Patrice Calégari

Frédéric Guidec

Pierre Kuonen

Urban Radio Network Planning for Mobile Phones

published or not. The documents may come

URBAN RADIO NETWORK PLANNING FOR MOBILE PHONES

by Patrice Calégari, Frédéric Guidec, Pierre Kuonen, EPFL -DI -GRIP/LITH La planification de réseaux radio pour la téléphonie mobile en milieu urbain est une nécessite de gros calculs, qu'il est préférable d'exécuter sur plusieurs processeurs en parallèle. D'une part, il faut simuler la propagation des ondes radio afin de pr dire les zones qui peuvent être couvertes. Le programme ParFlow++ a été développé dans ce but. D'autre part, il faut choisir l'ensemble d'antennes qui couvre une ville au meilleur coût. Ce dernier point est un problème d'optimisation combinatoire d'une grande complexité. Nous le traitons avec un algorithme génétique, ainsi nommé pour ses similitudes avec des systèmes biologiques.

Urban radio network planning for mobile phones requires costly computation that are better to run on processors in parallel. First, radio wave propagation must be simulated in order to predict the area that can be covered by a Base Transceiver Station (BTS). The ParFlow++ piece of software was developed with this goal. Second, the set of BTSs that cover a city with the lowest cost must be found. The latter task is a hard combinatorial optimization problem, that we try to solve with a bio-inspired genetic algorithm.

RADIO NETWORK PLANNING

One of the issues telecommunication operators must face when deploying a cellular network in a city is the selection of good locations for Base Transceiver Stations (BTSs). The problem comes down to finding out the best possible sites for BTSs, while guaranteeing that all -or at least a given percentage of the surface of-the streets are covered, and that the global cost of the radio network is kept at a minimum. Assuming that a set of potential sites is available, our goal is to select the best subset of sites capable of satisfying the coverage requirements. The first step, that is, the computation for each BTS of the zone that it can cover, is achieved by a radio wave propagation simulation piece of software called ParFlow++. The second step, that is, the selection of the best BTS sites, is done by a bio-inspired piece of software called Paragene. These two parallel pieces of software are parts of the STORMS 1 project, which aims at the definition, the implementation, and the validation of a software tool to be used for the design and the planning of the future UMTS 2 network.

RADIO WAVE PROPAGATION SIMULATION

The ParFlow method

The ParFlow method was designed at the University of Geneva by Chopard, Luthi and Wagen [START_REF] Luthi | Wave Propagation in Urban Micro-Cells: a Massively Parallel Approach using the TLM Method[END_REF]. It compares with the so-called Lattice Boltzmann Model, that describes a physical system in terms of the motion of fictitious microscopic particles over a lattice [START_REF] Benzi | The Lattice Boltzmann Equation: Theory and Applications[END_REF], and it permits the simulation of outdoor radio wave propagation in urban environment. As the ParFlow method operates on a 2D model of the terrain it is appropriate for simulating radio wave propagation when fixed antennas are placed below rooftops, as is the case in urban radio networks composed of micro-cells.

According to the Huygens principle, a wave front consists of a number of spherical wavelets emitted by secondary radiators. The ParFlow method is based on a discrete formulation of this principle. Space and time are represented in terms of finite elementary units ∆r and ∆t, related by the velocity of light C 0 3 . Space is modeled by a grid with a mesh size of length ∆r, and flow values are defined on the edges connecting neighboring grid points.

The flows entering a grid point at time t are scattered at time t+∆t among the four neighboring points. For each grid point, outgoing flows at time t are a linear combination of incoming flows at that time, and an incoming flow at time t corresponds to the outgoing flow calculated on a neighboring grid point at time t-∆t (see Figure 1). These rules apply for all grid points but those modeling the source (i.e., the BTS) and obstacles. The source point radiates a signal through its four outgoing flows, but it does not propagate incoming flows. Obstacles (typically, city

3 ∆t = ∆r / (C0. √2)
FOR SUPERCOMPUTING REVIEW 1997 buildings) are modeled by two kinds of grid points: wall points, and indoor points (see Figure 2). In the current version of the ParFlow model, it is assumed that radio waves do not penetrate buildings. As a consequence, indoor points are not involved in the computation: wall points are perfectly reflecting points that return any incident wave with opposite sign, and whose reflection coefficient and matrix elements can be modified in order to model different kinds of walls [START_REF] Luthi | Wave Propagation in Urban Micro-Cells: a Massively Parallel Approach using the TLM Method[END_REF].

Irregular implementation in ParFlow++

ParFlow++ is an object-oriented, irregular implementation of the ParFlow method, targeted at distributed memory parallel platforms. Its main originality with respect to former implementations of the ParFlow method [START_REF] Luthi | Wave Propagation in Urban Micro-Cells: a Massively Parallel Approach using the TLM Method[END_REF] is that it was implemented as an irregular application. Since the method does not allow for radio wave propagation through buildings, ParFlow++ does not model indoor points. Experience shows that this approach permits a significant reduction of memory space and of computational power (when modeling an urban area, buildings can represent up to 30 % of the surface considered). But such an approach inevitably leads to the creation and the management of an irregular data structure. As they provide powerful features to describe and to manipulate complex, irregular data structures, objectoriented languages are perfectly suited to an irregular implementation of the ParFlow method. This is the reason why ParFlow++ was implemented in C++. All kinds of non-indoor points are described in a hierarchy of C++ classes, whose instances are assembled at runtime so as to constitute an irregular structure that preserves the neighborhood relationships.

Data parallelism

A major advantage of the ParFlow method is that, although the calculations made during each iteration step are theoretically synchronous, updates of points require independent computation. The ParFlow algorithm is therefore a good candidate to parallel implementation.

The first parallel version of the ParFlow method was implemented by Chopard, Luthi and Wagen on Thinking Machine Corporation's CM-200, whose SIMD 4 architecture provides thousands of synchronous processors [START_REF] Luthi | Wave Propagation in Urban Micro-Cells: a Massively Parallel Approach using the TLM Method[END_REF]. The ParFlow method can be readily and efficiently implemented on SIMD platforms, because it is possible to take advantage of the regular grid data structure and of the synchronous progress of the computation. However, the main disadvantage of such an implementation is its lack of scalability. An irregular data structure such as that discussed in the former paragraph can hardly be mapped on the synchronous regular architecture of the CM-200. The consequence is that, on such a platform, many processing units (those modeling indoor points) remain idle throughout the entire computation. Moreover, since each point of the grid must be allocated to one processing element, the size of the grid is constrained by the size of the parallel machine.

MIMD platforms are more versatile than SIMD platforms when it comes to implementing irregular applications. Actually, the ParFlow method has already been implemented on several MIMD platforms by Chopard, Luthi and Wagen [START_REF] Luthi | Wave Propagation in Urban Micro-Cells: a Massively Parallel Approach using the TLM Method[END_REF]. Yet, every time it was implemented as a regular algorithm, in C or in Fortran. ParFlow++ contrasts sharply with these former implementations, not only because of its object-orientation, but also because it results from the first attempt to implement the ParFlow method for MIMD-DM platforms while operating on an irregular data structure with an irregular algorithm. Another characteristic of ParFlow++ is that it was developed so as to be easily portable on any kind of MIMD-DM platform.

