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Lecture 1: Incomplete Contracts and International Trade Economics 552 Esteban Rossi-Hansberg Princeton University ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 1 / 32

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Page 1: Lecture 1: Incomplete Contracts and International Tradeerossi/Trade/Lecture1_552.pdf · Lecture 1: Incomplete Contracts and International Trade ... I when contracts are incomplete,

Lecture 1: Incomplete Contracts and InternationalTrade

Economics 552

Esteban Rossi-Hansberg

Princeton University

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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.

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

y = Ap−1/(1−α), 0 < α < 1. (1)

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

y =(hη

)η ( m1− η

)1−η

, 0 < η < 1, (2)

where a higher η 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.

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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 δ) — property rights over input.

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

R (h,m) = A1−α

(hη

)αη ( m1− η

)α(1−η)

. (3)

Given the specification of the ex-post bargaining, F obtains share βO = β ofsale revenue under outsourcing and share βV = δα + β (1− δα) > βO underintegration.The optimal ownership structure k∗ is thus the solution to the followingprogram:

maxk∈{V ,O}

πk = R (hk ,mk )− ch · hk − cm ·mk − f · g (ch , cm)− U

s.t. hk = argmaxh{βkR (h,mk )− ch · h}

mk = argmaxm{(1− βk )R (hk ,m)− cm ·m}

(P1)

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

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A Useful Result

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

PropositionThere exists a unique threshold η̂ ∈ (0, 1) such that for all η > η̂, integrationdominates outsourcing (k∗ = V ), while for all η < η̂, 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 η̂ is independent of factor prices(Cobb-Douglas assumption important).

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Another Look at the Result

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

0 1

1

)(* ηβ

η

NVβS

Vββ

Mη Hη

Figure 1

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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

π`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{

β`kR(h,m`k

)− c`h · h

}m`k = argmaxm

{(1− β`k

)R(h`k ,m

)− c`m ·m

}(P2)

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Firms, Contracts and Trade Structure: Antràs (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)αdi

) µα(∫ nZ

0z(i)αdi

) 1−µα

, µ, α ∈ (0, 1).

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

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Firms, Contracts and Trade Structure: Antràs (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

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Firms, Contracts and Trade Structure: Antràs (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 supplier’s facility.

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

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Firms, Contracts and Trade Structure: Antràs (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

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Firms, Contracts and Trade Structure: Antràs (2003)

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

Homothetic cost functions: g `j

(r `,w `

)=(r `)ηj(w `)1−ηj

and f `k = f

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

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

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Firms, Contracts and Trade Structure: Antràs (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 `)ηj(w `)1−ηj

}.

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 certainintermediate input varieties and export them worldwide,

I but capital-abundant countries tend to produce a larger share ofcapital-intensive varieties than labor-abundant countries.

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

Intermediate inputs can be traded at zero cost, while final goods arenontradable so that each F (costlessly) sets J plants to service the J markets.

It can then be shown that, with FPE, for any country j ∈ J:I “probability” of imports being intrafirm is increasing in capital-intensity of theindustry.

I the share of capital-intensive (and thus intrafirm) imports in total imports isan increasing function of the capital-labor ratio of the exporting country.

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

log 

of (

Mif 

/ M

)

log of (Capital / Employment)3 4 5 6

­4.5

­3

­1.5

0

aud

bev

checlecom

dru

ele

fme foo

ima

ins

lum

och

oel

oma

pap

pla

pri

rub

sto

tex

tra

veh

Notes: The Y­axis corresponds  to  the  logarithm of  the share of intrafirm imports  in  total U.S.  imports  for 23 manufacturingindustries  averaged  over  4  years:  1987,  1989,  1992,  1994.  The  X­axis  measures  the  average  log  of  that  industry’s  ratio  ofcapital stock to total employment, using U.S. data. See Table A.1. for industry codes and Appendix A.4. for data sources.

y = ­6.86  + 1.17 x(1.02) (0.24)

R2 = 0.54

Share of Intrafirm U.S. Imports and Relative FactorIntensities

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

Notes: The  Y­axis  corresponds  to  the  logarithm  of  the  share  of intrafirm imports  in  total  U.S.  imports  for  28  exportingcountries in 1992. The X­axis measures the log of the exporting country’s physical capital stock divided by its total number ofworkers. See Table A.2. for country codes and Appendix A.4. for details on data sources.

log 

of (M

if / M

)

log of Capital­Labor Ratio7.5 9 10.5 12

­6

­4

­2

0

ARG

AUS

BELBRA

CAN

CHE

CHL

COL

DEU

EGY

ESP

FRA

GBR

HKG

IDN

IRL

ISR

ITA

JPN

MEXMYS

NDL

OAN

PAN

PHL

SGP

SWE

VEN

y = ­14.11 + 1.14 x(2.55)   (0.29)

R2 = 0.46

Share of Intrafirm Imports and Relative FactorEndowments

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Antràs (2003): Econometric Evidence

The last section of Antràs (2003) attempts to provide evidence that thepatterns in these Figures are not driven by third omitted factors. Thepurpose is also to unveil additional factors affecting the relative prevalence ofintrafirm trade.

