NBER WORKING PAPER SERIES FACTOR PRICES AND INTERNATIONAL TRADE: A UNIFYING PERSPECTIVE. Ariel Burstein Jonathan Vogel

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1 NBER WORKING PAPER SERIES FACTOR PRICES AND INTERNATIONAL TRADE: A UNIFYING PERSPECTIVE Ariel Burstein Jonathan Vogel Working Paper NATIONAL BUREAU OF ECONOMIC RESEARCH 050 Massachusetts Avenue Cambrige, MA 0238 March 20 We thank Arnau Costinot, Javier Cravino, Gene Grossman, Stephen Reing, an Anrés Roríguez-Clare for very useful comments an the National Science Founation (uner Grant SES ) for research support. A previous version of this paper circulate uner the name "International Trae Patterns, the Skill Premium, an Heterogeneous Firms." The views expresse herein are those of the authors an o not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulate for iscussion an comment purposes. They have not been peerreviewe or been subject to the review by the NBER Boar of Directors that accompanies official NBER publications. 20 by Ariel Burstein an Jonathan Vogel. All rights reserve. Short sections of text, not to excee two paragraphs, may be quote without explicit permission provie that full creit, incluing notice, is given to the source.

2 Factor Prices an International Trae: A Unifying Perspective Ariel Burstein an Jonathan Vogel NBER Working Paper No March 20 JEL No. F ABSTRACT How o trae liberalizations affect relative factor prices an to what extent o they cause factors to reallocate across sectors? We first present a general framework that nests a wie range of moels that have been use to stuy the link between globalization an factor prices. Uner some restrictions, changes in the "factor content of trae" are sufficient statistics for the impact of trae on relative factor prices. We then stuy the etermination of the factor content of trae in a specific version of our general framework featuring imperfect competition, increasing returns to scale, an heterogeneous proucers. We show how heterogeneous firms' ecisions shape the factor content of trae, an, therefore, the impact of trae liberalization on relative factor prices an between-sector factor allocation. Ariel Burstein Department of Economics Bunche Hall 8365 Box UCLA Los Angeles, CA an NBER arielb@econ.ucla.eu Jonathan Vogel Department of Economics Columbia University 420 West 8th Street New York, NY 0027 an NBER jvogel@columbia.eu

3 Introuction How o trae liberalizations a ect the skill premium, or relative factor prices more generally, an to what extent o they cause factors to reallocate between sectors an across proucers within sectors? This paper o ers a unifying perspective on the funamental forces that shape factor prices an factor allocation in a global economy. In the rst part of the paper we provie a set of su cient statistics for the etermination of factor prices across a wie range of international trae moels. To o so, we consier a general framework that imposes only one key restriction: all e ciency units of a given factor employe in a country receive a common price. Given its generality, this framework nests the traitional Heckscher-Ohlin moel, which emphasizes i erences in factor intensities across sectors an factor enowments across countries. It also nests other moels emphasizing, e.g., i erences in skill intensities between exporters an non-exporters within sectors, i erences in the traeability of skill-intensive an unskill-intensive goos, an complementarities between skille labor an trae goos such as capital 2 that have been use to stuy the link between international trae an the skill premium. 3 We show that within this framework, each factor price can be expresse as the prouct of two components. The rst component is the inverse of the trae-ajuste factor supply, which is the omestic supply of that factor less the factor content of trae (FCT); the FCT is the quantity of that factor emboie in the country s net exports. A ecrease in the trae-ajuste factor supply increases the factor s price, just like a ecrease in its omestic supply. The secon component is the factor payments for omestic absorption, which is the counterfactual payments to that factor if omestic sectoral absorption were prouce omestically; this component epens on omestic sectoral expeniture shares an factor shares in sectoral revenues. An increase in the average revenue share of a factor increases the price of this factor. We use this ecomposition to show how various mechanisms (which have been propose to link trae to factor price) operate through these two components. Uner some aitional restrictions, the ratio of factor payments for omestic absorption between any two factors is constant, so that changes in relative factor prices epen only on trae-ajuste factor supplies. In any moel satisfying these restrictions, changes in the FCT See e.g. Feenstra (2004) for a textbook presentation of this moel an its implications for trae patterns an factor prices 2 See e.g. Yeaple (2005), Matsuyama (2007), an Burstein an Vogel (200) for the rst mechanism, Epifani an Gancia (2006) for the secon, an Burstein, Cravino, an Vogel (200) an Parro (200) for the thir. 3 The restriction that all employe e ciency units of a given factor receive a common price is relaxe in the trae an search literature; see e.g. Davison, Matusz, an Shevchenko (2008) an Helpman, Itskhoki, an Reing (200).

4 are su cient statistics for the impact of trae on the relative price of any two factors if the omestic supplies of those two factors are xe: changes in the economic environment such as trae costs, foreign prouctivities, foreign factor supplies, foreign prouction functions, omestic prouctivities, or omestic supplies of other factors a ect omestic relative factor prices only through changes in the FCT. A similar result has been obtaine previously by Dearor an Staiger (988) an Dearor (2000) in perfectly competitive environments with constant returns to scale an common prouction technologies across proucers within sectors. 4 We show that this result applies more generally in moels with imperfect competition, increasing returns to scale, an heterogeneous proucers. While our general framework makes a clear link between the FCT an factor prices, it takes the FCT as given. Hence, it oes not provie insights into how changes in the economic environment, such as changes in trae costs, a ect the FCT an relative factor prices. Moreover, while the FCT is a powerful su cient statistic to assess the impact of trae on factor prices across a range of moels, measuring the FCT in the ata requires etaile information on factor employment an trae across highly isaggregate inustries, which may be unavailable in practice; see e.g. Feenstra an Hanson (2000). The secon part of the paper stuies the etermination of the FCT. To o so, we specialize the general framework above to an environment with two-countries, two-factors (skille an unskille labor), an two-sectors, as in the Heckscher-Ohlin moel; with sectoral prouctivity i erences across countries, as in the Ricarian moel; an with monopolistic competition an heterogeneous rms, as in Melitz (2003) an Bernar, Reing, an Schott (2007). In this moel, the ratio of factor payments for omestic absorption between any two factors is constant, so that the FCT fully etermines the relative price of skille to unskille labor (the skill premium), as in our general framework. Moreover, the FCT also fully etermines the extent of between-sector factor reallocation an between-sector trae. The FCT is shape by comparative avantage, which is etermine by cross-country i erences in factor enowments an sectoral prouctivities as in the stanar Heckscher- Ohlin an Ricarian moels, respectively. The strength of comparative avantage, however, is also shape by rms ecisions to enter an to operate in each market, which are absent in these stanar moels. In particular, an increase in the mass of country rms that sell in a given estination market in a given sector is equivalent in terms of its impact on the FCT, the skill premium, between-sector factor reallocation, an between-sector trae to an increase in country s exogenous Ricarian prouctivity in that sector. The mass of rms selling to a given estination increases either because of an increase in the mass of entering 4 Many empirical papers use this theoretical result to quantify the e ects of trae on the skill premium; see e.g. Katz an Murphy (992) an Krugman (995). 2

