DO UNIT LABOR COST DRIVE INFLATION IN THE EURO AREA? SANDRA TATIERSKÁ

Transcription

1 DO UNIT LABOR COST DRIVE INFLATION IN THE EURO AREA? SANDRA TATIERSKÁ WORKING PAPER

2 Naional Bank of Slovakia Imricha Karvaša Braislava research@nbs.sk December 21 ISSN The views and resuls presened in his paper are hose of he auhors and do no necessarily represen he official opinion of he Naional Bank of Slovakia. All righs reserved. 2

3 Do Uni Labor Cos Drive Inflaion in he Euro Area? Sandra Taierská 1 Absrac The purpose of his sudy is o analyze he relaionship beween uni labor coss and inflaion. We esimae an opimal price pah model based on a New Keynesian Phillips Curve for eleven euro area counries individually, under he assumpion ha uni labor coss are proporional o marginal coss. We seek such a model which minimizes he disance beween fied and acual price level flucuaions, wih parameers ha saisfy heoreical resricions. The economeric mehodology used is a wo-sep approach mehod. Esimaes show ha in eigh of he eleven euro area counries here is a plausible relaionship beween uni labor coss and price level dynamics. The average ime needed o adjus prices in line wih movemens in uni labor coss is esimaed o be around eigh monhs. In he case of Slovakia he resuls indicae raher flexible prices. JEL classificaion: C22, E12, E3, J3 Key words: inflaion, uni labor coss, NKPC, Euro area, VAR Reviewed by: Michal Horváh Marin Šuser Downloadable a hp:// 1 Research Deparmen of he NBS, sandra.aierska@nbs.sk. 3

4 1 INTRODUCTION Undersanding he naure and sources of inflaion in he euro area is imporan for more efficien preservaion of price sabiliy by he European Cenral Bank. The abiliy o define he drivers of price level flucuaion enables deeper undersanding of privae secor expecaions formaion and easier deerminaion of he role of nominal price rigidiies in an economy. The exisence of sicky prices makes moneary policy able o affec real economic aciviy by influencing he nominal ineres rae, a leas in he shor run. Nominal price rigidiies are a he foundaions of he New Keynesian heory following from he assumpion of imperfec compeiion among firms. In such an economic environmen monopolisic firms are price seers ha wan o maximize heir fuure profis and se heir prices above marginal coss. Therefore wha one really whishes o sabilize, in order o minimize he deadweigh losses, is he ime depended markup of price level over marginal coss. The assumpion of proporionaliy of marginal coss o uni labor coss (ULC) was used in various sudies due o he fac ha ULC includes wage rigidiies. 2 Chrisoffel, Kueser and Linzer (29) in heir paper abou he role of labor markes for euro area moneary policy claimed ha a lower degree of wage rigidiy makes moneary policy more effecive, i.e. a moneary policy shock ransmis faser ino inflaion. Rigid wages were defined as he main source of sluggish cyclical movemen in marginal coss in he U.S. and also in he euro area. Finally, some auhors like Sbordone or Galí, Gerler and López-Salido discovered ha o explain he majoriy of flucuaions in he price level i is sufficien o assume he marginal cos are proporional o ULC and flucuaions in he markup. The purpose of his sudy is o analyze he relaionship beween uni labor coss and inflaion. We esimae an opimal price pah model individually for every euro area counry observed; under mehodology used by Sbordone (22, 25). Such a model was no ye esimaed on euro area daa. Under Sbordone s mehod we es implicaions ha depend only on he firm s opimal pricing problem and herefore we can more easily undersand he effec of each assumpion on he resuls. We ake as given he evoluion of a number of sae variables and deermine wha pah of prices is prediced by he evoluion of he exogenous variables. The advanage is ha our resuls do no depend on arbirary idenificaion procedure o exrac srucural shocks from he residuals of an esimaed ime series model. By using his mehodology we seek a model ha minimizes he disance beween fied and acual price level flucuaions wih parameers which saisfy he heoreical resricions. In he economic environmen of forward looking monopolisic firms, covered by our model, agens believe ha dynamics of uni labor coss, proporional o movemens in marginal coss, are exogenous and Granger cause inflaion. Various inflaion indicaors will be esed, including also he core inflaion where we expec he mos significan resuls, since i excludes cerain iems ha face volaile price movemens like food producs and energy. The fi of he model wih nominal price rigidiies (New Keynesian Phillips Curve) will be compared wih a flexible price model based on real business cycle 2 The assumpion of he proporionaliy of marginal coss o uni labor coss can be jusified by he use of a Cobb-Douglas producion funcion; furher explanaion in Galí, Gerler and López-Salido (21) or Sbordone (1999, 22). 4

