Unions, Firing Costs and Unemployment

Transcription

1 DISCUSSION PAPER SERIES IZA DP No Union, Firing Cot and Unemployment Leonor Modeto May 004 Forchungintitut zur Zukunft der Arbeit Intitute for the Study of Labor

2 Union, Firing Cot and Unemployment Leonor Modeto FCEE, Univeridade Católica Portuguea and IZA Bonn Dicuion Paper No May 004 IZA P.O. Box Bonn Germany Phone: Fax: Any opinion expreed here are thoe of the author() and not thoe of the intitute. Reearch dieminated by IZA may include view on policy, but the intitute itelf take no intitutional policy poition. The Intitute for the Study of Labor (IZA) in Bonn i a local and virtual international reearch center and a place of communication between cience, politic and buine. IZA i an independent nonprofit company upported by Deutche Pot World Net. The center i aociated with the Univerity of Bonn and offer a timulating reearch environment through it reearch network, reearch upport, and viitor and doctoral program. IZA engage in (i) original and internationally competitive reearch in all field of labor economic, (ii) development of policy concept, and (iii) diemination of reearch reult and concept to the intereted public. IZA Dicuion Paper often repreent preliminary work and are circulated to encourage dicuion. Citation of uch a paper hould account for it proviional character. A revied verion may be available on the IZA webite ( or directly from the author.

3 IZA Dicuion Paper No May 004 ABSTRACT Union, Firing Cot and Unemployment In thi paper we conduct an analyi of the effect of firing cot in model that conider imultaneouly worker heterogeneity, imperfect information on their productivity and union power. We conider an OLG model where heterogeneou worker participate in the labour market both when young and old. Each generation of worker i repreented by it own union. Union et wage unilaterally taking into account firm behavior. Firm are atomitic and chooe employment treating wage parametrically. There i imperfect information about worker productivity. We find that at given wage firing cot increae youth unemployment and decreae old age unemployment. However, once we take the wage repone into account, we find that firing cot increae both youth and old age unemployment. Thi happen becaue union react trategically, and repond to higher firing cot. Indeed, when firing cot increae, firm refrain from hiring youth ince, if a young worker turn out to be inadequate, it will be more cotly to fire him. The union, knowing thi, reduce the wage of young worker in order to attempt to increae their employment propect. However, depite thi cut youth unemployment till increae with firing cot. In the econd period, on the contrary, higher firing cot give the union more power. In fact, knowing that firm will be le likely to cut their labour force when firing cot are high, the union increae the wage of old worker, and, therefore, old age unemployment increae. JEL Claification: D83, E4, J65 Keyword: firing cot, unemployment, union, worker heterogeneity Leonor Modeto FCEE Univeridade Católica Portuguea Palma de Cima Liboa Portugal lrm@fcee.ucp.pt

4 1 Introduction The purpoe of thi paper i to conduct an analyi of the effect of firing cot in model that conider imultaneouly worker heterogeneity, imperfect information on their productivity, and union power. The labour market conequence of firing cot have been analyzed in everal work. See for example Bentolila and Bertola (1990), Bertola, (1990), Hopenhayn and Rogeron (1993) and Modeto and Thoma (001). However, in all thee work labour i an homogenou factor. More recently Montgomery (1999), Canziani and Petrongolo (001), and Kugler and Saint-Paul (003) have introduced worker heterogeneity, and analyzed the effect of turnover cot on employment, when there i imperfect information about worker productivity. In thee paper, a in Gibbon and Katz (1991), the cae of private information by current employer vi-a-vi the market i conidered, i.e., it i aumed that current employer are better informed about the worker ability than propective employer. Therefore, if firm have dicretion over whom to lay off, whenaworkedifired the market infer that he or he i of low ability, o that pat employment hitorie become important determinant of future hiring deciion. Montgomery (1999) and Canziani and Petrongolo (001) analyze repectively the effect of hiring or firing cot on the level and compoition of unemployment. Montgomery (1999) olve hi advere election, earch model numerically, and find that, when hiring cot are low the ytem converge to a teady tate in which firm hire every period and mot of the unemployed are low-ability worker. On the contrary, when hiring cot are ufficiently large employment cycle emerge, and firm alternate between hiring and not hiring. Canziani and Petrongolo (001) ue an overlapping generation model with young and old heterogenou worker. They find that firing cot reduce the option value of hiring an young worker and therefore increae youth unemployment. Moreover they alo find that firing cot reduce the re-employment propect of dimied worker becaue propective employer infer that they are very low-productivity individual. Kugler and Saint-Paul (003), uing a matching model, explore the conequence of advere election on the relative job finding probability of unemployed and employed job eeker. They find that hiring and firing cot reduce the hiring of both unemployed and employed job eeker. However, the hiring of the former i more affected by turnover cot. Thi can explain why the ratio of employment-to-employment flow to unemployment-to-employment flow