First run ln(SUSA,ROWi−f

)k= θ1 + θ2 ln (K/L)k +W

′k θ3 + εk ,where the

implication is that θ2 > 0 (smoothed version of Proposition 1).

Then run ln(MUSA,ji−f

)= ω1 +ω2 ln

(K j/Lj

)+ω3 ln

(Lj)+W ′j ω4 + εj ,

where the implication is that ω2 > γ2.

The results are very supportive of the theory.

ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 18 / 32

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Antràs (2003): Econometric Evidence

Table 4a. Factor Intensity and the Share SUS ,ROWi−fDep. var. is Pooled Regressions

ln(SUS ,ROWi−f

)k

I II III IV V

ln(K/L)k 1.149∗∗∗ 0.996∗∗∗ 0.859∗∗∗ 0.852∗∗∗ 0.709∗∗∗

(0.272) (0.253) (0.192) (0.186) (0.177)ln(H/L)k 0.386∗ -0.000 -0.060 0.045

(0.197) (0.148) (0.162) (0.179)ln(R&D/Sales)k 0.468∗∗∗ 0.508∗∗∗ 0.569∗∗∗

(0.077) (0.089) (0.086)ln(ADV/Sales)k 0.098 0.141

(0.055) (0.096)ln(VAD/Sales)k -0.897∗

(0.527)R2 0.50 0.55 0.72 0.73 0.74No. of obs. 92 92 92 92 92

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Antràs (2003): Econometric EvidenceTable 6. Factor Endowments and the volume MUS ,j

i−f

Dep. var. is

ln(MUS ,ji−f

)I II III IV V

ln (K/L)j 2.048∗∗∗ 2.192∗∗∗ 2.188∗∗∗ 1.841∗∗∗ 2.096∗∗∗

(0.480) (0.458) (0.716) (0.623) (0.695)ln (L)j 0.607∗∗ 0.608∗∗ 0.435 0.700

(0.229) (0.268) (0.332) (0.419)ln (H/L)j 0.031 0.892 0.708

(3.289) (3.147) (3.052)OpFDI -0.624∗∗ -1.006∗∗

(0.259) (0.474)OpTrade 0.674

(0.560)CorpTax -0.647

(5.295)R2 0.44 0.52 0.52 0.42 0.49

No. of obs. 28 28 28 26 26

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Global Sourcing with Heterogenous Firms: Antràs andHelpman (2004)

Environment and Preferences: Consider a world with two countries, theNorth and the South, and a unique factor of production, labor. There is arepresentative consumer in each country with quasi-linear preferences:

U = x0 +1µ

J

∑j=1

X µj , 0 < µ < 1.

where x0 is consumption of a homogeneous good, Xj is an index of aggregateconsumption in sector j , and µ is a parameter.Aggregate consumption in sector j is a CES function

Xj =[∫

xj (i)αdi]1/α

, 0 < α < 1,

of the consumption of different varieties xj (i), where the range of i will beendogenously determined.This specification leads to the following inverse demand function for eachvariety i in sector j :

pj (i) = Xµ−αj xj (i)

α−1.

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Global Sourcing: The Model (cted.)

Technology: Producers of differentiated goods face a perfectly elastic supplyof labor. Let the wage in the North be strictly higher than that in the South(wN > wS ). The market structure is one of monopolistic competition.

I As in Melitz (2003), producers needs to incur sunk entry costs wN fE , afterwhich they learn their productivity θ ∼ G (θ).

I As in Antràs (2003), final-good production combines two specialized inputsaccording to the technology:

xj (i) = θ

(hj (i)

ηj

)ηj(mj (i)1− ηj

)1−ηj

, 0 < ηj < 1.

I h is controlled by a final-good producer (agent F ), m is controlled by anoperator of the production facility (agent S).

I Sectors vary in their intensity of headquarter services ηj . Furthermore, withinsectors, firms differ in productivity θ.

I Intermediates are produced using labor with a fixed coeffi cient.I hj (i) is produced only in the North, which implies that the headquarters H arealways located in the North.

I Productivity in the production of mj (i) is assumed identical in both countries.

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Global Sourcing: The Model (cted.)After observing θ, H decides whether to exit the market or start producing.In the latter case additional fixed cost of organizing production need to beincurred.

I It is assumed that these additional fixed cost are a function of the structure ofownership and the location of production.

