Reallocation Effects in the Specific Factors and Heckscher-Ohlin. Models under Firm Heterogeneity

Transcription

1 Reallocation Effects in the Specific Factors and Heckscher-Ohlin Models under Firm Heterogeneity Eddy Bekkers Johannes Kepler University Linz Robert Stehrer The Vienna Institute for International Economic Studies - wiiw ABSTRACT: We set up a two countries two sectors model with firm heterogeneity that nests both the the Heckscher Ohlin model and the specific factors model. We use this model to study: a) to what extent the analytical and numerical results in Bernard, et al. 2007) on firm heterogeneity and factor abundance extend to the specific factors model; b) the robustness of the numerical results in Bernard, et al. 2007) to different levels of trade costs and different relative factor abundances and factor intensities; c) the effect of intersectoral factor mobility on intrasectoral reallocation effects. We get the following results. ) The analytical result on the size of the reallocation effect in the two sectors in Bernard, et al. 2007) also holds in the specific factors model. 2) The magnification of productivity differences between the comparative advantage and disadvantage sector in the Heckscher-Ohlin model does not hold for trade cost reductions from all levels of trade costs. 3) The scarce factor of production does not unambiguously gain from trade liberalization in the Heckscher-Ohlin model under firm heterogeneity, especially for larger differences in relative factor abundance. The points 2) and 3) differ from Bernard, et al. 2007). 4) More intersectoral factor mobility has a small and ambiguous effect on intrasectoral reallocation effects. 5) The magnification effect rises when the forces of comparative advantage are more pronounced, measured by a larger difference in relative factor input prices. Keywords: Firm heterogeneity, Specific Factors Model, Heckscher-Ohlin Model, Factor Mobility, Reallocation Effect, Magnification Effect JEL codes: F2 printdate: April 3, 203 Address for correspondence: Eddy Bekkers, Johannes Kepler University Linz, Department of Economics, Altenbergerstr. 69, 4040 Linz, Austria. Tel.: +43 0) ; fax: +43 0) ; eddy.bekkers@jku.at

2 Reallocation Effects in the Specific Factors and Heckscher-Ohlin Models under Firm Heterogeneity ABSTRACT: We set up a two countries two sectors model with firm heterogeneity that nests both the the Heckscher Ohlin model and the specific factors model. We use this model to study: a) to what extent the analytical and numerical results in Bernard, et al. 2007) on firm heterogeneity and factor abundance extend to the specific factors model; b) the robustness of the numerical results in Bernard, et al. 2007) to different levels of trade costs and different relative factor abundances and factor intensities; c) the effect of intersectoral factor mobility on intrasectoral reallocation effects. We get the following results. ) The analytical result on the size of the reallocation effect in the two sectors in Bernard, et al. 2007) also holds in the specific factors model. 2) The magnification of productivity differences between the comparative advantage and disadvantage sector in the Heckscher-Ohlin model does not hold for trade cost reductions from all levels of trade costs. 3) The scarce factor of production does not unambiguously gain from trade liberalization in the Heckscher-Ohlin model under firm heterogeneity, especially for larger differences in relative factor abundance. The points 2) and 3) differ from Bernard, et al. 2007). 4) More intersectoral factor mobility has a small and ambiguous effect on intrasectoral reallocation effects. 5) The magnification effect rises when the forces of comparative advantage are more pronounced, measured by a larger difference in relative factor input prices. Keywords: Firm heterogeneity, Specific Factors Model, Heckscher-Ohlin Model, Factor Mobility, Reallocation Effect, Magnification Effect JEL codes: F2. Introduction Welfare gains from trade in models with heterogeneous firms are driven by a reallocation of resources from less productive to more productive firms Melitz 2003), Bernard, et al. 2003), Melitz and Ottaviano 2008)). Bernard, et al. 2007) incorporate Melitz 2003) firm heterogeneity in a standard Heckscher Ohlin factor abundance model showing that the reallocation effect is larger in the comparative advantage sector. More firms are squeezed out of the market in the comparative advantage sector leading to a magnification of productivity differences between the comparative advantage and disadvantage sector. Thus far firm heterogeneity has not been studied in another classical model in the trade literature, the specific factors model Viner 93), Haberler 950)). This model still plays a prominent role in many

3 textbooks of international trade see for example Krugman, et al. 202)). An important question arising in this context but not yet addressed in the literature is how the reallocation effect within sectors interacts with the ease of moving factors of production across sectors. On the one hand the intuition of the Melitz 2003) firm heterogeneity model might suggest that with a higher factor mobility trade liberalization does not drive up the price of inputs that much, so that more firms can continue surviving. On the other hand intuition suggests that higher factor mobility increases the profitability of entry inducing larger reallocation effects. In this paper we combine the integration of firm heterogeneity into the specific factors model and study the effect of intersectoral factor mobility on intrasectoral reallocation effects. In particular, we aim at three goals with this paper. First, we explore whether both the analytical and numerical results in Bernard, et al. 2007) on firm heterogeneity in a Heckscher-Ohlin model extend to firm heterogeneity and specific factors. Second, we study the robustness of the simulation results in Bernard, et al. 2007) to changes in trade costs for a larger range of trade costs and to differences in relative factor abundances and factor intensities. Third, we examine the impact of intersectoral factor mobility on the intrasectoral reallocation effect. To realise these goals we set up a two country two sectors model with firm heterogeneity nesting both the Heckscher-Ohlin model and specific factors model and apt to study the effect of intersectoral factor mobility on intrasectoral reallocation effects. Our model features two factors of production. Low skilled labor is fully mobile, whereas high skilled labor consists of a partially mobile part and a sectorspecific part in both sectors. By setting the factor intensity of the sector-specific factor at zero and the transformation elasticity of the partially mobile factor between the two sectors at infinity, we nest the factor abundance model. By setting the factor intensity of the partially mobile factor at zero, we nest the specific factors model. And by varying either the transformation elasticity of the partially mobile factor or the factor intensity of the sector-specific factor we can explore the effect of intersectoral factor mobility. We get the following results. For the specific factors model, we find that the analytical results in Bernard, et al. 2007) working with the factor abundance model also hold in the specific factors model. The reallocation effect is stronger in the comparative sector. More precisely, it can be shown that the domestic cutoff productivity rises more in the comparative advantage sector when reducing trade costs from the autarky level. This result implies like in Bernard, et al. 2007) that average firm output and the rate of creative destruction are also larger in the comparative advantage sector. Further it implies a magnification effect. As a result of the stronger reallocation effect in the comparative advantage sector, 2

4 the forces of comparative advantage are magnified. So, the reallocation effect raises average productivity more in the comparative advantage sector. Important is that these analytical results hold for a movement from autarky to a positive level of trade costs, dubbed costly trade by Bernard, et al. 2007). We can also replicate the main numerical result of Bernard, et al. 2007) in the specific factors model: the real reward of the scarce production factor can go up as a result of trade liberalization. This result implies that the - traditional - political economy implications of the specific factors model should be interpreted with caution, as it is very well possible that none of the production factors loses with trade liberalization. The real loss might be incurred not by production factors and capital owners), but by firm owners, with sunk investments in specific varieties. Our numerical analysis of the firm heterogeneity Heckscher Ohlin model of Bernard, et al. 2007) shows that there are ranges of trade costs where demagnification of productivity differences might arise. I.e., productivity differences between the comparative advantage and disadvantage sector can also fall. Bernard, et al. 2007) only present simulation results on trade cost reductions from 60% to 20%, i.e. iceberg trade costs τ falling from τ =.6 to τ =.2. When trade costs fall further below τ =.2 productivity differences get smaller again. This result is not at odds with the analytical result on magnification in Bernard, et al. 2007) and in our specific factors model. The magnification effect proved analytically in Bernard, et al. 2007) holds for a movement from autarky to a positive level of trade costs. What we claim is that there can be demagnification when reducing trade costs starting from a positive nonprohibitive level of trade costs. We also show that the scarce factor of production can also lose from trade liberalization in real terms. This happens when relative factor abundance differences are slightly) larger than in Bernard, et al. 2007). These authors show that the real factor reward of the scarce factor rises with trade liberalization from τ =.6 to τ =.2) when relative factor abundance H A L A / H B L B is.44, with H the abundant factor in country A. Our simulations show that raising relative factor abundance to 2.4 the scarce factor will unambiguously lose with trade liberalization. The numerical analysis of the firm heterogeneity Heckscher Ohlin model shows furthermore that the level of trade costs where magnification of productivity differences switches to demagnification varies with factor intensity differences between the two sectors. When the Cobb Douglas parameters in the two sectors are given by 0.6 and 0.4 on the two factors in one sector and 0.4 and 0.6 in the other sector the case considered by Bernard, et al. 2007)) productivity differences will magnify until trade costs are Bombardini 2008) focuses on the gains and losses of firm owners with trade liberalization, showing that in more concentrated industries there is more lobbying for protection, as larger firms can coordinate their lobbying efforts more easily. 3

5 reduced to about τ =.2. When Cobb Douglas parameters are given by 0.9 and 0. trade liberalization magnifies productivity differences only until about τ =.6 and for further reductions in trade costs will demagnify productivitiy differences. Chen and Novy 20) report widely varying trade cost estimates across sectors in a sample of European countries. In about /3 of the sectors trade costs are smaller than τ =.6, suggesting that demagnification of productivity differences as a result of trade liberalization is not just a theoretical phenomenon. The size of relative factor abundance differences does not have much impact on the point where magnification reverts into demagnification. Our analysis also shows that the size of the magnification effect varies considerably with both variations in factor intensity differences and relative factor abundance differences. Simulations with the specific factors model show that demagnification is also possible in this model. The level of trade costs where magnification switches to demagnification is larger than in the Heckscher Ohlin model, between τ =.5 and τ =.7 for different levels of factor intensity and relative specific factor abundance differences. Simulations based on the general model to study the effect of intersectoral factor mobility on intrasectoral reallocation effects show that there is not clear link between the two. A larger transformation elasticity of the partially mobile factor raises the reallocation effects from trade in the comparative advantage sector and reduces the reallocation effect in the other sector. So, the domestic cutoff productivity rises more with trade liberalization in the comparative advantage sector and less in the other sector. The implication is that a larger transformation elasticity reflecting more intersectoral factor mobility leads to a magnification of productivity differences between the comparative advantage and disadvantage sector. The effects are small, though. Changing the transformation elasticity from 0.3 to 3 raises the maximum magnification effect from 2% to 3%. A smaller factor intensity of the sector specific factor reduces the reallocation effect in the comparative advantage sector and raises it in the other sector. Thus, a smaller factor intensity of the fixed factor reflecting more intersectoral factor mobility demagnifies productivity differences between the comparative advantage and disadvantage sector. The effect is somewhat larger than for changes in the transformation elasticity: reducing the Cobb Douglas factor intensity of the fixed factor from 0.8 to 0.2 decreases the maximum magnification effect from 3% to %. The effect of larger intersectoral factor mobility on the strength of the reallocation effect is ambiguous. Modelled by a larger transformation elasticity larger factor mobility raises the reallocation effect in the comparative advantage sector and reduces it in the other sector. Modelled by a smaller factor intensity of the specific factor a larger factor mobility reduces the reallocation effect in the comparative advantage 4

