Odile Chagny
email: ochagny@ofce.sciences-po.fr

Frédéric Reynès
email: frederic.reynes@ofce.sciences-po.fr

Henri Sterdyniak
email: sterdyniak@ofce.sciences-po.fr.

The equilibrium rate of unemployment: a theoretical discussion and an empirical evaluation for six OECD countries

Keywords: labor market, equilibrium unemployment, Phillips curve, WS/PS model, Three Stage Least Squares estimation, OECD. JEL Classification: C13, C32, E24, E31

This paper examines theoretically and empirically the controversial notion of "equilibrium rate of unemployment" (ERU) which opposes proponents of the Phillips curve to those of the WS/PS models. Theoretically, this paper shows that the specification of the wage equation has a significant influence on the ERU. It also shows that an "asymmetric" wage-price setting using a Phillips curve and a price equation in level allows a clear distinction between the medium run ERU and the long run ERU that can be seen as a reconciliation between WS/PS models and the Phillips curve.

Moreover, this paper calculates ERU for 6 OECD countries (the United States, Germany, France, the United Kingdom, Spain and the Netherlands) for the period 1970-late 1990's by using a structural approach. As there are little studies that test directly the impact of institutional variables in a Phillips curve, the first empirical objective is to test this effect. The results in this matter are not really conclusive.

The second objective is to calculate medium run and long run ERU. The evolutions of the medium run ERU explain relatively well those of the actual unemployment rate until the late eighties. Its determinants are the slowdown of productivity growth, the 2 oil shocks, the increase of employer's social contribution and the change in the inflation target of the monetary authorities. In the nineties, the actual unemployment lies clearly above its equilibrium level suggesting that a big part of the European unemployment is due to an excess supply.

Introduction

The notion of "equilibrium rate of unemployment" 1 is the center of numerous economic policy debates. Did this rate decrease in the United States due to a new economy effect? Did it stay high in continental Europe? Could it be a factor explaining why the period of strong growth in continental Europe from 1997 to 2000 came to an end? Can we place this concept at the core of the economic policy debates in Europe, as recently proposed by Pisani-Ferry (2000)? Is it possible to decrease the equilibrium rate of unemployment through reforms strengthening the flexibility of the labor market, a decrease of the tax burden over labor factor, lower interest rates or even via a lower unemployment rate?

The evaluation of the equilibrium rate of unemployment (ERU) is theoretically and empirically controversial. Its determinants differ according to the specification of the model.

In particular, this notion opposes the proponents of the wage curve in level and those of the Phillips curve (see [START_REF] Sterdyniak | Le taux de chômage d'équilibre, anciennes et nouvelles approches[END_REF]).

In the first part, we will see that the debate can not be simply reduced to an alternative between Wage-Setting Price-Setting (WS/PS) models and the Phillips curve; we will also see the importance of the distinction between the medium run ERU and the long run ERU, that can be seen as a way of reconciliation between WS/PS model and the Phillips curve.

A lot of empirical and theoretical studies [START_REF] Bean | European unemployment: a survey[END_REF]; [START_REF] Blanchard | The Role of Shocks and Institutions in the Rise of European Unemployment: the Aggregate Evidence[END_REF]; [START_REF] Belot | Unemployment and labor market institutions: an empirical analysis[END_REF]; [START_REF] Burda | Complementarity of Labor Market Institutions, Equilibrium Unemployment and the Propagation of Business Cycles[END_REF]; Den [START_REF] Haan | Shocks and Institutions in a Job Matching Model[END_REF]) suggest that differences in OECD unemployment performances can be explained by institutional differences in the labor market. Two questions then arise: (1) Can we explain empirically unemployment differences by institutional differences? (2) To what extend have institutional changes in some countries led to a modification of the equilibrium rate of unemployment 2 ? Among the empirical studies that focus on the link between the institutional characteristics and unemployment, mainly two approaches can be distinguished: structural approaches of the WS/PS type, popularized by [START_REF] Layard | Unemployment, Macroeconomic Performance and the Labour Market[END_REF] and reduced approaches that establish a direct link between the unemployment and the institutional characteristics. Some studies have recently focused on the complexity of the link between the institutional characteristics and the real rigidity of nominal wages measured by a Phillips curve [START_REF] Passet | Flexibilité et performances comparées des marchés du travail dans les pays de l'O.C.D.E[END_REF]; [START_REF] Cadiou | La diversité des marchés du travail en Europe: Quelle conséquences pour l'Union Monétaire[END_REF]). However few empirical studies have directly tested the role of the institutional characteristics in a model where the wage setting relies upon the traditional Phillips curve, where the growth rate of wages is a function of the level of unemployment and the past inflation. We use this approach for six OECD countries (the United States, Germany, France, the United Kingdom, Spain and the Netherlands) for the period 1970-late 1990s. It allows us to estimate for these countries medium run and long run ERU based on a clear theoretical and empirical definition and to test the interaction between shocks and labor market institutions on the equilibrium rate of unemployment.

Part 1. Some considerations about the equilibrium rate of unemployment (ERU)

Several definitions of the ERU are proposed in the economic literature [START_REF] Blanchard | What We Know and Do Not Know About the Natural Rate of Unemployment[END_REF], [START_REF] Sterdyniak | Le taux de chômage d'équilibre, anciennes et nouvelles approches[END_REF], [START_REF] Mellis | The United Kingdom NAIRU: concepts, measurement and policy implications[END_REF], [START_REF] Richardson | The concept, policy use and measurement of structural unemployment: estimating a time varying NAIRU across 21 OECD countries[END_REF]).

Some specifications consider that the ERU depends solely on the growth rate of labor productivity. Other specifications put the emphasis on the role played by the trade unions, the impact of the level of unemployment benefits, the tax burden and the level of the interest rates [START_REF] Bean | European unemployment: a survey[END_REF]). The debate cannot be summarized by a simple alternative between the structural wage-price setting model developed by [START_REF] Layard | Unemployment, Macroeconomic Performance and the Labour Market[END_REF] and the Phillips curve 3 ; each branch of this alternative may be decomposed into several models and definitions.

We will show that it is necessary to distinguish between a long run ERU and a medium run ERU. Indeed, this distinction leads to some reconciliation of the WS/PS and the Phillips curve models. For a given specification, we define the long run ERU as the rate of unemployment prevailing in the long run equilibrium of the model and characterized by inflation and labor share stability. In some specifications, the long run ERU depends only on structural or institutional parameters of the economy and is therefore unique and relatively stable. In some others, it can be influenced by the economic policy choices (such as the level of public expenses, the desired price inflation); in such cases, the long run ERU (ERU LR ) may vary and 3. The structural Phillips curve we are using must be distinguished from the "triangle model" of [START_REF] Gordon | The Time-varying NAIRU and its Implications for Economic Policy[END_REF] where the Phillips curve relates directly the price inflation rate (and not the wage inflation) to inertia (measured by the past price inflation), excess demand (measured by the gap between the unemployment rate and the NAIRU) and supply shocks (import price, etc.). will be influenced by some pertinent parameters. In addition, given a certain initial state of the economy, it may be impossible to have an unemployment rate permanently equal to the long run ERU. We will see that this is the case in presence of hysteresis, when the inflation rate remains above the desired inflation rate, and when the real wage is too high. In this case, the path of the unemployment rate is influenced by a medium run constraint that can be defined as the medium run ERU (ERU MR ). The definition of the equilibrium rate of unemployment will be clarified in the following presentation of wage-price setting systems alternatives.

