Institutions as a Source of Comparative Advantage

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1 Institutions as a Source of Comparative Avantage Tomohiro Ara Fukushima University This Version: February 2013 Abstract Why oes the fraction of firms that eport 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 relatively more in a sector where prouction is more institutionally epenent. In aition, institution-inuce comparative avantage makes it relatively easier for orthern heterogeneous firms to incur eport costs in a more contract-epenent sector, thereby leaing to a higher eporters percentage. Keywors: Contracting institutions, firm heterogeneity, comparative avantage JEL Classification umbers: D23, F12, F14, L33, O43 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, icolas Schmitt, an seminar an conference participants at various institutions for helpful comments an suggestions. I have also benefite from financial support from USW an Hitotsubashi University. eeless to say, all remaining errors are my own responsibility. Faculty of Economics an Business Aministration, Fukushima University, Fukushima, , Japan. aress: tomohiro@econ.fukushima-u.ac.jp.

2 1 Introuction A growing boy of empirical evience using firm-level ata has etensively reveale that the etent to which firms participate in eporting varies systematically across countries an sectors. These works have foun that, in evelope countries, the percentage of firms that eport tens to be substantially higher in sectors where prouction technology is more comple an customize (such as chemical proucts), an the share of eporters steaily eclines as sectors prouction requires simpler an more generic technology (such as tetile proucts). In eveloping countries, on the other han, the opposite patterns are typically observe: the ratio of eporting firms to overall firms tens to be notably higher (resp. lower) in simpler (resp. more comple) sectors. At the same time, these stuies have also ocumente that eporting occurs in every major manufacturing sector of both evelope an eveloping countries: even in a strong comparative isavantage sector, a small fraction of firms o eport. 1 Why oes the fraction of firms that eport vary with countries comparative avantage? To answer this question, combining the recent empirical fining quantifie by Levchenko (2007) an unn (2007) with firm heterogeneity of Melitz (2003), 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. Furthermore, each firm is ifferent in terms of its prouctivity à la Melitz. These three-imensional ifferences in country, sector, an firm characteristics enogenously pin own the pattern of specialization an trae in equilibrium. To investigate the role of country an sector characteristics, I buil on the concept of partial contractibility, originally evelope by Acemoglu, Antràs, an Helpman (2007). I consier an environment in which orth has better institutions for partially e-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 eplicitly eamine the interaction between contractual incompleteness an technological complementarity by simply assuming that prouction in customize (generic) sectors is more (less) epenent on institutions. Instea, I eten 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 relatively more in a sector where prouction is more institutionally epenent. 1 See Bernar, Eaton, Jensen, an Kortum (2003) an Bernar, Jensen, Reing, an Schott (2007) for the Unite States, Tomiura (2007) for Japan, an Lu (2011) for China, respectively. For eample, Bernar et al. (2007, Table 2) report that, as of 2002, 36 percent (8 percent) of U.S. firms eport in a chemical manufacturing sector (an apparel manufacturing sector), whereby a more customize sector tens to ehibit a higher percentage of eporters among 21 sectors. Conversely, Lu (2011, Figure 1) shows that, as of 2005, aroun 60 percent (less than 20 percent) of Chinese firms eport in cloth an fur manufacturing sectors (a chemical manufacturing sector), inicating that there eists a clear negative relationship between eport participation an the capital-labor ratio among 29 sectors. Finally, Bernar et al. (2003, 2007), Tomiura (2007), an Lu (2011) all ocument that there eist some eporting firms in every manufacturing sector. 1

3 To formalize a higher tenency to eport participation in comparative avantage sectors, I incorporate firm-level ifferences in prouctivity. Since eporting requires fie eport costs that less prouctive firms cannot cover, only a small fraction of firms are able to eport. 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 a more (less) contract-epenent sector, which in turn softens the relative buren of incurring eport costs. As a result, compare to a comparative isavantage sector in a counterpart country, relatively less prouctive firms can eport in a country s comparative avantage sector. This mechanism eplains why the stronger institutional comparative avantage is, the smaller the prouctivity cutoff for eporting becomes, thereby leaing to a higher eporters percentage. 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 eport participation. There are at least three reasons for this. First, countries abilities to enforce contracts can have quantitatively larger impacts on comparative avantage than countries resource enowments. For instance, unn (2007) estimates that contract enforcement eplains more of the global pattern of trae than countries enowments of physical capital an skille labor combine. Secon, as rigorously emonstrate by Costinot (2009a), this empirical evience is appropriately capture by (Ricarian) institutional ifferences with log-supermoularity in country an sector characteristics. 2 In this specification, the characteristic of firms in terms of their prouctivity is an inepenent factor of the variation in eport participation as iscusse above. Finally, the Ricarian view of institutional ifferences gives a complementary eplanation for Bernar, Reing, an Schott s (2007) factor-enowment riven comparative avantage theory. Although the main result is strikingly similar, I show that some phenomena (e.g., home-market effects) are well unerstoo through a lens of Ricarian sources of comparative avantage. In this paper, I o not attempt to eplain 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 eplore how contracting institutions an heterogeneous firms jointly shape an enogenous pattern of trae. In so oing, the moel shows that orth with better institutions gains comparative avantage in contract-epenent sectors an is a net eporter of customize proucts in intra-inustry trae. South with worse contracting institutions, on the other han, is shown to be a net eporter of generic proucts. Moreover, within sectors in bilateral trae flows, the fraction of eporters is monotonically increasing in countries comparative avantage strength. These results, both of which are consistent with empirical evience, hol even if orth has absolute avantage in institutional quality in any sector, an there eists no technological ifference (in terms of firm prouctivity istributions) between the two countries. 2 As far as log-supermoularity in country an sector characteristics is central, the moeling of technological an institutional ifferences is isomorphic (Costinot, 2009a). This is because a country with better institutions faces less severe unerinvestment an thus has bigger cost avantage in prouction, which is a key presumption in empirical stuies by Levchenko (2007) an unn (2007). Although it is questionable whether institutions are more crucial than technologies for trae patterns, evience on these two ifferences is so far unavailable. 2

