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 y Sephen Millard Bank of England January 2010 Francesco Zanei z Absrac This paper esimaes a New Keynesian model wih maching fricions and nominal wage rigidiies on UK daa. The esimaion enables he ideni caion of imporan srucural parameers of he Briish economy, he recovery of he unobservable shocks ha a eced he UK economy since 1975 and he sudy of he ransmission mechanism. Resuls show ha wih maching fricions, wage rigidiies have limied e ec on in aion dynamics, despie improving he empirical performance of he model. The reason is he following. 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: Bayesian esimaion, labour marke search, wage rigidiies. We are graeful o Bob Hills, Thomas Lubik, Anonella Trigari and seminar paricipans a he Bank of England for heir 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. y Correspondence: Renao Faccini, Bank of England, Threadneedle Sree, London EC2R 8AH, U.K. Tel: Fax: renao.faccini@bankofengland.co.uk. z Correspondence: Francesco Zanei, Bank of England, Threadneedle Sree, London EC2R 8AH, U.K. Tel: Fax: francesco.zanei@bankofengland.co.uk.

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 UK economy, he unobservable shocks and sudy heir ransmission mechanism. Second, we invesigae how saggered 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 Frish elasiciy of labour supply, re ecing he fac ha employmen is more volaile along he exensive margin han he inensive margin. The esimae of he raio of he income value of non working aciviy over wages is abou 77%. As poined ou by Cosain and Reier (2008), his esimae is consisen wih a semielasiciy of unemploymen o unemploymen insurance equal o 2, which is in line wih empirical evidence. This nding cass doub on he argumen by Hagedorn and Manovskii (2008) ha a high opporuniy cos of working be a plausible soluion of he unemploymen volailiy puzzle in he UK. Similar resuls have been obained by Gerler e al. (2008) using US daa. The 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 e al. (2009a), Krause e al. (2008b), Zanei (2007a) and Ravenna and Walsh (2008). 1

3 elasiciy of he maching funcion wih respec o unemploymen is equal o 0.55, lower han he esimaes of 0.7 in Perongolo and Pissarides (2001), suggesing ha he number of new hires equally depends on he number of unemployed workers as well he number of vacancies posed. The esimae of he job desrucion rae is approximaely equal o 7%, higher han he esimaes from microdaa which range from 3%, as esimaed by Bell and Smih (2002), o 4.5%, as given by Hobijn and Sahin (2007). 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 and here is a mild degree of ineres rae ineria, while he response o oupu ucuaions is robus. 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 shocks o preferences and he labour supply are more imporan han echnology and moneary policy 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 shocks has somewha decreased since he mid-1990s, wih he excepion of preferences shocks, whose size has remained broadly unchanged. Furhermore, similarly o sudies for oher counries, we nd ha he volailiy of moneary policy shocks declined afer he mid-1990s. 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 UK during he pas decade. We esablish ha saggered wage seing enables he model o he daa more closely. We nd ha alhough a posiive degree of saggered wage seing is suppored by he daa, he model is unable o precisely idenify he frequency of wage adjusmen. Nominal wage rigidiies make wage dynamics more subdued, and have imporan implicaions for labour marke dynamics. For insance, in he saggered wage speci caion vacancies fall in reacion o a posiive echnology shock as prices fall a a faser pace han wages, inducing an increase in he real wage and a reducion in he value of a job o he rm. Similarly o Krause and Lubik (2007), we nd ha a he esimaed equilibrium wage rigidiies are irrelevan for in aion dynamics, despie being imporan in characerising labour marke dynamics. 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 a 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). 2

4 The paper is relaed o several sudies. As in Krause and Lubik (2007), Krause e al. (2008a, 2008b), Ravenna and Walsh (2009) and Zanei (2007a), 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 modeling of wage rigidiies following Thomas (2008). Moreover, we show ha by assuming ha newly hired workers become immediaely producive creaes a 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 wages and in aion. 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, marginal coss will only depend on hours. Bu when hours are e cienly bargained he marginal cos will depend only on he number of hours which is solely relaed o he raio beween marginal rae of subsiuion and he marginal produc of labour, which in urn are independen from wages. In order o inroduce a link beween wages and in aion, 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 e al. 2009a, Chriso el e al. 2009b, Maesini and Rossi 2009, and Zanei 2007b). 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. Finally, Secion 5 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 and 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 4 (c &C 1 ) =0 Z h 1+ j n j 1 + dj 5 ; (2) where is he discoun facor, is a preference shock and is a labour supply shock. The 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 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 Frish elasiciy 3 Noe ha U = R 1 ujdj and 0 V = R 1 jdj: 4 0 Noe ha N = R 1 njdj: 0 4

