Hélène Benghalem
email: helene.benghalem@gmail.com

Pierre Cahuc
email: pierre.cahuc@sciencespo.fr

Pierre Villedieu
email: pierre.villedieu@sciencespo.fr

The Lock-in Effects of Part-time Unemployment Benefits

Keywords: Unemployment insurance, Part-time unemployment benefits, Lock-in effects, Unemployment duration. JEL classification: H5, J64, J65

We ran a large randomized controlled experiment among about 150,000 recipients of unemployment benefits insurance in France in order to evaluate the impact of part-time unemployment benefits. We took advantage of the lack of knowledge of job seekers regarding this program and sent emails presenting the program. The information provision had a significant positive impact on the propensity to work while on claim, but reduced the unemployment exit rate, showing important lock-in effects into unemployment associated with part-time unemployment benefits. The extension of the duration of compensated unemployment counterbalanced the increase in the number of days worked while on claim so that the number of hours worked and the net expenditure of unemployment insurance remained unchanged.

Introduction

Part-time unemployment benefits provided to persons working on non-regular jobs who are seeking a regular job play an increasingly important role in unemployment insurance systems. 1 The rise in the incidence of such alternative work arrangements as temporary work, part-time work, self-employment, and the new kinds of work relationship emerging in the "online gig economy" has increased the part-time unemployment take-up in several countries. In France, almost one over two unemployment benefit recipients works while on claim during his unemployment spell. Part-time unemployment benefits are also widespread in Belgium, Finland, Austria and Germany. 2In principle, part-time unemployment benefits aim at supplying incentives to job seekers who are looking for regular jobs to accept non-regular jobs in the mean time. This may increase overall employment and shorten unemployment spells if non-regular jobs act as stepping stones toward regular jobs. However, such benefits may also induce lock-in effects by discouraging unemployed workers from searching for regular jobs. Knowing the relative importance of stepping stone and lock-in effects which condition the access to regular employment is essential to evaluate the impact of part-time unemployment benefits on labor supply and on unemployment insurance expenditure. Unfortunately, little is known on these issues because the potential selection into part-time unemployment of individuals with non-observable characteristics correlated with their exit rate from unemployment makes the evaluation of part-time unemployment insurance very difficult.

To evaluate the impact of part-time unemployment insurance, we ran a large randomized controlled experiment among about 150,000 recipients of unemployment insurance benefits in France in which we provide them with information about the existence of part-time unemployment benefits. Then, we deduce the impact of part-time unemployment insurance on the behavior of unemployed workers from the change in their behavior induced by the provision of information. The choice of this strategy is justified by the lack of knowledge about part-time unemployment insurance among job seekers. A survey conducted by the employment agency [START_REF] Unédic | Enquête auprès des allocataires de l'assurance chômage en activité réduite[END_REF]) has shown that 41,2% of job seekers do not know of the existence of the program and that 33,6% are aware of its existence, but do not know the rules. In our experiment, individuals who had recently entered unemployment were randomly allocated either to a treated group or to a control group. Individuals assigned to the treated group were sent emails that contained a description of the part-time unemployment insurance scheme. Individuals in the control group did not receive any message, while otherwise facing identical conditions in terms of employment services. To investigate how the treatment affects the behavior of unemployed workers, we combine administrative data from public employment services and from hiring intentions registers, which allow us to know whether individuals who exit unemployment do find jobs. Comparing the outcomes between treated and untreated individuals provides a clean identification of the average causal effects of providing information about part-time unemployment benefits.

To interpret the consequences of the provision of information, we propose a simple model of job search in which part-time unemployment insurance makes it possible to combine income from work with part of unemployment compensation and lengthen the potential duration of compensation thanks to the parts of unemployment compensation not received during periods of work while on claim. This model shows that the propensity to work while on claim decreases with the marginal tax rate on earnings from work while on claim.

The model shows how the marginal tax rate depends on the tax on current labor earnings and on the expectation of the duration of unemployment. We show that an information provision which raises the propensity to work while on claim can be interpreted as a revision of beliefs according to which the marginal tax rate drops. A drop in the marginal tax rate exerts effects on the search for regular jobs through two channels. The first is an anticipation channel reflecting the impact of part-time unemployment insurance schemes on the expected gains of unemployed workers. This channel necessarily reduces the exit rate from unemployment toward regular jobs if the drop in the marginal tax raises the expected gains of unemployed workers, which increases their reservation wage and reduces their job search effort. In addition, the model shows that this channel exerts a significant effect on the rate of exit from unemployment as the initial exhaustion date of benefits approaches, because the lengthening of the duration of unemployment benefits induced by work during the compensation period delays the increase in search effort that usually precedes the exhaustion date. The other channel arises from the direct effect of work while on claim on the exit rate from unemployment toward regular jobs. Working while on claim may generate more job opportunities than remaining on the dole. But working while on claim may also leave less time to look for regular jobs. Therefore, this second channel can either increase or decrease the exit rate from unemployment toward regular jobs when part-time unemployment becomes more remunerative.

We find that the information provision has a significant positive impact on the propensity to work on while on claim: The probability that treated individuals will take work while on claim increases by about 6% three months after receiving the information compared with non treated individuals. We explore the potential heterogeneity of the effects of the treatment to see whether the information provision has effects of different signs on the propensity to take work on non-regular jobs for different groups generated with the machine learning approach developed by [START_REF] Chernozhukov | Generic machine learning inference on heterogenous treatment effects in randomized experiments[END_REF]. We find no evidence that the information provision has negative effects on the propensity to work while on claim. For all groups, the effects are either non-significant or positive, suggesting that the treatment changed the beliefs of job seekers whose behavioral inattention [START_REF] Gabaix | Inattention[END_REF]) induced them to underestimate the returns from work while on claim.

The hike in the propensity to work while on claim is associated with a drop in the exit rate from unemployment toward employment. 3 In accordance with the predictions of the job search model, we find that the difference in the exit rate from unemployment toward unemployment between treated and untreated people is maximum near the initial exhaustion date and then declines. 4 The effect is significant: a 6% increase in the probability that job seekers will take work while on claim 3 months after the start of the treatment is associated with 1.5% drop in the probability that they will have exited unemployment toward regular employment the last month before the initial exhaustion date. Therefore, it is clear that lock-in effects of part-time unemployment dominate in our context.

It is possible that part-time unemployment insurance decreases the exit to regular employment in general but increases the exit to good quality regular jobs, characterized by employment spell of a longer duration. However, we find that treated people are less likely to experience long (i.e. more than 3 or 6 months) employment spells than untreated ones.

Regarding the number of hours of work and the total number of days compensated by unemployment insurance, we find that these lock-in effects counterbalance the increase in work while on claim. More specifically, on the one hand, part-time unemployment benefits induce unemployed workers to work while on claim, which reduces the number of days compensated during the period of unemployment, but, on the other hand, they delay the exit to employment. 5 All in all, the total number of hours worked and net unemployment insurance expenditure remained unchanged over the entire period.

Although, it is possible that the provision of information improved welfare as treated individuals had better information, we show, on the basis of the search model, that its welfare impact is ambiguous. It depends on the impact of the part-time unemployment insurance parameters on the expectations of job seekers regarding the job offer availability.

For example, the model shows that more generous part-time unemployment benefits can reduce the expected utility of job seekers and trigger more work while on claim if it is interpreted as signaling the scarcity of regular jobs. Therefore, in the absence of precise information on the expectations of job seekers, the assessment of the impact of unemployment insurance on their welfare is left for future research.

Our paper makes contributions to two strands of the literature. The first is the empirical literature on part-time unemployment insurance, which has used different approaches to identify the effects of part-time unemployment benefits. The seminal contribution of Mc-Call (1996) exploits variations in the design of part-time unemployment benefits across U.S.

states from 1986 to 1992. An increase in the disregard is estimated to raise the probability of part-time re-employment and to reduce expected joblessness. 6 Using kinks in the U.S. benefit-withdrawal schedule, Le [START_REF] Le | Taxes today, benefits tomorrow[END_REF] provides evidence that workers take into account the value of future benefit entitlement when they make their labor supply decision. [START_REF] Ait | Partial unemployment insurance and hour decisions: Evidence from administrative data[END_REF] rely on a regression discontinuity design to show that an increase in the tax on earnings from work while on claim which occurred in France in 2006 reduced the propensity to work while on claim. Several studies, focused on European countries, rely on the timing-of-events approach (Abbring and [START_REF] Jaap | The nonparametric identification of treatment effects in duration models[END_REF]) or matching methods.

They look at the effects of working on non-regular jobs on the access to regular employment in Austria [START_REF] Böheim | The effects of marginal employment on subsequent labour market outcomes[END_REF], [START_REF] Eppel | Getting a lot out of a little bit of work? the effects of marginal employment during unemployment[END_REF], Belgium [START_REF] Cockx | Can income support for part-time workers serve as a stepping-stone to regular jobs? an application to young long-term unemployed women[END_REF]), Denmark [START_REF] Kyyrä | The effect of receiving supplementary ui benefits on unemployment duration[END_REF]), Finland [START_REF] Kyyrä | Partial unemployment insurance benefits and the transition rate to regular work[END_REF]), France [START_REF] Fremigacci | Subsidized temporary jobs: lock-in and stepping stone effects[END_REF], [START_REF] Auray | Stepping-stone effect of atypical jobs: Could the least employable reap the most benefits?[END_REF]), Germany [START_REF] Caliendo | Earnings exemptions for unemployed workers: The relationship between marginal employment, unemployment duration and job quality[END_REF]), Norway [START_REF] Godøy | Unemployment insurance and underemployment[END_REF]), Slovakia [START_REF] Van Ours | The locking-in effect of subsidized jobs[END_REF]), Switzerland (Gerfin et al. (2005)). They find mixed results, showing generally significant lock-in effects while individuals work on non-regular jobs and more positive effects on the access to regular jobs after non-regular jobs end. It is clear that these approaches can potentially identify the effects of working on non-regular jobs on the exit rate from unemployment, but cannot identify the effects of any part-time unemployment benefits scheme per se, insofar as they do not account for the anticipation channel described above. The papers of O' Leary (1997), [START_REF] David S Lee | Are sufficient statistics necessary? nonparametric measurement of deadweight loss from unemployment insurance[END_REF] and [START_REF] Altmann | Do Job Seekers Understand the UI Benefit System (and Does It Matter)?[END_REF] are the most closely related to ours to the extent that they rely on randomized controlled experiments which allow a credible identification of the impact of part-time unemployment. O' Leary (1997) and [START_REF] David S Lee | Are sufficient statistics necessary? nonparametric measurement of deadweight loss from unemployment insurance[END_REF] analyze the consequences of the Washington State Unemployment Insurance Earnings Deduction Experiment in which for one year, starting in October 1994, Washington conducted a large randomized experiment to investigate the effects of reducing the amount of benefits deducted from claimants who worked while on claim. They find that the tax reduction had no positive effects on labor supply and increased the unemployment insurance expenditure because it raised the propensity to claim benefits. [START_REF] Altmann | Do Job Seekers Understand the UI Benefit System (and Does It Matter)?[END_REF] provide information on part-time unemployment benefits to job seekers in Denmark. They find that the provision of information promotes employment in part-time and non-regular jobs for individuals close to benefit expiration, but reduces their employment and earnings in the longer run. Our contribution provides a more complete picture of the impact of part-time unemployment insurance than O' Leary (1997) and [START_REF] David S Lee | Are sufficient statistics necessary? nonparametric measurement of deadweight loss from unemployment insurance[END_REF] insofar as we follow individuals over a period of 3 years instead of one year for O' Leary (1997) and [START_REF] David S Lee | Are sufficient statistics necessary? nonparametric measurement of deadweight loss from unemployment insurance[END_REF]. This allows us to analyze the impact of part-time unemployment insurance on unemployment survival over a sufficiently long period, which is key for the understanding of the consequence of a scheme that can increase the potential benefit duration well beyond the initial benefit exhaustion date.

Our contribution also adds to the literature devoted to the analysis of the consequences of information provision in a variety of economic applications, including job search [START_REF] Altmann | Learning about job search: A field experiment with job seekers in germany[END_REF], [START_REF] Belot | Providing Advice to Jobseekers at Low Cost: An Experimental Study on Online Advice[END_REF], [START_REF] Crépon | Information shocks and the empirical evaluation of training programs during unemployment spells[END_REF], [START_REF] Darling | Encouragement emails increase participation in reemployment services[END_REF]), labor supply and taxes [START_REF] Chetty | Teaching the tax code: Earnings responses to an experiment with eitc recipients[END_REF], [START_REF] Blaufus | Tax misperception and its effects on decision making -literature review and behavioral taxpayer response model[END_REF], [START_REF] Abeler | Complex tax incentives[END_REF], Kostøl and Myhre (2021)), the take-up of social benefits (Currie (2006), [START_REF] Bhargava | Psychological frictions and the incomplete takeup of social benefits: Evidence from an irs field experiment[END_REF], [START_REF] Finkelstein | Take-up and targeting: Experimental evidence from snap[END_REF]), unemployment benefits [START_REF] Blank | Recent trends in insured and uninsured unemployment: Is there an explanation[END_REF], [START_REF] Fontaine | Quasi-experimental evidence on take-up and the value of unemployment insurance[END_REF]Ketteman (2019), Altmann et al. (2021)), housing allowances [START_REF] Engström | Increasing the takeup of the housing allowance among swedish pensioners: a field experiment[END_REF]), retirement savings plans [START_REF] Dolls | Reprint of: Do retirement savings increase in response to information about retirement and expected pensions[END_REF]) and training programs [START_REF] Crépon | Information shocks and the empirical evaluation of training programs during unemployment spells[END_REF]). From this perspective, our paper is the first, with that of [START_REF] Altmann | Do Job Seekers Understand the UI Benefit System (and Does It Matter)?[END_REF], to provide information focused on part-time unemployment benefits.

