Melika Hinaje
email: melika.hinaje@univ-lorraine.fr

Olivier Bethoux

Guillaume Krebs

Bernard Davat

Non-intrusive Diagnosis of a PEMFC

Keywords: Proton exchange membrane fuel cell, Maxwell-Stefan diffusion, magnetic field, 3D PDE modeling, diagnosis

Many reasons may cause malfunction of a proton exchange membrane fuel cell stack. Moreover, a single defect cell can affect the whole stack functioning, therefore the localization of this cell is crucial as well as identifying the root causes for such malfunctioning. The diagnosis tool has to be non intrusive and to be easy to replicate to a new fuel cell system. This paper explores paths to achieve such monitoring based on the use of the magnetic field induced by the fuel cell stack internal currents. Designing and using a three-dimensional simulation tool allows to establish a cause and effect relationship between fuel cell defects and specific magnetic signatures. This preliminary work enables to determine the required magnetic sensor accuracy, the sensor orientation and location as well as the experimental precautions for relevant measurements.

I. AIM

Using polymer electrolyte membrane (PEM) fuel cells (FCs) is an attractive way to produce energy without greenhouse gas. A defect in the FC stack, such as drying, flooding, starvation, active layer deterioration, induces major negative effect on the operation of the overall energy conversion system (FC and its auxiliaries): performance decreases and may cause the FC system to shut down, with possible damages to the PEMFC or to one of the auxiliaries. Identification of the defect and understanding the physical processes involved are essential to diagnose accurately the reduced performance causes. The aim of this work is to compute the magnetic field created by a PEMFC in order to identify a specific signature in case of malfunctioning cell.

II. PEMFC MODELING

To predict the FC performance, the unknowns, w H2 , w H2O,a, w H2O,c , w O2 , w N2 , p a , p c , φ m , φ, and v have to be computed by solving the equations of mathematical physics that describe the overall cell; computational domain is given in Fig. 1.

It is assumed that: -Three species oxygen, nitrogen and water are present on the cathode side, while hydrogen and water are considered in the anode side. -The PEMFC is operating in steady state.

-Flow is considered laminar. -There is no condensation in the cell. The single phase model described here is sufficient for modelling the mass transport in the porous anode and cathode up to moderately high current densities [START_REF] Hu | Three dimensional, two phase flow mathematical model for PEM fuel cell: Part I. Model development[END_REF] [2]. -The FC temperature remains constant and homogeneous all over the cell. -The membrane is gas-tight.

-The channels are approximated by straight channels.

TABLEI NOMENCLATURE

A. Mass and Momentum balances (coupled)

In anode and cathode sides, the transport phenomena are similar, only the species differ. In channels, the velocity v and the pressure of the gas mixtures are described by Navier-Stokes equations, i.e. the conservation of momentum (1) and the conservation of mass known as mass continuity 2). As GDL and CL are porous media, the Navier-Stokes equations have to be modified that leads to the socalled Brinkman equations [START_REF] Sohn | Numerical analysis of convective and diffusive fuel transports in high-temperature protonexchange membrane fuel cells[END_REF] (3). In the channel, the following system has to be solved

      0 . 3 2 p . . ρ . c a, c , a c , a T c a, c , a c a, c , a c a, c a, c , a                      v v v v v (1)   0 ρ . c a, c , a   v (2)
(1) while in the GDLs and in the CLs the below-stated system of equations needs to be solved:

  0 κ μ .v ε μ 3 2 p . v ε μ . v ε μ v v ε ρ . Cl GDL, c a, c a, CL GDL, c a, c a, T c a, CL GDL, c a, c a, CL GDL, c a, c a, c a, CL GDL, c a,                                      (3) (2)   0 ρ . c a, c , a   v (4)
B. Mass and specifies balance The mass and molar fractions obey the Maxwell-Stefan equations which describe the multi-species diffusion and convection in channels (5-6) and electrodes. Pair of species (i,j) interactions are characterized by the binary diffusion coefficient D ij [START_REF] Serincan | Transient Analysis of PEMFC at Start -Up and Failure[END_REF]: to account for the electrodes' porosity, the effective diffusion coefficient (9) substitute the Dij coefficient in relation [START_REF] Springer | Polymer electrolyte fuel cell model[END_REF].

