ENDOGENOUS MARKET STRUCTURES AND THE BUSINESS CYCLE 1

Transcription

1 ENDOGENOUS MARKET STRUCTURES AND THE BUSINESS CYCLE Federico Ero and Andrea Colciago Universiy of Milano, Bicocca, Deparmen of Economics forhcoming on The Economic Journal Firs version: Sepember 7 Curren version: Ocober 9 Absrac We characerize endogenous marke srucures under Berrand and Courno compeiion in a DSGE model. Shor run markups vary counercyclically because of he impac of enry on compeiion. Long run markups are decreasing in he discoun facor and in produciviy, and increasing in he exi rae and in he enry coss. Dynamic ine ciency can emerge due o excessive enry under Courno compeiion. Posiive emporary shocks arac enry, which srenghens compeiion so as o emporary reduce he markups and increase real wages: his compeiion e ec creaes an ineremporal subsiuion e ec which booss consumpion and employmen. Endogenous marke srucures improve he abiliy of a exible prices model in maching impulse response funcions and second momens for US daa. JEL classi caion: L, E3. Keywords: Endogenous Marke Srucure, Firms Enry, Business Cycle. This work is par of a larger research projec which includes he companion paper "Ramsey Mees Courno" (Colciago and Ero, 7). We are graeful o seminar paricipans a he Universiy of Sain Andrews, CERGE-EI (Prague), Universiy of Amserdam, he IMT (Lucca), he Universiy of Rome, he Universiy of Milan, Bicocca, he Caholic Universiy of Leuven, he Universiy of Osaka, he Universiy of Tokyo and he Cenral Bank of Hungary for imporan suggesions. Guido Ascari, John Beah, Florin Bilbiie, Lilia Cavallari, Alex Cuckierman, Albero Dalmazzo, Mark Gerler, Fabio Ghironi, Mario Gilli, Sefano Gnocchi, Giammario Impullii, Piero Pereo, Tiziano Ropele and Parizio Tirelli provided insighful discussions on his opic. Correspondence: Federico Ero, Universiy of Milano-Bicocca, Deparmen of Economics, U6-36, Piazza dell Aeneo Nuovo, Milano 6, Ialy.

2 The neoclassical heory of he business cycle, which is well represened by he work of Kydland and Presco (98), is based on perfec compeiion, consan reurns o scale and he absence of xed coss of producion. In his environmen goods are priced a he marginal cos, here is no room for exrapro s and he srucure of he markes is indeerminae, i.e. mark ups are zero and he number of rms, heir individual producion and (sock marke) values are no deermined by he model. The New-Keynesian heory, saring wih Blanchard and Kiyoaki (987), has inroduced produc di ereniaion and imperfec compeiion in general equilibrium models wih nominal fricions o sudy he e ecs of aggregae demand and supply shocks. Mos of his lieraure depared from he neoclassical framework assuming monopolisic compeiion à la Dixi and Sigliz (977) beween an exogenous number of rms producing di ereniaed goods. This approach rapidly became he sandard framework for he analysis of macroeconomic policy, wih a focus on moneary policy. Neverheless, i also led o exogenous marke srucures. As such, i negleced he role of sraegic ineracions beween rms of he same secors, he endogeneiy of he number of compeiors, and he impac of enry on he same sraegic ineracions. The resul is ha he srucure of he secors of he economy remains a sor of black box whose main componens, mark ups, number of compeiors and heir individual producion level, are exogenous in he shor and long run. Building on recen imporan works on enry by Ghironi and Meliz (5) and Bilbiie, Ghironi and Meliz (7, BGM henceforh) we open he black box of he marke srucure, we inroduce sraegic ineracions and link he endogenous behavior of rms a he secorial level wih he general equilibrium properies of he economy, in paricular wih is business cycle properies. We consider an economy wih disinc secors, each one characerized by many rms supplying goods ha can be imperfecly subsiuable o a di eren degree, aking sraegic ineracions ino accoun and compeing eiher in prices (Berrand compeiion) or in quaniies (Courno compeiion). Sunk enry coss allow us o endogenize enry and he (sock marke) value of each rm in each secor. Therefore, in he shor run he degree of marke power depends endogenously on he form of compeiion, on he degree of subsiuabiliy beween goods and on he number of rms. In he long run, he equilibrium mark ups depend also on he srucural parameers of he economy: hey are decreasing in he discoun facor of consumers and in he produciviy level, and increasing in he rae of exi from he marke and in he size of he coss of enry. The long run endogenous marke srucure is ypically ine cien because of he endency oward excessive enry associaed wih imperfec compeiion. Moreover, since savings nance he process of business creaion, his can lead o a novel form of dynamic ine ciency (compared o he neoclassical framework or he BGM model). In paricular, under Courno compeiion, when he discoun facor is high enough, he number of rms is above he golden rule number ha would maximize seady sae uiliy: when consumers are exremely paien hey save oo much, inducing excessive creaion of rms ha produce oo lile individually. While he marke for goods is characerized by imperfec compeiion and endogenous enry, he res of our baseline economy operaes as in a sandard neoclassical ( exible price) model wihou accumulaion of physical capial. In his conex, a emporary supply shock iniially increases pro s, which aracs enry of rms and srenghens compeiion, which Early conribuions o his lieraure are Chaejee and Cooper (993), Devereux e al. (996), Cooper (999), Devereux and Lee (). More recen developmens are in BGM (7, 8a,b), Elkhoury and Mancini-Gri oli (7), Ero (7), Bergin and Corsei (8), Jaimovich and Floeoo (8) and Lewis (9). For oher applicaions of endogenous marke srucures in macroeconomic models see Ero (9a, ).

