Comparative Advantage and Heterogeneous Firms

Transcription

1 Comparatve Advantage and Heterogeneous Frms Andrew B. Bernard Tuck School of Busness at Dartmouth & NBER Stephen Reddng London School of Economcs & CEPR Peter K. Schott Yale School of Management & NBER June 2005 Abstract Ths paper examnes how country, ndustry and frm characterstcs nteract n general equlbrum to determne natons responses to trade lberalzaton. When frms possess heterogeneous productvty, countres dffer n relatve factor abundance and ndustres vary n factor ntensty, fallng trade costs nduce reallocatons of resources both wthn and across ndustres and countres. These reallocatons generate substantal job turnover n all sectors, spur relatvely more creatve destructon n comparatve advantage ndustres than comparatve dsadvantage ndustres, and magnfy ex ante comparatve advantage to create addtonal welfare gans from trade. The relatve ascendance of hgh-productvty frms wthn ndustres boosts aggregate productvty and drves down consumer prces. In contrast wth the neoclasscal model, these prce declnes dampen and can even reverse the real wage losses of scarce factors as countres lberalze. Keywords: Heckscher-Ohln, nter-ndustry trade, ntra-ndustry trade, trade costs, entry and ext, job creaton and destructon, product varety, Rcardan productvty, creatve destructon, exportng, mssng trade JEL classfcaton: F11, F12, L11 Bernard and Schott gratefully acknowledge research support from the Natonal Scence Foundaton (SES ). Reddng gratefully acknowledges fnancal support from a Phlp Leverhulme Prze. We would lke to thank Pol Antras, Rchard Baldwn, James Harrgan, Marc Meltz, Tony Venables, semnar and conference partcpants at the NBER Sprng Meetngs, CEPR, ETSG, the IMF, Htotsubash, Prnceton, Columba, the NY Fed and London School of Economcs for helpful comments. The vews expressed and any errors are the authors responsblty. 100 Tuck Hall, Hanover, NH 03755, USA, tel: (603) , fax: (603) , emal: andrew.b.bernard@dartmouth.edu Houghton Street, London. WC2A 2AE UK. tel: (44 20) , fax: (44 20) , emal: s.j.reddng@lse.ac.uk 135 Prospect Street, New Haven, CT 06520, USA, tel: (203) , fax: (203) , emal: peter.schott@yale.edu

2 Comparatve Advantage and Heterogeneous Frms 2 1. Introducton How do economes respond to trade lberalzaton? Neoclasscal trade theory, wth ts emphass on comparatve advantage, stresses the reallocaton of resources across ndustres and countres as well as changes n relatve factor rewards, but provdes no role for frm dynamcs. More recent research on heterogeneous frms emphaszes the relatve growth of hgh-productvty frms wthn ndustres but gnores comparatve advantage by consderng just a sngle factor and ndustry. Untl now, very lttle has been known about how these two sources of reallocaton combne n general equlbrum. Ths paper derves new and more realstc predctons about trade lberalzaton by embeddng heterogeneous frms n a model of comparatve advantage and analyzng how frm, country and ndustry characterstcs nteract as trade costs fall. We report a number of new and often surprsng results. In contrast wth the neoclasscal model, we fnd that smultaneous wthn- and across-ndustry reallocatons of economc actvty generate substantal job turnover n all sectors, even whle there s net job creaton n comparatve advantage ndustres and net job destructon n comparatve dsadvantage ndustres. We show that steady-state creatve destructon of frms also occurs n all sectors, but fnd that t s more hghly concentrated n comparatve advantage ndustres than comparatve dsadvantage ndustres. We demonstrate that the relatve growth of hgh-productvty frms rases aggregate productvty n all ndustres, but that productvty growth s strongest n comparatve advantage sectors. The prce declnes assocated wth these productvty ncreases nflate the real-wage gans of relatvely abundant factors whle dampenng, or even potentally overturnng, the real-wage losses of relatvely scarce factors. Fnally, we show that the behavor of heterogenous frms magnfes countres comparatve advantage and thereby creates a new source of welfare gans from trade. Our analyss contrbutes to two lteratures. We advance prevous work on mperfect competton and comparatve advantage, e.g. Helpman and Krugman (1985) 1,byrelaxngthe assumpton that frms are dentcal. We extend more recent research on heterogeneous frms and monopolstc competton, e.g. Meltz (2003), by ntroducng an addtonal ndustry and factor and the complex nteractons to whch they gve rse. 2 Our framework smultaneously explans why some countres export more n certan ndustres than n others (endowmentdrven comparatve advantage); why nonetheless two-way trade s observed wthn ndustres (frm-level horzontal product dfferentaton combned wth ncreasng returns to scale); and why, wthn ndustres engaged n these two forms of trade, some frms export and others do not (self-selecton drven by trade costs). These outcomes, as well as the assumptons underlyng the model, are consstent wth a host of stylzed facts about frmsandtradethathaveemerged across several emprcal lteratures. 3 The framework we develop consders a world of two countres, two factors and two n- 1 See also Krugman (1981), Helpman (1984) and Markusen and Venables (2000). 2 Other nternatonal trade models ncorporatng heterogeneous frms nclude Bernard et al. (2003), Helpman et al. (2004), Meltz and Ottavano (2003) and Yeaple (2005). 3 Taken together, these facts document substantal varaton n productvty across frms, frequent frm entry and ext, postve covaraton n entry and ext rates across ndustres, hgher productvty among exportng frms, the co-exstence of exportng and non-exportng frms n all sectors, no feedback from exportng to frm productvty, and substantal sunk costs of entry nto export markets. See, among others, Bartelsman and Doms (2000), Bernard and Jensen (1995, 1999, 2004), Clerdes, Lach and Tybout (1998), Davs and Haltwanger (1991), Dunne, Roberts and Samuelson (1989), and Roberts and Tybout (1997). For recent emprcal evdence of Heckscher-Ohln forces operatng at the level of ndvdual frms and products wthn ndustres, see Bernard, Jensen and Schott (2005).

