Firms, Contracts, and Trade Structure: Slides

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1 Firms, Contracts, and Trade Structure: Slides Alexander Tarasov University of Munich Summer 2010 Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

2 Motivation For the United States, about one-third of exports and over 40% of imports consist of intrarm trade between a U.S. or foreign rm and their afliates. In a cross-section of industries, the share of intrarm imports in total U.S. imports is larger the higher the capital intensity of the exporting industry. PICTURE 1. In a cross-section of countries, the share of intrarm imports in total U.S. imports is larger the higher the capital-labor ratio of the exporting country. PICTURE 2. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

3 Motivation These observations raise the following questions: Why are capital-intensive goods transacted within rm boundaries while labor-intensive goods are traded mostly at arm's length? Why is the share of intrarm imports higher for capital-abundant countries? Are these facts related? Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

4 What This Paper Does A property-rights model of the boundaries of the rm in which the endogenous benets of integration outweigh its endogenous costs only in capital-intensive industries! close to PICTURE 1 A general-equilibrium, factor-proportions model of international trade, with imperfect competition and product differentiation: in the general equilibrium, capital-abundant countries capture larger shares of a country's imports of capital-intensive goods PICTURE 2 follows from the interaction of transaction-cost minimization (PICTURE 1) and comparative advantage Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

5 The Sketch of the Model A nal-good producer needs to obtain a special and distinct intermediate input from a supplier. Production of the input requires certain noncontractible and relationship-specic investments in capital and labor. The nal-good producer contributes to some of these investments but cost-sharing is relatively more important in capital investments. The lack of ex-ante contracts implies that the bargaining over the terms of trade takes place after intermediate input has been produced and manufacturing costs are bygones. A two-sided holdup problem which results in underinvestment in both capital and labor. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

6 The Sketch of the Model There are two possible organizational forms: vertical integration or outsourcing. Ownership is dened as the entitlement of some residual rights of control. Inefciency in labor investments is shown to be relatively higher under integration than under outsourcing; and conversely for capital. This implies that rms will choose outsourcing only when the investment in labor is relatively important in production! close to PICTURE 1. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

7 The Sketch of the Model This partial equilibrium is embedded in a general equilibrium setup with imperfect competition and product differentiation. Countries specialize in certain intermediate input varieties and export them worldwide. Capital-abundant countries tend to produce a larger share of capital-intensive varieties than labor-abundant countries. The share of capital-intensive (and thus intrarm) imports in total imports is then shown to be an increasing function of the capital-labor ratio of the exporting country! close to PICTURE 2. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

8 Consider a two-factor (K, L), two-sector (Y, Z ) closed economy. K and L are inelastically supplied and freely mobile across sectors. In each sector, rms use K and L to produce a continuum of differentiated varieties. Preferences of the representative consumer are of the form: where µ, α 2 (0, 1). Z ny µ Z U = y(i) α α nz di 0 0 z(i) α di 1 µ α, Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

9 Demand for nal-good varieties is thus y(i) = z(i) = A Y, p Y (i) 1 1 α A Z, p Z (i) 1 1 α where A Y = µep α 1 α Y, A Z = (1 µ) EP α 1 α Z. E is the total expenditure and P Y and P Z are the industry price indexes. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

10 Sales revenues are given by R Y (i) = p Y (i)y(i) = A 1 α Y y(i) α R Z (i) = p Z (i)z(i) = A 1 α Z z(i) α. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

11 Technology: Each variety y(i) requires a special and distinct intermediate input x Y (i) (z(i) requires x Z (i)). The input must be of high quality, otherwise output is zero. If the input is of high quality, production of the nal good requires no further costs and y(i) = x Y (i), z(i) = x Z (i). Production of a high-quality intermediate input requires a combination of capital K x and L x : Kx (i) βk Lx (i) x k (i) = β k 1 β k 1 βk for k 2 fy, Z g. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

12 Technology: Let 1 > β Y > β Z > 0. Low-quality intermediate inputs can be produced at a negligible cost. There are also xed costs of production: fr β k w 1 β k, k 2 fy, Z g. The costs are split between the producer and the supplier (f S and f F ). Firm structure: The nal-good producer (F ) decides whether it wants to enter a given market, and if so, whether to obtain the input from a vertically-integrated supplier (S) or from a stand-alone S. F chooses the mode of organization so as to maximize its ex-ante prots. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

