(Un)Employment Dynamics: The Case of Monetary Policy Shocks

Transcription

1 (Un)Employmen Dynamics: The Case of Moneary Policy Shocks Helge Braun Norhwesern Universiy November 17 h, 25 Job Marke Paper Absrac This paper esimaes an ideni ed VAR on US daa o gauge he dynamic response of he job nding rae, he worker separaion rae, and vacancies o moneary policy shocks. I develop a general equilibrium model ha can accoun for he large and persisen responses of vacancies, he job nding rae, he smaller bu disinc response of he separaion rae, and he inerial response of in aion. The model incorporaes labor marke fricions, capial accumulaion, and nominal price rigidiies. Special aenion is paid o he role of di eren propagaion mechanisms and he impac of search fricions on marginal coss. Esimaes of seleced parameers of he model show ha wage rigidiy, moderae recruiing coss, and a high value of he opporuniy coss of employmen are imporan in explaining he dynamic response of he economy. The analysis exends o a broader se of aggregae shocks and can be used o undersand and design moneary, labor marke, and oher policies in he presence of labor marke fricions. 1 Inroducion Empirical research shows ha a key o undersanding business cycle ucuaions lies in labor marke fricions (Hall (1997), Galí, Gerler, and Lopez-Salido (22), Chrisiano, Eichenbaum, and Evans (25)). Knowledge of he exac naure of hese fricions is necessary o design, for example, labor marke and moneary policies (Levin, Onaski, Williams, and Williams (25)). Candidae labor marke fricions are conracual fricions and he ime and resource coss associaed wih searching for suiable employmen relaionships. Alhough he inegraion of search fricions held promise for he performance of business cycle models (Merz (1995), Andolfao (1996)), he abiliy of he canonical Morensen and Pissarides (1994) model o accoun for he srong cyclicaliy and persisence of vacancies, unemploymen, and worker ows ino and ou of unemploymen has recenly been quesioned (Shimer (25a), Pries (24), Fujia (24)). I develop and esimae a dynamic sochasic general equilibrium (DSGE) model ha incorporaes search fricions and wage rigidiy. The model is consisen wih he magniude and persisence of he responses of key macroeconomic variables, including in aion, vacancies, and he in ows and ou ows of unemploymen, o a moneary policy shock. I use he model o assess he conribuion of propagaion mechanisms ha are able o reconcile he Morensen and Pissarides (1994) (MP) model wih he daa. I analyze he role of search fricions and wage rigidiy in explaining he inerial response of in aion. I am graeful o Dale Morensen, Larry Chrisiano, Éva Nagypál, Riccardo DiCecio, Reinou De Bock, Giorgio Primiceri, Marin Eichenbaum, Peer Funk, Winfried Koeniger, Kripa Freias, Ambarish Chandra, and Kaspar Hennig. I would also like o hank seminar paricipans a Norhwesern Universiy and he S. Louis Fed and he research deparmen of he S. Louis Fed for is hospialiy and suppor. Conac: h-braun@norhwesern.edu 1

2 I nd ha he mechanisms which are consisen wih he ampliude and persisence of he responses of vacancies, unemploymen, he job nding rae, he separaion rae, and he inerial response of in aion are (i) wage rigidiy, (ii) large xed opporuniy coss of employmen relaionships, (iii) moderae recruiing coss, and (iv) adjusmen coss in vacancy creaion. The analysis is relevan no jus for moneary policy shocks, because unemploymen, vacancies, and he job nding and separaion rae respond similarly o oher aggregae shocks (Fujia (24), Fujia and Ramey (25), Braun, De Bock, and DiCecio (25)). This paper conribues o he recen lieraure on he evaluaion and reconciliaion of he Morensen and Pissarides (1994) model of search fricions and unemploymen wih worker ows and vacancy daa ha he model seeks o explain (see Morensen and Nagypal (25) for a summary). I develop new feaures and inegrae ones already proposed in his lieraure. I formulae wage rigidiy in a racable way ha ness he sandard Nash-Bargaining soluion used in he lieraure. I model vacancy adjusmen coss ha generae persisen, hump-shaped responses of vacancies and he job nding rae. Furhermore I analyze he role of overhead and urnover coss. I include capial accumulaion and model worker separaions ino unemploymen. The bulk of he lieraure has ignored he separaion margin of employmen adjusmen and framed he analysis in parial equilibrium. Even hough he hiring margin is quaniaively more imporan, separaions are no acyclical and clearly reac o moneary policy and oher shocks. The separaion decision is an economic one and should be par of any aemp o model worker ows. I nd ha ignoring he behavior of worker separaions ino unemploymen is no only inconsisen wih he daa bu may lead o erroneous conclusions abou he mechanisms a work. In addiion, explicily modelling capial coss as par of he surplus value of rms and workers clears up some misconcepions abou he role of capial overhead coss. Anoher conribuion of his paper lies in he exension of he analyses of search fricions in New-Keynesian models. 1 Closely relaed is he esimaed DSGE model of Trigari (24), who sudies job ows daa. Job ows daa poin o a more volaile separaion margin of employmen adjusmen. 2 Adjusmen on his margin can be relaively cheap and an evaluaion of he role of search fricions based on job ows may lead o di eren conclusions. Insead, I focus on he naure of he propagaion mechanisms ha can accoun for in aion ineria in conjuncion wih he observed responses of worker ows daa and vacancies. Capial and invesmen are included in he analysis because in addiion o recruiing coss, he cosliness of separaions, and he wage capial uilizaion coss are a key deerminan of marginal coss and hence he response of in aion. To esimae parameers of he model and idenify he dynamic response of he economy o a moneary policy shock, I follow he limied informaion sraegy in Chrisiano, Eichenbaum, and Evans (25) (CEE). I idenify moneary policy shocks in a vecor auoregression (VAR) represenaion of poswar US aggregae, worker ow, and vacancy daa. The ideni caion sraegy assumes ha he nominal ineres rae reacs conemporaneously o moneary policy shocks while he variables ordered before he ineres rae do no. The VAR includes oupu, he price level, hours, wages, he nominal ineres rae, invesmen, consumpion, measures of job nding and worker separaion raes consruced by Shimer (25b), and a measure of vacancy posing. The esimaed responses of in aion and oher aggregae variables are consisen wih hose repored in CEE and consisen wih esimaes using alernaive speci caions and idenifying assumpions (Chrisiano, Eichenbaum, and Evans (1999), Uhlig (25)). The esimaed responses of he job nding rae, unemploymen, and vacancies are hump shaped, large, and persisen. The response of he worker separaion rae is disinc bu less persisen, and conribues up o one hird of changes in unemploymen. These resuls are consisen wih 1 See Cooley and Quadrini (1999), Cheron and Lango (2), Krause and Lubik (23), Walsh (25), Trigari (24) and Chriso el, Kueser, and Linzer (25), who esimae Trigari (24) s model using a Bayesian approach on German daa. For an analysis in he absence of nominal price sickiness see Nason and Slosve (24). 2 For a comparison of he cyclical properies of job and worker ows daa see Braun, De Bock, and DiCecio (25). The nding ha job desrucion conribues more o employmen changes is no necessarily a odds wih he ndings from worker ow daa, as job desrucion perains o employmen losses a conracing esablishmens and does no imply ha he main margin of adjusmen is an increase in worker separaions. 2

