Amel Bennaceur

Valérie Issarny

Romina Spalazzese

Shashank Tyagi

Achieving Interoperability through Semantics-based Technologies: The Instant Messaging Case

Keywords: Interoperability, Composition, Ontology, Verification, Mediation, Universal Instant Messaging

The success of pervasive computing depends on the ability to compose a multitude of networked applications dynamically in order to achieve user goals. However, applications from different providers are not able to interoperate due to incompatible interaction protocols or disparate data models. Instant messaging is a representative example of the current situation, where various competing applications keep emerging. To enforce interoperability at runtime and in a non-intrusive manner, mediators are used to perform the necessary translations and coordination between the heterogeneous applications. Nevertheless, the design of mediators requires considerable knowledge about each application as well as a substantial development effort. In this paper we present an approach based on ontology reasoning and model checking in order to generate correct-by-construction mediators automatically. We demonstrate the feasibility of our approach through a prototype tool and show that it synthesises mediators that achieve efficient interoperation of instant messaging applications.

Introduction

Pervasive computing promises a future where a multitude of networked applications dynamically discover one another and seamlessly interconnect in order to achieve innovative services. However, this vision is hampered by a plethora of independently-developed applications with compatible functionalities but which are unable to interoperate as they realise them using disparate interfaces (data and operations) and protocols. Compatible functionalities means that at a high enough level of abstraction, the functionality provided by one application is semantically equivalent to that required by the other.

The evolution of instant messaging (IM) applications provides a valuable insight into the challenges facing interoperability between today's communicating applications. Indeed, the number of IM users is constantly growing -from around 1.2 billion in 2011 to a predicted 1.6 billion in 2014 [START_REF]The Radicati Group: Instant Messaging Market[END_REF] -with an increasing emphasis on mobility -11% of desktop computers and 18% of smartphones have instant messaging applications installed [START_REF] Nielsen | Games Dominate America's Growing Appetite for Mobile Apps[END_REF]-and the scope of IM providers is expanding to include social networking such as Facebook that embeds native IM services onto their Web site. Consequently, different versions and competing standards continue to emerge. Although this situation may be frustrating from a user perspective, it seems unlikely to change. Therefore, many solutions that aggregate the disparate systems, without rewriting or modifying them, have been proposed [START_REF] Issarny | Middleware-layer connector synthesis: Beyond state of the art in middleware interoperability[END_REF]. These solutions use intermediary middleware entities, called mediators [START_REF] Wiederhold | Mediators in the architecture of future information systems[END_REF] -also called mediating adapters [START_REF] Yellin | Protocol specifications and component adaptors[END_REF], or converters [START_REF] Calvert | Formal methods for protocol conversion[END_REF] -which perform the necessary coordination and translations to allow applications to interoperate despite the heterogeneity of their data models and interaction protocols.

Nevertheless, creating mediators requires a substantial development effort and thorough knowledge of the application-domain. Moreover, the increasing complexity of today's software systems, sometimes referred to as Systems of Systems [START_REF] Maier | Integrated modeling: A unified approach to system engineering[END_REF], makes it almost impossible to manually develop 'correct' mediators, i.e., mediators guaranteeing deadlock-free interactions and the absence of unspecified receptions [START_REF] Yellin | Protocol specifications and component adaptors[END_REF]. Starlink [START_REF] Bromberg | Starlink: Runtime interoperability between heterogeneous middleware protocols[END_REF] assists developers in this task by providing a framework that performs the necessary mediation based on a domain-specific description of the translation logic. Although this approach facilitates the development of mediators, developers are still required to understand both systems to be bridged and to specify the translations.

Furthermore, in pervasive environments where there is no a priori knowledge about the concrete applications to be connected, it is essential to guarantee that the applications associate the same meaning to the data they exchange, i.e., semantic interoperability [START_REF] Heiler | Semantic interoperability[END_REF]. Ontologies support semantic interoperability by providing a machine-interpretable means to automatically reason about the meaning of data based on the shared understanding of the application domain [START_REF] Baader | The Description Logic Handbook[END_REF]. Ontologies have been proposed for Instant Messaging although not for the sake of protocol interoperability but rather for semantic archiving and enhanced content management [START_REF] Franz | SAM: Semantics aware instant messaging for the networked semantic desktop[END_REF]. In a broader context, ontologies have also been widely used for the modelling of Semantic Web Services, and to achieve efficient service discovery and composition [START_REF] Mokhtar | Efficient semantic service discovery in pervasive computing environments[END_REF]. Semantic Markup for Web Services 4 (OWL-S) uses ontologies to model both the functionality and the behaviour of Web services. Besides semantic modelling, Web Service modelling Ontology (WSMO) supports runtime mediation based on pre-defined mediation patterns but without ensuring that such mediation does not lead to a deadlock [START_REF] Cimpian | WSMX process mediation based on choreographies[END_REF]. Although ontologies have long been advocated as a key enabler in the context of service mediation, no principled approach has been proposed yet to the automated synthesis of mediators by systematically exploiting ontologies [START_REF] Blair | The Role of Ontologies in Emergent Middleware: Supporting Interoperability in Complex Distributed Systems[END_REF].

This paper focuses on distributed applications that exhibit compatible functionalities but are unable to interact successfully due to mismatching interfaces or protocols. We present an approach to synthesise mediators automatically to ensure the interoperation of heterogeneous applications based on the semantic compatibility of their data and operations. Specifically, we rely on a domain-specific ontology (e.g., an IM ontology) to infer one-to-one mappings between the operations of the applications' interfaces and exploit these mappings to generate a correct-by-construction mediator. Our contribution is threefold:

-Formal modelling of interaction protocols. We introduce an ontology-based process algebra, which we call Ontology-based Finite State Processes (OFSP), to describe the observable behaviour of applications. The rationale behind a formal specification is to make precise and rigorous the description and the automated analysis of the observable behaviour of applications. -Automated generation of mediators for distributed systems. We reason about the semantics of data and operations of each application and use a domain ontology to establish, if they exist, one-to-one mappings between the operations of their interfaces. Then, we verify that these mappings guarantee the correct interaction of the two applications and we generate the corresponding mediator. -Framework for automated mediation. We provide a framework that refines the synthesised mediator and deploys it in order to automatically translate and coordinate the messages of mediated applications.

Section 2 examines in more detail the challenges to interoperability using the IM case. Section 3 introduces the ontology-based model used to specify the interaction protocols of application. Section 4 presents our approach to the automated synthesis of mediators that overcome data and protocol mismatches of functionally compatible applications and illustrates it using heterogeneous instant messaging applications. Section 5 describes the tool implementation while Section 6 reports the experiments we conducted with the instant messaging applications and evaluate the approach. The results show that our solution significantly reduces the programming effort and ensures the correctness of the mediation while preserving efficient execution time. Section 7 examines related work. Finally, Section 8 concludes the paper and discusses future work.

The Instant Messaging Case

Instant messaging (IM) is a popular application for many Internet users and is now even embedded in many social networking systems such as Facebook. Moreover, since IM allows users to communicate in real-time and increases their collaboration, it is suitable for short-lived events and conferences such as Instant Communities for online interaction at the European Future Technologies Conference and Exhibition5 (FET'11) that took place in May 2011.

Popular and widespread IM applications include Windows Live Messenger 6 (commonly called MSN messenger), Yahoo! Messenger 7 , and Google Talk 8 which is based on the Extensible Messaging and Presence Protocol9 (XMPP) standard protocol. These IM applications offer similar functionalities such as managing a list of contacts or exchanging textual messages. However, a user of Yahoo! Messenger is unable to exchange instant messages with a user of Google Talk. Indeed, there is no common standard for IM. Thus, users have to maintain multiple accounts in order to interact with each other (see Figure 1). This situation, though cumbersome from a user perspective, unfortunately reflects the way IM -like many other existing applications -has developed. A solution that guarantees interoperability between heterogeneous IM applications has to cope with the following heterogeneity dimensions:

-Data heterogeneity. MSN Messenger protocol (MSNP), the protocol used by Windows Live Messenger, uses text-based messages whose structure includes several constants with predefined values. On the other hand, the Yahoo! Messenger Protocol (YMSG) defines binary messages that include a header and key-value pairs. As for XMPP messages, they are defined according to a given XML Schema. -Protocol heterogeneity. Even though IM applications are simple and quite similar, each one communicates with its own proprietary application server used to authenticate and to relay the messages between instant messaging clients. Consequently, each application has its own interaction protocol.

Achieving interoperability between independently developed systems has been one of the fundamental goals of middleware research. Prior efforts have largely concentrated on solutions where conformance to the same standard is required e.g., XMPP. However, compliance to a unique standard is not always feasible given the competitive pressures in the marketplace.

Middleware-based approaches define a common abstraction interface (e.g., Adium10 ) or an intermediary protocol (e.g., J-EAI 11 and CrossTalk [START_REF] Motoyama | CrossTalk: scalably interconnecting instant messaging networks[END_REF]) promote interoperability in a transparent manner. However, relying on a fixed intermediary interface or protocol might become restrictive over time as new functionalities and features emerge. By synthesising mediators automatically and rigorously we relieve developers from the burden of implementing or specifying such mediators and further ensures their correctness.

Semantics-based solutions (e.g., SAM [START_REF] Franz | SAM: Semantics aware instant messaging for the networked semantic desktop[END_REF] and Nabu12 ) use ontologies to enhance the functionalities of IM application by reasoning about the content of messages and overcoming mismatches at the data level but assume the use of the same underlying communication protocol. Hence, even though an enormous amount of work is being carried out on the development of concrete interoperability solutions that rely on ontologies to overcome application heterogeneity, none propose an approach to generate mediators able to overcome both data and protocol heterogeneity. In the next section, we introduce our ontology-based approach to interoperability that automatically synthesises mediators to transparently solve both data and protocol mismatches between functionally compatible applications at runtime.

