Bruno Amable

Baptiste Françon

The Effect of the Hartz Reform on Unemployment Duration and Post-Unemployment Outcomes A Difference-in-Differences Approach

Keywords: unemployment benefits, unemployment duration, job matching, job quality, early retirement, difference-in-differences JEL codes: C41, J64, J26 assurance chômage, durée de chômage, appariement sur le marché du travail, qualité de l'emploi, dispositifs de pré-retraite, différence-de-différences Codes JEL: C41, J64, J26

In this paper, we investigate the microeconomic effects of one major feature of the German Hartz reforms (2003)(2004)(2005), namely the reduction in compensation duration for older unemployed above 45 years of age. We look at two potential effects of this measure: on job take-up rates, but also on post-unemployment outcomes, through various indicators of matching quality (job stability, skill adequacy) and job quality (type of job contract). Applying difference-in-differences estimators, we show that the effects of this specific feature were rather scant. Regarding unemployment duration, only unemployed within a specific age group (55 to 59 years old) were affected by the reform. Evidence suggests that this is because they previously used unemployment schemes as a bridge to early retirement. In addition, there is some evidence of detrimental effects on job or matching quality.

Introduction

Against the backdrop of the current Great Recession, Germany is commonly depicted in public debates as an economic 'success story' and a potential model for other European countries. Moreover, its current good labour market performances are often ascribed to the set of measures implemented by the Social Democratic-Green coalition from 2003 to 2005, usually referred to as the Hartz reforms (CAE, 2012, p. 5;OECD, 2012, pp. 10-11). These structural reforms have profoundly transformed the German unemployment insurance system and its administration, while they also brought minor changes to the employment protection legislation: they notably led to substantial cuts in unemployment benefits and increased pressures on unemployed.

The conventional view in economics posits that such measures should indeed decrease unemployment, by lowering the reservation wage of workers and by increasing the incentives for the unemployed to take up jobs. In this framework, generous benefits reduce work incentives because they alter the labour/leisure trade-off of unemployed. Moreover, they might lead unemployed to delay re-entry into the labour market as they wait for better job offers, as predicted by standard matching theories [START_REF] Mortensen | Job search and labor market analysis[END_REF][START_REF] Pissarides | Equilibrium unemployment theory[END_REF]. Cuts in benefits generosity should therefore decrease the duration of unemployment spells, but at the same time they might have detrimental effects on post-unemployment outcomes. As they would force unemployed to take up jobs where their skills are not optimally exploited, workers productivity might suffer and subsequent employment might be less stable. This mechanism might be especially relevant in the German context, where workers skills have the property of being very specific (Hall and Soskice, 2001): consequently, the amount and availability of jobs that would match their skills appears to be limited [START_REF] Iversen | An Asset Theory of Social Policy Preferences[END_REF]. Eventually, cuts in benefits might also negatively affect the well-being of workers, by forcing them into jobs of lower quality.

This paper focuses on one of the major feature of the Hartz reforms, namely the strong cuts in unemployment compensation duration for unemployed above 45 years of age. We take advantage of the particular design of this measure to evaluate its causal effect on job take-up rates and post-unemployment outcomes through a difference-in-differences estimation, using the German Socio-Economic Panel (SOEP). Results of duration models first show that this measure only had a limited impact on job take-up rates by the unemployed, and that this effect was concentrated on a specific age group (55 to 59 years old) who previously used Documents de Travail du Centre d'Economie de la Sorbonne -2014.20 unemployment compensation as a bridge to early retirement. Additional evidence is exhibited in support of this claim.

Furthermore, we analyse the potential impact of this reform on the quality of postunemployment outcomes, taking into account various measures of matching quality (job stability, skills adequacy) and job quality (type of contract). We also find re-employment duration to have significantly increased for the 55-59 age group specifically. While this comes in contradiction with job matching theories, it corroborates our point that contemporaneous changes in early retirement provisions caused workers to delay labour market exit.

Eventually, some detrimental effects of the reform on post-unemployment outcomes are found: skills inadequacy has increased for the oldest unemployed (60-64 years old) while unemployed aged 50 to 54 experienced slightly more exits toward part-time employment. This paper is organised as follows. The following section presents major features of the Hartz reforms. Section 3 reviews the main results of the literature that focuses on the microeconomic effects of benefits generosity on the job take-up rates by the unemployed.

Section 4 details the features of the measure that reduced compensation duration and presents our estimation strategy. Main results of this analysis are presented in Section 5. The final section concludes.

The Hartz reforms

The Hartz reforms consisted of four packages of measures (Table 1). They entailed substantial changes in various areas of the unemployment policy, such as the creation of single gateways for the benefit and employment administrations, the development of new training programmes or the introduction of government-sponsored jobs (the infamous Ein-Euro-Jobs). In this paper, we focus in particular on the potential effects of the Hartz IV package, implemented in January 2005, as it involved a drastic decrease of the unemployment insurance generosity.

Prior to the reform, the German unemployment insurance system was organised around three schemes; unemployed who were eligible based on their past contributions were entitled to earnings-related benefits from the unemployment insurance (Arbeitslosengeld I); once their rights were exhausted, they could still enjoy earnings-related benefits from the unemployment assistance (at a lower replacement rate though), virtually for an unlimited period of time (Arbeitslosenhilfe); only unemployed without entitlements to UI benefits had to rely on flatrate means-tested social assistance (Sozialhilfe). With the Hartz IV reform, unemployment Documents de Travail du Centre d'Economie de la Sorbonne -2014.20 assistance was merged with social assistance into a new flat-rate means-tested benefit (Arbeitslosengeld II), which implied significant benefit cuts for about two thirds of the unemployed that formerly depended on these two schemes [START_REF] Goebel | Nach der Einführung von Arbeitslosengeld II: Deutlich mehr Verlierer als Gewinner unter den Hilfeempfängern[END_REF]. The new scheme was particularly unfavourable to former recipients of the unemployment assistance, who represented about one half of all unemployed with compensation in 2003 (Chagny, 2005, p.14). The benefits of the new scheme were no longer earnings-related.

Moreover, criteria of job suitability were strengthened as references to conventional wages or geographical distance were removed. Those who formerly depended on the social assistance generally experienced monetary gains from the reform, but these gains were very marginal in most cases. Furthermore, these recipients also lost from the reform on other fronts. For example, many of these welfare recipients were not exempted from job search anymore and at the same time sanctions in case of job refusals were strengthened.

Finally, introduction of new rules for unemployment insurance compensation also implied less generosity. The necessary contributions for unemployment insurance were now calculated on the 2 years preceding dismissal (3 years before), strengthening the eligibility requirements. The maximum compensation duration for unemployed above 45 years of age was reduced to 18 months, compared to 36 months previously. 3 For unemployed without familial ties, reference to geographical distance was also removed from the criteria of job suitability after four months of unemployment and the burden of proof that a job was notsuitable was now on the unemployed. To sum up, opt-out options for workers were severely reduced as a result of the reform. This should increase employment according to conventional views in economics.

Benefits generosity, unemployment duration and job matching quality: empirical evidence in the literature

There is a large empirical literature dealing with the microeconomic effects of unemployment benefits generosity. Traditionally, these evaluations focus on the quantitative effects of a variation in the generosity of benefits on the time spent in unemployment. Their basic assumption is that unemployment insurance creates disincentives for job seekers to look actively for a job, leading to longer unemployment spells. Most of them use policy shifts or discontinuities as natural experiments to isolate the causal impact of variation in potential benefit duration or benefit level. They usually find robust evidence in line with theoretical predictions about the detrimental effects of generous benefits.