5 heory, where we assume perfecly compeiive oupu and inpu markes and prices ha adjus every period o he movemens in uni labor coss. I should be also noed ha he sensiiviy of inflaion o uni labor coss varies sysemaically across economic secors, e.g. he service secor ends o have sickier prices han he manufacuring secor. In view of his fac we expec ha he causaliy of flucuaions in ULC differs across secors and implies diverse significance levels of impacs on inflaion dynamics. For every euro area counry observed we search for a specific economic secor which validaes ha uni labor cos dynamics drive inflaion and hese secoral daa will be used o esimae he heoreical inflaion. We will show ha produciviy, wages and inflaion move largely ogeher as he New Keynesian heory suggess. In accordance wih our expecaions abou inflaion indicaors he use of core inflaion in he New Keynesian Phillips Curve (NKPC) is he mos significan. In line wih his fac in eigh of eleven euro area counries observed here is a plausible relaionship beween uni labor coss and he price level. Our esimaion resuls show ha he average ime needed o adjus prices o movemens in uni labor coss is around eigh monhs. Slovakia is specific in he sense of puing more weigh on he flexible price model. This esimaion resul coincides also wih analyses of Gerler and Senaj (28) on downward wage rigidiies in Slovakia based on micro foundaion, where hey concluded raher flexible nominal compensaions. The paper is organized as follows. In he secions 2 and 3 we will presen some heoreical background o he opic analyzed, and describe he models wih flexible and sicky prices in more deail. The empirical par in secion 4 will cover he daa used and he esimaion procedure on he basis of a wo-sep approach mehod where he forecasing VAR is esimaed separaely from he pricing parameers. Finally, he las wo secions comprise resuls and some concluding remarks. 2 LITERATURE OVERVIEW The New Keynesian models are ypically saic, designed mainly for qualiaive analyses. The indicaors added o he flexible real business cycle model, which form he New Keynesian model branches, are monopolisic compeiion and nominal rigidiies. In line wih Calvo (1983) price rigidiies follow from monopolisic compeiion among firms ha have heir own rules for changing heir price levels. The monopolisic firms are forward looking, se markup price over heir marginal coss (P>MC), and base heir pricing decision on he expeced fuure behavior of marginal coss. Such an economic environmen is covered by he New Keynesian Phillips Curve, where he log-linearizaion of opimaliy condiions around zero inflaion seady sae relaes inflaion o expeced fuure inflaion and real marginal coss. According o Galí and Gerler (1999) NKPC is of he form: 3 3 In he empirical implemenaion of Galí and Gerler (1999), hey use measures of real marginal cos in place of an ad hoc oupu gap, as heory sugges. A desirable feaure of a marginal cos measure is ha i direcly accouns for he impac of produciviy gains on inflaion, a facor ha simple oupu gap measures ofen miss. When he oupu gap is used, we ge he pricing equaion π = β E π κyˆ, where κ = ϕδ and δ measures oupu elasiciy of real marginal coss. For more deails on how o derive he equaions see Woodford (23,ch.3). 5

6 π = βe π ϕ rmc cons, (1) + where rmc represens he logarihm of average real marginal coss in he economy, β is a discoun facor, cons is a consan erm 4 ha is equal o ϕ ln( /( )), where represens he elasiciy of demand. 5 In his economic environmen here are wo ypes of firms. Le θ represen a fracion of firms which do no rese prices opimally a ime, in oher words i is an indicaor of nominal rigidiies. The frequency of opimal price adjusmens is hen defined by a fracion (1-θ) of firms, which can adjus heir prices each period, independenly of ex ane price dynamics, and he ime ha is needed o adjus he price is 1/(1-θ). The parameer ϕ from he NKPC equaion is he ineria coefficien which is in he simples form a nonlinear funcion of srucural parameers: ϕ = ( 1 θ )(1 βθ ) / θ. I follows ha he lower he frequency of price adjusmen, he fewer firms adjus prices in any period, and hence he less sensiive inflaion will be o marginal coss and he smaller is ϕ. A smaller ϕ also implies ha marginal coss are less sensiive o oupu and price adjusmen will be less sensiive 6 o movemens in oupu. As already menioned, in his monopolisic environmen firms se heir prices as a markup over curren and expeced marginal coss. Under flexible prices firms se heir prices each ime period due o a consan markup over nominal marginal coss. According o Roemberg (1982) an inroducion of nominal rigidiies deermined by price adjusmen coss he markup of a firm sars o flucuae. This means ha insead of a consan relaion beween price and nominal marginal coss, here exiss a ime period dependen markup. To sum up, prices are sicky because firms face subjecive cos of changing heir prices. Recen empirical implemenaions sress he idea ha he Calvo-syle models link inflaion o he behavior of labor share of income (real uni labor coss) used as a proxy of real marginal coss. Galí and Gerler (1999), Galí, Gerler and López-Salido (21,25), Kurmann (25), Rabanal and Rubio-Ramiréz (25), Woodford (21) and Sbordone (22,25) find evidence ha he New Keynesian Phillips Curve gives reasonable approximaion of US inflaion dynamics when labor share of income is used. Galí, Gerler and López-Salido (21) and Paloviia (24) ge he same conclusion for euro area inflaion dynamics. Following 4 Acually he consan erm can be ignored because we wan o compue inflaion deviaions from he mean, herefore in our calculaion his erm does no appear anymore. I should be also noed ha /( ) is he equilibrium markup μ*, derived from he firs order condiion for he opimal choice of price level evaluaed a a symmeric equilibrium based on price adjusmen cos a firm is facing. 5 Elasiciy of demand should be greaer han one due o he resuling bigger percenage change in demand han in price. This implies a profi maximizaion behavior of a firm which ses prices greaer han marginal cos. Bu in he case when he elasiciy of demand goes o infiniy individual producs become closer subsiues and he individual monopolisic firm has less economic power due o perfec compeiion. Then prices are se o be equal marginal coss and we ge a consan markup over ime equal o one. 6 Poenially relevan are pricing complemenariies ha may induce firms o minimize he variaion in heir relaive prices. These pricing complemenariies, known in he lieraure as real rigidiies, induce firms ha are adjusing prices o wan o keep heir relaive price close o he non-adjusers. The ne effec of real rigidiies is o reduce φ and hus reduce he overall sensiiviy of inflaion o oupu. (Woodford, 23). 6

