Globalization, Market Structure and Inflation Dynamics

Transcription

1 DIRECTION GÉNÉRALE DES ÉTUDES ET DES RELATIONS INTERNATIONALES Globalizaion, Marke Srucure and Inflaion Dynamics Sophie Guilloux-Nefussi 1 Working Paper #610 December 2016 ABSTRACT The sensiiviy of inflaion o domesic slack has declined in developed counries since he mid-1980s. This aricle shows why his migh resul from globalizaion favoring concenraion. To do so, I add hree ingrediens o an oherwise sandard general equilibrium wo-counry new-keynesian model. (1) Sraegic ineracions generae a ime-varying desired markup; (2) endogenous enry and (3) heerogeneous produciviy engender a self-selecion of he mos producive firms (which are also he larges ones) in inernaional rade. Hence, he weigh of large firms in domesic producion increases in response o a fall in inernaional rade coss. These large firms ransmi less marginal cos flucuaions o price adjusmens, raher absorbing hem ino heir desired markup o proec heir marke share. A he aggregae level, his leads o domesic inflaion reacing less o real aciviy flucuaions. Keywords: Inflaion; Impac of Globalizaion; Sraegic Ineracions; Marke Srucure; Phillips Curve. JEL classificaion: E31,F41,F62. 1 Banque de France Moneary and Financial Research Deparmen Moneary Policy Research Uni, 31 rue Croix des Peis Champs, Paris, France. address: sophie.guilloux-nefussi@banque-france.fr. Working Papers reflec he opinions of he auhors and do no necessarily express he views of he Banque de France. This documen is available on he Banque de France Websie. Les Documens de ravail reflèen les idées personnelles de leurs aueurs e n'exprimen pas nécessairemen la posiion de la Banque de France. Ce documen es disponible sur le sie inerne de la Banque de France.

2 NON-TECHNICAL SUMMARY 2 Despie he dramaic economic conracion following he Lehman collapse and he ensuing subdued growh dynamics, inflaion has displayed remarkable sabiliy. This missing disinflaion puzzle has drawn renewed aenion on he fundamenal forces behind he loosening of he inflaion/oupu radeoff observed in advanced counries since he mid-1980s. Improvemen in moneary policy making, moving owards enhanced cenral bank independence and inflaion argeing, has cerainly helped anchor inflaion expecaions and conribued o he growing sabiliy of inflaion over he pas hiry years. Recen empirical sudies have also poined o anoher, more srucural change: conrolling for inflaion expecaions, he magniude of he increase in inflaion resuling from a given expansion of domesic demand has become significanly lower oday han i was in he early 1980s, i.e., he Phillips curve have flaened. Among he possible explanaions for ha srucural ransformaion, globalizaion has sood as one of he prime suspecs. Inuiively, as openness o inernaional rade increases, some producers adjus heir pricing behavior for fear of losing heir marke share. This should in principle affec how inflaion responds o he slack/ighness of he domesic economy. However, despie is appeal, i has proven exremely difficul o formalize his simple sory. In his paper, I provide a novel analyical framework ha can replicae he declining sensiiviy of domesic inflaion o real aciviy in response o globalizaion. I build on a sandard wo-counry new- Keynesian model, in which he Phillips curve relaes inflaion o inflaion expecaions and he real marginal cos, he laer being a proxy for domesic slack. I include hree new ingrediens o his oherwise sandard framework. (1) Oligopolisic compeiion a he secor level allows for sraegic ineracions beween firms. They compee in prices à la Courno wihin secors and adjus sraegically heir markups in order o keep low relaive prices and preserve heir demand. This assumpion capures he impac of compeiion on he pricing behavior of producers. In addiion, (2) firms have differen produciviies and (3) hey have o pay boh a fixed cos and a variable per-uni rade cos o serve he foreign marke. Hence he se of exporers is endogenously deermined. I is profiable o expor only for a subse of firms (he mos efficien ones). Wih ha model in hands, I define globalizaion as a fall in inernaional per-uni rade coss. As a resul, he se of compeiors endogenously changes as i becomes profiable for new firms o expor. 2 This paper is a subsanially revised version of a manuscrip previously circulaed as ``Globalizaion, Marke Srucure and he Flaening of he Phillips curve. I have paricularly benefied from deailed discussions and commens by Thomas Chaney, Behzad Diba, Pedro Gee, Jean Imbs, Oleg Iskhoki, Philippe Marin, Isabelle Méjean, and Harald Uhlig. I hank as well Philippe Andrade, Pamfili Anipa, Jean Barhélemy, Vincen Bignon, Luca Guerrieri, Chrisian Hellwig, Julien Maheron, Eric Mengus, Adrian Penalver, Lionel Poier and Andrea Tambaloi for heir houghful remarks and feedback. All remaining errors are mine. I am also graeful o seminar paricipans a he 2014 ADRES docoral Conference in Economics, he 2014 Inernaional Symposium on Money, Banking and Finance, he 2014 European Economic Associaion Congress, he 2015 Theories and Mehods in Macroeconomics (T2M) Conference, he 2015 Dynamics, Economic Growh, and Inernaional Trade Conference, he 2015 Midwes Macro Meeings, he 2015 Bank of England/Banque de France Inernaional Macro Workshop, he 2016 Sciences-Po/Banque de France workshop on Granulariy, and he 2016 NBER Summer Insiue ITM. Banque de France Working Paper #610 ii

