WorkSim: An Agent-Based Model of Labor Markets

In thispaper,weprovideanoverviewof theWorkSimmodel, anagent-based frameworkdesigned to study labor markets. The first objective of thismodel is to reproduce, within rigorous stock-flowaccounting, the gross flows of individuals between important work-states: i.e., employment (distinguishing fixed term contracts and openended contracts), unemployment and inactivity. French legal institutions of the labor market are modelled in some detail and constrain the decisions of the agents on job flows and worker flows. Firms and individuals are heterogeneous and all decisions are taken on the basis of bounded rationality, yet employers aswell asworkers form imperfect anticipations. One important theoretical noveltyof themodel is thatweconsidermulti-job firms and shocks on the individual demandof the firms. Employers consider anticipated shockswhen they decide on the types of contract. Once themodel is calibrated, the secondary objective is to characterize the nature of the labormarket under study, and notably the di erentiated roles of the two types of contracts and their impact on unemployment. This is achieved, first by examining the patterns of flows and stocks of labor and secondly by sensitivity experiments, modifying certain exogenous parameters and variables such as total demand. We then use the model as a tool for experimenting labor market policies, including changes in the labor law in France.


Introduction
. Agent-based methodology o ers a very appropriate tool to model a labor market as a dynamic system of gross flows of workers between the three major states (or stocks) of employment, unemployment and inactivity (also called non participation). It also allows us to study the e ects of policies directly on these flows, a much finer analysis than the studies of the e ects on the stocks. Such a representation of the labor market has emerged as the most fruitful description to ground an analysis of a labor market since the 's and the development of search theory (Phelps et al. ), but its implementation remains partial in empirical work because data on gross flows are only partial . The move of a worker from one state to another is based on a decision of the agent or another agent (the employer), not a random process. The agent-based methodology allows us to base heterogeneous agents' decisions on theoretical ground and empirical knowledge about behavior, and then to build bottom up the aggregate flows and the stocks of individuals in di erent states in a natural way. Finally, we simulate all the flows, both measured and unmeasured, to obtain a complete gross flow system. The workers are always in a state of disequilibrium, by at least the e ect of experience gained or lost, although they do not move each period. Yet the market as a whole may show an aggregate quasi stability, or on the contrary may display important changes each period in terms of stocks and flows that inform us in the great detail on the labor market outcomes and their changes. In a similar manner to workers, jobs are treated using a stock-flow approach. .
Why can we consider the gross flows approach to labor markets so important as an investigation tool? Firms as agents make decisions about job creation, as well as job destruction. The resulting flows are the most important the formal apparatus uses calculus procedures under bounded rationality, since the heterogeneity of agents and a detailed modelling of firms' anticipations preclude the use of the analytic equilibrium methodology common to the search models (Phelps et al. ). Search Theory considers how economic actors find a partner for their transactions (here workers looking for a job in a company, and employers a worker for a vacant job) . In WorkSim, the basic concept of search is developed in several directions, some new. The rationale is first, to build the complete framework of job and workers' flows that is needed and secondly, to provide a new and detailed explanation of the choice of contracts by the employers, in order to make some policy experiments: . Matching emerges from bilateral meetings on a decentralized labor market. Both sides select and can prefer no match other than a poor one. Employers post vacant jobs with a contract and a wage and workers apply for these jobs (or not). Employers select among those who are high in productivity distribution. However, they would prefer to keep a job vacant than hire a worker with poor productivity, because of hiring and termination costs. A stopping rule in the form of a minimum productivity requirement or hiring standard is computed. Moreover, agents have an imperfect evaluation of the future match value: workers do not know the amenity of the job (conditions of work) before being hired, and the employer has an imperfect information on the worker's productivity. No aggregate matching function is then used, in opposition to the matching models now dominant in search theory (Mortensen & Pissarides ). An aggregate matching function introduces a fictitious intermediary on the labor market, and has weaker microeconomic foundations than our sequential double search framework, which can cope with heterogeneity and informational di erentiation . Moreover, matching function models are not robust to large changes in the labor market and do not reproduce the crowding out e ect a ecting some categories of workers .
. Firms are multi-jobs. This is new to the search literature and is a major feature key to the contribution of our model to the analysis of the employers' choices between the two types of contracts. We consider that shocks are on the demand of the firm, a realistic assumption, rather than on individual job productivity, as in the search literature. The firm faces a yearly idiosyncratic random trend (on its share of the market), and random weekly variations around that trend. The employer forms anticipations on future demand and, if the present demand rises, takes into account future cost and benefits of each type of contract before deciding to create a job. If employers forecast a demand fall, they prefer to create short FTC, since they will pay the worker only on the fixed term and so not lose much money. On the other hand, economic dismissals of OEC take delays (o en a year or more) caused by the labor law and jurisprudence generating hoarding costs and also induce severance pay. Hence hiring FTC can be a good choice for an employer who is uncertain about her future demand. However, FTC have their own problems such as limited renewal under the French law and a partial amortization of training costs. Considering firms with multiple jobs and demand shocks then makes it possible to model the choice by each firm of a profitable mix of the two types of contracts. Productivity changes in each job-worker match are modeled as improvements in workers' productivity, which is based on general experience and on-the-job learning with seniority. This is a non-random mechanism (as opposed to the standard search model assumption). We add an assumption of (real and nominal) downward wage rigidity to shocks (a known feature of the French labor market), which means that an employer does not solve a demand shock by lowering the wages of the incumbent workers. A justification based on the theory of e iciency wages can be invoked to give microfoundations (Shapiro & Stiglitz ).However entry wages are flexible to the labor market conditions, an assumption based on empirical studies such as Martins et al. ( ), which is compatible with the rigidity of incumbents' wages. The individual wage then increases on human capital accumulation. The multijobs feature induces the employer to take into account her stock of FTC when deciding on the creation of a new job, since FTC are a bu er against uncertainty. In the existing models, the firms have one job, it precludes to model in a realistic way the role of uncertainty and other factors on the mix of the two types of contracts. Moreover, the uncertainty concept has lead us to introduce subjectivity in forecasting, in the line of Tversky & Kahneman ( ), and Akerlof & Shiller ( ), a concept which also appears to be very relevant to job creation decisions, since it opens the way to the integration of employers' anticipations on the business cycle (le for future work).
. The search concept is extended and integrated in most other decisions on the labor market, which involve more than search costs. First, workers take other voluntary decisions than applying for a job, such as quits and on-the-job search (i.e., looking for a new job while remaining employed). Search calculus in terms of utility is also done about decisions of entry and exit of workers, but we have included some elaborate features such as taking into account the psychological cost of starting to search, and the total income of the household. The latter assumption brings non-market interactions between individuals (see below), an important topic in labor economics, yet one which cannot be treated by models based on representative agents. Secondly, firms also take into account the search costs of replacement when they consider firing a worker for lack of productivity. Demand shocks and workers' productivity changes allow us to explain the disequilibria and flows at the microeoconomic level. Demand shocks explain job creations and hires, part-time, economic dismissals, while productivity changes explain personal dismissals, promotions and transformations of FTC into OEC, since FTC can be also used as screening devices.
Search models and the dual labor market .
All these features put together yield a coherent search model which di ers very deeply from existing models, and is more useful to understand unemployment, as well as the mechanisms of dualism on the labor market and its persistence. Only recently search theory has started to integrate dualism. The model by Cahuc et al. ( ) appears to be the first, and up to the writing of the present paper, the only one to fully endogenize the choice between temporary and permanent contracts . They introduce the cost of paying the total remaining salary in case of termination of temporary contract before the contracted end date. It yields the needed trade o to the firing costs for permanent jobs, without which employers should always prefer FTC. However, they assume that each job is an independent project with an expected duration. Then the employer chooses FTC for short projects and OEC for long projects. The duration of FTC contracts is endogenous. The advance termination cost of FTC does not appear to us as substantial enough to explain that most jobs are OEC. If there is a trade-o , it is rather based on the impossibility to amortize substantial training costs on short contracts, to which one could add the building of trust for many jobs, and long on-the-job learning for complex jobs. Moreover, the independence of the expected duration of jobs in the Cahuc et al. ( ) model does not characterize the demand uncertainty that firms undergo in the real world. As mentioned above and modeled in WorkSim, firms anticipate shocks on their total demand for a good. They respond by choosing a mix of the two types of contracts according to a complex trade-o which takes into account dismissals costs on OEC, vacancy costs, training costs, renewal limitations on FTC and associated costs, as well as the current mix of OEC and FTC, with current FTC as a bu er for the current and future OEC. The duration of FTC is endogenous as in Cahuc et al. ( ). This comprehensive framework of the relative costs of the two contracts requires multi-jobs firms and therefore a profound change in search theory that we propose. Moreover it retrieves the spirit of the seminal dual labor markets model of Rebitzer & Taylor ( ) which is based on total demand uncertainty. The employer divides its employment into temporary and permanent jobs, but the model has an aggregate nature, and no search framework (no unemployment in the model). It also assumes among strong assumptions, di erent wages between FTC and OEC as well as the necessity of monitoring workers to deter them from shirking, and these assumptions are not needed in our model.

Related agent-based models .
WorkSim takes place in a multi-agent literature on labor markets, which has a long history, but remains underdeveloped compared to other fields in agent-based economics. Bergmann ( ) is probably the first to have developed a simple search model with both sides of the market and obtained simultaneously vacant jobs and unemployment, reproducing the imperfect matching by a labor market. Eliasson ( ) has built a macroeconomic agent-based model, MOSES, which has Keynesian, Schumpeterian and Wicksellian foundations and contains a labor market, even though workers do not appear as individual agents. Entry and exit of firms, and process R&D (incremental and radical) are the Schumpeterian factor and influence unemployment. Entry has an important positive influence on growth. Extensions introduce skills through training investment. Firms can raise wages to poach skilled labor from other firms (Ballot & Taymaz ) and competition is then not only on goods markets but also through wages. ARTEMIS (Ballot , ), the forerunner of WorkSim, is based on search decisions by individuals and multi-jobs firms. It is the first multi-agent model to have modeled the gross flows of individuals between the three main states (employment, unemployment, and inactivity), with the addition of on-the-job search.

