Comparative Advantage, Monopolistic Competition, and Heterogeneous Firms in a Ricardian Model with a Continuum of Sectors

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1 Comparative Avantage, Monopolistic Competition, an Heterogeneous Firms in a Ricarian Moel with a Continuum of Sectors Tomohiro Ara Fukushima University July 25 Abstract Why oes the fraction of firms that export vary with countries comparative avantage? To aress this question, I evelop a general-equilibrium Ricarian moel of orth-south trae in which both institutional quality an firm heterogeneity play a key role in etermining international trae flows. Because of contractual frictions that vary across countries an sectors, orth with better institutions prouces an exports relatively more in sectors where prouction is more institutionally epenent. In aition, institution-inuce comparative avantage makes it relatively easier for orthern heterogeneous firms to incur export costs in more contract-epenent sectors, thereby leaing to a higher exporters percentage. Keywors: Comparative avantage, firm heterogeneity, log-supermoularity, relative wage JEL Classification umbers: D23, F2, F4, L33, O43 This stuy is conucte as a part of the Project Trae an Inustrial Policies in a Complex Worl Economy unertaken at Research Institute of Economy, Trae an Inustry RIETI). I am eeply grateful to Arghya Ghosh an Hoaka Morita for invaluable guiance an encouragement, an to Richar Balwin, Anrew Bernar, Arpita Chatterjee, Qingyuan Du, Taiji Furusawa, Jota Ishikawa, Keith Maskus, Phillip McCalman, Devashish Mitra, Raymon Riezman, icolas Schmitt, an seminar an conference participants at various institutions for helpful comments an suggestions. I have also benefite from financial support from USW, RIETI an JSPS uner grant # All errors are my own. Faculty of Economics an Business Aministration, Fukushima University, Fukushima , Japan. aress: tomohiro.ara@gmail.com.

2 Introuction A growing boy of empirical evience using firm-level ata has extensively reveale that the extent to which firms participate in exporting varies systematically across countries an sectors. These works have foun that, in evelope countries, the percentage of firms that export tens to be substantially higher in sectors where prouction technology is more complex an customize such as chemical proucts), an this percentage steaily eclines as sectors prouction requires simpler an more generic technology such as apparel proucts). In eveloping countries, on the other han, the opposite patterns are typically observe: the ratio of exporting firms to overall firms tens to be notably higher resp. lower) in simpler resp. more complex) sectors. At the same time, these stuies have also ocumente that exporting occurs in every major manufacturing sector of both evelope an eveloping countries: even in strong comparative isavantage sectors, a small fraction of firms o export. Why oes the fraction of firms that export vary with countries comparative avantage? To aress this question, combining the recent empirical fining quantifie by Levchenko 27) an unn 27) with firm heterogeneity of Melitz 23), I evelop a general-equilibrium Ricarian moel of orth-south trae in which both institutional quality an firm heterogeneity play a key role in etermining international trae flows. Following Levchenko s an unn s fining, the moel assumes that each country is ifferent in terms of contracting institutions, an each sector is ifferent in terms of contract intensity. Moreover, each firm is ifferent in terms of its prouctivity à la Melitz. These three-imensional ifferences in countries, sectors an firms characteristics enogenously pin own patterns of specialization an trae in equilibrium. Although the current paper focuses on institutional factors as a source of countries comparative avantage, they can be interprete more broaly. All what matters for the main results is that labor prouctivity stemming from countries an sectors characteristics satisfies log-supermoularity. To investigate the role of countries an sectors characteristics, I buil on the concept of partial contractibility, originally evelope by Acemoglu, Antràs, an Helpman 27). I consier an environment in which orth has better institutions for partially ex-ante contractible activities than South, whereas customize sectors make use of relationship-specific investments intensively more than generic sectors. Because of these contractual frictions that vary across countries an sectors, aggregate output ifferences emerge. In contrast to Acemoglu et al., I o not explicitly examine the interaction between contractual incompleteness an technological complementarity by simply assuming that prouction in customize generic) sectors is more less) epenent on institutions. See Bernar, Jensen, Reing, an Schott 27) for the Unite States, Tomiura 27) for Japan, an Lu 2) for China, respectively. For example, Bernar et al. 27, Table 2) report that, as of 22, 36 percent 8 percent) of U.S. firms export in a chemical sector an apparel sector), whereby a more customize sector tens to exhibit a higher percentage of exporters across 2 sectors. Conversely, Lu 2, Figure ) shows that, as of 25, aroun 6 percent less than 2 percent) of Chinese firms export in cloth an fur sectors a chemical sector), inicating that there exists a clear negative relationship between export participation an the capital-labor ratio across 29 sectors. While the current paper tries to rationalize this relationship from log-spermoularity in countries an sectors characteristics, theoretical results shoul be interprete with caution as the sectors in question amittely iffer along several other imensions, an the ifferences in export participation observe in these ata cannot be purely attribute to this property.