5 tend to be higher in high-job-ecurity economie. Neverthele in thee model wage are exogenou or fixed at the competitive level. However, if the labour market i not competitive, but rather i unionized, then, a in Modeto and Thoma (001), one would expect union to behave trategically and to react to firing cot. Hence it might be expected that employment level and the relative incidence of youth and long-term unemployment will differ between competitive and unionized model, even in the preence of imperfect information. Therefore in thi paper we tudy the effect of firing cot in unionized economie with heterogenou worker. We conider a imple overlapping generation model where heterogenou worker participate in the labour market for two period. We have therefore two generation of worker: the young and the old. Each generation of worker i repreented by it own union. There i imperfect information about worker productivity, and current employer are better informed than propective employer. Firm, when hiring (firing) a worker, form expectation about the worker profitability, treating wage parametrically. Union announce wage unilaterally, taking into account firm behavior. We how that firing cot affect hiring and firing deciion at given wage, and alo through wage, ince wage etting repond to firing cot. Indeed, when firing cot increae, firm refrain from hiring youth ince, if a young worker turn out to be inadequate, it will be more cotly to fire him. Thi i eentially an option value effect. 1 The union, knowing thi, will reduce the wage of young worker in order to increae their employment propect. However, the effect of thi reduction i not ufficiently trong to change the final reult, and we till find that firing cot increae youth unemployment when wetakethewageeffect into account. Alo, when firing cot increae, the employment propect of old worker that were not hired when young improve at given wage. Thi happen becaue the tigma of having not been hired decreae with firing cot. However, when we take into account the repone of wage to firing cot, the previou reult i revered, i.e., firing cot decreae the employment propect of old worker that were unemployed a youth. Indeed, we find that when firing cot increae, the union alo increae the wage of old worker, o that firm will hire le, and thi lat effect dominate. In fact, when firing cot are higher firm refrain from 1 See on thi iue Canziani and Petrongolo (001). See alo Canzianni and Petrongolo (001). 3

6 firing. Thi give the union more power o that it increae the wage of old worker. Therefore, we find that firing cot increae old age unemployment, although at given wage firing cot increae the probability of employment of old worker. The ret of the paper i organized a follow. In ection we preent the model and derive the optimal hiring, firing and wage-etting policie. In ection 3 we analyze the repone of unemployment to wage. The effect of firing cot on wage and on the level and compoition of unemployment are preented and dicued in ection 4. Finally in ection 5 we conclude. Proof and imulation reult are preented in the Appendix. The Model The model ued i baed on Canziani and Petrongolo (001), where we have introduced collective bargaining to capture the phenomena dicued in the introduction. It i a imple overlapping generation model with heterogenou worker. Individual live and participate in the labour market for two period. Therefore, in every period there are two generation alive and participating in the labour market: the young and the old. Both generation have equal ma that we normalize to one. Worker have different productivitie. Let a i be the productivity of worker i that i contant over time. We aume that a i N(a, σ a). We further aume that the productivity draw are unoberved by both worker and firm. There are a large number of identical, (atomitic), infinitely lived firm. The output of firm j, y j, i linearly additive in the productivitie of it worker: y j = R n j 0 a id i, where n j denote the meaure of firm j labour force. Firm are forward-looking and decide whether to hire or fire a worker. For implicity we aume that the dicount rate i zero. A individual productivitie are not oberved, firm make their deciion, taking wage a given, and after oberving the worker age, employment hitory and current productivity ignal. Indeed every time a firm meet a worker 3 it receive an imperfect ignal of the worker productivity. Figure 1 how the ignalling tructure of the model. 4 When a firm meet a young worker it receive a ignal i = a i +ε i. We aume that ε i i independent of a i and that ε i N(0,σ e). Thi mean 3 We aume that every period all worker meet a firm with probability 1. 4 Note that the ignalling tructure i identical to the one conidered in Canziani and Petrongolo (001). 4

7 that i N(a, σ ) where σ = σ a+ σ e. If a firm hire a young worker it get better information (although till imperfect) of hi productivity. We model thi by auming that the firm receive, at the end of the period, a econd ignal, 5 0 i. The firm then decide on the bai of all the available information to fire or to keep the worker. If the worker i fired the firm bear a firing cot 6 f 0. Ifaworkerifired or ha not been hired when young, he meet again a firm at the beginning of the econd period, and a new productivity ignal 00 i i oberved. 7 The firm then decide to hire the worker or not, proceing optimally all the relevant information. We aume that each generation of individual i repreented by it own union. Thi mean that each period we have two union and two different wage, one for each generation, w 1 for the young and w for the old. We alo aume that union et wage unilaterally and that firm chooe employment at thoe wage. Hence, each firm ignore any effectofitowndeciionon wage..1 Employment A firm hire a worker when the expected profitability of the worker i non negative. Similarly it fire a worker when it expected profitability i negative and larger than the firing cot. Each firm treat wage parametrically, ignoring any effect of it behavior on wage..1.1 Young worker The expected profitability of a young worker i equal to the um of the expected profitability in the current and in the next period conidering the 5 Note that all ignal have exactly the ame tructure, i.e., they have the ame ditribution. Alo the error term of different ignal are independent. 6 A in Canziani and Petrongolo (001), Kugler and Saint-Paul (003) and Boeri and Jimeno (003) we model firingcotaataxthatipaidtoathirdparty,andthat cannot be internalized in the employer-employee relationhip (for example red-tape cot on employer), rather than conidering tranfer from employer to dimied worker. In thi way we abtract from the reditributive effect of everance payment. 7 Note that the ditribution of 0 i and 00 i exit and are defined over the entire population of worker, i.e., they are marginal and not conditional ditribution. The fact that we only oberve 0 i for young worker that were hired doe not mean we can not define a marginal ditribution for 0 i over the entire population of worker. Indeed, if thoe young worker that were not hired had been hired they could have produce a ignal, generated from the marginal ditribution of 0 i. 5

8 poibility that the worker may be fired. Therefore to olve the firm hiring problem we mut firt olve the firing problem. Firing Deciion At the end of each period firm mut decide whether to keep or to fire their young employee. A young worker will be fired if w E[a i \ i, 0 i ] >f (1) where w i the wage that a worker receive when old and E[a i \ i, 0 i ] i the mean of the poterior ditribution of a i after the two ignal. Note that before meetingaworkerafirm expect hi productivity to be a. However, once the firm get to know the worker better (i.e. after oberving one or more ignal) it revie it expectation about the worker productivity. We have that (ee Appendix A.): E[a i \ i, 0 i]= σ e σ a + a + σ a σ e σ a + e i () σ e where e i =( i + 0 i)/. Thi mean that the mean of the poterior ditribution of a i i a weighted average of the mean of the prior ditribution (a) andof the ignal received. The weight are inverely proportional to the repective variance. 8 Uing () we can rewrite (1) a: e i < 0 where (3) 0 = σ a + σ e (w σ f) σ e a. (4) a σ a Thi mean that there i a cutoff level for the average of the ignal, 0, uch that a worker will be kept (fired) if the average of the two ignal exceed (i below) the cutoff. Note that the firing cutoff i increaing in w and decreaing in f and a. Indeed, when average productivity decreae or the wage of an old worker increae, the option value of keeping an worker decreae and therefore firm will fire more. Alo when firing cot are higher, firing i more cotly and le productive worker are kept, i.e., the firing cutoff decreae. 8 Note that, to eae the tak of the reader, we provide in Appendix A.1 the joint ditribution of (a i, i, e i, 00 i ). 6