i i e 1 j c , a c , a j j j ij i R ρ w p p ) w x ( x D ρ.w .                           c a, v (5)
                         i e 1 j c , a c , a j j j ij i i w ρ p p ) w x ( x D ρ.w c a, v N (6)
Where ρ is the mixture density and D ij is defined by:

RT p M x c , a e 1 i i i             (7)   2 3 0 0 0 0 0 0 ij ij T T T P T , P D D        (8)
In the GDLs and CLs into account, the effective diffusion coefficients are computed by the Bruggeman relation:

2 / 3 ij eff ij CL , GDL D D   (9)
Using the Onsager reciprocal relation [START_REF] Daneshpajooh | Equation for membrane transport[END_REF], [START_REF] Monroe | Onsager reciprocal relations for Maxwell-Stefan diffusion[END_REF] also leads to the following relation:

eff ji eff ij D D  (10)
In the continuity equation ( 5), species production and consumption are represented by a source term (water production) and a sink term (reactant consumption) respectively. The corresponding R i terms is expressed in kg/(m 3 .s). Obviously R i =0 in flow channels.

M 4F j R 2 2 O c O  (11) 2 2 H a H M F 2 j R   (12) M 2F j R O H c O H 2 2   (13)
Where ja and jc are the transfer current densities at CLs. C. Redox reaction and produced current Indeed, hydrogen oxidation leads to charges' displacements: a proton one occurs through the membrane inducing a ionic current j H+ while electrons travel are conducted by the electrodes resulting in an electronic current, je. Current conservation is expressed as follows:

0 j . j . j . H e cell        (14)
Ohm's law links current ji densities to potentials i:

  c , a e eff j . e        (15)   c , a H eff j . H         (16)
In ( 15) and ( 16), the source terms ji derive from the electrochemical reactions described by Butler-Volmer equation. exp exp

H ref a c a v o a c t a c t ref H C F F j a j C R T R T                                  (17)                                      act c act a ref O O ref o v c RT F exp RT F exp C C j a j 2 2 (18)
The reference exchange current ref o j depends on several parameters such as operating temperature and requires a large number of experiments [START_REF] Parthasarathi | Temperature dependence of electrode Kinetics of oxygen reduction at Platinium/Nafion interface-A microelectronic investigation[END_REF][START_REF] Springer | Polymer electrolyte fuel cell model[END_REF] to be properly identified. act  is the voltage drop between electrodes and electrolyte:

At the anode side

      H e act (19) At the cathode side oc H e act V        (20)

D. Boundary conditions

The boundary conditions have to be specified for all variables in each domain. In anode and cathode channels, inflows are given by their velocity and their inlet mixtures:

in , c , a c , a v v  (21) in , 2 H a w w  (22)       in O H O c 2 in , 2 w w w ( 23
)
The outlet boundaries are given by: pa,c = pout (24) and

0 p p ) w x ( x D ρ.w . e 1 j c , a c , a j j j ij i                         n (25)
Elsewhere no slip conditions apply and no flux go out. Thus:

0 i  n.N ( 26
)
The potential is fixed at gas channel-gas diffusion layer interfaces:

At the cathode side: E. Magnetic formulation As discussed earlier, the main aim of this study is to propose a set of guiding principles that will support the implementation of non intrusive fuel cell malfunctioning detection. A default in the heart of the fuel cell might modify the current density repartition and consequently the resulting magnetic field. After computing the fuel cell electrical operating point, the magnetic field is calculated by means of the magnetic vector potential (32).

cell e V   (
In this part, the studied domain is the single fuel cell  FC and the air around it a. The air domain dimensions are chosen much larger than the cell ones.

FC a in        0 j A (32)
To ensure the uniqueness of the solution, a Coulomb gauge (33) has to be coupled to Poisson equation (32).

To obtain the PEMFC operating point (V, I), 3D coupling PDE, describing the mixture gas diffusion and the redox reactions, have to be solved under a given operating conditions. Subsequently, the resulting magnetic field is computed by means of MVP. All the equations have been implemented in FEM software.

III. SOME RESULTS

A. Defect cathode channel

The considered fuel cell features a 100 cm 2 active area. As one of its cathode channels is blocked, O 2 does no more diffuse correctly (Fig. 2) and consequently the electrochemical reaction as well as the current distribution are locally disturbed; finally the resulting magnetic field is modified (Fig. 3 and4).