The simple model

Starting with a simple model, the production technology is a Leontief technology (no factor substitution). Wages are determined by an "augmented" Phillips curve. The model is described by the following equations 4 : Labor demand equation:

(1.1)

tt ly t π =-
where y is the output, l is the employment and p the labor productivity growth.

Price setting equation:

(1. 4. In the rest of the paper, the lower-case variables are in logarithm, ∆ is the change in the variable and all coefficients are positive. Time t as suffix will be omitted in the rest of the paper. 5. This specification is equivalent to a constrained error correction model.

Rearranging equations (1.1) to (1.3) gives the unemployment rate consistent with a constant inflation:

(1.4) () / ELR Ucb π = -
The ERU depends positively on the constant of the wage setting equation and negatively on the growth rate of labor productivity.

This model does not precisely formalize the wage setting process. Nominal wages can be fixed by collective bargaining or by individual agreements involving each firm and each employee. Social partners agree to index the wages on the prices. The unemployment rate represents here either the bargaining power of workers and the firms or the pressures on the labor market. On one hand, the labor market leads to a real wage growth being a decreasing function of the rate of unemployment, on the other hand the equilibrium growth of the real wage is equal to the growth rate of the labor productivity. Thus, only one level of the unemployment rate allows the effective growth rate of wages to be equal to the medium run equilibrium growth rate of real wages.

This elementary model assumes that the parameter c is constant. It is an intrinsic characteristic of the labor market in a given country, for a given period. But this hypothesis has poor foundations and leads to three possible research fields. The first is to find empirical factors that can explain the variations of the parameter c -as for instance the bargaining strength of unions, the degree of mismatch, the reforms on the labor market. The second consists in studying econometrically changes in c, but without relating explicitly these changes to institutional or structural changes as in [START_REF] Gordon | The Time-varying NAIRU and its Implications for Economic Policy[END_REF]. The third is to study the microeconomic foundations of the wage setting process (as in [START_REF] Cahuc | Economie du travail: La formation des salaires et les déterminants du chômage[END_REF]).

Equation (1.3) postulates that nominal wages adjust fully to prices. This is often explained by the absence of nominal illusion of workers and firms. However, this may not be the case at least for two reasons. First, in periods of sustained inflation, the bargaining power of workers is weakened because they attempt to maintain their purchasing power. Second, in some countries, they may agree not to fully adjust wages to inflation in order to contribute to a lower inflation rate when trade unions internalize the effect of their bargaining posture on macro-economic performance [START_REF] Calmfors | Bargaining structure, corporatism and macroeconomic performences[END_REF] and [START_REF] Soskice | Wage determination: the changing role of institutions in advanced industrialized countries[END_REF]) or fear the reaction of the central bank. Assuming the wage equation is:

(1.3 bis) e wca p b U ∆=+∆ -, the ERU is given by:

(1.4 bis) ( (1 ) ) / o ELR Uc a p b π =---∆
This is a decreasing function of the inflation target of the monetary authorities ( o p ∆ ); the well known inflation-unemployment trade-off model developed by [START_REF] Samuelson | Analytical Aspects of Anti-Inflation Policy[END_REF]. The main problem is the stability of equation (1.3 bis) when the price inflation remains durably on a relatively high level. In such a case, there is a strong incentive to adopt automatic indexation rules ( 1 a = ), i.e. the inflation-unemployment trade-off disappears.

Hysteresis

Hysteresis occurs when part of the unemployed workers exert no influence on the wage setting. Proposed theoretical explanations include deterioration of human capital of long term unemployed workers, the reluctance of firms to hire long term unemployed workers as they are not able to evaluate their human skills or the fact that incumbent workers (insiders) afford to maintain their position in the wage negotiations (Blanchard andSummers (1986), Lindbeck (1993)). In this case, as the growth of wages depends also on the gap between the actual unemployment rate and its past trend, the Phillips curve equation can be rewritten:

(1.3 ter) 12 () e l wc p b Ub UU ∆=+ ∆ - - - with 1 li i i UU λ ∞ - - = = ∑ and 1 1 i i λ ∞ - = = ∑
Independently of the hysteresis phenomena, this equation can also refer to models where the wage setting is affected both by the level and the rate of change of employment.

Recovering periods, where firms hire a relatively high proportion of workers, may induce wage acceleration notwithstanding the high level of unemployment. The opposite situation, in periods of low unemployment rate but where firms begin to fire workers, is inauspicious to high wage increases (as in [START_REF] Lipsey | The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1862-1957: A further analysis[END_REF]). Two cases can be distinguished:

In case of full hysteresis ( 1 0 = b
), the model has no stable long run. Indeed, for any constant unemployment rate level, the real wage growth is c, which is not equal to π , except by chance. The specification of the model is therefore not correct.

In case of partial hysteresis ( 1 0 b > ), the long run equilibrium rate of unemployment is defined by:

(1.4 ter)

1 () / ELR Ucb π = -
Nevertheless, if at the initial situation the unemployment rate is not equal to the long run ERU, speed limit effects will affect the convergence of the unemployment rate towards its equilibrium level. The path (the medium run ERU) allowing the growth rate of wages to be consistent with the growth rate of productivity is the following:

(1.5)

+ = +
where , lt U is the past trend unemployment rate.

Let us assume, for instance, that 12 bb = . The long run ERU is equal to 8%; the past trend unemployment rate (average of the last four years) is equal to 12%. In such a case, the evolution of the unemployment rate will be: 10%, 9.75%, 9.35%, 9.14%, 8.77%.

The greater 2 b is relatively to 1 b , the longer the adjustment path of the unemployment rate level and the higher the gap between the medium run ERU and the long run ERU will be.

Price setting

In addition to an adequate growth rate of real wages, the macroeconomic equilibrium requires also an appropriate level of the real wages. When the wage equation is a Phillips curve, the wage and price settings are assumed to be asymmetric [START_REF] Debonneuil | La boucle prix-salaires dans l'inflation[END_REF]) and the consistency of the level of the real wages depends only on the price equation.

Firms set their desired prices as a mark up over labor costs. However, workers don't have any objective of real wage independent from the evolution of wages. This is a fundamental difference with WS/PS model and the main reason why we call the wage-price setting described here an asymmetric setting.

In our simple model, the transformation of the equation (1.2) gives a specific level of real wages, the available real wage. It corresponds to the real wage firms are ready to offer to their employees considering their price setting.

(1.6) (1 ) /

d cr tt k p ω π µ µ =--+ ∆-
where w is the real wage.

If we assume that at a given time period, the real wage lies above the available real wage level, firms will increase their prices. This reaction will induce a stagflation process, until the real wage level equals to the available real wage. Rearranging equation (1.3) gives:

(1.7) .( )

ELR bU U ω ∆= - -
Hence, if the effective real wage lies above the available real wage, and assuming that the convergence to the long run ERU will be obtained arbitrarily by an increase of the unemployment rate during T periods, the level of the equilibrium rate of unemployment at each of these T periods will be:

(1.5 bis) / EMR ELR UU b T ϖ =+ ∆
where ϖ ∆ is the gap between the actual real wage and the available real wage.