9 Hiring Deciion A young worker will be hired if hi expected profitability, given the current productivity ignal, i non negative, i.e. if E[π i \ i ] 0. We have een that the expected profitability of a young worker i obtained a the um of hi expected profitability in the current and next period, admitting that the worker may be fired, i.e. 9 E[π i \ i ] = E[a i \ i ] w 1 Pr[fire\ i ]f (5) +[1 Pr[fire\ i ]] [E[a i \e i 0, i ] w ]. We have that (ee Appendix A.) E[a i \ i ]= σ e a + σ a σ σ i (6) i.e. the mean of the poterior ditribution of a i after ignal i i oberved i a weighted average of the mean of the prior ditribution (a) andoftheignal received. The weight are inverely proportional to their variance. We alo have that µ 0 µ Pr[fire\ i ]=Pr[e i < 0 e\ \ i ]= (7) where (.) tand for the tandard normal cumulative ditribution, and where µ e\ and (ee Appendix A.3) are repectively the mean and the tandard deviation of the conditional ditribution of e i on i. Moreover we alo have that E[a i \e i 0, i ], the expected productivity of a worker that i not fired (e i 0 )andgiveignal i a a youth, i given by (ee Appendix A.3): E[a i \e i 0, i ]= σ e σ a + σ a σ i + σ a σ a + σ e 0 µ e\ (8) 1 0 µ e\ where (.) i the p.d.f. of the tandard normal ditribution. Thi mean that we can rewrite (5) a: 9 Note that we aume that firm have perfect foreight in what concern aggregate variable. 7

10 E[π i \ i ] = µ 0 µ e\ σ e σ µ 0 µ e\ f + σ a σ a + σ e µ 0 µ e\ 1 w. a + σ a i w σ 1 µ 0 µ e\ (9) Equation (9) i a continuou and increaing function of 10 i. Therefore we can define a the value of i uch that E[π i \ i ]=0, and only young worker with a ignal i will be hired. Thi mean that in thi model youth unemployment (YU) i imply given by: µ a YU =Pr[ i < ] =. (10) Note that a depend on w 1 and w (ee (9)) youth unemployment i affected by the union choice. In ection 3.1 we analyze the effect of wage on youth unemployment. Youth unemployment alo depend on firing cot through. See (9). The effect of firing cot on youth unemployment are dicued in ection Old Worker Hiring Deciion An old worker may be looking for a job for two reaon. Either he wa firedorhedidnotgetajobwhenyoung.in bothcaefirm, when hiring old worker will, a aid before, take into account all the relevant information, i.e., wage, their pat hitory and their current ignal. Firm will hire thoe worker whoe expected profitability i non-negative. In the cae of an old worker thi i imply hi expected current profitability. For an old worker that did not work when young ( i < ) and give now 10 Note that a E[π i \ i ]/ µ e\ = 0 we have that E[π i \ i ]/ i = h i 0 µ e\ σ a σ > 0. σ 8

11 ignal 00 i hi expected current profitability i given by (ee Appendix A.4): E[π i \ i <, 00 i ]=E[a i\ i <, 00 i ] w (11) σ a = σ e a + σ a 00 σ σ i σ a + σ e µ\ 00 µ\ 00 w where µ \ 00 and (alo given in Appendix A.4) are repectively the mean and the tandard deviation of the conditional ditribution of i on 00 i. A equation (11) i continuou and increaing in 00 i (proof in Appendix A.7) we can define a cutoff value nh uch that, for 00 i = nh, E[π i \ i <, 00 i ]=0. Therefore only old worker that did not work when young with a ignal 00 i nh willbehired.notealothatfrom(11)wehavethat nh i a function of w 1,w and f. 11 The expected current profitability of an old worker that worked when young ( i ), wafired (e i < 0 ) and give now ignal 00 i i given by (ee Appendix A.5): E[π i \ i, e i < 0, 00 i ]=E[a i\ i, e i < 0, 00 i ] w (1) µ\ = σ e a + σ a 00 σ σ i + σ 00 a σ σ a + σ \ 00 µ\ 00 e 1 µ 0 µ e\, 00 σ, 00 a σ 3σ a + σ e\, 00 µ w 0 µ e e\, 00, 00 where µ e\, 00 = E[e i \ i, 00 i ] and, 00 =[Var[e i \ i, 00 i ]] 1/ are alo giveninappendixa.5. A equation (1) i continuou and increaing 1 in 00 i we can define a cutoff value f uch that, for 00 i = f,e[π i \ i, e i < 0, 00 i ]=0. Therefore for thoe worker that did work when young and were fired, only the one with a ignal 00 i f will be hired when old. Note that from (1) we have that f i a function of w 1,w and f Remark that nh i a function of w 1 and f through. 1 Thi reult wa obtained by imulation. 13 Note that f depend on w 1 through and on f through and 0. 9