In a seminal paper, [START_REF] Katz | The impact of the potential duration of unemployment benefits on the duration of unemployment[END_REF]) use the differences in potential benefits duration across U.S. states and find significant and substantive disincentives effects. The size of these effects was discussed by follow-up studies. [START_REF] Card | Extended benefits and the duration of UI spells: evidence from the New Jersey extended benefit program[END_REF] notably raise the question of policy endogeneity bias, which relates to the fact that benefits are often targeted at individuals who have especially bad employment prospects. Exploiting an exogenous variation in benefit duration in New Jersey, they still find unemployment insurance to significantly enhance the length of the unemployment spell. But the size of this effect is more modest once policy endogeneity is accounted for. 4Some studies have specifically dealt with the impact of unemployment insurance in Germany. [START_REF] Hunt | The Effect of Unemployment Compensation on Unemployment Duration in Germany[END_REF] analyses the impact of the extension of potential benefits duration to unemployed older than 42 years of age in the 1980s. Her empirical strategy is very similar to the one used in this section, as it is also based on difference-in-differences estimators applied to the SOEP dataset. She notably finds that longer benefits entitlement had a significant negative impact on job take-up rates by unemployed. In a more recent evaluation of this reform, [START_REF] Fitzenberger | Unemployment durations in West Germany before and after the reform of the unemployment compensation system during the 1980s[END_REF] provide results in contradiction with [START_REF] Hunt | The Effect of Unemployment Compensation on Unemployment Duration in Germany[END_REF]. Using an administrative dataset, they do not find any impact of the extended benefit entitlement on unemployment spells that end with a new job. Besides, they show that this extension was in fact used by firms and older workers as part of early retirement schemes, which is in line with the results presented in this paper.

Beside disincentive effects, theoretical contributions have also emphasized the importance of unemployment benefits to enhance the efficiency of the job matching process. In this framework, more generous benefits give workers the opportunity to wait for jobs that fit their skills better [START_REF] Jovanovic | Job matching and the theory of turnover[END_REF][START_REF] Marimon | Unemployment vs. Mismatch of Talents: Reconsidering Unemployment Benefits[END_REF]. 5 Accordingly, this should be reflected in post-unemployment outcomes. More generous benefits should improve job matching quality, thus enhancing productivity (wages) and job stability. The empirical results about such effects are mixed. [START_REF] Addison | The effects of unemployment insurance on postunemployment earnings[END_REF] find weak effects of generous benefits on re-employment wages in a U.S. dataset, while [START_REF] Card | The spike at benefit exhaustion: Leaving the unemployment system or starting a new job?[END_REF] find no effects on re-employment wages or subsequent job stability in an Austrian dataset. Using a panel from eight European countries, [START_REF] Tatsiramos | Unemployment insurance in Europe: Unemployment duration and subsequent employment stability[END_REF] finds a positive effect of generous benefits on job stability. For Germany, Caliendo et al. (2009) use the discontinuity in unemployment benefits around age 45 (prior to the Hartz IV reform, see Table 2) to identify postunemployment outcomes. They find a positive effect of longer compensation duration on both re-employment wages and job stability. On the contrary, Fitzenberger and Wilke (2010) find that the 1980s reforms improved neither re-employment wages nor job stability.

Empirical strategy

In this paper, we investigate more thoroughly the microeconomic effects of one major feature of the Hartz IV package, namely the reduction in compensation duration for older unemployed. We look at two potential effects of this measure: on job take-up rates, but also on post-unemployment outcomes, through various indicators of matching quality (job stability, skill adequacy) and job quality (type of job contract). Applying difference-indifferences estimators, we show that the effects of this specific feature were rather scant.

Regarding unemployment duration, only unemployed within a specific age group were affected by the reform. Evidence suggests that this is because they previously used unemployment schemes as a bridge to early retirement. In addition, there is no convincing evidence of detrimental effects on job or matching quality. As already mentioned, many older unemployed were actually using the rather long compensation duration implemented in the 1980s as a bridge to early retirement. This strategy was particularly beneficial for firms, as they could more easily negotiate dismissals for older Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

Institutional background

and less productive workers. Besides, numerous regulations facilitated such early retirement schemes [START_REF] Müller | Beschäftigung und Arbeitslosigkeit älterer Arbeitnehmer: Eine mikroökonometrische Evaluation der Arbeitslosengeldreform von[END_REF]. In particular, persons who had already experienced one year of unemployment had the opportunity of entering early retirement without pension reductions at age 60, despite the legal retirement age of 65 in Germany. Moreover, unemployed aged 58 or older were exempt from active job search requirements, while nevertheless receiving unemployment benefits. Hence, workers with maximum entitlements could build a bridge to early retirement from the age of 57 years and 5 months, exhausting their 32 months of benefits. They could actually retire on benefits at an even earlier age, as they could still enjoy earnings-related benefits from the unemployment assistance scheme after insurance benefits exhaustion prior to 2005 (at a lower replacement rate though). These regulations were strengthened, which made early retirement strategy less attractive for workers. First, between 1997 and 2004 pensions were progressively reduced for individuals who retired before the legal age of 65. Eventually, individuals faced a 3.6 percentage points discount on their pensions for each year that separated them from the legal age of 65 years.

For instance, persons who entered unemployment at the age of 57 years and 5 months could still enjoy early retirement at age 60 after benefits exhaustion, but with a pension reduction of

Sample and main covariates

This paper assesses the effect of the cuts in benefits duration on the length of the unemployment spell and on post-unemployment outcomes. Our sample consists of 7846 unemployment spells from the SOEP dataset from 1997 to 2009 where we observe the entry into unemployment (i.e. not left-censored). 6 In this longitudinal panel, respondents answer 10 questions about various socio-economic characteristics relating to the interview year and also fill in a calendar about their labour force status in each month of the previous year.7

Individuals checking the box "registered as unemployed" (that is, at the employment office) are considered unemployed. We first focus on the job take-ups by these unemployed without distinguishing between type of exits to employment, full-time job, part-time job or mini-job.

Besides, exits to inactivity and retirement are treated as competing risks. Unemployment spells which end this way are accordingly coded as right-censored. 8 Similarly, unemployed reaching the legal retirement age of 65 years during their spell are right-censored, while unemployed age 65 or older are dropped.

In a second step, we investigate potential effects of the reform on three different postunemployment outcomes. We first investigate the reform impact on job stability, measured by the time spent in the first job after the end of the spell. It is a classical measure of job matching quality, as a quick separation possibly indicates that the workers' skills were illadapted to his new job. The SOEP yearly interviews also allow us to dispose of a rich variety of information about the type of job that is found. One interesting variable is the one about skill adequacy, where respondents assess whether they are actually working in the occupation they were trained for. This variable is thus particularly relevant to measure job matching quality. The last post-unemployment outcome we investigate is the type of contract (full-time job, part-time job or mini-job). The idea here is to see whether cuts in duration had the effect of fostering atypical employment.

Estimation strategy

Our estimation strategy relies on a difference-in-differences estimation. This is made possible by the change in the legislation that only affected unemployed aged 45 or older. Differencein-differences estimation is indeed well-suited to identify the causal impact of policy shifts where only a part of the population is affected by the law change. Basically, unemployed are divided into treatment and control groups using a dummy. The treated are the part of the population to whom the benefit duration cut applied, while the control group remained unaffected. We then compare outcomes for the treatment and control groups before and after the reform implementation. If the treated experienced a larger variation in one of these outcomes as compared to the control group, the difference is ascribed to the reform effect.

Hence, the identifying assumption behind difference-in-differences estimation is that trends in employment outcomes would have been the same for the treated and the control group in the absence of a change in the law. In particular, it implies that macroeconomic effects or other changes in the legislation had a similar impact on both groups as the reform was implemented. 9 In order to make this 'common trends' assumption more reasonable, we restrict our control group to individuals aged 35 to 44. Indeed, there are concerns that younger unemployed could still be marginally attached to the education system, Germans entering the labour market at a relatively high age.

In our empirical analysis, we first consider the impact of the reform on the job take-up rate by unemployed. In its most parsimonious form, our estimation strategy relies on the following unemployment-to-employment hazard rate (at a given time of the spell):

where is a vector of covariates and the baseline hazard. Formally, the policy effect is given by the interaction term between a time dummy ( ) taking the value one for spells commencing once the policy change was implemented (after February 2006) and a treatment group dummy ( ). 10 Covariates include basic demographic variables (age, sex, marital status, nationality and a dummy for East Germans). They also include categories for the highest obtained degree, the number of spells already experienced by the individual and year dummies to control for economic fluctuations.11

9 Important changes in unemployment compensation that concerned both the treatment and the control group include the merging of unemployment and social assistance and the reduction in the period used for entitlements calculation mentioned earlier. We want to emphasise here that our estimation strategy only allows us to assess the microeconomic impact of the cuts in duration, and not the impact of these two other features of the Hartz reforms.

