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1 Labour Economics 17 (2010) Contents lists available at ScienceDirect Labour Economics journal homepage:.elsevier.com/locate/labeco On-the-job search equilibrium ith endogenous unemployment benefits Arnaud Chéron a,b,, François Langot a,c,d,e a GAINS-TEPP (Université du Maine), France b EDHEC, France c Cepremap, France d IZA, Germany e ERMES (Université de Paris 2), France article info abstract Article history: Received 18 April 2006 Received in revised form 21 September 2009 Accepted 24 September 2009 Available online 8 October 2009 JEL classification: C51 J24 J31 J38 This paper develops an on-the-job search model ith age posting here unemployment benefits are proportional to past ages. We emphasize that this contributes to increasing the reservation ages of unemployed orkers and introduces a feedback effect of the distribution of ages on the distribution of unemployment benefits. We sho that the model predictions are consistent ith some stylized French facts and quantify the impact of inefficient rejections of lo-age offers by the unemployed. We find that, by reducing the indexing of unemployment benefits to previous earnings and increasing lump-sum transfers, it is possible to increase both employment and elfare Elsevier B.V. All rights reserved. Keyords: Unemployment benefits Wage posting Equilibrium unemployment 1. Introduction In their seminal paper, Burdett and Mortensen (1998) (BM henceforth) not only sho that pure age dispersion can exist at equilibrium ith the on-the-job search, but also that the interplay ith unemployment benefits dispersion gives rise to inefficient unemployment according to BM's definition. This means that some unemployed orkers reject lo-age offers, hich pushes up the unemployment rate. Although this dispersion of the unemployment benefits (UB) does not reflect any heterogeneity of orkers' ability, these job rejections are unambiguously inefficient. The distribution of UB should therefore collapse to a mass point. Hoever, it is obvious that there is also an insurance motive for the UB system because consumption-smoothing raises the ell-being of risk-averse orkers. 1 This argument favors the indexing of UB to previous earnings, Corresponding author. GAINS, Faculté de Droit et de Sciences Economiques, Avenue Olivier Messiaen, Le Mans Cedex 9, France. addresses: acheron@univ-lemans.fr (A. Chéron), flangot@univ-lemans.fr (F. Langot). 1 Since Shavell and Weiss (1979) and Hopenhayn and Nicolini (1997), it is ellknon that the optimal UB system reflects a trade-off beteen the positive impact of consumption-smoothing and the adverse moral hazard effect related to unobservable search efforts. hich ould lead to a dispersed distribution of UB. From another standpoint, Marimon and Zilibotti (1999) and Acemoglu and Shimer (2000) argue that a generous UB system can be considered as a subsidy to the search activity; this allos orkers to find high productivity jobs and contributes to raising output and elfare. Overall, the indexing of UB to previous earnings introduces a trade-off beteen inefficient unemployment on the one hand, and insurance/subsidy motives on the other hand. The aim of this paper is to quantitatively analyze this trade-off by extending the BM frameork to allo UB to be proportional to past ages. In most OECD countries (see OECD (1994)), the UB distribution is not a mass point. UB systems therefore differ according to average replacement rates but also according to the heterogeneity of the unemployment compensations. The UB system typically embodies to components: a Beveridge component (lump-sums) associated ith redistribution, and a Bismarck component associated ith the insurance i.e. the UB indexing to previous earnings. The extent of this indexing differs largely across countries (beteen 57.4% and 75% of gross ages in France, 60% of the net ages in Germany, 40% of gross ages in Italy ). Moreover, the UK, Australia and Ne Zealand are noticeable exceptions here there are only lump-sum transfers (the Beveridge component). The first goal of this paper is to sho ho the on-the-job search equilibrium ith endogenous age dispersion is affected by endogenous /$ see front matter 2009 Elsevier B.V. All rights reserved. doi: /j.labeco