6 sector and raises it in the other sector. This suggests that something else is driving the size of the reallocation effect. This turns out to be the strength of comparative advantage expressed by the difference in relative factor input prices in the two countries. More specifically, as a last result of the paper it is shown that a larger difference in relative input prices in the comparative advantage and comparative disadvantage sector in the two countries leads to a larger difference in cutoff productivity in the two sectors and hence a larger magnification effect. Using the relative input prices in the two countries as a measure for the strength of comparative advantage means that the result is not dependent upon how the factor market is modelled. The literature on the specific factors model starts with contributions by Viner 93), Haberler 950) other contributions include Jones 97) and Neary 978)). On the interaction between the gains from trade and factor mobility. Artuc, et al. 200) estimate in a structural model switching costs of workers between sectors. They show that from a lifetime perspective all factors gain from trade shocks, i.e. also the factors working in declining sectors, as the flows between sectors are large. Kambourov 2008), Dix- Carneiro 200) and Dix-Carneiro 200) also study the interaction of labor market frictions and trade liberalization, all showing that more labor flexibility raises the welfare gains from trade. In comparison to these papers our focus is on the effect of intersectoral factor mobility on the intrasectoral reallocation effect between firms as a result trade liberalization. So, we address the question how factor mobility interacts with the squeezing out of firms. The four papers mentioned do not address this question and focus on welfare effects and real wage effects of the immobile/scarce production factors. 2 Balistreri, et al. 2009) show in a CGE model with Melitz 2003) firm heterogeneity and endogenous labor supply that a larger factor supply elasticity of labor) leads to a bigger increase in the welfare gains from trade. Still, they do not examine the effect of intersectoral factor mobility on the intrasectoral reallocation effect. 3 2 Model We model an economy with two sectors indexed by m =, 2, two countries indexed by i, j = A, B and two factors of production indexed by S = L, H with Melitz 2003) firm heterogeneity in both sectors. One of the factors of production, L, is perfectly mobile and the other factor H is partially mobile between sectors. Preferences and technology are identical across the two countries. Country A has a comparative 2 We do not study the effects of imperfect factor mobility on the gains from trade liberalization for the different factors of production in our general model. The more structural models cited are better placed for such an analysis. But, to reiterate, in these papers the interplay between intrasectoral factor mobility and intrasectoral reallocation effects is not studied. 3 The main point in Balistreri, et al. 2009) is that in multisector simulations one cannot summarize the welfare gains from trade by a single statistic measuring the trade openness of a country as Arkolakis, et al. 2008) claim in single sector models. 5

7 advantage in sector. We nest two models with this setup. When both factors of production are fully mobile between sectors, we have a Heckscher-Ohlin model with firm heterogeneity in both sectors like in Bernard, et al. 2007). Second, with full immobility of the second factor of production, we get a specific factors model like in Jones 97) and Neary 978) with firm heterogeneity in both sectors. 2. Demand All consumers have the following identical utility function across the two composite goods X and X 2 : U i = X α i Xα2 i2 ) With α + α 2 =. X i and X i2 are both a function of a continuum of differentiated consumption goods x im ω) with substitution elasticity σ X im = σ x im ω) σ dω σ σ 2) ω Ω im Ω im is the set of available varieties in country i in sector m. With this setup demand for variety x im ω) is given by x im ω) = α mp σ im I i p im ω) σ 3) P im is the price index corresponding to the composite X im defined as P im = p im ω) σ σ 4) ω Ω im I i is total income in country i and will be defined below. P i is the price index corresponding to utility and defined as: P i = Pi ) α ) α2 Pi2 5) α α Production There is a mass of producers of varieties in each sector differing in productivity ϕ. Firms face an iceberg trade cost τ ijm for exports from i to j in sector m and a fixed export cost f ijm for producing in country i and selling in country j. Assuming f ijm τ σm ijm > f iim > 0, only a subset of domestic producing firms can 6

8 export. We assume τ iim = and τ ijm τ ikm τ kjm. Firms in sector m use homogeneous input bundles Z im as inputs with price q im. The cost function of a firm producing in country i and selling an amount x ijm in country j having productivity ϕ is given by ) τijm x ijm C x ijm, ϕ) = + f ijm q im 6) ϕ Each firm produces a unique variety, so we can identify demand for variety ω by the productivity of the firm producing this variety. Demand x ijm ϕ) and revenue r ijm ϕ) of a firm with productivity ϕ producing in i and selling in j in sector m) are equal to x ijm ϕ) = α mp σ jm I j p ijm ϕ) σ 7) r ijm ϕ) = α mp σ jm I j p ijm ϕ) σ 8) Maximizing profits using 6) and 8) generates the following markup pricing rule of a firm with productivity ϕ p ijm ϕ) = σ τ ijm q im σ ϕ 9) Entry and exit are like in Melitz 2003), i.e. potential firms can draw a productivity parameter ϕ from a distribution F ϕ) after paying a sunk entry cost f e q im. Hence, the input bundles to develop new varieties are identical to the input bundles used in production. Entering firms either decide to start producing for one or two markets or leave the market immediately. Firms face a fixed death probability δ each period. A cutoff productivity parameter ϕ ijm for production in country i and sales in country j in sector m can be defined. Firms drawing a ϕ ϕ iim enter the market in country i and all other firms leave the market immediately. 2.3 Sectoral Equilibrium We can characterize equilibrium in sector m by a supply equation its dual representation given by the definition of the price index), a demand equation, a free entry condition FE), a relation between the domestic and exporting zero cutoff profit condition ZCP) and an expression for the number of firms. We start with the price index, which consists of domestic and imported goods into country i: P im = N iim p iim ϕ iim ) σ + N jim p jim ϕ jim ) σ) σ 0) 7

9 N jim is the mass of firms producing in j and selling in i. Substituting the pricing rule in equation ) leads to the following expression for supply: P im = σ ) σ qim N iim + N jim σ ϕ iim τjim q jm ϕ jim ) σ ) σ ) ϕ jim is a measure for average productivity of firms producing in j and selling in i in sector m: ϕ jim = F ) ϕ jim ϕ jim ϕ σ f ϕ) dϕ σ 2) For completeness, we define average productivity of firms selling in country i in sector m as follows: 4 ϕ im = N iim + N jim N iim ϕ σ iim + N jim ϕjim τ jim ) σ )) σ 3) To derive an expression for demand we use that revenue R im in country i in sector m should be equal to the value of input bundles, R im = q im Z im : 5 R im = 2 N ikm r ikm ϕ ikm ) = q im Z im 4) k= Substituting the expression for revenue in equation 8) and the pricing rule in equation 9) generates the following expression for demand in country i in sector m: ) σ ) σ σ σ qimz σ im = N iim ϕ σ iim σ α mp σ im I i + N ijm σ τ ijm ϕ σ ijm α mp σ jm I j 5) The FE requires ex ante zero expected profit: V im = 2 j= F ϕ ijm )) r ijm ϕ ijm ) σ f ijm q im ) = δf e q im 6) V im is the ex ante expected value from entry. The ZCP dictates that a firm with cutoff productivity ϕ ijm can just make zero profit r ijm ϕ ijm ) = σfijm q im 4 With this definition we can express the price index in country i and sector m, P im, as a function of average productivity, P im = σ σ im / ϕ im with N im the mass of varieties available in country i in sector m, N im = N iim + N jim. 5 This can be shown using the steady state entry/exit conditions together with the free entry condition, implying that all revenues are spent on factor bundles, directly through production or indirectly through development of new varieties. σ N 8

10 Expressing average revenue r ijm ϕ ijm ) as a function of the cutoff revenue and the ratio of average revenues ϕ ijm and cutoff revenues ϕ ijm, the ZCP can be rewritten as r ijm ϕ ijm ) = )) σ ϕijm ϕ ijm σf ijmq im 7) ϕ ijm Substituting the ZCP in equation 7) into the FE in equation 6) leads to: V im = 2 j= )) σ )) ϕijm F ϕ ϕ ijm ijm f ijm = δf e 8) ϕ ijm Using equation 8) for revenues, the ZCP in equation 7) can also be written as: ϕ σ ijm = α m ) σ σ σ τ P σ jm ijmq I j im 9) σq im f ijm Dividing the exporting by the domestic ZCP generates an expression for the ratio of domestic cutoff ϕ iim and exporting cutoff ϕ ijm, Λ im: Λ im = ϕ ijm ϕ iim ) fijm σ = τ ijm f iim P im P jm Ii I j ) σ 20) Finally, to determine the mass of firms N ijm, we express the relative mass of firms as a function of the shares of the densities of productivities that can produce profitably in the market: N ikm = F im ϕ ikm ) F im ϕ ijm )N ijm 2) Substituting equation 2) into 4) and using the FE in equation 6), N ijm can be expressed as a function of the cutoff productivity and factor inputs: N ijm = )) F im ϕ Z im ijm σδf e + 2 F im ϕ ikm )) σf ikm k= 22) Goods market equilibrium solves for the price indexes P im, the use of input bundles Z im, cutoff productivities ϕ im and ϕ i2m and masses of firms N im and N i2m in each sector m for given price of input bundles q im determined by factor market equilibrium) using the expressions for supply equation )), demand equation 5)), the FE equation 8)), the ZCP ratio equation 20)) and expressions for the 9

11 masses of firms in each sector m. 2.4 Pareto Distribution In the simulations we will work with a Pareto distribution of productivities. The distribution of initial productivities from which entering firms draw is defined as follows: F im ϕ) = κθim 23) ϕ θim with θ im the shape parameter and κ im the size parameter in this case. Expressions for supply equation )), demand equation 5)) and the FE equation 8)) can be reformulated, respectively, as follows see for derivation Appendix A): P σ im = A imκ θim im Z imq σ im ϕ θim σ+ iim q σ im = α m A im κ θim i P σ im I i ϕ θim σ+ iim + τ σ A jm κ θjm jm Z jmq σ jm jim ϕ θjm σ+ jim + τ σ ijm P σ jm I j ϕ θim σ+ ijm ) 24) 25) with A im = δf eθ im σ+) σ ) σ. σ σ ) κ θim im f iim θ im σ ) ϕ θim iim + f ijm ϕ θim ijm ) = δf e 26) 2.5 Factor Market Equilibrium There are two factors of production in each country, S i = L i, H i. The price of production factor S in country i in sector m is indicated by w Sim. The input bundle Z im in country i and sector m is a Cobb Douglas function of the factors of production employed in country i and sector m, L im and H im : Z im = L β Lm im Hβ Hm im ; β Lm + β Hm = 27) The corresponding price of input bundles q im is a function of the factor prices w Li and w Him : q im = wli ) βlm ) βhm whim 28) β Lm β Hm 0