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This is achieved within an institutional framework distinguishing contracts, notably with some workers in OEC in internal labor markets, other workers in OEC without careers, termed secondary, and others in a temporary help firm. The model generates a temporary segmentation of the young workers, which has been since shown to be an important feature of the French labor market (see for instance Le Barbanchon & Malherbet ( )). Then, a negative demand shock (the first oil shock) a ects only slightly the male workers of prime age in OEC but crowds out the other categories of labor, such as low skilled and females, and, beyond temporary segmentation, precludes the progressive integration of some of the young workers in the internal labor markets. This result corresponds to the real e ects of this oil shock which has strongly influenced the rise of the dualism in France with for individuals lifecycle consequences . .
With the 's we have seen some multi-agents models of the labor market aiming at theoretical research (see Neugart & Richiardi ( ) for a review). The introduction of networks is a progress compared to random search in some contexts (Pingle & Tesfatsion ; Tassier & Menczer ). If massive microdata become available, this approach may give a better understanding of the labor market flows for segments of the workforce. Richiardi ( ) has modeled in more detail than before the matching process between workers and firms with on-thejob search, entrepreneurial decisions and endogenous wage determination. Neugart ( ) has developed an agent-based labor market model with sector-specific skill requirements. Barlet et al. ( ) have simulated the French labor market for the year , appearing as the closest empirical work to ours. They distinguish individuals and jobs, but not firms as such, although there is a labor demand side, with creation and destruction of jobs based on a desired margin and demand. Moreover, calibration by indirect inference is done. However, the most active agent-based field of research is not focused on the development of detailed labor markets models, but on building compact labor market modules in macroeconomic agent-based models, in order to experiment with alternative specifications of a very limited set of institutional and behavioral rules (unemployment benefits, wage flexibility), and examine the aggregate e ects on the whole economic system. Then the models are not calibrated to fit data for a specific country, but look for validation through the obtention of stylised facts.
. Fagiolo et al. ( ) do not propose a full macroeoconomic model, but put a loop between wages and consumption, and introduce process innovation to allow for GDP growth. The labor market is represented by a simple decentralised process to match workers and jobs, with some bargaining in the wage setting. The authors investigate two alternative behaviors when firms decide to open jobs (with dependence on past profits or not) and two for workers (trying to be reemployed by the same firm in last period or performing a random search). Combinations define two regimes, the Walrasian regime, and an Institutionally shaped regime (dependence of job openings on past profit and loyalty of workers). They show that some main stylised facts as the Beveridge, Wage and Okun Curves appear simultaneously only in the Institutionally shaped regime . The K+S model by Dosi et al. ( ) emphasizes the interaction of Keynesian demand factors with innovation (the Schumpeterian dimension) modeled as endogenous R&D to understand growth and business cycles. It has been the stepping stone for macroeconomic models which extend to new parts of the economic system and are more and more complete. Dosi et al. ( ) summarized recent work carried out with a labor market module. The labor market is decentralised but remains centered on hires and fires as far as flows are concerned. The focus is again on comparing alternative regimes, namely a Fordist and a Competitive regime. In the Fordist regime, fires are allowed only when losses are incurred as is the case in WorkSim (before the El Khomry law studied below) and more flexible firing rules are studied in the Competitive regime. Many stylised facts are obtained at the microeconomic and the aggregate level. However, the list given by the authors (in their Table ) makes it clear that almost all do not focus on the labor market detailed outcomes, and notably the competition between categories of workers. Finally, the EURACE model is a macroeconomic and stock-flow consistent model which contains a decentralised labor market module. The model displays a number of macroeconomic stylised facts for a prototype European economy. Dawid et al. ( , ) analyze a system of two regions with di erent or identical labor regimes (rigidity versus flexibility) to analyze convergence and inequality.

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WorkSim and these macroeconomic models are not opposed models of the labor market, and in the future, they may converge. Yet first, they currently have di erent interests. The macroeconomic models formalise some features of the labor market only in order to integrate its interactions with the other parts of the economy to analyze the aggregate outcomes. WorkSim aims at a better understanding of the dynamics of the detailed flows and stocks of the main categories of workers interacting in a fairly precisely defined institutional environment. To give an example, Dosi et al. ( ) study broad alternatives in firing laws (only FTC, no firing). Although theoretically interesting, these are much too radical alternatives to study historical policy changes in a country and especially in France, where they are o en marginal for political and sociological reasons. Modifying the French labor law just to make economic dismissals possible a er one, two, three, or four quarters of diminishing turnover instead of losses during one year has meant a semester of major demonstrations and strikes in France in as well as the dislocation of the socialist majority in parliament. Yet we will show that the "small" changes of the El-Khomri law have large distributional e ects since they a ect the gross flows in a major way and the age classes in an opposed manner. .
Secondly, our detailed analysis leads us to theoretical developments that are specific to our model. The modelling of a large number of decisions on the labor market for each agent requires a unified treatment of costbenefit outcome for each of these agents. This is why we have adopted a utility function with idiosyncratic weights for each individual in order to aggregate incomes and free time, with search costs and other variables. Individuals have a bounded rationality, yet they know what trade o they accept between income against free time, when these play a role in their di erent decisions. The utility function acts simply as an aggregator of two needs, and it enables the individual to decide between discrete choices, not to choose the values that maximize the utility. In the same manner, an employer has a unique profit function which applies to all her decisions, but also o en faces discrete choices such creating a job or not, hiring a candidate or not. The profit criterion then acts as part of a rule of decision.
. Finally, unlike the models surveyed and in part because the model is detailed, the empirical focus is very different. The validation goes through calibration by an algorithm on a large number of real labor market variables, rather than by obtaining macroeconomic regularities. Some of the latter are not always present in historical time (for instance the Phillips curve, or the Beveridge curve which may be flat or rising through structural change).
. The paper is organized as follows: In Section , we describe the main features of the model. In Section , we present our validation method -through calibration -and in Section a brief characterization of the simulated French labor market and some simulation experiments. We will show how WorkSim can be used to assess labor policies ex-ante as well as ex-post, including the "El Khomri law" that generated very hot political and union struggles in France as well as vivid debates among economists. Section will conclude and open the discussion.

Model Description
The agents in WorkSim . There are two types of agents: Private Firms and Individuals. At its creation, each firm starts with at least one worker to run the company, representing the managing director . The Individuals are grouped in households and the simulation evolves in a stationary population. The individuals can marry each other, have children and therefore the decisions of one member of the household may have an impact on the other members. In WorkSim, the agents are heterogeneous. They have specific attributes determined once and for all at their creation (e.g., gender, amenity,. . . ) and internal variables (e.g., age, salary, number of employees,. . . ) that evolve throughout the simulation.

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The agents under or over years belong to the households but are not instantiated as full agents and do not take decisions in the model. However, these non-instantiated agents indirectly participate through the economic decisions of the other members of the household (e.g., the number of dependent children is taken into account in decisions of transition to inactivity, the retirement pension is included in household income). The individuals under years become full agents in the model at the age of , and some remain in the school system while others enter the labor market. Finally, the period corresponds to a week, in order to capture very short spells on many FTC, and be as close as possible to real gross flows. % of all hires are on Fixed-Term Contracts that last one week or less in (ACOSS ).

Environment .
In addition to these agents, the model uses three artifacts : • JobAds, which lists job o ers from the firms and job applications from the job seekers. Dissemination of information, however, is based on the costly job search process described in more detail below (see Section . , according to the principles of search theory. • a Statistical Institute that calculates statistics from the simulation and disseminates some information (e.g. tension on the labor market). The information is imperfect for agents, and we specify what information is being broadcasted.
• a Public Sector that recruits (exogenously) employees and collects payroll taxes on businesses.

Institutional Framework
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Moreover, it also includes one institutional module. One distinctive feature of the WorkSim model is to integrate a fairly complete and flexible institutional framework that includes ( ) the necessary elements of the French labor Law, featuring two types of contracts -Fixed-Term contracts (denoted F T C) and open ended contracts (OEC), but also dismissals on personal and fires on economic grounds, redundancy payments, etc. and ( ) government decisions (minimum wages, welfare benefits, etc.). This institutional framework is described in more detail in Appendix B.

Individuals .
In WorkSim, each individual with index i is characterized by the following attributes : • Gender : female or male.
• Age, counted in weeks (a tick or period represents one week in the simulation).
• Preferences for free time : see Section . below.
• State in the labor market. The possible states are : inactive, unemployed, employed and not searching for another job (denoted ENS), employed and seeking a new job (denoted OTJS, for On-The-Job Searchers), student or retired.
• Occupation, denoted q in this paper. The number of possible occupations is denoted n q . In our simulations, we consider levels : = blue collar or employee, = middle level job, = manager. An individual can change his occupation during the simulation (upward or downward).
• Productivity kernel, kP rod i : it represents the "innate" abilities of the individual i.
• Condition factor cond i,t that represents his physical and psychological condition at time t. It evolves with time following a random walk : Hence ∀t, cond i,t ∈ [minC, maxC]. minC et maxC are two exogenous parameters and σ C ∈ [0, 0.3] is calibrated.
• Human capitals (HC) HC gen i,t , HC occ i,q,t , HC spec i,p,t , respectively for the general, occupational level q, and specific to the firm and job p human capitals . The general HC represents the abilities useful for all jobs, like problem solving or knowledge of a foreign language. It increases with experience (one more unit per period) and also with training. It decreases at each period when the individual is unemployed (or inactive) by a percentage Lxp a er T xp periods (loss of skills). Lxp ∈ [0, 0.1] and T xp ∈ [0, 500] are two calibrated parameters. The occupational HC is related to the occupation, and represents abilities specific to this occupation: engineering field or cra for instance. Like the general HC, it increases with experience (one more unit per period) and also with training, and decreases at each period if the individual is unemployed (or inactive) by a percentage Lxp a er T xp periods. The specific HC is related to the position and the firm. It represents abilities specific to the job in the firm, like a particular process or a so ware to use. It equals the number of periods the employee spends in the job. It is reset to zero when he exits this job to another job in the firm.

