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This is to certify that the

dissertation entitled

Essays on International Joint Ventures
And Foreign Wholly-Owned Subsidiaries

presented by

Wing-Fai Leung

has been accepted towards fulfillment
of the requirements for

PhD Economics

degree in

 

 

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ESSAYS ON INTERNATIONAL JOINT VENTURES AND
FOREIGN WHOLLY-OWNED SUBSIDIARIES

By

Wing-Fai Leung

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1993

ABSTRACT

ESSAYS ON INTERNATIONAL JOINT VENTURES AND
FOREIGN WHOLLY-OWNED SUBSIDIARIES

By

Wing-Fai Leung

Foreign direct investment (FDI) have grown very fast in the past several decades.
Apart from establishing wholly-owned subsidiaries, multinational enterprises frequently
join with local firms to form joint ventures. This dissertation emphasize three issues
related to wholly-owned subsidiaries and international joint ventures: coexistence of both
types of affiliates in a country, a comparison of host-country welfare under alternative
forms of FDI, and a comparison of the duration times of different kinds of affiliates in
a host country.

Chapter 3 uses a model of monOpolistic competition to explain why there are both
foreign wholly-owned enterprises and international joint ventures coexisting in a single
industry. The theory is based on the existence of both firm-specific knowledge and local
knowledge to explain the entry of a firm into a foreign country. In addition, differences
in production costs of different plants within a firm may be the reason of the coexistence
of both types of affiliates in a country.

Chapter 4 compares welfare between closed economies, free FDI and restricted FDI
under the assumption of intra-industry and interindustry spillovers. Preferences, the rate
of technology transfer, and technology gaps between the countries are factors affecting

the welfare level. Although it is found that under the minimum local ownership policy the

welfare effects are ambiguous, this policy is at least no worse than a closed economy.
Though joint-venturing allows the parents to contribute their own advantages, the
parents learn from the partners, implying that the benefits of a joint venture to a firm are
lower over time. On the other hand, the cooperation costs may not be easily eliminated.
It is hypothesized that on average, a foreign wholly-owned subsidiary should have a
higher stability rate than an international joint venture. In chapter 5, samples of U.S. FDI
and FDI in the United States are applied. On the whole, U.S. investment abroad supports

the hypothesis while the evidence of FDI in the United States is not strong.

ACKNOWLEDGMENTS

This dissertation is completed after valuable assistance from many people. At first,
Steven Matusz, my committee chairperson, has contributed a lot to this dissertation and
has shown special patience to read every draft. Thank you very much, Steve.

As committee members, Paul S. Segerstrom and Corinne Krupp also provide much
advice. I am very grateful to both of them. Carl Davidson read an earlier draft of a part
of this dissertation. Here is also a good place for me to thank him.

There are also other faculty in the department helping me on the papers at various
stages: Kenneth D. Boyer, Ching-Fan Chung, Peter Schmidt and Jeffrey Wooldridge.
Their kind assistance is very much appreciated.

Without my parents' encouragement and support, it might be impossible for me to
finish the degree. It is not enough to simply say thanks to them.

Many other friends inside or outside Michigan State University also helped me directly
or indirectly in achieving the degree. I fear that it would be a very long list if all of their

names appeared. I thank all of them.

iv

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES

CHAPTER 1: INTRODUCTION
1.1 What is Foreign Direct Investment?
1.2 A Few Facts about FDI
1.3 Purpose and Organization of This Thesis

CHAPTER 2: THEORIES OF FOREIGN DIRECT INVESTMENT:

REVIEW OF THE LITERATURE
2.1 "New Theory" of FDI
2.2 Choices of Entry Modes
2.3 Theories Related to Joint Ventures
2.4 Effects of FDI on the Host Country
2.5 Synthesis of Neoclassical International Trade Theory
and Foreign-Direct-Investment Theory

CHAPTER 3: A THEORY OF THE COEXISTENCE OF
INTERNATIONAL JOINT VENTURES AND
WHOLLY-OWNED ENTERPRISES

3.1 Introduction ‘
3.2 A General Equilibrium Model
3.3 Equilibrium in a Closed Economy
3.4 Equilibrium Condition under Free Trade but without FDI
3.5 Decisions on FDI
3.6 Coexistence of International Joint Ventures and
Foreign Wholly-Owned Subsidiaries in the Host Country
3.7 Extensions and Discussions
3.8 Concluding Remarks

vii

viii

«hoot—r—

19
22
23
25

27

34
34
36

50
57

76
78
80

CHAPTER 4: WELFARE ANALYSIS OF FOREIGN DIRECT

4.1
4.2
4.3
4.4

4.5
4.6
4.7

INVESTMENT UNDER SPELOVER EFFECTS
Introduction
The Model
Closed Economies
One-Sided Investment from the Developed Country
to the Developing Country
Evaluation of the Host Country's Welfare under FDI
Policy of Minimum Ownership Requirements
Concluding Remarks

Appendix 4A: The First Derivatives for Case 4.1
Appendix 4B: The First Derivatives for Case 4.5

CHAPTER 5: THE DURATION TIMES OF INTERNATIONAL

5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8

JOINT VENTURES AND FOREIGN
WHOLLY-OWNED SUBSIDIARIES

Introduction

Sources and Data Collection

The Proportional Hazards Model

The Estimated Model

Results

Test of the Appropriation of the Proportional Hazards Model

Parametric Models

Concluding Remarks

Appendix 5A: Maximum Likelihood of

the Proportional Hazards Model

Appendix 5B: Summary of the Data Set
Appendix 5C: Kaplan-Meier Estimates

LIST OF REFERENCES

vi

83
83
84
90

96
115
124
127
129
132

135
135
138
141
147
153
159
162
169

171
173
180

184

‘2‘“!

Table 1.1:
Table 1.2:
Table 1.3:

Table 1.4:

Table 3.1:
Table 5.1:
Table 5.2:
Table 5.3:
Table 5.4:
Table 5.5:
Table 5.6:

Appendix 5B:

LIST OF TABLES

Inflows and Outflows of FDI, 1980-1990
Transactions of FDI in the United States
Transactions of FDI China

Japanese MNEs Operating Both Wholly-Owned Subsidiaries
and Joint Ventures in the United States

The Summary of Forms of Ownership in Country H
Correlations between the Independent Variables (Sample (c))
U.S. FDI (Sample(a))

FDI in the United States (Sample (b))

Combined Data Set (Sample (c)) Results

Exponential Model - Combined Data (Sample(c))

Weibull Model - Combined Data (Sample (0))

Summary of the Data Set

vii

12

70
154
155
157
159
164
167

173

 

 

LIST OF FIGURES

Figure 1.1: FDI, Gross Domestic Product and Domestic Investment,
1970-1990 6

Figure 1.2: Index of Current Value of Exports and FDI Outflows, 1975-1989 7

Figure 3.1: The Organization of a Firm 39

Figure 3.2: The Profit-Wage Ratio with Respect to 9 56 4,

Figure 3.3: An Example of the Distribution of Ownership Forms 3::
inCountrwaith R>J+1>F-C+1>1 and F+1>J>F 71 E

Figure 4.1: Equilibrium Condition of Country H in a Closed Economy 94 :3;

Figure 4.2: An Example of Welfare Improvement in Country H
with the Displacement of the Domestic Monopoly
by a Foreign Monopoly in Sector X 118

Figure 4.3: An Example of Immiserizing Country with the Displacement
of the Domestic Monopoly by a Foreign Monopoly in Sector X 119

Figure 5.1: The Kaplan-Meier Survivor Functions of Foreign
Wholly-Owned Subsidiaries (Group 0) and
International Joint Ventures (Group 1) 152

 

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viii

 

Chapter 1

Introduction

1.1 What is Foreign Direct Investment?

Interest regarding foreign direct investment (FDI) has been renewed in recent years
for several reasons‘. The first reason is the rapid growth in global FDI flows. For
example, the flows were increased from $47 billion in 1980 to $139 billion in 1985.
Another reason is the large amount of FDI inflows into the United States during the
19808. Moreover, developing countries realize that FDI is an important source for their
economic development.

FDI implies that a person or an organization has some interests in a foreign country
or has influence in the management of an enterprise in a foreign country. That is, FDI
applies to the activities of foreign-oriented capital or resources which are at least partly
controlled by foreigners. On the other hand, foreign indirect investment is related to the
foreign oriented capital inflow with no participation in running a business locally.
Portfolio investments are typical examples of this kind of indirect investment.

A multinational enterprise (MNE) refers to a corporation operating in more than one

country. FBI is closely related to the concept of MNEs although the two may not be the

 

1The reasons were suggested by Lizondo (1993).

1

2

same thing. For example, licensing is a kind of FDI but the foreign licensor need not be
a MNE. From the viewpoint of the host country, FDI usually implies that a foreign
corporation participates in the local economy more actively and the local market structure
may be affected by the foreign firm; therefore, MNEs have become the main interest in
the recent literature about FDI.

One important point is that FDI is not necessarily related to capital inflowsz. Since the
financial market in the world is well connected, a subsidiary of a MNE may raise funds
locally and the headquarters may only provide management control and technological
advice.

To illustrate the effects of FDI, the first task is to define FDI. Several interpretations
have been mentioned above, but a primary problem is that a corporation will combine
stockholders of different nations. Conceptually, we can use the share of voting power as
a standard to determine whether the firm is foreign or local. As a practical matter,
however, it is very difficult to form a clear-cut definition. For example, the U.S.
Department of Commerce defines a foreign investment as direct investment when a single

foreign investor owns at least 10% of the shares in a U.S. firm’. A defect in this

 

2Here capital refers to the physical inputs to production. If "capital" includes the intangible assets, of
course FDI is still related to ”capital" flows.

