A note on firm entry, markups and the business cycle

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1 Universiy of Rome III From he SelecedWorks of Lilia Cavallari 23 A noe on firm enry, markups and he business cycle Lilia Cavallari, Universiy of Rome III Available a: hps://works.bepress.com/lilia_cavallari/6/

2 Economic Modelling 35 (23) Conens liss available a ScienceDirec Economic Modelling ournal homepage: A noe on firm enry, markups and he business cycle Lilia Cavallari Universiy of Rome III, Deparmen of Poliical Sciences, Via Chiabrera, 99, 45 Rome, Ialy aricle info absrac Aricle hisory: Acceped 3 July 23 Available online xxxx JEL classificaion: E3 E32 E52 This paper proposes a moneary model wih firm enry as a means for alleviaing he difficulies of real business cycle models in reproducing he smoohness and persisence of macroeconomic variables ogeher wih he volailiy of profis and markups. Simulaions show ha my baseline model maches he uncondiional momens of consumpion, oupu, hours, markups and profis in US daa fairly well. In addiion, i implies a posiive effec of a moneary expansion on business formaion as in he daa. Allowing for differences in he composiion of he invesmen and he consumpion baskes is essenial for hese resuls. 23 Elsevier B.V. All righs reserved. Keywords: Firm enry Business formaion Business cycle Macroeconomic dynamics Markup flucuaions. Inroducion I is a well-esablished fac ha business formaion moves procyclically. Recenly, Broda and Weinsein (2) have documened a pro-cyclical behavior also for he range of varieies. Moivaed by his evidence, a novel line of research sresses he role of firm enry and creaion of new varieies in propagaing business cycle flucuaions. In a number of conribuions, including Jaimovich and Floeoo (28), Colciago and Ero (2) and Bilbiie e al. (22), he presence of firm enry improves he capaciy o mach sylized business cycle facs compared o sandard (fixed-variey) real business cycle models. Ye, a lo remains o be done. Enry models are sill relaively unsuccessful in capuring a number of regulariies in he daa. They ypically fail o mach he smoohness of consumpion, invesmen and hours, oversae heir cyclicaliy and undersae heir persisence. In addiion, hey largely downplay he volailiy of markups and profis. This paper shows ha a moneary model wih firm enry can help alleviae hese difficulies. Early sudies combining firm enry and sicky prices include, among ohers, Bilbiieeal. (28), Bergin and Corsei (28), Lewis (29), Lewis and Poilly (22), Cavallari (27,2,in press) and Uusküla (28). Wih he excepion of Cavallari (in press) and Bilbiie e al. (28) ha will be discussed furher in he paper, hese works do no I wish o hank hree anonymous referees for useful commens on previous drafs. Remaining errors are mine. address: lilia.cavallari@uniroma3.i. In he US, ne business formaion and he incorporaion measures are srongly procyclical (see Chaeree and Cooper (993), Dunne e al. (988), Campbell (998) and more recenly Jaimovich and Floeoo (28), Bilbiie e al. (22) and Lewis (29)). provide a quaniaive assessmen of he performance of he model in erms of uncondiional momens as is done in his paper. The conribuion of he paper in he lieraure, however, can be read along more han one dimension. A firs dimension concerns he specificaion of he enry coss. As is now well undersood, modeling hese coss as wages has counerfacual implicaions in moneary models: a moneary expansion leads o a fall in business formaion a odds wih he empirical evidence. 2 The moneary easing, in fac, pushes on labor demand, hereby raising wages and enry coss. For his reason, Bergin and Corsei (28) propose enry coss in erms of capial goods while Lewis (29) considers wage sickiness in a seup wih labor enry coss. A conribuion of he presen paper is o clarify ha varying he composiion of he enry coss alers he ransmission of business cycle shocks. In he model, differences in he composiion of he consumpion and he invesmen baskes are essenial for reducing he gap wih he daa. The oher dimension relaes o enry as a form of invesmen. The poin ha firm enry acs much like invesmens a he inensive margin in sandard (fixed-variey) models was firs shown by Bergin and Corsei (28). In heir model, he presence of he exensive margin amplifies he real effecs of moneary policy. In a similar vein, business formaion amplifies he ransmission of produciviy shocks in my seup. In order o see why, consider a posiive shock o produciviy. The produciviy rise reduces he price of invesmen in erms of consumpion, shifing he allocaion of resources from he p- r- 2 Using US daa, Bergin and Corsei (28) documen ha a moneary easing, i.e. a drop o- in he nominal ineres rae, has a posiive impac on business formaion. See also Lewis (29) and Uusküla (28) /$ see fron maer 23 Elsevier B.V. All righs reserved. hp://dx.doi.org/.6/.econmod

