Physical Capital, Knowledge Capital and the
Choice Between FDI and Outsourcing
Yongmin Chen
Department of Economics, University of Colorado, Boulder
Ignatius J. Horstmann
Rotman School of Management, University of Toronto
James R. Markusen
Department of Economics, University of Colorado, Boulder
School of Economics, University College Dublin,
NBER and CEPR
March 2009

Abstract. There exist two approaches in the literature concerning the multinational …rm’s mode choice for foreign production between an owned subsidiary and alicensing contract. One approach considers environments where the …rm is transferring primarily knowledge-based assets. An important assumption there is that therelevant knowledge is absorbed by the local manager or licensee over the course oftime: knowledge is non-excludable. More recently, a number of in‡uential papers
have adopted a property-right view of the …rm, assuming the application abroad ofphysical capital, the owner of which retains full and exclusive rights to the capitalshould a relationship break down. In this paper we combine both forms of capital
assets in a single model. The model predicts that foreign direct investment (owned
subsidiaries) is more likely than licensing when the ratio of knowledge capital to physical capital is high, or when market value is high relative to the book value of capital(high Tobin’s-Q).

JEL codes: F2, L2
Key words: FDI, outsourcing, hold-up, knowledge capital, physical capital

The authors thank the participants and discussants at a number of seminars andconferences for helpful comments and suggestions. Presentations were at the NBER
ITO Working Group Meeting in Cambridge, the ERWIT conference in Appenzell, theETSG conference in Warsaw, and the Norface conference in Munich, all held in 2008.

1. INTRODUCTION
Foreign direct investment (FDI) has grown at rates greatly outpacing the
growth in world trade over the last several decades. This has naturally led to increased interest in FDI by academic researchers and policy makers. Part of thatinterest has been directed to the determinants of the choice of mode by which …rms
service foreign markets, including options such as exporting, owned foreign a¢ liates(FDI), licensing and subcontracting, and joint ventures. This in turn relates to moregeneral discussion in microeconomics about the “boundaries of the …rm”: decisions as
to which activities should be undertaken within the ownership structure of the …rm,
and which activities should be contracted or outsourced to arm’s-length …rms.
There is a rich and extensive literature on the boundaries of the …rm, andwe can make no attempt to survey it here. Instead, we will direct our e¤orts alonglines which have been productive in the …eld of international trade, where researchers
have attempted to model a multinational’s decision as to whether to establish aforeign subsidiary or contract with a foreign supplier to produce a good for local
sales or for export back to the parent …rm. This issue, previously referred to as the“internalization problem”and more recently as the “outsourcing problem”, addresses
the question of whether or not an activity should be internalized inside the …rm oroutsourced to an arm’s-length …rm.
Much of the more recent literature under the name outsourcing has drawn
from an approach which, we assert, focuses on properties of physical capital such as
plant and equipment. On the other hand, the empirical literature and other recent
theoretical literature has emphasized the importance of knowledge-based assets in explaining the decision to become a multinational …rm. An earlier theoretical literature1

under the internalization label also took the latter approach.
The purpose of this paper is to inquire whether or not the nature of the capitalrequired by a subsidiary makes an important di¤erence to the choice of mode, either
subsidiary or licensee. Speci…cally, we wish to di¤erentiate between physical capitaland knowledge-based capital assets, and ask whether a more physical capital-intensive…rm will be more or less likely to chose internalization via a subsidiary rather thanoutsource compared to a knowledge-capital-intensive …rm.
As just alluded to, the somewhat older literature assumed knowledge-based
assets and in particular assumed that the multinational …rm (the principal) cannot
prevent a licensee (the agent) from absorbing or learning the relevant knowledge overtime. Even though the multinational “owns”the knowledge-based asset, it gets transferred to a licensee. This literature emphasizes the jointness property of knowledge
capital, the ability of the …rm to use it fully in multiple locations at the same time(Markusen’s (2002) knowledge-capital model), which leads to multi-plant productionin the …rst place. It suggests that the jointness property also leads to the problem
of asset dissipation: knowledge-assets are easily transferred but also easily absorbedby the licensee. Formal models include Horstmann and Markusen (1987), Ethier andMarkusen (1996), Markusen (2001), Fosfuri, Motta and Rønde (2001) and Glass andSaggi (2002).
By contrast, more recent literature is focused around the Grossman-HartMoore property-right approach (Grossman and Hart (1986) and Hart and Moore(1990)), which seems (implicitly) more appropriate for physical capital in that therelevant asset has no jointness property and that the owner of the residual rights has
full control of the asset if a relationship or negotiation breaks down. Important papers

