Heterogeneous Markups, Growth and Endogenous Misallocation

Transcription

1 Heerogeneous Markups, Growh and Endogenous Misallocaion Michael Peers Yale Universiy December 206 Absrac This paper proposes a parsimonious model of growh, where imperfec produc markes allow firms o charge heerogeneous markups. Firms increase he produciviy of heir exising producs o raise markups and grow in size by expanding ino new markes. The inerplay beween hese forces deermines he saionary disribuion of markups and firm size and he long-run rae of growh. Policies ha raise firms coss o ener new markes increase misallocaion by lowering produc marke compeiion and reduce firm size by limiing he number of markes firms compee in. I apply he heory o panel daa from manufacuring firms in Indonesia and show ha seemingly large differences in he number of acive firms and heir average size are consisen wih empirically plausible differences in firms life cycle dynamics, enry raes and aggregae produciviy growh beween rich and poor counries. m.peers@yale.edu. I am especially graeful o Daron Acemoglu, Abhiji Banerjee and Rob Townsend for heir invaluable guidance. I also hank Ufuk Akcigi, Susano Basu, Penny Goldberg, Chang-Tai Hsieh, Sam Korum, Giuseppe Moscarini, Ezra Oberfield and Aleh Tsyvinsk as well as numerous seminar paricipans, whose quesions and suggesions benefied he paper subsanially. I am also graeful for he financial assisance of he George and Obie Shulz fund o acquire he daa necessary for his projec.

2 Inroducion One of he major developmens in he recen lieraure on growh and long-run economic developmen has been he focus on firm-level daa. Some of he key sylized facs, which emerged from his lieraure, are (i) ha firms in poor counies are small (bu ha here are los of hem), (ii) ha he small size of such firms is less a reflecion of heir small scale when enering bu raher due o slow growh dynamics over he life cycle and (iii) ha poor counries suffer from persisen misallocaion, whereby variaion in firms marginal producs reduces aggregae produciviy. A he same ime, enry raes do no vary sysemaically across counries. In his paper I show ha hese paerns are consisen wih a parsimonious model of firm growh, where imperfec produc markes allow firms o charge heerogeneous markups. I sar from he premise ha developing economies migh suffer from wha I call marke barriers, i.e. fricions, which will hamper firms abiliy o ener new markes. Such barriers can be relaed o policies like size-requiremens or lenghy approval processes for producion licenses. They could also be echnological in naure, whereby he coss of breaking ino markes firms previously did no caer o, are higher in developing counries. Such barriers reduce compeiion and increase markups and misallocaion by rendering produc markes capive o incumben firms. A he same ime, hey also limi he exen of firm growh, keep firms small and hence increase he number of acive firms. I find ha his mechanism can quaniaively go a long way when calibraed o cross-counry paerns on life cycle growh and enry raes. Imporanly, I also show ha hese paerns are consisen wih a sable world income disribuion: despie very differen processes of firm dynamics, he model is consisen wih counries growing a essenially he same rae in long-run. The heory has wo key ingrediens. I sar from recen models of firm based growh in he spiri of Klee and Korum (2004). This is an aracive framework which provides a racable way o connec firm-level growh and enry incenives o he resuling disribuion of firm size and enry and exi paerns. I hen augmen his framework wih a srucure of imperfec produc markes, where firms engage in non-compeiive pricing and charge variable markups. In paricular, firms can spend resources o increase he produciviy in heir exising markes o shield hemselves from compeiion and susain high markups in equilibrium. A he same ime, firms face he consan hrea of losing heir markes o eiher new enrans or oher firms, which ry o expand heir cosumer base. I i his join process of new firms enering he economy and exising firms expanding ino new markes and engaging in markup increasing qualiy improvemens, which will deermine he long-run disribuion of markups and firm size. The model has an analyic soluion and makes precise predicions how hese equilibrium objecs are relaed. In paricular, he disribuion of markups and firm size are fully characerized by wo endogenous summary saisics. The key saisic deermining he disribuion of markups is he wha I call inensiy of creaive desrucion, which is simply he rae a which firms lose heir exiing markes relaive o he speed a which hey increase heir marke power. In paricular, I show ha he saionary disribuion of markups akes a pareo form, whose shape parameer is increasing in his endogenous saisic. If creaive desrucion is inense, he cross-secional disribuion of markups is compressed because enering and expanding firms inroduce sufficien churning in he economy o keep monopoly power limied. If on he oher hand creaive desrucion is limied, he disribuion of markups has a fa ail because incumben firms are unlikely o be replaced and have ample ime o accumulae marke power. A similar saisic exiss for he properies of he firm size disribuion, which is fully paramerized by he inensiy of marke expansion, which is simply he rae a which exising firms break ino new markes relaive o he equilibrium rae of enry. The higher his inensiy, he larger will he average firm be and he less firms will be able o survive in equilibrium. Wih hese wo summary saisics a hand, i is easy o analyze differen policies. An equilibrium wih boh misallocaion and many small firms requires a low inensiy of creaive desrucion and a low inensiy of marke expansion. Marke barriers have his exac implicaion as hey reduce he exen o which exising firms expand 2