3 By he produciviy heerogeneiy assumpion, only highly producive firms choose o expor; hese firms also happen o be he larges firms. Because of he sraegic ineracions assumpion, he larges firms are he ones mos prone o acively adjus heir markup and hus have more sluggish prices. This specific behavior of large firms compared o small firms is crucial for undersanding he impac of globalizaion on inflaion dynamics. Large firms exhibi high markups and have room o acively play wih hem in order o mainain heir low relaive prices and hence heir marke share. On he conrary, small firms markups are iny and offer only limied room for sraegic adjusmens. Hence, when hi by he same cos shock, large firms ransmi only parially he shock o heir prices, raher adjusing heir markup. A he aggregae level, he magniude of he responsiveness of inflaion o real marginal cos depends on he proporion of large versus small firms, and on how much higher and more elasic heir markups are. Therefore, he remaining quesion regards he impac of globalizaion on he disribuion of firms size. In ha respec, openness o inernaional rade gives rise o wo forces. (i) On he one hand, holding consan he se of domesic firms, he enry of new foreign compeiors on he marke mechanically reduces domesic firms marke shares. This purely pro-compeiive impac of globalizaion squeezes he scope for markup adjusmens, hence renders prices more flexible and ighens he link beween inflaion and domesic slack. (ii) On he oher hand, as globalizaion is a long-run process, he se of domesic producers endogenously changes over ime. In response o a fall in inernaional rade cos, i becomes profiable for he mos producive (which also happen o be he larges) firms o expor. The leas producive ones (also he smalles) lose domesic marke shares due o foreign compeiion and canno access new markes. In he end, a larger share of domesic oupu is produced by large firms, wih more rigid prices. If his concenraion force dominaes he pro-compeiive one, hen globalizaion srenghens he overall degree of real rigidiies, which ranslaes ino inflaion responding less o domesic slack. For a parameerizaion of he model ha replicaes sandard feaures of inernaional rade, I show ha his migh indeed be he case. Specifically, I simulae a globalizaion shock in wo economies. The firs one is composed of firms ha all have he same produciviy, and he second one comprises heerogeneous firms bu exhibis he same average produciviy as he firs one. The slope of he Phillips curve responds in opposie direcion o he globalizaion shock in hose wo environmens. In he homogeneous-produciviy case, i.e., when only he pro-compeiive channel is acive and he concenraion channel is shu down, globalizaion seepens he slope of he Phillips curve by 1%. In he heerogeneous-produciviy case, he concenraion channel is a work (due o self-selecion of large firms) and offses he pro-compeiive one: he sensiiviy of inflaion o marginal cos drops by 11% in response o globalizaion. Banque de France Working Paper #610 iii

4 RÉSUMÉ : MONDIALISATION, STRUCTURE DE MARCHÉ ET DYNAMIQUE DE L INFLATION La sensibilié de l inflaion aux ensions sur les capaciés de producion domesique s es affaiblie dans les pays développés depuis le milieu des années Ce aricle explique en quoi ceci peu êre dû à la mondialisaion, via un accroissemen de la concenraion des enreprises. À cee fin, j incorpore rois nouveaux élémens dans un modèle sandard d équilibre général néokeynésien à deux pays : (1) des ineracions sraégiques enre les enreprises, qui se raduisen par des aux de marge variables ; (2) l enrée endogène d enreprises sur chaque marché e (3) des différences de producivié enre elles, qui génèren une auo-sélecion des plus producives (égalemen les plus grandes) à l expor. Par conséquen, quand les coûs de ranspor inernaionaux baissen, le poids des grandes enreprises dans la producion inérieure augmene. Or les grandes enreprises répercuen moins les chocs de coûs marginaux sur les prix, ayan pluô endance à les absorber dans leur marge afin de proéger leur par de marché. Au niveau agrégé, ceci implique que l inflaion domesique réagi moins aux flucuaions de l acivié réelle. Mos-clés : Inflaion ; Impac macroéconomique de la mondialisaion ; Ineracions Sraégiques ; Srucure de Marché, Courbe de Phillips. Banque de France Working Paper #610 iv

5 Inroducion In spie of he dramaic economic conracion following he Lehman collapse and he ensuing subdued growh dynamics, inflaion has displayed remarkable sabiliy. This missing disinflaion puzzle has drawn renewed aenion on he fundamenal forces behind he loosening of he inflaion-oupu radeoff observed in advanced counries since he mid 1980 s. 1 Improvemen in moneary policy making owards enhanced cenral bank independence and inflaion argeing has cerainly helped anchor inflaion expecaions and conribued o he growing sabiliy of inflaion over he las hiry years. Recen empirical sudies have also poined o anoher more srucural change: conrolling for inflaion expecaions, he magniude of he increase in inflaion resuling from a given expansion of domesic demand has become significanly lower oday han i was in he early 1980 s. 2 Among he possible explanaions for ha srucural ransformaion, globalizaion has sood as one of he prime suspecs. Inuiively, as openness o inernaional rade increases, some producers adjus heir pricing behavior for fear of losing heir marke share. This should in principle affec how inflaion responds o he slack/ighness of he domesic economy. Ye, despie is appeal, i has proven exremely difficul o formalize his simple sory. In his paper, I provide a novel analyical framework ha can replicae he declining sensiiviy of domesic inflaion o real aciviy in response o globalizaion. I include hree ingrediens ino an oherwise sandard wo-counry new-keynesian model: sraegic ineracions due o oligopolisic compeiion, endogenous enry on he expor marke due o fixed peneraion coss and heerogeneiy in firms produciviy. I define globalizaion as a fall in inernaional per-uni rade coss. The se of compeiors endogenously changes as i becomes profiable for new firms o expor (En- 1 A non-exhausive lis of publicaions on ha quesion includes Kohn (2006), Bernanke (2007), or, more recenly, Ball and Mazumder (2011), Peach e al. (2011), Gordon (2013), Inernaional Moneary Fund (2013), Frao and Uhlig (2014), Coibion and Gorodnichenko (2015), Blanchard e al. (2015). In a differen approach, Gopinah e al. (2012) also sudy he dynamic properies of prices over he business cycle, bu hey focus specifically on rade prices during he rade collapse from Augus 2008 o March They show ha he sharp drop in differeniaed goods rade came abou enirely hrough quaniies, while prices remained prey sable. 2 In a new-keynesian perspecive, his is referred o as he flaening of he Phillips curve. See Borio and Filardo (2007), Ball and Mazumder (2011), Inernaional Moneary Fund (2013), and Blanchard e al. (2015) for empirical evidence. Sbordone (2010) s inroducion also provides a deailed review of he lieraure documening such a srucural change. 1

