A New Phillips Curve for Spain 1

Transcription

1 A ew Phillips Curve for Spain Jordi Galí and J David López-Salido 2,3 Absrac In his paper we provide evidence on he fi of he ew Phillips Curve (PC) for Spain over he mos recen disinflaionary period (980-98). Some of he findings can be summarised as follows: (a) he PC fis he daa well; (b) however, he backward-looking componen of inflaion is imporan; (c) he degree of price sickiness implied by he esimaes is plausible; (d) he use of independen informaion abou he price of impored inermediae goods (which is influenced by he exchange rae) affecs he measure of he firm s marginal coss and hus also inflaion dynamics; and finally, (e) labour marke fricions, as manifesed in he behaviour of he wage markup, appear o have also played a key role in shaping he behaviour of marginal coss.. Inroducion In recen years much research has been devoed o he inegraion of Keynesian feaures ino he class of dynamic sochasic general equilibrium models generally associaed wih Real Business Cycle heory. Two imporan ingrediens of he resuling ew Keynesian models are he presence of imperfec compeiion and nominal rigidiies. The resuling framework has implied a new view on he naure of shor-run inflaion dynamics. In paricular, hese ew Keynesian models have given rise o he so-called ew Phillips Curve (PC). Two disinc feaures characerise he relaionship beween inflaion and economic aciviy in he PC: firs, he forward-looking characer of inflaion, which is a consequence of he fac ha firms se prices on he basis of heir expecaions abou he fuure evoluion of demand and cos facors; second, he link beween inflaion and real aciviy, which comes hrough he poenial effecs of he laer on real marginal coss. In his paper, we follow recen work by Sbordone (999), Galí and Gerler (999), and Galí e al (2000). Those auhors have found supporing evidence for he PC, and have shown ha real marginal coss provide imporan informaion o undersand inflaion dynamics in boh he Unied Saes and he euro area. The objecives of he presen paper are wofold. Firs, we provide evidence on he fi of he PC for a small open economy like Spain, and use i as a ool o undersand he recen Spanish disinflaion process (980-98). Tha exercise also allows us o compare he characerisics of Spanish inflaion dynamics wih hose observed for he euro area. The PC framework assigns a cenral role o movemens in marginal cos as a source of inflaion changes. Hence, undersanding he behaviour of marginal coss should shed ligh on he behaviour of inflaion iself. This moivaes he second par of he paper, in which we characerise he join behaviour of Spanish inflaion, oupu and marginal cos over he pas wo decades, in order o assess 2 3 Paper presened a he workshop on Empirical sudies of srucural changes and inflaion held a he BIS on 3 Ocober This paper is an English version of a paper presened a he XIII Simposio de Moneda y Crédio on El Análisis Económico frene a los problemas de la Sociedad Moderna, and o be published in issue 202 of Moneda y Crédio. Par of he research applied in his invesigaion is based on join work wih Mark Gerler. We are graeful for commens by Javier Díaz-Jiménez, Juanjo Dolado, Rafael Domenech, Angel Esrada, Javier Gardeazabal, Fernando Resoy, Vicor Rios-Rull, Javier Vallés, José Viñals, and especially Jeff Amao (our discussan a he BIS) on an earlier version of he paper. We also appreciae he commens of paricipans a he BIS workshop and he Seminar of he Bank of Spain. We also hank Angel Esrada for supplying us wih he daa. The views expressed here are hose of he auhors and do no represen he view of he Bank of Spain. Cenre de Recerca en Economia Inernacional (CREI), Universia Pompeu Fabra, CEPR and Bank of Spain. Bank of Spain, Research Deparmen. 74 BIS Papers o 3

2 quaniaively he conribuion of differen facors o he recen disinflaionary period. The srucure of he paper is as follows. In Secion 2 we describe he main differences beween he radiional Phillips curve and he PC. Secion 3 presens he main heoreical ingrediens underlying he PC. In Secion 4 we provide exensive evidence supporing he PC paradigm. Finally, in Secion 5 we analyse he facors underlying inflaion ineria by examining in deail he deerminans of he marginal coss. 2. Phillips curves, old and new 2. The radiional Phillips curve The radiional Phillips curve relaes inflaion o some cyclical indicaor plus lagged values of inflaion. For example, le F denoe inflaion and ŷ he log deviaion of real GDP from is long-run rend. A simple, largely aheoreical specificaion of he radiional Phillips curve akes he form: 4 h F i F yˆ () i where E is a random disurbance. Insead of he direc esimaions of expressions like (), mos of he available evidence on a Phillips curve relaionship in Spain was based upon he esimaion of wages and prices equaions. Given he naure of such a relaionship, he emphasis of he lieraure shifed from analysing he link beween inflaion and unemploymen (or oupu) in erms of a relaionship like () o a relaionship beween real wages and unemploymen (ie he so-called wage equaion). 5 Pioneers working on ha analysis in Spain are Sanchez (977), Espasa (982), Dolado and Malo de Molina (985), Dolado e al (986), De Lamo and Dolado (99), Andrés and García (993) and recenly Esrada e al (2000). everheless, i is sill possible o find some evidence of a Phillips curve relaionship which explicily emphasises he link beween inflaion and unemploymen and/or inflaion and oupu. Pioneering work is ha by Dolado and Malo de Molina (985), and specially Baiges e al (987). The laer consiues a clear example of esimaes of a Phillips curve relaionship like (). everheless, since he mid-970s, radiional Phillips curves have been he objec of inense scruiny on differen grounds. Firs, heir lack of rigorous micro-foundaions has made hem subjec o he Lucas criique, and quesioned heir validiy as a building block of any model used for he evaluaion of alernaive moneary policies. This issue is of paricular concern in Spain, o he exen ha he Bank of Spain has swiched beween differen policy regimes in he pas wo decades. 6 Second, is empirical performance has been raher unsaisfacory in many insances. Thus, he radiional Phillips curve seemed incapable of accouning for he combinaion of high inflaion and oupu losses experienced by indusrial economies in he 970s. 7 More recenly i failed o explain why he expansion of he lae 990s was no accompanied by any significan inflaionary pressures, a leas unil he recen hike in oil prices. The recen Spanish experience has no been an excepion from his poin of view. Figure displays he ime series for inflaion and derended oupu over he period As can be easily seen, low and seady inflaion characerising he lae par of he sample has no been perurbed despie he robus expansion in economic aciviy (refleced in posiive and For example, Rudebusch and Svensson (999) show ha a varian of equaion () wih four lags of inflaion fis well quarerly US daa over he period Galí e al (2000) compare his evidence wih he one obained for he euro area. For deails on he relaionships beween he wage equaion and he Phillips curve, see he recen paper by Blanchard and Kaz (999). Essenially he Phillips curve analysis for he Spanish economy was pursued under he approach described by Layard e al (99). For a deailed discussion, see Ayuso and Escrivá (999). This was already emphasised by Dolado and Malo de Molina (985) and Baiges e al (987). BIS Paper o 3 75