’This example is referred to in Graham and Krugman (1991, pp.9). The definition of U.S. FDI can
be drawn from the U.S. Department of Commerce (1992, pp.M-4). It is said that ”U.S. direct investment
abroad is the ownership or control, directly or indirectly, by one U.S. person of 10 percent or more of the
voting securities of an incorporated foreign business enterprise or an equivalent interest in an
unincorporated foreign business enterprise. . 'Person' is broadly defined to include any individual, branch,
partnership, associated group, association, estate, trust, corporation or other organization (whether or not
organized under the laws of any State), and any government (including a foreign government, the U.S.
Government, a State or local government, and any agency, corporation or financial institution, or other
entity or instrumentality thereof, including a government-sponsored agency). "

3

definition is that, for example, if a firm contains 12 foreign single investors, each having
5% of the shares, then according to the U.S. Department of Commerce, the firm is not
directly invested from foreign countries. It is ridiculous that a firm dominated by foreign
investments is not counted as a foreign investment. (Of course, who holds the
administrative rights is still an issue.)

In this thesis, only the concepts related to FDI theory are analyzed. The practical
difficulties of the official definition are ignored. For the sake of convenience, FDI is
defined as any local business activity with at least some decisions made by foreign
parties. Sometimes, the MNE is distinguished from other alternatives such as licensing,
franchising, subcontracting and joint ventures. However, here we will focus on two types
of MNEs: joint ventures with other firms in a foreign country and wholly-owned

subsidiaries.4

1.2 A Few Facts about FDI
The Recent Trend of FDI Outflows in the World
In the 19803, the growth of FDI in the world was very weak in the first half of the

decade while it grew very quickly in the second half. Table 1.1 summarizes the inflows

 

‘Omen's (1984) definition of FDI is broader - including "new forms" of international investments. The
so-called "new forms of investment“ refer to:

(a) Joint international business ventures in which foreign-held equity does not exceed 50%:

(b) various international contractual arrangements which involve at least some investment from the

foreign firm, but without equitable participation.
International investments comprise wholly-owned subsidiaries, joint ventures, licensing agreements.
franchising, management contracts, turnkey contracts, production-sharing contracts and international
subcontracting.

and outflows of FDI within this period.’

Figure 1.1 compares the trends of global FDI outflows and gross domestic product for
the last two decades. From the figure, we can see that at least from 1970 to 1985, the
outflows of FDI had been closely related to the cyclical fluctuations of national incomes.
After 1985, FDI grew at a much higher rate than national income. Not only does the
growth rate of FDI exceed gross domestic product growth in the second half of the
19805, but FDI also grows at a faster rate than exports as shown in Figure 1.2.

The unparalleled growth of FDI compared to global gross domestic product after 1985
may be explained in several ways.1 First, there was a strong recovery of the world
economy between 1985 and 1989. After 1985, the average annual rate of real gross
domestic product grew at 3.5 % in developed countries and 3.4 % in developing countries,
compared to 2.2% and 1.7% respectively between 1980 and 1984. The improved
economic performance of some developing countries, especially those which experienced
debt-servicing problems, relieved the inhibition of further investments. Increased profit

distribution provided the investors the opportunity to reinvest.

 

5From the global point of view, inflows and outflows of FDI should, in principle, be balanced. But
actually, there is some discrepancy between inflows and outflows. One reason is that the definition of FDI
is not the same in different countries. However, in 1990 the discrepancy reached US$41 billion, an amount
which is too significant for such a simple explanation. Several reasons have been cited by a recent report
(United Nations 1992) to explain the discrepancy: ”differences in the threshold definition between inward
and outward investment; differences in the treatment of unremitted branch profits between inward and
outward investment; treatment of unrealized and realized capital gains and losses, the recording of
transactions of 'offshore' enterprises; differences in the method of collection and reporting of [FDI]
between countries; and differences in the treatment of real estate and construction investment. "

Table 1.1: Inflows and Outflows of FDI, 1980-1990

i

 

Developed Countries I Developing Countries I All Countries II

 

 

 

 

 

 

 

Years
Billion USS or % Inflows Outflows Inflows Outflows Inflows Outflows
: 1986 64 86 14 2 78 88
y 1987 108 135 25 2 133 137
1988 129 161 30 6 158 167
1989 165 201 30 10 195 211
1990 152 217 32 8 184 225
1980-85 Growth -3 -2 4 l -1 -2
Rate (% )
1986-90 Growth 24 26 22 47 24 26
Rate (96)

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Source: Table 1.1, Transnational Corporations and Management Division, United Nations Department of
Economic and Social Development, World Investment Report 1991: Transnational Corporations as Engines of

Growth, United Nations, 1992, pp.14.

 

 

 

 

 

 

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Figure 1.1: FDI, Gross Domestic Product and Domestic Investment, 1970-1990

Reprinted from Figure 1.1, United Nations Centre on Transnational Corporations and Management Division,
United Nations Department of Economic and Social Development, World Investment Report 1992: Transnational
Corporations as Engines of Growth, United Nations, 1992, pp.17.

 

 

 

1975- 100

 

700

500

300

200

 

100

 

0 1111111
757877787980819293848586979999

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Sources: UNC'I‘C aatintataa, based on UNC’I‘Q World Investment Directory (New York, UNC’I‘C 1991).
Intarnational Monetary Fund balance-ofpaymanta taps, tab-Saved on 10 January 1991; and United Nations.
Monthly Bulletin ofStotistioa, Odobar 1984 (ST/EBA/B‘I‘A’Dst’lfl) and Octobar 1990
(ST/ESNSTA'IYSERMH).

 

 

 

Figure 1.2: Index of Current Value of Exports and FDI Outflows, 1975-1989

Reprinted from Figure 1, United Nations Centre on Transnational Corporations, World Investment Report 1991:
The Triad in Foreign Direct Investment, United Nations, 1991, pp.5.

8

Another factor of the unparalleled growth is that corporations in developed countries
are able to invest abroad, eroding the traditional leading positions of the United States and
the United Kingdom. The most significant case is Japan: from 1985 to 1989, Japanese
companies increased investments abroad at an annual rate of 62%. Apart from good
economic performances, the high Japanese incentive to invest abroad is partly due to the
appreciation of yen against other currencies.

On the other hand, the newly industrializing countries, particularly Singapore, Hong
Kong, Taiwan and South Korea, also seek to invest outwardly. This is partly due to the
appreciating currencies, current account surpluses, rising production costs at home, and
the threat of protectionism in the export markets.

Owing to technological and competitive forces, acquisitions and mergers across
borders also contribute to the rise of FDI. The plan to integrate the European Community
in 19926 attracted not only outside FDI but also investment between the European
Community members. Finally, the rise of the importance of service goods in recent
years, most of which are difficult to trade, also helped to promote FDI.

With the recession which came in 1991 (and by mid-1993 has not yet ended
completely), PD] is expected to grow at a much slower rate though the actual figures

have yet to be revealed.

 

6So far, the 1992 plan for the integration of the European Community has not succeeded.
Economically, the global recession (except for developing countries in East Asia) was a main reason for
the difficulty in carrying out the plan. Politically, worries about German domination in Europe was the
other reason.

9
Table 1.2: Transactions of FDI in The United States

 

 

 

 

 

 

 

 

 

 

~ Years Total Transactions' Joint Ventures as a Share of

, Total Foreign Subsidiaries
l981° | 806 8.56%

1982° 753 10.36%

? 1985d 801 6.12%

I 1986‘ I 832 6.97%

I 1987‘ I 1091 9.07%

I 1988‘ | 880 10.34%

 

 

Sources: U.S. Department of Commerce, International Trade Administration, Foreign Direct Investment in the
United States, 1986—1988 Transactions, U.S. Government, 1986-89.
Note: a: The number of total transactions excludes equity increase, plant expansion and real estate;

b: Others include the transaction of acquisitions and mergers, new plants and other terms;

c: For 1981 and 1982 data, both completed and pending transactions are included;

(I: For 1985-88 data, only completed transactions are included.

Table 1.3: Transactions of FDI in China, 1985-89

 

 

   
   

Joint Ventures' as a Share of
Total Foreign Subsidiaries

98.50%
98.80%
97.94%
93.10%
83.89%

  
 

 

 

 

 

 

 

 

Sources: The People's Republic of China Government, Almanac of China's Economy, 1987, 1988, 1990,
Economic Management Press, 1987, 88, 90 (Chinese Version).
Notes: a: Joint ventures here comprise the joint-venturing businesses, cooperating businesses and cooperating
explorations;
b: Referred to pp.653, Almanac of Otina's Economy, 1987;
c: Referred to pp.731, Almanac of China '8' Economy, 1988;
d: Referred to pp.603, Almanac of China 's Economy, 1990;

10

Joint Ventures in the United States and China in Recent Years

The United States is a developed country while China is a developing country. We
compare joint ventures as a share of total foreign subsidiaries in the United States and
China to see the different preferences of foreign firms in these two countries. Table 1.2
lists the data of international joint ventures in the United States while Table 1.3
summarizes the international joint ventures in China.

It is worthwhile to note that joint ventures are relatively insignificant in the United
States. In great contrast, joint ventures are the dominant form of FDI in China. It is also
interesting to note that the ratio of joint ventures in the United States increased slightly
between 1985 and 1988 while the share of joint ventures in China dropped in the same
period (though 1989 is included in the case of China). A possible explanation to this

difference will be given in the next section.