6 of labour supply. Consumpion c is a Dixi Sigliz aggregaor of a 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 p = R 1 B 1 p + Z 1 0 dj 1 A 1=(1 ) :! j 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 household expendiure is invesmen, I, consumpion, c, and he acquisiion of bonds, B =p. Households income is he sock of bonds B 1 from previous period 1 which pay a gross nominal ineres rae R 1, he proceedings from working in rm j, Z 1 0! j n j h j dj, 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 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, I = k +1 (1 k )k ; (4) where k denoes he rae of capial depreciaion. 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) 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 5

7 muliplier equals he marginal uiliy of consumpion. Equaions (6) and (7), once equaion (5) is subsiued in, are he 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: Wj E h 1+ j =! j h j 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 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 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 ouside he rm in + 1: This equaion saes ha he marginal value of unemploymen is he sum of unemploymen bene s plus he expeced-discouned 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: h 1+ j W j =! j h j b 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 producion echnology y j = A (n j h j ) k 1, where A is a sochasic variable capuring shocks j o oal facor produciviy. 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 6

8 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 a vacancy 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 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 h i ' +s y +s! j+s n j+s h j+s C(v j+s ) k j+s r+s k ; 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! j h j + (1 ) E +1 J j+1 : (14) Equaion (12) implies ha reurns o capial equalize 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, i.e., he marginal revenue produc of employmen ne of wage coss, plus he coninuaion value. Subsiuing equaion (13) ino equaion (14) yields he sandard job creaion condiion: C 0 (v j ) q ( ) = ' A (n j h j ) 1 k 1 j h j! j 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) 7

9 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 forward looking 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 wage negoiaions, meaning ha each period only a random fracion of rms, w, is allowed o renegoiae on wages. Following Thomas (2008) we assume ha he wage se by he renegoiaing rm j sais es he following sharing rule: J j = (1 ) W j ; (19) where is he 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 8

10 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), in an economy wih saggered wage negoiaions Nash bargaining implies ha, in he presence of saggered wage negoiaions, he share parameer in equaion (19) ucuaes over he cycle. 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: Wj =! +1 W j+1j jh j ~! j + E (1 ) w (1 w ) W j+1 ; (20) where he worker s opporuniy cos of holding he job, ~! j, is equal o: ~! 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 (eq. (20)), equals he ne ow income from employmen,! j h j ~! 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: Jj =! j! +1 jh j + (1 )E w J j+1j + (1 w )J j+1 : (21) where! 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. Ieraing equaions (20) and (21) forward i is possible o rewrie hem as follows: W j = E 1X s=0 s +s (1 ) s s w! jh j+s ~! j+s +(1 )(1 w )E 1 X s=0 s+1 +s+1 (1 ) s s Wj+s+1 w ; (22) +s+1 9

11 X 1 Jj = E s +s (1 ) s s w! j+s! jh j+s s=0 +(1 )(1 w )E 1 X Using he sharing rule in equaion (19), (22) and (23) imply ha: E 1 X s=0 s=0 s+1 +s+1 (1 ) s s wj j+s+1: (23) s +s (1 ) s s w! jh j+s! ar +s = 0; (24) where! ar j+s =! j+s + (1 )~! j+s is he oal wage paymen o he worker on which boh paries would agree if wages were fully exible: Subsiuing for! j+s and ~! j+s he arge real wage bill can be wrien:! 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 wage is given by: where! = R 1 0! jdj: 2.5 Hours bargaining! = w! 1 + (1 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 : 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 10