Demand .
Labor is the only production factor, a natural simplification in a stationary state model. As mentioned, there is one good, and each firm produces a certain amount of its own variety of this good. The price P is assumed unique (horizontal di erentiation between firms) and fixed at the arbitrary value of . Each firm responds to a quantity demanded of this good D j,t , which fluctuates randomly due to variations in consumers preferences. However, the total demand D tot is held constant because we aim to study our economy in a steady state.
. At time t = 0, the market share of a firm j is given by D j,t=0 /D tot . We assume that the distribution of this total demand is di erent in the initializations. We then apply a stochastic shock which defines the trend of this market share for each firm each year and another stochastic shock each period (random walk) using a normal law: ∀t, M S j,t = M ax(0, M S j,t−1 × (1 + N (µ M S,j,t , σ M S,j,t ))) ( ) with µ M S,j,t , σ M S,j,t specific trend and volatility factor assumed to be unknown by the firms. These coe icients are randomly reassessed every year for each firm.
Each firm has a managing director and a list of jobs per occupation. A job can be in di erent states : filled,vacant or pending. A pending job is typically a F T C contract that ended, but cannot be renewed immediately, because of the grace period .
. Each job p of the occupation q is characterized by specific attributes determined once for all at its creation : • a vector of required human capitals [HC gen req,p , HC occ req,p,q , HC spec req,p ], respectively for the general, the occupational level q, and the specific to the firm and job p human capitals. They represent the minimum skills required to work on this job and are randomly drawn according to uniform distributions respectively between and M axHC gen req , M axHC occ req and M axHC spec req . We will see in the next section that an individual can acquire these skills with experience or training.
• The duration of work HpW p , measured by the number of hours required per week for the job p.
• An hourly base production QH base j,q for all jobs in the firm at occupation q. It is randomly drawn at the creation of the firm j, to account for the di erences in production e iciency (technology, organization . . . ) between the firms. The weekly e ective production of an individual on a job depends on this hourly base production and the duration of work, but also on the individual characteristics described on Section . . The complementarity between the technological level of the job (related to the physical capital) and the individual skills (the human capital) has been shown in numerous studies starting with Griliches ( ). We assume that this base level of production does not depend on the type of contract assigned to this job. The weekly e ective production of an individual i on this job p at time t is given by with F β (HC gen i,t , HC occ i,q,t ) = 1 + β × HC gen i,t − β × (HC gen i,t ) 2 + β q × HC occ i,q,t − β q × (HC occ i,q,t ) 2 ( ) and F λ (HC spec i,p,t ) = 1 + λ × HC spec i,p,t − λ × (HC spec i,p,t ) 2 . ( ) β,β ,β q ,β q ,λ, λ are calibrated parameters greater than . The sensitivity functions F β and F λ are concave, in order to introduce diminishing returns of the human capital on the employee productivity. These diminishing returns are observed for example in the study of Kramarz et al. ( ) for France.
• An hourly base salary determined from the base production in the job for all jobs in the firm at occupation q : with P = 1 the exogenous price of the (unique) good and ζ ∈ [0, 1], an exogenous parameter that represents the share of the base productivity value kept by the firm (in order to pay expenses, taxes, interests, dividends, etc.). It reflects the balance of power between workers' and employers' unions in the country, since the model does not assume perfect competition and free entry, and workers are not paid their marginal productivity. This does not mean that the forces of competition do not play, since employers hire only workers who are profitable, while the workers themselves raise their reservation wages when the tension rises on the market. The weekly e ective salary of an individual i on this job p at time t is given by : S i,j,p,q,t = M ax(SMIC H * HpW p , SH base j,q ×HpW p ×F β (HC gen i,t , HC occ i,q,t )×F λ (HC spec i,p,t )×G(U q,t=crea )) ( ) where SMIC H is the hourly minimum wage in France (see Appendix B for details about the institutional framework in France), and G(U q,t=crea ) = ( Uq,t=crea U q,ref ) ω , with U q,t=crea the unemployment rate at the occupation level q when creating the job o er and U q,ref the reference unemployment rate during the current year. Estimations of the e ect of the unemployment level on the new worker's wages are not directly available in France, and rarely elsewhere (we mentioned Martins et al. ( ) for Portugal). In order to set this elasticity, that we assume constant, we use the wage curve, a relation between the levels of unemployment in di erent local labor market and the wage levels, although the change in the unemployment rate within an occupation over time is not exactly the same phenomenon (Blanchflower & Oswald ). ω has been found to be stable over a very large set of studies on the wage curve (Nijkamp & Poot ( )), and equal to −0.1 The e ective salary of an individual does not depend on its unobservable productivity kernel kP rod i nor on its condition factor cond i,t . The only di erentiation is due to measurable and therefore indisputable factors of human capital related to experience in the line of the human capital theory.
• A level of amenity. This represents non-monetary features perceived by the individual on the job (social recognition, working environment,. . . ). An hourly base amenity is randomly drawn at the creation of the firm as a percentage P rA of the base salary for all occupation level q.

Simulation cycle in the WorkSim Model
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The simulation cycle includes four main steps, as shown in Figure

Firm decisions .
Before describing the job creation process, we present the demand anticipation mechanism that is the core of the job creation process and the endogenous choice between the di erent contracts : F T C and OEC.
The central idea that governs job creation relies on the way the firm will estimate the future demand. If the demand is going to increase, a new job might be profitable, but not if there is a decrease in the demand. Hence, the firm will compute three scenariosbad (noted θ = −1), neutral (θ = 0) and good (θ = +1), which are depicted in Figure below. We see in this figure that in the bad scenario, the demand of the firm is below its production with the new job a er a certain time. As the firm cannot sell more than its demand, and the good is perishable, it may result in a loss because the firm has to continue to pay a salary if it is an OEC until economic dismissal is allowed (a year of delay in the reference experiment). In this example, we see that it may be more profitable for the firm to choose a contract with a shorter duration like a months F T C. Indeed, the firm will have the option to end this contract a er months in case of a bad scenario or to renew it if it goes well. F T C then act as a bu er against the shocks on demand. However with a shorter contract it is more di icult to amortize the cost of hiring and training a new employee. It therefore appears a trade-o depending on how the employer perceives the risks. A supplementary trade-o comes from the increase of productivity with tenure in a job, that the employer anticipates. Since this productivity increase is shared by the employer, this factor also favors OEC and counterweights the risks of a dismissal cost. .
Because of bounded rationality, the firms anticipate with finite horizons corresponding to the specifications of the di erent contract types. For each contract the decision process computes a net profit for each scenario, and then combines the three possible scenarios into a weighted profit. The weight of each scenario is calibrated at the aggregate level. The most profitable contract type and duration are selected (see Appendix A for details). Job creations (step in Figure ) .
The job creation proceeds in three steps: . First, the firm checks if there is a su icient demand margin to create a new job. Here it considers the actual (not anticipated) demand margin DM j,q,t for firm j and occupation level q at time t: if it exceeds the demand margin threshold DT (calibrated parameter), then the firm moves to the next step. Otherwise, no job is created.
. If there is in the firm a pending job in the occupation q, the firm considers to hire a new person for this job (taking into account the eventual grace period). Therefore the pending job becomes a vacant job. Otherwise, it moves to the next step.
. Here, DM j,q,t > DT and there are no pending jobs in occupation q. Hence, the firm considers to create a new job p of the occupation q. The characteristics of this new job are randomly drawn (cf. Section . above). From these job features, the firm must decide which type of contract suits better. .
In order to create a job and choose a contract, the firm proceeds as follow: . During a prospecting phase, the firm receives information about N P ros job seekers of the occupation q, who have applied to a job with a F T C and N P ros job seekers of the occupation q who have applied to a job with a OEC during the last period. The expected profit per period φ per i,j,p,q,c,t for a candidate i on a job p with a contract c is then computed for each contract (see Appendix A) : the OEC contract is JASSS, ( ) , http://jasss.soc.surrey.ac.uk/ / / .html Doi: . /jasss. compared with several F T C with di erent fixed terms ( week, month, months, months, months, months). As described in Appendix A, it takes into account the training costs for the job.
. Then the firm chooses to create the contract c with the best average positive profit, calculated along a set of potential candidates. These candidates are job seekers and the employer is informed via JobAds of their anticipated productivity level corresponding to their occupation, given their human capitals and the base production in the job (The information is based on equation but the productivity kernel and the condition factor are unknown to the firm and set at their average). The employer will choose the contract c * that gives the highest positive expected profit per period φ per i,j,p,q,c,t . If all the profits are negative, no new job is created.
. The firm continues to consider creating new jobs as long as DM j,q,t > DT . Figure ) .

Job destruction (step in
By contrast, when there is a significant reduction in its demand in one occupation (in our model, this is when DM j,q,t < −DT ), the firm reacts in the short-term by removing its pending jobs and vacancies. In the medium run (on a yearly basis), if this low cost adjustment is not su icient, the firm considers the possibility to dismiss workers.
. Moreover, independently of the demand level, pending jobs and the vacancies that remain unfilled and have a duration greater than a fixed threshold -a parameter that will di er for F T C and OEC -are destroyed since they have a cost.
. Economic dismissals : an evaluation of the financial viability of the company is performed on a yearly basis ( periods in the simulation). The first date of the balance sheet is drawn randomly, then this financial reporting occurs every year from this date. The company calculates its yearly return that is computed as the ratio of the yearly profit over the total labor cost . If this return falls below a certain profitability threshold (a fixed parameter P T , that will be calibrated, but has to be negative, representing losses), the firm can justify an economic dismissal procedure. This is the formal implementation of our interpretation of the French jurisprudence (before the El-Khomri law) over the serious economic di iculties that allow to dismiss. However, owing to the diversity of judgments when workers appeal for unfair dismissal, an employer, even though she respects the threshold, may be condemned in industrial courts. Therefore she anticipates penalties on the base of the probabilities of litigation and loosing the case, which are added to the severance costs: • all remaining vacancies are removed.
• a er all the vacancies have been removed, if DM j,q,t < −DT still holds, the firm considers dismissing employees. It selects one employee randomly, computes the associated profit Φ tot i,j,p,q,c,t and the firing cost EF C. If Φ tot i,j,p,q,c,t < −EF C, the firm dismisses the employee. This process is repeated until DM j,q,t > −DT or if all employees have been evaluated. .
In the event that the company has a return below P T and has no employees to dismiss, the managing director "dismisses" himself, which in this case leads to the bankruptcy of the firm that is removed from the simulation. The managing director becomes unemployed. However, we want to keep the number of firms constant . Hence, when a bankruptcy has occurred, we randomly select an active agent in the simulation to create a new firm and manage it. He will be the only producer in the firm (until he starts to recruit). Figure ) .

Employee evaluations (step in
In each period, the firm examines if some employees have to be evaluated. This individual evaluation may occur: . At the end of the probationary period for F T C and OEC; . Every year, at the anniversary date of the contract, for OEC employee; . At the end of F T C contract to decide if it should be renewed; . At the end of F T C contract, if the transformation of F T C to OEC is to be considered.
. Dismissal for personal reasons (insu icient productivity : the process takes two steps : . First, the firm evaluates if there is a case for considering the dismissal. That could be the case if the employee's production is below the firm's requirement. Thus, there is a chance that the firm considers to fire this employee for personal reasons if the annual production of the employee Q eval i,j,p,q,t satisfies : is the required level of production and ρ an exogenouscalibrated -parameter in [0.7, 0.9]. ρ encodes the tolerance the firm has with underproduction, or the maximum margin risk it accepts to take . . Then the firm decides whether such a dismissal is more profitable or less costly than keeping him. Figure ) .

Hiring phase and promotions (step -in
Once the firm has chosen which contract c to create, a hiring norm must be computed to evaluate the candidates. This hiring norm is the profitability threshold below which it prefers to refuse a candidate. To do so, it uses the positive expected profits Φ avg j,p,q,c,t calculated for each of the N P ros candidates during the prospecting phase and computes the average Φ M oy , the minimum Φ M in and the maximum Φ M ax values. .
The hiring norm of the firm is given by the main economic factors taken into account in search theory: • t = crea is the time of the creation of the contract.
• N 1 is calibrated in [0, 1]. The hiring norm increases with φ per M ax − φ per M in , so that the firm favors a large dispersion of candidates' qualities in order to increase the probability to get better candidates, as prescribed by search theory.
• N (d c ) = N 2 + N 3 × d c , an increasing function of the duration of the contract d c proposed for the job.
N 2 et N 3 are two calibrated parameters in [0, 1]. We assume that the firm will be more demanding for longer contracts, as they imply to keep the employee for a longer time.
• T IGH q,t=crea is the tightness on the labor market at the time of job creation and is given by Uq,t with V q,t the vacancy rate and U q,t the unemployment rate at time t for the occupation q. The higher this tension, the more the firm has to lower its requirements if it hopes to find a candidate. We assume that the impact of the tension to HN is limited to ±20%, because the hiring norm could be otherwise increased above the profitability of any worker, so H is a logistic function with values between . and . and given by H( This hiring norm above is then decreased by a percentage N 4 in each period until the job is filled, but never drops below .
. Hiring takes place in three steps: . Receiving applications -The firm receives applications from external and internal applicants.
. Selection and potential hiring -A two-step process takes place: (a) First, the firm computes a score for each candidate (internal or external), given by the expected profit per period Φ per i,j,p,q,c,t . Then the best candidate (highest score) is selected. (b) Therea er, the firm checks if this candidate's score exceeds the hiring norm. If this is the case, the candidate is hired, otherwise, the job remains vacant.
. Internal promotion -If the best candidate hired is an internal candidate of the company, it is a promotion. The employee acquires the occupation level of the job. .
When an individual is hired for the job, he is trained and receives the minimum required human capital for the job if he does not have it yet and the firm pays for it: HC gen i,t ← Max(HC gen i,t , HC gen req,p ) ( ) The costs are proportional to the weekly base salary in the job and the gaps in human capital to be filled (Appendix A). Yet the cost of training is deducted from the expected profit a candidate provides to the firm, so that a candidate who needs much training is unlikely to be selected (see Apppendix A) . This is an assumption which fits the facts: a worker who would not fit minimal norms of productivity could have a productivity below the minimum wage in the model, and also induce many other problems such as underutilising capital and slowing team work in the real world. The theoretical framework of ranking candidates according to the expected training costs has been developed by Thurow ( ) under the label of job competition, and fits easily as an extension of the search based concept of a hiring norm. The wage has a job specific base, and cannot be lower that this base, which is a component of the hiring norm. The expected profit provided by a candidate, net of the training costs, must be higher than the hiring norm. Figure ) .