12 It i intereting to compare the two hiring cutoff for old-age worker, i.e., nh and f.wehavethate[a i \ i <, 00 i ] >E[a i\ i, e i < 0, 00 i ] o that f > nh. 14 Thi mean that, conditional on a given ignal 00 i, firm are more willing to hire a worker that wa not hired in the pat than a worker that wa fired, ince the expected profitability of the former i higher than the profitability of the later. Old age unemployment It i now eay to ee that in thi model old age unemployment (OU) i imply given by: OU = Pr[Not hired when young] Pr[Not hired when old\not hired when young] +Pr[Hired when young] Pr[fired]Pr[Not hired when old\fired] that we can write a: OU = Pr[ i < ]Pr[ 00 i < nh \ i < ] (13) +[1 Pr[ i < ]] Pr[e i < 0 \ i ]Pr[ 00 i < f \e i < 0, i ] where (ee Appendix A.6): Ã! nh µ Pr[ 00 i < nh \ i < ] = \ (14) σ 00 \ µ 0 µ Pr[e i < 0 e\ \ i ] = Pr[ 00 i < f \e i < 0, i ] = µ f µ 00 \ 0, σ 00 \ 0, (15). (16) µ 00 \ = E[ 00 i \ i < ], µ e\ = E[e i \ i ], µ 00 \ 0, = E[ 00 i \e i < 0, i ], σ 00 \ = [Var[ 00 i \ i < ]] 1/, = [Var[e i \ i ]] 1/ and σ 00 \ 0, = [Var[ 00 i \e i < 0, i ]] 1/ are alo given in Appendix A.6. We found that (ee the imulation reult in Appendix A.11) Pr[ 00 i < nh \ i < ] < Pr[ 00 i < f \e i < 0, i ] i.e., the probability of unemployment for an old worker that wa hired when young and wa fired, i higher than the probability of unemployment for an old worker that did not work 14 Thi reult wa obtained by imulation. See Appendix A

13 while young. Indeed we have een that f > nh. Moreover, both the mean and the variance of the ditribution of the ignal of old worker that did not work when young, are higher than the mean and the variance of the ditribution of the ignal of old age worker that were employed a youth and fired, i.e. µ 00 \ >µ 00 \ 0, and σ 00 \ >σ 00 \ 0,. See alo Appendix A.11. Therefore from (14) and (16) it i eay to ee that old-age worker that were unemployed when young have better employment propect than thoe that worked while young, but got fired. Thi implie that, in thi model, having been fired affect more adverely future employment propect than having failed to obtain a job previouly. 15 From the previou expreion one can alo eaily ee that old age unemployment i affected by w 1,w and f. In ection 3. we dicu the repone of old age unemployment to wage. The effect of firing cot on old age unemployment are analyzed in ection 4... Wage Each generation i repreented by a union which i a wage-etter, allowing firm to chooe their employment level in repone. We aume that union wih to maximize the income of their member. 16 Thu, the union that repreent the generation born at time t maximize the following function: Ω t = w 1t (1 YU t )+wy U t + w t+1 (1 OU t+1 )+wou t+1 (17) where YU t and OU t+1 are given repectively by (10) and (13), and where we have aumed that the union alo ha a zero dicount rate and that w, the reervation wage, i contant. For implicity, in what follow we normalize the reervation wage to zero. We aume that a union at time t i unable to precommit to it future wage. Intead the union announce each period a wage, knowing that in the future it will reoptimie. A key feature of thi framework i time-conitency. 15 Note that in our model the productivity of worker i, a i, i contant in time, i.e., it doe not increae with experience. Therefore, being employed while young doe not increae productivity, while having been fired i perceived by potential employer a a ign of very low productivity. 16 Note that thi aumption i frequently ued in the literature, and i equivalent to the aumption that the union i a utilitarian one with rik neutral member. See Owald (198). 11

14 Therefore we have to olve the union problem backward, tarting with the determination of w. In the econd period the union olve the following problem: max wt+1 w t+1 [1 OU(w 1t,w t+1 )] (18) with OU(w 1t,w t+1 ) given by eq.(13). The FOC i: 17 (1 OU(w 1,w )) w OU(w 1,w ) w =0 (19) that i olved by w (w1 ). Note that equation (19) tell u that in the econd period the union wage-etting policy i uch that it elect the wage that make the wage elaticity of old age employment, η (1 OU),w,equalto-1, where η (1 OU),w = [1 OU(w 1,w )]/[1 OU(w 1,w )] w /w. In the firt period the problem of the union i the following: max w 1t 1 YU(w1t,w (w1 w1t )) + w (w1 ) 1 OU(w1t,w (w1 )) (0) with YU(w 1,w ) and OU(w 1,w ) given repectively by eq.(10) and eq.(13). The FOC i: 18 (1 YU(w 1,w (w1 ))) w 1 Y U(w1,w (w1 )) w 1 + Y U(w 1,w (w1 )) w dw (w1 ) dw 1 OU(w 1,w (w1 )) w (w1 ) =0 (1) w 1 where, from (19) we have that 19 dw (w1 ) dw 1 = OU(w 1,w ) w 1 + w OU(w 1,w ) w w 1 OU(w 1,w ) w + w OU(w 1,w ) w. () 17 We aume that the econd order derivative of problem (18) i negative, i.e. OU(w 1,w ) w + w OU(w 1,w ) > 0. Note that for the ake of implicity we have omitted w thetimeubcript. 18 We aume that the econd order derivative of problem (0) (ee Appendix A.9) i negative. Again, for the ake of implicity we have omitted the time ubcript. 19 Note that the denominator of expreion () i poitive. See footnote (16). 1