3 ino ino novel produc markes. This no only keeps markups high and dispersed, bu i also reduces average firm size and he rae of employmen growh over firms life cycle. In equilibrium, his direcly implies ha he economy will be populaed by many firms, mos of which are small, and ha resources will be misallocaed across firms. In conras, higher enry coss, i.e. fricions which raise he coss of new firms o ener he economy, have he opposie effec. While lower enry raes will also increase markups and hence cause misallocaion, firms will grow faser as hey face less compeiion from enrans. In equilibrium, enry coss will herefore increase average firm size and reduce he number of acive producers. I apply he heory o firm-level panel daa for formal manufacuring firms in Indonesia. Two imporan empirical momens o discipline he equilibrium inensiies of creaive desrucion and marke expansion are he increase of markups and firm size over he firm s life cycle. I find ha firms boh increase heir markups and heir size as hey age. To quanify he imporance of marke barriers and enry coss for he cross-counry daa, I calibrae he model and idenify differences in marke barriers and enry coss beween he US and Indonesia from wo cross-counry momens: he equilibrium enry rae and he rae of life cycle growh. The calibraion implies ha boh enry coss and marke barriers are lower in he US. While I esimae enry o be abou 5% less cosly in he US, he difference in expansion barriers amouns o more han 30%. The quaniaive effec of his variaion is sizable. The model predics ha he aggregae imporance of small producers declines by 75% and average firm size more han doubles. Moreover, fiercer compeiion reduces markups and misallocaion. This in urn increases aggregae TFP by abou 0.3% and reduces he monopoly ax on facor supplies (i.e. he labor wedge) by abou 2%. The implicaions for he equilibrium growh rae are suble. Higher enry coss and expansion barriers in Indonesia reduce he exen of creaive desrucion. This reduces he equilibrium growh rae. A he same ime, by increasing he survival probabiliies for exising firms, such barriers increase he incenives for firms o increase produciviy wihin heir markes. This ends o increase he equilibrium growh rae, albei a he cos of higher markups. In my calibraion, hese effecs essenially cancel ou, rendering he growh rae insensiive o enry coss and expansion barriers. Differences in firm size and misallocaion are herefore consisen wih a siuaion of balanced growh, where he disribuion of income across counries does no diverge in he long-run. This is in sark conras o a version of he model, which absracs from he markup channel. If firms were no engaged in markup increasing innovaion, he observed cross-counry variaion in enry raes and life cycle employmen growh would imply large differences in aggregae produciviy growh. Finally I use he variaion across differen provinces in Indonesia o give some direc evidence for he imporance of marke barriers. I show ha average firm size correlaes posiively wih boh he exen of life cycle employmen growh and average markups and negaively wih regional enry raes. This is consisen wih a view where expansion barriers are an imporan source of variaion across regions wihin Indonesia bu inconsisen wih varying coss of enry. Relaed Lieraure This paper provides a parsimonious heory, where he exen of saic misallocaion and he long-run disribuion of firm size are joinly deermined. Empirically, hese aspecs of he firm-level daa are negaively correlaed. In paricular, firms in poor counries are small bu numerous (see e.g. Hsieh and Olken (204), Poschke (20) or Beno and Resuccia (forhcoming)), hey experience slower growh as hey age (Hsieh and Klenow (204)) and misallocaion of resources across such firms is more severe (see e.g. Hsieh and Klenow (2009), Resuccia and Rogerson (2008), Barelsman e al. (203) and he survey aricle by Hopenhayn (202)). A recen lieraure has conneced hese wo observaions by exploring how changes in exogenous disorions affec firms innovaion incenives and he paerns of firm enry. Hsieh and Klenow (204), Buera and Jaef (206) and Beno and Resuccia (forhcoming) for example show how size-dependen policies, i.e. disorions, which are 3

4 exogenously correlaed wih firm size, reduce firms incenive o expand. Faal Jaef (20) and Yang (202) sudy he aggregae effecs of such disorions in environmens wih free enry. In his paper, I ake a differen approach. I consruc a model, where misallocaion is fully endogenous and hence emerges as an equilibrium oucome ogeher wih he firm size disribuion and he rae of enry. My heory is an endogenous growh model in he Schumpeerian radiion of Aghion and Howi (992) and Grossman and Helpman (99). In erms of modeling choices I build heavily on Klee and Korum (2004). This framework is analyically aracive, can raionalize many feaures of he daa and has been used o empirically sudy he exen of creaive desrucion in Denmark and he US (Lenz and Morensen, 2008; Garcia-Macia e al., 206), he welfare implicaions of indusrial policies (Acemoglu e al., 202), he imporance of differen margins of innovaion behavior a he firm-level (Akcigi and Kerr, 205) and differences in he process of firm dynamics across counries (Akcigi e al., 205). In conras o hese papers, I show how o exend his framework in a racable way o generae heerogeneous markups across producers. This exra margin does no only generae addiional esable predicions bu also has novel aggregae implicaions. In paricular, my model falls ouside of he class of models analyzed in Akeson and Bursein (205) as changes in innovaion policy will no only affec aggregae produciviy growh bu also change he naure of compeiion on oupu markes. While his is, o he bes of my knowledge, he only paper ha focuses on imperfec oupu markes in relaion o he lieraure on growh and misallocaion, here is a large and growing lieraure in he field of inernaional rade sressing he imporance of markups. On he heory side, Bernard e al. (2003), Meliz and Oaviano (2008) or Akeson and Bursein (2008) are examples of heories ha generae heerogeneous markups. In conras o he model of his paper, all hese frameworks are saic in he sense ha firm efficiency is exogenous. Tha rade migh have addiional welfare gains by reducing markup heerogeneiy and misallocaion is explicily sressed in Edmond e al. (205), Epifani and Gancia (20) and Holmes e al. (203). 2 firms. There is also large empirical lieraure which shows ha markups vary sysemaically in he cross-secion of In paricular, markups are low for enering firms (Foser e al. (2008)), high for exporers (De Loecker and Warzynski, 202) and increase in response o rade liberalizaions, which reduce he price of impored inpus (De Loecker e al., 206). Furhermore, firm-specific prices are argued o be an imporan source of variaion in revenue-based produciviy measures (De Loecker, 20a). The dynamic model in his paper is consisen wih hese facs as i predics ha markups are increasing in age and size and ha pass-hrough is imperfec. In order o explain he negaive correlaion beween firm size and misallocaion a he counry-level, my heory suggess an imporan role for fricions for exising firms o ener new produc markes. This is consisen wih a se of recen papers, which argue for he imporance of cosly consumer acquisiion (e.g. Arkolakis (2008), Gourio and Rudanko (204) and Perla (206)). In a saic model, Beno (206) also shows ha higher coss of enry for new firms will increase average firm size and sresses he imporance of fricions for firms enering muliple markes. The finding ha produc marke compeiion has ambiguous effecs on he long-run growh rae is also presen in Aghion e al. (200) and Aghion e al. (2005). 3 The res of he paper proceeds as follows. In he nex secion I presen he heory and show how misallocaion The reduced form of my model is isomorphic o hese papers and hence provides a micro-foundaion for he equilibrium disribuion of he modeling device of firm-specific wedges. There are, of course, oher heories of misallocaion. The vas majoriy of conribuions focuses on fricions in firm inpu choices, sudying models wih imperfec capial markes (Buera e al., 20; Moll, 204; Banerjee and Moll, 200; Midrigan and Xu, 200), conracual imperfecions (Acemoglu e al., 2007) or capial adjusmen coss Asker e al. (204). This is in conras o his paper, which argues ha he equilibrium disribuion of marginal producs reflecs monopolisic power and no binding inpu consrains. In he empirical analysis in Secion 3 I will presen evidence o disinguish some of hese explanaions. 2 Arkolakis e al. (202), however, find ha heerogeneous markups migh also reduce he gains from rade. 3 The mechanism, however, is differen. These papers sress he imporance of escape compeiion, whereby produc marke compeiion increases innovaion incenives by firms. In my heory, he ambiguous effec of marke barriers on he rae of growh is due o a wihin-firm composiion effec, whereby firms shif heir innovaion aciviy from marke expansion o produciviy increases of heir exising producs. 4