12 Demand for production factor S in country i in sector m is thus given by: S im = β Sm w Sim q im Z im 29) Production factor L is fully mobile across sectors implying the following factor market equilibrium: L i = L i + L i2 30) As production factor L is fully mobile across sectors, its price w Li is equal across sectors and so we can drop the sectoral subscript m. I i 2 i I i H L H 2 L2 2I H L L 2 H 2 ~ L L L ~ 2 ~ H H H 2 H 2 ~ ~ ~ ~ H H 2 H Figure : Overview of modelling setup Production factor H is partially immobile across sectors. To nest both the Heckscher-Ohlin model and the specific factors model and to study the effect of variation in factor mobility, we specify the supply of factor H im as follows. H im is a Cobb-Douglas aggregate of a factor fixed to sector m, H im, and a

13 factor that is imperfectly mobile across the two sectors, Him : H im = H γ H γ im im ; γ + γ = 3) With L indicating low skilled workers and H high skilled workers, our modelling setup can be interpreted in the following stylized way. The low skilled workers L are the mobile factor who can freely move between sectors, as they have few skills and hence also no sector-specific skills. The high skilled sector-specific workers H can be interpreted as high skilled technical workers whose skills are tied to the sector they are working in. The partially mobile high skilled workers H can be seen as high skilled management workers, who can move between sectors but not perfectly. We do not further use this stylized interpretation. The modelling setup is chosen to nest the two classical models in trade theory, the factor abundance model and the specific factors model, and to study the interaction of intersectoral factor mobility in intrasectoral reallocation effects. Figure summarizes the modelling setup. The price of factor H im, w Him, is a function of the price the fixed factor w Him and the price of the partially mobile factor w Him : w Him = whim ) γ ) γ whim γ γ 32) Demand for the fixed and partially mobile factor are defined as: H im = H im = γ w Him H im w Him 33) γ w Him H im w Him 34) The supply of H im is fixed. Him can be imperfectly substituted between the two sectors according to a constant elasticity of transformation function: H i = H ν+ ν i + ν+ ) ν ν+ ν H i2 35) θ is the elasticity of transformation governing the ease of substitution across sectors. The optimal allocation of production factors H i and H i2 across the two sectors requires: H i H i2 = whi w Hi2 ) ν 36) Factor market equilibrium solves for factor allocations L i, L i2, H i, H i2, H i, H i2 and factor prices w Li, 2

14 w Hi, w Hi2, w Hi, w Hi2, w Hi, w Hi2, q i and q i2 for given demand for input bundles Z i and Z i2 using factor demand in equation 29), factor demand for the fixed and partially mobile factors in equations 33) and 34), factor supply in equations 30) and 35), the definitions of the price of input bundles equation 28)) and factor prices equation 32)) and optimal allocation of the partially mobile factor in equation 36). With this specification we can nest the 2x2x2 Heckscher-Ohlin model perfect factor mobility) and the 2x2x3 specific factors model no factor mobility). The first case of perfect factor mobility requires setting γ = 0 and ν. Substituting equation 3) into equation 35) using these parameter values implies that we can replace equations 33), 34), 35) and 36) with: 6 H i = H i + H i2 37) The second case of no factor mobility, requires setting γ =. This implies simply the following equation replacing equations 33), 34), 35) and 36) to define equilibrium: H im = H im 38) We had to introduce two parameters to nest both models. Working with a specification without a fixed factor, i.e. setting γ = 0 we could not properly nest the specific factors model. With ν 0, equation 35) would become: H i = max Hi, H ) i2 Hence, there would be two fixed factors as in the specific factors model, but necessarily equal. 7 Therefore, we could not model comparative advantage in the specific factors model. 8 6 ν implies from equation 36) w Hi = w Hi2 or a corner solution for Hi, Hi2 ) with one of the factor supplies H im equal to zero. The factor is homogeneous across sectors with ν, so its price will be equal unless equilibrium is a corner solution. 7 ν 0 would imply from equation 36) Hi = Hi2. 8 Adding shift parameters to the CET function in equation 35) and differing them by country would make it possible to model the specific factors model with comparative advantage without introducing a fixed factor. Still, technology would be different across the two countries and we want to avoid modelling comparative advantage using technological differences between countries. 3

15 Table : List of Equilibrium Conditions and Associated Variables Equilibrium Condition Equation Associated Variable Dimension Goods Market JK Supply ) Sectoral price index P im M Demand 5) Supply of input bundles Z im M Free entry condition 8) Domestic cutoff ϕ iim M Zero cutoff profit condition 20) Exporting cutoff ϕ ijm M Mass of firms 22) Mass of firms N ijm M Factor market Aggregate factor demands 29) Factor demands S im MK Fixed factor demand 33) Fixed factor price w Him M Partially mobile factor demand 34) Partially mobile factor demands Him M Mobile factor supply 30) Mobile factor price w Li Partially mobile factor supply 35) Partially mobile factor price w Hi Partially mobile factor optimality 36) Partially mobile factor price w Hi2 Aggregate input bundles price 28) Aggregate input bundle price q im M Partially fixed factor price 32) Partially fixed factor price w Him M Identity Income identity 39) Income I i J indicates the number of countries, M the number of sectors and K the number of factors of production. 2.6 Equilibrium To define equilibrium, an expression is needed for total income. Total income in country i can be defined as the sum of payments to input bundles in both sectors: 9 I i = q i Z i + q i2 Z i2 39) We can define equilibrium in the general model as follows: Definition Equilibrium in the general model is defined by a tuple of vectors in both countries i = A, B {I i, P i, P i2, q i, q i2, ϕ i, ϕ i2, ϕ i2, ϕ i22, ϕ i, N i2, N i2, N i22, Z i, Z i2, w Li, w Hi, w Hi2, w Hi, w Hi2, w Hi, w Hi2, L i, L i2, H i, H i2, H i, H i2 } and is determined by the following equations in both countries i:. Goods market equilibrium: supply equation )), demand equation 5)), the FE equation 8)), the ZCP ratio equation 20)) and the number of firms equation 22)) in each sector m; 2. Factor market equilibrium: factor demand for each sector m and each factor S equation 29)), factor demand for the fixed and mobile factor in each sector m equations 33) and 34)), factor supply equations 30) and 35)), the definitions of the price of input bundles equation 28)) and factor prices equation 32)) for each sector m and the optimal allocation of the partially mobile 9 Alternatively, we could define income as the sum of payments to the different production factors. 4

16 factor in equation 36); 3. The income identity equation 39)) Table gives an overview of the equilibrium conditions and the associated variables.. 3 Specific Factors Model We start theanalysis with the study of the specific factors model in combination with firm heterogeneity. In particular, we examine two questions. First, is the increase in the cutoff productivity of a country opening up to costly trade larger in the comparative advantage industry? Second, does the real reward of the scarce factor rise in real terms, because of the productivity gains as a result of reallocation effects? We first define equilibrium in the specific factors model by a tuple of vectors in both countries i = A, B, {P i, I i, P i, P i2, q i, q i2, ϕ i, ϕ i2, ϕ i2, ϕ i22, Z i, Z i2, w Li, w Hi, w Hi2, L i, L i2, H i, H i2 }. Equilibrium is determined by the same equations for goods market equilibrium and the same income identity as in definition, respectively definition. and.3. Factor market equilibrium is determined by factor demand for each sector m and each factor S equations 29)) and factor supply of the mobile factor L i equation 30)) and immobile factors in each sector m equations 38)). Country A has a comparative advantage in sector. So, country A is abundant in the sector one specific factor, H A H A2 > H B H B2. Further, the two countries have identical amounts of the mobile factor and the Cobb Douglas parameters are equal across the two sectors. 0 We turn now to the first question, the size of the reallocation effect in the two sectors. It can be easily shown that trade liberalization leads to a higher cutoff productivity in both sectors. The proof is analogue to the proof of Proposition 4 in Bernard, et al. 2007) and is available upon request. However, the size of the reallocation effect displays an interesting pattern across the two sectors, similar to the pattern in Bernard, et al. 2007) for the factor abundance model: Proposition The opening of costly trade in both sectors from a situation of autarky leads to a larger increase in the domestic cutoff productivity in the comparative advantage sector, ϕ AA > ϕ AA2 and ϕ BB > ϕ BB2. 0 Comparative advantage in the specific factors model follows from the combination of working with sector-specific factors and differences in abundance of the sector-specific factors between the two countries. The mere fact that factors are specific plays the same role as factor intensity differences in the Heckscher-Ohlin model. Therefore, the Cobb Douglas parameters are set equal across the two sectors. 5

17 Proof. Under free trade, the relative price indices of the two sectors are identical in the two countries, by the law of one price, P A /P A2 = P B /P B2. Under autarky the relative price indices in country i are given by: P i P i2 = ) Ni N i2 σ p i ϕ i ) p i2 ϕ i2 ) ) 40) Under autarky, the mass of firms N im can be expressed as total revenues R im divided by average revenues r im ϕ im ), N im = R im /r im ϕ im ). Also, we have R im = α m R i. r im ϕ im ) follows from equation 7) and 28). Using the pricing rule in equation 9) and the expression for the input price q im in equation 28), the relative price indices can be written as: P i P i2 = α2 α ) σ ϕ i2 ϕ i ) fi f i2 σ w Hi w Hi2 ) βh σ σ 4) With identical fixed costs and identical technologies implying ϕ m = ϕ 2m, the relative price indices are determined by the relative wage of the specific factors, w Hi w Hi2. market equilibrium, H im = H im and using R im = α m R i, leads to: 2 Substituting equation 29) into factor w Hi2 w Hi = H i H i2 42) Substituting the relative wage under autarky, equation 42), into the relative price index under autarky, equation 4), implies that the relative price level of good is smaller in country A under autarky, P A /P A2 < P B /P B2. Using the definition for the price index under costly trade in equation 0) it can be easily shown that the relative price index under costly trade converges to its autarky value in equation 40) for τ ijm and f im. The relative price index converges to the common free trade values for τ ijm and f ijm f iim. For intermediate values of fixed and iceberg trade costs, the relative price indices lie in between the two countries autarky values and the free trade values, P A /P A2 < P B /P B2. For equal values of iceberg and fixed trade costs across the two sectors, Λ im in equation 20) is smaller in a country s comparative advantage sector, Λ A < Λ A2 and Λ B2 < Λ B. So, the ratio of exporting to domestic cutoff productivity is smaller in a country s comparative advantage sector, ϕ AB ϕ AA ϕ BA2 ϕ BB2 < ϕ AB2 ϕ AA2 < ϕ BA ϕ. As V im is monotonically decreasing in ϕ iim, the rise in ϕ iim in response to a reduction in BB trade costs starting from autarky has to be larger in a country s comparative advantage sector for equal values of τ ijm, f ijm and f e across the two sectors. Derivation available upon request. 2 Derivation available upon request. and 6