3 he responses o embodied echnology, neural echnology, demand, and moneary shocks ideni ed using sign resricions in Braun, De Bock, and DiCecio (25) and he responses o an aggregae shock esimaed in Fujia (24) and Fujia and Ramey (25). A key feaure of worker ows is he srong cyclicaliy and persisence of he job nding rae of unemployed workers and vacancy posing aciviy by rms. Saed di erenly, aggregae shocks enail large and persisen movemens along he Beveridge curve. The dynamic general equilibrium model used o undersand hese responses incorporaes a fricional labor marke based on Morensen and Pissarides (1994) in a New-Keynesian model along he lines of CEE. Search and maching fricions, endogenous worker separaions, wage and price rigidiies, variable capial uilizaion, and invesmen and vacancy adjusmen coss are key feaures of he model. Moneary policy follows a Taylor rule. I esimae he model parameers ha govern he dynamic response of he economy using a limied informaion minimum disance esimaor. The parameers are chosen such ha he model impulse responses mach he empirical impulse responses as closely as possible, where more weigh is aribued o he responses which are esimaed more precisely. The esimaed model impulse response funcions are able o mach heir empirical counerpars reasonably well. The secoral srucure of he model is similar o Trigari (24). A monopolisically compeiive inermediae good secor wih nominal price rigidiies in is oupu marke uses homogenous goods produced by mached rm-worker pairs ( jobs ) as an inpu. In he job secor, rms pos vacancies in order o hire unemployed workers in a fricional labor marke. The job nding probabiliy of unemployed workers is increasing in he number of vacancies relaive o he size of he pool of unemployed and searching workers. Endogenous worker separaions ino unemploymen are due o idiosyncraic shocks o he mach value. Cosly search and maching creaes a quasi-ren for exising jobs ha can be shared beween rm and worker via a wage paymen. This ren creaes he scope for wage rigidiy ha is consisen wih he paricipaion consrains of rms and workers. Alhough he wage does no have allocaional consequences for exising maches, i deermines he magniude of he response of rms pro s o aggregae shocks and hence vacancy posing and he creaion of employmen relaionships. Hall (25) and Shimer (24) argue ha he MP model s shorcomings in accouning for he large reacion of vacancies and he job nding rae o reasonably sized shocks can be aribued o he sandard assumpion of wage deerminaion via Nash-Bargaining. Along he lines suggesed in Hall (25), I model wage rigidiy in a racable way ha ness he Nash-Bargaining soluion. The esimaed degree of wage rigidiy conribues considerably o he model s abiliy o mach he empirical responses of vacancies and he job nding rae and is consisen wih he weak response of wages. However, high wage rigidiy alone does no su ce o explain he responses of he labor marke variables, including separaions. The opporuniy coss of employmen mus also be high. Wage rigidiy alone may induce an evenual increase of separaions afer an expansionary shock. The reason lies in he paricipaion consrain of he worker. If wage rigidiy is high, rms vacancy posing reacs srongly o shocks. This increases he value of workers ouside job-opporuniies hrough an increase in he job nding rae and may decrease he worker s surplus value of he mach. The e ec can be srong enough o reduce he join coninuaion value of a rm-worker mach and hence increase worker separaions ino unemploymen, which is incompaible wih he daa. The value of he paricipaion consrain of he worker encompasses no only he value of ouside job opporuniies, bu also of he opporuniy coss of employmen for example in he form of unemploymen bene s, he value of home producion, and he disuiliy of work ne of he disuiliy of search. A high value of non-responsive opporuniy coss of employmen implies ha he response of he paricipaion consrain of he worker is relaively small. Then, he counerfacual e ec on separaions ino unemploymen described above is absen. Accordingly, he esimae of he opporuniy coss of employmen is high relaive o sandard calibraions of he MP model. 3