Because of the large amount of outdoor points that must be considered in a simulation (typically, several thousands of outdoor points for a single city district), an appropriate policy must be chosen to allocate each point to a processing element of the target platform. Many partitioning policies can be considered for an irregular structure such as that of ParFlow++. Yet, exotic partitioning policies often require costly mechanisms for locating remote data, and for ensuring efficient data exchanges. For these reasons, and in order to obtain good load balancing, ParFlow++ relies on a simple, yet efficient static data distribution. The simulation zone is split in horizontal stripes, which are then allocated to processors based on a round-robin policy, as shown in Figure 3. FOR SUPERCOMPUTING REVIEW 1997 In ParFlow++ each stripe basically consists of a structured collection of points. It also manages two `frontiers' internally. A frontier can be perceived as a collection of references to points that are either on the northern edge or on the southern edge of a partition. The behavior of frontier points differs slightly from that of other points, for they have to interact with `neighboring' points that are actually stored on remote processors. A frontier thus ensures the propagation of flows between a partition and one of its neighbors. Communications between neighboring partitions are based on calls to routines of the PVM library [START_REF] Geist | PVM: Parallel Virtual Machine. A User's Guide and Tutorial for Networked Parallel Computing[END_REF].

Experimental results and performances

ParFlow++ was compiled and tested on the Cray T3D of the Swiss Federal Institute of Technology 5 . We ran an 800 step radio wave propagation simulation on a 500x500 point zone modeling a 1 km 2 district of the city of Geneva. Figure 4 shows snapshots of the simulation. Each picture is a path-loss map. On the Cray T3D we measured the speedups observed for various simulation zone sizes. Figures 5 and6 confirm the scalability of the parallel implementation. The table in Figure 5 shows the actual computation times observed on each test case, and Figure 6 shows the speedups calculated from these times. (For the 1024x1024 and 2048x2048 zones, the simulation was not possible on a single processor because of memory limitation, so we had to estimate the sequential reference times).

Covered cells computation

Once a propagation simulation is complete for a given BTS, the geographical area in which the coverage is good for mobile phone communication must be delimited. This area is called the covered cell of the BTS. A threshold value is determined based on different radio quality criteria (guessed traffic demand, etc.), and each grid point where the power of the received signal is bigger than the threshold value belongs to the covered cell. Such a covered cell is shown in Figure 7.

BTS SITING

Modelling

The aim of the first step was to generate the set of covered cells associated to a set of potential BTSs. These data will be used to find the best subset of BTSs that covers an area. In order to store the huge amount of information FOR SUPERCOMPUTING REVIEW 1997 about BTSs and covered cells, a data structure was developed. This structure connects a subset of BTSs to the intercells they can cover, where an intercell is a set of locations that are potentially covered by exactly the same BTSs. A simple example of such a structure is shown in Figure 8.

BTS1 BTS2 cell1 cell2 cell1∩ ∩ 2
Fig. 8 The covered cells associated to the BTSs are discretized on a grid. Each BTS is connected to the intercells it covers.

Complexity

Definition: A set system (X,ℜ) is a set X, with a collection ℜ of subsets of X Let us consider:

• X is the set of all intercells.

• ℜ is the set of all subsets R of X such that:

x i = One covered cell

x i ∈R U Definition: a set cover is a subcollection C ⊆ ℜ, whose union is X, and the size of C is the number of sets in C [START_REF] Brönnimann | Almost Optimal Set Covers in Finite VC-Dimension[END_REF].

With such a modelling, the problem of finding the minimum number of BTSs that cover an area comes down to finding a set cover of minimum size. Unfortunately, finding a set cover of minimum size is NP-complete [START_REF] Garey | Computers and intractability: a guide to the theory of NP-Completeness[END_REF]. Thus unless P=NP, if we want a polynomial time algorithm, we must use an approximation algorithm and look for possibly sub-optimal -yet satisfactory-solutions. To achieve this goal, we investigate several approaches, which are said to be 'bio-inspired' because they use heuristics that have some analogies with natural or social systems [START_REF] Colorni | Heuristics from nature for hard combinatorial optimization problems[END_REF].

The genetic approach

To date, we most especially focus on the so-called genetic approach. This work is done in cooperation with the LEOPARD6 project. A genetic algorithm is a populationbased algorithm, which means that its state at any time is a population of candidate solutions. A population is a set of individuals that represent candidate solutions for a given problem, and that are generally encoded as chromosomelike bit strings. The algorithm uses selection and recombination operators to generate new sample points in a search space [START_REF] Holland | Adaptation in natural and artificial systems[END_REF]. The bit strings we consider represent the whole set of possible BTS locations. Whether a location is actually selected in a potential solution depends on the value of the corresponding entry in the bit string. Figure 9 shows how a possible solution to our problem is encoded as the bit string of an individual. The first step in the execution of a genetic algorithm consists in the creation of an initial population. In our implementation, the initial population is built randomly. Each iteration step of the algorithm on the population (see Figure 10) is called a generation. During the execution of a genetic algorithm, a generation can be thought of as a two stage process. First, selection is applied to the current population to create an intermediate population. Then, crossover and mutation operators are applied to the intermediate population to create the next population. The execution terminates when a satisfactory individual has been produced or when a predefined number of generations has been run through. Figure 10 describes the different steps in the evolution of a population. The selection is achieved based on the fitness value associated with each individual, which may be perceived as an allocation of reproductive opportunities: the higher the fitness value of an individual, the likelier it is to `reproduce' . The function returning the fitness value is:

FOR SUPERCOMPUTING REVIEW 1997 fitness(individual) = CoverRate α number of selected BTSs
where CoverRate is the percentage of locations covered by the selected BTSs (in relation to the number of locations covered by the initial set of BTSs). The parameter α can be tuned to favor the cover rate with respect to the number of transmitters. Figure 11 shows the influence of the parameter α on the characteristics of the results. It shows that for α<1.5 the coverage is unacceptable, for 1.5<α<4 the coverage grows quickly while the number of BTS grows slowly, and for 4<α<10 the coverage remains almost constant while the number of BTSs keeps growing. A good value for α is thus 4 (this value will be used in the remainder of this article). The crossover operator we use achieves a 'one-pointcrossover'. It splits the bit strings of two randomly selected individuals at a randomly chosen position, and it then recombines the bit strings by exchanging their ends, hence producing two new bit strings. In the current implementation of Paragene, each couple of individuals taken from the intermediate population has a probability of 0.9 to achieve a crossover. In the case no crossover is performed, the couple of individuals is put back into the new population without changes. Our mutation operator simply flips the value of a randomly chosen bit of the bit string with a probability of 0.6 7 . The execution terminates after a predefined number of generations.

First experimental results

Experiments were conducted for the district of Geneva introduced in the first part of this article. Starting with 99 user-provided potential BTS locations, 99 cells were computed with ParFlow++. Figure 12 shows the coverage that would be obtained if these 99 BTSs were all selected in the final radio network. Locations that are covered exactly once are colored in blue, those covered twice are colored in green, those covered three times are colored in red and those covered four times and more are colored in pink. It can be noticed that the gray locations cannot be covered by any of the user-provided potential BTSs. As a lot of points are covered many times, it is clear that some of the proposed BTSs are useless. Moreover, too many transmitters covering a same zone can lead to radio interference. On the other hand it can also be useful to cover a same location with two different BTSs, as this permits roaming: when a user moves from one cell to another. Figure 13 shows a solution returned by Paragene after 320 generations of a 160 individual population. The algorithm meets our demand by returning solutions with large coverage and few BTSs. It has however two major shortcomings. First, it is too slow (3mn31s for this solution) to be used interactively, as required by telecommunication operators. Second, the solutions still contain quite too many BTSs in the operators opinion.

Island concept and parallelism

In order to improve the quality of the results obtained with the genetic algorithms, the population can be distributed in subpopulations that evolve independently. These subpopulations, called islands, increase the chances for the algorithm to find good solutions by having many genetic algorithms competing, each of them operating on small populations. In order to let some islands benefit from the information found by others, some individuals are allowed to move from an island to another. This mechanism is called migration.