18 Like in Bernard, et al. 2007) the result in Proposition implies a set of results on average firm output, endogenous changes in average productivity and creative destruction of firms in the comparative advantage sector relative to the comparative disadvantage sector. In particular, it can be shown that the opening of costly trade in both sectors from a situation of autarky leads to i) a larger rise in average firm output in the comparative advantage sector; ii) a magnification of ex ante cross country differences in comparative advantage because of endogenous Ricardian productivity differences at the industry level that are positively related to specific-factors-based comparative advantage; iii) a larger rise in steady-state creative destruction in the comparative advantage sector. The proofs of the three results are identical to the proofs of respectively Propositions 5, 6 and 9 in Bernard, et al. 2007) given the result in Proposition Proposition 4 in Bernard, et al. 2007)) of a larger rise in cutoff productivity in the comparative advantage sector. To illustrate the result in Proposition and the implied results, we solve the model numerically showing the effect of trade liberalization. We explore symmetric variations in trade costs in the two sectors from τ = 3 to τ =. Factor supply is set so that country A is relatively abundant in the sector specific factor. The exact values chosen are largely arbitrary and we set them in the benchmark, so that the total amount of L and H in the two countries is similar to the amounts chosen in Bernard, et al. 2007). In particular, we use the following values for factor supply, L A = L B = 000, H A = 800, H A2 = 200, H B = 200, and H B2 = 800. The Cobb Douglas parameters in the production of input bundles are set equal in the two sectors at β Sm = 0.5. The other parameter values are set symmetric across the sectors. They are discussed in Appendix D and are set as in Bernard, et al. 2007). As countries are symmetric we report only the results on country A in both sectors. We start with the rise in the cutoff productivity in the two sectors. The first panel of figure 2 displays the cutoff productivity in the comparative advantage and comparative disadvantage sector in country as a function of iceberg trade costs. 3 The increase in the cutoff productivity is larger in the comparative advantage sector in comparison to a situation of autarky. But at lower levels of trade costs the increase in the cutoff productivity is larger in the comparative disadvantage sector. The cutoff productivity increase is larger at higher trade costs, but smaller at lower trade costs. The second and third panels of figure 2 show that the average firm size and steady state creative destruction display a similar pattern across the two sectors. They rise more in the comparative advantage sector as trade costs fall from the autarky level, but the increase is larger in the comparative disadvantage 3 As the two countries are symmetric, we only report results for country. 7

19 STeady-State Creative Destruction Average Firm Output Cutoff Productivity 0.48 Domestic Cutoff Productivity Iceberg Trade Costs Average Firm Output Iceberg Trade Costs Creative Destruction Iceberg Trade Costs Comparative Advantage Sector Autarky Level in Two Sectors Comparative Disadvantage Sector Figure 2: Domestic Cutoff Productivities, Average Firm Output and Steady-State Creative Destruction in Comparative Advantage and Disadvantage Sectors in Specific Factors Model 8

20 Magnification Ratio sector, as trade costs approach zero Magnification Ratio Iceberg Trade Costs Magnification Ratio Figure 3: Magnification of Comparative Advantage in Specific Factors Model in Specific Factors Model Figure 3 displays the magnification effect defined by Bernard, et al. 2007) as the relative productivity in the two countries in the two sectors, ϕ A/ ϕ A2 ϕ B / ϕ B2. The figure shows that a reduction of trade costs from the autarky level first leads to a stronger pattern of comparative advantage, but at low levels of trade costs, the magnification effect shrinks again, with the magnification ratio converging to at zero trade costs. We can make the following observations based upon the simulations. Observation Lowering trade costs from the autarky level magnifies productivity differences between the comparative advantage and disadvantage sector in the specific factors model. There is a positive level of trade costs beyond which further trade cost reductions reduces demagnifies) productivity differences between the two sectors. The result in Proposition and the presented simulation results imply an interesting contrast in the effect of trade liberalization on the specific factors in the two sectors and on the sector-specific enterpreneurs. On the one hand, more enterpreneurs have to leave the market as a result of trade liberalization in the comparative advantage sector. So, in this sector there are more sector-specific enterpreneurs who suffer from trade liberalization. On the other hand, the specific production factor in the comparative advantage sector gains. So, the sector specific enterpreneurs have to be clearly distinguished from the sector specific factors. The first is the group of enterpreneurs who happen to be active in a certain sector having sunk investments in the sector, but able to move on to another sector 9

21 Real Factor Rewards when incurring again sunk investment costs, whereas the second group has sector specific skills and cannot move to the other sector. Real Reward Two Factors Iceberg Trade Costs Abundant Factor Scarce Factor Figure 4: Real Rewards of Scarce and Abundant Production Factor in Specific Factors Model We now move to the second question on the effect of trade liberalization on the real reward of the scarce factor of production. It can be easily shown that the relative nominal reward of the scarce abundant) factor falls rises) with lower trade costs proof available upon request). We remind that in the perfect competition specific factors model the scarce factor unambiguously loses in real terms. We use simulations to explore whether the scarce production factor can still gain from trade liberalization in real terms, because of the reallocation effect present with firm heterogeneity. This result cannot be proved analytically. Also Bernard, et al. 2007) have to use simulations to show that the scarce factor in the Heckscher-Ohlin model might gain from trade liberalization. Working with the same parameter values as in the simulations above, figure 4 shows that the real reward of the scarce factor displays a nonmonotone pattern. Lower trade costs first lead to a decline in the real reward of the scarce factor and at relatively low levels of trade costs τ =.2) real rewards of the scarce factor rise again. The real reward of the abundant factor is monotonically rising. 4 We summarize our result in the following Observation: Observation 2 The real reward of the scarce production factor can both fall and rise as a result of trade liberalization in the specific factors model with firm heterogeneity. 4 There seem to be a link with the strength of the reallocation effect: the rise in cutoff productivities is stronger in the comparative disadvantage sector for low levels of trade costs and this is also the area where the real reward of the scarce factor is rising. So, for low levels of trade costs we see the strongest reallocation effect in the comparative disadvantage sector and so the demand for the specific factor in this sector the scarce factor) woll rise most driving up its reward. 20

22 Our result in the specific factors model seems to contrast with the Heckscher-Ohlin model with firm heterogeneity in Bernard, et al. 2007), where the real reward of the scarce factor rises as a result of trade liberalization for all levels of trade costs Figure 6 in Bernard, et al. 2007)). In section 5 we will study how the real reward of the scarce factor as a function of trade costs behaves for different levels of relative factor abundance and factor intensity. We will see that also in the Hecksher-Ohlin model the real reward of the scarce factor does not always rise as a result of trade liberalization. Before moving to this topic, we will first replicate some of the simulations from Bernard, et al. 2007) for levels of trade costs not studied by Bernard, et al. 2007). 4 Heckscher-Ohlin Model In the specific factors model discussed in the previous section, the size of the reallocation effect in the comparative advantage sector relative to the comparative disadvantage sector displays a nonmonotone pattern. The rise in the cutoff productivity is larger in the comparative advantage sector for reductions in trade costs starting from the autarky level, but as trade costs fall and approach the free trade level, the cutoff productivity increase is larger in the comparative disadvantage sector. This raises the question whether a similar pattern emerges in the Hecksher-Ohlin model. Bernard, et al. 2007) explore variations in various outcome variables like the cutoff productivity for trade costs between τ =.6 and τ =.2 60% and 20%). In this range the largest increase in cutoff productivity occurs in the comparative advantage sector. This pattern also holds for other variables like weighted average productivity, probability of exporting and average firm output. The top panel of figure 5 displays the cutoff productivity in the comparative advantage and disadvantage sectors for trade costs ranging from τ = 3 to τ =. Parameter values are like in Bernard, et al. 2007), with country A abundant in factor H H A = 200, L A = 000, H B = 000 and L B = 200), sector H-intensive β H = 0.6 and β H2 = 0.4) and the other parameter values as in the specific factors model. For reductions in trade costs until τ =.2 the cutoff productivity increase is larger in the comparative advantage sector, replicating the finding in Bernard, et al. 2007). But for further reductions until free trade the cutoff productivity rises much stronger in the comparative disadvantage sector. We also see thatthe difference in reallocation effect between the two sectors is tiny for τ > 2. The second and third panels of figure 5 displays similar patterns for average firm output and steady-state creative destruction. 5 Figure 6 plots the magnification ratio, ϕ A / ϕ A2 ϕ B / ϕ B2, showing that comparative advantage is 5 The expression for average firm output in Bernard, et al. 2007), equation 30, is not fully correct. The reason is that it 2

23 Steady-State Creative Destruction Average Firm Output Domestic Cutoff Productivity 0.48 Domestic Cutoff Productivity Iceberg Trade Costs Average Firm Output Iceberg Trade Costs Creative Destruction Iceberg Trade Costs Comparative Advantage Sector Autarky Level in Two Sectors Comparative Disadvantage Sector Figure 5: Domestic Cutoff Productivities, Average Firm Output and Steady-State Creative Destruction in Comparative Advantage and Disadvantage Sectors in Factor Abundance Model 22

24 Magnification Ratio magnified for reductions in trade costs until 20% and then weakened for further trade cost reductions. Based on figure 6 we can state the following: Observation 3 Lowering trade costs from the autarky level magnifies productivity differences between the comparative advantage and disadvantage sector in the factor abundance model. There is a positive level of trade costs beyond which further trade cost reductions reduces demagnifies) productivity differences between the two sectors..05 Magnification Ratio Iceberg Trade Costs Magnification Ratio Figure 6: Magnification of Comparative Advantage in Heckscher-Ohlin Model in Factor Abundance Model Figures 5-6 do not contradict the analytical findings in Bernard, et al. 2007). Compared to a situation of autarky, the reallocation effect is larger in the comparative advantage sector, i.e. the domestic cutoff productivity, average firm output and the steady-state rate of creative destruction are larger in the comparative advantage sector and productivity differences between the two sectors are magnified by endogenous changes in average productivity, the claims in respectively Propositions 4,5,9 and 6 of Bernard, et al. 2007). In their simulations these authors display the cutoff productivity and related variables in the range of τ =.6 to τ =.2. In this range the reallocation effect is strongest in the comparative advantage sector. Our figures show that the reallocation effect can be larger in the comparative disadvantage sector when starting from trade costs below τ =.2. Figures 2-3 showed that in the specific factors model the reallocation effect is stronger in the comparative advantage sector for trade cost reductions ) ϕijm is not correct to write x ijm = ϕ x ijm. See for further discussion Appendix B. This also implies that our graph of ijm average firm output deviates somewhat from the graph in figure 4 of Bernard, et al. 2007). 23