Temporary shocks affecting wages or long lasting shocks affecting the level of desired prices will therefore temporarily alter the ERU. In our simple model, such a shock can only be an increase of the employer's social contribution rate but the model can easily be extended to other shocks.

Next we turn to the consequences of the precise specification of the price setting.

a) Super-neutrality

The price setting specification of equation (1.2) is such that in the long run, the actual mark up of the firms is a decreasing function of the inflation rate. The model is hence not superneutral. Such a result can be avoided under the assumption that firms incorporate a trend inflation rate in their price setting, as follows:

(1. where n is the ratio of imports to the output, supposed to be equal in both countries, s is the exchange rate and p * is the external price level.

The external balance is:

(1.8) The equilibrium exchange rate that equilibrates the external balance is:

(1.9) The available real wage level is therefore:

(1.6 bis) /(1 )

d cr tt kn n ωπ φ = --+ -
A decrease of the real exchange rate induced by a shock on the external balance requires a decrease of the real wage and therefore a temporary increase of the unemployment rate.

Assuming for instance that 0.3 n = and 1.5 ϕ = ; a negative external balance of 1 percentage point of the GDP induces a decrease of 2.2% of the real exchange rate and hence a decrease of 0.95% of the real wage. If

0.5 = b
, it involves a period of two years where the unemployment remains 0.95 point above the ERU.

c) The case of capital financing

Now assume that firms want to achieve a given ratio 0 γ between their indebtedness and their capital level. In the initial period, the ratio is γ. The desired price is:

(1.2 quater) 00 (( () ( 1 ) ( )( ) ) ) / p wL g r g p pK Y δ γ γ λ γ γ =+ +- + --∆ - -
where L is the employment level, δ is the depreciation rate of the capital, r is the nominal interest rate, g is the growth rate of the economy, Y is the level of real output and l the speed at which firms want to achieve their desired indebtedness ratio.

The available real wage is therefore a decreasing function of the real interest rate. An increase of the real interest rate induces a transitory period of higher unemployment.

A numerical example: assume that 0.5 = b

. In the initial period, the following hypothesis are made: the nominal interest rate has a value of 6%, the inflation is equal to 3%, the growth rate is equal to 3%. The production level is 100; the wages level is 70; the investment level is 30; the capital stock level is 200; the indebtedness level is 100 and the ratio of desired indebtedness is 0.5. Let us assume an increase of one percentage point of the interest rate level (7%) and a decrease of 0.05 percentage point of the ratio of desired indebtedness (0.45).

The long run ERU is not affected, but the available real wage is affected by a double effect.

On one hand, it declines from 0.7 to 0.691 (a decrease of 1.3%). On the other hand, as the desired indebtedness of the firms is now 90, it requires a decrease of the real wage of 14.3%.

There are many unemployment rate paths consistent with these results. The most abrupt way is to have one year where the unemployment rate remains 31.2 points above the initial value, followed by a year where it will be below its initial value by 28,6 points. The third year, the unemployment rate will return to its initial value. If the objective is to spread the shock over ten years, it will require a five-year period where the unemployment rate remains 1.87 point above the long run ERU, followed by a five-years period where the unemployment rate remains 1.35 point below the long run ERU.

In this respect, any supply shock induces a gap between the long run ERU and the medium run ERU. But the concept of medium run ERU is ambiguous as it relies on specific hypotheses about the duration and the type of convergence towards the long run equilibrium.

Capital-labor substitution

Now let's assume that the technology is a CES function with labor-saving technical progress:

Price setting:

(1.2 quinto) (1 )( ) Kc r p cw t t α απ =+ - + -
where a is the capital share.

Capital cost:

(1.10)

K cp r δ =++
where r is the real interest rate, δ the depreciation rate of capital.

Employment demand:

(1.11) ( )

cr K ly w t tc t ασπ π =- + -- -
where σ is the elasticity of substitution.

Capital demand:

(1.12) (1 ) ( )

cr K ky w t tc α σπ =-- + --
with a constant real interest rate, the real available wage is:

(1.6 ter) () 1

d cr tr t α ωπ δ α =- + - -
and the employment is:

(1.13) 1 ly r t ασ π α =+ - -
Here again an increase of the interest rate requires a transitory period of higher unemployment rate in order to achieve the decrease of the real wage. It induces a durably lower level of production once the unemployment rate level has returned to its long run equilibrium value. The labor productivity considered here for the evaluation of the ERU is the trend labor productivity and not the effective labor productivity which depends on the evolution of the relative price of factors.

In all Phillips curve based models, the real wage in the long run is equal to the available real wage, but the convergence of the real wage to this available real wage should not be incorporated into the wage equation, as it is not a behavior. The convergence is achieved by the interactions of all components of the model.

Wage setting

The Phillips curve has been criticized by the proponents of the structural WS/PS model, who consider that the wages are bargained in level and not in variation. The bargaining models [START_REF] Cahuc | Economie du travail: La formation des salaires et les déterminants du chômage[END_REF]) imply that wages are fixed as a "mark up" over a reservation wage, which represents the income opportunities of employees outside the firm. As this mark up is a positive function of the trade union membership density and a decreasing function of the unemployment rate, the wage setting equation is:

(1.3 quater) r s cf Tb U ω θω =+ - ++
where s T is the trade union density, r ω is the reservation wage and θ are the mandatory levies on wages which are not compensated by benefits proportional to the contributions (in France, family and sickness contribution for instance).

However, the main problem is the determination of the reservation wage. To address this problem, four proposals have been exposed in the literature.

In a first specification, following [START_REF] Sargan | Wage and prices in the United Kingdom: a study in Econometric methodology[END_REF] (1.4 quater) 0 () / ( 1 ) ()

s ELR cf T r t U b ω θα δ α τπ ++ + + + -+ - =
According to its proponents, this specification has the advantage to provide numerous candidate variables to explain the evolution of the ERU, as for instance the power of the unions, the social contributions, the interest rate, the labor productivity. Unfortunately, in most cases τ ≠ π , which induces a trended ERU that is not realistic in the long run. The slowdown of productivity growth in Europe from 1973 to 2000 would in that case have induced a permanent increase of the unemployment rate.

6. In order to simplify, we consider here that wage and price setting equations are super-neutral.

In a second specification, the reservation wage is equal to the unemployment benefits.

Assuming that the unemployment benefits are institutionally set as a percentage of the gross wages ( r r t ωω =+), the ERU becomes:

(1.4 quinto) s r ELR cf T t U b θ ++ + =
where t r is the net replacement ratio.

The ERU depends only on the labor market features and on the unemployment benefits. An increase of the labor productivity induces an increase of the real wage, but as it is integrated in the unemployment benefits, it does not affect the ERU. An increase of the social contribution rate affects the ERU only when it alters the net replacement ratio (see for instance Layard et al. (1991), p.107;[START_REF] L'horty | Identification de la courbe de salaire et déterminants du chômage d'équilibre dans un modèle de négociation salariale[END_REF]). In this model, the increase of the unemployment rate is explained either by the power of the trade unions or by an increase of the replacement ratio, an explanation which is hardly pertinent for the European countries.

