MICROECONOMIC PRICE ADJUSTMENTS AND INFLATION: EVIDENCE FROM SPANISH SECTORAL DATA

Transcription

1 MICROECONOMIC PRICE ADJUSTMENTS AND INFLATION: EVIDENCE FROM SPANISH SECTORAL DATA Ángel Esrada and Ignacio Hernando Banco de Esaña Banco de Esaña Servicio de Esudios Documeno de Trabajo n.º 992

2 MICROECONOMIC PRICE ADJUSTMENTS AND INFLATION: EVIDENCE FROM SPANISH SECTORAL DATA(* Ángel Esrada and Ignacio Hernando Banco de Esaña, Research Dearmen Ocober999 Absrac The urose of h aer o illusrae he imlicaions for aggregae rice dynamics of alernaive characerizaions of microeconomic rice adjusmen olicies. Wihin he hazard adjusmen framework develoed in Caballero and Engel (993a, we resen alernaive models of individual rice adjusmen ha are consen wih he redicions of he menu-cos models. We esimae hese models using a daa se of Sanh secoral rice indexes covering he eriod , and comare heir abiliy o exlain he behavior of he aggregae rice level, aking he arial adjusmen model as a benchmark. The main findings are he following: models wih non-consan hazard funcions slighly ouerform he arial adjusmen model; 2 here weak evidence regarding he exence of differences beween he magniudes of uward and downward rice rigidiies; and 3 he imac on he aggregae inflaion rae semming from he exence of nominal rigidiies in several subses of secors non-negligible. Keywords: rice adjusmens, inflaion, downward rice rigidiy. JEL Classificaion: E3, D49. (* We wh o hank Michael Binder, Mª de los Llanos Maea, Olimia Bover, Javier Vallés, Javier Andrés and David Lóez- Salido for very helful commens and suggesions.

3 - Inroducion The exence of nominal rice rigidiies a sandard assumion in macroeconomic modeling ha allows for nominal shocks o influence real variables. In urn, formal models of individual rice adjusmen are essenial o undersand aggregae rice sickiness. An adequae formalizaion of he dynamic behavior of he aggregae rice level would require boh aking ino accoun ha firms are heerogeneous and adoing a realic characerizaion of he rice adjusmen olicies a he firm level. However, he sandard framework o obain a sluggh behavior of he aggregae rice level has been o consider a reresenaive agen model wih quadraic adjusmen coss of changing rices. In h seing, individual firms adjus heir rices coninuously and in a consan roorion. The lack of realm of h conduc has led o alernaive characerizaions of he aggregae rice dynamics semming from a more acceed microeconomic behavior. Time-deenden adjusmen models, in which firms reve heir rices a resecified daes, reresened a firs se in h direcion. Models considering sae-deenden ricing rules rovide an alernaive aroach. Wihin h ye of models, he adjusmen hazard framework roosed by Caballero and Engel (993a ries o combine a more realic characerizaion of he microeconomic behavior wih more exlanaory ower a he aggregae level. In h framework, he adjusmen olicy a he firm level characerized by means of he adjusmen hazard funcion, which links he robabiliy of a firm adjusing rice o he size of he deviaion from arge rice. Considering ha firms are heerogeneous, he aggregae dynamics generaed by non-consan hazard funcions will deend on he cross-secional dribuion of rice deviaions. The adjusmen hazard framework quie general and i encomasses he arial adjusmen model or he menu-cos models as aricular cases. Ineresingly enough, he aggregae rice dynamics aring from a wide range of hazard funcions -i.e. hose hazard funcions ha are increasing wih resec o he absolue value of he rice deviaions- consen wih he macroeconomic imlicaions of he menu-cos models as hose develoed in Ball and Mankiw (994,995. Moreover, h aroach useful no only for esing reasonable conjecures abou individual adjusmen olicies (for insance, he exence of downward rice rigidiy bu also for comaring alernaive hazard funcions regarding heir abiliy o exlain he evoluion of he aggregae rice level. In h aer we ry o illusrae he imlicaions for aggregae rice dynamics of alernaive characerizaions of microeconomic rice adjusmen olicies, wihin he hazard adjusmen framework develoed by Caballero and Engel. For h urose, we esimae alernaive models of individual rice adjusmen, consen wih he redicions of he menu-cos models, using a daa se of Sanh secoral rice indexes covering he eriod BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

4 A key elemen o esimae hese adjusmen hazard models he sequence of cross-secional dribuions of rice deviaions. In h aer, we esimae hem using wo alernaive rocedures. Firs, we roxy he cross-secional dribuion of individual rice deviaions by he cross-secional dribuion of secoral rice deviaions. Second, following Caballero and Engel (993b, saring from an arbirary cross-secion densiy we simulae he whole sequence of rice deviaions using exclusively aggregae daa. In boh cases, we comare he abiliy of he alernaive hazard adjusmen models o exlain he behavior of he aggregae rice level, aking he arial adjusmen model as a benchmark. Finally, we resen simle simulaion exerces in order o rovide an assessmen of he imac on he aggregae rice level semming from he exence of nominal rigidiies in several subses of secors. The main resuls of he aer may be summarized as follows. Models wih nonconsan hazard funcions slighly ouerform he arial adjusmen model, i.e. he aggregae behavior of rices deends no only on he as average deviaion from arge rices (as i assumed when using a arial adjusmen model bu also on higher momens of he cross-secion dribuion of rice deviaions. Besides, here weak evidence regarding he exence of differences in he size of uward and downward rice rigidiies. Finally, he imac on he aggregae rice level semming from he exence of nominal rigidiies in several subses of secors non-negligible. The res of he aer organized as follows. Secion 2-a rovides an informal review of he microfoundaions of alernaive heories exlaining aggregae rice dynamics. Secion 2-b inroduces he adjusmen hazard framework and characerizes he imlicaions of alernaive hazard funcions for he evoluion of he aggregae rice level. Secion 3-a secifies he model for secoral fricionless rices. Secion 3-b describes he esimaion mehodology. Secion 4 resens an alicaion of he adjusmen hazard framework for Sanh secoral rice daa and secion 5 rovides a brief summary of he major findings. 2- Individual adjusmen olicies and aggregae rice dynamics 2-a Microfoundaions for aggregae rice sickiness The fac ha many individual rices are se in nominal erms and are no always readjused when here a change in he economic environmen far from conroversial. These characerics of he rocess of individual rice seing are enough o jusify he exence of aggregae nominal rigidiies. However, he assumions abou rice sickiness imlici in radiional Keynesian models have been criicized on he grounds of heir inconsency wih any reasonable model of microeconomic behavior. Much recen heoreical research has been devoed o analyze he microeconomic foundaions of he sluggh adjusmen of rices and, as a consequence, he characerizaion of he aggregae 2 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