15 Equation (19), (1) and () ummarize the wage-etting policy of the union. We can ee that the union behave trategically, taking into account the current and future effect of wage on employment. Alo, a employment react to firing cot, the union, knowing thi, will exploit thi fact, o that wage will alo repond to firing cot. In ection 4.1. we analyze the effect of firing cot on wage. 3 The repone of unemployment to wage We have een that wage affect hiring and firing deciion and therefore employment. In thi ection we dicu in detail the effect of wage on unemployment. We tart with the cae of youth unemployment. 3.1 Youth unemployment From (10) we have that Y U w j = 1 µ a with j =1,. (3) σ w j σ Now, a i the value of i uch that E[π i \ i ]=0, from(9)wehavethat w j = E[π i\ i ]/ w j E[π i \ i ]/ i which implie that: 0 w 1 = w = h h 1 h 1 0 µ e\ i 0 µ e\ i 0 µ e\ i σ σ a σ σ a > 0 (4) 0. (5) Thereforewehavethat Y U w 1 > 0, Y U w 0 and that Y U w 1 Y U w.aexpected higher wage for the young make the firm hire le youth. Alo, when econd period wage increae, the firm alo refrain from hiring young worker 0 Note that E[π i \ i ]/ 0 =0. 13

16 today, ince it anticipate that their future value will decreae. However, alo a expected, the effect of current wage on current employment i higher than the effect of future wage on current employment. Indeed when w increae a firm can react in two way. It can either hire le and/or fire more youth. When the Pr[fire\ i = ] = 0 µ e\ =0the firm will not fire and i = will only react uing the hiring margin. In thi cae the effect of w on youth unemployment i maximum and identical to the effect of w 1 on YU.Onthe contrary, when the Pr[fire\ i = ] = 0 µ e\ =1the firm will only i = react by firing youth, and will not change it hiring policy. In thi cae Y U/ w =0. Intheintermediatecae,i.e.when0 < Pr[fire\ i = ] < 1, the firm will ue both margin and therefore Y U w 1 > Y U w. Note that, ince 0 µ e\ increae with 0, we have that when firing cot are high the firm will ue le the firing margin. Therefore the repone of youth unemployment to future wage will be higher when firing cot are high. 3. Old age unemployment We now dicu the effect of wage on old age unemployment. We tart by analyzing the effect of w 1. Note that, due to the analytical complexity of our model, we decided in ome cae to perform numerical imulation. In Appendix A.11.1 the reader can find ome of the imulation performed The effect of w 1 on old age unemployment In our model there are two type of old age unemployed. See (13). Thoe worker who were never hired, and that from now on we will call long-term unemployed (LTU), and thoe worker that worked when young but got fired, and were not able to find a new job. We tart by analyzing the cae of longterm unemployment. We have that LTU = YU.Pr[Not hired when old\not hired when young]. (6) We have een that the probability that a worker i not hired when young (YU) increae with w 1. We alo have that the probability of unemployment for an old worker that did not get a job when young decreae with w The Pr[Not hired when old\not hired when young], i given by (14). We have that nh w 1 < 0, µ 00 \ w 1 > 0 and σ 00 \ w 1 > 0. See Appendixe A.8.1-A.8.3. Indeed, when the wage 14

17 Indeed, when the wage of youth are high the tigma of having not been hired when young decreae, and therefore, the probability of employment in old-age of thee worker increae. Therefore the effect of w 1 on long term unemployment i a priori ambiguou, ince it augment youth unemployment, but increae the employment propect in old age of thoe that were unemployed a youth. In the imulation we performed (ee an example in Appendix A.11.1) we found that the firt effect wa alway dominant, and therefore that an increae in w 1 increaed long term unemployment. We now addre the cae of thoe worker that were fired when young and not hired when old, i.e., we want to analyze the effect of w 1 on Pr[Hired when young]pr[fired]pr[not hired when old\fired]. Weawthattheprobability of a youth being hired decreae with w 1. The probability of a worker being firedigivenbyeq. (15). Althoughanincreaeinw 1 doe not affect the firing cutoff, 0, (ee (4)) it doe increae the hiring cutoff,, (ee (4)) o that fewer and better young worker are hired. A they are more productive firm will fire le. Therefore the probability of a worker being fired decreae with w 1. See the imulation reult in Appendix A The probability that a young worker that wa fired doe not get a job when old, Pr[Not hired when old\fired], i given by eq. (16). We found (by imulation) that thi probability decreaed, although only very lightly, with w 1. 3 The rationale for thi i the following. A w 1 increae only the more productive youngter are hired, and the expected productivity of both hired and non-hired worker increae. Therefore, a we have een, le worker will be fired. What happen to the profitability of the one that were fired i a priori ambiguou, but, in the imulation performed, we found that their productivity alo increaed, although not much. Therefore they will be more eaily hired by firm. All thi implie that the probability that an individual work when young of young worker increae fewer young worker are hired. Thi mean that the expected profitability of non-hired worker increae (and therefore nh decreae) and that the mean (µ 00 \ ) and the variance (σ 00 \) of the ditribution of the ignal of old worker that were not hired when young alo increae, implying that the Pr[Not hired when old\not hired when young] alo decreae. Thi in turn implie an increae in the mean (µ e\ ) and a decreae in the variance (σ e\ ) of the ditribution of the average of ignal of the worker that were hired. See Appendix A.8.4. and A Note that we found that µ 00 \ 0, w 1 > 0, σ 00 \ 0, w 1 < 0 and that f w 1 < 0. However, all thee effect are very mall. See the imulation reult in Appendix A