6 dogenous Enry assumpion). By he Produciviy Heerogeneiy assumpion, only he mos producive firms choose o expor, which also happen o be he larges firms. 3 Because of he Sraegic Ineracions assumpion, larges firms are he ones mos prone o ac sraegically by absorbing marginal cos movemens ino heir markup in order o proec heir marke share. Thus, hey ransmi less marginal cos flucuaions ino price adjusmens, compared o smaller firms. Evenually, openness o inernaional rade gives rise o wo forces: (i) pro-compeiive pressures, as foreign compeiors penerae he domesic marke, and (ii) greaer concenraion, as he weigh of large firms in domesic producion increases. If he concenraion force dominaes, hen globalizaion srenghens he overall degree of real rigidiies, 4 which ranslaes ino inflaion responding less o domesic slack. I furher demonsrae why each assumpion is necessary, bu no sufficien in iself, o produce he weakening of he relaionship beween inflaion and domesic slack in response o globalizaion. To esablish his poin, he mechanics can be decomposed ino wo pars: (1) How does he elasiciy of inflaion o marginal cos vary wih he marke srucure? (2) How does he marke srucure, i.e. he number of firms and heir relaive marke power, change wih globalizaion? How does he elasiciy of inflaion o domesic slack vary wih he marke srucure? The view ha he level of compeiion migh affec he responsiveness of inflaion o domesic flucuaions presumes ha firms ac sraegically, by adjusing heir markup in response o he perceived compeiion. In order o capure he sraegic ineracions channel, I relax he sandard fixed price elasiciy of demand assumpion. To ha end, I inroduce oligopolisic compeiion a he secor level, saing ha firms compee in quaniies, à la Courno, wihin secors. 5 Firms inernalize heir influence on he secoral oupu when seing heir opimal plans. As a resul, he perceived price-elasiciy of demand, and subsequenly he desired markup, 6 vary wih firm s marke share. 7 As in Amii e al. 3 This resul is in line wih sandard heerogenous-firm rade models à la Meliz (2003) or Chaney (2008) where he mos producive firm ses he lowes relaive price and hence capures he larges marke share. 4 Defined afer Ball and Romer (1990) as forces ha reduce he responsiveness of firms opimal prices o variaions in aggregae oupu resuling from variaions in real aggregae demand. 5 In he vein of Dornbusch (1987), Krugman (1987), Akeson and Bursein (2008), Benigno and Faia (2010), or Amii e al. (2015). 6 The one prevailing under flexible prices. 7 There exiss alernaive ways o accoun for ime varying markups. Insead of supply side sraegic complemenariies, Meliz and Oaviano (2008), Sbordone (2010) or Guerrieri e al. (2010) rely on demand side complemenariies, 2

7 (2015), large firms (wih high marke power) exhibi greaer sraegic complemenariies compared o small firms. They have more elasic markups and lower pass-hrough of he cos shocks. Coupled wih nominal rigidiies, he degree of firms marke power deermines he srengh of he relaionship beween inflaion and domesic slack. As in Woodford (2003), for a given degree of nominal rigidiies, he sronger he sraegic ineracions (also referred o as real rigidiies), he weaker he relaionship beween inflaion and real marginal cos. Inuiively, large firms respond o a marginal cos shock by absorbing par of ha shock ino heir desired markup, which mechanically reduces he pass-hrough of real marginal cos ino inflaion. Thus, if an economy is populaed by a few large firms (in each secor), he buffer-effec semming from sraegic markup adjusmens is very pronounced. On he conrary, if firms marke share becomes infiniely small, sraegic ineracions vanish. Knowing ha he link beween domesic inflaion and real aciviy loosens when firms have more marke power, he remaining quesion regards he impac of globalizaion on firms marke share/marke power. How does he marke srucure change wih globalizaion? The answer depends on how globalizaion is idenified. Sbordone (2010) and Benigno and Faia (2010) consider symmeric firms and model globalizaion as an increase in he overall number of varieies (or equivalenly firms), N. More compeiors enail a decline in each firm s marke share (ξ = 1/N). Such a definiion of globalizaion leads o a decline in firms marke power and consequenly reduces he scope for sraegic markup adjusmens. Thus inflaion reacs more srongly o marginal cos movemens. This effec is he purely pro-compeiive impac of globalizaion. Differenly from he previous papers, I borrow from he new rade lieraure and I argue ha globalizaion migh favor concenraion hrough he emergence of big players. In he spiri of Meliz (2003) and Chaney (2008), I rely on wo assumpions: he se of exporers is endogenous, due o fixed peneraion coss on he expor marke; and firms are heerogeneous in produciviy. When he iceberg rade cos falls, only he high-produciviy firms choose o expor and high-produciviy firms are also large ones as in Akeson and Bursein (2008) or Berman e al. (2012). Therefore new firms who ener he expor marke have more marke power han he average. They are consequenly relaively more prone o ac sraegically, by adjusing heir desired markup. Hence, in he inroducing demand funcions ha direcly relaes he elasiciy of subsiuion beween goods o he number of available goods. Differenly, Berman e al. (2012) assume disribuion coss in order o generae variable producer markups. In all cases, he resul is ha large firms would less pass-hrough aggregae shocks ino prices (relaive o small firms). 3

8 presence of nominal rigidiies in he shor run, heir price adjusmens respond less o cyclical flucuaions in real marginal cos. A he aggregae level, he proporion of large marke share firms producing domesic oupu increases wih globalizaion. As a resul, domesic inflaion becomes less responsive o domesic slack. In a new-keynesian seup, his means ha he Phillips curve flaens. The mechanism ha I highligh suggess ha, in he long run, economies have become more concenraed. This re-allocaion/concenraion channel 8 srenghens he overall degree of real rigidiies in he economy and can counerbalance he pro-compeiive force. This resul is in fac in line wih empirical findings. Decomposing he reasoning ino hree seps, I show ha each of hem is suppored by well-esablished micro evidence. (1) Large firms have higher and more elasic markups and, as a resul, do less pass-hrough cos shocks ino prices (Berman e al. (2012), Amii e al. (2015)). (2) The share of oupu produced by large firms increases wih globalizaion due o he self-selecion of exporers (Bernard e al. (2007), Eaon e al. (2011)). (3) Consequenly, he aggregae marke power -weighed by firms share in domesic oupu- increases wih globalizaion. This las poin is consisen wih De Loecker e al. (2016) findings, even hough i comes from a differen channel. They show ha he firm-level markup can increase afer rade liberalizaion as firms ake advanage of cheaper impored inpus o increase heir markups. This channel is absen from my seup, bu I show ha he aggregae markup in he economy can increase due o a reallocaion of producion owards large firms. The res of he paper proceeds as follows. Secion 1 reviews he relaed lieraure. Secion 2 describes he model. Secion 3 derives he new-keynesian Phillips curve (aggregaing heerogeneous firms behaviors) ha relaes domesic inflaion o marginal cos. Secion 4 provides a numerical example. Secion 5 reviews empirical suppor for an increase in he overall degree of firms marke power since he eighies. 1 Relaed lieraure My conribuion connecs differen srands of he lieraure. Firs, his paper shares ingrediens wih he inernaional rade lieraure on pricing-o-marke and imperfec exchange rae pass-hrough. The survey by Bursein and Gopinah (2013) poins ou 8 In he sense ha domesic producion is re-allocaed owards larger firms. 4