I In particular, if an organizational form is k ∈ {V ,O} and ` ∈ {N , S}, thesefixed costs are wN f `k and satisfy

f SV > fSO > f

NV > f NO . (4)

Contracting is as in the previous models, but they let δN ≥ δS .Following Antràs (2003), the ex-post division of surplus is as follows:

North South

Non-Integration βNO= β βSO= β

Integration βNV=(

δN)α+β

[1−

(δN)α]

βSV=(

δS)α+β

[1−

(δS)α]

Notice thatβNV ≥ βSV > βNO = βSO = β.

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Global Sourcing: EquilibriumAfter solving for investment levels (in the constraints), the general program in(P2) reduces to

maxβ`k∈{βNV ,β

SV ,β

NO ,β

SO}

π`k (θ,X , η) = X(µ−α)/(1−α)θα/(1−α)ψ`k (η)− wN f `k (5)

where

ψ`k (η) =1− α

[β`kη +

(1− β`k

)(1− η)

][1α

(wN

β`k

)η (w `

1−β`k

)1−η]α/(1−α)

.

By choosing k and `, H is effectively choosing a triplet(

β`k ,w`, f `k

). And:

I π`k is decreasing in w` and f `k .

I π`k is largest when β`k = β∗ (η), with β∗′ (η) > 0, β∗ (0) = 0 and β∗ (1) = 1(remember Figure 1). Intuitively, H wants to allocate relatively more power tothe party undertaking a relatively more important investment in production.

One can also solve for the industry equilibrium as in Melitz (2003) or HMY(2004).

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Global Sourcing: Relevant Trade-OffsThe choice of an organizational form faces two types of tensions.

I Location decision: variable costs are lower in the South, but fixed costs arehigher there — a firm’s productivity θ will turn out to affect crucially theparticipation in international trade;

I Integration decision: integration improves effi ciency of variable productionwhen the η is high, but involves higher fixed costs. This decision will thuscrucially depend on η but also on θ.

To simplify the discussion, focus on two types of sectors:

A Component-intensive sector (η < β∗−1(β) and

wN/wS <(f SO /f NO

)(1−α)/α(1−η)):

I This implies ψ`O (η) > ψ`V (η) for ` = N , S , which together with (4), impliesthat any form of integration is dominated in equilibrium.

A Heaquarter-intensive sector with η > β∗−1 (

βNV

), and

(wN/wS

)1−η

“high enough”I This implies the ranking of slopes

ψSV (η) > ψSO (η) > ψNV (η) > ψNO (η). (6)

which together with (4) leads to the Figure below.

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Global Sourcing

0

NOfNw−

SOfNw−

SOπ

)1/( ααθ −)1/( ααθ −

M)1/()( ααθ −N

MO

NOπ

Equilibrium in the Component-Intensive Sector

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Global Sourcing

0

NON fw−

SVN fw−

SOπ

)1/( ααθ −

)1/( ααθ −H

)1/()( ααθ −NHO

NOπ

SON fw−

NVN fw−

)1/()( ααθ −NHV

)1/()( ααθ −SHO

NVπ

SVπ

Equilibrium in the Headquarter-Intensive Sector

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Global Sourcing: Relative PrevalenceThe final section of the paper quantifies the relative prevalence of thedifferent organizational forms and how this prevalence varies across industries.This requires parameterizing the distribution of θ. Following HMY (2004),choose G (θ) to be a Pareto distribution with shape z , i.e.,

G (θ) = 1−(bθ

)zfor θ ≥ b > 0. (7)

I Remember that z is inversely related to the variance of the distribution.

In the component-intensive sector they find that, foreign outsourcing is moreprevalent:

I the higher is wN/wS (or the lower are transport costs τ),I the lower are z and η.

In the headquarter-intensive sector they find that:I the share of intrafirm imports in total imports should be higher in industrieswith higher η, but also in industries with higher productivity dispersion (lowerz) and higher transport costs (τ).

I a higher wN/wS (or lower τ) increase the amount of international sourcing,but also increase the share of foreign outsourcing in total foreign sourcing.

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0 θ

Outsourcingin N

Outsourcingin SExit

0 θ

Outsourcingin N

Outsourcingin SExit

Integrationin S (FDI)

Integrationin N

Component­Intensive Sector Headquarter­Intensive Sector

0 θ

Outsourcingin N

Outsourcingin SExit

0 θ

Outsourcingin N

Outsourcingin SExit

Integrationin S (FDI)

Integrationin N

Component­Intensive Sector Headquarter­Intensive Sector

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Empirical Tests and Other Applications

Yeaple (2006, JEEA, "Offshoring, Foreign Direct Investment, and theStructure of U.S. Trade") used the BEA dataset to test some of thecross-industry implications of the Antràs and Helpman (2004) model:

I he finds that the share of intrafirm imports in total U.S. imports (a measure ofthe relative prevalence of FDI over outsourcing) is higher in industries withhigh R&D intensity and high productivity dispersion.

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Yeaple (2006, JEEA)

ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 31 / 32

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Yeaple (2006, JEEA)

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