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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 = 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.
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 δ) — 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−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 .
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 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).
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 β ∈ (0, 1).
0 1
1
)(* ηβ
η
NVβS
Vββ
Mη Hη
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
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)
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 8 / 32
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).
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 9 / 32
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
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 10 / 32
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.
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 11 / 32
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.
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 15 / 32
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
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 16 / 32
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
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 17 / 32
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
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
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 19 / 32
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
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 20 / 32
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.
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 21 / 32
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.
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 22 / 32
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.
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 23 / 32
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).
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 24 / 32
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.
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 25 / 32
Global Sourcing
0
NOfNw−
SOfNw−
SOπ
)1/( ααθ −)1/( ααθ −
M)1/()( ααθ −N
MO
NOπ
Equilibrium in the Component-Intensive Sector
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 26 / 32
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
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 27 / 32
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.
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 28 / 32
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
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 29 / 32
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.
ERH (Princeton University ) Lecture 1: Incomplete Contracts and Trade 30 / 32
Yeaple (2006, JEEA)
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Yeaple (2006, JEEA)
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