5 and he firm size disribuion are joinly deermined in equilibrium. Secion 3 conains he empirical analysis using Indonesian micro daa and he calibraion exercise o quanify he aggregae effecs of marke barriers and enry coss. Secion 4 concludes. 2 Theory 2. The Environmen There is a measure one of infiniely lived households, supplying heir uni ime endowmen inelasically. Individuals have preferences over he unique consumpion good, which are given by U = =0 e ρ ln (c ) d. This final good, which I ake o be he numeraire, is a Cobb-Douglas composie of a coninuum of differeniaed varieies lny = 0 ln fεs i y fi di, () where y fi is he quaniy of variey i bough from firm f and S i denoes he number of firms acive in he marke for variey i a ime. Hence, differen varieies i and i are imperfec subsiues, whereas here is perfec subsiuabiliy beween differen brands wihin a variey. I will also refer o a variey as a marke. Firms can be acive in muliple markes and he only source of heerogeneiy across firms is heir facor-neural produciviy o produce differen varieies. In paricular, a firm f producing variey i wih curren produciviy q produces oupu according o y fi = q fi l, where l is amoun of labor hired. The marke for inermediae goods is monopolisically compeiive, so ha firms ake aggregae prices as given. However, firms compee a la Berrand wih producers offering he same variey. This sraegic ineracion across producers will be he source of heerogeneous markups and aggregae misallocaion. Boh he se of compeing firms [S i ] i and firms produciviies [q fi ] fi evolve endogenously hrough (i) he enry of new producers ino he economy, (ii) he expansion of exising firms ino new markes, i.e. ino varieies hey did no produce before and (iii) produciviy increases by curren producers in markes hey already serve. While he firs wo margins of growh are considered in Klee and Korum (2004), he hird aspec is novel. I is his inensive margin of innovaion ha allows firms o gain compeiiveness relaive o oher firms in he marke hey serve and will give rise o heerogeneous markups across producers. A he aggregae level, his ingredien provides he link beween growh, misallocaion and he disribuion of firm size. 2.2 Saic Allocaions, Markups and Misallocaion Consider firs he saic allocaions for a given number of firms and disribuions of produciviy q. Given ha producion akes place wih a consan reurns o scale echnology, firms compee in prices and differen brands of variey i are perceived as perfec subsiues, in equilibrium only he mos producive firm will be acive. However, he presence of compeing producers (even hough hey are less efficien) imposes a consrain on he leading firm s price seing. Because he demand funcion associaed wih () has a uniary price elasiciy, he mos efficien firm 5

6 will resor o limi pricing. Leing q i denoe he produciviy of he acual producer, i.e. he mos efficien firm wihin he marke, he equilibrium markup in marke i is given by µ i p i = w /qi F = q i w /q i w /q i q F i, (2) where w denoes he equilibrium wage and w /qi F is he marginal cos of he second mos producive firm, which I will refer o as he follower. 4 Inuiively, a bigger produciviy advanage shields he curren producer from compeiion and allows him o pos a higher markup. From (2) one can also derive he allocaion of labor a he firm-level. Leing N f be he se of markes firm f is acive in, oal employmen of firm f, l f, is given by l f = i N f l fi = i N f q if y if = i N f q if Y p i = Y n f w n f µ i i N f Y n f w µ f, (3) where () implies ha p i y if = Y, n f = N f is he number of markes he firm is acive in and he las equaliy defines he average markup a he firm-level as µ f n i N f µ i. Hence, expanding ino novel markes increases employmen a he firm-level. Conversely, for a given number of markes n f, higher markups reduce firm-employmen, so ha variaion in markups induce variaion in employmen holding he number of markes fixed. I is his variaion, which induces an inefficien allocaion of resources and hence aggregae misallocaion. To see his, noe ha firm f s revenue labor produciviy is given by MRP L f p fy f l f = n f Y l f = w µ f, (4) i.e. revenue produciviy is no equalized bu reflecs he variaion in equilibrium markups. In he framework of Hsieh and Klenow (2009) and Resuccia and Rogerson (2008), measured revenue produciviy is proporional o (+τ K,i ) α τ Y,i, where τ K,i and τ Y i are exogenous firm-specific axes on capial and oupu. Hence, firms charging a high markup have high produciviy and would be idenified as facing high disorionary axes. Given he above srucure, he economy has a ransparen aggregae represenaion. Leing L P, denoe he oal mass of producion workers, (3) implies ha L P, = f Similarly, equilibrium wages are given by l f = Y w f ( w = exp ln ( ) ( qi F ) di = exp ln 0 0 µ i i N f ( qi µ i = Y ( ) µ i w di. (5) 0 ) ) ( di = Q exp 0 ln ( ) µ ) i di, 4 I is a his poin where he assumpion of he aggregae producion funcion being Cobb-Douglas simplifies he exposiion. If he demand elasiciy was o exceed uniy, he firm migh wan o se he unconsrained monopoly price in case is produciviy ( advanage ) over is closes compeior is big enough. In paricular, if σ > was he demand elasiciy, he opimal price was p = w q F min σ q F σ q,. ( ) In he limi where σ, we ge min σ q F σ q, =. This assumpion ha leading firms will always se he limi price will make he dynamic decision problem of firms very racable. 6