2 384 A. Chéron, F. Langot / Labour Economics 17 (2010) unemployment benefits. Secondly, this paper aims at shoing the main trade-offs behind the definition of an optimal UB system in the context of the on-the-job search equilibrium. Previous orks in line ith BM assumed that the dispersion of unemployed reservation ages is exogenous. This implies that the position of orkers ithin the unemployment distribution does not depend on the orker's career and his previous age earnings (see, e.g. Bontemps et al. (2000), or Postel-Vinay and Robin (2002)). Unemployed benefits/reservation ages dispersion modifies the shape of the age distribution, but the latter has no feedback effect on the distribution of the unemployed. In this paper, e emphasize that the proportionality of UB to past ages implies an unexplored argument for the job search decision of the unemployed hich raises their reservation ages. An unemployed orker indeed expects that if he accepts a age equivalent to his benefits, this can imply loer unemployment compensation in the future event of the job's destruction; he ould earn only a fraction of the accepted age. Endogenous UB dispersion then introduces additional restrictions on the job contact rates: the probability of the orker accepting a age offer no depends only on the age dispersion and no longer on an ad-hoc distribution of the UB. From the empirical point of vie, a first objective is to assess the on-the-job search model's performance as regards its ability to replicate not only the distribution of ages but also the distribution of UB. As can be seen from Table 1 and Fig. 6 in Appendix A, the heterogeneity of UB is high in France. 2 More precisely, the dispersion is relatively higher for unemployed incomes than for age earnings: the coefficient of variation is larger for UB than for ages, hatever the skill of the orkers. Fig. 1 examines the value of the earnings decile over average earnings (both for ages and unemployment benefits) 3 and then shos that both for lo-skilled and mediumskilled orkers the distribution of UB is unambiguously flatter than the distribution of ages. Numerical experiments based on the French lo-skilled labor market sho that our model allos a good fit of both distributions (ages and unemployment benefits). It implies a large right-hand tailed of the UB distribution, hich is in some extent the outcome of job rejections by the unemployed. This suggests, therefore, that to explain a orker's upard mobility along the age distribution during his career it could be orthhile to consider indexing of UB to previous earnings (see Burdett et al. (2009) or Bagger et al. (2006) for alternative explanations of this mobility 4 ). Because the dispersion of the UB is endogenous, our model is a useful tool to examine the impact of reforming the UB system, on unemployment, productivity and elfare. First, our model is ell-suited to quantify the potential extent of inefficient unemployment. Moreover, because e consider endogenous productivity dispersion, as as first suggested by Mortensen (2000) 5 to generate the observed humpshaped age distributions, 6 our model also allos us to deal ith the productivity argument discussed in Marimon and Zilibotti (1999) and Acemoglu and Shimer (2000). Finally, e introduce risk-aversion in order to take into consideration the insurance motive related to the UB system. 2 See Appendix A for a detailed description of the data. 3 To read these graphs, notice for instance that the value of this ratio approximately equates 1 for the fifth decile of lo-skilled orkers, both for ages and unemployment benefits; that is, the average age (UB) is close to the median age (UB). 4 The papers of Burdett et al. (2009) or Bagger et al. (2006) rule out this problem by abstracting from the labor market institutions. In these models, upard mobility along the age distribution comes only from experience (human capital accumulation) and the on-the-job search. 5 At the time of job creation, firms invest in match-specific capital. 6 It is no ell knon that the standard BM frameork implies a strictly increasing age earnings density function. Exogenous productivity dispersion helps to generate hump-shaped age distributions (see, e.g., Bontemps et al. (2000)). Chéron et al. (2008) sho that endogeneous productivity dispersion is also able to fit the French distribution of ages. Table 1 Wages and unemployment incomes dispersion in France. Our quantitative analysis is based on the French lo-skilled fulltime labor market. We find that the impact of job-offer rejections on the unemployment rate is not very large but significant, around one percentage point. This gives an assessment of the inefficient unemployment for lo-skilled orkers in France. We then sho that the optimal UB system for this population ould correspond to a Beveridge system ith only lump-sum transfers ithout any indexing of the UB to previous earnings. The remainder of the paper is as follos. The first section presents the model. The second section is devoted to calibration, model assessment and policy analysis. The last section concludes. 