In order to speedup the execution, the parallelisation of the island-based algorithm was investigated. The fact that the islands evolve almost independently suggests that the algorithm is parallel in essence. The computation time can thus be decreased by distributing the islands on several processors. This MIMD-DM 8 approach enables to run the program on clusters of workstations, which are more commonly available and cheaper than parallel supercomputers. The islands are virtually positioned on an oriented ring, and migrations are only allowed along that ring (see Figure 14). This topology was chosen so as to minimize the amount of migrations, and thus to minimize the communication overhead due to migrations between remote islands. Every time a new generation is computed, a copy of the best individual (that with the best fitness value) ever met by each island is sent to the next island on the ring. Each island thus receives a new individual that replaces one of its individual selected randomly. The only requirement is that the number of islands be greater or equal to the number of available processors because each processor must be in charge of at least one island (see Figure 15). Our parallel implementation of Paragene [START_REF] Calégari | Radio Network Planning with Combinatorial Optimization Algorithms[END_REF] was designed using objectoriented techniques, and it was written in C++. It uses the PVM library [START_REF] Geist | PVM: Parallel Virtual Machine. A User's Guide and Tutorial for Networked Parallel Computing[END_REF] for inter-processor communications.

Quality of the results and speedup

Figure 16 shows a solution returned by our island-based genetic algorithm after 320 generations when running on 40 workstations that were in charge of one island each. The total population size (40 * 4 = 160 individuals) was the same as that used for computing the result shown in Figure 13. This new result is of better quality: its associated fitness value is 0.03051, whereas that of the previous solution was only 0.02177, and it was found in 10 seconds (against 3mn31s. for the previous solution).

CONCLUSION

In this article we have presented a cellular automaton approach to simulate radio wave propagation in urban environment on a MIMD-DM computer. A very good speedup was achieved by using an original static load balancing technique. The development was realized using object-oriented techniques, leading to a strict distinction between what belongs to the physical problem (radio wave propagation) and what belongs to the computing model (cellular automaton). In the future we intend to reuse this computing model to simulate other physical phenomena such as flowing fluids.

Using radio wave propagation predictions computed by the former algorithm, we tackled the problem of selecting optimal BTS sites for urban mobile phone networks. A parallel genetic algorithm was implemented on a network of up to 40 workstations. Taking into account that fact the links between the workstations are rather slow the efficiency of the parallel execution measured on 40 workstations (52.75%) is good. It was obtained with an island-based genetic algorithm which tries to minimize the communication between the workstations. Again, the development was realized using objectoriented techniques, because we intend to reuse this islandbased parallel genetic algorithm to solve other difficult combinatorial optimization problems.

BIBLIOGRAPHY

  1 STORMS (Software Tools for the Optimization of Resources in Mobile Systems) is an ACTS project funded by the EC and by the Swiss Government.

  2 UMTS: Universal Mobile Telecommunication System.

Fig. 1 :

 1 Fig. 1: Discretization of space and time in the ParFlow model

Fig. 2 :

 2 Fig. 2: Obstacles modelling in the ParFlow method. The input is a digital terrain model that permits to distinguish between outdoor points (blue), wall points (white), and indoor points (gray)

Fig. 3 :

 3 Fig. 3: Simulation zone partitioning and mapping

Fig. 4 :

 4 Fig. 4: Snapshots of a radio wave propagation simulation achieved with the ParFlow method. These pictures show how the wave propagates and covers a growing surface

Fig. 5 :Fig. 6 :

 56 Fig. 5: Parallel simulation duration on the Cray T3D, for 512 x 512, 1024 x 1024, and 2048 x 2048 point simulation zones (times given in seconds)

Fig. 7 :

 7 Fig. 7: Result of a radio wave propagation simulation on a district of the city of Geneva (left), and shape of the covered cell hence identified (right).

Fig. 9

 9 Fig. 9 Encoding of a candidate solution in an individual bit string.

Fig. 10

 10 Fig. 10 Global overview of a genetic algorithm. One iteration of the loop is called a generation.

Fig. 11 :

 11 Fig. 11: Average number of BTSs and average coverage of solutions found with different values of the parameter α.

Fig. 12

 12 Fig.12 Coverage obtained with the 99 potential BTSs. Pink locations are covered 4 or more times.

Fig. 13 A

 13 Fig. 13 A solution obtained, with a 160 individual population, after 320 generations. The 36 selected BTSs cover 94.09% of the initially covered surface.

I s l a nd- 4 I 2 I s l a nd- 1 Fig. 14

 42114 Fig. 14 Distribution of islands on an oriented ring. Migrations are only allowed along the oriented ring.

8Fig. 15

 15 Fig. 15 Parallel version of our island-based genetic algorithm.

Fig. 16 :

 16 Fig. 16: A solution obtained with 40 islands of 4 individuals, after 320 generations. The 19 selected BTSs cover 87.26% of the initial covered surface.

Figure 17 FORFig. 17

 1717 Figure17shows the speedup observed on a network of 40 workstations, when running 320 generations over 40 islands of 4 individuals each. It can be noticed that the speedup is almost linear for less than 10 workstations, and that the efficiency on 40 workstations amounts to 52.75%, which is satisfying.

The LEOPARD project (Parallel population-based methods for combinatorial optimisation) is funded by the Swiss National Science Foundation (project # 21-45070.95/1)

These probability rates have been carefully chosen, after a comprehensive study of their impact on the quality of the results returned by Paragene.


Fabrice Murtin
email: fabrice.murtin@oecd.org.

Alain De Serres

Romain Duval

Jørgen Elmeskov

John Martin

Giuseppe Nicoletti

Jean- Marc Robin

Stefano Scarpetta

Jean-Luc Schneider

Paul Swaim

How Do Policies Affect the Exit Rate out of Unemployment? Disentangling Job Creation from Labour Market Frictions

This paper assesses the effects of labour market policies on the unemployment outflow rate while disentangling two channels, namely labour market tightness and employer-employee matching efficiency. Using a sample of 11 OECD countries over the period 1985-2007, we treat the endogeneity of market tightness with business cycle shocks and the tax wedge as instruments. We find that the replacement rate of unemployment benefits, Active Labour Market Policies as well as the tax wedge in countries with poorly representative unions, have a significant, robust, and large impact on market tightness. Employment protection has a negative but small impact on matching efficiency. Overall, policy effects appear to be mostly channeled through market tightness and job creation.

Introduction

Nearly 4 years after the economic crisis, unemployment rates still remain significantly above their pre-crisis level in a majority of OECD countries. With the rise in unemployment being largely concentrated among specific categories of workers, one of the main concerns in countries most severely hit is that persistently high unemployment levels eventually lead to the emergence of a substantial pool of workers trapped in a situation of quasi-permanent unemployment or with tenuous attachments to the labour market. Put differently, there is a risk that the incidence of long-term unemployment remains high -or rises further -even as employment growth picks-up. Given that the incidence of long-term unemployment is directly related to the unemployment outflow rate, this paper aims to evaluate the influence that policies and institutions may have on the latter. This is done on the basis of macroeconomic data covering 11 OECD countries over the period 1985-2007. More specifically, the paper seeks to identify the structural determinants of unemployment outflow rates by using matching functions. The latter are used in labour economics to disentangle the influence of the pace of job creation or labour market tightness (measured as the ratio of job vacancies to unemployment) on unemployment outflows from that of the degree of labour market frictions or matching efficiency [START_REF] Blanchard | The Beveridge Curve[END_REF][START_REF] Mortensen | Job Creation and Job Destruction in the Theory of Unemployment[END_REF][START_REF] Petrongolo | Looking into the Black Box: A Survey of the Matching Function[END_REF][START_REF] Pissarides | Equilibrium Unemployment Theory[END_REF]. Factors contributing to stimulate labour demand and jobs creation will influence outflow rates through market tightness, whereas those affecting job search intensity are expected to impact on the outflow rate through matching efficiency.