9 ha sraegic ineracions are sufficien o generae pricing-o-marke and imperfec pass-hrough, even absen of any nominal rigidiies. This resul sill holds in my model. In he long run, when prices are flexible, he model boils down o Akeson and Bursein (2008) s framework. My resuls are also consisen wih oher models where he heerogeneiy in pass-hrough is driven by firm specific produciviy, as in Berman e al. (2012) for insance. However, my approach differs from he inernaional rade lieraure on imperfec pass-hrough as I consider a sicky price environmen. I am focusing on how he combinaion of sraegic ineracions and nominal rigidiies in he shor run affecs he inflaion/real marginal cos nexus. As opposed o Akeson and Bursein (2008) or Amii e al. (2015), I do no focus on he link beween prices and nominal marginal coss, bu I am looking a he relaionship beween inflaion and he level of he real marginal cos (as a proxy for domesic slack). Ye, he similariy sems from he underlying force (he role of large firms) ha can boh generae a decline in exchange rae passhrough in he long run and, as a corollary, make inflaion respond less o marginal cos shocks in he shor run. Second, his paper is relaed o he new-keynesian open economy lieraure. Sandard new- Keynesian open-economy models à la Gali and Monacelli (2008) show how impor prices have a direc effec on consumer price inflaion proporionally o heir share in he consumpion baske. Besides, domesic producer price inflaion is relaed o he erms of rade insofar as he laer influences he domesic real marginal cos. I consider anoher channel ha works hrough firms sraegic behavior and direcly affecs he slope of he Phillips curve. In ha sense, my work is very close o Sbordone (2010) 9, Benigno and Faia (2010) and Guerrieri e al. (2010) who embed sraegic ineracions ino oherwise sandard DSGE models in order o assess he impac of globalizaion on inflaion dynamics. However, i differs in a crucial aspec: insead of defining globalizaion as an increase in he number of goods, I define globalizaion as a fall in rade coss ha allows for boh (i) he enry of new varieies and (ii) for he selecion of he mos producive firms (a mechanism for which he inernaional rade lieraure provides solid evidence). Third, his work is relaed o he recen lieraure embedding endogenous varieies in a new- Keynesian seup. 9 Sbordone sudies a closed economy, bu he impac of he res of he world is capured hrough he number of varieies available o domesic cusomers. 5

10 A closely relaed series of papers deals wih opimal moneary policy under endogenous enry: Bilbiie e al. (2012), Bilbiie e al. (2014), and Bergin and Corsei (2013) sudy economies wih endogenous firm enry and sluggish price adjusmen o derive he opimal moneary policy. Par of his lieraure also inroduces sraegic complemenariies. In paricular, Cecioni (2010), Ero and Colciago (2010), Faia (2012), Lewis and Poilly (2012), or Ero and Rossi (2015) rely on he oligopolisic compeiion and endogenous firm enry assumpions in a closed economy framework. They find ha shor-run markups vary counercyclically because, afer a posiive produciviy shock, he enry of new firms reduces he average marke share. This sream of he lieraure concludes ha a cyclical increase in he number of operaing firms lowers CPI-inflaion in he shor run. My work differs from hose papers along hree dimensions: firs, I sudy an open economy; second, I suppose ha firms are heerogeneous in produciviy. As a resul, my model predics a weaker link beween inflaion and real aciviy in response o globalizaion if he concenraion force dominaes he pro-compeiive one. Third, he focus is differen since my goal is o undersand he long-run impac of he changes in he marke srucure while hey raher look a he shor-run impac of enry/exi of varieies. Fourh, his work is linked o he lieraure on granulariy in he vein of Gabaix (2011). The granular hypohesis ypically saes ha a few big firms maer for undersanding he macro variables dynamics. My work is very consisen wih Di Giovanni and Levchenko (2012) findings: openness o inernaional rade renders economies more granular. The reason is ha big firms are favored and heir weigh in he domesic oupu increases. Ye, I differ from he aforemenioned papers insofar as (i) I am focusing on inflaion dynamics in a sicky price environmen, whereas hey are sudying real variables in a flexible price world; and (ii) I consider heerogeneous firms behavior in response o a common aggregae shock, while hey look a idiosyncraic shocks. Neverheless, he fundamenal inuiion is very similar. A few big players accoun for a large par of aggregae movemens. Besides, as far as he pricing behavior is concerned, large firms do behave differenly from small firms because hey have room for playing sraegically wih heir markup. Fifh, in erms of modeling, his work is closely relaed o Ghironi and Meliz (2005) and Akeson and Bursein (2008) insofar as I consider a dynamic wo-counry economy wih an endogenous se of exporers driven by rade coss. The key difference is ha I am focusing on a sicky-price environmen while hey boh deal wih flexible prices. I simplify Akeson and Bursein (2008) framework by imposing symmery across secors. Assuming he same disribuion of produciviy 6

11 across secors renders he model racable enough o derive an analyical Phillips curve equaion. In seady sae, here exiss an endogenous cuoff produciviy value ha deermines he se of exporers, heir prices and he quaniies sold. Evenually he seady sae marke share of firms pins down heir marke power and incidenally deermines how much inflaion responds o real marginal cos in he shor run. 2 The Model I build on a very sandard wo-counry new-keynesian general equilibrium model wih nominal rigidiies à la Roemberg (1982). My objec of ineres is he parial equilibrium Phillips curve equaion ha relaes inflaion o real marginal cos and inflaion expecaions. 10 In such a framework, he response of inflaion o real marginal cos (i.e. he slope of he Phillips curve) is pinned down by he seady sae marke power of firms (inversely relaed o he price elasiciy of demand). The goal of his paper is o compare he slope of he srucural Phillips curve in a pre-globalizaion seady sae characerized by high inernaional rade coss, versus a pos-globalizaion seady sae low rade coss. To ha end, his secion sars from he sandard new-keynesian model and gradually amends he supply side in order o allow for endogenous changes in firms marke power. Noe ha in he long run, prices are flexible and here is no link beween real aciviy and inflaion. The slope of he Phillips curve only makes sense in he shor run when sochasic disurbances kick in and nominal fricions maer. Ye, he shor-run dynamics of inflaion is deermined by he long-run (seady sae) marke srucure of he economy (how many producers, wha heir respecive marke power is). Hence, he exercise I am carrying ou is in effec a comparaive saic analysis beween wo seady saes characerized by high versus low rade coss. 2.1 Supply side: basic elemens To begin wih, I describe he sandard version of he supply side, from which I will progressively 10 Admiedly his new-keynesian srucural Phillips curve is only one par of he overall aggregae Phillips curve relaing inflaion o oupu gap. As emphasized by Sbordone (2010), his link is he mos likely o be affeced by globalizaion. 7