3 growing derended oupu esimaes). In such an environmen a radiional Phillips curve would over predic inflaion The ew Phillips Curve Recen developmens in moneary business cycle heory have led o he developmen of a so-called ew Phillips Curve (PC). The PC arises in a model based on saggered nominal price seing, in he spiri of Taylor s (980) seminal work. A key difference wih respec o he radiional Phillips curve is ha price changes are he resul of opimising decisions by monopolisically compeiive firms subjec o consrains on he frequency of price adjusmen. A common specificaion is based on Calvo s model (983) of saggered price seing wih sochasic ime dependen rules. The firs building block is an equaion ha relaes inflaion, F, o anicipaed fuure inflaion and real marginal cos: F > E F mc (2) where mc is average real marginal cos, in percenage deviaion from is seady sae level, β is a discoun facor, and is a slope coefficien ha depends on he primiive parameers of he model, and in paricular he one measuring he degree of price rigidiy. As we will show below, equaion (2) can be obained by aggregaing across he opimal pricing decisions of individual firms. Equaion (2) is he firs of wo building blocks for he PC. The second is an equaion ha relaes marginal cos o he oupu gap. Under a number of assumpions ypically found in sandard opimisaion-based models wih nominal price rigidiies, i is possible o derive a simple relaionship beween real marginal coss and an oupu gap variable: 9 mc ( y y ) y and y are, respecively, he logarihms of real oupu and he naural level of oupu. The laer variable has a heoreical counerpar: i is he level of oupu ha would be observed if prices were fully flexible. Combining (2) wih (3) yields he sandard oupu gap-based formulaion of he PC: 0 F y y F > E (3) (4) 2.3 Implicaions and criicisms The PC, as exemplified by equaion (4), has been he subjec of considerable conroversy. Like he radiional Phillips curve, inflaion is prediced o vary posiively wih he oupu gap. Ye in he PC inflaion is enirely forward-looking, as can be easily seen by ieraing equaion (4) forward: F > k 0 k E y k y k (5) There is exensive evidence on his for he Unied Saes. Recen conribuions include Lown and Rich (997) and Gordon (998). See Roemberg and Woodford (997). See Yun (996), Woodford (996) and King and Wolman (997). See also Galí and Gerler (999) for a discussion of some of he issues involved. 76 BIS Papers o 3

4 Hence, pas inflaion is irrelevan in deermining curren inflaion under his new paradigm. As a resul, an economy may achieve disinflaion wihou he need for he cenral bank o engineer a recession, o he exen ha i can commi o sabilising he oupu gap. In oher words, here is no longer a rade-off beween price and oupu gap sabiliy. Many auhors have poined o ha predicion as being in conflic wih he evidence of subsanial oupu losses associaed wih disinflaions (eg Ball (994)). Furhermore, and as emphasised by Fuhrer and Moore (995) and ohers, he join dynamics of inflaion and oupu implied by equaion (5) appear o be a odds wih he empirical evidence. In paricular, (5) implies ha inflaion should anicipae movemens in he oupu gap, bu he evidence suggess ha he opposie relaionship holds: he oupu gap ends o lead inflaion insead, a leas when derended log GDP is used as a proxy for he former variable. In his sense, he evidence is consisen wih he radiional Phillips curve. 2.4 Recen evidence The previous criicisms nowihsanding, recen work by Sbordone (999), Galí and Gerler (999), and Galí e al (2000) has provided evidence favourable o he forward-looking naure of inflaion, and he link beween he laer variable and real marginal cos, and suggesed ha equaion (2) is largely consisen wih he daa. These resuls suppor he idea ha i is he failure of equaion (3) - he hypohesised link beween real marginal cos and he oupu gap - ha may be behind he claimed poor performance of he PC. Galí and Gerler (999) pu forward wo possible explanaions for his finding. One is ha convenional measures of he oupu gap may be poor approximaions. To he exen ha here are significan real shocks o he economy (eg shifs in echnology growh, fiscal shocks, ec), using derended log GDP as a proxy for y in expression (4) may no be appropriae. Second, even if he oupu gap is correcly measured, i may no be he case ha real marginal cos moves proporionaely o i, as assumed. In paricular, as we discuss in Secion 5, wih fricions in he labour marke, eiher in he form of real or nominal wage rigidiies, equaion (3) is no longer valid. These labour marke rigidiies, furher, can in principle offer a raionale for he inerial behaviour of real marginal cos. 2 Indeed, in Secion 5 we provide evidence ha labour marke fricions were an imporan facor in he dynamics of marginal cos in Spain. In he nex secion we skech he derivaion of he srucural relaion beween inflaion and real marginal cos. This will be he base of our esimaes in Secion 4. We do so under alernaive assumpions regarding he echnology available o firms. We also consider a varian of he baseline model which allows for a fracion of backward-looking firms. In Secion 4 we esimae he differen specificaions of he inflaion equaion using Spanish daa. Secion 5 provides some evidence regarding he sources of variaions in marginal coss. 3. The ew Phillips Curve: basic heory and alernaive specificaions We assume a coninuum of firms indexed by j [0,]. Each firm is a monopolisic compeior and produces a differeniaed good Y (j), which i sells a nominal price P (j). Firm j faces an isoelasic P demand curve for is produc, given by ( j) Y( j) Y, where Y and P are aggregae oupu P and he aggregae price level, respecively. Suppose also ha he producion funcion for firm j is given = byy ( j) A ( j), where ( j ) is employmen and A is a common echnological facor. oice ha allowing for decreasing reurns o labour will imply on he one hand increasing marginal coss, and on 2 As we discuss in deail in Secion 5, inerial behaviour of marginal cos opens up he possibiliy of a shor-run rade-off beween inflaion and oupu. See also Erceg e al (2000). BIS Paper o 3 77