3 Instea, I exten their framework by allowing countries institutional quality an sectors institutional epenency to obey the Ricarian law of comparative avantage. This elaboration makes it possible to capture the aggregate relationship between country an sector characteristics neatly in a way such that orth with better institutions prouces an exports relatively more in sectors where prouction is more institutionally epenent. 2 To formalize the higher tenency to export participation in comparative avantage sectors, I incorporate firm-level ifferences in prouctivity. Since exporting requires fixe export costs that less prouctive firms cannot cover, only a small fraction of firms are able to export. The variation in this fraction is further reinforce by institution-inuce comparative avantage in my setup, because orthern Southern) firms are relatively better at proucing in more less) contract-epenent sectors, which in turn softens the relative buren of incurring export costs. As a result, compare to comparative isavantage sectors of a counterpart country, relatively less prouctive firms can export in a country s comparative avantage sectors. This mechanism explains why the stronger each country s comparative avantage is, the smaller the prouctivity cutoff for exporting becomes, thereby leaing to a higher exporters percentage. Moeling the share of firms that export helps to unerstan whether ifferences in aggregate output ue to comparative avantage are achieve through ifferences in the extensive an intensive margins. Since the share of exporters is efine as the ratio of the mass of exporters to the mass of omestic firms, calculating this share requires both aggregate omestic sales an aggregate exports to be ecompose into the mass of firms extensive margin) an average sales per firm intensive margin). While it is not surprising that total omestic sales an total exports increase with countries comparative avantage strength, this increase comes mainly from the extensive margins net change in the intensive margins is generally ambiguous an is specially inepenent uner the case of a Pareto istribution). Further, the increase in these two extensive margins is not the same magnitue; inee, the fact that the share of exporters is increasing in the egree of comparative avantage suggests that the extensive margin of exports increases with comparative avantage more significantly than the extensive margin of omestic prouction. Clearly, these insights cannot be obtaine when simply analyzing how aggregate exports vary with comparative avantage. Following the new literature on institutions an trae, I employ contracting institutions more specifically contract enforcement rather than the classical eterminants of international trae such as capital or un)skille labor) to rationalize the stylize fact of export participation. There are at least three reasons for this. First, countries abilities to enforce written contracts can have quantitatively larger impacts on comparative avantage than countries factor enowments. For instance, unn 27) estimates that contract enforcement explains more of the global pattern of trae than countries enowments of physical capital an skille labor combine. Secon, as 2 There is mounting evience on the link between countries institutions an sectors types that affects the pattern of trae. For instance, evising a measure of input customization the share of a sector s inputs that are not sol in organize exchanges), unn 27) shows that countries with better contract enforcement export relatively more in sectors for which relationship-specific investments are more important. Similarly, Manova 28) fins evience that trae liberalizations inuce countries with better financial systems to export relatively more in sectors for which financial requirements are more important. 2

4 rigorously emonstrate by Costinot 29a), this empirical evience is appropriately capture by Ricarian) institutional ifferences with log-supermoularity in country an sector characteristics. 3 In this specification, the characteristics of firms in terms of their prouctivity are an inepenent factor of the variation in export participation as iscusse above. Finally, a Ricarian view of institutional ifferences can give a complementary explanation for Bernar, Reing, an Schott s 27) factor-enowment-riven comparative avantage theory. Although the main result is strikingly similar, I show that some phenomena e.g., home-market effects) are better unerstoo through a lens of Ricarian sources of comparative avantage. In this paper, I o not attempt to explain why orth has better institutions than South, why customize sectors epen heavily on institutions more than generic sectors, or why some firms are more prouctive than others. Taking these country, sector, an firm characteristics as given, I instea set out to explore how contracting institutions an heterogeneous firms jointly shape an enogenous pattern of trae. By so oing, the moel shows that orth with better institutions gains a comparative avantage in contract-epenent sectors an is a net exporter of customize proucts in intra-inustry trae. South with worse contracting institutions, on the other han, is shown to be a net exporter of generic proucts. Moreover, within sectors in bilateral trae flows, the fraction of exporters is monotonically increasing in countries comparative avantage strength. These results, both of which are consistent with firm-level empirical research, hol even if orth has an absolute avantage in institutional quality in any sector, an there exists no technological ifference in terms of firm prouctivity istributions) between the two countries. This paper is closely relate to two branches of the recent literature of international trae. The first is an emerging literature on institutions an trae e.g., Antràs, 25; Acemoglu et al., 27; Costinot, 29b). These papers show that, even in the absence of inherent technological ifferences, cross-country institutional ifferences can enogenously generate comparative avantage, which is at the heart of my moel as well. In this stran of the papers, however, all firms are generally treate as ientical an therefore every firm is able to export everywhere. 4 In the real worl, a large proportion of firms o not export even in strong comparative avantage sectors. The current paper emonstrates that not only is comparative avantage enogenously inuce by institutions, but the fraction of exporters is higher in stronger comparative avantage sectors, as suggeste by the existing evience. Another branch of the relate literature is the so-calle heterogeneous-firm moel of trae, especially evelope by the seminal work of Melitz 23). While the Melitz moel is successful in explaining the exporters behaviors among evelope countries orth-orth trae), recent empirical evience has pointe out that this moel is less suitable for the stuy of bilateral trae flows 3 As far as the pattern of specialization an trae is central, the moeling of technological an institutional ifferences is isomorphic Costinot, 29a). While I interpret institutions as a country s ability to alleviate contractual frictions between firms an suppliers as in Acemoglu et al. 27), the results o not change at all even if they are interprete as a country s ability to use a given technology as in usual Ricarian moels. All what matters is that labor prouctivity stemming from countries an sectors characteristics satisfies log-supermoularity. 4 Acemoglu et al. 27) introuce firm heterogeneity in the egree of complementarity among inputs, but all proucts are assume to be freely trae an hence all firms export in their moel. 3