7 where ln Q = 0 lnq idi is he usual CES efficiency index. Hence, aggregae oupu is given by ( Y = Q exp 0 ln ( µ ) ) i di L P, T F P L P,, (6) 0 µ i di so ha aggregae TFP is he produc of firms physical produciviy measure Q and a erm reflecing firms marke power. In paricular, (5) and (6) show ha he aggregae implicaions of he underlying disribuion of markups are summarized by he wo sufficien saisics M = Λ = ( exp ( 0 0 ln ( µ ) ) i di 0 µ i di = exp ( [ ( )]) E ln µ i E [ µ ] (7) i µ i di ) = E [ µ i ]. (8) While Λ measures he gap beween he equilibrium wage and he social marginal producs of labor (see (5)), M deermines aggregae T F P (see (6)). Hence, Λ and M are akin o he labor wedge and he efficiency wedge in he erminology of Chari e al. (2007). Equaions (7) and (8) sress ha he macroeconomic implicaions of marke power are fully summarized by he marginal disribuion of markups and ha differen momens of his disribuions have differen aggregae effecs. In paricular, (7) implies ha M and ha M = if and only if markups are equalized across markes. Hence, aggregae TFP depends on he dispersion of markups in he sense ha a common proporional increase in markups in every marke, will leave he efficiency wedge unchanged. Conversely, he labor wedge will decline by he exac same amoun and hence reflecs he average level of marke power (see (8)). 5 Noe also ha he canonical case of consan markups as generaed by a CES demand sysem wih differeniaed producs is a special case of his resul: TFP will be idenical o is compeiive counerpar bu monopolisic power reduces facor prices. As long as facors are in fixed supply, monopolisic power will no have any effecs on efficiency. 2.3 Dynamics: Enry, Innovaion and Marke Expansion Boh he producion possibiliy fronier (as summarized by Q ) and he disribuion of markups depend on he underlying disribuion of produciviy across firms. Following Aghion and Howi (992) and Grossman and Helpman (99), I model firms efficiencies as being ordered on a qualiy-ladder wih proporional produciviy improvemens of size λ >. 6 In a given marke i, produciviy increases can sem from hree disinc sources: (i) a new firm can ener marke i wih a new echnology, (ii) an exising firm, who is no currenly acive in marke i, can expand ino his marke and (iii) he curren producer in marke i can increase his produciviy o gain addiional monopoly power. I assume ha hese differen sources of growh are fully symmeric in ha hey improve upon he curren fronier echnology: if he curren produciviy in marke i is given by q i, he new produciviy is given by λq i. Treaing produciviy increases hrough curren and new producers symmerically is no only sandard in mos Schumpeerian models of growh, bu is paricularly appealing in he curren conex, in ha i sresses he differen allocaional consequences of enry, marke expansion and innovaion. While new producers and incumbens increase he fronier echnology by he same amoun, he implicaions for equilibrium markups and allocaional efficiency 5 See also Epifani and Gancia (20), who derive a similar resul in an economy wih inernaional rade. 6 Specifically, leing r denoe he rung of he ladder, qualiies are ordered according o q r+ = λq r. 7

8 are very differen. In paricular, he expression for equilibrium markups in (2) implies ha µ i = q i q F i λ i, (9) where i is he producer s produciviy advanage over he compeing firms in marke i. Hence, in case he innovaion sems from he curren producer of variey i, he equilibrium markup in marke i increases by a facor λ. In conras, when produciviy growh is induced by a novel producer (which can eiher be an enirely new firm or an exising firm, which did no produce in marke i in he pas), he equilibrium markup in marke i decreases by a facor λ (i,), as he new producer is only a single sep ahead on he qualiy ladder. 7 Given his srucure, he sae of he firm is a muli-dimensional objec: he number of producs n, he qualiy of each of hese producs [q j ] n j= and he qualiy-gaps in each produc line [ j] n j=. However, he Cobb-Douglas demand srucure in () implies ha equilibrium profis in marke i are given by π i = ( µ ) i Y = ( λ i) Y π ( i ), (0) i.e. hey only depend on he qualiy gap and no on he level of qualiy q( fi. Hence, I) resric aenion o equilibria where firm behavior only depends on he payoff relevan sae variables n, [ j ] n j=. Given his sae, he firm can spend resources o improve is produciviy in he markes i is currenly producing in and i can ry o break ino novel markes. I adop he usual sochasic formulaion, whereby he firm can chose he flow rae o increase he produciviy of exising producs, [I i ] n i=, and o expand in a novel, randomly seleced marke, X, a a cos Γ (X, [I i ] n i= ), which - consisen wih Bollard e al. (206) - I denoe in unis of labor. I is analyically convenien o formulae he problem in erms of he expansion inensiy per currenly served marke, x X /n. Opimal behavior is hen described by he value funcion V (n, [ i ] n i= ), which is given by r V (n, [ i ] n i= ) V n (n, [ i ] n i= ) = π ( i ) i= max x,[i i] n i= { n i= n τ [V (n, [ i ] n i= ) V i= (n, [ i ] j i )] + () [ { }) ] I i V (n, [ i ] j i, i + V (n, [ i ] ni= ) + nx [V ({n +, [ i ] n i=, }) V (n, [ i ] n i= )] Γ (nx, [I i] n i= ) w }. The value of he firm consiss of hree pars. Firs here is he oal flow payoff, which is simply he sum of profis across all markes. Second, here is he possibiliy of losing any of he n exising markes o oher firms. This happens a he endogenous rae τ, which will be deermined in equilibrium and which I refer o as he rae of creaive desrucion. Finally, here is he opion value of innovaing. Firs of all, he firm has he opion o increase he markup in each of is markes wih flow rae I i. Secondly, he firm can spend resources o break ino a new marke wih flow rae nx. Noe ha he qualiy gap in novel markes is always equal o uniy. Finally, he las erm in () capures he cos of innovaion and marke expansion. While he recursive formulaion for V in () looks somewha dauning, i urns ou ha () admis a simple closed form soluion. I assume a paricular funcional form for he cos funcion Γ (.), which is consisen wih 7 Noe ha he coninuous ime formulaion of he model precludes he possibiliy ha a variey experiences boh enry and a produciviy improvemen by he curren producer, which is of second order. 8