2. A age posting model ith unemployment benefits proportional to past ages This paper extends the job search-age posting frameork àla Burdett Mortensen to allo for endogenous unemployment benefits hich are proportional to past ages. Letting b denote this unemployed income, e assume: b = ρ 1 + all here 1 stands for the former age, and all is a lump-sum transfer. The benefit b has therefore to components: all the Beveridge component associated ith redistribution across the unemployed, and ρ 1 the Bismarck component associated ith insurance. Overall, this implies that the equilibrium age offer density function depends on the distribution of unemployed incomes, hich in turn depends on the distribution of age earnings. A first contribution of this paper is then to solve the corresponding fixed-point Labor market flos Wages UB UBb2Y standard deviation Lo-skilled mean 34.2% 40.2% 38.6% standard deviation Medium-skilled mean 36.3% 45.6% 44.5% standard deviation High-skilled mean 45.7% 53.7% 48.7% UBb2Y=UB for orkers unemployed for less than 2 years. We consider a minimum age hich bounds belo the age distribution and gives the level of the iso-profit. This suggests that ithout any variation of the minimum age, the number of vacancies is fixed as ell as contact rates. Therefore, for simplicity, e consider to exogenous arrival rates of age offers, λ 0 and λ 1 for the unemployed and the employed, respectively. We denote the steady-state number of employed orkers being paid a age no greater than by G()(1 u), here G() is the distribution of age earnings across employed orkers and u the overall unemployment rate. Let F() be the distribution of age offers, and s be the job destruction rate. At steady-state the flo of orkers leaving employers offering a age no greater than equals the flo of orkers hired ith a age no greater than : λ 0 ½FðÞ FðxÞŠuðxÞdx = ðs + λ 1 ½1 FðÞŠÞð1 uþgðþ ð2þ here F() F(x) is the probability that an unemployed orker ith reservation age x receives and accepts a age offer no greater than. u(x) gives the mass of unemployed orkers ith a reservation ð1þ

3 A. Chéron, F. Langot / Labour Economics 17 (2010) Fig. 1. Earnings deciles. age x. This mass depends on the distribution of ages according to the folloing steady-state equilibrium condition: uðrðρ + allþþλ 0 ½1 FðRðÞÞŠ = sð1 uþgðþ here g() G () and R(ρ+all) stands for the reservation age of an unemployed orker ho earn benefits ρ+all. Lastly, the overall unemployment rate is given by u = R R uðrþdr Wage posting and match-specific capital investments As in Mortensen (2000), each employer commits to both the age offered and the extent of its match-specific human capital investment. Let r be the real interest rate, since jobs are destroyed at rate s and employed orkers quit at rate λ 1 [1 F()] hen they receive a higher age proposal, the expected discounted present value of the employer's future flos of quasi-rents once a orker has been hired at age is yðkþ r + s + λ 1 ½1 FðÞŠ here k represents the match-specific investment per orker and the value of productivity y(k) is an increasing and concave function of this investment. Because investments are made after the orker and the employer have met, the ex ante asset value associated ith a job is given by: yðkþ max hðþ ;k 0 r + s + λ 1 ½1 FðÞŠ k here h() stands for the probability that a job ith age offer is accepted by the orker; using Eq. (2) it is defined by: ð3þ here u(x) isdefined by Eq. (3).If e let ŵ() denote the former age that ould lead an unemployed orker ho earns ρŵ+all to accept any age above, 7 the contact probability turns out to be ritten as follos: sλ hðþ = 0 ð1 uþ s + λ 1 ½1 FðÞŠ R s + λ 1 ½1 FðxÞŠ gð ˆxðxÞÞdx λ 0 ½1 FðxÞŠ This allos us to emphasize the fact that the age policy of the firm, hich is related to this contact probability, depends both on the UB system that determines ŵ() and the overall distribution of earnings. For any age offer, the optimal training investment policy is fully characterized by the first order condition: f ðkþ = r + s + λ 1 ½1 FðÞŠ k = kðþ From F () 0, because the expected duration of a job is positively related to the level of the age offer, employers ho post high ages also invest more in match-specific capital, i.e., k ()N0. 8 This implies in particular that k( ) k and k( ) k solve y ðk Þ = r + s + λ 1 ; y ðk Þ = r + s Because all jobs are ex ante identically productive, every age in the support of the equilibrium age distribution must yield the same profit (see BM). The on-the-job search equilibrium is then characterized by: " hð Þ yðk Þ k ðr + s + λ # 1Þ r + s + λ 1 = hðþ yðkðþþ kðþðr + s + λ 1½1 FðÞŠÞ r + s + λ 1 ½1 FðÞŠ ð5þ ð6þ ð7þ hðþ = ð1 uþλ 1 GðÞ + λ 0 uðxþdx R λ = 0 s + λ 1 ½1 FðÞŠ R ðs + λ1 ½1 FðxÞŠÞuðxÞdx ð4þ 7 As ill be stated hereafter, this corresponds to U()=W(ŵ). 8 See Mortensen (2000) for more details.

