexts. According to a literature in psychology, management, and marketing, simultaneous and sequential decision-making procedures induce people to reason differently, and to use cognitive skills that are not the same (Basu and Savani (2019), Bazerman and Moore (2013), Bruine de Bruin (2005)). This literature also shows that actual outcomes generally differ depending on whether they result from a sequential or simultaneous format. For instance, hiring decisions are not the same when job candidates are evaluated one after the other or jointly (Bohnet et al. (2016)).<fnref n="2" /> All these findings, obtained in various research fields, render it plausible that the two decision formats may also have differentiated effects in the courtroom.<fnref n="3" /> To what extent and in which direction simultaneous judicial decisions are biased by outcome simultaneity is, however, an open empirical question.

<footnote n="1">¹For instance, the Pennsylvania Commission on Sentencing, or the immigration courts dealing with asylum cases in the U.S., are courts where the decision-making is sequential. Decisions are instead made simultaneously in all labor and commercial courts in France. Similarly, appellate courts in the U.S., including the Supreme Court, often hear oral arguments in multiple cases before rendering their decisions on each of them at the session's end. On a more historical perspective, Langbein (1978) reports that until the 18th century, juries in England heard several criminal cases before deliberating on all of them.</footnote>

<footnote n="2">²Similarly, consumers choosing among sequentially presented goods are less satisfied with their chosen option than when choosing among simultaneously presented goods (Mogilner et al. (2013)); Eyewitness' ability to recognize a suspect depends on whether a simultaneous lineup is used or a sequential lineup (Dobolyi and Dodson (2013))</footnote>

<footnote n="3">³Admittedly, apart from the study on lineups, these papers and many others in this literature (see Basu and Savani (2019), for a survey) consider situations where decision makers have to choose optimally among several options presented to them (typically goods, job candidates, sports players, or musicians), explicitly requiring a comparison across these options. To the extent that there is evidence of path dependency in sequential judicial decisions –implying that different court cases are apparently compared or contrasted– and to the extent that such comparisons may similarly occur in simultaneous judicial decisions, this literature is relevant in our context.</footnote>
To address the question of whether judges fall prey to simultaneity biases, we use a new data set on decisions taken by judges of the Paris Labor Court. As all other French labor courts, the one in Paris deals with individual disputes affecting labor relations in the private sector. The judicial decisions at these courts are made by juries composed of four judges (two of them represent workers' unions and the other two represent employers' federations). They decide how much money defendants (employers) should pay to plaintiffs (employees), based on the claims filed by the latter and the evidence revealed in court. In the large majority of sessions, the juries have to examine multiple cases. They are heard one after the other, and at the end of the session the jury decides simultaneously how each plaintiff is to be compensated. The financial stakes are high in these courts. In our data, for instance, the awarded amount among plaintiffs who actually received a compensation is around € 28,000 on average (with a median of € 14,000).<fnref n="4" />

We compiled detailed information on all cases examined by the juries during the months of February of 2013-2017. We recorded not only the amounts of money awarded to plaintiffs, but also the monetary demands for relief they are seeking from their employers. Furthermore, we collected information on various characteristics of jury members (their gender, whether they represent a worker's union or an employer's federation, and the political orientation of this union or federation), of plaintiffs and defendants, of cases (e.g., the number and nature of complaints filed by plaintiffs), and finally of sessions (the number of cases within a session, their order of appearance, the Paris Labor Court section in which the session was held).

In order to test for the presence of outcome simultaneity, we consider regression models that relate the amount of money received by a plaintiff in a given session to the amounts received by other plaintiffs in that session. Since we are also interested in the possible effects of jury composition and session features, we add such variables to the econometric specifications. Lastly, we include plaintiff/defendant characteristics as controls. Exploiting the quasi-random assignment of cases and juries to sessions (juries are first randomly assigned to the different sessions programmed by the Paris Labor Court, and sessions are then filled with cases on a first-come, first-served basis), we first estimate linear models wherein other plaintiffs' amounts enter the specification through their mean. These models are estimated using ordinary least squares (OLS) and the instrumental variable (IV) method. OLS has the disadvantage of not accounting for the fact that the error term in the regression model is, for the same reason as in peer effect models, by construction correlated with the amounts given to others. We therefore also present IV estimates by instrumenting the average amount awarded to other plaintiffs by the average amount they demanded. Linear regression models are not fully appropriate in our context because the dependent variable has a lot of mass at zero (for about 40% of observations in the sample the plaintiffs did not get any compensation at all). Our main results are therefore based on estimation of a simultaneous Tobit model, which accounts for both the simultaneous nature of the decision process and the mass at zero of the dependent variable. This model is estimated using a method recently proposed by Xu and Lee (2015).

In contrast to previous results based on courts that adopt sequential decision procedures, our empirical results suggest that the decisions taken at the Paris Labor Court are not prone to simultaneity bias: we cannot reject the null hypothesis that the compensation received by a plaintiff is unaffected by the average amount the jury

<footnote n="4">⁴Cahuc et al. (2022) show that labor court decisions affect the survival prospects of medium-sized firms in France.</footnote>
awards to other plaintiffs. In a series of robustness checks, we do not find statistically significant effects either when other plaintiffs' amounts enter the specifications differently (e.g., through their total sum, or through the amount awarded to the plaintiff heard prior to the one being studied), or when outcome simultaneity is assumed to affect only specific plaintiffs (e.g., plaintiffs for whom it is difficult to assess what are the monetary costs of the damage incurred by them, or whose cases are somehow "complicated", rendering juries potentially more susceptible to be influenced by extraneous factors). Jury composition, however, does have strong and statistically significant effects: A plaintiff whose case is examined by a jury headed by a judge representing employees is awarded around €4,000 more; having a jury composed of one member of a left-wing orientated worker union leads to an increase of €1,500, while the increase is around €4,000 when two members belong to such a union. Finally, we find that a variable capturing session size is also significant: plaintiffs examined in a large session (more than 4 cases) receive around €3,500 less compared to those who are assigned to a small one (between 2 and 4 cases).

Our work is most closely related to a series of recent papers that test for the presence of path dependency in sequential judiciary decisions. Chen et al. (2016) study refugee asylum court decisions in the US and find that current and past outcomes are negatively autocorrelated. Bindler and Hjalmarsson (2019) study verdicts adjudicated by juries for criminal cases at London's Old Bailey criminal Court, and find instead evidence of positive autocorrelation. Leibovitch (2016) investigates sentencing data from the Pennsylvania Courts of Pleas. She shows that judges exposed to low levels of criminal gravity, at the beginning of their career, order longer sentences than those exposed to high levels of criminal gravity.<fnref n="5" />

There is also a strong connection with a literature studying the impact of judge/jury characteristics on judicial outcomes. Anwar et al. (2012) study felony trial outcomes in Florida and find that juries formed from all-white jury pools convict black defendants more often. Anwar et al. (2018) analyze the impact of juror political party on verdicts pronounced at a court in Gothenburg. They show that convictions for young defendants and those with Arabic names increase substantially when they are assigned to jurors from the Swedish far-right party. Cohen and Yang (2019) also study the impact of political affiliation using U.S. federal sentencing data, and show that Republican-appointed judges sentence black defendants and young defendants more harshly. Finally, Glynn and Sen (2015) have data from the U.S. Courts of Appeals and show that judges with daughters consistently vote in a more feminist fashion on gender issues than judges who have only sons.<fnref n="6" />

The remainder of the paper is organized as follows. Section 2 describes the institutional background, and Section 3 the data we collected from the Paris Labor Court. In Section 4 we present simple tests to verify that juries and cases are randomly matched with court sessions. Section 5 presents our empirical results and Section 6 concludes. Additional material can be found in an online appendix.

<footnote n="5">⁵Evidence of path dependency is also found in other contexts such as MBA admissions (Simonsohn and Gino (2013)), speed dating (Bhargava and Fisman (2014)), physician decisions (Jin et al. (2020)), and research grant attributions (Radbruch and Schiprowski (2022)).</footnote>

<footnote n="6">⁶Although not explicitly stated in these papers, all of them study sequential judicial decisions.</footnote>
# 2 The institutional setting

## 2.1 Organization of labor courts in France

French labor courts (Conseils de Prud'hommes) deal with individual disputes affecting labor relations in the private sector (regarding for example the validity of employment contracts, nullification of dismissals, compensations to be paid, levels of severance payments).<sup>7</sup> These courts are first level tribunals and are exclusively designed for labor disputes.<sup>8</sup> Created at the beginning of the 19th century, during Napoleon's reign, there are today 210 of them spread all over the territory. Each court is competent for a given geographical area in France, and plaintiffs are required to bring their claim before the court that covers the area in which their workplace is located.<sup>9</sup> All labor courts are divided into five different sections, each section representing a field of activity. The Paris Labor Court is by far the largest one in the country. It receives about 18,000 new cases per year while the average across all courts in France is around 900.<sup>10</sup> During our sampling period (2013-2017), 41.4% of new cases brought to the Paris Labor Court fell in the "Commerce" section, 30% in the "Executives" section, 21% in the "Diverse Activities" section,<sup>11</sup> 7.5% in the "Industry" section, and 0.05% in the "Agriculture" section.

## 2.2 Selection of labor court judges

Until recently, judges in French labor courts were selected through elections that were held separately in each section of each court. The judges of a given section were elected by employees and employers active in the field represented by the section (and in the geographical area covered by the court). They voted for different sets of candidates: employees for candidates representing workers' unions and employers for candidates representing employers' federations.<sup>12</sup> For each section the number of judges elected by employees had to be equal to the number elected by employers. Elected judges were nominated for a period of five years, and during their mandate they could keep on working in their original job at the same salary. In addition they were paid for each hour worked at the labor court, and employers were obliged to grant them time-off for their court duties.

The worker unions in France (the main ones are CGT, FO, CFDT, CFTC, and CFE-CGC)<sup>13</sup> generally established separate lists of candidates, while the five main employers' federations (CGPME, MEDEF, FNSEA, UNAPL,

<footnote n="7"><sup>7</sup>Disputes affecting collective labor relationships are resolved by ordinary civil courts. For a more detailed description of the organization of French labor courts, see Desrieux and Espinosa (2017) and Espinosa, Desrieux, and Ferracci (2018).</footnote>

<footnote n="8"><sup>8</sup>The United Kingdom, Germany and Belgium are some of the countries wherein such specialized courts exist as well.</footnote>

<footnote n="9"><sup>9</sup>Those working at home have to choose the court of the geographical area of their home address.</footnote>

<footnote n="10"><sup>10</sup>Source: French Ministry of Justice, http://www.justice.gouv.fr/statistiques.html</footnote>

<footnote n="11"><sup>11</sup>The "Diverse activities" section deals with claims brought by, for instance, people working in not-for-profit organizations, workers in lawyers' offices, and building caretakers.</footnote>

<footnote n="12"><sup>12</sup>Elections were held by universal suffrage (membership of a union or federation was not required to vote).</footnote>

<footnote n="13"><sup>13</sup>CGT stands for Confédération générale du travail, FO for Force Ouvrière, CFDT for Confédération Française démocratique du Travail, CFTC for Confédération Française des Travailleurs Chrétiens, and CFE-CGC for Confédération Française de l'Encadrement-Confédération générale des cadres. There are in addition a few smaller unions such as SUD (Union Syndicale Solidaire) and UNSA (Union nationale de Syndicats Autonomes), and some independent ones.</footnote>
UPA)<fnref n="14" /> mostly proposed a common list, thereby obtaining a majority in most elections. The last elections were held in 2008, and the mandate of the judges elected at that time was exceptionally extended to the end of December 2017. Due to the high costs of organizing these elections and because of high abstention rates, the National Assembly decided to change the system of selecting labor courts' judges: from the mandate starting in 2018, they were no longer elected but directly nominated both by the Ministry of Justice and the Ministry of Labor, for a four-year term.

