The Short-Time Compensation Program in France: an Efficient Measure against Redundancies? * Oana Calavrezo∗∗, Richard Duhautois∗∗∗, Emmanuelle Walkowiak∗∗∗∗

April 2008

Abstract The short-time compensation (STC) program aims at avoiding layoffs in case of short-term downturns. This paper investigates the relationship between the STC recourse and establishments’ redundancy behaviour over the period 1996-2004. We test panel data models with sample selection, endogenous explanatory variables and unobserved heterogeneity, developed by Semykina and Wooldridge (2006). We work with an unbalanced panel which results from the matching of four administrative databases. Our panel includes more than 36,000 establishments with at least 50 employees and 204,000 observations. We show that the participation in the STC program does not protect from redundancies.

Key words: Short–time compensation program, layoffs, fixed effects, instrumental variables, sample selection JEL classification: J22, J63, C23

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Acknowledgements: This paper is a prolongation of a project financed by the Statistical Department of the French Labour Ministry (DARES). We are very grateful to Anastasia Semykina and Jeffrey Wooldridge for their kindness and help in estimating the asymptotic variance. We would also like to thank participants at CEE’s seminar, LEO’s Wednesday Lunch Seminar, THEMA’s Lunch Seminar, DEVA CEREQ Seminar and LEO’s Thursday Research Seminar and in particular Jean-Paul Pollin, Régis Breton, Christophe Hurlin, Sébastien Ringuedé, Marianne Cornu-Pauchet, Emmanuel Duguet and Alberto Lopez. All remaining errors and shortcomings remain our own. Data availability: Final panel data is available on request from the authors and the initial databases can be requested from the institutions which produce them. ∗∗ Corresponding author: Laboratoire d’Economie d’Orléans (LEO) and Centre d’Etudes de l’Emploi (CEE). Address : LEO, Faculté de Droit, d’Economie et de Gestion, Rue de Blois, BP6739, 45067, Orléans, CEDEX 2 Telephone number : 01 45 92 69 72 - Fax : 01 45 92 69 97 E-mail: [email protected] ∗∗∗ CEE, CREST and Université de Marne-la-Vallée. [email protected] ∗∗∗∗ LEO and CEE. [email protected]

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1. Introduction A rich empirical literature regarding the evolution of flexibility practices has been developing since the eighties in Europe. Flexibility policies are related to external quantitative flexibility (for example, fixed-term contracts, temporary work, redundancies, etc.), internal quantitative flexibility (such as flexible working hours) and internal qualitative flexibility (workers’ polyvalence) (OECD, 1995). This paper studies the efficiency of the Short-Time Compensation (STC) program in France. STC gives the right to firms to reduce their activity below the legal working time duration in case of short-term downturns. The STC program provides internal and quantitative flexibility since it acts on the volume of worked hours and on the number of employees inside the firm. It represents a specific form of work-sharing. Two main characteristics distinguish it from broadly based job sharing policies. Firstly, firms participate voluntarily in the STC program and non-participants are not directly affected. Secondly, STC is a protective device since it aims at avoiding layoffs in case of short-term downturns or exceptional circumstances (disasters, important building work and restructuring, supplying difficulties, etc.). This paper investigates the relationship between the STC recourse and establishments’ redundancy behavior in France between 1996 and 2004 and discusses the efficiency of the program. Up to now, the STC programs have mainly been analyzed from a theoretical point of view with insurance models (Van Audenrode, 1994; Houseman and Abraham, 1993). Our contribution is empirical. We test panel data models with sample selection, endogenous explanatory variables and unobserved heterogeneity on an unbalanced panel of more than 36,000 establishments with at least 50 employees. Our work is an original application of a recent econometric panel data model developed by Semykina and Wooldridge (2006). We use a rich dataset obtained by matching four administrative data sources. The sample contains approximately 204,000 observations.

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The remainder of the paper is organized as follows. The second section describes the STC programs in Europe, the US and Canada. The third section presents the data. The fourth section outlines our econometric approach; the fifth one presents our findings. Finally, the conclusion in the sixth section discusses the efficiency of the STC program in France.

2. Short-time compensation and layoffs By applying STC, firms can temporarily reduce their activity below the legal working time or stop a part or their entire activity (for more details see appendix 1). STC is a tool of preventive economic aid, which allows employees to keep a contractual bond with their employer. Employees perceive a compensation for their wage loss caused by the temporary interruption of activity. Nowadays, most of the developed countries propose a STC program to avoid layoffs: the “chômage partiel” device in France, the “Short-Time Working” instrument in Great Britain, the Italian “Cassa Integrazzione Guadagni” (CIG), the German “Kurzarbeitergeld”, the “Short-Time Compensation Program” (United States), the “Work Sharing Program” (Canada), etc. Although STC programs in North America are relatively new and underutilized, they have been widespread in Europe since the 1920s. However, in both regions, STC remains a rare phenomenon. For example, between 1995 and 2005, the STC authorizations have affected less than 1 % of French establishments and 2 % of their employees (Calavrezo et al., 2007). Similarly, during the 80s, in the US, less than 1 % of the American employers have implemented STC. From a theoretical perspective, insurance models clearly distinguish the security and flexibility roles of the STC programs, which differentiate North America and continental Europe. However, each program shares the common primary goal of avoiding layoffs during

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short-term economic downturns. Van Audenrode (1994) shows that the STC program generates major fluctuations in working hours when the system is more generous than the traditional unemployment insurance system. Consequently, the speed of adjustment of the total worked hours is longer in Europe than in the US, despite a much slower adjustment in number of employed workers. Because it is more difficult in the European countries to fire a worker or to lay one off, STC is a mechanism that makes these discharges less necessary. The argument holds good for France and explains its internal flexibility role. Similarly, Houseman and Abraham (1993) argue that in France, STC constitutes a cheap labour force adjustment mode, which raises the firms’ cost of declaring redundancies. This is due to the low flexibility of the French labour market. The flexibility role of STC is not a predominant characteristic of the US system. External flexibility is there less expensive and the STC program is relatively more costly than in Europe1. STC represents mainly a job security instrument. From an empirical perspective, analyses of the efficiency of STC programs lead to mitigated results. According to European and Canadian experiences, the STC program would avoid or delay layoffs, while in the US experience, the STC would not fulfil a job protection role. Compared with the US, in Europe, the STC program improves essentially workforce adjustments (Houseman and Abraham, 1994). This “flexibility effect” passes through an increase in work sharing and avoids layoffs (Burdett and Wright, 1989). The French case offers a good example of this “work sharing effect” associated with STC. Indeed, in France between 1995 and 2005, the working time reduction policy represented the most important shock, which influenced the STC recourse. It led to a fall in the STC recourse. In 2005, French administration authorised 1.8 million STC days. Eight years before, with a similar economic situation, the number of STC authorized days was approximately six times higher. 1

In time, 19 states have implemented the STC program. In the some states of the US, extra taxes on employers using STC represent a disincentive to the use of this instrument.