2include Grossman and Helpman (2002, 2004), Antrás (2003, 2005), and Feenstra andHanson (2005).
Our model combines the two approaches in a simple two-period incompletecontracting model. A …rm requires both physical and knowledge capital for a foreignsubsidiary, along with non-contractible e¤ort by a foreign licensee or manager. E¤ort
is relatively more important as a complement to physical capital than knowledge capital, creating the well-understood advantage for using a licensee who owns the physicalcapital and thus captures the full bene…t of his or her e¤ort. However, knowledge
capital transferred by the multinational is absorbed by the licensee during the …rst
period regardless of who “owns” it. We assume that the value of this knowledge toa manager or licensee outside the relationship depends on working with the physicalcapital, the two assets being complements. Thus the advantage to the multinationalin owning the physical capital is that it reduces the incentives or ability of the licensee
to use the knowledge for private or outside uses in period 2.
This tension, ownership by the multinational reduces agent’s e¤ort while preserving the value of the knowledge capital, is the fundamental di¤erence between
the present paper and previous ones. Our result is that …rms that are more physicalcapital intensive will tend to license (outsource), while …rms that are more knowledgecapital intensive will tend to establish subsidiaries (internalize). We believe that thisis consistent with all available empirical evidence.
We are of course aware that some existing literature emphasizes that capitalintensive …rms are more like to establish subsidiaries (Antrás 2003), but this refers tocapital use relative to labor and materials, not to physical versus knowledge-capitalintensity. Our model does not o¤er cross-section predictions about mode choice as3

a function of industry or …rm capital-labor ratios. Rather, our predictions would
more appropriately be examined by using a type of Tobin’s q; speci…cally, the ratio ofa …rm’s market value (re‡ecting knowledge-based assets as well as physical capital)
to its book value of capital (largely re‡ecting physical capital only). Our prediction
would be that …rms/industries with higher q’s would be more likely to establish foreignsubsidiaries. Existing evidence, reviewed in Markusen (1995, 2002) and Caves (2007)
does indeed suggest that this is the case.1 Another implication of our theory is thatwhen there is stronger protection for knowledge capital, the incentive for licensing
tends to be higher relative to the incentive for FDI.2
2. THE MODEL
A multinational …rm (MNE) in the North, denoted as M , plans to produce a product (either intermediate or …nal) in the South due to cost advantages of manufacturing
there. There are two periods of production, t = 1; 2, and there is no discounting. Production in the South requires the services of a local agent/manager, denoted as A,
and two types of asset services: physical capital and knowledge capital or intellectual
property. There is an exogenous and …xed amount of physical capital, K, that can
1

See Morck and Yeung (1991, 1992) for evidence on the importance of information-related intangible assets in the FDI decision. For events in which …rms do transfer technology abroad, articles
by Davidson and McFetridge (1984), Mans…eld and Romeo (1980), Teece (1986), and Wilson (1977)
show technology is more likely to be transferred internally within the …rm by R&D intensive …rms
producing new and technically complex products.
2

Smith (2001) …nds that stronger foreign patent rights increase US …rms transfers of knowledge
more by licensing than by a¢ liate sales. Yang and Maskus (2001) …nd that countries with stronger
patent rights attract larger arm’s-length volumes of licensed technology, although licensing is notcompared to FDI. Maskus, Saggi and Puttitanum (2005) …nd that stronger patent protection increases the probability of inward FDI and has very little e¤ect on licensing; but they note that
this overall …nding is driven by high technology sectors, and that lower technology sectors have theopposite result (stronger protection increases licensing more than FDI).

4

only be acquired in the beginning of t = 1 and that is required for production in both
periods. Either M or A can own the physical capital K; whereas only M initiallyowns the knowledge capital, with a …xed and exogenous amount equal to S.
At the beginning of t = 1, M makes a once-for-all choice between two possibleorganizational forms: foreign direct investment (FDI) or outsourcing. With FDI, M
acquires (and owns) the physical capital used for production in the South and employs A under a sequence of one-period employment contract to manage a production
process utilizing M ’s capital. A’s hiring occurs at the beginning of t = 1 and A’s
employment contract is re-negotiated at the beginning of t = 2. M also decides eachperiod how much knowledge capital to transfer to A to be utilized in production.
With outsourcing, A acquires (and owns) the physical capital, with capital acquisition again occurring at the beginning of t = 1. M signs a one-period licensing
contract with A that licenses an amount s1 of M ’s knowledge capital to A for use inproduction at t = 1. This licensing agreement is re-negotiated at the beginning of
t = 2, with an amount s2 transferred at t = 2.
The cost of physical capital is rK: As in Grossman and Hart (1989), ownershipof physical capital bestows control rights on the owner. Speci…cally, the owner can
decide the uses to which the capital can be put and can exclude access to the capitalfor any other uses at any time. That having been said, e¤ort from the agent is often
required to improve or maintain the e¢ ciency (usefulness) of the physical capital.
We shall make these points clear shortly when we specify the payo¤ functions of theplayers.
Knowledge (or intellectual ) capital, by contrast, does not have the same excludability properties. The owner of knowledge capital may not be able to control to5the same extent the uses to which the capital is put and to capture the returns thatthe knowledge capital generates. In essence, property rights to knowledge capital are
harder to de…ne and protect than is the case for physical capital. We capture thesefeatures of knowledge capital in the following way. We assume that, at t = 1, there
exists a fraction< 1 of S that is “explicit knowledge”in the sense that the uses ofthis part of M ’s knowledge capital can be de…ned in a t = 1 licensing agreement, they
can be measured and the returns appropriated by M . In this sense, the fractionofM ’s knowledge capital can be “owned”in the same way as physical capital is owned.
A fraction 1of S is “tacit knowledge” and is not contractible at t = 1 in thesense that its current and future uses cannot be controlled by M in a t = 1 licensing
agreement and any returns that it generates cannot be speci…cally appropriated by
M in the agreement. The value ofis assumed to be exogenous to the …rm and canbe thought of as capturing either characteristics of the knowledge capital utilized by
M or a characteristic of the legal regime of the country in which M is contracting.
Note that this set of assumptions allows a simple characterization of the environment in which M and A operate. Speci…cally, the values of K, S andcompletely

