Institutions as a Ricardian Source of Comparative Advantage

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1 Institutions as a Ricarian Source of Comparative Avantage Tomohiro Ara Fukushima University June 2013 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 North-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, North with better institutions prouces relatively more in sectors where prouction is more institutionally epenent. In aition, institution-inuce comparative avantage makes it relatively easier for Northern heterogeneous firms to incur export costs in more contract-epenent sectors, thereby leaing to a higher exporters percentage. Keywors: Contracting institutions, heterogeneous firms, comparative avantage JEL Classification Numbers: 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, Raymon Riezman, Nicolas Schmitt, an seminar an conference participants at various institutions for helpful comments an suggestions. I have also benefite from financial support from UNSW, Hitotsubashi University, an JSPS uner grant # All errors are my own. 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 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 the share of exporters steaily eclines as sectors prouction requires simpler an more generic technology (such as textile 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. 1 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 (2007) an Nunn (2007) with firm heterogeneity of Melitz (2003), I evelop a general-equilibrium Ricarian moel of North-South trae in which both institutional quality an firm heterogeneity play a key role in etermining international trae flows. Following Levchenko s an Nunn 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 North has better institutions for partially ex-ante contractible activities than South, whereas customize sectors make use of relationshipspecific 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 contrac- 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 example, Bernar et al. (2007, Table 2) report that, as of 2002, 36 percent (8 percent) of U.S. firms export in a chemical manufacturing sector (an apparel manufacturing sector), whereby a more customize sector tens to exhibit a higher percentage of exporters among 21 sectors. Conversely, Lu (2011, Figure 1) shows that, as of 2005, aroun 60 percent (less than 20 percent) of Chinese firms export in cloth an fur manufacturing sectors (a chemical manufacturing sector), inicating that there exists a clear negative relationship between export participation an the capital-labor ratio among 29 sectors. Finally, Bernar et al. (2003, 2007), Tomiura (2007), an Lu (2011) all ocument that there exist some exporting firms in every manufacturing sector. 1

3 tual incompleteness an technological complementarity by simply assuming that prouction in customize (generic) sectors is more (less) epenent on institutions. 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 North 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 Northern (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 in 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. 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 contracts can have quantitatively larger impacts on comparative avantage than countries resource enowments. For instance, Nunn (2007) estimates that contract enforcement explains 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. 3 In 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), Nunn (2007) shows that countries with better contract enforcement export relatively more in sectors for which relationship-specific investments are more important. Similarly, Manova (2008) fins evience that trae liberalizations inuce countries with better financial systems to export relatively more in sectors for which financial requirements are more important. For the other relate papers in this literature, see Costinot (2009a). 3 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 Nunn (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 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 (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 explain why North 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. In so oing, the moel shows that North with better institutions gains 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 empirical evience, hol even if North has 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, 2005; Acemoglu et al., 2007; Costinot, 2009b). These papers show that, even in the absence of 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 (2003). While the Melitz moel is successful in explaining the exporters behaviors among evelope countries (North- North trae), recent empirical evience has pointe out that this moel is less suitable 4 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 export in their moel. 3

5 for the stuy of bilateral trae flows between ifferent countries (North-South trae), as exemplifie 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 North-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 factorproportions 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 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 (1980) home-market effect. I show that, ue to selection into omestic an export markets that varies with comparative avantage, the home-market effect works quite ifferently for the number of omestic firms (specialization) an the number of exporters (trae). 2 Setup Consier a worl composing of two large countries, North an South, i {N, 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 Dixit-Stiglitz within 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 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 ifferentials between the U.S. an eveloping countries: China s an Mexico s wages are respectively only 4 percent an 13 percent of the U.S. level. 4

6 sectors: where 1 0 U = 1 0 λ z ln X z z, [ ] 1/α λ z z = 1, X z = x z (v) α v. v V z λ z enotes the share of expeniture 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 x 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 North an South. 6 This structure of the preferences is similar to that of Krugman (1980), an more recently to that of Antràs (2005) an Okubo (2009). Notice 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. As is well-known, the above preferences generate eman functions in sector z, x = Ap 1/(1 α), where A = λe 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 inex 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 that prouce a ifferent variety v V z in sector z. Labor is the only factor of prouction to prouce a variety in each sector an firms face 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 across countries as in conventional Ricarian moels, w is the same across sectors within a country but 6 By excluing a homogeneous-goo sector, I can explicitly investigate the role of the relative wage or factoral terms of trae (Matsuyama, 2008) in comparative avantage, which is an orthoox 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. 5