4 Furhermore, any unresponsive cos componens of he mach, such as xed overhead, ring, and raining coss in addiion o he opporuniy coss lised above increase he response of rms surplus value of a lled job and hence of hiring aciviy o aggregae shocks. In he form of workers opporuniy coss, his mechanism is sressed by Hagedorn and Manovskii (25) in a model wihou endogenous separaions. In he form of xed capial coss, i is employed by Morensen and Nagypal (25) and Fujia and Ramey (25). Training coss appear in he hiring adjusmen cos speci caion of Yashiv (25). Anoher shorcoming of he MP model is is inabiliy o explain he persisence of vacancies and he job nding rae. In response o a posiive aggregae shock, he unemploymen pool diminishes quickly as unemployed workers nd jobs. In he sandard calibraions of he MP model, recruiing coss increase and vacancy creaion and hiring aciviy slump. I show ha adjusmen coss in he growh rae of vacancies generae persisen and hump shaped responses of vacancies and he job nding rae. This formulaion can be inerpreed as a reduced form of a ime-o-build model of vacancy creaion as discussed below. Yashiv (25) also assumes adjusmen coss in vacancy creaion and hiring aciviy. Fujia and Ramey (25) make vacancies a sae variable by assuming ha vacancy creaion is associaed wih sunk coss and show ha ogeher wih large xed overhead coss and recurren job loss he persisence of vacancies and he job nding rae increases. In Secion 2, I discuss he consrucion of he separaion and job nding raes and presen he esimaed impulse responses of he VAR o a moneary policy shock. Secion 3 lays ou he model. In Secion 4, I presen he esimaes of parameers of he model ha govern he dynamic responses of he variables of ineres. Secion 5 discusses he resuls and he mechanisms a work. I change parameer values from he poin esimaes o undersand he conribuion of he propagaion channels and conduc a sensiiviy analysis wih respec o he values of calibraed parameers. Secion 6 analyzes he role of overhead and raining coss as sources of ampli caion. Secion 7 exends and esimaes a varian of he model ha incorporaes an inensive margin of hours adjusmen. Secion 8 concludes and suggess avenues for furher research. 2 Srucural VAR Analysis 2.1 Daa The quarerly daa of he VAR analysis includes real GDP (Y ), he GDP de aor (P ), real wages (per capia, w), hours (H), consumpion (C), invesmen (I), he Fed Funds rae (R), a measure of vacancies (v), and job nding (hir) and separaion probabiliies (sep). In Secion 7 I consider an alernaive VAR speci caion by replacing hours wih employmen and average hours (per worker) o analyze he exensive and inensive margin of labor adjusmen. Because he response of average hours is small, he response of oal hours and employmen are similar. The separaion and he job nding rae are obained from Shimer (25b). 3 The separaion rae is consruced from CPS daa on he shor erm unemploymen rae. Using his separaion rae, he job nding rae is consruced from di erences in he unemploymen pool across monhs. Boh are adjused for ime-aggregaion bias. Since hey refer o exi raes from employmen o unemploymen and ou of unemploymen, ows beween non-paricipaion and he labor force are ignored. In paricular, assume ha here are only worker ows beween unemploymen (U) and employmen (E). Assume ha he separaion and job nding raes are consan wihin a ime period ; +1. Denoe hese Poisson arrival raes by fsep and f hir respecively. Consider he evoluion of he unemploymen pool a a dae 2 (; 1) 3 For addiional deails, please see Shimer (25b) and his webpage hp://home.uchicago.edu/~shimer/daa/ ows/. For he approach, see also Darby, Haliwanger, and Plan (1985). 4

5 beween periods and + 1 U + = fsep E + {z } INFLOW S fhir U + {z } ; (1) OUTFLOW S where X + denoes he ime derivaive. The CPS conains daa on he shor-erm unemploymen of less han 5 weeks, U s. Wihin a period, he pool of shor-erm unemploymen evolves according o s U + = fsepe + hir f U+ s ; (2) where U s + measures he pool of workers who have become unemployed since he beginning of period. Combining (1) and (2), and solving he resuling di erenial equaion using U s = yields U +1 = U e g hir + U s +1 (3) Given daa on U ; U +1, and U s +1, (3) can be used o consruc he job- nding rae f hir. The separaion rae hen follows from U +1 = (1 e g hir gsep ) fsep fhir + fsep L + e g hir gsep U ; (4) where L U + E is he labor force. Given he job nding rae f hir, and labor force daa L and U, equaion (4) uniquely de nes he separaion rae fsep. Noe ha he raes fsep and f hir are ime-aggregaion adjused versions of U s +1 E +1 and U U+1+U s +1 U +1 respecively. The consrucion of fsep and f hir akes ino accoun ha workers may experience muliple ransiions beween daes and + 1. The corresponding probabiliies used in he VAR are sep = 1 e gsep and hir = 1 e g hir. These correspond o he separaion and job nding raes in he discree-ime model formulaed in Secion 3. Using a sample overlapping wih BLS daa consruced by Bleakley, Ferris, and Fuhrer (1999) ha includes ows for he non-paricipaion sae, Shimer (25b) shows ha movemens in he separaion and job nding raes accoun for he bulk of unemploymen and o a lesser exen employmen changes. For a furher discussion of he consrucion, business cycle properies, sensiiviy o adjusmens necessiaed by he 1994 CPS redesign, and a comparison o job ows daa see Braun, De Bock, and DiCecio (25). Figures 1 and 2 from Braun, De Bock, and DiCecio (25) show he cyclical and rend behavior of he series, lered using an HP ler wih smoohing parameer 16. Shaded areas denoe NBER recession daes. Boh job nding and separaion probabiliies show a srong cyclicaliy. Spikes in he separaion rae are disinc during recessions, alhough heir magniude has decreased in he pas wo recessions. For he VAR, I use quarerly averages of he monhly daa. Vacancies are measured using he Conference Board Help Waned Index, scaled by he labor force. 4 he vacancy series. Figure 3 shows he business cycle and rend behavior of The sample used in he VAR covers he period 1954:Q3-23:Q4. All variables in he VAR excep for he Fed Funds rae have been logged. Deails of he remaining daa sources can be found in appendix A. 2.2 VAR Represenaion Consider he following reduced form VAR: 4 Scaling by working age populaion did no lead o signi can di erences. Y = + P p j=1 A jy j + u ; Eu u = V; (5) 5

6 A. Job Finding Probabiliy and Trend Q1 51Q3 53Q1 56Q3 58Q1 61Q3 63Q1 66Q3 68Q1 71Q3 73Q1 76Q3 78Q1 81Q3 83Q1 86Q3 88Q1 91Q3 93Q1 96Q3 98Q1 1Q3 3 B. Business Cycle Componen Job Finding Probabiliy Q1 51Q3 53Q1 56Q3 58Q1 61Q3 63Q1 66Q3 68Q1 71Q3 73Q1 76Q3 78Q1 81Q3 83Q1 86Q3 88Q1 91Q3 93Q1 96Q3 98Q1 1Q3 3 Figure 1: Job Finding Probabiliy A. Separaion Probabiliy and Trend.25 Q1 51Q3 53Q1 56Q3 58Q1 61Q3 63Q1 66Q3 68Q1 71Q3 73Q1 76Q3 78Q1 81Q3 83Q1 86Q3 88Q1 91Q3 93Q1 96Q3 98Q1 1Q B. Business Cycle Componen Separaion Probabiliy Q1 51Q3 53Q1 56Q3 58Q1 61Q3 63Q1 66Q3 68Q1 71Q3 73Q1 76Q3 78Q1 81Q3 83Q1 86Q3 88Q1 91Q3 93Q1 96Q3 98Q1 1Q3 3 Figure 2: Separaion Probabiliy 6

