Fragmentation and Wage Inequality: Insights from a Simple Model

Transcription

1 Fragmentation and Wage nequality: nsights from a Simple Model Juan Carluccio, var Ekeland, Roger Guesnerie March 27, 207 Abstract We develop a simple model to study ho globalization affects age inequalities. The model features three goods, one is an international goods, and to are local non-tradable goods. The non-tradable goods are produced by local labor, either skilled or unskilled, hile labor of all types and all origins contribute to the production of the international good. We find that increasing participation of the South in global production and consumption lead to an increase in age inequalities in the North. Higher South integration into global value chains reduces North-South age inequalities. KEY WORDS: Fragmentation of production, globalization, age inequalities. JE CASSFCATON: F62, F6, F23. We are grateful to Camilo Carluccio for helpful discussions. All remaining errors are our on. Banque de France and University of Surrey. CEREMADE and Chaire Finance et Développement Durable, Université Paris- Dauphine. Collège de France and Paris School of Economics.

2 ntroduction One of the hottest debates on the effects of the present so-called globalization concerns its consequences for income inequality, both beteen nations and ithin nations. Bourguignon and Guesnerie 996) asked hether globalization decreases inequalities beteen nations hile increasing inequalities ithin nations, in line ith the questions feeding the titles of the articles of Freeman 995), Rodrik 997) or more recently Ebenstein, Harrison and Mc Millan 204). The present paper attempts to shed light on the issue from a partial and in a sense naive viepoint. The viepoint is partial since the paper voluntarily leaves aside the questions associated either ith capital accumulation or technical progress, hose distributional dimension has raised a lot of recent debates and controversies. t is also naive, in the sense that it provides a simplistic image of international trade hich, although referring to the simplest version of the Heckscher-Ohlin model hich has come to dominate trade modelling after the 9th century episode of globalization, attempts to depart as much as possible from its defining features. n the Heckscher-Ohlin story, international trade concerns goods produced from immobile local factors. n our model, besides local non-traded goods, there is a single international good hich is internationally produced from all local factors and consumed in every place. Naturally, this model captures an extreme form of trade hich extrapolates from the present trend associated ith the continuous increasing role of multinational firms. t echoes the idea that the production of manufactures is associated ith a global value chain, hich in this model is an aggregate of the global value chains of many specific manufactured goods see Timmer et al 204)). Finally, for the sake of simplicity, our orld has to blocks, or regions, metaphorically the North and the South, echoing again the prospects of Timmer et al. et us sum up. Our orld has three goods: the international good produced nohere, and the to local non-traded goods. The non-traded goods are produced from local labor, either skilled or unskilled, hile labor of all types and all origins contribute to the production of the international good. The paper aims at providing a clear understanding of the forces shaping inequalities beteen the North and the South, as ell as beteen orkers of different skills in the North, in the admittedly simplistic orld under consideration. Most forms of globalization that e consider lead to an increase in age inequalities in the North, hile improving the age of South s unskilled orkers. We complement the theoretical analysis ith a simple numerical simulation of our model. t aims at capturing an operationally more plausible image of the orld under scrutiny, hile stressing hat e believe to be reasonable interpretations of the theoretical insights. Our paper contributes to a burgeoning literature analysing global values chains and offshoring, of hich closer to our ork is Acemoglu et al 205). Our approach is not in opposition, but rather attempts to provide a complementary vie, to papers modelling offshoring and international production in Heckscher-Ohlin frameorks, here visible contributions include Helpman 2