7 is ifferent across countries. 7 Following Krugman (1980) an Melitz (2003), firm technology is summarize in a linear cost function of output x: f + l = f x + x = f θ(ϕ,z,µ) + τx = f θ(ϕ,z,µ) x + x ϕµ(z) τx ϕµ(z) 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( 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 sectorspecific 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 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 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: 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 ln a(z, µ) 0), or equivalently z µ 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 7 I recognize that wage inequality exists across sectors as well as within sectors (Helpman, Itskhoki, Muenler, an Reing, 2013), 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 general-equilibrium Ricarian moel with a continuum of sectors. 6

8 i z 1 N z S z 0 Customize Generic 1 z Figure 1. Log-supermoularity in contractibility 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 North has partial contractibility strictly superior to South in any sector. Noting the inverse relationship between µ( ) an a(, ), logsupermoularity in terms of µ( ) is given by 1 < µn (z) µ S (z) < µn (z ) µ S (z ) < +, for z > z, µ N > 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 North 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 N (1) = µ S (1) = 1 an µ S (0) = 0. As epicte in the figure, logsupermoularity means in this framework that the gap between µ N an µ S is graually larger as sectors prouction becomes 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 N 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 North 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 Nunn (2007) is elegantly capture by log-supermoularity. 7

9 Finally, in this ecomposition θ(ϕ, z, µ) = ϕµ(z), I refer to a country s istribution G(ϕ) of firms prouctivity raws ϕ as technologies as in Melitz (2003), whereas a country s partial contractibility µ(z) on firms relationship-specific investments as institutions as in Levchenko (2007). 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 {N, S} an z (0, 1). 8 Consequently, 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. This istinction is not crucial for the analysis below an the following efinition is mae for the sake of convenience. Definition 1. Technologies are a country s istribution G(ϕ) of firms prouctivity raws ϕ, which is ientical across countries an sectors. Institutions are a country s partial contractibility µ(z) on firms relationship-specific investments, which varies across countries an sectors. Each firm chooses its price to maximize π = px wl. Solving this profit-maximizing problem yiels the following first-orer conitions: p = w ϕαµ, ( ϕαµ ) ɛ x = A, w ( µ ) ɛ 1 π = B ϕ ɛ 1 wf, w ( µ ) ɛ 1 π x = B ϕ ɛ 1 wf x, w where B = Aα ɛ 1 (1 α) = λe(αp ) ɛ 1 (1 α). For analytical simplicity, I assume that transport costs are zero (τ = 1) an thus p = p = p x. Section 5 iscusses how the following results are moifie if τ > 1. It is also assume that f x > f, which is require for the partitioning between exporters an nonexporters an, uner this assumption, only a subset of firms export 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 North an South, since countries are asymmetric an there is no freely traable 8 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 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). 8

10 homogeneous-goo sector in this moel. For instance, Melitz (2003) assumes symmetric countries, whereas Helpman, Melitz, an Yeaple (2004) introuce a homogeneous-goo sector to equalize wages 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 explicitly explore. As originally propose by Grossman an Hart (1986), the holup problem in relationship-specific investments occurs because 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 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 by itself. To prouce a variety, every firm asks a omestic input supplier to provie a specialize input. This input is relationship-specific in the sense that it has a higher value within the parties an a thir party (such as courts of law) cannot istinguish its true value. Because 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 1 β enote respectively the firm s an its supplier s bargaining power. Then, the firm s profit is π F = βpx+t an the supplier s profit is π S = (1 β)px wl T, where T is a transfer from the supplier to the firm. 9 This transfer works to make the supplier break-even an the firm s ex-post profit is π = π F + π S = px wl in a subgameperfect Nash equilibrium. The supplier chooses its price to maximize π S, so the optimal pricing rule is p = w ϕα(1 β). Comparing the two pricing rules reveals µ = 1 β in equilibrium. Thus, the above moel implies that the supplier s bargaining power is lower in a more customize sector because a fraction of ex-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 9 Note 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 (2012) for etails. 9