7 A. Vacancies Probabiliy and Trend Q1 51Q3 53Q1 56Q3 58Q1 61Q3 63Q1 66Q3 68Q1 71Q3 73Q1 76Q3 78Q1 81Q3 83Q1 86Q3 88Q1 91Q3 93Q1 96Q3 98Q1 1Q B. Business Cycle Componen Vacancies Q1 51Q3 53Q1 56Q3 58Q1 61Q3 63Q1 66Q3 68Q1 71Q3 73Q1 76Q3 78Q1 81Q3 83Q1 86Q3 88Q1 91Q3 93Q1 96Q3 98Q1 1Q3 3 Figure 3: Vacancies where p is he number of lags. In he analysis ha follows Y is de ned as: Y = " ln (Y ) ; ln (P ) ; ln (w ) ; ln (H ) ; ln (hir ) ln (sep ) ; ln (v ) ; ln (C ) ; ln (I ) ; R # : I esimae he reduced form VAR (5) including p = 3 lags using OLS. 5 The reduced form residuals, u, are relaed o he srucural shocks,, by = A u or equivalenly by u = C, where C = A 1. The srucural shocks are orhogonal o each oher, i.e., E = I. The las elemen of " is he moneary policy shock; The remaining elemens of are no ideni ed. Moneary policy shocks are ideni ed as in CEE by assuming ha he 1 h column of A has he following srucure: A (:; 1) = [ 19 ; a ] : The idenifying assumpion can be inerpreed as he moneary auhoriy following a Taylor rule like policy, which responds o all he variables ordered before he ineres rae in he VAR. The solid lines in Figure 4 display he impulse response funcions (IRFs) of oupu, in aion, he Fed funds rae, hours, he real wage, he job nding rae, he separaion rae, vacancies, consumpion, and invesmen o a one sandard deviaion moneary policy shock. Excep for he responses of he nominal ineres rae and in aion which are represened in annualized percenage poin deviaions, all variables are expressed in percenage deviaions. The shaded areas are boosrapped 95% con dence inervals around he poin esimaes. The alernaive speci caion of he VAR wihin his ideni caion framework ha imposes coinegraion relaionships beween variables (Alig, Chrisiano, Eichenbaum, and Lindé (25)) did no aler he esimaes of he impulse response funcions considerably. 5 The lag lengh was seleced wih he Akaike Informaion Crierion. 7

8 4 quarers 8 quarers 2 quarers Y oupu 9 (3; 18) 1 (4; 23) 6 (3; 18) in aion 3 (1; 11) 3 (1; 1) 4 (2; 11) R Fed Funds Rae 2 (11; 25) 13 (8; 19) 12 (7; 18) H hours 8 (3; 18) 15 (6; 3) 12 (5; 25) w wage 1 (:5; 2) 1 (:3; 2) 1 (:9; 2) hir job nding 5 (1; 11) 11 (4; 22) 9 (4; 19) sep separaions 7 (3; 16) 9 (4; 16) 6 (3; 13) v vacancies 1 (4; 2) 14 (6; 27) 11 (5; 22) C consumpion 1 (:2; 2) 2 (:3; 5) 2 (:5; 8) I invesmen 11 (5; 21) 12 (5; 24) 1 (5; 2) Table 1: Percenage of Variance of he Forecas Error due o Moneary Policy Shocks (95 percen boosrapped con dence inerval boundaries in parenheses) The las panel shows he response of unemploymen and he conribuions of he separaion and job nding probabiliies o unemploymen. Unemploymen is approximaed using he seady sae relaionship u +1 = gsep gsep + hir g. The approximaion is very accurae for he aggregae daa (Shimer (25b)). The conribuions of in ows and ou ows are calculaed using means. gsep gsep +hir and sep sep+ g hir respecively, where hir and sep are sample In response o an expansionary moneary policy shock, he fall in he ineres rae leads o a persisen, hump shaped increase in oupu, reaching a peak afer abou 5 quarers. In aion iniially falls before increasing slighly (he price puzzle ). The Fed Funds Rae reurns o is seady sae level afer abou 1 quarers. Similarly o oupu, hours respond in a hump-shaped manner, bu show slighly more persisence. There is no clear response of he real wage. The job nding rae and vacancies exhibi srong hump shaped responses, while he separaion rae s response is U-shaped and less persisen. Noice ha he larges e ec is reached earlier for he separaion rae han for he job nding rae. In he early phase following he shock, separaions conribue abou one hird o he change in unemploymen. This is in line wih he ndings in Braun, De Bock, and DiCecio (25) who idenify a broader se of shocks using sign resricions. The shape and magniude of he responses of oupu, in aion, he Fed Funds rae, hours, consumpion, and invesmen are consisen wih hose esimaed in CEE. Table 1 presens he percenage variance of he k-sep ahead forecas errors due o moneary policy shocks. As discussed in CEE, hese esimaes are imprecise, sensiive o he VAR speci caion and should hence be inerpreed wih cauion. Neverheless, moneary policy shocks conribue a non-rivial fracion o he variance of he variables of ineres. The volailiy of he job nding rae has increased relaive o he separaion rae (Shimer (25b)). This may be conneced o he pas wo jobless recoveries. (Schref and Singh (23), Groshen and Poer (23)). Furhermore, moneary policy or is ransmission may have changed in he pos Volcker period (Boivin and Giannoni (22)). Overall, volailiy of aggregae real variables has decreased since he early 198 s (Kim and Nelson (1999), Sock and Wason (22)). I esimaed a VAR on he pos 198:I sample: The magniude of he moneary policy shock and he persisence of is e ecs are somewha smaller and he price puzzle is absen. The fall in he separaion rae is smaller relaive o he increase in he job nding rae, bu remains disincly negaive. 8

9 Oupu 1 2 Hours 1 2 Separaion Invesmen Inflaion 1 2 Wage 1 2 Vacancies 1 2 Unemploymen Fed Funds 1 2 Job Finding 1 2 Consumpion 1 2 unemploymen job finding separaions Figure 4: IRFs o a Moneary policy shock (in % deviaions, annualized for in aion and he Fed Funds Rae). Dashed lines are model IRFs (see below). The las panel shows conribuions of changes in he job nding and he separaion rae o unemploymen changes. 3 The Model This Secion develops he general equilibrium model. Consumpion and invesmen goods are produced in a compeiive nal good secor using di ereniaed inermediae goods supplied by a monopolisically compeiive secor ( Inermediae Goods Secor ). The laer in urn uses goods produced by jobs as an inpu. Jobs combine capial services and labor o produce a homogenous good, sold in a compeiive marke. In he job secor, workers and rms mee in a fricional labor marke. Households supply labor, accumulae capial and ren capial services o jobs. Pro s of rms are rebaed o households. Unemploymen risk is diversi ed among families (Andolfao (1996) and Merz (1995)). Figure 5 summarizes he secoral srucure of he economy. Insead of modelling search fricions and nominal price rigidiies in separae secors, one could assume ha here are quadraic price adjusmen coss in conjuncion wih search fricions in he monopolisically compeiive secor (see e.g. Krause and Lubik (23)). The resuls would be equivalen. I use he secoral srucure o make he comparison o he exising lieraure immediae. 9