5 rms or because of an increase in the fraction of entrants that operate in the estination. Moreover, the extent to which changes in the mass of rms selling in each estination a ects the FCT epens on the egree of prouctivity heterogeneity. We use this logic to obtain the following results on the impact of trae liberalization on the FCT an, hence, on the skill premium an the extent of between-sector factor reallocation an between-sector trae. We rst show that a reuction in trae costs inuces countries to expan prouction an exports in their comparative avantage sector an contract prouction elsewhere, as in the Heckscher-Ohlin an Ricarian moels. This between-sector reallocation lowers the traeajuste supply of the factor use intensively in the comparative avantage sector (by raising its FCT) an hence raises its relative price. This e ect is often referre to as the Stolper- Samuelson e ect. We then stuy how the impact on the FCT an, hence, the change in the skill premium an the extent of between-sector trae an factor reallocation of moving from autarky to given aggregate trae shares is shape by the extent of prouctivity heterogeneity an by heterogeneous rms ecisions to enter an operate in each market. Greater within-sector prouctivity heterogeneity weakens ex-ante comparative avantage, reucing the magnitue of the change in the FCT an, hence, the change in the skill premium an the extent of between-sector trae an factor reallocation for a given change in trae shares. Given the extensive evience of large prouctivity i erences within narrowly-e ne sectors, this comparative static exercise provies a rationale for empirical results suggesting that the FCT is not very large for many countries like the US, an that the extent of between-sector factor reallocation inuce by trae an its impact on the skill premium are small in practice; see e.g. Golberg an Pavcnik (2007). Enogenous entry an enogenous selection of rms into markets increases the magnitue of the change in the FCT an, hence, the change in the skill premium an the extent of between-sector trae an factor reallocation inuce by a given change in trae shares. This result implies that measures of sectoral prouctivity an enowment i erences across countries woul unerestimate the impact of trae liberalization on the skill premium an between-sector factor reallocation if rm entry ecisions are not take into account. Note however that, given our earlier results, the extent of within-sector prouctivity heterogeneity, enogenous entry, an selection of rms into markets have no e ect whatsoever on changes in factor prices, between-sector factor allocation, or between-sector trae, for given changes in the FCT. Our results are relate to recent papers in international trae ientifying robust insights for welfare analysis across i erent moels; see e.g., Arkolakis, Costinot, an Roriguez- Clare (Forthcoming) an Atkeson an Burstein (200). Whereas these papers focus on the welfare implications of international trae, we focus on the istributional implications of international trae. We show that across a wie range of workhorse moels, the e ects of 3

6 international trae on the skill premium can be summarize by changes in the FCT. 5 Our paper is most closely relate to Bernar, Reing, an Schott (2007), henceforth BRS. Our contribution relative to BRS is as follows. First, we show that changes in the FCT are su cient statistics for the impact of international trae on the skill premium an betweensector factor allocation. Secon, we emonstrate analytically how the extent of within-sector prouctivity heterogeneity, enogenous entry, an selection of rms into markets each a ects the impact of trae on the skill premium, between-sector trae an factor reallocation. Thir, we revisit their ning that i erences in factor enowments inuce what BRS call "enogenous Ricarian prouctivity i erences" at the inustry level. 6 2 Factor Prices: A Unifying Framework In this section we present a general framework to examine the link between factor prices an trae. The key assumption in this framework is that in each country, all e ciency units of a given factor of prouction receive a common wage or price. We rst erive a simple expression relating equilibrium factor prices to two components: trae-ajuste relative factor supplies an the factor payments for omestic absorption. We then show how changes in relative factor prices within a range of workhorse moels of trae can be mappe into these two components. Finally, we escribe a set of assumptions that are stanar in the literature uner which changes in the FCT are su cient statistics for the impact of trae on relative factor prices. 2. General Framework There are N countries, inexe by n = ; :::; N; J sectors, inexe by j = ; :::; J; an K factors of prouction, inexe by k = ; :::; K. Let L k;i 0 enote the stock of factor k employe in country i. There is a common price, w k;i 0, for all units of factor k employe in country i. 7 We enote by E i (j) 0 country i s total expeniture on sector j, an by 5 A large literature stuies Vanek s (968) preiction that each country is a net exporter of the services of its abunant factors, using the FCT; see e.g. Tre er (993 an 995) an Davis an Weinstein (200). Our results are relate to Helpman an Krugman (985) an Tre er an Zhu (200), who show that Vanek s preiction hols across a wie range of moels. 6 Ho (200) uses a similar framework to stuy the implications of iiosyncratic istortions on betweensector factor allocation, the skill premium, an welfare, while Lu (200) uses it to stuy how export market participation ecisions of Chinese rms vary across sectors. 7 One stanar assumption uner which each e ciency unit of a factor receives a common price is that factors are perfectly mobile across proucers within a country. At this point we o not require an assumption regaring the mobility of factors across countries nor o we nee to istinguish between cases in which L k;i is in xe supply or not. 4