The Japanese firms in the United States Operating Both Wholly-Owned Subsidiaries and
Joint Ventures

The MNEs may not only choose either wholly-owned subsidiaries or joint ventures in
a foreign country. It is very common that a MNE operates both wholly-owned
subsidiaries and joint ventures joined together with the local firms. Instead of fully
covering the multinational firms which comprise both types of the affiliates, Table 1.4
lists the Japanese firms in the United States with both types of affiliates. The data of this
table were collected from Who Owns Whom (1993) which include 567 Japanese firms

having affiliates in the United States. However, only 42 of which are identifed to operate

11,

both wholly-owned subsidiaries and joint ventures (with U.S. firms).7 Though more
Japanese firms have joint interests with other firms in the United States, we screen out
those without U.S. partners. There are many cases that the Japanese firms joined with
other Japanese firms or MNEs based in other countries. Since this thesis concentrates on
the cases of the international joint ventures between foreign firms and local firms, the
other joint ventures are excluded for simplification.

The subsidiaries usually have their own subsidiaries. The subsidiaries of a parent firm
are belonged to "the first level". The subsidiaries of the first level subsidiaries are
belonged to "the second level" and so on. In Table 1.4, The second to fifth columns list
the number of wholly-owned subsidiaries for the first to fourth levels respectively. That
is, WSl refers to the first level subsidiaries and ’WS2 refers to the second level and so
on. Similarly JV 1 refers to the international joint ventures at the first level while JV2
refers to the second level. It should be noted that a second level joint venture may be the
affiliate of a first level wholly-owned subsidiary. However, for the samples in the table,
no wholly-owned subsidiaries are the affiliates of any joint ventures. There are many
cases that joint ventures may be joined by firms from all Japanese firms or between
Japanese firms and MNEs of other countries. Those cases are put in the last column -
JVU. If the joint ventures cannot be identified as who's affiliates, they are also put in

JVU.

 

7A Japanese firm may be the major-pewter, equal partner or minor-partner.

12
Table 1.4: Japanese MNEs Operating Both Wholly-Owned Subsidiaries and Joint

Ventures in the United States

 

 

 

Japanese MNEs in the I Wholly-Owned I Joint Others

United States Subsidiaries Ventures

    

 

 

I

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I Ajinomoto Co., Inc. 1 0 0 0 1 0 1
Asahi Glass Co., Ltd. 3 l 0 0 4 0 3
’ Bridgeston Corp. 3 7 0 0 0 1 1
The DAI-Tokyo Fire & Marine 2 0 0 0 1 0 0
Insurance Co. Ltd.
’ Fanuc Ltd. 4 0 0 0 1 0 1
. Fuji Photo Film Co. Ltd. 9 3 0 0 0 1 0
j Fujikura Ltd. 3 0 0 0 1 0 1
Fujitsu Ltd. 17 3 2 4 1 0 0
f Inoue Rubber Co. Ltd. 3 0 0 0 o 1 2
Ishikawaj ima-Harima Heavy 2 0 0 0 1 0 l
Industries
I Isuzu Motors Ltd. I 4 0 0 0 1 0 0
Itochu Corp. I 36 o 0 0 2 0 4
I Kansai Paint Co, Ltd. 1 0 0 0 1 0 0
2 Kawasaki Steel Corp. I 13 1 0 0 I 1 0 I 2
I Kubota Corp. 3 0 0 0 1 0 I 3
‘ Kyotaru Co., Ltd. a 3 0 0 0 I 1 0 I 0
j Matsushita Electric Industrial Co. 20 59 4 0 I 1 0 I 2
5 Ltd. I I
1 Mazda Motor Corp. 3 1 0 0 I 1 0 1
. Mitsubishi Corp. 12 0 0 0 I 1 0 I 12
Mitsubishi Heavy Industries 4 0 0 0 I 1 0 3
; Mitsubishi Kasei Corp. 1 6 2 0 I 1 0 0
I Mitsubishi Petrochemical Co. Ltd. 3 0 0 0 I l 0 2
’ Mitsubishi Rayon Co. Ltd. 6 0 0 0 I 1 0 0

 

 

13

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Japanese MNEs in the I Wholly-Owned 3 Joint I Others
United States I Subsidiaries I Ventures I
I W81 W82 W83 W84 JV 1 JV2 I

Mitsui & Co. Ltd. I 45 4 0 0 I 1 0 I 8
Mitsui Mining & Shelting Co. I 1 0 0 0 I 1 0 I 0
Nippon Lfe Insurance Co. 4 0 0 0 I 1 0 I 0
Nippon Sheet Glass Co. Ltd. 1 0 0 o I 1 0 I 1
Nippon Steel Corp. 1 0 0 0 I 1 0 l 2
Olympus Optical Co. Ltd. 5 0 0 0 I 1 0 I o
Settsu Corp. 4 o 0 0 1 0 I 1
Sumitomo Bank Ltd. I 3 0 0 0 1 0 I 2
Sumitomo Chemical Co. Ltd. I 1 o 0 o I 3 o I o
Sumitomo Electric Industries Ltd. 1 0 0 0 l 0 I 4
Takeda Chemical Industries Ltd. I 2 0 0 0 I l 0 I 1
Tanabe Seiyaku Co. Ltd. 3 0 0 0 1 l 0 I 0
The Tokio Marine & Fire I 8 2 0 0 l 0 I 1
Tokyo Electron Ltd. I 1 0 0 0 1 0 I 0
Toray Industries Inc. I 2 O 0 0 1 O I 1
Toshiba Corp. II 10 5 0 0 2 0 1
Tosoh Corp. 7 0 o 0 1 0 0
Toyota Motor Corp. 7 2 0 0 l 0 l
The Yokohama Rubber Co. Ltd. . 2 0 0 0 - l 0 I 0

 

 

 

 

 

 

14

We only look into one sample for a brief story. Toyota Motor Corporation (Toyota)
formed a joint venture located in the United States with General Motor in 1983. The joint
venture was named New United Motor Manufacturing, Ltd. and the production was
carried in Fremont, California. Both parent companies own equal shares and have equal
numbers of representatives within the board of directors although the president of the
joint venture is selected by Toyota. The first automobile produced in the joint venture,
Chevrolet Nova, was completed in November, 1984.

In 1986, Toyota established its wholly-owned plant in the United States - Toyota
Motor Manufacturing U.S.A. , Inc. The new plant is owned 20% by Toyota and 80% by
Toyota Motor Sales, USA. , Inc. which itself is 100% owned by Toyota. The production
was carried out in Georgetown, Kentucky and in May 1988, the first automobile, Camry,
was completed. Since then, Toyota has operated both wholly-owned subsidiary and

international joint venture in the United States.8

1.3 Purpose and Organization of This Thesis

This thesis compares foreign wholly-owned subsidiaries with international joint
ventures in a host country. This comparison is related to the decision of a firm to enter
a foreign market. Generally speaking, a firm compares the costs of exporting, licensing,

joint-venturing, and operating wholly-owned subsidiaries to determine which is the most

 

I"The details of the development of Toyota can be seen from Toyota J id osha Kabushiki Kaisha (1988).

15

appropriate form of entry to a foreign country. Apart from the explicit costs, implicit
costs are also very important in decision-making. The implicit costs include transaction
costs from external markets and internal organization, and getting local knowledge of a
specific location.

A firm can transfer management and research expertise, for example, to its
subsidiaries at a very low cost. Thus, a firm may find it profitable to extend production
to other locations. Such transfer of management and technology implies firm-specific
advantage". However, each location has different environments such as differences in
laws, cultures, facilities, etc. An outside firm needs time and incurs expenses to learn the
new environment. These are related to local knowledge which affects the efficiency of
production.10

From the previous section, it is evident that the growth of global inflows and outflows
of FDI exploded in the second half of the 1980s. However, the share of FDI inflows and
outflows is mainly concentrated among the developed countries. This thesis does not
explain this observation though some concepts central to this thesis such as firm-specific
advantage and local knowledge may help to understand it. A MNE based in a developed

country will find the investment environments in other developed countries more similar

 

9Firm—specific advantage refers to the efficiency raised by expanding the size of the firm and the
advantages cannot be transferred easily to the outsiders. More will be elaborated in section 2.1.

loLocal knowledge mainly refers to the specific advantages obtained by a plant at a certain location.
More explanations of local knowledge will be given in Section 3.1.

16

to the source country, so the firm must spend fewer resources collecting information
about the developed countries.

We noticed that international joint ventures are not important in the United States
while joint-venturing is a dominant form of FDI in China. In addition to the
encouragement of Chinese Government, local knowledge is also helpful in understanding
this fact. Since China opened its market to the outside world only at the end of the 19703,
other countries have very limited information about China's market. For this reason,
foreign corporations prefer to join local firms to avoid the high costs of adapting the
operation in China. On the other hand, the United States has had an open market for
many years, at least since World War II. Investing foreign firms know more about the
local market in the United States.

As the emphasis is placed on comparing international joint ventures and wholly-owned
subsidiaries, the theories explaining FDI are the stepping stones to illustrate this issue.
Chapter 2 briefly reviews the new theory of FDI after the 19608. Since the late 19803,
there has been much attention focused on entry modes. Literature on entry modes will be
mentioned in the same chapter. Some models on linking international trade theory and
FDI theory are also summarized in Chapter 2.

International trade theory incorporates the theory of FDI starting in the mid-19803.
However, the theory does not distinguish wholly-owned subsidiaries from joint ventures.

In Chapter 3, a model is set up in an attempt to fill this gap.

 

17

Attention of Chapter 3 is paid to answering why a firm may choose to operate both
wholly—owned subsidiaries and joint ventures in a foreign country. We have seen some
examples in the last section that it is not a rare case. In addition to the transaction costs
and local knowledge, the difference in operating costs of different subsidiaries is the
reason that a corporation establishes both foreign wholly-owned subsidiaries and
international joint ventures in a foreign country. Some extensions of the model are also
discussed in that chapter.

