Wage rigidities in an estimated DSGE model of the UK labour market

Transcription

1 Wage rigidiies in an esimaed DSGE model of he UK labour marke Renao Faccini Sephen Millard Bank of England March 2012 Francesco Zanei Absrac We esimae a New Keynesian model wih maching fricions and nominal wage rigidiies on UK daa. We are able o idenify imporan srucural parameers, recover he unobservable shocks ha have a eced he UK economy since 1971 and sudy he ransmission mechanism. We show ha in a model wih maching fricions, wheher nominal wage rigidiies are relevan or irrelevan for in aion dynamics depends on he paramerisaion. A he esimaed equilibrium, we nd ha wage rigidiies are irrelevan, despie improving he empirical performance of he model. The reason is ha wih maching fricions, marginal coss depend on uni labour coss and on an addiional componen relaed o search coss. Wage rigidiies a ec boh componens in opposie ways leaving marginal coss and in aion virually una eced. JEL: E24, E32, E52, J64. Keywords: DSGE models, Bayesian esimaion, labour marke search, wage rigidiies. Please address correspondence o: Renao Faccini, or Seve Millard, or Francesco Zanei, Bank of England, Threadneedle Sree, London EC2R 8AH, U.K., s: renao.faccini@bankofengland.co.uk, seve.millard@bankofengland.co.uk, francesco.zanei@bankofengland.co.uk. The auhors wish o hank Andrea Gerali, Bob Hills, Thomas Lubik, Anonella Trigari and seminar paricipans a he Bank of England, Durham Universiy, he Universiy of Noingham, he Sociey for Nonlinear Dynamics and Economerics 18h Annual Symposium, he Royal Economic Sociey meeings, he Third World Conference EALE-SOLE 2010, he 16h inernaional conference of he Sociey for Compuaional Economics, he 6h Dynare Conference, 23rd annual EALE Conference, and he 25h congress of he European Economic Associaion for exremely helpful commens and suggesions. This paper represens he views and analysis of he auhors and should no be hough o represen hose of he Bank of England or he Moneary Policy Commiee members.

2 1 Inroducion Dynamic, sochasic, general equilibrium models based on he New Keynesian paradigm have become a powerful ool o invesigae he propagaion of shocks and in aion dynamics. 1 In his framework price rigidiies esablish a link beween nominal and real aciviy: if nominal prices are saggered, ucuaions of nominal aggregaes rigger ucuaions of real aggregaes. Using his framework, seminal work by Gali and Gerler (1999) has documened ha he dynamic behaviour of in aion is ighly linked o rms marginal cos (represened by uni labour cos), whose dynamics crucially depend on he funcioning of he labour marke. Gali and Gerler (1999) assume fricionless labour markes. However, empirical evidence from virually all he major indusrialised counries, as surveyed by Bean (1994) and Nickell (1997), shows ha labour markes are characerised by fricions ha preven he compeiive allocaion of resources. As shown in Krause and Lubik (2007), hese fricions, once incorporaed in a New Keynesian model, enrich he noion of marginal cos, by incorporaing he coss of esablishing a work relaionship over and above he uni labour cos, hereby, in principle, alering he dynamics of in aion. A growing number of empirical sudies documen ha embedding labour marke fricions ino a sandard New Keynesian model increases he model s empirical performance and enables a more accurae descripion of in aion dynamics. 2 The conribuion of our paper is wo-fold. Firs, we build on hese previous sudies o esimae a New Keynesian model characerised by labour marke fricions using UK daa. This esimaion allows us o esimae he srucural parameers of he Unied Kingdom economy, he unobservable shocks and sudy heir ransmission mechanism. Second, we invesigae how saggered nominal wage negoiaions a ec he propagaion of shocks and he abiliy of he model o he daa. To his end, he heoreical framework allows, bu does no require, nominal wage rigidiies o a ec he model s dynamics, herefore leaving he daa o esablish he imporance of wage rigidiies. In paricular, his esimaion sraegy allows us o invesigae he e ec of nominal wage rigidiies on in aion dynamics. Our ndings are he following. Firs, we esimae imporan srucural parameers of he labour marke ha characerise he Briish economy. In paricular, we idenify a relaively low Frisch elasiciy of labour supply, re ecing he fac ha employmen is more volaile along he exensive margin han he inensive margin. The bargaining power of he workers is esimaed o equal abou 0.9. This esimae implies a rm s surplus of approximaely 10% relaive o produciviy, which is higher han he value of 2.5% in Hagedorn and Manovskii (2008) needed o mach he unemploymen volailiy in US daa. The habi persisence parameer is close o zero, di erenly from he high value of approximaely 0.6 in US daa. We nd ha on average prices adjus every wo quarers, in line wih UK micro-esimaes in Bunn and Ellis (2009), whereas he average frequency 1 See Smes and Wouers (2003, 2007) for an exensive applicaion of his framework. 2 Noiceable examples, documened below, are Gerler e al (2008), Chriso el, Kueser and Linzer (2009), Krause e al (2008b), Zanei (2010) and Ravenna and Walsh (2008). 1