By design, the paper of [START_REF] Altmann | Do Job Seekers Understand the UI Benefit System (and Does It Matter)?[END_REF] is mainly focused on the impact of the provision of information on beliefs, thanks to a survey that we do not have. However, its design makes it less informative than ours to look at the behavior of unemployed workers. From that perspective, these two contributions are complementary. In particular, we provide a model which shows how information provision can influence the beliefs held by individuals about part-time unemployment insurance rules from its impact on the behavior of unemployed workers. We find that the take-up of individuals who benefited from the information increased. This confirms the results of [START_REF] Altmann | Do Job Seekers Understand the UI Benefit System (and Does It Matter)?[END_REF] and of the literature which finds that the take-up of most social benefits programs is reduced by the lack of information, especially when rules are complex. We find that the lack of information persists over a long horizon (at least 36 months) after the start of our experiment, suggesting that the spread of information about the program among uninformed unemployed workers is very slow. We also bring new information by analyzing spillover effects. We compare the behavior of nontreated individuals registered with employment agencies where half of individuals have been treated with the behavior of individuals registered with employment agencies where nobody has been treated. These two types of non-treated individuals behave similarly, meaning that information provision had no spillover effects among unemployed workers. This suggests that the information about part-time unemployment benefits did not spread from treated to non-treated individuals registered with the same unemployment agency and that the hike in non-regular employment of treated individuals did not crowd out that of individuals of the control group. This result can be compared to that of [START_REF] Crépon | Do Labor Market Policies have Displacement Effects? Evidence from a Clustered Randomized Experiment[END_REF] and [START_REF] Gautier | Estimating equilibrium effects of job search assistance[END_REF] who do find important spillover effects from job placement assistance programs.

The paper is organized as follows. Section 2 presents the part-time unemployment benefits program and the knowledge of unemployment workers about the program. Section 3 presents the theoretical framework which allows us to interpret the consequences of providing information about the program. The experimental design and the data are presented in Section 4. The impact of the informational treatment on part-time unemployment, on the unemployment exit rate, the hours worked, the quality of jobs, the unemployment insurance payout and welfare are discussed in Section 5. Section 6 provides concluding comments.

Institutional Background

Program structure

At the start of their unemployment spell, eligible unemployed workers get an initial unemployment insurance capital B 0 which allows them to get unemployment benefits, denoted by b. Both the initial capital and the unemployment benefits depend on the individual's past employment history. 7 The benefits paid each month are deducted from the capital B t . This capital yields, in each month of unemployment t, unemployment benefits equal to

b(B t ) =    b > 0 if B t ≥ b max(B t , 0) otherwise (1)
The part-time unemployment insurance scheme allows unemployed workers to take work while on claim. There is no specific eligibility condition for part-time unemployment insurance. Claimants must only meet the usual eligibility requirements for unemployment insurance. They are allowed to work for any employer, including their past employers. For each euro earned from work, current benefits are reduced by the marginal benefit reduction rate τ =87%. 8 To put it differently, the part-time unemployment scheme allows individuals to combine their unemployment benefits and the share 1 -τ of their labor earnings z t in the periods where they work while on claim. More precisely, the monthly income of a worker whose labor earnings amount to z t in month t is equal to

max[b(B t ) + (1 -τ )z t , z t ] (2)
τ and b are set to ensure that by working while on claim job seekers cannot get a monthly income higher than the past monthly income used to compute their unemployment benefits.

Hence, individuals whose labor earnings in the current month are larger than the monthly income used to compute their unemployment benefits, do not get unemployment benefits at the end of the month.

Figure 1 illustrates the part-time unemployment insurance schedule. From a static point of view, there are low incentives to work while on claim: the blue line, which displays the relation between the monthly labor earnings of people working while on claim and their income, is almost flat. Yet the reduction in benefits is not lost, it can be paid in a later month. The corresponding benefit reduction delays the exhaustion date. Figure 2 illustrates the dynamic aspects of the part-time unemployment insurance schedule which are critical for understanding its incentivation effects. If job seekers are totally unemployed throughout their claim and receive their benefits each month, their benefits will lapse after their exhaustion 7 See Appendix A.1 for more details 8 For the sake of simplicity, we describe the rules in net terms for a job seeker who earned the minimum wage before unemployment. Appendix A.1 provides details on this point.

date. When job seekers are only paid part of their benefits in a given month b(B t ) -τ z t ≥ 0, the unpaid amount min[τ z t , b(B t )] is not deducted from their insurance capital B t . This implies that the earnings from the days worked while on claim make it possible to extend the duration of the claim. The exhaustion date can be delayed without any limitation.

Hence, the unemployment insurance capital evolves according to the law of motion9

B t+1 = max (B t -b(B t ) + min[τ z t , b(B t )], 0) (3)

Knowledge of unemployed workers about the program

A survey conducted by the employment agency (Unédic ( 2012)) as well as interviews from the field [START_REF] Issehnane | Le recours à l'activité réduite: déterminants et trajectoires des demandeurs d'emploi[END_REF]) show that the knowledge of unemployed workers about part-time unemployment benefits is very limited. The survey conducted in 2012 shows that 41,2% of job seekers do not know of the existence of the program and 33,6% know of its existence without being able to explain the rules framing the part-time unemployment benefits program. This lack of knowledge about the program is striking.

Le [START_REF] Le | Activité réduite: les allocataires sont-ils sensibles aux effets de seuil? Etudes et Recherches[END_REF] also conclude that a large proportion of job seekers do not know the rules. The authors study the rules prevailing before 2006. At this time, specific criteria had to be met to be eligible for part-time benefits. First, the number of hours worked could not exceed 136 hours per month, which amounts to 86% of a full-time job. Second, the corresponding gross wage could not go beyond 70% of the wage earned before the unemployment spell. This implies that earnings drop at those thresholds (136 hours per month or 70% of the last wage). These notches should create incentives to move from a point just above the notch, in particular in the dominated area, to a point just below the notch. However, the authors do not observe bunching at those cutoffs. The lack of knowledge regarding the rules may explain why a large proportion of job seekers do not bunch at cutoffs.

Theoretical framework

This section starts by presenting a simple job search model which explains the consequences of part-time unemployment benefits on the behavior of unemployed workers before analyzing the impact of the transmission and reception of information about the existence of this scheme.

The model

We analyze the behavior of unemployed workers who look for regular jobs that yield a present value higher than the present value of unemployment. The value of these jobs is denoted by W and the effort devoted to job search is denoted by e. 10 The per period utility derived from consumption c ≥ 0 and search effort e ≥ 0 is equal to

v(c) -e
where v is an increasing and concave function. Engaging in search effort e yields regular job arrival probability equal to λ(e), where λ(e) ∈ (0, 1) is an increasing and concave function of the search effort. Time is discrete and the discount factor is denoted by β ∈ (0, 1).

To account for the possibility of working on non-regular jobs, it is assumed that, in each period, unemployed workers can get an offer to work on a one-period job. 11 In each period t, the earnings z t associated with these jobs are independently drawn in a stationary distribution.12 There is a fixed cost of working denoted by κ > 0. Moreover, we start by assuming that λ(e), the exit rate from unemployment toward regular jobs, does not directly depend on the choice to work on non-regular jobs while on claim. This assumption, which will be modified later on, allows us to clearly exhibit an important source of lock-in effects.

As explained above, the part-time unemployment scheme allows individuals to combine 10 We neglect the heterogeneity of regular jobs for the sake of simplification insofar as we do not have precise information on wages in our data. Adding this heterogeneity would not alter the qualitative predictions of the model regarding the impact of part-time unemployment benefits on the unemployment exit rate.

11 It is possible to enrich the model by introducing a search effort for non-regular jobs in order to take into account the substitution between different job search channels (see e.g: [START_REF] Moscarini | Excess Worker Reallocation[END_REF], van den Berg and van der [START_REF] Van Den Berg | Counseling and monitoring of unemployed workers: Theory and evidence from a controlled social experiment[END_REF], [START_REF] Marinescu | Unemployment insurance and job search behavior[END_REF]). This would accentuate the negative effect on the unemployment exit rate of part-time unemployment benefits linked to anticipations but would not modify the qualitative predictions concerning the unemployment exit rate. We do not integrate this aspect of the behavior of job seekers for the sake of simplicity insofar as we do not have precise data on job search activity.

their unemployment benefits and the share 1 -τ of their labor earnings, implying that their monthly income in period t is equal to max[b(B t ) + (1 -τ )z t , z t ] where b(B t ) is defined by equation ( 1) and B t by the law of motion (3).

In every period, unemployed workers choose their search effort and whether to take work while on claim or not. The value function of unemployed workers is

U (B t ) = E t max (et≥0,Ωt) v(c t ) -e t + β [λ(e t )W + (1 -λ(e t ))U (B t+1 )] (4)
where

c t = Ω t (max[b(B t ) + (1 -τ )z t , z t ] -κ) + (1 -Ω t )b(B t )
subject to the law of motion (3). E t is the expectation operator with respect to the future values of z t conditional on the information available in period t; and Ω t ∈ {0, 1} is an indicator variable equal to 1 if the unemployed worker decides to work while on claim and to zero otherwise.

The optimal decision to work while on claim relies on the comparison of the gains, equal to the earnings z t , with the costs equal to the sum of the taxed earnings and the fixed cost κ. The tax on earnings from work while on claim depends on the tax τ on current labor earnings and on the probability that the taxed earnings will be retrieved after the benefits exhaustion date. More precisely, the marginal tax rate is 13

m t = τ 1 -β T -t E t T -1 j=t [1 -λ(e j )] (5)
where T > t denotes the benefits exhaustion date.

The model implies that it is worth working while on claim if the net gains, equal to

(1 -m t )z t , are larger than the costs κ, or

(1 -m t )z t > κ (6)
The decision to work while on claim crucially depends on the marginal tax rate m t , which has two components: the proportional tax rate τ on current earnings and the expected returns induced by current earnings reported at the end of the entitlement period, that will be obtained only if the person is still unemployed in this period. The marginal tax rate is higher for people who exit unemployment faster, because the probability that they will This corresponds to situations in which unemployed workers produce the minimum level of effort e t = 0 until the exhaustion date approaches and then increase their effort from this date. 16 The model predicts that the search effort reaches its maximum value at the exhaustion date and remains constant thereafter. [START_REF] Marinescu | Unemployment insurance and job search behavior[END_REF] show that this property is relevant on French data and that the drop in the rate of exit from unemployment to employment after the exhaustion date comes from composition effects, due to the exit around the exhaustion date of unemployed people who find a job more easily. To illustrate this point, the middle panel of Figure 4 displays the outflow rate from unemployment to employment for a population composed of two types of unemployed with different job search efficiency. The bottom chart shows the difference in exit rates between environments with and without part-time unemployment benefits for this population. The 14 Figures C6 and C7 display the distribution of the estimates of the marginal tax rate for each individual × month observation and the evolution of the average marginal tax rate over the employment spell for the population of our field experiment.

possibility of receiving unemployment benefits after the initial date acquired by work while on claim delays the date on which the unemployed increase their search effort. Thus, the bottom panel of Figures 4 and5 clearly show that the impact of part-time unemployment benefits on the exit rate from unemployment to employment and on the unemployment survival rate is significant close to the benefit exhaustion date.

To this point, the model implies that the possibility of working while on claim has lockin effects which arise only from the increase in the value of unemployment induced by the possibility of working while on claim. The stepping stone effect, which has so far been left out of consideration, can arise from the relation between work on non-regular jobs and the arrival rate of regular job offers. This relation can be incorporated into the model by assuming that the arrival rate of regular job offers λ is a function of the job search effort and of the decision to work while on claim: λ(e t , Ω t ). The stepping stone effect arises if the arrival rate of regular job offers increases when individuals work on non-regular jobs while on claim; this might happen because working on non-regular jobs improves work experience, sends good signals to employers, or facilitates the access to information about regular job offers through networks. The stepping stone effect induces individuals to work while on claim more frequently and sooner in the unemployment spell.17

However, the relation between the arrival rate of regular job offers and work on nonregular jobs while on claim can also amplify the lock-in effect if working on non-regular jobs reduces the time available to hunt for regular jobs or sends a negative signal about the quality of workers to employers [START_REF] Farber | Factors determining callbacks to job applications by the unemployed: An audit study[END_REF]). In this case, individuals have less incentives to work on non-regular jobs while on claim.

All in all, the model shows that there is a monotone mapping between the marginal tax rate on earnings from work while on claim and the propensity to work while on claim; and that part-time unemployment benefits programs influence the unemployment exit rate through two effects: the anticipation effect, which reflects the impact of the possibility of working while on claim on the search effort, and the direct effect of working while on claim, dλ(e t , Ω t )/dΩ t . 18 Moreover, the model predicts that the impact of part-time unemployment benefits on the exit rate from unemployment to employment is significant close to the benefit exhaustion date.

The consequences of information provision

The provision of information to the treatment group is justified by the assumption that individuals are not fully informed and may have biased beliefs about the part-time unemployment insurance scheme. A natural interpretation of bias in beliefs is given by the literature on behavioral inattention [START_REF] Gabaix | Inattention[END_REF]) which assumes that the belief in the marginal tax rate, m t , is a convex combination of the actual rate m a t and a "default" rate,

m d t , i.e., m t = αm a t + (1 -α)m d t ,
where α ∈ [0, 1] characterizes the degree of attention. In this framework, the provision of information increases the value of α.

Individuals can underestimate the gains from working while on claim, for instance because they think that they would lose all their labor earnings or their unemployment benefits if they were working while on claim. For these individuals, whose "default" tax rate is above the actual tax rate, the provision of information is equivalent to the announcement of a drop in the marginal tax rate, which should, according to our model, boost part-time unemployment.

Note that for those who did not use the scheme before the informational treatment simply because they were not aware that it existed, the "default" rate can be interpreted as being equal to one, since they thought that is was not possible to work while on claim before getting the information from our treatment.

For individuals who overestimate the gains, the information provision is equivalent to the announcement of an increase in the marginal tax rate which should induce less work on non-regular jobs while on claim.

The definition of the marginal rate m t shows that it can be influenced in different ways by the informational treatment, which can change beliefs on the tax rate τ on current labor earnings but also any anticipation which affects the future value of unemployment U t+1 . For instance, the informational treatment can be interpreted by some individuals as a message on the frequency of the offers of non-regular or regular jobs. According to the model, if individuals interpret the informational treatment as a good signal indicating the availability of non-regular jobs, this raises their expected utility E t (U t+1 ). They decrease their search effort for regular jobs and their marginal rate m t drops. The informational provision might also be interpreted as bad signal indicating the scarcity of regular jobs, which now reduces the expected utility of job seekers. 19 But, like the good signal, it decreases the search effort for regular jobs and the marginal tax rate m t .20 Whatever, all these changes affect the marginal rate m t , which is the key variable of interest to interpret the consequence of the informational treatment on the partial unemployment take-up as well as on the exit rate from unemployment. 21Hence, the fact that we find a positive impact of our treatment on the part-time unemployment benefits take-up, as will be shown below, means that treated individuals overestimated, on average, and for many different possible reasons, the marginal tax rate on earnings from work while on claim before the treatment. 22 The model shows that this decrease in the marginal tax rate has an impact of ambiguous sign on labor supply and on unemployment duration. Our empirical analysis aims at exploring this impact.

