Three Essays on International Trade and Monetary Economics
By
Sangwha Shin

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Economics – Doctor of Philosophy
2014

ABSTRACT
Three Essays on International Trade and Monetary Economics
By
Sangwha Shin
This dissertation consists of three studies in international trade and monetary economics. The first and third chapters study the impact of labor market rigidities on multinational firms’ choice between FDI and outsourcing. The second chapter proposes a
model that explores one of the motivations for using Bitcoin.
In the first chapter, I propose a two-country, two-sector model, where a firm’s decision on offshoring depends on labor market rigidities, due to which firms need to bear
not only wages, but also additional costs from the labor market. In this model, firms
endogenously choose their organizational form, considering their productivity level and
fixed organizational costs. The labor market cost generated by search frictions plays a
key role in changing the variable benefits of each choice, and thus works as a key determinant in the process of selecting the organizational form for offshoring. The model has
four different types of equilibria, depending on relative levels of two labor market costs
(domestic and foreign) and the price of the intermediate input. In all equilibria, a relative rise in the domestic labor market cost increases the share of offshoring firms, while
decreasing domestic integration. Furthermore, an economy with offshoring has a higher
welfare level and a lower unemployment rate than autarky.
The second chapter offers an explanation for how Bitcoin gained its success, by focusing on the anonymity of the Bitcoin transactions based on the Bitcoin system’s peer-topeer nature, among several other features that distinguish it from previous digital currency systems. In the model that I propose, there exist two currency markets, Bitcoin
and Debit, and agents are heterogeneous in their anonymity concerns. This heterogeneity
drives some agents to choose the Bitcoin market and others to choose the Debit market

in the benchmark model. When I introduce the intermediaries, which accept Bitcoin for
legal goods, the number of agents who choose the Bitcoin market increases, while the
share of Bitcoin users engaged in illegal activities decreases.
Finally, in the third chapter, I examine the key prediction that I make in the first chapter: the difference in labor market flexibility across countries can be a key determinant in
a firm’s offshoring decision. I use the data set for 2006 through 2012 from U.S. relatedparty trade data of 453 6-digit North American Industry Classification System (NAICS6)
level goods from 137 countries. For the labor market flexibility index, I use the Global
Competitiveness Report (GCR) by the World Economic Forum. The data yields supporting results for the first chapter: the U.S. intrafirm imports share is positively correlated
with the industry productivity dispersion only in countries that have the most flexible labor market. The supporting results stand out more with the data on developing countries
only, which are mostly host countries trading with U.S. multinationals.

ACKNOWLEDGMENTS

In every step of this dissertation, I have been indebted to my advisor, Dr. Carl Davidson.
His insight and continued work in the field motivated me to start this study, and his
probing questions and feedback allowed me to complete it. I am also deeply grateful to
my professors Dr. Luis Araujo and Dr. Susan Chun Zhu for their valuable suggestions
and advice. Their help throughout the research and writing process enabled me to refine
my ideas and reasoning. I am thankful to all three of my committee members for their
encouragement and for believing in me.
My friends in the Economics Department helped me in various ways. I valued the
helpful comments from my colleagues; and I am especially grateful to my friend, Hyeongjun
Bang, for his supportive company while I lived in East Lansing.
I want to express my deepest gratitude to my family. I am grateful for the love and encouragement of my wife, Yujin, who saw me through the ups and downs of dissertating;
she selflessly understood and took care of our small family in spite of her own doctoral
work. With my son, Ian, I was able to realize the importance of family, as he reminded me
how rich my life can be with him around. Finally, I want to express my admiration and
appreciation to my father and mother for their sacrifices and support. They have continued to be there for me despite having to cope with my father’s struggle with cancer in
the last five years. Thanks to all of my family members, I have been able to find a happy
balance between my work and my personal life.

iv

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
CHAPTER 1
Labor Market Structure and Offshoring . . . . . . . . . .
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 The Labor Market . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Choices of Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Domestic Integration (DI) . . . . . . . . . . . . . . . . . . . .
1.3.2 FDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Outsourcing . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Two Possible Paths . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 Equilibrium Conditions . . . . . . . . . . . . . . . . . . . . .
1.4.3 Equilibrium with DI, Outsourcing, and FDI (Type 4) . . . . .
1.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 FDI vs. Outsourcing . . . . . . . . . . . . . . . . . . . . . . .
1.5.2 Effect of the Domestic Labor Market Cost on Firms’ Decision
1.5.3 Economic Implications of Offshoring . . . . . . . . . . . . . .
1.6 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CHAPTER 3
FDI vs. outsourcing: the Role of Labor Market Flexibility
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Data Sources and Measurement . . . . . . . . . . . . . . . . . . . . .
3.4 Empirical Specification . . . . . . . . . . . . . . . . . . . . . . . . . .

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68

CHAPTER 2
Anonymity Concerns and Bitcoin
2.1 Introduction . . . . . . . . . . . . . . . . . .
2.2 Model . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Environment . . . . . . . . . . . . . .
2.2.2 Value Functions . . . . . . . . . . . .
2.2.3 Equilibrium . . . . . . . . . . . . . .
2.3 A Model with the Intermediary Market . .
2.4 CONCLUSION . . . . . . . . . . . . . . . .
REFERENCES . . . . . . . . . . . . . . . . . . . .

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3.5 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

vi

LIST OF TABLES

Table 1.1

Three Productivity Cutoffs . . . . . . . . . . . . . . . . . . . . . . . . . 25

Table 3.1

Labor Market Flexibility Index (2012) by Developed/Developing Countries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Table 3.2

Estimation Results with Data from All Countries . . . . . . . . . . . . 70

Table 3.3

Estimation Results with Data from Developed Countries . . . . . . . . 71

Table 3.4

Estimation Results with Data from Developing Countries . . . . . . . 72

Table 3.5

U.S FDI Inflows by Partner Country (2012) . . . . . . . . . . . . . . . . 73

vii

LIST OF FIGURES

Figure 1.1 Autarky vs. Offshoring equilibrium . . . . . . . . . . . . . . . . . . . . 29
Figure 2.1 Equilibrium in the Benchmark Model . . . . . . . . . . . . . . . . . . . 49
Figure 2.2 Equilibrium with the intermediaries . . . . . . . . . . . . . . . . . . . . 52
Figure 3.1 Equilibrium Type and The Labor Market Flexibility . . . . . . . . . . . 61
Figure 3.2 GDP per Capita and Labor Market Flexibility . . . . . . . . . . . . . . 64
Figure 3.3 Labor Market Flexibility in Rich/Poor Countries . . . . . . . . . . . . 65

viii

CHAPTER 1
Labor Market Structure and Offshoring
1.1

Introduction

Rapidly increasing international disintegration in production has gained attention in many
studies. When a firm decides to move part of its production process or tasks abroad, it
has two choices. It can forge an arm’s-length relationship with other intermediate goods
suppliers; or it can opt for vertical integration by setting up affiliates overseas. The former
is called ‘Outsourcing’ and the latter, ‘Foreign Direct Investment (FDI)’.
As some firms choose to outsource tasks while others choose FDI, a question naturally arises about the key determinants in each decision. Although many studies have
attempted to answer this question, the labor market structure has received little attention,
as most studies in the literature have assumed a frictionless labor market. Considering
the fact that saving variable costs is the fundamental motivation of firms choosing to offshore, models with a frictionless labor market may be missing an important factor that
affects a firm’s decision.
In this paper, I consider the labor market structure to be a key determinant in a firm’s
decision to offshore. In the model I propose, two sectors exist, in one of which the labor
market is under search and matching frictions. Specifically, the labor market structure
is based on Helpman and Itskhoki (2010), where homogeneous workers search firms for
jobs, while firms are heterogeneous across their skill levels. In this setting, it is costly for a
firm to hire or fire workers, and thus firms consider not only the wage level, but also the
labor market cost generated by the frictions. I show that a country with a relatively high
labor market cost will have more firms choosing to offshore; and firms with a high pro1

ductivity level will choose offshoring, while less productive firms remain in the domestic
market.
When I analyze the impact of allowing offshoring on the economy, I find that the
equilibrium with offshoring gives a weakly higher welfare level. Firms facing a higher
labor market cost in the domestic labor market in autarky try to reduce the production
to keep the profit level unchanged. Allowing offshoring, however, offsets the decrease in
the quantity level by structural changes in the economy, as more firms choose to offshore.
In an analysis of the total hiring and unemployment rate, I find that even though the total hiring in autarky is higher, the unemployment rate is also higher. These seemingly
contradictory results have originated from the fact that the unemployment rate depends
on not only the total jobs available, but also the number of job seekers in the labor market. When offshoring is available, workers realize that the number of jobs decreases; and
choose the other sector, where labor market frictions do not exist.
The proposed model lies in an intersection of two strands of literatures. One of them
focuses on the role of the labor market structure on issues in the international trade. Since
the seminal work of Davidson et al. (1999), there have been many studies on this topic and
now there exists well-developed literature on search-induced unemployment in different
trade environments. Among this literature, two studies from Mitra and Ranjan (2010,
2012) are closely related to the model. In both studies, the labor market is under search
and matching frictions. Mitra and Ranjan (2010) analyze the impact of offshoring on the
unemployment rate. Interestingly, they find the impact of offshoring on the unemployment rate depends on inter-sectoral labor mobility. Under imperfect inter-sectoral labor
mobility, unemployment may increase in the offshoring sector, while it may decrease in
the non-offshoring sector. When the economy is under perfect inter-sectoral labor mobility, however, the economy-wide unemployment decreases unambiguously. Mitra and
Ranjan (2013) analyze the role of offshoring in a model with fair wage consideration. In
their model, workers are heterogeneous in terms of skill level, while firms are homoge-

2

neous. When the fair wage constraint is binding and a firm hires two types of labor, a
distortion can arise in the production process. Mitra and Ranjan (2010) show that fairness
consideration can motivate offshoring, as it could be a way of resolving the distortion.
But neither study distinguishes FDI from Outsourcing as they do not focus on the firms’
choice between the two.
Davidson et al. (2008) also introduce search and matching frictions into the labor market and analyze the impact of Outsourcing in high-tech jobs on low-skilled workers’
wages. In their model, there exist two types of labor, high-skilled and low-skilled, and
firms endogenously choose their technology level. Interestingly, Davidson et al. (2008)
find that under certain conditions, Outsourcing can increase the wage level of low-skilled
labor in the long run. In the long run equilibrium, there will be more entry of firms and if
the new firms select the low-level technology, it will become easier for low-skilled labor
to find employment and their wage level can increase. In the short run, however, both
types of labor are worse off, as high-skilled labor now faces fewer job opportunities and
lowered wages, while low-skilled labor encounters greater competition for jobs.
Although many papers in the literature on trade issues related to labor market rigidities use novel models, several recent papers have attempted to introduce search-induced
unemployment into standard trade models.1 In particular, Helpman and Itskhoki (2010)
introduce Diamond-Mortensen-Pissarides-type search and matching frictions into the labor market. They use a two-sector model where one sector is monopolistically competitive. Firms become heterogeneous when they enter the market, and some choose to
export, while others decide whether to exit or remain in the domestic market. Helpman
and Itskhoki (2010) show that labor market flexibility can be a source of comparative advantage in trade, i.e., a country with lowered labor market inefficiencies can get welfare
improvement, while its trade partner becomes worse off.
Another strand of literature this paper relies on tries to answer the question of why
1 See

Cuñat and Melitz (2010), Cuñat and Melitz (2012), Davidson and Matusz (2012), and Felbermayr
et al. (2011).

3

some firms choose to outsource, while others choose FDI. In some studies, incomplete
contracts play a central role. Antràs (2003) focuses on the incomplete contract between
a firm and a supplier. With Outsourcing, a firm can have efficiency gains from having a
specialized supplier. However, due to incomplete contracts, hold-up problems occur, and
both sides tend to underinvest compared to the optimal level. Similarly, Grossman and
Helpman (2002) and Grossman and Helpman (2003) have modeled an economy where
firms are placed in a trade-off between extra governance costs in FDI and the incomplete
contract problem in Outsourcing.
In other studies, the heterogeneity of firms’ productivity level induces different sorting across firms. In Antràs and Helpman (2004), firms are heterogeneous in terms of
productivity. In this model, they make two choices. In choosing location between North
and South, they face a trade-off between the low fixed cost at home and low variable costs
in a foreign country. On the other hand, in the choice between vertical integration and
arm’s-length relationship, firms face a trade-off between an ownership advantage in vertical integration and better incentives in Outsourcing. These trade-offs, together with the
incomplete contract problem in Outsourcing, drive firms to choose certain organizational
forms depending on their realized productivity levels. In Antràs and Helpman (2004)
model, firms with high productivity level choose FDI, while less productive firms choose
Outsourcing.
While many studies focus on the role of incomplete contracts and productivity levels,
Chen (2011) places informational asymmetry at the center of the analysis. In this model,
firms face an adverse selection problem in choosing an intermediate goods supplier, while
they face an inefficient monitoring problem when they choose FDI. This model is helpful
in explaining why FDI is heavily concentrated in capital-intensive industries, in which
monitoring costs are significantly lower than in other industries, which alleviates the inefficient monitoring problem in FDI.
In this paper, I extend the model in Helpman and Itskhoki (2010). While following

4

the basic setup of their model, I allow firms to have offshoring choices, which include
both FDI and Outsourcing. Compared to previous studies, firms have a different source
of trade-off in choosing offshoring. They can lower their production costs by selecting a
foreign country with a low labor market cost, even though it would incur an additional
fixed organizational cost. Thus, the labor market cost directly affects a firm’s decision to
offshore.
The remainder of this paper is organized as follows. In Section 1.2, I develop the
model and in Section 1.3, I calculate the profit levels of the three different choices. In
Section 1.4, I derive four different types of equilibria and analyze them in Section 1.5.
Finally, in Section 1.6, I offer a summary of the analysis with concluding remarks. The
proof of the main results are in Appendices.