3 of wage negoiaions is abou hree quarers. We also provide esimaes for he moneary auhoriy s reacion funcion. We nd ha he moneary auhoriy s response o in aion is paricularly srong, here is a mild degree of ineres rae ineria and a weak response o oupu ucuaions. The esimaed model allows us o characerise he ransmission of shocks. We invesigae how he model variables reac o supply and demand shocks, and we nd ha neural and invesmenspeci c echnology shocks are more imporan han oher shocks in explaining he daa. Finally, using a Kalman ler on he model s reduced form we provide esimaes for he unobservable shocks ha characerised he pos-1970s Briish economy. In general, we nd ha he magniude of some shocks has somewha decreased in he period beween he mid-1990s and he mid-2000s. In paricular, similarly o sudies for oher counries, we nd ha he volailiy of moneary policy shocks declined during his period. These ndings corroborae he resuls of empirical sudies, such as Benai (2007) and Bianchi e al (2009), which deeced a period of macroeconomic sabiliy riggered by a lower volailiy of shocks in he Unied Kingdom during he same ime span. We esablish ha saggered wage-seing enables he model o he daa more closely. However, we nd ha a he esimaed equilibrium wage rigidiies are irrelevan for in aion dynamics. This resul echoes he ndings by Krause and Lubik (2007). In a fricional labour marke in aion depends on uni labour coss and on an addiional erm which is relaed o labour marke fricions, ha is, o he expeced change in he search coss incurred in nding a mach. Following a shock, wage rigidiies have a direc e ec on he uni labour cos. However, he conribuion of uni labour coss o marginal coss is o se by he conribuion of he componen relaed o labour marke fricions. We elaborae more on he inuiion in he main ex. This resul holds for all he shocks in our model economy and sands in sharp conras wih hose obained in New Keynesian models wih compeiive labour markes. Absen search fricions in he labour marke, he dynamics of in aion are only driven by he uni labour coss. I follows ha wage rigidiies generae in aion persisence by making uni labour coss more persisen (see Chrisiano e al (2005)). In his paper we also invesigae wheher he irrelevance of wage rigidiies for in aion dynamics is buil ino he model, which poenially may preven wage rigidiies from a ecing he dynamics of in aion, or i is a consequence of he speci c esimaion. To answer his quesion we simulae he heoreical framework by drawing 1,000 imes from he parameer priors and we compare he variance of in aion from he baseline model wih wage rigidiies and an oherwise idenical model where wages are exible. I clearly emerges ha he variance of in aion in he model wih exible wages is greaer han in he model wih sicky wages for a wide range of parameer values. So we nd ha in our model he irrelevance resul obained by Krause and Lubik (2007) only holds for some paricular calibraions. However, for he esimaed parameers he variance of in aion is idenical in he wo models. This shows ha he heoreical framework allows nominal wage rigidiies o have relevan consequences for in aion dynamics, bu he daa prefer a version of he model in which wage rigidiies are irrelevan for in aion dynamics. This resul sands in conras wih hose found by Gerler e al (2008) in a similar analysis of he US labour marke. 2

4 The paper is relaed o several sudies. As in Krause and Lubik (2007), Krause e al (2008a,b), Ravenna and Walsh (2008) and Zanei (2010), we inernalise he imporance of labour marke fricions o describe in aion dynamics, bu we also exend he framework o incorporae and es he empirical relevance of saggered wage-seing. In his respec, our approach is similar o Gerler e al (2008). However, our work di ers from heirs as we allow rms o change he labour inpu along boh he exensive and he inensive margin, and we simplify he modelling of wage rigidiies following Thomas (2008). Moreover, by assuming ha newly hired workers become immediaely producive we inroduce an insananeous channel from wages o in aion wihou deparing from e cien bargaining on hours. As shown by Trigari (2006), under e cien bargaining on hours and a delay in he iming of he maching funcion, here is no link beween curren period wages and marginal coss. The inuiion is sraighforward: if i akes ime for workers o conribue o producion, rms can change oupu only by changing hours. As a resul, curren period marginal coss will only depend on hours. Bu when hours are e cienly bargained he number of hours will depend only on he raio beween he marginal rae of subsiuion and he marginal produc of labour, which in urn are independen from wages. In order o inroduce a link beween curren period wages and marginal coss, a number of auhors have abandoned he assumpion of e cien bargaining o invesigae he implicaions of righ o manage (Chriso el and Kueser (2008), Chriso el and Linzer (2006), Chriso el, Kueser and Linzer (2009), Maesini and Rossi (2008) and Zanei (2010)). We build on his lieraure by showing ha a conemporaneous iming of he maching funcion resores a wage channel in he presence of e cien bargaining on hours. However, we nd ha a he esimaed equilibrium he wage channel is unable o a ec in aion dynamics. Finally, di erenly from all he aforemenioned sudies, we are he rs o esimae a model wih labour marke fricions and nominal wage rigidiies on he UK economy. The remainder of he paper is organised as follows. Secion 2 ses up he model and deails he speci caion of marginal coss. Secion 3 presens he resuls of he esimaion. Secion 4 uses impulse response funcions o lay ou he ransmission mechanism of he model. I hen evaluaes he imporance of each shock in explaining he dynamics of he endogenous variables, and nally uses he reduced form of he model o recover he dynamics of he unobserved shocks. Secion 5 invesigaes wheher he irrelevance of wage rigidiies for in aion dynamics is buil ino he heoreical framework. Finally, Secion 6 concludes. 2 The model The model combines he search and maching framework in Krause e al (2008a) wih he saggered wage-seing mechanism in Thomas (2008). The economy consiss of: households; rms, comprised of a coninuum of producers indexed by j 2 [0; 1] and reailers; a moneary auhoriy and a scal auhoriy. In wha follows we explain he srucure of he labour marke and he problems faced by households and rms. We conclude by deailing he speci caion of marginal coss. 3

5 2.1 The labour marke The maching of workers and rms is esablished by he sandard maching funcion M(U ; V ) = mu V 1, which represens he aggregae ow of hires in a uni period. 3 The variable U denoes aggregae unemploymen and V aggregae vacancies, m > 0 capures maching e ciency and 0 < < 1 denoes he elasiciy of he maching funcion wih respec o unemploymen. During each period, vacancies are lled wih probabiliy q( ) = M =V ; where = V =U denoes labour marke ighness. Consan reurns o scale in he maching funcion imply ha workers nd a job wih probabiliy q( ): We assume ha new hires sar working a he beginning of each period, and a he end of each period a consan fracion of workers loses he job wih probabiliy : Consequenly, he evoluion of aggregae employmen N is: 4 N = (1 )N 1 + M : (1) Workers who lose he job a ime 1 can look for a job a he beginning of ime : The sock of workers searching for a job a ime is herefore given by he number of workers who did no work in 1, 1 N 1 ; plus hose who los heir job a he end of he period, N 1. The evoluion of aggregae unemploymen is wrien: U = 1 (1 )N 1 : 2.2 Households The economy is populaed by a uni measure of households whose members can be eiher employed or unemployed. We follow Merz (1995) and Andolfao (1996) in assuming ha members of he represenaive household perfecly insure each oher agains ucuaions in income. The problem of he represenaive household is o maximise an expeced uiliy funcion of he form 2 X 1 E s +s 4 (c +s &C +s 1 ) s=0 +s Z h 1+ j+s n j+s 1 + dj 5 ; (2) where is he discoun facor, is a preference shock and is a labour supply shock. variable c denoes consumpion of he represenaive household a ime, while C 1 denoes aggregae consumpion in period 1, and & is an index of exernal consumpion habis. The variable n j denoes he number of household members employed in rm j; and h j denoes he corresponding number of hours. The parameer governs he degree of risk aversion and is he inverse of he Frisch elasiciy of labour supply. Consumpion c is a Dixi-Sigliz aggregaor of a 3 Noe ha U = R 1 ujdj and 0 V = R 1 jdj: 4 0 Noe ha N = R 1 njdj: 0 The 4