11 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 contracts. Firm Behavior The current paper analyzes a static version of the Melitz (2003) moel. To enter a sector in country i {N, 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 z(ϕ) = G(ϕ). 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 < 0, or woul prouce an serve its omestic market if π i 0. Moreover, among omestic firms, only the most prouctive firms woul earn πx i 0 an serve the foreign market in j as exporters because 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 0 an πx j 0 for some firms in i j {N, 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 0 for some firms an πx j < 0 for any firm, on the contrary, one-way (inter-inustry) trae occurs in this sector, whereby exporting from country i to country j takes place. 3 Partial Equilibrium In this section, I explore a partial equilibrium in which some important variables are exogenously given. The next 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 exporters from i. From the first-orer conitions in the previous section, the profit functions of these firms are respectively given by ( ) µ π j j ɛ 1 = (z) Bj ϕ ɛ 1 w j f, w j π i x = B j ( µ i (z) w i ) ɛ 1 ϕ ɛ 1 w i f x. Notice that, since they compete in j s market, aggregate eman B j is common for both of the profit functions. π j an πi x are measure by ifferent wage rates an contractibility 10

12 levels, however, because exporters from i 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 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 x is steeper (flatter) than π j if an only if µ i (z) µj (z) µ(z) ω if i = N, w i w j µ(z) ω if i = S, where µ(z) = µ N (z)/µ S (z) = a(z, µ S )/a(z, µ N ) an ω = w N /w S respectively enote the relative contractibility (or relative labor requirement) an relative wage in North. Following stanar Ricarian moels, I say that North (South) has institutional comparative avantage in sector z if it has a large (small) relative labor prouctivity in partial 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 sectors where the slope of exporters π i x is steeper than that of omestic firms π j. Definition 2. North (South) has institutional comparative avantage in sector z if µ(z) > ω (µ(z) < ω), or equivalently if the slope of π N x (π S x ) is steeper than that of π S (πn ). The left panel of Figure 2 epicts π N an πs x in Northern market uner the conitions that (i) µ(z) = ω an (ii) w S f x > w N f ω < f x f. From the first conition, the two profit functions are parallel in this sector. From the secon conition, Southern exporters bear the higher fixe costs (measure by the local labor wage) than Northern omestic firms. Following the same line of reasoning, the profit functions in Southern market, π S an π N x, are epicte in the right panel of the figure uner the conitions that (i) µ(z) = ω an (ii) w N f x > w S f ω > f f x. Notice that, ue to wage ifferentials, omestic firms in j might bear the higher fixe costs than foreign exporters from i in j s market. Because it is empirically well-known that f x is huge in any manufacturing sector, 10 I hereafter assume that: Assumption 1. f f x < ω < f x f. 10 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 fixe costs are (i) large enough to cause export hysteresis an (ii) remarkably similar across these sectors: the average export costs range from $412,000 (in U.S. ollars) for knitte fabrics to $430,000 for leather proucts. 11

13 , N S x, S N x N S S x N x 0 N S x 1 0 S N x 1 w N f w S f w S fx w N fx North South Figure 2. Profits from omestic sales an exports Figure 2 shows that Northern (Southern) firms with prouctivity above ϕ N x ( ϕ S x) export to South (North) an hence two-way trae occurs 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 occur in any sector z (0, 1) if the slopes of π N x an π S x are positive, i.e., B ( µ w) ɛ 1 > 0. As will be emonstrate in the next section, this observation survives even in a generalequilibrium setting, although the feeback among enogenous variables imposes some restrictions on exogenous variables. Next, 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 N (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 North 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 North (South) has institutional comparative avantage in relatively customize (generic) sectors. 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 12