5 between ifferent countries orth-south trae), as exemplifie by Lu 2) who analyzes Chinese firm-level manufacturing ata. A number of papers among others, Demiova 28), Fan, Lai, an Qi 2), an Okubo 29) incorporate the asymmetry of countries in this setting. My approach iffers from these papers, because I focus on the role of wage ifferentials in orth-south trae, 5 an because most results hol without specifying any parameterization of firm prouctivity istributions. More importantly, none of these papers shes new light on the interplay between institutions an comparative avantage. Although I restrict the analysis only to an open economy an abstract from welfare implications for expositional simplicity, it is straightforwar to exten the current setup to see the impact of trae on inter-/intra-sectoral resource allocations an welfare gains from trae. Finally, this paper is also relate to the heterogeneous-firm literature on factor-proportions theory, especially to Bernar et al. 27) as argue above. Using Helpman-Krugman s 985) two-factor moel, they provie a rich framework for analyzing istributional consequences from trae, a feature missing in this Ricarian one-factor moel. Their analysis, however, primarily applies to the situation in which two countries are not too ifferent, an numerical simulations are require for outsie factorprice-equalization regions. In contrast, it is possible in the current paper to analytically examine trae patterns between any two countries of arbitrary country size with enogenous wage ifferentials) by sacrificing istributional issues via trae liberalization. A further istinction of this paper is in aressing Krugman s 98) home-market effect. I show that, ue to selection into omestic an export markets that varies with comparative avantage, the home-market effect works oppositely for the extensive/intensive margins of omestic prouction an those of exports between orth an South, leaing the share of exporters to change oppositely to the relative country size. 2 Setup Consier a worl composing of two large countries, orth an South, i {, S}. For notational simplicity, country superscript i is roppe unless neee in this section. Deman Each country is populate by a mass L of ientical consumers who evote their income into ifferentiate goos of a continuum of sectors over an interval [, ]. The preferences of a representative consumer are Cobb-Douglas across sectors an C.E.S. Dixit-Stiglitz within sectors: U = λz) ln Qz)z, where Qz) = [ v V z) ] σ qz, v) σ v, 5 Wage ifferentials are one of the most prominent factors that have triggere large trae flows among issimilar countries in the past two ecaes. For instance, noting that in 26 for the first time the Unite States i more trae in manufacture goos with eveloping countries than evelope countries, Krugman 28) asserts that this is largely ue to the wage ifferentials between the U.S. an eveloping countries: China s an Mexico s wages are respectively only 4 percent an 3 percent of the U.S. level. 4

6 is aggregate consumption of varieties in sector z. V z) is the mass of available goos within the sector, which potentially inclues both omestic an foreign varieties. Given this aggregate goo Qz), its ual aggregate price is given by P z) = [ pz, v) σ v v V z) λz) enotes a constant share of expeniture spent on sector z, which is ientical between the two countries. Letting Rz) = P z)qz) an Y = wl respectively enote aggregate expeniture in sector z an aggregate labor income in the economy, λz) is efine as ] σ. λz) = P z)qz) Y = Rz) wl, which must satisfy λz)z =. Therefore, the sum of aggregate sector expeniture equals aggregate labor income Rz)z = wl). Letting Xz) = λz)y enote labor income spent on sector z, the above preferences generate eman functions for ifferentiate variety v in sector z: qz, v) = Az)pz, v) σ, where Az) = Xz)P z) is the inex of aggregate market eman. In the following, I focus on a particular variety in sector z an rop variety subscript v from relevant variables. Before proceeing further, it is important to note that there is no homogeneous-goo sector with nontrae costs, an wage rates w cannot be normalize between orth an South. 6 This structure of the preferences is similar to that of Krugman 98), an more recently to that of Antràs 25) an Okubo 29). ote also that while the elasticity of substitution between any two varieties within a sector is assume to be greater than one σ > ), the elasticity of substitution between any varieties across sectors is unity. The unit elasticity of substitution implies that firm behavior in each sector can be analyze inepenently. Prouction There is a continuum of firms that prouce a ifferent variety in each sector. Labor is the only factor of prouction to prouce a variety an firms face a perfectly elastic supply of labor at each country size L. Since labor is completely mobile across sectors but immobile across countries as in conventional Ricarian moels, a wage rate w is the same across sectors within a country but is ifferent across countries. 6 By excluing a homogeneous-goo sector, it is possible to explicitly investigate the role of the relative wage or factoral terms of trae Matsuyama, 28) in comparative avantage, which is an orthoox practice in Ricarian moels. While introucing a homogeneous goo à la Helpman an Krugman 985) woul help to simplify the analysis, empirical evience suggests that the bulk of recent trae flows cannot be capture without a terms-of-trae effect between evelope an eveloping countries as emphasize in Introuction. 5

7 Following Krugman 98) an Melitz 23), firm technology is summarize in a linear cost function of output q: f + q θϕ,z,µ) l = = f + f x + τq θϕ,z,µ) = f x + q ϕµz) τq ϕµz) if omestic prouction, if exporting, where θ,, ) is labor prouctivity, f is a fixe cost for omestic prouction, f x is a fixe cost for exporting, an τ ) is a iceberg transport cost note in particular that the fixe costs, f an f x, are being incurre in units of labor). These costs are ientical across countries an sectors. A few points are in orer for this specification. First, labor prouctivity θ,, ) epens on three factors: i) firm-specific ϕ; ii) sector-specific z; an iii) country-specific µ. In Melitz 23), he consiers symmetric countries, implying that a country-specific factor µ is ignorable. He also focuses on one sector within each country, leaing a sector-specific factor z to be absent from his analysis. Therefore, only a firm-specific factor ϕ is important in the Melitz moel. In the current moel, by contrast, since the two countries are asymmetric an there is a continuum of sectors, the three factors jointly affect labor prouctivity. It follows from this cost function that the country-specific factor µ ), ) affects firms variable costs only leaving fixe costs ientical) an labor prouctivity is greater if µ ) is closer to one. I assume that µ ) is relate to a country s ability to enforce written contracts between firms an suppliers as will be shown in the next subsection) an is referre to as partial contractibility in this paper. Secon, I aopt a reuce form of labor prouctivity: θϕ, z, µ) = ϕµz). While this form is use for simplicity, one can justify this simplification from Costinot s 29a) log-supermoular argument. He efines Ricarian technological ifferences as labor prouctivity that satisfies θϕ, z, µ) = fϕ) az, µ), where a, )> ) is the unit labor requirement efine as the inverse of labor prouctivity), an shows that Ricarian sources of comparative avantage hol if /a, ) is log-supermoular i.e., 2 z µ ln az,µ) 2 z µ ln az, µ) ), or equivalently az 2, µ ) az 2, µ 2 ) az, µ ) az, µ 2 ), for z z 2, µ µ 2, az, µ 2 ) an az 2, µ 2 ). My specification is restricte relative to Costinot s in that θϕ, z, µ) = fϕ)/az, µ) = ϕµz). 7 In aition to applying this reuce form, I further assume that orth has partial contractibility strictly superior to South in any sector. oting the inverse relationship between µ ) an a, ), log-supermoularity in terms of µ ) is given by < µ z) µ S z) < µ z ) µ S z ) <, 7 ote that µ is use in ϕµz) as a function of z, an countries characteristic µ is henceforth roppe from arguments. 6