Developing countries in recent years have encouraged FDI to promote their economic
development. However, the governments also fear that large MNEs will dominate the
local economies. Thus local participation in the foreign investment projects is preferred,
which may or may not be beneficial to the developing countries. Chapter 4 compares
host-country-welfare under foreign investment (in the form of a foreign wholly-owned
subsidiary or a joint venture) with that under autarky economy. Assuming both
interindustry and intra-industry technology transfers, a developing country may be better
off in most cases by requiring minimum local ownership. However, the mandatory
requirements may reduce the incentives of some foreign investors if joint-venturing is too
costly. The likelihood of some factors that increase the welfare is also analyzed in that
chapter.

Once an international joint venture or a wholly-owned subsidiary is set up, it is

interesting to compare the performances of the two kinds of affiliates. The difference is

18

important to the decision makers (at the governmental level and the firm level). This
paper will not cover the full comparison of performance. Instead, the relative stability of
international joint ventures and foreign wholly-owned subsidiaries is compared in Chapter
5. It is predicted that, on average, an international joint venture has a shorter duration
time than a foreign wholly-owned subsidiary. Data of U.S. direct investment aboard and
FDI in the United States are applied to test the instability of joint ventures. On the whole,
the results of U.S. FDI in other countries are consistent with the prediction but the

evidence of FDI in the United States is not strong.

Chapter 2

Theories Of Foreign Direct Investment:
Review Of The Literature

2.1 "New Theory" Of FDI

It is usually agreed that the new theory of FDI was first discussed by Stephen Hymer
in his doctoral dissertation‘. From then, the main concern of FDI has been related to
transaction costs. The basic reason for a firm producing goods in foreign countries is
because the firm can operate at a lower cost by controlling more subsidiaries in different
countries.

Hymer stresses the firm-specific advantage or the ownership advantage of U.S.
corporations in explaining the difference between FDI and portfolio investments. The
firm-specific knowledge mainly, refers to the ownership of intangible assets by a

corporation.2 When setting up subsidiaries in foreign countries, U.S. firms use their

 

|Hymer's dissertation was completed in 1960. But this important paper had not been published until
1976 (Hymer, 1976).

2An intangible asset may be technology or knowledge of how to produce more products or better
products at given input prices, or how to produce the same product at a lower price than other firms.
Examples are patented processes or designs, the know-how among the employees, marketing techniques,
or innovations.

Externalities arise from the intangible assets. The intangible assets have characteristics of public-good
nature, opportunism and uncertainty so that the supply of those assets may be less than optimal from the
social point of view. The concept of opportunism is referred to in Williamson (1971) and it will not be
explained here.

19

20

advantages in technology, management, marketing techniques, capital-abundance and
other areas to overcome the disadvantages inherent in the unfamiliar environment abroad.

Another question considered by Hymer is why some U.S. managers do not transfer
their technology by licensing. The answer is that the market for knowledge is not
perfectly competitive, and often a firm prefers direct control over a foreign subsidiary.

Many theorists have tried in recent years to provide the most general theory for FDI.
The most significant theory is John Dunning's ”eclectic theory".3

Intemalization within an industry of a certain size determines the number of firms and,
in turn, affects the market structure. Intemalization means that the firm absorbs the
transaction costs in markets internally, i.e. the firm includes different departments which
"trade" among themselves. The intermediate products, if not provided within the firm,
can be exchanged from the outside market. To include all the "marketing" internally,
some costs such as bargaining difficulties and suspicion arising from asymmetric
information will be avoided. The word ”internalization" implies that the transaction costs
are transferred within a firm.

Dunning's "eclectic model" mcludes not only internalization but also ownership-
specific advantage and location—specific advantage for viewing the decisions of a MNE.

Ownership-specific advantage means that the costs are lowered by the direct control of

 

3Dunning (1977, 1980, 1988). There may also be other "general theories": Rugman's (1980, 1981,
1985) generalized internalization theory and Teece's (1981, 1985) multinational version of Williamson's
"markets and hierarchies” theory. In this thesis we are not going to introduce either theory. Rugman
claimed that FDI was explained only by internalization but such theory has been criticized by many people.
For example, Parry (1985) argues that it cannot explain all the characteristics of FDI. Some counter
examples listed by Parry include reasons relating to trade barriers, the popularity of joint ventures and the
independence of the subsidiaries from the headquarters in administration. On the other hand, Teece argues
that the seeking for efficiency and organizational decisions of a firm are neglected by internalization theory.
But Teece's point is not sound since internalization implicitly implies that efficiency is necessary.

21

the MNE over subsidiaries while location-specific advantage refers to the higher profits
of production in a foreign country if that country has advantage in producing certain
products. (The ownership-specific advantage is similar to the firm-specific advantage.)
A firm may only export goods if there are only internalization-specific and ownership-
specific advantages. A MNE arises only if there is incentive to operate in a foreign
country due to the location-specific advantage.

For elaboration, Dunning uses the location-specific advantage to explain why U.S.
firms operate in Europe. Serving a foreign market by producing at the same location
makes it possible to avoid transport costs and tariffs. Sometimes, cheaper labor is also
available abroad.

But the firm investing abroad will face different environments compared to those of
the home country, making it costly for a foreign subsidiary to adapt production to the
local environment. Ownership advantage helps to explain why the U.S. firms can compete
with their European rivals in spite of the difficulties of local unfamiliarity. The U.S.
firms are able to survive thanks to the technological gap between the United States and
other countries, i.e. superior technology and efficient management.

A question arises as to why a U.S. firm does not choose to license its ownership
advantage to a local European firm. The answer is the existence of internalization
ad\rantage. As long as the costs saved by operating in a foreign country (from avoiding
monitoring, negotiation, etc.) is greater than the disadvantage of unfamiliarity, a NINE

will choose to establish subsidiaries.

22
2.2 Choices Of Entry Modes '

When a firm considers how to participate in a foreign market, broadly speaking, it has
four choices (entry modes): exporting, licensing, joint-venturing and setting up a wholly-
owned subsidiary. An older theory is developed around the fact that a firm chooses the
entry mode based on the trade—off between risks and returns. Under the assumption of
profit maximization, the firm makes the choice that offers the highest expected rate of
return at the same level of risk.

In addition to the risk-return analysis, more recently, it is also suggested that the firm
may consider resource availability and c0ntrol in the foreign country‘. Resource
availability is related to the extent of a firm's financial and managerial support to the
targeted foreign market. Control refers to the impact of a firm's influence on foreign
markets and operation of the foreign affiliate5. A firm can get greater control by entering
a market with a larger share of ownership. On the other hand, having a larger share of
the ownership always infers higher risk and requires more resources. Therefore, a firm
has to balance resource availability and control.

Comparing the four entry modes“, we can see that exporting has the lowest risk and
requires the fewest resources. Though the firm has operating control in exporting, it lacks

marketing control in the foreign market. Licensing is a low investment, low risk and low

 

‘Examples of such points of views are Cespedes (1988) and Stopford and Wells (1972).
’I'his definition follows Anderson and Gatignon (1986).
‘The comparison mainly follows the discussion of Anderson and Gatignon (1986) and Hill et a1. (1990)

which include the four choices. On the other hand, Hill and Kim (1988) and Rugman (1981) do not include
joint ventures in their analyses.

23

return alternative. But the firm has only limited control on the local licensee. On the
other side, establishing a wholly-owned enterprise is the highest-control option. The
trade-off is a high capital requirement and high risk. Joint-venturing is somewhere
between licensing and setting up a wholly-owned subsidiary in terms of control, resource

requirement and risk level.

2.3 Theories Related To Joint Ventures

Since this thesis concentrates on foreign wholly-owned subsidiaries and international
joint ventures, exporting and licensing will not be discussed. Moreover, as FDI theories
can be directly applied to wholly-owned subsidiaries, we are going to talk more about
joint ventures in this section.

A joint venture is a firm jointly created and run by two or more parent firms. A joint
venture comprises not only joint ownership from different firms but also joint control by
parent firms. Parent firms jointly contribute and control resources.’ The joint control of
different parents distinguishes joint ventures from other business combinations such as
mergers, takeovers, or acquisition of subsidiaries in which the relationship is one-sided.
All the parties contribute resources which include, but are not limited to, monetary
investment.

Since it is not easy for two individual organizations to join together under diversified

goals and separate plans, a joint venture must provide benefits to both parties. There are

 

7The definition of a joint venture may not be restricted to joint management; it can be under the
management of either or both parties (Clarke and Brennan (1990, pp.1)).

24
various internal factors leading to joint ventures.8 The first obvious factor is that each
party has its own strength which the other lacks. Some examples of the firm-specific
assets are financing power, ownership of raw materials, technology skills, managerial
talent and marketing intelligence. Firms usually do not have the same level of skills in
these firm-specific assets. I

The second reason is more market—oriented. In order not be pushed out of the market,
small firms will cooperate together to compete with large firms. The joint venture may
broaden product diversification by expanding product lines or achieving scale economies.
As a result, the volume of products increases. The other implied advantage is that the
market entry barriers of high sunk costs can be overcome. Conversely, the bigger size
of a firm due to joint-venturing may create entry barriers to other potential rivals.

The third reason is that the high costs of research and development and capital or
equipment investment can be shared with other firms, therefore, the risk will be reduced
and the cost burden of a firm is lowered.

However, the negotiations between two different-goaled parent firms lead to lower
efficiency. Cooperation between administrative staff from different parents is not easy and
then decision-making is not efficient. Even if the parents find it easier to compromise on
a plan, if the managers seek to maximize the benefits of their own companies, it may
affect cooperation within the administrative team.