3 L. Cavallari / Economic Modelling 35 (23) ducion of exising goods o he creaion of new varieies. This in urn ranslaes ino a persisen increase in he sock of producers. As is common pracice in models wih enry, I consider an economy where producers are subec o a sunk enry cos, a one-period producion lag and an exogenous exi shock. Each of hem produces a unique variey in a monopolisic compeiive marke and ses he price of his produc subec o price rigidiy à la Calvo (983).Following Bergin and Corsei (28), he seup of a new firm requires enrans o buy a baske of invesmen goods whose composiion may differ from ha of he consumpion baske. Enry coss herefore coincide wih he price of invesmen goods relaive o he price of exising varieies. This assumpion represens he main deparure from a seup à la Bilbiie e al. (28, 22) where he enry coss are specified as wages. I will argue below ha i plays an imporan role in he model. Simulaions show ha he baseline model maches key uncondiional momens in he daa. Remarkably, i aenuaes he difficulies common o sandard business cycle and endogenous enry models in capuring he persisence and smoohness of oupu, consumpion and hours worked. In addiion, i maches he cyclicaliy of profis and markups in he daa. On a less posiive one, he model undersaes he smoohness of markups and slighly oversaes he smoohness of profis. Differences in he consumpion and he invesmen baskes are essenial for hese resuls. The remainder of he paper is organized as follows. Secion 2 presens he model and discusses he soluion sraegy. Secion 3 illusraes he performance of he model in reproducing he uncondiional momens in he daa. Secion 4 conains conclusive remarks. 2. The economy I consider a closed economy version of he model in Cavallari (in press). The economy is populaed by a coninuum of agens of uni mass indexed by i. Firms are monopolisic compeiors, each producing a differen variey (, ), where is he number of firms acive a ime. The sock of producers is deermined endogenously in he model. A ypical agen supplies L hours of work each period for he nominal wage W and maximizes iner-emporal uiliy E β s UC ð s ; L s Þ, where C is consumpion, β is he subecive discoun facor and E is he expecaion operaor. The period uiliy is he addiive-separable funcion U ¼ ðcþ ρ φχ L ρ þφð Þ þφ φ wih ρ andφ. The consumpion baske akes he form C = X γ Z γ where X is a homogeneous endowmen good and Z is he CES aggregaor Z ¼ Z ðþ θ θ d θ ðθ Þ wih θ denoing he elasiciy of subsiuion among he varieies Z(). Wihou loss of generaliy, I normalize he price of he homogeneous good o one, so ha he welfarebased consumer price index is = P γ Z. The producer price index is P Z ¼ P ðþ θ ð θþ d where P() denoes he price of a variey. Producers face an idenical linear echnology in he labor inpu y () =A L (), where A is an aggregae shock o labor produciviy. In each period, in addiion o incumben firms here is a finie mass of enrans, e.asinghironi and Meliz (25), allfirms enered in a given period are able o produce in all subsequen periods unil hey are hi by a deah shock, which occurs wih a consan probabiliy δ (,). In order o sar he producion in period +,aime an enran needs o pay an exogenously given sunk enry cos f e.followingbergin and Corsei (28), his cos is specified in erms of produc prices. The creaion of a new firm requires purchasing f e unis of a composie baske s¼ of invesmen goods K = X σ Z σ a a price P K = P σ Z.oehahe composiion of he invesmen baske may differ from ha of he consumpion baske, namely γ σ. Clearly, when γ = σ enry coss are consan in real erms (i.e. in unis of consumpion), a case examined by Auray and Eyquem (2) and Bilbiie e al. (28). As will be clear soon, he composiion of invesmen goods has relevan consequences for he dynamics of he model. Ohers, as Bilbiie e al. (28, 22) and Cavallari (27), model enry coss as wages. 