18 and doen t work when old decreae with w 1. Since we have een that LTU increaed with w 1 we have that the total effect of w 1 on old age unemployment i a priori ambiguou. However, in the imulation we performed (ee an example in Appendix A.11.1) we found that the effect on long-term unemployment dominated, o that old age unemployment increae with w The effect of w on old age unemployment We tart again by analyzing the effect of w on LTU. We know that YU increae with w. In fact when w increae the firm refrain from hiring youth, which implie that the productivity of non-hired worker increae. However, it increae le than w and therefore the expected profitability of an old worker that wa not hired when young decreae. See (11). Thi in turn implie that the probability that a worker that wa not hired when young i again not hired when old increae with w. See (14) and Appendix A Since YU alo increae we have that LTU unambiguouly increae with w. We alo have that a w increae firm will tend to fire more. See (15) and Appendix A Indeed from (4) we have that the firing cutoff, 0, increae with w. 5 Alo the probability of unemployment for an old worker that wa fired, Pr[Not hired when old\fired], increaewithw. See (16) and Appendix A In fact a w increae the productivity of hired youth increae, and even thoe that are fired are more productive. However, a w increae more than the expected productivity, we obtain a decreae in the expected profitability of an old worker that wa fired, o that the Pr[Not hired when old\fired] increae with w. 6 4 Note that when the expected profitability of an old worker that wa not hired when young decreae we obtain an increae in nh. See Appendix A.8.1. Alo, a we have now more productive worker among the one that were not hired when young, we obtain an increae in the mean (µ \) and the variance (σ \) of the ditribution of ignal of old worker that were not hired when young. See Appendixe A.8. and A.8.3. However, the global effect (obtained by imulation) i uch that the probability that a worker that wa not hired when young i again not hired when old increae with w. 5 Note however that, a with a higher w le and better youth are hired, we oberve an increae in the mean (µ e\ ) and a decreae in the variance (σ e\ ) of the ditribution of the average of ignal of worker that were hired. See Appendix A.8.4. and A.8.5. However, the total effect (obtained by imulation) of w on the probability of a worker being fired i poitive. 6 Note that f increae and we alo oberve increae in the mean (µ 00 \,) andinthe 0 16

19 We have een that the probability of a worker being fired and the Pr[Not hired when old\fired] increae with w. But, a the probability of a worker being hired when young decreae with w the global effect on the Pr[Hired when young]pr[fired]pr[not hired when old\fired] i a priori uncertain. However, in the imulation performed (ee an example in Appendix A.11.1) we alway got a poitive effect of w on the probability of unemployment of old worker that were hired a youth and fired. A LT U alo increae with w we can conclude that old age unemployment increae with w. In hort, an increae in w decreae the employment propect of both dimied worker, and worker that were not hired when young, implying alo that firm will fire more. In fact, facing higher labour cot for enior worker, firm will want to reduce the amount of enior employment. They do o by imultaneouly hiring le old-age individual and firing more youth. Therefore, old age unemployment increae with w. 4 Theeffect of firing cot on unemployment and wage In thi ection we analyze the effect of firing cot on wage and unemployment. We tart with youth unemployment. Again, due to the complexity of the model, ome reult were obtained by imulation. In Appendix A.11. and A.11.3 the reader can find ome of the imulation performed. 4.1 Youth unemployment Youth unemployment i affected by firing cot in two different way. Both directly and, ince wage alo react to firing cot, through wage. Therefore, incewehavethatyu(w 1(f),w (f),f) we can write: dy U df = Y U f + Y U dw 1 w 1 df + Y U dw w df (7) where the firt term on the RHS of(7), Y U/ f, correpond to the effect of firing cot on youth unemployment at given wage, and where the two variance (σ 00 \0) of the ditribution of ignal of old worker that were fired. (Remark that thee reult were obtained by imulation). However, the total effect (obtained by imulation) wa that the Pr[Not hired when old\fired] increae with w. 17

20 other term correpond to the effect of firing cot on youth unemployment through wage The effect of firing cot on youth unemployment at given wage Uing (10) we have that Y U f = 1 µ a σ σ f = 1 µ a σ σ σ σ a 0 µ e\ h 0 µ e\ i > 0. (8) Therefore, in the abence of union, or if union did not react trategically to firing cot, an increae in firing cot would unambiguouly imply an increae in youth unemployment. Indeed, at given wage, if firing become more cotly, firm, anticipating higher cot in the future if a youth turn to out to be le productive than expected and hould be fired, will refrain from hiring youth today. Thi i eentially an option value effect 7. However, when union et wage trategically, the final outcome depend alo on union behavior toward firing cot and on the repone of firm to wage. In the previou ection we have analyzed the repone of unemployment to wage: Y U/ w 1 > 0 and Y U/ w 0 are given by (3)-(5). We mut now analyze how wage react to firing cot The effect of firing cot on wage In Appendix A.9 the reader can find the expreion for dw 1 /df and dw /df. Since thee expreion are very complex we decided to obtain by imulation the effect of firing cot on wage. (See an example in Appendix A.11.3). In the imulation performed we found that w 1 decreaed with firing cot while w increaed. The rationale for thi i the following. We have een that when firing cot increae, at given wage, firm will tend to employ le youth. Anticipating thi behavior, the union will repond by decreaing w 1 in order to boot youth employment. In the econd period, on the contrary, higher firing cot give the union more power. Indeed, knowing that firm will be 7 Note that thi effect wa already obtained by Canziani and Petrongolo (001). 18

21 le likely to cut their labour force when firing cot are high, the union will increae econd period wage The total effect of firing cot on youth unemployment The global effect of firing cot on youth unemployment i therefore a priori ambiguou. See (7). Indeed at given wage firing cot increae youth unemployment. Alo the anticipated increae in w will make firmhireleyouth. However, thee effect may be compenated by the fall in w 1. Subtituting (3)-(5) and (8) in (7) it i eay to ee that youth unemployment will decreae with firing cot if the repone of w 1 to firingcotiufficiently trong, i.e. if 0 µ e\ h 1 0 µ e\ i dw /df < dw 1 /df. Other- + wie youth unemployment will increae with firing cot. In the imulation performed we alway obtained an increae in youth unemployment. See an example in Appendix A Thi mean that, although union reduce the wage of youth when firing cot increae, thi cut i not ufficiently trong to imply a decreae in youth unemployment. 4. Old-age unemployment In thi ection we dicu the effect of firing cot on old age unemployment. Since firing cot affect old age unemployment both directly and trough their effect on wage we have that OU(w 1(f),w (f),f). Thereforewecanwrite: dou df = OU f + OU dw 1 w 1 df + OU dw w df (9) where the firt term on the RHS of(9), OU/ f, correpond to the effect of firing cot on old age unemployment at given wage, and where the two other term correpond to the effect of firing cot on old age unemployment through wage The effect of firing cot on old age unemployment at given wage We tart by dicuing the effect of firing cot on old age unemployment at given wage. A before, and again due to the complexity of our model, to get ome reult we relied on imulation. We tart with the effect of firing cot on long term unemployment. See (6). We have een that, at given wage, 19