3 Comparatve Advantage and Heterogeneous Frms 3 dustres. Each ndustry s populated by a contnuum of frms that each produce a sngle dfferentated varety wthn ther ndustry. Frms are heterogeneous n ther level of productvty (whch s constant durng ther lfetme), ndustres vary n relatve factor ntensty and countres dffer n relatve factor abundance. Frms from a compettve frnge may enter ether ndustry by payng a sunk entry cost. After ths sunk entry cost s pad, frm productvty s drawn from a fxed dstrbuton and observed. The presence of fxed producton costs means that frms drawng a productvty level below some lower threshold (the zero-proft productvty cutoff ) choose to ext the ndustry. Fxed and varable costs of exportng ensure that, of the actve frms n an ndustry, only those who draw a productvty above a hgher threshold (the export productvty cutoff ) fnd t proftable to export n equlbrum. Consderaton of the asymmetrc export opportuntes afforded by comparatve advantage s key to understandng our results. When countres smultaneously transton from autarky to costly trade, frms export opportuntes ncrease and therefore the expected value of enterng an ndustry rses. Entry from the compettve frnge ncreases wth ths expected value, and ths entry drves down the ex post proftablty of producng frms and ncreases the mnmum levelofproductvtyfrms must possess n order to survve. Ths ncrease n the zero-proft productvty cutoff rases the average productvty of frms n an ndustry, thereby nducng aggregate (.e., ndustry-level) productvty growth. In the presence of comparatve advantage, the relatve proftablty of servng export and domestc markets vares wth ndustry factor ntensty and country factor abundance. As a result, comparatve advantage ndustres experence greater productvty gans than comparatve dsadvantage ndustres as trade costs fall because frms n comparatve advantage ndustres fnd t easer to export. The ensung asymmetrc aggregate productvty growth amplfes ex ante comparatve advantage: pre-lberalzaton dfferences n the opportunty costs of producton wden as trade costs fall because countres comparatve advantage ndustres become even more productve than ther comparatve dsadvantage ndustres. Ths magnfes countres orgnal heterogenety and thereby boosts the welfare gans from trade. By ncreasng exporters profts, fallng trade costs also reduce the mnmum level of productvty frms need to export successfully. Export productvty cutoffs declne relatvely more n comparatve advantage ndustres, where potental export profts are hgher. As a result, the relatve range of productvtes over whch frms export s hgher n comparatve advantage ndustres than n comparatve dsadvantage ndustres. Trade lberalzaton also rases average frm sze by promptng exporters to sell more output abroad, and the ncrease n average frm output s largest n comparatve advantage ndustres. These fndngs contrast wth the homogeneous-frm, mperfect-competton model of Helpman and Krugman (1985), where ndustry productvty remans constant and ether all or no frms export followng trade lberalzaton dependng on the value of fxed and varable trade costs. They also dffer from exstng heterogeneous-frm models such as Meltz (2003) by demonstratng that the strength and mportance of frm self-selecton vares wth the nteracton of country and ndustry characterstcs. Our framework provdes a rch settng for analyzng the dstrbutonal mplcatons of nternatonal trade. 4 In the neoclasscal model, fallng trade costs lead to the well-known Stolper-Samuelson result,.e., a rse n the real reward of the abundant factor and a declne n the real reward of the scarce factor. Here, there are two addtonal nfluences on real wages, and both are affected by the endogenous ndustry-level productvty gans noted above. The 4 Dstrbutonal ssues cannot be addressed n the sngle-factor models studed to date n the heterogeneousfrm lterature.

4 Comparatve Advantage and Heterogeneous Frms 4 frst relates to consumers taste for varety. Trade lberalzaton, as n Helpman and Krugman (1985), makes foregn varetes avalable to consumers. Ths ncrease n product varety reduces consumer prce ndces and rases real ncome. In our framework, however, there s an addtonal consderaton: hgher average frm productvty ncreases average frm sze and reduces the mass of domestcally produced varetes. The second nfluence on real wages s unque to our approach and s a more drect consequence of aggregate productvty growth. Increases n ndustry productvty reduce the prce of the average varety n each ndustry and thereby elevate the real ncome of both factors. Thus, even f the real wage of the scarce factor falls durng lberalzaton n our model, ts declne wll be less than t would be n a neoclasscal settng. Moreover, t s possble that the productvty gans assocated wth self-selectng heterogeneous frms are strong enough to rase the real wage of both factors, rrespectve of the net change n varetes. The possblty of such an outcome, whch also depends on model parameters, represents a sharp departure from the neoclasscal model. Our approach also generates novel predctons about the mpact of trade lberalzaton on job turnover. In contrast to a neoclasscal model, whch predcts a smple flow of factors from comparatve dsadvantage to comparatve advantage ndustres, we show that a reducton n trade barrers encourages smultaneous job creaton and job destructon n all ndustres, but that gross and net job creaton vary wth country and ndustry characterstcs. Comparatve dsadvantage ndustres exhbt net job destructon as the layng off of workers by extng, lowerproductvty frms exceeds the hrng by expandng, hgher-productvty frms. Comparatve advantage ndustres, on the other hand, enjoy net job creaton as job loss due to extng frms s domnated by the entrance and expanson of hgher-productvty frms. Surprsngly, steady-state frm falure,.e., the creatve destructon of frms, s hghest n the comparatve advantage ndustry. Each perod a mass of ncumbent frmsdesexogenously whle a separate mass of entrants fals to draw productvty levels above the zero-proft productvty cutoff and therefore exts after employng factors to pay ther entry cost. Though the exogenous death rate s the same n both ndustres, overall steady-state creatve destructon rses wth the zero-proft productvty cutoff and s therefore hgher n comparatve advantage ndustres. Ths mplcaton of the model may explan why workers n comparatve advantage as well as comparatve dsadvantage ndustres report greater perceved job nsecurty as countres lberalze. 5 Fnally, our framework offers a more useful benchmark than exstng theory for predctng the pattern of trade. Recent research reveals that the poor emprcal performance of neoclasscal trade theory s drven by forces not captured n the standard Heckscher-Ohln-Vanek model, ncludng the exstence of trade costs, factor prce nequalty and varaton n technology and productvty across countres. 6 The model we develop here features these generalzatons of the neoclasscal model as endogenous outcomes of the nteracton of frm, ndustry and country characterstcs, and demonstrates how they gve rse to both nter- and ntra-ndustry trade. The remander of the paper s structured as follows. Secton 2 develops the model and solves for general equlbrum under free trade. Secton 3 explores the propertes of the free trade equlbrum, hghlghtng the ways n whch our analyss nests exstng results for homogeneous-frm models of nter- and ntra-ndustry trade. Secton 4 ntroduces fxed and varable trade costs nto the model and Secton 5 examnes the propertes of the costly trade equlbrum. Secton 6 provdes a numercal soluton to the model to llustrate the trajectory 5 See Slaughter and Scheve (2004). 6 See, for example, Bowen et al. (1987), Leamer (1984), Trefler (1993, 1995), Harrgan (1997), Davs and Wensten (2001) and Schott (2003, 2004).

