The Business Cycle with Nominal Contracts and Search Frictions

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1 MPRA Munich Personal RePEc Archive The Business Cycle wih Nominal Conracs and Search Fricions Weh-Sol Moon 10. June 2011 Online a hp://mpra.ub.uni-muenchen.de/57457/ MPRA Paper No , posed 22. July :53 UTC

2 The Business Cycle wih Nominal Conracs and Search Fricions Weh-Sol Moon Absrac I consruc a dynamic sochasic general equilibrium (DSGE model characerized by flexible prices, search fricions, and nominal wage conracs, and examine o wha exen he model can explain he quaniaive business cycle properies of real macroeconomic variables in he U.S. economy. I consider efficien bargaining ha he firm and he worker ener ino bargaining over he fuure nominal hourly wage rae and fuure hours worked under he generalized Nash bargaining framework. The Nash produc is assumed o consis of he discouned presen value of he expeced mach surplus. Under efficien bargaining, he model hardly produces unrealisically high volailiy of real variables or counercyclical produciviy because hours per worker are fixed ahead of ime and employmen is a slow-moving variable wih search fricions. Moreover, efficien bargaining requires firms o rely on job creaion heavily o adjus he wedge beween he marginal produc of labor and he real wage rae in response o shocks. As conrac lengh increases, he volailiies of he unemploymen rae and vacancy rae increase significanly, bu hose of oupu and oal hours worked do no appreciably change. I also invesigae he model under differen assumpions such as he righ-o-manage approach, he Nash produc wih he curren value of mach surplus, and insananeous hiring. Efficien and forward-looking bargaining are imporan in accouning for he U.S. business cycle properies. Keywords: Business Cycles, Search Fricions, Nominal Wage Conracs, Efficien Bargaining JEL Classificaions: E24, E32 I would like o hank he associae edior and wo anonymous referees for heir helpful commens ha grealy improved he paper. I also hank Jang-Ok Cho and Yoonsoo Lee for heir helpful suggesions. All remaining errors are my own. Correspondence: Deparmen of Economics, Seoul Women s Universiy, 621 Hwarangro, Nowon, Seoul, Republic of Korea; moon@swu.ac.kr. 1

3 1 Inroducion This sudy invesigaes a dynamic sochasic general equilibrium (DSGE model ha conains flexible prices, search fricions, and nominal wage conracs (Cho and Cooley Janko (2008 argues ha he equilibrium business cycle model wih wage conracs, which was moivaed by he work of Gary (1976 and Fischer (1977, does no capure he business cycle saisics of he US economy. This argumen considerably limis he heory. Nominal rigidiies improve moneary ransmission and amplificaion mechanisms when nominal wage conracs are incorporaed ino real business cycle models. However, hese models lead o unrealisically high volailiy among real variables and counercyclical produciviy. In his paper, a model economy wih wage conracing is examined o show ha search fricions and efficien bargaining have imporan roles in overcoming model limiaions. I follow he exising assumpion by adhering o he fuure nominal wage rae. However, my approach differs wih regard o he conrac regime. The nominal wage rae in Cho and Cooley (1995 is derived from he decision rule of he model wihou conrac by assuming ha he conrac wage rae is he expeced marke-clearing level of he wage rae. However, I derive he conrac wage counerpar from he soluion o a forward-looking Nash bargaining problem. This componen is imporan in explaining why firms and workers ener ino nominal conracs. In my model, wage conracs are based on bargaining conduced by workers and firms because of he coordinaion failure raised by labor marke fricions. Forward-looking bargaining is also imporan in maching he volailiy of vacancies wih nominal wage conracs and maching he conribuions of inensive and exensive margins of labor hours o oal hours worked. I consider an alernaive bargaining problem o examine he role of forward-looking bargaining. In his problem, he Nash produc consiss of he curren surplus of each pary. Moreover, only currenly employed workers and operaing firms ener ino bargaining. In he curren surplus bargaining model, he bargaining power of a worker varies wih conrac lengh in he seady sae. The seady-sae nominal wage rae decreases and per-period profis increase significanly wih conrac lengh. These feaures are no observed in he forward-looking bargaining model. A subsanial increase in he seady-sae value of per-period profis dampens he volailiies of per-period profis and vacancies. This paper also invesigaes why he incorporaion of nominal wage conracs ino he equilibrium business cycle model does no lead o resuls ha mach US daa. In doing so, he imporance 2

4 of labor marke fricions and efficien bargaining is emphasized. This approach reveals unexamined informaion in lieraure. Under he nominal conracing arrangemens following Cho and Cooley (1995, employees and firms agree on he nominal hourly wage rae in advance. Furhermore, firms are free o choose employmen on he hours margin a he wage rae. This approach is referred o as he righ-o-manage (RTM approach. Under he RTM framework, firms adjus o shocks during he conrac period by choosing hours o equae he marginal produc of labor o he realized real wage. Consequenly, he volailiies of hours worked and oupu are unrealisically high. This issue is raised no only for he flexible price model bu also for he New Keynesian model. Chrisoffel e al. (2009 examine a New Keynesian model wih saggered wages and repor ha he model, combined wih an RTM assumpion, does no replicae he dynamics of hours worked because hours per worker are oo volaile relaive o daa. On he oher hand, he exising RTM framework does no allow employmen o have an effor dimension despie being able o beer capure acual labor conracs. 1 If labor inpu varies because of responses in effor and hours, he effec of wage rigidiies on hours worked can be offse by variaions in effor a work. 2 Therefore, I assume ha efficien bargaining is a reasonable approximaion for bargaining. Under efficien bargaining, he nominal wage rae and work hours are joinly deermined. Lile aenion has been paid o he role of labor marke fricions wih efficien bargaining as a way o resolve an unrealisic degree of real variable volailiy. Hence, his paper conribues o he furher sudy of his issue. 3 The model no longer generaes unrealisically high volailiy among real variables and counercyclical produciviy when efficien bargaining and nominal wage conracs are incorporaed ino he flexible price model. Among all he models wih differen conrac lenghs, he volailiies of oupu and oal hours worked are less han hose found in US daa. Moreover, produciviy remains procyclical during he business cycle. The volailiies of unemploymen rae and vacancy rae rise significanly wih increasing conrac lengh. Efficien bargaining requires firms o rely on job creaion heavily o adjus he wedge beween he marginal produc of labor and he real wage rae in response o echnology and moneary shocks because hours per worker are fixed ahead of ime. Afer he realizaions of shocks, vacancies increase 1 Among ohers, see Trigari (2006 and Chrisoffel and Kueser ( Using a DSGE model wih endogenous effor, Bils and Chang (2003 show ha workers are willing o rade off exerion and hours in producion. 3 Krause e al. (2008 analyze a DSGE model wih price rigidiies, search fricions and efficien bargaining. Bu hey do no invesigae he relaionship beween nominal wage rigidiies and he volailiy of oupu hrough efficien bargaining. 3