12 amoun of hours, i.e., h j = h : Solving he rs order condiion for hours yields: h j = ' A 2 n 1 j kj 1! 1 1+ : (27) 2.6 Price and wage in aion 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 equaion (24) and (26) we obain he following equaion for wage in aion: w = k w h ^! ar where he coe cien k w is equal o: ^! + ^h i + (1 ) E w+1 ; (29) k w [1 (1 ) w] (1 w ) w : Equaion (29) saes ha wage in aion depends on he gap beween he acual and arge real wage bill, ^! + ^h and ^! 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). 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 11

13 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. Trigari (2006) shows ha whenever rms pos vacancies a ime o conrol employmen in he following period, he maching model wih e cien bargaining on hours lacks a ransmission channel from wages o prices since he real marginal cos is independen from wages. 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 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. I follows ha wages are irrelevan for 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 (2007b) 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 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 coss ' : ' =! h mpe + J E +1 (1 ) J 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. If we had 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 depend solely on he number of hours, which, due o e cien wage bargaining, are independen 12

14 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. 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 1975Q1-2009Q1 using ve shocks and ve daa series. We use quarerly observaions of real oupu scaled by he labour force. Real GDP is measured as seasonally adjused gross value added a basic prices. In aion is measured as percenage changes of he implied GDP de aor. We also use series on average hours, employmen in heads and Bank raes. All series, wih he excepion of he Bank rae, are passed hrough a Hodrick-Presco ler wih smoohing parameer The ve shocks in he model are a preference shock, a mark-up shock, a labour supply shock, a 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; ; ; Ag, 0 < < 1 and N (0; ) : Moneary policy shocks " R are i.i.d. Some parameers are xed, while oher are esimaed. We sar by discussing he xed parameers. The discoun facor is se a 0.99 implying a real ineres rae of 4%. Capial depreciaion k is se a 0.025, o mach an average annual rae of capial desrucion of 10%, and a 0.69 o mach he labour share over he period of he esimaion. The habis parameer, &, he bargaining power of he workers,, and he elasiciy of he vacancy cos funcion, " c, are also xed, due o ideni caion problems. Consequenly, he habis parameer is hen calibraed a 0.5, a value lying in he mid range of he esimaes repored in he lieraure for he UK economy, as deailed in Harrison, and Oomen (2009). The bargaining power of he workers is se a 0.5, in line wih he esimaes in Perongolo and Pissarides (2001). The elasiciy of he vacancy cos funcion 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. Table A summarises he values of he xed parameers. The remaining parameers are all 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, 13

15 poserior esimaes and 90% con dence inervals. The unemploymen bene s coe cien, b, is calibraed o mach a replacemen raio of 0:38 as in Nickell (1997). 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 his case he surplus of a job is very small and iny changes in he produciviy of he labour inpu produce a high change in he oal surplus of a mach, boosing he response of employmen. However, as deailed below, Cosain and Reier (2008) show ha a high value of b is empirically implausible. For his reason we choose a prior value for b which is low enough no o generae an addiional source of ampli caion. The prior of he 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 normalised o 1. The prior mean of he job desrucion rae,, is se o 0:03, in line wih he esimaes from he Labour Force Survey in Bell and Smih (2002). The Calvo parameer on wages,!, is se o mach a yearly average wage renegoiaion frequency, as in Dickens e al. (2007). Similarly, he Calvo parameer on prices, p, is chosen o mach an average duraion of prices of abou six monhs, in line wih he ndings by Bunn and Ellis (2009) for he UK economy. The elasiciy of demand,, is se o 11, a value suggesed in Brion, Larsen and Small (2000), which implies a seady sae mark-up of 10%. Finally, we choose he prior mean of he Taylor rule response o in aion, r = 1:5, and o oupu r y = 0:5: While he former value is sandard in he lieraure, he laer is somewha higher han he ypically repored values. Our reason for a relaively high value of r y lies in he ideni caion problems relaed o he use of more moderae priors. The model favours high values for r y and does no appear o be ideni ed for relaively low values of his prior. The prior mean of he ineres rae smoohing parameer is se o Parameer esimaes Table B shows poserior means of he srucural parameers ogeher wih 90% con dence inervals. The poserior mean of he unemploymen bene parameer equal o 0.6 is subsanially di eren from is prior of A he esimaed equilibrium, he replacemen raio, compued as he sum of unemploymen bene s and he disuiliy of working over he wage, equals This is remarkably close o he value of 0.75 suggesed by Cosain and Reier (2008), which is consisen wih an esimaed semielasiciy of unemploymen o unemploymen bene s around 2. This resul suggess ha a high opporuniy cos of working is unlikely o be a valid explanaion for he unemploymen volailiy puzzle, which is in line wih he resuls obained by Krause e al. (2008a) for he US economy. The esimae of he inverse Frish elasiciy of labour supply of 1.5 is considerably higher han 14