Ontology-based Modelling of Interaction Protocols

Automated mediation of heterogeneous applications requires the adequate modelling of their data and interaction protocols. In this section, we introduce OFSP (Ontology-based Finite State Processes), a semantically-annotated process algebra to model application behaviour.

Ontologies in a Nutshell

An ontology is a shared, descriptive, structural model, representing reality by a set of concepts, their interrelations, and constraints under the open-world assumption [START_REF] Baader | The Description Logic Handbook[END_REF]. Ontologies are defined by domain experts, not by the application developers, to represent shared knowledge about a specific domain.

The Web Ontology Language13 (OWL) is a W3C standard language to formally model ontologies in the Semantic Web. Many OWL ontologies have been developed for specific domains, e.g., Sinica BOW14 (Bilingual Ontological Wordnet) for English-Chinese integration. In addition, work on ontology alignment deals with the possible usage of distinct ontologies in the modelling of different systems from the same domain, as illustrated by the W3C Linking Open Data project 15 . OWL is based on description logic (DL), which is a knowledge representation formalism with well-understood formal properties [START_REF] Baader | The Description Logic Handbook[END_REF]. Concepts are defined as OWL classes. Relations between classes are called OWL properties. Ontology reasoners are used to support automatic inference on concepts in order to reveal new relations that may not have been recognised by the ontology designers. Traditionally, the basic reasoning mechanism is subsumption 16

Modelling Protocols using Ontology-based FSP

The interaction protocol of an application describes how the operations of its interface are coordinated in order to achieve a specified functionality. We build upon state-of-the-art approaches to formalise interaction protocols using process algebra, in particular Finite State Processes (FSP) [START_REF] Magee | Concurrency : State models and Java programs[END_REF]. FSP has proven to be a convenient formalism for specifying concurrent systems. Although another process algebra would have worked equally well, we choose FSP for convenience and to exploit the Labelled Transition System Analyser (LTSA) in order to automate reasoning and analysis of interaction protocols specified as finite processes. Table 1 gives an overview of FSP, while the interested reader is referred to [START_REF] Magee | Concurrency : State models and Java programs[END_REF] for further details.

Each process P is associated with an interface αP that defines the set of observable actions that the application requires from/provides to its running environment. We structure these actions and annotate them using a domain ontology O so as to specify their semantics, resulting in Ontology-based FSP (OFSP). An input action a =<op, I, O> specifies a required operation op ∈ O for which the application produces a set of input data I = {in ∈ O} and consumes a set of output data O = {out ∈ O}. The dual output action17 b =<op, I, O> refers to a provided operation op for which the application uses the inputs I and produces the corresponding outputs O. Note that all actions are annotated using the same domain ontology O describing the application-specific concepts and relations. The rationale behind this notation is to enable behavioural analysis based on the semantics of process actions. Indeed, only if both sides of communication assign the same semantics to their actions, can they interact correctly. In addition, τ is used to denote an internal action that cannot be observed by the environment. The concepts and properties defined in the IM ontology are used to specify MSNP and XMPP clients using OFSP, as illustrated in Figures 3 and4 respectively, focusing on message exchange. Each IM application performs authentication and logout with the associated server. Before exchanging messages, the MSNP application has to configure a chat room, which is an MSN conversation between the user that initiates the conversation (sender) and the user who accepts to participate in this conversation (recipient). In XMPP each message simply contains both the sender and the recipient identifiers.

Ontology-based Approach to Mediator Synthesis

In this section we consider two functionally-compatible applications, described through OFSP processes P 1 and P 2 , that are unable to interoperate due to differences in their interfaces or protocols. Functional compatibility means that their required/provided high-level functionalities are semantically equivalent [START_REF] Issarny | Middleware-layer connector synthesis: Beyond state of the art in middleware interoperability[END_REF]. Our aim is to enforce their interoperation by synthesising a mediator that addresses these differences and guarantees their behavioural matching. The notion of behavioural matching is formally captured through refinement [START_REF] Hoare | Communicating Sequential Processes[END_REF]. A process Q refines a process P if every trace of Q is also a trace of P , i.e., traces(Q) ⊆ traces(P ). However, this notion of refinement analyses the dynamic behaviour of processes assuming close-world settings, i.e., the use of the same interface to define the actions of both processes. What is needed is a notion of compatibility that takes into account the semantics of actions while relying on a mediator process M to compensate for the syntactic differences between actions and guarantees that the processes communicate properly.

To this end, we first reason about the semantics of actions so as to infer the correspondences between the actions of the processes' interfaces and generate the mapping processes that perform the necessary translations between semantically compatible actions. Various mapping relations may be defined. They primarily differ according to their complexity and inversely proportional flexibility. In this paper we focus on one-to-one mappings, i.e., direct correspondences between actions. During the synthesis step, we explore the various possible mappings in order to produce a correct-by-construction mediator, i.e., a mediator M that guarantees that the composite process P 1 M P 2 reaches an END state, or determines that no such mediator exists.

In this section we introduce the semantic compatibility of actions, and use it to define behavioural matching. Then, we present the automated synthesis algorithm.

Semantic Compatibility of Actions

A sine qua non condition for two processes P 1 and P 2 to interact is to agree on the data they exchange. However, independently-developed applications often define different interfaces. The mediator can compensate for the differences between interfaces by mapping their actions if and only if they have the same semantics. We first define the notion of action subsumption and then, use it to define the semantic compatibility of actions.

Definition 2 ( O : Action Subsumption). An action a 1 =<op 1 , I 1 , O 1 > is subsumed by an action a 2 =<op 2 , I 2 , O 2 > according to a given ontology O, noted a 1 O a 2 , iff: (i) op 2 op 1 , (ii) ∀i 2 ∈ I 2 , ∃i 1 ∈ I 1 such that i 1 i 2 , and (iii)

∀o 1 ∈ O 1 , ∃o 2 ∈ O 2 such that o 2 o 1 .
The idea behind this definition is that an input action can be mapped to an output one if the required operation is less demanding; it provides richer input data and needs less output data. This leads us to the following definition of semantic compatibility of actions: Definition 3 (≈ O : Semantic Compatibility of Actions). An action a 1 is semantically compatible with an action a 2 , denoted a 1 ≈ O a 2 , iff a 1 is subsumed by a 2 (i.e., a 1 is required and a 2 provided) or a 2 is subsumed by a 1 (a 2 is required and a 1 provided) .

The semantic compatibility between two actions allows us to generate an action mapping process as follows:

M O (a 1 , a 2 ) = a 1 O -→ a 2 if a 1 is subsumed by a 2 a 2 O -→ a 1 if a 2 is subsumed by a 1
The process that maps action a 1 to action a 2 , written a 1 O -→ a 2 captures each input data from the input action, assigns it to the appropriate input of the output action (i 2 ← i 1 ), then takes each output data of the output action and assigns it to the expected output of the input action (o 1 ← o 2 ). This assignment is safe since an instance of i 1 (resp. o 2 ) is necessarily an instance i 2 of (resp. o 1 ).

Let us consider a1=<InstantM essage,{U serID,ConversationID,M essage},∅> associated to the MSN client and a2=<InstantM essage,{SenderID,RecipientID,M essage},∅> associated to the XMPP client. The IM ontology indicates that (i) Sender is subsumed by User, and (ii) Conversation is associated with some Recipient. Consequently, a 1 is subsumed by a 2 .

Behavioural Matching through Ontology-based Model Checking

We aim at assessing behavioural matching of two processes P 1 and P 2 given the semantic compatibility of their actions according to an ontology O. To this end, we first filter out communications with third party processes [START_REF] Spalazzese | Towards a formalization of mediating connectors for on the fly interoperability[END_REF]. The communicating trace set of P 1 with P 2 , noted traces(P 1 )↑ O P 2 is the set of all successfully-terminating traces of P 1 restricted to the observable actions that have semantically compatible actions in αP 2 .

Definition 4 (↑ O : Communicating Trace Set). traces(P 1 )↑

O P 2 def = {s = a 1 , a 2 , ..., a n , a i ∈ αP 1 | P 1 s ⇒ END such that ∀a i , ∃b i ∈ αP 2 |a i ≈ O b i }
As an illustration, both the MSNP and XMPP IM clients perform their authentication and logout with their respective servers. Additionally, MSNP also performs the actions related to the ChatRooms with its servers. Consequently their communicating traces sets are restricted to instant message exchange.

Then, two traces s 1 = a 1 a 2 ...a n and s 2 = b 1 b 2 ...b n semantically match, written s 1 ≡ O s 2 , iff their actions semantically match in sequence.

Definition 5 (≡ O : Semantically Matching Traces).

s 1 ≡ O s 2 def = a i ≈ O b i 1 ≤ i ≤ n
The associated mapping is then as follows:

Map O (s 1 , s 2 ) = M O (a 1 , b 1 ); ...; M O (a n , b n )
Based on the semantic matching of traces, a process P 2 ontologically refines a process P 1 (P Behavioural matching is automated through ontology-based model checking. Model checking is an attractive and appealing approach to ensure system correctness that proved to be a very sound technique to automatically verify concurrent systems. The gist of model checking approaches is the exhaustive state exploration. This exploration is performed by model checkers using efficient algorithms and techniques that make it possible to verify systems of up to 10 1300 states in few seconds [START_REF] Clarke | Model checking and abstraction[END_REF]. However, even if these techniques effectively handle very large systems, the actions of the models they consider are usually simple strings and the verification matches actions based on their syntactic equality. We build upon these model checking techniques but further match actions based on their semantic compatibility. The semantic compatibility of actions is defined based on the domain knowledge encoded within a given ontology.