7 heir resuls i means ha cenral banks should raise ineres raes in response o increases in labor share of income. However, Tillman (25) presened in his paper ha he explanaory power of he saggered price seing scheme for euro area inflaion is limied due o a large degree of esimaion uncerainy and hey canno say wheher he Calvo model for euro area daa acually fis or fails. They also discovered ha he inclusion of backward looking componen ino he NKPC narrows confidence bands, bu sill canno generae sufficienly precise esimaes. Also he resuls of he approach of Paloviia (24) indicae here is more weigh on backward looking indexaion. On he conrary, Galí, Gerler and López-Salido (21) demonsraed wih heir resuls ha he forward looking NKPC fis he euro area daa very well, possibly beer han he U.S. daa. 7 In our paper we focus on he mehodology of Sbordone (22, 25) in is resriced form ha assumes only forward looking behavior of firms, where agens believe ha dynamics of marginal coss are exogenous and Granger cause inflaion. She combines he mehodology of Roemberg wih Calvo, wha allows one o inerpre he esimae of he cos of adjusing price of he Roemberg model as nominal rigidiies examined in erms of he average expeced ime beween price changes in he Calvo model. 3 REVIEW OF THEORY BEHIND THE MODELS WITH FLEXIBLE AND STAGGERED PRICING In our approach we es implicaions ha depend mainly on he firm s opimal pricing problem in line wih Sbordone (22, 25). She discovers ha models of imperfec compeiion wih nominal rigidiies deliver an exremely close approximaion o he dynamics of he inflaion process, even using a very simple measure of marginal coss, which are assumed o be proporional o uni labor coss. 3.1 MODEL WITH FLEXIBLE PRICES A firs we derive he model wih flexible prices, herefore we assume perfecly compeiive oupu and inpu markes. We assume ha each firm produces a single good Y and wans o 1 α maximize is profis, under Cobb-Douglas producion funcion: Y = Z H ), where H and ( Z represen labor inpus and aggregae labor-augmening echnological progress, where (1- α) is he share of labor in he producion funcion and α<1. The nominal marginal coss are derived by aking he firs order derivaive of he firm s cos funcion and are in he end proporional o uni labor coss, MC =(1/1-α)(ULC ). Uni labor coss are in our case equal o 7 The assumpion of forward looking behavior of he monopolisic firms was suppored for he U.S. daa by Sbordone (25), Galí and Gerler (1999), Galí, Gerler and López-Salido (25) and for he UK daa by Baini, Jackson and Nickell (25). The use of backward looking indexaion was dominan in papers of Rudd and Whelan (25) and Linde (25), working wih U.S. daa. Kurmann (25), who worked wih mehods of Galí and Gerler and Sbordone, discovered ha we canno definiely say if puing more weigh on forward or backward looking behavior is he righ decision, due o he resuling grea amoun of uncerainy abou he fi of heoreical inflaion wih daa. 7

8 (H,W )/Y, where H sands for hours worked and W is nominal compensaions paid. In a model wih flexible prices he opimal price should be equal o marginal coss (P=MC) wih a consan markup, µ =1. The equilibrium is hen defined by π = ulc, (2) represening he equaliy beween log deviaions of respecive growh raes from he mean. The prices adjus in relaion o he changes in uni labor coss, which are assumed o be exogenous and independen of movemens in price levels, and his will deermine our benchmark model. 3.2 MODEL WITH NOMINAL RIGIDITIES In his seing we have a coninuum of monopolisic firms, which produce differeniaed goods and wan o maximize heir fuure profis. By mainaining he Cobb-Douglas echnology he marginal coss can be sill measured by uni labor coss. The inroducion of nominal rigidiies deermined by price adjusmen coss leads o flucuaions in markup. So insead of a consan relaion beween price and nominal marginal coss, as we had before, here exiss a ime period dependen markup μ, MC = (μ /1-α)(ULC ). We expec convex price adjusmen coss where he minimum is deermined by consan inflaion ( ln( p / 1 ) = ). Afer log-linearizaion due o Sbordone (22, 25) we ge equilibrium p pricing condiion where he price level is deermined by pas price levels, uni labor coss, and he weighed sum of expeced uni labor coss: j p = 1 p + ( 1 λ1 ) ulc + (1 λ1) λ2 E ulc+ j j= λ (3) where all variables are expressed as log deviaions from he mean. 8 Afer rewriing he whole equaion ino a saionary model we ge: j j π = + + λ1 π ( 1 λ1) ulc (1 λ1 ) λ2 E ulc+ j λ2 E 1 ulc+ j (4) j= j= λ 1 and λ 2 in boh equaions (3) and (4) are he wo roos of he polynomial P(λ): 2 P ( λ) = βλ (1 + β + ϕ) λ + 1 =,whereλ 1 = θ, λ2 = 1/ βθ and he parameers should follow hese resricions <β<1 and <θ<1. Under hese condiions equaion 4 can be rewrien o: j j π = θπ + ( 1 θ ) ulc + (1 θ ) ( βθ ) E ulc+ j ( βθ ) E 1 ulc+ j (5) j= j= Profis are discouned using a sochasic discoun facor β, <β<1. For he firm o have he discoun facor less han one simply means ha i places less weigh on fuure losses han on oday s losses. 9 The parameer β should also coincide wih uiliy discoun facor of he 8 The derivaion of equaion 3 from equaion 1 is shown in he appendix. 9 One euro oday is worh more han one euro omorrow because i can be reinvesed. By he same argumen, one euro los oday is more imporan han a one euro los omorrow. 8