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This evolution is due to a substitution effect between STC and working time reduction. The working time reduction policy would have refocused STC on its initial job protection function (Calavrezo et al, 2007). However, Calavrezo et al. do not check the efficiency of STC in terms of employment protection in France. Vroman (1992) studies this question for the case of Germany between 1970 and 1991. He shows that STC stabilizes employment in the shortterm, but its effects do not necessarily last over time. The Canadian Ekos research (1993) provides similar results. Canadian employers report that on average, STC firms would have laid off 40% of their workforce in absence of STC. However, Canadian employers finally laid off 12% of their employees after program participation. The Ekos research also suggests that STC does not fully avoid layoffs but reduces them significantly. Discussions on how STC affected layoffs in the US inform only in an indirect way the debate in Europe. Kerachsky et al (1986) determine whether a STC use in cyclical situations implies higher costs for the unemployment insurance system than outright layoffs in three States (Oregon, California and Arizona). They show that layoffs remain predominant in STC firms. However, Schiff (1986) and Morand (1990) qualify these conclusion because they disapprove the methodology of the counterfactuals’ used by Kerachsky et al (1986). Needels et al. (1997) come across this conclusion again when they analyse the impact of STC on mass layoffs in five States (California, Florida, Kansas, New-York and Washington). STC firms are more likely to undergo large-scale workforce reductions than others, even when controlling for observable characteristics. Abraham and Houseman (1993) put these results into perspective by showing that unemployment effects depend on the layoff subsidy.

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3. Data To assess the impact of the participation to the STC French program on firms’ redundancy behaviour, we use a very original statistical dataset obtained from matching four administrative databases2. The monthly STC authorization databases: When facing a strong economic downturn an employer can administratively ask for a specified number of STC days. If the request is justifiable, the Departmental Directions of Work and Employment provides an authorization for a specified number of STC days. The files give information about the STC authorizations obtained by French establishments between 1995 and 2005. The authorized STC imperfectly measures the compensated STC that establishments really use and for which they get a financial compensation. Indeed, some establishments can decide not to use the STC authorized days. In the database, the number of compensated days is not available at establishment or firm level. Thus, we measure the number of authorized STC days. It is the superior limit of compensated days which represents an indicator of the entrepreneurial anticipations. Similar aggregated databases are used by Gray (1998) for analysing the determinants of the STC recourse in France between 1983 and 1987. Gray (1998) works at a 2 digits industry level. On the contrary, we analyse the STC behaviour at the establishment level with yearly indicators. From these databases we constituted an exhaustive STC panel. It covers more than 93,000 French establishments of all industries, which had at least one STC authorization between 1995 and 2005. This panel provides for each establishment i and for each year t information on the STC authorized days ( STC _ daysit ), the number of employees concerned by the authorizations ( STC _ empit ), the part of employees concerned by these authorizations ( P _ STCit ) and the average period of the STC per employee ( AP _ STCit ). 2

They are produced by the Statistical Department of the French Labour Ministry and the French National Institute of Statistics (INSEE).

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The “Déclarations des Mouvements de Main-d’Œuvre” (DMMO) files are quarterly exhaustive administrative databases over the period 1996-2004. They measure all workforce movements within establishments with at least 50 employees. These files inform about the general features of the establishment (size, industry, and region) and about all the workers’ entries and exits. We measure redundancy indicators (at a yearly level) by adding up establishment quarterly layoffs ( NB _ layoffsit ). The yearly establishment size indicator is the mean of the quarterly number of employees ( EST _ sizeit ). Finally, the redundancy rate ( REDit ) is the ratio of the establishment’s annual number of redundancies and the establishment’s annual average number of employees. We also calculate dummy variables for the presence of redundancies. LAYit is a dummy variable that takes the value 1 if the establishment has at least one layoff during the year and 0 otherwise. In the same way, LAY 10it is a mass redundancies dummy. In France, just like in the U.K., the threshold that releases mass layoffs is 10 layoffs during a month. We keep this threshold. The "Working Time Reduction" database contains the declarations and the agreements of the firms, which reduced their effective working time in order to benefit from the social security reduction. WTRit is a dummy variable which indicates if an establishment reduced its effective working time. It is our exclusion variable in the econometric model 4. Firm databases (the Bénéfices Réels Normaux files), over the period 1994-2003, give information about the firms to which establishments are belonging to. They contain the firm size ( F _ sizeit ) and various economic situation indicators: value-added ( VAit ); capital investment ( K _ INVit ); firm’s profits ( Π it ). Matching the four databases and cleaning out establishments with implausible values for the variation rates of the size, the value-added and the profitability reduces our sample 4

See section 4 for details on this dummy.

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around 204 000 observations. Appendix 1 details the cleaning procedure and appendix 2 explains the different indicators used. We finally work with an unbalanced panel of more than 36 000 establishments, which contains around 204 000 observations and covers the 19962004 periods. This sample includes establishments with at least 50 employees for which we have the information about their redundancy behavior. Establishments with at least 50 employees cover 70% of the total number of employees concerned by STC and approximately 64% of the total number of STC authorized days on the period 1996-2004.

4. The econometric model We implement an estimation of panel data models with sample selection, endogenous explanatory variables as well as unobserved heterogeneity. It is an original application of the econometric model proposed by Semykina and Wooldridge (2006). This relevant methodology takes into account the structure of our unbalanced panel. Longitudinal redundancy behaviour equations for firms are likely to suffer from heterogeneity, selection bias and endogeneity. Heterogeneity can be associated with individual ability, management behaviour, political orientations, and workforce managerial preferences of employers. Since these factors are likely to be correlated with the STC behaviour, simple estimation methods will not produce consistent estimators. There can also be a problem of endogeneity because the relationship or the causality between STC and layoffs is unclear. We can imagine that during a year, STC can be affected by the establishment’s redundancy behaviour5. Selection can also be a potential problem because establishments which choose to have STC authorizations might do it as a consequence of their internal strategy.

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This can be the consequence of a temporality problem in the data.

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4.1 The first stage of the model

We use a two-stage model. The first stage is represented by the selection rule standing for the STC program participation ( sit ). An establishment is considered to be a participant to the STC program if it has a number of STC authorized days superior to zero. The main problem here is the existence of an unobserved effect inside the index of the probit selection model. Provided we make appropriate linearity assumptions about the conditional expectations of the unobserved effect as in Mundlak (1978), we can obtain valid selection correction. In this way, the selection equation can be written as follows:

sit = 1[ s *it > 0] = 1[η + zitδ + ziξ + vit > 0]

(1)

1[ i] is the indicator function, t represents the time (t = 1,…,T), i the establishment (i = 1,…,N) and v it is the error term which follows a normal distribution. As for zit , it represents the set of exogenous explanatory variables: firm’s size variation rate (lagged by one year), establishment’s size, profitability rate (lagged by one year), value-added variation rate (lagged by one year), time dummies and establishment’s situation regarding to working time reduction. As we are working with an unbalanced panel, for each establishment, time dummies are weighted by the number of establishment’s appearances during the 1996-2004 period. Mundlak’s method (1978) is a method usually developed for unbalanced panels and it consists in calculating for each establishment and for each exogenous explanatory variable z the average value on the period of establishment’s appearance in the sample ( zi )6. The δ coefficient represents the within estimator that deals with individual effects.

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More precisely, Mundlak supposes that the individual effects can be written as a linear combination of individual explanatory variables’ means and an orthogonal component i.i.d. α i * .