The main contributions of this paper are of both a methodological and an empirical nature. Whereas the properties of the matching function have been extensively studied (e.g. [START_REF] Coles | A Test Between Stock-flow Matching and the Random Matching Function Approach[END_REF][START_REF] Gregg | Stock-flow Matching and the Performance of the Labor Market[END_REF], to the best of our knowledge it is the first time that the outflow rate is decomposed into a system of structural equations that identifies the channels through which the latter rate is affected by labour market policies and institutions. In this regard, we find that the bulk of policy and institution impact is channelled by market tightness, that is to say, through the pace of job creation.

In practice, our system of simultaneously determined equations allows for the treatment of the endogeneity of market tightness with respect to the unemployment outflow rate. In a first stage, we instrument labour market tightness by business cycles shocks as well as labour market institutions that are deemed to have an impact on market tightness but none on matching efficiency. These policy-based instruments include the tax wedge and its interaction with the characteristics of wage bargaining systems. In a second stage, we regress the unemployment outflow rate on predicted market tightness and on other institutional variables that may influence the degree of labour market frictions and matching efficiency, namely the characteristics of unemployment benefit systems and the degree of employment protection or product market regulation. Overall, this approach delivers a credible estimation of the relationship between unemployment outflows, labour market tightness, and labour market policies.

In terms of empirical results, we find three robust and economically important effects on market tightness stemming from the replacement rate of unemployment benefits, the volume of Active Labour Market Policies (ALMPs) as well as the tax wedge (especially among countries with intermediate or sector-based wage bargaining systems). The only policy variable found to have a robust (and negative) effect on the outflow rate through matching efficiency is employment protection on regular contracts. However, the latter effect is small in terms of magnitude.

The next section presents the analytical framework that underpins the empirical model as well as the related literature. The data are presented in Section 3, which is followed by the empirical framework, the results, and a discussion. The last section concludes.

The relationship between unemployment outflow, market tightness, and labour market policies and institutions

In this section, we explain the relationships between the unemployment outflow rate, labour market tightness and labour market institutions with the help of a simple framework, which is a simplified version of [START_REF] Mortensen | Job Creation and Job Destruction in the Theory of Unemployment[END_REF] job-search theory. A more elaborate model can be found in [START_REF] Mortensen | New Developments in Models of Search in the Labour Market[END_REF]. Then, we explain our identification strategy to assess the former relationships. Finally, we briefly review the literature dealing with labour market institutions and the unemployment outflow rate.

Theoretical framework

The basic features are as follows: Potential jobs can be either filled or vacant and workers can be either unemployed or employed (inactivity and job-to-job transitions are ignored). Job creation takes place when a firm with a vacant job and a worker meet and start producing. The rate at which vacant jobs and unemployed workers meet is determined by the homogeneousof-degree-one matching function f (u,v), where u and v represent the number of unemployed workers and vacancies respectively, normalized by the size of the labour force (assumed to be fixed). The higher the number of unemployed and the higher the number of vacancies, the more matches, the more hires. The number of new hires per period is determined by a Cobb-Douglas function of vacancies and the number of unemployed:

f u v u v t t t t ( , ) , = - φ η η 1 [1]
where the parameter η determines the elasticity of hires with respect to existing vacancies. The parameter ϕ is deemed to capture all the factors that affect the efficiency of the matching process. For instance, both a decrease in the job-search intensity of unemployed workers, or an increased mismatch between the skills of the unemployed and the skills desired by firms, lead to a decrease in ϕ.

Unemployed workers are identical and vacancies offer the highest wage, so that they are always accepted. The unemployment outflow (or exit) rate f is simply equal to the number of hires divided by the number of unemployed:

f f u v u v u t t t t t t = = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ( , ) , φ η [2]
where the ratio v/u is commonly referred to as market tightness. Conversely, the probability q that an employer fills a vacancy is:

q f u v v t t t t = (

, ) . [3]

A tax τ is levied on labour income in the form of personal income tax or social security contributions. Consider the choice between unemployment and employment. If unemployed, a worker receives bh, where b is unemployment benefits and h is the private cost of being unemployed. If employed, the same worker receives w -τ. Her surplus from working is therefore wb + h -τ. Conversely, if a firm employs this worker, it receives yw where y is the productivity of the match and w the wage paid to the worker. If it does not, the firm receives nothing. Thus, the firm's surplus is simply yw. Adding these two surpluses, the total surplus from the match is yb + h -τ. Workers and firms bargain repeatedly over wages. Defining β as the bargaining power of the worker, the latter obtains a share β of the total surplus via Nash bargaining. Hence, the surplus V that firms extract when a vacancy is filled and producing is:

V y b h t = - -+ - ( )( ). 1 β τ [4]
Firm's behaviour is as follows. There is a fixed cost c in posting a vacancy. The ex-ante profit of a firm when posting a vacancy is equal to -c + q•V. Applying [START_REF] Mortensen | Job Creation and Job Destruction in the Theory of Unemployment[END_REF] 'free-entry' condition that assumes the exhaustion of ex-ante profits, one has:

-+ = c qV t t 0.

[5]

Replacing q and V in [5] by their expressions respectively given by [3] and [4], then using [2], yields the following expression for market tightness:

v u V c y b h c t t t = ( ) = --+ - ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ - - φ φ β τ η η 1 1 1 1 1 ( )(
) .

[6]

The above relationship suggests to describe the relationship between labour market policies and institutions, market tightness and the unemployment outflow rate with the help of the following system of simultaneously determined variables:

log log log ( )( ) log log l v u y b h c f t t t = - + - - -+ - ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = + 1 1 1 1 1 η φ η β τ φ η o og . v u t t [7]

Identification strategy

As made clear by the above system of equations, market tightness is endogenous to the unemployment exit rate in the sense that important omitted variables (including matching efficiency ϕ) simultaneously determine the latter two variables. The identification of the effect of market tightness on unemployment outflow therefore requires an instrumental approach. Along this line, we instrument market tightness in a first stage, whereas in a second-stage, the unemployment outflow rate is regressed on predicted market tightness and a set of other variables that excludes first-stage instruments.

Our main identifying assumption is that business cycle shocks affect market tightness but have no direct effect on matching efficiency and unemployment outflow (i.e. that business cycle shocks have no effect on unemployment outflow other than the one transmitted by market tightness). To improve the quality of the first-stage regression, we consider one policy-based instrument, namely the tax wedge, which is a composite indicator of labour and personal income taxes (see Appendix S1). It is therefore assumed that the tax wedge has an impact on market tightness and job creation, but none on matching efficiency (i.e. no direct impact on unemployment outflows).

In practice, the above system of simultaneously determined equations separates out the effects of labour market policies on job creation (through market tightness) from other effects linked to labour market frictions (i.e. matching efficiency). Determining whether policies and institutions influence the unemployment exit rate mainly through job creation or through labour market frictions constitutes the main objective of this paper.

Related literature

Table 1 summarizes priors for the effects of each labour market institution on the outflow rate as reflected by existing empirical and theoretical studies. These priors are consistent with the identification strategy that was outlined above.