5 rice dynamics has been enriched. Th sub-secion rovides an informal review of alernaive microeconomic adjusmen olicies and heir imlicaions for he behavior of he aggregae rice level. Sandard models connecing he microeconomic behavior of individual rices wih aggregae rice dynamics include boh arial adjusmen models and ime-deenden rice-seing models. On he one hand, arial adjusmen models are based on he inroducion of quadraic adjusmen coss of changing rices, h assumion leading o a coninuous bu arial adjusmen a he firm level. Assuming idenical srucural arameers across firms, a arial adjusmen equaion obained for he aggregae rice level. There a clear lack of realm in he microeconomic behavior imlici in h framework given ha firms do no adjus heir rices coninuously o resond o he shocks hey suffer. An alernaive inerreaion of he arial adjusmen model would sugges ha a consan share of firms adjus fully (insead of all firms adjusing arially. As Roemberg (987 shows, boh inerreaions are observaionally equivalen if he robabiliy of adjusing indeenden of he deviaion beween firms rices and heir corresonding arges. However, h assumion does no hold as long as he likelihood of a rice change deends on he magniude of he deviaion beween acual and arge rices. On he oher hand, ime-deenden adjusmen models have relied on he assumion ha each firm leaves rice unchanged for a fixed amoun of ime 2. Considering ime-deenden ricing rules rovide a simle framework o derive he aggregae dynamics. Alhough hese models allow for he realic fac of nominal rice changes occurring in dcree jums, hey share he unsafacory assumion ha he ime beween rice changes rese, and firms are unable o adjus o any shock beween rice-adjusmen daes. An alernaive aroach o inroduce rice sickiness rovided by sae-deenden adjusmen models 3. In hese models a firm will change rice whenever i deviaes a cerain amoun from oimal value. The mos obvious jusificaion for h individual behavior he exence of a fixed cos in he adjusmen-cos funcion. Th he idea in which he menu-cos model of rice adjusmen based. According o h model, a firm will change acual rice only if he desired adjusmen large enough o warran aying he menu cos. The menu-cos model belongs o he class of non-convex adjusmen cos See chaer 6 in Romer (996 for a review of heoreical microfoundaions of nominal rigidiies and Sheshinski and Wes (993 for a collecion of aers dealing wih he ineracion of individual rice adjusmen olicies and aggregae rice sickiness. 2 See, for insance, Taylor (98. 3 See, for insance, Sheshinski and Wes (977,983 and Calin and Leahy (99. 3 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

6 models wih a fixed (S,s ricing rule 4. Some degree of flexibiliy may be inroduced in hese models by allowing differen hresholds for osiive and negaive deviaions. Th seing would be jusified, as Ball and Mankiw (994 sugges, by he resence of rend inflaion. When here rend inflaion, rices will be more flexible uwards han downwards, i.e. osiive shocks are more likely o rigger rice adjusmens han are negaive shocks. The reason ha, in he face of a negaive shock, he firm more likely o avoid he menu cos execing ha some of he desired adjusmen will come abou as a resul of rend inflaion. While menu-coss models rovide realic microfoundaions for rice dynamics a he firm level, hey do no seem o be adequae o exlain aggregae rice dynamics since dconinuous adjusmen a feaure of individual firms, no of he whole economy. The adjusmen hazard models, develoed by Caballero and Engel (993a, ry o address h roblem. These auhors inroduce he adjusmen hazard funcions ha link he robabiliy of an individual adjusmen o he size of he deviaion beween arge and acual rices. Th aroach rovides boh a reasonable microeconomic behavior and, by allowing heerogeneiy across individual firms, a realic characerizaion of aggregae rice dynamics. Furhermore, he arial adjusmen model and he menu cos model may be considered as aricular cases of he family of adjusmen hazard models 5. Thus, a direc comaron of hese models o alernaive hazard models ossible. For insance, Caballero and Engel (993b esimae an increasing hazard model for rice adjusmen ha ouerforms he arial adjusmen model in exlaining he dynamics of he aggregae manufacuring rice level in he U.S. 2-b The adjusmen hazard model In h sub-secion, we briefly describe he basic framework underlying he adjusmen hazard aroach develoed by Caballero and Engel (992 and 993a. Th aroach relies on wo basic feaures: firs, he robabiliy of an individual rice change deends on he dearure of he acual rice ( P i from wha i would be oimal ( i, and, second, firms are heerogeneous. The main macroeconomic imlicaion of h framework ha o exlain aggregae rice dynamics necessary o kee rack of he evoluion of he cross-secional dribuion of individual rice deviaions. P 4 A fixed (S,s ricing rule indicaes ha he deviaion of he acual rice from arge floas freely beween wo redeermined bounds and he adjusmen riggered only if one of he bounds reached. See Caballero and Engel (99 for a sudy of he imlicaions of individual (S,s olicies for aggregae dynamics. 5 More recely, in he arial adjusmen model he hazard funcion consan, i.e. he robabiliy of adjusmen indeenden of he magniude of he deviaion. In he simles menu-cos model he hazard funcion will ake value one if he deviaion (in absolue value larger han a secific hreshold, and zero oherwe. 4 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