3 As is now well-undersood, his may have counerfacual implicaions in moneary models: a moneary expansion may lead o a fall in business formaion a odds wih he empirical evidence. The reason is ha a moneary expansion pushes on labor demand, hereby increasing real wages and enry coss. I will show below ha he impulse responses o a moneary policy shock are in line wih he esimaed responses in my seup wih enry coss in erms of goods. Enrans are forward looking and decide o sar a new firm whenever is real value, v, given by he presen discouned value of he expeced sream of profis {d s } s = +, covers enry coss: " X ν ¼ E βð δþ C # ρ sþ d s ¼ f e P K : ðþ s¼þ C s The free enry condiion holds so long as he mass of enrans in posiive. Macroeconomic shocks are assumed o be small enough for his condiion o hold in every period. oe ha upon enry, firms' profis vary and may even urn negaive for a while. This is a key difference relaive o early models of fricionless enry, where he absence of sunk coss leads profis o zero in every period. The iming of enry and he one-period producion lag imply he following law of moion for producers: ¼ ð δþ þ e : ð2þ Finally, a ypical agen eners period wih nominal bond holdings B and muual fund share holdings s. He receives labor income, ineres income on bond holdings a he risk-free rae i and dividend income on muual fund share holdings and he value of selling his iniial share posiion. The agen allocaes hese resources beween purchases of bonds and shares o be carried ino nex period and consumpion. The period budge consrain (in unis of consumpion) is: B i þ s þ e ν B i ð þ i where ϖ ¼ W is he real wage. 2.. Equilibrium condiions 2... Consumers Consumers' firs order condiions are given by: " ðc Þ ρ C ρ # ¼ βe þ i þ þ ðc Þ ρ d ¼ βð δþe þ þ ν þ C ν Þþs ðν þ d Þþϖ L i C i ð3þ ρ C þ ðþ¼ P ðþ θ C ð6þ ϖ ¼ χðl Þ φ ðc Þ ρ : ð7þ 3 For a moneary model wih enry ha combines labor and capial enry coss see Cavallari (22). ð4þ ð5þ

4 53 L. Cavallari / Economic Modelling 35 (23) Firms Each producer ses he price for is own variey facing a downwardsloping marke demand: y ðþ¼ P ðþ θ ð γþðp Z Þ γ C þ ð σ ÞðP Z Þ σ f e e : ð8þ P Z I inroduce nominal rigidiy hrough a Calvo-ype conrac. In each period a firm can se a new price wih a fixed probabiliy α which is he same for all firms, boh incumben firms and new enrans, and is independen of he ime elapsed since he las price change. In every period here will herefore be a share α of firms whose prices are pre-deermined. In a symmeric equilibrium, pre-se prices a a given poin in ime coincide wih he average price chosen by firms acive in he previous period, i.e. ðp Z Þ θ ¼ P Z;. The assumpion ha enrans behave like incumben firms is wihou loss of generaliy. Allowing enrans o make heir firs price-seing decision in an opimal way would have only secondorder effecs in a seup wih Calvo pricing. In a conex where firms face coss of price adusmen, insead, his assumpion would inroduce heerogeneiy of he price level across cohors of firms enered a differen poins in ime (see Bilbiie e al. (28)). As he number of price-seers ha face no cos of adusing o a pas pricing decision moves over he cycle, he aggregae degree of price sickiness becomes endogenous. The analysis of endogenous changes in price sickiness is beyond he scope of his paper. Each firm ses he price for is own variey so as o maximize he presen discouned value of fuure profis, aking ino accoun marke demand and he probabiliy ha she migh no be able o change he price in he fuure, yielding: X ðþ¼ θ E ðαβð δþþ kw þk k¼ θ X E ðαβð δþþ k y þk ðþ k¼ y þk ðþ A þk þk C ρ þk þk C ρ þk Clearly, when α = opimal pricing implies a consan markup θ θ on marginal coss a all daes. Wih α, prices may respond more or less han proporionally o a marginal cos shock, implying imevarying markups. Recalling he definiion of P Z, he Calvo sae equaion correced for firm enry is given by: ðp Z Þ θ ¼ α ð P Z θ ð9þ Þ θ þ ð αþ ð ðþ Þ θ : ðþ oe ha an increase in he number of producers over ime reduces he aggregae price level and he more so he higher he elasiciy θ.this is a consequence of love for variey: a wider range of varieies raises he value of consumpion per uni of expendiure, implying a fall in aggregae prices Aggregae consrains Define real GDP as Y PðÞ y P ðþd where y() isgivenbyeq.