10 Final Good Secor uses inermediae good in CES Moneary Auhoriy Taylor Rule { P i } i [,1] { Y i } i [,1] Y R Inermediae Good Secor differeniaed good ypes monopolisically compeiive nominal price rigidies P j Y j Job Secor homogenous good use capial & labor search fricions real wage rigidiy Job finding Separaions Capial services Households supply labor & search capial accumulaion capial uilizaion Bond holdings Figure 5: Secoral Srucure of he Model Economy Afer developing he job secor, I describe he inermediae good secor, he nal good secor, households, and he policy of he moneary auhoriy. 3.1 Jobs and he Labor Marke A job is a rm-worker pair. 6 Job oupu is produced according o A k ; where k denoes capial services rened from households a renal rae r k, is he elasiciy of mach oupu wih respec o capial, and A measures aggregae produciviy, idenical across jobs. The goods produced by jobs are sold o inermediae good rms in a compeiive marke a relaive price p j : For exising jobs, he iming is as follows. capial o ren for ha period. A he beginning of he period, he rm decides how much Subsequenly, he worker draws an iid idiosyncraic uiliy cos of working, a F () : 7 The realizaion of his preference shock is observable o he rm. If he realizaion is less han a cerain endogenous hreshold a, mach coninuaion is joinly opimal for he rm-worker pair. Then, wages are deermined via a varian of Nash-Bargaining and producion akes place. If he value of he preference shock exceeds he hreshold, mach coninuaion would be oo cosly due o he paricipaion consrains of rm and worker, he worker separaes and eners he pool of unemployed and searching workers. The probabiliy of endogenous worker separaion is hence 1 F (a ) : The rm chooses he 6 The model absracs from job-o-job ransiions of workers. Hence, job and worker ows are ied. 7 Here I deviae from he muliplicaive produciviy shock speci caion of mos of he lieraure on endogenous job desrucion. In his lieraure, a lognormal disribuion of idiosyncraic mach produciviy shocks is assumed. This assumpion implicily pins down boh he elasiciy of he separaion rae wih respec o changes of he hreshold a which deermines he response of he separaion rae o shocks and he relaion of xed mach componens (such as unemploymen bene s) o average produciviy. Thus, he cosliness of separaions is ied o propagaion on he hiring margin due o xed cos-componens of he mach. A global disribuional assumpion is (i) no necessary for he local analysis underaken here and (ii) makes comparisons o he lieraure on exogenous desrucion di cul. The preference shock speci caion has also been used by Cooley and Quadrini (1999) and Trigari (24) and is similar o an overhead cos shock sepci caion on he rm side. 1

11 hreshold value a a he beginning of he period. As I show below, one can equally hink of a join decision of he rm and worker pair because he rm wans o disconinue he mach if and only if he worker nds separaion opimal. Furhermore, he assumpion ha he capial inensiy and separaion hreshold decisions are made before he realizaion of he idiosyncraic preference shock serves purely o simplify he exposiion. The mach survives ino he nex period wih probabiliy (1 probabiliy. x ), where x is he exogenous separaion Unmached rms ( vacancies ) and unemployed workers mee in a fricional labor marke described by a maching funcion. Firms decide weher or no o pos vacancies a he beginning of he period. If a rm mees a suiable worker, producion can ake place in he following period. Vacancy creaion is subjec o free enry. The vacancy lling probabiliy q and he job nding probabiliy hir depend on he measure of vacancies posed v and he size of he pool of searching (unemployed) workers u : In paricular, he number of maches in period is deermined by a sandard consan reurns o scale maching funcion mv u 1, where m is a maching e ciency parameer and 2 (; 1) : The probabiliy of lling a vacancy in a period sais es and he job nding probabiliy is q = min ( m v u hir = min m (1 ) ; 1) v u ; 1 : Noe ha he vacancy lling probabiliy is decreasing and he job nding probabiliy is increasing in marke ighness v u, re ecing congesion exernaliies on eiher side of he labor marke. The pool of employed workers evolves according o n = 1 1 n 1 + hir 1 u 1 ;, where = 1 (1 x ) F (a ) is he separaion rae. Since worker separaion akes place a he beginning of he period before producion akes place and new maches are formed, he period pool of unemployed workers is u = 1 (1 ) n. We now urn o he hree cenral economic decisions governing: (i) vacancy posing, (ii) separaions, and (iii) wage deerminaion. To spare noaion, I will specify he informaion available when he decisions are made afer laying ou he model. The informaion se is consisen wih he idenifying assumpions of he VAR Value Funcions Denoe he beginning-of-period rm value of being mached o a worker wih J and he worker s value of being mached o a rm wih W : All values are measured in consumpion unis. The relevan sochasic discoun facor for workers and rms (which are owned by households) is +1 = +1 ; where is he marginal uiliy of consumpion in period and < 1: The revenue produc of a mach ne of capial coss is = p j A k r k k: The value of a lled job o a rm before he preference shock is realized sais es he Bellman equaion J = max k Z max w + (1 x ) E +1 J +1 + x E +1 V +1 ; V df (a) ; (6) 11