de…ne the environment – characteristics of the relevant industry/product – underconsideration. The values of K and S give the physical relative to knowledge capitalintensity of the industry while

gives features of the appropriabilty of M ’s knowledge

asset. Subsequent analysis will consider how variation in the economic environment–variation in (K; S; ) –a¤ects the observed pattern of outsourcing and FDI.
For any given K and knowledge asset si for i = 1; 2; the maximum gross surpluses
that accrue to M and A from utilizing K and si at t = 1 and at t = 2 are U1 (K; s1 )and U2 (K; s2 ) + V (ej K) ; respectively, where Ui (K; 0)

60; e is A0 s e¤ort during

t = 1 that a¤ects the return in t = 2; and V (ej K) is a concave function of e for any
given value of K:3 We allow the possibility that Ui (K; 0) > 0; in which case agent
A can have alternative uses for K even if si = 0. That is, we allow the possibility
that K can either be used for producing M 0 s product or for some alternative purpose
bene…ting A (e.g., K can be used for A0 s private bene…ts). We assume that producing
M 0 s product always yields higher payo¤s than any alternative use when si

S; butthe alternative payo¤ could be higher if s < S:
There is a perfectly elastic supply of agents with opportunity cost W

0 in eachperiod. However, the agent not owning capital at t = 1 (M in the case of outsourcing
and A in the case of FDI) is not able to raise the amount K su¢ ciently quickly to beable to produce alone at t = 2. This fact produces a (potential) speci…c relationshipbetween M and A at t = 2:4 In this case, the t = 2 surplus is allocated based on
the Nash bargaining solution. Both A and M are risk neutral and make choices tomaximize expected income.
We assume that, at t = 1, M has access to perfect capital markets while A has only
limited ability to borrow against future income to …nance capital K and consumption
W (i.e., we assume that W is both an opportunity cost and a subsistence requirement).
Speci…cally, under outsourcing A is only able to cover a fraction

2 (0; 1] of t = 1

costs (rK + W ) via the capital market. The remainder must be covered out of t = 1
revenues. As will be seen later, this inability on A’s part to borrow against future
income limits M ’s ability to extract t = 2 surplus from A via the initial licensing
agreement. It also forces M to bear some of the costs of A’s capital investment.
3

We emphsize that K is a …xed parameter for our model, and we include it in the payo¤ functions
so that we can see the e¤ects of this parameter; on the other hand, both s1 and s2 are choice varialbes.
4This is relevant in the case of oursourcing, where the agent, who owns K; can demand thesharing of returns from using S in t = 2:

7

Throughout our analysis, we shall maintain:
Assumption 1. (i) Ui (K; si ) increases in both K and si for all si

S. (ii) V (ej K)

increases in e: (iii) U2 (K; 0) + V ( 0j K)

W:(1 + ) W: (iv) V (0j K)