Experimental Design and Data

Treatment

Our experiment consists in sending information about the part-time unemployment benefits scheme to unemployed workers eligible for unemployment benefits and recently registered at the unemployment agency. Individuals of the treated group received 3 successive emails on 31 January, 28 February, and 31 March 2017. The emails were sent from the employment agency's mailing platform. The main text of the emails is as follows:

We inform you that you can work without losing your unemployment benefits. This opportunity to combine your wage and benefits allows you to:

• Have earnings higher than your benefits, though without exceeding the amount of your former gross wage. Pôle Emploi only reduces your benefits by 70 cents per gross euro earned.

• Be entitled to benefits for a longer period. The number of days of benefits not received due to the accumulation of your earnings while on benefits are credited to your account.

At the exhaustion of your benefits, you will be able to get new entitlement to unemployment benefits if you have done at least 150 hours of salaried activity.

This main text is accompanied by an example which introduces a hypothetical worker and displays what happens to his benefits if he works while on claim. An attached file provides further information about the example. The message also comprises a link to a web page of the public employment agency where it is possible to simulate the disposal income as a function of labor earnings.23

Implementation

The experimental design relies on three experimental groups : treated workers (the "treated group"), untreated workers in treated areas (the "control group"), untreated job seekers in non-treated areas (the "super control" group).

The steps taken to implement the experiment were very similar to those described in [START_REF] Crépon | Do Labor Market Policies have Displacement Effects? Evidence from a Clustered Randomized Experiment[END_REF]. Randomization was implemented at both the labor market and individual levels. There are 856 public unemployment agencies, scattered across France. Each agency represents a small labor market, within which we may observe treatment externalities which may arise from information spillovers or displacement effects. On the other hand, the agencies cover areas that are sufficiently large, and workers in France are sufficiently immobile, that we can assume that no spillovers take place across areas covered by different agencies. To identify spillovers, we used a "super control" group as in [START_REF] Crépon | Do Labor Market Policies have Displacement Effects? Evidence from a Clustered Randomized Experiment[END_REF].

First we stratified our sample at the agency level. 24 Within each stratum we randomly divided the 856 agencies into two groups that covered areas similar in size and with comparable local populations. One of the two groups consists of the non-treated areas, i.e. the "super control" group. The other group consists of the treated areas. For each treated area, we stratified the job seekers. Within each stratum we randomly assigned treatment with a probability of one-half, making half of job seekers in the treated areas effectively treated (i.e. received emails). Table 1 summarizes the experimental lay-out.

Data

We use three sources of data. First, an administrative database on job seekers provided by the employment agency (Fichier National des Allocataires). These records provide the individual socio-demographic characteristics (age, gender, education level, family situation,living area) and detailed information about all previous registrations (date of registrations, reason for registration, start and end dates of unemployment spells, the level of unemployment benefits, earnings and hours of work while on claim...).

A second data set comes from the hiring intentions of firms (Déclarations Préalables A l'Embauche). Prior to hiring each employee, any employer from the private and semi-private sector has to fill out a form indicating the starting day, the type (permanent contract or fixed-term contract) and the expected duration of the contract. This allows us to acquire information about the employment status of all randomized individuals. As this form only reports the intention to hire, we do not know whether the individual has actually been hired25 and whether the individual stays in the firm for the entire expected contract duration.

Our third source of data is email tracking statistics. The information treatment was sent by email from the employment agency's mailing tool (Gestion des Messages Entrants).

For all treated individuals, it lists basic email activity: whether they have opened the email and/or clicked within the email.

Sample and summary statistics

The randomization was implemented in December 2016. The effects of the experiment critically depend on the knowledge of job seekers about part-time unemployment insurance.

Job seekers with multiple spells have a better knowledge of the unemployment system, and are thus less likely to react to our information intervention. We identified job seekers who are entitled for the very first time to unemployment benefits between 1 July 2016 and 30 November 2016. We excluded job seekers subject to very specific rules, such as recurrent temporary workers (in temp agencies), childminders, entrepreneurs, artists, and technicians working in the culture sector, as well as job seekers who had already worked while on claim between their entry into unemployment and November 2016. This procedure resulted in an experimental sample of 147,878 job seekers who have been randomized into treated (T), control (C) and super control groups (SC). In the treatment effect analysis, we apply an additional filter to the experimental sample, retaining only individuals who were still on claim and did not experience part-time unemployment between the randomization date and the first sending. Our final sample is then composed of 115,547 individuals. 26 Table 2 presents summary statistics regarding the final sample for the treated group, the control group and the super control group before program assignment, as well as balancing tests. 27 A large share of individuals (38%) is under 25 years old in our sample while they are 14% in the whole population of job seekers. This is not surprising given that we only select job seekers who have never been eligible for unemployment benefits. Nearly half of job seekers are women and 33% of the sample has a university degree. At the date of the first email (January 31, 2017), individuals have on average been unemployed for 108 days, which is consistent with the selection of job seekers who registered between 1 July 2016 and 30

November 2016. Finally, potential benefit duration -i.e. the difference between the initial date of benefit exhaustion and the starting date benefit entitlement -is equal to 621 days on average and this potential duration is longer than 2 years for 56% of job seekers (2 years being the maximum benefits duration for individuals under 53 years old). Figure 6 displays the distribution of potential benefit duration. 43% of individuals are entitled to 730 days of benefits against 30% in the whole population of job seekers. This also reflects the fact that we select individuals who are entitled to unemployment benefits for the first time. In this case, they are more likely to have experienced a long period of employment.

The last five rows of Table 2 present summary statistics about the employment agencies.

The average number of job seekers by employment agency is 4,362 among which 224 are in our sample. The unemployment rate is around 13.7%. Both the share of part-time unemployed workers and the share of recurrent job seekers is about 43%.

The last three columns of Table 2 report the p-values for the difference between those

26 The further away the entry into unemployment is from the treatment date, the higher the chances for an individual to have been filtered out from our final sample. Thus, for people with higher elapsed unemployment duration at treatment date, our sample is less representative of newly registered job seekers. We check below that the treatment effect does not significantly depend on the elapsed unemployment duration at treatment date.

27 Table B1 in Appendix B reports summary statistics for the whole sample, before dropping the observations for individuals who were not on claim or who had already experienced part-time unemployment at the date of the first sending. It shows that the share of individuals who were still on claim and the share of those who had never experienced part-time unemployment at the date of the first sending are not statistically different in the treated group, the control group and the super control group before program assignment. Figures C4 andC5 in Appendix C provide additional descriptive statistics on work while on claim by group.

assigned to treatment (T) and those assigned to control (C) (column 5), the difference between those assigned to treatment (T) and the non assigned (C + SC), and for the joint significance of assignment status (T, C and SC). We do not observe any significant differences between our groups.

Results

This section provides information about the intensity of the informational treatment before looking at its impact on work while on claim, on unemployment, on unemployment insurance expenditure and on welfare.

Treatment intensity

Results concerning treatment intensity are reported in Table 3. The share of treated individuals who opened at least one email after the three mailings is about 85%. This figure is relatively high and can be related to the fact that we targeted first time claimants. Furthermore, among these 85%, the vast majority opened the first email. The proportion of claimants who used the simulator is much lower: about 7.5% used it at least once.

Regarding the heterogeneity of the opening rate, we observe that the share of job seekers who opened at least one email is high, above 70%, among all groups reported in Table 3. The most substantial differences in opening rates are associated with education: + 18,1 percentage points for individuals with higher education levels compared to people with lower education levels; age: + 7,6 percentage points for prime age people compared to seniors; gender: + 4,1 percentage points for women; and the daily reference wage: + 3,7 percentage points for people with a daily reference wage above the mean.

Although compliance in the experiment is difficult to interpret for people who have opened the emails and used the simulator, the recent contribution from [START_REF] Altmann | Do Job Seekers Understand the UI Benefit System (and Does It Matter)?[END_REF] finds that the impact of providing information unemployment insurance rules has a significant impact on the knowledge of unemployed workers in a context similar to ours, where they have pronounced information gaps about complex part-time unemployment benefits. To the extent that a large proportion of the unemployed opened the emails we sent, this suggests that our provision of information may have altered the propensity to work while on claim.

Work while on claim

This section is devoted to the effects of the treatment on work while on claim. Work while on claim includes all those who work while continuing to receive unemployment benefits during the current month. 28 Hence, for our purposes hours of work while on claim are defined as the hours of work of individuals who do continue to receive unemployment benefits during the current month. We start by presenting our statistical model before looking at the effects of the treatment by comparing the treated, the control, and the super control groups. We also explore the potential heterogeneous effects of the treatment within the treated group.

We then go on to compare the characteristics of individuals who work while on claim in the treated and control groups, in order to gauge the external validity of our results.

Statistical model

The intention to treat (ITT) estimates are obtained from the following model :

y i = α + βZ i + δC i + γX i + ϵ i (7)
where Z i is a dummy for being treated and C i is a dummy for being in a treated area (i.e.

being either in the treated group or in the control group but not in the super control group).

Then, β is the difference between the treated group and the control group. δ is the difference between the control group and the super control group i.e. the effect of being untreated in a treated zone. X i is a vector of control variables that includes the variables reported in the summary statistics (Table 2) as well as entry months and regional fixed effects.

Treated group versus control group

Regarding the difference between the treated group and the control group (β), we first consider the impact of the treatment on work while on claim at the extensive margin (i.e. the choice between working or not working while on claim), which is measured by the indicator 28 According to the regulations, individuals whose monthly earnings exceed the earnings used to compute their unemployment benefits do not get any unemployment benefits in the current month but are still on claim if they continue to register with the unemployment agency at the end of the month. By definition, an individual continues to be registered in the current month only if he registers during that month. Individuals who do not register during the current month lose the benefits associated with registration. Registration at the unemployment agency can be beneficial for reasons other than receiving unemployment benefits, e.g. getting counselling to find a better job, avoiding the time-consuming process of launching a fresh entitlement period from scratch, getting free access to several public services... We take the view that such individuals -registered at the unemployment agency and eligible for unemployment benefits but not actually receiving them because their earnings are too high -are not unemployed, and therefore not part-time unemployed.

variable equal to one from the first month in which the individual starts working while on claim. Figure 7 shows that the treatment has a quick positive impact on the extensive margin, which becomes significant three months after the first email, where work while on claim increases by 0.4 percentage points, which corresponds to an increase of 6% compared to non-treated individuals -see Table B2, Column 1. Work while on claim increases until six months after the first email by about 0.5 percentage points. After six months, the impact of the treatment stops increasing and remains positive. The fluctuations in the effect of the treatment, which is stronger in spring and summer, is associated with the seasonality of work while on claim illustrated on Figure C3.

Figure 8 shows that the treatment has a significant effect on the cumulative number of hours of work while on claim. The impact amounts to about 7 supplementary hours after 36 months for people assigned to treatment. It is striking that the impact of the treatment does not dampen over a quite long period of time, up to three years. This suggests that whatever information members of the control group were able to acquire about part-time unemployment benefits over the period after the treatment did not sufficiently improve to catch up to the level of supplementary information provided by our emails.

Table 4 reports the results for the estimation of equation ( 7) for different outcomes and time horizons. From Panel A, we can see that the assignment to treatment increases the frequency of months in which individuals work while on claim by about 4.5% from 3 months to 36 months after the treatment. Panels B and C show that the treatment has about the same impact, in percentage terms, on the cumulative number of hours of work and on cumulative earnings from work while on claim, 3, 12 and 36 months after the treatment.

Table 5 reports the results for the effects of the treatment at the intensive margin, i.e. on the number of hours of work while on claim and on the earnings from work while on claim for the subset of job seekers who work at least one day while on claim. Table 5 shows that the impact of the treatment on the number of hours of work while on claim and on the earnings while on claim conditional on working while on claim is barely significant and very small. This means that the treatment has a negligible impact on work while on claim at the intensive margin. 29The robustness of these results to randomization based inference is presented in Appendix A.3 and in Table B3. Overall, the p-values obtained with randomization inference tests are very close to the cluster-robust model based p-values, which is not surprising, considering the sample size in our experiment. Both conventional and randomized based inference thus support the conclusion that the treatment did have a statistically significant effect on the propensity to work while on claim.

Control group versus super control group

The propensity to work while on claim of the control group can be impacted by the informational treatment through two effects: i ) The transmission of information from treated individuals, which can increase take-up in the control group, as well as in the treated group.

ii ) Displacement effects arising from the increase in the take-up of treated individuals. These displacement effects can decrease the take-up in the control group, as suggested by [START_REF] Crépon | Do Labor Market Policies have Displacement Effects? Evidence from a Clustered Randomized Experiment[END_REF], who show that unemployed workers more intensively supported by public employment services crowd out other job seekers in a context similar to ours.

Figure 9 shows that the number of hours worked while on claim is not statistically different in the control and the super control group at all available time horizons. This result is confirmed by Tables 4 and5 which show that there is no statistically significant difference between any outcome of the control group and of the super control group.

It is possible that the lack of spillover documented in Tables 4 and5 arises from the absence of any effects of the treatment on the control group. But it is also possible that the two effects cancel each other out. [START_REF] Crépon | Do Labor Market Policies have Displacement Effects? Evidence from a Clustered Randomized Experiment[END_REF] identify displacement effects from variations in the share of treated individuals in each unemployment agency. This does not help us to identify the relative impact of the two effects since the strength of both effects is expected to increase with the share of treated individuals: when more individuals are treated, both information transmission and displacement effects may increase. However, [START_REF] Crépon | Do Labor Market Policies have Displacement Effects? Evidence from a Clustered Randomized Experiment[END_REF] find displacement effects only in weak labor markets where the unemployment rate is high. Thus, in labor markets with a low unemployment rate, only the transmission of information is likely to have a significant impact on the control group if there are informational spillovers. This means that one should observe a positive impact of the treatment on the part-time unemployment take-up of the control group in labor markets where the unemployment rate is low if the provision of information spreads to the control group. To test this assumption, we estimate the following model for individuals in the control and the super control groups:

y i = α 0 + α 1 C i + α 2 U i + α 3 (C i × U i ) + α 4 X i + ϵ i (8)
where y i is a measure of part-time unemployment take-up of individual i, U i is an indicator function equal to one if individual i is located in a commuting zone in the bottom tercile of local unemployment rates ; C i is a dummy for being in the control group -i.e. in a treated area but not in the treated group since it is excluded from the sample here.