25 up to approximately τ =.6. For further trade cost reductions the reallocation effect is stronger in the comparative disadvantage sector. Empirical work inferring iceberg trade costs from actual trade flows finds large variation in trade costs across sectors. Chen and Novy 20) find in a sample of EU countries that trade costs range across sectors from τ =.08 up to τ > 0. So, in some sectors trade costs might be in the range where trade cost reductions induce stronger reallocation effects in the comparative disadvantage sector in both models. Before discussing the trade cost estimations further, we note that the point where the cutoff productivity starts to rise more in the comparative disadvantage sector might vary as a function of the strength of comparative advantage. Therefore, we explore this issue in the next section for both the specific factors model and the Heckscher-Ohlin model. 5 The Role of Factor Abundance and Factor Intensity In the previous two sections we have studied the strength of the reallocation effect by looking at the difference in cutoff productivity between the comparative advantage and comparative disadvantage sector as a function of trade costs. In the specific factors model we have explored how the real reward of the scarce production factor varies with trade costs. Both relations might also be influenced by the size of relative factor abundance differences in the two countries and by factor intensity differences. We first study the strength of the reallocation effect in the next subsection and then move on to the real reward of the scarce factor of production. 5. Strength of Reallocation Effect in Comparative Advantage and Disadvantage Sector The simulations in the previous two sections have shown that in both the specific factors and Heckscher- Ohlin model the change in the cutoff productivity as an indicator for the strength of the reallocation effect) as a result of lower trade costs is larger in the comparative advantage sector starting from large initial levels of trade costs and is larger in the other sector starting from trade costs close to free trade. In this section we explore how the strength of comparative advantage affects the sector in which the reallocation effect is strongest. Therefore we display the ratio of domestic cutoff productivities in the two sectors, ϕ AA ϕ, as a function of trade costs and the strength of comparative advantage. We employ AA2 two measures of the strength of comparative advantage. First, relative factor abundance differences and second, factor intensity differences. We report the ratio of domestic cutoff productivities, ϕ AA ϕ AA2 as an 24

26 Relative Factor Abundance HFA Cutoff Productivity Ratio indicator of the strength of the reallocation effect in the two sectors, but the magnification ratio, ϕ A/ ϕ A2 ϕ B / ϕ B2, follows the same pattern. 6 and magnification effect interchangeably. So, in our interpretation we use strength of reallocation in the two sectors Starting with the Heckscher-Ohlin model, we vary the difference in relative factor abundance. More specifically, we raise high skilled factor abundance in country A, HF A = H A/L A H B /L B, starting from equal factor supplies, H A = H B = L A = L B = 00 and keeping total factor supply, H + L, in each country constant and varying factor abundance within countries symmetric, i.e. imposing H A = L B and L A = H B. 7 The other parameters are as in the baseline with sector H-intensive β H = 0.6). Factor Abundance and Reallocation in HO Model Figure 7: Ratio of Cutoff Productivities in Comparative Advantage and Disadvantage Sector as a Function of Relative Factor Abundance in Heckscher Ohlin Model Figure 7 displays the results for trade costs ranging between τ = 2 and τ = and relative factor abundance HF A = H A/L A H B /L B between and 4. In the range of τ = and HF A = 4 part of the figure is missing, as the economy would move into a corner solution. The figure shows that the strength of 6 The reason is that ϕ AA ϕ AA2 and ϕ BB2 ϕ BB ϕ B2 / ϕ B follow the same pattern as respectively ϕ AA ϕ AA2 follow the same pattern with a symmetric modeling setup and ϕ A / ϕ A2 and and ϕ BB2 ϕ. BB 7 We vary H A, L A, H B and L B as follows, H A = L B = HF A 2 derivation available upon request). HF A 2 + H + L) and L A = H B = HF A 2 + H + L) 25

27 Cutoff Productivity Ratio factor abundance does not have much influence on the level of trade costs where the difference in cutoff productivities is largest. This is for different values of high skilled relative factor abundance around τ =.2. The figure does show that the difference in cutoff productivities rises with the strength of factor abundance as measured by HF A. So, the magnification effect is larger for more pronounced differences in factor abundance across the two countries. We summarize our findings in the following Observation: Observation 4 With a larger relative factor abundance difference in the Heckscher Ohlin model the level of trade costs where the magnification effect is largest and switches to demagnification) does not change. The size of the magnification effect becomes larger. Factor Intensity and Reallocation in HO Model Figure 8: Ratio of Cutoff Productivities in Comparative Advantage and Disadvantage Sector as a Function of High Skilled Factor Intensity in Sector in Heckscher Ohlin Model In figure 8 we vary factor intensity for the Heckscher Ohlin model. Keeping factor abundance at the baseline level of the previous section, H A = 200, L A = 000, H B = 000 and L B = 200, we raise high skilled factor intensity of sector, β H, and low skilled factor intensity in the other sector β H2, starting from β H = 0.55 and β H2 = In contrast to relative factor abundance differences across countries, factor intensity differences across sectors do affect the point where the cutoff productivity difference across the sectors is largest. A larger factor intensity difference across the two sectors increases the level of trade costs where cutoff difference is largest. So, for factor intensities of β H = 0.55 and 26

28 Cutoff Productivity Ratio β H2 = 0.45, the largest difference lies around τ =. and for β H = 0.9 and β H2 = 0. the largest difference lies around τ =.7. Furthermore, the figure shows that the magnification effect is stronger for smaller factor intensity differences between the two sectors. We can make the following Observation: Observation 5 With a larger factor intensity difference between the two sectors in the Heckscher Ohlin model the level of trade costs where the magnification effect is largest rises. The size of the magnification effect becomes smaller. Factor Abundance and Reallocation in Specific Factors Model Figure 9: Ratio of Cutoff Productivities in Comparative Advantage and Disadvantage Sector as a Function of Relative Specific Factors Abundance in Specific Factors Model In figure 9 we move to the specific factors model varying relative abundance of specific factors in the two countries. More specifically, we raise relative specific factors abundance in country A in sector, SF A = H A/H A2 H B /H B2 from to 4. We start from equal factor supplies, H A = H A2 = H B = H B2 = 500 and L A = L B = 000, keeping total factor supply, H +H 2 and also L, constant and varying factor abundance within countries symmetric, i.e. imposing H A = H B2 and H A2 = H B. 8 The figure makes clear that like in the Heckscher Ohlin model, the relative specific factors abundance does not affect the level of trade costs where the cutoff productivity difference is largest. So, for trade cost reductions until approximately τ =.6 there is a magnification effect. For further trade cost reductions, the cutoff productivities come 8 We vary H A, H A2, H B and H B2 as follows, H A = H B2 = SF A 2 SF A H + H 2 ) 2 + and H A2 = H B = SF A H + H 2 )

29 Specific Factors Intensity Cutoff Productivity Ratio closer to each other. Furthermore, the magnification effect becomes larger for bigger differences in relative factor supply of the two specific factors. We make the following Observation: Observation 6 With a larger difference in relative specific factors supply in the two countries in the specific factors model the level of trade costs where the magnification effect is largest does not change. The size of the magnification effect becomes larger. Factor Intensity Specific Factor and Reallocation Figure 0: Ratio of Cutoff Productivities in Comparative Advantage and Disadvantage Sector as a Function of Specific Factor Intensity in Both Sectors in Specific Factors Model Finally, in figure 0 we vary factor specificity of technology. Keeping factor supply at the baseline level, H A = H B2 = 800, H A2 = H B = 200 and L A = L B = 000, we raise the importance of the specific factor in the production function, β H = β H2, starting from β H = β H2 = 0.2 until β H = β H2 = 0.8. The figure makes clear that the trade cost level where the reallocation effect is largest rises somewhat with factor intensity of the specific factor from about τ =.35 for β Hm = 0.2 to τ =.6 for β Hm = 0.8. The size of the magnification effect rises only slightly with factor intensity of the specific factor. We summarize our findings with the following Observation: Observation 7 With a larger factor intensity of the specific factor in the specific factors model the level of trade costs where the magnification effect is largest rises. The size of the magnification effect also rises. 28

30 Real Factor Reward Scarce Factor We can confront our findings with the iceberg trade cost estimates in Chen and Novy 20) across manufacturing industries of EU countries. Table in Chen and Novy 20) shows that there are only a couple of sectors where iceberg trade costs are larger than τ =.2. So, for the large majority of the sectors further trade cost reductions will magnify productivity differences between comparative advantage and comparative disadvantage sectors if the economy can be described by a Heckscher-Ohlin setup with relatively equal factor intensities across the sectors. For large differences in factor intensity in the Heckscher-Ohlin model and for specific factor intensities larger than β Hm = 0.5 in the specific factors model, trade cost reductions beyond τ =.6 reduce the magnification effect. From table of Chen and Novy 20) iceberg trade cost levels below τ =.6 can be found in about /3 of the sectors. Hence, our simulations show that trade cost reductions will not always magnify productivity differences between comparative advantage and comparative disadvantage sectors. 5.2 Real Reward of Scarce Production Factor Scarce Factor Reward and Specific Factor Abundance Figure : Ratio of Cutoff Productivities in Comparative Advantage and Disadvantage Sector as a Function of Specific Factor Intensity in Both Sectors in Specific Factors Model We conduct the same experiments on relative factor abundance and factor intensity with the real 29

31 reward of the scarce factor as for the strength of the reallocation effect. Starting with the specific factors model, figure displays the real factor reward of the scarce production factor in country, w HA2, as a function of trade costs between τ = and τ = 2 raising relative factor abundance SF A = H A/H A2 H B /H B2 from to 4. For a relative factor abundance SF A of, of course, the real reward of the scarce factor rises for all levels of trade costs. The factor is not scarce as both specific factors are in equal supply. As the specific factor abundance differs more and more, trade cost reductions first reduce the scarce factor s real factor reward for larger levels of trade costs and then raise its real factor reward for lower levels of trade costs. The figure shows that the level of trade costs where the real factor reward is at its minimum and hence starts to rise again with further trade liberalization, becomes smaller as the relative factor abundance rises. Hence, whether the scarce factor gains or loses with trade liberalization depends on the interaction of the size of the trade costs and the relative specific factor abundance. We can make the following statement: Observation 8 For larger differences in relative specific factors supply in the two countries in the specific factors model, the real reward of the scarce factor first falls and then rises in reaction to trade cost reductions from the autarky level to the free trade level In a figure available upon request, it is shown that variations in the factor intensity of the specific factor have no impact on the response of the real reward of the scarce factor to trade liberalization. Next, we move to the Heckscher-Ohlin model. In figure 2 we expose how the real reward of the scarce factor of production in country, w LA varies with trade costs as a function of relative factor abundance, HF A = H A/L A H B /L B. For relative factor abundance HF A equal to the real reward of the scarce factor rises for all trade cost levels. The factor is not scarce as supply of the two factors are equal. Raising relative factor abundance until the level used in Bernard, et al. 2007), HF A = 200/ /200 =.44, the real reward of the scarce factor still rises unambiguously with lower trade costs. As relative factor abundance rises further, the real reward of the scarce factor displays a monotonically falling pattern with reductions in trade costs until the economy bumps into the corner of full specialization. Hence, the result of rising real rewards of the scarce factor of production in Bernard, et al. 2007) only holds for relatively small levels of relative factor abundance differences between countries. As relative factor abundance differences are somewhat larger, the scarce factor unambiguously loses in real terms with trade liberalization. The reason is that the scarce factor sees a larger drop in factor demand as a country liberalizes trade when factor abundance differences are more pronounced. We make the following Observation: Observation 9 With larger relative factor abundance differences in the Heckscher Ohlin model the scarce 30