7 in (j) 2 [0; ] the share of country n s total expeniture in sector j that is allocate to goos from country i, with P i in (j) =. Factor payments: Let L k;in (j) enote the quantity of factor k in country i, sector j that is employe in supplying estination market n. At this point, L k;in (j) is an accounting variable escribing how factor usage is istribute across estination markets. In Section 2.2 we iscuss how L k;in (j) can be constructe in a range of speci c moels. The quantity of factor k use in country i, sector j, across all estination markets is L k;i (j) = X n L k;in (j). The sum of L k;i (j) across inustries must equal total employment of factor k: L k;i = X j L k;i (j). () Denote by in (j) 2 [0; ] the share of country i revenues from sales in country n in sector j that is pai to factors, in (j) = P k w k;il k;in (j) in (j) E n (j), an enote by k;in (j) 2 [0; ] the share of these factor payments that are pai to factor k, k;in (j) = w k;i L k;in (j) Pk 0 w k 0 ;il k 0 ;in (j), where P k k;in (j) = for all n an j. Using these e nitions, we can re-express equation () as w k;i L k;i = X j X in (j) k;in (j) in (j) E n (j). (2) n Equation (2) is purely an accounting relationship, stating that the payments to a factor must equal the value of this factor use across all sectors in the prouction of goos boun for all estination markets. Factor content of trae: Denote by F CT k;i the factor content of trae for factor k in country i, i.e. the net exports of factor k emboie in country i s trae: F CT k;i = X j X n L k;in (j) L k;ii (j) ni (j). ii (j) Using our e nitions of in (j) an k;in (j), we can express the payments for the FCT, 5

8 w k;i F CT k;i, as w k;i F CT k;i = X j X [ in (j) k;in (j) in (j) E n (j) ii (j) k;ii (j) ni (j) E i (j)]. (3) n6=i We can unerstan this expression for the payments for the FCT, w k;i F CT k;i, as follows. The rst term in the summation in equation (3), in (j) in;k (j) in (j) E n (j), simply represents the payments to factor k emboie in country i s exports to estination market n. The secon term in the summation, ii (j) k;ii (j) ni (j) E i (j), represents the counterfactual payments to factor k in country i, ha country i prouce for itself the value of goos that it importe from country n. Note that constructing the FCT in the ata requires input usage by estination country, which may be i cult to observe in practice. In Section 2.2, we iscuss a range of moels in which the construction of F CT k;i is simpli e signi cantly. Factor prices: To show how F CT k;i is relate to w k;i, we procee as follows. By equation P (2), equation (3), an the ientity ii (j) = n6=i ni (j), we ecompose payments to factor k into two components: w k;i L k;i = w k;i F CT k;i + k;i. (4) The rst component is the payments for the FCT e ne in equation (3). The secon component is the factor payments for omestic absorption (FPD), k;i = P j ii (j) k;ii (j) E i (j), which is the counterfactual payments to the factor if omestic absorption were prouce omestically. By equation (4), factor k s price is w k;i = k;i /L k;i, (5) where L k;i = L k;i F CT k;i enotes the trae-ajuste supply of factor k. By comparing equations (2) an (5), it is apparent that for given values of ii (j), k;ii (j), an E i (j), the price pai to factor k in a trae equilibrium is equal to the price that woul have been pai to factor k in autarky ha country i s stock of factor k been L k;i rather than L k;i. If a country is a net exporter of factor k, then its factor price is etermine as if it has a smaller stock of this factor. In this sense, we can think of L k;i as the counterfactual stock of factor k available in economy i in the presence of international trae. Using equation (5), we express the price of factor k relative to factor k 2 as w k ;i=w k2 ;i = (L k2 ;i /L k ;i ) ( k ;i / k2 ;i ). (6) 6

9 Equation (6) ecomposes the relative price of factor k to factor k 2 into two terms: (i) the trae-ajuste supply of k 2 relative to k an (ii) the FPD of k relative to k 2. An increase in L k2 ;i /L k ;i, either through a ecrease in the relative supply of factor k or an increase in the FCT of k, increases the relative price of k. Similarly, an increase in k ;i / k2 ;i, either through an increase in expeniture shares in sector intensive in factor k or an increase in the average revenue share of factor k across sectors, increases the relative price of k. We summarize these results in the following proposition, which provies an equation for the change in the relative price of factor k to factor k 2 between any two equilibria. Proposition If w 0 k ;i w 0 k2 ;i, L0 k;i, an 0 k;i enote the relative price of factor k to factor k 2, the trae-ajuste supply of factor k, an the factor payments for omestic absorption of factor k in a counterfactual equilibrium, then w 0 k ;i w 0 k 2 ;i, w k ;i w k2 ;i = " L 0 k2 ;i L 0 k ;i, L k2 ;i L k ;i # " 0 k ;i 0 k 2 ;i k ;i k2 ;i #. (7) Of course, both L k;i an k;i are enogenous, an their equilibrium etermination an therefore, how they are a ecte by trae liberalization is outsie the scope of this accounting framework. In Section 3, we specialize our general framework to stuy the etermination of these variables. 2.2 Mapping Speci c Moels into Framework In this section we iscuss how a variety of moels of international trae, technological change, an the skill premium can be mappe into the general framework above. We also escribe a range of moel assumptions uner which expression (7) an the calculation of the FCT can be simpli e signi cantly. Heckscher-Ohlin-like perfectly competitive moels: Here we focus on perfectly competitive moels with constant returns to scale in which all proucers within a sector share a common factor intensity that oes not epen on the estination in which output is sol. These assumptions are satis e in the Heckscher-Ohlin moel see, e.g., Stolper an Samuelson (94) an its multi-sector an multi-factor extensions see, e.g., Ethier (984), Jones an Scheinkman (977), an Costinot an Vogel (200). In these moels, L k;in (j) can be constructe easily as the prouct of sector j s employment of factor k, L k;i (j), an the ratio of country i sector j revenues earne in market n to total revenues earne in that sector, in (j) E n (j) = ( P n 0 in 0 (j) E n 0 (j)). Hence, the share of factor payments accruing to factor k in sector j prouction i.e. the factor k intensity of prouction in sector j is the same 7