Importantly for this paper is that the French worker unions are ideologically quite distinct. The five main ones are usually divided into two categories: the so-called *reformist* unions (CFDT, CFE-CGC and CFTC) and, by opposition, the *non-reformist* unions (CGT and FO). The latter tend to take tougher positions in their negotiations with the employers' federations and the government, while the former are relatively moderate and more inclined to make concessions during negotiations (see Mouriaux (2013), Desrieux and Espinosa (2019)). At the national level, the *reformist* unions CFDT, CFE-CGC and the CFTC gathered respectively 22%, 8% and 9% in the 2008 elections. For *non-reformist* unions CGT and FO the scores were respectively 34% and 16%.<fnref n="15" /> On the other hand, the employers' federations are ideologically more homogeneous (explaining why the five major ones generally proposed joint lists of candidates), one of the exceptions being the fairly recently created AEES (*Association des Employeurs de l'Economie Sociale*), which is regarded as a relatively left-wing orientated federation. In 2008 the five main federations gathered together 72% of the votes, while AEES got 19%.

## 2.3 Dispute resolution

Dispute resolution in French labor courts is composed of several stages. Once a claim is opened, it has to go first through the conciliation board (*bureau de conciliation*). This first stage is mandatory, and is supervised by two judges, one representing employers and one representing employees. This first stage aims at forcing parties to listen to each other's viewpoint, and, if possible, to reach an agreement to avoid litigation. If parties fail to settle at this stage, the plaintiff may either drop the case, or the case is sent to the adjudication panel (*bureau de jugement*), comprising two judges representing employers and two representing employees. Decisions in each adjudication panel are made by majority rule, i.e., a verdict is pronounced on a case only if at least three judges approve it. When they do so the claim ends (for the first instance at least). In practice, however, judges sometimes fail to reach an agreement, either on the question of whether the plaintiff should be compensated, the amount of compensation or on the litigation cost allocation (Bardin-Fournairon and Barraut (2013)). The case is then again examined at some later date, by the same four judges of the adjudication panel, but to which is added a professional judge from the regional Court of First Instance (*Tribunal de Grande Instance*). Presided by the latter judge, this additional tie-breaking hearing (*audience de départage*) then decides on the claim. Note that professional judges therefore only intervene in French labor

<footnote n="14">¹⁴CGPME stands for *Confédération Générale des Petites et Moyennes Entreprises*, MEDEF for *Mouvement des entreprises de France*, FNSEA for *Fédération nationale des syndicats d'exploitants agricoles*, UNAPL for *Union nationale des professions libérales*, and UPA for *Union Professionnelle Artisanale*.</footnote>

<footnote n="15">¹⁵These aggregate scores hide strong discrepancies within and across labor courts. For instance, while the CFE-CGC dominates the *executives* section of labor courts, it receives a limited support in other sections.</footnote>
courts when the adjudication panels fail to reach an agreement. Figure 1 in the online appendix illustrates
these different stages.

## 2.4 Main principles governing the hearings

Several principles govern the hearings in French labor courts. First, in application of article 6-1 of the European Convention of Human Rights,<fnref n="16" /> all defendants and plaintiffs whose cases are being examined by an adjudication panel have the right to a fair and impartial trial (as for any kind of civil dispute or criminal case in France). Just before starting their mandate, all judges have therefore to take an oath whereby they commit themselves to take their decisions with diligence and integrity. Second, the assignment of cases to adjudication panels and sessions is done in a quasi-random way. The court office schedules all sessions that need to be held, and constitutes, for each session, the panel of judges that is going to examine the cases which belong to that session. In doing so it must respect the employer-employee parity for each panel, and the judges it nominates as presidents (who chair the session) should evenly come from the employers' pool and the employees' pool. Sessions are then filled up as new cases arrive at a court, on a first-come, first-served basis: a newly registered case is assigned to the session that still has a remaining slot.

Third, all hearings before the adjudication panel are oral and accessible to the public.<fnref n="17" /> Cases within a session are examined sequentially, one after the other, following the order in which they were registered by the court office.<fnref n="18" /> The adjudication panel listens to the arguments presented by the plaintiff and defendant of a case, and may ask clarifying questions, before proceeding with the next case. Only when all the cases have been heard, the panel retires to deliberate behind closed doors (art. 448 *Code de la Procédure Civile*). In the Paris Labor Court, juries take their decisions on the day of the session.

# 3 Data

## 3.1 Data collection

Our dataset is constructed by combining two sources. The first source contains detailed information on the decisions made by the adjudication panels at the Paris Labor Court. We had access to this information thanks to a partnership with this court, a partnership approved by the Ministry of Justice under the condition that all collected data would remain strictly confidential and anonymous. We compiled data on all decisions taken by the adjudication panels in the three main sections (Commerce, Diverse Activities, and Executives),

<footnote n="16">¹⁶This article states that "[...] in the determination of his civil rights [...] everyone is entitled to a fair and public hearing within a reasonable time by an independent and impartial tribunal established by law".</footnote>

<footnote n="17">¹⁷Hearings at the Paris Labor Court are held in the afternoon.</footnote>

<footnote n="18">¹⁸At the beginning of the session the panel judges determine which cases scheduled to be examined can actually be heard that day. Indeed, cases can be postponed (and handled at a later date) whenever the parties (or their representatives) do not show up at the session's start, or if they have not disclosed sufficiently in advance all necessary documents and material necessary for the judgment.</footnote>
accounting for more than 90% of all cases dealt by the Paris Labor Court, during February of the years 2013-2017.<fnref n="19" /> First, we extracted the agenda of each adjudication panel (sitting in February 2013-2017 for the three sections under scrutiny), that is to say the list of all cases that potentially had to be examined by the judges of the panel. Second, we downloaded from the court's local server two documents for each case: a two-page summary of the dispute, and the decision of the court. The information contained in these two documents was then hand-coded by several research assistants (who had received a training prior to their job). Using the agendas, we identify the date of each hearing, the composition of the adjudication panel (i.e., the names of the four judges), and the list of all cases actually handled by the judges on a given day (recall that some cases could be adjourned), together with the precise order in which they were heard. The two documents that were downloaded allowed us to collect information on characteristics of defendants and plaintiffs, their chosen type of judicial representation,<fnref n="20" /> and a short description of each claim a plaintiff has against a defendant together with the corresponding requested and received amounts of money.

The second source provides the identity of the judges elected in December 2008. We accessed a document via the Internet containing, for all electoral lists established by the worker unions and employer federations, the names of all candidates that got elected in that year. We then matched this second source with the first source thanks to the fact that judge names are also recorded in our first source.<fnref n="21" />

## 3.2 Descriptive statistics

Our sample consists of 2,331 cases, handled by 643 different adjudication panels, henceforth referred to as the juries. Out of these 2,331 cases, 916 (handled by 238 juries) were assigned to the "Commerce" section, 527 (167 juries) to the "Diverse Activities" section, and 888 (238 juries) to the "Executives" section. Table A1 in the online appendix shows the summary statistics of characteristics of plaintiffs and defendants. The upper panel concerns plaintiffs and the lower panel defendants. Note that some characteristics are not always observed. For example, defendant's age is missing and unknown for 351 observations (2,331 minus 1,980). Instead of dropping such observations from our sample, we will include in all regression models a set of missing-observation dummies. Thus, to capture that age is sometimes unknown, we add in our specifications a dummy "age missing" equal to one if age is missing and 0 otherwise. If age is missing we attribute a value 0 to this variable (arbitrary normalisation). This is the simplest solution to keeping a maximum number of observations for estimation purposes. Plaintiffs are on average 44 years old, and 54% of them are male (no missing observations for the gender variable). Most have the French nationality (77%),

<footnote n="19">¹⁹The remaining 10% of cases were handled in the two other court sections, namely "Agriculture" and "Industry". We focused on the month of February since, according to Paris Labor Court officials, this is a standard and representative month (in particular not subject to abnormal seasonality).</footnote>

<footnote n="20">²⁰Each party has the possibility to choose to be represented by a union representative, a lawyer, a colleague (or an employer from the same sector as the defendant) or a spouse/partner. But judicial representation is not mandatory: parties can also decide to defend their interests by themselves.</footnote>

<footnote n="21">²¹The full lists of candidates (including those who were not elected) are not available. If a judge's name could not be found in the second source we consulted the Internet to retrieve the affiliation (i.e., worker union or employer federation) of this judge. This occurs when those initially elected in 2008 were replaced, at some point during the (long) mandate, by non-elected candidates. We did not always succeed in retrieving these affiliations, explaining why information on judges is sometimes missing in our data.</footnote>
while those originating from North Africa (resp. sub-Sahara Africa) make up 7% (resp. 9%) of observations. Around 35% of the plaintiffs reported to live in Paris, 35% in a close suburb of Paris (petite couronne), 19% in a more distant suburb (grande couronne), and 11% in a place outside Ile-de-France (or IDF, one of the 13 regions in metropolitan France to which Paris and its suburbs belong). About 70% of the plaintiffs chose to be represented by a professional lawyer, 7% by a union representative, and 22% preferred to defend their interests by themselves. Regarding the defendants, about 85% of employers are firms or companies, 8% are liquidators,<fnref n="22" /> and 5% are associations. Employers' headquarters are mostly located in Paris (81%), 13% in a close or more distant suburb, and 6% in a place outside IDF. <fnref n="23" /> Defendants made relatively little use of lawyers (60%, 11 percentage points fewer than plaintiffs), while only 15% preferred to defend themselves without assistance (7 percentage points fewer than plaintiffs). Many of them asked a colleague to assist them (24%). All defendant/plaintiff characteristics listed in Table A1 will play the role of control variables in our regression analyses.

Table 1 displays summary statistics on jury decisions and claims filed by the plaintiffs. The statistics are based only on plaintiffs for whom the four judges of the jury managed to reach an agreement (2,111 observations). Unlike Table A1, the variables listed in Table 1 are either known for all observations, or missing for just a few of them. We see that the amount of money demanded by plaintiffs varies between zero<fnref n="24" /> and almost €5 million, and the amount actually awarded between zero and about €1 million. On average the demanded amount (around €104,000) is well above the awarded amount (€15,000), reflecting that plaintiffs and/or those who assist them tend to over-demand relatively to what judges find a justified compensation. The ratio of awarded amount to demanded amount is on average equal to 20% (calculated after dropping the four plaintiffs who demanded no money). This last statistic partly reflects, however, that 40% of plaintiffs receive no compensation at all. Considering only the sub-sample of plaintiffs who did get compensated, the average ratio goes up to 34%. Plaintiffs tend to have quite a high number of different claims against defendants, almost 7 on average, and there are only 29 cases out of 2,111 with a single claim, indicating that employees overwhelmingly take court action against their employers for multiple issues.<fnref n="25" /> Table 1 also contains statistics on what we call the primary claim, i.e., the claim for which the associated amount of demanded money is highest among all claims formulated by a plaintiff. The amount requested for this claim is on average around €52,000, about half of what plaintiffs request in total. The corresponding amount actually obtained is approximately €7,500, again about half of the total compensation awarded to plaintiffs.