3 984) and Grossman and Rossi-Hansberg 2008). Ho does this paper relate to Malinvaud s scientific ork? et us remind the division of labor promoted by the Econometric Society: theory leaning on appropriate modelling on the one hand, empirical analysis relying on statistical examination of existing data, on the other hand. Clearly, Malinvaud as one of the fe people of his generation able to undertake frontier research on each side of the line. Our paper, even if e sketch at the end a quantitative illustration of the model under scrutiny, is clearly on one side of the dividing line. t goes ithout saying that our subject has no close connections ith a number of subjects hich ere behind E. Malinvaud s theoretical ork, and does not concern, to take some examples, either intertemporal equilibrium, Malinvaud, 953) and planning. Our preocupations hoever echo a constant interest of Malinvaud, as a professional economist as ell as a policy adviser, for ages and income distribution problems. ndeed, the labor market is the explicit subject of a number of his contributions Malinvaud 980, 983, 984, 994) and a key implicit question behind his investigations in the economics of fixed prices and macroeconomics Malinvaud 98, 982, 99), or even groth Malinvaud 986, 987). And in a sense our text attempts to shed some different light on the functioning of labor markets in the ne context of globalization. We proceed in a standard ay: e present the model in Section 2, provide the equilibrium analysis in Section 3, discuss the comparative statics analysis in Section 4 and provide a simple numerical simulation in Section 5. Section 6 concludes. 2 Model Setup The orld is divided in to countries, the richer one, called North, and the poorer one, called South, ith different types of labor as factors of production. All variables pertaining to North are denoted in capitals, and all variables pertaining to South in loer-case. n North, there are H skilled orkers and unskilled orkers. n South, there are no skilled orkers and l unskilled orkers. abor is perfectly mobile across sectors ithin countries, but immobile across borders. abor markets are perfectly competitive. Wages W H, W, ) ill be determined in equilibrium. There are three goods. To of them are local non-tradable) goods: one is produced and consumed in the North and the other is produced and consumed in the South. The third one is an industrial good, consumed in both countries and produced by combining labor from both countries. The production of good can be thought of taking place nohere or in the air, capturing the idea that the disintegration of production across borders that happens ithin global value n recent ork, Carluccio et al 206) modify the factor-proportions model to include trade in inputs and heterogeneous firms. For a variety of vies of globalization, see e.g. Broda and Weinstein 2006), Costinot and Vogel 200), Thoenig and Verdier 2003). 3

4 chains implies goods are made in the orld 2. There is perfect competition in all goods markets. Preferences All inhabitants of North and all inhabitants of South have Cobb-Douglas utility. Respectively: U X 0, X ) = X α 0 X α in North u x 0, x ) = x β 0 x β in South here the subscript 0 refers to the non-tradable goods and the subscript refers to the industrial good. Notice that e allo the preference parameters α and β to be potentially different. This admittedly ad-hoc formulation ill allo us to study ho changes in consumption patterns that can be associated ith global economic integration affect ages in both locations. Production Denote by H and, respectively, the quantity of skilled and unskilled labor from North allocated to the production of the industrial good, and by l the quantity of unskilled orkers from South allocated to the production of the industrial good. Similarly, H 0, 0 ) and l 0 denote the quantity of orkers allocated to the production of the local good in each country. The production functions are the folloing. For the international good : Q = l + ) )/ H ith 0 The expression measures the elasticity of substitution beteen North s and South s unskilled labor. 3 t varies from to infinity hen goes from 0 to. The coefficient measures some kind of relative eight of the North and the South labor in the production of the industrial good. There are different possible explanations for the existence of this relative eight productivity or implicit embedded capital differences of the North and South labor inputs) and e ill come back to them later. Note that the production of our industrial good is fragmented, to use a ord of the policy debate, and that that fragmentation, hatever the precise meaning, ill intuitively increase, ith and, everything else being kept equal. 2...More and more firms no organize production on a global scale and choose to offshore parts, components or services to producers in foreign and often distant countries. The typical Made in labels in manufactured goods have become archaic symbols of an old era. These days, most goods are Made in the World. Antras 206, Ch. p. 4) 3 Note that hen goes to zero, e get Cobb-Douglas production functions elasticity of substitution equal to ): lim 0 l + ) ) / H = l ) H. 4