Referring to the IM case, all the traces of MSNP and XMPP processes semantically match. Subsequently, these two processes are in exact matching relation, and a mediator can be synthesised to perform action translations and enable their correct interaction.

Automated Mediator Synthesis

In the case where P 1 and P 2 match, that is exact matching in the case of peerto-peer communication or plugin matching in the case of client/server communication, we synthesise the mediator that makes them properly interact. The algorithm incrementally builds a mediator M by forcing the two protocols to progress synchronously so that if one requires an action a, the other must provide a semantically compatible action b. The mediator compensates for the syntactic differences between their actions by performing the necessary transformations, which is formalised as follows:

Mediator O (P 1 , P 2 ) = Map(s 1 , s 2 ) such that s 2 ∈ traces(P 2 )↑ O P 1 , s 1 ∈ traces(P 1 )↑ O P 2 : s 2 ≡ O s 1
In the IM case, we are able to produce the mediator for the MSNP and XMPP processes as illustrated in Figure 5. The mediator intercepts an instant message sent by an MSNP user and forwards it to the appropriate XMPP user. Similarly, each instant message sent by an XMPP user, is forwarded by the mediator to the corresponding MSNP user.

Map1 = (<InstantM essage, {SenderID, RecepientID, M essage}, ∅ > → <InstantM essage, {U serID, ConversationID, M essage}, ∅ >→ END). Map2 = (< InstantM essage, {U serID, ConversationID, M essage}, ∅ > → <InstantM essage, {SenderID, RecepientID, M essage}, ∅ >→ END). Mediator = (Map1 Map2).

Implementation

In order to validate our approach, we have combined the LTSA 18 model checker with an OWL-based reasoner to achieve ontological refinement leading to the OLTSA tool (Figure 6-). LTSA is a free Java-based verification tool that automatically composes, analyses, graphically animates FSP processes and checks safety and liveness properties against them. In the case where the processes match, a concrete mediator that implements the actual message translation is deployed atop of the Starlink framework [START_REF] Bromberg | Starlink: Runtime interoperability between heterogeneous middleware protocols[END_REF], see Figure 6-. Starlink interprets the specification of mediators given in a domainspecific language called Message Translation Logic (MTL). An MTL specification describes a set of assignments between message field s. The messages correspond to action names and the fields to the name of input/output data. Note that the OFSP description focuses on the ontological annotations and not the the actual name. Therefore, we refine the OFSP specification of the mediator so as to generate the associated MTL before deploying the mediator atop of Starlink, see Figure 6-. Let us consider the mapping Map 1 (see Figure 5), which transforms an XMPP input action to the associated MSNP action. Figure 7 shows a small fragment of the associated translation logic described in MTL and which corresponds to the assignment of the U serID field of the XMPP message (ReceivedInstantMessage) to the SenderID field of of the MSNP message (SDG) with the mediator transiting from state XS1 to state M R1.

The tool, the IM ontology, and a video demonstration are available at http: //www-roc.inria.fr/arles/download/imInteroperability/.

<t r a n s l a t i o n l o g i c > <assignment> <f i e l d > < s t a t e l a b e l >MR1</ s t a t e l a b e l ><m e s s a g e>SDG</m e s s a g e> <xpath >/ f i e l d / p r i m i t i v e F i e l d [ l a b e l = ' UserID ' ] / v a l u e </xpath> </ f i e l d > <f i e l d > < s t a t e l a b e l >XS1</ s t a t e l a b e l ><m e s s a g e>R e c e i v e d I n s t a n t M e s s a g e </m e s s a g e> <xpath >/ f i e l d / p r i m i t i v e F i e l d [ l a b e l = ' S e n d e r I D ' ] / v a l u e </xpath> </ f i e l d ></assignment> . . . . </ t r a n s l a t i o n l o g i c > Fig. 7. Translation logic to map MSNP and XMPP instant messages

Assessment

In this section we first report a set of experiments we conducted to evaluate the effectiveness of our approach when applying it to the instant messaging case. Then, we discuss some of its quality properties.

Experimental Results

We have evaluated the time for translating one protocol to the other by the synthesised mediator and the effort required by the developer to enable mediation. We have hand-coded a mediator that makes MSNP, YMSG, XMPP interoperable in order to gauge the complexity of the mediation. We considered the Windows Live Messenger for MSNP, Yahoo! Messenger for YMSG, and Pidgin 19 for XMPP. We run the OLTSA tool and the Starlink framework on a Mac computer with a 2,7 GHz processor and 8 GB of memory.

In the first experiment, we measured the time taken to translate from one protocol to another. We repeated the experiments 50 times and reported the mean time for each case in Table 2. The hand-coded mediator is approximately 3 times faster than the synthesised one. This is mainly due to the fact that the execution framework (Starlink) is interpreting the models at runtime whereas the hand-coded one is already compiled and hence more efficient.

In the second experiment, we measured the time for synthesising the mediator (see Table 3). One can note that action mapping is the most time consuming step as it necessitates ontology reasoning in order to infer semantically matching actions while the behavioural matching is performed is less than 1 ms. Nevertheless, this step needs to be performed once only and is definitely faster than hand-coding the mediator or even specifying it. Moreover, for each new version of one of the protocols, the hand-coded mediator has to be re-implemented and re-compiled, Starlink requires the specification of the translation logic to be respecified whereas the automated synthesis requires only the specification of the protocol to be re-loaded. The third experiment measures the effort demanded from the developer to produce mediators between different IM applications. We calculate the number of Java code lines of the hand-coded mediator, the number of lines of DSL specification that need to be specified for Starlink and those needed to specify the individual applications for the automated synthesis. The results are given in Table 4. One can notice that although Starlink reduces considerably (around 4 times) the lines of code that need to be written, the automated approach requires the OFSP specifications only and decreases this number drastically (around 10 times). This is mainly due to (i) the use of OFSP to model the interaction protocols, which introduces an ontology-based domain-specific language grounded in process algebra and especially targeted for concurrent systems. For example, the MSNP behaviour is described in Starlink using 30 XML lines and only 6 lines with our approach (ii) Further, the translation code need not be specified. More importantly, unlike the hand-coded or the Starlink versions where the developer is required to know both protocols and define the translation manually, the protocols are specified separately in the automated version. Thus, each IM provider can independently specify its own protocol. Finally, we are investigating within the Connect20 project learning-based techniques to infer such a specification automatically [START_REF] Blair | The Role of Ontologies in Emergent Middleware: Supporting Interoperability in Complex Distributed Systems[END_REF].

Handcoded

To sum up, our automated approach to interoperability significantly reduces the programming effort and ensures the correctness of the translation while requiring a negligible time for synthesising the mediator and guaranteeing good performances at translation time.

Qualitative Assessment

In addition to the above-mentioned performances, our approach satisfies the following properties:

-Correctness by construction. The correctness of the mediation, i.e., the absence of deadlock and unspecified receptions [START_REF] Yellin | Protocol specifications and component adaptors[END_REF], is guaranteed by construction. Indeed, if there is an exact match between P 1 and P 2 then the parallel composition P 1 M P 2 is deadlock free. Exact matching means that each trace of P 1 (P 2 ) has a corresponding semantically-matching trace in P 2 (P 1 ), which amounts to setting P 1 (P 2 ) as a safety property that needs to be verified by P 2 (P 1 ). This verification is performed by exhaustively exploring the state space. Note though that efficient model checkers use optimisation techniques to reduce the space if possible. The reduction techniques are even more efficient in the case of process algebra.

-Formal yet tractable DSL specification. OFSP introduces an ontology-based domain-specific language grounded in process algebra. Process algebra constitute a very expressive behavioural specification language for complex concurrent systems while ontologies are the model of choice to describe data semantics. Furthermore, standard modelling languages that developers are familiar with (e.g., BPEL or CDL) can be used to specify the interaction protocols and then automatically translate them to FSP using existing tools 21 . -Dealing with encryption. When encryption is enforced (e.g., Google Talk encrypts XMPP messages), the mediator cannot parse or modify these messages all the way between the initial sender and the ultimate receiver. Transparency cannot be ensured anymore. Instead, the user get involved and handles some of the translation tasks [START_REF] Vassilakis | A framework for adaptation in secure web services[END_REF]. In the Google Talk case, the mediator uses a robot (bot) that the user adds to its contact list. The robot manages a set of commands, e.g., IM <destinationID> <message> to send a message message to user destinationID.

Related Work

The problem of mediating applications has been studied in different domains. Middleware solutions focus on providing abstraction and execution environments that enable interoperation by providing an abstract interface and exploiting reflection [START_REF] Grace | ReMMoC: A reflective middleware to support mobile client interoperability[END_REF], by translating into a common intermediary protocol such as in the case of Enterprise Service Buses [START_REF] Menge | Enterprise Service Bus[END_REF] or by proposing a domain-specific language to describe the translation logic and automatically generate the corresponding gateways [START_REF] Bromberg | Starlink: Runtime interoperability between heterogeneous middleware protocols[END_REF]. However, these solutions require the developer to specify the translation to be made and hence to know both protocols in advance whereas in our approach, each protocol is independently specified and the translation is produced automatically. The Web Service Execution Environment (WSMX) performs the necessary translation on the basis of pre-defined mediation patterns.

