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  • Lecture 1: Incomplete Contracts and InternationalTrade

    Economics 552

    Esteban Rossi-Hansberg

    Princeton University

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 1 / 32

  • The Property-Rights Approach in International Trade

    What defines the boundaries of the firm?

    Grossman and Hart argue that incomplete contracts are key

    They suggest that ownership is a source of power when contracts areincomplete. What does this mean?

    I integration means acquisition of physical assets;I when contracts are incomplete, the parties will often encounter contingenciesthat were not foreseen in the initial contract;

    I in those situations, the owner of the asset has these residual rights of control;I these residual rights of control are important because they are likely to affecthow the surplus is divided ex-post (ownership = power).

    In the presence of relationship-specific investments, these considerations leadto a theory of the boundaries of the firm in which both the benefits and thecosts of integration are endogenous.

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 2 / 32

  • A Simple Property-Rights ModelConsumer preferences are such that F faces a demand given by

    y = Ap1/(1), 0 < < 1. (1)

    Production of good y now requires the development of two specializedintermediate inputs h and m. Output is Cobb-Douglas:

    y =(h

    ) ( m1

    )1, 0 < < 1, (2)

    where a higher is associated with a more intensive use of h in production.

    There are two agents engaged in production:I a final-good producer (denoted by F ) who supplies the input h and producesthe final good y ,

    I an operator of a manufacturing plant (denoted by S) who supplies the input m.

    F can produce h at a constant marginal cost ch ; S can produce m at cm . Inaddition, production requires fixed cost f g (ch , cm).Both inputs are tailored specifically to the other party and are useless toanybody else.

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 3 / 32

  • A Simple Property-Rights Model

    Contractual structure: before investments h and m, only contractibles arethe allocation of residual rights (i.e., the ownership structure) and alump-sum transfer between the two parties.

    Ex-post determination of price follows from generalized Nash bargaining.

    Ex-ante, F faces a perfectly elastic supply of potential S agents so that, inequilibrium, the initial transfer will be such that it secures the participation ofS in the relationship at minimum cost to F .

    Key features:1 ex-post bargaining takes place both under outsourcing and under integration;2 the distribution of surplus is sensitive to the mode of organization because theoutside option of F is naturally higher when it owns S than when it does not.

    Outside options are as follows:I under outsourcing, contractual breach gives 0 to both agents;I under integration, F can selectively fire S and seize input m (at a productivitycost ) property rights over input.

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 4 / 32

  • Formulation of the ProblemIn light of equations (1) and (2), the potential revenue from the sale of y aregiven by

    R (h,m) = A1(h

    ) ( m1

    )(1). (3)

    Given the specification of the ex-post bargaining, F obtains share O = ofsale revenue under outsourcing and share V =

    + (1 ) > O underintegration.The optimal ownership structure k is thus the solution to the followingprogram:

    maxk{V ,O}

    k = R (hk ,mk ) ch hk cm mk f g (ch , cm) U

    s.t. hk = argmaxh{kR (h,mk ) ch h}

    mk = argmaxm{(1 k )R (hk ,m) cm m}

    (P1)

    where U is the outside option of the operator S .First-best level of investments would simply maximize k .

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 5 / 32

  • A Useful Result

    The solution to the constrained program (P1) delivers the following result(see Antrs, 2003 for details):

    PropositionThere exists a unique threshold (0, 1) such that for all > , integrationdominates outsourcing (k = V ), while for all < , outsourcing dominatesintegration (k = O).

    As in Grossman and Hart (1986), in a world of incomplete contracts, ex-anteeffi ciency dictates that residual rights should be controlled by the partyundertaking a relatively more important investment:

    I if production is very intensive in the m input, then choose outsourcing toalleviate the underinvestment in the provision of the m input,

    I when production is intensive in the h input, F will optimally choose to tilt thebargaining power in its favor by obtaining these residual rights, thus giving riseto vertical integration.

    Convenient Feature: threshold is independent of factor prices(Cobb-Douglas assumption important).

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 6 / 32

  • Another Look at the Result

    Suppose that instead of choosing k {V ,O}, F could choose (0, 1).