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The ξ coefficient represents the difference between the within and the between estimators that informs about the existence of the individual effects. From the equation (1) we then estimate for each establishment i and for each year t the inverse Mills ratios ( λˆit )7. Among explanatory variables, we introduced the WTRit indicator to identify the model in an appropriate way. In fact, WTRit represents the exclusion variable. We assume that it does not explain establishments’ redundancy behaviour (the equation of the second stage of the model) but it explains only the STC recourse. Finding such an exclusion variable is a very difficult exercise because STC and layoffs are two devices that are used only when the establishment meets strong economic downturns. We can imagine that they have almost identical determinants. However, Calavrezo et al. (2007) showed that, excepting the economic situation, WTR is the only other major determinant of the STC use. On the other hand, the assumption that WTR does not have any effect on the establishments’ layoffs is very debatable, even incorrect. For this reason, we have to choose carefully the variable WTRit that has to satisfy the condition of independence from redundancies. First, we have to recall some elements of the French WTR legislation. WTR is a device that firms has implemented heterogeneously in a number of different stages: the “Robien” law in 1996, the “Aubry 1” law in 1998, the “Aubry 2” law in 2000, the “Fillon” law in 2003 and finally, the 2005 law. There is a rich French literature on the WTR behaviour that mainly focuses on its effects on employment or unemployment. The effects are very mixed. In general, establishments that reduced their working time are compared with those that did not. The identified effects depend on the WTR type and of the period of analysis: this literature shows an increase in employment between 3% and 6 % (Fiole, Passeron and Roger, 2000; Fiole and Roger, 2002, etc.) Nevertheless, the impact of WTR on employment is unclear: Crépon and Kramarz (2002) conclude that changes in the French 1982 legal standard 7

It is the ratio of the probability density function over the cumulative distribution function of a distribution.

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workweek led to employment losses contrary to the initial goals. Freeman (1998) shows that work-sharing generated by market forces can increase employment whereas legislated policies rather have negative effects. As for de Regt (2002), he shows that there is a U-shaped relationship between working time and the equilibrium unemployment rate. So according to this author, WTR can reduce unemployment only when working time is sufficiently long. Moreover, he suggests that the (un-)employment effects are rather limited. The “Robien” and the “Aubry 1” laws distinguished offensive and defensive sections. The offensive section aims at reducing firms’ working time and in the same time at creating new jobs. More precisely, the firm has to reduce its working time (by 10% at least) and to increase its workforce (by 6% at least according to the Aubry law) to receive benefits. In the defensive section, firms receive benefits when they reduce their working time (by 10% at least) in order to avoid layoffs. In addition, they have to maintain their workforce still during a certain period of time. Regarding WTR in general, Larrey (1998) develops a theoretical model and shows that reorganizing working time allows to stabilize the insecure employment and to delay postpone layoffs. A DARES paper suggests that the defensive section can be a means of calming the situation in the short-run but ultimately firms will layoff (there are no lasting effects). A recent OECD work (2004) points out that in the 90s, in Germany, WTR was used principally to avoid layoffs (the defensive section), but in France the central feature of this measure was to create employment (the offensive section). In conclusion, we have clear evidence that the defensive section of the WTR has the objective of avoiding redundancies. So, we can not assume that WTR, as a whole, does not have any effect on establishments’ layoff behaviour. We take into account this conclusion to construct the WTRit variable. The “Working time reduction” database informs about the WTR type: WTR for employment creation (offensive section), WTR in order to preserve from layoffs (defensive

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section), WTR in order to preserve from layoffs and to create employment (offensive and defensive sections) and WTR without the intention of creating employment or preserving from redundancies. We remove from the analysis the defensive section of the law. The WTRit binary indicator equals to 1 when the establishment reduced its working time but not for defensive reasons. From now on, when we will refer to WTR, we mean WTR without the defensive section. So, the direct relationship between WTR and layoffs does not exist anymore. If this type of WTR affects redundancies, we do not think that the effect transits through a direct transmission channel. To our knowledge, there is no empirical or theoretical proof regarding the direct relationship between this kind of WTR and establishments’ layoff behaviour. For all the reasons mentioned above, even if we are conscious that the WTRit variable can be criticisable, but taking into account the data and the difficulty of its identification, WTRit seems to be a good exclusion variable.

4.2 The second stage of the model In the second stage of the model, we concentrate on the establishments with sit = 1 and we estimate their redundancy behaviour8 by controlling the endogeneity bias. The estimated equation can be roughly written as follows:

yit = xit β + φ + zi µ + γλˆit + uit where the dependent variable, yit

(2)

is the number of layoffs ( NB _ layoffsit ) in the

establishment. The vector of explanatory variables xit includes a STC indicator, firm’s size variation rate (lagged by one year), establishment’s size, the profitability rate (lagged by one year), the value-added variation rate (lagged by one year) and time dummies. The STC

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We distinguish two samples: one for all the establishments with

sit = 1 (9,132 observations) and another for

the establishments having a STC recourse in at least two years (6,519 observations).

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indicator is not strictly exogenous and it can be expressed through three STC variables: the number of STC authorized days, the number of employees affected by the authorizations and the average period of the STC affectation per employee9. We introduced the inverse Mills ratios previously calculated in order to take in account a possible selection bias. If γ is significantly different from zero, it means that there is a selection bias and we control for it. However, the model can still suffer from an endogeneity bias due to the simultaneity of STC variables and the number of layoffs. We implement two different strategies to control the endogeneity bias. (i) On the one hand, we use a two-stage model. The first step of this kind of modelling consists in estimating STC indicators with STC variables lagged by one year, the inverse Mills ratio, zit without the WTR variable, zi and time dummies. As STC can be affected by the establishment’s redundancy behaviour, STC indicators lagged by one year represent our instrumental variables. By using them, we meet the conditions of controlling the endogeneity bias: they explain the STC recourse for the year t, but they are not correlated with the error term of the redundancy equation. Then, the second step of the modelling is to introduce the STC estimate in the redundancy equation. As NB _ layoffsit is a discrete number with a lot of zero values (more than 60%), we use in the second step of the modelling a zero inflated negative binomial (ZINB) model. Appendix 3 provides a presentation of ZINB models. With this method, we are able to discuss the impact of the STC participation of the French establishments at the date t on their redundancy behaviour at the date t, by controlling unobserved heterogeneity, selection and endogeneity biases.

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Among the layoff indicators we did not retain the redundancy rate ( REDit ) and among the STC indicators we

did not conserve the STC rate ( P _ STCit ). We used these two variables only for descriptive statistics. As these indicators are calculated from the establishment size and as we already control for this feature, introducing them can distort the results of the estimation.

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(ii) On the other hand, an alternative to the previous method is to estimate directly the redundancy behaviour by using STC indicators lagged by one year. With this method, we are able to discuss the impact of the STC participation of the French establishments on their redundancy behaviour, by controlling the endogeneity biases. Econometric procedures having several steps fail to account for the fact that the estimated covariance matrix contains errors, so hypothesis tests based on the estimated covariance matrix of the second-step estimator are biased, even in large samples. We implement the method developed by Semykina and Wooldridge (2006) to correct the bias. They fully detail this procedure in the appendix of their paper. Our methodology has two main differences with the model developed by Semykina and Wooldridge (2006). First, their application renders the model very intuitive and easy to understand (see for example other articles such as Dustmann and Rochina-Barrachina, 2000). They estimate earning equations for females to measure the return to labour force experience. Women’s wages can be observed only if they had positive work hours in a given year. In our case things are conceptually slightly different. We are analyzing the impact of the STC use on establishments’ layoffs behaviour. Having this information is not conditioned by the fact that an establishment had a STC recourse (our participation equation). Nevertheless, we consider this approach appropriate to our analysis because it permits controlling the STC selection bias. Second, in Semykina and Wooldridge’s paper (2006), the selection equation is estimated separately for each time period. So, they calculate for each time period an inverse Mills ratio for each individual (lambda). Finally in the main equation they introduce lambda but also the interaction terms between lambda and time dummies. In this way they control for the selection bias year per year. In our case, the inverse Mills ratios were directly calculated per year and per individual in a unique selection equation where we controlled by time

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dummies. Our model can be seen as a restricted form of the Semykina and Wooldridge’s model since we are controlling for the selection bias on the 1996-2004 period10. We preferred implementing this restricted version of their method because the phenomenon we are studying (STC) and even our exclusion indicator (WTR) are quite specific. Results are difficult to interpret when estimating the selection equation year by year and the necessary conditions of implementation cannot be met.

