Factor Prices and International Trade: A Unifying Perspective

Transcription

1 Factor Prices an International Trae: A Unifying Perspective Ariel Burstein UCLA an NBER Jonathan Vogel Columbia an NBER October 20 Abstract How o trae liberalizations a ect relative factor prices an to what extent o they cause factors to reallocate across sectors? We rst present a general accounting framework that nests a wie range of moels that have been use to stuy the link between globalization an factor prices an from which we obtain two su cient statistics that etermine factor prices. Uner some restrictions, changes in the "factor content of trae" (FCT) fully etermine the impact of trae on relative factor prices. We then stuy the etermination of the FCT in a speci c version of our general framework that uni es traitional moels of trae an factor prices featuring sectoral prouctivity an factor enowment i erences an new moels featuring imperfect competition an heterogeneous proucers. We show how heterogeneous rms ecisions shape the FCT, an, therefore, the impact of trae liberalization on relative factor prices an between-sector factor allocation. 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.

2 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 present a general accounting framework from which we obtain su cient statistics that etermine factor prices. In the secon part of the paper we stuy the impact of trae on these su cient statistics (an, hence, on factor prices an factor allocation) in a speci c moel, neste by our general framework, that uni es traitional moels of trae an factor prices featuring sectoral prouctivity an factor enowment i erences an new moels featuring imperfect competition an heterogeneous proucers. The general accounting framework that we present in the rst part of the paper nests a wie range of international trae moels such as 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 that have been use to stuy the link between international trae an relative factor prices. While we focus on factor prices an between-factor inequality, the framework also covers recent moels featuring unemployment, within-factor heterogeneity, an within-group inequality. 2 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 employment of that factor less the factor content of trae (FCT). The FCT of a given factor 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 speci c moels an mechanisms operate 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. 2 See e.g. Helpman, Itskhoki, an Reing (200).

3 through these two components. More generally, this ecomposition provies a single lens to view an compare a wie range of moels an mechanisms linking trae an technology to factor prices. Uner some restrictions, the ecomposition simpli es further. In particular, we provie conitions uner which the ratio of factor payments for omestic absorption between any two factors is constant across equilibria, so that changes in relative factor prices epen only on changes in trae-ajuste factor supplies. Hence, in any moel satisfying these restrictions, if the omestic supplies of two factors are xe, then changes in the FCT for these two factors are su cient statistics for the impact of trae on the relative price of those two factors: 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. Moreover, we show that uner these restrictions the FCT can be constructe using inustry-level trae an prouction ata. 3 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. Dearor an Staiger (988) motivate a substantial number of empirical stuies; see e.g. Katz an Murphy (992) an Krugman (995). We show that this empirical approach remains vali in signi cantly more general economic environments featuring, for instance, imperfect competition, increasing returns to scale, heterogeneous proucers, an/or xe costs of exporting. 4 While our general framework provies a single lens to view an compare a wie range of moels an mechanisms linking trae an technology to factor prices, an makes a clear link between the FCT an factor prices, it takes the FCT as given. Without any further structure, this accounting framework 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. In the secon part of the paper we stuy the etermination of the FCT an the impact of trae liberalization on factor prices an factor allocation in an environment that combines a number of key elements of an important class of workhorse moels in international trae. To maintain analytic tractability, we specialize the general framework above to an environ- 3 Note that even in cases in which the FCT can be constructe using inustry-level ata, measuring the FCT 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). 4 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. 2