12 deviae in he nex subsecions. Assume ha he economy is composed of wo counries, domesic (D) and foreign (F). Suppose for now on ha each counry is a closed economy (say here exiss fixed coss for exporing ha are infiniely high). I focus on counry D, bu everyhing holds symmerically in F (variables are denoed wih a superscrip sar). The final consumpion good is he aggregaion of differeniaed goods ha are imperfec subsiues. Each variey i is produced by a differen firm wih a consan reurn o scale producion funcion. Labor is he only inpu: x (i) = A z i h (i), where x (i) is he quaniy produced and h (i) is he amoun of work. A is he aggregae produciviy in he domesic counry, while z i is he firm i relaive produciviy facor. For exposiional simpliciy, I firs suppose ha all firms are idenical and I normalize z i o one. I will inroduce heerogeneiy laer on and show he consecuive changes. When choosing a ime he price P x (i) ha maximizes is expeced ineremporal discouned profi, a firm i incurs a price adjusmen cos, expressed in unis of final consumpion, PAC (i) = φ p 2 [ P x (i) ] 2 P 1 x (i) 1 P x (i) P x (i). This cos can be inerpreed as he amoun of maerial ha a firm mus purchase in order o change a price. If he price adjusmen cos coefficien, φ p, is zero, he model yields back flexible prices. In his very sandard framework wih price sluggishness à la Roemberg (1982), he opimal price chosen by a firm is a markup over marginal cos. Typically, in a monopolisic compeiion environmen where he final consumpion goods is he Dixi-Sigliz aggregaion of symmeric varieies wih elasiciy of subsiuion θ, hen he desired markup 11 is consan ( θ θ 1 ), and he acual markup flucuaes because prices adjus only sluggishly o economic condiions. Loglinearizing he acual markup around he seady sae gives he new-keynesian Phillips curve equaion: π = θ 1 φ p mc ˆ + βeπ +1, where π = Π 1 = P P 1 1 and mc denoes he real marginal cos, mc = W A P. Throughou he paper, he symbol ha denoes he log-deviaion of a variable o he seady sae. 12 The goal of his paper is o shed ligh on how globalizaion migh affec he response of inflaion o real marginal cos. I argue ha his change migh sem from globalizaion alering he degree of real rigidiies in he economy keeping he degree of nominal rigidiies, φ p, consan. To prove ha 11 i.e. he one ha would prevail absen nominal fricions. 12 Assuming gross inflaion is one in seady sae, I wrie he log-deviaion of inflaion as Π = π. 8

13 claim, he baseline model 13 needs o be amended. Precisely, I make firms behavior depar from he sandard seup along hree dimensions. Oligopolisic compeiion (assumpion A1) replaces he sandard monopolisic compeiion assumpion, which enails sraegic ineracions beween firms, rendering firms marke power endogenous. Besides, firms are heerogenous in produciviy (A2) and he se of exporers is endogenous (A3), due o he exisence of (finie) fixed coss for exporing. Those las wo assumpions engender a self-selecion of mos producive firms on he expor marke. 2.2 Assumpion A1: Sraegic Ineracions among Firms Semming from Oligopolisic Compeiion In inroducing oligopolisic compeiion, I follow a lieraure iniiaed by Dornbusch (1987) and Krugman (1987) or Roemberg and Woodford (1989), and more recenly developed by Akeson and Bursein (2008) in a flexible price environmen or Benigno and Faia (2010) in a sicky price seup. 14 The idea is ha he final consumpion good is sill he Dixi-Sigliz aggregaion of imperfec subsiuable goods, bu, differenly from he sandard case, here are wo layers of producion: 1. The final consumpion good, denoed Y, is composed of differeniaed [ secoral goods supplied by a coninuum of secors (indexed by k) on [0, 1]: Y = ] 1 0 Y (k) σ 1 σ σ 1 σ dk, where σ is he elasiciy of subsiuion beween goods from differen secors. The demand for ( ) secoral good is Y (k) = P (k) σ P Y, where P is he consumpion price index defined as [ ] 1 P = 0 P (k) 1 σ 1 1 σ dk and P (k) is he secoral price. 2. In each secor k, he secoral good is produced by a reailer firm ha combines all inermediae goods in Ω k o supply Y (k) = i Ω k x (i) θ 1 θ [ ] θ 1 θ. The elasiciy of subsiuion beween goods wihin a secor (θ) is greaer han he elasiciy of subsiuion across secors (σ), consisenly wih Broda and Weinsein (2006) findings. Ω k is a counable and finie se. The final good producer in secor k chooses is opimal producion plan o maximize is profi, ( ) P x which gives he demand for good i: x (i) = (i) θ ( ) P x Y P (k) = (i) θ ( ) P (k) σ (k) P (k) P Y, where 13 In which he responsiveness of inflaion o real marginal cos, θ 1 φ p, is purely fixed and exogenous. 14 See also, in a flexible price framework, Amii e al. (2015), or Auer and Schoenle (2015). Those papers rely on he oligopolisic compeiion assumpion o analyse he imperfec exchange rae pass-hough. Closer o my work, a recen srand of he new-keynesian lieraure is embedding he oligopolisic compeiion assumpion in a sandard Dynamic Sochasic General Equilibrium framework wih nominal rigidiies: Cecioni (2010), Ero and Colciago (2010), Faia (2012), Lewis and Poilly (2012), or Ero and Rossi (2015). 9

14 P (k) = and P x (i) is he price of he inermediae good i, belonging o secor k, a ime. [ i Ω k P x (i)1 θ ] 1 1 θ Sraegic Ineracions and Time Varying Desired Markup N k is he measure of Ω k and represens he number of differeniaed goods sold in secor k for producing Y (k). Since firms are no aomisic wihin a secor, hey ake ino accoun heir impac on secoral oucome. I assume ha producers compee sraegically in quaniies, à la Courno, inernalizing heir impac on he secoral oupu when choosing heir opimal quaniies plan. Consequenly, he perceived elasiciy of demand o a firm s own price, Θ (i), is no consan, alhough he elasiciy of subsiuion beween goods in secor k is consan (θ). Θ (i) = x (i) P x(i) [ 1 P x(i) x (i) = θ + ( 1 σ 1 ( θ ) P (k) P x(i) )] 1 P x(i) (1) P (k) [ ] where P (k) P x P x(i) (i) P (k) = Px (i)x (i) P (k)y (k) = P x (i) 1 θ P (k) = ξ (i), he marke share of good i in secor k. 15 The profi maximizaion program of firm i a ime is: max x +j (i) j=0 s.. P x (i) = [ ( E Q,+j P+j x (i)x +j(i) W +j x +j (i) φ p A +j z i 2 ( ) x (i) 1 θ P (k) Y (k) where Q,+j is a sochasic discoun facor defined in Appendix C. ( P+j x (i) )] ) 2P P+j 1 x (i) 1 x +j (i)x +j (i) The firs order condiion implies ha he opimal price is a markup over marginal cos: P x (i) = µ x (i) W A z i (2) 15 Noe ha here is a sligh abuse of noaion here since I should in principle explicily wrie ha i belongs o secor k. I ry o alleviae he noaion, bu he reader should keep in mind ha he marke share, ξ (i), is defined a he secor level. In he res of he paper I will use he symmery across secors and will be allowed o drop he noaion k anyway. 10