5 Comparatve Advantage and Heterogeneous Frms 5 of endogenous varables for whch closed-form analytcal solutons do not exst. Secton 7 concludes. 2. Free Trade Throughout ths secton we mantan the assumpton that nternatonal trade s costless. We consder a world of two countres, two ndustres, two factors and a contnuum of heterogeneous frms. We make the standard Heckscher-Ohln assumpton that countres are dentcal n terms of preferences and technologes, but dffer n terms of factor endowments. Factors of producton can move between ndustres wthn countres but cannot move across countres. We use H to ndex the skll-abundant home country and F to ndex the skll-scarce foregn country, so that S H /L H > S F /L F where the bars ndcate country endowments Consumpton The representatve consumer s utlty depends on consumpton of the output of two ndustres (), each of whch contans a large number of dfferentated varetes (ω) produced by heterogeneous frms. 7 For smplcty, we assume that the upper ter of utlty determnng consumpton of the two ndustres output s Cobb-Douglas and that the lower ter of utlty determnng consumpton of varetes takes the CES form 8, U = C α 1 1 Cα 2 2, α 1 + α 2 =1,α 1 = α (1) where, to smplfy notaton, we omt the country superscrpt except where mportant. C s a consumpton ndex defned over consumpton of ndvdual varetes, q (ω), wth dual prce ndex, P,defned over prces of varetes, p (ω), Z 1 Z 1 C = q (ω) ρ ρ dω, P = p (ω) 1 σ 1 σ dω, (2) ω Ω ω Ω where σ = 1/(1 ρ) > 1 s the constant elastcty of substtuton across varetes. For smplcty, we assume that the elastcty of substtuton between varetes s the same n the two ndustres, but t s straghtforward to allow ths elastcty to vary Producton Producton nvolves a fxed and varable cost each perod. Both fxed and varable costs use multple factors of producton (sklled and unsklled labor) whose ntensty of use vares across ndustres. All frms share the same fxed overhead cost but varable cost vares wth 7 Allowng one ndustry to produce a homogeneous good under condtons of perfect competton and constant returns to scale (e.g. Agrculture) s a specal case of ths framework where, n one ndustry, the elastcty of substtuton between varetes s nfnte and the fxed producton and sunk entry costs are zero. 8 We use the terms good, sector, and ndustry synonymously whle varety s reserved for a horzontally dfferentated verson wthn an ndustry. All we requre s a utlty functon wth an upper ter where ndustres outputs are substtutes and a lower ter where consumer preferences exhbt a love of varety. See Meltz and Ottavano (2003) for a sngle ndustry model where love of varety takes the quas-lnear form. We concentrate on the CES case to focus on the effects of relatve factor abundance wth homothetc preferences and to make our results comparable wth the exstng nter- and ntra-ndustry trade lterature (Helpman and Krugman 1985).

6 Comparatve Advantage and Heterogeneous Frms 6 frm productvty ϕ (0, ). To avod undue complexty, we assume that the cost functon takes the Cobb-Douglas form, 9 Γ = f + q (w S ) β (w L ) 1 β, 1 >β ϕ 1 >β 2 > 0 (3) where w S s the sklled wage and w L the unsklled wage, and ndustry 1 s assumed to be skll ntensve relatve to ndustry 2. We choose the sklled wage for the numerare and so w S =1. Thepresenceofafxed producton cost mples that, n equlbrum, each frm wll choose to produce a unque varety. The combnaton of monopolstc competton and varable costs that depend on frm productvty follows Meltz (2003). We augment that model by ncorporatng factor ntensty dfferences across sectors and factor abundance dfferences across countres. As a result, Heckscher-Ohln comparatve advantage now plays an mportant role n shapng heterogeneous frms adjustment to nternatonal trade. Consumer love of varety and costless trade mply that all producng frms also export. Snce frms face the same elastcty of demand n both the domestc market, d, andtheexport market, x, and trade s costless, proft maxmzaton mples the same equlbrum prce n the two markets, equal to a constant mark-up over margnal cost: p (ϕ) =p d (ϕ) =p x (ϕ) = (w S) β (wl ) 1 β. (4) ρϕ Wth ths prcng rule, frms equlbrum domestc revenue, r d (ϕ), wll be proportonal to productvty: µ ρp ϕ σ 1 r d (ϕ) =α R (w S ) β (w L ) 1 β. (5) For gven frm productvty ϕ, domestc revenue s ncreasng n the share of expendture allocated to an ndustry, α, ncreasng n aggregate domestc expendture (equals aggregate domestc revenue, R), ncreasng n the ndustry prce ndex, P, whch corresponds to an nverse measure of the degree of competton n a market, and ncreasng n ρ whch s an nverse measure of the sze of the mark-up of prce over margnal cost. Frm revenue s decreasng n own prce and hence n own producton costs. The equlbrum prcng rule mples that the relatve revenue of two frms wth dfferent productvty levels wthn the same ndustry and market depends solely on ther relatve productvty, as s clear from equaton (5): r d (ϕ 00 )=(ϕ 00 /ϕ 0 ) σ 1 r d (ϕ 0 ). Revenue n the export market s determned analogously to the domestc market and, wth frms chargng the same equlbrum prce, relatve revenue n the two markets for a frm of gven productvty, ϕ, wll depend on relatve country sze, R F /R H, and the relatve prce ndex, P F. Wth the prces of ndvdual varetes equalzed and all frms exportng under /P H costless trade, the prce ndces wll be the same n the two countres, P F = P H,andrelatve revenue wll depend solely on relatve country sze. Total frm revenue s the sum of revenue n the domestc and export markets. Under the equlbrum prcng rule, frm profts wll equal 9 The analyss generalzes n a relatvely straghtforward way to any homothetc cost functon, for whch the rato of margnal cost to average cost wll be a functon of output alone. The assumpton that fxed costs of producton are ndependent of productvty captures the dea that many fxed costs, such as buldng and equppng a factory wth machnery, are unlkely to vary substantally wth frm productvty. All the analyss requres s that fxed costs are less senstve to productvty than varable costs.