5 sharply and unemploymen decreases. Given ha hours per worker are fixed because of efficien bargaining, an increase in oal hours worked is driven primarily by employmen. However, employmen per se is unable o generae large flucuaions of oupu because employmen is dicaed by a law of moion in he search and maching framework. Wih regard o produciviy, echnology shocks and moneary shocks noably play differen roles in he model. Alhough echnology shocks direcly affec boh individual and aggregae oupus, moneary shocks indirecly increase aggregae oupu by expanding he number of mached firms. The oupu response o moneary shocks is slighly less han he response of oal hours worked. Hence, produciviy falls in response o moneary shocks. Wih regard o echnology shocks, which remain exremely srong wih increasing conrac lengh, he oupu response is much greaer han he response of oal hours worked. Thus, produciviy becomes procyclical for boh shocks. Several papers in real business cycle lieraure have sudied he implicaions of nominal wage conracs in he ransmission of moneary shocks. Cho (1993 firs examines he quaniaive implicaions of one-period nominal wage conracs. Cho and Cooley (1995 sudy he properies of model economies wih nominal wage conracs. Cho e al. (1997 quaniaively esimae he welfare cos of nominal wage conracing. Janko (2008 provides empirically plausible labor adjusmen coss o he equilibrium business cycle model wih wage conracing o overcome several shorcomings ha are presen wih nominal wage rigidiies. However, Janko (2008 does no discuss unemploymen and vacancies. Wih respec o labor marke fricions, Merz (1995 and Andolfao (1996 firs bring he concep ino a real business cycle model. Shimer (2005 discusses he lack of an amplificaion mechanism in he conex of he search and maching model of Morensen and Pissarides (1994. Shimer (2005 finds ha he wage bargaining process is a source of inabiliy ha amplifies shocks. The bargaining wage is exremely volaile because i absorbs mos of he shocks. Therefore, he cyclical movemens in he incenives of firms o hire are dampened. Consequenly, Hall (2005 proposes real wage rigidiy, which allows firms o achieve cyclical movemens in heir incenives o creae jobs. Following Shimer (2005 and Hall (2005, numerous sudies have inroduced real and nominal wage rigidiies ino he DSGE models. 4 To my knowledge, he curren paper is he firs work ha revializes DSGE models 4 Krause and Lubik (2007, Gerler and Trigari (2009, and Blanchard and Galí (2010 focus on real wage rigidiies based on he New-Keynesian DSGE model. Mos sudies employ Hall (2005 s noion of a wage norm, bu Gerler and Trigari (2009 assume ha in each period a subse of firms and workers renegoiae wage conracs, and modify he convenional Morensen and Pissarides (1994 model o allow for Calvo-ype saggered wage conracs. On he oher 4

6 characerized by nominal wage conracs in a fricional labor marke environmen. This paper is organized as follows. Secion 2 presens he model and shows how he nominal wage rae is derived. Secion 3 discusses he calibraion and seady-sae properies of he model. Secion 4 quanifies he model, presens he resuls, and compares he benchmark model wih various versions of he model. Secion 5 concludes. 2 Model The model economy used in his paper is a varian of he models of Morensen and Pissarides (1994 and Cho and Cooley (1995, which consiss of households, firms, and governmen. 2.1 Households A represenaive household consiss of a coninuum of expeced-uiliy-maximizing infiniely lived individuals wih a measure of one. Each member has ime-separable preferences over his/her consumpion c (i and her labor supply (h (i, n (i. Each person may be eiher employed by a firm n (i = 1 wih he hours of work h (i or unemployed n (i = 0. The period uiliy of each member is given by he following: ln c (i B 1 1+φ h (i 1+φ if n (i = 1, ln c (i if n (i = 0, where 1/φ denoes he elasiciy of ineremporal subsiuion of leisure. Following Merz (1995, I assume ha he household serves as a full insurance mechanism by pooling he resources of all is members. The household allocaes oal consumpion o maximize he sum of household uiliy, which can be obained by equalizing he marginal uiliy of consumpion of each household member. The household, which makes all members obain an idenical consumpion bundle, serves a uiliy funcion E 0 =0 { } β ln c B h1+φ 1 + φ n, where 0 < β < 1 is a discoun facor, c is consumpion, h is hours worked by each employed household member, and n is he fracion of employed household members. hand, Gerler e al. (2008 and Galí (2010 incorporae nominal wage rigidiies ino he New-Keynesian DSGE model. Noice ha nominal wage rigidiies are inroduced in he form of saggered nominal wage seing à la Calvo. 5

7 Households in his economy are required o hold money o purchase consumpion goods and face a cash-in-advance consrain wih he following form: c m 1 + T P, where m 1 is money carried over from he previous period, T is he lump-sum money ransfer, and P is he price level in period. The budge consrain of he represenaive household can be expressed as follows: c + i + m P = j W n h j + (1 n b + r k + π + m 1 + T, P P where i denoes invesmen in capial (k ; n is he fracion of employed household members; and h j W j are he nominal hourly wage rae and work hours, respecively, deermined in period j hrough bargaining; b is household producion; r is he real renal rae of capial; π is he profis received by household from firms. The issue of how bargaining occurs over nominal wages and hours worked will be furher analyzed in he nex secion. Employmen n evolves according o he following law of moion: n +1 = (1 s n + f (1 n, where s denoes an exogenous separaion rae in which employees lose heir jobs each period. The exising workforce a he beginning of period + 1 is denoed by (1 sn and new hires enering ino employmen agreemen in period + 1 are denoed by f (1 n, where f is he job-finding probabiliy of a worker. 2.2 Firms A firm (or enrepreneur produces oupu y by using capial k and hours h j echnology: y = z k α ( h j θ, under he following where z is an aggregae produciviy shock and h j is he hours of work deermined hrough bargaining in period j. Wihou loss of generaliy, we can convenienly assume ha a single firm or 6