4 386 A. Chéron, F. Langot / Labour Economics 17 (2010) here F( )=0 and k() solves Eq. (6). Using Eq. (4), this expression can be re-stated as follos: s + λ 1 ½1 FðÞŠ r + s + λ1 ½1 FðÞŠ s + λ 1 r + s + λ 1 " # = yðkðþþ kðþðr + s + λ 1½1 FðÞŠÞ f ðk Þ k ðr + s + λ 1 Þ R ðs + λ1 ½1 FðxÞŠÞuðxÞdx R ðs + λ 1 ½1 FðxÞŠÞuðxÞdx In addition, it is straightforard to derive by evaluating Eq. (8) hen F( )= Reservation ages It is ell knon that heterogeneity across contact rates implies that the reservation ages of the unemployed, R(b), can be either greater or smaller than their current income b (see BM). In our frameork, the proportionality of unemployment benefits to past ages also implies that the reservation ages of the unemployed no longer correspond to their current earnings. The basic intuition is that an unemployed orker expects that if he accepts a age corresponding to his current unemployed income, this ould lead to loer unemployment benefits in the future event of job destruction. This point can be stated clearly by considering the expected lifetime income of employed and unemployed orkers according to their current earnings, respectively: rvðþ = ruðbþ = ð + τþ1 σ 1 σ ðb + τþ1 σ 1 σ + λ 1 ½VðxÞ VðÞŠdFðxÞ s½vðþ UðbðÞÞŠ + λ 0 R ½VðxÞ UðbÞŠdFðxÞ here b is defined by Eq. (1), σ 0 and τ stands for lump-sum transfers (profits taxes to finance the UB system). The loest acceptable offer for unemployed orkers ith earnings b is then defined by U(b)=V(R). The unemployed orker's reservation age turns out to be given by the folloing condition: 9 ðr + τþ 1 σ 1 σ = ðb + τþ1 σ + ðλ 1 σ 0 λ 1 Þ R ½VðxÞ VðRÞŠdFðxÞ + s½uðbþ UðρR + allþš Consider at this stage σ=0 and τ=0. The main salient features are: λ 0 Nλ 1 accounts for a reservation age of the unemployed greater than unemployment benefits (as in BM), For ρ+allb, indexing of UB to previous earnings leads to U (b) U(ρR+all)N0, so that it also accounts for a reservation age of the unemployed greater than the unemployed income. 10 Otherise stated, even though λ 0 =λ 1, it is in the interest of the orkers to accept a age greater than their unemployed earnings b because they expect in the future to go back to unemployment ith earnings ρb+all loer than b. 11 This highlights a ne motive for age offer rejections and suggests that standard structural estimations of the unemployed contact rate, hich do not take this motive into account, are biased. 9 Replacing R by ŵ and b by, one gets ŵ() used in Eq. (5). 10 The proof is straightforard since U(b) is unambiguously increasing ith b. 11 This job search strategy does not exist in BM because orkers kno that they ill earn b hatever their former age. ð8þ ð9þ 2.4. Labor market equilibrium and evaluation criteria The labor market equilibrium is characterized by {u(b), g(), h(), f(), k(), R(b)} and b defined by Eq. 1, hich solves the system Eqs. (2), (3), (4), (6), (8) and (9), and here transfers to orkers τ, defined as profits π minus taxes T to balance the UB system, are defined by: τ = π T R π = ð1 uþ ½yðkðÞÞ ŠgðÞd λ 0 R x kðþf ðþd uðxþdx T = b b buðrðbþþdb; ithu = R R uðxþdx To evaluate the impact of the UB system, e then consider the three folloing criteria: The extent of inefficient unemployment as defined by the gap u in u ũ here ũ s s + λ 0 refers to the unemployment rate ithout any rejection. Aggregate output flo net of training costs, as defined by: R Y = ð1 uþỹ λ 0 R x kðþf ðþd uðxþdx here ỹ gives the average job-productivity: ỹ yðkðþþgðþd This allos us to take into consideration the impact of the UB system on training investment, hence on productivity and output. Aggregate elfare hich takes into account the risk aversion of orkers and the redistributive effects of the UB system, as defined by: R W = ð1 uþ VðÞgðÞd + R UðxÞuðxÞdx 3. Equilibrium distributions, inefficient unemployment and the optimal unemployment benefits system In our model age and UB distributions are interrelated. One may then onder to hat extent this explains the distribution of ages and UB in a orld here no other heterogeneity is introduced. Otherise stated, a first objective is to look at the empirical relevance of the model. A second objective is to sho the extent of the inefficient unemployment associated ith these rejections, and hat the optimal UB system could be Calibration We choose to calibrate annually the model on a French lo-skilled orkers data set, by considering the employed ith full-time jobs and the unemployed less for than to years. 12 As a preliminary step, e need to specify a functional form for the job-productivity; as in Chéron et al. (2008), e consider the folloing specification: yðkþ = y + p k α α ith pn0 and α2(0,1). Then, e distinguish to subsets of parameters, according to the calibration strategy (Table 2). A first subset Φ 1 ={r, σ, s, λ 1 } is based on external information. In particular, e use the values provided by Postel-Vinay and Robin (2004) to set the contact rate of the employed and the job destruction rate. A second subset Φ 2 ={λ 0, y, p, α} is set in order to reproduce the 12 We use the Labor Force Survey in 2002; see Appendix A for a detailed description of the data. A detailed explanation of the numerical procedure to compute the labor market equilibrium is also provided in Appendix B.