5. Empirical results 5.1 Description of the sample Tables 1 and 2 provide summary statistics and a more detailed description of the variables used in the models. On average, 4.5% percent of the observations of our sample participates to the STC program. It shows that using the device is a very rare phenomenon. In the total STC panel that includes more than 36 384 establishments and 204 396 observations, only 6% of the establishments (2 286 establishments that represent 6 519 observations) had at least two STC recourses during the whole period (cf. tables 1 and 2). We consider them as establishments with a recurrent STC recourse11. This distinction between recurrent and nonrecurrent resort to STC is interesting to analyse in order to check if recurrent users may recourse to STC to accommodate structural downturns in a specific way. Indeed, a recurrent use of STC is controversial according to the French STC legislation since STC program should not be used to face structural downturns. In this paper, we test the model over the sample of recurrent participants in STC. The latter constitute our selection sample. Then, to

10

Formally, we impose

γ t = γ for all t contrary to Semykina and Wooldridge. In order to check if these two

methods provide different estimators for the redundancy indicators, we have implemented exactly the Semykina and Wooldridge’s model (2006) and we finally obtained very similar results. 11 This definition of the STC recurrent recourse is very large. We consider this threshold of two STC uses because of the rarity of the phenomenon. STC recurrent establishments belong to industries in structural downturns most of the time. 5% from the 93 000 establishments of the STC panel are using 4 years the STC device.

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check the robustness of the model and to ensure that wan can generalize the results, we test the model on the sample of all STC participants (recurrent and non-recurrent). The average number of STC authorized days is 88 for the total sample, 1 914 for participants in the program and 2 319 for recurrent participants. This large difference in means is a consequence of the rarity of the phenomenon. Such differences also characterise the other STC indicators. For example, when establishments have STC authorizations, they affect in average 54% of their workforce (55% for recurrent participants), while only 2.4% of the establishments’ employees are concerned by STC on the total sample. Similarly, the average duration of the STC per employee equals to 7 days on the selection sample (for recurrent or not recurrent participants), while this duration is inferior to 3 hours on the total sample. The number of layoffs is our dependant variable in equation (2). On the global sample, the average number of layoffs per establishment (NB_layoffs) is slightly superior to 1 and reaches 5 on the selection sample. Participants in the STC program have higher average redundancy rates REDit (around 3%) than establishments from the global sample (less than 1%). To test the robustness of the results, we introduce other measures of redundancies in addition of the number of layoffs: a dummy indicating the existence of a layoff and dummy indicating mass layoffs. Less than 20% of the establishments of the total sample have at least one layoff during the year. Establishments that do not use STC have an lower proportion of redundancies (18%) and this figure reaches nearly 40% for those which make recourse to STC. This can be interpreted by the economic situation of these establishments. As expected, it seems that STC establishments have a worse economic situation. So, there are more chances for them to layoff. In France, we talk about a mass layoff when an establishment, for a given month, has at least 10 redundancies. In this paper, we consider that there is a mass layoff when an establishment fires 10 employees during a year. Imposing the 10 layoffs threshold is

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a consequence of the distribution of the number of layoffs: 75% of the establishments of the global sample that lay off had at maximum 5 layoffs during a year. So, our mass layoff indicator ( LAY 10it ) points out that, on the global sample, less than 3% of the establishments laid off at least 10 workers during the year. This value is much higher for the STC establishment sample (approximately 10%). Other variables constitute controls in our estimations. Since we work with establishments with at least 50 employees, the average establishment size on the total sample is quite high (177 employees). STC establishments are bigger than in the no-STC establishments (220 against 174 employees) and the recurrent STC establishments have an even more important size (239 employees). Establishments also differ in average as regards to their WTR behaviour. Fewer STC establishments have reduced their working time (by nearly 16%) than non-STC establishments (31%). This result confirms the conclusions of the Calavrezo’s et al. (2007) paper. Regarding the economic indicators, table 1 points out that STC establishments have stronger economic downturns in comparison to no STC establishments. For example, STC establishments have negative average firm’s size variation rate and negative average value-added variation rate. Profitability rate is also more important for the no STC establishments. We remark that no STC establishments are principally from the “Ile-de-France” region or the “Centre-North” region. As for the STC establishments, they are mainly from the “Centre-North” region and the “North-West Atlantic” region. There are also some differences at the industry level. Globally, as expected, agriculture is marginally represented. The STC establishments are mainly concentrated in the “manufacture of intermediate goods” industry (44% of the selection sample). Even if this industry is also strongly represented for non STC establishments the proportion is smaller (18%). These establishments are principally concentrated in the “wholesale and retail trade” industry. The

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STC specific industries such as “manufacture of motor vehicles” are overrepresented on the selection sample: 3% against 1% on the no STC sample.

[Insert tables 1 and 2]

To estimate our redundancy equation conditional on fixed effects, we need repeated layoff observations for the same establishment. Table 3 reports frequencies of the number of years of presence in the panel for each establishment of the total panel. Nearly 30 % of the establishments of the total sample appear on the whole period, from 1996 to 2004.

[Insert table 3]

5.2 Estimation results

The main question of this paper is to determine whether the participation in the STC program enables establishments to avoid layoffs. Before answering to this question, we begin to interpret selection regression estimates for STC recourse that control for unobserved heterogeneity. They are computed on the total sample, i.e. 204 396 observations. Table 4 presents results for this first stage of the model. Then, we answer our central question, by interpreting the estimates of redundancy equations for recurrent participants in the STC program. Table 5 summarizes the results that are computed on 6 519 observations. The size of the establishment, its economic situation and WTR choices are all significantly correlated with the probability to participate in the STC program (cf. table 4). More precisely, the probability to use the device increases with the size of the establishment. We can interpret this relationship in different ways. It can be due to increasing requirements in flexibility with the size of the establishment. Big establishment are more likely to have a

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personnel department better informed about STC rules and procedures. Poor economic health of the establishment also increases the probability to participate in the STC program. Indeed, this probability at the date t decreases with the variation of value-added rate and the profitability rate at the date t-1. This negative relationship is very easy to understand since the establishment has to provide the proof of strong unpredictable economic difficulties if it participates in the STC program. Finally, establishments that reduced their effective working time (for offensive reasons) participate less frequently in the STC program. The significance of the WTR variable partially confirms that it is a good exclusion variable12. This negative relationship between participation in STC and WTR confirms previous conclusions of Calavrezo et al. (2007). They empirically highlight a substitution effect between STC and working time reduction (WTR) due to their internal flexibility roles. Moreover, selection regression estimates for STC recourse informs about the existence of the individual effects. Indeed, the coefficients of the difference between the within and the between estimator are significantly different from zero (excepting for the EST _ size variable).

It confirms the relevance of the model.

[Insert table 4]

The second stage of the model enables to discuss the impact of a recurrent participation in the STC program on redundancies’ behaviour of establishments. Does the participation in the STC program avoid redundancies and, more generally, protect employment? The table 5 summarizes the results of nine regressions on the number of layoffs within establishments. We test the equation (2) of the model by considering successively three

12

By regressing directly

WTRit on the layoff indicators, its coefficient is not significatively different from zero.