9 balanced growh and allows me o derive an analyic soluion Γ (nx, [I i ] n i=, n) = n i= c I (I i ; i ) + c X (nx; n) where c I Iζ (I i ; i ) = λ ϕ I and c X (X; n) = n ζ X ζ ϕ x. (2) Here ϕ I and ϕ x paramerize he efficiency of he innovaion and expansion echnology and ζ > ensures ha he cos funcion is convex so ha here is a unique soluion. In addiion, boh cos funcions conain scaling variables, which make he model consisen wih balanced growh (Suon, 997; Lumer, 200). 8 As far as new enrans are concerned, I assume ha poenial enrans have access o a linear echnology, whereby each uni of hired labor generaes a flow of ϕ z markeable ideas. As firms ener in a single marke wih a uniary qualiy gap, he equilibrium degree of enry z is described by he free enry condiion V (, ) ϕ z w = 0 wih equaliy if z > 0. (3) For he remainder of he paper, I will focus on he case wih posiive enry, where he condiion in (3) holds wih equaliy The Saionary Equilibrium Given his se-up, I will now characerize he saionary (or balanced-growh-pah) equilibrium of his economy, which is defined in he usual way. Definiion. A saionary (or balanced-growh-pah) equilibrium is a se of allocaions [l i, I i, x i, z, y i, c ] i and prices [w, r, p i ] i such ha (i) all aggregae variables grow a a consan rae, (ii) consumers chose [y i, c ] i o maximize uiliy, (iii) firms chose [I i, x i, p i ] opimally, (iv) he free enry condiion is saisfied, (v) all markes clear and (vi) he cross-secional disribuions of markups and firm size are saionary. The firs useful resul o characerize he equilibrium is ha - along he BGP - he value funcion has a racable closed form soluion. In paricular, I show in Secion 6. in he Appendix ha V (n, [ i ] n π () + (ζ ) ϕ i= ) = x x ζ w n + ρ + τ n π ( i ) π () + (ζ ) λ i I ζ i= ρ + τ ϕ I w, (4) where x and I are he opimal innovaion and expansion raes and τ = z + x is he endogenous rae of creaive desrucion, i.e. he flow rae of which a firm in a given marke is replaced by eiher a new enran or an exising firm, who expands ino he respecive marke. The value of he firm has an inuiive srucure. In paricular i consiss of wo addiive pars. The firs erm is similar o he baseline model of Klee and Korum (2004) and capures he value of serving a marke wih a qualiy gap of uniy (and hence a markup of λ) plus he inframarginal rens of he concave expansion echnology. This par of a firm s value scales linearly in he number of markes n. The second erm capures he possibiliy of exploiing marke-power. I consiss of he flow value of being able o 8 The erm λ in c I (.) implies ha innovaions are easier he bigger he wihin-marke produciviy advanage and is similar in spiri o he assumpion of knowledge capial made in Klee and Korum (2004) or he seup in Akeson and Bursein (200). Inuiively: per-period profis are given by ( λ ) Y (see (0)) and hence concave in. For innovaion incenives o be consan, he marginal coss of innovaion have o be lower for more advanced firms. The leading erm in (2) ( λ ) is exacly he righ normalizaion o balance hose effecs. Noe ha firms only generae a high produciviy gap when hey have muliple innovaion in a row. Hence, (2) effecively posis ha firms can build on heir own innovaions of he pas. The erm n ζ in c X (.) serves a similar purpose and implies ha he cos of expanding a rae x per marke (i.e. nx = X) is linear in n. 9 I show in Secion 6. in he Appendix ha a sufficien condiion for he free enry condiion o be saisfied along he balanced growh pah is ρ > ((ζ ) /ζ) (ϕ x/ (ζϕ z)) ζ. 9

10 susain higher markups augmened by he possibiliy of increasing markups furher, which again is capured by he rens from he innovaion echnology. Because, firms are long-lived, he value funcion is given by he ne-presen value of hese flow payoffs, where he appropriae discoun rae is no only he rae of ime preference ρ, bu i also conains he rae of creaive desrucion τ, o accoun for he risk of losing markes o oher firms in he economy. Proposiion. Consider he seup described above. There exiss a unique saionary equilibrium, where he innovaion and expansion raes I and x and he rae of enry z are consan. The rae of creaive desrucion, i.e. he rae a which he producer in a given marke is replaced, is given by τ = z + x. The economy-wide growh rae is given by g = ln (λ) (I + τ). Proof. See Secion 6. in he Appendix. Proposiion esablishes ha his economy permis a unique saionary equilibrium. In ha equilibrium here is a consan flow of enering firms z and exising producers innovae wihin heir own markes and expand ino new markes a consan raes. As in any Schumpeerian model, he economy is characerized by creaive desrucion, whereby new producers replace incumben firms. In his economy, he flow rae of creaive desrucion is given by τ = z + x. 0 The aggregae rae of growh is simply given by he rae of growh of echnology Q (see (6)), because he efficiency wedge M is consan in a saionary equilibrium (see below). Because all hree sources of innovaion generae produciviy improvemens of he same size, g is proporional o he sum of creaive desrucion τ and firms markup increasing innovaion effors I. The cross-secional disribuions of markups and firm size Firms equilibrium enry, expansion and innovaion policies also deermine he equilibrium disribuion of markups and he disribuion of firm size. In a saionary equilibrium, boh hese disribuions are ime-invarian. Consider firs he disribuion of markups. Convenienly, markups only depend on he disribuion of qualiy gaps across markes (see (9)). Hence, he cross-secional disribuion of markups is fully characerized by {ν (, )} =, where ν (, ) denoes he measure of markes wih qualiy gap a ime. These measures solve he se of differenial equaions (τ + I) ν (, ) + Iν (, ) if 2 ν (, ) =, (5) τ ( ν (, )) Iν (, ) if = where ν (, ) denoes he ime derivaive. Inuiively, here are wo ways for a marke i o leave sae (, ): he curren producer could have an innovaion (in which case he qualiy gap would increase from o + ) or a new producer could ener (in which case he qualiy gap would decrease o uniy). The only way for a marke o ener he sae (, ) is by being in sae and hen having he curren producer experience an increase in produciviy (which happens a rae I). The sae = is special, because all markes where he producing firm ges replaced ener his sae. In addiion, all marke leave he sae (, ) if he curren producer increases his produciviy. Equaion (5) is he key equaion o characerize he equilibrium disribuion of markups. Three properies are noeworhy. Firs of all, noe ha he disribuion is fully deermined from he wo endogenous variables (I, τ) and is hence joinly deermined wih he economy-wide growh rae g. Secondly, he disribuion of firm size is no required o solve for he disribuion of markups across producs. This is due o he fac ha all firms innovae and expand a consan raes I and x per marke. Finally, (5) highlighs he pro-compeiive effecs of creaive 0 Recall ha he produc space has measure one. Because he aggregae rae of enry is given by z, his is also he rae a which each produc is subjec o enry by a new firm. Similarly, because each exising firm innovaes a rae x per produc, he aggregae rae a which exising firms expand ino he new markes is also given by x. 0