32 Real Factor Reward Scarce Factor Scarce Factor Reward and HO Factor Abundance Figure 2: Ratio of Cutoff Productivities in Comparative Advantage and Disadvantage Sector as a Function of Relative Factor Abundance in Hecksher Ohlin Model 3

33 factor unambiguously loses as a result of trade liberalization. A figure available upon request shows that for baseline levels of relative factor abundance, the response of the real reward of the scarce factor to trade liberalization is not affected by variations in factor intensity. 6 Intersectoral Factor Mobility and Intrasectoral Reallocation Effects Cutoff Productivity CA Industry Cutoff Productivity CD Industry Figure 3: Cutoff Productivities in Comparative Advantage and Comparative Disadvantage Sector as a Function of Transformation Elasticity of Partially Mobile Factor in General Model In this section we study the effect of intersectoral factor mobility on the reallocation effect within sectors. So, we explore the impact of factor mobility between sectors on the cutoff productivity. Therefore, we employ the full model and vary the transformation elasticity ν and the importance of the fixed factor in the production function, γ. We start with the transformation elasticity. Figure 3 displays the cutoff productivities in the comparative advantage and comparative disadvantage sectors, respectively ϕ AA and ϕ AA2, as a function of iceberg trade costs τ and the transformation elasticity ν. Factor supplies are given by L A = L B = H A = H B = 000, H A = H B2 = 800, H A2 = H B = 200 comparative advantage of country A in sector ) and β Hm = γ = 0.5. Comparative advantage is driven by the supply of the fixed factors and not by differences in factor intensity between the two sectors. Figure 3 shows that the transformation elasticity ν has only a marginal effect on the cutoff productivities, although the pattern is interesting. This pattern can be uncovered by studying the ratio of domestic cutoff productivities in the two sectors, ϕ AA ϕ AA2 Figure 4 shows that a larger ν leads for higher levels of trade costs to a larger increase in the cutoff productivity in the comparative advantage sector as a result of trade liberalization. 32

34 So, there is a magnification of productivity differences across the two sectors, although the effect is small. Transformation Elasticity and Cutoff Ratio in General Model Figure 4: Ratio of Cutoff Productivities in Comparative Advantage and Comparative Disadvantage Sector as a Function of Transformation Elasticity of Partially Mobile Factor in General Model As robustness check we can study the effect of increased factor mobility in the Heckscher-Ohlin model with imperfect factor mobility, so setting fixed factor supply H im at zero. Figures available upon request show that the pattern is similar as for the general model: a larger transformation elasticity θ magnifies productivity differences between the comparative advantage and comparative disadvantage sectors, but the effects are small. 9 We summarize our findings in the following Observation: Observation 0 A larger transformation elasticity between the two sectors in both the general model and in the Heckscher Ohlin model with imperfect factor mobility magnifies productivity differences between the comparative advantage and comparative disadvantage sector, but the effect is small. The results in figures 3-2 imply that the reallocation effect is stronger the more resources are drawn into the sector. The domestic cutoff productivity rises more in the comparative advantage sector as a result of trade liberalization when the transformation elasticity is larger. With a larger transformation elasticity 9 As a second robustness check we study the effect of the transformation elasticity θ if factor mobility of both factors, H and L, is imperfect. The results available upon request) are very similar to the results with imperfect factor mobility in only one factor. A larger factor mobility in both sectors magnifies productivity differences between comparative advantage and comparative disadvantage sectors, although the effect is small. 33

35 Domestic Cutoff Productivity Domestic Cutoff Productivity more resources will be drawn into the comparative advantage sector. The comparative disadvantage sector displays the opposite pattern. A larger transformation elasticity means less resources in the sector and therefore a smaller increase in the cutoff productivity as a result of trade liberalization. The implication is that a larger transformation elasticity magnifies productivity differences between the two sectors, as more resources are moving from the comparative disadvantage to the comparative advantage sector. Now we move to the effect of variation in the importance of the fixed factor relative to the partially mobile factor. We vary the Cobb Douglas parameter γ on the fixed factor in the composite of the fixed and partially mobile factor in equation 3). Factor supplies are given by L A = L B = H A = H B = 000, H A = H B2 = 800, H A2 = H B = 200 comparative advantage of country A in sector ). β Hm = 0.5 and γ varies between 0.2 and 0.8. Figure 5 displays the cutoff productivities in the comparative advantage and disadvantage sectors as a function of iceberg trade costs τ and the Cobb Douglas parameter on the fixed production factor γ. The figure shows that the cutoff productivity rises more as a result of trade liberalization in the comparative advantage sector when the fixed factor becomes more important corresponding with a higher γ) and it rises less in the comparative disadvantage sector. We see this pattern also in figure 6, where we display the ratio of cutoff productivities in the comparative advantage and disadvantage sectors as a function of trade costs and the Cobb Douglas parameter on the fixed factor, γ. So, as the fixed factor becomes more important, the productivity differences between the comparative advantage and disadvantage sectors are magnified. We make the following statement to summarize our findings: Observation A larger factor intensity of the fixed factor in the general model magnifies productivity differences between the comparative advantage and disadvantage sector, although the effect is small. Cutoff Productivity CA Industry Cutoff Productivity CD Industry Figure 5: Cutoff Productivities in Comparative Advantage and Comparative Disadvantage Sector as a Function of Cobb Douglas Parameter γ on Fixed Factor in Full Model 34

36 Our results seem to contradict the results on the transformation elasticity when more factor mobility would have the same effect on reallocation effects across sectors for variations in the transformation elasticity and variations in the Cobb Douglas parameter on the fixed factor. More factor mobility corresponds in the case of the transformation elasticity with a larger transformation elasticity and thus leads to larger productivity differences between the two sectors. More labor mobility in the case of the fixed factor Cobb Douglas parameter corresponds with a lower fixed factor Cobb Douglas parameter and therefore smaller productivity differences between the two sectors. This suggests that something else is driving the relative size of the reallocation effects in the two sectors, to which we turn in the next section. CD Parameter and Cutoff Ratio in General Model Figure 6: Ratio of Cutoff Productivities in Comparative Advantage and Comparative Disadvantage Sector as a Function of Cobb Douglas Parameter γ on Fixed Factor in Full Model 7 The Magnification Effect and Factor Input Prices We have studied how a range of parameters affects the magnification effect between the comparative advantage and disadvantage sector. A larger relative factor abundance difference in the Heckscher Ohlin model in figure 7, a larger specific factors abundance difference in the specific factors model in figure 9, a larger transformation elasticity in both the general model figure 4) and the Heckscher-Ohlin model with imperfect factor mobility figure 2) and a larger Cobb Douglas parameter on the fixed factor in the general model all lead to a magnification of productivity differences between the comparative advantage and comparative disadvantage sector under costly trade in comparison to autarky. The common element is 35

37 Relative Input Price Relative Input Price Relative Input Price Relative Input Price that in all these cases the relative input price difference, qi q i2, between the two countries is larger. In figure 7 we display how the relation between the ratio of relative input prices, q A q A2 / q B q B2 and trade costs varies with relative factor abundance in the Heckscher Ohlin model, relative specific factor abundance in the specific factors model, the transformation elasticity in the general model and the fixed factor intensity in the general model. Combining the graphs with the figures displaying the size of the magnification effect for the different models implies that for all the models a larger input price difference between the comparative advantage and comparative disadvantage sectors in the two countries leads to a stronger magnification of productivity differences between the two countries. Relative Input Price and HO Relative Factor Abundance Relative Input Price and Specific Factor Abundance Relative Input Price and Transformation Elasticity Relative Input Price and Fixed Factor Intensity Figure 7: The Relation between The Ratio of Relative Input Prices and Trade Costs as a Function of The Relative Factor Abundance in The Heckscher Ohlin Model, Relative Specific Factor Abundance in The Specific Factors Model, The Transformation Elasticity in The General Model and The Fixed Factor Intensity in The General Model We cannot prove this result analytically. This is discussed more formally in Appendix C. The reason is that a larger input price difference under autarky only implies that price index differences are larger in the case of autarky. We cannot prove that price index differences are also larger in the case of costly trade, which would imply a larger difference between the domestic and exporting cutoff in the 36

38 comparative advantage sector, therefore a larger domestic cutoff productivity in this sector and so a magnified productivity difference. We summarize our discussion in the following Observation: Observation 2 In the 2x2 model with two countries and two industries with firm heterogeneity in both sectors and comparative advantage defined according to the relative prices of input bundles in the two countries, a larger difference in the relative prices of input bundles between the comparative advantage and disadvantage sectors in the two countries, so a larger q A q A2 / q B q B2, leads to a larger difference in cutoff productivity between the comparative advantage and disadvantage sector and hence a larger magnification effect. 8 Concluding Remarks In this paper we set up a model with imperfect factor mobility that nests the classical factor abundance and specific factors models in international trade. We first studied the two nests separately. In the specific factors nest we showed that the analytical results in Bernard, et al. 2007) extend to the specific factors model. In both nests we runned a range of numerical exercises with as main results that there might be demagnification of productivity differences between the comparative advantage and comparative disadvantage sector in both models and that the scarce factor of production can both gain and lose in real terms from trade liberalization, both as a function of the range of trade costs for which trade liberalization is studied and as a function of relative factor abundance and factor intensity differences. We used the general framework to study the interaction of intersectoral factor mobility and intrasectoral reallocation effects. The size of the intrasectoral reallocation effect in the two sectors does not vary much with intersectoral factor mobility and is instead determined by the strength of comparative advantage as measured by relative input price differences References Arkolakis, Costas, Svetlana Demidova, Peter J. Klenow, and Andres Rodriguez-Clare 2008), Endogenous Variety and The Gains from Trade, American Economic Review: Papers & Proceedings 982), pp Artuc, Erhan, Shubham Chaudhuri, and John McLaren 200). Trade Shocks and Labor Adjustment: A Structural Empirical Approach. American Economic Review 003):