Part (i) of Assumption 1 is quite natural and simply states that returns are higher
with a higher amount of K or S. Part (ii) says that A0 s e¤ort during t = 1 would
improve (maintain) the e¢ ciency of physical capital K. Part (iii) will be required
later to ensure that A0 s payo¤ in t = 2 from production is high enough relative to its
opportunity cost (i.e., (iii) will be required as a sort of participation constraint): (iv)says that there cannot be too much improvement in the value of physical asset if A
exerts no e¤ort during t = 1:
Notice that we allow V (ej K) to be either positive or negative:5 For instance,
V (ej K) could be the depreciation (repair) cost of K in t = 2; as, for example,
V (ej K) =rK (1e)2 < 0; and e simply reduces this cost. Or e could be A0 se¤ort to …nd additional use for K that adds value in t = 2: For instance, a by-productmay be produced with K; in addition to the product already being produced using
K; in which case V (ej K) > 0:6 We shall later present examples where Assumption
1 is satis…ed.
To summarize, the timing of the game is as follows:
At the beginning of t = 1, M chooses between FDI and outsourcing. If M chooses
FDI, then M o¤ers A an employment contract involving payment to A of w1 ; if
5However, if V ( ej K) < 0; U2 (K; 0) will need to be high enough to satisfy (iii).
This positive V is to be distinguished from A0 s using K for private bene…ts that reduces thereturn of K to M: For convenience and to capture the idea that e¤ort is more important to improveor maintain the usefulness of physical capital, we assume V does not depend on s: This is certainly
the case, for instance, if V represents the depreciation of K: This assumption is not essential for themain insights of our analysis.
68M chooses outsourcing, M and A negotiate a contract involving a transfer to A of
knowledge capital, s1 , and a licensing payment from A to M of l1 . In either case,should A accept the contract, A chooses an e¤ort level e and M chooses the levelof knowledge capital to use (this level is determined by the licensing contract underoutsourcing). Finally, the gross surplus U1 (K; s1 ) is realized and payments are made.
At the beginning of t = 2, M o¤ers A a second employment contract involving apayment w2 under FDI. If A accepts, M again chooses a level of knowledge capitalutilization for A. Surplus U2 (K; s2 )+V (ej K) is realized. The employment contract inboth t = 1 and t = 2 can also specify the uses to which A can put M ’s physical capital.
Under outsourcing, M and A negotiate a second contract involving a transfer to A of
intellectual capital, s2 , and a licensing payment from A to M of l2 . If the contract isagreed to, M transfers intellectual capital s2 to A, and surplus U2 (K; s2 ) + V (ej K)
is realized: Transfers at t = 2 are determined via the Nash bargaining solution.
In all cases, the equilibrium levels of e; s1 ; s2 are the result of subgame perfect Nashequilibrium strategy choices by A and M ; and Ui is su¢ ciently large relative to K and
W so that in equilibrium it is pro…table for M to choose either FDI or outsourcing.
3. ANALYSIS
We begin by analyzing the complete contracting case where contracting on e andsi 2 [0; S] are feasible, so as to provide a benchmark for the subsequent analysis of
the incomplete contracting situation. For the incomplete contracting case, we analyze…rst the FDI contract equilibrium and then the outsourcing equilibrium. Finally, we
compare equilibrium payo¤s for M and determine the situations in which M prefers
FDI to outsourcing.

93.1 The complete contracting case
The complete contracting solution is given as the solution to the problem

max U1 (K; s1 ) + U2 (K; s2 ) + V (ej K)

e;s1 ;s2

e

rK

(1)

Since both U1 (K; s1 ) and U2 (K; s2 ) are increasing in s and M can control the use of
S with complete contracting, M chooses s1 = s2 = S: The level of e¤ort for A is given
by e , de…ned by the condition

Ve (e j K) = 1:(2)

3.2 Equilibrium under FDI
We begin by analyzing the equilibrium contract at t = 2. Since M owns the physicalasset under FDI, M can control the use of K at t = 2. Thus, M can prevent A fromusing S for purposes other than M 0 s project in t = 2: Consequently, A’s outside option
is simply W; and, since U2 (K; s2 ) is increasing in s2 , M chooses knowledge capitaltransfer of sF2 = S: As a result, the contract that M o¤ers A involves a payment
w2F = W . M ’s payo¤ at t = 2 is, therefore,FM 2 = U2 (K; S) + V (ej K)

W:

At t = 1; M will optimally choose sF1 = S, since U1 (K; s1 ) is increasing in s1 andthe payo¤ at t = 2 is independent of the value of s1 . Further, since e¤ort is costly
for A and A’s compensation at t = 2 is independent of e, A will choose eF = 0.

10

M , recognizing this fact, o¤ers a payment of w1F = W . M ’s two period payo¤ fromchoosing FDI is thusF
M = U1 (K; S) + U2 (K; S) + V ( 0j K)

2W

rK:

(3)

We summarize this discussion below:
Lemma 1 Under the FDI option, the unique equilibrium contract pair involves: i)transfers of knowledge capital of sF1 = sF2 = S, and ii) wage payments to A of w1F =w2F = W . Under this contract, A chooses e¤ort level eF = 0 and M ’s equilibrium
payo¤ isF
M given in equation (3).

Note that, under FDI, the equilibrium contract is a standard wage-employment
contract. The contract allows M , via control of physical capital, to control the useof M ’s knowledge capital.7 The agent employee exerts no (extra) e¤ort in improving(maintaining) physical capital and undertakes no tasks other than those involved inworking directly for M . The ine¢ cient choice of e by A obtains because M cannot
commit to compensating A for its investment in e: As such, the contract exhibits
the oft discussed features of an insourced activity: low-powered incentives (and so
problems of lower e¤ort) but control over asset use.
3.3 Equilibrium under outsourcing
Unlike the case of FDI, under outsourcing A now owns the physical capital while M
still owns the knowledge capital. This ownership di¤erence impacts both the abilityof M to control the use of knowledge capital and the incentives that A has to invest in7
M will also require A to use K only for M 0 s project. Otherwise, A may use K for its own
alternative purpose, given that he receives a …xed wage payment.