(8). Goods marke clearing requires oupu o equalize aggregae demand, Y = C + e ν. Labor marke clearing implies: Z Z y L L i di ðþ d: ðþ A The model is closed by specifying a moneary policy rule. I assume he moneary insrumen is he one-period risk-free nominal ineres rae, i, and moneary policy belongs o he class of feedback rules The log-model The model is log-linearized around a symmeric seady sae wih zero inflaion. In he seady sae sochasic shocks are mued a all daes, A = (he seady sae and he full log-linear model are in he Appendix A). The Euler equaion for bond holdings is given by: E b Cþ ¼ C b þ b i E ρ π þ ð2þ where a ha over a variable denoes he log-deviaion from he seady sae and π þ ¼ ln þ is he CPI inflaion. In Eq. (2), an increase in he real ineres rae raises he reurn on bonds, herefore making i more aracive o pospone consumpion in he fuure. The Euler equaion for share holdings is: E b Cþ ¼ C b þ bν þ ρ E i þ δ þ i d þ þ δ ν þ i b þ Arbirage in financial markes equalizes he real reurns on shares and bonds a all imes. Labor supply is given by: b L ¼ ρφ b C þ φ bϖ ð3þ Using he definiion of GDP and he labor marke equilibrium (),iis convenien o derive a log-linear approximaion o he aggregae producion funcion Y b ¼ b L þ A b þ P b C; where P b C; ln ðþ is he price of a variey in consumpion unis. Consider now he opimal price (9). Usingmarkedemand(8) and labor supply (7), re-arranging and linearizing gives: X E αβð δþ k PZ;þk b ρ þ bc φ þk þ þ ba φ þk φ b þk þ θ P φ b Z; ¼ k¼ where P b Z; ln ðþ P Z and P b Z;þk ln ðþ P Zþk.oehabydefiniion P b Z;þk ¼ P b Z; k s¼ π Z þs; where π Z þs ¼ ln P Zþs is he producer inflaion. Inuiively, he P Z change in he price of a variey (in unis of producion) is given by he so-called variey effec, he firs addend, less inflaion. Using Eq. (), he variey effec is: bp Z; ¼ α α πz þ ð αþðθ Þ b α ð αþðθ Þ b : Wih α =, an increase in he number of producers raises he price of each variey and he more so he lower he elasiciy of subsiuion θ.the presence of sicky prices affecs he variey effec along wo dimensions. Firs, i gives firms an incenive o adus heir markup o cyclical condiions (recall Eq. (9)). This implies ha P b Z; will increase in periods of high inflaion. Second, he slow adusmen of prices amplifies he persisence of P b Z;. Combining he wo equaions above and re-arranging gives he new-keynesian Phillips curve correced for firm enry: π Z ¼ ζ ρþ bc φ ð αþðθ Þ b ð þ φþ α A φ þ ð αþðθ Þ b þ βð δþe π Z þ ð4þ αβ δ where ζ ¼ ð ð ÞÞð αþ αφþθ ð Þ.Theinflaion rae depends on nex period expeced inflaion as well as on deviaions of consumpion, he number of producers and produciviy from heir seady sae values. These deviaions reflec changes in curren marginal coss as is usual in a new-keynesian Phillips curve. In order o see why, consider an increase in C. The rise in aggregae demand pushes up labor demand, hereby increasing real wages. The hike in marginal coss fuels inflaion. A rise

5 L. Cavallari / Economic Modelling 35 (23) in produciviy, on he conrary, direcly reduces marginal coss and inflaion. The number of producers is relaed o inflaion via he variey effec. A log-linear approximaion o he number of enrans is obained from he aggregae resource consrain: b e θ β δ ¼ ð ð ÞÞ θ β δ by βδ þ ð ð ÞÞ bc βδ ð5þ oe ha here is a rade-off beween invesmens in new varieies and consumpion of exising goods (he coefficien on C is negaive). As will become apparen soon, changes in he price of invesmens in new firm relaive o he producion of exising varieies consiue he main ransmission mechanism in he model. The law of moion of firms is: b ¼ ð δþ b þ δ b e : ð6þ Using he opimal price (9) ogeher wih he definiion of he aggregae markup μ ¼ P ðþa =W, one obains 4 : bμ ¼ αβð δþ E b PZ;þ bϖ þ A ð7þ In he model, markup flucuaions arise from a disconnec beween changes in he variey price and changes in marginal coss. As in ew- Keynesian models, variable margins of profis are powered by exogenous price sickiness (markups are consan wih flexible prices, i.e. wih α = ). In principle, sicky prices are by no means essenial for replicaing ime-varying markups. 5 I will discuss below he advanage of including sicky prices in a model wih firm enry. Using he propery ha markups coincide wih he inverse of he YP labor share, WL, ogeher wih he log-linear producion funcion, he real wage is given by: bϖ ¼ b A bμ þ b P C; : ð8þ The log-model is closed wih he Taylor rule b i ¼ ϕb ii þ ϕ π π Z þ ϕ b yy. 6 For ease of comparison wih flexible price models, I also consider a Wicksellian regime in which he nominal ineres rae reproduces a flexible price equilibrium wih zero inflaion. The Wicksellian ineres rae mimics changes in he naural (real) ineres rae e i ¼ ρ E Cþ b C b. As is well-known, he Wicksellian policy can be implemened by means of a credible hrea o deviae from a zero inflaion arge, i.e. i ¼ e i þ ϑπ wih ϑ. 3. Simulaions The model is simulaed using firs-order perurbaion mehods. For ease of comparison wih real business cycle models, I firs consider produciviy shocks as he exogenous source of business cycle flucuaions. I hen consider ineres rae innovaions wih he aim of clarifying he mechanism of moneary ransmission in he model. 