19

different dimensions of the STC authorizations (in raws): the number of authorized days, the number of employees concerned and the duration of STC per employee. Columns (I), (II) and (III) refer to the econometric method used. Estimates in the column (I) result from a zero inflated negative binomial model that we test by pooling the data and introducing some controls13. We do not control for unobserved heterogeneity, selection and endogeneity biases. We introduce these results as a benchmark to see what would be the “naïve” estimates of the relationships between participation in the STC program and the number of layoffs. Estimates of column (II) and (III) control for the different biases. Even if we do not report estimates associated with all introduced variables to simplify the presentation, one should notice that estimates associated with the inverse of Mills ratio are generally significantly positive. It indicates the presence of a selection bias that was controlled by the model. In column (II), once again, we use a two-stage model to control the potential endogeneity of the STC variables. Estimates give the contemporary impact of the participation in the STC program at the date t on the number of layoffs at the date t. In column (III), we estimate directly the redundancy behaviour by using STC indicators lagged by one year to control endogeneity bias.

[Insert table 5]

First, none of the estimates is negative. This strong result means that the recurrent participation in the STC program does not decrease layoffs. Even more unexpected, some coefficients are significantly positive. Thus, the recourse to STC seems to announce layoffs instead of avoiding them. From that point of view, the STC program does not appear to be an efficient instrument to protect employment when establishments come across economic 13

Establishment size, variation of the value-added (lagged by one year) and variation of the size of the firm (lagged by one year) that establishment belongs, profitability rate (lagged by one year) and time dummies

20

difficulties. To interpret this positive relationship between STC authorizations and the number of layoffs, we can imagine that the participation in the STC program is a way for establishments to calm the social tensions before a planned redundancy scheme. Another interpretation is to consider the resort to the STC authorizations as the ultimate (inefficient) solution to avoid layoffs. From that perspective, the STC authorization and redundancies would be complementary to face economic difficulties. We can also comprehend the STC program as a policy that aims at accompanying establishments in structural decline and at financially helping them. Another interpretation relates back to the population that we are studying: recurrent users of the STC authorizations. One could argue that this category face a structural decline which explains their redundancy behaviour. However, the econometric method that we use controls for such a selection bias. Robustness tests that we will implement in the following section will enable to check whether the same results could apply to nonrecurrent participants in the STC program or if the results are due to the econometric approach. Moreover, the considerable impact of the STC authorizations on redundancy has to be qualified. Indeed, each and every estimate associated with STC variables is not significant. Namely, the number of employees concerned by authorised days does not affect the number of layoffs during the period or the following one. On the contrary, the number of STC authorized days and their duration per employee involve more layoffs during the period. Moreover, the effect of the duration of STC per employee on the layoffs of the next period remains significant and positive. It shows that to put a large number of employees under the STC program for short duration has not the same consequences than to put a small number of employees under the STC program for long duration. Indeed, the former solution would involve more layoffs than the latter. Therefore, the longer duration of STC episodes for a

21

rather limited number of employees in the clothing industry is more worrying for employment than the shorter episodes that concern a large number of employees in the auto industry.

5.3 Generalisation and robustness of results We run several additional regressions to check that we can generalize the previous results and to test their robustness. First, we enlarge our selection sample by considering both recurrent and non-recurrent users of the STC authorizations. It allows to verify whether the impact of STC variables on the number of layoffs are specific or not to recurrent users. Second, we successively characterize the redundancy behaviour with new variables: the dummy variable LAYit indicates if the establishment had at least one layoff and the dummy variable LAY 10it indicates if the establishment had at least ten layoffs. We consider the latter variable as a mass layoffs dummy. At the second stage of the model, we run a probit estimation for each binary variable. Third, we introduce some supplementary explanatory variables: establishment’s industry (at an 11 level classification) and establishment’s region (following to the French National Institute of Statistics definition, we use the main 8 regions of France). As these variables do not change over time, we cross them with the firm’s valueadded variation rate. Indeed, we think that these crossed effects can capture some industrial characteristics like the structural decline of some sectors; even if they are difficult to interpret. Table 6 summarizes the results. Each coefficient comes from a different estimation. In columns denoted by (II) and (II’), we use a two stages model based respectively on ZINB and probit models. They inform about the “contemporary” impact of STC authorizations on redundancy behaviour of establishments. In columns denoted by (III) and (III’) we estimate directly the redundancy behaviour by introducing STC indicators lagged by one year. It allows determining lasting effects.

22

As regards to the number of layoffs, working on a larger sample strengthens our previous conclusions. Indeed, estimated coefficients become more significant. Whatever the STC indicator considered, it is associated with a contemporary increase in the number of layoffs. For the following period, the only lasting effect on the number of layoffs concerns the duration per employee of STC authorizations. Moreover, introducing new explanatory variables confirms our previous conclusions: they are quite general and robust. They characterize the behaviour of recurrent and non-recurrent participants in the STC program. When we consider other redundancy behaviour variables, once again, we find very similar results. None of the coefficients is negative. Moreover, the duration per employee of the STC authorizations is the key variable that produces lasting effect on the decision to lay off one or ten employees. More than the number of employees concerned by STC authorizations, it is their duration that “announces” some redundancies.

[Insert table 6]

6. Conclusion This paper shows that the participation in the STC program involves an increase in redundancies in French participant establishments (with at least 50 employees). More precisely, long durations of STC signal that the establishment will lay off. We can interpret this positive and significant relationship between STC authorizations and redundancies in different ways. Establishments would resort to STC to calm the social tensions before a planned redundancy scheme; resort to STC authorizations would be the ultimate inefficient solution to avoid layoffs; STC authorizations and redundancies could complement each other to face economic difficulties; or the STC program is a policy used to accompany establishments in structural decline. Whatever the true interpretation, the STC program does

23

not fully protect from redundancies in French establishments (with at least 50 employees) that face strong economic difficulties. Does this result come from the econometric approach used? The models that we test control for unobserved heterogeneity, selection bias and endogeneity. Moreover, we run several robustness tests. However, one can still suspect some biases since layoffs and duration per employee of STC authorizations are both contra-cyclical. A way to solve this problem would be to use a quarterly panel and to control for industrial economic situation. The problem with this approach is that we cannot control quarterly industrial economic situation in an appropriate way. Does it mean that the STC program is an inefficient policy? We do not think so. To measure the efficiency of this policy several additional studies have to be done. The most obvious is to check the impact of the STC program on survival of establishments. Besides, we also have to analyze the redundancy and survival behaviours of establishments with less than 50 employees. Finally, a comparison of the monetary costs and benefits of the STC program would be necessary to conclude on the efficiency of the STC program. This comparison would be macroeconomic since the volume of STC days really used and their total budget are only available at the national level.

References Abowd, J.M., Allain, L., 1997. The Washington State Short-Time Compensation Program and its Implication for European Work Share Programs. Mimeo. Abraham, K.G., Houseman, S.N., 1993. Does Employment Protection Inhibit Labor Market Flexibility? Lessons from Germany, France and Belgium. NBER Working Paper, No. W4390, june.