11 desrucion: while produciviy increases by exising producers are markup increasing, creaive desrucion shocks shif he disribuion of markups downwards. In addiion o his cross-secional disribuion of markups, he model also generaes a disribuion of firms over he number of markes hey serve. As he sochasic process of firms losing markes and expanding ino new markes is he same as in Klee and Korum (2004), he firm size disribuion akes exacly he same form. More precisely, he mass of firms who are acive in n markes a ime, ω (n, ), will be consan in he saionary equilibrium. Noe ha in conras o Klee and Korum (2004), oal sales and employmen are no longer proporional. While firm sales are proporional o he number of acive markes n, firm employmen is also affeced by he firm s average markup. Proposiion 2. Consider he economy above and le I, x and τ be he equilibrium raes of innovaion, expansion and creaive desrucion in a saionary equilibrium. Le ϑ I τ I and ϑ x x τ. Then he following is rue:. Le θ ln(+ϑ I ) ln(λ). The disribuion of markups µ = λ is given by G (µ) = µ θ, (6) and he efficiency and labor wedge M and Λ (see (7) and (8)) are given by Λ = θ + θ 2. The mass of firms serving n markes is given by and M = e /θ + θ. (7) θ ω (n) = n ϑ x ϑ x ϑ n x. The number of acive firm F and he share of aggregae oupu accouned for by firms wih a mos n markes, S n, is given by F = ϑ ( ) x ln ϑ x ϑ x and S n = (ϑ x ) n. Proof. See Secion 6.2 in he Appendix. Proposiion 2 conains he main heoreical resul of his paper: he cross-secional disribuion of markups G (µ), he exen of misallocaion M and Λ, he equilibrium mass of firms F and he shape of he firm size disribuion S k are joinly deermined from firms innovaion and enry incenives and ake a racable form. In paricular, wo endogenous saisics are crucial. The firs is he inensiy of creaive desrucion ϑ I, which measures he exen of firms being replaced by new producers relaive o firms innovaive effor in heir exising markes. The second is he inensiy of marke expansion ϑ x, which measures he share of aggregae creaive desrucion accouned for by exising firms. No only do hese wo endogenous saisics fully summarize he join disribuion of markups and firm size, bu hese wo aspecs nealy separae. See Secion 6.2 in he Appendix for deails.

12 The endogenous disribuion of markups akes a pareo form, whose shape parameer θ is fully deermined from he endogenous inensiy of creaive desrucion ϑ I. If creaive desrucion is inense, he shape parameer is large so ha boh markup heerogeneiy and he average markup decline. If on he oher hand creaive desrucion is of lile imporance, he resuling disribuion of markups has a fa ail and boh he average markup and heir dispersion is large. Hence, (6) is very differen from Bernard e al. (2003), who generae a Pareo disribuion of markups from firms exogenous produciviy draws. 2 The macroeconomic consequences of his endogenous markup disribuion are in urn fully summarized he wo sufficien saisics M and Λ, which only depend on ϑ I and have he closed form represenaion given in (7). 3 In paricular, i is easy o verify ha boh M and Λ are increasing in ϑ I. This capures he pro-compeiive effec of creaive desrucion: by reducing equilibrium markups, creaive desrucion reduces misallocaion and increases TFP and equilibrium facor prices. The equilibrium firm size disribuion in conras does no depend on firms inensive innovaion I, bu is enirely deermined by he equilibrium inensiy of marke expansion ϑ x. In paricular, if exising firms expansion aciviies are an imporan componen of he process of creaive desrucion, he equilibrium disribuion of firm size will be such ha a large share of oupu is produced in large firms. This direcly implies ha he number of acive firms will be small. Formally, boh F and S k are decreasing in he expansion inensiy ϑ x. 4 Proposiion 2 illusraes ha here is no a priori reason for he degree of misallocaion and he properies of he firm size disribuion o be relaed. However, Proposiion 2 makes precise predicions, which environmens are characerized boh by a muliude of small firms and a high degree of misallocaion - a siuaion, which is consisen wih he sylized facs on firm level oucomes in many developing counries. For his o be he case i has o be ha boh ϑ I and ϑ x are low in poor counries. In Secion 2.5 below I will argue ha his is he case if i is cosly for exising firms o break ino new markes, i.e. if ϕ x is low. In conras, fricions for new firms o ener he economy, i.e. barriers o enry, which lower ϕ z, have qualiaively differen effecs. The Dynamics of Markups and Firm Size Proposiion 2 focuses on he cross-secional implicaions of he heory. The model, however, also makes igh predicions for he resuling life cycle dynamics of markups and firm size and hese momens will be informaive o ake he model o he daa.. Consider firs he evoluion of markups. The underlying mechanism which generaes he endogenous pareo ail in my model is akin o he ciy-size dynamics of Gabaix (999), in ha markups wihin a marke have an inuiive life cycle inerpreaion: as long as oher firms do no replace he curren producer, markups sochasically increase. Once a new producer breaks ino he respecive marke, markups are rese o λ and he process begins afresh. In fac, as shown in Secion 6.4 he Appendix, he condiional disribuion of qualiy gaps as a funcion of he ime a marke is served by a paricular producer, which I will refer o as produc age a P, is a Poisson disribuion wih parameer Ia P, i.e. is given by h + (a P ) =! (Ia P ) e Ia P. (8) Hence, condiional on no being replaced, he disribuion of markups coninuously shifs ouwards as incumben firms engage in produciviy improvemens o rack up heir monopoly power. Equaion (8) also implies ha he average log markup in a marke condiional on being served by he same firm for a P years is given by E [ln (µ) produc age=a P ] = ln (λ) ( + Ia P ), (9) 2 I also wan o poin ou ha (6) describes he disribuion of markups across markes and no across firms. While he former is he welfare-relevan saisic, he laer is measured in firm level daa. I will come back o his in he empirical analyses below. 3 Noe ha is no a coninuous variable bu only akes ineger values. For simpliciy I rea markups as coninuous. See Secion 6.2 in he Appendix for he closed form expressions for he discree case. 4 Recall ha a saionary equilibrium requires ha x < τ so ha ϑ x <. 2