11

improving (maintaining) physical capital. To see the overall e¤ect of this ownershipdi¤erence, …rst consider the equilibrium contract at t = 2. Since A owns the physicalcapital, A can control the use of K and so can credibly threaten to use K for own
purposes. Indeed, A will choose this option unless the contract at t = 2 provides A
with su¢ cient inducement not to do so. Thus, the Nash bargaining solution at t = 2
must account for A’s alternative uses of K –these uses form A’s threat point in thebargaining –and compensate A appropriately.
To see how the bargaining solution is obtained, note …rst that, if M and A fail toreach an agreement at t = 2 and s1

S, then A can use the intellectual capital not

controlled by M under the initial licensing agreement and A’s own physical capital forother uses. Speci…cally, A can use K and s1

S to generate return U2 (K; s1S)+

V (ej K) ; through either producing an imitation of M ’s product, or putting the assets
for some alternative purpose, or both. Of course, A can also choose not to produce
and obtain its option value W: Thus A0 s disagreement payo¤ at t = 2 ismax fU2 (K; s1

S) + V (ej K) ; W g ;whereas M earns zero in t = 2 if no agreement is reached. From part (iii) of Assumption 1, we have

U2 (K; s1

S) + V (ej K)

U2 (K; 0) + V (0j K) > W:

On the other hand, the maximum joint surplus for M and A if they reach agreement
is U2 (K; S) + V (ej K) :Therefore, at t = 2; according to the Nash bargaining solution, which splits the12surplus equally between the two parties, M 0 s and A0 s payo¤s are, respectively:
O
M2
O
A2

U2 (K; s1
2
U2 (K; S) + U2 (K; s1=
2=

U2 (K; S)

S)

;

(4)

+ V (ej K) :

(5)

S)

Anticipating this, during t = 1 agent A will choose e to maximize

O
A2

e=

U2 (K; S) + U2 (K; s1
2

S)+ V (ej K)

e;and the equilibrium e under outsourcing is eO = e ; the e¢ cient e as de…ned inequation (2):Turning next to the t = 1 contract, since there is a perfectly elastic supply ofagents at t = 1 and knowledge capital is fully contractible for s1
all incremental returns to the use of knowledge capital for s1
M ’s licensing revenues at t = 1 are U1 (K; s1 )(1

S, M captures
S: for s1

S,)(rK + W ) (recall that A can

only borrow against future income to cover a fractionof …rst-period capital andconsumption costs (rK + W ). The rest must be covered out of …rst-period revenues
and hence reduces M ’s maximum licensing fee by (1)(rK + W )). Since U1 ( )is increasing in s1 , M will choose to license at least S units of knowledge capital.
Since M cannot commit to transferring any s1 > S (s1 > S is not contractible)
nor capture returns at t = 1 from doing so, and since M ’s return at t = 2 ( OM 2 ) isdecreasing for s1 > S, the equilibrium licensing contract at t = 1 has sO
1 = S. The
licensing payment by A to M is

l1O = U1 (K; S)(1

13)(rK + W ):(6)

From (5) and (6), and recalling that in t = 1 agent A receives U1 (K; S) but has
capital cost rK and e¤ort cost e ; we conclude that, under the equilibrium pair ofoutsourcing contracts, A’s payo¤ is

O
A

=
=

O
A2 e=ee + U1 (K; S)

U2 (K; S) + U2 (K; 0)+ V (e j K)
2
[U1 (K; S)

=

rK

(1

l1O
e + U1 (K; S)

rK

e)(rK + W ): (7))(rK + W )]U2 (K; S) + U2 (K; 0)+ V (e j K)2

rK + (1Since A has an opportunity cost of 2W to work with M under the licensing contract,OA

in equilibrium it is required that

2W; which we assume to hold:M 0 s equilibrium payo¤ from outsourcing is, from (4) and (6):U2 (K; S)O
M =U2 (K; 0)2+ U1 (K; S)(1)(rK + W ):(8)

The results for the outsourcing contract are summarized below.
Lemma 2 Under the outsourcing option, the unique equilibrium contract pair is

l1O = U1 (K; S)
l2O =U2 (K; S))(rK + W )]; sO
1 = S;[(1U2 (K; 0)2; sO
2 = S:The equilibrium e¤ort choice by A is e . Equilibrium payo¤s for A and M are
and

O
A

O
M given in equations (7) and (8).