6 bundle of di ereniaed goods: 0 c Z 1 0 c (j) ( 1)= dj 1 A =( 1) ; where is he sochasic elasiciy of subsiuion among di ereniaed goods. Denoing by p j he price of a variey produced by a monopolisic compeior j; he expendiure minimising price index associaed wih he represenaive consumpion bundle c is: 0 p Z 1 0 p (j) 1 The household faces he following budge consrain: I + c + B Z B 1 1 = R 1 + p p 0 dj 1 A 1=(1 ) : w j p n j h j dj + (1 n )b + r k k + d + T ; (3) which dicaes ha expendiure, on he lef-hand side (LHS), mus equal income, on he righ-hand side (RHS). The households expendiure is invesmen, I, consumpion, c, and he acquisiion of bonds, B =p. Households income is he sock of bonds B 1 =p from previous period 1 which pay a gross nominal ineres rae R 1, he proceedings from working in he rms indexed by j, R 1 0 (w j =p )n j h j dj, 5 and he unemployed bene s, b, earned by each unemployed member of he household. In addiion, he household earns proceedings from rening capial, k, o he rms a he rae r k, he real dividends from owning he rms, d, and he ne governmen ransfer T. The household chooses c ; B and k +1 o maximise he uiliy funcion (2), subjec o he budge consrain in equaion (3) and he law of moion for capial, k +1 = I + (1 k )k ; (4) where k denoes he rae of capial depreciaion and denoes an invesmen-speci c echnology shock. By subsiuing equaion (4) ino (3), and leing denoe he Lagrange muliplier on he budge consrain, he rs-order condiions wih respec o c ; B and k +1 are: = (c &C 1 ) ; (5) = E [ +1 R = +1 ] ; (6) 5 Noe ha wih his noaion w j, n j and h j are he wage employmen and hours of work a rm j a ime respecively. 5

7 and i = E +1 hr+1 k + (1 k ) ; (7) where +1 = p +1 =p denoes he gross in aion rae. Equaion (5) saes ha he Lagrange muliplier equals he marginal uiliy of consumpion. Equaions (6) and (7), once equaion (5) is subsiued in, are he sandard household s Euler equaions ha describe he consumpion and capial decisions respecively. To conclude he descripion of he household we need o de ne he marginal value of being employed and unemployed. The marginal value of employmen a rm j, Wj E ; is given by: W E j = w j p h j 1+ hj E +1 W U +1 + (1 )Wj+1 E ; (8) which saes ha he marginal value of a job for a worker is given by he real wage bill ne of he disuiliy of work plus he expeced-discouned value from being eiher employed or unemployed in he following period. The marginal value of unemploymen, W U ; is: W U = b + E +1 h(1 +1 q( +1 )) W U +1 + (1 ) +1 q( +1 ) ^W E +1 i ; (9) where E ^W E +1 = R 1 0 W j+1 E dj is he expeced value of employmen in + 1: This equaion saes ha he marginal value of unemploymen is he sum of unemploymen bene s plus he expeceddiscouned value from being eiher employed or unemployed in + 1. Using equaions (8) and (9) we deermine he household s ne value of employmen a rm j, W E j W U, denoed by W j, as: 1+ w j hj W j = h j b p E +1 (1 ) hw j+1 +1 q( +1 ) ^W i +1 ; (10) where E ^W+1 = R 1 0 W j+1dj. 2.3 Firms We assume wo ypes of rms: producers and reailers. Producers hire workers in a fricional labour marke and ren capial in a perfecly compeiive marke. They manufacure a homogeneous inermediae good and sell i o reailers in a perfecly compeiive marke. Reailers ransform inermediae inpus from he producion secor ino di ereniaed goods and sell hem o consumers. As i is sandard in he New Keynesian lieraure, we assume saggered price adjusmen à la Calvo (1983). In wha follows we describe he problems of he producers and reailers in deail. Producers There is a coninuum of producers of uni measure selling homogeneous goods a he compeiive price '. During each period, rm j manufacures y j unis of goods according o he following 6

8 producion echnology y j = A (n j h j ) k 1 j, where A is a sochasic variable capuring neural echnology shocks. We assume consan reurns o scale in producion implying ha all rms have he same capial-labour raio k j =n j h j = k =n h for all j. Consequenly, he marginal produc of labour is also equalised across rms such ha mpl j = mpl : Firms open vacancies a ime o choose employmen in he same period; he cos of opening vacancies is C(v j ) = av "c j ; where a > 0 is a scaling facor and " c > 1 is he elasiciy of hiring coss wih respec o vacancies: The vacancy cos funcion is assumed o be convex in order o produce an equilibrium where all he rms pos vacancies. If he vacancy cos funcion were linear all rms would face he same marginal vacancy posing cos. Since we assume saggered nominal wage negoiaions, i follows ha only he rm wih he lowes wage would hire a equilibrium. In our model wage dispersion implies ha rms wih high wages face low marginal reurn from search and low marginal vacancy posing coss since hey hire only a relaively small number of workers. The problem of he rm is o choose v j, n j and k j+1 o maximise he presen value of fuure discouned pro s: max E 1 X s=0 s +s ' +s y +s w j n j+s h j+s C(v j+s ) k j+s r+s k ; p subjec o he producion funcion and he law of moion for employmen: n j = (1 )n j 1 + v j q( ): (11) Since households own he rms, fuure pro s are discouned a he rae s +s = : Leing J j denoe he Lagrange muliplier on he employmen consrain (11), he rs-order condiions wih respec o k j+1, v j and n j are: r k = ' (1 ) A (n j h j ) k j ; (12) C 0 (v j ) q ( ) = J j; (13) J j = ' A (n j h j ) 1 k 1 j h j w j p h j + (1 ) E +1 J j+1 : (14) Equaion (12) implies ha reurns o capial equalise he marginal revenue produc. Equaion (13) implies ha he per period cos of lling a vacancy C 0 (v j ) imes he average vacancy duraion 1=q ( ) mus equal he shadow value of employmen J j : Equaion (14) shows ha he shadow value of employmen o he rm equals curren period pro s, ie, he marginal revenue produc of employmen ne of wage coss, plus he coninuaion value. Subsiuing equaion (13) ino equaion 7