4 ment with two-countries, two-factors (skille an unskille labor), an two-sectors, as in the Heckscher-Ohlin moel. We allow for sectoral prouctivity i erences across countries, as in the Ricarian moel, an we introuce monopolistic competition an heterogeneous rms, as in Melitz (2003) an Bernar, Reing, an Schott (2007). While this moel is signi cantly less general than our accounting framework, it provies a uni e environment to stuy analytically how the FCT, factor prices, the extent of between-sector factor reallocation, an the extent of between-sector trae are all shape by cross-country i erences in factor enowments an sectoral prouctivities, as in the stanar Heckscher-Ohlin an Ricarian moels, an by rms ecisions to enter an to operate in each market, as introuce in the recently evelope moels of monopolistic competition an heterogeneous proucers. In this moel, a reuction in trae costs inuces countries to expan prouction an exports in their comparative avantage sector an contract prouction elsewhere, as in the stanar Heckscher-Ohlin an Ricarian moels. This between-sector reallocation lowers the trae-ajuste supply of the factor use intensively in the comparative avantage sector (by raising its FCT) an hence raises its relative price, as in the Heckscher-Ohlin moel. This e ect, which is often referre to as the Stolper-Samuelson e ect, is the only channel through which trae a ects factor prices (in contrast to the general framework) because the ratio of factor payments for omestic absorption between any two factors is constant in this environment. Moreover, in this moel changes in the FCT fully etermine not only changes in the skill premium, but also changes in the extent of between-sector factor reallocation an between-sector trae. Our main objective in this secon part of the paper is to stuy how the impact of trae liberalization on the FCT, the skill premium, the extent of between-sector trae, an the extent of factor reallocation is shape by the new margins of heterogeneous- rm trae moels that are absent in stanar Heckscher-Ohlin an Ricarian moels; e.g., the extent of prouctivity heterogeneity an heterogeneous rms ecisions to enter an operate in each market. To provie intuition for these comparative static exercises, we n it useful to relate the implications of these new margins to the well-known e ects of changes in exogenous Ricarian comparative avantage. In particular, exploiting the moel s simple expressions for sectoral trae shares, we show that 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 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 3

5 the FCT epens on the egree of within-sector prouctivity heterogeneity. In this sense, the strength of exogenous sources of comparative avantage (resulting from sectoral prouctivity i erences an factor enowment i erences) is shape by the ecisions of rms to enter an to sell in each estination market. We use this logic to obtain the following results on the impact of trae liberalization on the FCT, the skill premium, the extent of between-sector factor reallocation, an the extent of between-sector trae. We rst show that greater within-sector prouctivity heterogeneity reuces the magnitues of the changes in the FCT, the skill premium, the extent of between-sector trae, an the extent of factor reallocation inuce by a given change in trae shares. This is because greater technological heterogeneity mitigates the relative importance of exogenous Ricarian technological i erences an factor price i erences in shaping sectoral trae patterns. 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). We next show that enogenous entry an enogenous selection of rms into markets each increases the magnitues of the changes in the FCT, the skill premium, the extent of betweensector trae, an the extent of factor reallocation inuce by a given change in trae shares. This is because the mass of entrants from country relative to the mass of entrants from country 2 an the fraction of these entrants from country relative to the fraction of these entrants from country 2 that choose to sell in any given market is relatively larger in country s comparative avantage sector than in country 2 s; an an increase in the mass of rms that supply a given market is equivalent to an increase in that sector s exogenous Ricarian prouctivity. These results imply 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 an selection ecisions are not taken into account. Note, however, that given our earlier results, the extent of withinsector 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 betweensector 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 4

6 international trae on the skill premium can be summarize by changes in the FCT. The secon part of our paper is most closely relate to Bernar, Reing, an Schott (2007), henceforth BRS, which consier a very similar framework. As in other moels with factor-enowment i erences across countries an factor-intensity i erences across sectors, we both obtain stanar Heckscher-Ohlin-like results: trae generates factor reallocation an a Stolper-Samuelson-type e ect. 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 between-sector factor allocation. Secon, we emonstrate analytically how the new margins in heterogeneous- rm moels (the extent of within-sector prouctivity heterogeneity, enogenous entry, an selection of rms into markets) a ect the impact of trae on the skill premium, between-sector trae, an factor reallocation. In particular, while propositions in BRS state that the new margins in heterogeneous rm moels o a ect the aggregate implications of trae liberalization, none of their analytic results establish how any of these margins a ects the skill premium, the extent of factor reallocation, or the extent of between sector trae, whereas this is the focus of the secon part of our paper. Thir, we revisit their ning that i erences in factor enowments inuce what BRS call "enogenous Ricarian prouctivity i erences" at the inustry level. 5 2 Factor Prices: A Unifying Framework In this section we present a general accounting framework to examine the link between factor prices an trae. We rst erive a simple expression relating equilibrium factor prices to two components: the trae-ajuste factor supply an 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, an J sectors, inexe by j = ; :::; J. Prouction requires inputs, an inputs are groupe into isjoint sets of factors, inexe by k = ; :::; K. Factors coul be highly aggregate, e.g. capital an labor, or highly isaggregate; e.g. workers with a given number of years of eucation. Inputs within a given 5 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. 5