However, the composition of these patterns is not considered, and there is no guarantee that it will not lead to a deadlock. Vaculín et al. [START_REF] Vaculín | The process mediation framework for semantic web services[END_REF] devise a mediation approach for OWL-S processes. They first generate all requester paths, then find the appropriate mapping for each path by simulating the provider process. This approach deals only with client/server Web service interactions. It is not able to deal with the heterogeneity of instant messaging applications for example. Calvert and Lam [START_REF] Calvert | Formal methods for protocol conversion[END_REF] propose an approach to reason about the existence of a mediator by projecting both systems into a common sub-protocol. However, this common sub-protocol needs to be specified using an intuitive understanding of the protocols. In their seminal paper, Yellin and Strom [START_REF] Yellin | Protocol specifications and component adaptors[END_REF] propose an algorithm for the automated synthesis of mediators based on predefined correspondences between messages. By considering the semantics of actions, we are able to infer the correspondences between messages automatically. Finally, Cavallaro et al.

[5] also consider the semantics of data and relies on model checking to identify mapping scripts between interaction protocols automatically. However, they do not take into account the actual semantics of the operations. Moreover, they propose to perform the interface mapping beforehand so as to align the vocabulary of the processes, but many mappings may exist and should be considered during the generation of the mediator. Hence, even though there exists a significant amount of work to achieve interoperability, none of the existing approaches proposes to generate automatically mediators that are able to deal with both data and protocol mismatches.

Conclusion

Achieving interoperability between heterogeneous distributed applications without actually modifying their interfaces or behaviour is desirable and often necessary in today's pervasive systems. Mediators promote the seamless interconnection of distributed applications by performing the necessary translations between their messages and coordinating their behaviour. In this paper, we have presented a principled approach to the automated synthesis of mediators at runtime. We first infer mappings between application interfaces by reasoning about the semantics of their data and operations annotated using a domain-specific ontology. We then use these mappings to automatically synthesise a correctby-construction mediator. This principled approach to generating mediators removes the need to develop ad hoc bridging solutions and fosters future-proof interoperability. We evaluated the approach using a case study involving heterogeneous instant messaging applications and showed that it can successfully ensure their interoperation. Work in progress involves the definition of many-to-many operation mappings to manage a broader set of heterogeneous systems. Our work further integrates with complementary work ongoing within the Connect European project so as to develop a framework to support the interoperability lifecycle by using semantic technologies to synthesise mediators dynamically and ensure their evolution to respond efficiently to changes in the individual systems or in the ontology. A further direction is to consider improved modelling capabilities that take into

Fig. 1 .

 1 Fig. 1. Interoperability issue between heterogeneous IM systems

Fig. 2 .

 2 Fig. 2. The instant messaging ontologyFigure 2 depicts the instant messaging ontology. An InstantMessage class has at least one sender hasSender{some}, one recipient hasRecipient{some}, and one message hasMessage. hasSender{some} and hasRecipient{some} are object properties that relate an instant message to a sender or a recipient while hasMessage is a data property associated with the InstantMessage class. The Sender and Recipient classes are subsumed by the User class. Indeed, any instance of the two former classes is also an instance of the latter. A Conversation is performed between a sender (who initialises it) and a recipient, and the conversation has its own identifier. An instant message isPartOf a conversation. A ChatRoom is a specific conversation and hence is subsumed by Conversation.

  MSNClient = (<M SN Authentication Request, {U serID}, {Challenge} > → <M SN Authentication Response, {Response}, {Authentication ok} > → ExchangeMsgs). ExchangeMsgs = (<CreateChatRoom, {U serID}, {ConversationID} > → <JoinChatRoom,{U serID},{Acceptance} >→P1 | < JoinChatRoom, {U serID}, {Acceptance} > → < {ChatRoomInf o, ∅, {ConversationID} > →P1), P1 = (<InstantM essage, {U serID, ConversationID, M essage}, ∅ > → P1 | <InstantM essage, {U serID, ConversationID, M essage}, ∅ > → P1 | <M SN Logout, {U serID}, ∅ > → END).

Fig. 3 .

 3 Fig. 3. OFSP specification of MSNP XMPPClient = (< XM P P Authentication Request, {U serID}, {Challenge } > → <XM P P Authentication Response, {Response}, {Authentication ok} > → ExchangeMsgs). ExchangeMsgs = (<InstantM essage, {SenderID, RecepientID, M essage}, ∅ >→ ExchangeMsgs | <InstantM essage, {SenderID, RecipientID, M essage}, emptyset > → ExchangeMsgs | < XM P P Logout, {U serID}, emptyset >→ END).

Fig. 4 .

 4 Fig. 4. OFSP specification of XMPP

Fig. 5 .

 5 Fig. 5. OFSP specification of the Mediator between MSNP and XMPP

Fig. 6 .

 6 Fig. 6. Mediation Architecture

Table 1 .

 1 FSP overview

	FSP Syntax

  1 |= O P 2 ) iff each trace of P 2 semantically matches a trace of P 1 : Definition 6 (|= O : Ontological Refinement). P 1 |= O P 2 def = ∀s 2 ∈ traces(P 2 )↑ O P 1 , ∃s 1 ∈ traces(P 1 )↑ O P 2 : s 2 ≡ O s 1 By checking ontological refinement between P 1 and P 2 , we are able to determine the following behavioural matching relations: -Exact matching-(P 1 |= O P 2 ) ∧ (P 2 |= O P 1 ): assesses compatibility for symmetric interactions such as peer-to-peer communication where both processes provide and require the similar functionality. -Plugin matching-(P 1 |= O P 2 ) ∧ (P 2 |= O P 1 ): evaluates compatibility for asymmetric interactions such as client-server communication where P 1 is providing a functionality required by P 2 . -No matching-(P 1 |= O P 2 ) ∧ (P 2 |= O P 1 ): identifies behavioural mismatch.

Table 2 .

 2 Translation time (ms)

			Mediator atop		Act.	Beh.
			Starlink		mapping	match.
	YMSG ↔ MSNP	22	69	YMSG ↔ MSNP	306	<1
	MSNP ↔ XMPP	52	131	MSNP ↔ XMPP	252	<1
	YMSG ↔ XMPP	44	126	YMSG ↔ XMPP	244	<1

Table 3 .

 3 Time for Synthesis (ms)

Table 4 .

 4 Development effort

		Hand-Coded	Starlink	Automated
	YMSG ↔ MSNP	1172	258	96
	MSNP ↔ XMPP	750	198	84
	YMSG ↔ XMPP	945	168	76

http://www.fet11.eu/

http://explore.live.com/windows-live-messenger/

http://messenger.yahoo.com/

http://www.google.com/talk/

http://www.xmpp.org/

http://adium.im/

http://www.process-one.net

http://nabu.opendfki.de/

http://www.w3.org/TR/owl2-overview/

http://BOW.sinica.edu.tw/

http://www.w3.org/wiki/SweoIG/TaskForces/CommunityProjects

The subsumption relation can be used to implement other inferences, such as satisfiability and equivalence, using pre-defined reductions.

Note the use of an overline as a convenient shorthand notation to denote output actions

http://www.doc.ic.ac.uk/ltsa/

http://connect-forever.eu/

account the probabilistic nature of systems and the uncertainties in the ontology. This would facilitate the construction of mediators where we have only partial knowledge about the system.


Gilbert Cette
email: gilbert.cette@banque-france.fr

Nicolas Dromel
email: nicolas.dromel@parisschoolofeconomics.eu]

Rémy Lecat
email: remy.lecat@banque-france.fr]

Anne-Charlotte Paret
email: anne.charlotte.paret@ensae.fr

Philippe Askenazy

Pierre Cahuc

Romain Duval

Denis Fougère

Eva Moreno-Galbis

Thomas Piketty

Labour relations quality and productivity: An empirical analysis on French firms

Keywords: Labour relation, collective bargaining, trade unions, productivity JEL Classification: J53, J52, J51

This analysis characterizes empirically how good labour relations can alleviate the negative impact on productivity of regulatory constraints or workforce opposition. Our evidence of good labour relations lies in the existence of binding collective agreements, at the firm or at the industry level. The estimations are based on a unique dataset collected by the Banque de France about the obstacles French firms may face in increasing their utilisation of production factors. Data are an unbalanced sample of 7,441 observations, corresponding to 1,545 companies, over the period 1991-2008. Our main results may be summarised as follows: i) 'workforce or union opposition' interacted with 'regulatory constraints' has a negative significant impact on total factor productivity (TFP). Regulatory constraints would become really binding when workers or unions use them as a tool to oppose management's decisions; ii) 'regulatory constraints' interacted with 'branch or firm agreement' has a positive significant impact on TFP. These agreements, which can only be obtained if labour relations are supportive, would be used by firms to offset the negative impact of regulatory constraints.

These results confirm that labour relations quality, at the branch or the firm levels, is an important factor of productive performance.

Introduction

A large amount of literature has been analysing the impact of worker voices, and more generally of work relations quality, on firm performances. An important part of this literature characterizes work relations by representative institutions, such as unions or works councils, and investigates their impact on firm performances. These performances are themselves characterized by labour productivity, total factor productivity or profitability. As a matter of fact, these studies do not really provide a unified and simple message.