9 (14) yields he sandard job creaion condiion: C 0 (v j ) q ( ) = ' A (n j h j ) 1 k 1 j h j w j p h j + (1 ) E +1 C 0 (v j+1 ) q ( +1 ) ; (15) which saes ha he cos of hiring an addiional worker (LHS) equals he marginal bene (RHS) ha he addiional worker brings ino he rm. Reailers There is a uni measure of reailers who ransform homogeneous goods from he producion secor ino di ereniaed goods. following demand for is own produc Monopolisic compeiion implies ha each reailer j faces he c j = pj c ; (16) p where c is aggregae demand of he consumpion bundle. Each reailer produces c j unis of oupu using he same amoun of inpus from he producion secor. We assume price sickiness à la Calvo (1983), meaning ha during each period a random fracion of rms, p, are no allowed o rese heir price. The problem of he reailers is o choose p j o maximise: max E 1 X s=0 s p s +s pj p +s ' +s c j+s ; subjec o he demand funcion (16). The opimal pricing decision is: E 1 X s=0 s p s +s p p +s 1 ' +s = 0; (17) where p is he opimal price chosen by all rms renegoiaing a ime. This implies ha forwardlooking rms choose he opimal price such ha he ime-varying mark-up is equal o = ( 1). Since rms are randomly seleced o change price, he law of moion for he aggregae price level is: p 1 = p p (1 p) (p ) 1 : (18) 2.4 Wage bargaining Similarly o he price-seing decision, we assume saggered nominal wage negoiaions, meaning ha each period only a random fracion of rms, 1 w, is allowed o renegoiae on nominal wages. Following Thomas (2008) we assume ha he wage se by he renegoiaing rm j sais es 8

10 he following sharing rule: J j = (1 ) W j ; (19) where " is he sochasic bargaining power of he workers and he superscrip * denoes renegoiaing workers and rms. This sharing rule implies ha renegoiaing workers obain a fracion of he oal surplus equal o heir bargaining power. Noice ha his is di eren from Nash bargaining. Wih Nash bargaining wages maximise a weighed average of he join surplus. Nash bargaining delivers he sharing rule, equaion (19), only if wages are coninuously renegoiaed. As shown by Gerler and Trigari (2009), Nash bargaining implies ha, in he presence of saggered nominal wage negoiaions, he share parameer in equaion (19) would ucuae over he cycle even if i were no subjec o shocks. This follows from he fac ha workers and rms face di eren ime horizons when hey consider he e ecs of di eren wages. However, Gerler and Trigari (2009) sugges ha his horizon e ec has quaniaively negligible implicaions. We herefore choose o follow Thomas (2008) and adop he sharing rule in equaion (19) as i simpli es he analysis considerably. Wih saggered wage negoiaions, he shadow value of employmen a rm j o he household ha is allowed o renegoiae can be rewrien from equaion (10) as follows: W j = w j +1 W j+1j h j ew j + E (1 ) w (1 w ) W j+1 ; (20) p where he worker s opporuniy cos of holding he job, ew j, is equal o: ew j = b + 1+ hj E +1 (1 ) +1 q( +1 ) ^W +1 : The ne value of employmen o he household condiional on wage renegoiaion a ime (equaion (20)), equals he ne ow income from employmen, (w j =p )h j ew j, plus he coninuaion value, which is he las erm on he RHS. The laer is equal o he sum of he marginal discouned value of employmen in + 1 condiional on he wage se a ime, if he rm does no renegoiae wih probabiliy w, and he value of employmen in +1 condiional on a renegoiaion, wih probabiliy 1 w : Similarly, he shadow value of employmen o he renegoiaing rm j can be wrien: J j = w j wj +1 h j + (1 )E w J p j+1j + (1 w )J j+1 ; (21) where w j = ' mpl h j denoes he marginal revenue produc: The marginal value of employmen for a renegoiaing rm equals he ne ow value of he mach plus he coninuaion value. In urn, his equals he marginal value of employmen in + 1 condiional on he previous period wage, wih probabiliy w, and he marginal value condiional on a wage renegoiaion, wih probabiliy 1 w. 9

11 and Ieraing equaions (20) and (21) forward i is possible o rewrie hem as follows: W j = E 1X s=0 +(1 )(1 w )E 1 X J j = E 1 X s=0 s +s w (1 ) s s j w h j+s p +s s=0 +(1 )(1 w )E 1 X ew j+s s+1 +s+1 (1 ) s s Wj+s+1 w ; (22) +s+1 s +s (1 ) s s w w j+s s=0 wj h j+s p +s s+1 +s+1 (1 ) s s wj j+s+1: (23) Using he sharing rule in equaion (19), equaions (22) and (23) imply ha: E 1 X s=0 s +s w (1 ) s s j w h j+s p +s w+s ar = 0; (24) where wj+s ar = +sw j+s + (1 +s ) ew j+s is he oal real wage paymen o he worker on which boh paries would agree if wages were fully exible: Subsiuing for w j+s and ew j+s he arge real wage bill can be wrien: w ar j+s = ' mpl h j + (1 ) " b + Equaion (25) is sandard in he search and maching lieraure. 1+ hj E +1 (1 ) +1 q( +1 ) ^W # +1 : (25) The arge real wage bill is expressed as a weighed average beween he marginal revenue produc of he worker and he opporuniy cos of holding a job a he level of hours worked h j. Given ha renegoiaing rms are randomly chosen, he law of moion for he aggregae nominal wage is given by: where w = R 1 0 w jdj: 2.5 Hours bargaining w = w w 1 + (1 w )w ; (26) We assume ha hours and wages are bargained simulaneously and ha bargaining on hours is e cien. Hence, hours saisfy he Nash bargaining crierion: W j h j = arg max J j 1 : 10