5 A. Chéron, F. Langot / Labour Economics 17 (2010) Table 2 Structural parameters. r σ s λ 1 λ 0 y p α ρ all 4% unemployment rate of 9% and three stylized facts hich characterized the distribution of ages; e use the mean age (=1.46 mandatory minimum age) and the value of to age deciles (5th and 6th), as shon in Fig. 2. Lastly, e normalize the mandatory minimum age to one, assume all=0 and set ρ in order to reproduce the observed average replacement rate of 53%. 13 To points then deserve discussion. First, it is orth stressing that the calibrated value for λ 0 is greater than λ 1. This is consistent ith the estimation of Postel-Vinay and Robin (2002) although the magnitude of the gap beteen contact rates is smaller here; slightly less than 2 instead of 3 in Postel-Vinay and Robin. Hoever, it seems consistent since, as e argued earlier, proportionality of UB to past ages increases the reservation ages of the unemployed, as is also implied by a higher value for λ 0. Secondly, the value of α is very close to the one obtained by Chéron et al. (2008) in a model ith endogenous productivity but exogenous UB (0.76 here instead of 0.72) Model properties Figs. 3 and 4 sho the results of model simulations, here the value of 1 refers to the value of the mandatory minimum age in France. Fig. 3 first shos that there exist some job offer rejections for unemployed orkers hose income is above 80% of the minimum age. For orkers ith loer unemployment compensations, all age offers turn out to be acceptable in our simulations. Then, for the unemployed ith the highest income (around the minimum age 14 ) the loest acceptable age is almost 20% higher than the minimum age. This figure also shos the value of job-productivity as implied by the training investment of the firms. This job-productivity is increasing ith ages, ith a range approximately from 1 to 4. Fig. 4 then shos the equilibrium distributions of ages and UB. Both density functions appear to be hump-shaped as found in the data. The main salient feature refers to the right-hand tailed of the distributions: the latter is larger for the UB than for ages. This result is clearly the outcome of job rejections by the unemployed ith high unemployment compensations; those orkers indeed stay longer in unemployment than the others. Are these model predictions consistent ith the data? Fig. 2 shos the value of earnings decile ith respect to average earnings (both for ages and unemployment benefits) in order to assess the model performance. Overall, the fit of the model is quite good. 15 Although it is obvious that the model is calibrated to mimic three moments of the distribution of ages, it remains hoever 6 deciles. The predictions of the model are not too inaccurate, even though it appears that the model understates (overstates) the 1st (9th) decile values, that is the fit is not perfect concerning the bottom and the top of the age distribution. Turning to the distribution of UB, the overidentification of the model is even greater since e use only one target to calibrate the model (the average replacement rate). While the model predictions are close to the data concerning the top of this distribution, the main failure refers to the bottom since the model again overstates the value of 1st 13 Although e consider the proportionality of UB to past ages, our model does not consider any eligibility criteria to access the standard unemployment compensation scheme. Hence, e choose to target the average replacement rate, and do not use the legal definition of the unemployment insurance and assume all=0. Our policy experiments ill then aim at shoing the equilibrium impact of alternative values for ρ and all. 14 This highest value is given by 0.51, here, is derived by considering F( )=1in Eq. (8). 15 To read this graph, notice for instance that the value of the computed ratio approximately equates 1 for the fifth decile of lo-skilled orkers, both for ages and unemployment benefits; that is, the average age (UB) is close to the median age (UB). 3rd deciles. These failures can be explained to some extent by the fact that the model does not incorporate any difference in contact rate and transferable human capital. It seems indeed intuitive that in the data some orkers ith lo ages and eligible for lo UB should obtain loer contact rates. Skill-obsolescence according to the length of the unemployment spell should also be introduced. Finally, UB typically decline over the course of an unemployment spell; it means that a orker may ell accept a loer age than his current benefittoescape before his benefits run out. Both could help to explain the bottom of age and UB distributions. Although some extensions ould have to be added, e think that the overall assessment of the model is good, given the large set of moments