3 GDP M ark up Ne Business Formaion Figure : Cyclical componen of GDP, Ne Business formaion and Price Markup. Shaded areas represen NBER recessions. in urn reduces he mark ups and (hrough a general equilibrium e ec) increases he real wages. The emporary reducion of mark ups and increase of real wages induces a sronger ineremporal subsiuion e ec in favor of curren consumpion and labor supply, which magni es he e ecs of he shock compared o a perfecly compeiive model à la Kydland and Presco (98). Our propagaion mechanism is even sronger when we augmen he model wih physical capial. There is convincing macroeconomic evidence in suppor of he business cycle implicaions of our approach. Bils (987), Roemberg and Woodford (999) and Galì e al. (7) documen price mark ups counercyclicaliy. Early references on he procyclicaliy of rms enry are Chaerjee and Cooper (993) for he US and Porier (995) for France. BGM (7) emphasize he procyclicaliy of real pro s. To provide addiional suppor o hese empirical ndings we performed a VAR analysis on US daa. We consruced a labor share based measure of he price mark up for he US along he lines suggesed by Roemberg and Woodford (999) in heir analysis of cyclical mark up behavior. 3 Figure plos he series of derended GDP, he markup and an index of ne business formaion a a quarerly 3 Roemberg and Woodford (999) assume he exisence of overhead labor L o so ha e ecive labor for he producion of consumpion goods is L c = L Lo where L oal labor supply. In his case he equilibrium markup in a model wih a producion funcion Y = A L c can be wrien as = A =w = (Y =w L ) L = (L L o ), whose log-linearizaion is b = lo ^L = ( l o ) bs, where l o L o =L represens he average share of overhead labor over oal labor inpu (assumed o be equal o.), s w L =Y is he labor share of income, and haed variables indicae percenage deviaions from is long run rend. 3

4 frequency from 948: o 995:3. 4 In line wih he evidence reviewed above, ne business formaion is procyclical and negaively correlaed wih he mark up, which is counercyclical. The conemporaneous correlaion beween GDP and new business formaion is posiive and equals.45, while ha beween GDP and he price mark up is Nex we considered a VAR() model including our mark up measure, a measure of he Solow residual correced for he presence of marke srucure endogeneiy, which we ake as he measure of echnology, 6 consumpion, GDP, pro s, and he index of ne business formaion. We idenify he echnology shock by imposing a recursive srucure on he sysem. In our baseline speci- caion variables are ordered as lised above. 7 The ordering is naurally suggesed by our heoreical framework. The echnology shock a ecs oupu and consumpion, his leads, for given markup, o a change in pro s which a ecs he enry decision of rms. The resuling number of compeiors will nally lead o a mark up change. Figure shows he esimaed responses o an expansionary shock o echnology. The responses of oupu and consumpion are similar o hose found in Dedola and Neri (7) and oher works in he lieraure. Mos relevanly for our purposes, boh pro s and rm enry respond posiively o he echnology shock, while he price mark up declines signi canly. This endogenous reacion is consisen wih he hypohesis formulaed in our approach. Our work is relaed o some recen heoreical and empirical conribuions sudying he role of rms enry and he creaion of new producs. 8 Recen empirical works on he manufacuring secor by Broda and Weinsein (9) and Bernard e al. (8) have emphasized he imporance of he exensive margin in he process of produc creaion or innovaion. For his reason BGM (7) design he enry process as a process of creaion of new producs wih limied subsiuabiliy which may depend on he same number of available producs. This relaion beween number of goods and heir subsiuabiliy can be microfounded hrough he ranslog preferences inroduced by Feensra (3), which are characerized by demand-side pricing complemenariies. While driven by di eren mechanisms, boh he BGM demand side explanaion and our supply side explanaion deliver dynamic responses of mark ups and pro s o a echnology shock which are consisen wih he VAR evidence presened above. Early works of he New Empirical Indusrial Organizaion lieraure saring wih Bresnahan and Reiss (987) and more recen research by Manuszak (), Campbell and Hopenhayn (5), Manuszak and Moul (8) and ohers have provided convincing evidence in 4 Variables have been logged. Since we use hese variables in subsequen ime series analysis we op for a polynomial of ime o derend variables insead of he HP ler, as suggesed by Galì e al. (7). However he signs of conemporaneous correlaions beween our measures of enry and he price mark up wih oupu are unchanged when variables are derended using he HP ler. 5 The 95 % con dence inervals are respecively (.33.56) and ( ). Boh correlaion coe - ciens are saisically di eren from zero. The conemporaneous correlaion beween GDP and he number of new incorporaions is posiive oo and equals., bu i is saisically di eren from zero a he percen signi cance level. However in he ime series analysis we adop he number of new incorporaions as a mesure of ne enry, since i is closer o wha we consider as new enrans. 6 Jaimovich (7) and Jaimovich and Floeoo (8) argue ha he Solow Residual is a biased measure of echnology in he presence of mark up variabiliy. See he Appendix for our derivaion of a model consisen correcion of he Solow Residual. 7 The lag lengh has been seleced according o a sequenial LR es saring wih a maximum number of lags equal o 8. However resuls do no change relevanly if we consider 3 or 4 lags. For robusness we experimened wih alernaive orderings of he variables ordered afer echnology. Also we have esimaed he dynamic behaviour of he model including he number of new incorporaions described above insead of he index measuring new business formaion. In all hese cases jus minor changes apply o he our baseline resuls. 8 An emerging heoreical lieraure is analyzing endogenous marke srucures in parial and general equilibrium conexs. Beween he recen works focusing on dynamic enry we should cie a leas Kováµc e al. (9) and Denicolò and Zanchein (). 4

5 .6 CONSUMPTION.8 GDP MARK UP.6 NEW INCORPORATIONS PROFITS ADJUSTED SOLOW RESIDUAL Figure : VAR() model. IRFs o a echnology shock wih 95 percen con dence bands. 5