14 the cutoff z. In contrast, this paper stuies monopolistic competition with ifferentiate proucts, an incomplete specialization (or intra-inustry trae) can occur in all manufacturing sectors. Seconly, the number an size of omestic firms an exporters are both ineterminate an irrelevant in their neoclassical moel, but it is enogenously etermine in the current framework in which the number of varieties exporte is only a subset of the number of varieties prouce in the home market. Finally, this paper s focus is on North-South trae where the ifference in economic evelopment plays a prominent role in countries comparative avantage. The result that a less evelope country nevertheless exports ifferentiate proucts in 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 exists a unique threshol z (0, 1) such that North (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 x in this sector, inicating that foreign exporters from i are more prouctive than omestic firms in j. This is not wholly surprising because foreign exporters are assume to incur the higher fixe costs uner Assumption 1, an this can be easily formalize by using a partial-equilibrium moel. However, ϕ i an ϕj or ϕ i x an ϕ j x are not comparable. Obviously, ϕ N an ϕs ( ϕn x an ϕ S x) are etermine at which π N = 0 an πs = 0 (πn x = 0 an π S x = 0), but these variables epen on the market eman B i as well as the wage rate w i, both of which are exogenous in partial equilibrium. Also, Proposition 1(ii) requires that ω shoul be greater than one if North- 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 examine the interaction among key variables an to see an enogenous pattern of trae. 13

15 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. 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 x = inf{ϕ : π i x(ϕ) > 0} in this static moel. Following Melitz (2003), I refer to this conition as a zero cutoff profit (ZCP) conition: ( ) µ π( i ϕ i ) = 0 B i i ɛ 1 ( ϕ i w ) ɛ 1 = w i f i, (ZCP i) ( ) µ πx( i ϕ i x) = 0 B j i ɛ 1 ( ϕ i x) ɛ 1 = w i f x, (ZCPx) i for i j {N, S}. In this conition, aggregate eman of exporters B j is ifferent from that of omestic firms B i as exporters from i compete in the foreign market in j. w i Seconly, a free entry (FE) conition must hol. Since potential entrants are ex ante ientical in the moel, this conition is efine as ϕ i π i (ϕ)g(ϕ) + ϕ i x π i x(ϕ)g(ϕ) = w i f e, (F E i ) where the first an secon terms in the left-han sie respectively enote the expecte operating profits from omestic prouction an exporting earne by potential entrants. The sum of these expecte profits shoul be equal to the fixe 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 x l i x(z, ϕ)g(ϕ)z = L i. 11 (LMC i ) The first an secon terms in the left-han sie respectively represent the sum of expecte labor emans use for omestic prouction an exporting by potential entrants, where l i (z, ϕ) an li x(z, ϕ) are etermine by the first-orer conitions of profit maximization in Section 2. Note that l i x(z, ϕ) is summe up over sectors of the economy as a whole, because two-way trae can occur in any sector z (0, 1) as seen in Proposition 1. The sum of these expecte labor emans has to be equal to the fixe labor supply L i in equilibrium. Now, 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 North 11 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 Note, the following result oes not change even if the LMC conition for investment is taken into account. 14

16 an South), these conitions provie implicit solutions for the following eight unknowns: ϕ N, ϕ S, ϕ N x, ϕ S x, B N, B S, w N, w S, where either LMC conition can be omitte by Walras law, thereby normalizing w i = 1 as a numéraire. 12 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), 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 1 that North-South trae occurs only if the relative wage in North ω is greater than one. Although ω is enogenously etermine in the moel, suppose first that ω > 1 hols 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 North has 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 North, an thus wages have to be greater in North 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, the relative ZCP conitions are efine by iviing Northern ZCP conition by Southern ZCP conition: ( ω ϕ = B ) 1/(ɛ 1) ω µ, (RZCP ) ϕ x = (Bω) 1/(ɛ 1) ω µ, (RZCP x) where all variables are represente by the relative terms in North (e.g., ϕ = ϕ N / ϕs ). It is easy to show that ϕ x ϕ B 1. Similarly, iviing Northern FE conition by Southern FE conition yiels the relative FE conition: B = B(µ, ϕ). (RF E) 12 As shown by Krugman (1980), another way to enogenize ω = w N /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). 15