15 where: Θ (i) µ (i) = [ ] (Θ (i) 1) 1 φ p 2 (Πx (i) 1)2 + φ p Π x(i)(πx (i) 1) Γ (i) [ 1 Θ (i) = θ + ( 1 σ 1 [ ] ] P θ ) x (i) 1 θ 1 P (k) [ Γ (i) = φ p E Q,+1 Π+1 x (i)2 (Π+1 x (i) 1) x ] +1(i) x (i) Π x (i) = Px (i) P 1 x (i) Under flexible prices, he markup becomes µ desired (i) = Θ (i) Θ. Unlike monopolisic compeiion, he desired markup is no consan over ime bu depends on he firm s price elasiciy (i) 1 of demand (Θ (i)) ha is negaively relaed o is marke share hrough equaion The sandard monopolisic case is nesed ino he model for specific parameers resricions. (1) If θ = σ, i.e. he elasiciy of subsiuion wihin a secor is equal o he elasiciy of subsiuion beween secors, hen he model collapses o he monopolisic case since he price elasiciy of demand becomes Θ (i) = [ 1 θ 0 ξ(i)] 1 = θ = σ and µ desired (i) = θ θ 1. Indeed, since here is an infiniy of secors, if he elasiciy of subsiuion wihin a secor is equal o he one beween secors, he sraegic ineracions -ha were aking place wihin a secor- vanish. (2) If he marke share ξ (i) ends o zero (he number of firms goes o infiniy for insance), hen he marke srucure also becomes monopolisic wih Θ(i) = θ. (3) If here is only one firm per secor, hen k, i Ω k : Px (i) = P (k) and hus Θ (i) = [ 1 θ ( 1 θ 1 σ ) 1] 1 = σ Impac of he Marke Srucure on he Slope of he Phillips Curve Loglinearizing equaion 2 around a zero inflaion seady sae wih symmeric firms ( i, z i = 1 and P x(i) = Px ) leads o an augmened Phillips curve similar o Benigno and Faia (2010) or Bilbiie e al. (2014): 17 π x = Θ ss 1 φ p }{{} slope [ mc ˆ x + ˆµ desired ] + βe π x +1 (3) 16 Noe ha σ 1 1 θ > 0 as he elasiciy of subsiuion across goods wihin a secor is greaer han he elasiciy of ( ) subsiuion beween secoral goods, and k, i Ω k : P x (i) 1 θ P (k) (0, 1). Thus σ < Θ (i) < θ. 17 Wih he difference ha here is no exi/enry on he domesic marke in my case. 11

16 where π x = Px P 1 x is he producion price inflaion, mc x = W A P x, ha symbol denoes logdeviaion from seady sae and subscrip s s sands for seady sae value. A ha poin, by incorporaing sraegic complemenariies (A1) in he new-keynesian framework, we have learned ha inflaion reacs less o real marginal cos movemens when firms marke power is high (i.e. Θ ss low). 18 This is in line wih Sbordone (2010) 19, Benigno and Faia (2010), or Bilbiie e al. (2014). In order o gauge he impac of globalizaion on firms seady sae marke power, I complee he model wih wo addiional assumpions (A2 and A3) in he vein of Meliz (2003) and Chaney (2008). 2.3 Assumpions A2 and A3: Heerogeneiy in Produciviy and Endogenous Enry of Exporers Firms are Heerogenous in Produciviy The produciviy z i is given for each firm and does no vary over ime. Each variey is produced by only one firm and one firm produces only one variey. Secors are symmeric: each secor comprises he same number of firms and he same produciviy disribuion prevails, k : S k = S = {, z 2, z 3,..., z N d}. Produciviy is ranked by sricly decreasing order: = z max > z 2 > z 3 >.. > z Nd 1 > z N = d z min. Thus, wihin a secor, a produciviy value uniquely pins down a producer (or equivalenly a variey). For convenience purpose, in he res of he paper, I use he produciviy ype z insead of he variey index i o refer o producers variables Inernaional Trade and Endogenous Enry on he Expor Marke The final consumpion good Y and he secoral goods Y (k) are non-radable, bu inermediae goods can be raded. The wo counries are idenical. They boh have heir own currency and he nominal exchange rae from F o D is e. 20 The real exchange rae is rer = e P P. Prices are se in local currency. In he secor k of counry D, inermediae inpus incorporaed for producing Y (k) can be supplied eiher by domesic or foreign firms: Y (k) = [ z N z d 1 x d θ 1 (z) θ + z N f x f θ 1 (z) θ ] θ θ 1, 18 Here he Phillips curve exhibis addiional erms on he righ-hand side since ˆµ desired flucuaes over ime, bu in he res of he paper, I sick o he common new-keynesian meaning of he slope of he Phillips curve, undersood as he link beween inflaion and real marginal cos. 19 When he markup elasiciy dominaes he price elasiciy erm in her seup. 20 To be read as one uni of counry F currency gives e unis of counry D currency. 12