12 where w is he wage bill. The rm value J is eiher equal o curren pro s w plus he expeced coninuaion value weighed by he relevan discoun facor, or equal o he value of a vacancy V if he laer exceeds he former. The wage bill may in urn depend on he realizaion of he preference shock. Equaion (6) akes ino accoun ha for some (high) realizaions of he preference shock, a separaion of he mach is opimal and he rm is lef wih a vacancy. Noe also ha capial coss are only incurred if he mach nds i opimal o produce. A vacan rm incurs vacancy posing coss of vac per period and is mached o a suiable worker wih probabiliy q. A new mach survives ino he following period wih probabiliy (1 x ), when producion akes place. The value of a vacancy sais es V = vac + q (1 x ) E +1 J +1 + (1 q (1 x )) E +1 V +1. (7) Vacancy posing coss vac will ener he resource consrain of he economy. The worker value of being mached o a rm a he beginning of he period sais es Z W = max w a + (1 where U is he value of being unemployed. x ) E +1 W +1 + x +1 U +1 ; U df (a) ; (8) When unemployed, he worker receives income b, measured in consumpion unis. The value b encompasses unemploymen bene s and home producion and is assumed o be xed ( non-responsive ). 8 Wih probabiliy hir, he unemployed worker is mached o a vacancy a he end of he period and he mach survives ino he following period wih probabiliy (1 x ). The unemploymen value U sais es: U = b + hir (1 x ) E +1 W +1 + (1 hir (1 x )) E +1 U +1. (9) De ne he expeced surplus value of an employed worker as = W Z = max w U. Combining (8) and (9) yields a b hir (1 x ) E (1 x ) E ; df (a). (1) Noe ha he value of coninuing a he curren job in he nex period is equal o he he value of nding a job a anoher rm for he nex period, because preference shocks are iid across maches and ime and here is no heerogeneiy across maches or rms. The iid assumpion is made in he business cycle lieraure wih few excepions (e.g. Hussey (25)) and grealy simpli es he analysis because knowledge of a disribuion of job- or worker - ypes is no necessary. I discuss he drawbacks of his assumpions in he conclusion Vacancy Creaion Vacancy creaion is subjec o free enry, such ha V = for all. Equaion (6) reduces o he vacancy creaion condiion vac q = (1 x ) E +1 J +1. (11) Recall ha he vacancy lling probabiliy q is decreasing in labor marke ighness, i.e., decreasing in he raio of vacancies o unemployed workers. An increase in labor marke ighness makes i harder for rms o nd 8 This assumpion would need o be modi ed if persisen shocks were considered. For example, unemploymen bene s would depend on previous or aggregae wages. 12

13 workers and increases e ecive recruiing coss on he lef hand side of (11). For sandard calibraions of he MP-model, ucuaions of he rm value J are no large enough in response o reasonably sized shocks o accoun for he observed volailiy of labor marke ighness (he Beveridge curve). Mos ampli caion mechanisms model discussed in he lieraure and in developed in his paper serve o direcly increase he variabiliy of J in he vacancy creaion condiion (11). One excepion is De Bock (25) who shows ha capial embodied echnology shocks increases he persisence of vacancies and improves he MP models abiliy o mach he business cycle facs. Anoher are ampli caion and persisence mechanisms inroduced hrough recurren job loss (Pries (24)) and job ladders (Krause and Lubik (24b)) which miigae he decrease in q hrough a delayed decrease in he number of searching workers. Also, mos of he recen lieraure on he evaluaion of he Morensen Pissarides Model does no direcly deal wih he persisence of he response of vacancies and he job nding rae o aggregae shocks. To accoun for he persisen, hump-shaped response of vacancies assume wih v and { >. v vac v = {, (12) v 1 Suppose a small adverising secor of he economy specializes in he provision of recruiing services. Suppose ha due o specializaion i akes ime for his secor o expand is services. We would expec he marginal coss and hence he service price o be decreasing in he resources available in ha secor a a given poin in ime. One can hink of v 1 as a proxy for hese resources. Hence, when v 1 is large, he coss associaed wih a given level of v are small. Vacancy posing coss are increasing in he growh rae of vacancies. A similar assumpion will be made for invesmen adjusmen coss, as in CEE. For invesmen, Lucca (25) shows ha random mauriy imeo-build or ime-o-plan in conjuncion wih imperfec subsiuabiliy beween invesmen projecs leads o a speci caion as in (12). In work in progress, Braun, De Bock, and Lucca (25) ie vacancy creaion and invesmen o explain he persisen and hump-shaped responses of vacancies and invesmen observed in he daa. Noe ha he e ec of vacancy posing on fuure vacancy posing coss is exernal o he vacancy creaion decision (11). The same is rue for he e ec ha curren vacancy posing has on q (he congesion exernaliy). One can formulae a model where rms of non-degenerae size inernalize he e ec of vacancy posing on vac. This does no aler he resuls qualiaively, alhough he esimaed value of v would change Endogenous Worker Separaions When he realized preference shock of exising maches is oo high, coninuaion of he mach is no pro able and worker and rm nd i opimal o separae. Consider he join surplus value of a mach, i.e., he sum of he rm and worker values of being mached, J + W, ne of he ouside opion of he rm and worker, V + U. V and U consiue he paricipaion consrains of he mach. Because V =, he surplus value of a mach is S = J + or using (6) and (1): S = J + Z = max a b (1 x ) hir E (1 x ) E +1 S +1 ; df (a) : (13) 13

14 The rs erm in braces is sricly decreasing in a. Hence, here exiss a hreshold value a, such ha a b (1 x ) hir E (1 x ) E +1 S +1 = : (14) This is he joinly privaely e cien separaion hreshold. Mach coninuaion is opimal i a a. Noe ha he wage paymen is absen from (13). The separaion hreshold is independen of wage ransfers beween rm and worker: I is joinly e cien. The varians of wage deerminaion considered below all saisfy his propery. Hence, he values can be expressed as J = max k;a Z a w + (1 x ) E +1 J +1 df (a) and Z a = w a b + (1 x ) (1 hir ) E df (a), and he joinly e cien separaion requiremen may be saed as argmax a J = argmax a = argmax a S Real Marginal Coss and Propagaion Recall ha job oupu is sold o he inermediae good secor in a compeiive marke a relaive price p j. For he monopolisically compeiive rms in he inermediae secor, p j represens real marginal cos. The response of real marginal coss is in urn he key deerminan of in aion and oupu responses o he moneary policy shock. Condiion (11) sheds ligh on how real marginal coss are relaed o he wage, he renal rae of capial services, and recruiing coss. Subsiuing he rm value (6) ino he vacancy creaion condiion (11) yields vac = max k E 1 q p j+1 A +1 k+1 r k vac +1k +1 w E ; (15) q +1 where w +1 = R a +1 df (a) w +1 F (a is he average wage. Noe ha p ) j+1 is relaed o curren and fuure (expeced) recruiing coss vac q. In paricular, if curren recruiing coss increase, p j+1 increases ceeris paribus. The exen o which p j+1 mus increase in percenage erms in urn depends on he response and level of w +1 : Hence here is a relaionship beween real marginal coss, wages, and vacancy creaion, hrough is posiive e ec of he laer on recruiing coss. Of course his relaionship is confounded by reacions of he ineres rae, he discoun facor, he separaion rae, expeced fuure recruiing coss, and wage deerminaion (see below). The model soluion will be approximaed by linearizing he equilibrium condiions around he non-sochasic seady sae. To gain inuiion for he propagaion mechanisms and deerminans of he dynamics of marginal coss, i is useful o consider he linearized version of (15). Assume ha aggregae echnology A is xed. As shown below, capial choice is joinly e cien also under he deviaion from Nash-Bargaining considered in his paper. Hence +1 = p j+1 Ak+1 r+1k k +1 = (1 ) p 1 1 j+1 rk 1 +1 A 1 1 and E bp j+1 = (1 ) + (1 ) w E b w +1 + E br k +1, w b vac bq (1 ) E b vac +1 bq +1 E " F;a ba +1 + E b +1 (16) where he ime index is dropped o signify seady sae values, bx +1 = x+1 x x, and " F;a = f(a)a F (a) is he seady 14