4 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, 2005; Acemoglu et al., 2007; Costinot, 2009b). These papers show that, even in the absence of technological ifference, 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 eport everywhere. 3 In the real worl, a large proportion of firms o not eport even in a strong comparative avantage sector. The current paper emonstrates that not only is comparative avantage enogenously inuce by institutions, but also that the fraction of eporters is higher in a stronger comparative avantage sector, as suggeste by the eisting evience. Another branch of the relate literature is the so-calle heterogeneous-firm moel of trae, especially evelope by the seminal work of Melitz (2003). While Melitz s moel is successful in eplaining the eporters behavior among evelope countries (orth-orth trae), recent empirical evience has pointe out that his moel is less suitable for the stuy of bilateral trae flows between ifferent countries (orth-south trae), as eemplifie by Lu (2011) who analyzes Chinese firm-level manufacturing ata. A number of papers, among others, Demiova (2008), Falvey, Greenaway, an Yu (2005), Fan, Lai, an Qi (2011), an Okubo (2009), 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, 4 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 epositional simplicity, it is straightforwar to eten 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. (2007) as argue above. Using Helpman-Krugman s (1985) 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 factor-price-equalization regions. In contrast, it is possible in the current paper to analytically eamine 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 (1980) home-market effect. I show that, ue to selection into omestic an eport markets that varies with comparative avantage, the home-market effect works quite ifferently for the number of omestic firms (specialization) an the number of eporters (trae). 3 Acemoglu et al. (2007) introuce firm heterogeneity in the egree of complementarity among inputs, but all proucts are assume to be freely trae an hence all firms eport in their moel. 4 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 2006 for the first time the Unite States i more trae in manufacture goos with eveloping countries than evelope countries, Krugman (2008) asserts that this is largely ue to the wage ifference between the U.S. an eveloping countries: China s an Meico s wages are respectively only 4 percent an 13 percent of the U.S. level. 3

5 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 There is a unit measure of ientical consumers in each country. The preferences of a representative consumer are Cobb-Douglas across sectors an Diit-Stiglitz within sectors: where 1 0 U = 1 0 λ z ln X z z, [ ] 1/α λ z z = 1, X z = z (v) α v. v V z λ z enotes the share of epeniture spent on sector z (0, 1). The representative consumer in each country evotes its income uniformly across sectors (i.e., λ i z = λ). X z enotes aggregate consumption in sector z, where z (v) is consumption of variety v from sector z an V z is the mass of available goos, which is enogenously etermine in equilibrium. It is important to note that there is no homogeneous-goo sector with nontrae costs, an thus wage rates cannot be normalize between orth an South. 5 This structure of the preferences is similar to that of Krugman (1980), an more recently to that of Antràs (2005) an Okubo (2009). otice also that, while the elasticity of substitution between any two varieties within a sector ɛ = 1/(1 α) is assume to be greater than one, 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. where As is well-known, the above preferences generate eman functions in sector z, = Ap 1/(1 α), λe A = n 0 p(v)1 ɛ v. E is total spening in the economy, n is the number (measure) of varieties available in a country, an p(v) is the consumer price of variety v. From the ieal price ine P = [ p(v) 1 ɛ v ] 1/(1 ɛ), this can be written as A = λep ɛ 1. Prouction There is a continuum of firms, each proucing a ifferent variety. Labor is only a factor of prouction an each supplier faces a perfectly elastic supply of labor at each country size L. Let w enote the wage rate. Since labor is completely mobile across sectors but immobile 5 By ecluing a homogeneous-goo sector, I can eplicitly investigate the role of the relative wage or factoral terms of trae (Matsuyama, 2008) in comparative avantage, which is an orthoo practice in Ricarian moels. While introucing a homogeneous prouct à la Helpman an Krugman (1985) 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. 4