8 i S z Figure Log-supermoularity in contractibility for z > z, µ > µ S, µ S z) an µ S z ). 8 Thus, not only oes µz) = /az, µ) satisfy log-supermoularity or Ricaro s classic inequality), but orth has an absolute avantage in µz) in any sector. Figure epicts µ i satisfying the above inequalities with the aitional assumptions that µ ) = µ S ) = an µ S ) =. As the figure inicates, log-supermoularity means that the gap between µ an µ S is graually larger as z is closer to zero. In the following, z is interprete as the egree of customization in sector z: the smaller is z, the greater is customization of prouction in sector z. An economic interpretation of this figure is as follows. In a more generic sector i.e., a sector with greater z), the severe holup problem is less likely irrespective of institutional quality because the prouction oes not rely heavily on relationship-specific investments. As a result, the gap between µ an µ S is relatively smaller an µ i is closer to one in a more generic sector. In a more customize sector i.e., a sector with smaller z), proucers are more likely to suffer from the holup problem an prouction efficiency is relatively more sensitive to institutional quality. Although µ i is significantly less than one for both countries, superior contractibility gives orth a relatively bigger cost avantage in a more customize sector. As formally establishe by Costinot 29a), this relatively more property which lies at the core of neoclassical trae theory an is also the pivotal element in the empirical evience reporte by Levchenko 27) an unn 27) is elegantly capture by log-supermoularity. Finally, in this prouctivity ecomposition θϕ, z, µ) = ϕµz), I refer to a country s istribution of firms prouctivity raws as technologies as in Melitz 23), whereas a country s contractibility on firms relationship-specific investments as institutions as in Levchenko 27). Further I restrict 8 It is known that if labor prouctivity is log-supermoular, aggregate output is log-supermoular Costinot, 29a); an in the current setup with the C.E.S. preferences, aggregate revenue is also log-supermoular. Thus, for z > z, Q z) Q S z) < Q z ) Q S z ), R z) R S z) < R z ) R S z ). This property plays a key role in examining the aggregate relationship between countries an sectors characteristics in the general equilibrium analysis. 7

9 attention to environments in which all firms have access to the same technologies across countries an sectors, i.e., G i ϕ, z) = Gϕ) for i {, S} an z [, ], where G ) enotes a cumulative istribution from which firms raw their prouctivity. 9 Thus, there are no technological ifferences across countries an institutional ifferences solely give rise to countries comparative avantage. In reality, technological an institutional ifferences coexist an these two ifferences are not precisely separable. To facilitate the analysis below, the following efinition is mae for the sake of convenience. Definition Technologies are a country s istribution Gϕ) of firms prouctivity raws ϕ, which is ientical across countries an sectors. Institutions are a country s partial contractibility µz) on firms relationship-specific investments, which varies across countries an sectors. Each firm chooses its price to maximize profits π = pq wl for omestic prouction an exporting. Solving profit-maximizing problem yiels the following first-orer conitions: where pϕ, z) = σ w σ ϕµz), ) σ ϕµz) σ qϕ, z) = Az), σ w ) µz) rϕ, z) = pϕ, z)qϕ, z) = σbz) ϕ, w ) rϕ, z) µz) πϕ, z) = wf = Bz) ϕ wf, σ w Bz) = σ ) σ ) σ σ Az) = σ σ Xz)P z), is aggregate market eman. For analytical simplicity, I assume that the variable trae cost is zero τ = ) an thus p = p = p x. Section 5 shows that the main result qualitatively hols even with the variable trae cost τ > ), an the supplementary note offers a etaile analysis that incorporates τ. It is also assume that the fixe trae cost is higher than the fixe prouction cost f x > f ) an, uner this assumption, only a subset of firms are able to export even in the absence of τ. While the above first-orer conitions are similar to those in the existing literature, two features of the current setup are worth emphasizing. First, wages w cannot be normalize between the two countries, since they are asymmetric an there is no freely traable homogeneous-goo sector in this moel. As note earlier, this assumption is mae to examine the role of enogenous factoral terms of trae in the Ricarian moel. Secon, institutional quality µ enters into these conitions. It is immeiate to see that the pricing rule is higher an the output level is lower in a more customize sector ue to the holup problem. 9 This means that, if firm prouctivity is rawn from a Pareto istribution, Gϕ) = ϕ min /ϕ) k, both shape an scale parameters, k an ϕ min, are ientical across countries an sectors. While both parameters are likely to vary with countries an sectors characteristics in evience Tybout, 2), the moeling of sector-variant istributions coul come at the cost of obscuring Ricarian sources of comparative avantage if these istributions are log-supermoular in sectors an firms characteristics Costinot, 29a). 8