10 across estination markets, k;in (j) = k;i (j) for all i, n, k, an j, where k;i (j) = w k;i L k;i (j) Pk 0 w k 0 ;il k 0 ;i (j). (8) Moreover, with constant returns to scale an perfect competition, rm pro ts are zero, so in (j) = for all i, n, an j. In any setting in which k;in (j) an in (j) are common across estination markets, we can simplify signi cantly the construction of net exports of factor k. In particular, we have F CT k;i = X j L k;i (j)! i (j), (9) where! i (j) = P n6=i [ in (j) E n (j) ni (j) E i (j)] P n in (j) E n (j) enotes the ratio of country i s net exports in sector j to country i s total revenue in sector j. The variables L k;i (j) an! i (j), an hence the factor k content of trae, can be measure in principle using sectoral prouction an trae ata. 8 In this environment, the expression in Proposition is simpli e only because k;in (j) = k;i (j) an in (j) =. However, we can further simplify this expression uner a few aitional assumptions. If preferences an prouction functions are Cobb-Douglas an the Cobb-Douglas share parameters are unchange across equilibria, then equation (7) simpli es to w 0 k ;i w 0 k 2 ;i, w k ;i w k2 ;i = L0 k 2 ;i L 0 k ;i, L k2 ;i. (0) L k ;i In this special case of our general framework, relative factor prices change only ue to changes in trae-ajuste factor supplies. For xe omestic supplies of factors k an k 2, any change in the economic environment such as trae costs, foreign prouctivities, foreign factor supplies, foreign prouction functions, omestic prouctivities, or omestic supplies of factors other than k an k 2 a ects omestic relative factor prices only through changes in the FCT. Expression (0) was also obtaine in Dearorf an Staiger (988) an Dearor (2000) in a perfectly competitive environment with constant returns to scale an common prouctivities across proucers within each sector. Our result allows for heterogeneous prouctivities 8 If factor intensities vary across highly isaggregate inustries, then constructing the FCT in practice requires highly isaggregate ata. See Feenstra an Hanson (2000) for an analysis of the bias in measuring the FCT using aggregate inustry ata. 8

11 within sectors, as in a multi-sector an multi-factor version of Eaton an Kortum (2002). 9 Common factor intensities across sectors: A particular class of moels neste by the perfectly competitive, constant returns to scale moels above are those in which factor intensity is ientical across proucers, sectors, an estination markets, k;in (j) = k;i. These assumptions are satis e in, e.g., Katz an Murphy (992), Krusell, Ohanian, Rios-Rul, an Violante (2000), an Burstein, Cravino, an Vogel (200). Uner these assumptions, equation (6) simpli es to w k ;i=w k2 ;i = (L k2 ;i /L k ;i ) ( k ;i / k2 ;i ) Moreover, because F CT k;i equals k;i =w k;i times country i s net aggregate exports (i s trae balance), we have L k2 ;i /L k ;i = L k2 ;i=l k ;i. Hence, equation (7) becomes w 0 k ;i w 0 k 2 ;i, w k ;i w k2 ;i = " L 0 k2 ;i L 0 k ;i, L k2 ;i L k ;i # " 0 k ;i 0 k 2 ;i, k ;i k2 ;i In this class of moels, changes in relative factor prices across two points in time are riven entirely by changes in relative factor supplies an by changes in relative factor intensities. Changes in relative factor intensities can be riven by technological change (see e.g. Katz an Murphy 992), 0 capital accumulation (see e.g. Krusell, Ohanian, Rios-Rul, an Violante 2000), an capital accumulation an international trae (see e.g. Burstein, Cravino, an Vogel 200). Factor intensity varies by estination market: In Matsuyama (2007) an Burstein an Vogel (200), markets are perfectly competitive, prouction is constant returns to scale, an average factor intensities vary epening on estination market. In Matsuyama (2007) proucers are homogeneous within a sector, an trae costs are assume to be skill intensive relative to prouction. In Burstein an Vogel (200), for a given proucer, skill intensity is inepenent of estination market, but the most prouctive proucers ten to export an to be more skill intensive. Hence in these moels, i (j) = but k;in (j) tens not to equal k;ii (j) for n 6= i. 9 An alternative assumption that simpli es equation (7) is that countries are symmetric. In this case, trae is balance sector-by-sector, so that! i (j) = 0 for all i an j, an F CT k;i = 0 for all k an i. Hence, changes in relative factor prices only epen on changes in factor supplies an relative payments for omestic absorption. 0 While some paper treat technological change as exogenous, there is a large literature on enogenous factor-biase technological change; see, e.g. Acemoglu (2002). The e ect of such changes on relative factor wages operate through changes in relative factor intensities (changes in s). Parro (200) consiers a moel similar to Burstein, Cravino, an Vogel (200) in which factor intensities vary across sectors. #. 9