6 suppor of he compeiion e ec on mark ups and he number of rms. However, while his empirical lieraure refers o a supply-side explanaion for counercyclical mark ups, is resuls may be consisen also wih he demand-side explanaion proposed by BGM (7). Fuure research may ry o idenify and disenangle demand and supply e ecs by means of microeconomic daa. Jaimovich and Floeoo (8) have independenly developed a exible price model wih endogenous marke srucures. Our analysis di ers from heirs wih respec o boh assumpions and focus. For wha concerns assumpions, as menioned above, we model endogenous enry à la Ghironi and Meliz (5) raher hen resoring o a saic zero pro s condiion. This allows us o sudy he ineracion beween enry coss and oligopolisic behavior in he shor and he long run. To accoun for he degree of business desrucion we assume ha an exogenous fracion of rms exis he marke in each period, which makes he number of acive rms an endogenous sae variable. This helps reproducing wo relevan empirical regulariies: he rs is a posiive correlaion beween pro s and oupu ogeher wih he negaive correlaion beween mark ups and oupu, and he second one is he nonlinear ime pro le of he correlaion beween he markup and he cycle. In our framework oupu jumps on impac in response o a TFP shock, while, since he number of rms increases slowly, he mark up does no change on impac and falls more in fuure periods. 9 This correlaion paern is consisen wih he VAR analysis presened above. Wih respec o he focus, we analyze endogenous marke srucures boh in he long and he shor run, and we emphasize heir role under di eren forms of compeiion for he propagaion of exogenous echnology shocks. Jaimovich and Floeoo (8) consider he e ecs of marke srucure endogeneiy for he measuremen of he Solow residual. More precisely, hey exploi he marke srucure endogeneiy o provide a decomposiion of TFP in an exogenous componen and in an endogenous one due o he variabiliy of mark ups. By ing a AR() process o he exogenous componen of echnology obained wih his mehodology, hey nd ha he laer has a lower variabiliy wih respec o ha esimaed using he radiional measures of he Solow residual. Nex hey impose he esimaed TFP process on model characerized by sraegic ineracions and show ha his can ouperform he sandard RBC model a replicaing he variabiliy of he main macroeconomic variables. The remainder of he paper is organized as follows. Secion describes he model and is dynamic properies in he shor and long run. Secion calibraes and simulaes he model. Secion 3 compares our supply-side explanaion for counercyclical mark ups wih he demand-side explanaion based on ranslog preferences. Secion 4 augmens he model wih physical capial. Secion 5 concludes. Technical deails are lef in he Appendix. The Model Consider a represenaive agen wih uiliy: U = E X ( Z log C k dk = ) L+=' + =' ; ' () 9 We hank a referee for poining his ou. Jaimovich and Floeoo (8) circulaed an online appendix wih a version of heir paper feauring sunk enry coss and a dynamic of he number of rms similar o ha adoped in he working paper version of his aricle ("Endogenous Marke Srucures and he Business Cycle", November 7, WP 6, Universiy of Milan, Bicocca). Our model has been developed independenly of heir analysis, and had already been circulaing when we became aware of heir exension. 6

7 where (; ) is he discoun facor, L is labor supply and C k is a consumpion index for a coninuum of goods produced in secors k [; ]. The represenaive agen supplies labor for a nominal wage W and allocaes his or her savings beween bonds or socks. The inraemporal opimaliy condiions for he opimal choices of C k and L require: P k C k = EXP for any k () W C k = L ' (3) P k where EXP is oal nominal expendiure allocaed o he goods produced in each secor in period and P k is he price index for consumpion in secor k: due o he uniary elasiciy of subsiuion, oal expendiure is equally shared beween he secors. Each secor k is characerized by di eren rms i = ; ; :::; N k producing he same good in di eren varieies, and he consumpion index C k is: C k = " Nk X i= C k (i) # (4) where C k (i) is he producion of rm i of his secor, and > is he elasiciy of subsiuion beween he goods produced in each secor. The disincion beween di eren secors and di eren goods wihin a secor allows o realisically separae limied subsiuabiliy a he aggregaed level, and high subsiuabiliy a he disaggregaed level. Conrary o many macroeconomic models wih imperfec compeiion, our focus will be on he marke srucure of disaggregaed secors: inrasecoral subsiuabiliy (beween goods produced by rms of a same secor) is high, while inersecoral subsiuabiliy is low. Each rm i in secor k produces a good wih a linear producion funcion. For he momen we absrac from capial accumulaion issues and assume ha labor is he only inpu. Oupu of rm i in secor k is hen: y k (i) = A L c k(i) (5) where A is oal facor produciviy a ime, and L c k (i) is labor employed for he producion of he consumpion good by rm i in secor k. This implies ha he producion of one good requires =A unis of labor, and he nominal marginal cos of producion is W =A. Since each secor can be characerized in he same way, in wha follows we will drop he index k and refer o he represenaive secor (furher deails are provided in Appendix A).. Endogenous Marke Srucures in he shor run In each period, he same expendiure for each secor EXP is allocaed across he available goods according o he direc demand funcion derived from he maximizaion of he consumpion index (4): C (i) = C p (i) P = p (i) C P = p (i) EXP P P i = ; ; :::; N (6) In paricular our funcional form implies uniary elasiciy of subsiuion beween secors. The same approach has been independenly proposed by Akeson and Burnsein (8) in a rade model. Even if hey allow for general subsiuabiliy across secors, heir numerical resuls are obained assuming a uniary inersecoral elasiciy of subsiuion. 7