8 enrepreneur corresponds o each worker. Therefore, he number of employees is 1 in he producion echnology of an individual firm. The produciviy shock follows an AR(1 process in logs: ln z = ρ z ln z 1 + ε z, where ε z is a normal random variable wih mean zero and variance σ 2 z. Technology shock is recognized a he beginning of each period before decisions are made. The expeced discouned sum of real profis for an individual firm is given by he following: J = z k α ( h j j θ W { } h j r k + β (1 s E [ψ +1 J +1 ] + se [ψ +1 O +1 ], (1 P where ψ +1 µ +1 /µ and O +1 is he value of a vacancy in period + 1. I assume ha mached firms and workers bargain on he nominal hourly wage rae and work hours. Given he hours of work, he firms choose he amoun of capial. The value of a vacancy O is given by he following: O = κ + β { q E [ψ +1 J +1 ] + (1 q E [ψ +1 O +1 ] }, where q is he probabiliy ha each vacancy will be filled and κ is he cos of posing a vacancy. Under equilibrium wih no enry barrier, he value of a vacancy mus be zero: κ = βq E [ψ +1 J +1 ]. (2 2.3 Governmen The governmen budge consrain for each period is expressed as follows: T = M M 1, where T is he lump-sum money ransfer and M is he sock of money. 5 The governmen budge consrain implies ha money is injeced ino he economy hrough lump-sum ransfers. If g denoes 5 As in Cooley and Hansen (1995, I se governmen spending and nominal governmen deb o zero for all. 7

9 he (gross growh rae of money beween periods 1 and, money is assumed o grow a rae g 1: M = g M 1. The growh rae of money g is known a he beginning of each period. The lump-sum money ransfer T is hen equal o (g 1 M 1. The growh rae g is assumed o evolve according o he following AR(1 process in logs: ln g = ρ g ln g 1 + ε g, where ε g is a normal random variable wih mean zero and variance σg. 2 I assume ha ε g is independen of ε z. 2.4 Maching In his economy, anoher echnology describes how maches occur. The so-called maching echnology or maching funcion can be expressed as follows: M (u, v = ηu ξ v 1 ξ, where M (u, v is he oal number of maches or hires, u is he number of unemployed workers, and v is he aggregae number of vacancies. Assuming ha he size of he labor force is fixed and normalized o uniy, he number of unemployed workers is u = 1 n. The probabiliy a firm fills is vacancy q is given by he following: q = M (u, v v. The probabiliy an unemployed worker finds a job f is expressed as follows: f = M (u, v u. 8

10 2.5 Resource Consrain Finally, he aggregae resource consrain is obained by combining he equilibrium budge consrain of he household and he value of he firm under he binding cash-in-advance consrain: c + k +1 + κv = y + (1 δ k, where y = n y is he sum of he oupu produced by he mached firms and k = n k is he sum of he capial sock of an individual firm. 2.6 Transformaion All consumpion mechanisms for household members are equal hrough full insurance arrangemens. I focus on he represenaive household s problem in equilibrium. To obain saionary variables in equilibrium, I divide all nominal variables, namely, m, P, and j W, by he aggregae money sock M. The maximizaion problem of he represenaive household is expressed as follows: subjec o max E 0 m P + k +1 = =0 ( } β {ln m 1 + g 1 B (h j 1+φ g P 1 + φ n W j P Π j i=1 g n h j + (1 n b + (r + 1 δ k + π +1 i n +1 = (1 s n + f (1 n, (3 where P P /M, W j j W /M j, and m 1 m 1 /M 1. Noe ha he expression Π j i=1 g +1 i links he real hourly wage rae o he moneary shocks realized beween period j and period. 6 The represenaive household aims o choose coningen plans for {k +1, m }, which akes he nominal hourly wage rae and work hours as given. The firs-order condiions for he maximizaion imply he following: 6 Le me define Π j i=1 g +1 i = 1 if j = 0. [ ] 1 P µ = βe, c +1 g +1 P +1 µ = βe [µ +1 (r δ], 9

11 where µ is he marginal uiliy of income in period, ha is, he muliplier aached o he budge consrain. In equilibrium, m = M = 1. The equilibrium cash-in-advance consrain implies ha consumpion is he reciprocal of he price level: c = 1 P. I denoe V as he worker s surplus when anoher household member is employed: 7 V = W j P Π j i=1 g i+1 h j [ ] b B (h j 1+φ 1 µ+1 + β (1 s f E V +1. (4 1 + φ µ µ For he value of a mached firm, Eqs. (1 and (2 provide he following expression: J = (1 α z k α ( h j θ W j P Π j i=1 g h j + (1 s κ. (5 i+1 q Given he hours of work, he firs-order condiion wih respec o k, which equalizes he marginal produc of capial o is renal rae, is expressed as follows: r = αz k α 1 ( h j θ. The per-period profis π is given by he following: π = (1 α z k α ( h j θ W j P Π j i=1 g h j. i Bargaining over Wages and Hours The nominal wage conrac esablished in his secion follows he sudy of Cho and Cooley (1995. The nominal wage conrac saes ha agens agree o a conrac arranged for j periods ahead a he beginning of each period. For example, consider j = 2. A, workers and firms agree o a nominal wage rae for period + 2 and firms pay o employees he nominal wage rae agreed in period 2. A + 1, workers and firms agree o a wage rae for period + 3. The firms hen pay o employees he 7 The worker s surplus can be obained by aking he derivaive of he indirec uiliy funcion of he household wih respec o n subjec o he budge consrain and he law of moion for employmen. I is expressed in erms of curren consumpion of final goods. 10