In a third specification, the reservation wage is the labor productivity [START_REF] Layard | Unemployment, Macroeconomic Performance and the Labour Market[END_REF]; [START_REF] Blanchard | Wage Dynamic: Reconciling Theory and Evidence[END_REF]). The basic idea is that workers can choose between dependent employment and domestic work, and that the productivity of domestic work increases at the same growth rate as the dependent work. The latter hypothesis does not seem very realistic. For other authors, unemployment benefits vary like the labor productivity (independently from wages). In both cases, the ERU is:

(1.4 sexto) 0 () / ( 1 ) s ELR cf T r U b ω θα δ α ++ + + + - =
This specification is "perfect": the ERU is a function of the desired variables.

Unfortunately, the theoretical underpinnings are not obvious, as they rely on arbitrary hypotheses relative to the productivity of the domestic work, or on false hypotheses about the evolution of unemployment benefits. The increases of the ERU are explained by increases in interest rates, unions power or social contributions. As the social contributions increase along with the unemployment rate in order to balance the social budgets, the long run econometric relation may hold.

In a fourth specification [START_REF] Manning | Wage bargaining and the Phillips Curve: The indentification and specification of aggregate wage equations[END_REF]; [START_REF] Blanchard | Wage Dynamic: Reconciling Theory and Evidence[END_REF]), the reservation wage is the lagged real wage, so that equation (1.3 quater) can be transformed into a Phillips curve.

A few words can be said about the theoretical underpinnings of those specifications. They do not study how actual wages are fixed. The idea that workers can choose between dependent employment and unemployment (or domestic work) is somehow unrealistic. For instance, let us consider a recently graduated student. He will take a job or not according to his idea about the normal level of wages and the level of unemployment. He will not base his decision on the level of productivity of domestic work. On the other hand, the firm will offer a wage that depends on the wages already prevailing in the firm and on the wages of the other firms and on the unemployment level. Such considerations lead to a Phillips curve specification, where the reservation wage is the current wage. Wage bargaining will depend on inflation, wages of other firms and the situation of the labor market. The trade off between dependent employment and the unemployment benefits or domestic work does not intervene.

In that sense, the Phillips curve theoretical underpinnings are as valid as those of the WS setting.

An attempt of synthesis

Let's assume that the general form of the wage equation is the following:

(1.14) Wages may be totally or partially indexed on prices; there may be or not hysteresis; wage setting may or may not integrate productivity growth or hikes of employer's social contribution.

The consumer price setting equation is the following:

(1.15) ( * ) (1 ) c p np s np =+ + -
and the value added price equation is:

(1.16) 1 (( ) / ( 1 ) ) ( ) o cr p kwt r tp p µα δ α π ν - ∆= + + + + --- + ∆
Let's assume that the real exchange rate:

(1.17) * p ps φ =-has no trend and that monetary authorities have an inflation target they impose in the medium term:

o p ∆ .
The long run ERU is:

(1.18) 1 (( 1) ( 1) ) / o ELR Ucd a p b π =-- --∆
As in the Phillips curve tradition, the ERU has few determinants. However, coefficient c can depend on specific characteristics of the labor market.

The available real wage is:

(1.19) ( ) /(1 ) (1 ) / d o cr tkt r n p ω πα δ α φ µ ν µ =--- + --+ --∆
The medium run ERU differs from le long run ERU when a shock widens the gap between the real wage and the available real wage affects:

(1.20) 1 () / ( )

d EMR ELR UU b T ωω =+ -
The same happens, in the presence of hysteresis, for any shock that widens the gap between the unemployment rate and the long run ERU.

So that:

(1.21) The equilibrium rate of unemployment has more determinants in the medium run than in the long run, as they include all supply shocks. Empirically, the differences between the Phillips curve model and the WS/PS model are narrowed, as the determinants of the medium run ERU in the Phillips curve model are the same as those of the long run in the WS/PS model. The difference between the two models lies in the determination of the long run.

A numeric example:

Let's assume that b is equal to 0.5 on a yearly basis and T is equal to 2 years. Let's assume that the employer's social contribution rate is raised by 1 point at the beginning of the first year.

When there is no hysteresis, the impact on the medium run ERU can be estimated in two ways. The first way is to consider that the medium run ERU has raised by 1 point over the 2 years. This method has the advantage and drawback to be determined ex ante: it is independent on the economic policy actually implemented by the authorities. The authorities are implicitly assumed to correct a gap after a shock in 8 trimesters. We use this method in our empirical part. In the second method, the difference between the medium and the long run equilibrium rate of unemployment is measured each quarter by the difference between the actual real wage and the equilibrium real wage divided by b 1 T (1 in the example). In this case, authorities are implicitly assumed to correct one eighth of the gap each quarters.

After a shock of employer's social contributions (a 1 percentage point increase), the unemployment rate must rise by 2 points in 2 years to meet the equilibrium (table 1). Inflation and the gap between the real wage (including social contributions) and the available real wage are progressively reduced.

1. Impact of an increase of the employer's social contribution of 1 percentage point The wage-price setting is assumed asymmetric as in the model previously developed. The wage equation is defined as a traditional Phillips curve (see below for the description of the variables):

T1 T2 T3 T4 T5 T6 T7 T8 T9 U 1 1 1 1 1 1 1 1 0 p ∆ 0.

Impact of an increase of the employer's social contribution of 1 point with hysteresis

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 U 1 1 1 1 1 1 1 1 0 0 p ∆ 0
(2.1)

11 2 1 () ( ) () ()( ) () n cl V c c r w w w wc a Lp b Ub UU d L e L p p f Lt Z k π α = ∆= + ∆ - - - + ∆+ ∆ - - ∆ + ∑
The consumer price equation is a linear function of the value added price and of the import price:

(2.2) () ( )

12 cV I p nL p n L p ∆= ∆+ ∆
The value added price setting results from a profit maximization in an imperfect competitive market. Firms have a desired price level determined as a mark up over labor and capital costs 7 [START_REF] Debonneuil | La boucle prix-salaires dans l'inflation[END_REF]):

(2.3) cr 12 3

.(1 ) ..

.

dI N V WT U C C PT Y β β β +  =+ +  Π 
and the adjustment process of prices follows a constrained Error Correction Model (ECM):

(2.4) 11 () ( )

Vd V d p Lp p p β µ -- ∆= ∆- - ,
the equation (2.4) being estimated by replacing d p by its specification in (2.3).