5 he oher ha marginal coss will differ across firms producing differen oupu quaniies. This is no he case under consan reurns o labour (ie = 0). Firms se nominal prices in a saggered fashion, following he approach in Calvo (983). Thus, each firm reses is price only wih probabiliy - G each period, independenly of he ime elapsed since he las adjusmen. Thus, each period a measure -G of producers rese heir prices, while a fracion G keep heir prices unchanged. Accordingly, he expeced ime a price remains fixed is G. Thus, he parameer G provides a measure of he degree of price rigidiy. I is one of he key srucural parameers we seek o esimae. Afer appealing o he law of large numbers and log-linearising he price index around a zero inflaion seady sae, we obain he following expression for he evoluion of he (log) price level p as a funcion of (he log of) he newly se price p and he lagged (log) price p. p G p G p Because here are no firm-specific sae variables, all firms ha change price in period choose he same value of p. A firm ha is able o rese in chooses price o maximise expeced discouned profis given echnology, facor prices and he consrain on price adjusmen (defined by he rese probabiliy -G ). I is sraighforward o show ha an opimising firm will se p according o he following (approximae) log-linear rule: k >G >G E mc n p, k 0 (7) where β is a subjecive discoun facor, n mc, is he logarihm of nominal marginal cos in period +k of a firm ha las rese is price in period, and log is he firm s desired markup. Inuiively, he firm ses price as a markup over a discouned sream of expeced fuure nominal marginal cos. oe ha in he limiing case of perfec price flexibiliy (G = 0), (6) p mc : price is jus a fixed markup over curren marginal cos. As he degree of price rigidiy (measured by G ) increases, so does he ime he price is likely o remain fixed. As a consequence, he firm places more weigh on expeced fuure marginal coss in choosing curren price. The goal now is o find an expression for inflaion in erms of an observable measure of aggregae marginal cos. Cos minimisaion implies ha he firm s real marginal cos will equal he real wage divided by he marginal produc of labour. Given he Cobb-Douglas echnology, he real marginal cos in +k for a firm ha opimally ses price in, MC,, is given by: n MC, ( W / P ) (=)( Y /, k, k ) where Y, and, are oupu and employmen for a firm ha has se price in a he opimal value P. Individual firm marginal cos, of course, is no observable in he absence of firm-level daa. Accordingly, i is helpful o define he observable variable average" marginal cos, which depends only on aggregaes, as follows: 3 3 oe ha his measure allows for supply shocks (enering hrough A in he producion). An adverse supply shock, for example, resuls in a decline in average labour produciviy, Y /. Also, he specificaion is robus o he addiion of oher 78 BIS Papers o 3

6 MC W / P = Y / (8) Following Woodford (996) and Sbordone (999), we exploi he assumpions of a Cobb-Douglas producion echnology and he isoelasic demand curve inroduced o obain he following log-linear relaion beween MC, and MC : = mc, mc p p = where mc, and mc are he log deviaions of MC, and MC from heir respecive seady sae values. Inuiively, given he concave producion funcion, firms ha mainain a high relaive price will face a lower marginal cos han he norm. In he limiing case of a linear echnology ( = 0), all firms will be facing a common marginal cos. We obain he primiive formulaion of he PC ha relaes inflaion o real marginal cos by combining equaions (6), (7), and (9), F > E F mc (0) wih G >G = G = oe ha he slope coefficien depends on he primiive parameers of he model. In paricular, is decreasing in he degree of price rigidiy, as measured by G, he fracion of firms ha keep heir prices consan. A smaller fracion of firms adjusing prices implies ha inflaion will be less sensiive o movemens in marginal cos. Second, is also decreasing in he curvaure of he producion funcion, as measured by =, and in he elasiciy of demand : he larger = and, he more sensiive is he marginal cos of an individual firm o deviaions of is price from he average price level; everyhing else equal, a smaller adjusmen in price is desirable in order o offse expeced movemens in average marginal coss. (9) () 3. A hybrid model Equaion (0) is he baseline relaion for inflaion ha we esimae. An alernaive o equaion (0) is ha inflaion is principally a backward-looking phenomenon, as suggesed by he srong lagged dependence of his variable in radiional Phillips curve analysis. As a way o es he model agains his alernaive, we follow Galí and Gerler (999) and Galí e al (2000) by considering a hybrid model ha allows a fracion of firms o use a backward-looking rule of humb. Accordingly, a measure of he deparure of he pure forward-looking model from he daa in favour of he radiional approach is he esimae of he fracion of firms ha are backward-looking. All firms coninue o rese price wih probabiliy - G. However, only a fracion - M reses price opimally, as in he baseline Calvo model. The remaining fracion M chooses he (log) price according o he simple backward-looking rule of humb: p b p b p F where p is he average rese price in - (across boh backward- and forward-looking firms). Backward-looking firms see how firms se price las period and hen make a correcion for inflaion, variable facors (eg impored goods), so long as he elasiciy of oupu wih respec o labour is consan, firms ake wages as given, and here are no labour adjusmen coss. BIS Paper o 3 79