1.2

Model

In this model, there exist two sectors. One sector produces a homogeneous good, while
the other produces differentiated goods. In the homogeneous-good sector, there are no
labor market frictions and all firms produce domestically. The price of the homogeneous
good is normalized to one and it serves as a numeraire. In the differentiated-goods sector,
search and matching frictions exist in the labor market. Firms in this sector can produce
domestically by using domestic labor, but they can also choose to offshore by paying the
fixed organizational cost of FDI or Outsourcing. As in many previous studies, I assume
that the fixed organizational cost of FDI is higher than that of Outsourcing.

5

1.2.1

Preferences

A representative household gets utility from consuming q0 homogeneous goods and a
continuum of differentiated goods,
1
β

β

Q =

i∈ I

q(i ) di

,

0 < β < 1,

(1.1)

where q(i ) denotes consumption of variety i, I denotes the set of varieties, and β is a measure of the elasticity of substitution between varieties. The total utility from consuming
them is defined as
1
U = q0 + Q ς ,
ς

0 < ς < β.

The restriction ς < β implies that differentiated goods are better complements to each
other than the homogeneous good.
It is well known that CES preferences yield the following constant elasticity demands:
p (i )
P

q (i ) = Q

− 1−1 β

.

(1.2)

And the price index for Q is defined as

P=

i

p (i )

β
− 1− β

−

1− β
β

di

.

With total spending E, the representative household maximizes its utility by choosing

Q = P

− 1−1 ς

q0 = E − P

6

,
− 1−ς ς

(1.3)
.

(1.4)

1.2.2

Technology

In the homogeneous-good sector, firms make one unit of good by using one unit of labor.
As the market is competitive, the wage is equal to the price of the homogeneous good,
one.
Following Melitz (2003), the market in the differentiated-goods sector is monopolistically competitive, and each firm needs to pay the entry cost, f e , to enter the market. After
paying the entry cost, firms realize their productivity level, θ, which is from a known
common distribution. The production function of a firm with θ is given by

q(θ ) = θh,

(1.5)

where h is the number of workers the firm hires. Firms can choose to offshore by hiring foreign labor (FDI) or buying intermediate inputs from intermediate-goods suppliers
(Outsourcing) to substitute h. In order to produce, firms also have to pay a fixed production cost, f d .
Using Equation (1.2) and Equation (1.5), we can calculate the price and revenue of a
firm with productivity level θ as a function of Q and h:
p(θ ) = (θh)−(1− β) Q−( β−ς) ,
R(θ ) = (θh) β Q−( β−ς) .

1.2.3

(1.6)

The Labor Market

In this economy, there is a continuum of identical households of measure one. As each
household has L units of workers, the total labor endowment of this economy is L. Workers can choose to work either in the homogeneous-good sector or in the differentiatedgoods sector. A household allocates its labor into two sectors. Out of L workers, it al-

7

locates N to the differentiated-good sector and L − N to the homogeneous-good sector.
As the wage in the homogeneous-good sector is equal to one, the average wage from
working in the differentiated-goods sector should be one.
In the differentiated-goods sector, labor market frictions exist, and as a result of which,
firms face a labor market cost, b, whenever it hires a worker. In this setting, firms consider
not only the wage level, but also the labor market cost when they make a decision on the
size of their labor.
The labor market cost can be decomposed into hiring and firing costs. When firms
hire workers, they have to pay costs in opening vacancies. As it is not possible to have
immediate matchings with potential workers, an inefficiency in the matching process also
incurs costs.
When a vacancy is filled, firms have to fire a fraction of workers they hired, as they
are assumed to realize whether workers are suitable or not for the jobs they are matched,
once they are hired. Thus, firms need to hire more than an optimal number of employees,
and they have to bear other costs related to the firing process.
Following the approach that is proposed in Helpman and Itskhoki (2010), I assume
that the hiring cost bh is a function of labor market tightness,

x=

H
,
(1 − σ ) N

where H is the total hiring in the differentiated-goods sector and σ is the fraction of job
openings which need to be fired. As firms anticipate to fire a fraction σ of total matches,
they hire

H
1− σ

to have H workers.

Hiring costs in this economy are defined as

bh = ax δ ,

a > 1 and δ > 0,

where a represents frictions in the labor market during the hiring process. Higher costs

8

of opening a vacancy or lower efficiency of matching technology will give us a higher a.
When firms fire a worker, they bear firing costs, ψ. Under the assumption that I made
regarding the firing process, the total labor market cost becomes

b=

1
(b + σψ)
1−σ h

(1.7)

and the economy-wide unemployment rate is defined as

u=

N−H
.
L

Following Stole and Zwiebel (1996a) and Stole and Zwiebel (1996b), firms engage in a
generalized Nash Bargaining procedure over the revenue they create with matches. For
simplicity, I assume equal bargaining power for a firm and a worker. As a result, the
equilibrium wage as a function of employment is the solution of the following equation:
∂
( R (h) − w (h) h) = w (h) ,
∂h

(1.8)

where R (h) is the revenue and h is the number of workers. As an additional worker
affects the overall wage level, Equation (1.8) yields a differential equation of w. With zero
outside option for a worker,2 the bargaining procedure makes the marginal gains from
the additional worker equal to the marginal gains to the worker.
2 Once

a worker enters the differentiated-goods sector, she cannot go back to the homogeneous-good

sector.

9

1.3
1.3.1

Choices of Firms
Domestic Integration (DI)

Firms in the differentiated-goods sector must pay a fixed cost, f d , regardless of their organizational choices when they decide to produce. This fixed cost may include costs
associated with headquarter services, such as accounting, finance operations, and R&D.
By using Equation (1.8), we can calculate equilibrium wages, w (θ ), as a function of
employment:
∂
[ R (θ ) − w (θ ) h] = w (θ ) .
∂h

(1.9)

By solving this, we get
w (θ ) =
Thus, a firm loses

β
1+ β R ( θ )

β R (θ )
.
1+β h

(1.10)

after the wage bargaining and faces

max

1
R (θ ) − bh − f d ,
1+β

(1.11)

and the optimal level of hiring becomes
β
h∗d (θ ) =
b (1 + β )

1
1− β

β−ς

Q

− 1− β

β

θ 1− β .

(1.12)

By plugging this into the wage equation, we get the wage and profit level from choosing
DI:3
w (θ ) = b,
3 In

∀θ,

more general settings where the bargaining power of two parties are not equal, the wage level is
proportional to the labor market cost. Specifically, with a relative bargaining power of firms µ, we get
w (θ ) = b/µ.

10

πd∗ (θ )

1
1− β

1
1+β

= (1 − β )

β
b

β
1− β

β−ς

Q

− 1− β

β

θ 1− β − f d

≡ Ad Θ − f d ,
where Ad = (1 − β)

1
1+ β

1
1− β

β
b

β
1− β

(1.13)
β−ς

Q

− 1− β

β

and Θ = θ 1−β

is a different measure of

productivity.

1.3.2

FDI

Instead of hiring domestic labor, a firm can hire foreign labor by engaging in FDI. Similar
to the domestic labor market, there also exist labor market frictions in the foreign labor
market, and firms have to bear b f whenever they hire workers.4
I assume that a firm engaging in FDI faces the same bargaining procedure as in Equation (1.9),
∂
R (θ ) − w f (θ ) h = w f (θ ) ,
∂h
and the resulting wage level becomes

w f (θ ) =

β R (θ )
.
1+β h

Therefore, the result of the wage bargaining is the same: a firm pays

β
1+ β R ( θ )

for the

total wage. A firm solves the same problem as in DI with the foreign labor market cost,
b f , but with an additional fixed organizational cost of FDI, f f , which is assumed to be
greater than that of Outsourcing, f u . Thus, a firm faces

max

1
R (θ ) − b f h − f d − f f
1+β

4 Same as in the domestic labor market,

b f is generated from search and matching frictions in the foreign
labor market. For example, we can think of a labor market structure in a foreign country to be the same as
a domestic labor market with different parameters, b f =

11

1
1− σ f

a f x δf + σ f ψ f .

and by solving this, we can derive the optimal hiring level,

h∗f (θ ) =

β
b f (1 + β )

1
1− β

β−ς

Q

− 1− β

β

θ 1− β .

With the optimal hiring level, we can derive the following wage and profit level from
choosing FDI:

∀θ,

w f (θ ) = b f ,

π ∗f (θ ) = (1 − β)

1
1+β

1
1− β

β
bf

β
1− β

β−ς

Q

− 1− β

≡ A f Θ − fd − f f .

1.3.3

β

θ 1− β − f d − f f
(1.14)

Outsourcing

Now suppose that a firm can buy intermediate goods from foreign suppliers to substitute
for labor.5 The intermediate goods market is assumed to be perfectly competitive, and
suppliers in the foreign country are assumed to have relative strength in dealing with
the foreign labor market compared to firms from the home country, as they have more
information about the labor market structure. Thus, they face a lower labor market cost
compared to firms engaging in FDI, i.e.,

bu < b f ,

where bu denotes the labor market cost that suppliers face.
With the competitive price of an intermediate good, pu , suppliers also has to bargain
5 For

simplicity, domestic Outsourcing is assumed to be dominated by domestic integration. Under an
assumption that domestic firms are exposed to the same information about the domestic labor market, this
is satisfied with the condition, p∗ /b>(1 + β)1/β , where p∗ denotes the unit price of a domestic intermediate
good.

12

with theirs labor forces,
∂
p h − wu h = wu ,
∂h u
and by solving this equation, we get

wu =

1
p .
2 u

Thus, after the wage bargaining, a supplier maximizes the following problem:
1
max pu h − bu h.
2
And as the market is perfectly competitive, the price of an intermediate good should be
at a level where the supplier gets zero profit, i.e.,

pu = 2bu .
By choosing Outsourcing, a firm can keep all of its revenue, as it does not have to
deal with the labor market anymore. However, it is assumed that it needs to pay the
adjustment cost, c, for every intermediate good to make it fit into its production process.
Thus, the unit price of the intermediate good, pu , becomes pu + c. So the problem that a
firm with Outsourcing faces is

max R(θ ) − pu h − f d − f u

13

and the resulting level of hiring and profit becomes

h∗u (θ )

=

β
pu

1
1− β

πu∗ (θ ) = (1 − β)

β−ς

Q

− 1− β

β
pu

β
1− β

≡ Au Θ − f d − f u .

1.4

β

θ 1− β

,

β−ς

Q

− 1− β

β

θ 1− β − f d − f u
(1.15)

Equilibrium

As firms are different in terms of productivity and three choices come with different levels
of fixed costs, we can observe different organizational types across firms in equilibrium.
With three choices, we could have seven different cases. Although it is theoretically possible to have equilibrium with only FDI or only Outsourcing, I consider them as extreme
cases and will discuss four other equilibria, which include at least Domestic Integration.
From here on, I refer to these equilibria as Type 1, Type 2, Type 3, or Type 4 equilibrium:
Type 1 has only DI and Type 2 has DI and Outsourcing. Type 3 is with DI and FDI and
Type 4 includes all three choices.

1.4.1

Two Possible Paths

As a thought experiment, we now consider what would happen if the home labor market
cost starts to increase from a very low level. When it is very low compared to pu and b f ,
firms located at home have no incentive to engage in offshoring. Thus, we would have
Type 1 equilibrium, where only DI exists. As b increases, while pu and b f remain fixed, the
relative benefits from choosing offshoring increase. When the gains from offshoring are
sufficient to cover its fixed organizational cost, firms would change their organizational
form into Outsourcing or FDI.
At this point, it is unclear which type of offshoring would be selected in the new

14

equilibrium without further analysis. But that choice depends on the relative size of pu
and b f . If the price of the intermediate good is relatively low compared to the foreign
labor market cost, it is reasonable to expect that the equilibrium will change to Type 2
because Outsourcing involves lower fixed organizational cost. If that is not the case, the
equilibrium will change to Type 3. This naturally gives rise to the following questions:
what would be the possible equilibrium paths as b changes? And what are the conditions
for each path? It turns out that two different paths exist in this model, depending on
certain parameter values.
The first path is from Type 1 to Type 2. This happens when the gains from FDI are
not sufficient to cover the additional fixed cost, f f − f u . In this path, as b increases, firms
choose Outsourcing and then it becomes impossible to have FDI in equilibrium. This is
because the relative variable benefits from having Outsourcing over FDI do not rely on
the domestic labor market cost. If we derive the relative ratio between two coefficients,
we get
Af
− 1
= ( 1 + β ) 1− β
Au

pu
bf

β
1− β

,

which is independent of b. This means that the relative gains from having Outsourcing
over FDI do not change as b increases. If A f /Au is smaller or equal to one, the gains from
FDI would never become larger than that of Outsourcing due to higher fixed organizational cost, and the equilibrium would stay in Type 2 as b increases.
Instead, if A f /Au is big enough, we would have another path which includes FDI.
In this path, FDI comes in first; and later we can see both choices in the equilibrium. In
other words, the equilibrium changes from Type 1 to Type 3 and then moves on to Type
4. As b increases, FDI becomes more attractive for the most productive firms, while other
firms stick to DI due to their inability to cover the fixed organizational cost of FDI. When
b further increases, some firms begin to change to Outsourcing as the relative variable
benefits from DI further shrink. In this equilibrium, firms with a high-productivity level

15

choose FDI and firms with a modest-productivity level choose Outsourcing, while firms
with a low-productivity level stay with DI. And as the condition of two paths cannot be
satisfied at the same time, we can derive the following results.
Lemma 1. In any path, Type 2 equilibrium cannot coexist with Type 3 or Type 4 equilibrium.
Proof. This is clear if we compare the equilibrium conditions of each type.6 To have Type
2 equilibrium, we need the condition, (1 + β)

− 1−1 β

pu
bf

β
1− β

Type 4 equilibrium, we must have the condition, (1 + β)

≤ 1. But to have Type 3 or

− 1−1 β

pu
bf

β
1− β

> 1. These two

conditions cannot be satisfied at the same time.
Proposition 1. If the domestic labor market cost keeps increasing from a very low level, while
keeping pu and b f fixed, the equilibrium would change as
1. Type 1 → Type 2, if (1 + β)

− 1−1 β

pu
bf

2. Type 1 → Type 3 → Type 4, if (1 + β)

1.4.2

β
1− β

≤1

− 1−1 β

pu
bf

β
1− β

>1

Equilibrium Conditions

To characterize the equilibrium in this model, let’s find the equilibrium conditions. For
each type of the equilibrium, there exists a zero profit cutoff productivity, Θd , and (possibly) other productivity cutoffs that are defined by the intersections of different profit
equations:
Ad Θd = f d ,
A d Θi − f d = Ai Θi − f d − f i ,
A f Θ f − f d − f f = Au Θ f − f d − f u .