15 sae elasiciy of he preference shock disribuion wih respec o he separaion hreshold a: Firs, noe ha for w = 1, he marginal cos equaion (16) collapses o one ha holds in an economy wihou search fricions. In ha case, he dynamics of marginal coss are governed by movemens in he wage and he renal rae of capial, as deermined by he capial share. In he presence of search fricions, erms involving curren and fuure recruiing coss, he separaion rae, and he discoun facor also deermine he reacion of marginal coss. Second, a value of w vac close o 1 implies a relaively small e ec of changes of curren recruiing coss q on real marginal coss. Saed di erenly, a given change in p j has a large e ec on recruiing coss. The same would be rue for a shock o aggregae produciviy A. E ecive recruiing coss are in urn an increasing funcion of vacancies for wo reasons: An increase in vacancies decreases he vacancy lling probabiliy q (he v v. congesion exernaliy), and increases vac = { v 1 Hence, vacancies reac srongly o shocks in pj if is close o one. A srong reacion of vacancies in urn implies a large e ec on he job nding rae. This w propagaion channel is sressed by Hagedorn and Manovskii (25) in a model wihou endogenous separaions. The expression 1 w represens ow pro s of he rm relaive o he ne revenue produc of he mach. In equilibrium, pro s compensae he rm for recruiing coss due o he free enry condiion. A small value of 1 w hence implies ha recruiing coss are small. As discussed in Secion 6, capial oulays in he form of xed overhead coss as in Fujia and Ramey (25) induce addiional ampli caion. Fixed capial coss are, however, grossly inconsisen wih he behavior of he capial share in income over he business cycle. A general equilibrium model mus ake ino accoun ha capial oulays are an endogenous variable. Third, noice ha a high elasiciy of he preference shock disribuion wih respec o he hreshold a reduces he response of real marginal coss for a given change in a: The elasiciy governs he cosliness of separaions. If " F;a is large, separaions can be reduced for a small increase in he hreshold a in response o an expansionary shock. Because every increase in a requires compensaion of he worker, a large elasiciy " F;a makes adjusmens on he separaion margin inexpensive for he mach. Finally, noe ha he presence of search fricions does no eliminae he in uence of wages on marginal coss. Of course, movemens in he hreshold ba +1 and he average wage bw +1 in urn depend on he endogenous variables: To pin down hese relaionships we now urn o he deerminaion of wages Wage Deerminaion Wages are ransfers from he rm o he worker. If here is no inensive margin of hours adjusmen, wages do no have allocaional implicaions for he curren rm-worker relaionship as long as hey do no induce ine cien separaions beween rm and worker. As explained above, I require ha wage deerminaion induces separaions ha are joinly privaely e cien. In oher words, separaions do no occur merely because he wage is no renegoiaed when i would be e cien o do so. Wage deerminaion ouside of he mach does have an impac hrough he ouside opion and paricipaion consrain of he worker (U) and he free enry condiion of rms (V = ). Recall ha he job nding rae (hir), he worker surplus value of ouside job opporuniies (), and he join coninuaion value (S) ener he separaion condiion (14). How wages are deermined in oher available jobs in uences he separaion decision, hrough rms vacancy creaion decision, he implied job nding probabiliy, and he worker value of ouside job opporuniies. Assume ha wage paymens are made afer choice of k has been made and afer he preference shock a a. has been realized. Denoe he rm, worker, and join surplus values a a paricular value of a a and a given wage schedule w (a) by (a; w (a)), J (a; w (a)), and S (a; w (a)) respecively. 15

16 We proceed by presening he Nash-Bargaining approach o wage deerminaion, which is sandard in he lieraure. 9 Nash Bargaining Nash-Bargaining wih worker share 2 (; 1) and rm share 1 implies 8a a : (1 ) (w (a) ; a) = J (w (a) ; a) : (17) Using he value expressions (6) and (1) and solving for he wage yields a w nash (a) = (1 ) + b + (1 x ) hir E (18) + (1 x ) E +1 J +1 (1 ) (1 x ) E : Because wages in period + 1 are also deermined via Nash-Bargaining, he di erence beween he las erms in vac q. Hence he average wage (18) is zero. Also hir (1 x ) E +1 = hir 1 (1 x ) E J +1 = hir 1 sais es Z a w nash = a df (a) F (a ) + b + hir 1 vac q +. (19) The worker is compensaed for uiliy coss, he value of non-marke aciviies, he rens she could appropriae hrough ouside job o ers, and obains a share of he mach revenue produc : The separaion condiion (14) becomes a b + 1 hir 1 vac q = : (2) Clearly, Nash-Bargaining sais es he requiremen ha separaions are joinly e cien, because he surplus S is shared: Linearizing (19) around he non-sochasic seady sae and using he expression for marginal coss (he linearized vacancy creaion condiion (16)) and (2) yields where 1 = R a a df (a) b H(a) b bp j+1 br +1 k = (21) b vac bq (1 ) (1 hir) b vac +1 bq b + b + (1 ) hirhir c +1 1 ; (1 ) (1 (1 )(1 hir)) H(a) b governs he response of marginal coss o search fricions, H (a) = F (a) is he runcaed mean of uiliy coss measured in consumpion unis, and = (1 (1 ) (1 hir)). Noe ha ba +1 does no ener (21). The level of wages relaive o revenue which deermines he magniude of he response of marginal coss in (16) is replaced by he level of cos componens of he mach, e b = H(a) + b, in relaion o he revenue. Training and overhead coss considered in Secion 6 ener in a similar fashion. The bargaining share eners (16) direcly only in conjuncion wih he ouside opion value of he worker. A higher increases he e ec of he job nding rae, reduces he magniudes of e ecs of curren and fuure e ecive hiring coss, b vac bq, and he magniude of he e ec of he marginal uiliy of consumpion. However, he bargaining share deermines H(a) +b. A higher worker share increases his raio. 9 Excepions are Delacroix (24) and Hall and Milgrom (25). Also see he discussion in Morensen and Nagypal (25). 16