In sum, transaction costs are the main consideration of a MNE contemplating a joint

venture with a local firm. On the positive side, a firm can use the advantage of the

 

I"The factors are synthesized from Pitt-Watson (1990), Harrison (1985), Walmsley (1982) and Wille
(1988).

25

partner's knowledge and the assets from a joint venture to lower its costs. On the negative
side, cooperation between two independent units may be inefficient and lead to higher
costs. A MNE compares the costs and benefits of a joint venture before the entry

decision.9

2.4 Effects Of FDI On The Host Country

Apart from the theory of FDI, the welfare effects for a host country also get attention.
The most important benefits to the host country are technology transfers or spillovers“).
Evidence also supports this point of view: for example, Twce (1977) and Mansfield and
Romeo (1980) find out that technological knowledge is "leaked" to the host countries by
the U.S.-based firms, and Globerman (1979) shows the positive spillover effects to
Canadian manufacturing industries from FDI. The literature generally emphasizes only
intra-industry spillovers.

Other discussions on welfare effects include both positive and negative sides. In
addition to technology spillovers, the reasons for increase in welfare owing to FDI are

quite broad: the inflow of factors of production into the host country“, promoting

 

’Beamish and Banks (1987) use the transaction cost paradigm to explain why joint ventures sometimes
may be preferred to wholly-owned subsidiaries. Contractor and Lorange (1988) discuss generally the costs
and benefits of forming a joint venture. In addition to the benefits of lowering transaction costs, a joint
venture can reduce a firm's risk or lower the requirement of capital inputs.

mQuite a lot of literature concerns technology transfer to host countries due to FDI. Some examples
are Blomstrém (1989), Caves (1971), Das (1987), Findley (1978), Georgantzas (1991), Hymer (1979),
Johnson (1970), Magee (1977) and Streeten (1971).

"Caves (1971).

26

competition in the host country”, lower transport costs”, higher employment rates“ and
transfer of marketing knowledge". On the other hand, the host country investment may
be immiserizing since the large MNEs can be anticompetitive“ and the costs of foreign
firms are not low enough to increase welfare". Therefore, whether FDI is beneficial to
the host country or not depends on the demand side of the market and technological
advantage”. Moreover, whether the technology is appropriate to the host country and the
extent to which local resources are used also determine the welfare effects”. From the
viewpoint of lobbying, if there are more MNEs, the importance of protecting local
markets from imports becomes lower and then the probability of more liberal policies is
higher.20

From the viewpoint of the host country, foreign investments can lead to higher

efficiency and inflows of capital, and then FDI is welcome. However, usually the foreign

 

”Cardoso and Dornbusch (1989), Horstmann and Markusen (1989).

'3Dei (1990).

"Meier (1976, p.373) and Brander and Spencer (1987).

”Streeten (1971).

“’I‘eece (1981).

”Levy and Nolan (1992).

"Mohtadi (1990).

l"Agarwal (1985).

”Hillman and Ursprung (1993). They know that their theoretical results lack evidence. One reason why
they have drawn this conclusion is that their model is based on the assumption that the lobbying expenditure
of the firms is spent on both liberal and conservative sides. If more MNEs produce locally in the host

cormtry, the firms will have lower incentive to spend on lobbying for protectionism, and so the share on
liberal lobbying expenses is increased.

27

firms push the local competitors out of the markets, thus the host country loses income
to the foreigners. Therefore, the host country may try to limit FDI using local ownership
requirements or foreign exchange outflow restrictions. In addition to economic reasons,
the political concern of preventing foreign dominance is also an important factor in those
restrictions.

Recently, there have been studies concerning the effects of FDI on stock values. For,
example, if a MNE spends a larger share of research and marketing expenditures on the
foreign subsidiaries, the stock returns are higher.21 From a study on U.S.-China joint
ventures (in China)”, the stock returns are higher for those firms with fewer subsidiaries

abroad.

2.5 Synthesis Of Neoclassical International Trade Theory And Foreign-Direct-
Investment Theory
For a long time, the development of theories on FDI has been independent from the
main-stream trade theories. One of the reasons is that trade theory is traditionally based

on perfect competition which cannot explain FDI”. With the emphasis that new trade

 

2|Morck and Yeung (1992). Their paper primarily aims to provide evidence to support the importance
of internalization for FDI.

2I’Hu et a1. (1992). They provide explanations for the higher stock returns on a relatively new MN E:
the people expect that more aggressive strategies of such a firm will make higher profits in the future. A
better established MNE, on the other hand, has only a small marginal benefit in its international presence.

2’Baxter (1992) claims that most phenomena of trade and FDI can still be explained by a neo-classical
model. She develops a two-good two-factor model with capital accumulation under constant returns to scale
and perfect competition. Since the steady state equilibria are reached in different combination of
consumption of the two goods, the long run production possibilities frontier is similar to the Ricardian
model: a downward sloping straight line. However, Baxter gives no details on how the so-called
neoclassical model can respond to the challenge of Helpman and Krugman (1985, Introduction) against the

28

theories place on imperfect competition, it is possible to use formal trade models to
discuss FDI“.

Krugman ( 1983), Markusen (1984) and Helpman (1984) are the pioneers in developing
models of MNEs. Their ideas are similar to the other major FDI theories: the "public
good" nature of the marketing, management and research and development (R&D) within
a firm is the main reason MNEs develop. Such intangible assets are firm-specific
knowledge. Since the management and research resources of the headquarters can be used
by the subsidiaries with little or no cost, a firm has the incentive to operate subsidiaries
in other countries. Since the firm-specific knowledge is usually a part of the fixed costs,
the transfer of the knowledge to other plants implies that the production is increasing
returns to scale”.

Krugman (1983) was the first to use a formal economic model based on firm-specific

 

traditional Heckscher-Ohlin (H-O) model.

For example, in Baxter's model, two identical countries need not have trade, and then the model has
the same difficulty as the H-0 model. Baxter remains helpless in explaining the volume of trade between
similar countries. If there is a little difference in the two countries (of Baxter's model), her model has the
same characteristics as the Ricardian model in which total specialization results.

In addition, intra-industry trade is not possible in Baxter's model. The assumption of perfect mobility
of capital may not be relevant to intra-industry trade.

For the aspect of trade liberalization, Baxter's model only points out that the removal of government
distortion will be beneficial to all. It does not face the real challenge from Helpman and Krugman: the
observation that international trade leads to all-around gains to all trade partners without significant
reallocation of resources which cannot be explained by the neo-classical model.

Perhaps Baxter's most unclear argument is that she provides no answer to whether FDI is possible in
her model. The model totally neglects the explanation of FDI although she claims that the model can
explain it.

2"Ethier (1992) provides a brief review of the recent development of formal models on F DI theory.

2‘8ubadditivity may be a better description in this case. Subadditivity of the cost function means that
the production cost of different products altogether is less than the sum of the cost of producing them
separately (Baumol 1977). By applying this concept to the case of existence of firm-specific knowledge,
an incumbent has the advantage over a new entrant by setting up an additional plant at a lower cost (since
the existing firm-specific knowledge can be transferred to the new plant). The production function is
therefore an example of subadditivity.

29
knowledge to explain the MNEs. He uses a model of differentiated products under the

assumption of the existence of firm-specific knowledge. In addition, there are
transportation costs and costs of overseas production. Transportation costs are positive for
exports while costs of overseas production are negligible. Due to the fact that firm-
specific knowledge can be transferred to different subsidiaries, if the transportation costs
are higher than the costs of overseas production, a firm finds it more profitable to
produce abroad rather than to export. Though Krugman's model can explain the choice
of a MNE on exporting or establishing a foreign subsidiary, the main dissatisfaction is
that there may be only exports or production in the foreign country but not both.26

In a two-country two-good two-factor model, Markusen (1984) further assumes that
one of the products is produced by a monopoly in each country. If a MNE operates a
plant in each country instead of the duopoly competition, it is possible (but not necessary)
for the world welfare to be increased because of the saving of the costs of producing the
firm-specific knowledge.

Helpman (1984) uses a monopolistic competition model (similar to Krugman's) by
assuming that the firm-specific knowledge is produced by a so-called general purpose
input. In a two-country, two-good, two-factor model (the two factors are the general
purpose input and labor), if the countries have different ratios of endowments in factors

and if there is complete specialization of production so that factor prices are not equal

 

z“Also realizing that existence of firm-specific knowledge is not sufficient for the appearance of MNE,
Horstrmnn and Markusen (1987a) compare the conditions of exports and FDI similar to Krugman's model:
the presence of transportation costs and tariff. But the model is closer to Markusen's (1984) model: a
homogeneous good with increasing returns to scale. 80 only a monopoly exists in a market. This paper has
the same problem as Krugman's paper: either exporting or FDI exists but not both.

30

under free trade, firms will operate subsidiaries in both countries. Therefore, whether or
not a MNE has the incentive to set up a subsidiary in the foreign country depends on the
endowments of factors apart from the firm-specific advantage.

Due to the ”public good” nature, Markusen's (1984) model is based on a market
dominated by a monopoly. It is because the expenses on the firm-specific knowledge are
similar to fixed costs that increasing returns to scale occur. In a homogeneous-good
market, the incumbent can monopolize the market by producing at a level that deters
potential rivals from entering. Potential entrants are discouraged if the required costs of
firm-specific knowledge cannot be covered by the new firm. In Krugman's (1983) or
Helpman's (1984) model, different firm-specific knowledge is required for producing
different varieties of a differentiated good, so more than one firm can exist within an
industry. Each variety is produced by at most one firm due to the increasing returns to
scale.