7 factor set k can be heterogeneous in all respects; e.g. the e ciency units provie by each input of factor k can vary within rms in a sector an across sectors. In a given equilibrium an at a given point in time, we enote by L k;i the mass of inputs of factor k employe in country i. Note that in the presence of ile inputs (e.g. labor unemployment), L k;i can be strictly less than the total supply of factor k in country i. Let L k;in (j) enote the mass of inputs of factor k in country i that are employe in supplying estination market n in sector j. The mass of inputs of factor k use in country i in sector j is L k;i (j) = P n L k;in (j), an the sum of L k;i (j) across inustries must equal total employment of factor k, L k;i = P j L k;i (j). At this point, L k;in (j) is an accounting variable escribing how factor usage is istribute across estination markets. Below we iscuss how L k;in (j) can be constructe in a range of speci c moels. In some cases it may not be straightforwar to allocate sectoral employment, L k;i (j), across estination markets, L k;in (j). As iscusse in etail below, this can be the case, for example, if rms must incur xe costs that o not epen on the set of estination markets they supply (or if marginal costs are not constant). We show, however, that in some of these cases we o not nee to construct L k;in (j) to apply our results that follow. We enote by E i (j) 0 country i s total expeniture on sector j, an by 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) =. Then total revenues by proucers in country i are P P n j in (j) E n (j). Factor payments: Let w k;in (j) enote the equilibrium average price pai in country i to inputs in factor group k employe in sector j in the prouction of goos boun for country n. This average price is equal to total earnings of these inputs ivie by the mass of these inputs L k;in (j). The average price pai in country i to inputs in factor group k employe in sector j can then be expresse as w k;i (j) = L k;i (j) X L k;in (j) w k;in (j). n Similarly, the average price pai in country i to inputs in factor group k, w k;i, can be expresse as w k;i = X L k;i (j) w k;i (j). L k;i j Note that we o not impose the restriction that two ientical inputs within a factor set (e.g. two ientical workers) are pai the same price within or across plants, rms, or sectors. Denote by in (j) the share of country i revenues from sales in country n in sector j that 6

8 is pai to all factors, in (j) = P k w k;in (j) L k;in (j). in (j) E n (j) Denote by k;in (j) the share of factor payments that are pai to inputs in factor set k, k;in (j) = w k;in (j) L k;in (j) Pk 0 w k 0 ;in (j) L k 0 ;in (j), where P k k;in (j) = for all n an j. If in (j) <, then any remaining revenues are pro ts or rents pai to an input that is not inclue in any set k = ; :::; K. Given these e nitions, it follows that w k;i L k;i = X j X k;in (j) in (j) in (j) E n (j). () n Equation () states that the total earnings of employe inputs within a factor set must equal the payments to these inputs in the prouction of goos boun for all estination markets an across all sectors. Factor content of trae: Denote by F CT k;i the factor content of trae for factor k in country i, e ne as F CT k;i = X j X n L k;in (j) L k;ii (j) ni (j) ii (j) w k;ii (j). w k;i To better unerstan the e nition of the FCT, we use our e nitions of in (j) an k;in (j) to express the payments for the FCT, w k;i F CT k;i, as w k;i F CT k;i = X j X [ k;in (j) in (j) in (j) E n (j) k;ii (j) ii (j) ni (j) E i (j)]. (2) n6=i The rst term in the summation in equation (2), k;in (j) in (j) in (j) E n (j), represents the payments to factor k emboie in country i s exports to estination market n. The secon term in the summation, k;ii (j) 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. Therefore, the FCT correspons to the net exports of factor k emboie in country i s trae. Note that constructing the FCT in the ata requires input usage an average factor prices 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 equations P () an (2), an using ii (j) = n6=i ni (j), we ecompose payments to factor k into 7