7 Comparatve Advantage and Heterogeneous Frms 7 revenue from the two markets together scaled by the elastcty of substtuton mnus fxed costs of producton: µ R F r (ϕ) = r d (ϕ)+r x (ϕ) = 1+ R H r d (ϕ) (6) π (ϕ) = r (ϕ) f (w S ) β (w L ) 1 β. σ To produce n an ndustry, frms must pay a fxed entry cost, whch s thereafter sunk. The entry cost also uses sklled and unsklled labor, and we begn by assumng that the factor ntensty of entry and producton are the same, so that the ndustry sunk entry cost takes the form: f e (w S ) β (w L ) 1 β, f e > 0. (7) It s straghtforward to relax the assumpton of common factor ntenstes across the varous stages of economc actvty wthn ndustres. We dscuss below how factor ntensty dfferences between entry and producton lead to addtonal nteractons between country comparatve advantage and the behavor of heterogeneous frms. After entry, frms draw ther productvty, ϕ, from a dstrbuton, g(ϕ), whch s assumed to be common across ndustres and countres. 10 Frms then face an exogenous probablty of death each perod, δ, whch we nterpret as due to force majeure events beyond managers control. 11 A frm drawng productvty ϕ wll produce n an ndustry f ts revenue, r (ϕ), atleast covers the fxed costs of producton,.e. π 0. Ths defnes a zero-proft productvty cutoff, ϕ, n each ndustry such that: r (ϕ )=σf (w S ) β (w L ) 1 β. (8) Frms drawng productvty below ϕ ext mmedately, whle those drawng productvty equal to or above ϕ engage n proftable producton. The value of a frm, therefore, s equal to zero f t draws a productvty below the zero-proft productvty cutoff and exts, or equal to the stream of future profts dscounted by the probablty of death f t draws a productvty above the cutoff value and produces: ( ) X v (ϕ) =max 0, (1 δ) t π (ϕ) (9) ½ =max t=0 0, π (ϕ) δ 10 Combnng the assumptons of dentcal cost functons wthn an ndustry across countres and a common productvty dstrbuton yelds the standard Heckscher-Ohln assumpton of common technologes across countres. It s straghtforward to allow for dfferences n productvty dstrbutons across countres and ndustres. As n prevous trade models wth heterogeneous frms, we treat each frm s productvty level as fxed after entry. Ths assumpton matches the emprcal fndngs of Bernard and Jensen (1999), Clerdes, Lach, and Tybout (1998) and others that there s no feedback from exportng to productvty at the frm level. 11 The assumpton that the probablty of death s ndependent of frm characterstcs follows Meltz (2003) and s made for tractablty to enable us to focus on the complex general equlbrum mplcatons of nternatonal trade for frms, ndustres and countres. An exstng lterature examnes ndustry dynamcs n closed economes where productvty affects the probablty of frm death (see, for example, Hopenhayn 1992 and Jovanovc 1982). ¾.

8 Comparatve Advantage and Heterogeneous Frms 8 The ex post dstrbuton of frm productvty, µ (ϕ), s condtonal on successful entry and s truncated at the zero-proft productvty cutoff: ( g(ϕ) µ (ϕ) = 1 G(ϕ ) f ϕ ϕ (10) 0 otherwse where G(ϕ) s the cumulatve dstrbuton functon for g(ϕ), and1 G(ϕ ) s the ex ante probablty of successful entry n an ndustry. There s an unbounded compettve frnge of potental entrants and, n an equlbrum wth postve producton of both goods, we requre the expected value of entry, V, to equal the sunk entry cost n each ndustry. The expected value of entry s the ex ante probablty of successful entry multpled by the expected proftablty of producng the good untl death, and the free entry condton s thus: V = [1 G(ϕ )] π = f e (w S ) β (w L ) 1 β, (11) δ where π s expected or average frm proftablty from successful entry. Equlbrum revenue and proft n each market are constant elastcty functons of frm productvty (equaton (5)) and, therefore, average revenue and proft are equal respectvely to the revenue and proft ofa frm wth weghted average productvty, r = r ( ϕ ) and π = π ( ϕ ), where weghted average productvty s determned by the ex post productvty dstrbuton and hence the zero-proft productvty cutoff below whch frms ext the ndustry: " Z # 1 eϕ (ϕ 1 σ 1 )= 1 G(ϕ ) ϕ σ 1 g(ϕ)dϕ. (12) ϕ It proves useful for the ensung analyss to re-wrte the free entry condton n a more convenent form. The equaton for equlbrum profts above gves us an expresson for the profts of a frm wth weghted average productvty, π = π ( ϕ ). Gven the equlbrum prcng rule, the revenue of a frm wth weghted average productvty s proportonal to the revenue of a frm wth the zero-proft productvty, r ( ϕ )=( ϕ /ϕ )σ 1 r (ϕ ), where the latter s proportonal to the fxed cost of producton n equlbrum, r (ϕ )=σf (w S ) β (wl ) 1 β. Combnng these results wth the defnton of weghted average productvty above, the free entry condton can be wrtten so that t s a functon solely of the zero-proft productvty cutoff and parameters of the model: V = f Z " µ ϕ σ 1 1# g(ϕ)dϕ = f e. (13) δ ϕ ϕ Terms n factor rewards have cancelled because average frm proftablty and the sunk cost of entry are each proportonal to factor costs, and entry and producton have been assumed to have the same factor ntensty. Snce the expected value of entry n equaton (13) s monotoncally decreasng n ϕ, ths relatonshp alone unquely pns down the zero-proft productvty cutoff ndependent of factor rewards and other endogenous varables of the model. If entry and producton have dfferent factor ntenstes, ths wll no longer be the case. The free entry condton wll then contan terms n factor rewards and, as dscussed further below, movements n relatve factor rewards wll have mportant mplcatons for heterogeneous frms decsons about whether or not to ext the ndustry based on ther observed productvty. Ths way of wrtng the free entry condton also makes clear how the zero-proft productvty cutoff s ncreasng n fxed producton costs, f, and decreasng n the probablty of frm