(1.16a)
i ∈ {u, f },

(1.16b)
(1.16c)

Equation (1.16a) set the zero-profit cutoff and Equation (1.16b) pin down the productivity
level which gives us the same profit from DI and FDI (or Outsourcing). Equation (1.16c)
6 In

Appendices, I list the sufficient conditions for each type.

16

only appears in Type 4 equilibrium, where profit equations of FDI and Outsourcing intersect each other.
As firms draw their productivity level after they pay the fixed entry cost, the free entry
condition equalizes the expected profit to the fixed entry cost:
f e = E[π (Θ)].

The total output in the differentiated-goods sector is derived as

Q=M

1
β

q(Θ) dG (Θ)
β

1
β

,

where M is the measure of firms in the sector and q (Θ) is the output of a firm with
productivity level Θ.
In the labor market, each household divides its labor endowment into two sectors,
and this process equalizes expected wages in both sectors, i.e.,

x (1 − σ )w¯ = 1.

The LHS simply indicates an expected wage from choosing the differentiated-goods sec¯ when she is hired, x, and is not fired,
tor. A worker expects to receive an average wage, w,
1 − σ. And the RHS is the wage level that a worker could get from the homogeneous-good
sector.
Total hiring in the differentiated-goods sector is defined as
H = M × E[h(Θ)]

and the average wage in the sector can be calculated by

w¯ =

M × E[w(Θ)h (Θ)]
.
H
17

Without an additional assumption on the distribution of Θ, these conditions will implicitly determine M, N, H, Q, and cutoff productivity levels.

1.4.3

Equilibrium with DI, Outsourcing, and FDI (Type 4)

In this section, I will characterize equilibrium conditions and firms’ decision under Type
4 equilibrium. As the equilibrium conditions depend on the distribution of Θ, I assume
that Θ follows the Pareto distribution with shape parameter α and minimum value Θm
for the rest of the discussion. I list the equilibrium conditions of the other three types in
Appendices.
To have Type 4 equilibrium, we should have sufficiently low foreign labor market
costs so that firms can cover the high fixed organizational cost in FDI. The unit price of
an intermediate good should also be low enough to cover the fixed organizational cost of
Outsourcing, but it should not be too low, as it would drive FDI out of the equilibrium.
Lemma 2. Sufficient conditions to have Type 4 equilibrium are
1. (1 + β)
2. (1 + β)
b
bf

1
1− β

1
1− β

β
1− β

b
pu
b
pu

β
1− β

β
1− β

− (1 + β )

> 1 & (1 + β )
−1 <

1
1− β

b
pu

fu
fd
β
1− β

− 1−1 β

pu
bf

β
1− β

> 1,

&

<

f f − fu
fu

(1 + β )

1
1− β

b
pu

β
1− β

−1 .

Proof. As f f > f u > 0, we should have A f > Au > Ad to have Type 4 equilibrium.
The first condition comes from Ad < Au < A f . The second condition is derived from
Θd < Θu < Θ f , where Θd , Θu , and Θ f are defined by




Ad Θd − f d ≡ 0




Au Θu − f u ≡ Ad Θu






 A f Θ f − f f ≡ Au Θ f − f u .

The first condition of this Lemma states that the variable benefits from FDI should be
greatest, while the second condition restricts the variable gains from FDI, so that we can
18

have both Outsourcing and DI in the equilibrium. If conditions in Lemma 2 are satisfied,
we can find the following decision rule for firms in Type 4 equilibrium.
Proposition
2. A firm with Θ will




exit
i f Θ < Θd







choose DI
i f Θd < Θ < Θu



choose Outsourcing







choose FDI

i f Θu < Θ < Θ f
i f Θ f < Θ.

This proposition tells us that a firm makes a decision over its structure by comparing
its realized productivity level with three productivity cutoffs. It is interesting to note that
this is similar to the segregation result of the headquarter intensive sector in Antràs and
Helpman (2004). Although both papers share the same assumption on the relative sizes
of fixed organizational costs, the fundamental source of the result is different. In Antràs
and Helpman (2004), a trade-off between the ownership advantages in FDI and better
incentive in Outsourcing, and the incomplete contracts in Outsourcing drive the results.
In this model, however, the labor market condition, along with the price of intermediate
goods, is the basis of the result as they determine three productivity cutoffs.
Using the equilibrium conditions that we discussed in the previous section, we can
get analytical solutions of Θd , Θu , and Θ f . Before proceeding further, it will be helpful to
express Θu and Θ f in terms of Θd by using three cutoff conditions:

Θu =

Θf =

fu 
(1 + β )
fd


1
1− β

f f − fu  b

fd
bf

b
pu

β
1− β

 −1

− 1

β
1− β

1

− ( 1 + β ) 1− β

19

Θd ≡ k1 Θd ,

b
pu

β
1− β

(1.17)

 −1



Θd ≡ k2 Θd .

(1.18)

With these, we can express three profit equations in terms of three productivity cutoffs:
πd (Θ) = f d

Θ
− fd,
Θd

Θ
− fd − fu,
k1 Θd
k2 − k1
Θ
fu + f f
− fd − f f .
k1
k2 Θd

πu (Θ) = ( f u + k1 f d )
π f (Θ) =

k2 f d +

If we plug these into the free entry condition and apply the Pareto distribution assumption, we get

fe =

Θu
Θd

+
=

fd
∞

Θf

Θf
Θ
Θ
− f d dG (Θ) +
− f d − f u dG (Θ)
( f u + k1 f d )
Θd
k1 Θd
Θu
k2 − k1
Θ
k2 f d +
fu + f f
− f d − f f dG (Θ)
(1.19)
k1
k2 Θd

(k 1 k 2 )−α

f f − f u kα1 + f u + f d kα1 kα2
α−1

Θm
Θd

α

,

where the last expression, which relates Θd in terms of k1 and k2 , is decreasing in Θd .
The labor market condition and the average wage condition are calculated as

x (1 − σ)w¯ = 1

(1.20)

and as
w=

M
H

Θu
Θd

w (Θ) hd (Θ) dG (Θ) =

bM
H

Θu
Θd

hd (Θ) dG (Θ) .

(1.21)

The second equality of the average wage condition holds because all domestic labor receives the same wage, b.
The total hiring, H, and the total output in the differentiated-goods sector, Q, are defined as
H=M

Θu
Θd

hd (Θ) dG (Θ)

20

(1.22)

and

Q=M

1
β

Θu
Θd

qd (Θ) β dG (Θ) +

Θf
Θu

qu (Θ) β dG (Θ) +

∞
Θf

1
β

q f (Θ) β dG (Θ)

,

(1.23)

where
qd (Θ) = Θ
qu (Θ) = Θ
q f (Θ) = Θ

1− β
β
1− β
β
1− β
β

hd ,
hu ,
hf.

Combining (1.20), (1.21), and (1.22), we get
1
H
= .
N
b

(1.24)

Using this result and Equation (1.7), we get the following equation that determines
the labor market cost:

b=

1
1
ax δ + σψ =
1−σ
1−σ

a

1
b (1 − σ )

δ

+ σψ .

(1.25)

Note that we can calculate b from Equation (1.25) as a function of labor market parameters. In other words, b does not depend on other fixed costs, nor the distribution of
productivity. This result is consistent with the result of the closed economy model in
Helpman and Itskhoki (2010).7
As the labor market cost is determined solely by exogenous labor market parameters,
we can calculate Θd from Equation (1.19). As the right hand side of Equation (1.19) is
decreasing in Θd , under the conditions of Proposition 2, there exists Θd , which is unique
7 Note

that this model focuses on not a horizontal FDI, but a vertical FDI. As discussed in Antras and
Yeaple (2013), it is useful to assume zero transportation costs to shut down the horizontal incentive in FDI.
Thus, if I introduce exports into this model, it will create unnecessary complications, while keeping the
main results the same, as it would only increase the market size that firms face.

21

at a given level of b. Then, we can calculate the total output in the differentiated-goods
sector using the zero profit condition:
1−β
β
1 + β b (1 + β )

β
1− β

β−ζ

Q

− 1− β

Θd = f d .

With Θd and Q, we can solve for M, N, and H using, (1.22), (1.23), and (1.24), while
Θu and Θ f can be solved from (1.17) and (1.18).

1.5
1.5.1

Analysis
FDI vs. Outsourcing

In this section, I attempt to analyze the trade-off between FDI and Outsourcing. To do
this, let me list three different profit equations in three different choices:
πd (Θ) = Ad Θ − f d ,

(1.26a)

π f (Θ) = A f Θ − f d − f f ,

(1.26b)

πu (Θ) = Au Θ − f d − f u ,

(1.26c)

where

A d = (1 − β )

1
1+β

A f = (1 − β )

1
1+β

A u = (1 − β )

β
pu

1
1− β

1
1− β

β
1− β

β
1− β

β
b

β−ς

Q

β
bf

− 1− β ,

β
1− β

β−ς

Q

− 1− β ,

β−ς

Q

− 1− β

.

By comparing three different expressions, we can see that all three choices have a
simple linear relationship with the productivity level and the three coefficients of Θ take

22

similar forms. If we calculate ratios between them, we get
Af
Ad

=

β
1− β

b
bf

, and

Af
Au

= (1 + β )

− 1−1 β

pu
bf

β
1− β

Au
Ad

1

= ( 1 + β ) 1− β

b
pu

β
1− β

,

. From here, we can see that the relative

levels of pu and b f along with b determine the relative variable benefits of each choice.
As

Af
Au

= (1 + β )

− 1−1 β

pu
bf

β
1− β

= (1 + β )

− 1−1 β

β
1− β

2bu +c
bf

, β and c affect the relative

attractiveness of two choices at a given level of bu and b f . The term with β originates
from the fact that in Outsourcing, firms do not have to bargain over their revenue with
their labor, as they can replace workers with intermediate goods. Thus, we can interpret
this term as an additional benefit of choosing Outsourcing over FDI.
Proposition 3. By choosing Outsourcing, a firm can avoid the labor market and this gives a
secondary benefit to the firm, which in turn increases as workers have more shares in the wage
bargaining process.
1

Proof. The term (1 + β) 1−β , which can be interpreted as a secondary relative benefit of
choosing Outsourcing over FDI, is an increasing function of β. It has a value of one when
β is zero, and it goes to infinity as β goes to one. As the worker’s share in the wage
bargaining,

β
1+ β ,

increases in β, the secondary benefit of having Outsourcing increases in

the workers’ share.
The intuition of this proposition is quite simple. The larger the share that workers
receive in wage bargaining, the more the gains that firms have as a result of avoiding it.
The other parameter that affects the trade off between two choices is c. If we have very
low c, Outsourcing will dominate FDI as it also has lower organizational cost. On the
contrary, if c is too high, Outsourcing would not be chosen by any firms, as the variable
benefits of choosing it would be lower than FDI and DI.
To be more specific, let’s rewrite the first sufficient condition of Type 4 equilibrium:
1

1

b f (1 + β) β − 2bu < c < b (1 + β) β − 2bu .

23

This condition tells us that, in Type 4 equilibrium, c has to be low enough to make Out1

sourcing a profitable option for some firms (c < b (1 + β) β − 2bu ), while it should not
1

be too low, as it would drive FDI out of the equilibrium (b f (1 + β) β − 2bu < c). If c
1

is larger than b (1 + β) β − 2bu , we will have Type 3 equilibrium and if c is smaller than
1

b f (1 + β) β − 2bu , it will become Type 2 equilibrium.
We can interpret c as a generality of a skill that a firm uses. If a firm uses unique
technology, it will be very costly for it to buy an intermediate good and adjust it to fit into
its production process. In this case, the firm would be better-off by choosing integration,
instead of an arm’s-length relationship. On the contrary, if the technology is a general
one, it will be profitable to choose Outsourcing. We can also think of c as a fixed cost of
producing an intermediate input as in Antràs (2003); but in my model firms have to bear
all of the cost as suppliers get zero profit.

1.5.2

Effect of the Domestic Labor Market Cost on Firms’ Decision

One benefit of using the proposed model is that we can derive analytic solutions of Θd ,
Θu , and Θ f in all types of equilibria. With these, we can analyze the effect of the domestic
labor market cost on individual firms’ decision.
Equilibrium values of the zero profit cutoff in all types are summarized in Table 1.1.
Note that unlike all the other equilibria, in Type 1, Θd does not depend on the domestic
labor market cost. This means that as long as b lies in a range which supports Type 1
equilibrium, changes in b do not change the zero profit cutoff. It turns out that changes in
b are completely offset by changes in the quantity index in the differentiated-goods sector,
Q, so that the profit level of an individual firm remains the same. For three other types
of equilibria, we can do comparative statics to determine the effect of changes in b on Θd
and it turns out that Θd decreases in b in all of them.