Unemployment insurance benefits are generally thought to have ambiguous effects on market tightness, matching efficiency, and the exit rate. Equation [6] underlines a negative effect of unemployment benefits b that may raise the reservation wage and lower the ratio v/u; however, other theoretical studies (e.g. [START_REF] Acemoglu | Productivity Gains from Unemployment Insurance[END_REF] isolate positive effects of unemployment insurance for the development of risky economic activities, which would imply an increase in the v/u ratio. Similarly, there is mixed empirical evidence that longer and/or more generous unemployment benefits may discourage job search [START_REF] Card | The Spike at Benefit Exhaustion: Leaving the Unemployment System or Starting a New Job?[END_REF][START_REF] Katz | The Impact of the Potential Duration of Unemployment Benefits on the Duration of Unemployment[END_REF][START_REF] Krueger | Job Search and Unemployment Insurance: New Evidence from Time Use Data[END_REF][START_REF] Petrongolo | What Are the Long-term Effects of UI? Evidence from the UK JSA Reform[END_REF], which in our framework would translate into a decrease in ϕ.

ALMPs may increase market tightness (i.e. the ratio v/u) insofar as for instance placement services reduce the cost c of posting a vacancy (see equation [6]). Similarly, training and employment incentives may increase the private (opportunity) cost of unemployment h, hence increase market tightness. ALMPs, and in particular Placement and Employment Services (labelled as PES), may also have an impact on matching efficiency ϕ. In the empirical literature, there is mixed evidence regarding the effect of ALMPs on the probability of finding a job, as it depends widely on the type of programme or training implemented and on the time horizon over which the treatment effect is measured (see [START_REF] Boone | Bringing Unemployed Back to Work: Effective Active Labor Market Policies[END_REF][START_REF] Card | Active Labor Market Policy Evaluations: A Meta-analysis[END_REF].

High degree of employment protection and product market regulation are deemed to have negative effects on the unemployment outflow rate [START_REF] Cahuc | Temporary Jobs, Employment Protection and Labor Market Performance[END_REF], mainly because they may lower the overall level of turnover on the labour market and reduce the degree of matching efficiency. Stricter product market regulation and employment protection are deemed to have an ambiguous impact on market tightness, as they may reduce the pace of new vacancy posting but they may also raise the number of unfilled vacancies. 1 The tax wedge τ, as well as any institution that reduces the profit share of firms 1 -β, unambiguously decrease market tightness and the unemployment exit rate as shown by equation [6] as well as by [START_REF] Mortensen | New Developments in Models of Search in the Labour Market[END_REF]. In this regard, de [START_REF] De Serres | Policies to Facilitate the Return to Work[END_REF] and Murtin et al. (2014) provide strong empirical evidence that the tax wedge reduces outflows more strongly among countries where wage bargaining takes place at the sectoral level rather than at the firm or at the economy-wide level. The intuition behind this empirical finding is that highly centralized or highly decentralized wage bargaining systems are prone to yield wage moderation and to mitigate the adverse effect of the tax wedge.

Excess demand, as captured by the output gap y, raises firms' profits, vacancy creation and unemployment outflows.

The data

Vacancy and unemployment outflow

The main data set on unemployment outflow is borrowed from Murtin et al. (2014). It covers 11 countries (Australia, Belgium, France, Germany, Japan, Norway, Portugal, Spain, Sweden, the UK, the USA) and spans the period 1985-2007. The data frequency is annual. In addition, vacancy data are extracted from various sources [OECD, Eurostat, Job Openings and Labor Turnover Survey (JOLTS)] to construct annual series of the vacancy rate (i.e. the number of vacancies divided by the number of employed workers plus vacancies) and of market tightness (i.e. the number of vacancies divided by the number of unemployed workers). As shown by the upper part of Table 2 as well as other studies (e.g. [START_REF] Elsby | Unemployment Dynamics in the OECD[END_REF], unemployment outflows are larger in most English-speaking and Nordic countries than in other countries. In particular, the USA appears to be an outlier as it displays a very large, albeit declining, outflow rate over time [START_REF] Murtin | Unemployment Dynamics with Labour Market Reforms[END_REF][START_REF] Robin | On the Dynamics of Unemployment and Wage Distributions[END_REF]. Countries with high outflow rates tend also to display tighter labour markets, as the correlation between outflow and market tightness equals 0.46 without the USA, and 0.82 with this country.

It is well known that the quality of vacancy data varies substantially across countries. Vacancy data usually refer to job opportunities notified by an employer to a Job Centre or Careers Office, which remained unfilled on the day of the count. Importantly, vacancies that are not notified to employment agencies are excluded, so that the vacancy figures do not represent the total number of vacancies in the economy. Moreover, national statistics differ in a number of dimensions such as the period of reference or the type of eligible position. For instance, vacancy data covers both the private and public sectors in France, whereas vacancies on government-sponsored programmes are excluded in the UK.

To appraise the quality of the vacancy data, we regress the log unemployment outflow rate on log market tightness country by country. If the vacancy rate is affected by measurement errors, the coefficient of log market tightness is expected to be biased towards zero and the R-squared of the regression to be low. The obtained results from these regressions are described in Appendix S1. Four countries turn out to have particularly low R 2 , namely Belgium, France, Germany, and Portugal. In the robustness analysis section, the main regressions are redone after excluding the latter four countries from the sample. For illustrative purposes, Figure 1 presents the Beveridge curves, which depict the vacancy rate with respect to unemployment, for four countries based on quarterly data. A negative correlation is expected between the two variables as a large number of unemployed workers would exhaust available vacancies. However, the relationship has generally been unstable, as for instance in Germany, the Netherlands, and Sweden. Figure 2 shows that a more stable relationship emerges when unemployment is related to market tightness instead of the vacancy rate. Indeed, market tightness relates the pool of vacant jobs to that of job-seekers, and such ratio would seem to be a better measure of job search conditions on the labour market than the vacancy rate. Indeed, the latter relates the pool of vacant jobs to that of employed workers, who do not necessarily look for another job, or do so with a lower intensity.

Labour market institutions

The data on labour market institutions include: (i) the replacement rate of unemployment benefits in the initial year of reception; (ii) the duration of unemployment benefits, as measured by the ratio of the average replacement rate during the first 5 years of reception to the initial replacement rate; 2 (iii) real spending on ALMPs per unemployed worker normalized by a proxy of average income (GDP per worker); 3 (iv) a measure of the tax wedge constructed by the OECD. 4 The tax wedge is in some cases interacted with a proxy for the degree of centralization/coordination embedded in the wage bargaining system, namely the difference (labelled as 'excess coverage of union agreements') between the share of workers covered by collective agreements (coverage rate) and union density; 5 (v) the OECD index of product

Vacancy rate

Unemployment rate USA market regulation (the PMR index); and (vi) the OECD index of employment protection legislation for regular contracts (labelled as EPR). The set of labour market institutions is complemented by a proxy for business cycle conditions, namely the OECD estimate of the output gap. In total, one obtains 189 usable observations for the econometric framework.

The identification of policy and institutional effects relies on the number of reforms over time. Indeed, country fixed effects will be systematically included in the panel data model. From that point of view, all indicators display a satisfactory degree of time variation as reflected by the simple decomposition of the variance between and within countries depicted in Table 3. Not surprisingly, the variance between countries is the largest component in a majority of cases with the noticeable exception of the PMR index. However, standard deviations within countries always represent significant policy changes. For instance, an increase in the replacement rate by 2.8 percentage points or an increase in the tax wedge by 2.4 percentage points are deemed to have observable consequences on labour market outcomes.

The policy and institutional determinants of the unemployment outflow rate

This section describes the empirical framework, which explains cross-country differences in outflow rates with the help of a matching function. The relationships between labour market institutions and two structural determinants of outflows, namely market tightness and matching efficiency, are examined. Then, a robustness analysis is proposed. Finally, the magnitude of the policy and institutional effects is assessed.