Individuals' decisions (step -in
The individuals take decisions in each period of the simulation. This decision process is modeled with a state machine, where one individual, at each tick, will be in one particular state: inactive, unemployed, employed and not searching for another job, employed and seeking a new job, student or retired. The transitions between these states can be caused by individual choices (for example: to look for a job, to quit a job, . . . ), by external events (firing, death, . . . ), or eventually by a sequence of multiple decisions (e.g. applying for a job, and the firm hires the candidate).

Utility functions .
Each individual uses a utility function, to decide whether he should stay in his current state or move to another one. The utility function has the generic form of a Cobb-Douglas function: It is a weighted aggregation of four factors : . Income: weekly income of the household in euros, divided by the number of consumption units (an adult counts for , a child . , as o en in consumers'studies). This specification means that we take into account that the partner' earnings a ect the participation decision of the individual. The family nature of the decisions is a fundamental element in labor economics and the theory of labor supply has studied the subject in depth. There are di erent theoretical possibilities. Models of joint decisions a er bargaining inside the household rely on heavy assumptions and are uneasy to generalize to all other workers' decisions on flows (such as quits). Our choice is in the line of Leuthold and Pollak as mentioned in the survey of family labor supply approaches by Killingsworth & Heckman ( ). It is a very simple specification but it predicts some facts which are important both at a microeconomic level and at a macroeconomic level for WorkSim. First non wage incomes of the household a ect the individual's decisions, and notably the hours and the participation decision negatively in France, and the specification implies this result (Kabatek et al. ). Secondly the partner's earnings decrease in the model the individual's participation probability. Kabatek et al. ( ) also find this result , which however remains debated (see Briard ( ) for a survey of the empirical knowledge for the French case) .
. Amenity: non-monetary features perceived by the individual (social recognition, working environment, job di iculty, . . . ). The factor is expressed as a percentage of the salary.
. Stability: criteria reflecting the preference of the individual for stability, i.e. for a job with the long contract duration. The maximum value is given for a permanent job (OEC). This stability is expressed as a percentage of the salary.
. Free time: free time per week available for the individual outside his working hours and search time. According to INSEE statistics , we deduct hours for sleep, eating, washing, from the total time per week. Then, the free time covers leisure but also caring for the children, and the model takes into account that the statistics show that women put more value on time for child care. .
The parameter α ∈ [0, 1] encodes the preference of the individual for free time against income, which depends, for a woman with young children, on the number of children. The INSEE statistics show that they still spend much more time than men on caring for children, and this is modeled as a higher "preference" for free time. A participation rate decreasing in the number of young children ensues.

Overview of the individuals' decisions
.
The decision-making process of individuals is sequential and summed up in the state transition diagram depicted in Figure . At each period, the individual agent computes the utility of his current state and the utilities of each reachable state. Each utility is evaluated using the generic form given by Equation above, and instantiated with the relevant values of income, amenity, stability and free time. Moreover, a factor ICHAN G ∈ [1, 2] is applied to several transitions to account for the psychological cost to do such a change (calibrated parameter). The higher ICHAN G > 1, the greater the new state utility must be to win the decision. A er describing the di erent decision mechanisms, we now detail the overall job search process: . Each period in the model, a job seeker spends time trying to get information on some jobs (wage, contract). JobAds sends a list of N V i,t vacancies matching his occupation or a level above. We assume that these incoming job o ers occur at a mean frequency that is known and independent of the time elapsed since the last o er. Therefore, we model the arrival of new job o ers with a Poisson law: at time t, this number of vacancies N V i,t is drawn from a Poisson distribution with parameter λ t = N SJ U × H(T IGH q,t ), where N SJ U is the average number of vacancies received by the unemployed at each period, and H is the same function of tightness as above. It can be the case that a job seeker does not obtain information on a single vacant job during the period.
. The individual sends an application for the first o er whose utility is above his reservation utility U T RES i,t . If there is no job o er corresponding to his occupation or if all his applications are rejected, he lowers his reservation utility U T RES i,t . Thus, at the end of each period, the reservation utility is updated : where Ru 3 ∈ [0, 0.005] is a calibrated parameter and Ru 4 a fixed parameter ( . ). The first term of the equation accounts for the diminution with time in unemployment and the second is driven by a modification of U T U EM , which is the utility for the unemployed (for instance a decrease of income will lower U T U EM and therefore U T RES, as the urge to find the job increases). We do not set di erent reservation utilities for the two types of contracts since the workers search for the two types of jobs simultaneously. Yet, we take into account the lower return to search provided by the FTC in terms of utility since they o er shorter contracts, by including the stability parameter. This information is known to the searcher before contracting for an FTC. For an OEC the mean duration is known. This method ensures that searchers prefer OEC ceteris paribus, but may accept to apply to FTC when their research does not meet success by lowering their reservation utility . Figure ) Household dynamics .

Demographic module (step -in
In Worksim, an individual can be in three di erent household states: . Child in a household, meaning that he stays with his parents. He can be in the labor market or not (when he is a student for example).
. Single person (with or without children).
. In couple (with or without children). .
At each turn, the individuals change their household state according to transition probabilities deriving from real demographic data measured by the French national institute of statistics (INSEE).

.
A simulation evolves over time with a stable population, therefore the agents marry each other and have children that can enter later in the labor market. These children can leave their household in order to create a new household.
The standard age of retirement is established to in WorkSim, but an agent aged between and can get early retirement. We reproduce the share of retired individuals by age range according to INSEE statistics. Let us note however that a retired agent does not leave the simulation as he may still be a member of a household.
The age of an individual is increased by one week every tick or period of the simulation (one year corresponds to ticks). The individuals leave definitely the simulation when they die at an age corresponding to the death rate by gender in France in .

Validation Process
. The WorkSim methodology uses a validation process at two levels: . model building : the way we design the model, and especially the agents' decision rules is rooted as much as possible in empirical data and facts. Following the psychomimetism methodology (Kant ), we ensure that these decision processes do not violate the cognitive principles we build our model on (e.g. bounded rationality).
. data reproduction: we want our simulation to account for most available data on the labor market we aim to study. To do so, we use an automatic procedure to calibrate the model parameters for which we do not have an empirical value (see Calibration section below).
First of all, we must set the number of agents in the simulation. It must be large enough to account su iciently for real behaviors, but not exceed our computational power . For the experiments described below, we initialized the agents population from the real data found for year 2014, at a scale of 1/4700. We obtained individuals and firm agents, for a total of agents in the simulation.

Calibration procedure .
In order to calibrate the parameters, we have to minimize a fitness function that is the weighted sum of the relative spreads between the outputs of our model and the real targets of the French labor market in (from multiple sources given by INSEE and DARES). We have chosen targets grouped in di erent categories : unemployment rates ( targets), activity rates ( ), salaries ( ), job flows ( ), FTC ( ), long-term unemployment ( ), mobility between occupations ( ), additional (part-time, vacancies, on-the-job searchers, training costs) ( ). In most cases, we have a target per occupation or age range (see Appendix C). .
To minimize this fitness function, we apply the evolutionary algorithm CMA-ES (Hansen & Ostermeier ), which is one of the most powerful algorithms to solve this kind of problem (Auger & Hansen ). CMA-ES means Covariance Matrix Adaptation Evolution Strategy. The principle of this evolutionary algorithm is to test step by step new generations of points in the parameters space. Each new generation of points is drawn stochastically according to the results obtained with the previous generation of points. The mean and the covariance matrix of the distribution of the new randomly drawn points are updated incrementally in order to move towards the best results obtained by previous generations. .
At each iteration, the CMA-ES algorithm sets the values of all the parameters. Then, to cope with the stochasticity we have in the model, simulations are run (they are usually called replications in a calibration process) with a di erent seed for the random generator, and the outputs are averaged over these simulations to obtain the fitness value of the iteration. We stop the calibration when the fitness does not improve (same minimum value) for iterations.

Computational power needs
.
The calibration process is costly in terms of computational resources, because the total number of simulations can be quite high: it is given by the product of the number of iterations by the number of replications. With WorkSim, it took iterations to converge, and as stated above each iteration is made of replications. Each replication takes about -minutes overall and the whole calibration process takes around two days to be completed on a processor with cores.

Results of the calibration on the main targets
. We obtain an average relative spread between all the outputs of our model and the real targets of . %. This can be deemed satisfactory for such a large non-linear model. We deal with a multi-objective optimization problem with many targets and parameters, and these problems are known to be hard to solve. The calibrated values of the parameters and the outputs of Worksim are shown in Appendix C (Tables and for the targets and Tables  and for the parameters).

Results and Policy Experiments
. In this section, we summarize the main results from a set of experiments we conducted with WorkSim. In this set, the model was calibrated to account for French data in . Note that each experiment result is averaged over simulations.