Concerning the effect of unionization, the literature surveys from [START_REF] Hirsch | What Do Unions Do for Economic Performance?[END_REF] and [START_REF] Morikawa | Labor unions and productivity: An empirical analysis using Japanese firmlevel data[END_REF] show that while a majority of analyses find a positive impact on productivity, some do find a nonsignificant impact or even a negative one. For example, both on US individual firm data, [START_REF] Brown | Trade unions in the production process[END_REF] find a positive impact and [START_REF] Clark | Unionization and firm performance: the impact on profits, growth, and productivity[END_REF] a negative one. On the same type of data, [START_REF] Cooke | Employee participation programmes, group-based incentives, and company performance: a union-nonunion comparison[END_REF] or [START_REF] Black | How to compete: the impact of workplace practices and information technology on productivity[END_REF] give an explanation of this contrast: they find a positive impact of unionization on productivity only in firms where the employer adopts some human resource practices that promote joint decision with incentive-based compensation, and a negative impact in firms that maintain more traditional labour management relations. The impact of unionization on average wage is found to be usually positive, but the impact on firm profitability is ambiguous, positive or negative depending on the study.

The survey from [START_REF] Addison | The determinants of firm performance: unions, works councils, and employee involvement/high-performance work practices[END_REF] also highlights contrasted conclusions in the literature regarding the impact of works councils on productivity. [START_REF] Addison | Worker Participation and Firm Performance: Evidence from Germany and Britain[END_REF] on German and British firms and [START_REF] Addison | Works councils in Germany: their effects on establishment performance[END_REF] on German firms obtain a positive impact in large firms only. [START_REF] Fairris | Works Councils and Firm Productivity in France[END_REF] find, on French firms, no evidence of a positive impact of works councils on firm productivity and even some limited evidence of a negative effect. [START_REF] Hübler | Works councils and collective bargaining in Germany: the impact on productivity and wages[END_REF] provide an empirical explanation of these different results. Based on German firms, their study shows a positive impact of works councils on productivity only within firms covered by collective agreements. This empirical result is actually in line with the theoretical paper from Freeman and Lazear (1994) which shows that works councils can improve firm productivity under certain conditions: "There are potential net social gains from works councils. But to work best and gain these potential benefits, the rules governing councils must be carefully written to bound the power of labor and management and 'fit' the broader labor system in which councils must function". It appears that works councils can improve firm productivity only in situations where the quality of labour relations is good enough to prevent some risks of inefficiency. The positive impact on productivity results in fact from the interaction between works councils and these good labour relations, works councils being however a negative productivity factor if taken individually.

The large literature on the quality of labour relations focused on indicators such as strikes [START_REF] Kleiner | How industrial relations affects plant performance: the case of commercial aircraft manufacturing[END_REF][START_REF] Mas | Labor Unrest and the Quality of Production: Evidence from the Construction Equipment Resale Market[END_REF], grievance fillings [START_REF] Ichniowski | The Effects of Grievance Activity on Productivity[END_REF][START_REF] Katz | Industrial Relations Performance, Economic Performance, and QWL Programs: An Interplant Analysis[END_REF], absenteeism [START_REF] Katz | Industrial Relations Performance, Economic Performance, and QWL Programs: An Interplant Analysis[END_REF], tough union leaders [START_REF] Freeman | An economic analysis of works councils[END_REF][START_REF] Kleiner | How industrial relations affects plant performance: the case of commercial aircraft manufacturing[END_REF] and labour climate surveys among managers or workers of a specific plant [START_REF] Katz | Industrial Relations Performance, Economic Performance, and QWL Programs: An Interplant Analysis[END_REF]Deery and Roderick 2005;[START_REF] Katz | Industrial Relations and Productivity in the U.S. Automobile Industry[END_REF]. These papers support the negative impact of a deteriorated labour climate on productivity or product quality. More precisely, [START_REF] Deery | Labor-management cooperation: antecedents and impact on organisational performance[END_REF] point out the building blocks of a good labour climate, as reflected by an employee survey: in particular, the union's willingness to adopt an integrative approach to bargaining and the management's willingness to share information freely with the union. However, these papers are based on case studies (different plants of the same firm in automobile, aircraft, paper mills...) and do not address the impact of firm or branch agreements or of the interactions between these agreements and labour relations. Our aim is to characterize the impact on productivity of good labour relations. In France, large margins of improvement in labour relations quality may exist, as compared to other countries. Trade union density is the lowest among OECD countries (7.6% in 2008 for 18.6% in Germany according to the OECD) and labour regulations at the national level rarely stem from union-employers negotiation. [START_REF] Aghion | Civil society and the state: The interplay between cooperation and minimum wage regulation[END_REF] highlight that in a cross-section of countries, state regulation of labour markets is negatively correlated with the quality of labour relations. They argue that state regulation crowds out the possibility for workers to experiment negotiation and learn about the potential cooperative nature of labour relations. This mechanism seems to be particularly relevant for France, where state intervention in the labour market regulation is widespread and pregnant.

Our empirical analysis is based on a unique survey of French firms, about the obstacles they may face in increasing their production factor utilisation: the survey on factor utilisation degrees (FUD hereafter). We merge these data with FiBEn, another individual company dataset collected by the Banque de France. FiBEn is a very large database that includes balance sheets and profit and loss accounts from annual tax statements, and can be used to compute total factor productivity (TFP) and changes in output. The FUD survey has been carried out every year since 1989 by the Banque de France at the plant level. It not only provides rich insights about firm-level factor utilisation, but also a unique appraisal of rigidities faced by firms in increasing their capital workweek. Firms are directly asked to declare the presence of such rigidities, and to characterize their legal, social or technical nature. More precisely, entrepreneurs answered the following question: « If you had to increase your capital operating time, and if your sales potential could justify it, would you meet obstacles or brakes such as… ? ». The considered obstacles are: worker opposition, union opposition, absence of qualified workforce, bottleneck on commodities or supply, technical obstacles, legal or regulatory constraint, branch agreement, firm agreement, and other. The merger of these two databases results in an unbalanced sample of 7,441 observations, corresponding to 1,545 companies, over the period 1991-2008. To our knowledge, this individual company database is unique for allowing an empirical analysis concerning the impact of these rigidities on TFP. As in [START_REF] Hübler | Works councils and collective bargaining in Germany: the impact on productivity and wages[END_REF], our evidence of good labour relations lies in the existence of binding collective agreements, at the firm or at the industry level. In France, the ability to conclude a collective agreement is a clear sign of good labour relations, between employers and at least some unions. Hence, even if it is declared as an obstacle to increase the capital operating time, the existence of a collective agreement (at the branch or the firm level) remains an appropriate proxy for good labour relations.

The empirical strategy consists in estimating a relation where firm-level TFP is explained by output changes, wages per employee, year, sector-year and firm-specific fixed effects along with different obstacles declared by firms, these obstacles being considered individually or interacted for some of them. These estimates may face a double causality bias: firms benefitting from high TFP may be able to provide higher wages. Employers could therefore overcome worker or union opposition, better secure supply, attract talents and negotiate more favourable firm agreements by being able to provide more generous compensations for increased flexibility. In order to address this bias, we implemented an instrumentation strategy based on Blundell and Bond (1998) using lagged obstacles levels and changes as instruments. We did also control for wages.

Our main results may be summarised as follows: i) 'workforce or union opposition' interacted with 'regulatory constraints' has a negative significant impact on total factor productivity (TFP). Regulatory constraints would become really binding when workers or unions use them as a tool to oppose management's decisions; ii) 'regulatory constraints' interacted with 'branch or firm agreement' has a positive significant impact on TFP. These agreements, which can only be obtained if labour relations are supportive, would be used by firms to offset the negative impact of regulatory constraints.

These results support the importance of labour relations quality, at the branch or the firm levels, as a powerful factor of productive performance. They provide an original confirmation to early insights in the literature (e.g. Freeman and Lazear, 1994). Section 2 presents the data. Section 3 details the empirical strategy and section 4 comments on the results. Section 5 displays the outcome of several robustness checks and section 6 concludes.

Data and obstacles to increase capital operating time

An original dataset

Our empirical analysis merges two firm-level annual datasets constructed by the Banque de France: FiBEn and a survey on factor utilisation degrees (FUD).

FiBEn is a large database built on fiscal documents, including balance sheets and profit-and-loss statements. It features all French firms with sales exceeding €750,000 per year, or with a credit outstanding higher than €380,000. Every year, these accounting data are available for about 200,000 firms. In 2004, FiBEn was covering 80 % of the firms with 20 to 500 employees, and 98 % of those employing more than 500 employees. This database allows calculating firm-level value added (Q), the capital stock (K), the volume of employment (L) and computing total factor productivity (TFP):

-The value added volume (Q) is calculated by dividing value added in value (production in value minus intermediate consumptions) by a national accounting index of value added price at the industry level (two digit decomposition level).

-The volume of capital (K) sums gross capital volumes for buildings and equipment. Gross capital at historical price (as reported in tax statements) is divided by a national index for investment price, lagged with the mean age of gross capital (itself calculated from the share of depreciated capital in gross capital, at historical price). This measure corresponds to the volume of capital, usually by the end of a fiscal year. For this reason, we introduce a one-year lag for capital to compute share-weighted factor growth.

-The average employment level (L) is directly available in FiBEn.

-Total factor productivity for firm i in sector j at date t (TFP ijt ) is obtained by dividing total value added Q ijt by the volume of production inputs V ijt , where:

with α j the labour share in revenue for sector j, calculated from the median over firms in this industry, on the dataset period.

The FUD survey has been carried out each September since 1989 1 . 1,500 to 2,500 plants 2 are covered by this survey, depending on the year. This dataset directly provides for each plant the annual growth rate of capital workweek (WK) and the level of labour workweek (WL).