Empirical framework

To empirically relate cross-country differences in outflow rates to differences in the institutional environment, it is convenient to log-linearize the matching function described by equation [2]. We assume a common vacancy elasticity (parameter η) across countries 6 and we allow for cross-country differences in matching efficiency ϕi,t and in market tightness ϕi,t = vi,t/ui,t. The econometric model is the following:

log log log , , , , , f w i t i t i t i t = + + φ η θ [8]
where w is a residual term. We denote as X and Y the two sets of labour market institutions that have an influence upon respectively market tightness and matching efficiency. As made clear by the 'free-entry' condition and system [7], any institutional variable affecting matching efficiency is also a determinant of market tightness, so that the set Y is included into X (and even strictly included as the tax wedge will be used as an instrument of market tightness). Moreover, business cycle shocks proxied by the output gap Z is taken as another instrument of market tightness. One has therefore the following system of equations:

log log , , , , , , lo θ
β γ β i t i v t v i t v i t v i t i t i f t f i t f a d X Z u f a d Y = + + + + = + + g g , , , log , φ η θ i t i t i t w + + ⎧ ⎨ ⎪ ⎩ ⎪ [9]
where ai denote country fixed effects and dt time fixed effects. The first equation can be labelled as the market tightness equation, the second one as the outflow equation.

In practice, labour market policy and institutions Y that are deemed to influence matching efficiency are the characteristics of unemployment benefits (replacement rate and duration), the level of employment protection of regular contracts, as well as the degree of product market regulation. As mentioned, these variables must be included both in the market tightness equation and in the outflow equation. Conversely, the set of institutions X includes Y plus the tax wedge and its interaction with the excess coverage variable.

The above system is estimated with a two-stage ordinary least squares (OLS) estimator (2-SLS). In the first-stage, the first equation of the system (market tightness) is estimated. In a second-stage, the second equation (outflow) is estimated while using the predicted market tightness variable derived from stage one.

Main results

Table 4 presents the instrumental variables (IV) estimation results with the first-stage market tightness equations on columns 1, 3, 5, 7, 9, 11, 13, and 15 and the second-stage outflow equations on columns 2, 4, 6, 8, 10, 12, 14, and 16. Selected instruments are in all cases the output gap and the tax wedge, as well as the interaction between the tax wedge and excess coverage in column 15. The tax wedge is lagged 3 years to increase its chance of being strictly exogenous to unemployment outflow. In all IV regressions, there is no evidence of weak instruments as F-statistics are comfortably large. Furthermore, our two (or three) instruments always pass the Sargan test of instruments validity, as the p-values never reject the null assumption of instruments joint exogeneity.

log V/U log f log V/U log f log V/U log f log V/U log f log V/U log f log V/U log f log V/U log f log V/U log f (1) (2) (3) (4) (5) (6) (7) (8) (9)
Starting with the determinants of market tightness (first-stage equations), the output gap always displays highly significant coefficients with an expected positive sign (excess demand fosters vacancy creation), whereas the tax wedge (as well as its interaction with excess coverage in column 15) displays in most cases a highly significant and negative coefficient. In addition, the initial replacement rate turns out to be (in two cases out of three highly) significant and negative, whereas ALMPs are always significantly and positively associated with market tightness. Other institutional variables, including the average replacement rates, the duration of unemployment benefits, the degree of employment protection and product market regulation, do not display robust coefficients.

Moving to the institutional determinants of matching efficiency (second-stage equations displayed on columns 4-6-8-10-12 and 14), we find that the duration of unemployment benefits is unambiguously and negatively related to matching efficiency and unemployment outflows. Moreover, the degree of employment protection displays a highly significant and negative coefficient in columns 12 and 14 whereas other institutions are controlled for, but fails to be significant on column 8.

Summing up, the tax wedge, ALMPs, and the initial replacement can be viewed as significant determinants of market tightness, whereas the duration of unemployment benefits and employment protection are linked to matching efficiency. The robustness of these results are examined in the next subsection.

Robustness analysis

The sensitivity of previous results relative to the quality of vacancy data is assessed in two ways. First, we trim the sample from outlier observations, deleting about 10 per cent of the sample for which unemployment outflow or market tightness take outlier values (either at the top or at the bottom or their respective distribution). Second, we restrict the sample to the countries that display higher quality data. In practice, we exclude the four countries (Belgium, France, Germany, and Portugal) in which vacancy data explain little of the unemployment exit rate. These are the countries for which a country-specific regression of log unemployment outflow on log market tightness displays a low R 2 (see Appendix S1). In a third set of regressions, we trim the data and we exclude the above four countries. In this case, the sample has a much smaller size (only 103 observations versus 189 formerly), so it is a priori uncertain whether the estimation would deliver better results because of higher-quality data or poorer estimates due to a smaller sample size.

The results depicted in Table 5 largely confirm the results obtained from Table 4, while offering some nuances. Across all regressions, ALMPs and the initial replacement rate are always significant determinants of market tightness, but the tax wedge is only significant in interaction with excess coverage. As already noticed by [START_REF] Calmfors | Bargaining Structure, Corporatism and Macroeconomic Performance[END_REF], [START_REF] Daveri | Unemployment, Growth and Taxation in Industrial Countries[END_REF] as well as de [START_REF] De Serres | Policies to Facilitate the Return to Work[END_REF], disentangling between countries with respect to their degree of coordination in wage bargaining is important when it comes to the analysis of the relationship between unemployment, labour taxes, and wages. Moreover, employment protection is always significant across outflow regressions, which highlights a robust adverse effect of employment protection on matching efficiency. In contrast, the duration of unemployment benefits loses its significance when the four countries are excluded from the sample. So the only one robust determinant of matching efficiency is employment protection. 7

Table 5. Robustness analysis

Accounting for hysteresis

The robustness of previous results is further evaluated in the light of a more general, state-dependent, matching function where time persistence in the outflow rate is introduced. Several theoretical and empirical studies point to a negative effect of the duration of unemployment spells on the probability to exit unemployment [START_REF] Bover | Unemployment Duration, Benefit Duration and the Business Cycle[END_REF][START_REF] Dantan | Can Public Policies Mitigate Unemployment Hysteresis: Evidence From OECD Countries[END_REF][START_REF] Elsby | Unemployment Dynamics in the OECD[END_REF][START_REF] Machin | The Causes and Consequences of Long-term Unemployment in Europe[END_REF][START_REF] Pissarides | Loss of Skill during Unemployment and the Persistence of Employment Shocks[END_REF][START_REF] Shimer | The Probability of Finding a Job[END_REF][START_REF] Van Den | Unemployment Dynamics and Duration Dependence[END_REF]. Intuitively, long spells of unemployment may imply a depreciation of human capital, or lead to lower job-search intensity and to discouragement effects.

The functional form of the matching function can easily be amended to allow for the possible influence of the time spent in unemployment on the probability of exiting unemployment. Let us write the outflow rate as:

f v u D t t t t t = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ( ) - φ η ρ , [ 10
]
where Dt is the time spent in unemployment at the beginning of period t, and ρt a positive coefficient that may eventually vary across countries and time. As f is expressed on a monthly basis, D represents the number of months spent in unemployment and it is strictly greater than one. Hence the larger ρ the smaller the outflow rate f. Assuming for simplicity that the time spent in unemployment can be proxied by the inverse of the lagged outflow rate (i.e. that

D f t t = - 1 1
), 8 the following system of equations is obtained from the log-linearization of [9]: log

β i t i v t v i t v i t v i t i t i f t f i t f a d X Z u f a d Y = + + + + = + + g g , , log , , , , , , lo θ β γ
φ η θ ρ i t i t i t i t i t f w + + + ⎧ ⎨ ⎪ ⎩ ⎪ -1 , , , log log .
[11]

The above system is identical to the former one except that the lagged unemployment outflow rate is introduced in the outflow equation. To estimate this new model, a two-stage procedure is adopted. In the first-stage, the market tightness equation is estimated via OLS and its predicted value is constructed. In the second-stage, the outflow equation is estimated by using the former predictor and an OLS estimator or [START_REF] Arellano | Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations[END_REF] first-difference generalized method of moments (DIF-GMM) estimator, while retaining a common and constant autocorrelation coefficient (i.e. ρi,t = ρ). 9,10 To conduct this empirical analysis, we use the sample that was trimmed from outlier observations. As shown by Table 6, the static results reported on Table 5 are relatively robust to the existence of persistence effects. 11 Regarding the determinants of matching efficiency presented on columns 2 and 3, we find that employment protection entails a robust adverse effect on unemployment outflows. As before, the negative effect of unemployment benefits duration is more fragile, as it is significant only in column 2.