Note that outsourcing generates e¢ cient e¤ort by the agent but leads to ine¢ cient
14

transfer of intellectual capital. Also, because of A’s limited access to capital markets,
M has a limited ability to extract payment at t = 1 for A’s hold-up surplus at t = 2.
This capital market restriction leads to a transfer of (1)(rK + W ) from M to A,

though note from (7) and (8) that this nets out and is not an e¢ ciency loss. FDI,
by contrast, leads to e¢ cient transfer of knowledge capital but shirking by the agent.
Also, M bears the full cost of physical capital. Below we investigate the circumstances
under which one option is preferred to the other.
3.4 Equilibrium Choice of Organization Form
To determine M ’s choice between FDI and outsourcing, one need only examine thepayo¤ di¤erence under the two options. From (3) and (8), this di¤erence is given by

F
M

O
M

= [U1 (K; S) + U2 (K; S) + V ( 0j K)[

U2 (K; S)= [U1 (K; S)[V (e j K)
In (9), the term U1 (K; S)

U2 (K; 0)
2U1 (K; S)] +

2W

rK]

+ U1 (K; S)(1)(rK + W )]U2 (K; S) + U2 (K; 0)+ V (e j K)
2

W

(W + rK)(9)

V ( 0j K)]

U1 (K; S) > 0 represents the gain from FDI due tobetter knowledge capital transfer. The term
U2 (K; S) + U2 (K; 0)+ V (e j K)
2

W > U2 (K; 0) + V (e j K)

W;

which is positive due to Part (iii) of Assumption 1, represents the increased surplus
accruing to M due to avoidance of hold-up under FDI created by the fact that M

15

owns the K under FDI.8 The third term,[V (e j K)

V (0j K)] ; represents the loss

to M due to the lower e¤ort under FDI. The …nal term,(W + rK) ; re‡ects theability of M to recapture some of A’s second-period hold-up rents under outsourcing
by requiring A to …nance a portion of (W + rK) in the …rst period: the higher ;the large this e¤ect which makes outsourcing more attractive (FDI less attractive).
When

F
M

O
M > 0, M chooses FDI; whenF
MO
M < 0, M chooses outsourcing.

Notice that for any given S; a lower K (and so a lower K); indicates an industry
S
that is more knowledge-capital intensive; by contrast, a higher K (and so a higherK); indicates an industry that is more physical-capital intensive.
S

Given Assump-tion 1, it is straightforward to show that FDI will be chosen by industries that aresu¢ ciently knowledge capital intensive –industries that have a su¢ ciently low capital requirement, K, for a given S. With some additional structure on the surplus
functions, one can also establish that outsourcing is chosen by an industry that is suf…ciently physical capital intensive – industries that have a su¢ ciently high physicalcapital requirement, K, for a given S. We now state out main results in the next two
propositions.
Proposition 1 Given any …xed S: (i) There exists some K1 > 0 such that when
K < K1 ;F
MO
M > 0: That is, M will choose FDI when the production (industry)is su¢ ciently knowledge-capital intensive. (ii) Suppose that, for si 2 [0; S] ; both@Ui (K;si )
@K

(K;S)
and d[U1 (K;S)dKU1 (K; S)] decrease in K and @Ui@K! 0 as K ! 1: Then,

there exists some K2

K1 > 0 such that when K > K2 ;FMO
M < 0: That is, M

will choose outsourcing when the production (industry) is su¢ ciently physical-capital
8

That is, under FDI, M only needs to pay A an amount equal to W in t = 2; whereas under
2 (K;0)outsourcing A will obtain U2 (K;S)+U+ V ( e j K) in t = 2 due to its ownership of K and can2hold up M in demanding a higher payo¤.

16

intensive.
F
M

Proof. (i) We can rewrite

U1 (K; S)O
M =U1 (K; S) +U2 (K; 0) + V ( 0j K)

U2 (K; S)

U2 (K; 0)
2

W (1 + )Since Ui (K; si ) increase in si ; we have U1 (K; S)

(10)

rK:

U1 (K; S) > 0; and U2 (K; S)

U2 (K; 0) > 0: From (iii) of Assumption 1, U2 (K; 0)+V ( 0j K)
when K (> 0) is su¢ ciently small, we must have+FM

(1 + ) W: Therefore,O
M > 0:(K;si )
(ii) Since @Ui@K
and @[U1 (K;S)@KU1 (K; S)] decrease in K;h@ U1 (K; S)

U1 (K;

2 (K;0)S) + U2 (K;S)+U
2i(W + rK)@K@ [U1 (K; S) U1 (K; S)] 1 @U1 (K; S) @U1 (K; 0)
=
+
+
@K
2
@K
@K

r

(K;S)
is decreasing and is negative when K is su¢ ciently large, due to @Ui@K! 0 asK ! 1: Thus U1 (K; S)

2 (K;0)U1 (K; S) + U2 (K;S)+U
2(W + rK) is a (strictly)

concave function that decreases when K > K 0 for some large enough K 0 : Therefore,
since V ( 0j K)
such thatF
M

W

0 by (iv) of Assumption 1, there must exist some K2

KO
M < 0 when K > K2 (or when S

K1

is su¢ ciently large).

Notice that for result (ii) in Proposition 1 to hold, we need the additional assumption that the marginal return of K is decreasing and becomes arbitrarily small
when K is su¢ ciently large, as well as the marginal return of K for the di¤erence
U1 (K; S)

U1 (K; S) is also decreasing.9 This guarantees that the gain from better

9For example, if the pro…tability of an industry with requirements (K; S) is given by Ui (K; S) =K S 1 ; this additional assumption is satis…ed.