7 using lagged inflaion as he predicor. oe ha hough he rule is no opimisaion-based, i converges o he opimal rule in he seady sae. 4 We defer he deails of he derivaion o Galí e al (2000) and simply repor he resuling hybrid version of he marginal cos-based Phillips curve: F mc (2) F C bf Cf E wih M G > G = ; B = ( ) where B G M G > ~ ; C b MB C f >GB. As in he pure forward-looking baseline case, relaxing he assumpion of consan marginal cos (ie = 0 ) affecs only he slope coefficien on average marginal cos. The coefficiens C b and C b are he same as in he hybrid model of Galí and Gerler (999). In his regard, noe ha he hybrid model ness he baseline model in he limiing case of no backward-looking firms (ie M 0 ). 3.2 Alernaive measures of marginal coss In his secion we keep he assumpion ha firms face idenical consan marginal coss, which grealy simplifies aggregaion, while relaxing he linear specificaion of he echnology. We consider various echnologies o generae differen measures of marginal cos. We ake as a baseline echnology a simple Cobb-Douglas producion funcion; we hen allow for overhead labour, as well as labour adjusmen coss. Finally, we consider a CES producion funcion and we also allow for labour adjusmen coss. Le Y be oupu, A be echnology, K capial and oal labour. Thus oupu is given by: Y A K = = Real marginal cos is given by he raio of he wage rae o he marginal produc of labour, ie MC coss: w P Y n ( W / P ) s MC (=)( Y / ) = Hence, given equaion (3), we have he following expression for he real marginal n W where s is he labour income share (or, equivalenly, real uni labour coss). Equivalenly, in PY erms of percenage deviaions from seady sae we have: mc s Consider nex he case where echnology is isoelasic in non-overhead labour: = Y = F K, A K yields he following expression for he marginal coss: 5 (3) (4) 4 5 oe also ha backward-looking firms free-ride off opimising firms o he exen ha p is influenced by he behaviour of forward-looking firms. In his regard, he welfare losses from following he rule need no be large, if he fracion of backwardlooking firms is no oo dominan. Overhead labour is represened by. The echnical deails of his secion are lef o a echnical Appendix. 80 BIS Papers o 3

8 mc n (5) / depends on he raio of overhead labour o oal labour in seady sae. Thus, / ' from expression (5) i is sraighforward o see ha allowing for overhead labour makes he real uni labour coss more procyclical. Le us assume nex a CES producion funcion: I Y (, ) F K = k K = Z I I I In his case he expression for he real uni labour cos has o be modified as follows: mc s D yk s I where yk is he deviaion from is seady sae of he produciviy of capial, and D, s I wih as he seady sae markup, s he seady sae labour income share and I he elasiciy of subsiuion beween labour and capial. Finally, we consider he effec of labour adjusmen cos on he compuaion of he real marginal coss. In ha case, he marginal coss ake he following form: (6) mc s C g Eg (7) C and is a consan ha depends upon he curvaure of he adjusmen coss (see he Appendix for deails). n, g log / 4. How well does he ew Phillips Curve fi Spanish daa? As a firs pass on he daa, Figure 2 plos he evoluion of inflaion (based on he GDP deflaor), as well as he labour income share which we ake as our baseline measure of real marginal coss, mc. Boh variables move closely ogeher, a leas a medium frequencies. The relaion appears o hold hroughou he hree key phases of he sample: (i) he disinflaion of he 980s; (ii) he seady inflaion of he lae 980s and early 990s; and (iii) he recen disinflaionary period and curren period of low inflaion since he lae 990s. Tha apparen posiive comovemen of marginal cos and inflaion suggess ha, as was he case for he Unied Saes (Galí and Gerler (999)) and he euro area (Galí e al (2000)), he PC may also fi he Spanish inflaion daa well, and hus may provide a useful ool for undersanding he dynamics of is differenial vis-à-vis he res of Europe. In order o confirm such an inuiion, we now proceed o provide formal reduced-form evidence of his conjecure. 6 The esimaed inflaion equaion for Spain during he period 980:I-998:IV is given by: 6 We begin by presening esimaes of he coefficiens in equaion (2). We refer o hese esimaes as reduced-form since we do no ry o idenify he primiive parameers ha underlie he slope coefficien. In he nex secion we proceed o relae hese coefficiens wih a srucural model wih sicky prices. The aim will be o idenify he degree of price rigidiies behind he observed evoluion of inflaion and real marginal coss. BIS Paper o 3 8

9 E F F (0.077) 0.5mc (0.052) (8) where sandard errors are shown in parenheses. 7 The main predicions of he model appear o be saisfied. The slope coefficien on marginal cos is posiive, as implied by he heory, and significanly differen from zero. The esimae of coefficien affecing expeced inflaion (he discoun facor) is raher low, bu has he righ sign and order of magniude. We view Figure 2 and he previous resuls as prima facie evidence of he poenial meris of he new inflaion paradigm. In Figure 3, we plo he real marginal coss under he differen assumpions abou echnology. In paricular, in he lef-hand panel we plo he Cobb-Douglas case agains wo cases: he firs allows for overhead labour, and he second for adjusmen cos in labour. In he righ-hand panel we compare he Cobb-Douglas case wih he CES and he CES wih labour adjusmen coss. I is clear ha here are few noiceable differences in he evoluion of he alernaive measures of real marginal coss. The mos remarkable feaure can be observed in he specificaion ha allows for labour adjusmen coss. In ha case, he marginal coss presen a higher volailiy over he period , induced by he large flucuaions in employmen experienced in Spain afer he inroducion of fixed-erm conracs among oher srucural reforms. 8 In a recen paper, Wolman (999) suggess ha allowing for feaures such as overhead labour, labour adjusmen coss and variable capial uilisaion would increase he empirical viabiliy of sicky price models. The analysis here ends o sugges ha such exensions may have very lile impac on he esimaes of he degree of price sickiness, as will become clear in he nex secion. 4. Srucural esimaes In his secion, we presen esimaes of he srucural parameer G, which measures he exen of price rigidiy. As expression () indicaes, he reduced-form coefficien is a funcion no only of G and >, bu also of he echnology curvaure parameer = and he elasiciy of demand. Our main aim is o use he model s resricions o idenify only wo primiive parameers: >, he slope coefficien on expeced inflaion in equaion (0), as well as one oher parameer among G, = and. Our sraegy is o esimae he degree of price rigidiy, G, and he discoun facor >, condiional on a se of = plausible values for = and. Le us define he consan (0,), which is condiional = ( ) on he calibraed values for = and. Given his definiion, we can express he slope coefficien on real marginal cos, in equaion (0), as follows: G G >G. In our baseline we repor esimaes under he assumpion of consan marginal coss across firms, which corresponds o. In his case idenificaion of G does no require he calibraion of any parameer. everheless, under increasing marginal cos, o esimae he parameers > and G, we rea as known wih cerainy. We obain measures of, ie of = and, based on informaion abou he seady values of he average markup of price over marginal cos, and of he labour income share S W / P Y. By definiion, he average markup equals he inverse of average real marginal S cos (ie, / MC ). I hus follows from our assumpions abou echnology ha: =. We can accordingly pin down = using esimaes of seady sae (sample mean) values of he labour income 7 8 We esimae his equaion by GMM. The mehod will be described in deail in Secion 4, where we presen our srucural esimaes of he model. Our insrumens se includes four lags of inflaion, derended oupu, wage inflaion and real marginal coss. We performed a number of diagnosic ess o evaluae he regression. To check for poenial weakness of he insrumens, we perform an F-es applied o he firs-sage regression; he resuls clearly sugges ha he insrumens used are relevan (F saisic = 5.7, wih a p-value = 0.00). ex we es he model s overidenifying resricions. Based on he Hansen es, we do no rejec he overidenifying resricions (J saisic = 7.59, wih associaed p-value of 0.9). See eg Benolila and Sain-Paul (992). 82 BIS Papers o 3