39 Balistreri, Edward J., Russell H. Hillberry and Thomas F. Rutherford 2009), Trade and Welfare: Does Industrial Organization Matter, Economics Working Paper Series CER-ETH, No. 09/9. Bernard Andrew B. and Jonathan Eaton and Samuel S. Kortum 2003), Plants and Productivity in International Trade, American Economic Review 93, pp Bernard, Andrew B., Jonathan Eaton, J. Bradford Jensen, and Samuel Kortum2003). Plants and Productivity in International Trade. American Economic Review 934): Bernard, Andrew B., Stephen J. Redding and Peter K. Schott 2007), Comparative Advantage and Heterogeneous Firms, Review of Economic Studies 74, pp Bombardini, M. 2008), Firm Heterogeneity and Lobby Participation, Journal of International Economics 75: Bowen, Harry P., Abraham Hollander, and Jean-Marie Viaene 997), Applied International Trade Analysis, The University of Michigan Press. Chen, Natalie and Dennis Novy 20). Gravity, Trade Integration, and Heterogeneity across Industries. Journal of International Economics 85: Dix-Carneiro, Rafael. 200). Trade Liberalization and labr market Dynamics. Mimeo Princeton University. Haberler, Gottfried 950). Some problems in the pure theory of international trade. Economic Journal 60: Jones, R.W. 97), A Three-Factor Model in Theory, Trade, and History, In Trade, Balance of Payments and Growth: Essays in Honor of C.P. Kindleberger ed. J.N. Bhagwati et al.). Amsterdam: North Holland. Kambourov, Gueorgui 2008). Labor Marke Regulations and the Sectoral Reallocation of Workers: The Case of Trade Reforms. Mimeo University of Toronto. Kerem Cosar, A. 200). Adjusting to Trade Liberalization: Reallocation and Labor Market Policies. Mimeo Pennsylvania State University. Krugman, Paul R., Marc Melitz and Maurice Obstfeld 202). International Economics, Theory and Policy. Pearson, 9th Edition. 38

40 Melitz, Marc J. 2003), The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity, Econometrica 7 6), pp Melitz, Marc J. and Gianmarco I.P. Ottaviano 2008), Market Size, Trade, and Productivity, Review of Economic Studies 75): J. Peter Neary 978), Short-Run Capital Specificity and The Pure Theory of International Trade, The Economic Journal 88, pp Viner, Jacob 93). Cost Curves and Supply Curves. Zeitschrift für Nationalökonomie 3:

41 Appendix A Sectoral Equilibrium with Pareto Distribution We start with the derivation of the FE with a Pareto distribution, equation 26). Using rϕ) rϕ 2) = ϕ ϕ 2 ) σ and the ZCP, the FE in equation 6) can be written as: 2 j= )) Fim ϕ ijm fijm ϕ ijm ϕ ijm ) σ = δf e A.) We impose θ im > σ to guarantee that expected revenues are finite. The implication of assuming a Pareto distribution is that ϕ is proportional to ϕ : ϕ ijm = θ im θ im σ ) ) σ ϕ ijm A.2) Under a Pareto distribution, the FE, equation 6) becomes: 2 F im ϕ σ ikm)) θ im σ ) f ikmq im = δf e q im k= A.3) Substituting the Pareto cdf in equation 23), the FE in equation A.3) becomes: σ ) κ θim im f iim θ im σ ) ϕ θim iim + f ijm ϕ θim ijm ) = δf e A.4) Next, we derive demand under a Pareto distribution, equation 25). Therefore, we substitute the Pareto cdf in equation 23) and the FE with Pareto, equation A.3), into the expression for the mass of firms, equation 22), to get: N ijm = κ im ϕ ijm ) θim σ σθ im δf e Z im A.5) Substituting equation A.2) and A.5) into equation 5) lead to: q σ imz im = q σ im = κ θim im ) θim ) σ κim σ σ θ im ϕ Z im iim σθ im δf e σ θ im σ ) ϕ σ iim α mp σ im I i ) θim ) σ κ im σ σ + ϕ Z im ijm σθ im δf e σ τ θ im ijm θ im σ ) ϕ σ ijm α mp σ jm ) σ σ P σ im I i θ im σ + ) δf e σ ϕ θim σ+ + τ σ ijm P σ jm I ) j iim ϕ θjm σ+ ijm I j A.6) In the main text we define A im as A im = δf eθ im σ+) σ ) σ. σ 40

42 Finally, to derive supply with a Pareto distribution, equation 24), we substitute equation A.2) and A.5) into equation ): P σ im = ) σ ) θim σ κim σ σ ϕ Z im iim σθ im δf e ) ) σ θim σ κ im σ + σ ϕ Z jm jim σθ jm δf e = A imκ θim im Z imq σ im ϕ θim σ+ iim q im θ im θ im σ ) + A jmκ θjm jm Z jmτ σ jim q σ jm ϕ θjm σ+ jim ) σ τ jim q jm θ jm θ jm σ ) ϕ iim ) σ ϕ jim σ σ Appendix B Expression for Average Firm Output The definition of average output x im follows from r ijm = x ijm p ijm and the pricing rule in equation 9) for the average firm: x im = = = σ σ r iim q im + ϕ iim θ im σ θ im σ ) θ im σ ) θ im σ ) F ) ϕ ijm r ijm F ϕ iim ) σ q im f iim σ σ q im + ϕ iim q im σ ϕ ijm θ im σ θ im σ ) ) ϕ ϕ θim iim iimf iim + ϕ ϕ ijm ϕ iim ϕ ijm ijmf ijm ) θim q im f ijm σ σ q im ϕ ijm B.) Alternatively average firm output can be defined directly from the ZCP. The ZCP for cutoff output x ijm can be written as: x ijm = ϕ ijmf ijm σ ) To get to the alternative expression, equation 30) in Bernard, et al. 2007), average firm output x ijm is written as follows: x ijm = = F ) ϕ ijm F ) ϕ ijm ϕ ijm ϕ ijm p ϕ) σ P σ j I j f ϕ) dϕ ) σ σ σ ϕ P σ j I j f ϕ) dϕ 4

43 = = = = = σ σ σ σ σ σ ϕ ijm ϕ ijm ϕ ijm ϕ ijm ϕ ijm ϕ ijm ) σ P σ j I j F ) ϕ ijm ) σ P σ j I j ) σ P σ j I j ϕ σ ijm ) σ σ ϕ σ ijm ) σ x ijm ϕ ijm F ) ϕ ijm σ ) σ ϕ ijmf ijm σ ) ) σ P σ j I j ϕ σ f ϕ) dϕ ϕ ijm ϕ σ f ϕ) dϕ σ σ We see that there is a small mistake in the fourth line, implying that it is not correct to write x ijm = ϕ ijm ϕ ijm ) σ ϕ ijmf ijm σ ) Using this equation average firm output can be written erronously as in equation 30) of Bernard, et al. 2007): x im = x im = ϕiim ϕ iim ) σ ϕ iimf iim σ ) + F ) ϕ ijm F ϕ iim ) ) σ σ σ ) ϕ iimf iim + θ im θ im σ ) ϕ ijm ϕ ijm ϕ iim ϕ ijm ) σ ϕ ijmf ijm σ ) ) θim ϕ ijmf ijm B.2) Comparing the expression in equation B.2) with the correct expression in equation B.), we see that for a Pareto distribution the mistake is relatively small. Appendix C Input Price Differences and Magnification Effect Consider the model with two countries and two sectors with Cobb Douglas preferences across the two sectors and Melitz type firm heterogeneity as in the main text, but with unspecified factor supply. So, equilibrium is defined by the tuple of vectors in both countries i = A, B, {I i, P i, P i2, q i, q i2, ϕ i, ϕ i2, ϕ i2, ϕ i22, Z i, Z i2 } and determined by supply, demand, a free entry condition and a zero cutoff profit condition in each sector m in each country i and the income identity in each country i, respectively equations ), 5), 8), 20) 42

44 and 39). The prices of the input bundles, q i, q i2, are determined by equilibrium on the factor market, which we leave unspecified. We can now follow exactly the same steps as in the proof of Proposition with equation 4) replaced by: P i P i2 = α2 α ) σ ϕ i2 ϕ i ) fi f i2 σ q i q i2 ) σ σ Suppose that country A has a comparative advantage in sector, corresponding with q A q A2 < q B q B2. This implies that the relative the relative price level of good is smaller in country A under autarky, P A /P A2 < P B /P B2. For intermediate values of fixed and iceberg trade costs, the relative price indices display the same pattern, P A /P A2 < P B /P B2. Therefore, for equal values of iceberg and fixed trade costs across the two sectors, Λ im in equation 20) is smaller in a country s comparative advantage sector, Λ A < Λ A2 and Λ B2 < Λ B. Hence, the ratio of exporting to domestic cutoff productivity is smaller in a country s comparative advantage sector, ϕ AB ϕ AA < ϕ AB2 ϕ AA2 and ϕ BA2 ϕ BB2 < ϕ BA ϕ, implying that the domestic cutoff productivity ϕ iim BB is larger in a country s comparative advantage sector for costly trade, ϕ AA > ϕ AA2 for equal values of τ ijm, f ijm and f e across the two sectors. So, we have shown that the magnification effect is driven by differences in factor prices. We can, however, not show that a larger difference in relative factor prices between the two countries under autarky driven by for example a more pronounced comparative advantage differences, a larger transformation elasticity or a larger Cobb Douglas parameter on the fixed factor) also implies a larger difference in cutoff productivities across the two sectors. The reason is that we are only able to show that the difference in relative price indexes, so P A/P A2 P B /P B2, is larger under autarky. We do not know how this difference evolves under costly trade. We only know that P A /P A2 stays larger than P B /P B2 until prices are equalized under free trade. Appendix D Simulations The baseline parameter values are set in accordance with the parameters in the numerical analysis of Bernard, et al. 2007). The baseline parameters can be found in Table 2. Without loss of generality the Cobb Douglas parameters of both sectors α m are set equal to each other, equal to /2. For the elasticity of substitution within sectors, σ, we work with a value of 3.8 and for the Pareto shape parameter θ m and size parameter κ m with values of 3.4 and 0.2, respectively, 43

45 Table 2: Baseline Parameter Values Baseline parameters Description Symbol Value shift parameter sector m α m 0.5 substititon elasticity sectors σ m 3.8 Pareto shape parameter θ m 3.4 Pareto shift parameter κ m 0.2 sunk entry costs f e fixed costs f 0. fixed export costs f x 0. death probability δ following estimates using plant-level US manufacturing data in Bernard, et al. 2003). The parameter value of the sunk entry cost f e scales the mass of firms and without loss of generality f e is set at. Fixed production costs, domestically and in the foreign market, f and f x respectively, are 0% of the sunk entry cost, 0.. The domestic and exporting fixed costs are equal in the baseline, implying equal domestic and exporting cutoff productivity when iceberg trade costs are. The death probability δ rescales the mass of entrants relative to the mass of producing firms and without loss of generality, a value of is chosen. 44