8 where P is he sandard price index: XN P = 4 p (j) j= ( ) 3 5 (7) such ha oal expendiure sais es EXP = P N j= p (j)c (j) = C P. Invering he direc demand funcions, we can derive he sysem of inverse demand funcions: p (i) = x (i) EXP XN x (j) j= i = ; ; :::; N (8) where x (i) is he consumpion of good i. We assume ha rms canno credibly commi o a sequence of sraegies, herefore heir behavior is equivalen o maximize curren pro s in each period aking as given he sraegies of he oher rms. Each good is produced a he consan marginal cos common o all rms. A main ineres of his aricle is in he comparison of equilibria where in each period rms compee in prices and in quaniies, aking as given heir marginal cos of producion and he aggregae expendiure of he represenaive consumer. Under di eren forms of compeiion we obain symmeric equilibrium prices saisfying: p = (; N )W A (9) where (; N ) > is he mark up depending on he degree of subsiuabiliy beween goods and on he number of rms N. In he nex secions we characerize his mark up under compeiion in prices and in quaniies aking sraegic ineracions ino accoun. 3.. Berrand compeiion Le us consider compeiion in prices (wih symmeric equilibria). In each period, he gross pro s of rm i can be expressed as: [p (i)] = [p (i) W =A ] p (i) EXP 3 XN 4 p (j) ( ) 5 j= () Firms compee by choosing heir prices. Conrary o he radiional Dixi-Sigliz (977) approach which neglecs sraegic ineracions beween rms, we will ake hese ino consideraion and derive he exac Berrand equilibrium. Each rm i chooses he price p (i) o maximize pro s aking as given he price of he oher rms. 4 The rs order condiion for Of course, boh of hem are endogenous in general equilibrium, bu i is reasonable o assume ha rms do no perceive marginal cos and aggregae expendiure in he secor as a eced by heir choices. 3 In he companion paper (Colciago and Ero, 7) we have examined oher forms of compeiion as imperfec collusion (hrough he model of quaniy compeiion wih conjecural variaions) and Sackelberg compeiion wih a leader choosing producion before he followers. 4 Since oal expendiure EXP is equalized beween secors by he consumers, we assume ha i is also perceived as given by he rms. Under he alernaive hypohesis ha consumpion is perceived as given, we would obain a higher mark up (as in Yang and Heijdra, 993) which would lead o similar qualiaive resuls. 8

9 any rm i is: p (i) p (i) W p (i) = A ( )p (i) hp (i) XN i= p (i) i W A p (i) Noice ha he erm on he righ hand side is he e ec of he price sraegy of a rm on he price index: higher prices reduce overall demand, herefore rms end o se higher mark ups compared o monopolisic compeiion à la Dixi-Sigliz. Imposing symmery beween he N rms, he equilibrium price p mus saisfy: p p W A p N p ( ) = ( )p p W p A Solving for he equilibrium we have p = W (N + )=A ( )(N ), which generaes he mark up: 5 P (; N ) = + (N ) ( )(N ) () where he index P sands for compeiion in prices. The mark up is decreasing in he degree of subsiuabiliy beween producs, wih an elasiciy P = N =( + N )( ). Moreover, he mark up vanishes in case of perfec subsiuabiliy: lim! P (; N ) =. Finally, he mark up is decreasing in he number of rms, wih an elasiciy P N = N= [ + (N )] (N ). Noice ha he elasiciy of he mark up o enry under compeiion in prices is decreasing in he level of subsiuabiliy beween goods, and i ends o zero when he goods are approximaely homogenous. Finally, when N! he markup ends o =( ), he radiional one under monopolisic compeiion (and adoped by BGM, 7). As well known, sraegic ineracions beween a nie number of rms lead o a higher markup han under monopolisic compeiion. In conclusion, wih compeiion in prices he individual pro s can be expressed in real erms (ha is dividing nominal pro s by he price index P ) as: P C (; N ) = () + (N ) which is a decreasing funcion of he number of rms and of he subsiuabiliy beween goods... Courno compeiion Le us consider compeiion in quaniies (again focusing on symmeric equilibria). Using he inverse demand funcion (8), we can express he pro funcion of a rm i as a funcion of is oupu x (i) and he oupu of all he oher rms: [x (i)] = p (i) W A = x (i) EXP XN x (j) j= x (i) = W x (i) A (3) 5 Jaimovich and Floeoo (8) allow for a general value of he inersecoral elasicy of subsiuion. In his case he individual rm also considers he e ec of is pricing sraegy on he secoral price level. 9

10 Assume now ha each rm chooses is producion x (i) aking as given he producion of he oher rms. The rs order condiions: x (i) EXP x (i) EXP Pj x h (j) P i = W j x (j) A for all rms i = ; ; :::; N can be simpli ed imposing symmery of he Courno equilibrium. This generaes he individual oupu: x = ( )(N )A EXP N W (4) Subsiuing ino he inverse price, one obains he equilibrium price p = W N =A ( )(N ), which is associaed wih he equilibrium mark up: Q (; N ) = N ( )(N ) where he index Q sands for compeiion in quaniies. For a given number of rms, he mark up under compeiion in quaniies is always larger han he one obained before under compeiion in prices, as well known for models of produc di ereniaion (see for insance Vives, 999). Noice ha he mark up is decreasing in he degree of subsiuabiliy beween producs, wih an elasiciy Q = =( ), which is always smaller han P : higher subsiuabiliy reduces mark ups faser under compeiion in prices han under compeiion in quaniies. In he Courno equilibrium, he markup remains posiive for any degree of subsiuabiliy, since even in he case of homogenous goods, we have lim! Q (; N ) = N =(N ). This allow us o consider he e ec of sraegic ineracions in an oherwise sandard seup wih perfec subsiue goods wihin secors. In he general formulaion he markup is decreasing and convex in he number of rms wih elasiciy Q N = =(N ), which is decreasing in he number of rms (he mark up decreases wih enry a an increasing rae) and independen from he degree of subsiuabiliy beween goods. Since Q N > P N for any number of rms or degree of subsiuabiliy, we can conclude ha enry decreases mark ups faser under compeiion in quaniies compared o compeiion in prices, a resul ha will have an impac on he relaive behavior of he economy under he wo forms of compeiion. Finally, only when N! he markup ends o =( ), which is he radiional markup under monopolisic compeiion. The individual pro s in real erms can be expressed as: Q (; N ) = (N + which is a decreasing funcion of he number of rms and of he degree of subsiuabiliy...3 Endogenous Enry In his model, households choose how much o save in riskless bonds and in he creaion of new rms hrough he sock marke according o sandard Euler and asse pricing equaions. Following Ghironi and Meliz (5) and BGM (7), he average number of rms per secor follows he equaion of moion: N )C (5) (6) N + = ( )(N + N e ) (7)