24

Table 1.1: Three Productivity Cutoffs
Θd
fd
f e ( α −1)

Type 1

1/α

Θu

Θf

-

-

Θm

k1 Θd 1

-

Θm

-

k3 Θd 3

k1 Θd

k2 Θd 2

Θm

1/α

Type 2

α
f d +k−
1 fu
f e ( α −1)

Type 3

α
f d +k−
3 ff
f e ( α −1)

Type 4

α
−α
f d +k−
1 f u +k2 ( f f − f u )
f e ( α −1)

1/α

1/α

Θm

1

k1 = f u / f d (1 + β)1/(1− β) (b/pu ) β/(1− β) − 1

2

k2 = f f − f u / f d

3

k3 = f f / f d

b/b f

b/b f
β/(1− β)

β/(1− β)

−1

−1

− (1 + β)1/(1− β) (b/pu ) β/(1− β)

−1

−1

To understand this result, let’s see the equilibrium conditions of Type 1. Once we
derive Θd as in Table 1.1, we use the zero profit cutoff condition,

π d ( Θ d ) = (1 − β )

1
1+β

1
1− β

β
b

β
1− β

β−ς

Q

− 1− β

Θd − f d = 0,

(1.27)

to get the equilibrium level of Q. From here, we can see that in Type 1 equilibrium, the
production index should be adjusted to cancel out the changes in b, as Θd is unaffected
by that. This means that if firms in Type 1 face a higher domestic labor market cost, they
reduce production quantities to make the profit level the same. And the reduced Q makes
the profit curves of Outsourcing and FDI steeper, as firms with either of them now enjoy
higher domestic prices.
When the profit curve of FDI or Outsourcing becomes steeper than DI, firms with
a high productivity level start to choose offshoring (Type 2 or Type 3). Now, firms that
choose offshoring are not affected by the changes in the domestic labor market cost as they
do not hire domestic labor. So the changes in Q cannot fully absorb all of the effects of the
changes in b, and the profit level of firms that choose DI start to decrease. This process in

25

turn forces more firms to exit (increase in Θd ), and thus the average productivity level is
increased.
And this process continues as b increases. The profit level of DI decreases, and that
of offshoring increases. Thus, in both Type 2 and Type 3 equilibria, more firms exit (Θd
increases), while more firms choose offshoring. This result implies that Θu in Type 2 and
Θ f in Type 3 decreases in b.
Even in Type 4 equilibrium, Θd will increase as b increases. Although it is difficult to
predict the movement of two other cutoffs, it turns out that we can prove both Θu and Θ f
decreases in b. Intuitively, this result is driven by the following fact: the relative benefits of
selecting FDI instead of Outsourcing do not depend on b. As we have seen in the Section
1.4.1,

Af
Au

does not include any terms containing b. As b increases, the relative benefits of

choosing Outsourcing or FDI compared to DI increases; but its effect is not biased toward
a certain choice, i.e., both Θu and Θ f decrease. Above discussion can be summarized in
the following proposition.
Proposition 4. As b increases, while keeping b f and pu fixed,
1. Θd is not affected in Type 1 equilibrium,
2. Θd increases in Type 2, Type 3, and Type 4 equilibrium,
3. both Θu and Θ f decrease,
4. average firm productivity in the differentiated-goods sector increases.
Proof. In Appendices

1.5.3

Economic Implications of Offshoring

This model predicts how firms’ organizational decision is made across heterogeneous
firms when three possible choices are given. To see the economic implications of having
these options, let’s think about an autarky equilibrium, where offshoring is not allowed.
26

In autarky, firms cannot choose offshoring, and thus the equilibrium will stay in Type
1. As discussed in the previous chapter, in Type 1, Θd remains at the same level and Q
decreases when b increases. Considering the indirect utility function of this economy,
V = E+

1− ζ ζ
ζ Q ,

these results imply that the welfare level of the autarky equilibrium

decreases.
To compare the welfare level in autarky with that of an economy where offshoring is
allowed, let’s check the zero profit cutoff condition in both cases. In both economies, Q is
defined by Equation (1.27):
− 1− β
QA

β−ζ

1 + β b (1 + β )
=
1−β
β

β−ζ

1 + β b (1 + β )
=
1−β
β

− 1− β
QO

β
1− β

β
1− β

fd
,
Θd,A
fd
,
Θd,O

where subscript A denotes the autarky equilibrium and O denotes an equilibrium with
offshoring. By dividing one equation with the other, we get
QO
QA

β−ζ

− 1− β

=

Θd,A
.
Θd,O

(1.28)

By Proposition 4, when b is sufficiently large, the right hand side of Equation (1.28)
is smaller than one, and thus QO is greater than Q A (they will be the same if b lies in
a region that support Type 1 equilibrium). Simply taking a derivative with respect to b
in Equation (1.28), we can prove that

QO
QA

increases in b.8 These are summarized in the

following proposition.
Proposition 5. The welfare level of an economy with offshoring is
1. higher than that in autarky
2. and the difference between the welfare levels increases in b.
8 It

can also be shown that Q in all types of equilibria decreases in b.

27

Now, let’s discuss the hiring level of domestic workers and the unemployment rate in
this model. By using the same trick of Equation (1.28) with Equation (1.12), we get
hO ( Θ )
=
h A (Θ)
As

QO
QA

QO
QA

β−ζ

− 1− β

.

(1.29)

> 1, we can see that the hiring level of individual firms in autarky is higher than

that of the offshoring equilibrium.
Moreover, under the Pareto assumption that I made, the number of firms that choose
DI is smaller in the offshoring equilibrium. Thus, we can conclude that the total hiring,
H, is smaller in an economy with offshoring (of course, if the economy stays in Type 1
equilibrium even though offshoring is allowed, Q and H will be the same).
The economy-wide unemployment rate is defined as

u = ( N − H ) /L = (b − 1) H/L,

(1.30)

where the second equality holds by Equation (1.24). From here, we can see that the unemployment rate equals zero when b = 1. When b goes to infinity, the term 1 −

1
b

will

get closer to one, but as H approaches zero, the unemployment rate will also go to zero.
Thus, as b increases, we would expect a bell-shaped unemployment rate curve.
The bell-shaped unemployment rate curve is driven by the labor movement across
two sectors. As b increases, more workers enter the differentiated-goods sector, as higher
b means a higher wage level. However, as the total hiring, H, decreases at the same time,
workers realize that the probability of getting a job in the differentiated-goods sector becomes lower and they choose the other sector. Even though this process hinders workers
from entering the diffentiated-goods sector in both the offshoring equilibrium and the autarky equilibrium, it is much slower in autarky. In the offshoring equilibrium, increased
labor market inefficiencies make firms choose offshoring, and thus adjustment in H is
more dramatic than in autarky. With lower H, more workers choose the homogeneous

28

sector, and thus the unemployment rate in the offshoring equilibrium becomes lower than
that in autarky. Analytically, this is an obvious result, as H in autarky is higher than that
in the offshoring equilibrium, and Equation (1.30) tells us, at a given level of b, higher H
leads to a higher unemployment rate.
Proposition 6. In an economy with offshoring, the total hiring in the differentiated-goods sector
and the unemployment rate are lower than those in autarky.
Figure 1.1: Autarky vs. Offshoring equilibrium
Q

d

0.020

4

Autarky
Offshoring

3

0.015

2

0.010
Autarky

1

0.005

Offshoring

1.5

2.0

2.5

3.0

b

1.5

2.0

H

2.5

b

3.0

Unemployment
0.8

Autarky
0.15

Offshoring

Autarky
Offshoring

0.6
0.10
0.4
0.05
0.2

1.5

2.0

2.5

3.0

b

2

4

6

8

10

b

For illustrative purposes, I simulate the model with parameter values that support
the second path (Type 1→Type 2→Type4).9 From Figure 1.1, we can see that the total
hiring in the differentiated-goods sector and the economy-wide unemployment rate are
lower in the offshoring equilibrium. We can also find that the total output is higher, and
the zero profit cutoff is increasing in b in the offshoring equilibrium. All of these results
are fundamentally driven by the fact that offshoring allows the economy more options to
used b f = 1.2, pu = 3, f d = 5, f u = 10, f f = 15, f e = 4, Θm = 1, α = 1.5, ζ = 0.2, β = 0.6 for this
example.
9I

29

react to the increased inefficiencies in the labor market. By choosing offshoring, firms can
prevent the quantity from dropping too much, and this is the main source of the welfare
gains in this economy.

1.6

CONCLUSION

In this paper, I studied an economy with two sectors where the labor market in one is
under search and matching frictions. By focusing on four types of equilibria, I find that
the welfare level of the economy decreases as the labor market inefficiency increases.
Increased labor market inefficiency makes more firms choose offshoring, in which foreign labor is used and more firms exit. As firms with a high-productivity level choose
to offshore and firms with a low-productivity level exit, the average productivity level
increases. Since fewer firms hire domestic labor, total hiring is reduced and total output decreases in the differentiated-goods sector. As the increased wage level and the
decreased total hiring cause the economy-wide unemployment rate to move in different
directions, it shows a bell-shaped curve.
I also analyzed the economic implications of offshoring by comparing the offshoring
equilibrium with the autarky equilibrium. In the offshoring equilibrium, the welfare level
is weakly higher and the economy-wide unemployment rate is weakly lower than those
in the autarky equilibrium. This implies that even though offshoring reduces the size of
total hiring, it does help the economy by lowering the unemployment rate and lifting the
welfare level. It is interesting to note that the clear prediction of the unemployment rate is
driven by the assumption of a frictionless labor market in the homogeneous-good sector.
With this assumption, the impact of the reduced total hiring in the differentiated-goods
sector can be absorbed by the homogeneous-good sector. This is similar to Mitra and
Ranjan’s (2010) finding that offshoring decreases the economy-wide unemployment rate
when perfect inter-sectoral mobility is satisfied. In both papers, the impact of offshoring
on the unemployment rate depends on whether or not the other sector can partly absorb
30

the negative effects of offshoring on unemployment.
It may be interesting to extend the proposed model in this study by relaxing the assumption of a frictionless labor market in the homogeneous-good sector; but the main
point of this model will still be the same: the difference in the labor market cost across
countries is the key factor that determines a firm’s decision on offshoring. Only with the
labor market frictions is this model able to produce the same segregation result that was
found in previous studies.10 This result hints that the full employment assumption which
was used in many previous studies could be too strong in analyzing the motivation of
offshoring.

10 See

Antràs and Helpman (2004) and Helpman et al. (2004).

31

APPENDIX

32

Appendix for Chapter 1
Equilibrium Conditions for Type 1, Type 2, and Type 3
Equilibrium with DI (Type 1)
Suppose that there only exist Domestic Integration in equilibrium. This happens when
gains from offshoring are not enough to cover the fixed organizational costs.
Lemma 3. The sufficient condition for Type 1 equilibrium are

(1 + β )

1
1− β

β
1− β

b
pu

≤ 1 and

b
bf

β
1− β

≤ 1.

Proof. The first condition comes from Au ≤ Ad and the second condition comes from
A f ≤ Ad . As I assume f f > f u > 0, these two conditions ensure Type 1 equilibrium.
In Type 1 equilibrium, there only exist zero profit cutoff, which is defined by Equation
(1.16a). Other equilibrium conditions for Type 1 will become as following:
∞
Θd

πd (Θ)dG (Θ)

(free entry)

fe =

(labor market)

x (1 − σ)w¯ = 1

(average wage)

w¯ =

(total hiring)

H=M

(total output)

∞
Θd w ( Θ ) hd ( Θ ) dG ( Θ )
∞
Θd hd ( Θ ) dG ( Θ )

M
H

Q=M

1
β

∞
Θd

qd

(Θ) β dG (Θ)

1
β

Equilibrium with DI and Outsourcing (Type 2)
Type 2 equilibrium exists when the benefits of choosing Outsourcing dominate those of
choosing FDI.
Lemma 4. Sufficient conditions to have Type 2 equilibrium are

33

1

1. (1 + β) 1−β
1

2. (1 + β) 1−β

b
pu
b
pu

β
1− β

β
1− β

> 1 & (1 + β )
−1 <

− 1−1 β

pu
bf

β
1− β

≤ 1,

fu
fd .

Proof. The first condition comes from Ad < Au & A f ≤ Au . And the second condition
comes from Θd < Θu .
In Type 2, there exist two cutoffs, zero profit cutoff, Θd , and Outsourcing cutoff, Θu .
Other equilibrium conditions will be modified as following:
Θu
Θd

πd (Θ)dG (Θ) +

(free entry)

fe =

(labor market)

x (1 − σ)w¯ = 1

(average wage)

w¯ =

(total hiring)

H=M

(total output)

πu (Θ)dG (Θ)

Θu
∞
Θd w ( Θ ) hd ( Θ ) dG ( Θ ) + Θu w ( Θ ) hu ( Θ ) dG ( Θ )
Θu
∞
Θd hd ( Θ ) dG ( Θ ) + Θu hu ( Θ ) dG ( Θ )

M
H

Q=M

∞
Θu

1
β

Θu
Θd

qd

(Θ) β dG (Θ) +

∞
Θu

qu

(Θ) β dG (Θ)

1
β

Equilibrium with DI and FDI (Type 3)
Type 3 equilibrium exists when the benefits of choosing FDI dominates those of choosing
Outsourcing.
Lemma 5. Sufficient conditions to have Type 3 equilibrium are
1.

b
bf

2.

b
bf

β
1− β

β
1− β

> 1 & (1 + β )
−1 <

ff
fd

&

ff
fu

− 1−1 β

pu
bf

(1 + β )

β
1− β

1
1− β

> 1,
b
pu

β
1− β

−1 <

b
bf

β
1− β

− 1.

Proof. The first condition comes from Ad < A f & Au < A f . The second condition comes
from Θd < Θ f & Θ f < Θu .
In Type 3, two cutoffs exist, zero profit cutoff, Θd , and FDI cutoff, Θ f . Other equilibrium conditions will be modified as following:

34

Θf
Θd

πd (Θ)dG (Θ) +

(free entry)

fe =

(labor market)

x (1 − σ )w¯ = 1

(average wage)

w¯ =

(total hiring)

H=M

(total output)

π f (Θ)dG (Θ)

Θu
∞
Θd w ( Θ ) hd ( Θ ) dG ( Θ ) + Θu w ( Θ ) hu ( Θ ) dG ( Θ )
Θf
∞
Θd hd ( Θ ) dG ( Θ ) + Θ f h f ( Θ ) dG ( Θ )

M
H

Q=M

∞
Θf

Θf
Θd

1
β

qd

(Θ) β dG (Θ) +

∞
Θf

qf

(Θ) β dG (Θ)

1
β

Proof of Proposition 4
The zero profit cutoff (Θd )
Before proceeding further, let’s define

R1 ≡

and
Af
R2 ≡
=
Ad
One can easily show that

dR1
db

b
pu

1
Au
= ( 1 + β ) 1− β
Ad

> 0 and

dR2
db

b
bf

β
1− β

β
1− β

.