17

knowledge transfer under FDI will be outweighed by the losses due to poor incentive
for e¤ort and the increased spending on physical capital.
FM

We can also say something about howOMchanges when other parametersof the model change, for any …xed K (and S): Notice that since a higher S will makeS larger, it is unlikely that U1 (K; S)S

Thus, if we assume that U1 (K; S)

U1 (K; S) is lower with a higher S:

U1 (K; S) is non-decreasing in S; 10 and noticethat U2 (K; S) is higher with higher S from part (i) in Assumption 1; we will haveF
MO
M higher with a higher S from equation (10). Next, again from equation (10),a higherlowers U1 (K; S)

U1 (K; S) ; thereby loweringF
MO
M . We have thus

established the following:
Proposition 2 (i) For any …xed K and S;…xed K;

F
M

O
M

F
M

O
M decreases withS
) if U1 (K; S)
increases with S (or with K: (ii) For any

U1 (K; S) is non-decreasing in S.
Mimicking Proposition 1, a more knowledge capital intensive industry (an industry
Swith a higher K) has a greater incentive to choose FDI. On the other hand, if a higher

portion of knowledge capital is contractible, there will be less problem with knowledge
capital transfer under outsourcing, which increases the incentive for outsourcing, allelse being equal.
Together, our results imply that FDI is the preferred choice for M when M ’s
product is intensive in knowledge capital and knowledge capital is di¢ cult for M tocontrol under a licensing agreement. When M ’s activity is either extremely intensive
in physical capital or knowledge capital is easy to protect under a licensing agreement,
outsourcing is M ’s preferred choice. Thus, for instance, we see the manufacturing of
10

This additional assumption is again satis…ed if Ui (K; S) = K S 1

18:

standard electronics equipment such as DVD players, CD players and regular TV’soutsourced as are items like Nike or Adidas athletic shoes. In all of these cases,
production is physical capital intensive or, what knowledge capital there is, is easily
controlled under a licensing agreement. But we do not see Microsoft outsourcing thewriting of its operating systems.
The following examples illustrate our payo¤ assumptions and …ndings.
Example 1 Suppose that Ui (K; S) = K (1 + S)1; and V (ej K) =

1
rK (1
5

40e)2 :

Then, part (i) and (ii) of Assumption 1 are always satis…ed; part (iii) and (iv) are1
rK > (1 +5satis…ed as long as K

) W: Furthermore, both the additional assump-tion used in part (ii) of Proposition 1 and the additional assumption used in part (i)of Proposition 2 are satis…ed. We have:

F
M

O
M

= U1 (K; S)= K (1 + S)1= K

U2 (K; S) + U2 (K; 0)+ V (0j K) W
(W + rK)2
K (1 + S)1 + K
1
K (1 + S)1 +rK W(W + rK)2
5
1
1(1 + S)1 ++rK (1 + ) W:
25U1 (K; S) +3
(1 + S)1
2

Suppose in addition that= 32 ; r = 0:5;

= 0:5; W = 0:5;

K 2 [0:94; 7:02] :11 Then, it is stragightforward to verify that K
F
M > 0;

O
M > 0; and= 0:3; S = 1; and1
rK > (1 +
5

) W;

O
A > 2W: Hence all the assumptions of our model are satis…ed,

11

As in the next two examples, here the interval restriction on K is due to the participationO
constraint that O
2W being concave in K for the relevant parameter values.
A > 2W; withA
This imposes a binding constraint on how high and low the parameter value K can be allowed.

19

and

F
M

O
M

= K 0:5

3(1 + 1)0:5
2(1 + 0:5)0:5 +

1
2

1 2
+
5 3

0:5K

1+

2
3

0:5

T 0 if K S 5: 915 5:That is, corresponding to Proposition 1, K1 = K2 = 5: 915 5:
Example 1 illustrates our …ndings in Propositions 1: for a given …xed S; M chooses
FDI when K (or K) is below some critical value, and chooses outsourcing when K
S(or K) is above some critical value. Notice that in this example the critical values areS
the same, i.e., K1 = K2 :Example 2 Suppose that everything is the same as in Example 1 above except that
now

F
M

= 0:7; then again all assumptions are satis…ed, andOM= K 0:5

3(1 + 1)0:5
2(1 + 0:7)0:5 +

1
2

1 2
+
5 3

0:5K

1+

2
3

0:5

T 0 if K S 4: 592 2:
Thus, with a higher ;FMO
M is lower for any given K; and K1 = K2 = 4: 592 2:

Example 2 illustrates Part (i) of Proposition 2: With a higher ; the incentive for
FDI becomes lower relative to that for outsourcing. This is re‡ected by the smaller
set of K for which