6 across countries as in conventional Ricarian moels, w is same across sectors within a country but is ifferent across countries. 6 Following Krugman (1980) an Melitz (2003), firm technology is summarize in a linear cost function of output : f + l = f + θ(ϕ,z,µ) = f + τ θ(ϕ,z,µ) = f + ϕµ(z) τ ϕµ(z) if omestic prouction, if eporting, where θ(,, ) is labor prouctivity, f is a fie cost for omestic prouction, f is a fie cost for eporting, an τ( 1) is a iceberg transport cost. 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 (2003), 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 Melitz s moel. In the current moel, by contrast, since 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( ) (0, 1) affects firms variable costs only (leaving fie 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 net subsection) an is referre to as partial contractibility in this paper. Secon, I aopt a reuce form of labor prouctivity: θ(ϕ, z, µ) = ϕµ(z). While this form is use for simplicity, one can justify this simplification from Costinot s (2009a) log-supermoular argument. He efines Ricarian technological ifferences as labor prouctivity that satisfies θ(ϕ, z, µ) = f(ϕ)/a(z, µ), where a(, )(> 1) is the unit labor requirement (efine as the inverse of labor prouctivity), an shows that Ricarian sources of comparative avantage hol if 1/a(, ) is log-supermoular (i.e., 2 z µ ln 1 a(z,µ) 0 2 z µ ln a(z, µ) 0), or equivalently a(z 2, µ 1 ) a(z 2, µ 2 ) a(z1, µ 1 ) a(z 1, µ 2 ), for z 1 z 2, µ 1 µ 2, a(z 1, µ 2 ) 0 an a(z 2, µ 2 ) 0. My specification is restricte relative to Costinot s in that θ(ϕ, z, µ) = f(ϕ)/a(z, µ) = ϕµ(z). In aition to applying this reuce form, I further assume that orth has partial contractibility strictly superior to South for any sector. oting the inverse relationship between µ( ) an a(, ), log-supermoularity in terms of µ( ) is 6 I recognize that wage inequality eists across sectors as well as within sectors (Helpman, Itskhoki, Muenler, an Reing, 2012), an that this is particularly serious in the presence of incomplete contracting (Levchenko, 2007). My assumption on wage equality raws from Antràs (2005), who stuies incomplete contracts in a generalequilibrium Ricarian moel with a continuum of sectors. 5

7 i z 1 z S z 0 Customize Generic 1 z Figure 1. Log-supermoularity in contractibility given by 1 < µ (z) µ S (z) < µ (z ) µ S (z ) < +, for z > z, µ > µ S, µ S (z) 0, an µ S (z ) 0. This implies not only that µ(z) = 1/a(z, µ) satisfies log-supermoularity (or Ricaro s classic inequality), but also that orth has absolute avantage in partial contractibility in any sector. Figure 1 illustrates µ i (z) that satisfies the above inequalities with the aitional assumptions that µ (1) = µ S (1) = 1 an µ S (0) = 0. As epicte in the figure, log-supermoularity means in this framework that the gap between µ an µ S is graually larger as the sector s prouction is more customize. An economic interpretation of this figure is as follows. In a generic sector, 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 customize sector, on the contrary, 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 relatively bigger cost avantage in a more customize sector. As formally establishe by Costinot (2009a), 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 (2007) an unn (2007) is elegantly capture by log-supermoularity. Finally, in this ecomposition θ(ϕ, z, µ) = ϕµ(z), I refer to countries partial contractibility µ(z) as institutions as in Levchenko (2007), whereas the istribution function G(ϕ) of firms prouctivity raw ϕ as technologies as in Melitz (2003). Furthermore, I restrict attention to environments in which all firms have access to the same technologies across countries an sectors, i.e., G i z(ϕ) = G(ϕ) for i {, S} an z (0, 1). 7 Consequently, there eists no technological 7 This means that, if the istribution of firm prouctivity is Pareto, G(ϕ) = 1 (b/ϕ) k, both the shape an scale parameters, k an b, are ientical across countries an sectors. While these parameters are more likely to vary with country an sector characteristics in evience (Tybout, 2000), the moeling of country-variant istributions 6

8 ifference across countries an institutional ifference solely gives rise to countries comparative avantage. In reality, technological an institutional ifferences coeist an these two effects are not precisely separable. This istinction is not crucial for the analysis below an the following efinition is mae for the sake of convenience. Definition 1. Technologies are the istribution function G(ϕ) of firms prouctivity raw ϕ, which is ientical across countries an sectors. Institutions are countries partial contractibility µ(z) on relationship-specific activities, which varies across countries an sectors. Each firm chooses to maimize π = p wl. Solving this profit-maimizing problem yiels the following first-orer conitions: p = w ϕαµ, ( ϕαµ ) ɛ = A, w ( µ ) ɛ 1 π = B ϕ ɛ 1 wf, w ( µ ) ɛ 1 π = B ϕ ɛ 1 wf, w where B = Aα ɛ 1 (1 α) = λe(αp ) ɛ 1 (1 α). For analytical simplicity, I assume that transport cost is zero (τ = 1) an thus p = p = p. Section 5 iscusses how the following results are moifie if τ > 1. It is also assume that f > f, which is require for the partitioning between eporters an noneporters an, uner this assumption, only a subset of firms eport even in the absence of transport costs. While these conitions are similar to those in stanar heterogeneous-firm moels of trae, there are two ifferent points. First, wage rates cannot be normalize between orth an South, since countries are asymmetric an there is no freely trae homogeneous-prouct sector in this moel. For instance, Melitz (2003) assumes symmetric countries, whereas Helpman, Melitz, an Yeaple (2004) introuce a homogeneous goo sector to equalize wage across countries. 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. Bargaining So far, bargaining issues have not been eplicitly eplore. As originally propose by Grossman an Hart (1986), the holup problem in relationship-specific investments occurs because parties cannot write every unforeseeable contingency into an initial contract e ante, an they have to renegotiate the contract e post. In what follows, builing on the seminal works of Antràs (2003, 2005) an Antràs an Helpman (2004, 2008), I briefly show that institutional quality µ plays a qualitatively similar (but istinct) role with incomplete contracting. Suppose, while letting perfect institutions (µ = 1) prevail in any sector of both countries, prouction of final goos now requires intermeiate inputs which each firm cannot manufacture coul come at the cost of obscuring Ricarian sources of comparative avantage if G i z(ϕ) is log-supermoular in country an firm characteristics (Costinot, 2007, 2009a). 7