10 Holup Problem So far, I have not explicitly explore how a country s institutional quality µ is relate to the enforcement of contracts between firms an input suppliers, an thus to the holup problem in relationship-specific investments. As originally propose by Grossman an Hart 986), the holup problem occurs because the parties cannot specify every unforeseeable contingency into an initial contract ex ante, an they have to renegotiate the contract ex post. In what follows, builing on seminal work of Antràs 23, 25) an Antràs an Helpman 24), I show that institutional quality µ plays a qualitatively similar but istinct) role with incomplete contracting. Suppose that, while perfect institutions µ = ) prevail in any sector of both countries, prouction of final goos now requires intermeiate inputs which firms cannot manufacture by themselves. To prouce a variety, each firm has to ask a omestic input supplier to provie a specialize input. This input is relationship-specific in that it has a higher value within the parties an a thir party cannot istinguish its true value. Since no enforceable contract will be signe ex ante in such a circumstance, the firm an its supplier have to bargain over the surplus after prouction takes place. Let β an β enote the firm s an its supplier s ex-post bargaining power, which vary across countries an sectors. Then, the firm s profit is π F = βpq + T an the supplier s profit is π S = β)pq wl T, where T is a transfer from the supplier to the firm. This transfer works to make the supplier breakeven an the firm s ex-post profit is π = π F + π S = pq wl in a subgame-perfect ash equilibrium. The supplier chooses its input level to maximize π S, so the first-orer conitions are pϕ, z) = σ w σ, qϕ, z) = Az) σ ϕ βz)) σ ) ϕ βz)) σ. w Comparing the two pricing rules reveals µ = β in equilibrium, an the istribution of bargaining power between the firm an its supplier is irectly relate to institutional comparative avantage. To see this in more etail, imagine what happens if the agents were able to sign complete contracts. In such an environment, the input level is ex ante verifiable an the supplier coul irectly bargain over the profit rather than the revenue. Then, the firm s profit is π F = βπ + T an the supplier s profit is πs = β)π T, where π = πf + π S is the joint profit uner complete contracting. The supplier woul choose its input level to maximize πs, so the first-orer conitions are p ϕ) = σ w σ ϕ, ) σ ϕ σ q ϕ) = A. σ w Eviently, the pricing rule is / β) times higher uner incomplete contracting because the supplier receives only a fraction of the marginal return to its investment for specialize input, leaing the input level to be β) σ times lower. Given this interpretation, the istribution of ex-post bargaining power has a irect impact on comparative avantage through ex-ante efficiency of specialize input prouction, i.e., the holup problem. In particular, across sectors, a fraction of ex-ante contractible activities woul be relatively smaller in a more customize sector an the supplier s holup problem is relatively severer in such a sector Acemoglu et al., 27). Furthermore, across countries, South woul have absolutely worse legal institutions in enforcing contracts an the supplier s holup problem in South is absolutely severer than orth Antràs an Helpman, 24). This is a theoretical justification 9

11 for log-supermoularity in institutional quality µ, with orth having an absolute avantage in it. Although I formalize µ from incomplete-contract perspectives, there are alternative mechanisms that may account for it. One of such caniates is financial constraints that exporters have to face when covering the fixe costs. As emonstrate by unn 27), sectors that are contract-intensive ten to be sectors that prouce more complex an technologically avance proucts that are more likely to require larger relationship-specific investments, relative to non-contract-intensive sectors that prouce simpler an technologically less avance proucts. ow, to the extent that countries iffer in the evelopment of their financial markets, cross-country ifferences in financial evelopment can lea to ifferences in comparative avantage Manova, 23). Moreover, constraints in financial markets can also reuce the share of exporters who must pay some entry costs in orer to access foreign markets, with potential larger impacts in comparative isavantage sectors Chaney, 23). In this context, µ may as well alternatively capture the egree of financial evelopment, an a more contract-intensive sector i.e., lower z sector) requires relatively better evelope financial markets i.e., higher µ country) which in turn confers orth a comparative avantage in these sectors. As is clear from this alternative explanation, the mechanisms at work are not necessarily restricte to partial contractibility. While the current paper focuses mainly on institutional factors as a source of countries comparative avantage, they can be interprete more broaly. All what matters for the main results is that labor prouctivity stemming from countries an sectors characteristics satisfies log-supermoularity. Firm Behavior The current paper analyzes a static version of the Melitz 23) moel. To enter a sector in country i {, S}, firms bear a fixe cost of entry f e, measure in country i s labor units. Upon paying this fixe cost, firms raw their prouctivity level ϕ from a known istribution G i ϕ, z) = Gϕ). After observing this prouctivity level, each firm ecies whether to exit or not. If the firm chooses to prouce, it bears aitional fixe costs f for omestic prouction an f x for exporting, as escribe before. An entering firm in country i woul then immeiately exit if π i <, or woul prouce an serve its omestic market if π i. Moreover, among omestic firms, only the most prouctive firms woul earn πx i an serve the foreign market in j as exporters uner the assumption f x > f. While this firm behavior is similar across countries an sectors, the prouctivity cutoffs for omestic prouction an exporting woul vary by reflecting countries comparative avantage. Regaring exporting participation, if πx i an πx j for some firms in i j {, S}, well-known two-way intra-inustry) trae occurs in this sector: trae occurs even in the same sector because proucts are ifferentiate an consumers are strictly better off by importing proucts unavailable in the omestic market. If πx i for some firms an πx j < for any firm, on the contrary, one-way inter-inustry) trae occurs in this sector, whereby exporting from i to j takes place. I am aware that the concept of partial contractibility, µ, here is not exactly the same as that evelope by Acemoglu et al. 27): they use µ as the fraction of tasks that are contractible for input provision, whereas I use it as the fraction of revenue that firms share at a bargaining stage. Most important for the pattern of trae, however, is not this moeling ifference but the fact that µ varies with countries an sectors characteristics, which also hols in their work.