7 Le z i denoe he difference beween acual and arge rice for firm i a ime and F (z he cross-secion dribuion of individual rice deviaions. The key elemen of h aroach he hazard funcion, Λ(z, which links he robabiliy of a firm adjusing rice o he size of he deviaion from arge rice. The ransiional dynamics of individual rice deviaions will be driven by hree elemens: firs, aggregae shocks shifing he whole dribuion of rice deviaions; second, he hazard funcion ha deermines he rice adjusmen; and, hird, idiosyncraic shocks affecing he deerminans of individual rice arges. Thus, he change in he aggregae rice level during he ime inerval [, would be equal o: ( = z z f Λ( ( z dz [] where reresens he aggregae shock (lower case leers meaning naural logarihms, and f (z he cross-secion densiy of rice deviaions a ime. The inuiion for h exression he following. Le us assume ha f (z he crosssecion densiy funcion of rice deviaions once firms have exerienced heir idiosyncraic shocks. Afer he realizaion of he aggregae shock (, every individual rice deviaion z shifed o ( z. Then, a fracion Λ( z of firms adjus heir rices by ( z. Exression [] obained by adding over he whole dribuion of z. Looking a exression [] i seems o be clear ha, in h framework, he evoluion of he aggregae rice level deends on wo elemens: he cross-secion dribuion of rice deviaions and he microeconomic hazard funcion. Nex, we ry o illusrae how he shae of he adjusmen hazard funcion condiions he aggregae rice dynamics. For h urose, firs we resen, as a benchmark case, he adjusmen when he hazard funcion consan, and hen we derive he aggregae dynamics for alernaive hazard funcions ha are consen wih a more realic microeconomic behavior. 2-b-a Consan Hazard: The Parial-Adjusmen Model Le us sar wih he simle case where Λ(z = λ. Relacing h exression for he hazard funcion in equaion [] yields: ( = λ ( z [2] 5 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

8 where z ( reresens he mean of he cross-secional dribuion of deviaions. Th equaion shows ha he change in he aggregae rice level in every eriod a consan share (λ of he average rice deviaion 6. Th aggregae aern he resul of a consan fracion of firms (λ adjusing fully in every eriod. As Roemberg (987 showed, h aggregae dynamics equivalen o ha derived from a reresenaive-agen model wih quadraic adjusmen coss (arial-adjusmen model 7. I worh noing ha in h case he aggregae rice dynamics deends only on he firs momen of he cross-secion dribuion of firms. 2-b-b Alernaive Hazards In h secion we inroduce alernaive hazard funcions o relax he consan hazard assumion ha he robabiliy of an individual rice adjusmen indeenden of he deviaion beween he acual and he arge rice. Wih hese alernaive hazards we look for a more realic microeconomic behavior 8. More recely, we seek o allow for he robabiliy of adjusmen being: (i increasing in he size of he rice deviaion and (ii differen for uwards and downwards rice adjusmens. Le us consider he following non-consan hazard funcions: I. Simle Quadraic-Hazard model Firs, as an examle of an increasing hazard funcion, we consider he simle quadraic-hazard funcion: 2 ( z = λ λ Λ [3] 2 z Subsiuing he hazard funcion [3] in equaion [] yields he following exression for he aggregae rice dynamics: z 6 Noe ha ( ( he average rice deviaion afer he realaion of he aggregae rice shock 7 Given ha ( z =, he level of observed rices would be:, = ( λ λ = ( λ λ, ha he usual reresenaion of he arial adjusmen model.., so equaion [2] may be rewrien as: 8 Neverheless, we are sill assuming ha once a firm adjuss rice, i adjuss fully, i.e. he size of he adjusmen equal o he rice deviaion. See Ariga and Okhusa (998 for a join esimaion of he robabiliy of zero rice change and he size of rice changes, boh condiional on he magniude of he deviaion of he rice from he arge level. 6 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

9 3 a a a (2 (3 2 = λ 3 zc, z c, λ [4] } a a ( where = ( z reresens he arial adjusmen erm in equaion [2], and (k z c denoes he kh cenered momen. Unlike he consan hazard case, he mean no he only momen of he cross-secional dribuion relevan for he aggregae dynamics. In h sense, wo ineresing feaures are from exression [4]. Firs, he resonse of he aggregae rice level o aggregae shocks osiively linked o he variance of he crosssecional dribuion. Th redicion consen wih Ball and Mankiw (994. These auhors show ha more variabiliy in he relaive-rice dribuion increases he effecs of asymmeric rice adjusmen -imlied by he resence of rend inflaion- on he aggregae rice level. Second, for a given aggregae shock, increases in he aggregae rice level are larger he more skewed o he lef he dribuion of deviaions. Again, h feaure consen wih Ball and Mankiw (995 who show ha inflaion res when he dribuion of relaive rice changes skewed o he side of relaive rice increases 9. II. Asymmeric Hazard models Nex, we exlicily model he ossible exence of asymmeries in he likelihood of rice adjusmens, ha, we allow he robabiliy of adjusmen being differen for osiive and negaive rice deviaions as suggesed by recen menu cos models. More recely we ry o caure he aforemenioned Ball and Mankiw s (994 redicion ha, in he resence of rend inflaion, he robabiliy of adjusing rices higher when he firm s deviaion negaive han when i osiive. In oher erms, in he resence of rend inflaion firms are more likely o increase heir rices han o cu hem. To es h ossibiliy we consider wo alernaive asymmeric-hazard funcions, which allow for wo differen origins of he asymmery. a Asymmeric-Consan-Hazard model Λ ( z = λ, λ, for z > for z < [5] 9 Noe ha in he comarons beween he imlicaions of Caballero and Engel s hazard funcion aroach and Ball and Mankiw s menu-cos models, we are idenifying he relaive rice shocks of he laer aroach wih he unadjused orion of individual shocks (i.e., he rice deviaions of he former. See Amano and Macklem (997 for evidence, using Canadian daa, suoring Ball and Mankiw s model of riceadjusmen. See also, Yaes (998 for evidence conrary o he exence of downward nominal rigidiy in rice adjusmen. 7 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