10 share and he markup. Given an esimae of he seady sae markup we can obain a value for by observing ha, given our assumpions, he seady sae markup should correspond o he desired or fricionless markup, implying he relaionship which allows us o idenify, ie.we esimae he models (0) and (2) by GMM using he following wo orhogonaliy condiions, respecively: E F > F E F M F G >G mc z 0 G M G >G mc z 0 >G F B where B G M G ( > ). oice ha in he hybrid model we can esimae an addiional parameer: M, he fracion of backward-looking price seers. As in he previous cases, we use calibraed values of = and o calibrae. This again allows us o idenify M, as well as he price rigidiy parameer G. In our empirical analysis we use insrumens daed or earlier for wo reasons: Firs, here is likely o be considerable error in our measure of marginal cos. Assuming his error is uncorrelaed wih pas informaion, i is appropriae o use lagged insrumens. Second, no all curren informaion may be available o he public a he ime hey form expecaions. Our insrumens se includes a consan and four lags of price and wage inflaion, derended oupu and he real marginal coss. Table repors esimaes of he model under consan reurns o labour, ie under consan marginal coss across firms, which corresponds o, as discussed above. In addiion, we proxy he real marginal coss using he real uni labour coss. The firs row (labelled ()) corresponds o he esimaes of he srucural parameers of he forward-looking model. The row (2) repors he srucural esimaes for he hybrid model. The firs wo columns repor he esimaes of he wo primiive parameers, G and >. The hird column repors he implied esimae for, he reduced-form slope coefficien on real marginal cos. ex we repor he average duraion of a price remaining fixed (in quarers), corresponding o he esimae of G (ie D /G)). Sandard errors (wih a ewey-wes correcion) for all he parameer esimaes are repored in brackes. The firs row of Table repors he baseline esimaes of he purely forward-looking model using Spanish daa from 980.I o 998:IV. The esimaed parameer G is a bi high leading o an average duraion of prices around 0 quarers. The esimae of he discoun facor > is again a bi low, bu no erribly so is we ake ino accoun he uncerainy surrounding he esimaes. The combinaion of hese wo parameers implies a low value for he slope of he Phillips curve,, posiive and significan. 9 Thus, alhough he resuls sugges ha real marginal cos is indeed a significan deerminan of inflaion, imposing a pure forward-looking model joinly wih he assumpion of consan reurns o labour yields a high esimae of he price sickiness parameer and so a high duraion of fixed prices. In he second row of Table we repor esimaes for he hybrid model. In his case, we repor he f esimaes for he primiive parameers M, G and >, as well as he reduced-form parameers, C b, C and while he las column again gives he implied average duraion of price rigidiy. The esimaes imply ha backward-looking price seers, measured by he size of M, have been a relaively imporan facor behind he dynamics of Spanish inflaion. The esimae of M, he fracion of backward-looking price seers, is around 0.7 leading o esimaes of C b and C f around 0.5. The esimaes of he oher srucural parameers, > and G are much more plausible under he hybrid specificaion. Again, afer accouning for sandard errors, we ge sound esimaes, being now he 9 Alhough no repored o save space, he overidenifying resricions are no rejeced under any specificaion. The resuls are available from he auhors upon reques. BIS Paper o 3 83