16 he prior, and in line wih microeconomeric esimaes. Since we use daa on average hours, he parameer appears o be well ideni ed. The 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 US, alhough heir esimae for is higher han ours. The poserior means of he consan of he maching funcion, m, equal o 0.92 and he consan of he vacancy cos funcion, a, equal o 6.5 are similar o heir prior means. The poserior mean of he rae of job separaions, ; which is approximaely equal o 0.7, is subsanially higher han is prior. These resuls imply a higher rae of unemploymen han under our baseline calibraion. The unemploymen rae implied by our esimaed model is around 19%. This is subsanially higher han he average rae measured in he Labour Force Survey in he period 1975Q1-2009Q1. However, since our model absracs from he paricipaion margin, he rae of unemploymen can be inerpreed as including workers who are passively searching and are no included in he sandard Inernaional Labour Organizaion de niion. In he calibraion of maching models a wide range of values is used and a rae of 19% would no be unprecedened. Trigari (2006) maches an unemploymen rae as high as 20% for he US economy. The poserior disribuion of he maching funcion elasiciy,, is equal o 0.55, which is signi canly lower han is prior. This is evidence ha he parameer is well ideni ed. The value of 0.55 is close o he sandard value 0.5 used in US sudies, and inside he range of plausible values 2 [0:5; 0:7] esimaed by Perongolo and Pissarides (2001). This low esimae suggess ha he number of new hires equally depend on he number of unemployed workers as well he number of vacancies posed. The poserior means of he Calvo parameers on he frequency of wage and price adjusmens,! and p, are equal o 0.75 and 0.5 respecively. These values imply an average frequency of wage negoiaions in he esimaed model is one year, in line wih Dickens e al. (2007), and an average frequency of price negoiaions is six monhs, in line wih Bunn and Ellis (2009) for he UK economy. Clearly, he esimaion is unable o idenify hese parameers precisely as he poserior and prior means are similar, irrespecive from he assumed priors. The parameers in he Taylor rule are well ideni ed. The poserior mean of he ineres rae response o in aion, r, equal o 1.46 indicaes a srong response o in aion and he degree of ineres rae smoohing, r, equal o 0.47 suggess mild degree of ineres rae ineria. Somewha more surprising he high esimae for r y, equal o 0.78 suggess a srong response o oupu. The esimaed value is larger han he ypical value of 0.125, and his is obained despie an already large prior of 0.5. Imposing lower priors impaired he ideni caion of he model. Table C shows esimaes of he shock parameers. The poserior means of he persisence parameers and, equal o 0.95 and 0.99 respecively, show ha shocks o he labour supply and preferences are highly persisen, while he esimaes of and a, equal o 0.32 and 0.69 respecively, display lower persisence of he mark-up and echnology shocks. The poserior means of, a and, equal o 0.015, and respecively, show ha he variances of he 15