e consider Eliminating inefficient unemployment A first objective is to focus on the unemployment rate to evaluate the impact of the UB system. More precisely, this section aims at addressing the folloing to issues: (i) What is the extent of inefficient unemployment? (ii) What should be the design of an unemployment insurance system to eliminate inefficient rejections? Actually, the anser to the former question is directly implied by our calibration procedure and the resulting value for λ 0. Inefficient unemployment corresponds to the gap beteen calibrated unemployment and equilibrium unemployment ithout any age offer rejections. Calibration of the model is done in order to match the observed unemployment rate. This means that the calibrated value for λ 0 is revealed by simulations of agents' behaviors and the labor market equilibrium, given the other set of structural parameters. Since e set s=0.1 and find λ 0 =1.13 to match the unemployment rate, this means that ũ s =8:1% s + λ 0 is the value of the unemployment rate in the context of no age offer rejection. Otherise stated, e can expect, at most, a 0.9 percentage point decrease of the unemployment rate by eliminating inefficient unemployment (u in ). The next issue deals ith the design of the UB system according to Bismarck/Beveridge components in order to eliminate rejections. There is a large set of combinations {ρ, all} hich ould deliver this outcome. On the one hand, one could choose to keep all=0 and search for the threshold value of ρ hich implies that the unemployed ith the highest benefits accept the minimum age; e find ρ=0.4. On the other hand, e can set ρ=0 and choose the highest value for the Beveridge component hich implies a reservation age for the unemployed consistent ith the minimum age (=1 from normalization); e find all=0.85 and the associated unemployment benefits distribution is a mass point at this level. Other combinations also exist and Table 3 shos values for unemployment and average replacement rates for some combinations that are consistent ith the fact that the unemployed at the top of the UB distribution accept the minimum age. It is obvious that for all these combinations, both the equilibrium unemployment rate and the distribution of ages are unchanged. Only the distribution of unemployment benefits is modified. Interestingly, e find that e can maximize the average replacement rate ithout introducing any inefficient unemployment rate hen the distribution of unemployment benefits is a mass point at a level corresponding to 85% of the minimum age; the associated replacement rate (rr) is 58%. Table 3 also shos values concerning productivity, output and elfare that take a orker's risk-aversion into account. Due to its redistributive impact on the unemployed, the set {ρ=0; all=0.85} allos us to reach the highest elfare in this context of no age offer rejection. 16 More generally, e ould like to go beyond unemployment to examine the optimal UB system. One may indeed onder to hat extent it could be orthhile to keep a UB system leading to some job offer rejections. 16 As could also be noticed, all the combinations {ρ, all} that eliminate inefficient unemployment leave productivity and output unchanged.

6 388 A. Chéron, F. Langot / Labour Economics 17 (2010) Fig. 2. Wage and UB deciles: model vs. data. Fig. 3. Individual decisions. Fig. 4. Equilibrium distribution of ages and UB Beyond unemployment: productivity, output and elfare Fig. 5 first emphasizes that a reform of the UB system hich leads to the elimination of all age offer rejections, pushes the age distribution slightly to the left. As as already emphasized by Chéron et al. (2008) hen examining the impact of tax exemptions on lo ages, such an impact on the distribution of ages can lead to reduced productivity. Indeed, due to the on-the-job search, the

7 A. Chéron, F. Langot / Labour Economics 17 (2010) Table 3 Impact of the UB system. UB system u in rr y Y W Reference {ρ =0.51; all=0} 0.9% 53% {ρ =0.4; all=0} 0% 42% {ρ =0.3; all=0.24} 0% 48% {ρ =0; all=0.85} 0% 58% Reference {ρ =0.40; all=0} 0% 41.5% {ρ =0.43; all=0} 0.1% 44.5% {ρ =0.46; all=0} 0.15% 47.7% {ρ =0.47; all=0} 0.2% 48.8% {ρ =0.48; all=0} 0.3% 49.8% {ρ =0.49; all=0} 0.6% 50.9% {ρ =0.51; all=0} 0.9% 53.0% {ρ =0.52; all=0} 1.3% 54.2% {ρ =0.55; all=0} 1.8% 57.6% {ρ =0.60; all=0} 3.7% 63.8% Fig. 5. The age distribution impact of inefficient unemployment. expected duration of jobs, and hence training investments, are increasing ith ages. In turn, by increasing the proportion of lo age offers, the policy shock leads to reduced training investments and average productivity. One may then first onder hether it is optimal to eliminate inefficient unemployment if it decreases output net of training costs, i.e. e take Y as a criterion. This is done by varying the Bismarck component of UB, considering values of ρ greater than 0.4 (the highest value consistent ith no rejection). 