9 by itself. To prouce a variety, every firm asks 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 (such as courts) cannot istinguish its true value. Because no enforceable contract will be signe e ante in such a circumstance, the firm an its supplier have to bargain over the surplus after prouction takes place. Let β an 1 β enote respectively the firm s an its supplier s e-post bargaining power. Then, the firm s profit is π F = βp + T, an the supplier s profit is π S = (1 β)p wl T, where T is a transfer from the supplier to the firm. 8 This transfer works to make the supplier break-even an leas to π = π F + π S = p wl in a subgame-perfect ash equilibrium. The supplier chooses to maimize π S, so the optimal pricing rule is p = w ϕα(1 β). Comparison of the pricing rules reveals µ = 1 β in equilibrium. It can thus be interprete that the supplier s e-post bargaining power is lower in a more customize sector because a fraction of e-ante contractible activities is smaller in such a sector (c.f., Acemoglu et al., 2007). The previous literature on organizations an trae typically assumes that the egree of the holup problem in relationship-specific investments is the same across sectors, but varies across organizational forms (i.e., vertical integration an outsourcing). Instea, I allow this egree to vary across sectors, while abstracting from the firm bounaries. The moel is evelope below, keeping in min the similarity between imperfect institutions an incomplete contracting. Firm Behavior This paper analyzes a static version of Melitz s (2003) moel. To enter a sector in country i {, S}, firms bear a fie cost of entry f e, measure in country i s labor units. Upon paying this fie cost, firms raw their prouctivity level ϕ from a known istribution G i z(ϕ) = G(ϕ). After observing this prouctivity level, each firm ecies whether to eit or not. If the firm chooses to prouce, it bears aitional fie costs f for omestic prouction an f for eporting, as escribe before. An entering firm in country i woul then immeiately eit if π i < 0, or woul prouce an serve its omestic market if πi 0. Moreover, among omestic firms, only the most prouctive firms woul earn π i 0 an serve the foreign market in j as eporters because f > f. While this firm behavior is similar across countries an sectors, the prouctivity cutoffs for omestic prouction an eporting woul vary by reflecting countries comparative avantage. Regaring eporting participation, if π i 0 an π j 0 for some firms in i j {, S}, well-known two-way (intra-inustry) trae occurs in this sector: trae arises even in the same sector because proucts are ifferentiate an consumers are strictly better off by importing goos unavailable in the omestic market. If π i 0 for some firms an π j < 0 for any firm, on the contrary, one-way (inter-inustry) trae happens, whereby eporting from country i to country j takes place in this sector. 8 ote that: (i) ue to incomplete contracting, the bargaining occurs over the revenue rather than the profit; an (ii) only the supplier unertakes (one-sie) relationship-specific investments. While this bargaining setup is amittely simplistic, even if both parties engage in relationship-specific activities thereby creating the two-sie holup problem, the key results o not essentially change. See Antràs an Staiger (2011) for etails. 8

10 3 Partial Equilibrium In this section, I eplore a partial equilibrium in which some important variables are eogenously given. The net section embes this analysis in a general-equilibrium setting. To see a traing equilibrium, consier country j s market where competition occurs between omestic firms in j an eporters from i. From the first-orer conitions in the previous section, the profit functions of these firms are respectively given by ( π j µ j ) ɛ 1 = (z) Bj ϕ ɛ 1 w j f, w j π i = B j ( µ i (z) w i ) ɛ 1 ϕ ɛ 1 w i f. otice that, since they compete in j s market, aggregate eman B j is common for both of the profit functions. π j an πi are measure by ifferent wage rates an contractibility levels, however, because eporters from i have to use omestic labor an institutions to prouce own variety. If there eist 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 profit functions graphically, they are rawn in (ϕ ɛ 1, π) space with slope B ( µ ) ɛ 1 w an intercept wf. Then, π i is steeper (flatter) than π j if an only if µ i (z) w i µj (z) µ(z) ω if i =, w j µ(z) ω if i = S, where µ(z) = µ (z)/µ S (z) = a(z, µ S )/a(z, µ ) an ω = w /w S respectively enote the relative contractibility (or relative labor requirement) an relative wage in orth. Following stanar Ricarian moels, I say that orth (South) has institutional comparative avantage in sector z if it has a large (small) relative labor prouctivity in contractibility µ(z), an/or a small (large) relative wage ω, i.e., µ(z) > ω (µ(z) < ω). Uner this efinition, country i s institutional comparative avantage is ientifie as the sector where the slope of eporters π i is steeper than that of omestic firms π j. Definition 2. orth (South) has institutional comparative avantage in sector z if µ(z) > ω (µ(z) < ω), or equivalently if the slope of π (π S ) is steeper than that of π S (π ). The left panel of Figure 2 epicts π an πs in orthern market uner the conitions that (i) µ(z) = ω an (ii) w S f > w f ω < f f. From the first conition, the two profit functions are parallel in this sector. From the secon conition, Southern eporters bear the higher fie costs (measure by the local labor wage) than orthern omestic firms. Following the same line of reasoning, the profit functions in Southern market, π S an π, are epicte in the right panel of the figure uner the conitions that (i) µ(z) = ω an (ii) w f > w S f ω > f f. 9