9 two components: w k;i L k;i = w k;i F CT k;i + k;i. (3) The rst component is the payments for the FCT e ne in equation (2). component is the factor payments for omestic absorption (FPD), The secon k;i = X j ii (j) k;ii (j) E i (j), which is the counterfactual payments to factor k if omestic absorption were prouce omestically. By equation (3), factor k s average price is w k;i = k;i /L k;i, (4) where L k;i = L k;i F CT k;i enotes the trae-ajuste supply of factor k. 6 By comparing equations () an (4), it is apparent that for given values of ii (j), k;ii (j), an E i (j), the average price pai to factor k in a trae equilibrium is equal to the average price that woul have been pai to factor k in autarky ha country i s employment of factor k been L k;i rather than L k;i. If a country is a net exporter of factor k, then its average 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 employment of factor k available in economy i in the presence of international trae. Using equation (4), we express the average 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 ), (5) for any k ; k 2 K. Equation (5) ecomposes the relative price of factor k to factor k 2 into two terms: (i) the trae-ajuste employment 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 employment of factor k or an increase in the FCT of k, increases the relative average price of k. Similarly, an increase in k ;i / k2 ;i, either through an increase in expeniture shares in sectors 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 6 While we use the term "trae-ajuste factor supply," it shoul be clear from the e nition of L k;i that in an environment in which some inputs remain ile, L k;i is really the trae-ajuste factor employment. 8

10 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 average 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 #. (6) 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 relative factor prices can be mappe into the general framework above. We also escribe a range of moel assumptions uner which expression (6) an the calculation of the FCT can be simpli e signi cantly. In the examples we consier, we follow the literature an assume that all inputs within a factor set are homogeneous. Moreover, because the labor market is perfectly competitive in the examples below, all inputs within a factor set receive a common price, w k;i. 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 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). (7) 9

11 Hence, constructing the k;in (j) terms requires only sectoral employment an factor prices. 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), (8) 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. 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 (6) 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. (9) L k ;i In this special case, 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 (9) was also obtaine in Dearor 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 within sectors, as in a multi-sector an multi-factor version of Eaton an Kortum (2002). 7 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 7 An alternative assumption that simpli es equation (6) 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 epen only on changes in factor supplies an relative payments for omestic absorption. 0

12 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 (5) 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 (6) 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), 8 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). 9 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. 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 (6) 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 8 While some papers 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). 9 Parro (200) consiers a moel similar to Burstein, Cravino, an Vogel (200) in which factor intensities vary across sectors. #.

13 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 xe 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 (8), an that equation (6) simpli es to equation (9). 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. 0 3 The FCT in a Heterogeneous Firm Moel While the framework in Section 2 provies a single lens to view an compare a wie range of moels an mechanisms linking trae an technology to factor prices, an links the FCT to relative factor prices, it takes the FCT as given. Without any further structure, this accounting framework 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. We now focus on unerstaning the etermination of the FCT an the impact of trae liberalization on factor prices an factor allocation in a speci c environment, covere by our accounting framework above, that combines key elements of an important class of workhorse moels in international trae. While this moel is signi cantly less general than our accounting framework, it provies a uni e environment to stuy analytically how the FCT, factor prices, the extent of between-sector factor reallocation, an the extent of betweensector trae are all shape by cross-country i erences in factor enowments an sectoral prouctivities, as in the stanar Heckscher-Ohlin an Ricarian moels, an by rms ecisions to enter an to operate in each market, as in moels of monopolistic competition an heterogeneous rms. We use this moel to obtain three sets of results. First, in Section 3, we show that in 0 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 (5). 2