12 Using he sharing rule (19), he rs-order condiion becomes: h j = ' A 2 n 1 j h 1 j k 1 j : This equaion saes ha he marginal rae of subsiuion, on he LHS, equals he marginal produc of hours, on he RHS. Since he marginal reurn o he labour inpu is equalised across rms a equilibrium, i follows ha members of he household employed in di eren rms work he same amoun of hours, ie, h j = h : Solving he rs-order condiion for hours yields: 2.6 Price and wage in aion h j = ' A 2 n 1 j kj 1! 1 1+ : (27) Following Calvo (1983), using equaions (17) and (18) we derive he sandard New Keynesian Phillips Curve: = k p (^' + ) + E +1 ; (28) where a ha superscrip denoes he variable s deviaion from is seady sae, and he coe cien k p is equal o: k p (1 p) (1 p ) p : Similarly, following Thomas (2008), using equaions (24) and (26) we obain he following equaion for wage in aion: w = k w h bw ar where bw denoes he real wage and he coe cien k w is equal o: bw + ^h i + (1 ) E w+1 ; (29) k w [1 (1 ) w] (1 w ) w : Equaion (29) saes ha he real wage in aion depends on he gap beween he acual and arge real wage bill, bw + ^h and bw ar, respecively. In aion maerialises whenever he real wage bill is below arge, ha is, whenever he wage bill is below he level ha would prevail if wages were perfecly exible. The appendix repors he derivaion of he wage Phillips curve, equaion (29). 11

13 2.7 Closing he model The moneary auhoriy ses he nominal ineres rae following he Taylor rule: R R = r R 1 r R ry 1 y y r " R ; where an aserisk superscrip denoes he seady-sae values of he associaed variables. parameer r represens ineres rae smoohing, and r y and r govern he response of he moneary auhoriy o deviaions of oupu and in aion from heir seady-sae value. The error erm " R denoes an i.i.d. moneary policy shock. The scal auhoriy is assumed o run a balanced budge: 2.8 Marginal coss B p = R 1 B 1 p + T + b (1 n ) : In his secion we compare he speci caion of marginal coss in our model agains alernaive formulaions in he lieraure. This is imporan o unveil some key properies of he model and undersand he ndings deailed in he nex secion. In a maching model wih e cien bargaining on hours, Trigari (2006) shows ha whenever rms pos vacancies a ime o conrol employmen in he following period, he real marginal cos a ime is independen from wages a ime. The independence of curren period marginal coss from curren period real wages is ypically referred o, in he lieraure, as he lack of a wage channel. The inuiion is sraighforward. Since curren hires conribue o nex period employmen, in he curren period rms can change producion only by adjusing hours. This implies ha he marginal cos of producion a ime depends solely on hours. Wih e cien bargaining he number of hours worked is deermined by he marginal rae of subsiuion beween consumpion and leisure and he marginal produc of labour, and herefore i is independen from wages in he curren period. I follows ha curren wages are irrelevan for curren period marginal coss. Following Trigari (2006), a number of auhors such as Chriso el and Kueser (2008), Chriso el and Linzer (2006), Maesini and Rossi (2009) and Zanei (2007) have resored he ransmission channel from wages o prices by resoring o alernaive bargaining schemes such as he righ o manage. In our model we are able o resore a wage channel a ime while preserving e cien Nash bargaining. We do so by changing he iming assumpion of he maching funcion. Tha is, we allow rms o conrol employmen a ime by choosing vacancies in he same period, as described by equaion (11). Under his iming assumpion, he cos of increasing producion a he margin depends on he cos of hiring an addiional worker, which is represened by he wage paid o he new hire. This can be seen by solving he job creaion condiion in equaion (14) for marginal The 12

14 coss ' : ' = w p h mpe + J E +1 (1 ) J +1 ; (30) mpe where mpe = A (n j h j ) 1 kj 1 h j denoes he marginal produc of employmen. From equaion (30), as shown by Krause and Lubik (2007), real marginal coss are equal o he sum of he uni labour cos and an addiional erm relaed o maching fricions. Given ha he shadow value of employmen J equals he expeced hiring cos, he second erm on he RHS of equaion (30) can be inerpreed as he expeced change in search coss. By equaion (13), his erm depends on he expeced value of labour marke ighness in he nex period relaive o he curren period. Had we assumed ha newly hired workers were unable o conribue o producion immediaely, he decision on vacancies would only a ec nex period marginal coss, leaving curren period marginal coss solely dependen on he number of hours, which, due o e cien wage bargaining, are independen from wages. 3 Esimaion The model is esimaed wih Bayesian mehods. I is rs loglinearised around he deerminisic seady sae. We hen solve he model and apply he Kalman ler o evaluae he likelihood funcion of he observable variables. The likelihood funcion and he prior disribuion of he parameers are combined o obain he poserior disribuions. The poserior kernel is simulaed numerically using he Meropolis-Hasing algorihm. 6 We rs discuss he daa and he priors used in he esimaion and hen repor he parameer esimaes. 3.1 Priors and daa The model is esimaed over he period 1971:Q1-2009:Q4 using seven shocks and seven quarerly daa series: consumpion, invesmen, in aion, average hours, employmen, he real wage and he nominal ineres rae. The daa series are from he O ce for Naional Saisics daa se; he acronyms are indicaed in ialics. For consumpion, we use daa on household nal consumpion expendiure (ABJR) and for invesmen we use daa on business invesmen (NPEL). We de ne oupu o be he sum of hese wo series and he price level o be he implici de aor associaed wih his measure of oupu ((NPEK +ABJQ)/(NPEL+ABJR)). Our employmen series comes from he Labour Force Survey (MGRZ ) and our series for average hours is calculaed as oal acual weekly hours worked (YBUS) divided by employmen. We de ne he nominal wage as wages and salaries (ROYJ ) divided by oal acual weekly hours worked. his series divided by our series for he price level. The real wage is hen Finally, our nominal ineres rae series is he 6 We use wo blocks of 250,000 draws. The sequence of draws is sable, providing evidence on convergence. An appendix ha deails evidence on convergence is available upon reques from he auhors. 13