17 B x B B, 1, x z 1 z Figure 3. Comparative avantage an prouctivity cutoffs In the above RFE conition, ϕ { ϕ N, ϕs, ϕn x, ϕ S x} 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 x as long as the ZCP conitions hol (see Appenix for proof): B = B = 0. ϕ ϕ x 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 exogenous µ in this setting (see also Appenix): B z = B µ µ z + B ϕ ϕ z + B ϕ x ϕ x z > 0.13 The intuition for B (z) > 0 is explaine by recalling that B is proportional to the price inex ratio P = P N /P S. 14 If z is close to one, the institutional ifferential is almost negligible but there exists the wage ifferential (i.e., ω > 1). Thus, South can prouce goos relatively cheaply, leaing to P N > 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 N < P S an B < 1 aroun z = 0. Note from Figure 2 that ϕ = ϕ N / ϕs an ϕ x = ϕ N x / ϕ S x are equal if an only if π i an πj x are parallel at z = z an therefore ϕ ( z) = ϕ x ( z) B( z) = 1. Roughly speaking, this mirrors the iea that a country has comparative avantage in 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 13 In the full general equilibrium moel, there shoul be B ω ω z in the right-han sie of this equation. Since the relative wage in North is the same across sectors, this has no effect on this relationship. 14 From B i = λe i (αp i ) ɛ 1 (1 α), the relative aggregate eman is B = ωlp ɛ 1 = B(µ, ϕ), which implies that etermining B = B N /B S are ientical with etermining P = P N /P S in equilibrium. 16

18 0 N N x N s 0 N N x N, 0 S S x S 0 S S x S 0 zz z z1 Figure 4. Relationships among ϕ across sectors with B (z) > 0 an B( z) = The secon quarant epicts the relationship between B, ϕ, an ϕ x 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 x (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 x, z = z B = 1 ϕ = ω 1/(ɛ 1) = ϕ x, z < z < 1 B > 1 ϕ < ω 1/(ɛ 1) < ϕ x, where either ϕ or ϕ x is greater than one uner the conition ω > 1. For instance, comparative avantage sectors of North, z (0, z), must satisfy ϕ > ω 1/(ɛ 1) > 1 but whether ϕ x 1 is ineterminate in this setup. Base upon this observation, Figure 4 illustrates the relationship among ϕ in comparative avantage sectors of North (left panel) an South (right panel). While the figure epicts the case of ϕ x > 1 an ϕ > 1 in the both panels, this might not hol in the sectors where z is close to zero an one. Regarless of whether or not they are greater than one, the gap ϕ i x ϕ i is narrower than the gap ϕj x ϕ j in country i s comparative avantage sectors. In aition, this former (latter) gap becomes smaller (bigger) as country i s comparative avantage is stronger. More formally, it follows from the ZCP conitions that ϕ N x ϕ N = ( B f ) 1/(ɛ 1) x, f ϕ S x ϕ S = ( ) 1/(ɛ 1) 1 f x. B f Since B (z) > 0, ϕ N x / ϕ N ( ϕ S x/ ϕ S ) is strictly increasing (ecreasing) in z. This means that, as country i s comparative avantage is stronger, 16 not only are omestic firms more prouctive, but also the prouctivity cutoff for exporting ϕ i x is closer to that for omestic prouction ϕ i an relatively less prouctive firms are able to enter the foreign 15 The figure epicts lim z 0 B(z) = 0 an lim z 1 B(z) =, but these are not necessarily true in the moel. 16 Noting that µ(z) = a(z, µ S )/a(z, µ N ) is the relative unit labor requirement satisfying µ (z) < 0, comparative avantage of North (South) is sai to be stronger if z is closer to zero (one) in this moel. 17

19 market. Consequently, the moel preicts a higher ratio of exporting firms to overall surviving firms in sectors where countries are relatively more prouctive. The above equations also inicate that the prouctivity cutoff for exporting is bigger than that of omestic prouction ( ϕ i x > ϕ i ) in the comparative isavantage sectors for i {N, S}. 17 In the comparative avantage sectors, the usual outcome ( ϕ i x > ϕ i ) occurs in both countries if whereas the perverse outcome ( ϕ i > ϕi x) occurs if f f x < B < f x f, (1) B < f f x if i = N, f x f < B if i = S. ϕ i > ϕi x 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 occurs in sectors where countries comparative avantage measure by B is strong enough relative to the fixe-cost ratio between f an f x. Proposition 2. (i) Relative to ϕ j x ϕ j, the gap ϕi x 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 x > ϕ i always hols in country i s comparative isavantage sectors, ϕi > ϕ i x is possible in extremely strong comparative avantage sectors. These two finings fit well with recent empirical research. The first fining among omestic firms, more firms export in stronger comparative avantage sectors is consistent with evience in Introuction. The logic of this result comes from the interplay between Ricarian prouctivity ifferences an relative burens of fixe export costs: log-supermoularity in country an sector characteristics allows relatively less prouctive firms to incur fixe export costs relatively more easily in comparative avantage sectors. Strictly speaking, this observation is not satisfactory because the percentage of firms that export cannot be aresse without the numbers of varieties prouce an exporte. Later I investigate what etermines these numbers in equilibrium. 17 From f x > f, comparative isavantage sectors of North, for example, must satisfy z < z < 1 B > 1 = ϕ N x > ϕ N. (Note also that Assumption 1 has an influence on the relationship between ϕ i an ϕj x for i j {N, S}.) 18