9 represenaive household. 1 This means ha when β<1 he represenaive household prefers o consume oday raher han omorrow due o a higher uiliy of presen consumpion. I is also an imporan assumpion for he analysis of opimal policy, e.g. if β=1 he household is indifferen beween consumpion oday and omorrow. Because we wan o assume ha more weigh is placed on fuure marginal coss he value of β should be close o 1. Besides his assumpion here exiss also anoher reason for a discoun facor near one: for he sake of β o be included in he deerminaion of he seady sae real ineres rae where r equals (β -1-1). Therefore i is more relevan o se β close o one o ge a plausible annual ineres rae, e.g. β=.99 wih r=4% or β=.98 wih r=8%. In our case we decided o calibrae he discoun facor β firs o he value of.99 in line wih Sbordone (25), Woodford (21), Rudd and Whelan (22), Rabanal and Rubio-Ramírez (25) and Lawless and Whelan (27), and laer on o β=.98 o es he robusness of our resuls. In he case of flexible prices, where he fracion of firms which se prices each period independenly of he pas price behavior (1- θ) is equal 1, equaion 5 simplifies o equaion 2. On he oher hand he higher he price adjusmen coss, he closer he fracion of firms which do no adjus prices opimally (θ) o 1. In such a case he firms pu more weigh on pas inflaion dynamics and expecaions play a negligible role. However, we have acually wo possibiliies how o derive he ineria coefficien φ: a) In he limiing case of a linear echnology where we expec consan reurns o scale wha leads o (1-α) equal o 1, all firms will be facing common marginal coss and he coefficien simplifies o he known equaion of srucural parameers: ( 1 θ )(1 βθ ) ϕ =. (6) θ b) Now by assuming increasing marginal coss ha vary across firms where <α<1 we ge he following relaionship for he ineria coefficien: (1 θ )(1 βθ ) (1 α ) ϕ =. (7) θ 1 α (1 ) The coefficien is decreasing in he curvaure of he producion funcion deermined by α and in he elasiciy of demand, є. The larger are α and є, he more sensiive are he marginal coss of an individual firm o deviaions of is price from he average price level (everyhing else equal). This means ha a smaller adjusmen in price is required o compensae expeced movemens in average marginal coss. (Galí, Gerler and López-Salido; 21) The assumpion of varying marginal coss produced more plausible esimaes of he degree of price rigidiy (θ) in compared o he case wih no wedge beween firm s and he average marginal coss (see Tab. 1). In his paper we analyze he impac of he use of consan reurns o scale as well as of decreasing reurns o scale on he value of nominal price rigidiies θ in he model. 1 Sbordone (1998, 22) and Kurmann (25) se β for example equal 1. In a poin sressed in Woodford (23) his amplificaion may seem appealing, in ha i implies a verical long-run inflaion-oupu rade off, bu correcly accouning for he presence of he uiliy discoun facor of he represenaive household has imporan consequences for he analysis of opimal policy. 9

10 Table 1 Various Resuls of he Degree of Price Sickiness (θ) wih Differen Parameers (α, є, μ) Used α є μ case θ 1/(1-θ) in quarers US: Sbordone (22) (b) (a) Galí, Gerler, López-Salido (21) (b) (a) Kurmann (25) (b) (a) Rudd and Whelan (22) (a) Rabanal and Ramiréz (25) (a) Euro Area: Galí, Gerler, López-Salido (21)* (b) (a) Lawless and Whelan (27) (b) (a) Paloviia (24) (a) Explanaory noe: (a) consan reurns o scale, (b) decreasing reurns o scale. *They derived he parameers from he following definiion: (1- α) equals he average labor income share of he euro area (3/4) imes he chosen markup (μ). 4 ECONOMETRIC METHOD AND DATA Differen economeric mehods were used o correcly esimae inflaion dynamics, such as: maximum likelihood (Roemberg, 1983; Linde, 25), wo-sep approach mehod (Sbordone, 22, 25; Kurmann, 25; Tillman, 25), Bayesian approach (Rabanal and Rubio-Ramírez, 25) and he widely used general mehod of momens (Galí and Gerler, 1999; Galí, Gerler and López-Salido, 21, 25; Rudd and Whelan, 25; Baini, Jackson and Nickel, 25; Paloviia, 24). In our paper we focus on he mehodology of Sbordone in is resriced form ha assumes only forward looking behavior of firms, where agens believe ha dynamics of uni labor coss are exogenous and Granger cause inflaion. We will es he Granger causaliy. In compuing he heoreical inflaion we use he minimum disance mehod based on a wo-sep approach, where he forecasing VAR is esimaed separaely from he pricing parameers β and ϕ. We ake as given he pahs of uni labor coss and oupu, and deermine he pah of prices prediced by he sicky price model (eq. 5). We choose four indicaors of inflaion: CPI (consumer price index), core CPI (excluding food and energy), HICP 1