    0 1

    1

    )(*

    NVS

    V

    M H

    Figure 1

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 7 / 32

  • A General Open-Economy Formulation

    Introduce the location decision of firms.

    Consider a two-country version of the model in which firms are allowed tolocate different parts of the production process in different countries.

    Denote by L the set of possible locational decisions (a mapping fromproduction processes to locations) and by ` L a particular one.Different locational choices will in general entail different values of keyparameters.

    The optimal ownership structure k and the optimal locational choice ` nowsolve the following program:

    maxk{V ,O},`L

    `k = R`(h`k ,m

    `k

    ) c`h h`k c`m m`k f `k g `

    (c`h , c

    `m

    ) U`

    s.t. h`k = argmaxh{

    `kR(h,m`k

    ) c`h h

    }m`k = argmaxm

    {(1 `k

    )R(h`k ,m

    ) c`m m

    }(P2)

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 8 / 32

  • Firms, Contracts and Trade Structure: Antrs (2003)

    J countries produce differentiated varieties in two sectors (Y ,Z ) using twofactors (K , L).

    Preferences of the representative consumer in each country are of the form:

    U =( nY

    0y(i)di

    ) ( nZ

    0z(i)di

    ) 1

    , , (0, 1).

    Demands are then y(i) = AY pY (i)1/(1) and z (i) = AZ pZ (i)1/(1).

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 9 / 32

  • Firms, Contracts and Trade Structure: Antrs (2003)

    Production is as described before with the following new features:

    h and m are nontradable, but combined yield a tradable composite input

    h is capital-intensive relative to m. Extreme factor intensity: c`h = r` and

    c`m = w`

    Key assumtion: S produces labor intensive good

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 10 / 32

  • Firms, Contracts and Trade Structure: Antrs (2003)

    Business practices suggest that cost-sharing is more common in capitalexpenditures than in labor expenditures.

    I Dunning (1993) - MNE with subcontractors - provision of machinery andspecialized tools, prefinancing of machinery, procurement assistance inobtaining capital equipment, labor training.

    I Milgrom and Roberts (1993) - GM paid for firm- or product-specific capitalequipment needed by the supplier to meet special requirements, even thoughthis equipment would be located at the suppliers facility.

    I Aoki (1990) - Japanese firms - close connections with suppliers butconsiderable autonomy in personnel administration.

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 11 / 32

  • Firms, Contracts and Trade Structure: Antrs (2003)

    Young, Hood, and Hamill (1985).

    Table 1. Decision-Making in U.S. based multinationals

    % of British affi liates in which parent influence on decision is strong or decisiveFinancial decisions Employment/personnel decisionsSetting of financial targets 51 Union recognition 4Preparation of yearly budget 20 Collective bargaining 1Acquisition of funds for working capital 44 Wage increases 8Choice of capital investment projects 33 Numbers employed 13Financing of investment projects 46 Lay-offs/redundancies 10Target rate of return on investment 68 Hiring of workers 10Sale of fixed assets 30 Recruitment of executives 16Dividend policy 82 Recruitment of senior managers 13Royalty payments to parent company 82

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 12 / 32

  • Firms, Contracts and Trade Structure: Antrs (2003)

    Tradable composite input can be produced in any country according toCobb-Douglas technology as in (2) with Y > Z

    Homothetic cost functions: g `j

    (r `,w `

    )=(r `)j (

    w `)1j

    and f `k = f

    Final goods are nontradable, but can be produced one-to-one with inputs

    `k is independent of `, same and apply to both sectors, and U`= 0.

    ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 13 / 32

  • Firms, Contracts and Trade Structure: Antrs (2003) cted.

    Under these assumptions the ownership structure and locational decisions in(P2) can be analyzed separately.

    I Optimal ownership structure in sector j {Y ,Z} solves (P1) Proposition 1applies;

    I Optimal location decision solves min`

    {(r `)j (

    w `)1j}

    .

    Pattern of specialization of intermediate inputs responds to Heckscher-Ohlinforces as well as Helpman-Krugman forces:

    I because of IRS and product differentiation, countries specialize in certaininte

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