9 Comparatve Advantage and Heterogeneous Frms 9 death, δ. Hgher fxed producton costs mply that frms must draw a hgher productvty n order to earn suffcent revenue to cover the fxed costs of producton. A hgher probablty of frm death reduces the mass of entrants nto an ndustry, ncreasng ex post proftablty, and therefore enablng frms of lower productvty to survve n the market Goods Markets The steady-state equlbrum s characterzed by a constant mass of frms enterng an ndustryeachperod,m e, and a constant mass of frms producng wthn the ndustry, M. Thus, n steady-state equlbrum, the mass of frms that enter and draw a productvty suffcently hgh to produce must equal the mass of frms that de: [1 G(ϕ )]M e = δm. (14) As noted above, under costless trade, frms charge the same prce n the domestc and export markets and all frms export. Hence, the ndustry prce ndces are equalzed across countres: P F = P H. A frm s equlbrum prcng rule mples that the prce charged for an ndvdual varety s nversely related to frm productvty, whle the prce ndces are weghted averages of the prces charged by frms wth dfferent productvtes, wth the weghts determned by the ex post productvty dstrbuton. Explotng ths property of the prce ndces, we can wrte them as functons of the mass of frms producng n the home country multpled by the prce charged by a home frm wth weghted average productvty, plus the mass of frms producng n the foregn country multpled by the prce charged by a foregn frm wth weghted average productvty: P = P H = P F = hm H p H (eϕ H ) 1 σ + M F p F (eϕ F ) 1 σ 1 1 σ. (15) The larger the mass of frms producng n the two countres, and the lower the prce charged by a frm wth weghted average productvty n the two countres, the lower the value of the common ndustry prce ndex. In equlbrum, we also requre the goods market to clear at the world level, whch requres the share of a good n the value of world producton (n world revenue) to equal the share of a good n world expendture: R 1 + R F 1 R + R F = α 1 = α. (16) 2.4. Labor Markets Labor market clearng requres the demand for labor used n producton and entry to equal labor supply as determned by countres endowments: S 1 + S 2 = S, S = S p + Se (17) L 1 + L 2 = L, L = L p + Le where S denotes sklled labor, L corresponds to unsklled labor, the superscrpt p refers to a factor used n producton, and the superscrpt e refers to a factor used n entry.

10 Comparatve Advantage and Heterogeneous Frms Integrated Equlbrum and Factor Prce Equalzaton In ths secton, we descrbe the condtons for a free trade equlbrum characterzed by factor prce equalzaton (FPE). We begn by solvng for the equlbrum of the ntegrated world economy, where both goods and factors are moble, before showng that there exsts a set of allocatons of world factor endowments to the two countres ndvdually such that the free trade equlbrum, wth only goods moble, replcates the resource allocaton of the ntegrated world economy. The ntegrated equlbrum s referenced by a vector of nne varables - the zero-proft cutoff productvtes n each sector, the prces for ndvdual varetes wthn each ndustry as a functon of productvty, the ndustry prce ndces, aggregate revenue, and the two factor rewards: {ϕ 1, ϕ 2, P 1, P 2, R, p 1 (ϕ), p 2 (ϕ), w S, w L }. All other endogenous varables may be wrtten as functons of these quanttes. The equlbrum vector s determned by nne equlbrum condtons: frms prcng rule (equaton (4) for each sector), free entry (equaton (13) for each sector), labor market clearng (equaton (17) for the two factors), the values for the equlbrum prce ndces mpled by consumer and producer optmzaton (equaton (15) for each sector), and goods market clearng (equaton (16)). Proposton 1 There exsts a unque ntegrated equlbrum, referenced by the vector {ˆϕ 1, ˆϕ 2, ˆP 1, ˆP 2, ˆR, ˆp 1 (ϕ), ˆp 2 (ϕ), ŵ S, ŵ L }. Under free trade, there exsts a set of allocatons of world factor endowments to the two countres ndvdually such that the unque free trade equlbrum s characterzed by factor prce equalzaton (FPE) and replcates the resource allocaton of the ntegrated world economy. Proof. See Appendx 3. Propertes of the Free Trade Equlbrum Under autarky, the relatve skll abundance n the home country leads to a lower relatve prce of sklled labor and of the skll-ntensve good. The openng of trade leads to a convergence n relatve goods prces and relatve factor rewards, so that the relatve sklled wage rses n the skll-abundant home country and falls n the labor-abundant foregn country. The rse n the relatve prce of the skll-ntensve good n the home country results n a reallocaton of resources towards the skll-ntensve sector, as each country specalzes accordng to ts pattern of comparatve advantage. All four theorems of the Heckscher-Ohln model (Rybczynsk, Heckscher-Ohln, Stolper- Samuelson, and Factor Prce Equalzaton) contnue to hold, wth only mnor modfcatons to take nto account monopolstc competton, frm heterogenety and ncreasng returns to scale. Factor prce equalzaton requres that countres endowments are suffcently smlar n the sense that ther relatve endowments of sklled and unsklled labor le n between the ntegrated equlbrum factor ntenstes n the two sectors (Samuelson 1949; Dxt and Norman 1980). Proposton 2 A move from autarky to free trade leaves the zero-proft productvty cutoff and average ndustry productvty unchanged (ϕ and eϕ ). Proof. See Appendx