11 (harmonized CPI) and GDP deflaor. We work wih daa 11 for 11 euro area counries (Ausria (AT), Belgium (BE), Spain (ES), Finland (FI), France (FR), Germany (DE), Ireland (IE), Luxembourg (LU), Neherlands (NL), Porugal (PT) and Slovakia (SK)) and for comparison also wih U.S. daa covering he ime period 1989Q2-28Q2. GDP deflaor is a sandard price level index used in new Keynesian macroeconomic sudies. We esed he assumpion ha GDP deflaor dynamics Granger causes inflaion and examined insignificancy in he case of U.S., Slovakia and some oher euro area counries. However, we prefer o analyze consumer price indexes, which are more closely moniored and more relevan for he ECB moneary policy objecive o mainain he price sabiliy in he euro area. We expec higher significance level of he use of core inflaion, which does no cover volaile prices of food and energy and hus conains a higher price level persisency. Wha should be also noed is ha he sensiiviy of inflaion o uni labor coss varies sysemaically across secors (for example he service secor ends o have sickier prices han he manufacuring secor) and also he causaliy of ULC differs across secors and implies diverse significance level of impacs on inflaion dynamics. We analyze he uni labor coss of 3 economic secors (privae secor excluding agriculure, manufacuring, and marke services) and he whole economy. For every counry we found a specific economic secor which validaed ha uni labor cos dynamics drive inflaion and hese secoral daa were used o esimae he heoreical inflaion (Tab. 2). Table 2 Significan Economic Secors where ULC Growh ( ulc ) Granger Causes Inflaion (π ) Significan Granger Causaliy : ulc π (cpi) π (ne_cpi) π (hicp) US oal oal - SK oal oal oal BE oal oal oal LU oal oal ms AT pri ms pri FI pri ms pri FR pri pri pri PT pri pri - IE ms ms - NL ms oal oal DE - ms - ES man oal man Source: Own calculaions. Explanaory noe: oal economy (oal), privae secor (pri), marke services (ms), manufacuring (man). 11 The daa used were exraced from he saisical daabases of OECD and EUROSTAT. 11

12 4.1 ESTIMATION METHOD As we have already menioned he forecasing VAR used for he esimaion of E ulc + j is esimaed separaely from he pricing parameers β and ϕ. In our esimaion procedure due o Sbordone we denoe X as he vecor of he following dependen variables: he rae of change of uni labor coss and oupu, and he raio of prices o uni labor coss, [ ulc y p ulc ] X = ( ). Our resuling VAR model is of he form Z = ΓZ + ε z, where he vecor Z is defined as [ ] elemen of he vecor Z Z = X X. Because he uni labor cos growh is he firs j = Γ + ε and E Z + j = Γ Z, he weighed sum of uni labor Z z I λ 1 1 Γ cos forecas ino he fuure is he firs elemen of he vecor [ 2 ] Z. For each value of he parameers ϕ and β in a chosen grid we solve for (βθ) and compue he forecas j= (βθ ) j E ulc+ j variance of he residual. We search for such parameer combinaions which minimize he e el = π mod π and fulfill hese heoreical resricions: ϕ >, β=.99 or β=.98 and <θ<1. We will focus also on he sandard deviaions of residuals of he flexible price model (eq. 2), where he lagged inflaion has no significan power and compare hem o he model wih nominal price rigidiies (eq. 5). 5 RESULTS The minimum disance mehod of he wo-sep VAR model wih a discoun facor β=.99 and consan reurns o scale provides plausible degree of fi. As expeced 12 he core inflaion in he New Keynesian Phillips Curve performs bes in comparison o he oher inflaion indicaors. In he case of core inflaion eigh euro area counries (AT, BE, ES, FI, FR, DE, NL, SK) underlined he imporance of he relaionship beween uni labor coss and price level by calculaing he heoreical inflaion dynamics o ge a closer fi o he acual inflaion. The resuls are given in Table 3. The probabiliy of equal variances beween he fied and acual inflaion of he eigh euro area counries was on average equal o 5% and he correlaion was around he value of Even wo of hem (SK, BE) pu more weigh on flexible price model by explaining a greaer par of he volailiy of inflaion, where we expec ha he firms change heir prices every quarer wih respec o movemens in uni labor coss. This is deermined by (1/1-θ)=1. For he remaining six euro area counries he average price duraion period is 14 monhs. 12 The resuls wih oher inflaion indicaors can be found in he Table A.1 in appendix. 13 For more deails see Table A.2 in appendix. 12