To assess the precise effects of the cuts in compensation duration, one would ideally want to build distinct treatment group dummies as older age groups were differently affected by the reform. Also, one would want to use distinct treatment period dummies to take into account the fact that the 2008 reform softened the initial cuts induced by Hartz IV for some age groups. This would require estimation of 10 distinct interaction terms (Table 2). This is not the strategy that we follow here because we want to keep a reasonable sample size in each treatment group.12 Still, we want to account for the fact that the effects of the cuts might differ across age groups, in particular because of early retirement strategies. We thus split the treated unemployed into four age groups of five years each. We end up with the following equation to estimate:

We present our estimation using two specifications, taking into account in different ways the interrelated issues of duration dependency and unobserved heterogeneity. We first present a Partial Likelihood method allowing for flexible duration dependency and then a parametric strategy with flexible specification for unobserved heterogeneity. The issues are related because if unobserved factors cause early exit (there are many frail individuals), the hazard rate will decrease rapidly over time as the frail individuals are removed from the sample.

We first estimate this equation using a Cox duration model. Such a model presents the advantage of being non-parametric with respect to the influence of spell duration, i.e. the model makes no assumption about the functional form of the baseline hazard, as long as it satisfies the proportional hazards assumption (i.e. the baseline hazard is multiplicatively separable).

We now focus on a strategy modelling flexibly the frailty distribution. An alternative to the Cox Partial Likelihood model thus specifies a flexible distribution of unobserved heterogeneity. We use the Gamma distribution, since [START_REF] Abbring | The unobserved heterogeneity distribution in duration analysis[END_REF] show equations from Tables 4 and5 without year dummies as a robustness check. Our conclusions remain valid (see table A2 in appendix).

that under certain conditions, all forms of unobserved heterogeneity converge to a Gamma distribution in the survivor population, providing a justification for this functional form. In a second step we thus estimate our model using an exponential model allowing for gammadistributed unobserved heterogeneity (frailty).

Finally, we use the same difference-in-differences identifying strategy for post-unemployment outcomes as for the hazard rate of finding a job out of unemployment. The model specifications are different though. For re-employment duration (job stability) we use a simple OLS regression. For skill adequacy and type of job contract we use multinomial logit regressions, as they allow for more than one possible outcome.

Results

Descriptive statistics

Kaplan-Meier survival curves are displayed in Figure 1. They depict the probability of not having found a job after a given duration of unemployment. Five different figures are displayed: one for each age group (according to the intervals defined previously) and one for these age groups taken together (aged 45-64). In each of these figures we also report the survival curves for the control group (aged 35-44), so that we can get a first idea of the potential reform impact. In the spirit of difference-in-differences, the reform impact is assessed by considering the difference in survival across the treatment and control groups against the backdrop of the reform. For instance, a sharper increase in the slope of the curves of the treated as compared to the control group would indicate faster exit from unemployment.

First, one can see from these figures that the survival curves of the control group are always below those of the treated. Older unemployed typically face more difficulties to find a new job, a feature we control for in subsequent regressions. Moreover, we observe that unemployment duration generally decreased after the reform implementation, as depicted by the increase in the slope or the convexity of the curves. This is true for all groups including the control group. The 'common trends' assumption implies that without the reform, survival curves of the treated age groups would have experienced an equivalent evolution as those of the control group. However, we observe a sharper increase in the slope (or convexity) for the treated age groups, which suggests a negative impact of the reform on unemployment duration. This is especially obvious for the 45-49 and 55-59 age groups. To some extent this For the older age groups (aged 55-59 or 60-64), we suspect that the reform, combined with contemporaneous changes in early retirement provisions, made early retirement strategies less attractive. This point has also been made by [START_REF] Dlugosz | Fixing the leak: Unemployment incidence before and after the 2006 reform of unemployment benefits in Germany[END_REF]. They show that the rate of separation of older workers significantly dropped after the 2006 reform. This suggests that firms and workers became less inclined to negotiate early dismissal. These findings are consistent with the descriptive statistics displayed in Table 3, which depicts the type of exits out of unemployment for different age groups, before and after the reform. We first observe that a significant share of the unemployed aged 55 or older were actually using unemployment benefits as a bridge to retirement before the reform. Furthermore, exits to retirement generally decreased after the reform: their share in total exits was more than halved. This decrease was particularly dramatic for unemployed aged 55-59 and 60-64, with respectively a drop of more than 30 and 20 percentage points in the share of total exits. This should strongly impact the average unemployment duration of these groups, but in a different way to the one predicted by job search theories. In job search models, cuts in benefits incite the unemployed to increase their job search efforts and/or to accept job offers earlier in their spell. The mechanism we observe here is different. Unemployed following an early retirement strategy were likely to fully exhaust their entitlement rights before entering retirement, in order to avoid future pension discounts. This enhanced average unemployment duration. As early retirement became less attractive with the reform implementation, the composition of the unemployed population changed: fewer workers entered unemployment to benefit from early retirement schemes. In turn, the share of unemployed actively looking for a job mechanically increased, and so did the unemployment-to-employment hazard rate. So the reform effect in this case is not to accelerate job take-up, but to prevent those who are likely to remain unemployed until benefits exhaustion from entering into unemployment. Source: SOEP, author's calculations education in particular) tend to exit faster from unemployment. This is also true for the unemployed who have already experienced spells of unemployment before. This can possibly be ascribed to the fact that they work in high turnover occupations, where both dismissal and hiring are frequent.

Reform impact on job take-ups

Looking at the coefficients of the non-interacted age group dummies, we see that the unemployment-to-employment hazard rate is significantly lower for older age groups prior to the reform, even after age is controlled for. The coefficients are especially large for the 55-59 and the 60-64 age groups. This is compatible with our assumption that many unemployed in these groups tended to exhaust their entitlement rights before retiring. As was already observable from the Kaplan-Meier survival curves, we see that the hazard rate generally increased after the implementation of the reform, as evidenced by the positive and significant coefficient for our treatment period dummy (Hartz). However, it cannot be ascribed to an effect of cuts in compensation duration as this coefficient also applies to the control group. 13The reform impact is given by the interactions of the age group and reform dummies. The results here are broadly consistent with the descriptive statistics. All estimated coefficients are positive, which could suggest a positive effect of the cuts on unemployment duration.

However, the interaction terms are only statistically significant for the 55-59 age group, at the 5% threshold. The coefficient for the 60-64 age group is actually positive but not significant, probably because the sample size is relatively small for this group. This is in line with our argument that the reform mainly had the impact of deterring early retirement schemes. On the contrary, we argue that the reform did not have the kind of effect predicted by job search theories, or at least that these effects were not sizeable. Indeed, we do not observe a significant increase in the hazard rate of age groups where early retirement strategies were less prevalent, although they were affected by equivalent cuts in the duration of benefits (see Table 2). Finally, Table 4 provides estimation results for men and women separately. The coefficients for the interaction terms indicate that the reform impact on the 55-59 age group is actually driven by male unemployed. This could be explained by the fact that employers used early retirement as a tool to dismiss workers with long work history within the same firm, in order to avoid too high severance payments. As men typically have more stable careers, this population was more severely affected by the reform.

Table 5 provides estimations of the unemployment-to-employment hazard rate using gamma frailty correction for unobserved heterogeneity. The estimate of the theta parameter indicates that heterogeneity is significant: the share of individuals with poor unobserved characteristics becomes larger as the length of the spell increase. Results from Table 5 are consistent with our previous findings. In particular, the differential effect of the reform for those aged 55-59 remains positive and statistically significant. The effect of the reform for those aged 60-64 is also large and positive, but insignificant. Again, we suspect that small sample size for this age group could potentially blur the results. In any case, this suggests that the reform operated mainly by deterring early retirement strategies, which were especially prevalent for these groups.

Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

Reform impact on job matching quality

We now turn to the regressions results for the three post-unemployment outcomes we have defined. For presentation purpose, we only display the coefficients for the interaction terms of interest. 14 In Table 7, we display the results for our second measure of job matching quality. This variable gives respondents assessment of whether they are working in the occupation they were trained for (the question relates to primary education, not training provided by employment services). Three possible answers are given: 'working in the occupation trained for', 'not working in the occupation trained for' and 'no training needed for this occupation'.