22 youth unemployment increae with firing cot. Alo, at given wage, the probability of unemployment for an old worker that did not get a job when young decreae with firing cot. 8 In fact, when firing cot are high fewer youngter are hired. Therefore remaining joble i not perceived by potential employer a a ignal of low productivity. In hort, higher firing cot decreae the tigma of having not been hired and increae the employment propect of worker who were unemployed when young. 9 But, ince youth unemployment increae with firing cot at given wage, the effect of firing cot on LTU i a priori ambiguou. In the imulation performed (ee an example in Appendix A.11.) the effect on youth unemployment dominated, and therefore we found that, at given wage, LTU increaed with firing cot. We analyze now the cae of an individual that worked when young, wa fired, and did not obtain a job in old age, i.e. we analyze now the effect of firing cot on Pr[Hired when young]pr[fired]pr[not hired when old\fired] at given wage. The probability of an youth being hired decreae with firing cot at given wage. The ame happen, at given wage, with the probability of an employed individual being fired. See Appendix A.11.. Indeed, at given wage, when firing cot increae not only the firing threhold, 0, decreae (ee (4)), but we alo oberve an increae in the hiring threhold,. See (8). Therefore, a only more productive worker are hired and firing i more cotly, firm will tend to fire le. When fewer worker are fired, having been fired i een by potential employer a a ure ign of very low productivity. Therefore the employment propect of dimied worker decreae with firing cot at given wage. 30 In other word, at given wage, higher firing cot increae the tigma of having been fired and reduce the re-employment probability of dimied worker The probability of unemployment for an old worker that did not get a job when young i given by (14). At given wage, ince firmhireleyouthwhenfiring cot increae, the expected profitability of non-hired worker increae with firing cot. Therefore, at given wage, nh decreae, and the mean (µ 00 \) and the variance (σ 00 \) of the ditribution of µ the ignal of old worker that were not hired when young increae, o that nh µ 00 \ σ 00 \ decreae. See Appendix A The ame reult wa obtained by Canziani and Petrongolo (001). 30 Indeed, at given wage, the expected profitability of an individual that wa fired decreae with firing cot. (See (1)). Therefore f increae, and the mean (µ 00 \,) 0 and the variance (σ 00 \ ) of the ditribution of ignal of old worker that were fired 0 decreae. See Appendix A On thi iue ee alo Canziani and Petrongolo (001). 0

23 However, in the imulation we performed (ee again an example in Appendix A.11.) thi lat effect wa not ufficiently trong to offet the effect of firing cot on the probability of an individual being hired when young and fired. Therefore we conclude that, at given wage, firing cot decreae the probability of an individual being employed when young and unemployed in old age. A, at given wage, firing cot increae LTU, the effect on old age unemployment are a priori ambiguou. Neverthele we found by imulation (ee an example in Appendix A.11.) that thi lat effect dominated the effect on LTU o that, at given wage, old age unemployment decreaed with firing cot, i.e. OU/ f < The total effect of firing cot on old age unemployment 3 A union behave trategically, to obtain the global effect of firing cot on old age unemployment we need to conider alo the effect of firing cot on old-age unemployment through wage. See (9). We have een in ection 4.1. that dw 1 /df < 0 and dw /df > 0. We alo have etablihed in ection 3. that OU/ w 1 > 0 and OU/ w > 0. Therefore, the econd term in the RHS of expreion (9) i negative, while the third term i poitive, i.e., firing cot increae old-age unemployment through their effect in w, but reduce old-age unemployment through w 1. In the imulation performed (ee an example in Appendix A.11.3) we found that the poitive effect of firing cot on old-age unemployment via w dominated the other two, o that,once we take into account wage behavior,firing cot increae old age unemployment. The total effect of firing cot on long-term unemployment i alo poitive. (See the imulation reult in Appendix A.11.3). Indeed, when we take the wage effect into account, YU till increae with firing cot (ee ection 4.1.3) and the probability of unemployment for an old worker that did not get a job when young alo increae with firing cot, o that LTU increae unambiguouly. In fact, although at given wage, higher firing cot decreae the tigma of having not been hired, both the decreae in w 1 and the increae in w imply an increae in the probability of unemployment for thoe old worker that were not hired when young 33 and thee effect dominate. 3 Note that all the reult in thi ection were obtained uing imulation. See Appendix A µ µ 33 Note that nh µ 00 \ σ / w 00 1 < 0 and nh µ 00 \ \ σ / w 00 > 0. See ection 3.. \ 1