13 Table 3 Resuls (consan reurns o scale, β=.99) core CPI σ(e)_flex σ(e)_rig IMPROVEMENT (β=.99) φ θ 1/(1-θ) VAR R 2 AT % AT ES % ES FI % FI FR % FR DE % DE NL % NL IE % IE LU % LU 1.84 PT % PT BE % BE ( ) () (1) SK % SK ( ) () (1) US % US 1.95 Source: Own calculaions Explanaory noe: σ(e)_flex sandard deviaions of residuals e of he flexible model (2); σ(e)_rig sandard deviaions of residuals e of he model wih nominal price rigidiies (4); IMPROVEMENT= 1-(σ_RIG/ σ_flex) measures he resuling improvemen in he fi of he daa due o he use of sicky prices assumpion; VAR R 2...is he R squared of he VAR model used o calculae expecaion of ulc growh. However, Ireland and Porugal did no confirm a significan connecion beween inflaion and ULC growh due o a degree of price rigidiy (θ) close o one. I should be menioned ha he closer is θ o one he higher is he ime needed o adjus a price and he less significan is he use of uni labor coss in he model. For Luxembourg and he U.S. 14 we have go an esimae of θ even equal 1. Figure 1 shows he acual and fied inflaion dynamics of he eigh counries were we examined ha flucuaions in uni labor coss have an impac on inflaion volailiy. As we can see he resuling fied inflaion evaluaed by using flexible or sicky price model is close o he real daa For he U.S. we have go more relevan esimaes under he use of CPI raher han core CPI as inflaion indicaor in he model. 15 The respecive residuals are ploed in figure A.1 in appendix. 13

14 Figure 1 Acual Inflaion and Fied Inflaion Deviaions from he Mean (π and π*) under Flexible Price Model (_flex) or Model wih Nominal Price Rigidiies (_rig) AT BE ES π π*_flex π*_rig π π*_flex π*_rig π π*_flex π*_rig.2 FI.15 FR.25 GE π π*_flex π*_rig π π*_flex π*_rig π π*_flex π*_rig NL SK π π*_flex π*_rig π π*_flex π*_rig Source: Own calculaion. To ge more plausible esimaes of he parameer θ we use he assumpion of decreasing reurns o scale, where firms face increasing marginal coss, which vary across he firms. I should be noed ha wha acually changes is only he value of he degree of price rigidiy while he behavior of he fied inflaion says he same. Following Galí, Gerler and López- Salido (21) who worked wih euro area daa we se α=.175 and є=11, and calculae he new values of he degree of nominal rigidiies. The resuls of θ in a model wih decreasing reurns o scale can be found in Table 4. 14

15 Table 4 Resuls (consan reurns o scale, β=.99) α= α=.175 α= α=.175 core CPI θ 1/(1-θ) θ 1/(1-θ) core CPI θ 1/(1-θ) θ 1/(1-θ) AT IE ES PT FI LU 1 1 FR BE () (1) () (1) DE SK NL () (1) () (1) Source: Own calculaions. The average price duraion period of 14 monhs decreased o 8 monhs for he counries in he euro area. I should be menioned ha he resuls coincide wih he lieraure where Galí, Gerler, López-Salido (21) esimaed θ=.7 (1 monhs), and Lawles and Whelan (27) θ=.59 (7.5 monhs). We also esed he robusness of our resuls wih a discoun facor β=.98. Regarding he resuls of he nominal price rigidiy model shown in Table 5, we can say ha, as expeced, lowering he value of β led o more price sickiness and an improvemen in he sandard deviaion of he esimaed residuals. The esimaed parameers of seven of he above menioned eigh euro area counries remained quie robus and he degree of price sickiness changed on average by 1%. Only Neherlands did no coincide wih he robusness of he esimaed parameers and he value of θ increased by 15%. The mos robus resuls are for Ausria followed by Finland and Germany. Finally we have o say ha on average he sandard deviaion of he esimaed residuals did improve only by.3% and so in he case of Belgium and Slovakia, he residual improvemen in he sicky price model was no sufficien o cover he beer finess of he model wih flexible prices. 15

16 Table 5 Resuls wih β=.98 in Comparison o β=.99 (β=.99) (β=.98) (β=.99) (β=.98) θ - change core CPI σ(e)_flex σ(e)_rig σ(e)_rig θ 1/(1-θ) θ 1/(1-θ) in % AT impr. 1.4% 1.2% ES impr. 9.87% 1.18% FI impr % 46.19% FR impr % 25.94% DE impr. 4.57% 4.73% NL impr % 24.96% BE impr % -1.3% 1 SK impr % -6.44% 1 1 Source: Own calculaions. Explanaory noe: σ(e)_flex sandard deviaions of residuals e of he flexible model (2); σ(e)_rig sandard deviaions of residuals e of he model wih nominal price rigidiies (4); IMPR.= 1-(σ_RIG/ σ_flex) measures he resuling improvemen in he fi of he daa due o he use of sicky prices assumpion. 6 CONCLUSION The purpose of our sudy was o analyze he relaionship beween he uni labor coss and inflaion. We esimaed an opimal price pah model individually for eleven euro area counries under wo-sep approach mehodology. We searched for a model ha minimized he disance beween fied and acual price level flucuaions wih parameers which saisfied heoreical resricions. We found ha inflaion and uni labor coss as an indicaor of marginal coss move largely ogeher. Following our expecaions abou inflaion indicaors he use of core inflaion in he New Keynesian Phillips Curve was he mos significan one. In line wih his fac in eigh of eleven euro area counries observed he heoreical inflaion dynamics indicaed a plausible relaionship beween uni labor coss and price level. Esimaed average ime needed o adjus quie flexible prices in line wih movemens in uni labor coss was around eigh monhs. Slovakia was specific in he sense of puing more weigh on he flexible price model, bu wih he highes sandard deviaions in comparison o he beer fi of he heoreical inflaion of he oher euro area counries. Despie he high level of uncerainy his 16

17 esimaion resul coincides also wih analyses of Gerler and Senaj (28) on downward wage rigidiies in Slovakia based on micro foundaions, where hey deeced raher flexible nominal compensaions. However, especially for Slovakia, i is imporan in he fuure o hink abou a model which will cover also he openness of a small economy and he implied impac of impored inflaion. 17