13 i.e. is increasing in age a a rae proporional o I. Markes, however, are no served by he same firm for eerniy. In paricular, creaive desrucion ignied by oher producers in he economy will limi how long exising firms can survive in a given marke. Because producers in a given marke are replaced a rae τ, he probabiliy of serving a marke for a P years is given by e τ a P. Hence, he exen o which old, high-markup markes exis in he economy depends crucially on he degree of creaive desrucion τ. If τ is high, i is rare o see firms serving a paricular produc marke for a long ime. The long-run disribuion of markups is shaped by he inerplay of hese wo processes, which lead o a pareo disribuion. 5 To link hese observaions o he dynamics of markups a he firm-level i is imporan o recognize ha firms are acive in many markes. Hence, he evoluion of firm-level markups is suble. Consider a firms of age a f. On he one hand, old firms end o have high markups for he reason encapsulaed in (9): old firms are he only firms wih he poenial of having had enough ime o build up markups wihin a marke over ime. On he oher hand, old firms also had ample ime o expand ino new markes. And as markups in new markes are lower han markups for he average variey he firm sells, expanding firms will end o have low average markups. Hence, he model implies a produc life cycle wihin he firm, where firms consanly accumulae marke power in heir exising producs and add new, low markup producs o heir porfolio. To see his more clearly, suppose ha firms never horizonally expand (i.e. x = 0) and hence never serve more han a single marke. In ha case, he age of he firm a f direcly corresponds o he ime a marke has been served by a paricular producer a P. Hence, he average log markup by firm age is also given by (9). Allowing firms o expand horizonally ino new markes breaks his igh link beween markups and firm age. In paricular, I show in Secion 6.4 of he Appendix ha he model implies ha he average log markup as a funcion of firm age is given by E [ln (µ f ) firm age = a f ] = ln (λ) ( + I E [a P a f ]), (20) where E [a P a f ] = τ ( e τa f ) x e τa f ( e xa f ( ( ) e xa f e (x+τ)a f γ (a f ) ln γ (a f ) )) ( + a f e xa f γ (a f ) ln γ (a f ) ), and γ (a) = x e (τ x) a. The expression in (20) has he same srucure as (9) - excep ha he mapping τ x e (τ x) a beween firm age a f and produc age a P is more complicaed and depends on boh he rae of marke expansion x and he exen of creaive desrucion. In paricular, he possibiliy of firms breaking ino new markes implies ha E [a P a f ] a f. Moreover, lim x 0 E [a P a f ] = a f, so ha (9) emerges as a special case. where The life cycle of employmen also has a closed form expression. In paricular, (3) implies ha ( ) Y E [ln (l f ) a f ] = ln + E [ln (n) a f ] E [ln (µ f ) a f ], (2) w E [ln (n) a f ] = γ (a f ) γ (a f ) ln (i) γ (a f ) i. Equaion (2) again shows he wo forces deermining he life cycle of firm-employmen. For a given number of markes n, older firm will be smaller as hey have higher markups. A he same ime however, older firms will caer o more markes as E [ln (n) a f ] is increasing in a f if x > 0. The wo relaionships in (20) and (2) will be imporan o ake he model o he micro daa as hey are 5 In a recen paper, Jones and Kim (206) exploi a similar srucure o argue ha creaive desrucion will limi income equaliy by reducing he ime enrepreneurs have o accumulae firm-specific human capial. i= 3