<footnote n="22">²²A liquidator (or a trustee) is an officer who is specially appointed to wind up the affairs of a closing company (typically when it goes bankrupt). Assets of the company are sold by the liquidator and the resulting funds are used to pay off the company's debts. The liquidator is legally empowered to act on behalf of the company in various contexts, including trials at court.</footnote>

<footnote n="23">²³The geographical jurisdiction of the Paris Labor Court covers the whole city of Paris. As such it is competent for handling cases of plaintiffs whose workplace is within the capital. The court documents we accessed mention the headquarters of firms where plaintiffs were employed, and these headquarters were not necessarily located in Paris itself. For plaintiffs working at home their personal address was mentioned.</footnote>

<footnote n="24">²⁴There are four cases where plaintiffs requested €0. The first case sought to rectify the documents of a previously established judgment. The second case required the reclassification of a short-term contract into a permanent contract. The third case challenged the refusal to grant a sabbatical leave, and the last one contains an empty decision document.</footnote>

<footnote n="25">²⁵This is a consequence of a ruling stipulating that a case has to gather all the different claims that a plaintiff has against a defendant. Since 2016, this rule is no longer mandatory, but it was nonetheless implemented during the full period covered by our study.</footnote>
We see that the primary claim mostly concerns unjustified layoff (67%) and unpaid wages (12%). Concealed work (4.0%), and discrimination/harassment (2.0%) represent smaller shares of cases.

Table A2 in the online appendix gathers analogous summary statistics but now based on the plaintiffs for whom the jury judges failed to agree (220 observations). The awarded amounts refer here to the decisions taken at the tie-breaking audiences. Plaintiffs demanded on average around € 130,000, about € 30,000 more than by plaintiffs whose cases were decided by the four-judge juries. The amount actually awarded is now on average around € 28,000, almost twice the amount listed in Table 1, and the probability of attributing no money at all is lower (30% instead of 40%). However, the amount awarded as a fraction of the amount demanded is similar in both tables. For instance, among plaintiffs who were awarded positive amounts of money, this fraction is 34% in Table 1 and 37% in Table A2. The statistics regarding the number of claims and the nature of primary claims are also comparable in both tables. All in all, while tie-breaking juries tend to handle comparatively more severe cases (and accordingly compensate plaintiffs more generously in absolute terms), they appear to behave similarly as the the four-judge juries in relative terms.

<table><caption>Table 1: Summary statistics on plaintiffs' claims and jury decisions</caption><thead><tr><th>Variable</th><th>Mean</th><th>Std. Dev.</th><th>Min</th><th>Max</th><th># Obs.</th></tr></thead><tbody><tr><td>Amount demanded (€)</td><td>104,424</td><td>219,231</td><td>0</td><td>4,777,106</td><td>2,111</td></tr><tr><td>Amount awarded (€)</td><td>15,483</td><td>42,420</td><td>0</td><td>931,107</td><td>2,111</td></tr><tr><td>Amount awarded/amount demanded</td><td>0.20</td><td>0.25</td><td>0</td><td>1.00</td><td>2,107</td></tr><tr><td>Amount awarded=0 (%)</td><td>40</td><td></td><td></td><td></td><td>2,111</td></tr><tr><td>Amount awarded/amount demanded if >0</td><td>0.34</td><td>0.25</td><td>0.00</td><td>1.00</td><td>1,261</td></tr><tr><td>Number of claims</td><td>6.86</td><td>3.92</td><td>0</td><td>35</td><td>2,111</td></tr><tr><td>Amount demanded primary claim (€)</td><td>52,413</td><td>89,644</td><td>200</td><td>1,300,976</td><td>2,107</td></tr><tr><td>Amount awarded primary claim (€)</td><td>7,509</td><td>21,197</td><td>0</td><td>426,240</td><td>2,107</td></tr><tr><td>Nature of primary claim :</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Unjustified layoff</td><td>0.67</td><td>0.47</td><td>0</td><td>1</td><td>2,111</td></tr><tr><td>Unpaid wages</td><td>0.12</td><td>0.33</td><td>0</td><td>1</td><td>2,111</td></tr><tr><td>Concealed work</td><td>0.04</td><td>0.19</td><td>0</td><td>1</td><td>2,111</td></tr><tr><td>Discrimination or harassment</td><td>0.02</td><td>0.13</td><td>0</td><td>1</td><td>2,111</td></tr><tr><td>Other</td><td>0.15</td><td>0.36</td><td>0</td><td>1</td><td>2,111</td></tr></tbody></table>

Table 2 gives information on jury characteristics. Female members are in the minority in 401 out of 643 juries (these juries have either 1 female member or none), in 161 juries there are exactly two female and 2 male members, while in only 81 of them women are in the majority (these juries are either composed of 3 women or 4). Although there are many more male than female jury members the sex ratio for presidents is perfectly balanced: half of the juries are presided by a woman. Presidents are also equally represented by employees and employers: 51% of juries are presided by a worker's union member and 49% by a employer's federation member. There are quite a lot of non-reformist union members (henceforth referred to as left-wing worker union) in the juries. Both worker representatives are from this union in 22% of juries, while 43% of juries are made up of one such representative. There are, however, relatively few left-wing federation members participating in juries: for 91% of them there is no such representative (in the remaining 9% of juries there are either one or two members of the left-wing employer federation).<fnref n="26" /> Recall here that judges were selected

<footnote n="26">²⁶Information on union affiliation is missing, for one or both union representatives, in 93 juries (643 minus 550); information of</footnote>
through elections, and that consequently our statistics on jury composition reflect these elections.

Finally, Table A3 in the Appendix shows that the number of cases handled per jury varies between 1 and 20. The majority of juries (72%) had to make decisions on between 2 and 5 cases, while the average number of cases is 3.63.

<table><caption>Table 2: Jury characteristics</caption><thead><tr><th>Variable</th><th>Frequency</th><th>Relative frequency (%)</th><th># obs.</th></tr></thead><tbody><tr><td># female jury members:</td><td></td><td></td><td></td></tr><tr><td>0</td><td>160</td><td>25</td><td>643</td></tr><tr><td>1</td><td>241</td><td>37</td><td>643</td></tr><tr><td>2</td><td>161</td><td>25</td><td>643</td></tr><tr><td>3</td><td>74</td><td>12</td><td>643</td></tr><tr><td>4</td><td>7</td><td>1</td><td>643</td></tr><tr><td>Identity President:</td><td></td><td></td><td></td></tr><tr><td>Woman</td><td>325</td><td>50</td><td>643</td></tr><tr><td>Member of left-wing worker union</td><td>328</td><td>51</td><td>643</td></tr><tr><td># members of left-wing worker union:</td><td></td><td></td><td></td></tr><tr><td>0</td><td>196</td><td>36</td><td>550</td></tr><tr><td>1</td><td>234</td><td>43</td><td>550</td></tr><tr><td>2</td><td>120</td><td>22</td><td>550</td></tr><tr><td># members of left-wing employer federation:</td><td></td><td></td><td></td></tr><tr><td>0</td><td>382</td><td>91</td><td>418</td></tr><tr><td>1</td><td>33</td><td>8</td><td>418</td></tr><tr><td>2</td><td>3</td><td>1</td><td>418</td></tr></tbody></table>

# 4 Checking for random assignment of juries and cases to sessions

In this section we first verify that jury composition is not systematically related to characteristics of cases. We then verify that cases belonging to a same session are unrelated to each other. Finally, we check that the number of cases examined during a session is unrelated to characteristics of cases and juries. These results are an immediate consequence of the random assignment of cases and juries to sessions (see Section 2.4). As argued below, these results are crucial since they are needed to identify the causal effects of our key variables. The following notations are used:

$M_{ij}^d \equiv$ Amount of money demanded (in euros) by the plaintiff of case i handled by jury j

$M_{ij}^a \equiv$ Amount of money awarded (in euros) by jury j to the plaintiff of case i

$N_j \equiv$ Number of cases in the session handled by jury j

$J \equiv$ Number of juries

<footnote>federation affiliation is missing, for one or both federation representatives, in 225 juries (643 minus 418). Whenever the affiliation of a given member is unknown we set a missing-dummy variable equal to one (like we did for the plaintiff/defendant characteristics).</footnote>
$$N \equiv \text{Number of cases } (N = \sum_{j=1}^{J} N_j)$$

$X_{ij} \equiv$ A row-vector of variables characterizing i and j (characteristics of plaintiff/defendant, case, session, and jury; dummies for missing variables)

The analysis in this section is based on the full sample, thus $J = 643$ and $N = 2,331$. Table A5 in the online appendix examines whether variation in the composition of the jury is uncorrelated to variables characterizing cases. We do this by running regressions of various jury composition measures on variables such as the average amount demanded by plaintiffs within a session ($\sum_{i=1}^{N_j} M_{ij}^d / N_j$), the fraction of female plaintiffs in a session,<fnref n="27" /> dummies for the year in which the case is examined, etc. We also add an indicator for the "Commerce" section and another one for the "Diverse Activities" section ("Executives" being the default section). Controlling for the court section wherein a session is held is important because the profiles of elected judges (especially in terms of their ideological orientation) tend to vary across sections, but at the same time various case characteristics, such as plaintiffs' demanded amounts of money, are correlated with section indicators (e.g., demanded amounts are relatively large in the "Executives" section). Finally, we included year indicators.

Columns 1 and 2 gives results of a Probit regression. In column 1 the dependent variable is a dummy indicating whether the jury is presided by a woman, and in column 2 it is a dummy equal to one if the president is a worker union member and zero otherwise. Columns 3 and 4 report results of an ordered probit regression, with the dependent variable in column 3 being the number of female jury members (ranging between 0 and 4), and in column 4 the number of members of a left-wing worker union (ranging between 0 and 2).<fnref n="28" /> Focusing first on the variables characterizing cases, there are only three that are statistically significant (two at the 10% level, and one at the 5% level) out of 44 possibilities. Furthermore, for each of the four models, we cannot reject the null hypothesis that all coefficients on these variables are jointly equal to zero using a Wald test (p-values between 0.32 and 0.99). While the year dummies are never statistically significant, the two section indicators mostly do have significant effects. In column 4, for instance, both coefficients are significant and positive, suggesting that there are relatively less judges of left-wing worker unions in the "Executives" section. Note that the reported pseudo-R² is low in each column, indicating that the regressors included in the different models have little explanatory power. The main conclusion to be drawn from Table A5 is that, conditional on our two section indicators, jury characteristics appear uncorrelated to observed features of cases. It is then plausible to assume that jury composition is also unrelated to unobserved attributes of cases, which ensures that the estimated jury effects we find in Section 5 have a causal interpretation.