24 The probability of an worker having a job when young, being fired and failing to obtain a job in old age, till decreae with firing cot when we take the wage effect into account. In fact, the probability of a worker being fired, taking into account the reaction of wage to firing cot, till decreae with firing cot although thi probability increae both through w 1 and w with firing cot. 34 We alo found that the re-employment probability of dimied worker till decreae with firing cot, when we conider the effect through wage. Indeed, the effect of firing cot on thi probability through w 1 and w are both negative 35 o that the total effect of firing cot on the re-employment probability of dimied worker i till negative. A the employment probability of young worker decreae with firing cot (ee ection 4.1) the total effect on the Pr[Hired when young]pr[fired]pr[not hired when old\fired] i a priori ambiguou. Neverthele, a tated before, in the imulation performed taking alo into account the effect through wage, we alway found a negative effect of firing cot on the Pr[Hired when young]pr[fired]pr[not hired when old\fired]. See an example in Appendix A However, firing cot, a we have een, increae LTU and thi effect dominate, o that old-age unemployment, when we conider alo the effect though wage, increae with firing cot. See again Appendix A Empirical evidence and further dicuion on the effect of firing cot on unemployment and wage According to the model preented above, both at given wage and when we take the wage effect into account, firing cot increae youth unemployment. Moreover, firing cot not only reduce the hiring of young job eeker, but they alo reduce the firing of employed youth, i.e., firing cot reduce the flow of youth into and out of employment. Therefore, our reult on the effect of firing cot on youth hiring and firing are conitent with the finding of Bentolila and Bertola (1990). Let u now invetigate whether the prediction of our model receive empirical upport. The fact that firing cot reduce flow into unemployment i a well documented fact. For example the OECD 1999 Employment Outlook, uing cro-country data, conclude that tricter employment protec- 34 Note that 0 µ e\ / w 1 < 0 and 35 Note that f µ 00 \ 0, σ 00 \ 0, / w 1 < 0 and 0 µ e\ / w > 0. See ection 3.. f µ 00 \ 0, σ / w 00 \ 0 > 0. See ection 3..,

25 tion i aociated with lower flow into unemployment. 36 Turning now to the hiring of youth we found that firing cot reduce the hiring of youth, depite the decreae in the wage of young worker induced by higher firing cot. Previou empirical work eem to upport thi outcome. Scarpetta (1996) conclude that youth unemployment i adverely affected by tricter employment protection legilation, particularly in the preence of wage compreion. Thi i a very intereting finding, which i in accordance with our model. Indeed, if exiting legal or other intitutional arrangement prevent wage adjutment, according to our model youth unemployment would be more everely affected by firing cot. 37 Alo, the OECD 1999 Employment Outlook, find a poitive bivariate aociation between tricter employment protection legilation and higher youth unemployment that i alo (weakly) confirmed when multivariate regreion technique are ued. Turning now to old-age worker our model predict, both at given wage and alo when the wage effect i conidered, that firing cot reduce the reemployment propect of dimied worker. Thi i the tigma effect of dimial on the future career, that i exacerbated when firing cot are high ince, in thi cae, only the le able are fired. Notice that Canziano and Petrongolo (001) found, uing microeconomic data for Spain, that indeed worker who lot their job through cotly firing procedure have wore reemployment propect. Alo, according to our model, although at given wage firing cot increae the employment propect of old worker that were not hired a youth, the oppoitehappenoncewetakeintoaccountthewageeffect. Indeed, the tigma aociated with having not had a job decreae with firing cot. However, a the wage of enior work increae with firing cot, firm hire le enior worker and thi lat effect dominate. Therefore, the employment propect of worker that were unemployed a youth decreae with firing cot. Note that thi reult i confirmed by the finding that tricter employment protection lengthen the time pent unemployed. Indeed, the OECD 36 Note that thi concluion i obtained both by examining the imple aociation between everal employment protection legilation indicator and meaure of labour market dynamic, and alo when multivariate regreion technique are ued to control for other factor that might influence the reult. 37 Note that, in ome countrie, the exitence of a minimum wage, that we know to be particularly binding in the cae of youth, may prevent the type of wage adjutment for youth conidered in thi paper, neutralizing therefore the poitive wage effect of firing cot on youth unemployment. See alo on thi iue Bertola and Rogeron (1997). 3

26 1999 Employment Outlook report that mean unemployment duration are higher in countrie with tricter employment protection. Our model prediction that firing cot, both at given wage and conidering the wage effect, increae long term unemployment i alo confirmed empirically. The OECD 1999 Employment Outlook how that the hare of the unemployed who have been joble for at leat a year, i.e. long term unemployment, i higher in countrie with tricter employment protection, and Machin and Manning (1999) find that long term unemployment tend to be higher in countrie with higher firing cot. The OECD 1993 Employment Outlook alo find that job ecurity i aociated with higher long term unemployment rate, and that in ome countrie (notably in Southern Europe and Ireland) job ecurity account for more than half of the long term unemployment rate. In what concern the effect of firing cot on wage empirical evidence i more difficult to find. Depite the widepread notion that, due to inider effect, wage will be higher in the preence of firing cot, 38 Bertola (1990) doe not find that wage are higher in high-job ecurity countrie. However, both the OECD 1993 Employment Outlook, uing data for 0 countrie between 1970 and 1991, and Layard et al. (1991), uing data for Britain, find that wage increae much fater when long term unemployment i important. Combining thi finding with the exitence of a poitive relation between firing cot and long term unemployment, we obtain a poitive aociation between firing cot and wage, in accordance with the view that higher firing cot increae the bargaining power of worker. Moreover, Elmekov et al (1998) find, uing data for 0 OECD countrie between 1983 and 1995, that different collective wage bargaining arrangement influence ignificantly the way in which employment protection legilation affect unemployment. They how that the poitive impact of employment protection legilation on unemployment i tronger and tatitically ignificant in countrie where inider have trong bargaining power in wage determination, while employment protection legilation doe not affect o ignificantly employment in countrie with either a decentralized or highly coordinated (among employer and trade union) wage bargaining ytem. Thi finding upport our claim that wage etting influence ignificantly the way firing cot affect unemployment, and confirm our model prediction in what concern the effect of firing cot on 38 Note that thi view i in accordance with our finding that, a with higher firing cot incumbent worker are more protected, union will puh up the wage for old worker. 4