The third category of outcome is more difficult to interpret. For some respondents it might indicate a mismatch, because they have been trained for an occupation but are working in an occupation that does not necessitate any. But for those who did not receive any training such a match would be considered as normal. The only age group that is significantly affected are those aged 60-64 years old, whose exits to employment are more headed towards occupations they were not trained for. This increase in job mismatches might be ascribed to the increased pressures to take-up jobs induced by the reforms. Nevertheless, this result should be interpreted cautiously, as it does not concern a large number of cases in our sample. Finally, Table 8 provides results about the type of job contracts after exits to employment, distinguishing between part-time job, full-time job and mini-job. The results here are rather scant. Exits to part-time, as compared to full-time, tend to increase for most age groups (45-49, 50-54 and 55-59), but the coefficient is only significant for the 50-54 age group, and only at the 10% threshold. While there was a contemporaneous increase in the total number of atypical jobs in Germany during that period, it does not seem that the duration cuts particularly contributed to enhance this trend. The coefficients of the 60-64 age group for exits toward part-time and mini-jobs are negative, which would suggest that this particular category was more likely to find a full-time job. While the coefficients are pretty large, they are not significant though.

Conclusion

To sum up, we have shown that the recent cuts in compensation duration induced by the Hartz reforms did not have the kind of sizeable effects on unemployment duration expected by job search theories. Only one specific age group, aged 55 to 59, had significant lower unemployment duration after the reform. But as we argue, this can better be ascribed to the deterring effect the reform had on early retirement strategies, in combination with other changes in early retirement provisions. Besides, we also found evidence that the reform had some effects on post-unemployment outcomes. Again re-employment duration of the 55-59 age group has been substantially and positively affected. While this comes in contradiction with job matching theories, it corroborates our point that the contemporaneous rise in the legal age for early retirement had a substantial impact on workers decisions to delay their exit from the labour market. Eventually, some detrimental effects of the reform on post-unemployment outcomes have been found: skills inadequacy has increased for the oldest unemployed (60-64 years old) while unemployed aged 50 to 54 experienced slightly more exits toward part-time employment.

To conclude, we would also like to acknowledge some limits of our empirical strategy. First, we are only assessing here the average effect of the entitlement cuts for the relatively large Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

  schemes were still commonly used by older workers until the 2006 unemployment benefits reform (see Figure1p. 10). More recently, the minimum age for early retirement was progressively raised over a transition period(2006)(2007)(2008)(2009)(2010)(2011)(2012) from 60 to 63 years. Combined with the reform of unemployment benefit duration and the end of earning-related unemployment assistance, this change has significantly lowered the incentives for older workers to enter early retirement. Indeed, it is now possible to use unemployment benefits as a bridge to retirement only from the age of 61 years onwards, while still facing a pension discount of 7.2 percent.

Figure 1 :

 1 Figure 1: Probability of remaining unemployed by length of unemployment spell

Table 1 :

 1 Synthetic presentation of Hartz reforms

Law Main features Time of implementation Hartz I (23/12/2002)

	Reform of public employment service	01/01/2003
	Creation of PSA (Personal-Service-Agentur), private
	employment placement agencies in charge of placing
	unemployed people into temporary agency jobs
	Temporary agency work
	Restrictions in the use of temporary agency work are
	cancelled (no duration limit (maximum of 2 years before))
	Reform of unemployment benefits system
	Time duration before the first appointment at the
	employment agency is shortened. Criteria of acceptation of
	a job are strengthened for unemployed with no family; the
	burden of proof is reversed.
	Reform of public employment service
	Training vouchers are introduced: creation of a new tool
	for the unemployed.
	Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

Hartz II (23/12/2002)

	Reform of subsidized jobs: mini and midi jobs	01/04/2003
	The aim is to remove poverty traps and to develop low-
	paid jobs.
	Reform of subsidized jobs: Ich AG
	Supporting schemes for one-man enterprises -targeted at
	people who receive unemployment benefits (either from
	insurance or assistance schemes) or who are in subsidized
	jobs (ABM and SAM)
	Reform of public employment service
	Job Centers are created. Regional employment agencies
	become "one-stop" centers.

Hartz III (23/12/2003)

	Reform of public employment service	01/01/2004
	New monitoring tools are created at the federal level; local
	agencies are given more autonomy. Control and
	supervision of the unemployed increase.
	Reform of unemployment benefits system
	The period of reference used to calculate unemployment
	benefits is reduced to two years.
	Reform of subsidized jobs
	ABM and SAM schemes are merged. The maximum
	duration for subsidized jobs is reduced.

Laws on labour market reforms (24/12/2003)

	Dismissal rules : more flexibility	01/01/2004
	The minimum number of employees required for the	01/02/2006
	application of unfair dismissal procedures increases from 5
	to 10 employees.
	Change in rules governing dismissal of workers in case of
	dismissal for economic reasons
	Reform of unemployment benefits system
	The maximum duration of unemployment benefits is
	reduced from 32 to 18 months

Hartz IV (24/12/2003)

	Reform of unemployment benefits system
	Social assistance and unemployment assistance are merged
	into a single scheme.
	For people who are able to work, social assistance benefits
	and unemployment assistance benefits are transformed into
	a means-tested minimum income scheme that requires
	active job search.
	Source: Chagny (2005, Table 3 p.8)
	Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

  Table 2 depicts the drop in the potential compensation duration induced by the Hartz IV package. This feature was actually implemented in February 2006, and was targeted at

unemployed aged 45 or older, who previously enjoyed longer compensation duration. Its impact on benefits generosity was quite dramatic, as maximal benefits duration was more than halved for some age groups (52-54), with duration reductions ranging from 6 to 14 months.

Potential benefit duration was eventually re-extended by 3 to 6 months for some age groups by the Grand Coalition in January 2008, but still remained significantly below its original level, with duration reductions (compared to 2005 levels) ranging from 6 to 14 months.

Table 2 :

 2 Summary of institutional changes in the potential compensation duration

		Maximal duration of benefits in months
	Age group	From January 1, 1997	From February 1, 2006
			Since January 1, 2008
		to January 31, 2006	to December 31, 2007
	Under 45	12	12	12
	45-46	18	12	12
	47-49	22	12	12
	50-51	22	12	15
	52-54	26	12	15
	55-56	26	18	18
	57-57	32	18	18
	58 or older	32	18	24

Table 3 :

 3 Type of exits out of unemployment (number and percent of observations)

	Before February 2006
	Age	Full-time job Part-time job	Mini-job	Retirement	Inactivity	Total
	35-44	1661	406	80	45	520	2712
		61.2%	15.0%	3.0%	1.7%	19.2%	100.0%
	45-49	609	139	43	58	217	1066
		57.1%	13.0%	4.0%	5.4%	20.4%	100.0%
	50-54	463	97	26	128	143	857
		54.0%	11.3%	3.0%	14.9%	16.7%	100.0%
	55-59	216	69	24	600	87	996
		21.7%	6.9%	2.4%	60.2%	8.7%	100.0%
	60-64	18	6	6	116	10	156
		11.5%	3.8%	3.8%	74.4%	6.4%	100.0%
	Total	2967	717	179	947	977	5787
		51.3%	12.4%	3.1%	16.4%	16.9%	100.0%
	From February 2006
	Age	Full-time job Part-time job	Mini-job	Retirement	Inactivity	Total
	35-44	297	59	30	2	56	444
		66.9%	13.3%	6.8%	0.5%	12.6%	100.0%
	45-49	130	30	14	4	19	197
		66.0%	15.2%	7.1%	2.0%	9.6%	100.0%
	50-54	97	28	13	9	24	171
		56.7%	16.4%	7.6%	5.3%	14.0%	100.0%
	55-59	49	16	10	33	12	120
		40.8%	13.3%	8.3%	27.5%	10.0%	100.0%
	60-64	16	2	5	29	2	54
		29.6%	3.7%	9.3%	53.7%	3.7%	100.0%
	Total	589	135	72	77	113	986
		59.7%	13.7%	7.3%	7.8%	11.5%	100.0%

  Table4presents the results from estimation of the Cox Partial Likelihood model, where we assess the reform impact on job take-ups. Covariates which are typically associated with poor labour market outcomes have the expected signs on their coefficients and are statistically

significant: being East German, non-German citizen, female, married, of old age, married and female, having no degree. On the contrary, individuals with good qualifications (in higher Documents de Travail du Centre d'Economie de la

Sorbonne -2014.20

Table 5 :

 5 Unemployment-to-employment hazard rate analysis (exponential distribution of duration dependency, gamma-distributed frailty)

  Table6provides the results of the reform impact on job stability, assessed by the duration of the job that directly follows unemployment. According to job matching quality arguments, less generous benefits should increase pressures on unemployed to take up jobs for which they are less qualified: in turn, this should decrease the stability of the match. At first sight, our results are at odds with this prediction. All coefficients for the interacted terms are positive, indicating longer re-employment duration for the treated age groups. This statement should be nuanced, as the estimates are only significant for the 55-59 age group, at the 1% threshold. The coefficient for the 60-64 age group is relatively large also, but not significant. However, we do not interpret these findings as an increase in job matching quality. We argue that this effect should in fact be assigned to the parallel evolution in retirement regulations, when the legal age threshold for early retirement was raised from 60 to 63. Prior to 2006, re-employment duration was shorter because re-employed could retire at a younger age. Postponing the age threshold for early retirement eventually led to a substantial increase in re-employment duration for those individuals closer to this age threshold.