> 0. It is also convenient to define k1 , k2 , and

k3 as

k1 =
k2 =
k3 =

For Type 2 equilibrium, Θd =

fu
( R 1 − 1 ) −1 ,
fd
f f − fu
( R 2 − R 1 ) −1 ,
fd
ff
( R 2 − 1 ) −1 .
fd

1/α
α
f d +k−
1 fu
f e ( α −1)

35

Θm . By taking a derivative with respect to

b, we get



dΘd
dΘd dk1
=
= −

db
dk1 db

α
f d + k−
1 fu

1
α −1

f e ( α − 1)

For Type 3 equilibrium, Θd =




fu
fu
dR1
α −1
k−
Θm
−
1
2

f e ( α − 1)
f d ( R1 − 1) db

α
f d +k−
3 ff
f e ( α −1)

1/α

> 0.

Θm . By taking a derivative with respect to

b, we get



dΘd dk3
dΘd
=
= −

db
dk3 db

α
f d + k−
3 fu

f e ( α − 1)

For Type 4 equilibrium, Θd =

1
α −1




fu
dR2
fu
α −1
−
k−
Θm
3
2

f e ( α − 1)
f d ( R2 − 1) db

−α
α
f d +k−
1 f u +k2 ( f f − f u )
f e ( α −1)

1/α

Θm . As both k1 and k2 depend

on b, we have to check the sign of
∂Θd dk1 ∂Θd dk2
dΘd
=
+
,
db
∂k1 db
∂k2 db
where

dk1
db

= −f

fu
d ( R1 −1)

2

dR1
db

< 0. We can find signs of other three parts as

−α
α
f f − fu
f d + k−
1 f u + k2
f e ( α − 1)

1/α−1

∂Θd
=−
∂k1

α
−α
f d + k−
f f − fu
1 f u + k2
f e ( α − 1)

1/α−1

∂Θd
=−
∂k2

f f − fu
dk2
=−
db
fd

1
R2 − R1

2

Θm

fu
k−α−1 < 0,
f e ( α − 1) 1

Θm

f f − f u − α −1
k
< 0,
f e ( α − 1) 2

β ( R2 − R1 )
< 0.
(1 − β ) b

The inequality of the last equation holds because, in Type 4, R2 =

36

> 0.

Af
Ad

>

Au
Ad

= R1 .

Outsourcing cutoff (Θu ) and FDI cutoff (Θ f )
In Type 2 equilibrium, we have one additional cutoff,
Θu = k1 Θd .

Taking a derivative with respect to b, we get
0) and

dk1
db (<

dΘu
db

dk1
d
= k1 dΘ
db + Θd db . As the sign of

dΘd
db (>

0) are different, we have to solve for each term to see whether we could

determine the sign of the whole equation.
Let’s define B2 as

α
f d +k−
1 fu
.
f e ( α −1)

1/α
α
f d +k−
1 fu
f e ( α −1)

Then, Θd =

Θm ≡ B21/α Θm . Using this equa-

tion, we get
dΘu
dk1
dΘd
=
Θd +
k1
db
db
dk1
1
1
dk1
fu
−1
B2α Θm − B2α Θm
k −α
=
db
f e ( α − 1) 1
dk1 α1 −1
fd
=
B2 Θm
,
db
f e ( α − 1)
which is negative as α assumed to be greater than 1 and

dk1
db

< 0.

In Type 3 equilibrium, we have FDI cutoff,
Θ f = k3 Θd .
Let’s denote Θd = B31/α Θm by defining B3 ≡
dΘ f
db

α
f d +k−
3 fu
.
f e ( α −1)

Then, we get

dk3
dΘd
Θd +
k3
db
dk3
1
1
dk3
fu
−1
=
B3α Θm − B3α Θm
k −α
db
f e ( α − 1) 1
dk3 α1 −1
fd
B3 Θm
,
=
db
f e ( α − 1)

=

37

which is negative as

dk3
db

< 0.

Now, we have to check how two cutoffs react to changes in the labor market cost in
Type 4 equilibrium. Offshoring and FDI cutoffs are defined as
Θu = k1 Θd ,
Θ f = k2 Θd .
And by defining B4 ≡

α
−α
f d +k−
1 f u +k2 ( f f − f u )
,
f e ( α −1)

Θd =

we get

α
−α
f f − fu
f d + k−
1 f u + k2
f e ( α − 1)

1/α

Θm

≡ B41/α Θm .
As both k1 and k2 depend on b, we have to check the sign of
d(k1 Θd )
dΘ
dk
dΘu
=
= k1 d + Θd 1
db
db
db
db
to determine the sign of

dΘu
db .

We can calculate each part as

β
fu
R1
dk1
= −
,
db
b (1 − β ) f d ( R1 − 1)2
f f − fu
β
1
dk2
= −
,
db
b (1 − β ) f d ( R2 − R1 )

1
∂Θd
fu
−1
α −1
= −Θm B4α
k−
,
1
∂k1
f e ( α − 1)
1
∂Θd
−1 f f − f u − α −1
= −Θm B4α
k
.
∂k2
f e ( α − 1) 2

38

(1.31)

If we plug these four equations into the original equation, we get
2

1
f f − fu
dΘd
R1
−1
α −1
α −1
= B4α C
f u2 k−
+
k−
2
1
2
db
R
−
R
2
1
( R1 − 1)

where C = Θm f
k1 =

fu
fd

1

β
. If we
b (1− β )
f − fu
k 2 = f f ( R2
d

e f d ( α −1)

( R1 − 1)−1 and

plug this into (1.31), we getFinally, if we plug in

− R1 )−1 into the above equation, we get

1
dΘu
−1
= B4α C − f dα f u f f − f u
db

− α +1

R1 f d f u
( R2 − R1 ) α
−
( R1 − 1)2
( R1 − 1)2

which is negative as R2 > R1 and f f > f u .
Similarly, we can simplify
dΘ f
db

=

d(k2 Θd )
db

= k2
B4

as

dΘd
dk
+ Θd 2
db
db

1
α −1

=

dΘ f
db

C

R1

2

f 2 k − α −1 k 2
2 u 1

f f − fu
+
k −α
R2 − R1 2

( R1 − 1)
1
f f − fu
−1
α
−α
− B4α C
f + k−
f f − fu
1 f u + k2
( R2 − R1 ) d
1
fd f f − fu
f u f f − f u −α
R1
−1
2 − α −1
f
k
−
B4α C
k
k
−
2
u
1
1
( R2 − R1 )
( R2 − R1 )
( R1 − 1)2

=

.

If we plug in k1 and k2 into the above equation, we get
1
dΘ f
−1 f d f f − f u
= B4α C
db
R2 − R1

As α > 1 and

fu 1
f d R1 −1

fu 1
f d R1 − 1

is greater than one by the Lemma 2,

is also decreasing in b.

39

1− α

−1 .

1− α
fu 1
f d R1 −1

< 1, and thus Θ f

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40

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42

CHAPTER 2
Anonymity Concerns and Bitcoin
2.1

Introduction

Bitcoin is a peer-to-peer network-based electronic currency system. The key structure of
Bitcoin was initially proposed in Nakamoto (2008). After that, an open-source project was
initiated, and the first Bitcoin was created in January 2009. Since then, Bitcoin has gained
much attention from users and has had huge success. At the time of this writing, around
65,000 transactions are taking place each day using Bitcoin, grossing about 88 million USD
per day. While Bitcoin is a topic of interest in the media, its economic implications have
not been much studied.
A key question regarding Bitcoin is whether it can be a substitute for the traditional
currency system or not. To answer this question, we need to check how well Bitcoin can
perform the function of a medium of exchange. Even though it is being used for various
types of goods, this is not obvious. Indeed, the number of merchants who accept Bitcoin
is still relatively small and most of them are Internet-based merchants.
Moreover, considering the fact that we already have various types of currencies which
do not require additional knowledge on the technology essential for using Bitcoin, the
question naturally arises: why do people choose Bitcoin instead of traditional currencies? There could be different explanations; in this study, I use one of the most essential
properties of Bitcoin, its anonymity, to answer this question.
By using recent technical inventions on digital cryptography, Bitcoin has become the
first electronic currency system without having a trusted third party (e.g., central bank).
Instead, the system stands on a peer-to-peer network, allowing users to send Bitcoin with43

out having to go through financial institutions. Furthermore, Bitcoin users can hide their
identity by using different public keys when carrying out different transactions. This
property confers the most cash-like status to Bitcoin among the electronic currency systems.
At the same time, Bitcoin’s anonymity raises concerns regarding its role in illegal activities. Several governments regard using Bitcoin in some cases as unlawful because it
can be used for illegal activities.1 The online market ‘Silk Road,’ which intermediated
many prohibited goods with Bitcoin before it was shut down by the FBI, serves as a good
example of how Bitcoin can be associated with illegal activities. However, the relationship between the two is not clear, in the sense that people may still want anonymity in
legal activities. Even the ‘Silk Road’ had many categories of legal goods like art, books,
computer equipment, etc.
In this study, I propose a model in which an agent’s choice over currencies depends on
her anonymity concerns. In the model, two currency markets exist. In the Debit market,
Debit is used for trading goods; and in the Bitcoin market, Bitcoin is used for transactions. In the Debit market, agents have to reveal their identity in a transaction, while
in the Bitcoin market, they can hide their identity by using Bitcoin. At the beginning of
the economy, agents compare the expected value of entering each currency market and
choose one of them. Under this setting, I find that agents with high anonymity concerns
choose the Bitcoin market, while others choose the Debit market.
When I extend the model by adding intermediaries which accept Bitcoin only for legal
goods, I find that the number of agents who use Bitcoin increases, while the share of
Bitcoin users who are engaged in illegal activities decreases. This result tells us a way
of resolving concerns regarding the usage of Bitcoin in illegal activities: even though it
is not fully possible to control each individual’s use of Bitcoin due to its anonymity, it is
possible to reduce the extent of illegal activities associated with Bitcoin by regulating the
1 See

http://en.wikipedia.org/wiki/Legality_of_Bitcoins_by_country

44

intermediaries.
This study is related to several studies in the literature on search-theoretic models. The
basic structure of the model that I propose is based on Kiyotaki and Wright (1993), which
shows the existence of a monetary equilibrium where fiat currency solves the ‘double coincidence of wants problem’ in a pure barter. To introduce the role of intermediaries into
the model, I introduce a new currency market, where agents can trade legal goods with
Bitcoin. In the literature, intermediaries are introduced in several different ways. Rubinstein and Wolinsky (1987) introduce intermediaries as agents with the ability to buy
goods from producers and sell them to consumers; Shevchenko (2004) introduces middlemen to be agents who can hold inventories of several goods; and Li (1998) analyzes the
role of middlemen in a model with private information where agents become middlemen
by investing to acquire quality-testing technology.
The remainder of this paper is organized as follows. Section 2.2 introduces the environment and solves the model. Section 2.3 adds intermediaries. Section 2.4 offers a
summary of the analysis with concluding remarks.

2.2
2.2.1

Model
Environment

Consider an economy with a continuum of agents, measure one. Time is continuous and
agents live infinitely. Agents are heterogeneous in terms of their preference with respect
to anonymity concerns. More specifically, an agent i ∈ [0, 1] incurs a cost ci by revealing
herself to the other party during a trade, and the cumulative distribution function of ci ,
F (ci ), is common knowledge. ci and Agents’ preferences over goodsare specified in the
below. To motivate agents to trade, it is assumed that they cannot consume the good they
produce, i.e., they produce and engage in a pairwise random meeting to trade with other
agents.

45

In the economy, there exist two currency markets, the Debit market and the Bitcoin
market. Only one type of currency circulates in each market. In the Debit market, agents
produce a good X, which is not related to any illegal activities, while in the Bitcoin market, they produce a good Y, which is potentially associated with both legal and illegal
activities. For the purpose of this study, it is important to note that in the Bitcoin market,
it is not possible to distinguish legal from illegal activities.
At the beginning of the economy, agents choose one of the markets to produce and
consume goods. Debit and Bitcoin are randomly distributed after agents have made this
decision. Let µ be the measure of agents who choose the Debit market; and let 1 − µ be the
measure of agents who choose the Bitcoin market. Total D units of Debit and B units of
Bitcoin are distributed to each market. I assume that

D
µ

= d ∈ (0, 21 ] and

B
1− µ

= b ∈ (0, 21 ]

are constant over µ. Agents cannot produce currencies.
As in Kiyotaki and Wright (1993), all currencies and goods are assumed to be indivisible. Moreover, agents cannot hold more than one unit of goods or currencies. Thus, at
any given point in time, agents are holding either one unit of currency (Bitcoin or Debit)
or good.
Agents in each economy meet pairwise in a random meeting with an arrival rate of β.
When two agents meet, they observe the other agent’s inventory and decide whether to
trade or not. It is assumed that with probability x ∈ (0, 1), agents find a good that they
like, in which case a trade occurs and their inventories are swapped. Once a trade takes
place, agents who have consumed a good return to the production process. The production cost is assumed to be zero.2 Agents who received Debit or Bitcoin keep searching
until they find a counterpart with a desirable good.
Lastly, let me explain ci and agents’ preferences in more detail. ci is ordered to be
increasing in i so that it has the lowest value of zero when i = 0, and it has the highest
2 See

Kiyotaki and Wright (1993) for the same assumption.