(C i × U i ) denotes the interaction between C i and U i . As previously, X i is a vector of control variables that includes the variables reported in the summary statistics (Table 2) as well as unemployment entry months and regional fixed effects. Coefficient α 3 is positive if the provision of information spreads to the control group.

Table 6 shows that there is no evidence that the part-time unemployment take-up of the control group increases, compared with the super control group, when the local unemployment rate is low. This suggests that there are no significant information spillovers to the control group arising from the treatment. Accordingly, the absence of spillover -from both displacement effects and information transmission -reported in Tables 4 and5 is likely the consequence of the absence of any significant impact of the informational treatment on the control group. Hence, we can be confident that the comparison of the outcomes of the treated group and the control group yields the net effect of the treatment on those who were assigned to it.

Heterogeneous effects of the treatment

To investigate the heterogeneity of the treatment effect in a disciplined fashion, we apply the machine-learning approach developed by [START_REF] Chernozhukov | Generic machine learning inference on heterogenous treatment effects in randomized experiments[END_REF]. This allows us to analyze potential heterogeneous effects while being agnostic about the source of heterogeneity, which can arise from any combination of our covariates. More specifically, we test for the presence of heterogeneity and estimate average treatment effects sorted by groups as well as average characteristics of the most and least affected units. To analyze treatment effect heterogeneity, we restricted our analysis to observations from the treated group and the control group. Details for the estimation procedure are presented in Appendix A.4.

Table B5 shows that the absence of heterogeneity can be rejected (at 10% significance level) for one outcome, namely the probability to work while on claim at least once one year after the treatment. Apart from this, we do not detect any significant heterogeneity for the other outcomes of interest (cumulative part-time unemployment activity and exit from unemployment). Overall, these results provide only limited evidence of heterogeneity in the treatment effect. This may be due to the absence of such heterogeneity or to the inability of our machine-learning proxies to detect it.

Focusing on the heterogeneity in the treatment effect on the probability to work while on claim at least once one year after the treatment, Figure 10 reports the estimated conditional average treatment effect (CATE) for five heterogeneous groups induced by our machinelearning proxy. Although point estimates show some evidence of heterogeneous effects, differences across groups are not statistically different from the whole average effect. Looking at each group separately, confidence intervals indicate that the treatment had no significant effect on part-time unemployment benefits take-up among the four least affected groups, but a significantly positive effect among the most impacted group, which corresponds to the top 5% (p-value = 0.038 with Linear Regression proxy). If we focus on the most affected group vs. the least affected group (bottom 50%), we are able to reject the null hypothesis that the two coefficients are equal at 5% significance level (p-value = 0.047) (see Table B6). Finally, we can observe that all point estimates are positive (or very mildly negative), indicating that our informational treatment did not induce any group to work less while on claim.

Table 7 provides 2) as well as month of entry into unemployment and regional fixed effects for individuals belonging to the super control group. 30 This allows us to rely on out-of-sample untreated units to predict the probability to work while on claim conditional on these covariates. 31 Overall, Table 9 shows that the impact of the treatment on all measures of the intensity of the propensity to work while on claim is more important for individuals whose observable characteristics are associated with a probability above the median to work while on claim. This indicates that the treatment induces individuals to work while on claim whose observable characteristics are similar to those who have a high propensity to work while on claim, which is a situation that should arise if the marginal tax on work while on claim drops.

Unemployment

According to the theoretical job search model, part-time unemployment benefits have an ambiguous impact on unemployment duration, which can either decrease if work while on claim significantly boosts the access to regular jobs or increase if lock-in effects dominate.

Specifically, as shown in Figure 5, the model predicts that the impact of part-time unemployment benefits on the unemployment survival rate is significant around the benefit exhaustion date if part-time unemployment benefits slows the exit rate. In what follows, we begin by analyzing the impact of the informational treatment on the survival in compensated unemployment, on the survival in unemployment -whether compensated, non-compensated or part-time -, on the total number of hours of work, and finally on job quality.

Compensated unemployment

In our context, it is clear that part-time unemployment is associated with longer unemployment spells. Figure 11 shows that the probability to be in compensated unemployment significantly increases among treated individuals around 26 months after the treatment date.

Figure 12 further indicates that this pattern is driven by job seekers with potential benefit duration equal or above 2 years whose treatment effect is stronger in magnitude and significant on a longer period. 32

30 Tables B8, B9, B10 report the results of this first stage for our outcomes of interest measured one 3, 12 and 36 months after the start of the treatment respectively. We can perceive that most of the characteristics associated with a higher probability to work while on claim at least once are also the characteristics that are prevalent in the most affected group from the CLAN analysis in Table 7. The only exception is the potential benefit duration, which is positively associated with part-time unemployment whereas it is on average lower in the most affected group.

31 [START_REF] Abadie | Endogenous stratification in randomized experiments[END_REF] stress the importance of using out-of-sample untreated units to proceed to this type of analysis.

32 By potential benefit duration we mean here the duration scheduled at the start of the entitlement period which corresponds to duration for individuals who do not work while on claim. As explained above, working

In line with the properties of the job search model, this increase occurs when the majority of individuals of the control group are exhausting their benefits since the potential duration of benefits of a large fraction of job seekers is around two years (cf. Figure 6). Figure 13 and 14 show more precisely how the treatment effects evolve around the initial exhaustion date of benefits. The probability to remain in compensated unemployment starts to be higher in the treated group than in the control group a few months before the initial date of benefits exhaustion and reaches a peak around this date that is statistically significant at 95% confidence level 1 and 2 month after (Figure 13). The same pattern, of greater amplitude, arises for job seekers entitled to 2 years or more of unemployment benefits (Figure 14).

Exit toward regular employment

The results concerning survival in compensated unemployment may simply reflect the fact that job seekers in the control group exhausted their unemployment benefits faster without necessarily finding regular jobs. We investigate this question by directly looking at exits toward regular employment, or in other terms at survival in unemployment including compensated, non-compensated and part-time unemployment. 33 Still in line with the job search model, survival in unemployment of treated individuals begins to increase relative to that of the control group around 18 months of unemployment and becomes significantly higher by 0.5 percentage points at 95% confidence level around 25 months (Figure 15). After 29 months, the treatment and control group difference in the survival rate diminishes. Then, it vanishes after 33 months.

The impact of the treatment on the exit rate toward regular employment is further documented by Table 10 which shows that the treatment has a negative impact on the probability to have a regular job in the last quarter and in the last month before the initial date of benefits exhaustion. Hence, the treatment has significant and sizeable lock-in effects: it increases by 6% the share of job seekers working while on claim about 3 months after the start of the treatment and reduces by 1.5% (Table 10, Panel B col. 1) the probability to have a regular job the last month before the initial exhaustion date. The lock-in effects are larger for individuals whose potential benefit duration is longer: the treatment decreases the probability to have a regular job the last month before the exhaustion date by 2.8% when the potential benefit duration is between 2 and 3 years whereas the effect on the propensity while on claim delays the exhaustion date.

33 Unemployed people who have stopped registering on the public employment service lists but have not found a job are counted as unemployed in this estimate.

to work while on claim 3 months after the start of the treatment is only slightly higher than for the overall sample (+6.7%).

The robustness of these results to randomization based inference is presented in Appendix A.3 and in Table B4. As previously, for the effects of the treatment on the propensity to work while on claim, the p-values obtained with randomization inference tests are very close to the cluster-robust model based p-values. Therefore, both conventional and randomized based inference indicate that the treatment had a statistically significant effect on both the exit from compensated unemployment and the exit toward regular jobs.

Hours of work

In order to better gauge the impact of the informational treatment on overall labor supply, we compute the difference in the number of hours worked (both in part-time unemployment and in regular employment) between the treated group and control group. 34Figure 16 shows that there is a non-significant decrease in cumulative working hours in the treatment group 3 years after treatment. The absence of an increase in hours worked in the first year after the start of treatment suggests, in accordance with Figure 15, that small lock-in effects appear from the start of the unemployment spell insofar as the treatment has a positive effect on the cumulative number of hours worked during the compensation period from four months after the start of treatment (see Figure 8). Treated unemployed, for whom the potential duration of benefits is at least equal to 24 months show an increase (although not significant) in their number of hours of work accumulated until the date of initial exhaustion of benefits (see Figure 17). But it is then wiped out because they are more often unemployed close to the exhaustion date than the untreated unemployed.

Job quality

It is possible that part-time unemployment decreases the exit to regular employment in general but increases the exit to good quality regular jobs. To explore this possibility, we decompose the exit toward regular jobs according to the length of the employment spell. As an alternative measure, one could think of contract type to analyze job quality. However, the hires recorded as "permanent contracts" often end up to last only a few weeks for individuals in our sample. Hence, we do not consider it as truly informative about job quality and we prefer to focus on the effective employment spell duration.

In particular, we consider the probability to be in an employment spell that lasts at least 3 months (Figure 18), at least 6 months (Figure 19) or at least 12 months (Figure 20). For all durations, we observe a drop in the probability to be employed for treated individuals which is around the same period (twenty to thirty months after the treatment) as for the drop in regular employment in general (see Figure 15). Thus, these results suggest that the lock-in effects found in the previous section do not mask stepping stone effects toward better quality jobs, but rather are driven by a lower exit rate to longer employment spells.

Unemployment insurance expenditure

In order to evaluate the impact of the informational treatment on unemployment insurance expenditure, we compute the difference in cumulative unemployment benefits net of taxes between the treated and control groups. Since we have limited information on tax receipts, we also provide information about the effect of the treatment on cumulative unemployment benefits gross of taxes as well as the number of days of compensated unemployment. 35 In line with the findings on hours of work, Table 11 shows that the treatment has no statistically significant effects on cumulative unemployment insurance payments, either net (Panel A) or gross (Panel B), at any time horizon. Three years after the start of the treatment, the cumulative benefits-net-of-taxes difference between the treated and the control group is very small and not significant: it is equal to the tiny amount of 62 euros (p-value = 0.50 for the null hypothesis of difference equal to zero) compared to the average cumulative amount equal to 13,746 euros. Table 11, Panel B, also shows that there is a non-significant increase in cumulative benefits in the treated group from the first year after the treatment.

The positive sign reflects the lock-in effects, implying that the increase in part-time unemployment (which should generate a drop in benefit payments) is counterbalanced by less 35 Tax receipts from unemployment insurance are computed by applying the unemployment insurance payroll tax rate to labor earnings, equal to 6.5%, for all hourly wages below about 25 euros, and to zero above this threshold. We have no information on earnings of individuals who definitively exit unemployment in our period. The monthly earnings are estimated by assuming that they are equal to the past daily wage used to compute the unemployment benefits times 30, which corresponds to the monthly earnings of a person working full time for the corresponding daily wage. It is likely that this overestimates the amount of tax receipts since all job seekers do not work full-time when they exit unemployment, meaning that we get a lower bound of the effect of the treatment on unemployment insurance expenditure net of taxes. For this reason, we provide results for the impact of the treatment on gross unemployment insurance payments (i.e. neglecting tax receipts), which yields an upper bound for the effect of the treatment on unemployment insurance expenditure net of taxes. exits toward employment. Then, as time elapses, cumulative benefits tend to be larger in the treated group, although the difference is not statistically significant. Panel C of Table 11 confirms the previous results by showing that the cumulative number of days of compensated unemployment does not significantly differ between the treated group and the control group.

The absence of a significant difference in unemployment insurance expenditures between treated and control group confirms that both the positive (lock-in effects) and negative (supplementary days of work while on claim) effects of the treatment on the expenditure cancel each other out. 36

Welfare

According to the model, improving information about unemployment insurance can only improve welfare because this helps to make better decisions. Therefore, the informational treatment improves welfare if it provides better knowledge on the unemployment insurance parameters without changing the expectation on the arrival rate of job offers. In this context, improved welfare is associated with a longer spell because the informational treatment induces a drop in the expected tax τ on current earnings from work while on claim and job seekers find it optimal to work more while on claim and to search for regular employment less intensely. But as discussed above, it is possible that the informational treatment was interpreted as a negative signal suggesting the scarcity of regular jobs, which now reduces the expected utility of job seekers, but induces them to work more while on claim and to look less intensely for regular jobs. The job search model clearly shows that this effect is not specific to our experiment. It is a consequence of part-time unemployment insurance which is likely to modify the expectations of the unemployed on job offers. Therefore, assessing the impact of part-time unemployment insurance on the welfare of the unemployed requires knowing how it affects their expectations regarding their employment prospects. 37 According to another mechanism, not accounted for by our job search model, the information treatment may also have a negative impact on welfare even though it improves knowledge of unemployment insurance parameters if working while on claim creates lock-in effects in unemployment that 36 It should be noted that our experience does not take into account the possible increase in entries into unemployment induced by part-time unemployment benefits since the information was transmitted to those entering unemployment. Recent empirical evidence in France suggests that this channel could increase unemployment insurance expenditure [START_REF] Khoury | Unemployment Benefits and the Timing of Redundancies[END_REF]).

37 Papers on the signalling effects of monetary policy of [START_REF] Melosi | Signalling Effects of Monetary Policy[END_REF] and Nakamura and Steinsson (2018) might be a source of inspiration.

are not anticipated by job seekers. These two issues,which are beyond the scope of this paper, are left for future research.

Conclusion

Our paper shows that the transmission of information about part-time unemployment benefits which raises the take-up rate induces significant lock-in effects into compensated unemployment. It is striking that these lock-in effects exist despite the positive correlation between the part-time unemployment take-up and the exit from compensated unemployment, documented by the previous literature in France [START_REF] Fremigacci | Subsidized temporary jobs: lock-in and stepping stone effects[END_REF] and [START_REF] Auray | Stepping-stone effect of atypical jobs: Could the least employable reap the most benefits?[END_REF]) and in other countries. 38 Our results, are in line with those contributions focused on the causal impact of part-time unemployment insurance (Lee et al. ( 2019), Le Barbanchon (2020), [START_REF] Altmann | Do Job Seekers Understand the UI Benefit System (and Does It Matter)?[END_REF]) which also find significant lockin effects associated with part-time unemployment benefits. Insofar as we find that the lock-in effects are important and can last for several years, our contribution underlines the importance of taking them into account in order to design effective part-time unemployment insurance schemes.