<footnote n="27">²⁷To facilitate the interpretation of results we have only included average plaintiff/defendant characteristics for which there are no missing observations.</footnote>

<footnote n="28">²⁸The ordered probit models contain a full set of cutpoints (estimates omitted from both column 4 and 5), hence the constants cannot be identified and have been normalized to zero. We did not manage to run an ordered probit regression on the number of members of left-wing oriented employer federations since there is too little variation in this variable (see Table 2)</footnote>
In Table A6 we report our tests of within-session case independence. We do this through estimation of the following type of model:

$$Variable_{ij} = X_{ij}\beta + \gamma \frac{1}{N_j - 1} \sum_{l \neq i} Variable_{lj} + \epsilon_{ij} \quad (1)$$

We are thus regressing *Variable*<sub>*ij*</sub>, a scalar variable characterizing case *i* examined by jury *j*, on the average of this variable over all other cases handled by *j*,<sup>29</sup> and the variables in *X*<sub>*ij*</sub> defined earlier (except that it does not include *Variable*<sub>*ij*</sub>). Within-session independence is tested using a standard t-test of the null hypothesis $\gamma = 0$. Naturally, estimation is here based exclusively on sessions with at least two cases. The table gives OLS estimates of $\gamma$ together with standard errors clustered at the session level, for nine choices of *Variable*<sub>*ij*</sub>. Column 1, with results for *Variable*<sub>*ij*</sub> = $M_{ij}^d$, indicates that $\hat{\gamma}$ is 0.067 with a standard error equal to 0.103, so the null hypothesis that $M_{ij}^d$ and $\sum_{l \neq i} M_{lj}^d/(N_j - 1)$ are uncorrelated cannot be rejected at any conventional significance level. The null cannot be rejected either for most of the other choices.<sup>30</sup>

The variable $M^d$ is arguably the single best predictor of case severity, so the non-correlation result found in column 1 is particularly welcome. Indeed, the result suggests that plaintiffs have not been grouped together in sessions on the basis of this observed determinant of case severity. It seems then unlikely that cases are bunched together along unobserved determinants of case severity, which in turn implies that we should be able to identify a key parameter in our empirical analysis, namely the effect on $M_{ij}^a$ of the amounts awarded to plaintiffs other than *i* (as measured by the parameter $\lambda$ in regression models (3) and (4)). If sessions had instead been formed on the basis of unobserved determinants of case severity (say the most severe cases in half of the sessions, and the least severe ones in the other half), identification would not be feasible, and the estimated parameter would (in part) reflect a spurious association between the amounts awarded to plaintiffs within sessions.

The last results discussed in this section are collected in Table A7. Reported therein are estimation results from an ordered probit regression of $N_j$ on the same regressors as in Table A5 together with variables characterizing juries (those for which there are no missing observations). All year dummies are statistically significant, suggesting that sessions included more cases during the years 2013-2016 relatively to 2017 (the omitted indicator variable). One of the two section indicators is also significant. More importantly, however, among our case and jury characteristics, only the fraction of plaintiffs form whom the primary claim corresponds to a layoff is statistically significant. Furthermore, using a Wald test we cannot reject the null that all coefficients associated with the case/jury variables jointly equal zero (p-value equals 0.52). It is then plausible that unobserved jury/case characteristics are unrelated to $N_j$ as well, suggesting that we can

<footnote n="29"><sup>29</sup>This average is calculated over all observations *l* such that *Variable*<sub>*lj*</sub> is not missing. If it is missing for at least one *l* ≠ *i*, then $N_j$ is adjusted downwards accordingly).</footnote>

<footnote n="30"><sup>30</sup>The null hypothesis is rejected only twice: at the 1% level for the dummy indicating that a plaintiff is assisted by a lawyer (column 8), and at the 10% level for the dummy indicating that a defendant is assisted by a lawyer (column 9). This may be explained by the presence of serial cases in our data. Whenever several employees working for the same employer file their complaints simultaneously they have a high chance of being grouped together in the same session, thereby creating bunching along the two variables (plaintiffs of a group tend to choose the same type of legal representation; similarly, the defendant often chooses the same type of representation for each case in this group).</footnote>
estimate the effect of the latter variable on $M^a$ (captured by the parameter $\alpha$ in models (3) and (4)) without confounding bias.

# 5 Empirical analysis

The objective of this section is to analyze what are the determinants of $M_{ij}^a$. We focus in particular on the role played by the amounts awarded to other plaintiffs, i.e., the amounts $M_{i'j}^a$ for $i' \neq i$. We also study closely the effects of session and case characteristics, and jury composition. Section 5.1 presents OLS and IV estimates of a linear regression model wherein other plaintiffs' amounts enter the specification through their mean. Linear models are, however, not well suited when the dependent variable equals zero for a large fraction of observations, as is the case in our data. To account for the clumping at zero, Section 5.2 then considers a simultaneous Tobit model and discusses the results that are obtained using a recent estimation method proposed by Xu and Lee (2015). Finally, Section 5.3 contains a robustness analysis: the simultaneous Tobit model is estimated under different assumptions regarding i) the plaintiffs $i$ actually affected by simultaneity; ii) the plaintiffs $i' \neq i$ having an influence on $M_{ij}^a$. All analyses are based on a sub-sample of observations that excludes from the full sample the 220 cases that were sent to the tie-breaking juries (since we do not model their decisions). We then discarded all sessions with just one case (since we wish to test for the presence of simultaneity in decision making). Altogether our resulting estimation sample contains $N = 2,010$ cases which were examined by $J = 535$ juries.

## 5.1 OLS and IV estimation results

Table A8 in the Appendix presents estimation results of the following linear regression model

$$M_{ij}^a = X_{ij}\beta + \delta M_{ij}^d + \alpha 1\{N_j > 4\} + \gamma 1\{i \text{ is first case in session}\} + \lambda \frac{1}{N_j - 1} \sum_{l \neq i} M_{lj}^a + \epsilon_{ij} \quad (2)$$

where $\epsilon_{ij}$ is an error term with mean equal to zero, $\beta$ a column-vector of parameters including a constant, and $\delta$, $\alpha$, $\gamma$, and $\lambda$ four scalar parameters. The amounts of money $M_{ij}^a$ and $M_{ij}^d$ are measured in 10 k euros for all $i$ and $j$ (the original amounts have thus been divided by 10,000). Each element in $\beta$ represents the effect of the corresponding variable in $X_{ij}$, while $\delta$ corresponds to the effect of $M_{ij}^d$, the variable that is intended to capture the severity of case $i$. The parameter $\alpha$ measures the impact of large sessions (containing more than 4 cases), $\gamma$ the effect of being the first case examined in a session, and $\lambda$ the impact of the average amount of money attributed to other plaintiffs in the same session as $i$.<fnref n="31" /> If $\lambda \neq 0$ then jury decisions regarding compensation levels given to plaintiffs simultaneously affect each other. When instead $\lambda = 0$ there is no such simultaneity and the model collapses to a standard linear regression model. Note that when $\lambda \neq 0$, the

<footnote n="31">³¹It would be tempting to add jury-specific fixed effects into the specification. However, as shown by Nickell (1981), panel data methods applied to a dynamic model such as (2) produce downward-biased estimates of $\lambda$ whenever fixed effects are included. We performed a small Monte Carlo study showing that the inclusion of fixed effects causes the IV estimator of $\lambda$ to be inconsistent as well.</footnote>
error term $\epsilon_{ij}$ is by construction correlated with $M_{lj}^a$ for each $l \neq i$. We assume though that this error term is independent of all other regressors appearing in (2), and those appearing in the model for which $M_{i'j}^a$ is the dependent variable, for each $i' \neq i$.

Column 1 reports OLS estimates together with standard errors clustered at the jury-level in parentheses. Note that OLS ignores the correlation between $\epsilon_{ij}$ and $M_{lj}^a$ for each $l \neq i$. To account for this endogeneity, column 2 gives IV estimates (again with clustered standard errors) where $\sum_{l \neq i} M_{lj}^a/(N_j - 1)$ is instrumented by $\sum_{l \neq i} M_{lj}^d/(N_j - 1)$, an instrument which is uncorrelated with $\epsilon_{ij}$ under our assumptions on the error terms. We only report the estimates of our key parameters, that is to say $\delta, \alpha, \gamma$, and $\lambda$, and the elements in $\beta$ that correspond to jury composition effects. We thus omit the estimated coefficients associated with defendant/plaintiff characteristics and the year/section indicators.

The OLS results in column 1 show that the null hypothesis $\lambda = 0$ cannot be rejected at any conventional significance level, hence we do not find evidence of simultaneity in juries' decision making. Among the case/session characteristics, only the variable $M^d$ is statistically significant: plaintiffs whose cases are more severe get awarded larger amounts of money. Among the jury characteristics, only the dummy indicating that both worker representatives are from a left-wing worker union is significant (at the 1% level). The estimate suggests that such juries award almost € 6,000 more to a plaintiff (compared to juries where none of the worker representatives is from a left-wing union). The IV results reported in column 2 are qualitatively the same as the OLS results. However, the impact of having two left-wing orientated worker union members in a jury is now a bit stronger (almost € 6,800). The first-stage estimate of the coefficient associated with the excluded instrument is 0.073 and the standard error equals 0.026. The p-value is 0.005, suggesting that the average amount demanded by plaintiffs (other than $i$) is an appropriate instrument for the average amount awarded to them.

As is well known, estimating linear regression models may lead to misleading interpretations when the dependent variable is heavily censored. As will be seen in the next section, estimation of a simultaneous Tobit model – a model that is well suited to account for the important mass at zero of $M^a$ – produces results that differ markedly from those presented here. In particular, several of our key variables no longer have statistically insignificant effects.

## 5.2 Simultaneous Tobit model

Table 3 reports the estimation results of the following simultaneous Tobit model:

$$M_{ij}^a = \max \left( 0, X_{ij}\beta + \delta M_{ij}^d + \alpha 1\{N_j > 4\} + \gamma 1\{i \text{ is first case in session}\} + \lambda \frac{1}{N_j - 1} \sum_{l \neq i} M_{lj}^a + \epsilon_{ij} \right). \quad (3)$$

Although we have used the same Greek letters to define the parameters as in (2), their quantitative interpretations differ from those in the linear model. Note that when $\lambda = 0$ there is no simultaneity in
decision making and the model collapses to a standard Tobit model. Qu and Lee (2012) derive the likelihood function under the assumption that the error terms $\epsilon_{ij}$ are i.i.d. (across $i$ and $j$) and with $\epsilon_{ij} | (X_{ij}, M_{ij}^d, 1\{N_j > 4\}, 1\{i \text{ is first case in session}\}) \sim N(0, \sigma^2)$. Each error term $\epsilon_{ij}$ is thus normally distributed and independent from all regressors appearing in (3) except $M_{ij}^a$ for $l \neq i$. Appendix A reproduces the expression of this likelihood function (actually the likelihood corresponding to the slightly more general simultaneous Tobit model (4) discussed below). Xu and Lee (2015) establish the asymptotic normality of the ML estimator of the parameters. As indicated by these authors, a limitation of their method is that the error terms $\epsilon_{ij}$ are assumed to be i.i.d. normally distributed across all $i$ and $j$. In particular, within-session error terms are thus independent, i.e., $\epsilon_{ij}$ and $\epsilon_{i'j}$ are restricted to be uncorrelated random variables for all $i \neq i'$. Our preferred results are therefore based on the full set of explanatory variables (reported in column 4), a specification that limits as much as possible the possibility of the restriction not holding. Note that indirect evidence in support of the restriction comes from the OLS and IV results where the clustered standard errors and those that are not clustered turn out to be comparable.