12 With constant returns to scale it is straightforwar to allocate aggregate sectoral factor employment, L k;i (j), to each estination market, L k;in (j). Hence, these moels t into the general framework presente above. However, equation (7) simpli es only because ii (j) =. In general, changes in trae costs will a ect relative factor prices through both trae-ajuste factor supplies an the factor payments for omestic absorption. Heckscher-Ohlin-like imperfectly competitive moels: In Section 3 we consier a range of moels featuring imperfect competition, heterogeneous rms, an increasing returns to scale, as in, e.g., Romalis (2004) an BRS (2007). With imperfect competition, rms may earn pro ts, so in (j) is not generally equal to one. Moreover, in some cases it is not straightforwar to allocate sectoral employment, L k;i (j), across estination markets, L k;in (j). This can be the case, for example, if a rm must incur entry costs that o not epen on the set of estination markets it supplies. However, we show that in the moel of Section 3, Proposition hols with the FCT being constructe using equation (9), an that equation (7) simpli es to equation (0). It is straightforwar to show that the same results hol in a two-factor version of Bernar, Eaton, Jensen, an Kortum (2003), which is an extension of Eaton an Kortum (2002) with Bertran instea of perfect competition. Since there are constant returns to scale (an no xe costs), allocating factors across estination markets is straightforwar. With Frechet istribute prouctivities an CES eman, in (j) is constant an equal across estination markets. 2 3 The FCT in a Heterogeneous Firm Moel While the framework in Section 2 links the FCT to relative factor prices, it takes the FCT as given. Hence, it oes not provie insights into how changes in the economic environment such as changes in trae costs a ect the FCT, an therefore, relative factor prices. We now focus on unerstaning the etermination of the FCT. To o so, we specialize the general framework above to an environment with two sectors, two factors (skille an unskille labor), two countries, an monopolistic competition, in which heterogeneous rms choose whether or not to enter an which markets to supply. We use this moel to obtain three sets of results. First, in Section 3, we show that in this environment, Proposition hols, the FCT is given by equation (9), an the calculation of 2 Epifani an Gancia (2008) consier an alternative moel of international trae an monopolistic competition. In their moel, changes in relative factor wages are riven by changes in the FCT an sectoral expenitures. Trae raises expenitures, E i (j), in the skill-intensive sector relative to the unskill-intensive sector in all countries, which tens to increase the skill premium in all countries, as is evient in equation (6). 0

13 the FCT in equation (7) simpli es to equation (0). Secon, in Section 4, we emonstrate that the FCT an factor enowments fully etermine not only the relative price of skille to unskille labor (the skill premium), but also the extent of between-sector factor reallocation an between-sector trae. Finally, in Section 5, we show how the extent of prouctivity heterogeneity between an within sectors, an heterogeneous rms ecisions to enter an operate in each market shape the impact of trae liberalization on the FCT, an, therefore, on factor allocation an the skill premium. 3. Moel Our moel economy features two countries, i = ; 2; two factors, which we refer to as skille labor an unskille labor; an two sectors, j = x; y, where x is skill intensive. While factors are perfectly mobile across proucers within a country, they are internationally immobile. The exogenous an xe enowments of skille an unskille labor in country i are enote by L s;i an L u;i, respectively. Each country prouces a nal non-traeable goo using output of both sectors. Output in each sector is prouce using a continuum of i erentiate intermeiate goos, which are prouce by rms using skille an unskille labor. International trae of intermeiate goos is subject to variable an xe costs. Factors are perfectly mobile across rms an sectors but are immobile across countries. Preferences: The representative consumer s utility is e ne over a non-traeable nal goo, Q i, that (for expositional purposes) places equal weight on the output of each sector Q i = Q i (x) =2 Q i (y) =2, where Q i (j) enotes the output of sector j. The aggregate price inex is P i = 2 P i (x) =2 P i (y) =2, where P i (j) is the price of sector j. Deman for the sector j goo is Q i (j) = E i = Q i P i enotes total expeniture in country i. Sectoral aggregates: Sector j s output, Q i (j), is a CES aggregate of varieties E i 2P i (j), where Q i (j) = Z!2 j q i (!; j) ( )=!! =( ). Here, q i (!; j) enotes country i consumption of variety (!; j), an > is the elasticity of h R substitution between varieties. The price inex in sector j is P i (j) = p!2j i (!; j)! where p i (!; j) enotes the price of goo (!; j) in country i. Deman for variety (!; j) is q i (!; j) = Qi (j). pi (!;j) P i (j) Intermeiate goo technologies: There are a continuum of rms, each proucing a i =( ),

14 unique variety (!; j). Firms face variable costs of prouction, xe (market access) costs of selling in each country, an iceberg costs of international trae. Both xe an variable costs use skille an unskille labor, where the factor intensity of prouction varies across sectors but is constant across rms within a sector an across xe an variable costs within a rm. A sector j rm from country i with Hicks-neutral prouctivity z that hires l s units of skille labor an l u units of unskille labor in variable prouction activities prouces y = za i (j) ls s(j) lu u(j) units of output, where s (j) + u (j) =. Here, k (j) enotes the share of skille (k = s) an unskille (k = u) labor in prouction of all country i rms in sector j, where we omit the epenence of k (j) on i since factor intensities are equal in both countries. Because x is skill intensive, we have s (x) > s (y). A i (j) > 0 enotes country i s exogenous total factor prouctivity in sector j. To facilitate exposition in our results below, we ecompose A i (j) into two components national TFP, T i, an sectoral TFP, T i (j) so that A i (j) = T i T i (j). We normalize T =. We e ne a = A (x) A 2 (y) =A (y) A 2 (x) to be a measure of country s relative prouctivity avantage (if a > ) or isavantage (if a < ) in sector x. Firms from country i must ship in q units of output in orer for q units to arrive in country n, with ii = an in = ni =. We refer to as the iceberg transportation cost. Aitionally, in orer to supply a positive amount of goos to country n, a country i rm incurs a xe market access cost of f in 0 units of the sectoral composite input bunle in country i; we assume that these xe costs are prouce using the same input bunle as the prouction of intermeiate goos in that sector. For simplicity, but without loss of generality for our results, we assume that variable an xe trae costs are common across sectors. We enote by f = f 2 =f = f 2 =f 22 the relative xe costs of international versus intra-national trae in all sectors an countries. Uner these assumptions on technology, a sector j rm with prouctivity z from country i incurs a cost h q i in C in (q) = v i (j) + f in z to supply q > 0 units of goos to country n. We refer to v i (j) as the cost of the sector j composite input bunle in country i, where v i (j) = s(j) u(j) ws;i wu;i. () A i (j) s (j) u (j) an where country i s wages for unskille an skille labor are w s;i an w u;i, respectively. We enote by c in (z; j) = v i (j) in =z the marginal cost of a rm with prouctivity z, sector 2