17 where he superscrips d or f indicae he origin of goods. 21 For goods ha are consumed in counry F, he superscrip d or f is followed by a symbol, referring o he desinaion marke. 22 A domesic firm wih produciviy z can serve he domesic marke as well as he foreign marke if i is profiable o do so. Since here is no fixed cos for firms o serve heir home marke, N d is fixed over ime because every firm chooses o acually produce and serve is home marke. Firms face a fixed peneraion cos on he expor marke, f X, paid in unis of consumpion. 23 is he number of inermediae goods produced by foreign firms (and consumed in counry D as inpus for a secor k). N f varies over ime depending on he endogenous expor decision of foreign firms. Symmerically for counry F: N f is fixed over ime and N d N f is endogenous. In addiion o he fixed marke peneraion cos f X, an exporer also faces a meling-iceberg cos (τ 1). To sell one uni of good o he foreign counry, an exporer mus produce and ship τ unis because τ 1 unis mel on he way. Because of rade coss, markes are segmened and a domesic firm z can se differen prices on domesic and foreign markes in order o maximize is oal profi. Compared o he homogeneous case in equaion 2, he opimal price and markup are firm-specific, depending on he relaive produciviy facor, z. The opimal price se by a domesic firm z on he domesic marke is P d (z) = µ d (z) W A z, wih: µ d Θ (z) = d (z) (4) [ ] (Θ d (z) 1) 1 φ p 2 (Πd (z) 1)2 + φ p Π d (z)(πd (z) 1) Γd (z) and Θ d (z) and Γd (z) defined in 2. For serving he foreign marke, he iceberg rade cos scales down firm s effecive marginal cos. Firms fix heir price in local currency. Hence he opimal price is P d Deails of he program are given in Appendix B. (z) = µ d (z)τ W A z rer 1. [ 21 And he associaed secoral price becomes P (k) = z N z d 1 P d(z)1 θ + z N f P f 1 (z)1 θ] 1 θ. 22 See in Appendix A a summary of he noaions. For insance, x d refers o goods produced and consumed in D, x d sands for goods produced in D and sold o F, whereas x f are goods produced and consumed in F, and x f are produced in F and consumed in D. 23 Differenly from Ghironi and Meliz (2005), I choose he consumpion uni (insead of effecive labor uni) in order o keep he model as ransparen as possible and o isolae he mechanisms rough which globalizaion affecs he pricing behavior of firms. For clariy, I don wan he impac of globalizaion o be driven by a change in fixed coss induced by a move in he real wage, because his effec is of second order compared o he channels I am highlighing. Anyway, as long as he expor peneraion coss are low enough, he wo specificaions should predic he same qualiaive impac of globalizaion on he marke srucure. 13

18 For a firm z in counry D, he dividend (expressed in unis of domesic consumpion) is he sum of he profi, in real erms, from sales on he domesic marke and he profi from sales on he foreign marke: d (z) = d d d d (z) = d d (z) = [ 1 1 (z) + dd (z), where: ] 2 [Πd (z) 1] 2 µ d (z) φ p x d (z) Pd (z) P 0 if he firm does no expor. ] rer [1 1 (z) 1] 2 x d (z) Pd (z) f X oherwise. µ d (z) φ p 2 [Πd Sequenial Enry of Exporers In he res of he paper, I follow Akeson and Bursein (2008) and resric o sequenial enry. Suppose ha firms are ranked by decreasing order of produciviy (as in S) and consider enry sequenially. 24 Say ha he n h mos producive firms are already exporers, hen he n + 1 h firm in S can choose wheher i is profiable o pay he expor peneraion cos. If i is profiable o do so, hen he nex n + 2 h firm in S can decide. And so on and so forh. When he profi of he n + j h mos producive firm urns ou negaive, hen he equilibrium is reached and involves he n + j 1 mos producive firms being acive in inernaional rade. By definiion, N d P is he number of exporers a ime. Thus he cuoff produciviy (ha pins down he leas producive exporer) is denoed z N d. By consrucion, all firms more producive han z N d are exporers oo. And firms below he hreshold are no. 2.4 Closing he General Equilibrium and Solving for he Seady Sae I aim a comparing he shor-run responsiveness of inflaion o marginal cos around a pre-globalizaion seady sae high τ and a pos-globalizaion seady saes low τ. This new-keynesian Phillips curve relaionship is a parial equilibrium objec. 25 However I need o solve for he whole general equilibrium (in seady sae) in order o pin down he seady sae marke power of firms ha deermines he slope of he Phillips curve. This echnical par is repored in Appendix and involves wo seps: (i) closing and defining 24 As noiced by Akeson and Bursein (2008), his is one among many oher poenial equilibria. 25 The general equilibrium relaionship beween inflaion and domesic slack migh also be affeced by moneary policy, inflaion expecaions, ec. 14

19 he general equilibrium (see Appendix C), and (ii) solving for he seady sae (in Appendix D). Compared o he previous lieraure ha incorporaes oligopolisic compeiion (A1) in a new- Keynesian framework, he seady sae of my model is a bi more complicaed o solve due o heerogeneiy across firms (A2). This is he reason why I dedicae a full Appendix secion o he compuaion of he seady sae equilibrium. Wih hose ools in hands, I am able o deermine he seady sae for differen values of iceberg rade coss, τ. When τ falls, he se of firms involved in inernaional rade expands. Nex secion provides analyical resuls characerizing how he dynamics of inflaion evolves when he seady sae marke srucure changes. 3 Analyical Resuls on he New-Keynesian Phillips Curve The goal of his secion is o compare he dynamics of he shor-run inflaion around he preglobalizaion seady sae (high τ) and he pos-globalizaion sae (low τ). A decline in he sensiiviy of inflaion o marginal cos has been observed in he daa 26 and I show ha a drop in he iceberg rade cos, τ, can generae he same feaure in my model. As firms are differen in erms of produciviy and consequenly in size and in marke power, hey adjus heir opimal price differenly. To shed ligh on he domesic inflaion dynamics, I aggregae hose heerogeneous price adjusmen behaviors. Resuls regarding he firm-level price adjusmen dynamics are derived in sub-secion 3.1. The impac of globalizaion on he aggregae Phillips curve is discussed in subsecion Dynamics around he Seady Sae for an Individual Firm z Loglinearizing he acual markup µ d (z) from equaion (4) around he seady sae gives he augmened Phillips curve in (5). Noe ha in his secion, I refer o he Phillips curve in a loose way since I am considering firm-level behaviors whereas he Phillips curve commonly refers o he dynamics of inflaion a he aggregae level. This erminology abuse aims a highlighing he link beween aggregae resuls and he micro-foundaions. 26 See for insance Maheson and Savrev (2013) or Blanchard e al. (2015). 15