3.. Calibraion The model is calibraed o he Unied Saes. In he simulaions, periods are inerpreed as quarers and β =.99 as is usual in quarerly 4 I used he following log-linear approximaion o Eq. (9) in deriving he expression for markups: P b ðþ ¼ ð αβð δþþ W c A þ αβð δþe P b ðþþ. 5 In a seup wih flexible prices, Akeson and Bursein (28) show ha firms adus heir markups o local marke condiions. Alessandria (29) poins o consumers' search as a reason for variable markups. 6 Taylor rules have been widely used in he las decades when he obecive of price sabiliy has gained a maor role in moneary policy-making. Ineres rae smoohing reflecs a need o reduce he swings in ineres raes in an environmen characerized by long and variable lags in moneary ransmission. models of he business cycle. The size of he exogenous exi shock is δ =.25 as in Bilbiie e al. (22) o mach he rae of firm disappearance in he US. To he bes of my knowledge, here is no evidence abou he shares of homogenous and differeniaed goods in he consumpion and he invesmen baske. In he absence of a prior on he values of γ and σ,i se raher arbirarily γ =.2 and σ =.6 in he baseline calibraion and hen experimen wih a full range of admissible values for hese parameers. In paricular, I will focus on he special case γ = σ where enry coss are fixed in unis of consumpion. The elasiciy of subsiuion among varieies is θ = 7.88 as in Roemberg and Woodford (999) o mach he average margin of profis of 8% in US daa. Sudies based on disaggregaed daa usually find a much lower θ, roughly around 4, implying profi margins above 4%. I have experimened wih θ = 3.8 as in Bilbiie e al. (22), obaining qualiaively idenical resuls (available upon reques). Oher preference parameers are φ = 4 and ρ =asinbilbiie e al. (22). The degree of price sickiness is α =.49 o mach he middle poin in he range of values esimaed by Galì e al. (2) for he US. This implies an average duraion of nominal conracs of 2.3 quarers. The vecor of produciviy shocks A follows a univariae auoregressive process wih persisence.975 and sandard deviaion of innovaions.72 as in King and Rebelo (999). The parameers of he Taylor rule draw on Bilbiie e al. (28), ϕ i =.8, ϕ y = and ϕ π =.3. I have also considered posiive values for he coefficien on oupu in he Taylor rule, in he range ϕ y (.,.5), wihou remarkable changes in qualiaive resuls. Finally, as fixed coss do no affec he dynamics of he model I se f e =wihoulossofgeneraliy Produciviy shocks This secion assesses he performance of he model a replicaing he dynamics in US daa in he wake of a produciviy shock. In comparing he model o properies of he daa, all he variables expressed in unis of consumpion are divided by he relaive price P() / so as o ne ou he effec of changes in he range of available varieies (for any variable X in unis of consumpion he empirical-relevan measure will be X R = X /P() ). As sressed by Ghironi and Meliz (25), he correcion is necessary because saisical measures of CPI inflaion are unable o adus for he availabiliy of new producs as in he welfare-based price index. In wha follows, all variables are Hodrick Presco filered wih a smoohing parameer equal o 6 as in he daa. 7 I sar wih an inuiive accoun of he funcioning of he model in he wake of a posiive echnology shock. Fig. displays he impulse response funcions of seleced macroeconomic variables o a one sandard deviaion increase in produciviy. For consisence wih he second momens below, he shock has a persisence of.975. The verical axis shows percenage deviaions from he seady sae (a value of, say, denoes a percen deviaion) and he horizonal axis shows he number of periods afer he shock. The impulse responses are calculaed wih he baseline calibraion. More favorable business condiions arac new enrans in he economy. oe ha he response of enrans is very large (5 imes as large as he shock) and concenraed in he iniial phase of he ransiion. Business formaion ranslaes ino a gradual increase in he number of producers over ime, amplifying he effecs of he produciviy shock and he persisence in he model. The increase in he sock of producers, in urn, pushes on labor demand, raising wages and marginal coss (no shown in Fig. ). On he oher side, i reduces inflaion hrough he variey effec. As a consequence, firms' markups decline. The produciviy rise reduces he real ineres rae inducing agen o anicipae 7 I have also experimened wih a Band-pass filer as well as wih non-filered variables. The properies of he model are robus o he filering mehod.