15 London clearing banks base rae (AMIH ). The series for consumpion, invesmen, average hours, employmen and real wages are logged and hen all series are passed hrough a Hodrick-Presco ler wih smoohing parameer 1,600. The seven shocks in he model are a preference shock, a mark-up shock, a labour supply shock, a neural echnology shock, a bargaining power shock, an invesmen-speci c echnology shock and a moneary policy shock. All shocks, wih he excepion of moneary policy shock, are assumed o follow a rs-order auoregressive process wih i.i.d. normal error erms such ha ln +1 = ln +, where he shock 2 f; ; ; A; ; " g, 0 < < 1 and N (0; ) : Moneary policy shocks " R are i.i.d. The model conains 19 srucural parameers, excluding he shock parameers. A rs aemp o esimae he model showed ha he esimaion procedure was unable o provide plausible esimaes for some srucural parameers. As in oher similar sudies, we calibraed hese parameers in order o mach imporan sylised facs in he daa. We sar by discussing he xed parameers, whose values are summarised in Table A. The discoun facor is se a 0.99 implying a real ineres rae of 4%. The labour share parameer is se equal o 0.69 in order o mach he observed labour share over he period of he esimaion and he capial depreciaion parameer k is se a o mach an average annual rae of capial desrucion of 10%. The elasiciy of he vacancy cos funcion, " c, is also xed. This parameer is se a 1.1, a value which is relaively close o he sandard assumpion of linear adjusmen coss, and sais es he assumpion of convexiy. The unemploymen bene s coe cien, b, is calibraed o mach a replacemen raio of 0:58, as in OECD (2007). This parameer is imporan o generae ampli caion of labour marke variables. As shown by Hagedorn and Manovskii (2008), values of b close o uniy generae responses of unemploymen and vacancies o produciviy shocks ha are close o he daa. When b is high, he value of a job o he worker is very close o he value of unemploymen. In such insance he surplus of a job is very small and iny changes in he produciviy of he labour inpu produce a high percenage change in he oal surplus of a mach, boosing he response of employmen. The elasiciy of he maching funcion,, is se o 0:7, as esimaed by Perongolo and Pissarides (2001) for he UK economy. The consan of he maching funcion, m, is se equal o 0.5 o mach he job- nding rae of 35%, in line wih evidence from he Labour Force Survey (LFS). The job desrucion rae,, is se o 0:03, as esimaed by Bell and Smih (2002) using LFS daa. Finally, he elasiciy of demand,, is se o 11, a value suggesed in Brion e al (2000), which implies a seady-sae mark-up of 10%. Finally, he seady-sae gross in aion rae,, is se equal o 1. The remaining parameers are esimaed. We use he bea disribuion for parameers ha ake sensible values beween zero and one, he gamma disribuion for coe ciens resriced o be posiive and he inverse gamma disribuion for he shock variances. Tables B and C repor priors, poserior esimaes and 90% con dence inervals for he srucural and shock parameers respecively. The prior mean of he relaive risk aversion,, is se equal o The prior mean of he index of exernal habi, &, is se a is middle value of 0.5, as in Gerler e al (2008). The prior mean of he 14

16 inverse of he Frisch elasiciy of labour supply,, is se equal o 1, as in Krause e al (2008a). The prior mean of he scaling facor of he cos of posing a vacancy, a, is se equal o 3 such ha he cos of posing a vacancy is approximaely 1% of oal oupu a he seady sae, as in Blanchard and Gali (2010). The prior mean of he worker bargaining power,, is se o 0.5, such ha he rm and he worker hey equally spli he surplus from working. The prior mean of he Calvo parameer on prices, p, is se o 0.5 in order o mach an average duraion of prices of abou six monhs, in line wih he evidence in Bunn and Ellis (2009) for he UK economy. We ake an agnosic view on wheher wages are more exible han prices, and herefore se he prior mean of he Calvo parameer on wages, w, o 0.5. We choose he prior means of he Taylor rule response o in aion, r, oupu, r y, and he ineres rae smoohing parameer, r, equal o 1.5, and 0.5 respecively. These values are commonly used in he lieraure. Finally, Table C repors he prior disribuions of he shock parameers. The prior mean of he auoregressive parameers is se equal o 0.8 and he prior mean of he sandard errors is se equal o for all he shocks. For he prior mean of he auoregressive parameers we choose values ha are in beween hose seleced by Gerler e al (2008) and Krause e al (2008a). 3.2 Parameer esimaes The hird, fourh and fh columns of Table B show he poserior means of he srucural parameers ogeher wih heir 90% con dence inervals. The poserior mean of he relaive risk aversion is equal o 0.73, in he range of esimaes in Brown and Gibbons (1985) for he Unied Saes. The poserior mean of he index of exernal habis & is equal o 0.04, which is subsanially lower han he esimae of 0.57 in Smes and Wouers (2003), herefore ruling ou habi in consumpion as an imporan source o generae persisence in he model. The poserior mean of he inverse of he Frisch elasiciy of labour supply is equal o 1.6, which is subsanially higher han is prior, and in line wih microeconomic esimaes as surveyed by Card (1994). This high esimae re ecs he fac ha employmen volailiy is higher a he exensive margin han a he inensive margin. Krause e al (2008a) obain similar resuls for he Unied Saes, alhough heir esimae is higher han ours. The poserior mean of he consan of he vacancy cos funcion a is equal o 1.88, lower han is prior, which indicaes ha he model prefers a low cos of posing a vacancy, which is equal o 0.3% of oal oupu a he esimaed equilibrium, similarly o he esimaes in Silva and Toledo (2009) of approximaely 0.2% on US daa. The poserior mean of he bargaining power of he workers is equal o 0.87, hereby indicaing ha wages are closer o he marginal produc of labour. This esimae is remarkably close o he value of 0.90 in Gerler e al (2008) based on US daa. Noe ha he value of and b deermine he equilibrium rm s surplus ha is a key variable for he response of labour marke variables o shocks, as shown in Hagedorn and Manovskii (2008). In paricular, 15