20 The secon fining is also in keeping with Lu s (2011) empirical evience that manufacturing exporters in China are typically less prouctive than omestic firms in labor-intensive sectors, but exporters 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 North-South trae. Although my theoretical focus is apparently ifferent from hers, the central message is surprisingly similar: exporters can be less prouctive than omestic firms in comparative avantage sectors, whereas exporters 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, exporters from i must be sufficiently prouctive, not only because they have to cover the fixe export cost, but also because they have to compete with more efficient foreign rivals in the export 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 export status might not be inuce only with f x > f in comparative avantage sectors. If ϕ i > ϕi x were true, however, all surviving firms in i coul export, which is not supporte by evience. 18 This result shoul be interprete as meaning that aggregate prouctivity premia of exporters relative to omestic firms are smaller in stronger comparative avantage sectors. I exclue ϕ i > ϕi x by assuming that f x 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 explores full general-equilibrium interactions by explicitly incorporating the LMC conitions. I show that the relative wage in North is greater than one, a sufficient conition of North-South trae require in Proposition 1. Recall that, while the ZCP an FE conitions must hol for each sector, the LMC conition must hol for sectors as a whole. To obtain the corresponing LMC conition for each sector, I use the assumption that consumers expeniture 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 l i (ϕ)g(ϕ) + ϕ i ϕ i x l i x(ϕ)g(ϕ) = λl i, 18 In Lu s (2011) ataset, ϕ i > ϕi x occurs because it inclues Chinese exporters involve in processing trae. If firms engage in final-goo trae only as in the current moel, this possibility woul not exist. 19

21 where 1 0 λli z = L i. Notice 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 exporting by an iniviual firm with prouctivity ϕ are respectively given by l i (ϕ) = (ɛ 1)Bi (w i ) ɛ ( ϕµ i ) ɛ 1 + f, l i x(ϕ) = (ɛ 1)Bi (w i ) ɛ ( ϕµ i ) ɛ 1 + fx. Substituting these values into the above LMC conition an iviing Northern LMC conition by Southern LMC conition, the relative LMC conition is efine as below (see Appenix 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 ξ summarizes the labor-market-clearing conition in each country. If z is higher for a given ω, there are more labor emans in North an Southern prouction is less likely. For North-South trae to occur, therefore, ξ must be increasing in z so that Northern labor is more expensive, thereby ensuring some Southern labor emans in equilibrium. Figure 5 epicts ξ curve in (z, ω) space. The other conition that pins own z an ω is the relative partial contactibility µ = µ N /µ S. Among µ s properties, µ > 1 (Northern absolute avantage) an µ > 0 (log-supermoularity) are of particular importance. Figure 5 epicts µ curve in the same space an the intersection of ξ an µ curves shows that ω is greater than one. These two curves intersect at ( z, ω) because ω = ω(b(z), ϕ (z), ϕ x (z)) is expresse in terms of ω at z = z, i.e., B( z) = 1 an ϕ ( z) = ϕ x ( z) = ω 1/(ɛ 1), implying also that ω is enogenous. This ω in turn leas to enogenous solutions of B, ϕ, an ϕ x, which completes the characterization of the eight unknowns in equilibrium. Proposition 3. The relative wage in North 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 N /L S, better contracting environments in North lea to the higher relative wage in general equilibrium. As in his moel, the equilibrium outcome ω > 1 irectly reflects that North has superior partial contractibility which helps mitigate the serious 20