24

Burdett, K., Wright, R., 1989. Unemployment Insurance and Short-Time Compensation: The Effects on Layoffs, Hours per Worker, and Wages. The Journal of Political Economy. Vol. 97, No. 6 (Dec.), pp. 1479-1496. Calavrezo, O., Duhautois, R., Walkowiak, E., 2007. The Effect of Working Time Reduction on Short-Time Compensation: a French Empirical Analysis, Document de travail CEE, n°88, juin. Crépon, B, Kramarz, F., 2002. Employed 40 hours or Not-Employed 39: Lessons from the 1982 Workweek Reduction in France. Journal of Political Economy, 110, 6, 1355-1389. de Regt, E.R., 2002. Employment, Wages and Working Time. Printed in The Netherlands by Alberts Drukkerij VOF, Gulpen. Dustman, C., Rochina-Barrachina, M.E., 2000, Selection Correction in Panel Data Models: An Application to Labour Supply and Wages, IZA Working paper, june. Ekos Research Associates, Inc. 1993. Work Sharing Evaluation: Technical Report. Ottawa, Canada: Insurance Programs Directorate, Program Evaluation Branch, Strategic Policy and Planning. Fiole, M., Passeron, V., Roger, M., 2000. Premières évaluations quantitatives des réductions collectives du temps de travail », DARES working paper, no. 35. Fiole, M., Roger, M., 2002. Les effets sur l’emploi de la loi du 11 juin 1996 sur la réduction du temps de travail : une analyse microéconométrique. Economie et Statistique, no. 357358, p. 3-22. Freeman, R.B., 1998. Work-Sharing to Full Employment: Serious Opinion or Populist

Fallacy?, pp. 195-222 in Freeman R.B. and P. Gottschalk (eds.), Generating Jobs, How to Increase Demand for Less-Skilled Workers, New York. Gray, M., 1998. When Might a Distressed Firm Share Work? Evidence from the Short-Time Compensation Programme in France, British Journal of Industrial relations. No. 36:1, march, pp. 43-72. Kerachsky, S., W. Nicholson, E. Cavin, A. Hershey. 1986. An Evaluation of Short-Time Compensation Programs Occasional Paper 86-4. Washington, D.C.: U.S. Department of Labor and Mathematica Policy Research.

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Larrey, J., 1998. Les effets sur l’emploi de la flexibilité du temps de travail. CSERC working

paper, no. 98.01. Morand, M. 1990. Unemployment Insurance and Short-Time Compensation, Edited by W. Lee Hansen and James F. Byers. Unemployment Insurance: The Second Half-Century. Madison, WI: University of Wisconsin Press. Mundlak, Y., 1978. On the pooling of time series and cross section data, Econometrica 46, 69-85. Needels, K., Nicholson, W., Kerachsky, S., Walsh, S., London, R., McCanne, D., 1997.

Evaluation of the Short-Time Compensation Programs. Final report. U.S. Department of Labor, Mathematica Policy Research and Berkeley Planning Associates. OECD, 1995. Flexible Working-time: Collective Bargaining and Government Intervention, Paris. OECD, 2004. The 35-hour week: Portrait of a French exception. The OECD Observer, no. 244, September. Schiff, F.W., 1986. Short-time compensation: assessing the issues. Monthly Labor Review, may. Semykina, A., Wooldridge, J.M., 2006, Estimating Panel Data Models in the Presence of Endogeneity and Selection: Theory and Application. Mimeo, Michigan State University Department of Economics, june. Van Audenrode, M.A., 1994. Short-Time Compensation, Job Security, and Employment Contracts: Evidence from Selected OECD Countries. The Journal of Political Economy, Vol. 102, No. 1. (Feb.), pp. 76-102. Vroman, W. 1992. Short-Time Compensation in the U.S., Germany, and Belgium. The Urban Institute.

26

Table 1: Summary statistics Variable

STC

Description

Total sample (204 396 obs.)

Establishments with STC participation at least one year (9 132 obs.)

Establishments with STC participation at least two years (6 519 obs.)

STC=1 if the establishment participate, 0 otherwise

0.04 (0.21) 88.19 (2228.86) 4.75 (80.00) 0.02 (0.13) 0.32 (1.87) 0.19 (0.39) 0.03 (0.16) 1.25 (8.09) 0.01 (0.05) 0.31 (0.46) 0.10 (0.30) 0.11 (0.31) 0.11 (0.31) 0.11

1.00

1.00

1974.01 (10367.26) 106.42 (363.93) 0.54 (0.31) 7.11 (5.47) 0.39 (0.49) 0.10 (0.30) 4.76 (20.20) 0.03 (0.10) 0.16 (0.37) 0.24 (0.42) 0.19 (0.39) 0.12 (0.33) 0.12

2318.68 (12166.39) 117.14 (423.46) 0.55 (0.31) 7.12 (5.38) 0.40 (0.49) 0.11 (0.31) 5.20 (22.60) 0.03 (0.10) 0.15 (0.36) 0.20 (0.40) 0.19 (0.40) 0.14 (0.35) 0.13

STC_days

Number of STC authorized days

STC_emp

The number of employees affected by the authorizations

P_STC

The part of employees concerned by the STC authorizations The average period of the STC affectation per employee

AP_STC LAY LAY10 NB_layoffs RED

Dummy variable indicating if the establishment had at least one layoff during the year Dummy variable indicating if the establishment had at least ten layoffs during the year Establishment’s number of layoffs

Id96

Redundancy rate (yearly number of layoffs divided by the establishment size) Dummy variable indicating for each year if the establishment reduced its effective working time duration Dummy variable for the year 1996

Id97

Dummy variable for the year 1997

Id98

Dummy variable for the year 1998

Id99

Dummy variable for the year 1999

WTR

27

Establishments with no STC participation (195 264 obs.)

0.18 (0.39) 0.02 (0.15) 1.08 (6.99) 0.01 (0.05) 0.31 (0.46) 0.09 (0.29) 0.10 (0.31) 0.11 (0.31) 0.11

Id00

Dummy variable for the year 2000

Id01

Dummy variable for the year 2001

Id02

Dummy variable for the year 2002

Id03

Dummy variable for the year 2003

Id04

Dummy variable for the year 2004

EST_size

Establishment number of employees

Var_F_size1

The variation rate of the firm size lagged by one year

Var_VA1

The variation rate of the value-added lagged by one year

PR1

Profitability rate lagged by one year

Reg1

Dummy variable with value 1 if the region is “Ile-de- France”

Reg2

Dummy variable with value 1 if the region is “Centre- North”

Reg3

Dummy variable with value 1 if the region is “Nord-Pas De-Calais”

Reg4

Dummy variable with value 1 if the region is “East”

Reg5

Dummy variable with value 1 if the region is “North West Atlantic”

Reg6

Dummy variable with value 1 if the region is “South West”

Reg7

Dummy variable with value 1 if the region is “Centre South”

Reg8

Dummy variable with value 1 if the region is “Midi Mediterranean”

28

(0.32) 0.11 (0.32) 0.12 (0.32) 0.12 (0.32) 0.12 (0.32) 0.11 (0.31) 176.50 (332.52) 0.03 (0.25) 0.05 (0.34) 0.22 (0.35) 0.20 (0.40) 0.20 (0.40) 0.07 (0.25) 0.10 (0.30) 0.14 (0.35) 0.08 (0.28) 0.14 (0.34) 0.07

(0.33) 0.06 (0.24) 0.07 (0.26) 0.08 (0.26) 0.07 (0.26) 0.05 (0.21) 219.75 (658.51) -0.002 (0.20) -0.01 (0.32) 0.13 (0.32) 0.06 (0.24) 0.26 (0.44) 0.10 (0.31) 0.13 (0.34) 0.17 (0.37) 0.09 (0.28) 0.15 (0.35) 0.04