To explore further the link between policies and persistence, the coefficient ρ can be conditioned on a set of institutional variables W. A logit functional form is used to ensure that ρ is always strictly smaller than 1. The following non-linear system can be estimated by combining the two-stage estimation approach with non-linear least squares (NLS) for the outflow equation:

+ + = + ⎧ -1 1 ⎨ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ [12]
As mentioned above, the higher the degree of persistence (ρ), the lower the outflow rate (as log ft-1 < 0). Hence, variables positively linked to the coefficient of persistence can be viewed as raising the duration of unemployment spells and reducing the outflow rate. Table 6 column 4 reports the results of this non-linear estimation. Several potential determinants of hysteresis are tested, in particular our proxy for the duration of unemployment benefits. We find that longer benefit duration increases the length of unemployment spells and the time persistence of unemployment outflows. In this regression, the significance of the adverse effect of employment protection on matching efficiency is preserved, whereas the replacement rate of unemployment benefits displays a positive sign. This may be interpreted as a positive effect of unemployment insurance on the quality of employer-employees match, or be disregarded as a statistical anomaly. 12 Furthermore, the business cycle may affect directly the exit from unemployment over and above its effects on labour market tightness, as in a bad recession the unemployed may get discouraged and become non-employed and, in parallel, in good times non-employed people may be encouraged to come back to the labour market. Similarly, if a high tax wedge creates unemployment traps, then matching efficiency may decrease together with labour market tightness. Both views challenge the assumption that our main instruments, namely the output gap and the tax wedge, are valid and affect the outflow rate only through their effect on market tightness. To provide a quick check, we have tested for the significance of our instruments when they are included in the second-stage regression. Both failed to be significant, which supports our main exclusion restriction.

Magnitude of policy effects

To gauge the magnitude of the estimated policy effects, we calculate the variation in outflows associated with the increase in each policy indicator by one within-country standard deviation. We select three different specifications extracted from the various tables. We differentiate the policy effects according to the channel of transmission, namely market tightness or matching efficiency. The calculated effect on market tightness are multiplied by the estimated market tightness's elasticity in the outflow equation.

Table 7 displays the results for each policy or institution while also indicating the respective channels of transmission. We used the point estimates of each coefficient, while highlighting with significance thresholds of these estimates (denoted as */**/*** for the 10/5/1 per cent confidence levels respectively). This table offers a quick overview of the policy and institutional reforms that matter from the perspective of a policy-maker. 13 Overall, we find that market tightness carries the bulk of policy and institutional effects. The replacement rate, ALMPs, and the tax wedge among countries with high excess coverage (intermediate wage bargaining systems) have a large effect on market tightness and unemployment outflows. Regarding matching efficiency, the effect of employment protection has a small magnitude. The adverse effect of unemployment benefits duration on matching efficiency is a bit larger, but as mentioned above, it does not always rely on robust estimates. Hence, market tightness and more generally job creation can be viewed as the main channel through which policies and institutions have an impact upon the unemployment outflow rate.

Conclusion

This paper explores the policy and institutional determinants of the unemployment outflow rate using a sample of 11 OECD countries observed between 1985 and 2007. We use matching functions to identify the effects of policies or institutions on the outflow rate via two channels, namely the number of job vacancies relative to the pool of unemployed (market tightness), and the degree of employer-employee matching efficiency. We treat the endogeneity of market tightness to unemployment outflow with the help of a system of simultaneously determined equations, using business cycle shocks and the tax wedge as instruments of market tightness. We find that the replacement rate of unemployment benefits, ALMPs as well as the tax wedge in countries with intermediate or sector-based wage bargaining systems, have a large impact on market tightness. Employment protection and the duration of unemployment benefits may reduce matching efficiency, but these effects are deemed to have a smaller magnitude. Overall, the bulk of policy and institution action on unemployment outflows appear to be channeled by market tightness and job creation.

Notes

1 The impact of employment protection on unemployment is more ambiguous. For instance, strict employment protection may lower the creation of vacancies but also the rate of job destruction, with little effect on unemployment.

2 If the replacement rate is assumed to decrease exponentially over time, its half-life is equal to 69 per cent of the ratio used in this study.

3 In order to remove cyclical variations in ALMPs that result from cyclical unemployment variations, we apply a Hodrick-Prescott (HP) filter to the series and use only this trend component in subsequent regressions. Thus this procedure corrects for the endogeneity that arises from the fact that ALMP spending has traditionally been relatively insensitive to cyclical changes in the unemployment rate. However, it does not address the endogeneity problem that may arise when the variation in ALMP spending falls short of the variation in the structural rate of unemployment. 4 The OECD tax wedge is a summary index of labour and personal income taxes. It was preferred to a simple labour tax index as the latter series is affected by a break in the late 1990s. However, our main results are largely unaffected if we replace the tax wedge by labour taxes. 5 In the presence of 'excess coverage' of collective agreements, union members receive a higher 'outside option' (fall-back income) as they have the possibility to reallocate in the non-unionized sector covered by collective agreement. This raises their bargained wage as well as unemployment, all the more so as payroll taxes are large (see Murtin et al., 2014). In spirit, this is the idea as in [START_REF] Calmfors | Bargaining Structure, Corporatism and Macroeconomic Performance[END_REF], who argue that largely centralized (economy-wide) and largely decentralized (firm-level) wage bargaining systems lead to a lower unemployment rate relative to intermediate systems where bargaining takes place at the sectoral level. Indeed, the variable 'excess coverage' tends to be higher among intermediate systems, and lower among both centralized and decentralized ones. Hence, it can be seen as a convenient proxy for the so-called 'Calmfors-Driffill' hypothesis. With respect to ad-hoc indices of the degree of coordination of wage bargaining systems, it is a continuous variable that does not rely on subjective judgement. 6 In unreported calculations we show that cross-country differences in parameter η explain little of the cross-country differences in unemployment outflows compared with cross-country differences in matching efficiency and market tightness. These calculations are available from the authors upon request.

7 All regressions pass the overidentifying restrictions test and there is no evidence of weak instruments in first-stage regressions.

8 Actually, unemployment duration should depend on all lags of the outflow rate. Introducing only the first lag aims to preserve a parsimonious model. 9 GMM have advantages and drawbacks. They allow a stronger claim that our estimates represent causal effects under the assumption of weak exogeneity of the explanatory variables. However, DIF-GMM may suffer from weak instruments problems. To remedy for that problem, [START_REF] Blundell | Initial Conditions and Moment Restrictions in Dynamic Panel Data Models[END_REF] system GMM (SYS-GMM) propose additional instruments that would hardly be valid in our context, as their use relies on the assumption that country fixed effects are independent of the unemployment's growth rate. As emphasized by [START_REF] Blanchard | The Role of Shocks and Institutions in the Rise of European Unemployment: The Aggregate Evidence[END_REF], this is highly unlikely so we refrain from using SYS-GMM in this study. 10 The DIF-GMM regression reported here passes the Arellano-Bond specification test for the autocorrelation of residuals as well as the Hansen test of joint exogeneity of instruments. However, the latter test is weak due to the small number of groups (countries). For the IV and NLS regressions, the autocorrelation of residuals was estimated and found to be not significantly different from zero.