Tables displaying all explanatory variables can be found in appendix (Tables

A3 to A9

) Documents de Travail du Centre d'Economie de la

Sorbonne -2014.20

Table 6 :

 6 Re-employment duration (OLS regression)

		All	Men	Women
	Hartz*Age 45-49	3.787	5.223	1.938
		[3.056]	[4.166]	[4.493]
	Hartz*Age 50-54	4.745	6.807	2.557
		[3.327]	[4.597]	[4.841]
	Hartz*Age 55-59	11.612**	13.162*	9.252
		[4.353]	[5.265]	[8.077]
	Hartz*Age 60-64	11.287	13.407	10.104
		[8.504]	[9.843]	[20.709]
	Number of obs.	4578	2611	1967
	Sample: SOEP, individuals aged 35-64. Notes: reference groups are aged 35-44 for age groups. Year dummies
	are included. Adjusted robust standard errors in brackets. Significance level: +p<0.10, *p<0.05, **p<0.01,
	***p<0.001.

Table 7 :

 7 Matching between skills and occupation after unemployment (multinomial logit, reference is 'exit to an occupation matching with skills') Sample: SOEP, individuals aged 35-64. Notes: reference groups are aged 35-44 for age groups. Year dummies are included. Significance level: +p<0.10, *p<0.05, **p<0.01, ***p<0.001.

		Not in the	No training needed
		occupation trained for	for this occupation
	Hartz*Age 45-49	-0.134	-0.274
		[0.244]	[0.861]
	Hartz*Age 50-54	0.123	0.265
		[0.270]	[0.786]
	Hartz*Age 55-59	-0.010	-0.478
		[0.351]	[1.189]
	Hartz*Age 60-64	2.328**	1.702
		[0.781]	[1802.926]
	Number of obs.	4578	4578

Table 8 :

 8 Type of first employment contract after unemployment (multinomial logit, reference is 'exit to full-time employment') Sample: SOEP, individuals aged 35-64. Notes: reference groups are aged 35-44 for age groups. Year dummies are included. Significance level: +p<0.10, *p<0.05, **p<0.01, ***p<0.001.

		Part-time job	Mini-job
	Hartz*Age 45-49	0.170	-0.136
		[0.299]	[0.417]
	Hartz*Age 50-54	0.603+	0.218
		[0.313]	[0.444]
	Hartz*Age 55-59	0.508	0.099
		[0.394]	[0.511]
	Hartz*Age 60-64	-0.806	-0.991
		[0.941]	[0.784]
	Number of obs.	4578	4578

Centre d'Economie de la Sorbonne, bruno.amable@univ-paris1.fr

Centre d'Economie de la Sorbonne, baptiste.francon@univ-paris1.fr (corresponding author), Maison des Sciences Economiques, bureau 208, 106-112 bld de l'Hôpital, 75013 Paris Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

These two latter features were enacted contemporaneously to the Hartz reforms, but were implemented in February 2006.

In an analysis of the 1989 unemployment insurance reform in Austria, a country which shares more similarities with Germany than the U.S., the results of[START_REF] Lalive | How changes in financial incentives affect the duration of unemployment[END_REF]Lalive et al. ( , p. 1029) also suggest that the magnitude of these effects, while significant, is not very large. They notably find that an additional week of benefit duration leads to a 0.05 weeks increase in unemployment duration, while an increase by one percentage point of the replacement rate leads to a 0.15 weeks increase in unemployment duration. Documents de Travail du Centre d'Economie de laSorbonne -2014.20

See also[START_REF] Acemoglu | Productivity gains from unemployment insurance[END_REF]. In this paper, the authors provide a theoretical framework where benefit generosity raise the incentives for the unemployed to wait for jobs with high wages, which in turn increases the incentives for firms to propose such high-wage jobs. Documents de Travail du Centre d'Economie de laSorbonne -2014.20

See Table A1 in appendix for descriptive statistics. Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

The design of the SOEP dataset makes it difficult to compare wages before and after the unemployment spell, although this is often used as a measure of job matching quality in the literature. Indeed, information on wages is contained within the yearly interviews only. We would lose a too large number of observations in the process of recovering this information from the yearly interviews -especially for long-term unemployed not interviewed before entering unemployment.

Exits to inactivity and retirement amount to less than one third of total exits (see Table3). Besides, we do not observe any exits for about 15% of all spells, because of individuals' drop-out of the survey. Documents de Travail du Centre d'Economie de laSorbonne -2014.20

More precisely, the time dummy Hartz takes the value one for unemployment spells beginning in February 2006 or later, because it is the date of entry into unemployment which determines benefit entitlements. Individuals who entered unemployment prior to that date were still subject to the old regulation, even when their spell continued after February 2006.

Recall that the Hartz time dummy refers to the calendar time of entering unemployment whereas the year dummies refer to the time of leaving unemployment. Thus identification of both year dummies and the Hartz time dummy is ensured as individuals entering unemployment at different points in time and are subject to the same macroeconomic shocks affecting recruitment out of unemployment. Nevertheless, we re-estimate the main Documents de Travail du Centre d'Economie de laSorbonne -2014.20

Moreover, the age variable we derive from the SOEP is not very accurate because it is based on the birth year only, whereas benefits entitlements are defined by actual age at entry into unemployment. It thus makes little sense to build narrow age groups with this variable. Note that this also leads us to exclude individuals celebrating their 45 th birthday in a given year, as we cannot know for sure if they are treated (aged 45) or not (aged 44). Documents de Travail du Centre d'Economie de laSorbonne -2014.20

Source: SOEP, author's calculations. Analysis time is months. Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

While this indicates that unemployment duration was generally lower from 2006 onwards, it is out of or scope to ascertain whether this is an effect of the other features of the Hartz reforms mentioned earlier, or whether it is linked to more favourable labour market conditions. Documents de Travail du Centre d'Economie de laSorbonne -2014.20

Sample: SOEP, individuals aged 35-64. Notes: reference groups are aged 35-44 for age groups and basic vocational training for education. Year dummies are included. Adjusted robust standard errors in brackets. Significance level: +p<0.10, *p<0.05, **p<0.01, ***p<0.001. Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

age groups we have defined. Thus we cannot exclude that the reform had a negative effect on unemployment duration for some narrower age groups. Also, we cannot rule out the possibility that the effect would have been larger if the initial stronger cuts in compensation duration of 2006 would have been maintained. While this implies that our results cannot be easily generalised to other reforms where cuts in benefits have been sharper, our point remains that in this case the reform impact on unemployment duration was not very sizeable. Documents de Travail du Centre d'Economie de laSorbonne -2014.20

Sample: SOEP, individuals aged 35-64. Notes: reference groups are aged 35-44 for age groups. Year dummies are included. Adjusted robust standard errors in brackets. Significance level: +p<0.10, *p<0.05, **p<0.01, ***p<0.001. Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

Sample: SOEP, individuals aged 35-64. Notes: reference groups are aged 35-44 for age groups. Year dummies are included. Significance level: +p<0.10, *p<0.05, **p<0.01, ***p<0.001. Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

Sample: SOEP, men aged 35-64. Notes: reference groups are aged 35-44 for age groups. Year dummies are included. Significance level: +p<0.10, *p<0.05, **p<0.01, ***p<0.001. Documents de Travail du Centre d'Economie de la Sorbonne -2014.20

Sample: SOEP, women aged 35-64. Notes: reference groups are aged 35-44 for age groups. Year dummies are included. Significance level: +p<0.10, *p<0.05, **p<0.01, ***p<0.001. Documents de Travail du Centre d'Economie de la Sorbonne -2014.20


Antoine Varet

Nicolas Larrieu

How to generate realistic network traffic ?