11 where N e is he average number of new rms and (; ) is he exogenous rae of exi. 6 The real value of a rm V is he presen discouned value of is fuure expeced pro s, or in recursive form: V+ + + (; N + ) V = ( )E (8) + r + where r is he real ineres rae. We assume ha enry requires a xed cos of producion in unis of labor. This implies ha echnology shocks a ec he produciviy of he workers ha produce goods and also of he workers ha creae new business: his appears as he mos naural hypohesis, bu our main resuls would go hrough in case of xed coss in unis of consumpion. Therefore, we assume ha he enry cos equals =A unis of labor, wih >. In each period enry is deermined endogenously o equae he value of rms o he enry coss. Since he real cos of a uni of labor can be derived from he equilibrium pricing relaion (9) as: A p w = = A N =( ) (9) (; N )P (; N ) =( ) where we used he fac ha P = p N in he symmeric equilibrium, he endogenous value of a single rm mus be equal o he xed cos of enry, or: V = N =( ) (; N ) () The represenaive agen supplies labor which is employed o produce goods and o creae new rms. Marke clearing in he markes for goods, labor and credi deermines he dynamics of he economy, which can be expressed in erms of a sysem of wo equaions for he evoluion of N and C (evenually depending on he evoluion of oal facor produciviy A ). We leave he deails of he derivaion o he Appendix and repor here he equilibrium relaions for he number of rms and for consumpion of he represenaive agen, derived by subsiuing all he equilibrium condiions ino (7) and (8). In paricular, under compeiion in prices we have: E 8 < : C+ C N + = ( ) 4N + A+' 4 ( )(N )N + (N ( )(N )N A [ + (N )] C ' N C =( ) 3 5 () 39 C = (N + ) ; = ( )(N )N ( ) [ + (N )] () which characerizes he corresponding evoluion of he endogenous marke srucures in he shor run. Under compeiion in quaniies we have: N + = ( ) 4N + ( )(N )N A C ' N C =( ) 3 5 (3) 6 I would be ineresing o endogenize he exi rae as a counercyclical facor: his would srenghen our propagaion mechanism, since i would enhance he counercyclicaliy of mark ups.

12 E 8 < : C+ C 4 ( )(N )N + (N + )C + N + 39 = 5 ; = ( )(N )N ( ) (4) In general, one can show ha he dynamic sochasic general equilibrium is saddlepah sable and convergen o a seady sae endogenous marke srucure. Saring from a siuaion wih a low number of rms, he equilibrium implies monoonic convergence o he seady sae hrough an increase of boh consumpion and he number of rms.. Endogenous Marke Srucures in he Long Run In his secion we will brie y analyze he dynamic properies of he deerminisic model (wih A = A for any ) along he ransiional pah and in seady sae. For simpliciy we will focus on he case of inelasic labor supply (' = ), in which he equaion of moion of he number of rms does no depend on he form of compeiion and boils down o:! N + = ( ) N + A C =( ) N Solving i for he consumpion index in seady sae, we obain: C = AN N A leas for low levels of subsiuabiliy (low ), his is an invered-u relaion in N : wih few rms in seady sae, he consumpion index increases wih he number of producers because of he love for variey e ec, bu wih a large number of rms he index is negaively a eced by a furher increase in he number of producers because of he high savings necessary o replace he rms ha exi in each period. 7 The seady sae number of rms ha maximizes he seady sae consumpion index (and herefore uiliy) can be derived as N GR = ( )A=, where we refer o his as he golden rule number of producers. Any seady sae wih N > N GR would be dynamically ine cien, in he sense ha higher levels of consumpion could be permanenly reached by reducing enry of rms... Seady sae under Berrand compeiion Under compeiion in prices he deerminisic equilibrium sysem is given by (5) and (). Evaluaing he laer in seady sae we have: (5) (6) C = ( )[ ( )]N (N ) ( ) (7) which is a posiive and convex relaion in N due o he role of he rms in producing consumpion goods. The wo expressions (6) and (7) could be represened in a phase diagram (N ; C ) as for he radiional Ramsey model. Solving for he seady sae endogenous marke srucure we obain an explici soluion for he number of rms and, using (), for he 7 When subsiuabiliy beween goods is high, he second e ec always prevails and he above relaion is monoonically decreasing; in paricular, when goods are homogenous (! ), we have C = A N =( ), which is linearly decreasing in N.

13 seady sae mark up: P (; N ) = ( )A + ( ) ( ) ( ) [( )A ] (8) One can easily verify he comparaive saics. Higher produciviy A leads o higher demand and pro s and herefore o more business creaion, which increases he seady sae number of rms and enhances compeiion while reducing he mark ups. When he coss of enry are high, pro abiliy is low and he long run equilibrium is characerized by high concenraion and high mark ups. When agens are more paien ( is larger), he ineres rae is lower and he discouned sum of fuure pro s is higher, which aracs more enry, srenghens compeiion and ulimaely reduces he mark ups. When he risk of bankrupcy is high ( is larger), here are only few rms in he long run and hey apply a high mark up o heir goods. Finally, higher homogeneiy beween goods (higher ) induces sronger compeiion and lower mark ups, wih a negaive impac on he number of rms. As in he Ramsey model wih perfec compeiion, he equilibrium is always dynamically e cien. 8 However, he number of rms is excessive compared o he welfare maximizing soluion - which BGM, 8,b, have shown o be equivalen o he equilibrium emerging wih consan mark ups = =( ). Opimaliy can be resored wih sales subsidies ha are inversely relaed o he number of rms: herefore i is opimal o increase he sale subsidy when here are less rms han in he opimal seady sae, and o decrease i when here are more rms, which corresponds o a counercyclical axaion. 9.. Seady sae under Courno compeiion Under compeiion in quaniies he deerminisic equilibrium sysem is given by (5) and (4). In seady sae he second relaion becomes: C = [ ( )]( )N ( ) [ + =(N )] (9) The seady sae endogenous marke srucure can be derived in a similar way o he previous case, wih a mark up Q (; N ) exibiing he same comparaive saics as before. However, he equilibrium wih Courno compeiion can be characerized by dynamic ine ciency (N > N GR ) when he discoun facor is high enough or he degree of subsiuabiliy is high enough. This oucome, which does no maerialize in he baseline BGM model wih monopolisic compeiion (whose equilibrium is acually fully e cien), is due o he endency 8 I can be veri ed ha when he discoun facor is small we have N N GR, and when! he seady sae number of rms converges o N GR + =. Therefore, aking he ineger consrain in consideraion, i urns ou ha he seady sae number of rms canno be larger han he golden rule number. 9 In paricular, inroducing an ad valorem sale subsidy a rae s s nanced wih lump sum axes on he rms as in BGM (8,b), he opimal scal policy requires a counercyclical subsidy a he rae s s = =(N ), which is clearly decreasing in he number of rms and in he degree of subsiuabiliy beween goods (See Ero, 9). In case of elasic labor supply also he opimal labor ax would be counercyclical. Recenly, Ghironi and Chug (9) have sudied opimal scal policy in a relaed model focusing on proporional dividend and labor axaion wih sae coningen deb. There is no an explici soluion for he long run number of rmsmark up (excep in he case of homogenous goods, analyzed in Colciago and Ero, 7). This can be veri ed in he limiing case of! which leads o N > N GR. A relaed case of dynamic ine ciency due o an excessive number of rms in a dynamic general equilibrium framework emerges in Ero (4, 8). 3