While the FUD survey is carried out at the plant level, FiBEn gives information at the firm level. A difficulty in the data merge lies in the fact that some firms are multi plants. When several plants of a single firm were covered by the FUD survey, we aggregated for each year all plants of this firm, weighting them by their share in the firm's total employment. We considered the FUD survey answers to be representative enough when the employment level corresponding to this aggregation was higher than 50 % of the one reported in FiBEn (otherwise, the firm was dropped from the final dataset 3 ). Each time one observation was missing for a given firm, we interpolated its value taking the average of its one-period past and one-period next observations.

The sample used in this paper is an unbalanced firm panel of 7,441 observations, corresponding to 1,545 companies, over the period 1991-2008. The criteria underlying this sample selection are detailed below.

Obstacles to shifts in capital operating time

Our dataset not only provides rich insights about firm-level factor utilisation, but also a unique appraisal of rigidities faced by firms in increasing their capital workweek. Firms were directly asked to declare the presence of such rigidities and to characterize their legal, social or technical nature. More precisely, entrepreneurs answered the following question: « If you had to increase your capital operating time, and if your sales potential could justify it, would you meet obstacles or brakes such as…? »:

1-Worker opposition (WOPP) 2-Union opposition (UOPP) 3-Absence of qualified workforce (ABS) 4-Bottleneck on commodities or supply (BOTT) 5-Technical obstacles (TOBS) 6-Legal or regulatory constraint (REG) 7-Branch agreement (BRA) 8-Firm agreement (FIR) 9-Other Beyond reporting obstacles, firms were also asked to rank them. Given the potential heterogeneity in the firms' understanding of this ranking exercise, we preferred to particularly focus on the presence of an obstacle and made some methodological choices: in particular, some firms ranked systematically all obstacles, while some others selected just one, two or three obstacles. On the one hand, considering that an obstacle is present as soon as it is reported may be misleading, as some firms ranked all obstacles. On the other hand, considering only obstacles ranked in first position may rule out any possibility to analyse firms facing several rigidities. To deal with this "question understanding" potential bias, we choose to consider an obstacle as present if it is declared and ranked either in first, second or third position.

A strong correlation and possible confusion between different obstacles led us to adopt an aggregation procedure, so as to reduce some potential interpretation and multicollinearity biases. We first decided, in an arbitrary way, to aggregate ABS, BOTT and TOBS in a single variable named « Skills, supply or technical constraints (TEC) », since the relevance of distinguishing these obstacles was weak in terms of policy implications. Then, we undertook a hierarchical clustering procedure, represented in Figure 1, to further aggregate obstacles while keeping a strong explanatory power.

Documents de Travail du Centre d'Economie de la Sorbonne -2012.52 The first obstacles to be aggregated were branch and firm agreements, then workforce and union opposition. Not only these two aggregations seem intuitively relevant, they also allow explaining more than 80 % of the variance associated with the non-aggregated model. We therefore decided to stop aggregating variables at this threshold, to avoid losing too much explanatory power with respect to the non-aggregated model. Table 1 summarizes the aggregation procedure outcome. Looking at the evolution of obstacle declarations through time yields interesting insights (Graph 1).

4

For instance, the OPP variable takes value 1 if workforce opposition (WOPP) and / or union opposition (UOPP) are / is declared, 0 otherwise. Other aggregates were built the same way, from their corresponding components. First, it appears that the different obstacles can easily be ranked in terms of reporting frequency, this hierarchy being quite stable through time. Each year, between 40% and 70% of firms signalled the presence of skills, supply or technical constraints (TEC), which makes them the most frequently reported obstacles. Workforce or union oppositions (OPP) were signalled by nearly 45% of firms every year, while regulatory obstacles were declared by a third of firms on average (with a peak at 47% in 2001). Obstacles linked to collective agreements at the branch or firm level (AGR) would be the least reported rigidities, but would nevertheless be faced by around 15% of firms every year.

Second, aside from these hierarchical considerations, we observe a kind of common trend between obstacle reporting, stemming probably from the business cycle and its perception by firms. A global increase in obstacle declarations can be highlighted between 1998 and 2001. It is easily understandable that during expansions, firms perceive constraints in a stronger way, precisely because they feel the need to increase their production and, therefore, their capital operating time. As a matter of fact, the TEC obstacle showed the strongest cyclical component over 1991-2008.

Interestingly, the larger the firm, the more frequently obstacles are declared as regards workforce or union opposition (OPP) and branch or firm agreements (AGR) (see Graph 2). In contrast, the smaller the firm, the more frequently entrepreneurs report obstacles linked to skills, supply or technical constraints (TEC) and regulatory constraints (REG). This tends to show that large firms have developed means to adapt technical shortages and regulatory obstacles, but would suffer more than smaller firms from workers' oppositions. Small firms in France are generally operating in a less unionized environment than big firms. This may explain why their reporting of obstacles linked to workforce or union opposition, and branch or firm agreements, is lower with respect to larger firms. Further descriptive statistics about the variables used may be found in the appendix. We now explain and detail in the following section our empirical strategy.

Empirical methodology

In the FUD survey, obstacles to increase capital operating time provide some rich information on the constraints that may prevent total factor productivity (TFP) improvements. In our estimations, these obstacles will therefore be used as TFP regressors, on the sub-sample of firms reporting at least one obstacle 5 .

Skills, supply or technical constraints (TEC) bear on human capital and on capital utilisation in the upper phase of the cycle, which will impact our TFP measure. These shortages may constrain firms to adopt some sub-optimal production organisation or process, which could have an impact on TFP.

Workforce or union opposition (OPP) directly bears on TFP through a lower effort from the workers, or indirectly through a resistance to reorganisations of the production process. Regulatory constraints (REG) or branch/firm agreements (AGR) may hinder TFP-improving reorganisations. On the other hand, AGR testifies of a significant worker involvement, alleviating information asymmetries between employees and management and reducing economic inefficiencies [START_REF] Freeman | An economic analysis of works councils[END_REF], and more globally of good labour relations quality, which can have a positive productivity impact. Indeed, unionization [START_REF] Brown | Trade unions in the production process[END_REF] or worker voices [START_REF] Fairris | Works Councils and Firm Productivity in France[END_REF] have been shown to have a positive impact on firm productivity.

5

There may be a bias in using this sub-sample as firms reporting obstacles need to increase capital operating time and hence may be in a tense production phase. To deal with this potential issue, we control for the firmspecific production cycles through its value added growth as an explanatory variable, and for the firm structural situation through firm fixed effects. The whole sample cannot be used since firms that report no obstacle may do so because they do not need to increase their capital operating time, not because they do not face any obstacle. Some interactions between obstacles may be relevant. Indeed, workforce or union opposition may be more detrimental to TFP if this opposition can use regulatory constraints to prevent reorganisations of the production process (OPP*REG). On the contrary, firm or branch agreements may have an ambiguous role, either acting as a kind of regulatory constraint in interaction with workers' opposition, or alleviating the degree of workforce opposition (OPP*AGR) and helping overcome rigidities stemming from regulation (REG*AGR).

The estimated equation is the following:

݂ݐ ,௧ ൌ ߙ ߙ ଵ ݍ∆ ,௧ ߙ ଶ ݓ ,௧ ∑ ߚ ܵܤܱ ,,௧ିଵ ߛܺ ,௧ ߜ ߝ ,௧
ୀସ ୀଵ

(1)

with variables:

• tfp: total factor productivity (in log)

• q: value added (in log)

• w: wages per employee (in log)

• OBS k : obstacles to increasing capital operating time • X: a vector of controls including sector-year dummies

• δ: firm fixed effects

• ߝ: error term and subscripts:

• i for firm • j for industry • t for year

We use sector-year dummies to control for industry cycles and TFP trends 6

.

Value added growth controls for potential mismeasurements of factor utilisation in the TFP regression (cf. [START_REF] Cette | Production factor returns: the role of factor utilisation. Banque de France Working paper n°317[END_REF], firm-specific cycles or activity trends. Wages per employee control for the unmeasured quality of human capital, but also for the favourable impact of a generous wage policy on labour climate. We also use firm-specific fixed effects, which control for time-invariant firm unobserved heterogeneity such as management quality.

We may face a double causality bias: firms benefitting from high TFP may be able to provide higher wages, overcoming worker or union opposition, to better secure supply, attract talents and negotiate more favourable firm agreements by being able to provide more generous compensations for increased flexibility. In order to address this bias, we implement an instrumentation strategy based on Blundell and Bond (1998) using lagged obstacles levels and changes as instruments. Changes in value added may be endogenous and are also instrumented the same way. As we may face heteroscedasticity and serial correlation, we use the generalised method of moments with robust standard errors.

Results

The main estimates are presented in Table 2. It is noteworthy to emphasise that OLS results are consistent with 2SLS ones in terms of sign if not significance.

'Value added growth' has a positive and significant impact on the TFP level, with stable coefficients, around 0.28 for 2SLS estimates (columns 2 and 4). This result, usually found in empirical studies, indicates the existence of short-term increasing returns to production factors. [START_REF] Cette | Production factor returns: the role of factor utilisation. Banque de France Working paper n°317[END_REF] argue they can be due to omitted variables, particularly the intensity of factor utilisation. With the very same data set, they show how increasing returns to scale disappear when working time, capacity utilisation rate and mainly capital operating time are introduced in the production function.

'Wages per employee' has a positive and significant impact on the TFP level, with quite stable coefficients, around 0.26 for 2SLS estimates (columns 2 and 4), which is consistent with the literature. 'Skills, supply or technological constraints' have no significant impact on the TFP level, which may not be surprising. Shortages may constrain firms to adopt a non-optimal production organisation or process, which could decrease or increase, depending on the situation, the TFP level compared to a situation without such shortages. For example, a shortage in labour or capital may lead to a more intensive use of the available quantity of these two factors, and increase TFP. Moreover, as this obstacle is reported by many firms throughout the period (cf. Graph 1), its impact may be captured by firm fixed effects as it may reflect the usual recruitment policy or supply management of the firm.