A brief characterization of the French Labor Market
.
We first comment on some calibrated parameters. We do it briefly since most of them do not have known empirical counterparts (Tables and ). Several concern the labor supply and careers. In order to start to search for a job, the expected utility must be at least % higher than his present utility, a jump high enough to avoid repetitive moves between unemployment and inactivity. An unemployed starts losing human capital a er months, a delay which makes sense although data are missing. Then the rate of decrease is , % per week, which appears a very high rate. The decline in reservation utility Ru 3 is % per year of unemployment, a high rate, allowing for the acceptance by former OEC workers of FTC jobs a er some time. However they are much more reluctant to look for jobs in the next lower broad occupation since it takes almost years to accept this downgrading. The probability to look for a better occupation is higher at . % per week. The wage careers are increasing and only slightly concave in general experience, since we do not consider the ceiling e ect that obsolescence of human capital and illness or fatigue put on blue collars. However the managers do obtain a steeper career than intermediate level workers and blue-collars. Internal promotions from a broad occupation to another is low since it takes an average of years. These figures are in agreement with the low social mobility in the French society in the XXIth century, compared to the previous century. On the employer's side, a major parameter is the weight of the pessimistic scenario in the anticipation of demand. At . %, it dominates the two other scenarios (neutral and optimistic), and means that the employers have a strong aversion to loss, which will deserve a sensitivity analysis below. Tolerance to a worker's underproduction is fairly large at %, but within the bounds we have set. The parameter of the labor share in productivity ζ may look very low at %, but the ratio concerns net wages and, if it is computed at the aggregate level in the model, it is higher since the workers at the minimum wage earn a higher share of their productivity, and then it matches the real French figure. Finally the profit threshold under which firms may layo on economic grounds without too much legal risk PT is -%, a loss, and clear evidence of serious economic di iculties. .
The targets in Tables and are reasonably well fitted for our purpose. The unemployment rate and the activity rate are especially important for the model and well fitted. However the long term unemployment is under the targets, but it should be mentioned that the measure of unemployment tenure is given in the French labor force survey by the worker, who may forget very short contracts during a long spell of unemployment. The flows are also essential but di icult to calibrate since in our labor flows comprehensive system, they are interdependent and therefore determined by the complete set of behavioral parameters and legal constraints. The results can be deemed satisfactory. Economic layo s are very low at . % per year, since they are very costly in France before the ELK law, much lower than the layo s for insu icient productivity, the exits at the end of the trial period, or the quit rate. .
The model generates some important specific characteristics of the French Labor Market such as the very important share of FTC in terms of total entry flows, %, and the contrasting fairly low figure of the share of the workers employed in such contracts: only %. The unemployment of the young is also much higher than the unemployment of the older workers. These results reproduce the known stylized facts of the French Labor Market, and the targets. These major stylised facts are not imposed by the assumptions of the model but emerge from the interactions of the agents during the simulation, given the calibration of the parameters on a large number of targets. .
This confirms the dualism in the French Labor Market, which is displayed by the di erences in the patterns of gross flows of the categories of workers. The model computes all the simulated flows, but allows for comparison with those which can be measured by the published statistics, and the results fit roughly. Most workers are stable in their OEC, while a minority undergoes short spells of employment in FTC and spells of unemployment between them. Moreover this dualism persists for a small proportion of young workers. The others obtain more stable OEC. It can be in the same firm in which they had an FTC through the experience (human capital) gained in FTC, as well as a screening process since the employers gather more precise information on their kernel productivity. This is a significant gross flow in the model. It can be through direct recruitment in OEC in other firms as the result of their increased experience.
. Many more results are obtained, some of them novel in the sense that we simulate the entire gross flows matrix of labor while only some of the flows are documented in the statistics. They will not be detailed here, due to lack of space and the focus of the presentation of the results on the sensitivity of the main variables to the parameters, and on policy design.

Sensitivity analysis
. In order to validate the mechanisms at play in the model, we undertake the sensitivity analysis of some important parameters. The sensitivity analysis consists in launching a set of simulations by changing each time the value of a parameter while the others remain at their calibrated value. For each point, we measure the outputs of the model a er periods ( years) starting with the baseline calibrated model. We examine three types of parameters having a substantial impact on unemployment. First, we study the impact of a major parameter for individual's choice: the base preference for free time. Secondly, we analyze a parameter playing an important role in unemployment theory and relating to workers' behavior, the rate of decrease of the reservation utility with time spent in unemployment. These two parameters, being the workers' choice, may have a considerable responsibility in unemployment. In a simple aggregate model, a preference of the workers for free time or a reluctance to accept jobs which are not so well paid (or not so stable) as the former job as time goes on, yield more unemployment. A systemic model like WorkSim may yield more nuanced results. Finally, we focus on one parameter a ecting employers's choices between the di erent contracts, relating to the formation of anticipations under uncertainty, a neglected topic in labor market models. The results reveal a huge impact on unemployment. This is in line with the focus of anticipations that macroeconomics now displays.
Preference for free time .
The parameter α 0 represents the base mean preference for free time in the computation of the free time parameter α (c.f. Section . above). The higher this parameter is, the more individuals prefer free time to labor incomes and the non-monetary characteristics of jobs (see Equation of the utility function). As expected, an increase of α 0 , starting from the calibrated value, leads to a substantial decrease in the activity rate and the employment rate since individuals prefer free time (see Figure below). For the unemployment rate, the expected move is less straightforward since it depends on the relative elasticities of the activity and employment rates to the preference for free time. The figure shows that the unemployment rate comes to a standstill. When α 0 decreases from the calibrated value, the activity rate increases, more individuals want to work, but most of these individuals do not find a job since total demand is fixed, so that we see an increase in the unemployment rate. To summarize the situation, the e ects of a change in the preference for free time are asymmetric (starting from the calibrated value) as far as employment is concerned, bad if the change favors free time, and null if the change disfavors free time. This asymmetry shows that agent-based methodology uncovers nonlinear e ects that standard aggregate models would not reveal.
Figure : Sensitivity of activity rate (blue), employment rate (green) and unemployment rate (red) to the basic mean preference for free time α 0

Reservation utility decline with seniority in unemployment .
In a model that embodies search behavior by the workers, the parameter Ru 3 -entering in Equationplays a crucial role. It corresponds to the percentage of decline of reservation utility each week spent in unemployment. The higher the value of this parameter, the faster the reservation utility of unemployed decreases in the model. It represents the acceptance of unemployed to revise downwards the minimum utility at which they accept to work, as time elapses. Search theory makes two predictions. First, if the distribution of wages is known to the worker entering unemployment, and the rate of arrival of vacancies in which he would be selected, he should not lower his reservation wage. Secondly, if his household income falls unexpectedly over the spell of unemployment, he should lower his reservation wage. Concerning the first prediction, the elasticity of the reservation wage to unemployment seniority in Europe appears to be quite low, and in France, not significantly di erent from zero (Addison et al. ). .
This study therefore appears to validate the first prediction of search theory. However, many studies show that workers, a er being laid o , and recovering another job, are subject to a wage loss, which requires that they have lowered their reservation wage. We then considered that workers may be overoptimistic, not necessarily in terms of wages, but in terms of the possibility for them to access OEC. Since a worker learns about this di iculty over the spell by being not selected by employers, he accepts FTC more easily, which provide less stability. Since  stability is a factor of the individual's utility in the model, this means that he decreases his reservation utility. We have then let the calibration decide over the rate of decline, which appears finally as non zero.
. Figure b shows that the higher the decrease rate of the reservation utility, the lower the unemployment rate, since the unemployed revise faster their reservation utility and accept to apply to a higher number of job o ers. When the reservation utility is rigid, search unemployment becomes a major component of total unemployment, the latter reaching % in the model. Such search unemployment is caused by the time that workers take to find a job that satisfies their requirements. It decreases when the reservation utility is more flexible with time elapsed in unemployment. The di erence of points in unemployment between the case in which reservation utility is rigid and the calibrated case could suggest that the behavior of unemployed is a major factor of unemployment. However we observe here a non linear e ect: it would not decrease by more than one point if the rate of decline doubled beyond the calibrated case, so that a policy forcing unemployed to be less choosy would have a some e ect. However it would not solve the unemployment problem, caused by a lack of demand and possibly by employers' requirements as well as the minimum wage. Moreover the decrease in unemployment we can see on the right of Figure b is also due partly to a greater discouragement of the unemployed, because we observe a small decrease in the activity rate a. When the reservation utility declines, at some level, it falls under the utility of inactivity, and triggers exit from unemployment. There are , discouraged workers for the highest rate of decline of the reservation utility. Finally the directions of the e ects are clear but the sensitivity of unemployment to the rigidity (or flexibility) of the reservation utility to the time spent in unemployment should be lower on the real labor market, since the model underestimates the structural mismatches between supply and demand. We have only three broad occupations, hence very large labour segments, inside which only human capital, hiring norms of firms, and reservation utilities of workers matter for matching. Cra s or geography are not obstacles.

Sensitivity to the pessimistic scenario weight in demand anticipation
.
Employers form anticipations on the future of their own demand, based on past estimated trend and volatility. Bounded rationality leads them to consider only three scenarios, one neutral, meaning the trend remains the same, and two others, one with an upward deviation of standard errors, and one with a downward deviation with standard errors. They give weights to these scenarios which have asymmetric e ects on profits since the bad scenario involves possible termination of OEC at a cost. The weights are calibrated and the value of the bad scenario ω −1 is . %. The domination of this scenario in the anticipations corresponds to an aversion to the loss (see Equation ).
. We then vary the coe icient ω −1 , the other coe icients remain to their calibrated value and the three of them are re-normalized in order to make them sum to one. When ω −1 increases, the employers reduce their hires on OEC in favor of more hires in FTC (Fig. a). Termination costs of OEC are so much higher than those undergone when having to pay an FTC until the end of his contract while he is producing in excess of demand. The employers also hire increasingly on short FTC of one week (Fig. d), because these contracts are the least risky in case of future decline in demand. The role of bu er of the FTC against the uncertainty is then highlighted by this experiment.
(a) Sensitivity of entry rates to ω−1.
(b) Sensitivity of activity and employment to ω−1.
(d) Sensitivity of the share of one week FTC to ω−1.
Figure : Sensitivity to ω −1 parameter (weight on the bad demand scenario). .
A reduction of this parameter could have a substantial impact on unemployment (Fig. c). In a hypothetical scenario, if it is set at the value of 0, the unemployment rate falls to the value of . %. It highlights the importance to take into account psychological factors determining the employers' behaviors in an economic model, as suggested by Keynes and recent Nobel prizes G. Akerlof and R. Shiller (Akerlof & Shiller ). These factors have a very strong impact on the choice of contract, FTC or OEC, and then on the functioning of the labor market. .
The fact that companies are sensitive to uncertainty about demand helps explain how they will react to a change in labor market legislation, in particular with the ELK law (see the following section). The aversion to the risk of having to pay significant redundancy costs in the event of a fall in demand can limit part of the job creation with OEC contracts. With a so ening of dismissal conditions, we therefore expect a higher rate of OEC contracts on the labor market.

Assessment of some labor public policies .
We have conducted several simulation of labor policies, and since most of them had not been implemented at the time of the study, nothing was known on their e ects at the moment of the decisions. In fact, one of the major purpose of WorkSim is to be a prototype for a generation of new models which advice policy decisions on employment and labor, by simulating them ex-ante and understanding the e ects of one particular policy, or, better, joint policies. This requires structural model building because complex interactions occur.

Reduction of social charges
.
The level of social charges on employment is frequently discussed, especially by employers' syndicates. In , French Minister F. Fillon has passed a law that reduces the charges paid by the firms on wages, for salaries lower than . times the minimum wage (SMIC) . The decrease is % for firms with employees or more, and . % for the others. To study the e ect of this policy, we compared the results of the baseline experiment with a new experiment in which these reductions of charges are removed. We measured a drop of . points in the unemployment rate, and a gain of , jobs, thanks to the reduction of charges. This result sets the gain within the range of the empirical studies on this policy, with between , to , jobs created or saved (Ourliac & Nouveau ). This experiment may be compared to ex post results has, beyond its intrinsic interest, the advantage of giving some validation to the model.

.
However, it might be more e icient to target the policy on lower wages. Therefore, we vary the maximum wage which can benefit from the policy, from . SMIC to . SMIC. The results are displayed in Table below. It appears that the . SMIC target gives the most e ective policy: the smallest unemployment rate (9.55%), , more jobs, , fewer unemployed and also the lowest costs.