46 Supplementary Appendices of Derivations Appendix E Specific Factors Model Proof of Cutoff Productivity Rising with Lower Trade Costs The expected value of entry under costly trade, V im in equation 8), is equal to the expected value of entry under autarky, Vim A A, plus a positive term reflecting the expected value from exporting. Vim is defined as: Vim A = F ϕ ϕiim ϕ iim iim)) ) ) σ ) It can be shown Appendix B in Melitz 2003)) that V im is monotonically decreasing in ϕ iim. Therefore, ϕ iim must be higher in both industries m under costly trade than under autarky for V im to be equal to the unchanged sunk entry cost δf e. Equation 4) ϕ iim f ijm B.) Substituting N im = R im /r im ϕ im ), R im = α m R i. and equation 7) for r im ϕ im ) and 28) for q im and using the pricing rule from equation 9), equation 40) can be rewritten as: P i P i2 = = = = = = Ri r i2 ϕ i2 ) R i2 r i ϕ i ) α α 2 α2 α α2 α α2 α α2 α ϕi2 ϕ i2 ) σ fi2 q i2 ϕi ϕ i ) σ fi q i ) σ ) σ ) σ ) σ ϕ i2 ϕ i ϕ i2 ϕ i ϕ i2 ϕ i ϕ i2 ϕ i ) σ q i q i2 ϕ i2 ) fi f i2 fi f i2 fi σ ϕ i ) σ q i ) σ f i2 ) fi f i2 ) σ ) qi ϕ i2 q i2 ϕ i ) σ σ q i2 wli ) βli w Hi β Li ) βli2 ) βhi2 wli w Hi2 β Li2 β Hi2 β β Li2 Li2 β β Li Li σ w Hi w Hi2 ) σ β Hi ) βhi σ β β Hi2 Hi2 ) βh σ σ β β Hi Hi σ σ ) σ σ wli β Li ) ) βli β Li2 w β σ Hi σ Hi w β Hi2 Hi2 Equation 42) Substituting equation 29) into factor market equilibrium, H im = H im and using R im = α m R i, leads

47 to: H i H i2 = H i H i2 = β H w Hi q i Z i β H w Hi2 q i2 Z i2 α R i w Hi α 2R i w Hi2 H i = w Hi2 H i2 w Hi Proof of Relative Nominal Reward of Scarce Factor Falling with Lower Trade Costs The relative nominal reward of the abundant factor under costly trade is in between the two countries autarky values. As trade costs become infinite, τ ijm, the relative nominal rewards converge to each country s autarky value and as trade costs become zero, τ ijm, the relative nominal rewards converge to the common free trade value. Country A is relatively abundant in sector specific labor, H A H A2 > H A+H B H A2 +H B2 > H B H B2. Therefore, the opening of costly trade leads to an increase in the relative nominal reward of the abundant factor in country A, w HA w HA2. Variation in Factor Supplies in Factor Abundance Model Simulations We impose that H + L = H A + L A = H B + L B is constant, varying relative factor abundance HF A = H A/L A H B /L B with factor abundance within countries symmetric, i.e. H A = L B and L A = H B. We can then express H A and L A as follows: HF A = H A/L A H B /L B = H A /L A ) 2 = H A / H + L) H A ) 2 Solving for H A = L B and L A = H B gives: HF A 2 = H A H + L H A HF A 2 H + L HA ) = H A ) H A HF A 2 + = HF A 2 H + L) H A = L B = HF A 2 H + L) HF A 2 + L A = H B = H + L) HF A 2 + 2

48 Appendix F Model with CES Functions In the main text we have worked with Cobb Douglas functions for consumer demand across sectors and 2, factor demand across factors L and H and factor demand across fixed and partially mobile factors, H and H. To run robustness checks, we also programmed the different models full model; Heckscher-Ohlin model; Heckscher-Ohlin model with partial factor mobility of one of the factors, H; and specific factors model) with CES specifications. The utility function U i is a CES function of sectoral aggregates X i and X i2 with substitution elasticity ρ: U i = α X ρ ρ i + α 2 X ρ ρ i2 ) ρ ρ, 0 < α <, 0 < α 2 <, ρ > 0 B.2) The input bundle Z im in country i and sector m is a CES function of the factors of production employed in country i and sector m, L im and H im with substitution elasticity η: Z im = β Lim L η η im + β HimH η η im ) η η ; 0 < βlim < ; 0 < β Him < ; η > 0 B.3) Factor H im is a Cobb-Douglas aggregate of a factor fixed to sector m, H im, and a factor that is imperfectly mobile across the two sectors, Him with substitution elasticity υ: H im = γ im H υ υ im ) υ υ υ υ + γ 2im H im, 0 < γim <, 0 < γ 2im <, υ > 0 B.4) The equilibrium is defined for the same set of variables as in the Cobb Douglas model, with price index P i added. Equilibrium values are determined by the following set of equilibrium equations. Goods market: P σ im = A imκ θim im Z imq σ im ϕ θim σ+ iim q σ im = α ρ ma im κ θ i P σ ρ im A jm κ θjm + τ σm jm Z jmq σ jm jim ϕ θjm σ+ jim ) P ρ U i ϕ θim σ+ iim I i + τ σ ijm P σ ρ jm P ρ U j I j ϕ θim σ+ ijm B.5) B.6) σ ) κ θim im f iim θ im σ ) ϕ θim iim + f ijm ϕ θim ijm ) = δf e B.7) ) σ ρ ϕ ijm = ϕ Pim σ I i f ijm iimτ ijm P jm I j f iim ) σ P i P j ) ρ σ B.8) 3

49 Factor market: q im = ) β η Lim w η Lim + βη Him w η η Him B.9) ) η βsim q im S im = Z im B.0) w Sim L i = L i + L i2 w Him = γ υ w υ Him + γυ 2 w υ ) υ Him B.) B.2) H im = H im = ) υ γ w Him H im B.3) w Him ) υ γ2 w Him H im B.4) w Him H i = H ν+ ν i + ν+ ) ν ν+ ν H i2 B.5) H i H i2 = whi w Hi2 ) ν B.6) Identities: P i = I i = q i Z i + q i2 Z i2 α ρ P ρ i ) + α ρ 2 P ρ ρ i2 B.7) B.8) Appendix G Additional Simulation Results The Effect of Variations in Factor Intensity on the Scarce Factor s Real Rewards Response to Trade Liberalization in the Specific Factors Model In figure 9 we explore the role of the intensity of the specific factor, raising the importance of the specific factor in the production function from β H = β H2 = 0.2 to β H = β H2 = 0.8. The real factor reward moves almost identically with trade costs for different values of specific factor intensity. So, the real factor reward falls for trade liberalizations until about τ =.2 and for further trade cost reductions rises. As expected the real factor reward rises with the specific factor intensity, as the specific factor becomes more important in the production process. So, we can conclude that a larger factor intensity of the specific factor in the specific factors model has no impact on the response of the real reward of the scarce factor to trade liberalization. The Effect of Variations in Factor Intensity on the Scarce Factor s Real Rewards Response to Trade 4

50 Real Factor Reward Scarce Factor Scarce Factor Reward and Factor Intensity in HO Model Figure 8: Ratio of Cutoff Productivities in Comparative Advantage and Disadvantage Sector as a Function of High Skilled Factor Intensity in Sector in Heckscher Ohlin Model 5

51 Real Factor Reward Scarce Factor Scarce Factor Reward and Specificity Figure 9: Ratio of Cutoff Productivities in Comparative Advantage and Disadvantage Sector as a Function of Specific Factor Intensity in Both Sectors in Specific Factors Model 6

52 Liberalization in the Heckscher-Ohlin Model We study how factor intensity affects the variation of the scarce factor s real reward with trade costs. We raise high skilled factor intensity in sector and reduce it in sector 2, starting from a level of β H = 0.55 and β H2 = Figure 8 displays the simulation results. Like in the specific factors model factor intensity has hardly any effect on how the real factor reward of the scarce factor moves with trade costs. The scarce factor s real reward rises with trade liberalization for all values between β H = 0.6 β H2 = 0.4) and β H = 0.95 β H2 = 0.05). 2 The scarce factor s real reward rises as factor intensity differences in the two sectors become more pronounced. The reason is that the scarce factor L becomes more important in sector 2, which drives up its real reward. So, we can conclude that for baseline levels of relative factor abundance variations in factor intensity do not affect the response of the real reward of the scarce factor to trade liberalization. Varying Transformation Elasticity in the Heckscher-Ohlin Model with Imperfect Mobility of One Production Factor We study the effect of increased factor mobility in the Heckscher-Ohlin model with imperfect factor mobility, so setting fixed factor supply H im at zero. Figure 20 displays the ratio of cutoff productivities in the comparative advantage and disadvantage sectors of country, ϕ AA ϕ, as a function of iceberg trade AA2 costs τ and the transformation elasticity ν. Comparative advantage is modelled by a difference in factor intensities, β H = β L2 = 0.6 and so β L = β H2 = 0.4), combined with a difference in relative factor abundance, H A = L B = 200 and H B = L A = 000. So, one of the production factors, H, is imperfectly mobile and the other production factor L is perfectly mobile. The figure reveals the same pattern as in the full model: a larger transformation elasticity θ magnifies productivity differences between the comparative advantage and comparative disadvantage sectors. This becomes clearer by studying the ratio of cutoff productivities in the comparative advantage and disadvantage sectors, ϕ AA ϕ AA2 in figure 2 Varying Transformation Elasticity in the Heckscher-Ohlin Model with Imperfect Mobility of Both Production Factors In an additional robustness check we introduce imperfect factor mobility of both factors of production, H and L. Figure 22 displays the ratio of cutoff productivities in the comparative advantage and disadvantage sectors of country, respecively ϕ AA and ϕ AA2, as a function of iceberg trade costs τ and the transformation elasticity θ. There is no fixed factor supply, H im = 0, and comparative advantage is modelled by a difference in factor intensities, β H = β L2 = 0.6 and so β L = β H2 = 0.4), combined 20 Remember that we keep factor abundance differences at the Bernard, et al. 2007) baseline level. 2 Only for β H = 0.55 β H2 = 0.45) there is a small area at very low levels of trade costs, τ =.05, where the scarce factor s real reward falls with trade liberalization. 7

53 Transformation Elasticity Cutoff Productivity Ratio Transformation Elasticity Cutoff Productivity Cutoff Productivity Transformation Elasticity Cutoff Productivity CA Industry Cutoff Productivity CD Industry Iceberg Trade Costs Iceberg Trade Costs Figure 20: Cutoff Productivities in Comparative Advantage and Comparative Disadvantage Sector as a Function of Transformation Elasticity of Partially Mobile Factor in Heckscher Ohlin Model Transformation Elasticity and Reallocation Iceberg Trade Costs Figure 2: Ratio of Cutoff Productivities in Comparative Advantage and Comparative Disadvantage Sector as a Function of Transformation Elasticity of Partially Mobile Factor in Heckscher Ohlin Model 8

54 Transformation Elasticity Cutoff Productivity Cutoff Productivity Transformation Elasticity with a difference in relative factor abundance, HA = L B = 200 and H B = L A = 000. Results are similar to imperfect factor mobility of one of the production factors. As figure 23 illustrates, a larger transformation elasticity θ magnifies productivity differences between the comparative advantage and comparative disadvantage sectors. Cutoff Productivity CA Sector Cutoff Productivity CD Sector Iceberg Trade Costs Iceberg Trade Costs Figure 22: Cutoff Productivities in Comparative Advantage and Comparative Disadvantage Sector as a Function of Transformation Elasticity in Factor Abundance Model 9