(0.34) 0.06 (0.24) 0.07 (0.26) 0.08 (0.27) 0.75 (0.26) 0.05 (0.21) 238.94 (762.21) -0.01 (0.18) -0.02 (0.30) 0.12 (0.32) 0.05 (0.21) 0.27 (0.44) 0.12 (0.32) 0.14 (0.34) 0.18 (0.38) 0.08 (0.28) 0.14 (0.35) 0.03

(0.32) 0.12 (0.32) 0.12 (0.32) 0.12 (0.32) 0.12 (0.33) 0.11 (0.31) 174.48 (308.82) 0.03 (0.25) 0.05 (0.34) 0.22 (0.35) 0.21 (0.41) 0.20 (0.40) 0.06 (0.24) 0.10 (0.30) 0.14 (0.34) 0.08 (0.28) 0.14 (0.34) 0.07

Ind1 Ind2 Ind3 Ind4 Ind5 Ind6 Ind7 Ind8

Dummy variable with value 1 if the industry is “Agriculture, forestry and fishing” Dummy variable with value 1 if the industry is “Manufacture of food products” Dummy variable with value 1 if the industry is “Manufacture of consumer goods” Dummy variable with value 1 if the industry is “Manufacture of motor vehicles” Dummy variable with value 1 if the industry is “Manufacture of capital equipment” Dummy variable with value 1 if the industry is “Manufacture of intermediate goods” Dummy variable with value 1 if the industry is “Construction”

Ind9

Dummy variable with value 1 if the industry is “Wholesale and retail trade; repairing” Dummy variable with value 1 if the industry is “Transportation”

Ind10

Dummy variable with value 1 if the industry is “Services to firms”

Ind11

Dummy variable with value 1 if the industry is “Services to individuals, education and health”

Sample standard deviations are in parentheses below sample averages. Field: French establishments with at least 50 employees.

29

(0.25) 0.01 (0.08) 0.06 (0.24) 0.08 (0.27) 0.01 (0.12) 0.08 (0.28) 0.20 (0.40) 0.08 (0.26) 0.19 (0.40) 0.08 (0.27) 0.14 (0.34) 0.07 (0.26)

(0.20) 0.00 (0.06) 0.04 (0.20) 0.18 (0.38) 0.03 (0.18) 0.12 (0.33) 0.42 (0.49) 0.11 (0.32) 0.01 (0.11) 0.01 (0.12) 0.04 (0.20) 0.02 (0.12)

(0.18) 0.00 (0.06) 0.04 (0.19) 0.20 (0.40) 0.03 (0.18) 0.12 (0.32) 0.44 (0.50) 0.11 (0.31) 0.01 (0.08) 0.01 (0.08) 0.04 (0.19) 0.01 (0.10)

(0.26) 0.01 (0.08) 0.06 (0.24) 0.08 (0.26) 0.01 (0.12) 0.08 (0.27) 0.19 (0.39) 0.07 (0.26) 0.20 (0.40) 0.08 (0.27) 0.14 (0.35) 0.08 (0.26)

Table 2: Distribution of the participation in the STC program of establishments Number of years Number of establishments Percent 0 31 485 86.53 1 2 613 7.18 2 1 197 3.28 3 603 1.65 4 276 0.75 5 111 0.30 6 53 0.14 7 32 0.08 8 11 0.03 9 3 0.01 Total 36 384 100 Field: French establishments with at least 50 employees.

Table 3: Number of years of presence in the sample for establishments that participate to the STC program Number of years Frequency Percent 2 6 165 16.94 3 4 711 12.95 4 4 399 12.09 5 3 665 10.07 6 2 770 7.61 7 2 293 6.30 8 2 088 5.74 9 10 293 28.29 Total 36,384 100 Field: French establishments with at least 50 employees..

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Table 4: Selection regression estimates for STC recourse

Intercept EST_size Var_VA1 Var_F_size1 PR1 WTR

-1.3829 0.000190 -0.0501 -0.00538 -0.0790 -0.1218

Standard error 0.0133 0.000068 0.0198 0.0286 0.0258 0.0186

EST _ size

-0.00008

0.000070

ns

Var _ VA1

-0.6346

0.0534

***

Var _ F _ size1

-0.2991

0.0722

***

PR1 WTR

-0.4145

0.0325

***

Variable

Estimation

*** *** ** ns *** ***

-0.0901 0.0227 *** Chi² 3052.05 N total 204 396 Field: French establishments with at least 50 employees. Note: Probit coefficients estimates. Regression also includes time dummies (weighted by the establishment’s presence in the sample). * indicates significance at 10%, ** indicates significance at 5%, *** indicates significance at 1% and ns indicates non-significance at 10%.

Table 5: Summary of results for the number of layoffs (I)

Number of STC authorized days (STC_days) Number of employees concerned by STC( STC_emp) Duration of STC authorized day per employee (AP_STC)

Naïve ZINB model 0.0003*** (0.0000) 0.0072*** (0.0005) 0.1378*** (0.0045)

(II) ZINB model (two step method) 0.0000 ** (0.0000) 0.0012 ns (0.0007) 0.1011 *** (0.0266)

(III) ZINB model (with lagged STC variable) 0.0000 ns (0.0000) 0.0008 ns (0.0008) 0.0201 ** (0.0090)

Field: French establishments with at least 50 employees. Note: Standard errors are given in parentheses. * indicates significance at 10%, ** indicates significance at 5%, *** indicates significance at 1% and ns indicates non-significance at 10%. In column (I) data are pooled and we run a zero inflated binomial model on the total sample that includes 204 396 observations. Introduced controls are : variation in the size of the firm that establishment belongs to (lagged by one year), variation in the value-added (lagged by one year), profitability rate (lagged by one year). In column (II) and (III), we report estimates from equation (2) of the second stage of the model. The sample includes 6 519 observations. The inverse Mills ratio is significant at 10% in almost all the regressions. In column (II), we use a two-stage model to control the endogeneity of the STC variables. In column (III), we estimate directly the redundancy behaviour by using STC indicators lagged by one year.

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Table 6: Summary of robustness tests Nb_layoffs Lay Lay10 (III) (II') (III') (II') (III') Sample of recurrent establishments STC_days ++ 0 0 0 0 0 STC_emp 0 0 0 0 + + AP_STC +++ ++ +++ +++ +++ +++ Sample of establishments that participate in the STC program (recurrent+ non recurrent establishments) STC_days +++ 0 0 0 +++ 0 STC_emp ++ 0 0 0 0 0 AP_STC +++ +++ +++ +++ +++ +++ Introduction of new explanatory variables (sample of recurrent establishments) STC_days ++ 0 0 0 0 0 STC_emp 0 0 0 0 0 0 AP_STC +++ ++ +++ +++ +++ +++ Field: French establishments with at least 50 employees. Note: The inverse Mills ratio is significant at 10% in almost all the regressions. The sample of recurrent establishments includes 6 519 observations. The sample of recurrent and non recurrent establishments includes 9132 establishments. + represents a positive significant impact at 10%, ++ at 5% and +++ at 1% and finally 0 is a sign of no impact. (II)

32

Appendix 1 The cleaning procedure In order to obtain the final sample, we impose five stages in the “cleaning” process. The first stage consists in replacing the missing values of the establishment size calculated from the DMMO databases with the values from the UNEDIC files (only if the information regarding the redundancy indicator is available). In the second stage, in order to obtain a coherent sample, we will erase the establishments which on the 1996-2004 period have two or more years with missing information. This choice was conditioned by the econometric model because otherwise we could not control correctly the unobserved heterogeneity14. For establishments having a missing year, we replace the absent values for the firm’s size, value-added, capital investment, firm’s profits and establishment size by the mean of these variables calculated on the previous and next year. Concerning the number of redundancies, we preferred replacing the missing values by 015. In the third stage, we calculated some economic indicators for the firms the establishments are belonging to: the variation rate of the firm size ( Var _ F _ sizeit ); the variation rate of the value-added ( Var _ VAit ) and the profitability rate ( PRit ). Appendix 2 details

these

variables.