Variant with FTC renewable twice .
We o er here a new experiment, by studying a policy formulated by the French government and adopted in June (Rebsamen Law, article ). It relates to the possibility to renew an FTC twice, but always within the cumulative limit of months. We still keep the assumption made in the model that the renewal of an FTC is of the same duration as the initial duration of the contract. In the evaluation of a new contract, it adds a new option to renew the FTC twice. Hence, the FTC has three potential durations: its initial duration, twice this duration (one renewal) and three times this duration (two renewals), always within the cumulative limit of months. .
The results of this variant are presented in Table . It appears that this policy raises the unemployment by . points, due to a stronger turnover e ect of the workforce (+ . points). There are fewer entries in OEC (-. points) and more entries in FTC (+ . points). It can be explained by the supplementary option of renewal making the FTC more attractive for the employers compared to OEC. In the simulation, the individuals in FTC are less likely to be hired in an OEC at the end of their first contract. This probability decreases from % to % because it becomes more beneficial for the employers to renew the contract, knowing that another renewal option remains possible in the future. However we observe that this policy lowers the share of long term unemployed (-. points) by increasing the turnover rate on the labor market, hence recruitment. The objective of the government was to increase the flexibility of labor adjustment to demand change, but this seems to be at the cost of raising unemployment, ceteris paribus (aggregate demand being unchanged).

Evaluation of the facilitation of dismissals in the El Khomri Law
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The El Khomri (name of the Minister of labor) law has been presented in March by the French government as the major labor law of François Hollande's presidency. This law has set the war not only on the French political scene, but also between groups of highly recognized French economists such as Philippe Aghion, Olivier Blanchard, Jean Tirole, or Thomas Picketti and many others who have not hesitated to take a categorical position in favor or against it. Its final version was voted on July , . There are many articles in the law, and several would be very di icult to implement in the model such as a much higher possibility to bargain within the firms for instance. Here we focus on the facilitation of the economic dismissals, considered as one of the main elements of the law, as it is likely to have an important impact on the labor market. The aim of the government was to encourage the employers to hire on OEC since dismissals would require less stringent but also more precisely defined economic conditions, hence less uncertainty on the industrial courts decisions in case of litigation and lower severance costs.

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In the El Khomri Law (ELK), article , the conditions to allow economic dismissals are explicitly specified. The economic conditions and therefore the delay change. Economic dismissals are allowed in case of a decline either in the firm's demand or its turnover, computed over a certain period of time, which depends on the firm's size. For firms under employees, the period is quarter, for those between and under the period is quarters, for firms between and under , the period is quarters, and for firms with employees or more the period is quarters. The law therefore so ened the former conditions for economic dismissals, which implied that firms had to undergo serious economic di iculties to be allowed to fire. Let us keep in mind that we formalised in a simple and rough way the jurisprudence before the law as the requirement for firms to undergo losses during one year. However, even if respecting this condition, the employers could be taken to industrial courts. They could then be ordered to pay a much higher severance pay than computed by applying the regular indemnities by judges, if the latter estimated that the economic di iculties were not serious enough, or the legal procedures not perfectly respected (advance notice,. . . ), and the fires unjustified.

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In the reference experiment without the law, we had integrated the anticipated supplementary costs, taking into account the probabilities to lose in courts, and the mean extra severance pay. For experiment with the ELK law, for the period a er the ELK law was passed, we have modeled the new conditions and we have suppressed the litigation costs. The real data justify ex post this assumption since they show that the legal conflicts over fires have strongly declined since the law was passed. The French controversy indeed focused on the facilitation of dismissals, but more specifically on the decrease of the litigation risks. Aghion et al. ( ) supported the clearer conditions for dismissals and the consequent diminution in the litigation risk and costs as an incentive for the employers to hire on OEC, but did not mention adverse e ects such as the increase of unemployment that faster adjustment to a decrease in firm own demand can generate. Both increases in hire and in economic fires are predicted by theoretical models of firing costs (see Bentolila et al. ( )), with no clear prediction on the net e ect on unemployment. The empirical evidence is mixed (Boeri et al. ). Askenazy et al. ( ) argued on theses bases that firing costs have not been proved to be a source of unemployment in Europe, that restrictive fiscal policy was the source of unemployment, and that FTC should be severely restricted to diminish the segmentation on the French labor market. Our model studies the French labor market as a complex system in which the El Khomri law modifies the rules of the game, and the results are more complex than in the quoted papers which are not based on models .

E ects under a stable aggregate demand .
To begin with, we simulate the ELK law for a steady state of the exogenous aggregate demand . The ELK law yields e ects which change over time a er the introduction of the law. They evolve during the first years to stabilize a er years. This comes from the fact that it takes time for the firing conditions to be filled even under the new law. The immense majority of French firms are small or very small, and it takes time for such firms to face a cumulated change large enough to be allowed by the new law to fire at least one employee. The results are displayed in Table . .
The law has no aggregate e ect on the unemployment rate or the employment rate. Hires on OEC increase to reach % but the rate of exit increases in an identical manner. This is in accord to the empirical results as mentioned. However the law has strong distributive e ects. It is very favorable to the young ( -), both in the short and the long run, with a decline in unemployment of , a er years (it drops over points). The impact is not significant for the prime age class ( -). A er years, there is a small decrease in unemployment (-, ) and an increase in employment (+ , ). However a er years the law has no significant e ect on this age class. Finally the seniors ( -) undergo a substantial rise in unemployment (+ , ), rising from . to %, i.e. . points, and a decrease in employment (-, ).
. Moreover, the mobility on the labor market is found to change very deeply, and the nature of the labor market is then transformed: . The share of FTC in the hires falls from % to %. The OEC becomes the dominant hiring contract.
. the hiring rate in OEC doubles, as predicted by economic analysis as a result of lower firing costs (Bentolila & Bertola ).
. The proportion of FTC in ongoing contracts falls from % to . %, which makes it a minor contract in terms of employment share. There is a decrease of the mean duration (renewal not included) from . weeks to . weeks. This double change means that FTC are now mainly used by firms having a really bad future demand forecast and no requirement in training for these jobs.
. The entry rate in FTC falls to a quarter of its value before the law. Hence less training costs for job specific training are lost.
. The economic dismissal rate jumps from . % to %, a major change in a French labor market which has been characterized by an extremely low and decreasing economic dismissal rate during the present century. The decreases in the uncertainty of the cost and the delay induce this explosion in the rate. This rise is predicted by economic analysis, but its rate is a surprise. The diminution of hoarding that the high firing delays induced raise the firms' average benefits by %.
. As a consequence of higher dismissals, the OEC become shorter (the median duration of OEC falls from . to years) and more precarious, as the probability to lose one's job within a year jumps from . to . (+ . points, + % relative increase), and more frequent spells of unemployment for the OEC. This consequence seems to dominate the favourable e ects and lead to a small decrease in average utility.
. The integration of the remaining FTC employees into OEC is improved since the increased turnover on OEC makes opportunities higher. This result has been also obtained in cross section studies which compare countries with di erent FTC rates (Bentolila et al. ).
. Two major conclusions can be drawn. First, a significant substitution of the young to the seniors takes place. Secondly the new adjustment rules on the OEC have the logical e ect of making the FTC a much less useful flexibility tool for the employers except when demand expectations are very bad and no training required. A main objective of the law is then achieved: the FTC are no longer the mean to get around the dismissal costs of OEC. They serve the legal purpose for which they have been allowed, namely to bu er temporary increases in demand. .
The explanation of the opposed e ects over the young versus the other categories is simple. The young were much more o en than the others in FTC ( % against . % for the -and . % for the seniors) and benefit from their fall. The e ect is enhanced (in the model) by the two e ects on the seniors. First these are mainly in OEC and the latter become much more precarious, so that many seniors are now fired. Second they are then unemployed and employers are reluctant to hire seniors on OEC when training for the job is required since the proximity of retirement makes amortization di icult . Young compete seniors out. The e ects of the ELK law then go much beyond the higher flexibility of OEC. The law raises the integration of the young into (more precarious) OEC, and this shows that the screening and experience enhancing roles of FTC before the ELK were not a su icient factor of integration for the young. The consequence of the substitution of OEC to FTC, namely the substitution of young workers to seniors, who are penalised, has been overlooked by the non quantitative analysis of the ELK law we mentioned .

Sensitivity of adjustment to aggregate demand
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We now change aggregate demand exogeneously in order to examine if the ELK law influences the e ect on unemployment di erently. Figure gives values a er years. It shows that the adjustment of the labor force is predicted to be more important a er the law. First, when demand declines under its value in the reference experiment, economic dismissals are more important, the suppression of the hoarded labor is more complete, and unemployment rises more under El-Khomri's law. The e ect reaches points if demand is to fall by %. Secondly when demand rises above the reference value, the employers hire more easily on OEC, and unemployment decreases more under ELK law. For a symmetric increase in demand the decrease is points. The responses are not symmetric for large changes since if demand is very high, there always remains some search unemployment caused by workers who raise their reservation utility. This higher sensitivity to demand could be predicted, yet its importance could not be, since FTC were a substantial bu er before the law, but finally less e ective than the reduction in dismissal delays for OEC. Figure : Sensitivity of employment rate to demand shocks. x-axis displays the demand factor df ∈ [0, 5; 2], where the total demand D tot becomes df × D ref tot

Discussion
. In this synthetic paper, we present the WorkSim framework, a comprehensive model of the labor market. First the stock-flow accounting of individuals, based on gross flows, is complete and endogenous. It is supplemented by a stock-flow accounting of jobs for further analysis. The institutional environment is modeled and based on labor law, which sets constraints at the agent level on the possible decisions, taking into account the specific characteristics of each agent in his type, worker or employer. Therefore the simultaneous existence of unfavorable characteristics including the agent's history may result in the exclusion of the labor market, a highly non linear e ect that cannot be obtained in aggregate models in a realistic manner. .
Secondly it implements numerous essential economic mechanisms that were not integrated before within a single labor market model: search on both sides of the market with multi-jobs firms, inter-temporal decision processes under bounded rationality, anticipations of demand shocks with risk aversion, learning, endogenous contract choices, endogenous salaries and productivities, di erent types of human capital. All are found to have major e ects on activity, employment and unemployment.