18 REFERENCES Baini, N., Jackson, B., Nickell, S., 25. An Open-Economy New Keynesian Phillips Curve for he U.K.. Journal of Moneary Economics 52, pp Calvo, G.A., Saggered Prices in a Uiliy-Maximizing Framework. Journal of Moneary Economics 12, pp Chrisoffel, K., Kueser, K., Linzer, T., 29. The Role of Labor Markes for Euro Area Moneary Policy. Kiel Insiue for he World Economy. Kiel Working Paper No.1513 / March 29. Galí, J., Gerler, M., Inflaion Dynamics: A Srucural Economeric Analysis. Journal of Moneary Economics 44, pp Galí, J., Gerler, M., López-Salido, J.D., 21. European Inflaion Dynamics. Naional Bureau of Economic Research, NBER Working Paper Series, Working paper 8218 Galí, J., Gerler, M., López-Salido, J.D., 25. Robusness of he esimaes of he hybrid New Keynesian Phillips curve. Journal of Moneary Economics 52, pp Galí, J., Gerler, M., 27. Macroeconomic Modeling for Moneary Policy Evaluaion. Journal of Economic Perspecives, Volume 21, pp Gerler P., Senaj M. 28. Downward Wage Rigidiies in Slovakia. Naional Bank of Slovakia. Working Paper No. 7/28. - downloadable a hp:// Kurmann, A., 25. Quanifying he Uncerainy abou he Fi of a New Keynesian Pricing Model. Journal of Moneary Economics 52, pp Lawless, M., Whelan, K., 27. Undersanding he Dynamics of Labor Shares and Inflaion. European Cenral Bank, Working Paper Series, NO 784 Lindé, J., 25. Esimaing New-Keynesian Phillips Curves: A Full Informaion Maximum Likelihood Approach, Journal of Moneary Economics 52, pp Paloviia, M., 24. Inflaion Dynamics in he Euro Area and he Role of Expecaions: Furher Resuls. Bank of Finland Discussion Papers 21/24 Rabanal, P., Rubio-Ramírez, J.F., 25. Comparing New Keynesian Models of he Business Cycle: A Bayesian approach. Journal of Moneary Economics 52, pp Roemberg, J.J., Sicky Prices in he Unied Saes, The Journal of Poliical Economy. Vol.9, No.6., pp Roemberg, J.J., Woodford, M., The Cyclical Behavior of Prices and Coss. Handbook of Macroeconomics, Volume 1, Elsevier Science B.V., pp

19 Rudd, J., Whelan, K., 22. Should Moneary Policy Targe Labor s Share of Income? Finance and Economic Discussion Series, Board of Governors of he Federal Reserve Sysem (U.S.), Second Draf Rudd, J., Whelan, K. 25. New Tes of he New-Keynesian Phillips curve. Journal of Moneary Economics 52, pp Sbordone, A., Prices and Uni Labor Coss: A New Tes of Price Sickiness. Insiue for Inernaional Economic Sudies, Sockholm Universiy, Seminar Paper No Sbordone, A., 22. Price and Uni Labor Coss: A New Tes of Price Sickiness. Journal of Moneary Economics 49, pp Sbordone, A., 25. Do Expeced Fuure Marginal Coss Drive Inflaion Dynamics? Journal of Moneary Economics 52, pp Tillman, P., 25. The New Keynesian Phillips Curve in Europe: Does I Fi or Does I Fail? Deusche Bundesbank, Discussion Paper No 4/25 Woodford, M., 21. The Taylor Rule and Opimal Moneary Policy. American Economics Review 91, pp Woodford, M., 23. Ineres and Prices: Foundaion of a Theory of Moneary Policy. Princeon Universiy Press. 19

20 APPENDIX 2

21 The evaluaion of he eq. 3 due o Sbordone (1998) π + ϕ rmc = βeπ +1 π = βe π + + ϕ ( ulc p ) 1 ( ulc p ) = ϕ ( π βeπ + 1) ulc ulc ulc = ( 1+ ϕ + βϕ ) p ϕ p 1 ϕ βe p = ϕ βe 1 L + L p+ 1 ϕ β β = ϕ βe (( 1 λ1l)(1 λ2l)) p+ 1 β 2 Where λ 1 and λ 2 are wo roos of he polynomial P(λ): P ( λ) = βλ (1 + β + ϕ) λ + 1 =. Implying λ 1 = θ, λ2 = 1/ βθ and ϕ which underlie following resricions: φ -1 >, <β<1, <λ 1 <1 and λ 2 > β -1 >1 Defining x+ 1 = ( 1 λ 1L) p+ 1, we can rewrie ulc as ulc = ( ϕ βλ2 ) x ( ϕ β ) E x+ 1 The use of he equaliy ( ϕ βλ ) = (1 λ )(1 λ ) and solving forward we ge x = (1 λ )(1 λ2 ) λ2 E ( ulc+ 1 j j= j p = λ p 1 + (1 λ1)(1 λ2 ) λ2 E ( ulc + Using he fac ha E 2 1 j j= 1 j j + = = ) λ ulc ( 2 j ulc E λ ulc j j j (1 λ2 ) j= We ge he equaion 3: j p = λ 1 p + ( 1 λ1 ) ulc + (1 λ1) λ2 E ulc+ j j= ) 1 2 ) 21