F
M >

O
M as

increases from 0.3 to 0.7, as compared to Example

1.
Example 3 Suppose again that everything is the same as in Example 1 above, exceptthat now S = 2 and K 2 [0:94; 11: 045] : Then again all assumptions are satis…ed,
20

includingO
A

2W > 0 if K 2 [0:6; 11: 04] :We have:

F
M

O
M

3
(1 + 2)0:5
2= K 0:5(1 + 1)0:5 +

1
2

1 2
+
5 3

0:5K

1+

2
3

0:5

T 0 if K S 10: 915:
Thus, with a higher S;

FMO
M is higher for any given K; and K1 = K2 = 10: 915:

Example 3 illustrates Part (ii) of Proposition 2: With a higher S; the incentive for
FDI becomes higher relative to that for outsourcing. This is re‡ected by the larger
set of K for which

F
M >

O
M as S increases from 1 to 2, as compared to Example 1.

Our theoretical …ndings have potentially testable implications. In particular, both
Propositions 1 and 2 suggest that …rms produce products that are more knowledgecapital intensive and/or have a lower

tend to choose FDI. Such a …rm will have ahigher return at t = 1 (U1 (K; S) > U (K; S)), and a lower replacement value (physical capital value plus the value of explicit intellectual capital). Consequently, such a…rm will have a higher Tobin’s q:12 This suggests a relationship between Tobin’s q andoutsourcing –…rm’s with high Tobin’s q are more likely to be using FDI while …rm’s
with low Tobin’s q are more likely to be outsourcing. This prediction is supported
by some existing empirical evidence. Morck and Yeung (1991), for example, show
12

Recall that Tobin’s q is de…ned asq=market value of the …rm:
replacement cost of …rm assets

21

that controlling for explicit knowledge capital such as R&D and advertising expenditures, …rms with more owned foreign subsidiaries have a higher Tobin’s q. Our theory
provides directions for further empirical studies.
Our results also have implications for the choice of organizational mode over the
product life cycle. Speci…cally, the product life cycle is often characterized in terms ofrecently innovated products being relatively intensive in intellectual assets and established products being relatively intensive in physical assets. Under this interpretation,a recently introduced product is one with K=S small and so it’s manufacturer is likely
to choose FDI; an established product is one with K=S large and so its manufacturer
is likely to choose outsourcing. Again, we have some observations of this pattern inthe data. Sharp, for instance, produces it’s latest ‡at-panel and Plasma TV’s for Europe in an owned facility in Eastern Europe. Its standard TV’s and older ‡at-panel
models are produced by outsourced manufacturers in Asia.
Markets in which technologies evolve rapidly so that knowledge capital quickly
depreciates are ones that the model also predicts should feature more outsourcing. In
this case, markets with rapid technological change will feature low values for U2 (K;S)
2
W as rents from knowledge capital decline quickly with time. As a result, the holdup problem that FDI solves is less severe in markets with rapid technological change.
This makes outsourcing a more attractive option. Similarly, products that require
highly skilled agents that are in scarce supply in the foreign country – products forwhich W is large relative to U2 (K; S) –are also more likely to be outsourced. Again,
the reason is that the value that FDI generates in terms of reduced hold up is lower
since the agent already captures a large share of second-period rents due to the highvalue of W .

22

To the extent that stronger intellectual property protection or contract enforcement
is likely to lead to a higher ; Proposition 2 further suggets that outsourcing to a
country is likely to increase as it implements stronger intellectual property protection.
Finally, note that the larger is , the larger is the amount of the second-period
surplus earned by A under outsourcing that M can claim in the …rst period licensing
contract and the larger is the share of physical capital costs borne by A. As a result, as
becomes larger, outsourcing becomes a more attractive option. Since low values ofare associated with greater capital market imperfections in the foreign country, FDI
is more likely when capital market imperfections are signi…cant whereas outsourcing
is more likely when capital market imperfections are less signi…cant.
4. CONCLUSION
In this paper we have examined how the non-excludability of knowledge capitalleads to the ownership of a complementary asset, in our case physical capital, as ameans of protecting intellectual property. The result we …nd is that …rms that arelargely dependent on knowledge capital for their returns will protect these returns byengaging in FDI rather than outsourcing. The ownership of physical capital protects
the returns of the complementary asset, knowledge capital. The cost of this ownershipis weak incentives for …rm management. Firms whose returns rely little on knowledge
capital and mainly on physical capital outsource to provide stronger management
incentives.
We conclude the paper by summarizing six empirical implications of the model.
Three relate to the …rms and their technologies. (1) Firms that choose FDI will havelarger values of Tobin’s q, all else equal, than …rms that outsource, (2) …rms and23

products that are subject to product cycles are likely to use FDI early in a cycle andoutsourcing later, and (3) …rms in industries with rapidly developing technologies
may be more likely to choose outsourcing. Three predictions relate to host-market
characteristics. FDI is more likely chosen in markets where (4) skilled labor has alow opportunity cost, (5) intellectual property rights and contract enforcement are
relatively weak, and (6) capital markets are relatively under-developed.

24

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