11 esimaed average duraion around six quarers, lower han obained in he purely forward-looking specificaion. Thus, using he hybrid model prices are more flexible (ie he average duraion of price rigidiy is shorer), bu he backward-looking behaviour is more imporan. We have hus far esed our forward-looking model agains he hybrid model under he hypohesis of consan marginal coss and using he real uni labour coss as our measure of real marginal coss. In he nex wo secions we exend our analysis in wo direcions. Firs, we analyse he effec of alernaive measures of marginal coss on he esimaes of he srucural parameers. Second, we focus on he effecs of allowing for increasing marginal coss in order o esimae our parameers, paying special aenion o he degree of price rigidiy. Table 2 presens he resuls for he consan marginal coss model, ie, under alernaive specificaions of marginal coss. We repor, for each definiion of marginal coss, he esimaes of he forward-looking model (row ()) as well as he hybrid model (row (2)). Overall, i appears ha he previous resuls hold. Thus, as anicipaed from Figure 3, alernaive specificaion of he marginal coss have no significan effecs on he esimaion of he srucural parameers. The forward-looking specificaion ends o overesimae he degree of price rigidiy. The hybrid model seems o work beer. The esimaes confirm ha backward-looking price seing, measured by he size of M, is around 0.7, and ha his corresponds o esimaes of C b and C f of around 0.5. The duraion is esimaed a around six quarers. We now exend he analysis o he model where we allow for increasing marginal coss ( ie ). Table 3 repors he srucural parameers under wo differen calibraions of he labour income share. In he firs wo rows we se s = 0.75, while in he second we se s = 0.70 corresponding o he average over he esimaion period. We fix he seady sae markup =.2 wihin he range of he empirical esimaes (see, for insance, Roemberg and Woodford (995) and Basu and Fernald (997)). Below we will show how he srucural esimaes depend upon he calibraion of hose parameers. From Table 3 wo main feaures are worh noing. Firs, as anicipaed in he heoreical Secion 3, he exisence of increasing marginal coss allows us o esimae a more plausible degree of price sickiness. This value leads o a esimaed duraion beween hree and four quarers, in line wih he esimaes for he Unied Saes and he euro area (see Galí e al (2000)). Moreover, hese esimaes are quie robus o he exisence of backward-looking firms (ie he esimaion of he hybrid model yields only slighly lower values). Second, allowing for decreasing reurns o labour yields lower esimaes of boh he degree of price rigidiy and he fracion of backward-looking price seers han hose obained under he consan reurns assumpion (corresponding o ). These laer esimaes, alhough heoreically appealing, render is idenificaion o he calibraion of he parameers = and using informaion on he seady sae labour income shares, s, and he markup,. We have carried ou a robusness check of he increasing marginal coss model, by analysing how he esimaes of he parameer of price sickiness, G, depends upon changes in he seady sae of boh s and. Thus, we have esimaed he parameers of he model for differen values of s and, boh in he purely forward-looking model and in he hybrid model. The resuls are presened in Figures 4a and 4b. The op panels of Figure 4a presen he esimaes of he parameer G wih he 95% confidence inervals, for boh he forward-looking and he hybrid model under differen values of he seady sae labour income share (he values ranged from 0.6 o 0.75, which cover he evoluion of he variable over he sample period we use in our analysis; see he righ-hand scale of Figure 2). For hese exercises we keep =.2 as in he esimaes of he previous Table 3. The boom panels presen he esimaes (and he 95% confidence inerval) of he duraion associaed o he values of G. These figures end o suppor he resuls previously discussed. Overall, changes in he labour income share of 5 percenage poins slighly affec he esimaes of he parameer G, so he esimaed duraion ranges from hree o four quarers. everheless, a higher seady sae labour income share leads o a higher esimaes of he price sickiness parameer. In he hybrid model, he differences, across differen values of he labour share, in he poin esimaes of G are even lower han in he forwardlooking model. In addiion, under he hybrid model we end o esimae a lower degree of price rigidiy. Figure 4b carries ou a similar exercise. ow we fix s = 0.7, bu allowing changes in he seady sae markup,. Values of he seady sae markup near one (perfec compeiion) end o reduce significanly he esimaes of he price sickiness. everheless, for values of he markup beween 20% 84 BIS Papers o 3

12 o 50%, here is no significan effec on he esimaion of parameer G, and so on he duraion. Again his is rue for boh models, alhough under he hybrid specificaion we end o esimae a lower degree of price rigidiies across differen values of. 4.2 A measure of fundamenal inflaion In his secion we follow Galí and Gerler (999), Sbordone (999) and Galí e al (2000), o assess he exen o which our esimaes of he model consiue a good approximaion o he dynamics of inflaion in Spain. We consider boh he pure forward-looking and he hybrid model given by equaions ((0) and (2)), since he hybrid model yields esimaes ha are slighly differen. The above-menioned auhors define he concep of fundamenal inflaion F, as he one obained by ieraing equaions (0) and (2). For simpliciy, we focus on he pure forward-looking case. In his case, solving forward yields: 20 F k 0 > k Emc k F (9) Fundamenal inflaion F is a discouned sream of expeced fuure real marginal coss, in analogy o he way a fundamenal sock price is a discouned sream of expeced fuure dividends. To he exen ha our baseline model is correc, fundamenal inflaion should closely mirror he dynamics of acual inflaion. The quesion we address in his secion is: o wha exen can observed flucuaions in inflaion be accouned for by our measure of fundamenal inflaion, ie how far is our model from realiy? Figure 5a displays our measure of fundamenal inflaion for Spain ogeher wih acual inflaion in he forward-looking model. The measure of fundamenal inflaion is consruced using he esimaed srucural form presened in Table 3. Overall, fundamenal inflaion racks he behaviour of acual inflaion quie well, especially a medium frequencies. In paricular, i seems o succeed in accouning for he high inflaion in he early 980s and he subsequen disinflaion in he mid-980s and 990s. everheless, he recen episode of low inflaion, in he lae 990s, is overesimaed. Thus, as expeced, he purely forward-looking model fails o fully capure he shor run movemens of inflaion. In Figure 5b we presen he fundamenal inflaion calculaed for he hybrid model. In his case, he model seems o work very well boh a he medium and high frequencies. Again, as expeced allowing for such an inerial behaviour (backward-looking price seers) in inflaion improves he previous model so as o capure he shor-erm movemens of inflaion over he sample period. 4.3 Measuring marginal coss in an open economy: he role of impored maerials Openness of he economy may affec he dynamics of inflaion, because movemens in he exchange rae can fuel domesic inflaion behaviour hrough impor prices. I is imporan o sress here, however, ha neiher he derivaion of equaion (0), relaing domesic inflaion o real marginal coss, nor he relaionship beween he laer variable and he labour income share (given a Cobb-Douglas echnology), relied on any assumpion on he degree of openness of he economy. Bu, as we will show nex, once we depar from he assumpion of a consan elasiciy of oupu wih respec o labour, he labour income share may no longer be a suiable indicaor of real marginal coss when oher non-labour inpus are used. In paricular, if some of he inermediae inpus are impored, informaion abou heir relaive price (which is influenced by he exchange rae) may be needed o measure he firm s marginal coss. For concreeness, le us assume he following CES producion funcion: 20 The hybrid case can be found in Galí and Gerler (999). We leave all he echnical deails of his secion o he previous paper. BIS Paper o 3 85