12 nominal wage rae agreed upon in period 1. This process is repeaed over ime. Efficien bargaining is assumed once he labor marke is characerized by search fricions. In his approach, he firm and worker ener ino bargaining over he nominal hourly wage rae and hours worked under he generalized Nash bargaining framework. The nominal hourly wage rae W +j and hours worked h +j in ime + j are agreed upon in period by boh paries, where he hourly wage rae and hours worked joinly maximize he Nash produc afer he aggregae shocks are realized: ( γ ( 1 γ W +j, h +j = arg max (β j µ +j E V +j β j µ +j E J +j, (6 µ µ where γ denoes he worker s bargaining power in wage negoiaions and he surpluses for a mached worker and firm are given by Eqs. (4 and (5, respecively. A he ime of he conrac, he nominal wage is paid o all employees and employees supply he work as specified in he conrac. Under his nominal wage conrac rule, new hires are paid he same nominal wage rae ha is predeermined hrough bargaining beween firms and workers. The firs-order condiions wih respec o he nominal hourly wage rae W +j and hours of work h +j a ime + j are expressed by he following: [ ] µ+j (1 γ E V +j µ B ( h +j [ ] µ+j = γe J +j, (7 µ [ ] µ+j θz +j k α µ +j(h +j θ 1. (8 φ 1 µ = E The nominal hourly wage rae chosen by a firm worker mach is derived from he expeced discouned surplus of firms and workers. The hours of work are chosen by he mach such ha he marginal rae of subsiuion beween consumpion and leisure is equaed o he expeced discouned value of he marginal produc of labor. In his paper, he economies are approximaed by he log-linearizaion around he seady sae because models wih nominal conracs canno be solved analyically. I also consider he following alernaive bargaining problem: ( W +j, h +j = arg max V γ J 1 γ. (9 Unlike Eq. (6, wherein firms negoiae wih all poenial workers who will be working in period + j regardless of curren employmen saus, Eq. (9 assumes ha currenly operaing firms negoiae 11

13 only wih currenly employed workers. Under he alernaive bargaining problem, he firs-order condiions wih respec o he nominal hourly wage rae and hours of work a ime + j (j 1 are expressed as follows: [ ] µ +j h j +j γj E µ P j +j i=1 g (1 s f +i 1 +i i=1 [ ] µ +j h +j = (1 γ V E µ P j +j i=1 g (1 s j, (10 +i [ µ +j j { γj E (1 s f +i 1 B ( } ] h φ 1 +j µ µ i=1 +j [ { µ+j }] = (1 γ V E (1 s j θz +j k α µ +j(h θ 1 +j. (11 The hours of work deermined hrough bargaining equae he expeced discouned value of he marginal rae of subsiuion beween leisure and consumpion wih he expeced discouned value of he marginal produc of labor. 8 Wih regard o he seady sae under he alernaive bargaining problem, he seady-sae nominal wage rae varies wih changing conrac lengh. The mached firms and households place differen weighs on he coninuaion values because of he differen probabiliies of he coninuaion of heir employmen relaionships. In he seady sae, conrac lengh deermines hose probabiliies. The seady-sae nominal wage rae saisfies he following for j 1: γj (1 s f j = (1 γ V (1 s j. I call he model wih bargaining problem of Eq. (6 he benchmark model and he model wih bargaining problem of Eq. (9 he curren surplus bargaining model. 3 Calibraion I se he discoun facor β o.99 o imply an ineres rae of 1% per quarer. The capial s share of oal income α is calibraed o be.33, and δ is se equal o.025. I assume ha he echnology of he 8 The log-linearized versions of he hours of work are equalized for Eq. (6 and Eq. (9. 12

14 represenaive firm exhibis decreasing reurns-o-scale. Thus, I se α+θ o.9. 9 The worker s bargaining power in wage negoiaions γ is se o.5, and household producion b is se o approximaely 40% of he seady-sae (real bargaining wage. The elasiciy of he maching funcion ξ is se o.5; his value is consisen wih lieraure. I se he seady-sae value of he worker s job-finding probabiliy f o.6 o imply an average duraion of unemploymen of 1.67 (Cole and Rogerson The seady-sae unemploymen rae u is se o 6% per quarer. Moreover, he labor force size is normalized o uniy. Given he job-finding rae and employmen rae, he exogenous separaion s is made consan from he seady-sae version of he law of moion for employmen n = f/ (s + f such ha s = The seady-sae level of hours worked h is normalized o 1/3, and uiliy parameer B is adjused accordingly. Following Cho and Cooley (1995, I se he ineremporal subsiuion elasiciy of leisure o.5, hus implying φ = 2. This value is exremely close o Chang and Kim (2006. The parameers governing he money growh rae, namely, ρ g and σ g, are se o.49 and.00623, respecively (Cooley and Quadrini Finally, parameers ρ z and σ z, which conrol he process for echnology shocks, are se o.95 and.007, respecively. These values are commonly used in relaed lieraure. Table 1 summarizes he se of parameers used in he simulaion. I follow Shimer (2005 by calibraing household producion b o 40% of he seady-sae real compensaion per employee W h, ha is, b =.4 W h. The seady-sae real bargaining wage W/P is p p given by Hence, he value of household producion is.27. The endogenously deermined parameer of he uiliy funcion B is Therefore, disuiliy from working in erms of curren consumpion of final goods is The sum of household producion and disuiliy from working is equal o.49, which corresponds o he flow uiliy from leisure or nonmarke aciviy in he sandard search and maching model. The benchmark model generaes he capialized value of a mached job J of.277 and producion per period ne of capial cos (1 α k α h θ of.68. Noe ha he surplus from employmen V is equal o J because he worker s bargaining power is se o.5. Thus, per-period profis (π and vacancy posing cos (κ are given by.013 and.165, respecively. 9 This assumpion is no criical in his sudy, bu is made for he comparison wih he model economies wih wage bargaining only (he righ-o-manage approach. The value of a mached firm becomes zero under he RTM approach if he firm s echnology exhibis consan reurns-o-scale. 10 See Appendix for he seady-sae condiions for he benchmark model. 13