11 Comparatve Advantage and Heterogeneous Frms 11 The ntuton for ths result s that, under free trade, all frms export and are affected symmetrcally by the openng of trade. Frms of all productvtes experence ncreased demand for ther products n export markets and reduced demand n domestc markets as a result of entry by mported varetes. The mass of frms producng domestcally n each ndustry, M, wll change as countres specalze accordng to comparatve advantage, and ths wll change the mass of frms producng at each level of productvty, µ (ϕ )M,whereµ (ϕ ) s the ex post productvty dstrbuton. Because frms of all productvtes are affected symmetrcally, there s no change n the zero-proft productvty cutoff below whch frms ext the ndustry and no change n average ndustry productvty. Ths result provdes an mportant benchmark and clarfes the analyss of costly trade below, where we show that wthn-ndustry reallocatons of resources between frms of dfferent productvtes are drven by the uneven effects of trade on exporters and non-exporters. However, we cauton that the zero-proft productvty cutoff and average ndustry productvty wll be affected even under free trade f entry and producton have dfferent factor ntenstes. Relatve factor rewards change followng the openng of trade, and f entry and producton have dfferent factor ntenstes, these changes n relatve factor rewards wll affect the value of entry (through frm profts) and entry costs dfferentally, resultng n a change n the equlbrum zero-proft productvty cutoff. 12 As countres specalze accordng to comparatve advantage, the mass of frms actve n the comparatve advantage ndustry wll rse relatve to the comparatve dsadvantage ndustry. Snce n equlbrum the flow of successful entrants equals the flow of dyng frms, the mass of entrants n an ndustry s proportonal to the mass of frms, M e =(δ/ [1 G (ϕ )]) M,andso the rse n the relatve mass of frms n the comparatve advantage ndustry wll be reflected n a rse the relatve amount of entry and ext. 4. Costly Trade The assumpton that trade s perfectly costless s at odds wth recent emprcal evdence of szeable trade costs. 13 Ths emprcal lterature suggests that there are mportant fxed costs of enterng foregn markets, such as the costs of acqurng nformaton about foregn markets, developng approprate marketng strateges and buldng dstrbuton networks. 14 In ths secton, we ntroduce fxed and varable costs of trade as n Meltz (2003). The basc setup remans the same as under free trade. However, n order to export a manufacturng varety to a partcular market, a frm must ncur a fxed export cost, whch uses both sklled and unsklled labor wth the same factor ntenstes as producton. In addton, the frm may also face varable trade costs, whch take the standard ceberg form whereby a fracton τ > 1 unts of a good must be shpped n ndustry n order for one unt to arrve. These fxed and varable trade costs mean that, dependng on ther productvty, some frms may choose not to export n equlbrum. We show how these trade costs nteract wth comparatve advantage to determne responses to trade lberalzaton that vary across frms, ndustres and countres. Factor ntensty and fac- 12 For example, f entry s more skll-ntensve than producton, the fall n the relatve sklled wage n the labor abundant country followng the openng of trade wll reduce the sunk costs of entry relatve to the expected value of entry, nducng ncreased entry, an ncrease n the zero-proft productvtycutoff, andanmprovementn aggregate ndustry productvty. See Flam and Helpman (1987) for an exploraton of factor ntensty dfferences between fxed and varable producton costs n a homogeneous frm model of trade. 13 See, n partcular, Anderson and van Wncoop (2004) and Hummels (2001). 14 See, for example, Roberts and Tybout (1997) and Bernard and Jensen (2004).

12 Comparatve Advantage and Heterogeneous Frms 12 tor abundance, whch have tradtonally been vewed as determnng reallocatons of resources between ndustres, also play an mportant role n shapng wthn-ndustry reallocatons of resources from less to more productve frms Consumpton and Producton Proft maxmzaton mples that equlbrum prces are agan a constant mark-up over margnal cost, wth export prces a constant multple of domestc prces due to the varable costs of trade: 15 p H x(ϕ) =τ p H d (ϕ) =τ (ws H)β (w H L ) 1 β. (18) ρϕ Gven frms prcng rules, equlbrum revenue n the export market s proportonal to that n the domestc market. However, the prce dfferences between the two markets mean that relatve revenue n the export market now depends on varable trade costs. Furthermore, prce ndces now vary across the two countres due to varaton n the mass of frms producng n an ndustry, dfferent prces charged by frms n domestc and export markets (varable trade costs), and the exstence of both exporters and non-exporters (fxed and varable trade costs). As a result, relatve prce ndces enter as a determnant of relatve revenue n the export market: r H x(ϕ) =τ 1 σ µ P F σ 1 µ R F P H R H rd H (ϕ). (19) The wedge between revenue n the export and domestc markets n equaton (19) wll typcally vary across countres and ndustres, and wll prove mportant n determnng how trade lberalzaton ncreases the expected value of entry nto an ndustry. Total revenue receved by a home frm s: r r H d H(ϕ) f t does not export (ϕ) = ³ rd H(ϕ) 1+τ 1 σ P F σ 1 ³ R F (20) f t exports. R H P H Consumer love of varety and fxed producton costs mply that no frm wll ever export wthout also producng for the domestc market. Therefore, we may separate each frm s proft nto components earned from domestc sales, π H d (ϕ), and foregn sales, πh x (ϕ), wherewe apporton the entre fxed producton cost to domestc proft andthefxed exportng cost to foregn proft: 16 π H d (ϕ) = rh d (ϕ) σ π H x(ϕ) = rh x (ϕ) σ f (w H S ) β (w H L ) 1 β (21) f x (w H S ) β (w H L ) 1 β 15 In the analyss below, we wrte out expressons for home explctly; those for foregn are analogous. 16 Ths s a convenent accountng devce whch smplfes the exposton. Rather than comparng revenue fromexportngtothefxed cost of exportng, we could equvalently compare the sum of domestc and export revenue to the sum of fxed producton and exportng costs.