7. In our empirical model, we test the impact of the interest rates only via the price equation. However, because of capital-labor substitution, this effect could transit via the labor demand equation (equation (1.11) in our theoretical model). Moreover, we did not test the influence on prices of the firm indebtedness ratio as suggested in equation (1.2 quater). These are two possible extensions of our empirical work. In order to eliminate the simultaneity bias, equations (2.1), (2.2) et (2.4) have been estimated with Non Linear Three Stage Least Squares method. Equation (2.3) is incorporated in equation (2.4). In the case of the European countries, we use the data before the revisions of the National Accounts except in the case of the United-Kingdom. The estimation period is as far as this is possible 1970 -late 1990's. The data for Germany refer to West Germany. First, we estimate the wage-price setting using the standard Phillips curve used in most French macroeconomic model [START_REF] Economie | Structure et propriétés de cinq modèles macroéconomiques français[END_REF]) (table A-1). In a second step, we estimate the wage-price setting using alternative specifications for the wage setting, in order to test the influence of institutional variables. The institutional characteristics we have tested are often mentioned in the literature (OECD (1994(OECD ( , 1997)); [START_REF] Layard | Unemployment, Macroeconomic Performance and the Labour Market[END_REF]): the average unemployment benefit replacement ratio, the trade union membership density, the number of days lost because of strikes and when existing the minimum wage. The existence of hysteresis phenomena has been tested through the effect of the long term unemployment on the wage setting process. Finally, we tested non linearities of the Phillips curve 8 . 8. We also tested the impact of unemployment rates by sex, age, qualification and region in order to test insider or mismatch phenomena. We did not find any robust results.

The evolution of some institutional variables

Some of the institutional variables, we tested here, have been varying significantly over the last thirty years. So, if they play a significant role over the wage-setting, we can expect econometric significant results.

The replacement ratios are estimated as the ratio of the unemployment benefits (assistance and insurance) to the average per head wage in the business sector. These do not include minimum income benefits or other social benefits that are not related to a former work, as our approach refers more to macro-economic bargaining models than to micro-economic labor supply models. As a consequence, our replacement ratio calculations differ from those of the OECD (1994) that conclude to an increase of the French replacement ratio until the middle of the 1980's.

In most countries, the replacement ratio has decreased since the mid seventies (see graph 2.1). The American replacement ratio is the most stable but also the lowest at the beginning of the period. In France, between 1979 and 1995, it has decreased of about 30%. A similar decrease was observed in Spain and in the United Kingdom. At the end of the 1990's, the French unemployment benefit system would be less generous than in the United States. Sources: [START_REF] Ebbinghaus | Trade Unions in Western Europe since 1945[END_REF].

Graph 2.1 -Replacement ratios

MAIN EMPIRICAL RESULTS

Hysteresis (table A-2)

The presence of hysteresis has been tested under two specifications. The first one consists of testing directly the influence of the short term unemployment rate versus the long term unemployment rate where the unemployment duration is respectively inferior and superior to one year. In the second one, the impact of a polynomial structure of the unemployment rate on the wage setting is tested in addition to the current unemployment rate. In this case, we test the respective significance of U and of 11 1 , w i t h 1

nn ii i ii CD U U λ λ -- - == = -= ∑∑ .
In presence of hysteresis, in the first test, we expect that the long term unemployment has no effect on the wage setting and that the coefficient of the short term unemployment is high and significant. In the second test, in case of partial hysteresis, we expect that both coefficients (U and CD1) are negative and significant. In presence of full hysteresis, we expect that the coefficient of U is not significant. As in other empirical studies, the results of the tests are not very conclusive (Elmeskov and Mac Farlan (1993)). Germany is the only country where the direct test of the impact of the short term unemployment rate provides conclusive results. No hysteresis is detected in France, Netherlands, the United-States and in Spain. In the United-Kingdom, a full hysteresis is detected.

Non linearity (table A-21)

A log linear specification of the wage setting implies that the Phillips curve is convex. The main implications of the convexity of the wage equation are that economic policies inducing a high volatility of the business cycle are costly in terms of unemployment. This rate can lie above the ERU, as the cost of reducing inflation is higher than the benefits of a lower unemployment rate [START_REF] Clark | Phillips curves, Phillips Lines and unemployment Costs of Overheating[END_REF].

A non linear Phillips curve specification is accepted in three countries (Germany, France and Netherlands). But the results for France are weak and lead to no improvements of the equations in Germany. The Netherlands is the only country where a non linear specification improves the equation.

Employer's social contribution rate and minimum wages (table A-3)

According to our estimations, in some countries, employers manage to obtain a wage moderation after an increase of the employer's social contribution (Germany, Spain, France and the United-Kingdom). So employees pay a part of this increase by a decrease of their real wage. This effect has an influence on the ERU, as the decrease of the available real wage induced by an increase of the social contribution rate is partly directly paid in terms of lower wage increases. This wage moderation would be rather modest in Germany and France compared to Spain and the United-Kingdom. The integration of employer's social contribution rate improves the results in two cases: the United-Kingdom and Spain.

No impact of the employee's social contribution rate or of the income tax rate were found. They are therefore entirely paid by employees. This result of non homogeneity of the impact of the tax wedge on gross wages is in opposition to the WS/PS models 9 .

Among the countries under review, France, Spain, the Netherlands, the United-States and the United-Kingdom have a minimum wage. In the United-Kingdom, its creation is too recent to be tested. We tested the influence of the variation of the purchasing power of the minimum wage. It is only significant in France and in the Netherlands and the effects are of the same magnitude: one percentage point increase of the minimum wage leads to an increase of 0.1 point of the nominal wages. This result is standard in the case of France. In the case of the Netherlands, the presence of the minimum wage alters the significance of other variables.

Wage bargaining variables (table A-4)

The United-Kingdom is the only country where an effect of either the level of the replacement ratio or the level 10 of the trade union membership density can be observed. 9. WS/PS models often test the impact on wages of the "wedge" defined as the difference between the real labor cost paid by employers and the after-tax real consumption wage received by employees. In most studies, a restriction of homogeneity of the impact of the tax wedge components on the real wage is imposed (for instance, [START_REF] Layard | Unemployment, Macroeconomic Performance and the Labour Market[END_REF][START_REF] L'horty | Les déterminants du chômage d'équilibre: estimation d'un modèle WS-PS sur données trimestrielles Françaises[END_REF][START_REF] L'horty | Les causes du chômage en France: Une ré-estimation du modèle WS-PS[END_REF], 2001)). As far as we know, only [START_REF] Tyrväinen | Real wage resistance and Unemployment: Multivariate Analysis of Cointegration Relations in 10 OECD countries[END_REF] tests this restriction.

10. In WS/PS model, wage bargaining variables are specified in level. As far as we know, [START_REF] Fabiani | NAIRU: Incomes Policy and Inflation[END_REF] is the only study, with ours, that directly tests institutional variables in a Phillips curve. These authors specify the replacement ratio and strikes in variation which, to a certain extend, respect the WS/PS framework. We tested both specifications. Institutional variables in level in a Phillips curve may explain structural evolutions in the wage bargaining system. The higher the trade union membership density and the replacement ratio are, the higher the bargaining power of workers is: the trade union membership density reflects the level of organization of workers and a worker can refuse a job offer more easily if the replacement ratio is high. On the other hand, the replacement ratio in variation in a Phillips curve reflects that the replacement income growth is taken as a wage growth target by employees, whereas the interpretation of the trade union membership density or strikes in variation is not very logical.