Column 1 presents results for a version of the model without explanatory variables besides the average amount awarded to other plaintiffs, i.e., $\beta$, $\delta$, $\alpha$, and $\gamma$ are set to zero. We reject the null hypothesis that $\lambda = 0$ at the 5% level, and the sign of this parameter is positive. A possible explanation for this finding is that our first specification does not include any variables characterizing sessions or juries. As shown below, some of these variables are strong determinants of $M^a$, hence excluding them from the model generates a positive correlation between $\epsilon_{ij}$ and $\epsilon_{i'j}$ for $i' \neq i$. This is turn may cause a spurious positive relationship between $M_{ij}^a$ and $\sum_{l \neq i} M_{lj}^a / (N_j - 1)$. Column 2 confirms this intuition: after adding case/session characteristics and our two section indicators to the specification, we can no longer reject that $\lambda$ equals zero (although it still has a positive sign). Like the OLS and IV results (A8) we find that $M^d$ has a positive and statistically significant effect. Unlike our earlier results, being examined in a large session now has a significant (at the 1% level) and negative impact on a plaintiff's awarded amount. The hypothesis $\gamma = 0$ cannot be rejected at any conventional significance level: analogously to Bruine de Bruin (2005) we do not find that a plaintiff examined first in a court session is treated differently compared to those examined later.

Results in column 3 correspond to a specification where jury characteristics have been added. The estimate of $\lambda$ is now negative but the null hypothesis that this parameter equals zero can still not be rejected. All findings regarding our case/session variables are very similar to those reported in column 2. Concerning our jury variables we see that, like in Table A8, the dummy indicating that both worker representatives are from a left-wing worker union has a positive and statistically significant impact. Unlike the OLS and IV results, however, the variable indicating whether the jury is presided by a worker's union member is significant as well. When this is the case a plaintiff is awarded a higher amount of money. Like our previous estimations, all other jury characteristics remain non-significant: the president's gender, the jury's gender composition, and the political colour of the members representing employers' federations, do not affect awarded amounts. Finally, column 4 contains our results for the richest specification, i.e., those obtained after including plaintiff/defendant characteristics and year indicators to the model as well. Adding these variables does not alter the conclusions obtained from column 3 except that the variable indicating that
one jury member is from a left-wing union turns significant also, albeit only at the 10% level. Its estimated coefficient is positive and, as expected, smaller than the effect of having two members from a left-wing union (the latter effect is bout twice as large as the former).

Using well known formulas for Tobit models (see for instance Wooldridge (2010)) and the parameter estimates of column 4, we can calculate the partial effect of each explanatory variable on the expectation of $M^a$ and the expectation of $M^a$ given that $M^a > 0$ (for simplicity we omit that these two expectations also depend on all explanatory variables of model 3). We will do this exercise only for variables that are statistically significant (except the demanded amount $M^d$). Since these variables are all 0-1 dummies, we calculate this effect by comparing the (conditional) expectation of the awarded amount at the two values of each dummy, holding other regressors fixed (see the online appendix for details). Table A4 contains these calculations. We find that the partial effect of being examined in a large session decreases $E(M^a)$ by € 3,485. A plaintiff whose case is examined by a jury headed by a worker's union member can expect to receive € 4,026 more than when the jury is headed by a employer's federation member. The effect of having a jury composed of two (resp. one) members of a left-wing worker union leads to an increase of € 4,068 (resp. € 1,517). The partial effects of these variables on $E(M^a|M^a > 0)$ take the same sign but are smaller in magnitude (roughly 1/3 smaller in absolute value compared to the effects on the unconditional expectation).

## 5.3 Robustness analysis

The purpose of this section is to present several robustness checks. To do this we now consider a slightly more general version of the simultaneous Tobit model:

$$M_{ij}^a = \max \left( 0, X_{ij}\beta + \delta M_{ij}^d + \alpha 1\{N_j > 4\} + \gamma 1\{i \text{ is first case in session}\} + \lambda \sum_{i'=1}^{N_j} W_{ii',j} M_{i'j}^a + \epsilon_{ij} \right) \quad (4)$$

Here $W_{ii',j}$ is a weight attributed to the variable $M_{i'j}^a$, with $W_{ii',j} \ge 0$ for all $i \ne i'$ and $W_{ii,j} = 0$ for all $i$. Note that when $W_{ii',j} = 1/(N_j - 1)$ for all $i \ne i'$ we get again model (3). The weights are allowed to depend on variables that are exogeneous (i.e., variables that are independent of the error terms $\epsilon_{ij}$), and for model coherency they should verify the restriction $|\lambda| \times \max_{i,j} \sum_{i'=1}^{N_j} W_{ii',j} < 1$ (see Qu and Lee (2012)). The assumptions that were previously made on the error terms remain unchanged.

Table A9 gives the ML results for different weighting matrices $W$. Column 1 corresponds to those for $W_{ii',j} = 1\{\text{case } i \text{ is handled right after case } i'\}$. This choice of the weights amounts to assuming that jury $j$'s decision regarding the amount $M_{ij}^a$ is only affected by the amount awarded to the plaintiff whose case was examined in court just before $i$. This specification thus assumes that juries fall prey to the same kind of bias as observed in sequential judicial decision procedures (see the three papers discussed in the introduction). Column 2 corresponds to results for $W_{ii',j} = 1\{\# \text{ claims from } i \text{ is above sample median}\} 1/(N_j - 1)$. Our intention here is to capture the idea that a jury may be more likely to be influenced by extraneous factors
<table><caption>Table 3: Estimation of simultaneous Tobit model (3)</caption><thead><tr><th>Variable</th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>Av. awarded amount to others (10 k €): λ</td><td>0.0820**<br>(0.0390)</td><td>0.00220<br>(0.0389)</td><td>-0.0149<br>(0.0391)</td><td>-0.0137<br>(0.0390)</td></tr><tr><td>Characteristics of case/session:</td><td></td><td></td><td></td><td></td></tr><tr><td>Amount demanded (10 k €): δ</td><td></td><td>0.0786***<br>(0.00590)</td><td>0.0787***<br>(0.00588)</td><td>0.0802***<br>(0.00594)</td></tr><tr><td>Large session: α</td><td></td><td>-0.798***<br>(0.275)</td><td>-0.812***<br>(0.279)</td><td>-0.740***<br>(0.280)</td></tr><tr><td>First case in session: γ</td><td></td><td>-0.303<br>(0.305)</td><td>-0.304<br>(0.303)</td><td>-0.279<br>(0.305)</td></tr><tr><td>Characteristics of jury:</td><td></td><td></td><td></td><td></td></tr><tr><td>President is from worker union</td><td></td><td></td><td>0.882***<br>(0.278)</td><td>0.854***<br>(0.279)</td></tr><tr><td>President is female</td><td></td><td></td><td>-0.150<br>(0.352)</td><td>-0.0944<br>(0.353)</td></tr><tr><td>Female majority</td><td></td><td></td><td>-0.260<br>(0.482)</td><td>-0.354<br>(0.482)</td></tr><tr><td>Male majority</td><td></td><td></td><td>-0.231<br>(0.387)</td><td>-0.280<br>(0.388)</td></tr><tr><td>One member is from left-wing worker union</td><td></td><td></td><td>0.442<br>(0.301)</td><td>0.507*<br>(0.303)</td></tr><tr><td>Two members are from left-wing worker union</td><td></td><td></td><td>0.984**<br>(0.403)</td><td>1.043**<br>(0.405)</td></tr><tr><td>One member is from left-wing employer federation</td><td></td><td></td><td>0.642<br>(0.619)</td><td>0.690<br>(0.625)</td></tr><tr><td>Two members are from left-wing employer federation</td><td></td><td></td><td>-0.223<br>(1.821)</td><td>-0.372<br>(1.847)</td></tr><tr><td>Constant</td><td>-0.607***<br>(0.165)</td><td>0.0150<br>(0.304)</td><td>-0.731<br>(0.545)</td><td>-1.067<br>(0.924)</td></tr><tr><td>σ<sup>2</sup></td><td>3.587***<br>(0.0428)</td><td>3.386***<br>(0.0428)</td><td>3.376***<br>(0.0428)</td><td>3.360***<br>(0.0428)</td></tr><tr><td>Characteristics of plaintiff/defendant</td><td>No</td><td>No</td><td>No</td><td>Yes</td></tr><tr><td>Section indicators</td><td>No</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Year indicators</td><td>No</td><td>No</td><td>No</td><td>Yes</td></tr><tr><td>Number of observations</td><td>2,010</td><td>2,010</td><td>2,010</td><td>2,010</td></tr><tr><td>Log likelihood</td><td>-4,371.1</td><td>-4,255.5</td><td>-4,242.7</td><td>-4,223.0</td></tr></tbody></table>

Standard errors in parentheses. * p<0.10, ** p<0.05, *** p<0.010.
if case *i* is relatively “complicated”, that is to say if the plaintiff of this case has many claims against the defendant. Column 3 gives results for *W*<sub>ii',j</sub> = 1{primary claim from *i* does not concern unpaid wages}1/(N<sub>j</sub> - 1), column 4 for *W*<sub>ii',j</sub> = 1{primary claim from *i* is not an unjustified layoff}1/(N<sub>j</sub> - 1), and column 5 for *W*<sub>ii',j</sub> = 1{primary claim from *i* is neither an unjustified layoff nor a matter of unpaid wages}1/(N<sub>j</sub> - 1). We have in mind here the possibility that jury *j* is more likely to be influenced by amounts awarded to others when the claims filed by the plaintiff of case *i* can easily be interpreted in multiple ways, or when it is hard to objectively assess what are the monetary costs of the damage incurred by this plaintiff (think for example of claims concerning discrimination). In such situations the jury may have a harder time to reach an agreement on the amount *M*<sup>*a*</sup><sub>*ij*</sub> it wishes to award, which in turn increases the likelihood that it falls prey to simultaneity biases. For example, the specification corresponding to column 3 postulates that *j* is influenced by other amounts only if the primary claim does not concern unpaid wages, which is arguably a claim such that the monetary compensation is easy to determine (either *j* awards the salary times the number of unpaid months to *i*, or it does not compensate this plaintiff if the claim is deemed unjustified). Columns 4 and 5 are based on similar ideas. Finally, column 6 reports results for *W*<sub>ii',j</sub> = 1 for all *i* ≠ *i'*. It is thus assumed here that jury *j*'s decision regarding *M*<sup>*a*</sup><sub>*ij*</sub> is influenced by the total amount awarded to others (∑<sub>*l*≠*i*</sub> *M*<sup>*a*</sup><sub>*lj*</sub>) instead of the average amount (1/N<sub>j-1</sub> ∑<sub>*l*≠*i*</sub> *M*<sup>*a*</sup><sub>*l'j*</sub>).

As Table A9 shows, practically all results are similar as those reported in the previous section. One exception is that the null hypothesis $\lambda = 0$ can be rejected in column 4. The evidence in favor of simultaneity is weak, however, since the hypothesis can only be rejected at the 10% level. Furthermore, it can not be rejected in columns 3 and 5, in spite of the fact that the corresponding specifications draw on the same idea as the specification corresponding to column 4. The other exception is that, unlike in Table 3, the variable “One member is from left-wing worker union” is now sometimes no longer statistically significant (in three out of 6 specifications the null can not be rejected at any conventional significance level).