B. Defect anode channel

The same default is simulated at the anode side; a stopper at anode channel is located at the top or the middle of the single fuel cell as shown in Fig 5.

Indeed, due to the stopper, hydrogen diffuses hardly in the default channel. However for a specified current of 27A, as shown in Fig. 5, the same default at anode side does not alter significantly the magnetic field distribution compared to cathode side. IV. CONCLUSIONS This study has allowed to build a 3-dimensional computer model of a fuel cell whose originality is to be able to compute the induced magnetic field inside and around the fuel cell. This model has been used in different steady state scenarios.

Among other things, it permits to compare the magnetic field maps of a good operating cell and a defect one. The final purpose is obviously to determine which defect can be easily detected by magnetic measurement means and understand the precautions to be taken to achieve relevant measurements and diagnosis.

At a few tens of percent of rated current (a few amps to a few tens of amps for the studied cell), a defect at the cathode can be detected by measuring the tangential component of B with a sensor located closed to the cell. By contrast, a defect placed at the anode side produces a weak effect on the magnetic field B; it would be difficult to achieve a relevant diagnosis of such situation.

Experimental facility has to be led to demonstrate the scientific and technical feasibility of detecting a cell default among a fuel cell stack. Specifically, the present study shows that, regarding the rated cell current density (approximately 0.5 to 0.7 A.cm -2 ), the resulted magnetic field does not exceed the 10 -6 T range which can be challenging to measure especially considering that FC system auxiliaries may distort the measuring results. It is therefore essential to choose a Hall probe featuring a high sensitivity (in the order of mG) with relatively small active area due to the thickness of a single fuel cell.

According to all these considerations, the experimental setup has to be carried out so that the two current collectors do not disturb the measurement of the magnetic field induced by the fuel cell. One way to do so is to shield magnetically the fuel cell. Another promising way consists in correcting the measurements using the computation of auxiliaries' noises.

In sum, the simulation results allow to check the feasibility of diagnosis by means of magnetic field measurement and size the test bench and the associated sensors. This experimental stage is a key step and is the next phase of this work.

V. AKNOWLEDGEMENT We wish to acknowledge the research group SEEDS for partially fund this work.

Fig. 1 .

 1 Fig. 1. Cell detail: zoom on the GDLs and the MEA.

  Boundary conditionsThe boundary surface is denoted by Γ air . Zero Dirichlet boundary conditions can be applied .

Fig. 2 .Fig. 3 .Fig. 4 .

 234 Fig. 2. O2 diffusion: (a) healthy cell and (b) defective cathode channel

Fig. 5 .

 5 Fig. 5. Comparison between the tangential component of the magnetic induction for a healthy and defective anode channel

  cathode channel blocked in the central area) Bx of the defect cell *

TABLE II

 II

	GEOMETRY PARAMETERS
	Parameters	Value
	Active area	100 cm²
	Anode GDL thickness	380 µm
	Cathode GDL thickness	380 µm
	Membrane thickness	100 µm
	Anode catalyst layer thickness	50 µm
	Cathode catalyst layer thickness	50 µm
	GDL porosity	0.4
	Catalyst layer porosity	0.3
	Anode and cathode channel width	1mm
	Anode and cathode channel depth	1 mm
	Cog height of bipolar plates	0.9 mm
	GDL conductivity	220 S/m
	Membrane conductivity	10 S/m

TABLE III

 III

		OPERATING CONDITIONS
	Parameters	Value
	Fuel cell temperature	60 °C
	Hydrogen flow rate	624 mL/min
	Air flow rate	1.56 L/min
	Inlet H2 mass fraction


Gaëtan Stephan
email: gaetanstephan@hotmail.fr

Julien Lecumberry

The German Unemployment since the Hartz Reforms: Permanent or Transitory Fall?

Keywords: C32, E32 business cycle, unobserved components, Hartz reforms

The Hartz reforms were designed to make the German labor market more flexible in order to reverse the increasing trend of unemployment. This paper employs unobserved components models in order to distinguish permanent from transitory movements in the German unemployment rate. Our results show that the permanent component of the German unemployment was reduced in the range of 1.1 and 2.6 percentage points after the Hartz reforms.