13 Comparatve Advantage and Heterogeneous Frms 13 where the fxed cost of exportng requres both sklled and unsklled labor, f x (ws H)β (w H L ) 1 β. 17 A frm whch produces for ts domestc market also exports f π H x (ϕ) > 0, andtotalfrm proft s gven by: π H (ϕ) =π H d (ϕ)+max 0,π H x(ϕ) ª. (22) 4.2. Decson to Produce and Export After frms have pad the sunk cost of enterng an ndustry, they draw ther productvty, ϕ, from the dstrbuton g(ϕ). There are now two cutoff productvtes, the costly-trade zero-proft productvty cutoff, ϕ H,abovewhchfrmsproduceforthedomestcmarket and the costly-trade exportng productvty cutoff, ϕ H x,abovewhchfrms produce for both the domestc and export markets: rd H (ϕ H ) = σf (ws H ) β (wl H ) 1 β (23) rx(ϕ H H x ) = σf x (ws H ) β (w L H ) 1 β. Combnng these two expressons, we obtan one equaton lnkng the revenues of a frm at the zero-proft productvty cutoff to those of a frm at the exportng productvty cutoff. A second equaton s obtaned from the relatonshp between the revenues of two frms wth dfferent productvtes wthn the same market, r d (ϕ 00 )=(ϕ 00 /ϕ 0 ) σ 1 r d (ϕ 0 ),andfromthe relatonshp between revenues n the export and domestc markets, equaton (19). The two equatons together yeld an equlbrum relatonshp between the two productvty cutoffs: ϕ H x = Λ H ϕ H µ P where Λ H H τ P F µ R H f 1 σ 1 x. (24) R F f The exportng productvty cutoff wll be hgh relatve to the zero-proft productvty cutoff,.e. only a small fracton of frms wll export, when the fxed cost of exportng, f x, s large relatve to the fxed cost of producton, f. In ths case, the revenue requred to cover the fxed export cost s large relatve to the revenue requred to cover the fxed producton cost, mplyng that only frms of hgh productvty wll fnd t proftable to serve both markets. The exportng productvty cutoff wll also be hgh relatve to the zero-proft productvty cutoff when the home prce ndex, P H, s hgh relatve to the foregn prce ndex, P F, and the home market, R H, s large relatve to the foregn market, R F. Agan, only hgh-productvty frms receve enough revenue n the relatvely small and compettve foregn market to cover the fxed cost of exportng. Fnally, hgher varable trade costs ncrease the exportng productvty cutoff relatve to the zero-proft productvty cutoff by ncreasng prces and reducng revenue n the export market. For values of Λ k > 1, there s selecton nto markets,.e. only the most productve frms export. Snce emprcal evdence strongly supports selecton nto export markets and the nteror equlbrum s the most nterestng one, we focus throughout the rest of the paper on parameter values where Λ k > 1 across countres k and ndustres We assume that fxed export costs use domestc factors of producton, consstent wth the dea that resources must be set asde to acqure nformaton about and to enter foregn markets. One could also ntroduce a component of fxed export costs that employ factors of producton n the foregn market. However, ths would ntroduce Foregn Drect Investment (FDI) nto the model and dstract from our focus on the relatonshp between nternatonal trade, heterogeneous frms and comparatve advantage. See Helpman, Meltz and Yeaple (2004) for an analyss of FDI n a sngle-factor model of heterogeneous frms. 18 For emprcal evdence on selecton nto export markets, see Bernard and Jensen (1995, 1999, 2004), Clerdes, Lach and Tybout (1998), and Roberts and Tybout (1997).

14 Comparatve Advantage and Heterogeneous Frms 14 Frms decsons concernng producton for the domestc and foregn markets are summarzed graphcally n Fgure 1. Of the mass of frms Me H who enter the ndustry each perod, afracton,g(ϕ H ), draw a productvty level suffcently low that they are unable to cover fxed producton costs and ext the ndustry mmedately; a fracton, G(ϕ H x ) G(ϕ H ), draw an ntermedate productvty level such that they are able to cover fxed producton costs and serve the domestc market, but are not proftable enough to export; and a fracton, G(ϕ H x ), draw a productvty level suffcently hgh that t s proftable to serve both the home and foregn markets n equlbrum. The ex ante probablty of successful entry s [1 G(ϕ H )] and the ex ante probablty of exportng condtonal on successful entry s: χ H = [1 G(ϕ H x )] [1 G(ϕ H )]. (25) 4.3. Free Entry In an equlbrum wth postve producton of both goods, we agan requre the expected value of entry, V H, to equal the sunk entry cost n each ndustry. The expected value of entry s now the sum of two terms: the ex ante probablty of successful entry tmes the expected proftablty of producng the good for the domestc market untl death and the ex ante probablty of successful entry tmes the probablty of exportng tmes the expected proftablty of producng the good for the export market untl death: V = [1 G(ϕ )] δ H π d + χ H π H x = fe (w S ) β (w L ) 1 β (26) where average proftablty n each market s equal to the proft ofafrm wth weghted average productvty, π H d = πh d (eϕh ) and π H x = πh x (eϕh x). Some lower-productvty frms do not export whch leads to hgher weghted average productvty n the export market than n the domestc market. Weghted average productvty s defned as n equaton (12), where the relevant cutoff for the domestc market s the zero-proft productvty, ϕ, and the relevant cutoff for the export market s the exportng productvty, ϕ x. Followng the same lne of reasonng as under free trade, we can wrte the free entry condton as a functon of the two productvty cutoffs and model parameters: V H = f δ Z ϕ H " µ ϕ σ 1 ϕ H 1# g(ϕ)dϕ + f Z x δ ϕ H x " µ ϕ σ 1 ϕ H 1# g(ϕ)dϕ = f e. (27) x The expected value of entry under costly trade equals the expected value of entry under autarky plus a second term reflectng the expected profts to be derved from servng the export market. The closer the exportng productvty, ϕ x, les to the zero-proft productvty cutoff, ϕ, the larger ths second term and the larger the ncrease n the expected value of entry from openng the economy to costly trade. In equlbrum, ϕ x and ϕ are related accordng to equaton (24). The dstance n productvty between the least productve frm able to survve n the domestc market and the least productve frm able to survve n the export market depends on ndustry prce ndces and country sze, and wll hence vary systematcally across countres and ndustres as consdered further below.