Our contribution, focused on unemployment duration, hours of work and unemployment insurance expenditure, does not draw conclusions on the impact of part-time unemployment insurance on welfare. Such an analysis, which is beyond the scope of this paper, is an important area for future research insofar as part-time unemployment insurance, which is already an important component of unemployment insurance in many countries, is expected to play a growing role in the face of the development of unstable jobs.

38 See the references provided above in the introduction.

Alwyn Young. Channeling fisher: Randomization tests and the statistical insignificance of seemingly significant experimental results. The Quarterly Journal of Economics, 134(2): 557-598, 2019. 2), ( 3) and ( 4) report the means of individual characteristics for the treatment, the control and the super control sub-samples, respectively. Columns ( 5)-( 7) report the p-values for the difference between assigned to treatment (T) and assigned to control (C) (column 5), the difference between assigned to treatment (T) and non assigned (C + SC), and for the joint significance of assignment status (T, C and SC). Note: Columns (1), ( 2), (3), and (4) report the share of treated participants who opened the first email (1), the second email (2), the third email (3) or at least one email (4). Columns ( 5), ( 6), ( 7), and ( 8) report the share of treated participants who used the simulator in the first email ( 5), in the second email ( 6), in the third email (7) or at least in one email (8). See Table 2 for a description of the variables. Columns (1), ( 2), ( 3) and ( 4) report the means of characteristics of individuals working while on claim at least once after the start of the treatment in our final sample, for the treatment, the control and the super control group, respectively. Columns ( 5)-( 8) report the p-values for the difference between assigned to treatment (T) and assigned to control (C) (column 5), the difference between assigned to treatment (T) and non assigned (C + SC), and for the joint significance of assignment status (T, C and SC). See Table 2 for a description of the variables. Note: Levels of significance: * < 0.10, * * < 0.05, * * * < 0.01. Standard errors, reported in parenthesis below the coefficients, are robust and clustered at the local agency level. p-values are reported in brackets. Each panel (outcome) * column (duration) displays the results from a different regression. Each regression include the list of covariates reported in the summary statistics (see Table 2) as well as entry months and regions fixed effects. "Treated" designates individuals who were assigned to treatment (ITT estimate). "Above median" designates individuals for whom the predicted outcome is above the median. For each outcome * duration, the predicted outcome is estimated by an OLS regression using individuals from the super control group only. Individuals from the super control group are not included in the regressions presented in this table to avoid potential bias arising from endogenous stratification as described in [START_REF] Abadie | Endogenous stratification in randomized experiments[END_REF]. The number of observations N corresponds to the number of individuals.

Tables

8 Figures These earnings are taxed at rate τ , implying that benefits are reduced by the amount τ z in month four. These saved benefits are carried over to the end of the initial entitlement period. The job search model is simulated assuming that the monthly discount factor β = 0.996, which corresponds to an annual discount rate equal to 5%; v(c) = log(c); λ(e) = λ 0 λ 0 -exp -γe ; the value of benefits is normalized to one: b = 1; the replacement ratio is equal to 0.5 implying that the wage of regular jobs, the duration of which is infinite and which yield the value W is equal to 2; the initial potential benefit duration equals 24 months; the tax rate on earnings from work while on claim τ = 0.85; the share α of current earnings reported at the end of the entitlement period, that will be obtained only if the person is still unemployed in this period, is equal to τ ; the distribution of earnings from work while on claim zt is uniform on the interval [0, b]; the fixed cost of work while on claim κ = 0.12; individuals still unemployed after the benefits exhaustion date get an income equal to 0.01 to ensure that they can choose to optimally produce a positive effort after the benefits exhaustion date. The top panel displays the case where γ = 0.1; λ 0 = 0.05; λ 1 = 1.4 which implies that the exit rate of unemployed workers increases around 24 months when there is part-time unemployment benefits and around 19 months otherwise. In this example, unemployed workers work 5 months while on claim in the 24 first months of unemployment when there is part-time unemployment benefits. The middle panel displays the exit rate from unemployment of a population composed of 95% of unemployed workers described in the top panel and 5% whose search effectiveness is too low to induce a positive search effort, implying that their exit rate from unemployment is equal to 1%. The bottom panel displays the difference between the exit rates of the middle panel.

Figure 5: The unemployment survival rate in the job search model Note: The job search model is simulated assuming that the monthly discount factor β = 0.996, which corresponds to an annual discount rate equal to 5%; v(c) = log(c); λ(e) = λ 0 λ 1 -exp -γe ; the value of benefits is normalized to one: b = 1; the replacement ratio is equal to 0.5 implying that the wage of regular jobs, the duration of which is infinite and which yield the value W is equal to 2; the initial potential benefit duration equals 24 months; the tax rate on earnings from work while on claim τ = 0.85; the share α of current earnings reported at the end of the entitlement period, that will be obtained only if the person is still unemployed in this period, is equal to τ ; the distribution of earnings from work while on claim zt is uniform on the interval [0, b]; the fixed cost of work while on claim κ = 0.12; individuals still unemployed after the benefits exhaustion date get an income equal to 0.01 to ensure that they can choose to optimally produce a positive effort after the benefits exhaustion date. The top panel displays the case where γ = 0.1; λ 0 = 0.05; λ 1 = 1.4. In this example, unemployed workers work 5 months while on claim in the 24 first months of unemployment when there is part-time unemployment benefits. The middle panel displays the unemployment survival rate of a population composed of 95% of unemployed workers described in the top panel and 5% whose search effectiveness is too low to induce a positive search effort, implying that their exit rate from unemployment is equal to 1%. The bottom panel displays the difference between the survival rates of the middle panel. 7)) on the indicator variable equal to one from the first month in which the individuals starts working while on claim (the variable remains equal to one in months in which the individual does not work while on claim but has worked while on claim previously). The green lines denote 95% confidence interval for the corresponding point estimate where standard errors are clustered at the agency level. All estimations include covariates that correspond to stratum variables reported in Table 2 as well as entry months and regional fixed effects. The results for 3, 6, 12 and 36 months durations are presented in Table B2 in Appendix B. 7)). The green lines denote 95% confidence interval for the corresponding point estimate where standard errors are clustered at the agency level. All estimations include covariates that correspond to stratum variables reported in Table 2 as well as entry months and regional fixed effects. 7)). The green lines denote 95% confidence interval for the corresponding point estimate where standard errors are clustered at the agency level. All estimations include covariates that correspond to stratum variables reported in Table 2 as well as entry months and regional fixed effects.

Figure 10: GATES of prob. to work while on claim at least once q q q q q -0.03

Elastic Net

Note: The outcome -probability to work while on claim at least once -is measured 12 months after the treatment date. The results are presented for the two best ML methods regarding this outcome : Linear Regression and Elastic Net. Heterogeneity groups are formed using the ML proxy distribution Ŝ(X i ) which we cut at 50 th , 75 th , 90 th , 95 th percentiles. For example, Group 1 corresponds to the bottom 50% of Ŝ(X i ) and Group 5 to the top 5%.

The parameter estimates and confidence intervals are computed as medians over 100 splits, with nominal levels adjusted to account for the splitting uncertainty. 7)) on the probability to be in compensated unemployment in the month. The green lines denote 95% confidence interval for the corresponding point estimate where standard errors are clustered at the agency level. Estimations do not include covariates but include entropy balancing weights that ensure identical outcome between the treated group and the control group at date zero [START_REF] Hainmueller | Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies[END_REF]). 7)) on the probability to be in compensated unemployment in the month. The green lines denote 95% confidence interval for the corresponding point estimate where standard errors are clustered at the agency level. Estimations do not include covariates but include entropy balancing weights that ensure identical outcome between the treated group and the control group at date zero [START_REF] Hainmueller | Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies[END_REF]). 7)) on the probability to be in compensated unemployment in the month. The green lines denote 95% confidence interval for the corresponding point estimate where standard errors are clustered at the agency level. Estimations do not include covariates but include entropy balancing weights that ensure identical outcome between the treated group and the control group at date zero [START_REF] Hainmueller | Entropy balancing for causal effects: A multivariate reweighting method to produce balanced samples in observational studies[END_REF]).

A Appendix

A.1 Unemployment Insurance in France Eligibility conditions

To qualify for unemployment benefits, the claimant must satisfy the following conditions:

• reside in France,

• have worked at least 122 days or 610 hours (4 months) in the last 28 months (or in the last 36 months for job seekers aged 50 and over) before becoming unemployed,

• have involuntarily lost his/her job (termination by the employer, the end of a fixed-term employment contract or an assignment contract, termination by mutual agreement or resignation for a valid reason),

• be registered as a job seeker with "Pôle emploi",

• be actively seeking employment.

Potential benefit duration

The potential benefit duration is computed based on the principle of "a day of work equals a day of compensation". Claimants must have worked at least 4 months before becoming unemployed. Benefits are then paid for a minimum period of 4 months and a maximum period of 24 months for job seekers aged under 50, and 36 months for job seekers aged over 50.

Benefits

Benefits are calculated on the basis of a daily reference wage. The reference wage is based on earnings subject to contributions during the 12 calendar months prior to the last day of paid work39 . It is calculated as follows:

Daily reference wage = Earnings during the past 12 months Number of working days during the past 12 months (up to 365 days)

The daily benefit is equal to the highest of the following amounts:

• 40.4% of the daily reference wage + a set amount (11.84 euros in 2017)

• 57% of the daily reference wage This amount cannot be below 28.86 euros or exceed 75% of the daily reference wage.

Monthly benefits, denoted b in the text, are then computed as the number of days in a month times daily benefit.

Part-time benefits

The part-time unemployment insurance scheme allows unemployed workers to work on non-regular jobs while on claim. They are allowed to work for any employer, including their past employers. For the sake of simplicity, the text only describes the rules in net terms for a job seeker who earned the minimum wage before unemployment. Nevertheless, the rules have been designed in gross terms. The marginal benefit reduction rate in gross terms is 70%, meaning that for each euro earned from work, 0.70 cents are deducted from the benefits.

When both the social contributions paid on the wage and on the benefits are deducted, the net financial gain of working is much lower as explained in the text. The contributions on wage amount to around 23% of the gross wage. Moreover, the social contributions on benefits for a job seeker who earned the minimum wage before unemployment represent 4.5%. For job seekers who earned more than the minimum wage before unemployment, the social contributions on benefits represent 9.6%. The net marginal benefit reduction rate is then comprised between 82% (= 70% 1-23% (1 -9.6%)) and 87%(= 70% 1-23% (1 -4.5%)).

Evolution of the unemployment insurance capital

At the beginning of her claim, the job seeker is informed about her monthly benefits b and about her potential benefit duration. The initial unemployment insurance capital B 0 is equal to the potential benefit duration times the level of benefits. If job seekers are totally unemployed all along their claim and receive their benefits each month, their benefits will lapse after their potential benefit duration. When job seekers are only paid part of their benefits in a given month, the unpaid amount is rolled over to a later month in the claim, so the capital depreciates at a slower pace.

Working while on claim is thus a way to delay the initial exhaustion date. The exhaustion date can be delayed without any limitation. Besides, after the initial benefit entitlement has expired, individuals can be eligible for a new entitlement period at the exhaustion of the unemployment benefits related to their current entitlement period. To do so, job seekers must meet less restrictive eligibility requirements. They must have worked at least 1 month while on claim (instead of 4 months for a first claim). The new potential benefit duration is still calculated on the principle of "a day of work while on claim equals a day of compensation".

A.3 Randomization Inference

This appendix evaluates the robustness of our results to randomization based inference. Contrary to conventional inference (cluster-robust p-value based on large sample approximations) which aims to account for sampling uncertainty, randomization based inference accounts for the uncertainty created by the treatment assignment itself. This method, first proposed by [START_REF] Ronald | Design of experiments[END_REF], is increasingly used in experimental papers as an alternative method to perform statistical inference [START_REF] Bloom | Contracting for health: evidence from cambodia[END_REF], [START_REF] Ichino | Deterring or displacing electoral irregularities? spillover effects of observers in a randomized field experiment in ghana[END_REF], [START_REF] Fujiwara | Can informed public deliberation overcome clientelism? experimental evidence from benin[END_REF]). Moreover, Young (2019) recently demonstrated that a substantial part of seemingly significant results, obtained with conventional methods, appear to be insignificant when statistical tests are conducted with randomization based methods.

The idea behind randomization inference is intuitive. It makes use of the knowledge that the researcher has on the randomization process to generate placebo estimates of the treatment effect. Thus, the observed ITT estimate, coming from the actual treatment assignment, can be compared to the distribution of these placebo estimates to test for its statistical significance.

A.3.1 Implementation

First, we randomly re-assigned "treatment" in the same way as was done in the experimental setting, that is, a 2 levels stratified sampling as described in section 4.2. Then, we re-estimate the two placebo treatment effect parameters: β r (Treated vs Control) and δ r (Control vs Super-control) based on the same estimating equation as equation ( 7):40

y i = α r + β r Z r,i + δ r C r,i + γ r X i + η r,i
where Z r,i is a dummy for being assigned to the treated group and C r,i is a dummy for being assigned to a treated area (i.e. being either in the treated group or in the control group but not in the super control group) in random re-assignment r.

We repeat this procedure 5000 times.41 Finally, for a given outcome, randomization based pvalue are obtained by computing the share of randomized based placebo estimates that are superior or equal (in absolute value) to the corresponding experimental estimate. For instance, we have for β:

p -value RI ( β) = R r=1 1( βr ≥ β) R
where R is the total number of random draws (i.e. R = 5000 in our setting).

A.3.2 Results

Tables B3 andB4 present the results of randomization inference tests. In particular, Table B3 presents the results for part-time unemployment and Table B4 presents the results for unemployment. We only present the results for outcomes on which we measured a statistically significant treatment effect with cluster-robust p-value.

Overall, the p-values obtained with randomization inference tests are very close to the clusterrobust model based p-values. To some extent this was expected, considering the relatively large sample size in our experiment. In particular, almost all (i.e. 7 out of 8) estimates that are statistically significant at 5% with model based inference are still significant at 5% with randomization based inference. Both conventional and randomized based inference thus support the view that the treatment had a statistically significant effect on both the propensity to work while on claim and the probability to exit from unemployment (i.e. lock-in effect). B Supplementary Tables 2), ( 3) and (4) report the means of individual characteristics for the treatment, the control and the super control sub-samples, respectively. Columns ( 5)-( 7) report the p-values for the difference between assigned to treatment (T) and assigned to control (C) (column 5), the difference between assigned to treatment (T) and non assigned (C + SC), and for the joint significance of assignment status (T, C and SC).