# 6 Conclusion

"Fair and impartial justice" is a cornerstone of many legal systems around the world. Identifying the factors that could influence judicial decision-making is then fundamental. In particular, it is important to investigate whether extraneous factors (i.e., variables that are unrelated to the intrinsic features of cases) play a role in court decisions, since this could reflect inequality before the law. The main objective of this paper is to test for the presence of a specific kind of extraneous factor, namely caseload exposure. We thus study whether decisions by judges are affected by the decisions they make on other cases in their caseload. We use a new data set on verdicts pronounced at the Paris Labor Court. Decisions in this court are made simultaneously, i.e., at the end of the session when all cases in a caseload have been heard. Exploiting the random assignment of cases and juries to sessions, we estimate simultaneous Tobit models using the method proposed by Xu and Lee (2015). We do not find any statistically significant relationship between the amount awarded to a given plaintiff and the average amount awarded to the other plaintiffs heard during the same session. As robustness checks, we explore other possible impacts of cases' exposure (through the total awarded amount
instead of the average, or through the money awarded to the case heard just before the one being studied), and consider alternative model specifications where outcome simultaneity is assumed to affect only specific subgroups of plaintiffs (e.g., plaintiffs for whom it is difficult to determine the monetary costs incurred by them, or whose cases are complex to evaluate because they contain many claims), but our empirical findings remain unchanged. A policy implication of our findings is that court officials should consider switching from a sequential to a simultaneous decision procedure, especially when court verdicts have far-reaching consequences. Such switches would require some administrative reorganization in each court, but would not entail important monetary costs. Some caution is needed here though, as further research is necessary to investigate if outcome simultaneity is absent not just in labor courts but in courts handling other issues as well.

While the exposure to other cases does not seem to affect judicial decisions in our setting, our investigation shows that jury composition has significant effects: larger amounts of money are awarded to plaintiffs if the jury is presided by a judge representing employees, or if it is made up of one or two judges of left-wing orientated worker unions. This last finding is reminiscent of Anwar et al. (2018) and Cohen and Yang (2019) who show that judges representing (extreme) right wing parties are harsher towards young defendants and those from minority groups. Such sources of biases are, unlike biases caused by decision formats used in courts, hard to address by policy makers, simply because judges’ political beliefs and preferences cannot be changed. However, an interesting direction for future work would be to analyze whether the impact of political affiliation has diminished now that labor judges in France are no longer elected by employers and employees, but nominated jointly by the Ministries of Labor and Justice. Although judges now still belong to either the worker unions or employer federations, these direct nominations may weaken their ties with the employees or employers they represent. This in turn may cause judges to take court decisions that are less aligned with the preferences of the groups of agents they represent, thereby reducing the impact of political affiliation on their decisions.
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A Log-likelihood function for the simultaneous Tobit model

In this appendix we reproduce the log-likelihood function derived by Qu and Lee (2012) and Xu and Lee (2015). Let $\theta = (\beta, \delta, \alpha, \gamma, \lambda, \sigma)$ be the vector of parameters to be estimated. The log likelihood function of $M_{ij}^a$ for all i and j, conditional on $(M_{ij}^d, X_{ij}, 1\{N_j > 4\}, 1\{i \text{ is first case in session}\})$ for all i and j, is

$$ \ln(L(\theta)) = \sum_{\forall i,j} 1\{M_{ij}^a = 0\} \ln(1 - \Phi(Z_{ij}(\theta))) - \frac{1}{2} \sum_{\forall i,j} 1\{M_{ij}^a > 0\} [\ln(2\pi\sigma^2) + (M_{ij}^a/\sigma - Z_{ij}(\theta))^2] + \ln(|\det(I_N - \lambda GWG)|) \quad (5) $$

where $\Phi$ is the distribution function of the standard normal random variable, $|\det(A)|$ the absolute value of the determinant of A, $I_N$ the identity matrix of dimension N (with N being the total number of observations, i.e., $N = \sum_{j=1}^J N_j$), G the N-dimensional diagonal matrix with first element being $1\{M_{11}^a > 0\}$ and last element $1\{M_{N_j J}^a > 0\}$, W the N × N block diagonal matrix with the j-th block being the $N_j \times N_j$ matrix $W_j \equiv (W_{ii'}, j)^{32}$ and

$$ Z_{ij}(\theta) = \left( X_{ij}\beta + \delta M_{ij}^d + \alpha 1\{N_j > 4\} + \gamma 1\{i \text{ is first case in session}\} + \lambda \sum_{i'=1}^{N_j} W_{ii',j} M_{i'j}^a \right) / \sigma. $$

Apart from some differences in notations, the log-likelihood function (5) is exactly the one that can be found in Qu and Lee (2012) and Xu and Lee (2015). Note that when $\lambda = 0$, the last term of (5) equals 0, and we get the log-likelihood function for data generated by a standard Tobit model. Xu and Lee (2015) have shown that the ML estimator of $\theta$ is consistent and asymptotically normally distributed.

ONLINE APPENDIX

B STAGES OF DISPUTE RESOLUTION IN FRENCH LABOR COURTS

Figure 1 illustrates the different stages of dispute resolution in French labor courts. The percentages in parentheses concern the Paris Labor Court during 2013-2017, but the proportions are similar for other French labor courts. Most of the cases (84%) went through the standard procedure, whereby the parties first try

$$ W_j = \begin{pmatrix} W_{11,j} & \cdots & W_{1N_j,j} \\ \vdots & \ddots & \vdots \\ W_{N_j 1,j} & \cdots & W_{N_j N_j,j} \end{pmatrix}. $$

<footnote>$^{32}$We thus have</footnote>
<figure><img src="image_3.png" /><figcaption>Figure 1: Organization of French labor courts (% from the Paris Court, 2013-2017)</figcaption></figure>

to conciliate. The remaining 16% went through the so-called interlocutory proceedings: these are cases for which an urgent decision has to be made and for which the plaintiff can disclose incontestable evidence to support his claim.<fnref n="33" /> For only 5% of cases the conciliation phase was successful. Among the cases for which conciliation did not work out, 62.5% ended up being examined by an adjudication panel, and 37.5% were either withdrawn or considered invalid. Finally, for 74% of disputes handled by the adjudication panel a decision was made by the four judges, in the remaining 26% of disputes they did not come to an agreement (they were hence examined at a tie-breaking hearing).

<footnote n="33">³³For instance, the case of a woman who is laid off during her maternity leave would be treated in the interlocutory proceedings. According to Ray (2015), 75% of the cases in interlocutory proceedings correspond to plaintiffs who have unsuccessfully requested from their employers documents such as labor certificates.</footnote>
C PARTIAL EFFECTS FOR THE SIMULTANEOUS TOBIT MODEL

To facilitate the calculations we will derive the partial effects under the assumption that $\lambda = 0$, which seems a reasonable assumption given that this hypothesis cannot be rejected at the usual confidence levels (column 4 of Table 3. Under this assumption the expectation of $M_{ij}^a$, and the expectation of $M_{ij}^a$ conditional on $M_{ij}^a > 0$, are given by (see Wooldridge (2010))

$$E(M_{ij}^a|X_{ij}, M_{ij}^d, 1\{N_j > 4\}, 1\{i \text{ is first case in session}\}) = \sigma(\Phi(Z_{ij}(\theta))Z_{ij}(\theta) + \phi(Z_{ij}(\theta))) \quad (6)$$

and

$$E(M_{ij}^a|M_{ij}^a > 0, X_{ij}, M_{ij}^d, 1\{N_j > 4\}, 1\{i \text{ is first case in session}\}) = \sigma(Z_{ij}(\theta) + \phi(Z_{ij}(\theta))/\Phi(Z_{ij}(\theta))) \quad (7)$$

where $\Phi$ is the distribution function of a standard normal random variable, $\phi$ its density function,

$$Z_{ij}(\theta) = (X_{ij}\beta + \delta M_{ij}^d + \alpha 1\{N_j > 4\} + \gamma 1\{i \text{ is first case in session}\}) / \sigma,$$

and $\theta = (\beta, \delta, \alpha, \gamma, \sigma)$. Note that both expectations are also conditional on the regressors appearing in model 3. Note also that the terms $Z_{ij}(\theta)$ and $\theta$ were already defined in the appendix but are now somewhat simpler since $\lambda = 0$.

We will only outline how to calculate partial effects of variables on the unconditional expectation (6), the effects on the conditional expectations are obtained in a similar way. Furthermore, we focus on determining partial effects of 0-1 dummy variables since in the main text we only consider partial effects for binary variables. These correspond to three of our jury variables included in the vector $X$, and the indicator $1\{N_j > 4\}$. Let us now obtain the formula for one of the jury variables. Suppose that it corresponds to variable $k$ in the vector $X$. Let $X_{ijk}$ denote this variable for case $i$ handled by jury $j$, and let $\beta_k$ be the associated coefficient (an element of $\beta$). Furthermore, let $X_{ij-k}$ correspond to $X_{ij}$ without $X_{ijk}$, and similarly let $\beta_{-k}$ correspond to $\beta$ from which the element $\beta_k$ is excluded. For observation $i, j$, the partial effect of variable $k$, denoted $PE_{ij}$, is the expected awarded amount at $X_{ijk} = 1$ minus the expected amount at $X_{ijk} = 0$, keeping all other regressors fixed at the values observed for this observation:

$$PE_{ij} = E(M_{ij}^a|X_{ij-k}, X_{ijk} = 1, M_{ij}^d, 1\{N_j > 4\}, 1\{i \text{ is first case in session}\}) - E(M_{ij}^a|X_{ij-k}, X_{ijk} = 0, M_{ij}^d, 1\{N_j > 4\}, 1\{i \text{ is first case in session}\}).$$

Using (6) we thus get

$$PE_{ij} = \sigma(\Phi(Z_{ij}^1(\theta))Z_{ij}^1(\theta) + \phi(Z_{ij}^1(\theta))) - \sigma(\Phi(Z_{ij}^0(\theta))Z_{ij}^0(\theta) + \phi(Z_{ij}^0(\theta))),$$

where

$$Z_{ij}^1(\theta) = (X_{ij-k}\beta_{-k} + \beta_k + \delta M_{ij}^d + \alpha 1\{N_j > 4\} + \gamma 1\{i \text{ is first case in session}\}) / \sigma,$$
and

$$Z_{ij}^{0}(\theta) = (X_{ij-k}\beta_{-k} + \delta M_{ij}^{d} + \alpha 1\{N_{j} > 4\} + \gamma 1\{i \text{ is first case in session}\})/\sigma.$$

Instead of calculating a partial effect for a given observation i, j, we actually determine the average partial effect, denoted AVPE, which is simply the average of PE$_{ij}$ over all observations:

$$AVPE = \frac{1}{\# \text{ of obs.}} \sum_{i,j} PE_{ij} \qquad (8)$$

After replacing $\theta$ by the ML estimate $\hat{\theta}$ we obtain an estimate of the AVPE. The AVPE is analogously derived for the variable $1\{N_j > 4\}$. The numbers given in column 1 of Table A4 correspond to this AVPE for each of the four regressors. The AVPE on the conditional expectation (7) is obtained in an analogous way except that the summation in (8) is only over observations i, j such that $M_{ij}^a > 0$, and we divide by the number observations for which this is the case.
D ADDITIONAL TABLES