5 For the local good in the North, e assume a Cobb-Douglas production function 4 : Q 0 = H θ 0 θ 0 ith 0 < θ < For the local good in the South: q = l 0. abor market clearing conditions The balance equations for the labor force are: Skilled orkers in North: H = H 0 + H Unskilled orkers in North: = 0 + Unskilled orkers in South: l = l 0 + l Cost-minimizing input choices The quantity of each type of labor allocated to each good is determined folloing a cost-minimization process. Absolute ages are denoted by W, W H, ). t ill prove useful to ork ith relative ages of northern to southern orkers, hich are defined as: W =, W H = H. The next emma reflects the input choices made for the production of the international good, as functions of the prices of the North s skilled and unskilled labor, and of the South s unskilled) labor. emma The cost-minimizing inputs for the production of one unit of industrial good, are: ) + l = / + = H = ) / ) / + ) ) + + ) ) + / H ) ) / H ) + / H Proof. See the Appendix. 4 As in the case described in footnote 3, this function obtains in the limit hen ρ 0 of θh ρ 0 + θ) ) /ρ ρ 0 = H θ 0 θ 0. n a previous version, e have orked ith this general form, obtaining similar results. We choose a Cobb-Douglas formulation here to ease the exposition. 5

6 The derivation of the unit cost functions for the to local goods is straightforard. We present the three unit cost functions in the folloing emma: emma 2 The unit costs functions are: For the international good : C = ) / + ) For the North s local good: C 0 = θ θ θ) θ W θ H W θ. For the South s local good: c 0 = ) / H We chose the the industrial good as the numéraire and normalize its unit cost hich equals its and price) to : C =. At this point it is useful to come back to the idea of fragmentation. One natural ay to measure it is ith the ratio l / : the higher it is, the larger is the participation of sourthen okers in the global value chain. Note that, using the expressions above, it can be expressed as ). Everything else being kept equal, fragmentation increases ith and. Such changes do modify endogenous ages, a fact that has to be captured by the investigation of the equilibrium. 3 The equilibrium equations The balance-of-payments equation Strictly speaking, e have no such thing as a balance-of-payments equation, since the production of good is made nohere. Hoever, note that consumption of the industrial good must be financed by the revenue of those orkers ho are engaged in the production of the industrial good. Therefore, in each country, the value of consumption of must equal the age bill of orkers engaged in the global value chain. Denoting Q the total production of good, and remembering that its unit price is normalized to, e obtain, for the North: and similarly, for the South: α HW H + W ) = Q H W H + W ) ) βl = Q l 2) Dividing one equation by the other, e eliminate Q, so that: α H β l H + ) l = H H + l l 6

7 Taking into account the above expressions for H,, and l, e get: α H β l H + ) l = ) ) ) + + We rerite this as: α H β l H + ) l ) = 0 3) A simple relation beteen and H, to hich e come back later. We ill refer to it as the Balance-of-payments equation. Note that this equation expresses the fact that the ratio of consumption of the industrial good beteen the North and the South equals the ratio of their contribution to the value added of this good. The skilled labor market equilibrium Assuming, as above, that the production function for the local good in the North is Cobb-Douglas, e can rite that the total age bill of skilled orkers HW H as HW H = α) θ + α )) HW H + W ) + ) βl The expression is made up by to parts: α) θ HW H + W ): the income received from the production of the local good in the North. ) [α HW H + W )+βl]: the income received for the participation in the global value chain of good. We thus obtain a a linear relation beteen the relative ages H = W H / and = W /, namely: H H = α) θ + α )) H H + ) + ) βl hich can be reritten as ; H = A A) H ) βl + A) H 4) ith A = α) θ + α ). A belongs to the segment [θ, ]. We ill refer to equation 4) as the Skilled labor market equation. 7

8 The good s market equilibrium The third equation reflects the equilibrium in the international good s market, equating its price to the unit cost P = C. As stated above, e normalize to price to : P =, and e have C = : ) / + ) ) / ) H ) = 5) We ill refer to equation 5) as the Normalization equation. Definition of equilibrium An equilibrium is a vector of ages W, W H, ) that constitutes a solution to the three-equation system formed by equations 3), 4), and 5). 3. Solving the system Theorem An equilibrium exists and it is unique. Equation 3) is of the form H = f ), ith f decreasing note that this is independent of the Cobb-Douglas assumption). Equation 4) is of the form H = f 2 ) ith f 2 increasing note again that this is independent of the Cobb-Douglas assumption). So f f 2 is decreasing, and: 0 f ) f 2 ) + hich implies that there is a single point such that f ) f 2 ) = 0. Figure provides an illustration of the equilibrium in the h, l ) space, hich is represented by point E. After solving for, H ) e can use normalization relation C = to obtain. Finally, absolute ages can then be recovered using the fact that WH = H and W =. This completes the solution of the model s equilibrium. We next study to important properties of the equilibrium. 3.2 Equilibrium properties To go further into the study of the equilibrium, it proves useful to rite equations 3), 4), and 5) in a more compact fashion. Respectively: 8