15 Comparatve Advantage and Heterogeneous Frms Goods and Labor Markets Agan, n steady-state, the mass of frms that enter an ndustry and draw a productvty hgh enough to produce equals the mass of frms that de. Usng the equlbrum prcng rule, the ndustry prce ndces may be wrtten as: P H = M H ³ p H d (eϕh ) 1 σ + χ F M F 1 ³ 1 σ τ p F 1 σ d (eϕf x). (28) In general, the prce ndces for an ndustry wll now vary across countres because of dfferences n the mass of domestc and foregn frms, dfferences n domestc and export prces (varable trade costs captured by τ ), and dfferences n the proporton of exportng frms (fxed and varable trade costs reflected n χ F and eϕ F x ). In equlbrum, we also requre that the sum of domestc and foregn expendture on domestc varetes equals the value of domestc producton (total ndustry revenue, R )foreach ndustry and country: R H = α R H M H µ p H d ( ϕ H ) P H 1 σ + α R F χ H M H µ τ p H d ( ϕh x ) 1 σ (29) where, wth free entry nto each ndustry, total ndustry revenue equals total labor payments, R H = ws HSH + wl HLH. Requrng that equaton (29) holds for all countres and ndustres mples that the goods markets clear at the world level. The frst term on the rght-hand sde of equaton (29) captures home expendture on home varetes, whch equals the mass of varetes sold domestcally, M H, tmes expendture on a varety wth weghted average productvty. 19 The second term on the rght-hand sde of equaton (29) captures foregn expendture on home varetes. The key dfferences between the two terms are that only some of the varetes produced n home are exported to foregn (captured by the probablty of exportng χ H ), the prce charged by home producers n the export market s hgher than n the domestc market (varable trade costs τ ), and the weghted average productvty n the export market s greater than n the domestc market because of entry nto export markets only by hgher productvty frms. P F 4.5. Costly Trade Equlbrum The costly trade equlbrum s referenced by a vector of thrteen varables n home and foregn: {ϕ k 1, ϕ k 2, ϕ k 1x, ϕ k 2x, P 1 k, P 2 k, pk 1 (ϕ), pk 2 (ϕ), pk 1x (ϕ), pk 2x (ϕ), wk S, wk L, Rk } for k {H, F}. All other endogenous varables may be wrtten as functons of these quanttes. The equlbrum vector s determned by the followng equlbrum condtons for each country: frms prcng rule (equaton (18) for each ndustry and for the domestc and export market separately), free entry (equaton (27) for each sector), the relatonshp between the two productvty cutoffs (equaton (24) for each sector), labor market clearng (equaton (17) for the two factors), the values for the equlbrum prce ndces mpled by consumer and producer optmzaton (equaton (28) for each sector), and world expendture on a country s varetes equals the value of ther producton (equaton (29) for each sector). 19 Expendture on a varety wth weghted average productvty depends negatvely on the domestc prce of such a varety, p H d( ϕ H ), postvely on the prce of competng varetes (ncludng those produced n foregn and exported to home) as summarzed n the domestc prce ndex, P H, postvely on the share of consumer expendture devoted to a good n equlbrum, α, and postvely on aggregate home expendture (equals aggregate home revenue, R H ).

16 Comparatve Advantage and Heterogeneous Frms 16 Proposton 3 There exsts a unque costly trade equlbrum referenced by the par of equlbrum vectors, {ˆϕ k 1, ˆϕ k 2, ˆϕ 1x, k ˆϕ k 2x, ˆP 1 k, ˆP 2 k, ˆpk 1 (ϕ), ˆpk 2 (ϕ), ˆpk 1x (ϕ), ˆpk 2x (ϕ), ŵk S, ŵk L, ˆR k } for k {H, F}. Proof. See Appendx. 5. Propertes of the Costly Trade Equlbrum The combnaton of multple factors, multple countres, country asymmetry, frm heterogenety, and trade costs means that there are no longer closed form solutons for several key endogenous varables of the model. Nonetheless, we are able to derve a number of analytcal results concernng the effects of openng a closed economy to costly trade. We begn by developng these analytcal results. In secton 6, we numercally solve the model, llustrate the analytcal results for a partcular parameterzaton of the model, and trace the evoluton of the endogenous varables for whch no closed form soluton exsts Productvty and Exportng Proposton 4 The openng of costly trade ncreases the zero-proft productvty cutoff and average ndustry productvty n both ndustres. (a) Other thngs equal, the ncrease n the zero-proft productvty cutoff and average ndustry productvty wll be greater n a country s comparatve advantage ndustry. (b) Other thngs equal, the exportng productvty cutoff wll be closer to the zero-proft productvty cutoff n a country s comparatve advantage ndustry. Proof. See Appendx Ths proposton s drven by the fact that, wth trade costs, not all frms fnd t proftable to export. As a result, trade has a dfferental effect on the profts of exportng and nonexportng frms. Movng from autarky to costly trade, the ex post profts of more productve exportng frms rse. Ths ncreases the expected value of entry n each ndustry because there s a postve ex ante probablty of drawng a productvty suffcently hgh to export. Ths nduces more entry and so rases the mass of actve frms n the ndustry. As a result, the ndustry becomes more compettve and the ex post profts of low-productvty frms that only serve the domestc market are reduced. Therefore, some low-productvty domestc frms no longer receve enough revenue to cover fxed producton costs and ext the ndustry. The zero-proft productvty cutoff, ϕ, and average ndustry productvty, eϕ,bothrse. 20 Profts n the export market are larger relatve to profts n the domestc market n comparatve advantage ndustres. Therefore, followng the openng of trade, the ex post profts 20 Startng from autarky and reducng trade costs, the zero proft productvtycutoff wll rse as long as there s selecton nto export markets. As trade costs contnue to fall, there wll eventually come a pont where all frms export. From ths pont onwards, further reductons n trade costs ncrease ex post proftablty for all frms, reducng the value of the zero proft productvty above whch frms can proftably produce, untl free trade s attaned at whch pont the cutoff takes the same value as under autarky. The same values for the zero proft productvty cutoff under autarky and free trade follow from the cutoff beng ndependent of market sze and relatve factor prces (under free trade, the world s a sngle ntegrated market). We focus on parameter values where there s selecton nto export markets snce ths s the emprcally relevant case.