The three mentioned models are mainly related to horizontal integration. All of them
are related to the concepts of firm-specific knowledge. On the other hand, Krugman
(1983), Helpman (1985) and Ethier (1986) provide quite different reasons for vertical
integration.

Krugman (1983) uses a monopsony model to explain vertical integration. If an
intermediate product (produced in a foreign country) of the monopsony is characterized
by increasing marginal costs, the equilibrium marginal cost of any independent supplier
(equal to the marginal revenue of the monopsony) will be higher than the market price

of the product because any increase in purchase of the intermediate products will bid up

 

pr<

Inf

31

the price (of the intermediate goods) for all units. The monopsony therefore has the
incentive to acquire the independent foreign suppliers. The MNE can save costs by paying
the upstream subsidiaries only the marginal cost on each unit (with a different marginal
cost for each unit) rather than paying the unified price on all units in an open market. In
this model, firm-specific knowledge nwd not play a role.

Instead, Helpman's (1985) model is still based on firm-specific knowledge. He
develops the model by assuming that the varieties of a differentiated product are
continuous, which can be represented by a real number line. Each firm produces a
number of varieties such that a variety further away from the central variety has a higher
production cost. The firm—specific knowledge is incorporated into the production of
intermediate goods, but both kinds of inputs (the firm—specific knowledge and the
intermediate goods) can be separated from the production of the final goods. By also
assuming that there are only two basic factors (as in the 1984 model), it is possible for
a firm to have downstream integration in a foreign country when the factor prices are not
equalized under trade.

Ethier (1986) follows Dunning's argument on the role of internalization. He
emphasizes the importance of uncertainty and asymmetric information on vertical
integration. In the model, uncertainty affects R&D in a way that the turnout of production
may be either high- or low—cost. The possibility of low-cost production is higher if more
labor is involved in R&D. The problem of asymmetric information arises in the
production of the downstream final good. The supplier of the upstream good has better

information on the production costs than the manufacturer of the final good, thus a

32

contract has to be designed to be incentive compatible so that the supplier has no
incentive to tell lies and the supplier bears the whole risk. FDI is possible if the wage
rates are different in the two countries. If the dispersion of research is so large that the
high-cost turnout leads to negative profits but the possible low-cost turnout leads to
positive profits, the supplier may prefer to set up a downstream subsidiary abroad. This
is because, in this case, more labor in the source country can be put into R&D while the
foreign wage rate will be lowered under the MNE's direct control over downstream
production.

One insight from the Krugman-Markusen-Helpman (K-M-H) model is that general
equilibrium can give a clear map of the role of firm-specific knowledge. Generally
speaking, the firm-specific knowledge alone may not lead to FDI. Due to input
constraints (mainly immobility of labor), a firm will choose to operate in foreign
countries for the purpose of maximizing profits due to the location-specific advantage in
a foreign country (in addition to the firm-specific advantage).27

There are authors applying formal models on entry modes. Horstmann and Markusen
(1987b) compare licensing and FDI. Under a world of imperfect information and
asymmetric costs, they show the conditions for a firm choosing licensing or FDI. The
model includes high- and low-quality of a good and the techniques in producing the high-

quality good can only be supplied by the MNE. The price and cost are higher for the

 

27One other explanation of the rise of MNEs is that the service sectors require production in the local
areas. Boddewyn et a1. (1986) provide a good description of the investment in services. The main
characteristics of services include: intangibility (a telephone call), perishability (a flight ride), customization
(an engineering plan of a factory), simultaneity of production and consumption (a bank loan), consumer
participation in production (remote computer data-processing), and use without ownership (a car rental),
etc.

33
high—quality good while the price and cost are lower for the low-quality good. If the local

firm in the host country can produce economies of scale by combining the high- and low-
quality goods so that the cost combined is lower than the sum of producing the goods
separately, licensing is more attractive. However, when the market is larger, the local
firm has higher incentive to produce low-quality goods, and the reputation of the MNE
is damaged. Since the multinational firm finds it hard to detect such cheats, FDI is
preferred. One problem is that this paper takes transferability of firm-specific knowledge
to other firms for granted but in reality, the transferability is not generally true.

Ethier and Markusen (1991) further compare exporting, licensing and establishing a
wholly-owned subsidiary (not including joint ventures). They stress the technology
transfer from a MNE to the host country, and they analyze the different entry modes in
a two-period model. Under the assumption that exports are costly while licensing or
establishing a subsidiary leads to an earlier loss of advanced knowledge, a MNE has to
compare costs of different entry modes to achieve the highest profits.

In addition to the explanation of appearance of MNEs, Horstmann and Markusen
(1989) work out a model on welfare effects based on the existence of firm-specific
knowledge. Since the firm-specific costs can be saved in the host country, if the price is
forced down to the average cost due to competition among MNEs and the market of the
host country is too small to support a domestic firm, FDI is beneficial to the host

country.

Chapter 3

A Theory Of the Coexistence Of
International Joint Ventures And
Wholly-Owned Enterprises

3.1 Introduction

The previous chapter explained briefly that a joint venture is set up if joint-venturing
is beneficial to all the partners. For international joint ventures, the local partner can
provide a special benefit to the foreign partner. From recent empirical work investigating
the incentives for multinational firms based in Sweden to form joint ventures‘, it is found
that the firms with less experience in FDI and with more diversified products are more
likely to participate in joint ventures. It is advantageous for a foreign firm to cooperate
with the local firm when the multinational enterprise has less experience in FDI.
Moreover, the set-up costs will be much higher for an international corporation when the
firm needs to develop more different types of knowledge. For example, when a firm
produces more diversified products, it needs more information on the local market. Local
knowledge is a special kind of asset the local firms own, so an international corporation
with less experience or more diversified products should find it profitable to form a joint

venture with a local firm. Therefore, it is reasonable to suggest that there exists local

 

'Blomstrém and Zejan (1991).

34

 

 

35

knowledge in contrast to firm-specific knowledge.

Local knowledge is available to a firm after getting experience in production at a
certain location. In such a case, the firm has the advantage over other late comers to a
particular location. One example of an advantage is better knowledge of the local labor
market (so that recruitment and training of workers is more efficient). Another example
is better connection to other local suppliers and a better developed network with local
distributors. Moreover, a local firm has the advantage over foreign firms if there are
language and cultural barriers. The importance of cultural factors in a multinational
enterprise choosing between a wholly—owned subsidiary and a joint venture (with a local
firm) has already been pointed out’.

This chapter concentrates on the existence of local knowledge as an explanation of
why a multinational enterprise chooses to establish wholly-owned subsidiaries or joint
ventures in a foreign country; furthermore, this chapter tries to identify the conditions that
determine why a multinational enterprise sets up both wholly-owned subsidiaries and joint
ventures in a foreign country. The problem of internalization is not considered here. It
is simply assumed that all the subsidiaries of a firm can utilize the firm—specific advantage
of a firm without costs. Local advantage is assumed to be reflected in the difference in

marginal costs.

ZKogut and Singh (1988).

36
3.2 A General Equilibrium Model

The model can be taken as a revised version of Krugman (1983)3 while including some
elements of the set-up of Markusen (1984) and Helpman (1984). The model includes two
countries with only one differentiated good (as in Krugman) and two inelastically supplied
factors of production (similar to Helpman) while the firm-specific knowledge is produced
by labor from the headquarters (Krugman and Markusen). The factors are labor and
plant-specific input. The latter refers to the advantages of local knowledge which is
assumed non-transferable to other plants.

It is assumed that the two countries have different technology levels such that country
8 has higher labor productivity than country H. This assumption projects the investment
flows from developed countries to developing countries.

Good X is assumed to be differentiated in any number of varieties and all varieties are
symmetric to satisfy a typical consumer. An unusual assumption critical to the conclusion
is that N of the varieties produced have lower production costs than the other varieties.
In other words, it is assumed that the production of a fixed number of varieties has local
advantage such that the costs are lower. Each country is assigned N varieties with plant-
specific input.

The rationale of assuming two types of production costs can be seen in a historical
way. We may consider that there were only N firms entering the market in the previous
period with each firm producing one variety. Each firm developed local knowledge by

producing the certain variety. In the present period, the N old varieties can be produced

 

3Krugman's model of a differentiated good is adopted from his earlier papers (Krugman (1979, 1980)).

37

at lower costs and then less labor is hired. Therefore, new varieties (without local
knowledge) can be produced by using the ”leftover" labor. Although it is interesting to
look into a two-period model, only the static condition is considered here since a static
model is simple enough to fulfill the purpose in distinguishing the entry modes of wholly-

owned subsidiaries and joint ventures.

(A) Assumptions of the production side
The supply of possible varieties of good X can be unlimited but the feasible number

is constrained by the production and consumption functions. There are M and M‘
varieties available in country H and country 8 respectively. Each variety is assumed to
be produced by only one plant. But one firm can operate more than one plant. The
industry consists of a finite number of firms (at most N) with multiple plants within each
firm. The rest of this chapter assumes that in equilibrium, M>N and M'>N. These
conditions can be fulfilled if the amount of labor supply is very large.‘

Each country is endowed with L units of labor and N units of the plant-specific input.
Labor is freely mobile within a country but immobile across countries. Firm-specific
knowledge (an aggregate input representing marketing, technology and management
skills) is produced by labor. It is assumed that F units of labor are required to produce
the minimum amount of firm-specific knowledge nwded to operate any number of plants.
The location of manufacturing can be separated from the headquarters which provide the

firm-specific services, so each firm uses only F units of labor to produce the firm-specific

 

‘Please refer to equation (28) of a working paper with the same title.

38
knowledge.