11 , S, S S S 0 S 1 0 S 1 w f w S f w S f w f orth South Figure 2. Profits from omestic sales an eports otice that, ue to wage ifferentials, omestic firms in j might bear the higher fie costs than foreign eporters from i in j s market. Because it is empirically well-known that f is huge in any manufacturing sector, 9 I hereafter assume that: Assumption 1. f f < ω < f f. Figure 2 shows that orthern (Southern) firms with prouctivity above ϕ ( ϕ S ) eport to South (orth) an hence two-way trae arises in sector of µ(z) = ω. While this figure epicts only a particular sector where the two profit functions are parallel, one can easily imagine from this partial-equilibrium framework that two-way trae woul happen in any sector z (0, 1) if the slopes of π an π S are positive, i.e., B ( µ w ) ɛ 1 > 0. As will be emonstrate in the net section, this observation survives even in a general-equilibrium setting, although the feeback among enogenous variables imposes some restrictions on eogenous variables. et, I erive the conition uner which the two profit functions are parallel, i.e., µ(z) = ω. From Figure 1, the ratio of contractibility µ(z) = µ (z)/µ S (z) has to satisfy µ(z) > 1, µ (z) < 0, µ (z) > 0, lim z 1 µ(z) = 1, an lim z 0 µ(z) = +, where the first conition stems from the absolute avantage assumption an the thir stems from µ i (z) s log-supermoular property. The relative wage in orth ω, on the other han, shoul be the same for all sectors z (0, 1), because labor is completely mobile across sectors in the Ricarian moel. This suggests that, if ω is greater than one, these two curves intersect at a unique threshol z = µ 1 (ω) such that: (i) 0 < z < z µ(z) > ω; (ii) z = z µ(z) = ω; an (iii) z < z < 1 µ(z) < ω. It is then immeiate from Definition 2 that orth (South) has institutional comparative avantage in relatively customize (generic) sectors. 9 Das, Roberts, an Tybout (2007) econometrically estimate the average costs of foreign market entry among three Colombian manufacturing sectors (leather proucts, knitte fabrics, an basic chemicals), an fin that these fie costs are (i) large enough to cause eport hysteresis an (ii) remarkably similar across these sectors: the average eport costs range from $412,000 (in U.S. ollars) for knitte fabrics to $430,000 for leather proucts. 10

12 While this outcome is reminiscent of Dornbusch, Fischer, an Samuelson s (1977) Ricarian moel with a continuum of goos, there are three notable istinctions between the current paper an theirs. First, since they analyze perfect competition with homogeneous proucts, complete specialization (or inter-inustry trae) occurs below/above the cutoff z. In contrast, this paper stuies monopolistic competition with ifferentiate proucts, an incomplete specialization (or intra-inustry trae) can arise in all manufacturing sectors. Seconly, the number an size of omestic firms an eporters are both ineterminate an irrelevant in their neoclassical moel, but it is enogenously etermine in the current framework in which the number of varieties eporte is only a subset of the number 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 founational role in countries comparative avantage. The result that a less evelope country nevertheless eports ifferentiate goos in the customize sectors seems to be consistent with recent trae flows (see, e.g., Krugman, 2008). Proposition 1. (i) Two-way trae can occur in any sector z (0, 1). (ii) If ω > 1, there eists a unique threshol z (0, 1) such that orth (South) has institutional comparative avantage in z (0, z) (z ( z, 1)). 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. This figure epicts ϕ j < ϕi in this sector, inicating that foreign eporters from i are more prouctive than omestic firms in j. This is not wholly surprising because foreign eporters are assume to incur the higher fie costs uner Assumption 1, an this can be easily formalize by using a partial-equilibrium moel. However, ϕ i an ϕj or ϕi an ϕ j are not comparable. Obviously, ϕ an ϕs ( ϕ an ϕ S ) are etermine at which π = 0 an πs = 0 (π = 0 an π S = 0), but these variables epen on the market eman B i as well as the wage rate w i, both of which are eogenous in partial equilibrium. Also, Proposition 1(ii) 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 moel is embee into a general-equilibrium framework to eamine the interaction among key variables an to see an enogenous pattern of trae. General-Equilibrium Setup This subsection outlines several conitions that play a central role in enogenizing variables in general equilibrium. In the subsequent subsections, I solve this full general-equilibrium moel with some restrictions. 11