12 3 Partial Equilibrium In this section, I first explore partial equilibrium in which some important variables are exogenously given. The next section embes this analysis in a general-equilibrium setting. To see an equilibrium of sector z, consier country i s market where omestic firms in i an foreign exporters from j engage in monopolistic competition. From the first-orer conitions in the previous section, the profit functions of these firms are respectively given by µ π i i ) ϕ, z) = z) µ Bi z) ϕ w i f, πxϕ, j z) = B i j ) z) z) ϕ w j f x. w i otice that, since these firms compete in i s market, aggregate eman B i is common for both profit functions. π i an πj x are measure by ifferent wage rates an contractibility levels, however, because exporters from j have to use omestic labor an institutions to prouce own variety. If there exist multinational enterprises that irectly employ local labor an have internal contractibility within the firm bounaries, this argument is no longer true. See Section 5 for the possibility of foreign affiliate prouction in the current setup. To compare these two profit functions graphically, they are rawn in ϕ, π) space with slope B µ w ) an intercept wf. Then, π i is steeper than π j x in i s market or π i x is steeper than π j in j s market) if an only if µ i z) w i µj z) w j w j µz) ω if i =, µz) ω if i = S, where µz) = µ z)/µ S z) = az, µ S )/az, µ ) an ω = w /w S respectively enote the relative contractibility or the relative labor requirement) an the relative wage in orth. Following stanar Ricarian moels, I say that orth South) has an institutional comparative avantage in sector z if it has a large small) relative labor prouctivity in terms of partial contractibility µz), an/or a small large) relative wage ω, i.e., µz) > ω µz) < ω). Uner this efinition, country i s institutional comparative avantage is ientifie as sectors where π i is steeper than π j in each country s market. Definition 2 orth South) has an institutional comparative avantage in sector z if µz) > ω µz) < ω), or equivalently if π π S ) is steeper than π S π ) in each country s market. Since this efinition inicates neither orth nor South has a comparative avantage in a sector where µz) = ω, I first erive the conition uner which this equality hols. From Figure, the ratio of contractibility µz) = µ z)/µ S z) has to satisfy µz) >, µ z) <, µ z) >, lim z µz) = an lim z µz) =, where the first conition stems from absolute avantage of orth an the thir conition stems from log-supermoularity of µ i z). The relative wage in orth ω, on the other Following the literature e.g. Melitz an Reing, 24), I assume that all prouction costs, incluing the fixe export cost f x, are measure in terms of a source country labor.

13 , S x, S x S S x x S x S S x w f w S f w S fx w fx orth South Figure 2 Profits from omestic sales an exports han, shoul be the same for all sectors z [, ] because labor is completely mobile across sectors within a country in the Ricarian moel. This suggests that, if ω is greater than one, these two curves intersect at a unique cutoff z = µ ω) such that: i) z [, z) µz) > ω; ii) z = z µz) = ω; an iii) z z, ] µz) < ω. It is then immeiate from Definition 2 that orth South) has an institutional comparative avantage in relatively customize generic) sectors z [, z) z z, ]). ext I consier the equilibrium in the cutoff sector z as a benchmark. Figure 2 illustrates the profit functions of π i an πj x in this sector for orth left panel) an South right panel). As is well-known, this figure epicts prouctivity sorting: firms with prouctivity ϕ > ϕ i prouce in i, whereas firms with prouctivity ϕ > ϕ i x export to j. Since these two profit functions must be parallel in this sector, if some omestic firms prouce in i i.e., ϕ i is finite), some foreign firms export from j i.e., ϕ j x is also finite). Thus, two-way trae occurs in sector z: trae occurs even in the same sector, because proucts are ifferentiate an consumers are strictly better off by importing proucts that are not available in the omestic country. This argument helps unerstan what happens in sectors other than the cutoff sector z. In sectors z [, z) where orth has a comparative avantage, for example, π an π x are respectively steeper than πx S an π S in both omestic an export markets. This however oes not always imply that the prouctivity cutoffs, ϕ an ϕ x, become smaller than the counterpart cutoffs in the cutoff sector z an less prouctive firms are more likely to fin it profitable to operate in these sectors. This is because the slope of the profit functions epens not only on µ/w but also on aggregate eman B, which is so far exogenously given. I will show in the next section that orth s comparative avantage allows the profit functions to change as epicte by the otte lines in Figure 2. As a consequence, while ϕ x becomes smaller an less prouctive firms can enter the export market, ϕ becomes larger an only more prouctive firms can survive in the omestic market. Similarly, two-way trae woul 2