See Table 2 for the definition of each covariate. Note: Levels of significance: * < 0.10, * * < 0.05, * * * < 0.01. Standard errors, reported in parenthesis below the coefficients, are robust and clustered at the local agency level. Each column displays the results from an OLS regression of the associated outcome on the listed covariates as well as entry months and regional fixed effects. The number of observations N corresponds to the number of individuals. The small number of observations per bin implies that the differences observed between groups are usually not significant. Only 2 bins display a significant difference between the supercontrol and the control groups. As for differences between the treated group and the supercontrol group or the control group, the few significant differences indicate that the treated are less present in the bottom of the distribution. Cox proportional hazards model with covariates including gender, age, education, the reference wage, and the local unemployment rate. The monthly discount factor β is equal to =0.996, which corresponds to an annual discount rate equal to 5%.

  further evidence by comparing the characteristics of individuals in the most affected vs. less affected groups. Looking at demographic characteristics, the most affected are more likely to be young and to have an intermediate educational level. Regarding unemployment spell related variables, individuals in the most affected group are found to have a higher daily reference wage, entering unemployment after shorter duration contracts and having a lower potential benefit duration. Looking at local environment characteristics, people are more impacted by the treatment when unemployment is lower and part-time unemployment more frequent.The heterogeneity of the impact of the informational treatment on the probability to work while on claim may arise from differences in dealing with information received by email, and from differences in the propensity to work while on claim. The next section examines this issue.5.2.5 Characteristics of individuals working while on claim in the treated groupIt is possible that the informational treatment impacted individuals particularly sensitive to information received by email, implying that those induced to work while on claim by the treatment are very different from those who work while on claim in the absence of our treatment. Knowing whether individuals induced to work while on claim because they received our information about part-time unemployment benefits resemble other individuals working while on claim is important when it comes to gauging the external validity of our analysis; or, to put it differently, when it comes to gauging whether the effect of the treatment can be compared to the effect of changes in the marginal tax on earnings from work while on claim. We examine this issue in two different ways. First, we compare the characteristics of individuals working while on claim in the treatment and in the control groups. Second, we use the super control group to predict the individual characteristics associated with the propensity to work while on claim and we analyze how treated individuals react to the treatment depending on these characteristics.Comparison of individuals working while on claim in the treated group and control group Table8reports the means of the characteristics of individuals who worked while on claim at least once six months after the treatment, which corresponds to the period in which the treatment has the largest impact on the number of job seekers working while on claim. It is clear that the characteristics of treated individuals working while on claim do not differ from those of other individuals also working while on claim, except for the duration of the last contract before the entry into unemployment. Individuals of the treated group in part-time unemployment had contracts whose duration was more frequently below 3 months before starting their unemployment spell compared with other individuals in parttime unemployment. This means that the informational treatment has larger effects on the propensity to work on non-regular jobs for individuals who worked on such jobs in the past. This is likely because those individuals are more inclined or have more opportunities to work on non-regular jobs. Apart from this difference, the characteristics of individuals of the treated group in part-time unemployment are not statistically different from those of other individuals who work while on claim. Treatment impact conditional on predicted characteristics associated with work while on claim Now, let us analyze whether the informational treatment has a stronger impact on the probability to work while on claim for individuals more likely to work while on claim in the absence of the treatment. We start by regressing the probability to work while on claim on the covariates displayed in the summary statistics (Table

Figure 1 :

 1 Figure 1: The relation between earnings when working while on claim and income

Figure 2 :

 2 Figure 2: The dynamic aspects of the schedule

Figure 3 :

 3 Figure 3: Survival rate in unemployment and exit rate from unemployment to employment of non-treated individuals

Figure 4 :

 4 Figure 4: The exit rate from unemployment in the job search model

Figure 6 :

 6 Figure 6: Potential benefit duration at registration date (left panel) and treatment date (right panel)

Figure 7 :

 7 Figure 7: Intention to treat effects on work while on claim at the extensive margin

Figure 8 :

 8 Figure 8: Intention to treat effects on the cumulative number of hours worked while on claim

Figure 9 :

 9 Figure 9: Comparison of the cumulative number of hours worked while on claim between control and super control group

Figure 11 :

 11 Figure 11: Intention to treat effects on survival in compensated unemployment

Figure 12 :

 12 Figure 12: Intention to treat effects on survival in compensated unemployment among job seekers with potential benefit duration superior or equal to 2 years

Figure 13 :

 13 Figure 13: Intention to treat effects on survival in compensated unemployment

Figure 14 :

 14 Figure 14: Intention to treat effects on survival in compensated unemployment among job seekers with potential benefit duration superior or equal to 2 years

Figure 15 :

 15 Figure 15: Intention to treat effects on survival in unemployment (compensated, noncompensated or part-time)

Figure 16 :

 16 Figure 16: Intention to treat effects on the number of accumulated hours of work

Figure 17 :

 17 Figure 17: Intention to treat effects on the number of accumulated hours of work among job seekers with potential benefit duration superior or equal to 2 years

Figure 18 :

 18 Figure 18: Intention to treat effects on the probability to have a regular job for at least 3 months

Figure 19 :

 19 Figure 19: Intention to treat effects on the probability to have a regular job for at least 6 months

Figure 20 :

 20 Figure 20: Intention to treat effects on the probability to have a regular job for at least 12 months

Figure A2 :

 A2 Figure A2: Screenshot of the message received by job seekers (example with gains in net terms)

Figure C4 :

 C4 Figure C4: Distribution of the number of months in part-time unemployment among those who worked while on claim

Figure C5 :

 C5 Figure C5: Distribution of the monthly number of hours worked in part-time unemployment among those who worked while on claim

Figure C6 :

 C6 Figure C6: The distribution of marginal tax rates

Figure C7 :

 C7 Figure C7: Evolution of the average marginal tax rate over the employment spell

Table 1 :

 1 Experimental lay-outNote: The upper part of this table reports the assignment to treatment probability of local agencies, the number of agencies and the number of job seekers assigned to treatment. The bottom part displays the assignment to treatment probability of job seekers in agencies assigned to treatment and the number of workers belonging to the treatment group (i.e. who received the emails), to the control group (i.e. who did not receive the emails but who were located in agencies in which other job seekers received emails) and to the super-control group (i.e. who were located in agencies in which nobody received the emails).

	1 st level of randomization : Local agencies assignment
		Treated areas	Untreated areas	All
	Assignment prob.	4/5		1/5
	Number of agencies	687		171	858
	Number of job seekers	118 229	29 649	147 878
	2 nd level of randomization : Job seekers assignment
		Treated (T) Control (C) Super-control (SC)	All
	Assignment prob.	1/2	1/2
	Number of job seekers	59 112	59 117	29 649	147 878

Table 2 :

 2 Summary statistics on the final sampleNote: This table reports descriptive statistics for the sample of individuals in January 2017, after dropping observations for individuals who were not on claim or who had already worked while on claim on 31 January 2017. Columns (1), (

		Means			p-value of the difference
	All	T	C	SC	T -C T -(C + SC) T = C = SC
	(1)	(2)	(3)	(4)	(5)	(6)	(7)

  Female equals 1 if the participant is female. Age is the age of the participant when the first email was sent. Young equals 1 if the participant is younger than 25 years old. Prime age equals 1 if the participant is between 25 and 50 years old. Senior equals 1 if the participant is above 50 years old. Lower education level equals 1 if the participant did not pass the Baccalauréat. Intermediate education level equals 1 if the participant passed the Baccalauréat. Higher education level equals 1 if the participant has a university degree. Potential benefit duration represents the maximum duration of unemployment when the participant does not work while on claim. Daily reference wage represents the daily wage earned prior unemployment. Days since entry represents the number of days since entry into unemployment when the first email was sent. Unemployment entry month represents the starting month of the participant's unemployment spell. Variables mentioning < mean (> mean) equal 1 for participants whose value of the variable in question is respectively below or above the mean. Last contract duration ≤ n months equals 1 for participants who entered into unemployment after a contract shorter than n months. Unemployment rate: unemployment rate in the area of the employment agency in December 2016. Share of part-time unemp: agency share of job seekers working while on claim in December 2016. Share of long-term unemp: agency share of job seekers whose unemployment duration is longer than one month in

the area of the employment agency in December 2016. Exit rate from unemp: agency average unemployment exit rate in December 2016. Number of claimants: number of job seekers by agency in December 2016. Number of participants: number of individuals included in our sample by agency.

Table 3 :

 3 Treatment intensity in the final sample % of treated ind. who opened the email % of treated ind. who used the simulator At 1 st

	At least	once	(8)
	At 1 st At 2 nd At 3 rd	sending sending sending	(5) (6) (7)
	At least	once	(4)
	At 2 nd At 3 rd	sending sending sending	(1) (2) (3)

Table 6 :

 6 Spillover effects on part-time unemploymentNote: This table reports the estimates of coefficients α 1 , α 2 and α 3 of equation (8). Levels of significance: * < 0.10, * * < 0.05, * * * < 0.01. Standard errors, reported in parenthesis below the coefficients, are robust and clustered at the local agency level. p-values are reported in brackets. Dependent variables are the same as in Table4. Each duration (i.e. 3, 12, and 36 months) indicates the elapsed time since treatment. Covariates include all stratum variables reported in Table2as well as entry months and regions fixed effects. The sample comprises the control group and the super control group only. "Control" (coefficient α 1 ) is a dummy for individuals in treated area but not treated. "Low" (coefficient α 2 ) is a dummy for areas in the bottom tercile of the unemployment rate. "Low × Control" (coefficient α 3 ) is the interaction term. The number of observations N corresponds to the number of individuals.

		3 months	12 months	36 months
		(1)	(2)	(3)	(4)	(5)	(6)
	Panel A : Cumulative number of months with work while on claim
	Control	-0.0015	0.0006	0.0047	0.0142	-0.0367	-0.0114
		(0.0043) (0.0041)	(0.0187)	(0.0162)	(0.0545)	(0.0430)
		[0.725]	[0.891]	[0.799]	[0.379]	[0.501]	[0.790]
	Low	0.0025	-0.0035	0.0545**	-0.0219	0.2887***	-0.0278
		(0.0066) (0.0075)	(0.0236)	(0.0276)	(0.0691)	(0.0754)
		[0.707]	[0.638]	[0.021]	[0.429]	[0.000]	[0.713]
	Low X Control	-0.0005 -0.0003	-0.0018	0.0012	0.0316	0.0309
		(0.0079) (0.0073)	(0.0301)	(0.0267)	(0.0879)	(0.0723)
		[0.946]	[0.970]	[0.953]	[0.965]	[0.719]	[0.669]
	Mean super control	0.10		0.57		1.70
	Panel B : Cumulative number of hours worked while on claim
	Control	-0.2188 -0.0466	-0.4772	0.2655	-3.7746	-1.3492
		(0.3031) (0.2926)	(1.5610)	(1.3726)	(5.2196)	(4.1148)
		[0.471]	[0.873]	[0.760]	[0.847]	[0.470]	[0.743]
	Low	0.7206	-0.0510	8.7680***	0.2101	39.7589***	3.5531
		(0.5002) (0.5525)	(2.1647)	(2.3707)	(7.4701)	(7.7616)
		[0.150]	[0.926]	[0.000]	[0.929]	[0.000]	[0.647]
	Low X Control	-0.0246 -0.0472	-0.8199	-1.0094	-1.1072	-3.0131
		(0.5859) (0.5532)	(2.7197)	(2.4288)	(9.3550)	(7.6591)
		[0.966]	[0.932]	[0.763]	[0.678]	[0.906]	[0.694]
	Mean super control	5.75		40.76		135.85
	Panel C : Cumulative earnings (in euro) from work while on claim
	Control	-2.9422 -0.9830	-7.4255	0.2810	-38.7499	-12.8498
		(3.9135) (3.6114) (22.1168) (17.4544) (73.9316)	(53.5499)
		[0.452]	[0.786]	[0.737]	[0.987]	[0.600]	[0.810]
	Low	13.4765* 2.6427 142.4420*** 15.2339 641.1864*** 106.4218
		(7.1747) (7.7183) (31.2417) (31.7882) (112.2593) (104.2902)
		[0.061]	[0.732]	[0.000]	[0.632]	[0.000]	[0.308]
	Low X Control	-4.9249 -5.9131	-24.7816	-33.4379	-71.7663	-122.5675
		(8.0957) (7.6851) (38.4159) (33.3205) (137.1450) (107.4938)
		[0.543]	[0.442]	[0.519]	[0.316]	[0.601]	[0.255]
	Mean super control	69.46		501.78		1709.82
	Covariates	No	Yes	No	Yes	No	Yes
	N	69356	69356	69356	69356	69356	69356

Table 8 :

 8 Summary statistics on individuals working while on claim at least once 6 months after the start of the treatment

			Means			p-value of the difference
		All	T	C	SC	T -C T -(C + SC) T = C = SC
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Job seekers characteristics
	Female	.504	.508	.501	.5	.503	.431	.728
	Age	31.169	31.08 31.213 31.266 .547	.451	.751
	Young	.418	.422	.413	.42	.345	.447	.636
	Prime age	.462	.461	.466	.456	.639	.895	.774
	Senior	.12	.117	.121	.125	.474	.308	.563
	Lower secondary education	.236	.234	.239	.235	.53	.625	.805
	Upper secondary education	.488	.488	.489	.486	.92	1	.978
	Higher education	.276	.278	.272	.279	.477	.661	.732
	Last contract inf to 12 m	.353	.357	.347	.354	.272	.365	.535
	Last contract inf to 3 m	.103	.108	.098	.104	.077	.137	.18
	Potential benefit duration	611.635 611.155 612.156 611.589 .833	.852	.975
	PBD inf to 730 days	.448	.451	.448	.445	.759	.664	.905
	PBD sup or eq to 730 days	.552	.549	.552	.555	.759	.664	.905
	Daily Reference Wage	60.125 60.546 59.673 60.155 .281	.422	.547
	DRW below the mean	.66	.663	.663	.648	.994	.554	.581
	DRW above the mean	.34	.337	.337	.352	.994	.554	.581
	Days since entry in unemp	105.976 106.241 105.793 105.789 .569	.548	.835
	Tenure inf to 3 months	.423	.426	.423	.416	.772	.586	.754
	Tenure between 4 and 6 months	.577	.574	.577	.584	.772	.586	.754
	Local agencies characteristics
	Number of participants	214.148 217.323 214.428 206.974 .177	.18	.33
	Number of claimants	4356.972 4371.09 4340.28 4361.041 .322	.706	.637
	Share of part time unemp	.444	.443	.443	.449	.797	.46	.571
	Share of long-term unemp	.431	.431	.431	.431	.866	.962	.988
	Exit rate from unemp	.064	.064	.064	.064	.535	.547	.781
	Unemployment rate	13.817 13.761 13.917 13.733 .102	.48	.296
	N	13240	5419	5218	2603