17 a low rm s surplus increases he response of labor marke variables. The poserior means of he model implies a rm s surplus of approximaely 10% relaive o produciviy, which is higher han he value of 2:5% in Hagedorn and Manovskii (2008). 7 The unemploymen rae is abou 10% a he esimaed equilibrium, slighly higher han he average value of 7% observed in he daa, possibly accouning for he exisence of workers who are only marginally aached o he labour force, and as such do no qualify as unemployed according o he ILO de niion. This higher unemploymen rae implies ha he job nding rae, around 28%, is somewha lower han our calibraion arge based on LFS daa. The poserior means of he Calvo parameers on he frequency of wage and price negoiaions, w and p, are equal o 0.63 and 0.52 respecively, showing ha prices adjus more frequenly han wages. These values imply an average frequency of wage negoiaions of hree quarers, in line wih Dickens e al (2007), and an average frequency of price negoiaions of wo quarers, in line wih Bunn and Ellis (2009) for he UK economy. However, alhough he model prefers higher wage rigidiies han price rigidiies, he esimaion shows a sizable uncerainy around is poserior mean. Finally, he esimaes of he Taylor rule parameers are as follows. The poserior mean of he ineres rae response o in aion, r, equal o 1.48 indicaes a srong response o in aion and he poserior mean of he degree of ineres rae smoohing, r, equal o 0.53 suggess a mild degree of ineres rae ineria. The poserior mean of he response o oupu, r y, equal o 0.31 shows a weak response o oupu. The hird, fourh and fh columns of Table C show he poserior means of he shock parameers ogeher wih heir 90% con dence inervals. The poserior means of he persisence parameers and, equal o 0.84 and 0.88 respecively, indicae ha shocks o he labour supply and preferences are subsanially more persisen han he oher shocks. The poserior means of he shocks variance is close o 1% for all he shocks, wih he excepion of invesmen-speci c echnology shocks, i, and bargaining shocks,, which are more volaile. In order o esablish wheher saggered wages are imporan o mach he daa, Table D repors he value of he marginal likelihood funcion for he esimaed models wih sicky and exible wages respecively. Since he value of he marginal likelihood funcion associaed wih he model wih sicky wages is equal o 3466, and subsanially higher han he value of 2944 associaed wih he exible wage model, saggered wage-seing enables he model o he daa more closely, hereby suggesing ha wages rigidiies are imporan o replicae UK daa. 7 Noe ha when we esimaed he model including ime series for vacancies, he rm s surplus was similar o Hagedorn and Manovskii (2008), alhough he overall of he model was worse. 16

18 4 Impulse response funcions, variance decomposiion and unobserved shocks In his secion we invesigae, by use of impulse responses, how he shocks are ransmied o he endogenous variables. In order o disenangle he e ec of nominal wage rigidiies we use our baseline model and an oherwise idenical model where he Calvo parameer on wages is se o zero ( w = 0). Figures 1-7 plo he impulse responses of seleced variables o a one sandard deviaion shock. Each enry compares he responses of he model wih sicky wages (solid line) agains hose wih exible wages (doed line). Figure 1 shows ha a one sandard deviaion mark-up shock leads o an increase in in aion. In urn, he resuling increase in he ineres rae decreases consumpion and invesmen. In reacion o he shock, he rm reduces he labour inpu along boh he inensive and he exensive margin o decrease producion. The qualiaive responses of he variables in he saggered wage model are similar o hose in he model wih exible wage-seing, since mark-up shocks do no induce he rm o adjus labour marke variables di erenly. However, i is worh noing ha wage rigidiies a ec he behaviour of nominal and real wages considerably, bu he reacion of marginal coss and in aion remains remarkably similar in he wo seings. Why are he in aion dynamics so similar? As deailed in Secion 2.8, search fricions inroduce an addiional erm ino marginal coss, over and above uni labour coss, which re ecs he expeced change in search coss. Following a posiive mark-up shock, nominal wage rigidiies aenuae he drop in uni labour coss and induce a fall in he fricional componen of marginal coss compared o a exible wage regime. As a resul, marginal coss and in aion dynamics behave similarly in he wo seings. Wage rigidiies aenuae he reacion of uni labour coss as rms are no allowed o renegoiae lower wages. A he same ime, wage rigidiies induce labour marke ighness o fall on impac and hen seadily increase. As a resul, he rm s cos of searching for a worker falls on impac and i hen rises over ime. 8 The rising pro le in expeced search coss implies ha he rm can save on fuure hiring coss by increasing curren period hiring. From equaion (30), higher expeced search coss nex period, ranslae in lower marginal coss in he curren period. As a resul, he impac of wage rigidiies on he fricional componen of marginal coss compensaes he impac on uni labour coss, leaving oal marginal coss unchanged compared o he case of exible wages. Figure 2 shows ha in reacion o a one sandard deviaion neural echnology shock oupu rises and, due o he downward sloping demand curve, prices and in aion fall. Lower in aion riggers a lower nominal ineres rae, which fosers consumpion and invesmen. The qualiaive reacions of hese variables are similar in he exible and saggered wage models. However, he presence of saggered wage-seing inroduces imporan di erences in he reacion of labour marke variables. Following he shock, he increase in real wages is more persisen in he presence of nominal wage 8 Noe ha he average duraion of a vacancy, 1=q( ), depends only on labour marke ighness. 17

19 rigidiies. Wih sicky wages, price de aion ranslaes ino persisenly high real wages. Wih exible wages, afer an iniial increase on impac, nominal wages fall sharply, empering he increase in real wages. I is noiceable ha vacancies, employmen and labour marke ighness increase by less in he presence of sicky wages. The inuiion for his is sraighforward. A neural echnology shock increases boh he marginal produc of labour and he real wage. The di erence beween hese wo deermines he incenives for posing vacancies, as dicaed by equaion (15). Boh wih sicky and exible wages he marginal produc of labour increases by more han real wages. Wih sicky wages, persisenly high real wages imply ha he presen value of a job is lower, which induces he rm o open fewer vacancies. Figure 3 shows ha a one sandard deviaion labour supply shock reduces hours and exers upward pressure on nominal wages by increasing he disuiliy of work. Wih exible nominal wages, real wages increase, leading o a reducion in vacancies and employmen. The sharp reducion in unemploymen raises labour marke ighness. On he conrary, wih saggered wage bargaining nominal wage in aion is lower han price in aion, which implies ha real wages fall. Consequenly, in he sicky wage model, vacancies and employmen increase. The fall in unemploymen increases labour marke ighness. Wage rigidiies do no have a signi can impac on marginal coss and in aion since he e ec produced hrough uni labour coss is o se by he e ec of he fricional componen of marginal coss. Figure 4 shows ha a one sandard deviaion moneary policy shock causes an increase in he nominal ineres rae, and a fall in boh in aion and oupu. As in he cases of mark-up shocks, nominal wage rigidiies do no aler he qualiaive responses of he variables on impac, wih he excepion of he reacion of real wages and uni labour coss. In he presence of sicky wages, vacancies and employmen fall in reacion o he shock and price de aion generaes higher real wages. When wages are coninuously renegoiaed insead, nominal wages fall a a faser pace han prices and real wages. Once again nominal wage rigidiies have a di eren impac on uni labour coss in he wo seings, whose movemens are o se by he reacion of search coss. This generaes a remarkably similar response in marginal coss and price in aion in he wo seings. Figure 5 shows impulse responses o a one sandard deviaion preference shock. The qualiaive responses of he variables are he same for he sicky and exible seings. The preference shock generaes an increase in consumpion and upward pressure on prices. As price in aion increases, he nominal ineres rae rises, and boh invesmen and oupu fall. The preference shock induces he workers o work a lower number of hours, hereby generaing lower reurn from employmen. Hence, he rm poss fewer vacancies, conracing employmen and labour marke ighness. Finally, also in his insance, nominal wage rigidiies do no produce any impac on marginal coss, since search fricion coss o se movemens in uni labour coss. As a resul, in aion dynamics remain subsanially una eced by nominal wage rigidiies. As shown in Figure 6, also in he case of a one sandard deviaion bargaining power shock, he qualiaive reacion of labour marke variables is unchanged by wage rigidiies. Higher bargaining 18