14 oward excessive enry ha characerizes models of compeiion in quaniies wih endogenous enry and o he dynamic link beween savings and business creaion in our model. When consumers are exremely paien hey save oo much, inducing excessive creaion of rms ha produce oo lile individually. The problem is more radical when he goods are highly subsiuable because in ha case he economy wases resourses o creae new rms ha produce very similar goods. Welfare could increase boh in he shor and long run wih a reducion of he number of rms and an increase in he producion of each rm. Moreover, even if dynamic e ciency holds, he equilibrium pah is always characerized by excessive enry compared o he social planner soluion. Again, full opimaliy can be resored wih sales subsidies ha are inversely relaed o he number of rms. Finally, noice ha, given he same srucural parameers, he endogenous marke srucure in seady sae wih compeiion in quaniies implies a larger number of rms compared o he case of compeiion in prices. Even if, ceeris paribus, Courno compeiion generaes higher mark ups, endogenous enry aracs more rms and srenghens compeiion. Business Cycle Analysis This secion has muliple purposes. Firs of all, we wish o evaluae he relaive success of he models considered above a replicaing he empirical facs described in he inroducion, namely counercyclical markups ogeher wih procyclical pro s and procyclical rms enry. Second, we wan o idenify he exen o which he marke srucure in uences he propagaion of echnology shocks hroughou he economy. Calibraion of srucural parameers is as follows. The ime uni is mean o be a quarer. The discoun facor,, is se o he sandard value for quarerly daa.99, while he rae of business desrucion,, equals.5 o mach he U.S. empirical level of per cen business desrucion a year. The value of is such ha seady sae labor supply is equal o one. In his case he Frish elasiciy of labor supply reduces o ', o which we assign a value of four as in King and Rebelo (). We se seady sae produciviy o A =. The baseline value for he enry cos is se o =. Our model allows for a large variey of combinaions of subsiuabiliy beween goods () and mark up (), which in urn depends on he mode of compeiion. In in he remainder we will ake = 6 as our baseline value since i is in line wih he ypical calibraion for monopolisic compeiion and delivers markups levels belonging o he empirically relevan range. 3 Neverheless, o evaluae he dependence of he model s implicaions on he elasiciy of subsiuion and for comparisons purposes wih oher models, we will also consider alernaive values of. Noice ha he combinaion of A and a ecs he endogenous level of marke power because a low enry cos compared o he size of he marke leads o a larger number of compeiors and hus o lower markups, and viceversa. However, he impulse response funcions below are no qualiaively a eced by values of wihin a reasonable range. In wha follows we will rs sudy he impulse response funcions o emporary supply shocks, and hen we will evaluae he second order momens. Inroducing an ad valorem sale subsidy a rae s s nanced wih lump sum axes on he rms as in BGM (8,b), he opimal scal policy requires a counercyclical subsidy a he rae s s = =(N ), again decreasing in he number of rms. 3 Oliveira Marins and Scarpea (999) provide esimaes of price mark ups for US manufacuring indusries over he period In broad erms mos of he secoral markups de ned over value added are in he range 3-6 per cen, while when de ned over gross oupu hey are in he range 5-5 per cen. In he laer case, high mark ups, over 4 per cen, are observed in few secors. 4