46

value of cmax when i = 1:
ci ∈ [0, cmax ],

∂ci
> 0, ∀i.
∂i

When agents consume a good X, they obtain utility u. When they consume a good Y,
however, the utility level that they get depends on their level of anonymity concerns.
Agents with high anonymity concerns are assumed to get higher utility from consuming
a good Y because it can be purchased with Bitcoin, and thus they can hide their identity.
Specifically, an agent i gets utility of αci from a good Y. As an agent i perceives costs ci in
a transaction associated with Debit, the utility that an agent i gets from each good can be
summarized as

2.2.2

u X (i ) = u − ci

(2.1)

uY (i ) = αci , α > 0,

(2.2)

Value Functions

We can write the flow returns of choosing the Debit market as
g

rVD (ci ) = β (1 − d) x u X (i ) + VD (ci ) − VD (ci ) ,
g

g

rVD (ci ) = βdx VD (ci ) − VD (ci ) ,

(2.3)
(2.4)
g

where VD (ci ) denotes the value function of an agent who is holding a Debit, and VD (ci )
denotes the value function of a good producer in the Debit market. Equation (2.3) states
that the flow return to a Debit holder, VD (ci ), equals the probability that she meets someone who is holding a good that she likes, β (1 − d) x, multiplied by the sum of gains from
g

the trade and value changes, u X (i ) + VD (ci ) − VD (ci ). Equation (2.4) sets the flow return
g

to a good holder in the Debit market, rVD (ci ), equal to the probability of meeting a Debit
holder who likes the good that she produced, βmx, multiplied by changes in the value
g

functions, VD (ci ) − VD (ci ).
47

Similarly, we can denote the value functions of choosing the Bitcoin market as
g

rVB (ci ) = β (1 − b) x uY (i ) + VB (ci ) − VB (ci ) ,
g

g

rVB (ci ) = βbx VB (ci ) − VB (ci ) ,

(2.5)
(2.6)
g

where VB (ci ) denotes the value function of an agent who is holding a Bitcoin and VB (ci )
denotes the value function of a good producer in the Bitcoin market.

2.2.3

Equilibrium

Agents compare the expected values of entering either market and choose the market
with greater expected value. Using Equations (2.3), (2.4), (2.5), and (2.6), we can express
the expected values of entering each market as
g

EVD (ci ) = dVD (ci ) + (1 − d) VD (ci ) = d (1 − d) βxu X (ci ) /r,
g

EVB (ci ) = bVB (ci ) + (1 − b) VD (ci ) = b (1 − b) βxuY (ci ) /r,

(2.7)
(2.8)

where EV j (ci ) denotes the expected value entering the market j of an agent i. From the
above two equations, we can calculate the relative gain of choosing the Debit market as
d (1 − d ) u X ( c i )
EVD (ci )
=
.
EVB (ci )
b ( 1 − b ) uY ( c i )

(2.9)

The ratio depends on two components. The first component is the relative utility level of
a good X to a good Y for an agent i,

u x ( ci )
.
uY ( c i )

By setting Equation (2.10) equal to one, we can

derive the cutoff c∗ , with which the agent i∗ is indifferent between two currency systems
as
c∗ =

d (1 − d )
u.
αb (1 − b) + d (1 − d)

48

(2.10)

Figure 2.1: Equilibrium in the Benchmark Model
EVj

EVD
EVB
1

i

An agent i will simply compare her anonymity cost ci with the cutoff cost, c∗ , then decide
which currency system to enter. If ci is higher than c∗ , it will be better for the agent to
enter the Bitcoin market, while if it is lower than c∗ , she will be better off to choose the
Debit market.
The second component of Equation (2.9) is the relative matching efficiency of the
Debit market compared to that of the Bitcoin market,

d (1− d )
,
b (1− b )

which is governed by the

market structure. As the relative size of d compared to b increases, the relative matching
efficiency of the Debit market increases, and thus more agents choose the Debit market.
In other words, c∗ is an increasing function of d, and a decreasing function of b. We can
summarize this discussion in the following proposition.
Proposition 7. With the cutoff c∗ =

d (1− d )
u,
αb(1−b)+d(1−d)

agents with ci > c∗ choose the Bitcoin

market, while agents with ci < c∗ choose the Debit market. Moreover,

49

∂c∗
∂d

> 0 and

∂c∗
∂b

< 0.

2.3

A Model with the Intermediary Market

In this section, I extend the benchmark model into a model with the intermediary market.
I introduce the intermediary market as a place where agents produce a good X and trade
it with Bitcoin. As agents are forced to produce only good X in this market, unlike in
the Bitcoin market, no illegal activities are associated with Bitcoin. This is the key benefit
of using the intermediary market, i.e., agents can consume the legal goods and still keep
their identities. I assume that to participate in the intermediary market, agents pay a
fixed fee of p when they consume a good X. The total money supply of the intermediary
market is exogeneously given by B I .
The flow returns of an agent i who chooses the intermediary market are
g

rVI (ci ) = β (1 − b I ) x u − p + VI (ci ) − VI (ci ) ,
g

g

rVI (ci ) = βb I x VI (ci ) − VI (ci ) ,

(2.11)
(2.12)

where b I denotes the fixed share of Bitcoin holder; VI (ci ) is the value function of holding
g

Bitcoin; and VI (ci ) is the value function of a good producer in the intermediary market.
The interpretation of the value functions are similar to those of the other two currency
markets, except that agents can obtain u without losing ci , and in return for that they pay
the fixed transaction cost, p, whenever they consume goods.
Similar to the benchmark model, agents choose the currency market that gives the
highest expected value. Let µ1 and µ2 denote the measure of agents who choose the Debit
market and Bitcoin market, respectively. Then, we can express the expected value of

50

entering each market as

where d =

D
µ1 ,

b=

B
µ2 ,

EVD (ci ) = d (1 − d) βx (u − ci ) /r,

(2.13)

EVB (ci ) = b (1 − b) βxαci /r,

(2.14)

EVI (ci ) = b I (1 − b I ) βx (u − p) /r,

(2.15)

and b I =

BI
1− µ1 − µ2 .

By equalizing three pairs of equations, we can derive the three cutoff values of ci as
b (1 − b I )
b I (1 − b I )
u+ i
p,
d (1 − d )
d (1 − d )
b (1 − b I )
= I
( u − p ),
αb (1 − b)
d (1 − d )
u,
=
αb (1 − b) + d (1 − d)

c1 = u −
c2
c∗

where c1 is the cutoff value that equalizes the expected value of choosing the Debit and
intermediary markets; c2 is the cutoff value that gives the same expected value of choosing the intermediary and Bitcoin markets; and c∗ is the cutoff value that divides the Debit
and Bitcoin markets in the benchmark model.
Depending on realized parameter values, we can have different types of equilibria. In
Figure 2.2, I graph an example of equilibria with and without the intermediary market.
If c1 becomes equal or greater than c∗ , we have an equilibrium where no one chooses the
intermediary market. Instead, if c1 is smaller than c∗ , the intermediary market is used
by a positive mass of agents in the equilibrium. We can find the condition to have the
equilibrium with the intermediary market by solving the condition, c1 < c∗ < c2 , which
is identical to the following condition:

u>

a1 + αa2
p,
a1 + αa2 − αa3

51

(2.16)

where a1 = d (1 − d) b I (1 − b I ), a2 = b (1 − b) b I (1 − b I ), and a3 = d (1 − d) b (1 − b).
Lemma 6. Depending on the realized values of parameters, there exist two types of equilibria.
When u >

a1 +αa2
a1 +αa2 −αa3 p,

a1 +αa2
a1 +αa2 −αa3 p,

we have an equilibrium with the intermediary market; and when u ≤

we have an equilibrium without the intermediary market.

The economic interpretation of the condition in Equatioin (2.16) is quite simple: the
fee for using the intermediary market should be low enough to attract agents from Debit
or Bitcoin markets. If p is too high, no one will choose the intermediary market and
the equilibrium becomes the same as the benchmark case. On the other hand, as the fee
approaches zero, the expected value of choosing the intermediary market increases, and
thus more agents enter the intermediary market.3
Another parameter that affects the condition in Equation (2.16) is d, b, and b I . By taking the derivative of
b I (1− b I )
d (1− d )

or

b I (1− b I )
b (1− b )

a1 +αa2
a1 +αa2 −αa3 p with respect to the three parameters, we can verify that as

increases, it becomes easier to satisfy the condition in Equation (2.16).

The intepretation of this result is similar to the benchmark case: as the relative matching
efficiency in the intermediary market increases, it becomes easier to attract agents to the
intermediary market.
Figure 2.2: Equilibrium with the intermediaries
EVj

EVj

EVD
EVB
EVI

EVD
EVB
EVI
1

i

1

3 If

i

α ≤ 1, all agents choose the intermediary market. If α > 1, a positive mass of agents choose the
Bitcoin market.

52

Let us focus on the equilibrium with the intermediary market. As we can see in Figure
2.2, agents with ci between c1 and c2 , who would have chosen the Debit or Bitcoin markets
in the benchmark model, choose the intermediary market. They choose the intermediary
market to seek either Bitcoin’s anonymity or to consume the legal goods. Agents from
c1 to c∗ are the first case, and agents from c∗ to c2 are the latter case. Thus, compared to
the equilibrium of the benchmark model, we can see that more agents use Bitcoin as a
medium of exchange, but fewer agents choose the Bitcoin market. So among the agents
who use Bitcoin, the share of agents who are possibly associated with illegal activities
becomes smaller than that in the benchmark model.
This result implies that the existence of a well-regulated intermediary market can not
only enhance the acceptability of Bitcoin, but also reduce the size of Bitcoin usage associated with illegal activities. Considering the fact that it is almost impossible to regulate an
individual agent’s activities with Bitcoin, this result shows an alternative way of controlling the illegal usage of Bitcoin, while keeping the benefits from the electronic currencies.
Let us summarize the above discussion by the following propositions.
Proposition 8. When u >

a1 +αa2
a1 +αa2 −αa3 p,

an agent i chooses

1. the Debit market if ci < c1 ,
2. the intermediary market if c1 < ci < c2 ,
3. the Bitcoin market if c2 < ci .
Proposition 9. As the benefit from choosing the intermediary market increases, fewer agents
choose Debit and more agents choose Bitcoin as currency. Also, as more agents choose the intermediary market, the number of agents who are associated with illegal activities decreases.

53

2.4

CONCLUSION

In this study, I propose a simple search-theoritic model where Debit and Bitcoin compete
with each other. In the model, agents compare the expected values of entering each market and decide which currency market to enter. In the benchmark model, where only
the Debit and Bitcoin markets exist, I show that the agents’ preferences regarding the
anonymity concerns drive some agents to choose the Bitcoin market. In the extended
model where the intermediary market is introduced, agents choose the intermediary market to have both Bitcoin’s anonymity and consumption of legal goods.
The results of this model are quite simple, but they are meaningful, considering the
general concerns regarding the relationship between Bitcoin and illegal activities. The
model shows that even if the fundamental motivation of using Bitcoin lies in the anonymityseeking behaviors, its relationship with illegal activities is not clear and can be reduced
by having well-regulated intermediaries. It also shows that introduction of intermediaries
has a positive effect on the acceptability of Bitcoin among agents.
As this study is based on quite a simple model, it cannot capture various aspects of the
demands of Bitcoin. However, by focusing on the key aspects of Bitcoin that distinguish
it from other electronic currency systems, this model clearly shows that agents’ desire
to protect their identity can be a source of fundamental motivation to use anonymous
electronic currencies, and the demand can be enhanced and controlled by having wellregulated intermediaries.

54

REFERENCES

55

REFERENCES

Kiyotaki, N., and R. Wright. 1993. “A Search-Theoretic Approach to Monetary Economics.” American Economic Review, 83(1): 63–77.
Li, Y. 1998. “Middlemen and private information.” 42(December 1996): 131–159.
Nakamoto, S. 2008. “Bitcoin : A Peer-to-Peer Electronic Cash System.”
Rubinstein, A., and A. Wolinsky. 1987. “Middlemen.” The Quarterly Journal of Economics,
102(3): 581–594.
Shevchenko, A. 2004. “Middlemen.” International Economic Review, 45(1): 1–24.

56

CHAPTER 3
FDI vs. outsourcing: the Role of Labor
Market Flexibility
3.1

Introduction

The literature has focused on multinational firms’ activities, and many studies have tried
to identify the key determinants of the decision between foreign direct investment (FDI)
and outsourcing when multinationals offshore. Several aspects in heterogeneity across
industries have been identified as the key determinants in that decision.
However, institutional heterogeneity across countries, which can possibly be an important factor, has not been discussed much. Suppose that a multinational firm tries to
enter several foreign markets. If there exists a substantial heterogeneity in the institutional structures across those markets, then the organizational choice in each market can
depend on each markets’ institutional structure.
In particular, this study takes heterogeneity in labor market flexibility across countries
to be the key factor that affects the decision. Chapter 1 proposed a theoretical model that
shows how labor market flexibility affects firms’ organizational decision. Under the assumption that the fixed cost of FDI is greater than that of outsourcing, the model predicts
that for a country with low labor market flexibility, outsourcing is the optimal choice for
all firms, while for a country with high labor market flexibility, FDI can be chosen for the
most productive firms.
In this study, I test the above prediction by using the data set for 2006 through 2012
from the U.S. Census related-party trade and the Global Competitiveness Report (GCR)

57

on labor market flexibility. The data yields supporting results for the first chapter: the
share of intrafirm import is positively correlated with the industry productivity dispersion only in the countries with the most flexible labor market. For countries with a rigid
labor market, I cannot find a positive relationship between the two.
This study is related to several studies in the literature. Most studies on this topic
focus on the relationship between a multinational firm (the headquarter) and an intermediate goods supplier. In their model, a multinational firm and a supplier produce
relationship-specific inputs. As inputs produced in the relationship have zero value outside the relationship, if the contract between the two parties is not complete, a typical
‘hold-up’ problem arises, and both parties tend to under-invest. Under these circumstances, when the headquarter firm provides more services, motivating the headquarter
firm reduces the size of underinvestment. As FDI gives higher outside options when the
bilateral bargaining breaks down, choosing FDI becomes optimal. Similarly, when the
service from the supplier is more important, choosing outsourcing becomes optimal.
Antràs (2003) developed the incomplete-contract and property-rights model with the
idea, and also found supporting estimation results by using the U.S. trade data from the
Bureau of Economic Analysis (BEA). This study is further developed in Antràs and Helpman (2004) and Antràs and Helpman (2006). In their 2004 study, Antras and Helpman
introduced heterogeneity in firms’ productivity level; and in their 2006 study, they allowed partial contractibility in the relationship.
Several studies have tried to empirically test theoretical results in the above models. Yeaple (2006) tested Antràs (2003) and Antràs and Helpman (2004) with the 1994
Benchmark Survey from BEA. This paper examined how industry-specific variables affect the intrafirm import/export of U.S. multinationals, and found that capital intensive
industries and R&D intensive industries are associated with higher intrafirm trade. It
also found that an industry with higher productivity dispersion has a greater share of intrafirm trade. This result is further strengthened in Nunn and Trefler (2013), which used

58

a much larger number of data from the 2005 U.S. Census trade and found supporting
results. Nunn and Trefler (2013) also tested the key implication of Antràs and Helpman (2006), that better contracting leads to more internalization, and found consistent
results. However, all of the empirical studies above have focused on industry characteristics rather than country characteristics, a key focus of this paper.
This study is organized as follows. Section 3.2 introduces the theoretical model and
summarizes its key implications. Section 3.3 explains the primary measures and data
used, and Section 3.4 sets up the empirical specification. Section 3.5 shows and explains
the estimation results, and finally Section 3.6 summarizes the analysis.