Every unit of plant-specific input is used for producing a certain variety, non-
transferable to other varieties, and affixed to only one plant. Each firm in the market (at
most N firms) owns 1 unit of plant-specific input. While plant-specific input is not
necessary in the production of a variety, utilizing a unit of plant-specific input makes the
production costs lower for the same quantity of output. That is, the production of a plant
(apart from the firm-specific knowledge) may either include labor and plant-specific input
or include only labor. Accordingly, there are at most N varieties of good X produced
with plant-specific input while the other varieties are produced by using labor and firm-
specific knowledge only. The organization of a firm is shown in Figure 3.1.

Let us call the plants using plant-specific input low-cost-plants and the plants without
plant-specific input high-cost—plants. Each firm has at most one low-cost-plant but it can
operate any number of high-cost-plants. Firm-specific knowledge is provided by the
headquarters to the subsidiary plants so each plant need not produce the firm-specific
knowledge. The total number of plants in country H is M but each firm nwd not have
the same number of plants. Since the profit of a high-cost-plant is assumed to be zero
(which will be discussed in section 3.2), a firm cannot make more profits by operating

more plants.

39

 

 

Headquarters

 

 

 

Firm—specific Knowledge

 

 

 

Eow-cost-plant] I High-cost-plant]

 

 

 

High-cost-plant:

 

Labor & Labor
Plant-specific

Input

 

Labor

 

Figure 3.1: The Organization of a Firm

 

 

40
As all the N units of plant-specific input are owned by N different firms, an oligopoly

of at most N firms arises in the product market. Although entry is potentially possible,
the new entrants cannot compete with the incumbents. The existence of plant-specific
input and firm-specific knowledge makes the incumbents efficient enough to block
potential rivals from entry because an existing firm need not produce the firm-specific
knowledge for operating a new plant. But new entrants have the additional costs of
producing the firm-specific knowledge for operating the first plant. Moreover, the
additional profits from a low-cost-plant allow an existing firm to survive under zero
profits in each new plant (high-cost—plant), so the incumbents have the advantage over all
potential rivals.’

It is more convenient to use cost functions in the supply side to describe the
production of good X. The difference between low-cost—plants and high-cost-plants is only
reflected in marginal costs. Fixed costs are the same for all plants. The labor required
in producing a variety can be summarized as:

Low-cost—plants:

L, =A + B,x,, i= 1, ,N, (3.1a)

 

’This is related to the contestable market theory (please refer to Baumol et al.(l982)). Under this
theory, a monopoly cannot make profits in the face of potential rivals because the monopoly keeps the price
low enough to block entrants; consequently no profits are made if all firms have the same technology. But
as Shepherd (1984) points out, the contestable “competition“ holds only in some restrictive conditions.

In this model, the producer of each variety has some monopoly power. Due to the entry of new plants
for producing different varieties, the profits of all the plants without plant-specific inputs will be equal to
zero, however, the plants with local knowledge can make positive profits by operating at a lower cost.

41

High-cost-plants:

LJ=A+th, j=N+l,...,M,

BI: > B! , (3.1b)

where A, B. and B, are constants; x, and x,- are outputs of a low-cost-plant and a high-
cost-plant respectively. Due to the lower costs from using plant-specific input, B, is
smaller than Bh. B. denotes the marginal cost of a low-cost-plant which has a lower cost
while B, denotes the marginal cost of a high-cost-plant which has a higher cost. Li and
Lj are the labor required in producing good X by a low-cost-plant and a high-cost-plant
respectively. When producing the same quantity of outputs, a low-cost—plant uses less
labor than a high-cost-plant, i.e. L,<Lj if x,=x,-.

To get total cost functions, one simply multiplies (3.1a) and (3. lb) by the wage rate:

Low-cost-plants:

TCI. = Liw = (A + B,x,)w, i = l, ,N , (3.2a)

High—cost—plants:

.2
TC]. =ij=(A +thj)w, j =N+1,...,M, (3 b)

where w is the wage rate. By assuming that labor is perfectly mobile within a country and
all workers are identical, the wage rate is the same for all workers. The total cost of a
plant is simply equal to the amount of labor used multiplied by the wage rate. Let AC.
and AC, be the average costs of a low-cost-plant and a high-cost-plant respectively; MC.

and MC, are the marginal costs of a low-cost-plant and a high-cost-plant respectively. It

42
can be easily seen that AC.<AC,, and MC.<MC,, in the same quantity produced.

Furthermore, AC. and AC, decrease as outputs increase.

Country 8 is only different from country H at the technology level. It is assumed that
the only difference is shown by the fixed costs, therefore, in country 8, the total cost
functions of low-cost-plants and high-cost-plants are:

Low-cost—plants (country 8):

TCI.‘ = Li‘w‘ = (A‘ + B,x,‘)w‘ , i= 1, ,N ,

High-cost-plants (country 8):

TCJ.‘ = Lj‘w‘ = (A‘ + thfW' , j = N+1, ,M‘ ,
A‘ <A ,

where the asterisks represent the different values in country 8. All the difference is due

to the technology gaps, i.e. A'<A.

(B) As um 'on f he demand sid

The consumers are divided into workers and entrepreneurs. Each worker owns 1 unit
of labor while each entrepreneur owns 1 unit of plant-specific input and 1 unit of labor
and operates at most 1 firm. Each entrepreneur may choose to maintain his status or
choose to be a worker but he cannot play both roles. If all the plant-specific inputs are
utilized, there are L workers and N entrepreneurs in a country. Let ci denote the
consumption of variety i of good X by a worker and (1, denote the consumption of variety

i by an entrepreneur. And by assuming that preferences of all individuals are identical,

43
an individual (of country H) has the utility function:

M (3.3)

where Q is the number of varieties of good X consumed. (In autarky, it should be noted
that Q=M.) It is easily seen that the first derivative of the utility function with respect
to ei is positive but the second derivative is negative. As everyone has the same utility
function as (3.3), it is well-known that the elasticity of demand for each variety becomes:

1
8:—
1-eI

Analogously, a consumer in country 8 has the following utility function:

Since the incomes may be different in the two countries, the consumption level may also

be different.

(C) Fpll employment

The full employment condition is fulfilled by the assumption of perfectly mobile labor.
The labor is used in the two types of plants and in production of firm-specific knowledge.

If all the plant-specific input is used, there are N firms with totally N low-cost-plants and

44

(M-N) high-cost-plants. The full employment condition in country H is represented by:

N ll
L = 2 (A + B,x,) + 2 (A + 3,15.) + NF (3.4)
1-1 j-N+l _

The full employment condition in country 8 is represented by:

N u:
L = E (A‘ + B,x,‘) + z (A‘ + thj‘) +NF
i-r j-N+1

It is possible that not all units of plant-specific input are used or no high-cost-plants

are operating.

3.3 Equilibrium In A Closed Economy

In this section, only country H is analyzed. The equilibrium conditions of country 8
follow straight-forwardly. In addition to the assumptions of profit maximization and free
entry (new plants, not new firms), a rather strict assumption is that the firms from the
same country cannot cooperate together, and there is no strategic interdependence
between firms. This assumption may not be realistic as the firms have the incentive to
join together for saving firm-specific costs and yielding more profits from greater
monopoly power. To partly solve this problem, it is assumed that the firms are prohibited
from joining together or merging together locally by law (but joint-venturing with or
taking over foreign firms is allowed). And N is assumed to be large enough to make
strategic behaviors insignificant.

In order to guarantee that an entrepreneur does not choose to be a worker, the profit

45

rate must not be less than the wage rate. Let 1: be the profit earned by a representative
entrepreneur (we will see that the profits of all firms are the same) and w be the wage

earned by a typical worker; the condition for a firm staying in the market is that 1t:.>.w.‘S

Demand fimctions

All consumers are assumed to maximize their utilities. The workers earn only wages
and the entrepreneurs earn only profits. Let U‘” be the utility of a worker. Every worker
maximizes his utility function of (3.3) subject to his budget constraint:

u
Max UW=Z cf

i=1

I!
Subject to w = 2 pic, ,
t-l

where pi is the price of ith variety of good X. Using the Lagrange Multiplier A and

solving the first order condition, we have:

6c;H = 1p, . (35)
Similarly, let U" be the utility of an entrepreneur. Every entrepreneur maximizes his

utility function subject to the budget constraint as follows:

 

‘The meaning of profits is different from the usual definition. The accounting concept is adopted in this
chapter. Let EP be the economic profits; it is easy to see that 1: 2 w as EP 2 O and vice versa.

46

U
Max U" = 2 di"
:-1

11
Subject to 1! = E pid, .
1-1

The main difference between a worker and an entrepreneur is that the profit rate may not
be the same as the wage rate. Using the Lagrange Multiplier I‘ and solving the first order

condition, we have:

6d,“ = m. (3.6)

There are two kinds of varieties to be consumed: low-cost or high-cost, i.e. i=0 or
h. From either (3.5) or (3.6), the ratio between the prices of a low-cost-variety (output
of a low—cost-plant) and a high-cost-variety (output of a high-cost-plant) can be written
in terms of the ratio between the quantity demanded of a low-cost-variety and a high-cost-

variety:

5 = (5)” (3.7)
Pb

Profit maximization
By assuming that all firms seek profit maximization, we have the following condition

for sector X:

47
MC, = MR, , i = 1, ,M , (3.8)

where MC, and MRi are respectively the marginal cost and the marginal revenue of either
a low-cost-plant or a high-cost-plant. Since the marginal cost of a low—cost-plant is lower
than that of a high-cost-plant, we will see that the output of low-cost-plant is larger than
a high-cost-plant. Let the total revenue for variety i be TR,-=p,xi, the marginal revenue

for variety i can be derived by using the fact that e=1/(1-6):

MR, = p,(1 - .3] = piB (3.9)
From (3.2a) and (3.2b), we have the marginal costs as follows:
Low-cost-plants:
MC, = B,w , i = 1, ,N , (3.108)
High-cost-plants:
MC]. = Bhw , j = N+1, ,M . (3.10b)

Therefore, from the profit maximizing (3.8), combining (3.9) with (3. 10a) and (3. 10b)
separately, the equilibrium prices of a low-cost-variety and a high-cost-variety are in
terms of the wage rate:

Low-cost-varieties:

B
P,- = “61W 9 i = 1, ,N , (3.118)

48

High-cost-varieties:

p, = .géw, j = N+1, ,M. (3.1111)

Determination of the number of plants
The profit of each plant is the difference between the total revenue and the total cost
of the respective plant:

Low—cost-plants:

.12
n, =p,x, —- (A + B,x,)w, 1°: 1, ,N, (3 a)

high-cost-plants:

. (3.12b)
nj=pjxj-(A +thj)w, J =N+1,...,M.