15 4 Findings I invesigae he exen in which he model economy wih wage conracs, as well as fricional labor markes, amplify moneary and real shocks (Cho and Cooley Table 2 presens he sandard deviaions of oupu and oher key variables of ineres. To evaluae predicive accuracy, I firs presen he relevan saisics obained from quarerly US daa beween 1956 and The oupu measure (y is producion (real oupu in he non-farm business secor. Consumpion (c is he sum of he personal consumpion expendiures of nondurables and services, which are deflaed by he associaed price indexes plus real governmen consumpion expendiures. Invesmen (i is he sum of he real privae domesic invesmen and real personal consumpion expendiures of durables. Employmen (n is measured by using he quarerly average number of non-farm employees. Hours (h are he average weekly hours for he non-farm business secor. Unemploymen (u is he quarerly averages of monhly daa from he Curren Populaion Survey. Vacancy (v is he quarerly average of monhly help-waned indexes consruced by he Conference Board. The real wage (w is he real hourly compensaion in he non-farm business secor. Finally, he level of price (P is measured by he CPI divided by M1 money sock for consisency wih he counerpar of he model. All daa are seasonally adjused and HP filered wih smoohing parameer 1,600. The summary saisics for he models subjec o boh moneary and echnology shocks, moneary shock only, and echnology shock only are presened. Saisics for he model economies are compued by simulaing for 200 periods and by repeaing he simulaion 1,000 imes. 11 This approach highlighs he role of each shock and enables he deerminaion of he relaive imporance of each shock wih he inroducion of nominal wage conracs and search fricions. 4.1 Wage Conracs and Role of Search Fricions I begin by invesigaing a DSGE model wih money and nominal rigidiy following Cho and Cooley (1995. I also inroduce search fricions ino he model in which firms choose he amoun of hours, such as Trigari (2006, Chrisoffel and Kueser (2008, and Chrisoffel and Linzer (2010. Blanchard and Fischer (1989 argue ha acual labor conracs appear only o se wages and leave he employmen decision o he firm. This approach is referred o as he RTM approach, wherein he firm and union bargain over he wage, and he firm chooses employmen freely o maximize profi. Hence, Cho and 11 I generae a se of arificial ime-series daa of he lengh of 1,000 periods and drop he firs 800 periods. 14

16 Cooley (1995 examine nominal conracs wih he RTM approach. From a DSGE model wih money and nominal conracs following Cho and Cooley (1995, I find unrealisically high flucuaions in oupu and oal hours worked upon he incorporaion of nominal wage conracs. 12 In he case of wo-period conracs, oupu is more han wice as volaile as in he model wihou conracs. Table 2 shows ha he volailiy of oupu increases from 1.30 for no conrac o 2.83 for wo-period conracs. On he oher hand, oal hours worked in he wo-period conrac case flucuae more han oupu. The relaive volailiy of oal hours worked is 1.30 for wo-period conracs, which is greaer han.46 for no conrac. These dramaic increases in volailiy are aribued o he RTM approach and he srong moneary ransmission mechanism induced by nominal wage conracs. Under he nominal conracing arrangemens in Cho and Cooley (1995, households and firms ener ino a wage conrac and agree upon he nominal wage se in advance. The workers are assumed o cede he firm he righ o deermine he aggregae hours, hus leaving firms o maximize profis. The firms adjus o shocks during he conrac period by choosing oal hours worked Q o equae he marginal produc of labor o he realized real wage as follows: W c P = (1 α z k α Q α, (12 where W c denoes he specified equilibrium nominal wage and Q = n h. Nominal wage and oal hours worked become highly volaile even for relaively minor shocks upon he inroducion of nominal conracs. This increase can be aribued o he response of firms o shocks by choosing aggregae hours worked along Eq. (12. Consequenly, he volailiies of oal hours worked and oupu are unrealisically high. In he model wih conracs, moneary shocks play significan roles in generaing high volailiies in oupu and oher variables compared wih echnology shocks as conrac lengh increases. For insance, he volailiy of oupu by boh shocks is 3.60 for he case of four-period conracs. The volailiy of oupu driven only by moneary shocks is Hence, a sizable share is explained by moneary shocks. Table 3 repors he correlaions wih oupu. One of he noable feaures of he model characerized by he RTM seup is ha oal hours worked are srongly posiively correlaed wih oupu. The 12 See Appendix for a deailed descripion of he model. 15

17 correlaions of oal hours worked wih oupu are.94 and.96 for wo-period conracs and four-period conracs, respecively. On he oher hand, he correlaion of labor produciviy wih oupu becomes negaive wih nominal conracs. Alhough posiive echnology shocks cause higher labor produciviy, a posiive shock o he money growh rae decreases nominal and real wages. The cyclical behavior of labor produciviy and real wages are idenical. Thus, labor produciviy becomes counercyclical. 13 Procyclical oal hours worked and counercyclical labor produciviy imply a negaive correlaion beween labor produciviy and aggregae labor. I inroduce search fricions ino he model wih money and nominal conracs and assume ha bargaining occurs over he nominal hourly wage rae only o maximize he Nash produc: ( γ ( 1 γ W+j = arg max β j µ +j E V +j β j µ +j E J +j. µ µ The resuling opimaliy condiion wih respec o he nominal wage rae is he same as Eq. (7. The employmen decision is lef o he firm. Hence, he amoun of hours worked is chosen by he firm. The condiion saes ha hours per worker are deermined o equae he marginal produc of labor wih he bargained wage: W j P j i=1 g i+1 = θz k α h θ 1, where he lef-hand side is he real bargained wage and he righ-hand side is he marginal produc of labor. Unlike fricionless labor markes wherein firms choose oal hours worked (Q = n h, employmen (n in fricional labor markes is a sae variable and no an individual firm s choice variable. The cyclical changes in real wages induced by boh echnology and moneary shocks are absorbed mainly by he movemens of hours per worker. Therefore, he high volailiy of oal hours worked is prediced. Anoher feaure is he lack of an amplificaion mechanism associaed wih flucuaions in unemploymen and hiring aciviy. Under he RTM approach, period profis of mached firms are given by (1 α θ z k α h θ, which can be expressed as follows: ( 1 α θ θ W j P j i=1 g h. (13 i+1 13 Bils and Chang (2003 also show ha a model wih sicky wages bu no effor response predics a srong negaive relaionship beween labor produciviy and hours worked. 16