15 j, in country i to supply a goo to country n. Conitional on a country i rm paying the xe cost to access market n, pro t maximization implies that it charges a constant markup over its marginal cost, p in (z; j) = c in (z; j). In this case, a rm s market-speci c revenue is proportional to its marginal cost, r in (z; j) = E n 2P n (j) c in (z; j), (2) an its market-speci c variable pro t is proportional to its revenue in (z; j) = r in (z; j) =. Selection of rms into markets: A country i rm chooses to supply market n if the variable pro t it earns there covers its xe market access cost, in (z; j) v i (j) f in (j). Denote by z in (j) the prouctivity threshol at which the least prouctive sector j rm from country i sells in country n: ( ) zin in 2 f in (j) = max P n (j) ( ) vi (j) ;. (3) E n In orer to unerstan the implications of enogenous selection for trae patterns an relative factor rewars, we consier speci cations in which enogenous selection into markets is an is not active. In the speci cation in which enogenous selection is not active, we assume that f in = 0 for all i; n 2 I, so that every entrant sells to each market: z in (j) = for all i; n 2 I an j 2 J. 3 We refer to this as the case "without selection." This case correspons to a multi-factor extension of Krugman (980), as in Helpman an Krugman (985) an in Romalis (2004). In the speci cation in which enogenous selection is active, we assume that f in is suf- ciently large for all i; n 2 I an j 2 J such that there is selection into every market, i.e. z in (j) > for al i; n 2 I an j 2 J. We refer to this as the case "with selection." This case correspons to a multi-factor extension of Melitz (2003) as in BRS or of Chaney (2008). Note that the two cases we consier are not exhaustive. There are parameter values for which there exist country-pairs an sectors such that z in (j) = an z kl (j0 ) >. We e ne t to be the relative size of international versus intra-national trae costs, ( without selection t = f + with selection. It is this relative cost t that matters for our results throughout the paper, rather than an 3 Uner this speci cation, our results remain unchange if market access costs are stricty greater than zero an all rms sell in all markets. 3

16 f separately. We assume that relative costs of international trae are strictly greater than those of intra-national trae, so that t >. Uner this assumption, any rm that exports also sells omestically. Entry: In orer to unerstan the implications of enogenous entry for trae patterns an relative factor prices, we consier two alternative speci cations on the etermination of the mass of entering rms in each sector, M i (j); we refer to these speci cations as exogenous an enogenous entry. The i erence between the two speci cations is the timing regaring when entrepreneurs (potential entrants) realize their prouctivities. In the speci cation with exogenous entry, we assume that entrepreneurs know their prouctivities ex-ante. In this case, the mass of entrepreneurs is xe at M i (j), since if it were unboune then only the most prouctive woul enter. Firms in each sector/country raw their prouctivity z from a Pareto istribution with shape parameter an location parameter one: G (z) = Pr (Z z) = z. This case correspons to, e.g., Chaney (2008), Arkolakis (Forthcoming), an Eaton et. al. (Forthcoming). For simplicity an without loss of generality, we assume in the exogenous entry case that M i (j) = M i. 4 In the speci cation with enogenous entry, we assume that entrepreneurs are ientical ex-ante. In this case, in each country/sector there is an unboune mass of ex-ante ientical potential entrants. To enter, an entrepreneur incurs a xe entry cost of f e > 0 units of the sectoral composite input bunle (in the exogenous entry case, we assume that f e = 0 for all j). That is, sector j startup costs in country i are f e v i (j). Upon entry, rms raw their prouctivity z from the same istribution G (z) e ne above. This case correspons to a version of Melitz (2003) an BRS (2007) with Pareto istribute prouctivities. The free entry conition, for all j, is given by IX n= Z z in (j) [ in (z; j) v i (j) f in ] G (z) v i (j) f e with equality if M i (j) > 0. Finally, in all that follows we focus exclusively on cases with incomplete specialization; i.e. in which M i (j) > 0 for all i 2 I an j 2 J. Trae balance: We assume trae balance in both countries. This implies that total expeniture equals total income (wages an pro ts) in each country, E i = X k=s;u w k;i L k;i + X j ( X Z ) M i (j) [ in (z; j) v i (j) f in ] G (z) v i (j) f e zin (j) n 4 This assumption implies that there are only two inepenent sources of comparative avantage: relative enowments an sectoral prouctivities. Alternatively, we coul combine i erences in M i (j) an A i (j) into a single parameter, e Ai (j). The parameter a in this case woul be e ne using the e A i (j)s. 4

17 3.2 Equilibrium Characterization In this section we erive the equations that we use to solve for equilibrium factor prices an trae patterns. We consier speci cations (i) with enogenous or exogenous entry an (ii) with or without selection. International trae: Denote by in (j) the sector j expeniture share in country n on goos from country i. By e nition, we have in (j) = Substituting in for G (z) an r in (z; j) yiels M i (j) R r zin (j) in (z; j) G (z) P I k= M k (j) R r zkn (j) kn (z; j) G (z). in (j) = M i (j) v i (j) zin (j) in P I k= M. (4) k (j) v k (j) zkn (j) kn In the speci cation without selection, in which z in (j) = for all i; n 2 I an j 2 J, Equation (4) implies M i (j) v i (j) in in (j) = P I k= M. (5) k (j) v k (j) kn In the speci cation with selection, in which z in (j) > for al i; n 2 I an j 2 J, Equation (4) implies in (j) = + M i (j) [v i (j)] fin P I k= M + k (j) [v k (j)] + fkn in kn. (6) We enote by i = 2 [ ni (x) + ni (y)], for n 6= i, country i s trae share. Note that i is the share of country i s expeniture allocate to imports from country n 6= i. We also enote by i = ni (y) ni (x), for n 6= i, the share of country i s expeniture allocate to imports in sector y minus the share of expenitures allocate to imports in sector x. The greater in absolute value is i, the greater is the i erence between net imports in the x an y sectors. Hence, for a given trae share i, i inicates the importance of between sector trae relative to within sector trae. Labor market clearing: In Appenix A we show that the labor market clearing conitions when entry is enogenous or exogenous an with or without selection are given by w k;i L k;i = X j X k (j) in (j) n En 2, (7) 5