13 Firm structure: It is assumed that, upon entry, S makes a lump-sum transfer T k (i) to F (it is to simplify the description of equilibrium). The labor investment L x is undertaken by S. The capital investment K x is undertaken by F. These investments are incurred upon entry and are useless outside the relationship. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

14 Contract Incompleteness: No outside party can distinguish between a high-quality and a low-quality intermediate input x k. This implies that F and S cannot sign enforceable quality-contingent contracts specifying the purchase of a certain type of intermediate input for a certain price. Similarly, it is assumed that K x (i), L x (i) are not veriable and the parties cannot write contracts on R Y (i) and R Z (i). The only contractibles ex-ante are the allocation of residual rights and the ex ante transfer T k (i). Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

15 Contract Incompleteness: If the supplier incurs all variable costs, the contract incompleteness gives rise to a standard holdup problem: the nal-good producer will want to renegotiate the price after x k (i) has been produced. Foreseeing this renegotiation, the supplier will undertake investments in capital and labor. If the nal-producer shares capital expenditures with the supplier, the holdup problem becomes two-sided. Therefore, its investment in capital are also suboptimal. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

16 Contract Incompleteness: Because no enforceable contract is signed ex-ante, F and S will bargain over the surplus of the relationship ex-post, when manufacturing costs are bygones. The extent of the underinvestment by each party will be inversely related to the share of surplus the obtain in the bargaining. Assume that Generalized Nash Bargaining leaves the nal-good producer with a fraction φ 2 (0, 1) of the ex-post gains from trade. Bargaining will occur even when the parties are integrated. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

17 When the supplier is a stand-alone rm, then if the parties fail to agree on a division of surplus, the nal-good producer is left with nothing. Under integration, the nal-good producer can re the manager of the supplying division and seize some amount of input produced. In particular, the nal-good producer obtains the residual rights over only a fraction of δ 2 (0, 1) of the input. If δ = 1, then integration would never be chosen (the nal-good producer just takes the whole amount of input implying zero investment in labor). PICTURE! Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

18 Integrated pairs: The potential revenues are given by R Y (i) = A 1 Y α y(i) α If there is no agreement, then the revenues are δ α R Y (i). Therefore, the quasi-rent is R Y (i) δ α R Y (i) = (1 δ α )R Y (i). Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

19 Integrated pairs: The nal-good producer receives δ α R Y (i) + φ(1 δ α )R Y (i) = φr Y (i) The supplier receives 0 + (1 φ)(1 δ α )R Y (i) Note that φ > φ. That is, under integration, the nal-good producer receives a higher fraction of sale revenues. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

20 Integrated pairs: Given the choice of labor, the nal-good producer solves max f φr Y (i) rk Y (i)g. K Y (i) Given the choice of capital, the supplier solves max f(1 φ) R Y (i) wl Y (i)g. L Y (i) We can solve for the interception of these two best response functions. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

21 Integrated pairs: The solution implies that p Y,V = β Y r β Y w 1 α φ β. Y (1 φ) 1 β Y The distortionary effect of incomplete contracting takes the form of a markup that is 1 φ β Y (1 φ) 1 β Y times higher than the "traditional" markup. The lump-sum transfer T Y,V is equal to the supplier prots. While the nal-good producer prots are given by π F,V,Y = const V A Y (p Y,V ) 1 α fr β Y w 1 β Y α Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

22 Non-Integrated pairs: The potential revenues are given by R Y (i) = A 1 Y α y(i) α If there is no agreement, then the revenues are equal to zero. Therefore, the quasi-rent is R Y (i). The nal-good producer gets φr Y (i) and the supplier (1 φ)r Y (i). Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

23 Non-Integrated pairs: Given the choice of labor, the nal-good producer solves max fφr Y (i) rk Y (i)g. K Y (i) Given the choice of capital, the supplier solves max f(1 φ) R Y (i) wl Y (i)g. L Y (i) We can solve for the interception of these two best response functions. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

24 Non-Integrated pairs: We have now that r p Y,O = β Y w 1 β Y αφ β Y (1 φ) 1 β. Y The nal-good producer's prots are π F,O,Y = const O A Y (p Y,O ) 1 α fr β Y w 1 β Y. α Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