17 As could be noticed from Table 3, an increase in ρ unambiguously raises the unemployment rate and average productivity, but it is clear that the overall impact on output is negative. From this point of vie, there is no justification for inefficient unemployment. In turn, if e no consider elfare W, the redistributive motive related to the concavity of the utility function leads to a nonmonotonous relationship beteen elfare and proportionality of UB to past ages, hich is increasing for ρ (0.4; 0.48) and decreasing for ρ Otherise stated, if e take all=0 as given, the optimal value for UB indexing is ρ=0.48, hich is only slightly loer than the reference value e used (ρ=0.51). Hoever, this elfare ( 3.307) remains loer than the highest value obtained by using the Beveridge component ( 3.197) alone, that is by setting {ρ=0, all=0.85}. Lastly, to remaining points deserve discussion. First, it is obvious that the fact that our policy assessment emphasizes the prominent role played by the Beveridge component depends on the calibrated Table 4 Impact of the minimum age (ith {ρ=0.51; all=0}). MW u in y Y W % % % % value of risk-aversion. Robustness analysis shos that for the value of σn0 it remains unambiguously the case that the highest elfare value can be reached by setting ρ=0 and all at its highest value so that it prevents job rejection. For σ=0 e find that the to alternative policies are equivalent. That is, the highest social elfare can be reached either by setting ρ or all so that it prevents job rejection. Secondly, one may also onder to hat extent the minimum age legislation could also be used to improve efficiency and/or reduce inefficient unemployment. Table 4 shos some simulation results. As in BM, the higher the minimum age the loer the inefficient unemployment. Indeed, the highest age paid increases less than the minimum age, and this induces a higher age concentration at the bottom of the distribution. In our frameork, this also implies higher concentration of the UB distribution so that it could be orthhile for the unemployed orkers at the top of this distribution to accept even the minimum age. This higher concentration at the bottom also leads to a reduction in average training investments, hence in productivity. Overall, even though a higher social elfare could be reached by increasing the minimum age and eliminating inefficient unemployment (W= 3.291), e find that it ould remain more efficient to reduce the Bismarck component of UB and simultaneously increase the Beveridge one (W= hen {ρ=0, all=0.85}). This is more efficient than increasing the minimum age, because the riskaversion of orkers gives more value to the unemployed incomes than to the employed earnings Conclusion The contribution of this paper is tofold. It is first to provide an extension of the on-the-job search frameork to account for endogenous unemployment benefits as a result of UB indexing to previous earnings. This allos us to emphasize ne determinants of the job search decision and to assess the model's ability to fit the distribution of ages and UB. Secondly, the paper argues that the proportionality of UB to past ages can undermine ell-being. Simulations based on French loskilled orkers indeed sho that a decrease of UB indexing together ith an increase of lump-sum transfers can improve elfare. This is due to the fact that the negative elfare impact of the related fall in productivity is more than offset by the positive elfare impact of the rise in employment as ell as in unemployed orkers' incomes at the bottom of the UB distribution. These results suggest that in an economy ith a binding minimum age, the optimal UB is close to that in, for instance, the UK and the Australia. This ork could be extended in several directions. First, ithout a mandatory minimum age, the loest age ould become endogenous and determine iso-profit value, so that the UB system should modify contact rates. Second, e do not consider the adverse moral hazard effect of UB. This could be discussed by introducing an additional labor market status such as long-term unemployed ith loer UB. By controlling the UB gap beteen the short-term and long-term, the UB system could also be optimized. 17 In turn, if e vary all ith ρ=0 this has no impact on equilibrium, because this does not lead to any age offer rejection. Furthermore, this should modify the loest age paid by firms and accordingly should have an impact on the labor demand (vacancy decision); this is beyond the scope of this paper. 18 Furthermore, e do not take into account the fact that an increase of the minimum age should also result in a decrease of contact rates.