17 Real Wage Rigidiy The Nash-Bargaining assumpion pins down he ransfer from rm o worker in one paricular way. An alernaive is proposed by Hall (25). Suppose here exiss a social norm wage paymen w s and assume ha whenever possible workers receive he norm wage. Deviaions from w s only ake place if he join surplus value S is non-negaive and w s violaes he paricipaion consrains of rms or workers (and would hence lead o ine cien separaions). Eiher aggregae or idiosyncraic shocks could necessiae such deviaions. 1 Similarly o Hall (25), I re ne his form of wage rigidiy by inroducing a noion of he degree of real wage rigidiy. Assume ha wages are equal o he normed wage w s unless he worker s surplus share induced by his wage becomes eiher oo high or oo low. In ha case, he surplus is divided wih he respecive boundary shares max and min. The degree of wage rigidiy is governed by he exen o which hese boundary shares di er from each oher and could be loosely inerpreed as a reduced form semming from coss associaed wih he bargaining process. Suppose a realizaion ea is associaed wih a wage paymen ew. Denoe he worker value induced by his wage and shock realizaion wih ( ew; ea) and he join surplus value of he mach wih S (ea) : S (ea) does no depend on wages, because he wage schedule sais es he joinly e cien separaion condiion. Inuiively, he wage adjuss in regions close o he paricipaion consrains. The share of he worker surplus in he oal surplus is ( ew;ea) S (ea) : Under Nash bargaining, ( ew;ea) S (ea) is equal o he xed fracion he worker s bargaining share for all realizaions of ea a. In oher words, he wage adjuss o changes in ea or aggregae condiions and ( ew;ea) S (ea) remains consan. Le min and max denoe he minimum and maximum worker shares ha do no lead o a renegoiaion of he wage. Implicily, hese de ne cuo s for he realizaion of he preference shock. In paricular, for realizaions of he preference shock in he range a min ; a max, he normed wage induces a worker share beween min and max ; where he former are de ned by he condiions (ws ;a min ) S(a min ) = max and (ws ;a max ) S(a max ) = min, or w s = 1 min a max + b (1 x ) (1 hir ) E min ( + (1 x ) E J +1 ) (22) and a w s = (1 max min ) + b (1 x ) (1 hir ) E max ( + (1 x ) E J +1 ) ; (23) Now consider a realizaion of he shock ha is smaller han a min. If he worker were paid w s, her share would be less han min. Assume ha in such a case, he wage is rese o a value ha guaranees he share min. For a < a min : w (a) = 1 min a + b (1 x ) (1 hir ) E min ( + (1 x ) E J +1 ) : (24) Expression (24) is equivalen o wage deerminaion via Nash-Bargaining wih worker share min. An analogous expression holds for wage paymens for realizaions of he preference shock above he hreshold a max and below he desrucion hreshold a This is one di erence o he Calvo-Pricing ha will be assumed in he inermediae goods marke. Furhermore, paricipaion consrains are no violaed ex-pos. Noe ha endogenous wage adjusmens ake place in he non-sochasic seady sae due o idiosyncraic shocks. 11 Noe ha he wage schedule is disconinuous a he cuo s a max and a min : 17

18 De ne w = R a df (a) w (a) F (a). For given choices of (k; a), expeced wage paymens w saisfy: Z a min a + (1 max ) Z a + a max w = w s (25) df (a) + b (1 x ) (1 hir ) E max ( + (1 x ) E J +1 ) F (a ) 1 min a + b (1 x ) (1 hir ) E min ( + (1 x df (a) ) E J +1 ) F (a ) where w = F (amax ) F(a min ) F (a ) is he fracion of maches ha does no experience a wage adjusmen in period : We can verify ha he wage schedule given by (25) sais es he condiion of joinly privaely e cien separaions by subsiuing (25) ino he rm value (6): Di ereniaing wih respec o he hreshold yields he separaion condiion (14). How should wage rigidiy be parameerized? Given a disribuion of idiosyncraic preference shocks and given shares max and min, de niions (22) and (23) would pin down seady sae values of he adjusmen hresholds a max and a min. Condiion (25) would hen pin down a value of he norm wage w s consisen wih he disribuional assumpion and a given level of he average wage. I follow a di eren roue here which is feasible because he model soluion is approximaed by a rs order linear approximaion. I allows a parsimonious parameerizaion of wage rigidiy wih a single parameer. More imporanly, changes in he degree of wage rigidiy do no a ec he level of wages. As discussed above, he level of wages is a propagaion mechanism iself and needs o be isolaed from he rigidiy of wages. Insead of specifying a disribuion and he boundary shares, I parameerize wage rigidiy by he fracion of wages adjused in seady sae, w, and assume ha 1. he seady sae social norm wage is equal o he seady sae average wage, w = w s (26) 2. he mass of seady sae adjusmens and he boundary shares are symmeric wih respec o he runcaed preference shock disribuion, where he runcaion poin is he separaion hreshold a: In paricular, assume max + min 2 F (a) F (a max ) F (a) = (27) = F amin F (a) = 1 w ; (28) 2 where is he worker share ha deermines he seady sae division of and J. In Appendix B, I show ha given resricions (26), (27) and (28) he linearized version of he average wage equaion (25) around he seady sae is: bw = w bw s +!! a " F;a ba + (1 w ) bw nash ; (29) w where " a = f(a)a F (a), w = b (1 x ) (1 hir), and bw nash is derived from he linearized version of (18). 12 The dynamics of he real wage are governed by he weighed average of he normed wage and he Nash bargained 12 The erm (1 x ) E +1 J +1 (1 ) (1 x ) E in (18) is no zero here because fuure values are no shared via Nash bargaining. Expression (29) di ers from he one posulaed in Krause and Lubik (23) because i (i) akes ino accoun ha fuure wages are no Nash bargaining wages and (ii) sais es he requiremen of joinly e cien separaions. 18