17 preference, echnology and moneary policy shocks are of a similar magniude, while he esimaes of and R, equal o 0.31, 0.21 respecively, display subsanial higher variance of labour supply and mark-up shocks. Boh he values of he persisence and sandard deviaion of shocks are well ideni ed, wih he poserior disribuions being largely shifed from he priors. Ineresingly, he persisence of he preference shock is close o uniy, suggesing ha despie wage rigidiies he model has a weak an inernal mechanism of propagaion and requires persisence in he underlying shocks in order o mach in aion persisence. We now discuss how he parameer esimaes change when we impose exible wages, while keeping he priors unchanged. The esimaes are in Tables D and E. Table D shows ha he consan of he vacancy cos funcion is lower han in he sicky wage economy, while he consan of he maching funcion and he job desrucion rae are higher. This implies higher urn over a he saionary equilibrium han we esimae in he sicky wages economy. The poserior mean of unemploymen bene s parameer is well ideni ed and somewha higher han in he sicky wage economy. All oher esimaes remain subsanially unchanged. Imporanly, he esimaion reveals ha he model wih sicky wages is preferred o he model wih exible wages by abou 17 likelihood poins. (The marginal likelihood is 2053 for he exible wages economy and 2070 for he sicky wages economy). 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 (! = 0). Figures 1-5 plo he impulse responses of seleced variables o a one-sandard-deviaion shock. Each enry compares he responses of he model wih exible wages agains hose wih sicky wages. Figure 1 shows ha oupu raises in reacion o a posiive echnology shock 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. On he conrary, he presence of saggered wage seing inroduces imporan di erences in he reacion of labour marke variables. Following he shock, real wages increase by more in he presence of nominal wage rigidiies. Wih sicky wages, price de aion ranslaes ino higher real wages. Wih exible wages, nominal wages fall, empering he increase in real wages. I is noiceable ha vacancies, employmen and labour marke ighness fall in he presence of sicky wages, while hey raise when wages are exible. The inuiion for his is sraighforward. A echnology shock increases boh he marginal produc of labour and he real wage. The di erence beween hese wo deermines he incenives for posing 16

18 vacancies, as dicaed by equaion (15). Wih sicky wages, real wages increase by more han he marginal produc of labour, and remain elevaed during he sluggish process of adjusmen. Wih exible wages insead, real wages increase below he marginal produc of labour and freely adjus in he afermah of he shock, preserving he rms incenives o pos vacancies. Even hough wage rigidiies a ec he ransmission of echnology shocks o labour marke variables hey are unable o produce sizeable changes o he dynamics of in aion. Why are he in aion dynamics similar in he wo seings? 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 echnology shock, nominal wage rigidiies aenuae he drop in uni labour coss and amplify he 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 since real wages hold up on impac as rms are no allowed o renegoiae lower wages. A he same ime, as menioned above, 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 raises over ime. 5 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 a one-sandard-deviaion mark-up shock leads o an increase in in aion. As he ineres rae increases, consumpion and invesmen fall. In reacion o he shock, he rm reduces he labour inpu along boh he inensive and he exensive margin o decrease producion. Noe ha he 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, as in he case of echnology shocks. Noneheless, similarly o he case of echnology shocks, he reacion of marginal coss and in aion remains subsanially unchanged in he wo seings. Figure 3 shows ha 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. 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. Wih coninuous wage negoiaions higher nominal wage in aion ranslaes ino higher price in aion, which leads o higher ineres raes and lower consumpion and invesmen. Wage rigidiies appear o have somewha sizeable impac on marginal coss since he e ec produced hrough uni labour coss is only parially o se by he e ec of he fricional componen of marginal coss. 5 Noe ha he average duraion of a vacancy, 1=q( ), depends only on labour marke ighness. 17

19 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. In boh seings, in reacion o he shock, vacancies and employmen fall, while in he presence of sicky wages 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 fall. 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 similar 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 raises, and boh invesmen and oupu fall. The preference shock induces he worker 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 produce only a minor impac on marginal coss, since search fricion coss o se movemens in uni labour coss. As a resul, in aion dynamics remain similar wih and wihou saggered wage seings. To summarize, 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 reached a similar conclusion in a calibraed model wih an adhoc saggered wage seing 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. However, his nding is a odds wih he resuls obained by Gerler e al. (2008), who esimae a similar model on he US economy and nd ha wage rigidiies are imporan for he dynamics of in aion. This suggess ha he link beween in aion and marginal coss migh depend on he esimaed parameer values, and in paricular on he degree of nominal wage and price rigidiies. Fuure sudies should invesigae his issue furher. To undersand he exen o which cyclical movemens of each variable are explained by he shocks, Table F repors he variance decomposiions for he model wih sicky wages. Enries reveal ha mos of he movemens in he model s variables are driven by preference shocks. Preference shocks exhibi an auocorrelaion coe cien of 0.99, as deailed in Table C, which is higher han in all oher shocks, and herefore magni es he imporance of preference shocks. This suggess ha he model has a weak inernal propagaion mechanism and he ucuaion of he endogenous variables 18