25 Complete contractibility: In the case of complete contracts, when the quality-contigent contracts could be enforced (the quality of the input is veriable), the investments in capital and labor would be set to maximize the total surplus given by: R Y (i) rk Y (i) wl Y (i) fr β Y w 1 β Y. It can be shown that the impossibility of writing contracts lead to underinvestment in capital and labor. PICTURE! Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

26 Ownership Structure: Let Θ(β k ) be operating prots under integration relative to outsourcing. That is, Then, Θ(β k ) = Θ(β k ) = π F,V,k + fr β k w 1 π F,O,k + fr β k w 1 α(1 φ)δ α (1 2β 1 + k ) 1 α(1 β k ) + αφ(1 2β k ) δ α αβ k 1 α 1 + φ(1 δ α (1 δ α ) α 1 α. ) β k β k Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

27 Ownership Structure: It can be shown that Θ(β k ) is increasing in β k, Θ(0) < 1, and Θ(1) > 1. Theorem Therefore, there exists a unique threshold capital intensity ˆβ, such that all rms with β k < ˆβ choose to outsource production of the intermediate output, while all rms with β k > ˆβ choose to integrate their suppliers. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

28 The theorem provides an explanation for the rst picture: vertical integration of suppliers occurs mostly in capital-intensive industries. Hence, one would expect the share of intrarm trade to be relatively higher in those industries. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

29 Some Important points: Θ(β k ) is independent of factor prices because of the Cobb-Douglas assumption in production. In general, the decision would depend on factor prices. Why is F providing K x? It can be shown that if φ > 1/2 then nal-good producers will always decide to provide capital required for production the supplier is never given full control Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

30 Industry Equilibrium: Free entry implies that no rm makes positive expected prots. There are two types of equilibria (depends on β k ): integrated and non-integrated. In the integrated equilibrium: the ex-ante transfer T Y,V is equal to the supplier's prots. All prices are the same and given by Then, β Y r p Y,V = β Y w 1 α φ β. Y (1 φ) 1 β Y A Y,V = µe (p Y,V ) α 1 α n Y,V Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

31 Industry Equilibrium: The free entry implies that In the case of outsourcing, n Y,V = 1 α(1 β Y ) + α φ (1 2β Y ) fr β Y w 1 β µe Y p Y,O = β Y r β Y w 1 αφ β Y (1 φ) 1 β. Y This implies that n Y,O = 1 α(1 β Y ) + αφ (1 2β Y ) fr β Y w 1 β µe Y Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

32 General Equilibrium We assume that β Y > ˆβ > β Z. That is, in one industry we have the integrated equilibrium, while in the other non-integrated. First, E = rk + wl Equilibrium conditions are such that the capital and labor markets clear. By Walras' law we can focus on the equilibrium in the labor market. The labor market clearing condition is given by: L = n Y L Y + n Z L Z where L Y and L Z are labor demand by each pair in the industries. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

33 General Equilibrium Therefore, L Y = L x,y,v + L f,f,y + L f,s,y L Z = L x,z,o + L f,f,z + L f,s,z where L x,k,j is labor used by the supplier for production, L f,k,j + L f,k,j is labor used to cover xed costs (k 2 fy, Z g and j 2 fv, Og). It is possible to derive that where σ L is some constant. w r = σ L 1 σ L K L Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

34 Open Economy Now suppose the world is divided in J 2 countries, with country j receiving an endowment (K j, L j ). Assume that preferences are identical in all J countries. Factors of production are internationally immobile. Factor price equalization is attained (the endowments are not too different) and we can use the general equilibrium above to characterize the aggregate allocations in the world economy. Final goods are not tradable. Trade is in intermediate inputs only. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

35 Open Economy: Conclusion Capital-abundant countries tend to produce a larger share of capital-intensive varieties than labor-abundant countries. The share of capital-intensive (and thus intrarm) imports in total imports is then shown to be an increasing function of the capital-labor ratio of the exporting country! close to PICTURE 2. Alexander Tarasov (University of Munich) Antràs (2003) and Antras and Helpman (2004) Summer / 35

Firms, Contracts, and Trade Structure: Slides

Firms, Contracts, and Trade Structure: Slides Alexander Tarasov University of Munich Summer 2012 Alexander Tarasov (University of Munich) Antràs (2003) Summer 2012 1 / 34 Motivation For the United States,