Without taking into account the potential interactions between explanatory variables (columns 1 and 2), 'workforce or union opposition' is the only obstacle which would have a significant impact on productivity. The existence of such an opposition would decrease TFP by around 2% (column 2). 'Regulatory constraints' do not have a significantly negative direct impact on productivity. Nonetheless, it appears (columns 3 and 4) that these regulatory constraints do have a negative impact on TFP when 'workforce or union opposition' are reported, leading to a -2% decrease in TFP on average (column 4). This suggests that 'regulatory constraints' would only become significantly binding when workers or unions use them as a tool to oppose management decisions. For example, working time rules are complex and workers or unions, through the threat of legal procedure, may lead to a stricter application of these rules in cases of deteriorated labour relations.

Besides, 'branch or firm agreement' has no direct impact on TFP (columns 1 to 4) but the interaction between 'branch and firm agreement' and 'regulatory constraints' has a positive and significant impact (columns 3 and 4). These puzzling results can receive two explanations. First, a branch or firm collective agreement can organize efficient working organisations, thus alleviating regulatory constraints. Secondly, the French labour code allows softening specified regulatory constraints through a collective agreement. This was emphasised in the context of the 35-hour workweek policy implemented in France from 1998, after the left-wing electoral victory of 1997 7 . This policy consisted in a decrease from 39 to 35 hours, in 2000 for firms of more than 20 employees (which represent more than 97% of our sample) and in 2002 for other firms, of the legal weekly working time threshold from which firms have to pay an overtime wage premium. For a firm decreasing to 35 hours or less the usual weekly working time of its employees, it was possible to get generous financial subsidies from the State if this decrease was organised through a collective agreement between social partners, at the firm level for firms of more than 50 employees and also possibly at the branch level for other firms. To get these subsidies, the agreements had to be signed by unions representing at least 50% of the employee votes at union elections. But the 35 hour workweek laws allowed firms to implement through a collective agreement some flexible labour organisation with a possible positive impact on TFP. For instance, it was possible through agreements to exclude some breaks of the accounted working time, or to account daily rather than hourly the working time for white collars, or to respect the 35 hours threshold in average over the year or even in average over several years. But the use of these disposals needed good quality labour relations, employee unions having the choice not to allow it. The results also indicate that 'branch or firm agreement' would have offset the significant negative impact of the interaction between 'regulatory constraints' and 'work force or union opposition', as it yields a positive impact of 4% on TFP. The interaction between 'branch or firm agreement' and 'work force or union opposition' is not significant when instrumented: indeed, 'branch or firm agreement' may actually be alleviating 'work force or union opposition' and hence neutralising its impact.

Table 3 displays estimates where branch and firm agreements are separated. It is difficult to identify separately both types of agreements which are highly correlated but it appears that the positive interacted impact of 'agreements' with 'regulatory constraints' would result mostly from 'firm agreements' rather than 'branch agreements' (table 3, column 6). This result indicates that it is mainly at the firm level that good quality labour relations can allow to use some complex regulation disposals to improve the firm's productive performance.

These results support the role of labour relations quality, mainly at the firm level, as a powerful factor of productive performance. They provide an original confirmation to early insights in the literature (e.g. Freeman and Lazear, 1994).

Robustness checks

Our flagship result is the structural regression in Table 2, column 4, which emphasises the role of interactions between regulatory constraints, branch or firm agreements, and employee or union opposition. In Table 4, we present several robustness checks for this regression, on different subsamples:

• First, we exclude firms which TFP level lies in the first or last 5 percentiles. That way, we assess whether our results are driven by a small number of extreme observations. The coefficient signs are not altered, although their significance changes: REG * AGR is still significant, but OPP * REG is not. • Then, we exclude one by one all sectors representing more than 5% of the sample, to evaluate the sensitivity of our results to specific activities (although we already had firm fixed effects and year-industry dummies in the reference equation). Significance and magnitude of the coefficients are barely altered, especially for REG*AGR. OPP * REG is however not significant for a large number of subsamples.

We provide in Table 5 further robustness estimates with different specifications:

• We remove year*sector dummies (column 1), while keeping year dummies which are necessary to avoid a spurious regression of a time series (TFP) on stationary variables. Our main results are not altered: REG*AGR and OPP*REG keep the same signs significance and magnitude. The magnitude is stronger for REG*AGR, although less precise. • We remove the firm production cycle control, .ܣܸ∆ Indeed, this control may encompass a lot of relationships beyond the firm production cycle (in particular supply shocks due to our variables of interest). Coefficients in the reference equation are not altered in their signs or magnitude, but the OPP*REG is no longer significant. • We remove the control for wage per head, which may be collinear with labour relations.

Coefficients are practically unaltered in signs or significance.

Our main result, showing that the negative effect of regulatory constraints on productivity can be alleviated by branch or firm agreements, appears to be fairly robust. However, the fact that regulatory constraints may be more stringent when employees or unions use them to prevent TFP improvements tends to be non-significant under some robustness checks, although the sign and magnitude of this effect is unaltered.

Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

Conclusion

Our aim was to analyse the impact on productivity of good labour relations. We have used an original database containing 7,441 observations, corresponding to 1,545 French companies, over 1991-2008.

To our knowledge, this company-level database is unique in allowing such an analysis. We assume the existence of a collective agreement (at the branch or the firm level) to be a proxy for good labour relations.

The main results from our empirical investigation are the following: i) 'workforce or union opposition' interacted with 'regulatory constraints' has a negative significant impact on total factor productivity (TFP). Regulatory constraints would become really binding when workers or unions use them as a tool to oppose management's decisions; ii) 'regulatory constraints' interacted with 'branch or firm agreement' has a positive significant impact on TFP. These agreements, which can only be obtained if labour relations are supportive, would be used by firms to offset the negative impact of regulatory constraints. These results support the importance of labour relations quality and provide an original confirmation to early insights in the literature.

Nevertheless, we must remain cautious in generalising these results, since France is a particular country concerning working relations. Among OECD countries, France has the lowest union membership rate. Related with that, France is probably the country (or at least one of the countries) where labour market regulation is the most stringent and where collective bargaining processes are the poorest and the weakest. Labour relations get conflictual more quickly, leading more easily to strikes for example, in France than in other countries. In such circumstances, the ability to conclude a collective agreement is probably a stronger indication for good labour relations in France than elsewhere. We cannot exclude that the impact of collective agreement, taken as a proxy of good labour relations, could have a positive but lower impact on productivity in other countries. Our result would need to be confirmed on a database covering other countries, for it to be generalised.

Bibliography:

0 0 1 1 1 0,

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

Figure 1 :

 1 Figure 1: Hierarchical clustering procedure result

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

Table 1 :

 1 Aggregation procedure

	Aggregated obstacles	4	…	… from originally declared obstacles
	Workforce or union opposition (OPP)	-Workforce opposition (WOPP)
				-Union opposition (UOPP)
	Skills, supply or technical constraints (TEC)	-Absence of qualified workforce (ABS)
				-Bottleneck on commodities or supply (BOTT)
				-Technical obstacles (TOBS)
	Regulatory constraint (REG)			-Legal or regulatory constraint (REG)
	Branch or Firm Agreement (AGR)	-Branch agreement (BRA)
				-Firm agreement (FIR)

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.52 Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

	Industry (control variables)					Frequency
	B0			Agriculture and food industry (AFI)				10.1
	C1			Clothing, leather and footwear				5.7
	C2			Paper, printing and publishing				7.0
	C3			Chemical, rubber, plastics and fuel				1.7
	C4			Household equipment industries				5.4
	D0 E1			Industry Shipbuilding, aeronautic and railway industries			2.2 1.5		50	0,50
	E2 E3	REG	Regulatory constraints	FUD survey Mechanical equipment industries Electric and electronic equipment industries 0	0	0	1	14.5 3.4	1	0,31	0,46
	F1 F2	AGR	Branch or firm agreement	Mineral products industry FUD survey Textile industry	0	0	0	0	3.8 3.7	1	0,16	0,37
	F3 F4 F5	BRA	Branch agreement	Wood and paper industry FUD survey Chemicals and plastics industry Metallurgy and metal transformation 0	0	0	0	9.8 7.9 20.0	1	0,12	0,33
	F6	FIR	Firm agreement	FUD survey Electric and electronic components industry 0	0	0	0	3.3	1	0,13	0,33
	OPP x REG		FUD survey	0	0	0	0		1	0,20	0,40
	OPP x AGR		FUD survey	0	0	0	0		1	0,13	0,33
	OPP x BRA		FUD survey	0	0	0	0		0	0,10	0,30
		OPP x FIR		FUD survey	0	0	0	0		1	0,11	0,31
	REG x AGR		FUD survey	0	0	0	0		1	0,12	0,32
	REG x BRA		FUD survey	0	0	0	0		1	0,10	0,30
	REG x FIR		FUD survey	0	0	0	0		0	0,09	0,28
			Total factor
		TFP	productivity in	FiBEn
			log		2,43	2,62	2,84	3,10		3,38	2,87	0,40
			1 st difference
		△ △ △ △q	value added in	FiBEn
			log		-0,17	-0,06	0,02	0,11		0,21	0,02	0,20
		w w w w	Labour cost per employee in log	FiBEn	3,13	3,30	3,47	3,64		3,80	3,46	0,28

Table 2

 2 * p < 0.05, *** p < 0.01 Firm fixed effects, two stage least square estimates when specified, generalized method of moments. Lagged levels and lagged difference of obstacles used as instruments. Year, Sector X Year dummies and constant included but not reported.