6 532 L. Cavallari / Economic Modelling 35 (23) GDP Consumpion umber of enrans umber of producers Markups Producer inflaion Fig.. Impulse responses o a one sandard deviaion increase in labor produciviy. heir consumpion plans in he early par of he ransiion. The boos in consumpion ogeher wih he hike in invesmen lead GDP above he seady sae level. ex, I compare he second momens of key macroeconomic variables in he model wih US daa and wih he momens implied by he ranslog model of Bilbiie e al. (22), BGM hereafer. The saisics on US daa are aken from Colciago and Ero (2). These auhors follow he approach of Roemberg and Woodford (999) in calculaing he aggregae markup as he inverse of he labor share, consisenly wih he propery of markups in my model. Panels A, B and C in Table repor, respecively, he sandard deviaion (raio o GDP), he correlaion wih GDP and he firs order auo-correlaion of consumpion C, hours worked L, invesmensν e,markupsμ and profis Π. The columns in Table refer o he baseline model, he model wih flexible prices (α = ), he model wih fixed enry coss (σ = γ), a calibraion wih σ =.2 and γ =.6, he BGM Translog and US daa. The momens of he BGM model reproduce Table 3 in Bilbiie e al. (22) augmened wih my own simulaions for profis and markups in heir model. US daa are from Table in Colciago and Ero (2). The benchmark model maches he momens of oupu, hours and invesmens fairly well. 8 The heoreical measures of smoohness, cyclicaliy and persisence for hese variables are close o US daa, ouperforming he BGM model. 9 In addiion, he baseline model capures couner-cyclical markups and pro-cyclical profis as in Roemberg and Woodford (999) and in previous models of firm enry (see, for insance, Bilbiie e al. (22) and Colciago and Ero (2) in a seup wih flexible prices and Faia (22) in a sicky price conex). On a less posiive one, he model undersaes he 8 Enry behaves similarly o invesmens (Lewis, 29). In US daa, he correlaion beween oupu and ne enry as measured by e Business Formaion, BF, is.7. The sandard deviaion of BF relaive o ha of oupu is Bilbiie e al. (22) show ha he inroducion of physical capial ouperforms heir baseline model in erms of he variabiliy of oupu and hours. The variabiliy of consumpion and he correlaions peraining o enry and markups, however, remain almos unalered. Given he unobservable naure of he marginal cos, he cyclical properies of markups may vary wih he mehodological approach. Mos sudies find couner-cyclical markups (see Roemberg and Woodford (999) and Bils (987) in he US and Marins e al. (996) in a panel of OECD economies). In conras wih hese sudies, ekarda and Ramey (23) documen pro-cyclical or a-cyclical markups in he US. smoohness of markups and slighly oversaes he smoohness of profis. The performance of he model is almos idenical in he specificaion wih σ =.2 and γ =.6. Simulaions no repored in Table show ha i is robus o changes in he values of σ and γ in he admissible range provided ha σ γ. As will be clear soon, changes in he real coss of invesmens play a key role in he model. A comparison beween he baseline model and he flexible price economy provides ineresing insighs on he role of sicky prices. The performance of he model deerioraes wih flexible prices. I undersaes he volailiies of hours and invesmens in he daa while oversaing he volailiy of consumpion. The low volailiy of hours reflecs a small incenive o smooh labor effor over ime when real wages are consan. The volailiies of invesmens and consumpion, on he oher side, reflec he abiliy of agens o shif resources a no cos beween he producion of exising goods (used for consumpion) and he creaion of new varieies (used for invesmen). A posiive shock o echnology, by increasing he marginal value of curren consumpion above he marginal value of fuure consumpion, moves producion effors owards he curren period. Wih sicky prices, on he conrary, he produciviy rise increases he araciveness of creaing new varieies, ranslaing ino a higher volailiy of invesmens. A his poin, i is worh analyzing he role of enry coss in more deail. To his end, consider hespecificaion wih enry coss fixed in unis of consumpion, i.e., γ = σ so ha P K /P =. The performance of he model deerioraes as in he flexible price economy and essenially for he same reason. Wih fixed enry coss, a rise in aggregae produciviy implies a higher produciviy in he secor ha produces exising goods relaive o he secor ha creaes new varieies. Agens herefore move resources owards he producion of exising goods. Two consequences may be driven from he analysis above. Firs, firm enry amplifies he ransmission of produciviy shocks, bringing he model closer o he daa. Second, endogenous movemens in enry coss, i.e. changes in he price of invesmens relaive o he producion This is analogous o a wo-secor real business cycle model where agens move producion effor in he secor wih a high echnology shock. Clearly, in my seup he shif occurs over ime as he allocaion of resources beween he producion of exising goods and he creaion of new varieies is given in each period.