Introduction

After having peaked at 11.4 % in 2005, the German unemployment rate recorded a sharp trend reversal and declined steadily until reaching 5.5 % at the end of 2013. This labor market performance has received considerable attention, especially during the Great Recession where unemployment slightly increased [START_REF] Burda | What Explains the German Labor Market Miracle in the Great Recession[END_REF]). One popular reason among economists is to give credit to the wideranging Hartz reforms implemented in [2003][2004][2005]. The reforms aimed to reverse the increasing trend of unemployment, particularly by getting long-term unemployed back to work. The four laws Hartz I-IV consist of a set of measures such as lowering benefits during unemployment, restructuring the federal labor agency or reducing the social security contributions on labor. [START_REF] Krebs | Macroeconomic Evaluation of Labor Market Reform in Germany[END_REF] show that Hartz reforms led to a substantial reduction in the trend component of unemployment. This paper attempts to know how much of this fall can be attributed to the trend component.

Unobserved components models allow to distinguish permanent (trend) from transitory (cyclical) movements in macroeconomic fluctuations. Traditional unobserved components models, employed by [START_REF] Clark | The Cyclical Component of U.S. Economic Activity[END_REF][START_REF] Clark | Trend reversion in real output and unemployment[END_REF] or [START_REF] Harvey | Forecasting, Structural Time Series Models and the Kalman _lter[END_REF], set to zero correlation between shocks to the trend and the cycle. Nevertheless, [START_REF] Morley | Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different[END_REF] (MNZ) show that the correlation could be identified and free estimated by specifying transitory component as an AR (2) process. [START_REF] Sinclair | The Relationships between Permanent and Transitory Movements in U.S. Output and the Unemployment Rate[END_REF] extends MNZ method to a multivariate analysis with real GDP and unemployment rate. This methodology suggests a substantial role for permanent movements unlike traditional models which imply a larger role for transitory movements. We estimate unobserved components models consisting of unemployment and real GDP following both [START_REF] Sinclair | The Relationships between Permanent and Transitory Movements in U.S. Output and the Unemployment Rate[END_REF] and a more conservative approach similar to [START_REF] Clark | Trend reversion in real output and unemployment[END_REF]. Moreover, [START_REF] Perron | Let's take a break: Trends and cycles in US real GDP[END_REF] show that permanent movements become secondary in explaining overall fluctuations when allowing a structural break in the trend component. Therefore, our models include structural breaks in the trend component of unemployment and real GDP. This paper assesses how much the reduction of the German unemployment rate can be attributed to a permanent component. To anticipate our findings, the permanent component of unemployment was reduced in the range of 1.1 and 2.6 percentage points after the implementation of the Hartz reforms, even in the most conservative estimate. Furthermore, the Great Recession accounts for a permanent loss on the German real GDP. The rest of the paper proceeds as follows. Section 2 describes unobserved components models employed in our empirical analysis. Section 3 presents and discusses the results while Section 4 concludes.

Model and data

In order to distinguish trend component from cycle component, we resort to a bivariate unobserved components representation. Building on [START_REF] Clark | Trend reversion in real output and unemployment[END_REF] and [START_REF] Sinclair | The Relationships between Permanent and Transitory Movements in U.S. Output and the Unemployment Rate[END_REF], the model consists of unemployment rate and real GDP. Unemployment rate ! is disentangled into permanent " #! and transitory components $ #! :

% & = ' ( %& + ) %& '''*,)
Berger (2011) argues that trend component of unemployment cannot be specified as a simple random walk for European countries. Following Berger, we represent the trend component of unemployment as a random walk with drift:

( %& = -%& + ( %&., + / %& (2) 0 #! = 0 1# + 2*3 > 4 # 56 (3) *Manuscript
where 7 #! 'is the innovation of permanent component of unemployment. Berger finds for Euro area unemployment one break occurred in 1985Q1. Before the break, the drift term is estimated to be 0.125 implying an upward trend in unemployment over the first period. After the break, the drift is estimated to be close to zero. Thus, the permanent component of Euro area unemployment collapses to a simple random walk. In equation (3), drift equals 0 1# before the break date labelled by 4 # and 0 1# + 6'*0 8# 5 after. Based on univariate break tests1 , we find one break in 1983Q2. Real GDP 9 ! is also the sum of permanent " :! and transitory components $ :! : 9 ! = ' " :! + $ :! (4) Permanent component of real GDP is specified as a random walk with drift 2 , where 0 9! is the average growth rate of real GDP and 7 9! represents the innovation as:

" :! = 0 :! + " :!.1 + 7 :! (5)

0 :! = 0 1: + 2;3 > 4 : <6 (6)
Following [START_REF] Perron | Let's take a break: Trends and cycles in US real GDP[END_REF], equation ( 5) accounts for one structural break in the drift term. This specification aims to capture potential shift in the trend component of output. Average growth rate equals 0 1: before the break denoted''4 : , 0 1: + 6'*0 8: 5 after. Univariate break tests find a shift in 1991Q1 corresponding to the German reunification. Transitory component of unemployment and real GDP are modeled as an AR (2) process:

$ #! = ? 1# $ #!.1 + ? 8# $ #!.8 + @ #! (7) $ :! = ? 1: $ :!.1 + ? 8: $ :!.8 + @ :! (8)
The shocks (7 :! A 7 #! A @ :! A @ #! ) are assumed to be normally distributed with mean zero. The variancecovariance matrix allows no restrictions on the correlations between any of the contemporaneous shocks. The variance-covariance matrix is:

B C C D E F G 8 E 7 9 7 E 7 9 @ 9 E 7 9 @ E 7 9 7 E F H 8 E 7 @ 9 E 7 @ E 7 9 @ 9 E 7 @ 9 E I G 8 E @ 9 @ E 7 9 @ E 7 @ E @ 9 @ E I H 8 J K K L
We confront this correlated unobserved components model to a more conservative approach which impose restrictions on the variance-covariance matrix, similar to [START_REF] Clark | Trend reversion in real output and unemployment[END_REF] :

B C D E F G 8 M M M M E F H 8 M M M M E I G 8 E @ 9 @ M M E @ @ 9 E I H 8 J K L
These restrictions assume that the off-diagonal elements of the matrix are set to zero. [START_REF] Okun | Potential GNP: Its Measurement and Significance[END_REF] shows that real GDP and unemployment are negatively related through their transitory movements. Thus, we only allow E I G I H to be free estimated as transitory component of real GDP and unemployment are linked via Okun's law.

Equations ( 1)-( 8) are cast into state-space form. The parameters of the model are estimated by using the Kalman Filter algorithm and maximum likelihood estimation.

Quarterly data are extracted from OECD.Stat and covering the period from 1970Q1 until 2013Q4. Unemployment corresponds with unemployment rate. Real GDP is defined in millions of dollars, volumes estimates, OECD reference year, annual levels and seasonally adjusted. Real GDP is expressed in logarithm and multiplied by 100.

3 Results

Parameters and components estimates

Table 1 reports the maximum likelihood estimates of our different specifications. The first column presents estimates of Model (1) which allows no restrictions on the variance-covariance matrix. Model (2) includes structural breaks3 in the drift term of unemployment rate and real GDP. A likelihood ratio test with a p-value of 0.002 rejects the null hypothesis of no structural breaks. Finally, Model ( 3) is a restricted model with zero-covariances between permanent and transitory shocks including structural breaks.

Figure 1 shows the estimated permanent component of unemployment rate based on Model (2). Movements in the unemployment rate appear to arise mainly from permanent shocks as the estimated permanent component is quite volatile. In particular, the standard deviation of the permanent innovation (0.566) is higher than the standard deviation of the first difference of the series (0.281) and slightly larger than the transitory innovation (0.547). The permanent and transitory innovations show negative correlation O F H I H with an estimate of -0.958. Allowing correlations between shocks to the trend and the cycle conduct to a significant part of permanent movements in the unemployment fluctuations.

The drift term 0 1# is found to be 0.158 % for Model (2) and 0.165 % for Model (3) on the pre-1983 sample. After the structural break, the drift term is estimated to be close to zero and not significant. We assume that this parameter is subject to one structural change rather than modeling the drift term as a random walk, implying that the permanent component of unemployment is I(1).

According to the bottom of Figure 1, Model (3) suggests that the increase of the German unemployment is explained by the permanent component until 1983. After the break, most of the movements arise mainly from transitory shocks although a decrease in the permanent component is observed since the mid-2000. Especially, the standard deviation of the transitory innovation (0.159) is larger than the standard deviation of the permanent innovation (0.148). Without surprise, the persistence of the transitory unemployment, as measured by the sum of the autoregressive parameters ? 1# and'? 8# , presents a high value relative to Model (2).