Keywords: Traffic generation, Network experimentation, Network performance analysis, Network measurement

Network engineers and designers need additional tools to generate network traffic in order to test and evaluate, for instance, application performances or network provisioning. In such a context, traffic characteristics are the most important part of the work. Indeed, it is quite easy to generate traffic, but it is more difficult to produce traffic which can exhibit real characteristics such as the ones you can observe through the Internet. With the lack of adequate tools to generate data flows with "realistic behaviors" at the network or transport level, we needed to develop our tool entitled "SourcesOnOff". The emphasis of this article is on presenting this tool, explaining how we implemented it and outlining the methodology it follows to produce traffic with realistic characteristics.

INTRODUCTION

Network engineers and designers need additional tools to generate network traffic in order to test and evaluate application performances or network provisioning for instance. In such a context, traffic characteristics are the very important part of the work. Indeed, it is quite easy to generate traffic but it is more difficult to produce traffic which can exhibit real characteristics such as the ones you can observe in the Internet. With the lack of adequate tools to generate data flows with "realistic behaviors" at the network or transport level, we needed to develop our tool entitled "SourcesOnOff 1 ". In this paper, "realistic behavior" means to generate traffic similar to the traffic a network administrator can capture on his network backbone, end-systems, etc... Previous research conducted us to design new methodologies and tools to generate network data traffic as close as possible to what we can find on Local Area Networks (LAN) and on the Internet. It can be necessary for instance to evaluate performances of new network entities. In this specific context, it is mandatory to face them to generated traffic with characteristics as close as possible as the Internet traffic. However, depending on what you mean by "Internet network" and where you perform the study, measurements may completely differ: Internet cannot be solely characterized with a small set of parameters such as some mathematical distributions and additional factors. Indeed, there is not currently one unique mathematical modeling able to embrace the different characteristics and the complexity of the Internet traffic [START_REF] Olivier | Flow Level IP traffic characterization[END_REF]. Anyway, Internet traffics hopefully show some common properties and trends that help to its modeling. For 1 We would like to thank Benoit Sainct (MS student) for his work in implementing statistical tools for traffic characterization.

Contact email: Nicolas.Larrieu@enac.fr instance, an Internet Service Provider (ISP) providing access for software engineering companies manage a different profile of data communications than an ISP for private individuals [START_REF] Gebert | Internet Access Traffic Measurement and Analysis[END_REF]. However, there are some common characteristics between both profiles. The goal of the tool we have developed is to handle most of Internet traffic profiles and to generate traffic flows by following these different Internet traffic properties.

The rest of this paper is structured as the following. The first section presents the mathematical model this tool is based on for traffic generation: the ON/OFF sources. We chose to consider different stochastic processes in order to model the complexity of the original traffic we want to replay. General approaches consider only one law for the On process and another law for the Off process. In our approach, we are able to consider several laws and to combine their effects to model accurately the original behavior we analyzed in the real data. We then select the right parameters to consider as inputs for our SourcesOnOff tool. This approach gives really good traffic characteristics and, consequently, the generated traffic is really close to reality as results presented at this end of this paper demonstrate it. In the second section, we present why the other tools currently available were not usable in our case. The third section describes how our tool works plus some specific points the user should know about its implementation. The fourth section is dedicated to the validation of our tool with different methods in order to conclude if the generated traffic has the same properties than the original one. We have, in particular, investigated the traffic characteristics generated by our software and we demonstrate that it is able to generate network traffic with realistic properties such as these we can capture on the Internet. Different parameters have been considered to match generated traffic characteristics with the original traffic. First, we considered classical traffic parameters such as throughput, delay or losses but we have also investigated more advanced statistical parameters such as the correlation level of generated packets or their long range dependence (by computing the Hurst factor).

How to characterize an "Internet-like" profile?

Different studies were published with results related to Internet-like traffic characterization: the word "Internet" can cover very different profiles, but some common trends can be highlighted. Thus, we will examine two of them: high variability and self-similarity, respectively called the Noah and Joseph Effects.

High variability is characterized by an infinite mathematical variance and means that sudden discontinuous changes can always occur. Some mathematical distributions like Pareto and Weibull are heavy-tailed (i.e. the tail of the distribution is not exponentially bounded) and thus can be used to generate sets of values with high variances and also high-variability. Different studies have shown that classical distributions such as the Gaussian and the Poisson distribution have failed to reproduce a LAN-like throughput [START_REF] Olivier | Flow Level IP traffic characterization[END_REF][START_REF] Taqqu | On the Self-Similar Nature of Ethernet Traffic[END_REF]. One of them [START_REF] Olivier | Flow Level IP traffic characterization[END_REF] proposes to use Pareto's and Weibull's heavytailed distributions and proved that the generated traffic shows properties closer to real network traffic characteristics than other mathematical distributions.

Figure 1: Emission process of ON/OFF traffic sources

Self-similarity is defined by a long-range dependence characteristic, which means there are bursts of traffic any time over a wide range of time scales. In other words, a small sub-range of values is "similar" to the whole range of values. W. Willinger found in [START_REF] Taqqu | On the Self-Similar Nature of Ethernet Traffic[END_REF] a relation between self-similarity and high variability for Ethernet Local Area Network (LAN) throughputs: in particular, he showed that the Noah and the Joseph effects are linked with a degree-1 polynomial relation. In other words, using ON/OFF sources with heavy-tailed distributions causes the traffic streams to be highly variable and, consequently, the aggregation of these streams to be also self-similar and highly variable.

ON/OFF sources to generate realistic throughputs

W. Willinger proposed in [START_REF] Taqqu | On the Self-Similar Nature of Ethernet Traffic[END_REF] to generate data following packet-train models, i.e. with strictly alternating, independent and identically distributed ON-and OFF-periods and proved that these ON/OFF sources generate data similar to experimental measurements on real networks. A source corresponds to one network flow. The flow is associated with a source and destination couple and also with data, transmitted as a set of packets called a train of packets. In our case, we use the transport protocols TCP and UDP. The data stream is thus exchanged as a set of IP packets. The source is associated to a departure time and a duration time. The departure time of any source is computed with the departure time of the preceding source plus a random duration. This randomness follows the user-defined "Doff distribution" (also named "distribution of inter-train durations"). The first source starts at the beginning of the process. Duration times should be similar for all sources. They should follow a user-defined random distribution called "Don distribution" (also named "distribution of train duration" or "distribution of flow duration"). This Don distribution is independent of the Doff distribution. For feasibility constraints and to reduce the complexity of implementation, we use the Don distribution to generate random values, not for time duration in seconds but for quantity of transmission in bytes. Because of TCP congestion control mechanisms, source durations are correlated with quantities of transmitted data.

We can summarize the ON-OFF source generation algorithm we use in our tool by:

Start the transmission of Don_value bytes to a remote host (do not wait the end to perform the next iteration, loop as soon as data are sent into the transmission buffer)

End_For

Algorithm 1: Traffic generation with ON/OFF sources

In algorithm 1, the Don_value is the length (in bytes or multiples of bytes) of each data flow, also called a "train". This train is exchanged between the local (transmitter) system and a remote (receiver) system. The Doff_value (in seconds or more often in milliseconds) is a duration called the inter-train distance (i.t.d). This i.t.d. represents the time between two consecutive flow creations. The Doff_values and the Don_values are completely independent. They are issued from random number generators, which follow respectively the "Don" and the "Doff" distributions. These distributions should be heavy-tailed to ensure the selfsimilarity of the generated data throughput [START_REF] Taqqu | On the Self-Similar Nature of Ethernet Traffic[END_REF]. Distribution parameters are defined by the user on the command-line. Figure 1 illustrates an example of the total throughput we can expect on the network following the ON/OFF sources generation process.

STATE OF THE ART OF TRAFFIC GENERATORS

Network simulators

Different tools are available to simulate networks and their behaviors, with integrated ON/OFF sources (for instance, NS-2 [START_REF]The Network Simulator -ns-2[END_REF]). Most of them provide "Internet-like" flow generators, some of them based on ON/OFF source generation processes. However, the aim of our research work was to face new network systems to real traffic. It means we wanted to perform our system evaluation in real time and do not want to evaluate a model of our system. Simulators cannot do this kind of real time experiments, only emulators can do it. However, it is complex to deal with most network emulators as they are complex to install, to configure with the real network environment, and consume as well many CPU resources. This is why we searched for and studied tools not to simulate or emulate but to generate a realistic traffic load on real networks.