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Thirdly, WorkSim is calibrated on a large number of targets of the French labor market, by using a powerful evolutionary algorithm that has not already been used in economic models. On average and satisfactorily it reproduces these targets to conduct some economic analyses. Moreover, it reproduces the gross flows measured by di erent statistical sources and with di erent types of measures with a fairly satisfactory approximation. This gives us an estimation of the model accuracy, and is part of the model's validation process.
. Fourthly, we have conducted several analyzes and policy evaluations. These helped us to identify some core mechanisms in the French Labor Market: segmentation, screening and bu er roles of FTC, importance of employers' loss aversion, among others. Each labor policy appears to have contrasting results for the di erent categories of workers in terms of employment improvements, benefits and costs. The complexity of the labor market has naturally led us to omit some more or less important institutions, and the number of targets remains small compared to this complexity. The e ects of the policies should then be considered with the necessary scientific caution. The results are mainly meant to suggest new mechanisms, and the possibility of some e ects of policies, which has not been highlighted before. One of the main conclusions is that institutions matter. Our agent-based model enabled us to simulate ex-ante e ects of various policies, making it a precious tool to help policy design.
. WorkSim in its present state has no equivalent in the agent-based models. These have macroeconomic goals that WorkSim does not have, and set assumptions on the labor market a minima. They mainly play with the wage setting mechanisms, comparing opposed theoretical assumptions such as wage rigidity versus flexibility, as our survey has shown (Dawid et al. , ; Dosi et al. ), and obtaining the standard macroeconomic stylised relations such as the Beveridge curve, the Phillips curve, and Okun's curve. Devoided of a complete macroeconomic setting, WorkSim has not such goals. Those models who are closer in spirit to WorkSim as they are interested in the structure of the labor market, study specific mechanisms such as networks (Tassier & Menczer ; Pingle & Tesfatsion ). They have theoretical purposes and do not intend to model the mechanisms of a real labor market. Reproducing the main mechanisms of such a real market and their interactions requires a framework rich enough: an heterogenous population of individuals and households with a demographic module, the main states (employment, unemployment, inactivity), the gross flows system, some main institutions like the di erent contracts, the minimum wage and benefits (and some others), some main constraints that labor law imposes, and finally, a calibration algorithm. The only agent-based models with such an agenda are our own previous models. ARTEMIS (Ballot , ) presented such a model but was calibrated by hand. The first version of WorkSim was calibrated by the powerful algorithm CMA-ES that we described. Goudet et al. ( ) present the model, and Goudet et al. ( ); Ballot et al. ( b) study policy experiments. In ARTEMIS and the first version of WorkSIm the choice between OEC and FTC was exogeneous . The present paper provides a major improvement, by making the choice between permanent jobs (OEC) and temporary jobs (FTC) completely endogeneous. .
Then the meaningful comparison is between WorkSim and the analytical search models of a dual labor market, which have gross flows between the employment and the unemployment states (the inactivity state is missing). Only one, (Cahuc et al. ), features a truly endogenous choice between OEC and FTC. The two models have at least two essential di erences. There is first a fundamental conceptual di erence between independent expected shocks on individual jobs in Cahuc et al. ( ) and the global demand shock for a multi-jobs firm in WorkSim. The second di erence lies in the types of costs when ending a job. In Cahuc et al. ( ), FTC cannot be extremely short because there is a cost of writing a contract. This cost is calibrated as . hour of production, significant enough to preclude extremely short contracts in the model. These would reduce to almost zero the possibility of a demand shock before they end, and could be repeated to compete out OEC . In fine an exogenous Poisson distribution of projects durations must determine the mix of contract types, if one repeats the draw for many jobs (the authors do not do this exercise). Our model considers firms which anticipate di erent evolutions of their total demand, weight them through risk aversion, and choose a mix of the two types of contracts: some FTC to avoid the risk of dismissing many OEC and paying advance notice and firing costs, but also OEC because FTC have also important drawbacks: they cannot amortise training costs on a short FTC, they cannot renew the incumbent more than once and undergo a waiting period before re-creating the job. Moreover the present mix of contracts is important for the choice in the dynamic context of the employer's choice since it provides a low or high bu er according to the proportion of present FTC in the employment of the firm. Some results are common to the two models, namely the large ratio of FTC in hires, the lack of sensitivity of aggregate unemployment to firing costs, and the substitution of OEC to FTC if the firing cost is decreased. Yet WorkSim, which is also calibrated to a much larger number of targets than the Cahuc et al. ( ) model, can study in more depth the microeconomic and aggregate e ects of the legal rules, as has been done with the ELK law, and previously with the generation contract in Ballot et al. ( b). It has also made possible to consider the heterogeneity of workers, and the divergent e ects that a change in the rules induces on them, a fundamental topic when it comes to assess the e ects of a policy on the young. This is not only a medium run phenomenon as it could appear in the present paper. Ballot et al. ( b) have been able to show that a cohort carries over its lifetime policy shocks undergone early, a result obtained by longitudinal studies (Schwandt & Von Wachter ), and a major topic since the Great Recession and the Covid.

Future directions
. The model can be extended in several directions. Firstly we can add more labor market institutions and mechanisms: temporary employment agencies, social networks, and lifelong training for instance. We can also integrate more organizational elements, including more detailed competences and tasks based production functions, as well as the monitoring role of the hierarchy. Secondly, WorkSim would benefit from being plugged into an agent-based macro-economic framework, in order to have consumption, investment and financial e ects as well (this is work in process). The outcomes on wages and profits have e ects which in turn modify aggregate demand and employment. One way to look at this is to assume, as done in this paper, that they are second order e ects, but this might not be true. .
Thirdly, tools to help analyzing and explaining the simulations are still to be developed further: visualization (improving the graphical interface in WorkSim), analyses of the agents' decisions, automatic classification of agents' trajectories to study individuals' careers (cohort analysis). Another issue is the link with micro-econometrics, to improve the agents' measures of elasticities and enhance the validation process. Fourthly, if the current version of WorkSim is primarily designed to account for the French Labor Market, most of its components and mechanisms could be re-used to describe labor markets in other countries. The elements specific to the French institutions (labor law) can be adapted when dealing with another country.

Acknowledgments
We are grateful to the reviewers for their useful comments and suggestions which helped us to significantly improve the paper.

Notes
The main empirical methodology relies on transition probabilities with a frequency no smaller than at least one month. This deletes short term contracts. The OEC correspond to the Contrats à durée indéterminée (CDI) and the FTC correspond to the Contrats à durée déterminée (CDD).
FTC and other non regular employment are even more important in Spain, Portugal, and Netherlands, according to OECD data (Bentolila et al. ).
Temporary help is the subject of a work in process (Ballot et al. ).
The exact rules are in Appendix B.
A previous version by Goudet et al. ( ) used an exogenous mix.
This has consequences since a centralized labor market has di erent outcomes from a decentralized labor market. The real labor markets have some intermediaries such as Employment Agencies and temporary help firms, but they should be introduced in a decentralized environment with their specificities.
The search concept is necessary to distinguish the two states of "unemployed" and "inactive" on the basis of rational (boundedly or not) decisions of agents. The unemployed looks for a job and the inactive does not. There is indeed a flow from unemployment to inactivity, because the value in terms of unemployment utility (expected gains from search minus time foregone) may become lower than the utility of inactivity (non wage income, welfare and free time). In that case, the individual stops search and becomes inactive. The reverse can occur. Search costs and not only non wage income influence the choice between inactivity, unemployment and employment. When an agent has decided to search, while on-the-job or as an unemployed, search concepts define stopping rules to be a candidate for a vacant job or not.
For instance an employer, when hiring on an OEC, has more information on a worker with whom she has a FTC contract than on an external candidate, hence FTC can be a stepping stone for OEC.
For evidence of the bias introduced by a matching function as a result of an employment policy, see (Neugart ). Bentolila et al. ( ) confirm this state of the research. They propose a simpler version of the Cahuc et al. ( ) paper. Several papers had proposed before models of this choice but either the choice is not fully endogenous, or they make assumptions much too far from the French rules to be useful to discuss here. Cahuc et al. ( ) o er a survey.
Briard ( ) presents a typology of careers based on a large number of individual trajectories which suggests a persistent segmentation over the life cycle. Be y et al. ( ) show by use of econometrics on transitions that around % of prime age population cannot get a stable job.
This work has spurred an extension by Silva et al. ( ) to distinguish routine and non routine workers, and in a framework with unbiased technical progress, explain the rise of unemployment with a paradoxical rise in o ered wages in some countries such as the US and Portugal.
The managing director works full time for the firm, and at the three occupations. The director never leaves the firm, except to retire or when the firm goes bankrupt.
Artifacts in multi-agent systems are the passive (non-proactive) entities providing the services and functions that make individual agents work together (Omicini et al. ), and must be distinguished from proactive autonomous entities like the individuals or the firms.
N (µ, σ) denotes a normal law distribution, with mean µ and standard deviation σ.
There are now many studies that support all these three types of human capitals (e.g. Kambourov & Manovskii ; Crook et al. ). It appears as covering better the heterogeneity of skills types than the traditional Beckerian dichotomy between general and firm specific human capitals, and it has important e ects on the evaluation of the workers and their selection. For instance mobility between occupations is much less than between jobs in the same occupation, and promoting workers from one job to another may involve some training costs within a firm.
The firm does not want to destroy the job, if there is still a potential demand margin for it, so it becomes a pending job. We have here an important feature of WorkSim: unlike other models, we distinguish the job and the contract, several employees (and therefore several contracts) may have occupied the same job since its creation.
using estimates of Phillips's curves would be inappropriate in the context of an economy with fixed prices, and downward rigid incumbents' wages.
The labor cost represents here the capital funds the firm has to pay in advance. Hence, the return is the ratio of the profit over this capital.
We keep the number of firms constant for two main reasons. First, we do not aim to model the determinants of firm creation, way too complex and out of the scope of WorkSim. Secondly, we are looking for a stationary state with a scale-up for year , to apply and assess policies, and this will not be possible if the number of firms evolves constantly.
This tolerance has necessarily a minimum, and a maximum < to ensure a non-zero tolerance. Moreover, if ρ is too high, it will create a lot of dismissals and the firm will run a higher risk to face litigation and a higher risk to lose if it underestimated the real employee's productivity.
In absence of empirical data, we assumed this function to be linear.
We assume that this training has no duration. One should have in mind that most training in firms is only a few hours.
More precisely amenity and stability are "monetized" for the sake of adding up to income, a fairly standard procedure in economics, which could be justified by enquiries on the "wage reduction" that workers would accept to have more stability or more amenity. Then the "total income " obtained and free time have di erent weights in the utility function.
The correlation appears for women in the econometric studies, even if the husband's earnings are made endogenous. In our specification, the man's decisions are also a ected by his wife's earnings. These may a ect such variables as his reservation utility. Decisions of a partner then depend on the other partner's status by an iterative process which fits well bounded rationality rather than a joint decision as in the game models of family labor supply. A transaction cost ICHANG avoids frequent changes that such an iterative process could induce.
INSEE Statistics on physiological time in France in (https://www.insee.fr/fr/statistiques/ 1281050#titre-bloc-1) The concept of reservation utility (or of reservation wage) is an important concept in labor economics, and more specifically in search theory. It is the equivalent of the hiring norm, for the individual, as it represents the minimum level of utility (or wage) to make it acceptable to an agent. Most models use the reservation wage concept, but then the state inactive cannot be endogenous. In WorkSim, if the reservation utility falls below the utility given by the inactivity state, the unemployed stops search.
Ru 3 is positive and calibrated on the basis of the French experience. More details are given in the section on the sensitivity experiment on Ru 3 . Ru 4 is inspired by the evidence of the Addison et al. ( )'s study that shows that reservation wages in France respond positively and very significantly to unemployment benefits. Since we consider reservation utility, the coe icient . reflects that its rise is less than the computed change in utilities, as all measures of elasticities show, and based on our ignorance on a precise value between and .
Population in France in (https://www.insee.fr/fr/statistiques/3137409) As we show below, the simulation itself does not take too much time and power to run. The critical point is the calibration as it has to launch thousands of simulations to reach an acceptable solution.
These results are based on a past calibration of the model on year , but there should not be qualitative changes with .
As noted above, the baseline experiment is performed with parameters set to their calibrated values. One must bear in mind that an experiment result is the average of simulations.
Our simulation has been done in April and presented in newspapers, workshops and working papers shortly a er, and is therefore really ex ante (Ballot et al. a). One could object that in an econometric study of the e ects of the El Khomri law could be undertaken. However the law was only implemented at the beginning of , and the time series would be short. Moreover the main problem would be the elimination of the other shocks and employment policy changes that the economy has undergone since. At the level of the aggregate e ects these obstacles may be overcome, but at the level of more disaggregated groups, where we find strong e ects, it is more di icult. Finally, given the complexity of the topic, the two methodologies can be regarded as complementary tools when ex post.
We used for the ELK experiment in a scale of / , half the one in more recent experiments, with a total number of , agents: , individuals and , firms.
The bias against hiring seniors on OEC is very strong in France and statistical discrimination based on alleged risks of health problems, lower motivation, or less ability to cope with change add in employers'decisions to the training problem which is the only one we model. However a caveat on the magnitude of these substitution results is in order. We have assumed that any job can be an FTC or an OEC, even if we take into account that employers should be deterred from FTC when training costs are high. In the real world, some jobs require trust and/or long experience and cannot be FTC, so that substitution is overestimated in the model. However ARTEMIS has an exogeneous choice between primary and secondary jobs, both permanent, and and endogeneous choice between the former jobs and temporary help jobs Very short contracts, of a maximum of one day, represent a large part % of the FTC contracts in (DARES ). Moreover in some sectors they can be renewed indefinitely without a waiting period or any other cost under the name of customery FTC (CDD d'usage in french). We have included these in WorkSim • Q i,j,p,q,t (d) the anticipated productivity of the individual a er d period on the job • S i,j,p,q,t (d) the anticipated salary of the individual a er d period on the job and SalC the payroll charges (in %) • P is the fixed exogenous price of the good (set to in the simulations) When summing this profit from the start of period d v (expected vacancy duration) to the end of d c ( expected duration of the contract) and applying the discount rate r, we get the total profit : with EndC c (d c ), the cost to end the contract (di erent for OEC and FTC).
Then, for a given evaluated contract c the firm chooses the best duration, that is the one that gives the highest profit: The net profit per period for a contract c with a duration d c in scenario θ is : with V C the vacancy cost required to open this position and T C the training costs, paid a er d v periods. V C is given by: with V ac c,j,q,p = P rV ac c × SH base j,q × HpW p , where P rV ac c is the percentage of the vacancy cost for a contract c with respect to the base salary. These percentages, P rV ac OEC for OEC and P rV ac F T C for FTC, are calibrated parameters The training costs T C is proportional to the amount of human capital that the firm must invest in the employee in order to reach the required levels of the job: T C spec = P T r spec × SH base j,q × HpW p × Max(0, HC spec Req,p − HC spec i,p,t ) ( ) T C gen = P T r gen × SH base j,q × HpW p × Max(0, HC gen Req,p − HC gen i,t ) ( ) T C occ = P T r occ × SH base j,q × HpW p × Max(0, HC occ Req,p,q − HC occ i,q,t ).
( ) P T r spec , P T r gen and P T r occ are calibrated scale parameters (human capitals are not measured in the same units).
A profit per period is then computed: φ per i,j,p,q,c,t = Φ tot i,j,p,q,c,t dtot with d tot the average expected duration of the contract. When the algorithm is used to compare contracts with di erent duration for the same job, and choose a type of contract for this new job, it is repeated for a set of potential candidates.