13 Y I I F(, M) = Z I = M I where M represens impored maerials (ie inermediae goods), and I is he elasiciy of subsiuion beween he wo inpus. From cos minimisaion we know ha he following equilibrium condiion holds: M P I, (20) M W where P M, is he price of impored maerials, and W is he nominal wage. In ha case, and as described in he Appendix, one can derive he following expression for he real marginal coss as: s mc Y M I Subsiuing expression (20) ino expression (2) and log-linearising he resuling expression yields he following specificaion for he real marginal coss: mc s B pm, M cons (22) s where B I. oice ha now real marginal coss depend upon real uni labour cos and s an addiional erm relaed o he relaive price of he wo inpus. The parameer B deermines how changes in he raio of relaive prices would ranslae ino movemens in he marginal coss, and so in inflaion. Thus, when I > an increase in he prices of impored maerials below he increase in he nominal wage will increase he marginal coss. 2 Finally, i is worh poining ou ha movemen in he exchange rae would affec he evoluion of he impor prices, and so he dynamic of he marginal coss. In Figure 6 we plo he evoluion of he (log) relaive price of impors ( p (2) M, M ) ogeher wih domesic annual inflaion. As he figure makes clear, he wo variables display a similar paern. This evoluion suggess ha his componen can be an addiional and independen source of movemens in he marginal coss ha is relevan o undersand he recen Spanish disinflaion. Bu, wha is behind his downward rend in he relaive prices? To answer ha quesion we have decomposed his variable in erms of real impor prices and real wages: pm, M M, p p M p Figure 6b presens he evoluion of hese wo componens. As can be seen from ha figure, he downward rend ha dominaes he behaviour of relaive inpu prices during he 980s was he resul of a decrease in real impor prices (ie a real exchange rae appreciaion), as well as an increase in real wages. Ineresingly, he nominal depreciaion of he pesea in 992 and subsequen years was no fully ranslaed ino real impor prices and, in addiion, i was offse by a reducion in real wages. These wo facors are behind he evoluion his second componen of he marginal cos. As a firs approximaion we proceed o esimae he imporance of he open economy facor as a source of variaions in marginal cos and, hus, in he dynamics of inflaion by esimaing he following reduced-form equaion: 2 oice ha when I he producion funcion is Cobb-Douglas so he marginal coss are independen of he movemens in he relaive prices of labour and impored maerials. 86 BIS Papers o 3

14 F > E mc F > EF s 2pM, M where parameers and 2 are funcions of he srucural parameers. The GMM esimae of he previous equaion is: 22 F 0.56 E F } 0.032s 0.442( p M ) (0.058) { M, (0.009) (0.083) oice ha he esimaed sign of he relaive impor price coefficien is posiive and highly significan. Given he observed behaviour of ha variable, we can conclude ha he Spanish disinflaion of he pas wo decades can be parly accouned for by he decrease in he relaive price of impored inpus (as we describe in Figures 6a and 6b). Given (22), he esimaes also imply an elasiciy of subsiuion beween employmen and impored maerials ha is significanly larger han one ( I ). Finally, he coefficiens on expeced inflaion and real uni labour coss are sill clearly significan, as prediced by he heory. We now urn o esimae our srucural parameers for differen values of he elasiciy of subsiuion. In paricular, in Figure 7 we plo how differen values of I affec he behaviour of he marginal coss. Thus, in he hree panels of Figure 7 we plo he evoluion of inflaion and hree measures of marginal coss ha have been obained for: I = 0.8, I (he Cobb-Douglas case), and I =.5. Overall, he medium-run behaviour of he marginal coss is very similar o he baseline case, ie he Cobb-Douglas. everheless, in he shor run here are some differences, especially during he period In paricular, i is worh noing ha a higher elasiciy of subsiuion leads o a less volaile behaviour of he marginal cos, ie he marginal coss remain essenially fla over ha period, hence conribuing o he reducion in inflaion. Finally, in Table 4 we presen he corresponding srucural esimaes for hese wo values of I. The esimaes confirm he previous assessmen ha accouning for he movemens in he relaive price of inpus in a non-cobb-douglas seing does no affec appreciably he basic resuls of he paper regarding he value of he srucural parameers (G and M ). 5. Marginal cos dynamics: he role of labour marke fricions 5. Measuring wage markup In his secion we decompose he movemen in real marginal cos in order o isolae he facors ha drive his variable. 23 Our resuls sugges ha labour marke fricions are likely o play a key role in he evoluion of real marginal cos in Spain. Our decomposiion requires some resricions from heory. Suppose he represenaive household has preferences given by 5 0 > U C,, wherec is non-durables consumpion and is labour, and where usual properies on he uiliy are assumed o hold. Wihou aking a sand on he naure of he labour marke (eg compeiive versus non-compeiive, ec), we can wihou loss of generaliy express he link beween he real wage and household preferences in he following log-linear way: w ( M p ) mrs (23) In he GMM esimaion we add four lags of he relaive price of inpus as insrumens. The coefficien affecing he relaive price of inpus has been muliplied by 00. These reduced-form esimaes correspond o he model wih consan marginal coss across firms. We follow here he analysis of Galí e al (2000). BIS Paper o 3 87

15 U, where mrs log( ) is he log of he marginal rae of subsiuion beween consumpion and UC, labour. Because ha variable is he marginal cos o he household in consumpion unis of supplying w addiional labour, he variable can be inerpreed as he wage markup (in analogy o he price markup over marginal cos, ). Assuming ha he household canno be forced o supply labour o he poin where he marginal benefi ( M p ) is less han he marginal cos mrs we have 0. Condiional on measures of ( M p ) and mrs, equaion (23) provides a simple way o idenify he role of labour marke fricions in he wage componen of marginal cos. If he labour marke were perfecly compeiive and fricionless (and here were no measuremen problems), we should observe w w 0 0 ie he real wage adjuss o equal he household s rue marginal cos of supplying w labour. Wih labour marke fricions presen, we should expec o see 0 and also possibly varying w over ime (ie 0 ). Siuaions ha could produce his oucome include: households having some form of monopoly power in he labour marke, saggered long-erm nominal wage conracing, disorionary axes, and informaional fricions ha generae efficiency wage paymens. Using equaion (23) o eliminae he real wage in he measure of real marginal cos yields he following decomposiion: w ( W / P ) (=)( Y / ), = C, / w log MC log log U ( / U ) Y (24) w According o equaion (24), real marginal cos has wo componens: (i) he wage markup, and (ii) he raio of he household s marginal cos of labour supply o he marginal produc of labour, U, / UC,. In his secion, we analyse in deail he 20 deerminans of he wage markup, leaving o (=) Y / he nex secion he analysis of he raio of he marginal rae of subsiuion o he marginal produc of U, / UC, labour,, and is implicaions for measuring he oupu gap" in a economy wih boh price (=) Y / and wage rigidiies. In his paper, we exend he analysis of Galí e al (2000) considering a ype of preferences ha imply he absence of income effec on he labour supply decisions. 24 This model has proved useful in gaining an undersanding of some moneary business cycle feaures. In paricular, we use he following specificaion for preferences U C, log i i C A (25) As anicipaed, his specificaion implies ha he MRS is independen of consumpion. Following King and Wolman (997) A can be undersood as a random preference shifer ha also acs as a produciviy shock, so guaraneeing balanced growh. Log-linearising equaion (24) and ignoring 24 Among ohers, see Chrisiano e al (997) and Dosey e al (999). 88 BIS Papers o 3