18 Wage coss are proporional o he revenue and per-period profis; hus, he percenage flucuaions in wages are equal o he percenage flucuaions in per-period profis. If wages per employee W j P j i g i+1 h do no flucuae significanly over he business cycle, per-period profis will no flucuae enough o generae incenives for he firms o creae jobs. Table 2 shows ha he model wih wage bargaining only is unable o amplify he effec of shocks on unemploymen and vacancies. Table 2 presens he sandard deviaions of oupu and oher variables. The resuls from he model wih wage bargaining only are similar o hose from he model wihou search fricions. Hours per worker and oal hours worked flucuae more han oupu and heir daa counerpars. For example, in he four-period conrac case, hours worked and oal hours worked flucuae more han one and a half imes oupu. The volailiy of oupu also rises wih increasing conrac lengh because hours worked are volaile. Table 2 also shows ha he model wih RTM bargaining fails o amplify he effec of echnology and moneary shocks on unemploymen and vacancies over he business cycle. In he four-period conrac case, he relaive sandard deviaions of unemploymen and vacancies are.21 and.39, respecively. Wih regard o correlaions wih oupu, he model wih search fricions along wih RTM bargaining also predics ha oal hours worked are significanly posiively correlaed wih oupu, labor produciviy is negaively correlaed wih oupu, and labor produciviy and oal hours worked move in opposie direcions (Table 3. The resuls show ha he model characerized by he RTM regime is unable o accoun for reasonable flucuaions in real variables and correlaions wih oupu over he business cycle regardless of he exisence of search fricions. I employ he model wih search fricions and efficien bargaining in his sudy. The nominal wage rae and hours of work are joinly deermined in his model. 4.2 Wage Conracs and Efficien Bargaining Table 5 presens he resuls from he benchmark model wih period-by-period wage bargaining. The resuls show ha labor marke variables have low volailiy. Compared wih he oupu volailiy, he relaive sandard deviaions of oal hours worked (nh, unemploymen (u, and vacancies (v are.26,.94, and 1.78, respecively. Hence, he model in which he nominal wage rae and hours of work are Nash-bargained in every period lacks amplificaion mechanisms. 14 This resul is consisen 14 In order o have highly volaile labor marke variables, Cooley and Quadrini (1999 se he worker s bargaining power (or he sharing parameer in heir paper in he range of Decreasing his parameer leads o he higher 17

19 wih ha of Galí (2010, who saes ha realisic labor marke fricions have limied effecs on he equilibrium dynamics of he economy. The benchmark model shows ha moneary shocks are no propagaed in his economy. Technology shocks generae mos of he observed volailiy in oupu (y. The benchmark model wih boh shocks produces essenially he same resuls as he model wih echnology shocks only. When search fricions and efficien bargaining are considered in he model, nominal wage conracs increase he volailiy of variables bu do no produce unrealisically high volailiies in oupu and oal hours worked. In he four-period conrac case, he volailiy of oupu and he relaive volailiy of oal hours worked are 1.03 and.43, respecively. As regards labor marke variables, nominal wage conracs resul in high degrees of volailiy. The volailiies of employmen (n, unemploymen, and vacancies increase o.41, 6.35, and under he four-period conrac scenario, respecively. The corresponding effec on he volailiies of unemploymen and vacancies is noably large. Table 5 also shows ha nominal wage conracs along wih efficien bargaining play imporan roles in amplifying moneary shocks. In he case of four-period conracs, moneary shocks have more weigh in generaing flucuaions in employmen, unemploymen, and vacancies han echnology shocks. The effec of moneary shocks on he volailiies of he labor marke variables, including real wages, is more significan han he effec of echnology shocks. Under efficien bargaining, he inroducion of nominal wage conracs slighly decreases he volailiy of oupu from 1.09 o 1.01 for wo-period conracs because hours worked are predeermined hrough bargaining. All else being equal, he volailiy of hours worked plays an imporan role for capuring he volailiy of oupu. The hours of work for he muli-period conrac case are less dependen on he sae variables, including shock componens, han hose for he period-by-period conrac case. For example, in he case of wo-period conracs, he hours of work in period +2 are deermined in period when workers and firms form heir expecaions abou he shocks o be realized wo periods volailiy of boh employmen and unemploymen. Noe ha he weaker bargaining power workers hold, he more rigid real wages become when he worker s period value from unemploymen is no ime-varying. Hagedorn and Manovskii (2008 also se he worker s bargaining power o.052 in heir proposed calibraion sraegy. As discussed by Hagedorn and Manovskii (2008, he he bargaining weigh parameer deermines he volailiy of real wages. All else being equal, lower values of he bargaining parameer imply more cyclical real wages and less cyclical profis. The purpose of his paper is no o accoun for he cyclical properies of unemploymen and vacancies, bu o show ha he search and maching model wih nominal wage conracs and efficien bargaining is able o predic a low volailiy of hours worked and oupu as well as generae procyclical produciviy. 18

20 laer. The log-linearized model expresses hours worked as follows: (φ + 1 θ ĥ +2 = E µ +2 + E ẑ +2 + αe k+2. Given ha all shocks have zero mean, he second erm of he righ-hand side represening he expeced value of fuure echnology shocks is equal o ρ 2 zẑ. Moreover, under he raional expecaions assumpion, he curren sae variables become less persisen. The hours of work for muli-period conracs are also less dependen on he sae variables, hus generaing less volaile work hours and leading o less volaile oupu (Table 5. Nominal wage conracs and efficien bargaining lead o significan changes in he relaive volailiy of real wages. None of he models wih differen conrac lenghs is able o mach he relaive volailiy observed in US daa. For example, for four-period conracs, he real wage rae depends on he nominal wage rae deermined in period 4, moneary shock componens, and oher sae variables. Wih increasing conrac lengh, he long-erm moneary shocks realized from 4 hrough lead o significan flucuaions in he real wages. Table 6 shows he correlaions wih oupu. Under he RTM seup, I observe ha produciviy is negaively correlaed wih oal hours worked and ha real wages and produciviy are negaively correlaed wih oupu (Table 3. By conras, he benchmark model wih differen conrac lenghs correcly predics a posiive correlaion beween oupu and produciviy, wih.97 for wo-period conracs and.90 for four-period conracs. However, in response o moneary shocks, produciviy exhibis a counercyclical behavior. This counercyclical behavior becomes srong wih increasing conrac lengh. If moneary shocks dominae, counercyclical produciviy will occur. The las column of Table 6 shows he correlaion beween produciviy and oal hours worked. The correlaion coefficien of.98 suppors a srong posiive relaionship wih oal hours worked in he benchmark model of period-by-period bargaining. However, correlaion decreases wih increasing conrac lengh. The correlaion simulaed from he model wih four-period conracs (i.e.,.15 is close o he observed level from he daa (i.e.,.27. The real wage rae is highly procyclical in he benchmark model of period-by-period bargaining wih a correlaion of.99 bu is procyclicaliy weakens wih increasing conrac lengh. The correlaion beween oupu and real wages is.02 for four-period conracs; hus, real wages appear acyclical. The model predics he low volailiy of hours worked (h, and he volailiy of hours worked 19