9 Figure : Equilibrium Balance-of-payments Skilled labor market 45 9

10 α βl H H + ) m g g = 0 6) A) H H A ) βl = 0 7) ) + m m + g ) + m g g ) g H = 8) ith g =, m = and = ) Note that g, m, ) are all strictly positive. g) is monotonically increasing in and m) is monotonically increasing in. We can rite equation 6) in the form: H = βl [ αh m g g + ] H 9) The right-hand side, as noted above, is a strictly decreasing function of > 0. ts derivative is: H g βl [ ] αh m g g Write equation 7) in the form: H = A A) H ) βl + A) H 0) The folloing proposition gives to results concerning the equilibrium, in line ith our introductory presentation. The first one gives a simple and eak condition on the relative populations of skilled and unskilled orkers in the North, hich ill imply that, in equilibrium, unskilled orkers have a loer age than the skilled ones and hich is true in all numerical simulations available upon request). The second one, > /m), states that, in equilibrium, the age of the unskilled orkers in North relative to the unskilled orkers age in the South is higher than hat is implied by their apparent relative productivity in the production of the industrial good. This relies on a eak condition concerning the number of orkers in the South. Proposition The folloing statements hold:. f H > A A, then H >. 2. f m < and βl >, then > /m Proof. See the Appendix. 0

11 Point ) is obvious, since the affine function defined by 0) has slope greater than. Regarding point 2), e note that m = is an increasing function of, and that the condition m < / limits attention to the case here m is either smaller than, hich e have in mind for this setting, or not too much larger. From no on, e assume m < hich is equivalent to < /2). 4 Comparative statics We are no able to proceed to the core of our analysis, i.e. the comparative statics. Dependence on α An increase in α reflects a higher level of consumption of the industrial good by northern orkers. t implies a donard shift of equation 9). The change in equation 0) depends on other parameters: f θ <, an increase in α increases A and A and implies that d < 0, and d H / ) > 0 f θ >, d H is negative, and d H / ) < 0 The result is expressed in the folloing emma: emma 3 f dα > 0, then f θ, then d < 0, and d H / ) > 0 if θ >>, then d H < 0 and d H / ) < 0 Dependence on β An increase in β implies a higher consumption of the industrial goods by southern orkers. t has to effects. t shifts up the curve defined by 9), and shifts up the line defined by 0), respectively by: d H = l [ αh m g g + ] dβ d H ) l = A) H dβ Note that since α < A, e have d H > d H. Geometrically, it is obvious that the ne intersection is such that d H > 0, but also d > 0, and the price normalization condition implies that d < 0. What about d H / )? The anser is not obvious and requires some computations, hich are provided in the appendix. t is clear that dw H has to be positive. The fact that dw > 0 results from additional computations. We sum up:

12 emma 4 f dβ > 0,then d H > 0, d > 0 and d < 0. t is also the case that d H / ) > 0, dw H > 0 and dw > 0 Dependence on m The parameter m gives the eight of the South s unskilled orkers in the global value chain. The curve 9) shifts don in the relevant area and the line 0) is unaffected. Then, it is geometrically straightforard that d H < 0, d < 0, and from the price normalization condition, it follos that d > 0. t is also clear that d H / ) > 0. n terms of absolute ages, it follos that dw < 0. emma 5 f dm > 0, then d H < 0, d < 0, and d > 0. t is also the case that d H / ) > 0 and dw < 0 n terms of absolute ages, it is intuitively plausible that dw H > 0. This is not generally true, but the situation obtains in our numerical computations henever β becomes high enough. Dependence on g An increase in the synthetic parameter g implies an increase in, hich represents the elasticity of substitution beteen North s and South s unskilled orkers in the global value chain. Geometrically, hen g increases, it loers the curve 9) if m >, hile leaving equation 0) unaffected. emma 6 f dg > 0, then d H < 0, d < 0, and d > 0. We also have d H / ) > 0. Dependence on A decrease in i.e. an increase in )), implying a loer eight of skilled orkers in the production of good, increases A and A A ), shifting up the curve 9). Then the folloing obtains. emma 7 f decreases, then d H > 0. One can also prove d > 0, and d H / ) > 0,unless /l is small, see the orking paper version. Dependence on θ An increase in θ implies a higher share of skilled orkers in the production of the North s local good. t increases A and leaves the curve 9) unaffected. emma 8 f dθ > 0, then d H > 0, d < 0, and d H / ) > 0. 2

13 4. Summary Consider the forces behind globalization. n our model, they are intuitively reflected by an increase in, ), associated ith the relative productivity and substitutability of South s labor, and also ith an increase in β, α), the income shares of the industrial good. We find: A- Whenever there is an increase in the forces of globalization, through the competitiveness of the South, i.e henever, )increase, d H / ) > 0 obtains, i.e. there is a deterioration of the situation of the North lo skilled orkers relatively to the North high skilled. ndeed, in both cases d > 0 and dw < 0 B- d H / ) > 0 also obtains hen the South s income share of the industrial good, β, increases. For the North, an increase in α, the sign of d H / ) is the sign of θ). C- The same d H / ) > 0 is true henever increases, such a change being possibly interpreted as the effect of increasing innovation triggered by globalization. D- The result d H / ) > 0 still holds henever θ increases although such a move does not a priori reflect the forces of globalization). 5 A simple quantitative analysis n this section e use our model to perform a simple quantitative analysis. The objective is not to provide a fully-fledged calibration, but rather to help grasping the plausibility of our model hen contrasted ith real-orld data. We base this section on the empirical analysis of Timmer et al 204), ho provide an estimation of value added shares of different productive factors ithin global value chains henceforth GVC). An interesting point in their analysis is that they are able to calculate value-added shares ithin geographical regions. They divide the orld in to groups, placing high income countries on one side and the rest in a second group. We ill identify high income countries ith the North, and the second group, ith the South. 5 We use 995 as our benchmark year. We no discuss ho e obtain the parameter values. First, notice that, in our simple model, e have assumed that the production function for the internationally traded good Q uses only labor. n order to account for the share of capital e proceed as follos. For the North, e multiply the value added by each type of labor by a factor z, here z is the value added share of capital. This method then allocates the capital stock to each type of labor, allocating more per-capita capital to skilled orkers i.e. those ith higher ages). For the South, e follo the model and consider that it has only one 5 The countries listed as high income are the folloing: Australia, Canada, and the United States; Japan, South Korea, and Taian; and all 5 countries that joined the European Union before