By multiplying the drift term 0 : of real GDP by four, it can be interpreted as the average annual growth rate of the permanent component. Based on Model (2), the drift term is estimated to be 0.655 before 1991Q1 and 0.354 thereafter. Thus, the permanent component of real GDP has annually grown by 2.6 % on average before the structural break and 1.4 % after. These estimates are quite similar in Model (3). Both models agree on a fall of almost 50 % of average annual growth rate after the process of reunification.

Similar to unemployment, movements in the German real GDP are mainly driven by permanent shocks in Model (2). The permanent component of real GDP is highly variable as shown by Figure 2 and very close to the series itself. The standard deviation of the permanent innovation (1.213) is larger than the standard deviation of the transitory innovation (0.395) and the standard deviation of the first difference of the series (0.993). These findings suggest a minor role for transitory shocks. Conversely to common detrending methods, such as bandpass or Hodrick-Prescott filters, Model (2) cannot remove low frequency movements in real GDP series. Therefore, the transitory component of real GDP, presented in the Figure 3, looks like small in amplitude and noisy. In addition, the transitory component of real GDP appears to match poorly recessions4 .

Another interesting fact is the variability of the permanent component of the German real GDP during recessions. The permanent component falls in accord with ECRI recessions, while the transitory component takes some positive values. Obviously, these facts cast serious doubts about the ability of Model (2) to generate business cycle. Both Models ( 1) and ( 2) found that the correlation O F G I G between the permanent and transitory components of real GDP is strongly negative: -0.823 in Model ( 2). This pattern is consistent with other studies that have examined correlation between trend and cycle using correlated unobserved components models [START_REF] Morley | Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different[END_REF], [START_REF] Morley | The Slow Adjustment of Aggregate Consumption to Permanent Income[END_REF], [START_REF] Sinclair | The Relationships between Permanent and Transitory Movements in U.S. Output and the Unemployment Rate[END_REF], [START_REF] Mitra | Output Fluctuations in The G-7: An Unobserved Components Approach[END_REF]].

Third column of Table 1 presents estimated parameters of Model (3). The results are striking: the parameters of the restricted model deviate strongly from Models ( 1) and ( 2). Fluctuations in real GDP are primarily due to transitory movements. The standard deviation of the permanent innovation (0.670) decreases of almost 50 % relative to Model (2) and becomes lower than the standard deviation of the first difference of real GDP. Consequently, the permanent component of real GDP acts more like a smooth trend. The transitory component, measured by the sum of the autoregressive parameters, becomes more persistent: 0.925 versus 0.623 in Model (2). Moreover, the declines in the transitory component match reasonably well with ECRI recessions, as shown by Figure 3. The restricted unobserved components approach implies a large and persistent cycle in agreement with business cycle.

Unemployment downward trend in Hartz reforms

Figure 4 shows the estimated permanent component of unemployment rate based on Model (2) and Model (3). The picture is limited to 1999 to investigate trend unemployment movements during implementation of the Hartz reforms and the Great Recession. From 2001 to 2005, the German unemployment rate rose from 7.8 % to 11.1 % and fall to 8.7 % in 2007 before the onset of the Great Recession. A striking feature is the slight increase of unemployment during the Great Recession and its ongoing decrease after the crisis. It is noteworthy to highlight that both models agree on a decrease of the permanent component of unemployment. We assess the fall in the permanent component from 2007 to 2013 as it corresponds to the onset of the Great Recession5 and the end of the 2005-2007 recovery6 .

According to Model (3), the permanent unemployment was reduced by 1.1 percentage points ranging from 7.8 % in 2007 to 6.7 % in 2013. Considering Model (2), the permanent unemployment fell from almost 2.6 percentage points between 2007 and 2013. In addition, the Great Recession appears to have not any adverse effect on the permanent component on both Models although the unrestricted estimate provides some volatility during the Great Recession. The decrease of the trend components could be easily attributed to lagged effects of the Hartz reforms. Although Models (2) and ( 3) differ strongly about the importance of permanent and transitory shocks, both models point out a steady fall in the permanent component of unemployment, even in the most conservative estimate, in the aftermath of the Hartz reforms7 .