13 First of all, a zero profit conition must be satisfie for the cutoff firm in equilibrium, which is achieve by setting ϕ i = inf{ϕ : πi (ϕ) > 0} an ϕi = inf{ϕ : π i (ϕ) > 0} in this static moel. Following Melitz (2003), I refer to this conition as a zero cutoff profit (ZCP) conition: ( ) µ π i i ɛ 1 ( ϕi ) = 0 Bi w i ( ϕ i )ɛ 1 = w i f, (ZCP i) ( ) µ π( i ϕ i ) = 0 B j i ɛ 1 ( ϕ i ) ɛ 1 = w i f, (ZCP) i for i j {, S}. In this conition, aggregate eman of eporters B j is ifferent from that of omestic firms B i since eporters from i compete in the foreign market in j. w i Seconly, a free entry (FE) conition must hol. Since potential entrants are e ante ientical in the moel, this conition is efine as ϕ i π i (ϕ)g(ϕ) + π(ϕ)g(ϕ) i = w i f e, (F E i ) ϕ i where the first an secon terms in the left-han sie respectively enote the epecte operating profits from omestic prouction an eporting earne by potential entrants. The sum of these epecte profits shoul be equal to the fie entry cost w i f e in equilibrium. Finally, a labor market clearing (LMC) conition must be taken into account: 1 0 ϕ i l i (z, ϕ)g(ϕ)z ϕ i l i (z, ϕ)g(ϕ)z = L i. 10 (LMC i ) The first an secon terms in the left-han sie respectively represent the sum of epecte labor emans use for omestic prouction an eporting by potential entrants, where l i (z, ϕ) an l(z, i ϕ) are etermine by the first-orer conitions of profit maimization in Section 2. ote that l i (z, ϕ) is summe up over the whole sectors in the economy because two-way trae can occur in any sector z (0, 1) as seen in Proposition 1. The sum of these epecte labor emans has to be equal to the fie labor supply L i in equilibrium. 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, ϕs, ϕ, ϕ S, B, B S, w, w S, where either LMC conition can be omitte by Walras law, thereby normalizing w i = 1 as a numéraire To be more precise, this is the LMC conition for prouction an the LMC conition for investment in f e shoul be inclue in this conition. As shown in Supplementary ote, the following result oes not change even if the LMC conition for investment is taken into account. 11 As shown by Krugman (1980), another way to enogenize ω = w /w S in general equilibrium is to look at the balance-of-payments (BOP) conition, an the LMC an BOP conitions are equivalent for this etermination. Okubo (2009) uses the BOP conition in the asymmetric-country version of Melitz (2003). 12

14 Relative ZCP an FE Conitions This subsection sets forth the characterization of the eight unknowns from the eight conitions. It is challenging, however, to solve the full general equilibrium moel with asymmetric countries. In particular, without specifying the functional form of the firm size istribution G(ϕ), eplicit solutions of these unknowns cannot be obtaine. In the following, instea of obtaining the eact values of each of them, the main focus is evote to the characterization of the relative terms of these unknowns. Recall from Proposition 1 that orth-south trae arises only if the relative wage in orth is greater than one. Although this ratio is enogenously etermine in equilibrium, for epositional purposes, suppose first ω > 1 hols in the moel. In other wors, the LMC conitions are left out as if the moel were partial-equilibrium. As will be clear, this inequality must be true in general equilibrium, because I assume that orth has absolute avantage in partial contractibility µ. 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 countries. This intuition will be confirme later by integrating the LMC conitions. Uner the circumstance, the relative ZCP conitions are efine by iviing orthern ZCP conition by Southern ZCP conition: ( ω ) 1/(ɛ 1) ω ϕ = B µ, (RZCP ) ϕ = (Bω) 1/(ɛ 1) ω µ, (RZCP ) where all variables are represente by the relative terms in orth (e.g., ϕ = ϕ / ϕs ). It is easy to show that ϕ ϕ B 1. Similarly, iviing orthern FE conition by Southern FE conition yiels the relative FE conition: B = B(µ, ϕ). (RF E) In the above RFE conition, ϕ { ϕ, ϕs, ϕ, ϕ S } must satisfy the ZCP conitions an hence B is enogenously etermine (for given ω). Furthermore, B in the RFE conition shoul be inepenent of ϕ an ϕ as long as the ZCP conitions hol (see Appeni for proof): B ϕ = B ϕ = 0. Shifts in ϕ have only a secon-orer effect on B in the RFE conition for any istribution G(ϕ), since the prouctivity threshols are etermine to satisfy the ZCP conitions in equilibrium. A first-orer effect comes solely from eogenous µ in this setting (see also Appeni): B z = B µ µ z + B ϕ ϕ z + B ϕ ϕ z > In the full general equilibrium moel, there shoul be B ω in the right-han sie of this equation. Since ω z the relative wage in orth is the same across sectors, this has no effect on this relationship. 13