22 Table A.1 Resuls for Oher Inflaion Indicaors (consan reurns o scale, β=.99) CPI σ(e)_flex σ(e)_rig IMPROVEMENT (β=.99) φ θ=λ1 1/(1-θ) VAR R 2 AT % AT BE % BE PT % PT ES % ES FI % FI IE % IE 1.88 LU % LU 1.84 NL % NL 1.98 FR % FR ( ) () (1) SK.133 FLEX SK 1.93 US % US ( ) () (1) HICP σ(e)_flex σ(e)_rig IMPROVEMENT (β=.99) φ θ 1/(1-θ) VAR R^2 AT % AT BE % BE FI % FI NL % NL ES % ES LU % LU 1.77 FR % FR ( ) () (1) SK.19 FLEX % SK 1.93 Source: Own calculaions. Explanaory noe: σ(e)_flex sandard deviaions of residuals e of he flexible model (2); σ(e)_rig sandard deviaions of residuals e of he model wih nominal price rigidiies (4); IMPROVEMENT= 1-(σ_RIG/ σ_flex) measures he resuling improvemen in he finess of he daa due o he use of sicky prices assumpion; VAR R^2...is he R squared of he VAR model used o calculae expecaion of ulc growh. 22

23 Table A.2 Sandard deviaions of residuals σ(e), probabiliies of variance σ² equaliy and correlaions ρ beween fied (π *) and acual (π) inflaion Probabiliy of Correlaion e=(π*-π) σ²(π *)=σ²(π) ρ(π*,π) core CPI σ(e)_flex σ(e)_rig IMPROVEMENT σ²_flex σ²_rig IMPROVEMENT ρ_flex ρ_rig IMPROVEMENT AT YES YES YES ES YES YES NO FI YES.1.89 YES YES FR YES.58.2 NO YES DE YES YES YES NL YES..67 YES YES IE YES..63 YES YES LU YES.2.98 YES YES PT YES.2.44 YES YES BE NO.1.5 YES.6.45 NO SK NO.6.59 NO NO US YES YES YES Source: Own calculaions. Explanaory noe: σ(e)_flex sandard deviaions of residuals e of he flexible model (2); σ(e)_rig sandard deviaions of residuals e of he model wih nominal price rigidiies (4); IMPROVEMENT measures he resuling improvemen in he finess of he daa due o he use of sicky prices assumpion. 23

24 Figure A.1 Residuals (e) wih heir Sandard Deviaions under Flexible Price Model (_flex) or Model wih Nominal Price Rigidiies (_rig) AT Q3 199Q2 1991Q1 1991Q4 1992Q3 1993Q2 1994Q1 1994Q4 1995Q3 1996Q2 1997Q1 1997Q4 1998Q3 1999Q2 2Q1 2Q4 21Q3 22Q2 23Q1 23Q4 24Q3 25Q2 26Q1 26Q4 27Q3 e_flex e_rig BE Q3 199Q2 1991Q1 1991Q4 1992Q3 1993Q2 1994Q1 1994Q4 1995Q3 1996Q2 1997Q1 1997Q4 1998Q3 1999Q2 2Q1 2Q4 21Q3 22Q2 23Q1 23Q4 24Q3 25Q2 26Q1 26Q4 27Q3 e_flex e_rig ES Q 3 199Q Q Q Q Q Q Q Q Q Q Q Q Q 2 2Q 1 2Q 4 21Q 3 22Q 2 23Q 1 23Q 4 24Q 3 25Q 2 26Q 1 26Q 4 27Q 3 e_flex e_rig 24

25 FI Q3 199Q2 1991Q1 1991Q4 1992Q3 1993Q2 1994Q1 1994Q4 1995Q3 1996Q2 1997Q1 1997Q4 1998Q3 1999Q2 2Q1 2Q4 21Q3 22Q2 23Q1 23Q4 24Q3 25Q2 26Q1 26Q4 27Q3 e_flex e_rig FR Q3 199Q2 1991Q1 1991Q4 1992Q3 1993Q2 1994Q1 1994Q4 1995Q3 1996Q2 1997Q1 1997Q4 1998Q3 1999Q2 2Q1 2Q4 21Q3 22Q2 23Q1 23Q4 24Q3 25Q2 26Q1 26Q4 27Q3 e_flex e_rig DE Q 3 199Q Q Q Q Q Q Q Q Q Q Q Q Q 2 2Q 1 2Q 4 21Q 3 22Q 2 23Q 1 23Q 4 24Q 3 25Q 2 26Q 1 26Q 4 27Q 3 e_flex e_rig 25

26 NL Q 3 199Q Q Q Q Q Q Q Q Q Q Q Q Q 2 2Q 1 2Q 4 21Q 3 22Q 2 23Q 1 23Q 4 24Q 3 25Q 2 26Q 1 26Q 4 27Q 3 e_flex e_rig SK Q1 1995Q3 1996Q1 1996Q3 1997Q1 1997Q3 1998Q1 1998Q3 1999Q1 1999Q3 2Q1 2Q3 21Q1 21Q3 22Q1 22Q3 23Q1 23Q3 24Q1 24Q3 25Q1 25Q3 26Q1 26Q3 27Q1 27Q3 28Q1 e_flex e_rig Source: Own calculaions. 26