10 8 The aggregae rice dynamics imlied by he hazard funcion [5] given by: = ( ( ( ( z F z F λ λ [6] where z (- and z ( denoe he means of he cross-secional dribuion condiional on z being smaller and larger han. b Asymmeric-Quadraic-Hazard model ( < > = Λ for, for, z z z z z λ λ λ [7] Subsiuing he hazard funcion [7] in equaion [] yields he following exression for he aggregae rice dynamics: } } (3, (2, 3 2 (3, (2, = c c a a c c a a a z z F z z F λ λ λ [8] where ( ( = a z and ( ( = a z. ( k c z and ( k c z denoe he kh cenered momens of he cross-secional dribuion condiional on z being smaller and larger han. 3- Emirical framework Las secion ses clearly he wo ieces of informaion we need o imlemen he general aroach o model he aggregae behavior of rices: firs, he rofile for aggregae arge rice (or aggregae shock, ; second, he individual deviaions of observed BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

11 rices from arge rices (z i, from which we can calculae he differen momens of he dribuion (F (z. In h aer, we use wo alernaive rocedures o esimae he alernaive hazard models. Our firs rocedure exlo he informaion conained in a secoral daabase. As a firs se we esimae secoral arge rices. For h urose, we firs characerize how firms deermine he fricionless rices (ha, he rices he firm would se if here were no rigidiies for he roducs hey sell in he markes making use of he coinegraion condiion beween fricionless and observed rices. Then we calculae he oimal rice (having in mind ha if he firms are no going o adjus every eriod heir rices hey need o incororae heir ersecives for he fuure evoluion of he fricionless rice deerminans and deviaions from he observed rice. In a hird sage, we define he aggregae shock as a weighed average of he changes in secoral oimal rices. Finally, we ake he ah of he momens of he cross-secional dribuion of secoral rice deviaions afer he realizaion of he aggregae shock as a roxy for he differen momens required o esimae he aggregae rice dynamics equaions corresonding o he models described in secion 2. As an alernaive sraegy, we follow Caballero and Engel (993b. Their aroach avoids he use of individual informaion abou rices and deerminans. Using h second rocedure, we use he same aggregae shock bu we assume a secific dribuion for he individual shocks. Thus, we only need an iniial dribuion of deviaions from arge rices o run he whole model 2. We consider as iniial dribuion he average cross-secional dribuion of secoral rice deviaions. 3-a A model for fricionless rices and oimal rice deerminaion The model we use o exlain rice formaion a a secoral level follows very closely a model roosed by Layard e al. (99. Firms have marke-ower in he roduc marke and hey ry o maximize heir revenue. For h urose, hey decide oimally he selling rice of heir roducs, he emloymen and he inermediae inus hey use. Firms ake wages, rices of he comeing firms (including he rice of imored goods, rices of he inermediae inus, he secoral level of demand and he caial sock as given. I should be sressed ha, if he hazard funcion a consan, we only need o know he mean of h dribuion o imlemen he model. As he mean a linear combinaion of he individual z, we do no need individual informaion o calculae i. 2 Caballero and Engel (993b considered as he iniial densiy he ergodic densiy ha would ex if aggregae shocks followed a random walk wih drif equal o ha of he aggregae shock rocess and (insananeous variance equal o he sum of he idiosyncraic variance and he variance of he series of aggregae shocks. 9 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

12 The reresenaive firm (i of a secor (s has a echnology reresened by a Cobb- Douglass roducion funcion wih consan reurns o scale. Th echnology he same for all he firms in he secor. The roducion made wih wo facors, caial (K -ha we consider fixed-, and a variable facor (FV ha includes boh labor and inermediae inus. Thus, he ouu (Y would be given by: Y = A FV [9] ( βs where A = A K [] ' s βs being A s he echnological rogress of he secor. We assume ha firms demand funcions deend osiively on he rices of he oher firms in he secor (P j -including he rices of he exernal goods ha are subsiues for he domesic roducion- and negaively on he rice charged by he own firm (P i in an oelasic way: Y P η s = YDs [] Pjs where YD s an indicaor of he secoral demand level. In h seing, he roblem faced by he reresenaive firm can be saed as follows: Max s.. Π = P Y CV s FV Y Y = A P = P FV js (β s ηs YD s [2] where CV reresens he rice of variable inus, being equal for every firm of he secor. Assuming he exence of a symmerical equilibrium in he secor (P =P js, he exression for secoral rices (in logs can be wrien as follows: =. η s s cns Ln η s cvu s [3] BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

13 wih cvu reresening he uni variable coss. Th equaion imlies ha rices are a mark-u over marginal coss, which we roxy by he uni variable coss. In h model he mark-u consan, bu a growing heoreical and emirical body of research indicaes ha demand flucuaions can influence he marku. For examle, Roemberg and Woodford (99 showed ha he organizaion of he roduc marke and he individual references had an imac on he size and sign of ha coefficien. Besides, he oenness degree of some secors we are considering very high, and i has been suggesed ha an increase in inernaional comeiiveness makes he domesic demand less elasic: when exernal rices are high, domesic firms can rae heir rices and exand heir mark-us. We secify he following equaion for he mark-u: η s Ln η s = cns. γ ( yd y γ ( e x s s s s 2 s s [4] where x s he exernal rice in foreign currency and e he nominal exchange rae. Subsiuing h equaion in [3], yields he following exression: s x = cns µ cvu ( µ ( e τ ( yd y [5]. s s s s s s s Thus, secoral rices are a weighed average of variable coss and exernal rices in domesic currency lus an addiional erm reresening demand ressure in he secor. The relaive weighs of he firs wo comonens deend on he secoral oenness degree, and hey have o add one. Th consrain, called nominal homogeneiy, imosed in he emirical model. If he secor has no exernal comeiion we dro he exernal rice comonen and we imose a coefficien of one for he uni variable coss. On he conrary, we have no a riori believe abou he size and sign of τ, he arameer for demand ressure, so we will le he daa o deermine h quesion. Now we can use he exression [5] o consruc he fricionless rice ( * i for each secor. If firms are forward-looking, h rice no going o be he oimal rice ( i, because here a non-null robabiliy of no adjusing rices in he following eriods. Thus, firms will also ake ino accoun he execaions of fuure develomens in he fricionless rice. Assuming ha he firm knows he robabiliy of adjusing rice and ry o minimize he flow of deviaions beween he oimal and he fricionless rices Caballero and Engel (993b showed ha he relaion beween h wo rices he following: m γ E ( * im * i = i m= β [6] BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