Traffic replay tools

Some software enables the user to replay previously captured network traffics. This is done in two steps: the user captures data on the networks he wants to reproduce (with tools called "sniffers" such as the reference tool Wireshark [START_REF]Wireshark[END_REF]), then the user needs to replay the captured traces, i.e. by retransmitting the sniffed packets in the same order, and separated with the same delays as these measured during the capture (cf. the "tcpreplay" 2 tool for instance). Harpoon 3 is another existing Open Source flow-level traffic generator, but this tool requires the user to define flow per flow the data weight he wants to transmit on the network. The automatic generation of the network profile is limited to constant and uniform distributions. Moreover, Harpoon seems to be not maintained since 2005. This is why we did not consider this tool for our experiments.

This traffic replay process has different advantages. The two steps may be done independently by two different users and at any time (as long as the first step is started before the second one). The capture may be filtered before being replayed and replay parameters may be set up. However, replaying has also important drawbacks. Indeed, before replaying any network trace, the user must make or acquire the capture he wants to replay. Most of the time, this is a difficult task: user privacy issues restrain the administrators in allowing captures on the router they administer; often ISPs do not want to extract advanced statistics from their networks… The public data we have found on Internet are often so anonymized that they not longer contain the useful information we need to replay them. Moreover, if you continuously replay the same trace you will reproduce periodically the same "events" (throughput bursts, specific packet sequences or behaviors…).

Network throughput estimation tools

This is why different techniques and tools have been elaborated to load a network and evaluate its capacity. One of the existing tools we have studied is "iperf" [START_REF]iperf, a modern alternative for measuring maximum TCP and UDP bandwidth performance[END_REF]. It can generate TCP or UDP flows to load the network. In TCP mode, an iperf client transmits to the server an infinite quantity of data through one TCP flow. After a user-defined duration, the iperf tool aborts the TCP connection and prints on the screen different statistics and the total quantity of data it succeeded in transmitting correctly.

A network capture shows often that mostly all the network resources are used by the TCP flows [START_REF] Gebert | Internet Access Traffic Measurement and Analysis[END_REF]. Indeed, the TCP protocol efficiently exploits the network and transmits data in an optimal time span. However, in LAN captures, external and unexpected events interact with the flow, they generate segment delays and losses impacting the TCP connection which becomes longer than the optimal time span expected. This drawback affects most of methodologies based on studies using only one TCP flow. We can cite, for example, when the tester uses an SSH or an FTP 2 Tcpreplay website: http://tcpreplay.synfin.net/ 3 Harpoon website: https://github.com/jsommers/harpoon connection to transmit a big file and consequently to artificially load the network.

When configured to transfer multiple TCP streams, iperf starts the different flows simultaneously at the beginning of the program. This behavior is not realistic because in Internet later flows are penalized at their start by the flows already established. Moreover, this tool "iperf" performs measurements on "long" TCP connections (100+ segments), allowing the TCP congestion control mechanism to adjust the data throughput efficiently. However, in most ISP studies the TCP connections are very numerous and the majority is short (e.g. in study [START_REF]iperf, a modern alternative for measuring maximum TCP and UDP bandwidth performance[END_REF] 81% of TCP connections carry less than 310 bytes), disabling the congestion control mechanisms optimizations. Consequently, congestion control mechanisms do not have the time to optimize the connection. In UDP mode, the client transmits data periodically: the period is computed depending on the user-defined quantity of data per second to transmit. However, for the same reason than previously, a single flow with constant throughput is not realistic [START_REF] Olivier | Flow Level IP traffic characterization[END_REF][START_REF] Gebert | Internet Access Traffic Measurement and Analysis[END_REF].

Consequently, we have searched for other tools to generate data throughput: BWPing [START_REF] Bwping | Open Source bandwidth measurement tool[END_REF], NetPerf [START_REF]The NetPerf HomePage[END_REF]… All differ more or less on the set of supported protocols, on the maximum admissible throughputs and on the statistics printed on the screen for the user. However, all have the same drawbacks as explained above. This is why, in the rest of this article, we chose the tool "iperf" as a comparison reference for our SourcesOnOff tool, because most measurement tools are based on the same assumptions and work in a similar manner: one or multiple identical and simultaneous TCP and UDP flows in order to load the network at its maximum available capacity. case, all generated values are equal to a user-defined constant. This method enables the user to generate a more predicting behavior (note that this behavior is similar to iperf behavior in UDP mode).

Multiplying factors enables users to convert the randomly generated values into Bytes (for Don distributions), nanoseconds (for Doff distributions) and their multiples (kB, MB, GB, us, ms, s…). Distributions may be bounded by minimum and maximum user-defined values. Our tool enforces also user-defined minimum and maximum values for the generated random numbers, by increasing values lower than the minimum boundary and decreasing values greater than the maximum boundary.

Generation of the network flows

First of all, different sets of Don and Doff random values are generated. They are then used for data communications. These data flows can be fully parameterized in order to enable the user to refine the tool behavior. Different sets of sources may run simultaneously, each set is associated with independent Don and Doff distributions and parameters. Contrary to programs like iperf, this tool is only intended to generate data. It was not developed to provide itself advanced statistics on the network: we use our tool to generate background traffic and we use additional passive and active measurement tools to evaluate network performances and collect statistics.

Statistic profile extraction from a real traffic trace

Before experimenting traffic generation, we have to define what kind of traffic we want to generate. This step may be done arbitrarily by choosing appropriate values or by selecting values from existing studies like [START_REF] Olivier | Flow Level IP traffic characterization[END_REF][START_REF] Gebert | Internet Access Traffic Measurement and Analysis[END_REF]. We chose an alternative solution: given that we belong to a research entity, we have easily access to real data. Thus, we asked to our local network administrator to capture the entire incoming and outgoing traffic, generated by people from the university (students, administrative people, teachers and researchers) on our local area network. The data were captured on the firewall protecting the access link between our LAN and other networks: REMIP and RENATER which are our links to the Internet. Thus, we captured all data from our LAN to Internet and all associated responses. We captured different network traces: between 10 minutes and 10 hours. We chose to capture traffic only on working days and between working hours given that the point of presence is at the output of a research entity and so, the main network activity is spread from 8AM to 8PM (Monday to Friday). For concise purposes, we will describe in the next subsections only one of the different traffic traces we collected, but other captures showed the same conclusions. Thus, in the next subsections we analyze a set of 9 millions of IPv4 packets (97.7% of TCP, 2.2% of UDP and 0.1% of ICMP), collected during 10 hours between 8:00AM and 6:00PM, Tuesday the 29 th of January, 2013. UDP datagrams are negligible in our case (less than 2.2% of our traffic in packet numbers, less than 0.5% of our traffic in bytes), so we replayed only TCP sources and we will just model and reproduce the TCP traffic in our study case (cf. section 4). We used the tool tcpdump [START_REF]Tcpdump & LibPcap public repository[END_REF] to capture the raw packets and then the tool ipsumdump [START_REF]IPsumDump and IPaggCreate website[END_REF] to ensure the anonymity. We finally conducted a complete statistical analysis with bash and R scripts. These tools enabled us to retrieve different statistical characteristics of the captured data. This process is detailed in the next subsection.

Statistic profile extraction process

Previous research work (such as [1, 2, 3 and 4] for instance) have demonstrated that one unique statistical law cannot figure out all the complexity of an original Internet traffic trace. This is why we chose to decompose and to model the Internet traffic trace we want to replay by using several different statistical laws. Thus, we need, firstly, a decomposition algorithm and, secondly, a distance criterion to evaluate the differences between real original data and data generated by our tool. This distance criterion will help us to select the best statistic laws to decompose original data.

Traffic trace decomposition

We developed an algorithm able to detect a lack of continuity in any data we want to characterize. This algorithm is mainly based on the quantmod4 tool developed by Jeffrey A. Ryan. Based on this algorithm, we are able to select different basic distributions (Weibull, Pareto, Exponential, Gaussian…) that we can combine to reproduce the whole complexity of the original data we want first to characterize and finally to replay. To assess the distance between selected statistical distributions and real data, we used the Bayesian Information Criterion which is introduced in the next subsection. We are thus capable of combining the different values of the traffic to generate by considering those different distributions in the SourcesOnOff tool.

BIC (Bayesian Information Criterion) distance assessment

The goal of this step is to quantify the statistical distance that exists between our original data and the data generated by our tool. To compute this distance we introduce the Bayesian Information Criterion [START_REF] Schwarz | Estimating the dimension of a model[END_REF]. This criterion is computed as BIC = k * ln(n) -2 * ln(L), where:

n is the size of analyzed data; -L is the likelihood of the model (Weibull, Pareto, Exponential…) regarding the different original data;

k is the total number of estimated parameters.