20 power increases wage and price in aion. The real wage increases, and consequenly vacancies fall. A higher ineres rae decreases consumpion and invesmen, which riggers a fall in oupu. Saggered wage negoiaions dampen he reacion of boh nominal and real wages and, as a resul, of uni labour coss. However, also in his insance, he reacion of he fricional componen of marginal coss largely o ses he impac of wage rigidiies on uni labour coss, hereby generaing a similar in aion dynamics across he wo models. Figure 7 plos impulse responses o a one sandard deviaion invesmen-speci c echnology shock. As in he case of oher previous shocks, nominal wage rigidiies do no a ec he qualiaive response of he endogenous variables, wih he excepion of nominal wage in aion and real wages. An invesmen-speci c echnology shock makes invesmen more e cien. Given ha oupu is demand consrained, due o imperfec compeiion on he goods marke, and he low degree of consumpion smoohing makes consumpion increase on impac, invesmen falls. As oupu gradually increases over ime, vacancies and employmen increase. Saggered wage negoiaions a ec he response of nominal wage in aion and he real wage, bu as for he oher shocks, here is virually no impac on real marginal coss and price in aion. To summarise, we nd ha while wage rigidiies migh a ec he response of labour marke variables, hey are subsanially irrelevan for he dynamics of in aion. This echoes he ndings in Krause and Lubik (2007), who reach a similar conclusion in a calibraed model wih a wage norm and fewer shocks. This is in sark conras wih he predicions of he sandard New Keynesian model wihou labour marke fricions, as in Chrisiano e al (2005). In heir model uni labour coss are he only deerminan of marginal coss, implying ha wage rigidiies naurally generae in aion persisence. Our analysis shows ha in a model wih search fricions, he conribuion of uni labour coss for marginal coss is o se by movemens in search coss, which become an addiional componen of marginal coss. To undersand he exen o which cyclical movemens of each variable are explained by he shocks, Table E repors he asympoic variance decomposiion for he model wih sicky wages. Enries show ha neural and invesmen-speci c echnology shocks explain approximaely 60% of ucuaions in oupu, which is similar o he ndings in Gerler e al (2008) on US daa. Invesmen-speci c shocks are he main drivers of ucuaions in he nominal ineres rae, in aion, employmen, vacancies and wages, while labour supply shocks explain approximaely 57% of ucuaions in hours. Finally, i is ineresing o noe ha he conribuion of preference shocks is sizeable for mos variables, while he conribuion of mark-up and bargaining shocks is limied. This is due o he high auocorrelaion coe cien of 0.88 for he preference shocks and he low auocorrelaion coe ciens for he mark-up and bargaining shocks, as deailed in Table C. To deail how he exogenous shocks have evolved during he sample period, Figure 6 plos he esimaes of he shocks using he Kalman smoohing algorihm from he sae-space represenaion of he model wih sicky wages. The esimaes show ha he magniude of shocks has somewha decreased from mid-1990s unil mid-2000s, wih he excepion of labour supply shocks, whose size 19

21 has remained broadly unchanged. Furhermore, similarly o sudies for oher counries, we nd ha he volailiy of moneary policy shocks declined during he same period. These ndings corroborae he resuls of empirical sudies, such as Benai (2007) and Bianchi e al (2009), which deeced a period of macroeconomic sabiliy riggered by a lower volailiy of shocks in he Unied Kingdom during he same ime horizon. 5 Discussion From he analysis i clearly emerges ha wage rigidiies are irrelevan for he dynamics of in aion, similarly o he ndings in Krause and Lubik (2007) based on a model calibraed on US daa. This resul is in conras o Gerler e al (2008), who esimae a search and maching model wih saggered wage-seing on US daa and deec wage rigidiies as imporan for in aion dynamics. Is our resul driven by he speci c model ha we develop, which poenially prevens wage rigidiies from a ecing he dynamics of in aion? Or is i a consequence of he speci c esimaion of he model? To answer his quesion, we simulae he heoreical framework by drawing 1,000 imes from he parameers priors in Table B and we compare he variance of in aion from he baseline model wih wages rigidiies and an oherwise idenical model where he Calvo parameer on wages is se o zero ( w = 0). To eliminae exreme responses, we discard he regions of he wo disribuions below and above 2.5 and 97.5 perceniles respecively. In his way, we are able o esablish if he wo models deliver he same variance for in aion across a broad range of plausible calibraions, hereby suggesing ha he irrelevance resul is mechanically generaed by he model. Figure 9 repors he scaer plo of he variance of in aion in he model wih sicky wages (y-axes) agains ha wih exible wages (x-axes), and he 45 degree line indicaes he values for which he saisics in he wo models are idenical. I clearly emerges ha mos of he scaered poins lie below he 45 degree line, suggesing ha he variance of in aion in he model exible wages is greaer han in he model wih sicky wages for a wide range of parameers values. However, for some parameers values he variance of in aion in he models is idenical, since some of he poins lie on he 45 degree line. In paricular, he gray do in he gure ideni es he variance of in aion in he esimaed baseline model and in he oherwise idenical model wih exible wages, showing ha he wo models generae similar saisics. 6 Conclusion We have esimaed a New Keynesian model characerised by labour marke fricions on UK daa o idenify some key feaures of he UK economy. Firs, we esimaed imporan srucural parameers of he Briish economy, which enabled he invesigaion of he ransmission mechanism of shocks and how i is a eced by wage rigidiies. We esablished ha neural and invesmen-speci c echnology 20