20 heavily depends on exrinsic sources of persisence, similarly o Krause e al. (2008a). However, while in Krause e al. (2008a) in aion persisence is generaed by a number of shocks, in our model preference shocks are he main source of persisence. In addiion, since he persisence of he preference shock is equally large boh in he sicky and in he exible wage model, we conclude ha wage rigidiies alone are unable o produce in aion persisence. Table F also shows ha mark-up shocks play a limied role in explaining movemens of variables, suggesing ha demand shocks are he main driver of economic ucuaions in he UK. Labour supply shocks appear o play a role, albei a minor one, in driving vacancies and employmen. Hours insead are mosly driven by labour supply shocks. To deail how he exogenous shocks have evolved during he esimaion period, Figure 6 plos shocks esimaes using he Kalman smoohing algorihm from he sae-space represenaion of he esimaed model wih sicky wages. The esimaes show ha he magniude of shocks has somewha decreased since he mid-1990s, wih he excepion of preferences shocks, whose size has remained broadly unchanged. Furhermore, similarly o sudies for oher counries, we nd ha he volailiy of moneary policy shocks declined afer he mid-1990s. 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 UK during he pas decade. As in Gerler e al. (2008), our model allows us o recover he naural rae of unemploymen, ha is, he rae of unemploymen ha would be observed if prices and wages were perfecly exible. Figure 7 shows ha he unemploymen gap, de ned as he di erence beween he acual and he naural rae of unemploymen, increases drasically in recessionary periods. Figure 8 shows ha he cyclical componen of he log-unemploymen rae is much less volaile in he exible price economy han in he sicky price economy. As a consequence, he level of he unemploymen rae ha would be observed in a exible price economy is no very di eren from wha we could obain by HP- lering he acual rae of unemploymen (see Figure 9). 5 Conclusion We have esimaed a New Keynesian model characerized 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 changes due o wage rigidiies. We esablished ha shocks o preferences and he labour supply are more imporan han echnology, moneary policy, or mark-up shocks in explaining movemens in he daa. In addiion, using a Kalman ler on he model s reduced form we provided esimaes for he unobserved shocks ha characerised he pos 1970s Briish economy. Similarly o sudies for oher counries, we found ha he volailiy of shocks declined afer he mid-1990s, corroboraing he evidence ha his facor migh have conribued o he macroeconomic sabiliy of he pas decade. 19

21 Second, we esablished ha saggered wage seing a ecs he behaviour of labour marke variables and enables he model o he daa more closely, despie playing an irrelevan role for he dynamics of in aion. In a search and maching model he marginal cos depends on he uni labor cos as well as on he fricional coss of searching. We show ha inroducing wage rigidiies ino an oherwise idenical model wih exible wages generaes o seing reacions in he fricional coss of employmen and in he uni labor cos. As a resul, in aion dynamics remain subsanially una eced. This nding, which echoes he resuls by Krause and Lubik (2007), is obained despie esablishing a link beween wage and in aion by assuming ha newly hired workers become immediaely producive. However, his resul is in conras o Gerler e al. (2008), who, using a similar iming assumpion, nd ha wage rigidiies a ec in aion dynamics in a model esimaed on he US. This discrepancy suggess ha fuure research should invesigae he role of he esimaed parameer values in deermining he link beween in aion and marginal coss. Furhermore, he nding is also di eren from sudies ha have resored he ransmission channel from wages o prices by resoring o alernaive wage bargaining schemes, such as righ-o-manage bargaining. Fuure research needs o esablish wha bargaining scheme he daa suppor more srongly. While he resuls do unveil key feaures of he UK economy, i should also be noed ha he esimaion was unable o precisely idenify imporan parameers of he model, such as he degree of nominal wage and price adjusmens, calling for re nemens o he heoreical seing ha could improve he empirical performance of he model. Furhermore, alhough he model developed here allows for a variey of supply and demand shocks o have e ecs on he economy, in pracice, a variey of oher aggregae shocks may play a role. The amendmen of he model and he inclusion of addiional disurbances remain ousanding asks for fuure research. 20