14 where γ he robabiliy of adjusing rices and β he dcoun rae. Th exression esablhes ha he fricionless rice should be increased wih he dcouned flow (correced by he robabiliy of non-adjusmen of i execed increases o obain he oimal rice. Jus aggregaing hrough individual firms we ge a similar resul a he secoral level. 3-b Daa and esimaion rocedures Our daabase includes rices, uni variable coss, imor rices and an indicaor of he demand ressure for fory differen caegories of goods and services 3. These rices corresond o wholesale rices of agriculural and indusrial firms in domesic (IPPA and IPRI and foreign markes (IVUX, reail rices for consumer goods (CPI-G and consumer rices for services (CPI-S, all of hem correced from changes in indirec axaion. Thus, he aggregae rice we are considering slighly differen from he rice indexes we usually look a. Char comares he annual ercenage changes of our aggregae rice indicaor, he CPI (ha, he aggregaion of CPI-G and CPI-S lus indirec axaion and he IPRI. No surringly, our indicaor lies, for mos of he samle eriod, beween he oher wo. Besides, he rofiles are very similar and main differences aear in 986, when he indirec axaion sysem was changed, and beween 989 and 993, when he inflaion differenial in goods and services was he highes ever recorded. Uni variable coss are an average of uni labor and uni inermediae coss, weighs coming from he Inu-Ouu ables for he Sanh economy. Uni inermediae coss include rices for all he inermediae goods and services each secor buys from oher secors and from he exernal markes. A secial case he inermediae coss for he differen caegories of consumer goods, because main comonens are he domesic and imored wholesale rices for each caegory. The secoral imor rices are our roxy for exernal rices in domesic currency 4, and he indicaor for demand ressure obained averaging inermediae and final demand for each aricular secor, using, again, he Inu- Ouu ables o calculae he weighs. Using h daabase, we imlemen a hree-se rocedure o esimae he differen hazard models roosed in secion 2. In he firs sage, we esimae he fricionless rice * ( s for he fory goods and services we are considering. In order o do ha, we exloi he coinegraion condiion ha should be ke (ill a consan beween observed and fricionless rices. As fricionless rices are given by he model described in las sub- 3 See Aendix for deails on he secoral classificaion. 4 We assume exernal roducion and domesic roducion o be homogenous. 2 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

15 secion, we run fory regressions in levels of observed rices on uni variable coss, exernal rices (if he secor oen o foreign markes and demand ressure 5, and we define as he fi of each aricular regression. The deailed OLS esimaes 6 of equaion [5] could be found in able A. (Aendix. In general, mos of he secors safy he coinegraion condiion, bu some of hem require arificial variables o obain saionary residuals. As execed, he influence of exernal rices larger for exor han for domesic rices. The imac of ressure demand almos always osiive for rices of goods (more han 5% of he cases, bu for rices of services we have hree secors wih ro-cyclical margins and one wih couner-cyclical margins. Defining he aggregae observed and fricionless rices (, * as he weighed averages of he secoral observed and fricionless rices ( s, s * resecively, we can comare he realized inflaion wih he inflaion rae we would observe if firms did no face adjusmen coss of changing rices. For ha urose, char 2 comares he annual ercenage changes of and *. As we would exec, he correlaion coefficien beween boh series very high (.97 -in a long-erm view, every shock should be incororaed in rices- and he series of fricionless rice changes dlays a slighly higher volailiy 7 -in he shor-erm, nominal rigidiies hel o smooh he imac of shocks-. I worh noing he exence of significan differences beween boh series in some eriods. For insance, in he hird quarer of 984 he observed inflaion rae was 2.2 % higher han he fricionless inflaion rae, whereas in he second quarer of 997 he observed rae was almos 2 % lower han he fricionless rae. Char 2 suggess ha nominal rigidiies may have significan imlicaions in erms of aggregae inflaion, a leas for some eriods. * s In he second se we consruc he oimal secoral rice ( s using exression [6]. The secoral execaions for he increases in he fricionless rices are derived from bivariae VARs of observed and fricionless rices for each secor. The dcoun arameer equal across secors (β=.25 and he robabiliy of adjusmen (γ aken from a esimaed arial adjusmen model beween observed and fricionless rices for each secor. Now we can calculae he secoral deviaions from arge rices (z s as he difference beween observed and oimal rices, so we can derive he cross-secional dribuion of z for every quarer and he aggregae shock ( as he weighed average of secoral oimal rices. Char 3 dlays he kernel densiy for he cross-secional dribuions of 5 These regressions are run searaely because he coefficiens could deend on he secor; in he esimaion we only imose ha he arameers for uni variable cos and exernal rice add o one. 6 We ried more sohicaed mehods as Fully-Modified Esimaors, bu he resuls were broadly he same. 7 The sandard deviaions for he annual changes of he fricionless and realized rices are 4.3 and 4.2, resecively. 3 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