3.2

Theoretical Model

Let us begin by reviewing the key features of the model proposed in the first chapter. A
firm located in the home country produces differentiated goods and the demand is set
by CES preferences. A firm produces by using the only input, labor. When it decides to
produce, it has three different options regarding its organizational form. It can produce
in the home country by hiring domestic workers or it can offshore the production process
by forging an arm’s-length relationship with a supplier (outsourcing) or hiring foreign
labor (FDI). As in Helpman and Itskhoki (2010), the production technology is defined to
be linear to the number of inputs, h,

q(θ ) = θh,

(3.1)

where θ is the productivity parameter and h represents either domestic labor (domestic
integration), intermediate inputs (outsourcing), or foreign labor (FDI).
There are two countries in the model, home and foreign. Labor markets in both countries are under search and matching frictions, and thus a firm bears not only wages, but
also an additional cost (labor market cost) when it hires workers. This additional cost

59

from the labor market is assumed to be different across countries. So, when the labor
market cost of the foreign country is lower than that of the home country, a firm has an
incentive to choose offshoring as it can reduce the variable cost indirectly (outsourcing)
or directly (FDI).
Wage is determined in a generalized Nash bargaining procedure. It is also assumed
that offshoring comes with an additional fixed organizational cost, where the fixed cost of
outsourcing is lower than that of FDI. Under this setting, a firm faces a new tradeoff that
was not recognized in previous studies: outsourcing allows a firm to avoid dealing with
the labor market directly, and thus it can keep all of the revenue without sharing it with
the labor. With FDI, a firm has to share the total revenue with the labor, but FDI offers a
lower variable cost than outsourcing.
Specifically, with the constant measure of the elasticity of substitution β,1 the profit
function of each choice is given as
πu (θ ) = Au ( Q, b, pu ) Θ − f u ,

(3.2)

π f (θ ) = A f Q, b, b f Θ − f f ,

(3.3)

β

where Θ = θ 1−β is the measure of productivity, Q is the quantity index in the differentiated goods sector, b is the labor market cost of the home country, pu is the unit price of
an intermediate input, and b f is the foreign labor market cost that a final good producer
from a home country faces.
Figure 3.1 shows two types of equilibria depending on the relative size of Au and A f .
Both graphs plot two profit curves, outsourcing and FDI, as a function of productivity
β

measure Θ = θ 1−β . Given the assumption of the fixed cost, f f > f u , we know that an
offshoring firm always chooses outsourcing if Πu (Θ) is steeper than Π f (Θ) . This case
is shown in the left-hand graph of Figure 3.1, where choosing outsourcing always gives a
1 The

elasticity of substitution σ is defined to be

1
1− β .

60

Figure 3.1: Equilibrium Type and The Labor Market Flexibility
Πj

Πj

1

Θ

1

Πu
Πf

Θ

Πu
Πf

higher profit level for all firms.
When b f is sufficiently lower than pu , Π f (Θ) becomes steeper than Πu (Θ). This case
is shown in the right-hand graph of Figure 3.1. In this case, two profit curves must cross
once, and firms with a productivity level to the right of the crossing point choose FDI,
while firms to the left of the point choose outsourcing.
From this figure, we can see that the relationship between the productivity level and
the share of firms that choose FDI is only valid when A f > Au . In other words, if the
underlying conditions do not support the equilibrium with FDI, heterogeneity in productivity does not affect firms’ organizational choices. More specifically, the ratio between
Au and A f is given as
1
Au
= ( 1 + β ) 1− β
Af

bf
pu

,

(3.4)

where pu is the unit price of intermediate input, which is assumed to be greater than b f .
In this equation, we can see that the ratio increases in b f , while it decreases in pu . As the
labor market cost that an FDI firm faces becomes smaller, the relative benefits from FDI
increase, when pu is fixed.
These results lead us to an interesting empirical prediction about offshoring firms’
organizational decision: the productivity level of an offshoring firm affects its organizational choice only for the host (foreign) countries with a sufficiently low labor market

61

cost.

3.3

Data Sources and Measurement

To test the hypothesis, we need a proper measure to compare the size of FDI and outsourcing. For this, I use the related-party trade data from the U.S. Census Bureau. This
data is compiled from U.S. customs documentation which includes a yes or no mandatory question whether a shipment is between related parties or not. For U.S. imports,
related-party trade is defined to be a trade between two parties in which one party has,
directly or indirectly, “5 percent or more of the outstanding voting stock or shares of any
organization.” For U.S. exports, two parties are defined to be ‘related’ if one party owns,
directly or indirectly, “10 percent or more of the other party”.2
This information allows me to distinguish intrafirm imports from all imports as I can
treat the related-party imports as intrafirm, while I treat the non-related party import
as outsourcing. All data is at the 6-digit North American Industry Classification System
(NAICS6) level and each observation has information on the origin (country) of the goods
and whether the import is from a related party or not. With the data, I set up the key
dependent variable, the share of intrafirm imports, as
V
I Mict
V + I MO
I Mict
ict

,

(3.5)

where I MV denotes the related-party imports and I MO denotes the unrelated-party imports. Subscripts i, c, and t mean industry, country, and year.
2 See Ruhl (2013) for more detailed information on the comparison between the U.S. Census Bureau
related-party data and the BEA intrafirm trade data.

62

Table 3.1: Labor Market Flexibility Index (2012) by Developed/Developing Countries
Developing Countries

Developed Countries

Name
Flexibility
Name
Venezuela
2.54
Kuwait
Zimbabwe
2.54
Senegal
Bolivia
3.09
Nicaragua
Mozambique
3.15
Mali
Uruguay
3.25
Jamaica
Ecuador
3.31
Gambia
Sri Lanka
3.44
Suriname
Egypt
3.52
Malawi
Indonesia
3.55
Serbia
Ghana
3.58
Cambodia
Nepal
3.61
Chad
Zambia
3.64
Albania
Honduras
3.69
Taiwan
South Africa
3.71
Peru
Sierra Leone
3.72
India
Iran
3.82
Madagascar
Algeria
3.84
Benin
Thailand
3.96
Costa Rica
Philippines
3.99
Cameroon
Trinidad And Tobago
4.02
Ukraine
Libya
4.1
Mauritania
Montenegro
4.1
Nigeria
Turkey
4.11
Kenya
Bangladesh
4.18
Haiti
Botswana
4.19 Bosnia And Herzegovina
Liberia
4.19
Timor-Leste
Paraguay
4.21
Macedonia
Brazil
4.22
Guyana
Yemen
4.24
Malaysia
Pakistan
4.24
Mauritius
Dominican Republic
4.26
Bulgaria
Mexico
4.27
Kyrgyzstan
Ethiopia
4.28
Jordan
Russia
4.29
Azerbaijan
Lesotho
4.29
Burkina Faso
China
4.3
Rwanda
Morocco
4.33
Cote D’Ivoire
Swaziland
4.33
Lebanon
Moldova
4.35
Saudi Arabia
Romania
4.35
Mongolia
Burundi
4.36
Guinea
Gabon
4.39
Kazakhstan
El Salvador
4.42
Georgia
Colombia
4.44
Armenia
Panama
4.45
Uganda
Guatemala
4.45
Oman
Namibia
4.46
Bahrain
Vietnam
4.46

Flexibility
Name
Flexibility
4.46
Argentina
2.9
4.5
Portugal
3.38
4.5
Greece
3.62
4.51
South Korea
3.85
4.53
Spain
3.91
4.53
Italy
3.94
4.54
Germany
3.97
4.59
Slovenia
4
4.59
Croatia
4.13
4.62
France
4.15
4.66
Slovakia
4.17
4.67
Lithuania
4.23
4.7
Belgium
4.25
4.71
Czech Republic
4.25
4.71
Israel
4.32
4.73
Sweden
4.32
4.73
Malta
4.33
4.74
Australia
4.35
4.75
Luxembourg
4.4
4.76
Austria
4.51
4.77
Finland
4.57
4.79
Hungary
4.58
4.79
Barbados
4.6
4.81
Norway
4.6
4.81
Poland
4.71
4.82
Seychelles
4.76
4.86
Netherlands
4.76
4.89
Chile
4.76
4.9
Cyprus
4.85
4.9
Latvia
4.91
4.91
Ireland
5.01
4.92
Japan
5.07
4.92
Iceland
5.09
4.93
Qatar
5.16
4.94
Estonia
5.28
4.96
United Kingdom
5.33
5.01
Denmark
5.37
5.02
Canada
5.38
5.08
New Zealand
5.45
5.15
Brunei
5.52
5.16 United Arab Emirates
5.88
5.22
Switzerland
5.91
5.26
5.28
5.34
5.41
5.61

For labor market flexibility, I use the Global Competitiveness Report (GCR) by the
World Economic Forum. Even though there are several other measures to compare labor
market flexibility across countries, the GCR report covers the greatest number of countries
in its survey. In the period of 2012-2013, 144 countries are included. By using this data, I
63

can utilize most of the U.S. import data in the following empirical test.
In the GCR report, the labor market flexibility is compiled with four different measures: hiring and firing practices, flexibility of wage determination, cooperation in the
labor-employer relationship, and redundancy cost. Except for redundancy cost, all measures report numbers from 1 to 7, where 1 is the most rigid and 7 is the most flexible.
The redundancy cost is reported as ‘weeks of salary,’ and to use this properly, we have
to recalculate it in terms of ‘cost’ by multiplying it by the average weekly salary. However,
as average wage data cover a small number of countries compared to the GCR report, I
do not use the redundancy cost measure in the analysis.
With these measures, the GCR report produces the overall labor market flexibility
index, which I list in Table 3.1 for both developing and developed countries. As we can
see in the table, there exists substantial variation across countries in both groups.
Figure 3.2: GDP per Capita and Labor Market Flexibility

2

3

4
Flexibility (7 is the most flexible)

GDP per Capita

5

6

Fitted values

Source: Global Competitivenes Report (2012)

In Figure 3.2, I plot the relationship between the labor market flexilibity and the GDP
per capita (nominal) of all countries listed in Table 3.1 for 2012. In this figure, we can find

64

that there exists a high correlation between the labor market flexibility and a country’s
income level. However, when I divide them into smaller groups by income level, I can
still find a significant heterogeneity in the labor market flexibility index. In Figure 3.3, the
left-hand side graph shows the labor market flexibility of the richest countries, while the
right-hand side graph shows that of the poorest countries.

Flexibility
3
0

0

1

2

2

Flexibility

4

4

5

6

Figure 3.3: Labor Market Flexibility in Rich/Poor Countries

ARE
AUT
CAN DEU
ESP
FRA
IRL
ISR
JPN
NLD
NZL SWE
AUS
BEL
CHE DNK
FIN
GBR
ISL
ITA
LUX NOR SAU

BGD BOL EGY GHA HND IDN JOR KHM MAR NIC PAK SLE UKR
BIH CMR GEO GTM HTI IND KEN LKA NGA NPL PHL SLV VNM

GDP per Capita > 25,000

GDP per Capita < 5,000

The last key variable in this study is the productivity measure. Chapter 1 assumes that
the distribution of productivity measure Θ follows the Pareto distribution with the minimum value of Θm and the shape parameter α. Specifically, the cumulative distribution
function of Θ is given as
G (Θ) = 1 −

Θ
Θm

α

.