However, because of multicollinearity problems, it is not possible to have simultaneously both variables in the wage equation. The integration of the trade union membership density leads to better results. The Netherlands is the only country where the variation of the replacement ratio has an impact on wages as in [START_REF] Broer | The equilibrium rate of unemployment in the Netherlands[END_REF]. It is also a country where the replacement ratio, very high at the beginning of the period, has been significantly reduced.

Synthesis of the results

As in other empirical studies, our results show that it is difficult to proof the effect of temporal changes of institutional variables on wages [START_REF] Blanchard | The Role of Shocks and Institutions in the Rise of European Unemployment: the Aggregate Evidence[END_REF]). Recent empirical studies concluding in favor of the role of institutional variables [START_REF] Fitoussi | Réduction du chômage, les réussites en Europe[END_REF], Fitoussi et al. (2000), [START_REF] Cadiou | La diversité des marchés du travail en Europe: Quelle conséquences pour l'Union Monétaire[END_REF]) use pooled country data and are hence not very useful for providing estimations of the impact of institutional variables on wages and hence on the ERU [START_REF] Richardson | The concept, policy use and measurement of structural unemployment: estimating a time varying NAIRU across 21 OECD countries[END_REF]). However, they underline the complex link between institutional features and unemployment that cannot be captured by a simple integration of variables, such as the trade union membership density or the number of days lost because of strikes. For example, the trade union density membership gives no information about the level of co-ordination of the trade unions, which according to some empirical studies, may have a negative influence on the unemployment level, but a positive one on the persistence of the unemployment [START_REF] Fitoussi | Réduction du chômage, les réussites en Europe[END_REF]).

Taking a closer look at the bargaining systems of the countries we have studied, a few remarks can be made. In Spain and in Germany, no major changes occurred in the bargaining system over the period under review. The bargaining system in Germany is centralized and co-ordinated. In Spain, there has been no constant wage co-ordination since the return of democracy. Tri-partite agreements including wage moderation have played a role in different periods of time (mid eighties, early nineties), through pay growth bands, but in the late eighties trade unions obtained wage increases above the inflation [START_REF] Ebbinghaus | Trade Unions in Western Europe since 1945[END_REF]). In the Netherlands and in France, wage moderation has become a strategy against inflation since the beginning of the eighties. In the United-Kingdom, the numerous laws against the power of the trade unions and in favor of the decentralization of wage negotiations (the employment acts in 1980, 1982 and 1988, the trade union acts in 1984 and 1992, the wage act in 1986 11 ) may instead have had concrete consequences on the wage bargaining. This could explain why this country is the only one where wage bargaining variables are significant in our estimations.

Part 3. Estimations of medium and long run equilibrium unemployment rate using an asymmetric wage-price setting model

The main assumptions

A lot of attempts to define different time horizon ERU can be found in the literature (for example, [START_REF] Mellis | The United Kingdom NAIRU: concepts, measurement and policy implications[END_REF] or [START_REF] Richardson | The concept, policy use and measurement of structural unemployment: estimating a time varying NAIRU across 21 OECD countries[END_REF]). However, these definitions rely more on technical considerations than on theoretical foundations. For instance, according to [START_REF] Richardson | The concept, policy use and measurement of structural unemployment: estimating a time varying NAIRU across 21 OECD countries[END_REF], the concept of "short-term NAIRU" corresponds "to the value of unemployment which stabilizes inflation over two consecutive periods" (p.35). The calculation of such a ERU generally give extremely erratic series dependant on the frequency used. Moreover the economic interpretation of such series is difficult since there is no reason for a shock to be absorbed in one period.

By focusing on inflation stability, proposed time horizon ERU definitions are often disconnected from the notion of macroeconomic equilibrium. They generally explain differences between the medium and the long run ERU with temporary shocks and inertia phenomena, but the link between the different ERU is vague and does not rely on hypotheses relative to the reactions of the economic authorities. In some studies [START_REF] Richardson | The concept, policy use and measurement of structural unemployment: estimating a time varying NAIRU across 21 OECD countries[END_REF]), the way that the medium run ERU converges to its long run path is omitted, in some others [START_REF] Mellis | The United Kingdom NAIRU: concepts, measurement and policy implications[END_REF]), this convergence follows an ad hoc dynamic through the introduction of the past unemployment rate.

Assuming that the wage-price setting are asymmetric allows to distinguish between a medium run and long run ERU based on a clear theoretical definition.

11. See [START_REF] Brown | The economic effects of industrial relations legislation since 1979[END_REF], Freeman and [START_REF] Pelletier | The Impact of Industrial Relations Legislation on British Union Density[END_REF] or [START_REF] Edwards | Grait Britain: From Partial Collectivism to Neo-Liberalism to Where?[END_REF].

The equilibrium rate of unemployment: a theoritical discussion and an empirical evalutaion for six OCDE countries -25 -

In the long run, we suppose that the growth rates of price set by firms and of their costs are the same. There is no temporary shocks affecting wages or long lasting shocks affecting the level of desired prices. Equations (2.1) to (2.4) can be simplified:

(3.1) 11 (1) (1) (1)( ) cV c wc a p b Ud e p p π ∆= + ∆ - + ∆+ ∆ -∆ 12 (3.2) 12 (( 1 ) ( 1 ) ) cV p nn p ∆= + ∆ (3.3) V pw π ∆= ∆ -∆ If 12 (1)
(1) 1 nn += , the long run ERU is: 1) is not equal to 1, as it is the case here for France, the inflation-unemployment tradeoff does not disappear in the long run. The ERU depends on the inflation target o p ∆ of the central bank.

(3.4) 1 1 (1 (1)) (1 (1)) o ELR ca p d U b π -- ∆ -- ∆ = If a(
Because the value added price equation is not super-neutral, in the long run, the actual mark up of firms is a decreasing function of the inflation target:

(3.5) 1( 1 ) o Vd p pp β µ - -= - ∆
Rewriting equation (2.2), gives the following equation (if the hypothesis 12 (1) (1) 1 nn += is not rejected):

(3.6) 21 1 (1) (1 (1)) cV I p cn p n p =+ +-
Rearranging equations (2.3), (2.4), (3.5) and (3.6) gives the available real wage:

(3.7) 2 21 1( 1 ) ( ) (1)( ) ( ) log( ) do cc r I V I N V wp t p n p p F T c β π β µ - -= -+ ∆ - - - - -
where 12. a(1) is the long run coefficient:

0 (1) ( ) l L aa L = = ∑ . 3 1 () l o g 1 (1 ) INV INV cr FT T WT β β  Π =+  + 
is a measure of the investment effort 13 .

Any shock that widens the gap between the real wage and the available real wage affects the medium run ERU:

(3.8) 1 () () d cc EMR ELR wp wp UU bT --- =+
As explained in the paragraph 1.6 of the part 1, authorities are implicitly assumed to correct the gap caused by the shock in 8 quarters, so that T is equal to 8 and the empirical estimation of the medium run ERU is given by: In presence of partial hysteresis (case of Germany), an additional term is incorporated in the medium run ERU:

(3.8 bis) 1 1( 1 ) o EMR ELR UU p bT β µ - =- ∆ ∆ 1 11 1 () ( ) (1 (1)) (1 ( 1
(3.9)

2 12 () () ELR bU U bb T - +
which captures the speed limit effects that affect the convergence of the unemployment rate towards the long run equilibrium rate of unemployment. In the case of full hysteresis, as it is the case for the United-Kingdom, our structural model does not allow to estimate an ERU.