Conclusion

In this paper, we focus on identifying the importance of permanent versus transitory movements in the German unemployment since the implementation of the Hartz reforms. The reforms aimed to make the German labor market more flexible in order to reverse the increasing trend of unemployment. Using quarterly data from 1970 to 2013, we estimate unobserved components models consisting of unemployment and real GDP. Considering different specifications, our results show that unemployment trend was reduced in the range of 1.1 and 2.6 percentage points since the implementation of the Hartz reforms, although the importance of permanent shocks depends on the estimates. In addition, the results suggest that Great Recession accounts for a permanent loss on the German real GDP.

Figure 5

 5 Figure 5 presents the permanent component of the German real GDP based on Model (2) and Model (3) between 1999 and 2013. During the Great Recession, Germany suffered a real GDP decline of almost 6.7 %, the most severe recession in the post-war era. Model (3) suggests that real GDP experienced a permanent loss of 4.1 %, we conclude that the major part of the recession was captured by the permanent component. Both Models point out a fall in the permanent component of real GDP during the Great Recession conversely to the 2001-2003 recession.

Figure 1 :

 1 Figure 1: Unemployment rate and permanent component

Figure 2 :

 2 Figure 2: Real GDP and permanent component

Figure 3 :

 3 Figure 3: Real GDP and transitory component

Figure 4 :

 4 Figure 4: Permanent components of unemployment rate(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)

Figure 5 :

 5 Figure 5: Permanent components of real GDP(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)

Table 1 :

 1 Parameter estimates

	standard errors are in parentheses
			Model (1)	Model (2)	Model (3)
			Correlations	Correlations	No correlations
			No breaks	Breaks	Breaks
	Log-likelihood		-204.678	-196.629	-199.989
	Real GDP
	Standard deviation of Permanent Shocks	! "	1.408 (0.231)	1.213 (0.146)	0.670 (0.049)
	Standard deviation of Transitory Shocks	# "	0.682 (0.436)	0.395 (0.424)	0.644 (0.036)
	AR (1)	$ %&	1.029	1.005	1.099
			(0.184)	(0.197)	(0.036)
	AR (2)	$ '&	-0.329	-0.382	-0.174
			(0.161)	(0.136)	(0.020)
	Drift 1970-1990	( %&	0.528	0.655	0.606
			(0.074)	(0.113)	(0.082)
	Drift 1991-2013	( '&	0.528	0.354	0.334
			(0.074)	(0.109)	(0.074)
	Unemployment rate
	Standard deviation of Permanent Shocks	! )	0.660 (0.147)	0.566 (0.101)	0.148 (0.005)
	Standard deviation of Transitory Shocks	# )	0.654 (0.319)	0.547 (0.228)	0.159 (0.003)
	AR (1)	$ %*	0.785	0.751	1.645
			(0.068)	(0.070)	(0.014)
	AR (2)	$ '*	-0.023	-0.029	-0.670
			(0.038)	(0.045)	(0.011)
	Drift 1970-1983	( %*		0.158	0.165
				(0.074)	(0.055)
	Drift 1994-2013	( '*		-0.025	-0.008
				(0.052)	(0.018)
	Correlations
	Permanent GDP/Transitory GDP	! " # "	-0.844 (0.090)	-0.823 (0.304)
	Permanent unemployment/Transitory	! ) # )	-0.971 (0.062)	-0.958 (0.058)
	unemployment
	Permanent GDP/Permanent	! " ! )	-0.636 (0.108)	-0.713 (0.089)
	unemployment
	Transitory GDP/Transitory	# " # )
	unemployment

We use tests proposed by[START_REF] Bai | Estimating and Testing Linear Models with Multiple Structural Changes[END_REF]

2003) and[START_REF] Andrews | Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative[END_REF].2 The Augmented Dickey-Fuller test with GLS detrending (ADF-GLS) cannot reject the null hypothesis of unit root for real GDP.

Including structural breaks reduce the size of the permanent and transitory innovations for both unemployment rate and real GDP.

Recessions are defined by the Economic Cycle Research Institute (ECRI).

Another reason for this choice is to compare the competing effects of Great Recession and labor market reforms on unemployment trend.

Conversely to 2005, permanent components and actual series are close in 2007.

We would like to thank our anonymous referee for suggesting this comment.