Table 9 :

 9 Treatment heterogeneity conditional on predicted part-time unemployment activity

		After 3 months After 12 months After 36 months
		(1)	(2)	(3)
	Panel A : Prob. to work while on claim at least once
	Treated	0.001	-0.000	0.001
		(0.0018)	(0.0032)	(0.0037)
		[0.611]	[0.892]	[0.873]
	Treated × Above median	0.010**	0.010*	0.007
		(0.0040)	(0.0055)	(0.0060)
		[0.011]	[0.069]	[0.218]
	Mean super control	0.06	0.19	0.30
	Panel B : Cumulative number of months with work while on claim
	Treated	0.001	0.006	0.038
		(0.0032)	(0.0114)	(0.0250)
		[0.833]	[0.574]	[0.133]
	Treated × Above median	0.013**	0.048**	0.100
		(0.0063)	(0.0234)	(0.0649)
		[0.037]	[0.039]	[0.123]
	Mean super control	0.10	0.57	1.70
	Panel C : Cumulative number of hours worked while on claim
	Treated	-0.102	-0.565	1.696
		(0.1952)	(0.8271)	(1.8660)
		[0.601]	[0.494]	[0.364]
	Treated × Above median	1.591***	7.105***	12.116*
		(0.5294)	(2.1583)	(6.3581)
		[0.003]	[0.001]	[0.057]
	Mean super control	5.75	40.76	135.85
	Panel D : Cumulative earnings (in euro) from work while on claim
	Treated	-0.445	-7.187	14.584
		(2.1089)	(8.4265)	(18.8816)
		[0.833]	[0.394]	[0.440]
	Treated × Above median	21.132***	102.325***	210.609**
		(7.0557)	(28.4939)	(84.0406)
		[0.003]	[0.000]	[0.012]
	Mean super control	69.46	501.78	1709.82
	Covariates	Yes	Yes	Yes
	N	92391	92391	92391

Table B1 :

 B1 Summary statistics on the overall sampleNote: This table reports descriptive statistics for the sample of individuals on January 2017 before dropping observations for individuals who were not on claim or who had already worked while on claim on 31 January 2017. Columns (1), (

			Means		p-value of the difference
		All	T	C	SC	T -C T -(C + SC) T = C = SC
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
	Job seekers characteristics
	Worked while on claim before treatment	.127	.126	.126	.13	.868	.371	.414
	Still on claim at treatment date	.901	.901	.9	.905	.858	.354	.404
	Female	.477	.479	.479	.472	.946	.403	.138
	Age	31.5	31.511	31.498	31.484 .863	.97	.977
	Young	.419	.416	.418	.43	.436	.514	.265
	Prime age	.442	.446	.445	.429	.735	.24	.237
	Senior	.139	.139	.137	.141	.531	.342	.632
	Lower education level	.224	.224	.222	.228	.321	.237	.462
	Intermediate education level	.435	.431	.433	.446	.332	.531	.195
	Higher education level	.341	.345	.345	.326	.887	.219	.365
	Last contract duration ≤ to 12 months	.367	.365	.365	.375	.941	.374	.567
	Last contract duration ≤ to 3 months	.106	.105	.106	.109	.898	.669	.754
	Potential benefit duration	601.958 602.089 602.836 599.949 .632	.522	.807
	... < 730 days	.469	.47	.468	.471	.659	.677	.891
	... ≥ 730 days	.531	.53	.532	.529	.659	.677	.891
	Daily Reference Wage	60.245	60.457	60.472	59.371 .957	.603	.866
	... ≤ the mean	.669	.667	.669	.673	.492	.964	.698
	... > the mean	.331	.333	.331	.327	.492	.964	.698
	Unemployment entry month
	July 2016	.156	.157	.154	.156	.146	.17	.315
	August 2016	.161	.161	.163	.157	.352	.091	.126
	September 2016	.288	.288	.288	.289	.89	.774	.938
	October 2016	.232	.231	.233	.231	.389	.398	.648
	November 2016	.163	.163	.162	.167	.781	.401	.522
	Local Agencies characteristics
	Unemployment rate	13.705	13.712	13.712	13.678 .983	.922	.994
	Share of part time unemp	.435	.434	.434	.44	.245	.329	.318
	Share of recurrent job seekers	.429	.429	.429	.428	.37	.958	.612
	Exit rate from unemp	.064	.064	.064	.064	.215	.526	.416
	Number of claimants	4365.983 4367.24 4378.652 4338.219 .227	.701	.398
	Number of participants	223.505 225.884 226.813 212.166 .172	.119	.129
	N	147878	59112	59117	29649

Table B8 :

 B8 Correlations between individual / local characteristics and part-time unemployment activity 3 months after the treatment in the super control group < 0.10, * * < 0.05, * * * < 0.01. Standard errors, reported in parenthesis below the coefficients, are robust and clustered at the local agency level. Each column displays the results from an OLS regression of the associated outcome on the listed covariates as well as entry months and regional fixed effects. The number of observations N corresponds to the number of individuals.

	Outcome measured 3 months	Prob. to work	Cumulated nb. of	Cumulated nb. of	Cumulated earnings
	after the treatment	while on claim at least once	months worked while on claim	hours worked while on claim	from work while on claim
		(1)	(2)	(3)	(4)
	Job seekers characteristics
	Female	0.012***	0.023***	1.044**	14.795**
		(0.0033)	(0.0055)	(0.4290)	(6.2267)
	Young	0.006	0.002	-0.868*	-5.699
		(0.0040)	(0.0070)	(0.4909)	(6.4642)
	Senior	-0.021***	-0.032***	-2.207**	-24.535*
		(0.0058)	(0.0103)	(0.8530)	(12.4490)
	Higher education	-0.015***	-0.026***	-0.801	-4.669
		(0.0040)	(0.0068)	(0.4973)	(6.2285)
	Lower secondary education	-0.009**	-0.017**	-1.177***	-10.093*
		(0.0042)	(0.0070)	(0.4414)	(5.3815)
	Potential benefit duration	0.000	0.000	0.001	0.016
		(0.0000)	(0.0000)	(0.0014)	(0.0193)
	Daily Reference Wage	0.000**	0.000***	0.035***	0.698***
		(0.0000)	(0.0001)	(0.0072)	(0.1613)
	Last contract inf. to 3 m.	0.009	0.018	1.483*	15.822
		(0.0075)	(0.0116)	(0.8350)	(9.8805)
	Last contract inf. to 12 m.	0.013**	0.012	0.941	10.170
		(0.0055)	(0.0094)	(0.6926)	(9.3814)
	Local agencies characteristics
	Number of participants	-0.000	-0.000	-0.006	-0.034
		(0.0001)	(0.0001)	(0.0051)	(0.0830)
	Number of claimants	0.000*	0.000*	0.000	0.002
		(0.0000)	(0.0000)	(0.0003)	(0.0038)
	Share of part-time unemp.	0.049	0.055	1.488	0.951
		(0.0431)	(0.0704)	(5.5228)	(88.3497)
	Exit rate from unemp	-0.133	0.022	3.992	-75.241
		(0.3174)	(0.4961)	(37.5766)	(492.3760)
	Share of recurrent job seekers	-0.057	-0.067	3.723	68.471
		(0.0684)	(0.1109)	(7.2266)	(103.8840)
	Unemployment rate	-0.000	-0.000	-0.052	-0.826
		(0.0004)	(0.0006)	(0.0429)	(0.5294)
	N	23156	23156	23156	23156
	R 2	0.007	0.006	0.006	0.009

Note: Levels of significance: *

Table B9 :

 B9 Correlations between individual / local characteristics and part-time unemployment activity 12 months after the treatment in the super control group < 0.10, * * < 0.05, * * * < 0.01. Standard errors, reported in parenthesis below the coefficients, are robust and clustered at the local agency level. Each column displays the results from an OLS regression of the associated outcome on the listed covariates as well as entry months and regional fixed effects. The number of observations N corresponds to the number of individuals.

	Outcome measured 12 months	Prob. to work	Cumulated nb. of	Cumulated nb. of	Cumulated earnings
	after the treatment	while on claim at least once	months worked while on claim	hours worked while on claim	from work while on claim
		(1)	(2)	(3)	(4)
	Job seekers characteristics
	Female	0.035***	0.193***	13.562***	169.492***
		(0.0052)	(0.0231)	(2.1664)	(28.2983)
	Young	0.008	-0.103***	-12.496***	-117.510***
		(0.0068)	(0.0250)	(2.3262)	(31.3109)
	Senior	-0.109***	-0.300***	-24.269***	-285.148***
		(0.0100)	(0.0446)	(4.1396)	(58.4379)
	Higher education	-0.039***	-0.124***	-4.981*	-16.307
		(0.0067)	(0.0274)	(2.5520)	(32.9411)
	Lower secondary education	-0.004	-0.048*	-5.076**	-38.191
		(0.0059)	(0.0248)	(2.1947)	(28.0274)
	Potential benefit duration	0.000***	0.000***	0.027***	0.307***
		(0.0000)	(0.0001)	(0.0061)	(0.0788)
	Daily Reference Wage	0.000**	0.002***	0.355***	6.632***
		(0.0001)	(0.0004)	(0.0510)	(0.9395)
	Last contract inf. to 3 m.	0.012	0.039	1.774	14.672
		(0.0111)	(0.0345)	(2.8504)	(33.7341)
	Last contract inf. to 12 m.	0.002	-0.040	-2.660	-39.970
		(0.0089)	(0.0348)	(3.0241)	(38.5039)
	Local agencies characteristics
	Number of participants	-0.000***	-0.001***	-0.075***	-0.889**
		(0.0001)	(0.0002)	(0.0237)	(0.3426)
	Number of claimants	0.000***	0.000***	0.003***	0.043**
		(0.0000)	(0.0000)	(0.0012)	(0.0170)
	Share of part-time unemp.	0.165***	0.578***	24.608	210.025
		(0.0605)	(0.2168)	(21.7140)	(324.3254)
	Share of recurrent job seekers	0.091	0.426	54.738	638.739
		(0.0978)	(0.3727)	(35.4824)	(476.4667)
	Exit rate from unemp.	0.290	0.507	94.238	809.370
		(0.4377)	(1.7558)	(174.9111)	(2261.9591)
	Unemployment rate	0.001	-0.002	-0.307	-5.034*
		(0.0005)	(0.0022)	(0.1964)	(2.6034)
	N	23156	23156	23156	23156
	R 2	0.018	0.019	0.026	0.035

Note: Levels of significance: *

Table B10 :

 B10 Correlations between individual / local characteristics and part-time unemployment activity 36 months after the treatment in the super control group

	Outcome measured 36 months	Prob. to work	Cumulated nb. of	Cumulated nb. of	Cumulated earnings
	after the treatment	while on claim at least once	months worked while on claim	hours worked while on claim	from work while on claim
		(1)	(2)	(3)	(4)
	Job seekers characteristics
	Female	0.058***	0.754***	58.392***	733.635***
		(0.0062)	(0.0641)	(6.2670)	(80.8263)
	Young	0.018**	-0.430***	-43.769***	-354.968***
		(0.0075)	(0.0667)	(6.5472)	(87.0175)
	Senior	-0.154***	-0.538***	-50.469***	-581.447***
		(0.0126)	(0.1187)	(12.4086)	(182.4914)
	Higher education	-0.076***	-0.366***	-23.598***	-150.368
		(0.0080)	(0.0713)	(7.6686)	(102.1160)
	Lower secondary education	0.009	-0.126*	-18.880**	-149.567
		(0.0076)	(0.0743)	(7.4010)	(94.7158)
	Potential benefit duration	0.000***	0.002***	0.125***	1.399***
		(0.0000)	(0.0002)	(0.0155)	(0.2088)
	Daily Reference Wage	0.000***	0.010***	1.548***	29.057***
		(0.0001)	(0.0012)	(0.1536)	(2.7619)
	Last contract inf. to 3 m.	0.027*	0.109	3.562	3.077
		(0.0139)	(0.0809)	(7.1952)	(89.1138)
	Last contract inf. to 12 m.	-0.003	-0.166**	-14.454*	-198.793*
		(0.0102)	(0.0793)	(8.2918)	(110.1325)
	Local agencies characteristics
	Number of participants	-0.000**	-0.003***	-0.268***	-3.381***
		(0.0001)	(0.0007)	(0.0780)	(1.0473)
	Number of claimants	0.000	0.000**	0.009**	0.125**
		(0.0000)	(0.0000)	(0.0042)	(0.0581)
	Share of part-time unemp.	0.164*	2.404***	177.679**	2327.809**
		(0.0923)	(0.6474)	(75.8056)	(1098.0432)
	Exit rate from unemp	1.199**	1.979	48.165	-3301.319
		(0.5670)	(5.2555)	(547.9057)	(7248.3622)
	Share of recurrent job seekers	0.239*	1.044	92.367	528.277
		(0.1225)	(1.0487)	(111.2905)	(1566.6654)
	Unemployment rate	0.001	-0.008	-1.070*	-18.106**
		(0.0007)	(0.0060)	(0.5970)	(8.1095)
	N	23156	23156	23156	23156
	R 2	0.031	0.043	0.051	0.065

Regular jobs usually include permanent full-time jobs or full-time temporary jobs of long duration.

See Ek[START_REF] Spector | Should unemployment insurance cover partial unemployment?[END_REF] and[START_REF] Cahuc | Wage insurance, part-time unemployment insurance and short-time work in the xxi century[END_REF].

Note that the anticipation channel highlighted by the model implies that it is not possible to use the informational treatment as an instrument to study the effect of part-time work on the exit rate from unemployment since the treatment can change the exit rate from unemployment of individuals who do not work while on claim.