21 relaive o employmen (n decreases wih increasing conrac lengh. This reducion in volailiy comes a he expense of reducing he correlaion of oupu and hours per worker and he correlaion of oupu and employmen. A rade-off beween he capabiliy of he model o mach volailiies and is capaciy o generae correlaions is emphasized. Alhough models wih nominal wage conracs and efficien bargaining overcome he limiaions observed in Cho and Cooley (1995 successfully, he seup predics he weak correlaions of unemploymen and vacancies wih oupu as conrac lengh increases. The correlaions of unemploymen and vacancies are.84 and.90 for period-by-period bargaining, respecively, bu are.49 and.18 for four-period conracs, respecively. Neverheless, he model wih four-period conracs shows significan negaive correlaions of unemploymen for each shock, wih.99 for moneary shocks and.71 for echnology shocks. 15 A similar rade-off beween correlaions and volailiies is apparen in unemploymen and vacancies wih increasing conrac lengh. Compared wih he model of he RTM regime or oher models invesigaed in he following secions, his rade-off does no seem o be common o all models wih nominal rigidiies. Table 7 shows he correlaions wih unemploymen. For differen conrac lenghs, he model can accoun for a negaive relaionship beween unemploymen and oal hours worked. The correlaion beween unemploymen and oal hours worked in he model wih four-period conracs is.93, which is close o he level seen in he US daa (i.e.,.94. As conrac lengh increases, he volailiies of employmen and unemploymen become more driven by moneary shocks han echnology shocks, whereas hours worked remain less volaile for eiher shock. Thereafer, he cyclical behavior of oal hours worked is explained mainly by he cyclical behavior of employmen, ha is, employmen moves in he opposie direcion of unemploymen over he business cycle. The model is unable o produce a negaive relaionship beween unemploymen and vacancies (i.e., he Beveridge curve. To observe he Beveridge relaionship, unemploymen should be significanly counercyclical and vacancies should be significanly procyclical. All he models invesigaed in his paper do no generae such feaures successfully. Moreover, he benchmark model predics a posiive relaionship beween unemploymen and real wages. The correlaion is.13 for he US economy over he las 50 years, whereas he correlaion is.21 for wo-period conracs and.69 for four-period 15 As conrac lengh increases, vacancies are more correlaed wih oupu for moneary shocks only and similarly correlaed for echnology shocks only. When boh shocks are in place, however, he aggregae correlaion somehow goes down. This can happen because boh posiive shocks produce couneracive effecs on he correlaions of oupu wih vacancies as in Table 6. The impulse response funcions in Figure 1 also show hese couneracive effecs. 20

22 conracs. The resuls are differen from he daa, bu he model wih echnology shocks only predics a weak negaive correlaion beween unemploymen and real wages. Impulse Response Funcions This sudy invesigaes how shocks are propagaed by nominal conracs and efficien bargaining in he model economy. For several key variables, such as oupu, hours worked, and produciviy, he impulse response funcions for innovaions in moneary shocks and echnology shocks are shown in Figure 1. The wo-period and four-period conracing economies, as well as he economy wih period-by-period efficien bargaining, are displayed in Figure 1. The impulse response funcions o innovaions in echnology shock are shown in Figure 1(a. Wih regard o oupu, oal hours worked, and produciviy, he model economy wih nominal conracs does no increase he propagaion of echnology shocks dramaically. However, for unemploymen and vacancies, he model is able o propagae echnology shocks. Under efficien bargaining, per-period profis of mached firms (Eq. (13 flucuae significanly in response o shocks. Thus, he incenives generaed by an increase in per-period profis lead he firms o pos vacancies. The second panel (Figure 1(b shows he impulse response funcions o innovaions in moneary shocks. The model economy wih period-by-period efficien bargaining confirms he fac ha he basic real business cycle model characerized by fricional labor markes does no propagae moneary shocks a all. However, he inroducion of nominal wage conracs makes a significan difference. In response o moneary shocks, oupu and oal hours worked exhibi a hump-shaped paern. In he wo-period and four-period conracing economies, he response of oal hours worked is slighly greaer han he response of oupu. Thus, produciviy falls. Considering he nominal wage rae and hours of work hrough bargaining, innovaions in moneary shocks have a srong negaive effec on real wages, hus decreasing real wages. This siuaion in urn increases he incenive of firms o pos vacancies. As a consequence of moneary shocks, vacancies increase and unemploymen decreases. Sensiiviy Analysis I repor a sensiiviy analysis conduced o examine he robusness of resuls o he use of oher parameer values. I consider differen values of γ o represen he bargaining power of workers, differen values of ξ o represen he maching funcion elasiciy wih respec o unemploymen, and differen 21