20 π d (z) = Θd ss(z) 1 [ φ p ] ˆµ d (z) ˆµ d,desired (z) + βe π+1 d (z) (5) Then, π d (z) = Θd ss(z) 1 [ ] mc ˆ d (z) + ˆµ d,desired (z) + βe π+1 d (z) (6) φ p where mc ˆ d (z) = Ŵ  ˆP d(z) = ŵ  ˆp d (z) and he desired markup is no consan and flucuaes wih he price elasiciy of demand: µ d,desired (z) = Θd (z) Θ d (z) 1, so ha ˆµd,desired (z) = 1 ˆΘ d Θ d ss(z) 1 (z). Thus: π d (z) = Θd ss(z) 1 φ p mc ˆ d (z) 1 ˆΘ d (z) + βe π+1 d (z) (7) φ p Equaion 7 resembles closely he one presened in secion 2.2.2, bu i holds a he firm level. The same key properies are verified: he sensiiviy of price adjusmens o marginal cos depends negaively on a firm s seady sae marke power, and cyclical adjusmens in he desired markup influence price adjusmens. Bu he seady sae demand elasiciy, Θ d ss(z), varies for differen producers, depending on heir relaive produciviy. Thus price adjusmens respond differenly o marginal cos flucuaions for each producer. Mos producive firms have a larger marke share and exhibi a flaer Phillips curve as Θ d ss(z) is low. They are less prone o ransmi marginal cos flucuaions ino inflaion compared o smaller firms. Inuiively, larger firms are he ones who are he mos concerned abou losing marke share as he markup elasiciy o relaive prices is increasing in he marke share. Therefore, he real rigidiies are increasing wih firm size, and he pass-hrough of marginal cos ino inflaion declines. Proposiion 1. (Cyclical flucuaions in he price elasiciy of demand maer for inflaion dynamics) In a sicky price environmen à la Roemberg, under oligopolisic compeiion, individual firm inflaion depends posiively on changes in he real marginal cos and on inflaion expecaions and negaively on he cyclical flucuaions in he perceived price-elasiciy of demand, ˆΘ d. A decline in ˆΘ d should be inerpreed as a srenghening of firm s marke power, which pushes up inflaion. Conversely, an increase in ˆΘ d reduces inflaion. Proof. See equaion (7). The shor-run flucuaions in he price elasiciy of demand are posiively relaed o he firm 16

21 relaive price. ˆΘ d (z) = ( 1 σ 1 θ )ξd ss(z) ˆξ Θ d ss3 d (z) = Θd 1 ss (z) θ 1 (z) Θ d ss3 ξ d (z) (z) = Θd 1 ss (z) θ 1 Θ d ss3 (θ 1) ˆp d (z) (z) Thus π d (z) = Θd ss(z) 1 φ p mc ˆ d (z) 1 Θ d 1 ss (z) θ 1 φ p Θ d ss3 (z) (θ 1) ˆp d (z) + βe π+1 d (z). (8) Corollary 1. (Cyclical flucuaions in he compeiive pressures maer for inflaion dynamics) In a sicky price environmen à la Roemberg, under oligopolisic compeiion, individual firm shor-run inflaion is decreasing in is relaive price (ha capures he flucuaions in he perceived compeiive pressures). Proof. See equaion (8). An increase in he relaive price is equivalen o a srenghening in compeiive pressures faced by a firm. Conversely, a decline in he relaive price corresponds o alleviaing compeiive pressures, which pushes up inflaion. The previous Proposiion 1 and he associaed Corollary 1 describe he deerminans of he shor-run inflaion dynamics a he firm level. Imporanly, he weighs on each facor (marginal cos and relaive price) are firm-specific. Noe ha he coefficien governing he sensiiviy of inflaion o he relaive price is he seady sae demand elasiciy wih respec o he relaive price. Indeed, denoing ε u,v he elasiciy of variable u wih respec o v, I ge: Thus equaion (8) becomes: ε µ,p x = 1 Θ x ss 1 } {{ } ε µ,θ ( 1 Θ 1 ss x θ Θss x 3 ε Θ,ξ ) (1 θ) }{{}}{{} ε ξ,p x } {{ } ε Θ,p x (9) The erm ε µ,p x π d (z) = high for small firms {}}{ Θ d ss(z) 1 φ p mc ˆ d (z) high for large firms {}}{ 1 ε φ Θ,p d(z) ˆp d (z) + βe π+1 d (z) (10) p connecs his paper o he lieraure sudying real rigidiies in a flexible prices environmen, as Amii e al. (2015). In he long run, nominal rigidiies vanish and he model yields similar predicions: he markup elasiciy wih respec o he relaive price (ε µ,p x) is increasing in 17

22 marke share. And he markup elasiciy wih respec o he nominal price is a hump-shaped funcion in he marke share. I is zero for infiniely small firms. Then he markup elasiciy increases wih firm s marke share. Ulimaely, for firms ha are sufficienly large (almos monopoly in heir secor), he elasiciy decreases as hey end up compeing agains he coninuum of oher secors (insead of compeing wih oher firms wihin heir secor). 27 Differenly from he flexible prices lieraure, he focus of his paper is on he shor-run flucuaions of inflaion. Bu he long-run degree of real rigidiies (i.e. he seady sae marke power of firms) pinpoins he shor-run dynamics. Proposiion 2. (The seady sae price elasiciy of demand perceived by a firm pins down he sensiiviy of price adjusmen o marginal cos) Under oligopolisic compeiion wih sicky prices à la Roemberg, he lower a firm seady sae price elasiciy of demand (or equivalenly he higher is marke power), he less reacive he price adjusemen o marginal cos flucuaions. Proof. See equaion 10. The coefficien pondering he real marginal cos erm is he slope of he new-keynesian Phillips curve. Noing ha he seady sae marke share of a firm is increasing in is produciviy ype z, he previous proposiion can be re-saed as follows: Corollary 2. (Large firms exhibi a flaer individual Phillips curve) High-produciviy firms are larger and exhibi a flaer Phillips curve compared o less producive (also smaller) firms. Proof. The sensiiviy of inflaion o marginal cos is increasing in he seady sae price elasiciy of demand, and he laer is decreasing in firm s produciviy. Secion 3.1 has emphasized ha he sensiiviy of price adjusmen o real marginal cos is lower for large firms. Consequenly, a he aggregae level, he link beween domesic inflaion and real marginal cos depends on he proporion of big versus small firms producing domesic oupu. 27 Precisely, for he benchmark parameerizaion of he model, he urning poin -afer which he markup elasiciy sars decreasing as a funcion of he marke share- is ξ 95%. Wih he produciviy disribuions I am considering in he calibraion, no firm can acually be ha big. Thus, he markup elasiciy can be hough of as monoonically increasing in firm size, which is consisen wih Berman e al. (2012), Gareo (2014), or Amii e al. (2015) empirical findings. 18