16 98, 989 and As i could be seen, here are some differences no only in he mean of hese dribuions, bu also in he variance and skewness; according o he model, hese differences could hel us o undersand he aggregae behavior of rices. For examle, alhough in 989 he mean was higher and he variance was lower han in 98, inducing a bigger downward adjusmen, he dribuion was less skew o he righ, imlying a movemen o he oosie side. In any case, in inerreing he resuls, we mus be secially cauious given he few observaions (fory or even less in he case of asymmerical hazard funcions available o calculae he momens. In he hird sage we consider wo alernaives. Firsly, we use hese quarerly crosssecional dribuions -o aroximae he differen momens required- and he aggregae observed and oimal rices (,, o esimae he models described in secion 2. We esimae hese models by he generalized mehod of momens (GMM aking he hird lag of he variables in he regression as insrumens, o avoid roblems of endogeneiy wih he aggregae shock. Secondly, we imlemen a rocedure very similar o he one roosed by Caballero and Engell (993b assuming a normal dribuion, wih zero mean and sandard deviaion σ I, for he individual shocks and using he same aggregae shock as before. Unlike hese auhors, we consider he average cross-secional dribuion of secoral rice deviaions as he iniial dribuion. Th alernaive sraegy imlemened as a gridsearch rocedure o esimae he arameers in he equaions of secion 2. Th rocedure selecs hose values of he arameers ha minimize he squared sum of he residuals. 4- Resuls 4-a Esimaes of alernaive hazard funcions Table resens he esimaes of he alernaive adjusmen hazard models for he eriod 98:-998:4 obained using he sequence of cross-secional dribuions esimaed from secoral daa. The corresonding esimaed hazard funcions are dlayed in Char 4. Column shows he esimaes of equaion [2] corresonding o he arial adjusmen model (Λ(z = λ. The esimaed consan hazard arameer.36 and i significan. Column 2 resens he esimaes of he simle quadraic-hazard model (equaions [3] and [4]. The quadraic hazard arameer osiive and significan imlying ha he hazard funcion increasing. However, he exlanaory ower for he aggregae rice level does no imrove. The sum of squared residuals indeed larger han in he arial adjusmen model. Column 3 resens he esimaes of he asymmeric-consanhazard model (equaions [5] and [6]. The esimaed non-consan arameer corresonding 8 In he emirical work we use he quarerly cross-secional dribuions, bu in order o reduce volailiy, in h char we consider he whole year. 4 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

17 o rice increases ( λ.49 whereas he esimaed non-consan arameer corresonding o rice decreases ( λ.33. Th resul would sugges ha he resuling hazard funcion asymmeric: for a given rice deviaion in absolue value, firms are more likely o increase heir rices han o decrease hem. However, he hyohes of equaliy of λ and λ canno be rejeced. Again, he exlanaory ower wih resec o he symmeric consan hazard model does no imrove. Finally, column 4 resens he esimaes of he asymmeric-quadraic-hazard model (equaions [7] and [8]. In h case, alhough he arameer for rice increases larger han he corresonding for rice decreases, i no significan. Moreover, wih h esimae, we also rejec ha he hazard funcion asymmeric. Table 2 dlays he resuls for he adjusmen hazard models esimaed following he rocedure roosed by Caballero and Engel (993b. The corresonding esimaed hazard funcions are dlayed in Char 5. Column shows he esimaes corresonding o he arial adjusmen model (Λ(z = λ. The esimaed long-run consan hazard arameer.58, subsanially higher han he esimaed wih he former aroach. Column 2 resens he esimaes of he simle quadraic-hazard model. The long-run quadraic hazard arameer osiive and significan imlying ha he hazard funcion increasing. Moreover, he exlanaory ower for he aggregae rice level slighly imroves. The sum of squared residuals for he dynamic quadraic hazard model around 3% smaller han for he arial adjusmen model. Column 3 resens he esimaes of he asymmeric-consanhazard model. The esimaed long-run non-consan arameers for rice increases ( λ significanly larger han he esimaed long-run non-consan arameers for rice decreases ( λ. Thus, he asymmery of he hazard funcion no rejeced in h case. Unlike wha haened wih he firs esimaion aroach, he exlanaory ower wih resec o he symmeric consan hazard model imroves. The sum of squared residuals for he asymmeric-consan-hazard model subsanially smaller (2% han for he arial adjusmen model. Finally, column 4 resens he esimaes of he asymmeric-quadraichazard model. In h case, he arameer for rice increases ( λ larger han he corresonding for rice decreases ( λ, bu hey are no significanly differen. Thus, wih 2 h esimae, we canno rejec ha he hazard funcion increasing, bu we rejec he asymmery roery again. The dynamic asymmeric-quadraic-hazard model has a sum of square residuals larger han he arial adjusmen model. The difference beween he wo aroaches o esimae he alernaive hazard models relies on he way o comue he sequence of esimaed cross-secion dribuions of individual rice deviaions. In he firs aroach, i roxied by he sequence of crosssecion dribuions of secoral rice deviaions. In h rocedure, here no needed an 2 5 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