7 L. Cavallari / Economic Modelling 35 (23) Table Second momens of consumpion, labor, invesmen, markups and profis. Baseline Flex prices σ = γ σ =.2 γ =.6 BGM ranslog US daa A: sandard deviaion (raio o GDP) C R L v R e μ Π R B: correlaion wih GDP C R L v R e μ Π R C: firs order auo-correlaion C R L v R e μ Π R of exising goods, play a key role in his conex. In he model, sicky prices ogeher wih differences in he composiion of he consumpion and invesmen baskes imply a real rigidiy of he enry coss. This in urn exacerbaes he volailiy of invesmens in new varieies and helps reducing he gap wih he volailiy of invesmens in he daa. These findings consiue a relevan deparure from Bilbiie e al. (28). The heoreical momens in heir baseline model or in a specificaion wih ranslog preferences are very similar wih sicky and flexible prices. The reason is he exen o which sicky prices affec enry coss and invesmen behavior. In he BGM framework, labor enry coss imply a direc link beween asse prices and inflaion ha is absen in my seup. Consider for insance a emporary drop in he nominal ineres rae ha reduces he real reurn on bonds and shares. In he BGM model, he fall in he reurn on shares is brough abou by an increase in oday's price of equiy relaive o omorrow's. This discourages enry of new firms in conras wih wha found in he daa. The price of equiy (he value of he firm) is ied o labor marginal coss by he free enry condiion, herefore marginal coss rise, markups fall and, hrough he Phillips curve, inflaion booss. Sicky prices will have only a small effec on enry whenever inflaion is moderae, as is he case wih Taylor rules. In my seup, on he conrary, he price of equiy is no direcly relaed o labor marginal coss. Sicky prices imply a rigidiy in he real coss of enry ha affecs he allocaion of resources beween he creaion of new varieies and he producion of exising goods. This mechanism is obscured when enry coss are fixed in unis of consumpion (γ = σ) or when prices are flexible (so ha P and P K move a he same pace) Moneary policy shocks In order o provide furher insigh on he mechanism of moneary ransmission in he model, his secion describes he effecs of a emporary moneary expansion. Fig. 2 displays he impulse response funcions of seleced variables o a one sandard deviaion fall in he nominal ineres rae. The impulse responses are calculaed under he sandard calibraion (solid line) and in a specificaion wih σ =.2 and γ =.6 (dashed line). The moneary expansion booss aggregae demand so long as prices are sicky, leading o a spike in consumpion and a burs in inflaion. Over ime, as prices slowly reurn o heir naural levels, consumpion converges o he seady sae. The rise in consumpion reflecs a drop in he real ineres rae, i.e. a drop in he reurn on bonds. Arbirage in financial markes requires he real reurn on shares o fall as well. The decrease in he real reurn on shares is brough abou by a fall in he reurn (v + + d + ) relaive o oday's price of equiy v. The price of equiy is ied o he cos of acquiring invesmens goods by he free enry condiion in he model (). The moneary expansion, by producing inflaion, reduces enry coss in real erms and favors invesmens in new firms. The impulse responses in Fig. 2 are almos idenical in he baseline and he alernaive specificaion for enry coss. As already discussed, he dynamics of he model is robus o changes in he values of he parameers σ and γ. I have also experimened wih a posiive value for oupu in he Taylor rule (no shown in Fig. 2) in he range (.,.5). Simulaions show ha a posiive weigh of he oupu arge does no GDP umber of enrans Consumpion Enry coss ominal ineres rae.5 Producer inflaion Fig. 2. Impulse responses o a one percen fall in he nominal ineres rae in he sandard calibraion (solid line) and wih σ =:2andγ =:6(dashedline).