15 . Temporary produciviy shocks In his secion we show he qualiaive reacions of he economy o a persisen echnology shock. Technology is assumed o follow a rs order auoregressive process given by ^A = A ^A + " A, where A (; ) and " A is a whie noise disurbance, wih zero expeced value and sandard deviaion A. Figures 3-4 depic percenage deviaions from he seady sae of key variables in response o a one percen echnology shock wih persisency A = :9 in case of alernaive marke srucures; ime on he horizonal axis is in quarers. We repor he impulse response funcions for di eren values of under respecively compeiion in quaniies and in prices. Le us consider he baseline value for he elasiciy of subsiuion beween goods, = 6. Under Berrand and Courno compeiion he marke srucure is generaed endogenously and he seady sae mark ups are respecively per cen and 36 per cen. As well known, when rms compee in prices he equilibrium mark ups are lower, which in urn allows for a lower number of rms o be acive in he marke: his implies ha he model is characerized by a lower number of goods compared o he model wih compeiion in quaniies. Since his requires a smaller number of new rms o be creaed in seady sae, lower mark ups are associaed wih a lower savings rae as well. In spie of hese subsanial di erences in he seady sae feaures of he economy, Figures 3 and 4 show ha he quaniaive reacions of he main aggregae variables o he shock are surprisingly similar in hese wo models wih low subsiuabiliy. Under boh frameworks, he emporary shock increases individual oupu and pro s on impac, which creaes large pro opporuniies. This aracs enry of new rms, which in urn srenghens compeiion and reduces he equilibrium mark ups. Therefore, our model manages o generae individual and aggregae pro s ha are procyclical despie mark ups being counercyclical, in line wih he empirical evidence on business cycles. Noice ha he dampening e ec of compeiion on he mark ups is sronger under compeiion in quaniies, where enry erodes pro s margins faser han under compeiion in prices: 4 his jusi es higher enry and lower mark ups under compeiion in prices. The number of rms and he sock marke value of he represenaive rm remain above heir seady sae levels along all he ransiion pah. While he shock vanishes and enry srenghens compeiion, oupu and pro s of he rms drop and he incenives o ener disappear. A some poin ne exi from he marke occurs and he mark ups sar increasing oward he iniial level. The impac of hese reacions on he real variables resembles ha of a basic RBC model, even if i derives from largely di eren mechanisms. Aggregae oupu jumps up and gradually revers o he seady sae level, being iniially fueled by he reducion in he mark ups associaed wih enry and by he increase in labor supply associaed wih higher wages. Par of he increase in income (from higher wages and pro s) is saved because he ineres rae is increased by he sudden improvemen of he pro opporuniies. Savings are invesed in rm creaion, which in urn pushes oupu up and he ineres rae down: he feedback e ec on consumpion generaes is hump shaped pah. However, conrary o sandard models, here he impac of he shock on consumpion is srenghened by a new compeiion e ec. Enry of new rms srenghens compeiion and emporarily reduces he mark ups, which in urn booss consumpion. To sum up, he produciviy shock reduces no only he marginal cos (as already happens in he RBC model), bu also he equilibrium mark up (which is zero in he RBC model and consan in he models wih monopolisic compeiion), herefore he ineremporal subsiuion oward curren consumpion is sronger when he marke srucure is endogenous. In 4 Recall ha he mark up elasiciy o he number of rms is larger under compeiion in quaniies, as poined ou in he previous secion. 5

16 .8 Consumpion Hours.5 Wage 3 Oupu Number of firms New enrans Mark up Sock Marke Value Individual oupu Individual profis.8 Aggregae profis Technology θ= θ=6 Figure 3: Berrand compeiion. Impulse response funcion o a emporary echnology shock. oher words, he impac of a emporary shock on consumpion is magni ed in he presence of endogenous marke srucures. 5 As noiced earlier, our general model should be inerpreed as a model of a represenaive secor wih a poenially high degree of subsiuabiliy beween goods. For his reason we consider an elasiciy of subsiuion beween goods =. In his case mark ups are markedly lower hen in he previous case, 5 per cen under Berrand compeiion and 8 per cen under Courno compeiion, bu he same qualiaive resuls hold. Also, we consider he exreme case of homogenous goods (! ), ha corresponds o he ypical assumpion of he RBC lieraure: in such a case, our model wih compeiion in quaniies is compaible wih posiive (Courno) mark ups and, as we can see in Figure 4, i is able o reproduce a similar propagaion mechanism o he one we have jus seen. On he conrary, under compeiion in prices and homogenous goods, he model collapses o one where mark ups vanish and enry does no ake place because of he posiive xed coss of producion (herefore we did no display his case in Figure 3). For his reason, and conrary o a long sanding lieraure, we consider he model wih compeiion in quaniies as a more exible ool for macroeconomic analysis of he business cycles in he presence of realisic (and endogenous) marke srucures. The above comparison beween wo models feauring he same srucural parameers bu di eren modes of compeiion can be ineresing in is own, bu is inerpreaion is limied by he fac ha in di eren markes di eren forms of compeiion ake place - and mos of he imes we are no even able o screen beween hem. An alernaive comparison which 5 As well known, his e ec is limied by he logarihmic preferences in consumpion, which imply a uniary elasiciy of ineremporal subsiuion. Wih an isoelasic uiliy funcion, he compeiion e ec would be sronger when he elasiciy of subsiuion is larger han uniy. 6

17 .8 Consumpion.5 Hours Wage Oupu Number of firms New enrans Mark up.4 Sock Marke Value Individual oupu.5 Individual profis.6 Aggregae profis Technology Homogeneous goods θ=6 θ= Figure 4: Courno compeiion. Impulse response funcion o a emporary echnology shock. can be useful o undersand he implicaions of endogenous marke srucures emerges when models wih equal seady sae mark ups are sudied. In such a case all he aggregae raios are he same as well, and di eren responses o a shock reveal fundamenal di erences of alernaive modes of compeiion. To sudy a comparison of his second ype, le us consider he model wih compeiion in prices under he baseline calibraion. (Figure 3). This model is characerized by a seady sae mark up of per cen. Under our paramerizaion, he same mark up emerges endogenously in a model of compeiion in quaniies when he goods are homogenous, ha is wih! (Figure 4). A comparison beween he impulse response funcions of hese wo cases wih a mark up of per cen (and herefore wih equal seady sae values) shows ha he e ec of compeiion on he markup is sronger in he case where rms compee in quaniies and goods are homogenous. This a ecs he impac response of consumpion, which has a sronger impac response under homogenous goods and compeiion in quaniies raher han under low subsiuabiliy and compeiion in prices. 6. Second Momens To furher assess he implicaions of endogenous marke srucures for he business cycle, we compue second momens of he key macroeconomic variables. In his exercise we follow he RBC lieraure and assume ha he only source of random ucuaions are emporary exogenous echnology shocks. We calibrae he produciviy process as in King and Rebelo (), wih persisence A = :979 and sandard deviaion A = :7. We use he same 6 The same holds compared o low subsiuabiliy and compeiion in quaniies, as we can see from Figures 3 and 4 joinly. 7