18 exlici assumion abou he dribuion of he idiosyncraic shocks. In fac, he aggregae shock, he hazard funcion and wo consecuive cross-secion dribuions would imlicily allow esimaing hese idiosyncraic shocks. In he second aroach, however, an exlici assumion abou he dribuion of he idiosyncraic shocks used o derive he whole sequence of cross-secional dribuions. As he comaron of ables and 2 reveals, boh rocedures generae, o a cerain exen, differen resuls. Overall, when we make use of he secoral daa we esimae models wih higher exlanaory ower (lower sum of he squared residuals han when we use only aggregae daa, he only exceion being he asymmeric-consan hazard model. I also worh noing ha he esimaed robabiliy of adjusmen using he firs aroach ends o be smaller. Th suggess ha allowing for a ime-varying dribuion in he idiosyncraic shocks leads o a higher degree of sickiness a he individual level. Finally, he asymmery roery no rejeced in he asymmericconsan hazard model esimaed using he second aroach. 4-b Simulaion: he imac of nominal rigidiies on he aggregae rice level As i has been already menioned, Char 2 comares he observed inflaion rae wih he inflaion rae ha we would observe if firms did no face adjusmen coss of changing rices. Tha char shows ha he differences beween boh raes may be fairly large, a leas for some eriods, suggesing ha when rice adjusmen cosly, firms do no adjus o every shock in heir rice deerminans. A sraighforward imlicaion ha he evoluion of fuure inflaion will be condiioned no only by he fuure shocks o he fricionless rice deerminans bu also by he delayed rice adjusmens and he execaions of firms. In order o assess he size of he delayed rice adjusmen, we resen some simulaion exerces. In hese exerces we comare he evoluion of he inflaion rae in a model wih adjusmen coss of changing rices in every secor of he economy, wih he inflaion rae ha we would observe in he absence of nominal rigidiies in a subse of secors. In oher words, we allow for differences in he rice-seing behavior across secors. More recely, in some secors he rice rule given by he esimaed hazard funcions, while in ohers, rices immediaely adjus o changes in heir deerminans. Table 3 resens he resuls of hese simulaion exerces. Each of hese exerces comares he secoral conribuion o he aggregae inflaion rae ha are from he fied quadraic hazard model 9 wih he secoral conribuion o he aggregae inflaion rae 9 The resuls obained using he fied values of he consan hazard model are slighly differen. Th means ha he choice of he secific hazard funcion maers. Alhough here no imrovemen in he goodness-of-fi of he quadraic hazard model wih resec o he consan hazard model, he resuls of he simulaions using boh models differ o some exen. Presumably, he exlanaory ower of he non-consan hazard models would be more relevan for eriods in which shocks ha have a large variance and are asymmeric across secors redominae. Similarly, Caballero and Engel (993b found ha he quadraic hazard model ouerforms he consan hazard one during large shock eodes. 6 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

19 comued assuming ha here are no nominal rigidiies during he eriod in ha subse of secors. Four subses of secors are considered: indusrial and agriculural domesic rices, indusrial and agriculural exor rices, consumer rices of goods and consumer rices of services. In Table 3, for each of hese subses of secors, he firs row ( quadraic hazard reresens he conribuion (of ha subse of secors o he aggregae inflaion rae ha ares from he fied quadraic hazard model. The second row ( full adjusmen reresens ha conribuion comued assuming ha here are no nominal rigidiies during he eriod in ha subse of secors. Finally, he following rows (hird o fifh or hird o fourh, deending on he secors reresen he decomosiion of h las conribuion ino he conribuions of he differen rice deerminans (uni variable coss, exernal rices and demand ressure. Therefore, we can read he difference beween he firs and he second row as he imac on he aggregae inflaion rae semming from he exence of nominal rigidiies in a subse of secors. A firs look a he resuls suggess ha he magniude of he effec of he nominal rigidiies on he aggregae inflaion rae nonnegligible. Le us now go ino he deails of he secific simulaions. The firs se of resuls corresonds o he simulaion of absence of rigidiies in he adjusmen of agriculural and indusrial domesic wholesale rices. We observe ha if firms in hese secors did no face adjusmen coss of changing rices during he eriod , he aggregae inflaion rae would have been around.2% and.7% higher in 996 and 997, and almos.5% lower in 998. The resuls of he simulaion for h subse of secors fi quie well wih he exence of nominal rigidiies. Firs, in 997 firms in hese secors delayed he ranslaion ino heir rices of he incremen in demand ressure. Similarly, in 998 hese firms did no resond lowering heir rices o he fall in he uni variable coss and demand. The second se of resuls dlays he imac on aggregae inflaion of he exence of nominal rigidiies in he adjusmen of agriculural and indusrial exor wholesale rices. In he absence of nominal rigidiies, he aggregae inflaion rae would have been.23% lower in 996 and.5% higher in 997. Th delayed adjusmen imlied ha in 998 firms in hese secors did no reac fully o he fall in exernal rices and demand ressure by lowering heir rices. The hird se of resuls, corresonding o he reail rices of consumer goods, suggess ha in he absence of nominal rigidiies he aggregae inflaion rae would have been slighly lower (under. % on average. Finally, he las se of resuls corresonds o he simulaion of absence of rigidiies in he adjusmen of reail rices of services. We observe ha, in h case, he aggregae rice level would have been higher in he firs wo years (.22% and.3%, resecively and lower in 998(.%. 7 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

20 5- Conclusions The arial adjusmen model reresens he sandard aroach o induce aggregae rice sickiness. Th model, based on he inroducion of quadraic adjusmen coss of changing rices, assumes a coninuous bu arial rice adjusmen a he firm level. Th behavior a odds wih he unconroversial fac ha individual firms do no adjus coninuously heir rices o all he shocks hey erceive in heir rice deerminans. The search for alernaive characerizaions of he aggregae rice dynamics semming from a more realic microeconomic behavior has led o models considering sae-deenden ricing rules. The adjusmen hazard framework roosed by Caballero and Engel (993a rovides an examle of h ye of models. In h framework, he adjusmen olicy a he firm level characerized by means of he adjusmen hazard funcion, which links he robabiliy of a firm adjusing rice o he size of he deviaion from arge rice. Considering ha firms are heerogeneous, he aggregae dynamics generaed by nonconsan hazard funcions will deend on he cross-secional dribuion of rice deviaions. Using h hazard adjusmen framework, h aer ries o illusrae he imlicaions for aggregae rice dynamics of alernaive characerizaions of microeconomic rice adjusmen olicies. For h urose, we follow wo differen aroaches. Firsly, we esimae alernaive models of individual rice adjusmens using a daa se of Sanh secoral rice indexes covering he eriod We use a hree-se rocedure o esimae he differen models. In he firs se, we esimae secoral rice equaions and ake he fi of each regression as he secoral fricionless rice, ha, he rice ha would be observed in he absence of nominal rigidiies. In he second se we calculae he oimal rices, having in mind ha if firms are forward-looking and hey have a non-null robabiliy of no adjusing rices he following eriods, hey need o ake ino accoun heir execaions on rice evoluion. In he hird sage, we use he cross-secional dribuion of he rice deviaions from oimal rices o roxy for he differen momens required o esimae he aggregae rice equaion. In he second aroach, we imlemen a similar rocedure as in Caballero and Engel (993b ha avoids he use of secoral informaion. Under boh aroaches we comare he abiliy of he esimaed hazard models o exlain he behavior of he aggregae rice level, aking he arial adjusmen model as a benchmark. Finally, we resen simle simulaion exerces in order o rovide an assessmen of he imac on he aggregae inflaion rae semming from he exence of nominal rigidiies in several subses of secors. The main resuls of he aer may be summarized as follows. Models wih nonconsan hazard funcions slighly ouerform he arial adjusmen model, i.e. he aggregae behavior of rices deends no only on he as average deviaion from arge rices (as i assumed when using a arial adjusmen model bu also on higher momens of he cross-secion dribuion of rice deviaions. Alhough he imrovemen in 8 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