14 production factor, hich accounts for 00% of South s value added of Q. We recalculate value added shares using the data in Table 3 in Timmer et al 204): Table : Value Added Shares in Global Value Chains H l 995 9% 54% 27% % 36% 44% For factor endoments e use the data provided in the Socio-Economic Accounts of the World nput-output Database WOD, available at.iod.org). We use hours orked by labor type, and adjust the size of orkforces to account for capital in the manner described above. We normalize l = 200 and set H = 0 and = 36 to account for the relative sizes of orkforces in the North and the South. Equation ) provides a relationship beteen the North s consumption of the industrial good Q and the revenue obtained by orkers in the North from the production of that good. Similarly for equation 2) that concerns the South. This means that e can back up α and β using data on the share of value added of Q produced in each region, as ell as each region s GDP. 6 Timmer et al. estimate that GVC value added accounted for 23% of the World s GDP in 995. That year, the GDP from the North and that of the South accounted for 77% and 23% of World GDP Source: World Bank Development ndicators database). Using this information it is easy to sho that equations ) and 2) imply α = 0, 2 and β = 0, 26 respectively. We set θ = 0, 6, calculated using the average share of skilled labor in total compensation in the North in non-tradable industries for the high-income countries Source: WOD). We set = 0, 8 to match the share of value added by skilled labor from Table. Parameters, ) are central to our analysis, as they determine the level of international fragmentation. The parameter governs the elasticity of substitution beteen North s and South s unskilled orkers in the global value chain, hich is given by σ: e have = σ σ. For our tentative experiment, e set = 0.75 hich corresponds to σ = 4, folloing a somehat bold interpretation of a value close to) the mean estimate for the US 4.7) provided by Broda et al 2006) in their estimations of trade elasticities for intermediate inputs. 7. We take as a free parameter, choosing the value required to match the shares in Table, hich is = Specifically e use α = Q H W H + W ) and β = Q l. HW H +W 7 ) l The estimates in Broda et al are obtained from data covering Given the lack of more recent data, e use the same value for 995 and Similar results obtain using different combinations of the pair, ), for example the folloing: 0, 4; 0, 2), 0, 5; 0, 9). t is easy to see that both higher and imply higher equilibrium values of and l, hich in turn generates a larger participation of the South both in the production of Q i and in global GDP. Thus, larger values of require loer values for and viceversa. 4

15 Table 2 summarizes the parameter values ith hich our model exactly replicates the 995 factor shares of Table, as ell as the observed division of orld s GDP beteen the North and the South. We repeat the exercise for 2008, using the parameter values given in Table 2. 9 Table 2: Parameter values α β θ H l 995 0,2 0,26 0,6 0,8 0,75 0, ,3 0,8 0,6 0,80 0,75 0, We can no discuss hat insights our model can provide to understand the changes shon in Table. The main message arising from the comparison of the numbers for 995 and 2008 is that, quantitatively, the increase in the share of the South s unskilled orkers, from 27% to 44%, is driven exclusively by the increase in the fragmentation parameter, hich changes from 0.4 to 0.23, i.e. a 64% increase. There is no straightforard empirical proxy for unfortunately 0. Still, our simple model generates patterns hich are quite reasonable in light of the real-orld data. n line ith the comparative statics presented in the previous section, the increase in the value-added share of South s orkers arising from higher is accompanied ith a reduction the ages of orkers in the North, both in absolute terms and ith respect to that of orkers in the South. Wage inequalities in the North increase ith the participation of the South in the global value chain. These effects of globalization have been ell documented see e.g. Harrison et al, 20). The impact of changes in consumption patterns, as given by α and β, modify ages in line ith the predictions of Section 4, but their impact on value-added shares looks small. Changes in factor endoments, namely the increase in the relative size of the South and the increase in the relative endoment of skilled orkers in the North, are relatively minor in size and have little explanatory poer for the factor shares. The numerical version of the model therefore points to the changes in the production function of global value chains as the main driver of the evolution of ages and the distribution of global value added. 9 n 2008, the South s share of World s GDP increased to 37%. Value-added in global value chains accounted for 5% of World s GDP. Using equations ) and 2) ith these values e obtain the values for α and β provided in Table 2. 0 There is no trade in a strict sense in the model. Hoever, the GVC s value-added originating in each country can be thought of as exports. n the connection beteen GVC value-added and,, simple in the case ith close to zero), can serve to provide a proxy to exports of the South for hich it is most likely that gross trade flos are larger than value-added terms) Such an analysis provide some ligth on. see discussion paper) 5