23 values of θ o represen he hours elasiciy of he producion funcion. Figure 2(a shows ha he volailiies of oupu, oal hours worked, unemploymen, and vacancies rise sharply wih increasing worker bargaining power. However, his phenomenon does no occur for he model wih period-by-period bargaining. A high value of γ wih four-period conracs produces unrealisically volaile unemploymen and vacancies. If he bargaining power of workers is srong under efficien bargaining, a relaively small amoun of rigidiy will be necessary o cause he real side of he economy o generae he volailiies of he magniude observed. When considering correlaions, he conemporaneous relaionships among oupu, hours, and produciviy are sensiive o a significan change in γ in he four-period conrac case (Figure 2(b. In he four-period conrac case, he srong posiive correlaions beween oupu and hours per worker and beween oupu and produciviy disappear when he bargaining power of workers is close o one. Furhermore, he weak posiive relaionship beween produciviy and oal hours worked becomes a negaive correlaion. Figure 3 shows he resuls of a sensiiviy analysis conduced wih respec o maching funcion elasiciy. Figure 3(a shows ha he volailiies of oupu, oal hours worked, unemploymen, and vacancies increase wih decreasing unemploymen elasiciy. Similar o he bargaining power of workers, his phenomenon occurs only o he model wih nominal rigidiy. For example, a low ξ value wih four-period conracs leads o large flucuaions in unemploymen and vacancies. The posiive correlaion coefficiens beween oupu and hours per worker and beween oupu and produciviy decrease subsanially wih low ξ values (Figure 3(b. Figure 4 shows he resuls of a sensiiviy analysis wih respec o he labor share ha deermines he reurns-o-scale of he producion funcion. The benchmark parameer is se o.66; hus, he producion funcion exhibis decreasing reurns-o-scale of.99. Unlike he sensiiviy analyses wih respec o he bargaining power of workers or he maching funcion elasiciy, a change in he labor share does no show a noiceable change in he volailiies of key variables and he conemporaneous correlaions among hem. Under he RTM approach, he producion funcion should have decreasing reurns-o-scale; oherwise, he value of a mached firm is zero and he firm has no incenive o pos a vacancy. The assumpion of a decreasing reurns-o-scale producion funcion is required under he RTM approach. However, Figure 4 shows ha he resricion is unnecessary under efficien bargaining. Conrac lengh really maers because a sensiiviy analysis depends on conrac lengh. The resuls are more likely o be sensiive o he changes in parameer values wih increasing conrac 22

24 lengh. Neverheless, he simulaion resuls are insensiive o he sligh changes in parameer values around he benchmark calibraion. 4.3 Bargaining over Curren Surplus In his subsecion, I consider an alernaive bargaining problem under which he Nash produc consiss of he curren surplus of each pary (Eq. (9. Only currenly employed workers and currenly operaing firms ener ino bargaining and negoiae over he curren join surplus. One of he major differences in bargaining over curren surplus compared wih bargaining over fuure surplus is ha some probabiliies are aached o he firs-order condiion wih respec o he nominal hourly wage (Eq. (10. The probabiliies aached o he curren surplus of firms denoe he weighs on he fuure mach surplus of workers. The probabiliies aached o he curren surplus of workers denoe he weighs on he fuure mach surplus of firms. This resul leads o an ineresing feaure ha he seady-sae bargaining wage rae depends on he exogenous separaion rae and jobfinding probabiliy, which play imporan roles in decreasing he acual bargaining power of workers wih increasing conrac lengh. The seady-sae nominal wage rae saisfies he following equaion: [ ( ] j 1 s f γ J = (1 γ V, 1 s where γ denoes he ex-ane bargaining power of workers and j denoes he conrac lengh. When conrac lengh increases, he acual bargaining power of workers decreases. Thus, he seady-sae nominal wage rae decreases. However, he mach surplus of firms increases wih conrac lengh because per-period profis increase. In he seady sae, I observe ha per-period profis significanly rise wih increasing conrac lengh. Per-period profis are.075 for wo-period conracs and.214 for four-period conracs. An increase in he seady-sae value of per-period profis decreases he volailiies of per-period profis and vacancies. Table 5 shows ha real wages and hours worked flucuae significanly wih increasing conrac lengh. Thus, he real compensaion per employee w h also flucuae significanly. 16 However, an increase in he volailiy of he real compensaion per employee is aenuaed by he increase in he seady-sae value of per-period profis. This phenomenon can be undersood by ex- 16 The sandard deviaion of he real compensaion per employee increases from 1.65 for wo-period conracs o 2.18 for four-period conracs. 23

25 amining he percenage flucuaions in per-period profis π : π = y π (ŷ n rk π ( r + k n wh π ( ŵ j + ĥ j, where variables wih has denoe log deviaions from heir seady-sae values. The coefficien on he real compensaion per employee wh/π plays an imporan role in decreasing he ampliude of flucuaions in per-period profis. The coefficien is 8.19 for wo-period conracs, bu decreases o 2.20 for four-period conracs because he nominal wage rae decreases and per-period profis increase significanly in he seady sae. The decrease in he coefficien dominaes he increase in volailiy of he compensaion per employee. Thus, per-period profis and vacancies flucuae less for four-period conracs han for wo-period conracs. The second momens of variables from he model wih bargaining over curren surplus are shown in he second panel of Table 5 o 7. Compared wih he resuls from he model wih bargaining over discouned expeced fuure surplus, he model wih bargaining over curren surplus seems o have similar quaniaive implicaions. Neverheless, he curren surplus bargaining model has a limiaion on maching he volailiy of vacancies wih nominal wage conracs and maching he conribuions of inensive and exensive margins of labor hours o oal hours worked. However, he benchmark model wih forward-looking Nash bargaining performs beer in such dimensions. When hours worked are fixed ahead of ime hrough forward-looking Nash bargaining, firms have o rely on job creaion more heavily o adjus he marginal produc of labor in response o shocks. 4.4 Insananeous Hiring In he sandard search and maching model, a one-period lag is observed beween hiring and employmen. For he model economy analyzed in his sudy, a one-period lag is equivalen o a lag of hree monhs because he model runs a quarerly. Given ha he nominal wage rae and hours of work are predeermined hrough bargaining, economic aciviy does no respond in he period when he shocks occur. Thus, I inroduce insananeous hiring ino he model and examine how much of he aenuaion in oupu flucuaions is driven by a lag beween hiring and employmen. Following Blanchard and Galí (2010 and Krause e al. (2008, I assume ha vacancies are filled immediaely by paying he hiring cos. Separaion occurs a he beginning of period. Job searchers in period consis of hose who separae a he beginning of period and hose who are unemployed 24