15 B B B, 1, z 1 z Figure 3. Comparative avantage an prouctivity cutoffs The intuition for B (z) > 0 is eplaine by recalling that B is proportional to the price ine ratio P = P /P S. 13 If z is close to one, the institutional ifferential is almost negligible but there eists the wage ifferential (i.e., ω > 1). Thus, South can prouce goos relatively cheaply, leaing to P > P S an B > 1 in the neighborhoo of z = 1. If z is close to zero, the ifferential in µ is sufficiently large to ominate the ifferential in ω (ue to log-supermoularity), resulting in P < P S an B < 1 aroun z = 0. ote from Figure 2 that ϕ = ϕ / ϕs an ϕ = ϕ / ϕ S are equal if an only if π i an πj are parallel at z = z an therefore ϕ ( z) = ϕ ( z) B( z) = 1. Roughly speaking, this mirrors the iea that a country has comparative avantage in the sectors where the aggregate price is relatively lower. Figure 3 illustrates the relationships among the key variables. The first quarant epicts the relationship between z an B. As shown above, B satisfies the ZCP conitions with B (z) > 0 an B( z) = The secon quarant epicts the relationship between B, ϕ, an ϕ from the RZCP conitions. In this figure, once B is enogenously etermine in the first quarant, the horizontal line of the RFE conition is rawn in the secon quarant since B is inepenent of ϕ an ϕ (although it is not epicte in the figure). From the intersections among these three curves, it follows that 0 < z < z B < 1 ϕ > ω 1/(ɛ 1) > ϕ, z = z B = 1 ϕ = ω 1/(ɛ 1) = ϕ, z < z < 1 B > 1 ϕ < ω 1/(ɛ 1) < ϕ, where either ϕ or ϕ is greater than one uner the conition ω > 1. For instance, comparative avantage sectors of orth z (0, z) must satisfy ϕ > ω 1/(ɛ 1) > 1 but whether ϕ 1 is ineterminate in this setup. Base upon this observation, Figure 4 illustrates the relationship among ϕ in comparative avantage sectors of orth (left panel) an South (right panel). While the figure epicts the case of ϕ > 1 an ϕ > 1, this might not hol in the sectors where z is close to zero an 13 From B i = λe i (αp i ) ɛ 1 (1 α), the relative aggregate eman is B = ωlp ɛ 1 = B(µ, ), which implies that etermining B = B /B S are ientical with etermining P = P /P S in equilibrium. 14 The figure epicts lim z 0 B(z) = 0 an lim z 1 B(z) =, but these are not necessarily true in the moel. 14

16 0 s 0, 0 S S S 0 S S S 0 zz z z1 Figure 4. Relationships among ϕ across sectors one. Regarless of whether or not they are greater than one, the gap ϕ i ϕ i is narrower than the gap ϕ j ϕ j in country i s comparative avantage sectors. In aition, this former (latter) gap becomes smaller (bigger) as countries comparative avantage is stronger. More formally, it follows from the ZCP conitions that ϕ ϕ = ( B f ) 1/(ɛ 1), f ϕ S ϕ S = ( ) 1 f 1/(ɛ 1). B f Since B (z) > 0, ϕ / ϕ ( ϕs / ϕ S ) is strictly increasing (ecreasing) in z. This means that, as country i s comparative avantage is stronger, 15 not only are omestic firms more prouctive, but also the prouctivity cutoff for eporting ϕ i is closer to that for omestic prouction ϕ i an relatively less prouctive firms are able to enter the foreign market. Consequently, the ratio of eporting firms to overall surviving firms graually becomes higher in the stronger comparative avantage sectors. The above equations also inicate that the prouctivity cutoff for eporting is bigger than that of omestic prouction ( ϕ i > ϕ i ) in the comparative isavantage sectors for i {, S}.16 In the comparative avantage sectors, the usual outcome ( ϕ i > ϕ i ) occurs in both countries if whereas the perverse outcome ( ϕ i > ϕi ) arises if f f < B < f f, (1) B < f f if i =, f f < B if i = S. ϕ i > ϕi implies that, among surviving firms in i, less prouctive firms serve the foreign market in j only, while more prouctive firms serve the foreign market in j an the home market in i. Clearly, this arises in a sector where countries comparative avantage measure by B is strong enough relative to the fie-cost ratio between f an f. 15 oting that µ(z) = a(z, µ S )/a(z, µ ) is the relative unit labor requirement satisfying µ (z) < 0, comparative avantage of orth (South) is sai to be stronger if z is closer to zero (one) in this moel. 16 From f > f, comparative isavantage sectors of orth, for eample, must satisfy z < z < 1 B > 1 = ϕ > ϕ. (ote also that Assumption 1 has an influence on the relationship between ϕ i an ϕ j for i j {, S}.) 15