13. As in none of the six countries an effect of the financial costs was found.

The ERU estimations

The medium and long run ERU for the six countries are shown in the graphs (3.1) to (3.5).

In order to identify separately the effect of shocks, three ERU are represented: UEL represents the long run ERU, UEM1 is the medium run ERU excluding the inflation target effects, UEM2 is the medium run ERU that incorporates all shocks (hence including the variation of the inflation target).

As expected, the slowdown of productivity growth since the mid seventies has led to an increase of the long run ERU in European countries (a little more than five percentage points in France between 1970 and 1998, more than 15 points in Spain, 4.5 points in the Netherlands, but less than one point in Germany, where the productivity slowdown was stopped during the eighties). On the other hand, it is quite stable in the United-States, at an average standard level of 5%. In the case of France, the long run ERU incorporates the trend variation of the purchasing power of the minimum wage. The effect of the minimum wage has progressively declined over the period. In the first half of the 1970's, it induced an increase of 1 percentage point of the ERU whereas the impact is only of 0.25 point in the late 1990's.

The inclusion of shocks and of the variations of the inflation target leads to substantial gaps between the long run and the medium run ERU in most countries in the seventies and especially in the first half of the eighties. The gap in the seventies is explained by the first oil shock and the increase of employer's social contribution rate that followed the first oil shock.

The sharpest increase of the employer's social contribution rate has been observed in Spain, but its effect on the medium run ERU has been partly compensated by the fact that it is partly paid by the employees according to our estimations. Because of the non linear specification of the wage equation, the unemployment cost of the shocks is the biggest in the Netherlands, albeit the relative import prices variations were similar to the other countries (the first oil shock has induced an increase of around 3% of the relative prices, the second oil shock an increase of 2%).

In most countries, except in Spain and to a smaller extend in Germany, the change in the inflation target of the monetary authorities achieved by higher real interest rates at the beginning of the eighties explains nearly all the increase of the unemployment rate of that period.

In all countries, the medium run ERU was near to the long run ERU and to the actual unemployment rate in the late eighties, following the counter oil shock of 1986 and the recovery of the second half of the eighties. The nineties are characterized by somehow different evolutions. In the United-States, the sharp decrease of the employer's social contribution rate, but also the improvement of the terms of trades have allowed a sharp decline of the medium run ERU until 1997, so that the decrease in inflation was mainly explained by identified favorable supply shocks. On the other hand, in European countriesexcept for Germany -, the medium run ERU lies close to the long run ERU. Therefore the gap between the actual and the long run ERU results from the effects induced by the restrictive economic policies conducted to achieve the monetary union.

The case of Germany is specific. Because of a very sluggish price adjustments and the presence of hysteresis -which leads to lower responsiveness of wages to the level of unemployment -, the medium run ERU is highly sensitive to supply shocks. Another particular feature of Germany is that it had the lowest gap between the actual unemployment and the medium run ERU in 1994 (one percentage point), because of the negative supply shocks induced by the financial cost of the reunification. We capture this shock through the increase of the employer's social contribution rate.

Concluding remarks

This paper had one theoretical objective and two empirical objectives. The first was to distinguish in a Phillips curve based model between the long run ERU and the medium run constraint that supply shocks impose to the path of the unemployment rate. The first empirical objective was to test the impact of institutional variables in an asymmetric wage-price setting.

In contrast to most of the TV-NAIRU reduced approaches 14 , our approach provides explanations to the evolutions of the unemployment rate within an explicit structural model.

As in other studies, the empirical results concerning the impact of institutions are not very conclusive. The second empirical objective was to estimate long run and medium run ERU based on a clear theoretical definition. Even if our estimations do not reveal the direct impact of the interest rate, our medium run ERU calculations intercept relatively well the increase of the unemployment rate due to the restrictive monetary policy of the first part of the eighties.

They also show a clear excess supply in most European countries in the nineties.

14. See [START_REF] Gordon | The Time-varying NAIRU and its Implications for Economic Policy[END_REF] and [START_REF] Richardson | The concept, policy use and measurement of structural unemployment: estimating a time varying NAIRU across 21 OECD countries[END_REF].

Graph 3.1 -United-States

Percent Sources: calculation of the authors, BLS.

Graph 3.2 -France

  where ϕ is the price elasticity of the external balance, 0 b is an exogenous shock on the external balance, y and y* are respectively the output level in the national country and abroad.

  , L'Horty and Sobczak (1996),[START_REF] Cotis | Le chômage d'équilibre en France: Une évaluation[END_REF][START_REF] L'horty | Les déterminants du chômage d'équilibre: estimation d'un modèle WS-PS sur données trimestrielles Françaises[END_REF][START_REF] L'horty | Les causes du chômage en France: Une ré-estimation du modèle WS-PS[END_REF], 2001)). In such a case, combining the wage equation with equations (1.2 quinto) and (1.10), the ERU is 6

  In this specification, the mark-up comes back to its initial value after 2 years. However, firms don't recover the profit losses during the period. This would be the case if the price setting incorporated a target of indebtedness. of the estimated wage-price settingThe wage-price setting model we have estimated is made of three equations. Results are presented in the annex for six countries (the United States, Germany, France, the United Kingdom, Spain and the Netherlands).

  sector (hourly or per capita) labor productivity L: lag operator P c : consumer price level P d : firm's desired price level P I : import price level P V : value added price level T cr : employer's social security rate. T INV : ratio between the investment in the business sector (excluding housing) and the volume of value added in the business sector. U: unemployment rate U l : trend unemployment rate UCC: net financial costs in the business sector W: business sector nominal (hourly or per capita) wage, Zk w : potential other variables influencing the wage setting process (union power, replacement ratio, mismatch, employee social contribution, etc...)

  In order to capture the effects of the trend investment effort, the variable ( )INV FThas been smoothed over with a HP filter. The inflation target is supposed to be equal to the trend inflation calculated with a HP filter. Other shocks are fixed at their average level over the last eight quarters, which is consistent with the hypothesis that authorities correct the shocks in eight quarters: one eighth of the shock is corrected in one quarter. The equations we use are those presented in the tables A.5, B and C of the annex.

  (L): trade union membership density; CD: short term unemployment rate (less than one year); LD: long term unemployment rate (= 20, Germany i=5), U: unemployment rate.

A.2.1. -Non linearity

	Country	c 1		a(L)	B 1	B 2	d(L)	e(L)	G(L)	R 2	Statistics SEE DW
			L			L	L
	Germany	-0.006	0	1**	-0.003 log	_	0.58	0.31	_	0.61 0.76% 2.1
	Quart.: 70:1-94:4	(3.8)			(3.91)		(5.6)	(2.65)
	France	-0.031	0	0.85	-0.0094 log	_	0.121	_	0.0948	0.94 0.31% 1.14
	Quart.: 70:1-98:3	(10.9)	3	(22.6)	(11.2)		(1.8)		(2.8)
	NLD	-0.019	0	1**	-0.086 log	_		_	_	0.66 0.70% 2.11
	Quart:70:1-96:4	(4.55)	4		(5.43)

Notations: g(L): minimum wage; log: log of unemployment rate.