11 The market tightness equation described on Table 6 column 1 is identical to that presented in Table 5 column 3. 12 Actually, equation [7] shows that any variable affecting matching efficiency ϕ, such as the replacement rate, should be included in both the first-stage and second-stage equations. It is therefore a bit surprising that such a variable switches sign across the two regressions. However, equation [7] also shows that this may happen if the latter variable affects structural coefficients b, h, or c in opposite direction. For instance, a higher replacement may indeed increase matching efficiency ϕ as suggested by column 4, but it may also reduce the match's surplus yb and lower market tightness overall as reported on column 1. 13 It is recalled that we used for each simulation the within-country standard deviation of each institution, rather than its cross-country and cross-time sample standard deviation.

Figure 1 .

 1 Figure 1. Beveridge curves in four OECD countries

Figure 2 .

 2 Figure 2. Market tightness and the rate of unemployment in four OECD countries

  */*** for the 10/5/1 per cent confidence levels respectively.

  */*** for the 10/5/1 per cent confidence levels respectively.

Table 1 .

 1 Analytical priors on the relationship between institutions and the unemployment outflow rate

			Market	Matching	Unemployment
			tightness	efficiency	outflow rate
	Institution	Parameter	V/U	E( f |V/U )	E( f )
	Unemployment benefits	b	+/-		+/-
		φ		+/-
	ALMPs:
	PES and administration	φ, 1/c	+	+	+
	Employment incentives, training	φ, h	+	+	+
	Employment protection	φ	+/-	-	-
	Product market regulation	φ	-	-	-
	Tax wedge	τ	-		-
	Excess coverage of wage bargaining	β	-		-
	agreements
	Output gap	y	+		+

Table 2 .

 2 Descriptive statistics -average values 1985-

2007 AUS BEL DEU ESP FRA GBR JPN NOR PRT SWE USA Unemployment variables

	Unemployment rate	7.52 8.64 8.02 16.52 10.16 7.44 3.93 4.09 6.18 5.78 5.68
	Unemployment outflow	22.60 6.77 6.61 7.90 7.90 13.92 17.66 40.23 7.83 24.94 56.73
	rate 15+
	Market tightness	0.15 0.11 0.11 0.04 0.08 0.20 0.26 0.15 0.04 0.16 0.61
	Labour market institutions
	Initial replacement rate 23.34 49.09 38.45 65.43 56.49 24.98 32.87 51.55 48.16 77.94 28.20
	Unemployment benefits	1.01 0.86 0.72 0.47 0.60 0.80 0.31 0.60 0.48 0.35 0.46
	duration
	EPL regular contracts	1.26 1.70 2.70 3.10 2.39 1.01 1.87 2.25 4.46 2.87 0.17
	ALMPs	0.05 0.14 0.14 0.05 0.11 0.06 0.09 0.19 0.10 0.41 0.03
	Tax wedge	28.14 41.25 35.45 30.05 41.42 28.95 22.77 49.66 26.79 52.21 23.60
	Excess coverage	42.21 37.43 46.94 55.76 71.99 13.99 -5.06 14.16 39.65 3.50 3.77
	PMR	3.25 4.39 4.08 4.12 4.95 3.03 3.98 4.20 4.88 3.75 2.54
	Observations	20	20	20	20	16	19	15	20	17	17	5

EPL, employment protection legislation.

Table 3 .

 3 Analysis of variance for labour marketinstitutions -1985-2007

		Standard deviation	Standard deviation
		between countries	within countries
	Initial replacement rate	20.30	2.80
	Unemployment benefits duration
	EPL regular contracts	1.10	0.20
	ALMPs	0.10	0.06
	Tax wedge	10.00	2.40
	Excess coverage	27.00	5.90
	PMR	0.60	1.10

Table 4 .

 4 The institutional determinants of market tightness and matching efficiency

			All	IV
			All	IV
			Active ALMPs	IV
		Product market	regulation	IV
	Employment	protection for	regular contracts	IV
	Initial replacement	rate and unemployment	benefits duration	IV
		Average	replacement rate	IV
			Baseline	IV
		Policy or	institution:	Procedure:	Dependent	variable:

Table 6 .

 6 The institutional determinants of market tightness, matching efficiency, and hysteresis effects

		First-stage		Second-stage
	Equation:	(market tightness)	(matching efficiency)
	Dependent variable:	log V/U		log f
		OLS	IV	DIF-GMM	NLS
	Estimator:	(1)	(2)	(3)	(4)
			Conditional persistence
				(coefficient of log f -1)
	Constant		0.695***	0.277***	-1.335
			(0.042)	(0.090)	(1.212)
	Initial replacement rate				0.013
					(0.012)
	Duration of unemployment benefits				2.007*
					(1.027)
				Other variables
				(matching efficiency)
	Instrumented log market tightness		0.259***	0.314***	0.275***
			(0.051)	(0.057)	(0.053)
	Initial replacement rate	-0.066***	0.011*	0.005	0.017**
		(0.009)	(0.006)	(0.008)	(0.007)
	Duration of unemployment benefits	0.696	-0.623**	-0.254	0.336
		(0.572)	(0.252)	(0.321)	(0.555)
	EPL regular contracts	0.290***	-0.111***	-0.224*	-0.137**
		(0.100)	(0.042)	(0.135)	(0.058)
	PMR	0.017	0.024	0.085	0.023
		(0.070)	(0.033)	(0.072)	(0.034)
	ALMPs	6.102***	-0.631	-0.362	-0.458
		(1.099)	(0.404)	(0.698)	(0.546)
	Tax wedge	-0.023
		(0.015)
	Tax wedge × excess coverage	-0.002***
		(0.000)
	Output gap	0.130***
		(0.016)
	Time effects	Yes	Yes	Yes	Yes
	Country fixed effects	Yes	Yes	Yes	Yes
	R 2	0.95	0.98	-	0.98
	N	170	170	159	170
	*/**/*** for the 10/5/1 per cent confidence levels respectively.

Table 7 .

 7 Relative effect of one standard deviation increase in policy and institutional indicators on the unemployment outflow rate (variation expressed in percentage)

Table 4 columns 15-16 Table 5 columns 3-4 Table 5 columns 11-12 Market tightness Matching efficiency Total Market tightness Matching efficiency Total Market tightness Matching efficiency Total

 4

	-6.36	0.62	-0.04	22.83	-4.53	-11.51
	1.39	-2.48	-4.82***	5.07
	-7.75***	3.10*	4.78**	17.76***	-4.53*	-11.51***
	-8.64	-3.58	-0.53	18.86	-3.05	-9.24
	1.67	-5.42***	-4.48***	-2.41
	-10.31***	1.84	3.94***	21.26***	-3.05	-9.24***
	-8.57	-4.46	-2.41	13.97	-4.64	-10.83
	1.11	-6.87***	-4.50***	-4.43
	-9.69***	2.41	2.09	18.40***	-4.64***	-10.83***
	Replacement rate	Duration of benefits	EPL regular	ALMPs	Tax wedge -all countries	Tax wedge -countries with	high excess coverage a

*/**/*** for the 10/5/1 per cent confidence levels respectively. a Australia, France, Germany, Portugal, Spain.

Supporting Information

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