	-Main results
		(1)	(2)	(3)	(4)
		Without	Without	With	With
		interactions	interactions -	interactions	interactions -
			2SLS		2SLS
	∆.Value added (log)	0.526 ***	0.285 ***	0.527 ***	0.279 ***
		(0.00970)	(0.0226)	(0.00970)	(0.0229)
	Wage per head (log)	0.224 ***	0.263 ***	0.225 ***	0.259 ***
		(0.0147)	(0.0326)	(0.0147)	(0.0328)
	Worforce or union opposition (OPP -1 )	-0.0091 *	-0.0217 **	-0.00150	0.00377
		(0.0048)	(0.0092)	(0.0060)	(0.0080)
	Skills, supply or technical constraints	0.0058	0.0198	0.00438	-0.0058
	(TEC -1 )	(0.0045)	(0.0286)	(0.0045)	(0.0074)
	Regulatory constraints (REG -1 )	0.0059	0.00858	0.0070	0.0119
		(0.0049)	(0.0082)	(0.0073)	(0.0106)
	Branch or firm agreement (AGR -1 )	-0.0091	-0.0105	-0.0067	-0.0494
		(0.00585)	(0.0104)	(0.0132)	(0.0323)
	Worforce or union opposition and			-0.00994	-0.0208 *
	regulatory constraints (OPP -1 X REG -1 )			(0.0095)	(0.0122)
	Worforce or union opposition and branch			-0.0216 *	0.0096
	or firm agreement (OPP -1 X AGR -1 )			(0.0128)	(0.0238)
	Regulatory constraints and branch or firm			0.0217 *	0.0420 **
	agreement (REG -1 X AGR -1 )			(0.0120)	(0.0208)
	N° Observations	7,441	7,441	7,441	7,441
	Adj. R²	0.222	0.226	0.222	0.221
	Sargan-Hansen		14.90		6.031
	Sargan-Hansen p-value		0.313		0.420
	Robust standard errors in parentheses

* p < 0.1, *Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

Table 3

 3

	-Separating branch and firm agreements
		(1)	(2)	(3)	(4)
		Without	Without	With	With
		interactions	interactions -	interactions	interactions -
			2SLS		2SLS
	∆.Value added (log)	0.526 ***	0.284 ***	0.527 ***	0.283 ***
		(0.00970)	(0.0226)	(0.00971)	(0.0227)
	Wage per head (log)	0.225 ***	0.263 ***	0.225 ***	0.262 ***
		(0.0147)	(0.0326)	(0.0147)	(0.0328)
	Worforce or union opposition (OPP -1 )	-0.00934 *	-0.0240 **	-0.00204	0.00440
		(0.00487)	(0.00964)	(0.00602)	(0.00777)
	Skills, supply or technical constraints	0.00620	0.0270	0.00463	-0.00691
	(TEC -1 )	(0.00451)	(0.0343)	(0.00461)	(0.00758)
	Regulatory constraints (REG -1 )	0.00644	0.00921	0.00850	0.0141
		(0.00503)	(0.00855)	(0.00729)	(0.0104)
	Branch agreement (BRA -1 )	-0.0103	-0.0146	-0.0131	-0.0257
		(0.00794)	(0.0106)	(0.0198)	(0.0571)
	Firm agreement (FIR -1 )	-0.000200	0.00118	0.00927	-0.0564
		(0.00769)	(0.0100)	(0.0167)	(0.0403)
	OPP -1 X REG -1			-0.0114	-0.0232 *
				(0.00981)	(0.0138)
	OPP -1 X BRA -1			-0.0108	-0.00640
				(0.0171)	(0.0329)
	OPP -1 X FIR -1			-0.0263	0.0317
				(0.0177)	(0.0348)
	REG -1 X BRA -1			0.0103	0.0143
				(0.0185)	(0.0417)
	REG -1 X FIR -1			0.0245	0.0465 **
				(0.0162)	(0.0200)
	N° Observations	7,441	7,441	7,441	7,441
	Adj. R²	0.222	0.224	0.222	0.223
	Sargan-Hansen		14.05		11.69
	Sargan-Hansen p-value		0.297		0.232
	Robust standard errors in parentheses; * p < 0.1, ** p < 0.05,

*** p < 0.01 Firm fixed effects, two stage least square estimates when specified, generalized method of moments. Lagged levels and lagged difference of obstacles used as instruments. Year, Sector X Year dummies and constant included but not reported.

Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

Table 4

 4 p < 0.1, ** p < 0.05, *** p < 0.01 Firm fixed effects when specified, two stage least square estimates, generalized method of moments. Lagged levels and lagged difference of obstacles used as instruments. Year, Sector X Year dummies when specified and constant included but not reported.

		-Robustness to exclusion of specific observations
			(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
	Exclusion of…	Reference	First and	Food	Textile	Printing	Households	Mecanical	Wood	chemicals	metal
			equation	last 5	products			equipment	equipments			products
				percentiles
	∆.Value	added	0.279 ***	0.195 ***	0.295 ***	0.274 ***	0.272	0.276 ***	0.281 ***	0.278 ***	0.272 ***	0.282 ***
	(log)		(0.0229)	(0.0170)	(0.0130)	(0.0129)	(0.0129)	(0.0129)	(0.0138)	(0.0131)	(0.0129)	(0.0143)
	Wage per head	0.259 ***	0.245 ***	0.261 ***	0.261 ***	0.260 ***	0.284 ***	0.269 ***	0.257 ***	0.263 ***	0.243 ***
	(log)		(0.0328)	(0.0334)	(0.0162)	(0.0160)	(0.0157)	(0.0163)	(0.0168)	(0.0159)	(0.0155)	(0.0169)
	OPP -1		0.00377	-0.000475	0.00216	0.00475	0.00273	0.00288	0.00710	0.00608	0.00366	-0.00161
			(0.00803) (0.00754) (0.00842) (0.00844) (0.00845) (0.00841) (0.00875) (0.00869) (0.00837) (0.00919)
	TEC -1		-0.00576	0.00429	-0.00874	-0.00522	-0.00425	-0.00685	-0.00705	-0.00436	-0.00306	-0.00420
			(0.00737) (0.00483) (0.00785) (0.00779) (0.00793) (0.00790) (0.00824) (0.00802) (0.00784) (0.00876)
	REG -1		0.0119	0.00402	0.00974	0.0106	0.0149	0.0118	0.00570	0.0115	0.0139	0.0122
			(0.0106)	(0.00964)	(0.0106)	(0.0106)	(0.0107)	(0.0106)	(0.0113)	(0.0108)	(0.0106)	(0.0123)
	AGR -1		-0.0494	-0.0589 *	-0.0684 **	-0.0535	-0.0527	-0.0307	-0.0409	-0.0226	-0.0352	-0.0554
			(0.0323)	(0.0330)	(0.0330)	(0.0325)	(0.0337)	(0.0336)	(0.0337)	(0.0341)	(0.0316)	(0.0356)
	OPP -1 X REG -1	-0.0208 *	-0.00913	-0.0216 *	-0.0209 *	-0.0210	-0.0183	-0.0188	-0.0147	-0.0172	-0.0250 *
			(0.0122)	(0.0115)	(0.0123)	(0.0124)	(0.0128)	(0.0125)	(0.0129)	(0.0127)	(0.0124)	(0.0142)
	OPP -1 X AGR -1	0.00963	0.0255	0.0270	0.0135	0.00853	-0.00351	0.00161	-0.0114	-0.00506	0.0182
			(0.0238)	(0.0271)	(0.0244)	(0.0240)	(0.0245)	(0.0248)	(0.0253)	(0.0247)	(0.0235)	(0.0267)
	REG-1 X AGR-1 0.0420** 0.0415** 0.0498**	0.0417*	0.0432*	0.0344	0.0435** 0.0254	0.0334	0.0491**
			(0.0208)	(0.0196)	(0.0214)	(0.0214)	(0.0222)	(0.0217)	(0.0219)	(0.0226)	(0.0208)	(0.0229)
	N° Observations	7441	6567	6715	7009	6937	7047	6345	6683	6868	5902
	Adj. R²		0.221	0.191	0.246	0.223	0.217	0.226	0.161	0.232	0.234	0.223
	Sargan-Hansen	6.031	5.454	6.044	6.784	5.270	7.154	4.647	4.262	5.761	4.607
	Sargan-Hansen p-	0.420	0.487	0.418	0.341	0.510	0.307	0.590	0.641	0.450	0.595
	value

* Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

is unfortunately not present in the dataset since accidentally, paper questionnaires for the 2002 survey are no longer available at Banque de France. 2 These plants are the ones usually covered by the Banque de France monthly survey on business climate. 3 In the final dataset, only 55 observations correspond to multi-plants firms. ܸ ௧ ൌ ܭ ௧ିଵ ଵିఈ ೕ ܮ ௧ ఈ ೕ Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

With an upward-trending TFP regressed on obstacles taking values 0 or 1, year dummies are needed to avoid estimating a spurious relationship. Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

The 35-hour workweek policy change is captured in our analysis by the year fixed-effect. Documents de Travail du Centre d'Economie de la Sorbonne -2012.52

Robust standard errors in parentheses; * p < 0.1, ** p < 0.05, *** p < 0.01; Firm fixed effects, two stage least square estimates when specified. Lagged levels and lagged difference of obstacles used as instruments. Year, Sector X Year dummies and constant included but not reported. Documents de Travail du Centre d'Economie de la Sorbonne -2012.52