14 occur in any sector z [, ] as long as the slope of πx an πx S is positive, although this might not always true once B is taken into account. ote in Figure 2 that the intercept of πx i lies below the intercept of π j for both countries, i.e., w S f x > w f ω < fx f in orth an w f x > w S f ω > f f x in South, ensuring that foreign exporters from i must bear the higher fixe cost measure by the source country labor wage) than omestic firms in j. Because it is empirically well-known that f x is huge in any manufacturing sector, I hereafter assume that these two inequalities hol in any sector z [, ], which will be shown to be necessarily satisfie in the general-equilibrium setting where ω is enogenous. Assumption f f x < ω < f x f. While the existence of the unique cutoff sector z in the absence of variable trae cost is reminiscent of Dornbusch, Fischer, an Samuelson s 977) Ricarian moel with a continuum of goos, 2 there exist three noteworthy istinctions between the current paper an theirs. First, since they analyze perfect competition with homogeneous goos, complete specialization or inter-inustry trae) occurs below/above the cutoff z; in contrast, this paper stuies monopolistic competition with ifferentiate goos an incomplete specialization or intra-inustry trae) can occur in all manufacturing sectors. Seconly, the mass an size of omestic firms an exporters are both ineterminate an irrelevant in their neoclassical trae moel, but it is enogenously etermine in the current framework in which the mass of varieties exporte is only a subset of the mass of varieties prouce in the home market. Finally, this paper s focus is on orth-south trae where the ifference in economic evelopment plays a prominent role in shaping countries comparative avantage. The result that a less evelope country nevertheless exports ifferentiate goos in customize sectors seems to be consistent with recent trae flows see, e.g., Krugman, 28). Proposition i) If ω >, there exists a unique cutoff sector z, ) such that orth South) has an institutional comparative avantage in sectors z [, z) z z, ]). ii) Two-way trae can occur in any sector z [, ]. It is important to emphasize that this partial-equilibrium analysis cannot clarify the interplay among key variables of the moel. To see this, it is useful to go back to Figure 2. The figure epicts ϕ j < ϕi x in the cutoff sector z, inicating that foreign exporters from i are more prouctive than omestic firms in j. This outcome is not wholly surprising because foreign exporters are assume to incur the higher fixe cost uner Assumption, an it can be easily formalize by using a partialequilibrium framework. However, ϕ i an ϕj or ϕi x an ϕ j x are not comparable. Obviously, ϕ 2 The iea of bringing firm heterogeneity into the Dornbusch et al. 977) moel is not entirely new, although the moels setups in the existing literature are less general than the current one. For instance, Okubo 29) uses a specific istribution of firm prouctivity levels, whereas Fan et al. 2) abstract from enogenous wage ifferentials between countries by introucing the homogeneous-goo sector. 3 an

15 ϕ S ϕ x an ϕ S x) are etermine at which π = an πs = π x = an πx S = ), but these variables epen on the aggregate market eman B i as well as the wage rate w i, both of which are exogenous in partial equilibrium. Also, Proposition i) requires that ω shoul be greater than one if orth-south trae is to occur, but it is not clear whether this hols or not. In this sense, the above partial-equilibrium setting is restricte, an a general-equilibrium approach is necessary to enogenize these variables. 4 General Equilibrium In this section, the partial-equilibrium analysis is embee into a general-equilibrium framework to examine the interaction among the key variables an to see enogenous patterns of specialization an trae. General-Equilibrium Setup This subsection first outlines several equilibrium conitions that play a central role in characterizing the enogenous variables in general equilibrium. In the subsequent subsections, I solve this general-equilibrium moel with some restrictions on the exogenous variables. Firstly, a zero profit conition must hol for all sectors z [, ] of omestic an export markets. The prouctivity cutoff that satisfies this conition is ientifie by ϕ i z) = inf{ϕ : πi ϕ, z) > } an ϕ i xz) = inf{ϕ : πxϕ, i z) > } for omestic firms an exporters respectively. This conition is referee to as a zero cutoff profit ZCP) conition: µ π i i ) ϕi, z) = z) Bi z) w i ϕ i z)) = w i f, ZCP i) µ πx i ϕ i x, z) = B j i ) z) z) ϕ i xz)) = w i f x, ZCPx) i for i j {, S}. In this conition, aggregate market eman of exporters B j ) shoul be ifferent from that of omestic firms B i ) because exporters from country i have to face aggregate market eman in country j. w i Seconly, a free entry FE) conition must be satisfie for all sectors. Since potential entrants are ex ante ientical in the current moel, this conition is efine as ϕ i z) π i ϕ, z)gϕ) + πxϕ, i z)gϕ) = w i f e, F E i ) ϕ i xz) where the first an secon terms in the left-han sie respectively enote the expecte operating profits from omestic sales an exports earne by potential entrants in sector z. The sum of these expecte profits has to be equal to the fixe entry cost w i f e. Finally, a labor market clearing LMC) conition must be taken into account: Mez) i l i ϕ i z) ϕ, z)gϕ)z+ Mez) i lxϕ, i z)gϕ)z+ ϕ i xz) M i ez)f e z = L i, LMC i ) 4

16 where Me i enotes the mass of potential entrants, which varies across sectors in country i. In this equation, the first an secon terms in the left-han sie are the sum of expecte labor emans use for omestic prouction an exporting by potential entrants, whereas the thir term is expecte labor emans use for investment by potential entrants. ote that lx i is summe up over sectors of the economy as a whole because two-way trae can occur in any sector z [, ] as seen in Proposition ii). The sum of these expecte labor emans that aggregate the use of labor across all sectors in i has to be equal to the fixe labor supply L i. ow, it is possible to enogenize the important variables in general equilibrium. Since there are the eight equations the ZCP, FE, an LMC conitions that must hol in orth an South), these conitions provie implicit solutions for the following eight unknowns: ϕ z), ϕs z), ϕ x z), ϕ S xz), B z), B S z), w, w S, 3 where the LMC conition in South can be omitte by Walras law, thereby normalizing w S = as a numéraire. The mass of potential entrants M i e can be written as a function of these eight unknowns as will be shown later.) Relative Equilibrium Conitions This subsection sets forth the characterization of the eight unknowns from the eight equilibrium conitions. It is challenging, however, to solve a full general equilibrium moel with asymmetric countries. In particular, without specifying the functional form of the firm size istribution Gϕ), explicit solutions of these unknowns cannot be obtaine. In the following, instea of obtaining the exact values of each of them, the main focus is evote to characterizing the relative terms of these unknowns. Recall from Proposition i) that orth-south trae occurs only if the relative wage in orth ω is greater than one. Although this relative wage is enogenously etermine in the moel, suppose first that ω > in equilibrium. In other wors, the LMC conitions are left out from the moel as if it were partial-equilibrium. As will be clear, this inequality must be true in general equilibrium because I assume that orth has an absolute avantage in partial contractibility µ in any sector. This means that the marginal prouct of labor is higher on average across heterogeneous firms) in orth, an thus wages have to be greater in orth than South if trae is to occur between the two countries. This intuition will be confirme later by integrating the LMC conitions. Uner the circumstance, I first examine the sectoral ifference in the relative prouctivity cutoffs ϕ = ϕ /ϕs, ϕ x = ϕ x /ϕ S x) an the relative market eman B = B /B S ) by focusing on the ZCP an FE conitions recall these two conitions must hol for all sectors). To o this, using the ZCP conitions, rewrite the FE conition as f J ϕ i z)) + f xj ϕ i xz)) = f e, 3 As is evient from the epenence on z, the first six enogenous variables are allowe to vary across sectors in this moel; in contrast, wages are inepenent of z ue to perfect intersectoral mobility of labor. Relate to this, it woul be more accurate to say that the ZCP an FE conitions are the six equations that hol for each sector, an the LMC conitions are the aitional two equations that aggregate the use of labor in all sectors for each country. 5