16 consans yields an expression for marginal cos and is componens ha is linear in observable variables: w mc a n y n wih he wage markup defined as follows: (26) u w w p a n Figure 8 presens he evoluion of he marginal coss and he wage markup for Spain under alernaive parameerisaion of he labour supply elasiciy, respecively. We ake hree values for, namely, 5 and 0, implying a labour supply elasiciy ( / ) of, 0.2 and The op panel in each case illusraes he behaviour of he (log) inefficiency wedge relaive o (log) real marginal cos and he boom panel does he same for he (log) wage markup. In general a robus feaure is ha over he whole period here is a seady decline in he wage markup behind he decline in marginal cos. This circumsance is robus across he differen values we use for he labour supply elasiciy. Perhaps mos sriking feaure is he change in he wage markup, from he high values a he beginning of he 980s o an apparen downward drif from 985 o 999. This behaviour seems consisen wih he popular noion ha labour union pressures produced a seady rise in he real wage in he lae 970s and during he beginning of he 980s. The impac of his labour marke disorion is mirrored in he seady increase in he inefficiency wedge over he same period. The increase in he wage markup during he laes recession is consisen wih he idea ha workers change heir expecaions slowly in response o changes in economic condiions. Finally, he reducion in he marginal coss we observe during he 990s is mosly due o he reducion in he wage markup. 6. Conclusions In his paper we provide evidence on he fi of he ew Phillips Curve (PC) for Spain over he mos recen disinflaionary period (980-98). Some of he findings can be summarised as follows: (a) he PC fis he daa well; (b) however, he backward-looking componen of inflaion is imporan; (c) he degree of price sickiness implied by he esimaes is plausible; (d) he use of independen informaion abou he price of impored inermediae goods (which is influenced by he exchange rae) affecs he measure of he firm s marginal coss and so inflaion dynamics; and finally, (e) labour marke fricions, as manifesed in he behaviour of he wage markup, appear o have also played a key role in shaping he behaviour of marginal coss. 25 A low value of he labour supply elasiciy is more in line wih he microeconomic empirical evidence (see eg Pencavel (986)). In he analysis, he variable z is a measure of he produciviy rend obained from a regression of produciviy on a ime rend. BIS Paper o 3 89

17 Appendix: Derivaion of various marginal cos measures The purpose of his appendix is o derive alernaive measures of firm s marginal coss. In his case, M real marginal coss, mc, (ie he inverse of he markup) are given by: mc, where M is he real F wage and F is he parial derivaive of he producion funcion (ie of oupu) wih respec o labour. Under he previous assumpions, he real marginal coss can be expressed as follows: w mc F s C where s is he labour income share, and C is he elasiciy of oupu wih respec o labour. In s log-deviaions from seady sae ( mc, where is he seady sae markup), he previous C expression is jus: mc s C The benchmark case used in his paper is based upon he assumpion of no adjusmen coss, and a Cobb-Douglas producion funcion ie Y FK (27) collapses o: mc s. = = Z K (27), ). In his case, C =, hus expression I I = = I Assuming a CES producion funcion: Y FK, K I Z, he elasiciy of oupu wih respec o labour can be wrien as a funcion of he average produciviy of capial Y K Y / K : C YK I. Log-linearising around seady sae his yields o: C D yk, wih s I D. s I Using expression (27) we ge: mc s D yk We calibrae he model following Roemberg and Woodford (999). Thus, s = 0.7, =.25, I = 2, which implies a value of D = 0.4. Roemberg and Woodford (999) also consider he case where = echnology is isoelasic in non-overhead labour: Y FK Z K =,. In his case, / C =, and in log-deviaions from he seady sae: n, so he new / expression for he marginal coss is: s n To calibrae he model we follow Roemberg and Woodford (999) using a zero profi condiion in seady sae. In paricular, i can be shown ha he raio of average coss o marginal coss can be (28) (29) 90 BIS Papers o 3

18 BIS Paper o 3 9 wrien as follows: X MC AC =. This implies he following seady sae relaionship: s on-negaive profis require AC, implying ha ) ( 0 s x We in expression (29) following Roemberg and Woodford (999). Under zero profis, and using s = 0.7, =.25, and X =, his = 0.4. Finally, we consider he effec of including he cos of adjusing labour. These coss ake he form: ) / ( U B, where U is he price of he inpu required o make he adjusmen. In his case, he real adjusmen cos associaed wih hiring an addiional worker for one period is given by: P U q E P U / ' / / / ' / / / 2, B B B Leing ) / ( ) / (, P U P U q, and ) / ( g, we can approximae he previous expression by: "() ) / ( g E g P U B Assuming ha he raio W U / is saionary, he real marginal coss are given by: "() / g E g W U s mc B C which in erms of deviaions from seady sae yields: g E g s mc C (30) where ) "( ) / ( B W U. Under he assumpion ha he employmen follows a random walk, hen g s mc C.

19 Figure Inflaion and Derended Oupu Figure 2 Inflaion and Marginal Cos 92 BIS Papers o 3

20 Figure 3 Comparing alernaive marginal coss BIS Paper o 3 93