14 this environment, Proposition hols, the FCT is given by equation (8), an the calculation of the FCT in equation (6) simpli es to equation (9). 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. Here we assume, without loss of generality for our results, that within each factor, all inputs are homogeneous. 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. To focus on cases in which changes in the FCT fully etermine the impact of trae on factor prices, we assume that intermeiate goos prouction functions an the nal non-traeable goo aggregator are Cobb Douglas. 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. E i 2P i (j), where We impose that there are two countries an two sectors for analytic tractability. We believe that the intuition for our results exten to more general environments. For an analysis of Stolper-Samuelson-like results in environments with many factors an sectors, see Costinot an Vogel (200). 3

15 Sectoral aggregates: Sector j s output, Q i (j), is a CES aggregate of varieties 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 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). i =( 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 ), 4

16 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. (0) 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 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), () 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) ;. (2) 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. 2 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. 2 Uner this speci cation, our results remain unchange if market access costs are stricty greater than zero an all rms sell in all markets. 5

17 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 ) >. 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 but the number of operating rms in each sector is enogenous because rms must pay a xe cost to sell in each market. 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. 3 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 an subsequently chose whether or not to pay a xe cost to sell in each market. This case correspons to a version of Melitz (2003) an BRS (2007) with Pareto istribute prouctivities. conition, for all j, is given by IX n= Z The free entry 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 expen- 3 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. 6

18 iture equals total income (wages an pro ts) in each country, E i = X k=s;u w k;i L k;i + X j 3.2 Equilibrium Characterization ( X Z ) M i (j) [ in (z; j) v i (j) f in ] G (z) v i (j) f e zin (j) n 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. (3) 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 (3) implies M i (j) v i (j) in in (j) = P I k= M. (4) 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 (3) implies in (j) = + M i (j) [v i (j)] fin P I k= M + k (j) [v k (j)] + fkn in kn. (5) We e ne t to be the relative size of international versus intra-national trae costs, t = ( without selection f + with selection. It is apparent from inspection of equations (4) an (5) that it is this relative cost t that matters, rather than an f separately. We assume that relative costs of international trae are strictly greater than those of intra-national trae, so that t >. We enote by i = 2 [ ni (x) + ni (y)], for n 6= i, country i s trae share. Note that 7

19 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 where is the share of revenues pai to all factors in both sectors, E i = X k=s;u 2, (6) w k;i L k;i, (7) an is given by 8 >< with enogenous entry + = with exogenous entry an with selection >: with exogenous entry an without selection (8) 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 in (j) n En where e = = without selection an e = ( ) = () 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 (6) (note that, by Walras law, one equation is reunant), equation (7), expeniture shares in (j) as given by Equation (4) without selection an by Equation (5) with selection, an the free-entry conitions (with enogenous entry) as given by Equation (9). 4 4 After solving for an equilibrium assuming that the moel is either with selection or without selection, 2 (9) 8

20 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 = y. Mirror symmetry makes the moel more tractable because w s = w u2, w u = w s2, an E = E Mapping to General Framework 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 () from the general framework of Section 2 is simpli e to equation (6) 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, in this speci cation we o not nee to construct L k;in (j) to use the results in Section 2. This is because 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 simplify equations () from the general framework of Section 2 to equation (6) in our moel. To obtain equation (6), 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 (6), it follows that we can express the FCT using equation (8) in all speci cations of our moel. Finally, one must verify that all cuto s are either greater than one or equal to one, respectively, using equation (2). 9

21 with Cobb-Douglas preferences an prouction functions an unchange share parameters ( k (j) = 0 k (j)), equation (6) from the general framework simpli es to equation (9), 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. 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 (0), from the factor-market clearing conition in equation (6), 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 liter- 20