17 B x B, x / ) z z Figure 3 Market eman an prouctivity cutoffs where J ϕ) = ϕ [ϕ/ ϕ) ]Gϕ). J ) is monotonically ecreasing with lim ϕ J ϕ) = an lim ϕ J ϕ) =. 4 Since the equality of this conition must hol in any sector, changes in z shift the prouctivity cutoffs in opposite irections, an thus ϕ i x/ ϕ i must be strictly increasing or ecreasing in z. ote that these changes in z affect ϕ s an B s while they have no impact on w s as wages are inepenent of z so long as labor is completely mobile across sectors), an the equilibrium analysis here oes not rely on the exogenous ω assumption. Moreover, iviing the ZCP conition of omestic prouction by that of exporting for each country, the relative market eman B = B /B S is given by Bz) = ) ϕ x z) f ϕ z) ϕ S z) ϕ S x z) f x if i =, ) fx f if i = S. Using the property of the FE conition erive above, it can be shown that B is strictly increasing in z see Appenix). The intuition behin this result is explaine by recalling that B is proportional to the relative aggregate price P = P /P S ). If z is close to one, the institutional ifferential is almost negligible whereas there exists the wage ifferential i.e., ω > ). South is thus able to prouce goos relatively cheaply, thereby leaing to P > P S an B > in the neighborhoo of z =. If z is close to zero, on the other han, the institutional ifferential is sufficiently large to ominate the wage ifferential ue to log-supermoularity), resulting in P < P S an B < in the neighborhoo of z =. Roughly speaking, this intuition mirrors the iea that country i has a comparative avantage in sectors where the aggregate price P i is relatively lower than P j. 5 The first quarant of Figure 3 epicts this relationship in z, B) space. 4 I have so far assume that the fixe cost parameters f, f x an f e are common across all sectors z [, ]. As inicate earlier, it woul be more realistic to allow the fixe costs to be systematically correlate by the egree of customization z: contract-intensive sectors ten to require large relationship-specific investments in evience. In Appenix, I show that the following result continues to hol if these fixe costs increase proportinately with the customization measure, i.e. faz) = afz) for any positive number of a. 5 This statement is not precise because the aggregate price P i inclues prices of both omestic an foreign varieties in the presence of two-way trae. Given log-supermoularity, this woul hol in a close-economy version of the moel. 6

18 x s x, S S x S S S x S zz z z Figure 4 Relationship among prouctivity cutoffs ext, iviing the ZCP conition of orth by the corresponing conition of South, the relative prouctivity cutoffs ϕ = ϕ / ϕs an ϕ x = ϕ x / ϕ S x satisfy the following relative ZCP conition: ϕ z) = ω ) Bz) ω µz), ϕ xz) = Bz)ω) ω µz), RZCP ) where all variables are represente by the relative terms in orth. It is easy to show that ϕ ecreases with B while ϕ x increases with B, an that ϕ x z) ϕ z) Bz). Further, simple geometry in Figure 2 suggests that ϕ an ϕ x are equal if an only if π i an πj x are parallel in the cutoff sector z. Thus, the relative market eman an relative prouctivity cutoffs respectively satisfy B z) = an ϕ z) = ϕ x z) = ω /) using µ z) = ω) in that sector. The secon quarant of Figure 3 epicts this relationship in B, ϕ) space. Finally, combining the first an secon quarants, Figure 3 highlights the sectoral ifference among the six enogenous variables represente in the relative terms) that are erive from the ZCP an FE conitions: in any sector z [, ], the relative market eman B is etermine in the first quarant, an the relative prouctivity cutoffs ϕ an ϕ x are subsequently etermine in the secon quarant. It is immeiately seen that z < z Bz) < ϕ z) > ω z = z Bz) = ϕ z) = ω z < z Bz) > ϕ z) < ω > ϕx z), = ϕx z), < ϕx z). In this relationship, either ϕ or ϕ x is necessarily greater than one uner the conition that the relative wage ω is greater than one. For instance, ϕ is greater than one in sectors where orth has a comparative avantage z [, z); however whether ϕ x is greater than one or not is ineterminate in the current setup. Base on this observation, Figure 4 illustrates the relationship among the prouctivity cutoffs in the comparative avantage sectors of orth left panel) an South right panel). While the figure shows that ϕ x = ϕ x / ϕ S x > left panel) an ϕ = ϕ / ϕs > right panel), these might not hol 7