8 534 L. Cavallari / Economic Modelling 35 (23) aler he qualiaive feaures of he moneary ransmission in he model. I leads o more persisence in he impulse responses of all he variables considered and o a larger response of inflaion. When he weigh of he oupu arge is larger han ha of he inflaion arge (.3), consumpion drops on impac. 4. Conclusions This paper proposes a moneary model wih firm enry as a means for alleviaing he difficulies of sandard real business cycle models in reproducing he smoohness and persisence of macroeconomic daa ogeher wih he volailiy of profis and markups. Simulaions show ha he baseline model maches he second momens of consumpion, oupu and hours in US daa fairly well while a he same ime capuring he cyclicaliy of profis and markups. In addiion, i implies a posiive effec of a moneary expansion on business formaion as found in he daa. A differen composiion of he invesmen and he consumpion baskes is essenial for hese resuls. The abiliy o reduce he gap beween he heoreical economy and he daa is imporan especially for he sake of policy evaluaion. The findings in he paper sugges wo implicaions. Firs, sicky price models wih firm enry may perform beer han was previously hough. Second, varying he composiion of enry coss alers he ransmission of business cycle flucuaions. Rehinking he way enry coss and nominal rigidiy are oinly modeled remains high on he research agenda. Appendix A A.. Seady sae The model is solved in log-deviaions from a symmeric seady sae equilibrium wih zero inflaion. Assuming A =, he seady sae of he economy is such ha: θ β δ ¼ ð ð ÞÞ δβ βð δþ θ 2 θ : Oher variables are given by: i ¼ β β ; v ¼ f e P γ σ Z β δ ; d ¼ ð ð ÞÞ βð δþ PðÞ ¼ θ P Π ¼ d Z β δ C ¼ θ ð Þ δ ; L ¼ θd βð δþ θð δþ e ¼ δ ð δþ P Z ¼ μ θ φ C ρ : L A.2. Loglinear model 2 θ θ ; μ ¼ θ ðθ Þ ; ; Y ¼ θd; Loglinearized condiions for households are: E b Cþ ¼ C b þ b i E ρ π þ E b Cþ ¼ C b þ bν þ ρ E i þ δ bd þ i þ þ δ ν þ i b þ L ¼ ρφc b þ φ bϖ : Loglinearized condiions for firms are: b ¼ ð δþ b þ δ ce bμ ¼ αβð δþ P b Z;þ bϖ þ A π Z ¼ ζmc þ βð δþe π Z þ where mc denoes an index of curren marginal coss defined by he erm in squared brackes in Eq. (4) in he main ex. Oher log-linear equilibrium condiions are: bp Z; ¼ α α πz þ ð αþðθ Þ b α ð αþðθ Þ b bp C; ¼ α þ γð αþ π Z þ α ð αþðθ Þ b α ð αþðθ Þ b π ¼ ð γþπ Z by ¼ A b þ b L þ P b C; b e θ β δ ¼ ð ð ÞÞ θ β δ by βδ þ ð ð ÞÞ bc βδ bν bϖ ¼ A b bμ þ P b C; b d bπ ¼ þ b d bν ¼ ðγ σ Þπ Z The model is closed wih he ineres rae rule in he ex. Appendix B. Supplemenary daa Supplemenary daa o his aricle can be found online a hp://dx. doi.org/.6/.econmod References Alessandria, G., 29. Consumer search, price dispersion and inernaional relaive price flucuaions. Inernaional Economic Review 5 (3), Akeson, A., Bursein, A., 28. Pricing o marke, rade coss and inernaional relaive prices. American Economic Review 98 (5), Auray, S., Eyquem, A., 2. Do changes in produc varieies maer for flucuaions and moneary policy in open economies? Inernaional Finance 4 (3), Bergin, P., Corsei, G., 28. The exensive margin and moneary policy. Journal of Moneary Economics 55 (7), Bilbiie, F., Ghironi, F., Méliz, M., 28. Moneary policy and business cycles wih endogenous enry and produc variey. In: Acemoglu, D., Rogoff, K., Woodford, M. (Eds.), BER Macroeconomic Annual 27. MIT Press, Cambridge (MA), pp Bilbiie, F., Ghironi, F., Méliz, M., 22. Endogenous enry, produc variey, and business cycles. Journal of Poliical Economics 2 (2), Bils, M., 987. The cyclical behavior of marginal cos and price. American Economic Review 77 (5), Broda, C., Weinsein, D., 2. Produc creaion and desrucion: evidence and price implicaions. American Economic Review (3), Calvo, G., 983. Saggered prices in a uiliy-maximizing framework. Journal of Moneary Economics 2, Campbell, J., 998. Enry, exi, embodied echnology and business cycles. Review of Economic Dynamics, Cavallari, L., 27. A macroeconomic model of enry wih exporers and mulinaionals. The B.E. Journal of Macroeconomics 7, ((Conribuions), Aricle 32). Cavallari, L., 2. Expors and FDI in an endogenous-enry model wih nominal and real uncerainy. Journal of Macroeconomics 32, Cavallari, L., 22. Modelling enry coss: does i maer for business cycle ransmission? CREI Working Paper o.7/22. Cavallari, L., 23. Firms' enry, moneary policy and he inernaional business cycle. Journal of Inernaional Economics. hp://dx.doi.org/.6/.ineco (in press). Chaeree, S., Cooper, R., 993. Enry and exi, produc variey and he business cycle. BER Working Paper Colciago, A., Ero, F., 2. Endogenous marke srucures and he business cycle. The Economic Journal 2, Dunne, T., Robers, M.J., Samelson, L., 988. Paerns of firm enry and exi in U.S. manufacuring indusries. The RAD Journal of Economics 9 (4), Faia, E., 22. Oligopolisic compeiion and opimal moneary policy. Journal of Economic Dynamics and Conrol 36 (),

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