21 he goodness-of-fi wih resec o he arial adjusmen model only modes, i may be imoran esecially for hose eriods in which shocks ha have a large variance and are asymmeric across secors redominae. Besides, here weak evidence of asymmeries in he rice adjusmen, ha, in he shor-erm he robabiliy of adjusing rices uwards higher han downwards. Finally, he magniude of he effec of he nominal rigidiies on he aggregae rice level non-negligible. 9 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

22 APPENDIX SECTORAL DESEGREGATION Our daa base includes informaion for weny one secors of he economy (agriculure, energy, en manufacuring secors, building, reail rading and seven secors from services ha covers he cororae non-financial side of he economy, bu we manage o consider fory secors. We do ha sliing he selling rices for some of he secors. In he case of manufacuring, agriculure and energy, we can searae rices of goods sold in he domesic and foreign markes, so we incororae welve more secors. Th has a drawback: he deerminans of hem in each secor (uni variable coss and exernal rices are he same in he wo markes. In reail rading we can dinguh he rices of eigh differen roducs, so we add oher seven secors. In h case, he uni variable coss in each caegory are differen, because he mos imoran ar of hem are he buying wholesale rices for he raded goods, bu uni labor coss and inermediae inu coss are he same. Table A. dlays he deailed resuls for he secoral coinegraion regressions ha we use o obain he secoral fricionless rices. The regressions were run by OLS, and all of hem included a consan and hree seasonal dummies. The saical ess we use o es coinegraion are he mos usual: Augmened Dickey-Fuller (ADF and Phill-Perron (PP. 2 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

23 TABLE A.. DETAILED RESULTS FOR COINTEGRATION REGRESSIONS. ESTIMATION METHOD: OLS Cvu e x (yd-y deerminic comonen Sandard Deviaion Agriculural and Indusrial Domesic Wholesale Prices (IPPA and IPRI Agriculure Energy S 86Q Basic Meal Mineral T Chemical Equimen Trans. Eq Food Texile Wood -.53 T 9Q Paer S 84Q Plasic Agriculural and Indusrial Exor Wholesale Prices (IVUX Agriculure -.3 T Energy - - S 86Q Basic Meal Mineral S 82Q Chemical Equimen S82Q Trans. Eq T Food Texile Wood S 95Q Paer Plasic T Reail Prices for Consumer Goods and Services (CPI-B and CPI-S Food Energy - - S 86Q Equimen Chemical - - S 86Q Trans. Eq. -.7 S 86Q Texile - - S 86Q Wood -.23 S 8Q Paer - - S 86Q Consrucion -.8 T 94Q Reairs -.7 S 89Q Hosess - - T Trans.Serv T86Q Communic Educaion -.67 T Healh - - T 84Q O. Services S 84Q Noes: ADF, augmened Dickey-Fuller es; PP, Phill-Perron es; S, se dummy; T, rend dummy. ADF PP 2 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

24 TABLE. GMM RESULTS FOR DIFFERENT HAZARD FUNCTIONS. DESAGREGATED APPROACH. Consan-Hazard (Exression [2] Quadraic-Hazard (Exression [4] Asymmeric- Consan- Hazard (Exression [6] Asymmeric- Quadraic- Hazard (Exression [8] λ.36 ( ( (3.47 λ λ ( ( λ ( λ 2 λ ( (.84 R RSS* DW Sargan Tes [v] 3.82 [.28] 8.46 [.2] 3.7 [.22] 9.7 [.42] Tes for λ - =λ [v] [.69].2 [.89] Noes: The insrumens cons of lag 3 of he variables ha aear in each equaion. Esimaion eriod: 979: o 998:4. TABLE 2. CABALLERO & ENGEL PROCEDURE FOR THE ESTIMATION OF DIFFERENT HAZARD FUNCTIONS. Consan-Hazard (Exression [2] Quadraic-Hazard (Exression [4] Asymmeric- Consan- Hazard (Exression [6] Asymmeric- Quadraic- Hazard (Exression [8] λ.58 ( ( (.8 λ λ ( ( λ ( λ 2 λ ( ( σ I R RSS* Tes for λ - =λ [v] [.].75 [.46] -raios beween brackes. 22 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992

25 Indusrial Domesic Prices Indusrial Exor Prices Consumer Prices of Goods Consumer Prices of Services TABLE 3. SECTORAL CONTRIBUTIONS TO THE AGGREGATE INFLATION RATE THE IMPACT OF NOMINAL RIGIDITIES Average Quadraic hazard Full adjusmen Uni variable cos Exernal rice Demand ressure Quadraic hazard Full adjusmen Uni variable cos Exernal Price Demand ressure Quadraic hazard Full adjusmen Uni variable cos Demand ressure Quadraic hazard Full adjusmen Uni variable cos Demand ressure Noes: Quadraic hazard reresens he conribuion (of he subse of secors o he aggregae inflaion rae ha ares from he GMM esimaed quadraic hazard model. Full adjusmen reresens ha conribuion comued assuming ha here are no nominal rigidiies during he eriod in ha subse of secors. Finally, uni variable coss, exernal rices and demand ressure reresen he decomosiion of h las conribuion ino he conribuions of he differen fricionless rice deerminans. 23 BANCO DE ESPAÑA / DOCUMENTO DE TRABAJO nº 992