18 process as in King and Rebelo () for comparison purposes wih he RBC lieraure and o verify he addiional impac of our propagaion channel for a given shock. We also compued and esimaed a model based Solow residual (see Appendix B on daa sources and Appendix C on a second momen analysis of a version of our model wih capial accumulaion where we paramerize he Solow residual according o our own esimaes). We repor in Table he saisics on US daa (947: / 7:3) for oupu Y, consumpion C, invesmen I, labor force L, aggregae pro s and he mark up. 7 We compued wo alernaive measures of he price markup. Since our model feaures a sunk cos in erms of unis of labor, boh of hem allow for overhead labor coss. The measure repored in Table is he labor-share based measure considered by Roemberg and Woodford (999). A second one is a model based measure and leads o similar qualiaive resuls bu is subsanially more volaile and displays sronger counercyclicaliy. 8 V ariable (X) (X) = (Y ) E (X ; X ) Corr (X; Y ) Y :66 :84 C :9 :75 :78 :76 I 4:97 ; 99 :87 :79 L :8 : :9 :88 8:8 4:87 :76 :67 :99 :6 :79 :8 Table : Second momens. US daa Table repors second momens of Y, C, I N e V, L,, and mark up for our model wih compeiion in quaniies and wih compeiion in prices under he baseline parameerizaion for he degree of subsiuabiliy beween goods. 9 Boh frameworks provide a similar performance a reproducing some key feaures of he U.S. business cycle. Endogenous mark up ucuaions ogeher wih endogenous enry deliver a subsanially higher oupu volailiy wih respec o he sandard RBC model (.5/.5 agains.39), 3 almos maching he one emerging from US daa. As emphasized above, we can capure procyclical pro s and enry ogeher wih counercyclical mark ups as in he daa. Our model provides a good mach for he correlaion of pro s and mark ups wih oupu, bu i underesimaes heir variabiliy, emphasizing he need for furher work on he microfoundaion of he endogenous marke srucures o beer explain he high volailiy of boh pro s and mark ups. 7 Variables have been logged. We repor momens of HP lered variables wih a smoohing parameer equal o 6. Pro s include boh he remuneraion of capial and he exra-pro s due o marke power: while we could no disinguish beween he wo, fuure research may ry o do i. 8 The model based measure of he price mark up akes ino accoun ha in our model he mark ups can be expressed as = C =w (L L e ), i.e. as he inverse of he share of labor in consumpion beyond he sunk quaniy used o se up new rms (noice ha L e represens hours required o produced new rms). Accordingly, we obain () = :6, E ; = :8 and Corr (; Y ) = :63. The measure of he labor share used in our compuaion is given by he raio of he compensaion of employees in he nonfarm business secor o GDP. None of he cyclical properies we repor are subsanially alered using (GDP- PROPRIETORS INCOME) insead of GDP. For boh he markup measures we consider, he raio of he overhead quaniy of labor o he seady sae aggregae labor inpu is assumed o be.. This is wihin he range of values endogenously delivered a he seady sae by our model under boh compeiive frameworks. 9 Following BGM (7) we repor momens of daa consisen variables, i.e. de aed using he average price index raher han he consumpion based price index. 3 The benchmark RBC model we consider is ha by King and Rebelo (). Our uiliy funcion di ers from heirs in he subuiliy from labour supply, bu he second momens are equivalen under he same calibraion. 8

19 Moreover, mark up counercyclicaliy allows o srenghen he propagaion of he shock on consumpion hrough he compeiion e ec. Boh models display an absolue and relaive (wih respec o oupu) variabiliy of consumpion larger han ha delivered by he RBC model (absolue:.78/.78 agains.6; relaive:.5/.5 agains.43). Since low variabiliy of consumpion is a well known shorcoming of he RBC heory, he compeiion e ec delivered by sraegic ineracion and endogenous enry appears o be a relevan channel o overcome i. Compared o he RBC framework, our model wih endogenous marke srucures slighly improves he performance in erms of variabiliy of hours (.85/.77 agains.67). Finally noice ha he variabiliy of oupu increases furher (bu ha of consumpion goes down) when lower degrees of subsiuabiliy beween goods are aken in consideraion, while i decreases (and he variabiliy of consumpion goes up) for higher degrees of subsiuabiliy, under boh forms of compeiion. V ariable (X) (X) = (Y ) E (X ; X ) Corr (X; Y ) Y :5; :5 :68; :68 C :78; :78 :5; :5 :77; :76 :94; :95 I 5:89; 7:56 3:87; 5: :65; :64 :97; :97 L :85; :77 :56; :5 :65; :64 :96; :96 :7; :74 :46; :49 :7; :7 :99; :98 :5; :3 :; :8 :95; :94 :7; :7 Table : Second momens under he baseline parameerizaion. Lef: Courno Compeiion; Righ: Berrand Compeiion 3 Supply-side versus Demand-side Models BGM (7) have o ered an explanaion for he empirical correlaion of mark ups and pro s wih he business cycle resoring o a class of ranslog preferences, inroduced by Feensra (3) and characerized by demand-side pricing complemenariies. In such a framework goods become closer subsiues as he number of varieies produced in he economy increases. Ne enry, which amouns o creaion of new producs, leads hus o a higher elasiciy of subsiuion beween goods which evenually ranslaes ino a lower mark up (which is given by (N ) = + =(N ) where > is a free parameer deermining he ime-varying elasiciy of subsiuion beween varieies, ha correspodns o = + N ). For his reason we refer o his approach as o a demand-side explanaion for mark up conercyclicaliy as opposed o he approach adoped in he our work, where counercyclicaliy resuls from sraegic ineracions on he supply side of he economy. The purpose of his secion is ha of comparing he demand side and he supply side alernaives from boh a qualiaive and a quaniaive poin of view. To economize on space we will focus on Berrand compeiion, however similar consideraions as hose made below apply o Courno compeiion. 3 We se he value of he elasiciy of subsiuion,, o 3:8, as in BGM (7). This delivers a seady sae mark up under Berrand compeiion equal o 4 %. 3 Given our purpose we need o paramerize he value of for he ranslog framework. 3 Boh a graphical and a quaniaive comparison beween he Courno and he ranslog framework is available from he auhors. 3 This value of delivers a high mark up level compared o he esimaes. We choose i for homogeneiy 9