18 where is the share of revenues pai to all factors in both sectors, E i = X w k;i L k;i, (8) k=s;u an is given by 8 >< with enogenous entry + = with exogenous entry an with selection >: with exogenous entry an without selection (9) in the i erent speci cations of the moel. Equilibrium rm entry: In Appenix A we show that with enogenous entry, the mass of entering rms in each sector is given by M i (j) v i (j) f e = e X n where e = = without selection an e = ( in (j) En 2 ) = () with selection. Solving for an equilibrium: Equilibrium factor prices, total expenitures E i, expeniture shares in (j), an entrants M i (j) can be solve for using factor market clearing as given by equation (7) (note that, by Walras law, one equation is reunant), equation (8), expeniture shares in (j) as given by Equation (5) without selection an by Equation (6) with selection, an the free-entry conitions (with enogenous entry) as given by Equation (20). 5 We compute prouction an consumption of the nal non-traeable goo, Q i, as follows. Given factor prices, nominal expenitures, an entry levels, the solution for sectoral price inices is provie in Appenix B. Using sectoral price inices an the e nition of the aggregate price level, P i, above we obtain Q i. Our moel an this solution proceure can be extene to any number of factors, sectors, an countries. In some comparative static exercises, in Section 5, we simplify the moel solution by assuming that countries an sectors are mirror symmetric: A (x) = A 2 (y), A (y) = A 2 (x), L s = L u2, L u = L s2, an x = because w s = w u2, w u = w s2, an E = E 2. (20) y. Mirror symmetry makes the moel more tractable 5 After solving for an equilibrium assuming that the moel is either with selection or without selection, one must verify that all cuto s are either greater than one or equal to one, respectively, using equation (3). 6

19 3.3 Mapping to General Framework Since there is a common wage, w k;i, for factor k in country i, the moel clearly ts into the general framework presente in Section 2. In the speci cation with exogenous entry, constructing L k;in (j) is straightforwar. It is the sum of factor k employment in variable prouction an market access costs for supplying estination market n. With CES sectoral aggregators, the share of variable costs in total sectoral revenue is constant. With CES sectoral aggregators an Pareto-istribute prouctivity, the share of market access costs in total sectoral revenue is also constant. Hence, with common an across sectors an countries, in (j) = for all estination markets an in each sector, where = ( + ) = () with selection an = ( ) = without selection. Since factor intensity is common across xe an variable costs as well as across source an estination markets, we have k;in (j) = k (j). Hence, equation (2) from the general framework of Section 2 is simpli e to equation (7) in our specialize moel. In the speci cation with enogenous entry, constructing L k;in (j) is more subtle because there are multiple ways of allocating entry costs, f e, across estination markets. However, for any construction of L k;in (j) consistent with equilibrium sectoral factor allocation (i.e., L k;i (j) = P n L k;in (j)), we can again simplify equations (2) from the general framework of Section 2 to equation (7) in our moel. To obtain equation (7), we make use of two results: (i) free entry implies that revenues are equal to total costs (incluing entry, market access, an variable costs) in each sector, an (ii) xe an variable costs have a common factor intensity in each sector. Note that to obtain this result in the speci cation with enogenous entry, we o not make use of Pareto istribute prouctivity or CES aggregators. Given that factor market clearing conitions are given by equation (7), it follows that we can express the FCT using equation (9) in all speci cations of our moel. Finally, with Cobb-Douglas preferences an prouction functions an unchange share parameters ( k (j) = 0 k (j)), equation (7) from the general framework simpli es to equation (0), so that the change in the skill premium across two equilibria is given by w 0 s;i w 0 u;i ws;i = L0 u;i Lu;i. w u;i L 0 s;i L s;i Hence, in all speci cations of our moel, changes in the skill premium are fully etermine by changes in trae-ajuste factor supplies. Moreover, since we impose that factor supplies are xe parameters (L k;i = L 0 k;i ), changes in the FCT are su cient statistics for the impact of trae on the skill premium: changes in trae costs or in prouctivities a ect the skill premium only through changes in the FCT. 7

20 4 The Skill Premium, Factor Allocation, an Trae We now investigate the impact of trae liberalizations on the skill premium, factor allocation, an trae patterns in our moel. We rst show that if country has a comparative avantage in the skill intensive goo, then the trae-ajuste relative supply of skill, L s;i =L u;i, falls in country an rises in country 2 when countries open to trae. We then show that changes in L s;i =L u;i fully etermine the impact of trae liberalization not only on the skill premium, as shown in the previous section, but also on between-sector factor allocation an betweensector trae. Through these results, we obtain a generalize version of what is often referre to as the Stolper-Samuelson e ect. The Stolper-Samuelson e ect relates changes in factor prices to exogenous changes in goos prices, whereas we relate changes in factor prices, factor allocation, an trae patterns to changes in trae costs, via changes in trae shares. We say that country has a comparative avantage in sector x if the cost of the composite input bunle in sector x relative to sector y is relatively lower in country than in country 2 in autarky: v (x) =v (y) < v 2 (x) =v 2 (y) in autarky. Accoring to this e nition, country has a comparative avantage in the skill-intensive sector if an only if x H =L y a >. (CA) H 2 =L 2 Conition CA follows from the e nition of v i (j) in equation (), from the factor-market clearing conition in equation (7), an from the observation that 2 (j) = 2 (j) = 0 in autarky. Without loss of generality, we impose Conition CA throughout the remainer of the paper. To unerstan Conition CA, consier two special cases that are stanar in the literature. First, if a = so that there is no Ricarian comparative avantage, then country has a comparative avantage in sector x if an only if H =L > H 2 =L 2, exactly as in the Heckscher-Ohlin moel. Secon, if enowment ratios are the same across countries so that there is no Heckscher-Ohlin-base comparative avantage, then country has a comparative avantage in sector x if an only if a >, exactly as in the Ricarian moel. The consequences of moving from autarky ( ; 2 = 0) to positive trae shares ( 0 ; 0 2 > 0) on the trae-ajuste relative supply of skill in country are state in the following proposition. Proposition 2 If ; 2 = 0 an 0 ; 0 2 > 0, then L 0 s;=l 0 u; < L s; =L u; = L s; =L u;. Country is a net exporter in the sector in which it has a comparative avantage, sector x: = 2 (y) 2 (x) > 0 if > 0. Because the x sector is skill intensive, country s 8