(3.6)

With the Pareto assumption, we can easily show that in the model, the share of production
by FDI compared to that by outsourcing decreases in α . In other words, as the productivity dispersion increases, i.e., α decreases, the relative quantity produced by FDI firms
increases. Increases in the productivity dispersion move more firms to the extreme, where
they find it more profitable to choose FDI when the host country’s labor market flexibility
is high enough. Thus, the share of production from FDI should increase in the degree of
productivity dispersion for host countries with low labor market cost.
As shown in Antràs and Helpman (2004), the difference in the sales of final goods
65

across firms can be a measure of the difference in firm productivity. This idea is accepted
in several empirical studies. Especially, Helpman et al. (2004) and Yeaple (2006) construct
a measure of productivity dispersion by using firm sales. Both studies use the standard
deviation in the logarithm of firm sales within an industry to construct industry-specific
productivity dispersion.
However, as the unit of observation in my data is not at the firm-level, I propose an
alternative way to follow the idea in Antràs and Helpman (2004). One method is to adapt
Nunn and Trefler (2007) approach, in which they use U.S. export data instead of firm
sales in calculating the productivity measure. As more productive firms produce more
and export more, the variation in exports can be thought of as a measure of productivity
dispersion.
Nunn and Trefler (2007) substitute the firm-level data with industry-level data, by taking the more aggregated industry level to be ‘notional’ industries and the less aggregated
industry level to be ‘notional’ firms. For example, with the data that I use, their approach
takes NAICS6 level data to be ‘notional’ firm data within an industry of the NAICS4
level. In an industry of NAICS4 code 3262 (rubber product manufacturing), there are
five NAICS6 categories: 326211 (tire manufacturing except retreading), 326212 (tire retreading), 326220 (rubber and plastics hoses and belting manufacturing), 326291 (rubber
product manufacturing for mechanical use), and 326299 (all other rubber product manufacturing). All of the observations in those 5 NAICS6 codes will be taken to be ‘notional’
firm exports, and the standard deviation in their logarithm becomes the productivity dispersion measure of the NAICS4 3262 industry.
However, this approach has two limitations. First, there exists an aggregation error
in this method. Even within a single NAICS6 code, there are many different goods, and
firms that differ in size. As this method aggregates all firms into one number, the resulting standard deviation can be smaller than the actual one. Second, the calculated measure
in the method is closer to the productivity dispersion of U.S. final goods, rather than that

66

of U.S. intermediate goods. Except for firms whose NAICS4 codes of intermediate and
final goods are the same, this is not a proper dispersion measure corresponding to the
key dependent variable, intrafirm imports, which is mostly intermediate goods. For example, if we look at the share of intrafirm imports in the tire industry from China in the
dependent variable, a proper measure will be the U.S. motor industry’s productivity dispersion or the Chinese tire industry’s productivity dispersion. The above method leads
to a productivity dispersion of the U.S. tire industry.
To alleviate these limitations, I choose an alternative method that utilizes additional
information, the destination country of U.S. exports. I calculate the productivity dispersion of NAICS4 industries with ‘notional’ NAICS6 firms in each destination country. In
other words, I distinguish the NAICS6 exports by their destination country, and calculate
the standard deviation for each.
This method can alleviate the two limitations of the method in Nuun and Trefler
(2007). According to the comparative advantage, the composition of goods in the same
NAICS6 exports is very different from each other, depending on the destination country.
Thus, separating exports by their destination countries gives us more detailed data and
alleviates the aggregation error of the above method.
The new method creates a productivity dispersion that varies by country dimension,
which I interpret to be a productivity dispersion of suppliers or subsidiaries of each country. This interpretation is also exposed to the problem that the above measure has; however, as we take foreign countries to be suppliers of intermediate goods in the model, this
method is more consistent with the theory. It is also justified by the fact that the total productivity level comes from not only a headquarter firm, but also its counterparts (either
subsidiaries or suppliers). ? also measure productivity dispersion of the counterparts and
use it as a proxy of productivity dispersion in the headquarter firm.
More specifically, let X denote export, subscript i, g(i ), and c denote NAICS4 level
industry, NAICS6 level goods, and the destination country of the export respectively.

67

Then, the measure of the productivity dispersion of an industry i in year t by a destination
country c is calculated as
prodict =

3.4

Var lnXg(i),c,t .

(3.7)

Empirical Specification

The main focus of this study is to check whether the positive correlation between the
productivity dispersion and the intrafirm trade is only valid for the countries with the
most flexible labor market or not. As mentioned in the previous section, I expect the
relationship to be zero when b f is large, while I expect it to be positive when b f is low.
Even though the theoretical model shows a clear prediction on the cutoff foreign labor
market flexibility level over which the relationship becomes positive, I cannot predict
where the cutoff b f will be in the data, but let the data determine its location.
To do this, I rank all countries by labor market flexibility. They are measured by all
four different labor market flexibility indexes: hiring and firing practice, flexible wage determination, cooperation in the labor-employer relationship, and the overall index. With
this ranking, I divide the countries into five sub-groups. Let p index the groups, where
p = 1 means the least flexible countries and p = 5 means the most flexible countries.
p

With the indicator function Ict , which equals 1 if Country c belongs to Group p in year
t, I estimate the following regression:
V
I Mict
V
I Mict

+

O
I Mict

5

= Di + D c + D t +

5

∑ β I Ict + ∑ β Ip

p =1

p

p

prodict · Ict +

cit ,

(3.8)

p =1

where Di , Dc , and Dt denote industry, country, and year dummies, respectively.
The sign and size of the coefficient β Ip are the main focus of this regression. The model
predicts that for low p, β Ip should be zero as all the offshoring firms find outsourcing
to be more profitable, and thus the productivity dispersion has no effect on the share of
intrafirm import. For high p, the model predicts that β Ip should be positive, as the most
68

productive firms choose FDI over outsourcing.

3.5

Empirical Results

Table 3.2 shows the result of estimating Equation (3.8) using all countries in the sample.
V / I MV + I MO and each column
In all four regressions, the dependent variable is I Mict
ict
ict

shows a regression result by using four different labor market flexibility measures. More
specifically, the first column shows the regression result of Equation (3.8) by using the
‘overall’ labor market flexibility index when we divide countries into five groups. Similarly, the second column uses the ‘hiring and firing practice’ index, the third column uses
the ‘flexibility in wage determination,’ and the last column uses the ‘cooperation in the
labor-employer relationship.’ All of the regressions reported in the table include country,
industry, and year fixed effects.
In this table, we expect the coefficient to be zero for countries with a rigid labor market, while we expect it to be positive for countries with a flexible labor market. With
the productivity measure in Equation (3.7), we find a consistent result for the prediction
in columns (1), (2), and (3). In all three columns, the coefficient jumps to positive and
becomes significant when we move from Group 4 to Group 5. In other words, the productivity dispersion only affects the intrafirm import share when the host countries have
the most flexible labor market. With the flexibility measure, cooperation in the laboremployer relationship, I cannot find a supporting result.
As I report the beta coefficient, we can interpret the coefficients more easily. For example, the coefficient for I 5 in the first column means that as we increase the productivity
index as 1 standard deviation, the intrafirm import share increases as 0.012 standard deviation in Group 5 countries. As the standard deviation of the dependant variable is 0.317,
the intrafirm trade share increases about 0.4 percent.
To explore the relationship in more detail, I divide countries into two different groups,
developed and developing countries. Surprisingly, I find very different results in each
69

Table 3.2: Estimation Results with Data from All Countries
V / I M V + I MO
Dependent Variable: I Mict
ict
ict

Using labor market index of
Prodcit interacted with:
I1
I2
I3
I4
I5
Country fixed effect
Industry fixed effect
Year fixed effect
Observations
R-squared

(1)
overall

(2)
hiring firing

(3)
flexible wage

(4)
cooperation

0.001

-0.016***

-0.018***

0.002

(0.002)

(0.002)

(0.002)

(0.002)

-0.019***

-0.003

0.004

-0.010*

(0.002)

(0.002)

(0.002)

(0.003)

0.001

0.008

-0.002

-0.007

(0.002)

(0.002)

(0.002)

(0.003)

-0.000

-0.000

0.001

0.008

(0.003)

(0.002)

(0.002)

(0.002)

0.012**

0.011**

0.014**

-0.002

(0.002)

(0.003)

(0.002)

(0.002)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

151,146
0.18

151,146
0.18

151,146
0.18

151,146
0.18

Notes: This table shows the estimation results of Equation (3.8) by using data from
V / I MV + I MO . The productivity
all countries. The dependent variable is I Mict
ict
ict
measure in Equation (3.7) is used. Beta coefficients are reported and standard errors
are in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1.

group. Table 3.3 shows the result of the estimation using developed countries only. In
columns (1), (2), and (3), I find a positive coefficient for the most flexible countries, but
none of them are significant. In the estimation with the flexibility measure, ‘cooperation
in the labor-employer relationship,’ I find a positive and significant coefficient for Group
3 and Group 4, but the coefficient for Group 5 is negative and significant.
However, when I estimate Equation (3.8) only using data from developing countries, I
get dramatically different results. Table 3.4 reports the result where coefficients for Group
1 through Group 4 are either zero or negative, while the coefficients for Group 5 are positive, and three of them are significant. These results strongly support the prediction of
the model in the first chapter.

70

Table 3.3: Estimation Results with Data from Developed Countries
V / I M V + I MO
Dependent Variable: I Mict
ict
ict

Using labor market index of
Prodcit interacted with:
I1
I2
I3
I4
I5
Country fixed effect
Industry fixed effect
Year fixed effect
Observations
R-squared

(1)
overall

(2)
hiring firing

(3)
flexible wage

(4)
cooperation

-0.012

-0.022***

-0.013*

-0.007

(0.003)

(0.003)

(0.003)

(0.003)

-0.023***

-0.013

-0.026***

-0.021***

(0.004)

(0.003)

(0.003)

(0.003)

-0.022***

0.002

-0.006

0.013*

(0.003)

(0.003)

(0.004)

(0.004)

0.006

-0.010

0.005

0.014*

(0.003)

(0.004)

(0.003)

(0.004)

0.011

0.008

0.004

-0.033***

(0.003)

(0.003)

(0.004)

(0.003)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

77,737
0.15

77,737
0.15

77,737
0.15

77,737
0.15

Notes: This table shows the estimation results of Equation (3.8) by using data from
developed countries. The productivity measure in Equation (3.7) is used. Beta coefficients are reported and standard errors are in parentheses. *** p < 0.01, ** p <
0.05, * p < 0.1.

When we compare the coefficient in Table 3.4 with the result in Table 3.2, we find
that the coefficients are greater in magnitude and they are more statistically significant
in Table 3.4. The beta coefficient of Group 5 in the first column is 0.027, which means
that a standard deviation increase in the productivity dispersion gives about a 0.9 percent
increase in the intrafirm trade share, which is about twice the increase that we get in the
estimation from all countries.3
3 The

standard deviation of the intrafirm import share is about 0.33.

71

Table 3.4: Estimation Results with Data from Developing Countries
V / I M V + I MO
Dependent Variable: I Mict
ict
ict

Using labor market index of
Prodcit interacted with:
I1
I2
I3
I4
I5
Country fixed effect
Industry fixed effect
Year fixed effect
Observations
R-squared

(1)
overall

(2)
hiring firing

(3)
flexible wage

(4)
cooperation

0.010

0.002

0.019**

-0.000

(0.003)

(0.003)

(0.003)

(0.003)

-0.023***

0.000

-0.019**

-0.003

(0.003)

(0.003)

(0.003)

(0.004)

0.008

0.005

-0.008

-0.011

(0.003)

(0.003)

(0.003)

(0.004)

-0.006

-0.015*

-0.004

0.000

(0.004)

(0.003)

(0.003)

(0.003)

0.027***

0.016*

0.022***

0.013

(0.004)

(0.004)

(0.004)

(0.003)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

73,409
0.16

73,409
0.16

73,409
0.16

73,409
0.16

Notes: This table shows the estimation results of Equation (3.8) by using data from
developing countries. The productivity measure in Equation (3.7) is used. Beta
coefficients are reported and standard errors are in parentheses. *** p < 0.01, ** p <
0.05, * p < 0.1.

Although the reason behind the huge difference in the results shown in Table 3.3 and
Table 3.4 is not clear, I can point to a possible cause of it in the U.S. Census data that I use.
The U.S. Census trade data includes information which tells us whether a certain trade is
between a related party or not; but it does not give any information on which one is the
headquarter and which one is the subsidiary. This is a drawback of the U.S. Census data
compared to the BEA intrafirm trade data as I want to focus on the case where the U.S.
firms are the headquarters.

72

Table 3.5: U.S FDI Inflows by Partner Country (2012)
Country / Organization

Inflows (Million Dollars)

Share

Netherlands
France
United Kingdom
Japan
Canada
Belgium
Luxembourg
South Korea
Hungary
Germany

29934
21664
20547
19169
16460
11876
6216
5240
3640
3103

18.64
13.49
12.80
11.94
10.25
7.40
3.87
3.26
2.27
1.93

OECD
Non-OECD

150595
9974

93.79
6.21

Source: OECD
As firms in foreign countries also do FDI in the U.S., there are many cases, in the
related-party data from those countries, in which U.S. firms are subsidiaries, and thus
weaken the result that we are looking for. Also, considering the fact that in 2012 about 94
percent of FDI inflow to the U.S. came from other OECD countries, we can think of the
data set only with developing countries to have more cases where U.S. firms are headquarters.4 This explanation is also consistent with the result that the coefficient in Table
3.4 is greater and significantly stronger than the coefficients in Table 3.2. Considering this,
the size of the coefficients that I get in Table 3.2 and 3.4 is not economically negligible.
We can find similar results in Yeaple (2006). Yeaple found generally supporting result
that the higher the dispersion across firms, the greater the intrafirm import share. But
when the countries were divided into three different groups, developing, emerging, and
developed, a positive correlation in the developed country group was not found.
4 See

Table 3.5, which is from OECD FDI in/outflows data by partner country in 2012.

73

3.6

Conclusion

The model in the first chapter suggests that cross-country heterogeneity in labor market
flexibility can be a source of different organizational forms of multinational firms. The key
prediction is that the productivity dispersion affects a firm’s decision only for countries
with a flexible labor market, as outsourcing is a dominant choice for all multinationals,
otherwise. I analyze this prediction using the U.S. Census data on the U.S. related-party
trade data of 453 NAICS6-level products from 137 countries from 2006 to 2012.
I find strong support for the prediction in the benchmark model: the productivity dispersion increases the intrafirm share only in countries with a more flexible labor market.
This result stands out more with the data set with developing countries, which are mostly
host countries in trade with U.S. multinationals. Overall, findings in this study provide
evidence for and confirm the prediction in the first chapter.

74

REFERENCES

75

REFERENCES

Antràs, P. 2003. “Firms, contracts, and trade structure.” Quarterly Journal of Economics,
118(4): 1375–1418.
, and E. Helpman. 2004. “Global sourcing.” Journal of Political Economy, 112(3):
552–580.
, and
Paper, 12747.

. 2006. “Contractual frictions and global sourcing.” NBER Working

Helpman, E., and O. Itskhoki. 2010. “Labour market rigidities, trade and unemployment.” Review of Economic Studies, 77(3): 1100–1137.
, M. J. Melitz, and S. R. Yeaple. 2004. “Export Versus FDI with Heterogeneous
Firms.” American Economic Review, 94(1): 300–316.
Nunn, N., and D. Trefler. 2007. “The Boundaries of the Multinational Firm : An Empirical Analysis.”
, and
. 2013. “Incomplete contracts and the boundaries of the multinational firm.” Journal of Economic Behavior & Organization, 94 330–344.
Ruhl, K. J. 2013. “An Overview of U . S . Intrafirm-trade Data Sources.”
Yeaple, S. R. 2006. “Offshoring, foreign direct investment, and the structure of US trade.”
Journal of the European Economic Association, 4(2-3): 602–611.

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