A.3.

-Wage equations with minimum wage and employer's social contribution rate

	Country	c 1		a(L)	b 1	b 2		d(L)		e(L)		f(L)	g(L)	Statistics R 2 SEE DW
			L				L		L		L
	Germany	0.0076	0	1**	-0.40	-0.40	0	0.57	0	0.27	0	-0.17	_	0.64 0.73% 2.3
	Quart.: 70:1-99:4	(4.43)	2		(3.97)	(1.42)	1	(6.4		(1.69)		(3.05)
	Spain	0.051	0	1**	-0.21	_		_		_	0	-0.84	_	0.88 2.1% 1.4
	Ann.: 1970-1998	(6.2)			(4.25)							(4.09)
	France	0.0196	1	0.794	-0.62	_		0.135		_	0	-0.329	0.112	0.95 0.3% 1.12
	Quart.: 70:1-98:3	(10.5)	3	(17.6)	(11.2)			(1.9)			1	(2.3)	(3.5)
	NLD	0.0081	0	0.846	-0.317		4	0.187		_		_	0.123	0.68 0.65% 2.21
	Quart.: 70:1-96:4	(1.62)	2	(2.71)	(1.5)	_	7	(1.84)					(3.15)
	UK	0.0094	0	1**	-0.177	_		_		_	0 -0.836	_	0.63 0.95% 1.84
	Quart.: 70:1-99:2	(5)	3		(1.75)							(2.7)

Notations: f(L): employer's social contribution rate; g(L): minimum wage.

A.4.

-Wage equations with wage bargaining variables

	Country	c 1		a(L)	b 1	b 2		d(L)	g(L)	i(L)	j(L) 1	k(L)	Statistics R 2 SEE DW
			L				L
	UK	-0.006	0	0.607	-0.302	_		_	_	0.066 N	_	_	0.73 0.79% 1.85
	Quart.: 70:1-98:4	(1.1)	3	(7.4)	(2.4)					(3.8)
		0.005	0	1**	-0.144	_		_	_	0.102 V	_	_	0.63 0.95% 1.81
	Quart.: 70:1-98:4	(2)	3		(0.7)					(1.5)
		0.0086	0	0.828	-0.159	_		_	_	_	0.0116 N	_	0.69 0.87% 1.87
	Quart.:70:1-98:4	(2.9)	3	(11.2)	(1.4)						(2.96)
		-0.003	0	0.843	-0.134	_		_	_	_	_	0.052 N	0.68 0.88% 1.88
	Quart.: 70:1-99:2	(0.5)	3	(8.4)	(1.2)							(3)
	NLD	0.021	0	1**	-0.23	_	1	0.29	_	_	_	0.27 V	0.91 1.2% 1.44
	Ann.: 1970-1996	(2.6)			(2.2)			(1.86)				(1.8)

Notations: g(L): minimum wage ; i(L): trade union membership density; j(L): strikes; k(L): replacement ratio; N: level; V: growth rate. 1. Days lost because of strikes per employee: moving average (20 quarters).

A.5.

-Wage equations with "all" institutional variables

  L): employer's social contribution rate; g(L): minimum wage; i(L): trade union density; log, CD1, U: see table A.2 and A.21.

	Country Germany = hysteresis Quart.: 70:1-94:4 France Quart.: 70:1-98:3 Spain = employ. Social contr. Rate Ann.: 70:1-98:3 UK Quart.: 70:1-98:4 NLD = non linearity Quart.: 70:1-98:4 Country Germany* Spain * USA * France * NLD * UK * * The restriction n 1 (1) + n 2 (1) =1 is not rejected. c 1 a(L) b 1 L 0.0064 (3.47) 0 2 1** -0.29 U (2.53) -0.0306 (10.9) 1 3 0.875 (23.2) -0.0092 log (11.2) 0.051 (6.2) 0 1** -0.21 (4.25) -0.024 (4.2) 0 3 0.64 (5.8) _ -0.019 (4.55) 0 4 1** -0.0086 log (5.43) Estimation period Quart.: 1970:1-1994:4 Annual.: 1970-1998 Quart.: 1970:1-1999:4 Quart.: 1970:1-1998:3 Quart.: 1970:1-1996:4 Quart.: 1970:1-1999:2 C -Value added price equations b 2 d(L) e(L) L L -1.55 CD1 (3.04) 0 1 0.48 (4.67) 1 0.43 (2.67) _ 0.118 (1.81) _ _ _ _ -0.64 CD1 (3.8) _ _ _ _ _ n 1 (L)∆p V L L 0-4 0.84 (40.3) 0-3 0 0.916 (119) 0 0-3 0.9455 (112.2) 0 0-1 0.879 (74.2) 0-1 0-4 0.905 (3.85) 0-1 0-1 0.913 (61.4) 0 β(L) β 4 (L) 0 1 -0.83 f(L) _ -0.331 (2.6) (4.09) -0.564 (1.82) _ n 2 (L)∆p I 0.16 (7.9) 0.084 (10.83) 0.0545 (6.5) 0.121 (10.2) 0.095 (3.8) 0.087 (5.8) Country L µ β 1 β 3 β 2 β 5 L Dummies g(L) _ 0.0979 (3) _ _ _ Germany Quart.: 70:1-94:4 0 0.24 (8.1) -0.072 (4.8) 1.51 (17.3) 0.91 (2.7) _ --Spain Ann.: 1970-1998 0 1 0.684 (5.74) -0.21 (2.7) 2.4 (2.7) _ n.a. -_ USA Quart.: 70:1-99:4 0 0.442 (8.83) -0.08 (3.7) 1.99 (11.5) _ _ 1 5 0.09 (4.3) _ France Quart.: 70:1-98:3 0 0.288 (5.4) -0.106 (8.9) 1.679 (21.5) 0.872 (2.8) _ -_ NLD Quart.: 70:1-96:4 0 0.419 (2.79) -0.123 (3.4) 1.54 (5.78) 1.417 (2.1) _ -_ UK Quart.: 70:1-99:2 0 1 0.442 (7.6) -0.134 (6.8) 1.75 (21.2) 0.589 (1.54) _ -D732741 D793 Notations: f(B -Consumer price equations Notations: β	i(L) _ _ _ 0.11 (6.6) _ Statistics Statistics R 2 SEE DW 0.69 0.72% 2.4 0.95 0.298 % 1.18 0.88 2.1% 1.4 0.75 0.77% 1.97 0.66 0.70% 2.10 R 2 SEE DW 0.51 0.4% 2.1 0.99 0.4% 1.2 0.9 0.19% 1.16 0.9 0.33% 2.3 0.50 0.65% 2.35 0.84 0.55% 2.07 Statistics R 2 SEE DW 0.44 0.43% 1.97 0.92 1.4% 1.22 0.71 0.35% 1.83 0.84 0.41% 1.47 0.32 1.78% 2.77 0.81 0.67% 2.3

5 : capacity utilization rate; n.a.: Non available data.