21 net exports emboy a positive amount of skille labor, F CT s; > 0, an a negative amount of unskille labor, F CT u; < 0, if > 0. Hence, moving from autarky to any positive trae shares reuces the trae-ajuste relative supply of skill in country. For given trae shares an 2, the level of the trae-ajuste relative supply of skill in either country, L s;i =L u;i, etermines important economic outcomes in both countries: the skill premium w s;i =w u;i ; between-sector factor allocation L k;i (j); an between-sector trae (the absolute value of i ). The following proposition states speci cally how these economic outcomes vary across two equilibria with equal trae shares but i erent trae-ajuste factor supplies. Proposition 3 In any two trae equilibria with equal trae shares 0 = > 0 an 0 2 = 2 > 0, the following eight statements are equivalent: (i) L 0 s;=l 0 u; < L s; =L u; (ii) L 0 s;2=l 0 u;2 > L s;2 =L u;2 (iii) ws;=w 0 u; 0 > w s; =w u; (iv) ws;2=w 0 u;2 0 < w s;2 =w u;2 (v) L 0 k; (x) > L k; (x) for k = s; u (vi) L 0 k;2 (x) < L k;2 (x) for k = s; u (vii) 0 > (viii) 0 2 < 2 The intuition behin Proposition 3 can be unerstoo as follows. A lower trae-ajuste relative supply of skill in country (statement i) increases the skill premium in country (statement iii), as state in Proposition. For xe factor supplies, a lower trae-ajuste relative supply of skill requires a higher absolute value of the FCT of skille an unskille labor in country, which requires that the extent of between-sector trae be greater (statement vii, since > 0 from Conition CA). More between-sector trae requires that a greater share of factors be allocate to country s comparative avantage sector (statement v). With trae balance an xe trae shares, more between-sector trae in country (statement vii) requires more between-sector trae in country 2 (statement viii, since 2 < 0), a greater share of factors allocate to country 2 s CA sector (statement vi), an a greater absolute value of the FCT of skille an unskille, which is associate with both a higher trae-ajuste relative supply of skill (statement ii) an a lower skill premium (statement iv). Combining Propositions 2 an 3, we establish the following corollary. Corollary Reucing trae costs so that countries move from autarky ( ; 2 = 0) to any positive level of trae ( 0 ; 0 2 > 0) raises the skill premium in country an reuces it in country 2, reallocates factors towars the x sector in country an towars the y sector in country 2, an generates positive net exports in the x sector in country an in the y sector in country 2. 9

22 Intuitively, starting in autarky, a reuction in trae costs increases each country s net exports in its comparative avantage sector. This requires factors to reallocate towars that sector, which increases the relative eman an, therefore, the relative price of the factor that is use intensively in the comparative avantage sector. 5 Technology, Selection, an Entry Changes in the trae-ajuste relative supply of skill are etermine by changes in the FCT, which are enogenous. Our next goal is to stuy how key margins in our moel the extent of prouctivity heterogeneity between an within sectors, an heterogeneous rms ecisions to enter an operate in each market shape the impact of trae liberalization on the FCT, an, therefore, on factor allocation an the skill premium. These margins matter for equilibrium outcomes only through their impacts on expeniture shares in (j). This follows from Proposition 3, which shows that for given factor supplies an trae shares, changes in trae-ajuste relative factor supplies in each country are fully etermine by changes in the extent of between-sector trae, which is itself etermine by changes in in (j). Equation (4) illustrates the various exogenous an enogenous eterminants of these expeniture shares. First, composite input costs, v i (j), have a irect e ect on expeniture shares through the prices charge by active rms. All else equal, lowering v i (j) increases in (j) for all n. From equation (), composite input costs can be ecompose into two components: (i) factor prices an intensities, w k(j) k;i, as in the Heckscher-Ohlin moel, an (ii) exogenous sectoral technologies, A i (j), as in the Ricarian moel. Secon, the mass of operating rms from each country shapes expeniture shares: an increase in the mass of country i rms operating in country n increases in (j), holing all else xe. This mass of rms can be ecompose into two components: (i) the mass of entering rms in country i, given by M i (j), an (ii) the fraction of country i entrants that operate in country n, which is negatively relate to z in (j). All else equal, an increase in the mass of operating rms, either through an increase in M i (j) or a ecrease in z in (j), is equivalent, in terms of expeniture shares, to an increase in sectoral prouctivity A i (j). Thir, the extent of prouctivity heterogeneity a ects the elasticity of expeniture shares to a change in the prouctivity cuto, z in (j). In particular, a greater ispersion of prouctivity, a lower, ecreases the concentration of rms aroun the cuto. This implies a smaller ecrease in the mass of operating rms for a given increase in the prouctivity cuto. In what follows, we stuy how each of these margins a ects the impact of trae liberalization on trae-ajuste relative supplies of skill, an therefore on the skill premium an the 20