The final goal of this comparison is to select the smallest BIC (minimum BIC value is -∞) according to the different candidate statistic profile (Weibull, Pareto, Exponential, Gaussian…). Thus, the tool can conclude that the selected model (which might be a composition of different distributions) is the closest from the original data.

SOURCESONOFF VALIDATION:

The objective of this section is to validate the traffic profile generated by our tool by verifying its correctness according to the real profile. We could have presented complex and realistic topologies, but the goal of this section is to analyze in details the traffic generation process provided by our tool. By introducing additional complex topologies, the statistical analysis of the generated traffic would have been too complex given that we would have had difficulties to link a specific parameter variation with a specific cause: our tool or the complex topology. This is why we chose a simple experimental topology with only two hosts and one router. The SourcesOnOff tool has been deployed on the different hosts: the sender part on the transmitter host and the receiver part on the receiver host. For this experiment, we use two Linux Debian hosts (mono-core processor @1.2 GHz, 1GB of RAM), connected to a Linux Debian router (quad-core processor @3.8 GHz, 4 GB of RAM). The links between hosts are Ethernet RJ45 connections manually configured to 10baseTx-HD, in order to easily limit the link capacities without any software solution and thus to capture all the traffic without any loss. For each original trace replayed thanks to the SourceOnOff tool, we captured, on our experimental topology, the same quantity of generated data in order to be consistent between original and generated data. As a reminder, we present only one set of results related to data collected on 01/29/2013. The validation of our tool needs to analyze its generated traffic. This is why this section analyzes the original captured traffic and explains how generated traffic is really close to the original network traffic. Thus, we performed different quantitative and qualitative verifications on the generated traffic to answer the following questions: does the generated traffic comply with the original one? By applying the algorithm described in section 3.3, the tool is able to detect several different statistic profiles in the same original data as described in the Figure 2. We studied both Doff and Don values but, to be concise, we describe in this section only Doff (i.e. the inter-train durations) results. The Doff distribution is a complex statistical process that we have modeled based on the function composition algorithm described in the previous section. Our algorithm chose a composition between Weibull and Dirac functions (as plotted by the black curve). In the following sub section, we are going to validate how this function composition fits very well the original statistical process.

Statistic profile detection

Qualitative analysis : quantile-quantile plots

As qualitative estimators, we used quantile-quantile plots diagrams (also called "QQPlots") to represent on the same diagram the measured values on the real network (i.e. the original data) and the measured values on the experimental network (i.e. the SourcesOnOff generated data). QQPlot diagrams sort independently X and Y values, and then represent points to the sorted coordinates. When the X and Y series are correlated, a linear tendency is visible on the diagram. On our QQPlot diagrams, we will represent a diagonal blue line of equation y=x, in order to represent a perfect correlation between x and y values.

The set of values used for the X data is the set of durations between two consecutive TCP connections observed in the capture in the real network. The set of values used for the Y data is the set of durations between two consecutive TCP connections measured in the traffic generated by our tool SourcesOnOff. In other words, the Y values are the durations our tool waited between starting two TCP connections. We can conclude that our tool shows very good trends for the generated traffic compared to the original one. However, it is necessary to analyze more accurately how the generated traffic is close to original. This is why we used additional tools (BIC distance and Hurst factor) to check quantitatively these results in the following section.

Quantitative analysis

BIC distance

Table 1 shows BIC distance analysis. We can note that original and generated traffics are the closest when the statistic model combines both Weibull and Dirac profiles. The qualitative similarity between original and generated traffics provided by QQPlot is thus confirmed by BIC distance computations for both Don and Doff profiles. This result validates that a combination of both Weibull and Dirac distributions is the right statistical profile to consider with our original data.

Hurst exponent computation

We wanted also compute quantitatively the long-term memory of the generated traffic compared to the original one. This can be showed with the Hurst exponent computation: this value is an indicator of long-term memory. In our case, we used the Wavelet-based joint estimator of the Hurst exponent, as described by D. Veitch and P. Abry in [START_REF] Veitch | A Wavelet Based Joint Estimator of the Parameters of Long-Range Dependence[END_REF] to study the Long-Range Dependence. In table 2, we compare the Hurst exponent estimation for the throughput generated by our tool with the throughput of the real capture at different time scales (from 100 us to 10 s).

Conforming to [START_REF] Veitch | A Wavelet Based Joint Estimator of the Parameters of Long-Range Dependence[END_REF], data (see table 2) exhibit Long Range Dependence (LRD). Indeed, data show LRD when 0.5 < H < 1. Moreover, the dependence is stronger when H is closer to 1. Thus, we can conclude than in our case, we have a strong Long Range Dependence in both series of throughput, whatever the time window is defined. We can also conclude that both generated and original traffics exhibit the same LRD level (considering a 12 % error interval).

CONCLUSION AND FUTURE WORK

In this paper, we have introduced a methodology to generate network traffic with realistic characteristics. A tool has been developed, based on the application of ON/OFF sources with different statistical profiles. Parameters of the distributions can be defined by the user or extracted from real traffic analysis. We have completed this paper with a validation of both the traffic generation methodology and the SourcesOnOff tool. Different experiments have been conducted. All of them appear to validate the proposition that our tool is able to generate traffic with the same characteristics as real ones.

The tool is freely available and may be utilized for a wide variety of network traffic profiles. We hope users can appreciate the wide range of applications where SourceOnOff can be utilized. This tool is currently unable to generate traffic other than TCP and UDP protocols. In the future, the tool may be developed further in order to support ICMP protocol. Moreover, the tool may support other statistical distribution profiles and may provide additional statistics for the users. Having completed the validation of this tool, we can now take into account more complex network topologies (cloud computing applications for instance) and distribute different SourcesOnOff sender and receiver agents among them for the future experiments we plan to conduct.

For n from 1

 1 to infinite do: /* start a new source here */ 1. Don_value := get a random value of distribution Don; 2. Doff_value := get a random value of distribution Doff; 3. Wait for the duration Doff_value 4.

Figure 2 :

 2 Figure 2: Fitting of original (red curve) and generated (black curve) for Doff traffic distributions

Figure 3 :

 3 Figure 3: QQPlot for Doff values (generated traffic vs. real traffic)We can see on figure7that the values are very well correlated: most of the 9,700 points drawn on this figure are near the diagonal blue line of equation y=x. This means most values measured in the real network were successfully reproduced in our experimental network. The correlation factor is 99.8% in our case for Doff values. A few points with high values are not well correlated: they come from the tail of the Weibull distribution densities.

Table 1 : BIC distance between original and generated traffic

 1

	Statistic model	Doff BIC distance	Don BIC distance
	Weibull (+ Dirac)	0.01558	0.02527
	Pareto (+ Dirac)	0.0209	0.03834
	Exponential (+ Dirac)	0.08892	0.06222
	Gaussian (+ Dirac)	0.1027	0.07535

Table 2 : Hurst exponent estimations (H) Sample duration for throughput measurements

 2

		H	H for real	Error
		for our tool	throughput	ratio
		SourcesOnOff
	100 us	0.88	0.83	7 %
	10 ms	0.97	0.95	2 %
	100 ms	1.00	1.00	0 %
	1 second	1.00	0.88	12 %
	10 s	1.00	1.00	0 %

Quantmod website: http://quantmod.r-forge.r-project.org

THE SOURCESONOFF TOOL

We did not find in the state of the art we performed any tool to generate data flows based on exact ON/OFF sources. This is why we developed this one in C language and validated it with the Debian Operating System. The tool we propose is free and Open Source, under the General Public License v3 (GPLv3). Source code can be downloaded at http://www.recherche.enac.fr/~avaret/sourcesonoff.

Generation of the random values

ON/OFF sources are based on the generation of random values following well-determined distributions. The following distributions are currently implemented in the program. The Uniform distribution is based on the drand48() and the random() Linux functions, with corrections to ensure an exact uniformity on any range. The Normal/Gaussian distribution is computed with the help of the Box-Muller transformation. We use the Knuth's algorithm for the Poisson distribution. The Pareto, Weibull and Exponential distributions use internally a transformation on the uniform distribution. The generation process of all these distributions have been statistically validated with the R statistical software [START_REF]The R Project for Statistical Computing[END_REF] and its comparison function qqplot(). An additional pseudo-distribution is available: the Constant distribution. In this