8 390 A. Chéron, F. Langot / Labour Economics 17 (2010) Acknoledgements We thank Fabien Postel-Vinay and to anonymous referees for helpful comments. This ork has also benefited from financial support of the European Commission ( TAXBEN program). Errors and omissions are ours. Appendix A. Stylized facts We use the French Labor Force survey 2002 to examine the properties of age distributions and unemployment benefits as ell. To that end, e distinguish three types of orkers: Lo-skilled orkers=manual orkers Medium-skilled orkers=intermediary professions High-skilled orkers=managers Fig. 6 shos the distribution of ages and unemployment benefits for each type, and Table 5 computes some related statistics. We consider separately the hole unemployed set on the one hand, and the distribution of unemployment benefits for orkers ith less than 2 years in unemployment (unemployedb2 years) on the other hand. The distribution of ages is hump-shaped, and the average age is increasing ith a orker's skill. It is also obvious that average unemployment benefits are increasing ith a orker's skill, hile the average replacement rate slightly decreases ith skill level. Appendix B. Model resolution The model resolution implies the solution of to fixed points. The first aims at determining the joint distributions of equilibrium age offers and unemployed incomes, hile the second aims at determining the reservation ages of unemployed orkers from value functions. 1. Consider a guess for (i) unemployed orkers' reservations ages R (b), (ii) distribution of unemployed orkers among possible income values u(x) x (so that it involves also a guess u R R uðxþdx), and (iii) contact rates h(). Fig. 6. Distributions of earnings.

9 A. Chéron, F. Langot / Labour Economics 17 (2010) Table 5 Wages and Unemployment incomes in France. Lo-skilled Medium-skilled High-skilled Wages UB UBb2Y Wages UB UBb2Y Wages UB UBb2Y Average , , S.D S:D: 34.2% 40.2% 38.6% 36.3% 45.6% 44.5% 45.7% 53.7% 48.7% Average Replacement rate 50.7% 53.1% 48.2%s 51.3% 48.4% 49.5% S.D.: standard deviation. UBb2Y: UB for unemployed for less than 2 years. 2. Grids for ages and corresponding unemployment benefits are defined according to Eq. (1) for b, and here the highest age offer solves: P = f ð P kþ P r + s hðþ kðr + sþ r + s + λ 1 hð P ðf ðk Þ P Þ P k ðr + s + λ 1 ÞÞ Solves for F() Eq. (7). 3. Iterate on value functions to determine reservation ages=determine the function R(b) b hich verifies simultaneously for both values of unemployed incomes V(R(b))=U(b) b by using F() determined at step According to F(), R(b) and u(r(b)), determine the distribution of earnings G() from Eq. (2). 5. According to G() and R(b) determine u(r(b)) from Eq. (3). 6. According to F() and u(r()) calculate a ne guess for the contact rate h() from Eq. (4). 7. Iterate from step 2 until convergence. References Bagger, J. and Fontaine, F. and Postel-Vinay, F. and Robin, J.-M. (2006), A feasible equilibrium search model of individual age dynamics ith experience accumulation, Working paper. Bontemps, C., Robin, J.-M., Van den Berg, G.J., Equilibrium search ith continuous productivity dispersion: theory and non-parametric estimation. International Economic Revie 41 (2), Burdett, K., Mortensen, D.T., Wage differentials, employer size, and unemployment. International Economic Revie 39 (2), Burdett, K. and Carrilo-Tuleda, C. and Coles, M. (2009), Human capital accumulation and labour market equilibrium, Working paper. Chéron, A., Hairault, J.-O., Langot, F., A quantitative evaluation of payroll tax subsidies for lo-age orkers: an equilibrium search approach. Journal of Public Economics 92 (3 4), Hopenhayn, H., Nicolini, J.-P., Optimal unemployment insurance. Journal of Political Economy 105, Marimon, R., Zilibotti, F., Unemployment vs. mismatch of talents: reconsidering unemployment benefits. Economic Journal 109 (455), Mortensen, D.T., Equilibrium unemployment ith age posting. Panel Data and Structural Labor Market Models. Elsevier, Amsterdam. Postel-Vinay, F., Robin, J.-M., Equilibrium age dispersion ith orker and employer heterogeneity. Econometrica 70 (6), Postel-Vinay, F., Robin, J.-M., To match or not to match? Optimal age policy ith endogenous orker search intensity. Revie of Economic Dynamics 7 (2), Shavell, S., Weiss, L., The optimal payment of unemployment insurance benefits over the time. Journal of Political Economy 87, Acemoglu, D., Shimer, R., Productivity gains from unemployment insurance. European Economic Revie 7,