We

made

some

controls

for

outliers

concerning

the

Var _ VAit and PRit indicators. For the variation of the value-added rate, we eliminated establishments which had at least for one year a value-added rate inferior to -5 or superior to 5. Concerning the profitability rate, establishments with yearly values out of the interval [-2, 2] were also eliminated. For the implementation of the econometric model we lagged by one year the values of these economic indicators. 14

If we do not deal with this kind of problem, the same establishment will be considered as two or more different establishments and so this will bias estimations. 15 Working with the average on the previous and next year could be dangerous for this indicator. In general very few establishments are laying off their workers for economic reasons.

33

In a forth stage, due to their small proportion among the STC establishments, establishments belonging to the following four industries were eliminated: manufacture of electricity, gas and water supply; financial intermediation; real estate activities and administration. For the same motivation, we also grouped together the “services to individuals” industry and the “education and health” industry. In the last stage, we paid a particular attention to establishments which for a year have 0 employees16. This can indicate that the establishment has just opened or it has just closed and so it exists only an administrative way but without having any employees. This type of value needs a particular control. We eliminated establishments that for one year had 0 employees but figured with layoffs. For the establishments which had a number of layoffs superior to the number of employees we preferred replacing the establishment size for this year with the establishment size of the previous year17. The final check was on the establishment size. We decided to eliminate establishments that on two following years had a strong increase (or a strong decrease) of at least 50 employees and they had an initial (respectively final) size was inferior to 10 employees. In this way we could verify if these establishments “were born” or “died”. According to this control, we erased the incoherent values (31 observations).

16

According to the data collecting rules, the establishment size can be inferior to 50 employees. Nevertheless, we have to precise that this case a figure does not represent an incoherence in the data. There are only 279 observations in this situation. These situations are due to the fact that we summed up the number of layoffs over the year, but we are working with the average establishment size over the quarters. We have still preferred to do this changing in order to harmonize the indicator. 17

34

Appendix 2 The main indicators Short-Time Compensation indicators STC authorized days ( STC _ daysit )

This indicator is the sum of the monthly STC authorized 12

days: STCit = ∑ STCij , where i represents the establishment, t the j =1

year and j the month.

Number of employees concerned by the STC authorizations ( STC _ empit )

This indicator is an average and it is calculated over the months during which the establishment is using the STC program. 1 STC _ empit = ∑ STC _ empij k j where i represents the establishment, t the year, j the month and k is the number of months during which the establishment has STC.

Part of employees concerned by the STC authorizations ( P _ STCit )

This measure is an average. EMPij is the total number of employees of an establishment i for the month j, then STC _ empij 1 P _ STCit = ∑ , k j EMPij where t defines the year and k is the number of months were the establishment has STC. The indicator is calculated exclusively over the months during which the establishment has STC authorizations. The values of this indicator are included in the interval [0, 1].

Average period of the STC affectation per employee ( AP _ STCit )

This indicator is an average of durations computed over the months during which the establishment recourses to STC STC _ daysij 1 AP _ STCit = ∑ . k j STC _ empij where k is the number of months during which the establishment has recourse to STC

Establishment size indicator Yearly establishment size indicator ( EST _ sizeit )

If i is the establishment, t the year, q the quarter and k is the number of quarters where the establishment appears in the database, the 1 indicator is calculated as follows: EST _ sizeit = ∑ EST _ sizeiq . k q

Layoff indicators Yearly layoffs ( NB _ layoffsit )

This indicator is obtained by adding up establishment quarterly layoffs. If i is the establishment, t the year, q the quarter, the indicator is calculated as follows: NB _ layoffsit = ∑ NB _ layoffsiq . q

35

Redundancy rate ( REDit )

It is the ratio of the establishment’s annual number of redundancies and the establishment’s annual average number of employees: NB _ layoffsit REDit = . EST _ sizeit

Presence of redundancies within the year ( LAYit )

Dummy variable indicating if the establishment had at least one 1 if NB_layoffsit >0 layoff during the year: LAYit =  0 if NB_layoffsit =0

Presence of mass layoffs ( LAY 10it )

Dummy variable indicating if the establishment had at least 10 layoffs during the year as a proxy of mass layoffs: 1 if NB_layoffsit >=10 LAY 10it =  0 if 0<=NB_layoffsit <10

Working Time Reduction (WTR) indicator Reducing working time not for a defensive reason ( WTRit )

Binary indicator equals to 1 only when the establishment reduced its working time for the following reasons: WTR for employment creation or WTR without the intention of creating employment or preserving from redundancies: 1 if WTR not for defensive reasons WTRit =   0 otherwise

Firm performance indicators Variation rate of the firm size ( Var _ F _ sizeit ) Variation rate of the added-value ( Var _ VAit ) Profitability rate ( PRit )

Var _ F _ sizeit =

F _ sizeit − F _ sizeit −1

1 ( F _ sizeit + F _ sizeit −1 ) 2 where F _ sizeit represents the firm size. Var _ VAit =

,

VAit − VAit −1

, 1 (VAit + VAit −1 ) 2 where VAit represents the value-added. Π it , where Π it represents firm’s profit and K _ INVit −1 K _ INVit represents capital investment. PRit =

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Appendix 3 Zero-Inflated Negative Binomial models One of the most popular ways to estimate models for count data involves the use of negative binomial regression models. The negative binomial model is typically motivated as a modification of the Poisson regression model that relaxes the assumption that the variance of the observed random variable is equal to its mean. Zero-Inflated Negative Binomial (ZINB) models allow for excess zeros by assuming that zero counts are generated by a process different from the generating positive counts. In ZINB models the population is assumed to consist of two groups. An establishment belongs to group 1 with probability η and it is in group 2 with probability 1 − η . Establishments in group 1 always have zero counts (because they do not have layoffs). In the second group, we suppose counts are generated by a negative binomial process. The probability η can be modeled as ηi = F ( ziγ ) , where z is a set of covariates predicting group membership. In our case F is the logistic cumulative distribution function. The ZINB model is: 1/α   1  ηi + (1 − ηi )  for yi = 0    1 + αµ   Pr( yi xi ) =  1/α yi  Γ( yi + 1/ α )  1/ α   µi  (1 − ηi ) y !Γ(1/ α )  1/ α + µ   1/ α + µ  for yi > 0 i i  i    

where µ =exp(xβ ) with x a matrix of covariates. α is a dispersion parameter to be estimated. N

The model is fitted using maximum likelihood : L(β , γ y, X, Z) = ∑ Pr( yi xi , zi ) . i =1

By substitution, Pr( yi xi , zi ) is defined as :

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1/α   1  F ( ziγ ) + (1 − F ( ziγ ))  for yi = 0    1 + αµ   Pr( yi xi , zi ) =  yi 1/α  Γ( yi + 1/ α )  1/ α   µi  (1 − F ( ziγ )) y !Γ(1/ α )  1/ α + µ   1/ α + µ  for yi > 0 i i  i    

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