14 informaive abou he differen margins of firm growh. In paricular, he relaive speed a which older firms increase heir markups and heir size idenifies he relaive imporance of firms expanding heir scope of producion horizonally, i.e. in novel produc markes, or verically, i.e. hrough produciviy improvemens in heir exising markes. The more imporan firms markup increasing innovaions I relaive o heir expansion rae x, he seeper he age-profile of markups and he flaer he exen of life cycle employmen growh. To see his, noe firs ha for a given age, he average markup is increasing in I and average employmen is decreasing in I. Secondly, he effecs of he rae of expansion x is more suble. A decrease in he rae of marke expansion x raises he exen of life cycle growh for markups bu lowers he growh rae of employmen. The effec on markups sems precisely from he composiion effec menioned above: if firms ener novel markes only very infrequenly, a small fracion of heir sales is accouned for by new and hence low-markup markes. As far as employmen is concerned, wo effecs are a play: no only are firms only acive in few markes, bu in addiion he average markups is also higher. Boh of hese effecs reduce he exen o which firms increase heir employmen as hey age. In he limi, as x = 0, firms only serve a single marke irrespecive of heir age. Hence, E [ln (n) a f ] = 0 so ha (2) implies ha employmen and markups are inversely proporional. As markups increase in age, firms would - condiional on survival - decrease in size while hey increase heir markups and profiabiliy. Similarly, more creaive desrucion τ will lead o slower life-growh for boh markups and firm size: if firms lose heir exising markes a a fas rae, hey say small and will no have ime o build-up marke-specific monopoly power The Effecs of Enry Coss and Marke Barriers So far he heory provides a racable dynamic model, where misallocaion, growh, he firm size disribuion and he life cycle dynamics of markups and firm size are joinly deermined in equilibrium. In his paper I wan o use his framework o sudy he consequences of wo paricular fricions, which are arguably imporan in developing economies. These are marke barriers, i.e. fricions for exising firms o expand ino new produc markes, and enry coss, i.e. coss for new firms o ener he economy. 7 For simpliciy I model boh of hese fricions in he following reduced-form way. Consider firs he case of marke barriers and le φ x be he probabiliy ha an expanding firm replaces he exising producer condiional on having generaed a superior echnology. A low level of φ x can for example reflec license requiremens, bureaucraic red ape, which have o be overcome before a new firm can be acive in a new marke, or oher policies aimed o shield exising producers from poenial compeiors. I adop a similar sraegy for he case of enry coss, i.e. new firms replace an exising firm wih probabiliy φ z : he lower φ z, he more cosly i is for new firms o acually ener he economy. This srucure is convenien because i is nesed in he heory laid ou above. In paricular, defining he realized expansion and enry flows raes above as x = φ x x and z = φ z z, where x and z are he gross expansion and enry raes, he model above incorporaes hese fricions once we define he expansion and enry cos shifer ϕ x and ϕ z as ϕ x ϕ x φ ζ x and ϕ z ϕ z φ z, (22) 6 I was no able o show hese comparaive saics analyically. I is possible o analyically show ha E [ ln (n) a f ] is increasing in x and decreasing in τ. For E [ ln ( µ f ) af ], I could no find any example where he average markup is increasing in τor x. This direcly implies ha E [ ln (l) a f ] is increasing in x. I also could no find any example where average employmen was increasing in τ, i.e. where he effec of lower markups were o dominae he effec of losing markes a a faser rae. 7 One widely used measure of enry coss is developed in Djankov e al. (2002). They measure he fees and ime coss o legally operae a business for a variey of counries. Such variaion in he regulaion of enry has been linked o cross-counry income differences in Barseghyan (2008), Barseghyan and DiCecio (2009) or Herrendorf and Teixeira (20). There are also sudies focusing on paricular epsiodes of delicensing. The dismanling of India s Licence Raj, for example, has been sudied in Aghion e al. (2008). Even hough all hese sudies refer o enry coss, he empirical variaion is likely o capure boh marke and enry barriers in he sense of my heory. 4

15 where ϕ x and ϕ z denoe he echnological efficiency of he enry and expansion echnology. Hence, expansion barriers and enry coss are akin o a reducion in expansion and enry efficiency. I can hen use he resuls from above o derive he aggregae effecs of changes in enry coss and marke barriers. Proposiion 3. Consider a saionary equilibrium in he economy above and suppose ha ζ ζ > and ρ < ρ. Then,. Higher enry coss and marke barriers reduce creaive desrucion, i.e. τ φ z > 0 and τ φ x > 0, 2. Higher enry coss and marke barriers increase misallocaion by reducing he inensiy of creaive desrucion, i.e. ϑ I φ z > 0 and ϑ I φ z > 0, 3. Higher enry coss increase average firm size and reduce he number of firms by increasing he expansion inensiy, i.e. ϑx φ z < 0, 4. Higher marke barriers reduce average firm size and increase he number of firms by reducing he expansion inensiy, i.e. ϑx φ x > 0, 5. The effec of enry coss and marke barriers on he equilibrium growh rae is ambiguous. Proof. See Secion 6.3 in he Appendix. The resricions ha ζ ζ and ρ < ρ are a sufficien condiions. I can be shown ha ζ < 2. Proposiion 3 summarizes he consequences of marke barriers and enry coss on he saionary equilibrium in his economy. To undersand how firms equilibrium incenives are affeced by changes in such barriers, i is helpful o hink abou heir dynamic opimaliy condiions. Consider firs he opimal rae of marke expansion x. Recall ha he value funcion in (4) is addiively separable across markes. Hence, he marginal value of expansion for an exising firm is exacly he same as he value of enry, which - given he linear enry echnology - is equal o he enry coss. This direcly implies ha he equilibrium rae of expansion x equalizes he marginal cos of expansion and he marginal cos of enry and is herefore only a funcion of parameers ( ϕx φ ζ x x = ϕ z φ z ζ Naurally, x is decreasing in markes barriers and increasing in he coss of enry. ) ζ. (23) The incenives for firms o verically innovae o increase heir markups are more suble. The value funcion implies ha he marginal reurns o increase markups in marke i are given by { }) V (n, [ j ] j i, i + V (n, [ i ] n i= ) = π ( i + ) π ( i ) ρ + τ + (ζ ) [c I (I, i + ) c I (I, i )] w. ρ + τ The firs erm is he benefi of being able o pos higher markups, which will resul in higher profis. The second erm reflecs changes in he innovaion echnology: according o (2), increases in qualiy will increase he efficiency of fuure innovaion, which represens a capial gain. Simplifying erms and seing his equal o he marginal cos of innovaion implies ha he opimaliy innovaion rae I is deermined from [ λ λ Y = ζi ζ + ρ + τ w ϕ I λ λ ] (ζ ) I ζ. (24) ρ + τ This shows ha firm s incenives o increase markups depend on wo endogenous aggregae variables - he rae of creaive desrucion τ and size of he marke Y w (relaive o he cos of innovaion). In paricular, an increase in 5