16 6 Conclusion We have provided a simple, perhaps too simple model, hich allos us to exhibit more clearly the respective role of different forces relating to our present globalization, as factors of the inequalities increases in the North. The conclusions may look unsurprising given the modelling input. The mechanics of the model differs significantly from the standard Heckscher-Ohlin story and its actual mechanics is far from straightforard. To equations govern equilibrium, the second one expresses in a rather intuitive ay the determination of the age of skilled labor in the North. The first one expresses the equality of the ratio of the contribution of the North and the South in the production of the industrial good ith the ratio of its consumption. We are aare that a better intuition on this equality is a prerequisite to the generalization of the model, left for future research. We believe that the comparison of the theoretical perspectives ith the stylised facts concerning the evolution of the orld trade, as measured in the ork of Tillmer et al., supports or at least illustrates) the theoretical story developed here. Again, although the context differs much of the context of the seventies, eighties or nineties, in hich Malinvaud developed his vies on ages, e hope that our attempt at shedding light on the present forces in the labor market, echoes Malinvaud s example and lessons. Appendix A: Proof of emma Minimizing W + W H H + l under the constraint: ) ln H + ln l + ) ) = 0 e find: W H = λ H ) W = λ l + ) l = λ l + ) Hence: W W H = = = H = ) l l + ) H l 6

17 t follos that; = H = = = H H H ) l l + ) l + + ) ) ) l l ) The quantity l needed to produce one unit is given by: ) / H = l + ) = / + ) ) / l = / + ) = / H l l ) ) / l H + Hence l. Substituting, e get H and ) H ) ) l + ) +/ l ) ) l l B: Proof of emma 4 Note that the slope of the curve 9) in H, β) + d H,, β), is approximately: H g βl [ ] αh m g g so that at the intersection ith line 8 in, β) + dν, d = dν) ) ) ldβ) A A) H + dν = l [ A H αh m g g + ] dβ) H + g βl ) αh [ m g g ] dν [ ) α + g βl ] A αh αh m g g ) dν = Multiplying by αh l : [ ] α A l ) + gβ[ m g g dν = 7 l [ αh m g g + [ m g g + ] ) α dβ) A) ] ) α dβ) A)

18 Remembering that: α βl H H + ) m g g = 0 so that: [ ] [ α A l ) + gβ[ m g g α dν = βl H H + ) As: e get: H = [ α βl H H + ) A A) H ) βl + A) H ] ) α A) = α A βl [ α + gβl A)[ ] m g g dν = [α β ]dβ) ] ) α dβ) A) We no have to compare the slope H at the initial point *) forget *) no) i.e ith ) lβ + A A) H A to the slope of the line connecting the ne equilibrium to the initial one, i.e t is enough to compare: d H/dν + A A H ) ldβ/dν) A) H ) ldβ/dν) A) H H + A A H dβ/dν) = [α + gβl A)[ m g g ] [α β ] > i.e hich is alays true. dβ/dν) > β [ ] [α + gβl A)][ m g g ] > [α] 8

19 C: Proof of Proposition The condition > /m) holds true iff the value of the right-hand side for = /m is higher in equation 9) than in equation 0), namely: [ βl αh m g m +g + ] A ) βl H m > A) H m + A) H or: βl m α [ A) ] α βl f m <, then a sufficient condition is: [ α ] > ] A) βl > βl ) βl ) + > α A) [ α A) At this point one should note that A < implies that α < A. So the right-hand side is negative. Substituting βl > in the left-hand side, e find that it is positive. So the inequality holds true, and the result is proved. References [] Acemoglu, D., Gancia, G and Zilibotti F, 205) Offshoring and Directed Technical Change, American Economic Journal: Macroeconomics, 73), pp [2] Antràs, P. 206) Global Production: Firms, Contracts and Trade Structure, Princeton University Press. [3] Bourguignon F. Guesnerie R. 996) Mondialisation : moins d inégaltiés entre les nations, plus d inégalités au sein des nations? [4] Broda, C., Greenfield J. and Weinstein, D. 2006)?From Groundnuts to Globalization: A Structural Estimate of Trade and Groth? NBER Working Paper No [5] Carluccio, J., Cunat, A, Fadinger, H. and Fons-Rosen, C. Offshoring and Skill-upgrading in French Manufacturing: A Heckscher-Ohlin-Melitz Vie, mimeo. [6] Costinot A and Vogel J, 200) Matching and nequality in the orld economy, Journal of Political Economy, 8, [7] Ebenstein A, Harrison A, Mc Millan M 204), Why are American orkers getting poorer? China, trade and offshoring, mimeo. [8] Freeman R. 995), Are your ages set in Beijing? Journal of Economic Perspectives, 9,3, 5-32 ] 9

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