Main contracts of the French labor law
There are two main types of contracts in France in : fixed duration contracts (FTC) and open ended contracts (OEC).
The main FTC features implemented in WorkSim are: . A maximum duration of months, including the possibility to be renewed once.
. A small probationary period of one day per working week with a limit of weeks, if the expected duration of the contract is below months, and of a limit of month, if the expected duration of the contract is over months.
. A special allowance that the employer must pay at the end of the contract and corresponding to % of the total gross salary paid during the contract.
. An FTC cannot be broken without heavy penalties (paying the remaining salary part).
The main OEC features implemented in WorkSim are: . No duration limit, except retirement.
. A probationary period of months for blue collars, months for middle level jobs and months for managers.
. No termination costs if the employee is quitting.
. Firing costs depending on employee salary and seniority: • No firing costs if the employee seniority is below one year, but dismissals must respect the Labor law.
• A er one year the firing costs correspond to a fi h of a monthly wage per year of seniority. The firing costs are increased by two fi eenth of a monthly wage per year of seniority a er ten years (cf. French labor law L.
-). The reference salary used to compute these firing costs is the maximum between the average gross salary of the last twelve months and the average salary of the last three months.
. In case of firing, a legal dismissal advance notice period has to be respected. It corresponds to one month, if the employee seniority is below two years, and two months otherwise.

Social policy
The main parameters of the French social policy in implemented in WorkSim are the following: Welfare allowance: people become eligible for the French welfare allowance (RSA) if one of the following conditions is met: • to be years old or older.
• to be a lone parent with one or more children.

Number of children Single person Couple
• to be years old or older and have worked at least two years during the last three years.
The monthly amount of the RSA for a household with no activity income depends on the number of children and is given in the Table . The children of the household in this evaluation must be years old or lower and be at the actual charge of the individual (children that perceive no income in the model). For a household with an activity income, the welfare allowance is a complement of resources, if the revenues of activity are below a guaranteed minimum amount (not detailed here).
Unemployment benefit: an individual becomes eligible for unemployment benefits if all of the following conditions are met: • he has been fired or he has completed a fixed duration contract.
• he is looking for a new job.
• he has worked days (full time) in the months preceding the end of the employment contract, if he is less than years old, or months before the end of the employment contract, if he is years old or older.
An individual receives the unemployment benefits over a period of time corresponding to his contribution period with a maximum of months, if he is less than years old, or months if he is more than years old.
The calculation of the allowance received depends on an average reference salary received in the past twelve months. We refer the reader to the o icial website of the French administration for more details on the allowance evaluation .
Legal work time: the legal work time per week for a full time job is hours.
Retirement pension: in WorkSim the minimum retirement age for a full-rate pension is years. The retirement pension is taken into account in the household utility evaluations. For the reason of simplicity in this work, we assume that this retirement pension is the same for all agents and equal to % of the average salary of the last years for employees in the private sector and equal to % of the average salary of the last months for employees in the public sector.
Minimum wage: the monthly net minimum wage for a full-time job (SMIC) is . euros in .
Social security contributions: employers and employees have to pay social security contributions. In , the percentage of the employer's social security contributions on net wage is %. The percentage of the employee's social security contributions on net wage is %. There is a reduction of employer's charges at the SMIC level corresponding to % of the gross wage for firms with employees or more and . % of the gross wage for firms with less than employees. . . annual layo for other reasons rate (%) . . Annual end of probationary period rate (%) . . Long term unemployment (more than yr) --yr (%) . . Long term unemployment (more than yr) --yr (%) . . Long term unemployment (more than yr) --yr (%) . . Share of FTC in employment (%) . . Share of FTC of less than one week in hiring (%) . . Share of FTC of less than one month in hiring (%) . . Share of customary FTC in employment (%) . . Share of employed on the job search (%) . . Half-time job share in employment (%) . . Average cost of specific training in euros Average cost of global training in euros Average number of vacant jobs in thousands Share of blue collars/employees in age class -yr (%) . . Share of middle level jobs in age class -yr (%) . . Share of managers in age class -yr (%) . . Share of blue collars/employees in age class -yr (%) . . Share of middle level job in age class -yr (%) . . Share of managers in age class -yr (%) . . Share of blue collars/employees in age class -yr (%) . . Share of middle level job in age class -yr (%) . . Share of managers in age class -yr (%) . . Annual internal promotion rate (%) . Annual external promotion rate (%) . Annual downgrading rate (%) . Table : Calibration targets and WorkSim ouputs -job flows, FTC, long-term unemployment, mobility (between occupations and additional targets).

Parameter Description Value α0
Average base factor for individual preference for free time . α old Increment of the factor for individual preference for free time every year . α child Sensitivity parameter of the preference for free time to the number of children for women . αyw Specific preference for free time for young women under having children . σ kernelP rod Standard deviation of the individual productivity kernel .

T xp
Time before loosing experience when unemployed (in weeks) Lxp Ratio of human capital loss every week a er these T xp periods . % β Linear coe icient of production in general human capital . β Quadratic coe icient of production in general human capital 6.42 × 10 −7 β0 Linear coe icient of production in general human capital for blue collars . β 0 Quadratic coe icient of production in general human capital for blue collars 5.87 × 10 −7 β1 Linear coe icient of production in general human capital for middle level jobs . β 1 Quadratic coe icient of production in general human capital for middle level jobs 3.88 × 10 −9 β2 Linear coe icient of production in general human capital for managers . β 2 Quadratic coe icient of production in general human capital for managers 7.22 × 10 −8 ICHAN G Psychological cost of starting to search for a job .

Ru1
Parameter entering in reservation utility initialization for unemployed .

Ru2
Parameter entering in reservation utility initialization for PARAE .

Ru3
Ratio of decline of reservation utility each week spent in unemployment or inactivity .

F ailT
Time without job before downgrading occupation level (in weeks) P rBQ Probability to look for a job with a better occupation level during job search . σC standard deviation of random factor entering in physical condition of the individual .

ET
Employability threshold for an individual

Parameter Description Value µ0
Average base hourly production for blue collar jobs . µ1 Average base hourly production for middle level jobs . µ2 Average base hourly production for manager jobs . ζ Share of the base productivity value kept by the firm . P T Profit ratio threshold -. µΨ 0 Average demand share allocated to blue collar jobs . % µΨ 1 Average demand share allocated to middle level jobs . % µΨ 2 Average demand share allocated to manager jobs . % µmax Maximum of the demand trend factor . σµ Standard deviation of the demand trend factor . µ alea Maximum of the demand volatility factor . Maximum of the specific human capital units required for a job P T r gen technical coe icient for training cost evaluation in general human capital . P T r occ technical coe icient for training cost evaluation in occupational human capital . P T r spec technical coe icient for training cost evaluation in job specific human capital . σ0 Standard deviation of base estimated productivity by the firm . δσ Decreasing factor of σ0 with seniority on the job . ω−1 Weight of pessimistic scenario in firm profit evaluation . % ω0 Weight of neutral scenario in firm profit evaluation . % ω+1 Weight of optimistic scenario in firm profit evaluation . % N1 Parameter entering in hiring norm evaluation .

N2
Parameter entering in hiring norm evaluation .

N3
Parameter entering in hiring norm evaluation 4.73 × 10 −5 N4 Decreasing factor of hiring norm every week . % InitV Share of demand allocated to vacancy creation at initialization . P rV acF T C Parameter entering in FTC vacancy cost evaluation .

P rV acOEC
Parameter entering in OEC vacancy cost evaluation .

SenT
Required level of seniority for a promotion (in weeks) DT Demand threshold beyond which the creation of a post is considered ρ Tolerance of the employer to employee's underproduction .