17 Proposition 2. (i) Relative to ϕ j ϕ j, the gap ϕi ϕ i is narrow in country i s comparative avantage sectors an this gap is monotonically ecreasing in countries comparative avantage strength. (ii) While ϕ i > ϕ i always hols in country i s comparative isavantage sectors, ϕi > ϕi is possible in etremely strong comparative avantage sectors. These two finings fit well with recent empirical research. The first fining among omestic firms, more firms eport in stronger comparative avantage sectors is consistent with evience in Introuction. The logic of this result comes from the interplay between Ricarian institutional ifference an relative buren of fie eport costs: log-supermoularity in country an sector characteristics allows relatively less prouctive firms to incur fie eport costs relatively easily in comparative avantage sectors. Strictly speaking, however, this is not satisfactory because the percentage of firms that eport cannot be aresse without the number of varieties prouce an eporte. Later I investigate what etermines this number in equilibrium. The secon fining is also in keeping with Lu s (2011) empirical evience that manufacturing eporters in China are typically less prouctive than omestic firms in labor-intensive sectors, but eporters are more prouctive in capital-intensive sectors. To rationalize this evience, Lu evelops a Heckscher-Ohlin moel with heterogeneous firms, emphasizing that allowing factor intensity to vary across sectors is crucial for the Melitz moel of orth-south trae. Although my theoretical focus is apparently ifferent from hers, the central message is surprisingly similar: eporters can be less prouctive than omestic firms in comparative avantage sectors, whereas eporters are always more prouctive in comparative isavantage sectors. The rationale for this outcome is as follows. In comparative isavantage sectors of i, a foreign market in j is more competitive than a omestic market in i since foreign firms are relatively better at proucing. Thus, eporters from i must be sufficiently prouctive, not only because they have to cover the fie eport cost, but also because they have to compete with more efficient foreign rivals in the eport market. In comparative avantage sectors of i, on the other han, foreign competitors are relatively less efficient an hence relatively less prouctive firms in i coul fin it profitable to enter the foreign market. This is the reason why the partitioning of firms by eport status might not be inuce only with f > f in comparative avantage sectors. If ϕ i > ϕi were true, however, all surviving firms in i coul eport, which is not supporte by evience. 17 This result shoul be interprete as meaning that aggregate prouctivity premia of eporters relative to omestic firms are smaller in a stronger comparative avantage sector. I eclue ϕ i > ϕi by assuming that f is large enough to satisfy (1) in any sector. Full General Equilibrium The previous subsection provies implicit solutions of B an ϕ for given ω (an z). This subsection eplores full general-equilibrium interactions by eplicitly incorporating the LMC conitions. I show that the relative wage in orth is greater than one, a sufficient conition of orth-south trae require in Proposition In Lu s (2011) ataset, ϕ i > ϕ i occurs because it inclues Chinese eporters involve in processing trae. If firms engage in final-goo trae only as in the current moel, this possibility woul not eist. 16

18 Recall that, while the ZCP an FE conitions must hol for each sector, the LMC conition must hol for all sectors. To obtain the corresponing LMC conition for each sector, I use the assumption that consumers epeniture is equally istribute across sectors in both countries, i.e., λ i z = λ. Uner this assumption, the previous LMC conition can be written as ϕ i l i (ϕ)g(ϕ) + l(ϕ)g(ϕ) i = λl i, ϕ i where 1 0 λli z = L i. otice that the result of Proposition 1(i) (i.e., two-way trae can occur in any sector) greatly simplifies the analysis. From the first-orer conitions in Section 2, labor emans for omestic prouction an eporting by an iniviual firm with prouctivity ϕ are respectively given by l i (ɛ 1)Bi ( (ϕ) = ϕµ i ) ɛ 1 + f (w i ) ɛ, l(ϕ) i (ɛ 1)Bi ( = ϕµ i ) ɛ 1 + f (w i ) ɛ. Substituting these values into the above LMC conition an iviing orthern LMC conition by Southern LMC conition, the relative LMC conition is efine as below (see Appeni for etails): ( Bµ ɛ 1 ) 1/ɛ Ψ ξ =, (RLMC) Γ where both Ψ an Γ are a function of prouctivity cutoffs ϕ, an Γ is also a function of labor supply L i. It is verifie that ξ is an increasing function of z satisfying lim z 1 ξ(z) > 1 (for B an ϕ seen in the last subsection). Intuitively, these properties follow from the fact that orth has stronger comparative avantage in the sectors where the relative wage (summarize in ξ) is relatively lower. Figure 5 epicts ξ curve in (z, ω) space. The other conition that pins own z an ω is the relative partial contactibility in orth µ = µ /µ S in Section 3. Among µ s properties, µ > 1 (orthern absolute avantage) an µ > 0 (log-supermoularity) are of particular importance. It is clear from the figure that ω is always greater than one. ξ an µ curves shoul intersect at ( z, ω) because ω = ω(b(z), ϕ (z), ϕ (z)) is epresse in terms of ω at z = z, i.e., B( z) = 1 an ϕ ( z) = ϕ ( z) = ω 1/(ɛ 1), implying also that ω is enogenous. This ω in turn leas to enogenous solutions of B, ϕ, an ϕ, which completes the characterization of the eight unknowns in equilibrium. Proposition 3. The relative wage in orth is greater than one in general equilibrium, i.e., ω > 1. It is worthwhile to stress that the above channel is akin to that evelope by Antràs (2005), who shows (with homogeneous firms) that, irrespective of the relative country size L = L /L S, better contracting environments in orth lea to the higher relative wage in general equilibrium. As in his moel, the equilibrium outcome ω > 1 irectly reflects that orth has superior partial contractibility which helps mitigate the serious holup problem. This in turn gives rise to better prouction efficiency an overall higher prouctivity (i.e., wage) in orth. 17