<table><caption>Table A1: Summary statistics on characteristics of plaintiffs and defendants</caption><thead><tr><th>Variable</th><th>Mean</th><th>Std. Dev.</th><th># Obs.</th></tr></thead><tbody><tr><td></td><td></td><td><u>Plaintiffs</u></td><td></td></tr><tr><td>Age (in years)</td><td>44.22</td><td>11.10</td><td>1,980</td></tr><tr><td>Gender (1=Man)</td><td>0.54</td><td>0.50</td><td>2,331</td></tr><tr><td>Nationality:</td><td></td><td></td><td></td></tr><tr><td>French</td><td>0.77</td><td>0.42</td><td>1,845</td></tr><tr><td>North-African</td><td>0.07</td><td>0.25</td><td>1,845</td></tr><tr><td>Sub-Saharan African</td><td>0.09</td><td>0.29</td><td>1,845</td></tr><tr><td>Other</td><td>0.07</td><td>0.26</td><td>1,845</td></tr><tr><td>Place of residence:</td><td></td><td></td><td></td></tr><tr><td>Paris</td><td>0.35</td><td>0.48</td><td>2,315</td></tr><tr><td>Close suburb of Paris</td><td>0.35</td><td>0.48</td><td>2,315</td></tr><tr><td>Farther-away suburb of Paris</td><td>0.19</td><td>0.40</td><td>2,315</td></tr><tr><td>Outside IDF</td><td>0.11</td><td>0.32</td><td>2,315</td></tr><tr><td>Legal representation:</td><td></td><td></td><td></td></tr><tr><td>Lawyer</td><td>0.71</td><td>0.45</td><td>2,331</td></tr><tr><td>Union representative</td><td>0.07</td><td>0.25</td><td>2,331</td></tr><tr><td>Other</td><td>0.004</td><td>0.06</td><td>2,331</td></tr><tr><td>No representative</td><td>0.22</td><td>0.41</td><td>2,331</td></tr><tr><td></td><td></td><td><u>Defendants</u></td><td></td></tr><tr><td>Type of employer:</td><td></td><td></td><td></td></tr><tr><td>Firm/company</td><td>0.85</td><td>0.36</td><td>2,290</td></tr><tr><td>Liquidator</td><td>0.08</td><td>0.27</td><td>2,290</td></tr><tr><td>Association</td><td>0.05</td><td>0.21</td><td>2,290</td></tr><tr><td>Other</td><td>0.03</td><td>0.16</td><td>2,290</td></tr><tr><td>Employer's headquarter:</td><td></td><td></td><td></td></tr><tr><td>Paris</td><td>0.81</td><td>0.39</td><td>2,318</td></tr><tr><td>Close suburb of Paris</td><td>0.10</td><td>0.30</td><td>2,318</td></tr><tr><td>Farther-away suburb of Paris</td><td>0.03</td><td>0.17</td><td>2,318</td></tr><tr><td>Outside IDF</td><td>0.06</td><td>0.24</td><td>2,318</td></tr><tr><td>Legal representation:</td><td></td><td></td><td></td></tr><tr><td>Lawyer</td><td>0.60</td><td>0.49</td><td>2,331</td></tr><tr><td>Colleague</td><td>0.24</td><td>0.43</td><td>2,331</td></tr><tr><td>Other</td><td>0.01</td><td>0.09</td><td>2,331</td></tr><tr><td>No representative</td><td>0.15</td><td>0.35</td><td>2,331</td></tr></tbody></table>
<table><caption>Table A2: Summary statistics on plaintiffs' claims and tie-breaking jury decisions</caption><thead><tr><th>Variable</th><th>Mean</th><th>Std. Dev.</th><th>Min</th><th>Max</th><th># Obs.</th></tr></thead><tbody><tr><td>Amount demanded (€)</td><td>132,500</td><td>200,307</td><td>1,724</td><td>1,983,336</td><td>220</td></tr><tr><td>Amount awarded (€)</td><td>28,441</td><td>97,257</td><td>0</td><td>1,392,357</td><td>220</td></tr><tr><td>Amount awarded/amount demanded</td><td>0.26</td><td>0.27</td><td>0</td><td>1.38</td><td>192</td></tr><tr><td>Amount awarded=0 (%)</td><td>30</td><td></td><td></td><td></td><td>220</td></tr><tr><td>Amount awarded/amount demanded if >0</td><td>0.37</td><td>0.25</td><td>0.01</td><td>1.38</td><td>153</td></tr><tr><td>Number of claims</td><td>7.64</td><td>4.48</td><td>2</td><td>23</td><td>220</td></tr><tr><td>Amount demanded primary claim (€)</td><td>69,091</td><td>123,575</td><td>1,000</td><td>1,403,316</td><td>220</td></tr><tr><td>Amount awarded primary claim (€)</td><td>14,979</td><td>58,003</td><td>0</td><td>812,337</td><td>220</td></tr><tr><td>Nature of primary claim :</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Unjustified layoff</td><td>0.59</td><td>0.49</td><td>0</td><td>1</td><td>220</td></tr><tr><td>Unpaid wages</td><td>0.12</td><td>0.33</td><td>0</td><td>1</td><td>220</td></tr><tr><td>Concealed work</td><td>0.05</td><td>0.21</td><td>0</td><td>1</td><td>220</td></tr><tr><td>Discrimination or harassment</td><td>0.03</td><td>0.18</td><td>0</td><td>1</td><td>220</td></tr><tr><td>Other</td><td>0.2</td><td>0.4</td><td>0</td><td>1</td><td>220</td></tr></tbody></table>

<table><caption>Table A3: Number of cases per jury</caption><thead><tr><th>Number of cases</th><th>Frequency</th><th>Relative frequency (%)</th></tr></thead><tbody><tr><td>1</td><td>77</td><td>12</td></tr><tr><td>2</td><td>124</td><td>19</td></tr><tr><td>3</td><td>139</td><td>22</td></tr><tr><td>4</td><td>125</td><td>19</td></tr><tr><td>5</td><td>77</td><td>12</td></tr><tr><td>6</td><td>59</td><td>9</td></tr><tr><td>7</td><td>25</td><td>4</td></tr><tr><td>8</td><td>9</td><td>1</td></tr><tr><td>9</td><td>6</td><td>1</td></tr><tr><td>10</td><td>1</td><td>0.2</td></tr><tr><td>11</td><td>1</td><td>0.2</td></tr><tr><td>12</td><td>1</td><td>0.2</td></tr><tr><td>20</td><td>1</td><td>0.2</td></tr></tbody><tfoot><tr><td>Total</td><td>643</td><td>100</td></tr></tfoot></table>

<table><caption>Table A4: Partial effects on $E(M^a)$ and $E(M^a)|M^a > 0$</caption><thead><tr><th>Variable</th><th>Effect on E(M<sup>a</sup>)</th><th>Effect on E(M<sup>a</sup>)|M<sup>a</sup> > 0</th></tr></thead><tbody><tr><td>Large session</td><td>€-3,485</td><td>€-2,660</td></tr><tr><td>Jury presided by worker-union representative</td><td>€4,026</td><td>€3,087</td></tr><tr><td>One judge from left-wing worker union</td><td>€1,517</td><td>€1,093</td></tr><tr><td>Two judges from left-wing worker union</td><td>€4,068</td><td>€3,114</td></tr></tbody></table>
<table><caption>Table A5: Testing for random assignment of juries</caption><thead><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td colspan="5">Characteristics of cases:</td></tr><tr><td>Average of M<sup>d</sup></td><td>0.00310<br>(0.00808)</td><td>-0.0117<br>(0.00824)</td><td>-0.0000446<br>(0.00672)</td><td>0.00602<br>(0.00811)</td></tr><tr><td>Std. dev. of M<sup>d</sup></td><td>-0.00176<br>(0.00541)</td><td>0.0133**<br>(0.00608)</td><td>0.0000894<br>(0.00445)</td><td>-0.00893<br>(0.00586)</td></tr><tr><td>Average number of claims</td><td>0.0391*<br>(0.0225)</td><td>0.0105<br>(0.0223)</td><td>0.0192<br>(0.0188)</td><td>0.0137<br>(0.0213)</td></tr><tr><td>% primary claim is unjustified layoff</td><td>0.170<br>(0.172)</td><td>0.267<br>(0.171)</td><td>-0.0226<br>(0.144)</td><td>0.0654<br>(0.167)</td></tr><tr><td>% female plaintiffs</td><td>-0.111<br>(0.164)</td><td>-0.205<br>(0.162)</td><td>0.0122<br>(0.137)</td><td>-0.195<br>(0.157)</td></tr><tr><td>% plaintiffs assisted by lawyer</td><td>0.0132<br>(0.148)</td><td>-0.252*<br>(0.148)</td><td>-0.00552<br>(0.125)</td><td>-0.0116<br>(0.144)</td></tr><tr><td>% defendants assisted by lawyer</td><td>0.0219<br>(0.169)</td><td>-0.0142<br>(0.168)</td><td>0.0839<br>(0.142)</td><td>0.198<br>(0.163)</td></tr><tr><td colspan="5">Year indicators:</td></tr><tr><td>2013</td><td>0.179<br>(0.158)</td><td>0.0840<br>(0.157)</td><td>0.114<br>(0.132)</td><td>-0.127<br>(0.156)</td></tr><tr><td>2014</td><td>0.0534<br>(0.168)</td><td>0.0837<br>(0.168)</td><td>0.0548<br>(0.141)</td><td>-0.0344<br>(0.166)</td></tr><tr><td>2015</td><td>0.159<br>(0.187)</td><td>0.258<br>(0.186)</td><td>0.0703<br>(0.156)</td><td>-0.235<br>(0.187)</td></tr><tr><td>2016</td><td>0.00535<br>(0.164)</td><td>0.241<br>(0.163)</td><td>0.00531<br>(0.138)</td><td>-0.162<br>(0.164)</td></tr><tr><td colspan="5">Section indicators:</td></tr><tr><td>"Diverse activities"</td><td>0.338**<br>(0.150)</td><td>0.0816<br>(0.150)</td><td>0.194<br>(0.125)</td><td>0.555***<br>(0.150)</td></tr><tr><td>"Commerce"</td><td>-0.238*<br>(0.139)</td><td>0.00767<br>(0.140)</td><td>-0.364***<br>(0.118)</td><td>0.872***<br>(0.138)</td></tr><tr><td>Constant</td><td>-0.434*<br>(0.249)</td><td>-0.0744<br>(0.246)</td><td></td><td></td></tr><tr><td>Number of observations</td><td>643</td><td>643</td><td>643</td><td>550</td></tr><tr><td>Pseudo R<sup>2</sup></td><td>0.031</td><td>0.015</td><td>0.018</td><td>0.060</td></tr><tr><td>Wald test [p-value]</td><td>8.16 [0.70]</td><td>12.6 [0.32]</td><td>3.1 [0.99]</td><td>8.11 [0.70]</td></tr><tr><td>Log likelihood</td><td>-431.7</td><td>-438.7</td><td>-857.7</td><td>-549.7</td></tr></tbody></table>

The Wald statistic corresponds to a test of the null hypothesis that all coefficients equal zero (except the coefficients on our two section indicators, the constant in columns 1 and 2, and the cutpoints of the ordered probit model in columns 3 and 4). Demanded amount $M^d$ is divided by 10,000. Standard errors in parentheses.