As explained below, working while on claim moves the exhaustion date of the unemployment benefits scheduled at the date of entry into unemployment. Throughout this paper, by initial exhaustion date we mean the exhaustion date which is scheduled at the start of the unemployment spell.

Note once again, that this results is in line with the prediction of the job search model.

Recipients accepting part-time jobs can earn up to a specific amount, called the "disregard", with no reduction in benefits during the reference period, which can be the week or the month. Above the disregard, the current benefits are reduced in proportion to the labor earnings. There is a disregard in several U.S. states, in Australia, Austria, Belgium, Canada, Czech Republic, Germany, Luxembourg, Poland.

Note that part-time unemployment insurance drastically changes the possibility of renewing the entitlement period. In the absence of part-time unemployment, when the insurance capital is exhausted, individuals must have worked at least 150 hours while on claim over the last 28 months to be eligible for a new entitlement period. The new initial capital is computed on the basis of the daily wage of periods of work and according to the rule "one day of work yields one day of compensation". In the presence of part-time unemployment, the hours worked during the entitlement not only make it possible to delay the end date of entitlements but also to accumulate hours for the opening of a new entitlement period. We neglect the opening of a new entitlement period to lighten the presentation, but it is taken into account when we come to compute the marginal tax rate in Section C, FiguresC6 and C7.

Note that this distribution may have a support including zero earnings which could be interpreted as a situation without job offer.

The differences between treated and non-treated individuals will be shown in Section 5.3.

Note that the value zero of the minimum level of effort is a normalization. This minimum effort level can correspond to the minimum effort that the public employment agency can require.

The gain from working while on claim with earnings z t , equal to∆ ≃ [z t (1 -τ ) -κ] v ′ (b) + τ zU ′ (B t ) + β [λ(e t , 1) -λ(e t , 0)] [W -U (B t+1 )]is higher in the presence of stepping stones effects, i.e. λ(e t , 1) -λ(e t , 0) > 0.

Hence, as stressed by[START_REF] Kyyrä | Partial unemployment insurance benefits and the transition rate to regular work[END_REF], the timing-of-events approach, which estimates the direct effect of working while on claim can be relevant to an estimate of the effect of working on non-regular jobs under the existing unemployment insurance scheme, but cannot estimate the full impact of part-time unemployment insurance schemes.

To the best of our knowledge, this type of channel, which has been analyzed in the context of monetary economics which have exhibited signalling effects of monetary policy[START_REF] Melosi | Signalling Effects of Monetary Policy[END_REF],[START_REF] Nakamura | High-Frequency Identification of Monetary Non-Neutrality: The Information Effect[END_REF]), has not been studied in labor economics.

Note that an effective variation in the marginal tax rate τ on current labor earnings can be interpreted by job seekers as a sign of changes in the rate of arrival of job offers anticipated by the government. As such, the diversity of possible interpretations of the informational treatment can also concern changes in the effective rules of part-time unemployment insurance.

It is very unlikely that our information provision could have been interpreted as a threat likely to modify job search behavior in the French context where there is almost no control of job search activity. In line with our interpretation,[START_REF] Crépon | Information shocks and the empirical evaluation of training programs during unemployment spells[END_REF] do not find any threat effect of notifications of training proposals in France.

[START_REF] Altmann | Do Job Seekers Understand the UI Benefit System (and Does It Matter)?[END_REF] find similar results in Denmark.

The exact contents of the emails is presented in appendix A.5. We sent two different types of email. One type presents the gains from labor earnings in net terms (i.e. after payment of the employee's social contributions. Income taxes, which depend on the situation of each person, cannot be computed at this stage) and the other type in gross terms. Insofar as we do not detect any statistically significant difference between the effects induced by these two types of message, we do not consider this heterogeneity of treatment in what follows.

We present summary statistics for the variables that were used for stratification in Table2.

90% of hiring intentions do become effective hires.

As remarked above, for people with higher elapsed unemployment duration at treatment date, our sample is less representative of newly registered job seekers. However, as shown in TableB7, the treatment effect does not significantly depend on the elapsed unemployment duration at treatment date.

We know the exact number of hours worked for individuals who are still registered at employment agencies but we have no information on the number of hours worked of individuals who definitely exit unemployment in our period. In this case, the number of hours worked is computed by assuming that individuals who exit toward regular employment are working at the same intensity as before their unemployment spell.

Up to a limit of 4 times the social security ceiling (13,076 euros per month).

e t = 0 for all t ≤ t 0 ∈]0, T [, e t > 0 for all t > t 0 , e t < e t+1 for all t ∈ [t 0 , T [ and e t = e T for all t ≥ T if e T > 0,. This situation arises when the expected gains from job search effort at the start of the unemployment spell are low because the initial expected value of unemployment

All the results reported below are based on the specification including covariates.

As a comparison Young (2019), used 10 000 repetitions but did not detect any appreciable difference above 2000 draws.

* This project has been approved and funded by the chair Sécurisation des Parcours Professionnels. It has been administratively supported by the Institut Louis Bachelier. Hélène Benghalem has benefited from financial support through Swiss National Science Foundation Grant No.100018 178878. We thank Pôle Emploi for the operational support and especially Anita Bonnet, Stéphane Ducatez, Cyril Nouveau and participants in a Pôle Emploi seminar. The pre-analysis plan, approved by the chair Sécurisation des Parcours Professionnels, is available here.

Note: Levels of significance: * < 0.10, * * < 0.05, * * * < 0.01. Standard errors, reported in parenthesis below the coefficients, are robust and clustered at the local agency level. p-values are reported in brackets. Each duration (i.e. 3, 12, and 36 months) indicates the elapsed time since treatment. Covariates include all stratum variables reported in Table 2 as well as entry months and regional fixed effects. "Treated" designates individuals who were assigned to treatment (ITT estimate), "In treated area" refers to those registered at employment agencies where half of individuals have been treated and "super control" designates individuals registered at employment agencies where nobody has been treated. The number of observations N corresponds to the number of individuals. 2as well as entry months and regional fixed effects. "Treated" designates individuals who were assigned to treatment (ITT estimate), "In treated area" refers to those registered at employment agencies where half of individuals have been treated and "super control" designates individuals registered at employment agencies where nobody has been treated. The number of observations N corresponds to the number of individuals.

A.2 Job search model solution

Maximization of program (4) with respect to the search effort e t yields the first order condition:

where η t ≥ 0 stands for the multiplier associated with the constraint e t ≥ 0. This equation defines the optimal search effort e t in each period. In order to analyze how e t evolves over time one needs to know how U (B t+1 ) evolves. We know that B t decreases over time. Therefore, it suffices to know the sign of the derivative of U to know how e t evolves. One can show that U ′ (B) > 0. The envelope theorem implies that

In equation (A2), the case where U ′ (B t ) = v ′ (c t ) arises the period just before the total exhaustion of the unemployment insurance capital

) in the top of the right hand side of equation (A2) shows that U ′ (B t ) > 0 in all periods, implying that U (B t ) decreases over time since B t decreases over time.

Let us first consider the case where η t > 0. We get from equation (A1)

We just showed that U (B t ) decreases with t for all t < T and reaches the minimum value U (0) for all t ≥ T where T stands for the benefits exhaustion date T . Thus, this equation implies that η t > 0 and then e t = 0 for all t iff

This situation can arise when the gap between the value of employment and the value of unemployment after the date of exhaustion of benefits is small. Now, let us consider the case where U (0) is small enough to yield a positive search effort at the benefits exhaustion date T and assume that ∃t < T such that e t > 0. In this case, e t is defined by equation (A1) with η t = 0. Since λ ′′ (e t ) < 0, differentiation of equation (A1) implies that

and then that the search effort e t increases over time since U (B t ) decreases over time. Therefore, the optimal search effort can take 3 different types of time profiles depending on the values of parameters:

1. e t = 0 for all t if e T = 0. This situation arises when the expected gains from job search effort are low.

is high, but declines enough over time to trigger positive search effort before reaching the date of exhaustion of benefits.

3. e t > 0 for all t, e t < e t+1 for all t < T and e t = e T for all t ≥ T if e T > 0,. This situation arises when the expected gains from job search effort are high from the start of the unemployment spell.

Now, let us look at the choice of working while on claim. Since we look for the reservation level of earnings from work while on claim in situations where individuals accumulate unemployment benefits b and earnings from work while on claim z t , which arise when z t < b+(1-τ )z t , we can focus on the case z t < b/τ without loss of generality to determine this reservation level. Maximization of program (4) with respect to Ω t implies that individuals prefer to work while on claim (i.e. choose Ω t = 1) if and only if this yields utility gains ∆ 0. The first order approximation of the utility gains from work while on claim with earnings z t can be computed using equation ( 4):

Equation (3) implies that dB t+1 = τ z t , when an individual earns z t from working while on claim compared with the situation in which she does not work. Using equation (A2) we get:

The first term of the right hand side, [z t (1 -τ ) -κ] v ′ (b), corresponds to the increase in the marginal utility of the current period induced by the increase in current consumption and the second term, τ z t U ′ (B t ), corresponds to the increase in the future expected consumption. From equation (A2) we know that U ′ (B t ) increases along the unemployment spell, because β(1 -e t λ) < 1 implies that U ′ (B t ) < U ′ (B t+1 ). This property, together with equation (A4), implies that the incentives to work while on claim increase over time. Now, let us show that equation (A4) implies that the effects of the part-time unemployment insurance scheme on the propensity to work while on claim depend on a single parameter, the marginal taxation rate, which encapsulates all the parameters of the part-time unemployment insurance scheme.

The expected discounted income from work while on claim in period t for an individual who gets benefits until the exhaustion date T -i.e. period T where B T = 0 and B T -1 > 0 according to the law of motion (3)-is equal to the instantaneous income, z t (1 -τ ), plus the future income that the individual can expect T if she is still unemployed in that period T -1. Note that, for the sake of simplicity in this discrete time framework, we assume that the taxed earnings from work while on claim increase the income in the last period before the exhaustion date, and neglect the situation where these taxed earnings move the exhaustion date, without loss of generality. Thus, the expected discounted income from earnings z from working while on claim in period t in the neighborhood of c T = b is equal to

By definition, the marginal taxation rate in period t, denoted by m t , is equal to 1 -(dy t /dz t ), which yields, from the previous equation

Using equation (A2) to compute U ′ (B t ) recursively from the last period T in which unemployed benefits are collected, we get, in the neighborhood of c T = b:

From equations (A5) and (A6), we get

where m t is defined by equation (A5). Equation (A8) implies that it is worth working while on claim in period t if and only if

A.4 Heterogeneous treatment effects

This appendix describes the estimation of heterogeneous treatment effects following the approach of [START_REF] Chernozhukov | Generic machine learning inference on heterogenous treatment effects in randomized experiments[END_REF]. The Conditional Average Treatment Effect (CATE) function is:

where X denotes a vector of covariates and Y is the outcome of interest.

We start by splitting evenly the whole sample into a main subsample, used to predict s 0 (X), and an auxiliary subsample, used to estimate the key features of s 0 (X). The auxiliary sample is used to predict s 0 (X) with machine learning (e.g. Elastic Net, Random Forest). We estimate the model separately for observations in the treatment and control groups, resulting in two prediction models. We then compute the estimated outcome for each observation in the main sample under both treatment statuses, i.e. Ŷ T (X i ) and Ŷ C (X i ) and the estimated propensity score p(X i ). Finally we compute Ŝ(X i ) = Ŷ T (X i ) -Ŷ C (X i ) our proxy for the true CATE, s 0 (X i ). However, except under strong assumptions about the ML estimator, this proxy predictor is likely to be an inconsistent estimate of s 0 (X i ). This motivates the second step of the procedure where the ML proxy is postprocessed into the estimates of the key features of s 0 (X i ).

To estimate the best linear predictor of the conditional average treatment effect function we run the following weighted regression

where Z i is an indicator variable equal to 1 for treated individuals, E denotes the empirical expectation with respect to the main sample and the weights are equal to [START_REF] Chernozhukov | Generic machine learning inference on heterogenous treatment effects in randomized experiments[END_REF] show that β 1 + β 2 ( Ŝ(X i ) -E Ŝ(X i )) identifies the best linear predictor of the conditional average treatment effect s 0 (X i ). Besides, β 1 identifies the average treatment effect (ATE) and rejecting the null hypothesis that β 2 = 0 therefore means that there is both heterogeneity and Ŝ(X i ) captures a relevant part of this heterogeneity. Table B5 presents our estimates of the best linear predictor of the conditional average treatment effect.

Next we estimate the sorted group average treatment effects. Here the parameters of interest are E[s 0 (X i )|G], where G is an indicator of group membership based on our proxy predictor Ŝ(X i ). As shown by [START_REF] Chernozhukov | Generic machine learning inference on heterogenous treatment effects in randomized experiments[END_REF], we can recover these parameters by estimating the following weighted regression:

where the weights are the same as in equation (A9) and 1(G k ) is equal to 1 if Ŝ(X i ) lies in the k th interval and 0 otherwise. We cut Ŝ(X i ) at 50 th , 75 th , 90 th , 95 th percentiles. In particular, Group 1 corresponds to the observations that lie in the bottom 50% of Ŝ(X i ) and Group 5 corresponds to the observations that lie in the top 5% Ŝ(X i ). Table B6 displays the results we obtained by estimating equation (A10). 2 as well as entry months and regional fixed effects. "Treated" designates individuals who were assigned to treatment (ITT estimate), "In treated area" refers to those registered at employment agencies where half of individuals have been treated and "super control" designates individuals registered at employment agencies where nobody has been treated. The number of observations N corresponds to the number of individuals. Note: Levels of significance: * < 0.10, * * < 0.05, * * * < 0.01. Standard errors, reported in parenthesis below the coefficients, are robust and clustered at the local agency level. p-values are reported in brackets. Each column displays the results from an OLS regression of the associated outcome based on equation (7). "Treated" designates individuals who were assigned to treatment (ITT estimate). "Above median" designates individuals whose elapsed unemployment duration at treatment date is above median, which corresponds to ∼4,5 months. Each regression include the list of covariates reported in the summary statistics (see Table 2) as well as regions fixed effects. Entry months fixed effects are not included in these regressions to avoid collinearity issues with the "Above median" regressor. The number of observations N corresponds to the number of individuals.

A.5 Emails contents

C Supplementary Figures