* p<0.10, ** p<0.05, *** p<0.010.
<table><caption>Table A6: Testing for random assignment of cases</caption><thead><tr><th>Variable</th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th></tr></thead><tbody><tr><td>M<sup>d</sup></td><td>0.0674<br>(0.103)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td># claims</td><td></td><td>0.0323<br>(0.0463)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Primary claim concerns unjustified layoff</td><td></td><td></td><td>0.0765<br>(0.0504)</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Female plaintiff</td><td></td><td></td><td></td><td>-0.0004<br>(0.0466)</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Age of plaintiff</td><td></td><td></td><td></td><td></td><td>0.0599<br>(0.0464)</td><td></td><td></td><td></td><td></td></tr><tr><td>French plaintiff</td><td></td><td></td><td></td><td></td><td></td><td>0.0638<br>(0.0580)</td><td></td><td></td><td></td></tr><tr><td>Defendant represents a firm/company</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.0804<br>(0.0523)</td><td></td><td></td></tr><tr><td>Plaintiff is represented by lawyer</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.6950***<br>(0.0291)</td><td></td></tr><tr><td>Defendant is represented by lawyer</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.0831*<br>(0.0456)</td></tr><tr><td>N</td><td>2,254</td><td>2,254</td><td>2,254</td><td>2,254</td><td>1,870</td><td>1,721</td><td>2,212</td><td>2,254</td><td>2,254</td></tr><tr><td>R<sup>2</sup></td><td>0.133</td><td>0.037</td><td>0.042</td><td>0.052</td><td>0.061</td><td>0.175</td><td>0.099</td><td>0.487</td><td>0.087</td></tr></tbody></table>

Main entries are the OLS estimates of $\gamma$ in model (1) and in parentheses are standard errors clustered at the session level. * p<0.10, ** p<0.05, *** p<0.010
<table><caption>Table A7: Testing for random assignment of the number of cases N<sub>j</sub></caption><thead><tr><th>Variable</th><th></th><th></th></tr></thead><tbody><tr><td>Characteristics of case:</td><td></td><td></td></tr><tr><td>Average of M<sup>d</sup></td><td>-0.000786</td><td>(0.00419)</td></tr><tr><td>Average number of claims</td><td>0.00320</td><td>(0.0180)</td></tr><tr><td>% primary claim is unjustified layoff</td><td>-0.284**</td><td>(0.141)</td></tr><tr><td>% female plaintiffs</td><td>-0.0622</td><td>(0.134)</td></tr><tr><td>% plaintiffs assisted by lawyer</td><td>-0.123</td><td>(0.121)</td></tr><tr><td>% defendants assisted by lawyer</td><td>0.0235</td><td>(0.138)</td></tr><tr><td>Jury characteristics:</td><td></td><td></td></tr><tr><td>President is female</td><td>-0.0660</td><td>(0.115)</td></tr><tr><td>President is from worker union</td><td>0.0668</td><td>(0.0814)</td></tr><tr><td>Number of female jury members</td><td>-0.0269</td><td>(0.0584)</td></tr><tr><td>Year indicators:</td><td></td><td></td></tr><tr><td>2013</td><td>0.279**</td><td>(0.128)</td></tr><tr><td>2014</td><td>0.389***</td><td>(0.136)</td></tr><tr><td>2015</td><td>0.318**</td><td>(0.151)</td></tr><tr><td>2016</td><td>0.272**</td><td>(0.133)</td></tr><tr><td>Section indicators:</td><td></td><td></td></tr><tr><td>"Diverse activities"</td><td>-0.344***</td><td>(0.121)</td></tr><tr><td>"Commerce"</td><td>-0.0441</td><td>(0.113)</td></tr><tr><td>Number of observations</td><td>643</td><td></td></tr><tr><td>Pseudo R<sup>2</sup></td><td>0.012</td><td></td></tr><tr><td>Wald test [p-value]</td><td>8.14 [0.52]</td><td></td></tr><tr><td>Log likelihood</td><td>-1246.7</td><td></td></tr></tbody></table>

The Wald statistic corresponds to a test of the null hypothesis that all coefficients equal zero (except the coefficients on the year and section indicators, and the cutpoints of the ordered probit model). Standard errors in parentheses.

* p<0.10, ** p<0.05, *** p<0.010.
<table><caption>Table A8: OLS and IV estimation of model (2)</caption><thead><tr><th>Variable</th><th>(1)</th><th>(2)</th></tr></thead><tbody><tr><td>Av. awarded amount to others (10 k €): λ</td><td>-0.0149<br>(0.0548)</td><td>-0.156<br>(0.143)</td></tr><tr><td>Characteristics of case/session:</td><td></td><td></td></tr><tr><td>Amount demanded (10 k €): δ</td><td>0.0721**<br>(0.0295)</td><td>0.0717**<br>(0.0291)</td></tr><tr><td>Large session: α</td><td>-0.3283<br>(0.2006)</td><td>-0.3622<br>(0.2235)</td></tr><tr><td>First case in session: γ</td><td>-0.1709<br>(0.2261)</td><td>-0.1755<br>(0.2108)</td></tr><tr><td>Characteristics of jury:</td><td></td><td></td></tr><tr><td>President is from worker union</td><td>0.1836<br>(0.1679)</td><td>0.2190<br>(0.1920)</td></tr><tr><td>President is female</td><td>0.0256<br>(0.1847)</td><td>0.0452<br>(0.2106)</td></tr><tr><td>Female majority</td><td>-0.2418<br>(0.2236)</td><td>-0.2680<br>(0.2516)</td></tr><tr><td>Male majority</td><td>-0.0243<br>(0.1946)</td><td>-0.0075<br>(0.2187)</td></tr><tr><td>One member is from left-wing worker union</td><td>0.3729<br>(0.2530)</td><td>0.4264<br>(0.2710)</td></tr><tr><td>Two members are from left-wing worker union</td><td>0.5945***<br>(0.2218)</td><td>0.6770***<br>(0.2444)</td></tr><tr><td>One member is from left-wing employer federation</td><td>0.2192<br>(0.1958)</td><td>0.2205<br>(0.2166)</td></tr><tr><td>Two members are from left-wing employer federation</td><td>-0.0265<br>(0.3533)</td><td>-0.0641<br>(0.4016)</td></tr><tr><td>Constant</td><td>0.1822<br>(0.5038)</td><td>0.4648<br>(0.6454)</td></tr><tr><td>Characteristics of plaintiff/defendant</td><td>Yes</td><td>Yes</td></tr><tr><td>Section indicators</td><td>Yes</td><td>Yes</td></tr><tr><td>Year indicators</td><td>Yes</td><td>Yes</td></tr><tr><td>Number of observations</td><td>2,010</td><td>2,010</td></tr><tr><td>R<sup>2</sup></td><td>0.199</td><td>0.192</td></tr></tbody></table>

Standard errors clustered at the session-level in parentheses. * p<0.10, ** p<0.05, *** p<0.010.
<table><caption>Table A9: Robustness analysis: Estimation of model (4) for different weighing matrices W</caption><thead><tr><th>Variable</th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th></tr></thead><tbody><tr><td>Awarded amount to others (10 k €): λ</td><td>0.0353<br>(0.0322)</td><td>0.0490<br>(0.0415)</td><td>-0.00448<br>(0.0387)</td><td>-0.0839*<br>(0.0487)</td><td>-0.0724<br>(0.0496)</td><td>0.00878<br>(0.0122)</td></tr><tr><td>Characteristics of case/session:</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Amount demanded (10 k €): δ</td><td>0.0804***<br>(0.00593)</td><td>0.0800***<br>(0.00594)</td><td>0.0803***<br>(0.00594)</td><td>0.0803***<br>(0.00593)</td><td>0.0802***<br>(0.00593)</td><td>0.0803***<br>(0.00593)</td></tr><tr><td>Large session: α</td><td>-0.726***<br>(0.280)</td><td>-0.723***<br>(0.280)</td><td>-0.735***<br>(0.280)</td><td>-0.749***<br>(0.280)</td><td>-0.743***<br>(0.280)</td><td>-0.763***<br>(0.283)</td></tr><tr><td>First case in session: γ</td><td>-0.202<br>(0.310)</td><td>-0.263<br>(0.305)</td><td>-0.261<br>(0.305)</td><td>-0.259<br>(0.305)</td><td>-0.259<br>(0.305)</td><td>-0.256<br>(0.305)</td></tr><tr><td>Characteristics of jury:</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>President is from worker union</td><td>0.840***<br>(0.279)</td><td>0.839***<br>(0.279)</td><td>0.852***<br>(0.279)</td><td>0.848***<br>(0.279)</td><td>0.847***<br>(0.279)</td><td>0.842***<br>(0.279)</td></tr><tr><td>President is female</td><td>-0.100<br>(0.352)</td><td>-0.0976<br>(0.352)</td><td>-0.0960<br>(0.353)</td><td>-0.0913<br>(0.352)</td><td>-0.0991<br>(0.352)</td><td>-0.0991<br>(0.353)</td></tr><tr><td>Female majority</td><td>-0.342<br>(0.482)</td><td>-0.340<br>(0.482)</td><td>-0.352<br>(0.482)</td><td>-0.357<br>(0.482)</td><td>-0.360<br>(0.482)</td><td>-0.337<br>(0.483)</td></tr><tr><td>Male majority</td><td>-0.286<br>(0.388)</td><td>-0.280<br>(0.388)</td><td>-0.281<br>(0.388)</td><td>-0.275<br>(0.388)</td><td>-0.281<br>(0.388)</td><td>-0.282<br>(0.388)</td></tr><tr><td>One member is from left-wing<br>worker union</td><td>0.492<br>(0.303)</td><td>0.490<br>(0.303)</td><td>0.504*<br>(0.303)</td><td>0.509*<br>(0.302)</td><td>0.507*<br>(0.302)</td><td>0.495<br>(0.303)</td></tr><tr><td>Two members are from left-wing<br>worker union</td><td>1.027**<br>(0.405)</td><td>1.018**<br>(0.405)</td><td>1.038**<br>(0.405)</td><td>1.049***<br>(0.404)</td><td>1.041**<br>(0.404)</td><td>1.026**<br>(0.405)</td></tr><tr><td>One member is from left-wing<br>employer federation</td><td>0.692<br>(0.625)</td><td>0.695<br>(0.625)</td><td>0.690<br>(0.625)</td><td>0.701<br>(0.624)</td><td>0.699<br>(0.624)</td><td>0.691<br>(0.625)</td></tr><tr><td>Two members are from left-wing<br>employer federation</td><td>-0.355<br>(1.846)</td><td>-0.349<br>(1.846)</td><td>-0.368<br>(1.847)</td><td>-0.366<br>(1.844)</td><td>-0.363<br>(1.845)</td><td>-0.361<br>(1.847)</td></tr><tr><td>Constant</td><td>-1.171<br>(0.922)</td><td>-1.171<br>(0.922)</td><td>-1.090<br>(0.924)</td><td>-1.058<br>(0.919)</td><td>-1.056<br>(0.920)</td><td>-1.144<br>(0.922)</td></tr><tr><td>σ²</td><td>3.359***<br>(0.0428)</td><td>3.358***<br>(0.0428)</td><td>3.360***<br>(0.0428)</td><td>3.356***<br>(0.0428)</td><td>3.357***<br>(0.0428)</td><td>3.359***<br>(0.0428)</td></tr><tr><td>Characteristics of plaintiff/defendant</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Section indicators</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Year indicators</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Number of observations</td><td>2,010</td><td>2,010</td><td>2,010</td><td>2,010</td><td>2,010</td><td>2,010</td></tr><tr><td>Log likelihood</td><td>-4,222.5</td><td>-4,222.4</td><td>-4,223.1</td><td>-4,221.6</td><td>-4,222.0</td><td>-4,222.8</td></tr></tbody></table>

Column 1: $W_{ii',j} = 1${case i is handled right after case i'}; Column 2: $W_{ii',j} = 1${# claims from i is above sample median}1/(N_j - 1); Column 3: $W_{ii',j} = 1${primary claim from i ≠ unjustified layoff}/(N_j - 1);

Column 4: $W_{ii',j} = 1${primary claim from i ≠ unpaid wages}/(N_j - 1); Column 5: $W_{ii',j} = 1${primary claim from i ≠ unjustified layoff or unpaid wages}/(N_j - 1); Column 6: $W_{ii',j} = 1$.

Standard errors in parentheses. * p<0.10, ** p<0.05, *** p<0.010.