Let us assume that the profit rate of a low-cost-plant net of the firm-specific costs is not
less than the wage rate. Under free entry, the profits of all high-cost-plants are equal to
zero, i.e. 1t,-=O. Because the demands for all varieties are symmetric and the marginal
costs of all plants of the same kind are equal, the prices, outputs and profits of all high-
cost-varieties are the same: pj=ph, xj=xh and 1tj=1th=0, j=N+l,...,M. Similarly, for
all low-cost-varieties: pi=p,, x,=x, and 1t,=1t., i=l,...,N. (The total profits of a firm
combines the profits from all subsidiary plants minus the firm-specific costs. The firm
profit function will be shown later in (3.16).) Then from the zero profit condition of a

high-cost-plant and applying (3.11b), we have:

— (3.13)

Let

B L
p=-"-]“°>l
(31 .

Substituting the equilibrium prices ((3.11a) and (3.11b)) and the equilibrium output of a
high-cost-variety (equation (3.13)) into the demand function (equation (3.7)), the

equilibrium output of a low-cost-plant is in terms of the exogenous variables:

6 A
= _ — >
Jr: 1-6 B,” x, (3.14)

The next variable we want to solve for is the equilibrium profit of a low-cost—plant.

Substituting (3.11a) and (3.14) into (3.12a), we have:

1:, = (p -1)Aw (3.15)

1: is the total profit for the firm:

1t=n,-Fw

(3.16)

[(B-1)A - Flw.

Substituting the equilibrium prices ((3. 11a) and (3.11b)) and outputs ((3. 13) and (3. 14))
into the full employment condition (equation (3.4)), the number of varieties available in

country H is:

50

M = (1-6)(L-NF) + emu-p)

A (3.17)

 

As all the owners of plant-specific input choose to be entrepreneurs, it must be nzw.

Comparing 1c (i.e. (3.16)) and w, we have:

 

 

W)
- 6 2 = 4) (3.18)

 

This chapter assumes that (3.18) holds. The equilibrium conditions for (3.18) not

holding are discussed in a working paper with the same title.7

3.4 Equilibrium Condition Under Free Trade But Without FDI

Suppose that trade is allowed freely in both countries but FDI is prohibited. From the
utility functions we can see that the consumers prefer more varieties within the same
budget constraint. A variety produced in either country will be consumed by all
consumers, therefore, there is intra-industry trade between the two countries“.

Because there is no mechanism to ensure that the incomes of the workers will be equal

 

7Please refer to pp.22-28 of the working paper.

'This is the basic result under a model of monopolistic competition (Krugman 1979, 1980).

51

in both countries (and indwd they are different), the demand functions for the varieties
produced in country H may be different from those in country S, and then the prices are
different in the two countries. But it can be shown that the price elasticities of demand
for all varieties are still the same (e=1/(1-9)). The output of a variety is then the same

as in a closed economy:

 

 

_ e A
- _9_fi
19 H, a,” . (3.14)
. _ 6 A‘
x, —1-6 B. (3.19)
. _ 6 A‘
x, —l -6 B: D (3.20)

Since A'<A, the output of a variety (produced by a same-class-plant) in country S is
smaller than that in country H, i.e. xh'<x,, and x,’<x,.

On the other hand, the output can be represented as the sum of consumption by all
consumers. Let the variables with superscripts H be consumption of the varieties
produced in country H; the variables with superscripts S are consumption of the varieties

produced in country S. Then we have:

 

52

x, = L(c,f’+c;") + N(d,”+d,") k = h or 1, (3.21)

x; = Label“) + N(d,;‘+d,") k = h or z. (3.22)

The subscript h denotes the output or individual consumption on high-cost—variety while
the subscript t denotes a variable on a low-cost-variety.
Taking the first derivative of the utility function of a country H worker, the following

first order conditions can be found:

66*” 0-1 = Apt
ticks“ = 1p; k = h or I,

where p, and pf are the prices of the varieties produced in country H and country S

respectively. From the first order condition, accordingly, the relationship between q," and

cks is:

 

The similar relationship for the other type of consumers (entrepreneurs) in country H can

be derived in the same way:

 

1
d: = P): H) dkH
PI:

The relationships also apply to the consumers in country S. Then substituting all the four

53
relationships into (3.21) and dividing the result by (3.22), the relationship between the

prices and the outputs is:

 

1
Pk T3
.—
x1: '( , 3‘1:

1’1:

From (3.13) and (3.19), we already know that xh'<xh, and because O<6<1, the

following relationship can be seen:

 

1
pl! 1‘0 < 1 _. phi. >ph
p.‘

 

Similarly, P,‘> P,. Since the wage rate has the same positive relationship with the
respective price, we have w' > w.

It is interesting to note that the lower fixed cost in country H leads to a higher price.
A possible explanation is that as a higher fixed cost of a variety requires a larger
production of that variety so that the disadvantage of higher cost is compensated for by
the economies of scale. We already have the fact that x,,'<xh and x,‘<x,. Because the
demands for all varieties are symmetric, when the supply of a variety is larger, the price
will be lower. The reverse is true for a lower fixed cost.

The profit rates of a firm H and a firm S are respectively:

 

54

1t =[(B-1)A - F]w. (3.16)

no ___ [(p_l)A-t _ Flwt . (3.23)

Comparing the profit rate between a firm S and a firm H, we have:

A‘ 0 1-6
1 1-1 W1) w]
A A‘ .

u' < 1|: since both the first and the second terms within the braces are negative (recall that

n‘—rt=A

 

 

 

A > A'). This result implies that the profit rate in the advanced country is lower.
Intuitively, when the fixed cost is lower for producing a variety, more varieties can be
produced with the same resources but each variety is sold in lower quantity. Though the
prices are higher for the products from country S, the higher revenue per unit may not
compensate for the loss in the quantity sold. Moreover, since the production is subject
to increasing returns to scale, as the quantity produced is smaller, a firm loses the
advantage of the economies of scale. As a result, the profit rate of a firm S is lower than
that of a firm H.

Dividing (3.16) and (3.23) by w, we have the following relationship:

55

 

 

3 =113-1)A — F = 331A)

W W ’
“Z =(1s-1)A' -F= “:(A‘)
W W

The relationship between n/w and 9 (or n'lw' and 0) is shown in Figure 3.2. 1t/w(A) and
it‘lw‘(A') represent the above relationship in which the former depends on A while the
latter depends on A'. From (3. 18), we have seen that if all N firms stay in one country,
02¢ for ensuring 1:2w. Therefore, if 6 < 11), some entrepreneurs become workers and the
remaining firms can earn a profit rate equal to the wage rate only. So both curves are
horizontal at the level equal to 1t/w=1 or n‘lw'= 1. If 92¢, the difference between 11: and
w (or 1t' and w') becomes larger and both curves rise upwardly. As O < 6 < 1, the curves
have a rightward bound of 6: 1. The income distribution is more uneven in country H
than in country S, so 1t/w(A) is laid above n'lw'(A') at the portion of 9>¢.

It is interesting to note that if the technology level is higher (the fixed cost is lower),
the relative income differential between the two kinds of consumers is narrower. It is
directly implied by the fact that 1t>1t° but w< w’. One further reason for this result is
that when the supply of varieties of good X is larger, the competition for labor is tighter
and then the income is more likely to be transferred from the entrepreneurs to the

workers.

56

 

 

 

 

 

3: 3!:
I
l
l
11" ,..
3:113)
I
l
I
1 3 I
I
I
I
I
I
0 It 1

 

Figure 3.2: The Profit-Wage Ratio with respect to 6

 

57
3.5 Decisions On FDI

Now suppose that the two countries agree to trade freely and FDI is allowed with no
impediments (but labor is not mobile across countries). Since country S is the developed
country (A' < A), it is clear that country S may find it profitable to set up subsidiaries in
country H as the production costs are lower in country H (w < w’). It is assumed that the
technology level is based on the firm-specific knowledge, therefore, although the wage
rate is lower in country H so the firm-specific knowledge can be produced in that country
more cheaply, country S has to be the headquarters of multinational enterprises in order
to get the advanced technology.

A firm S (a firm with the headquarters in country S) can choose the following activities
to get into the market in country H: exporting, setting-up a new plant, acquiring a local
plant or forming a joint venture with a local firm.

While a multinational enterprise can get benefits by joint-venturing, there will be
additional costs within a joint venture because the parent firms may have different targets
or both try to get a larger share of profits at the expense of the partner(s)9. We will not
go in details into these matters but simply assume a fixed labor usage, J, being the
c00peration cost.

An acquisition or merger is an alternative to setting up a new plant or joint-venturing.
Buyout of an existing firm has a purpose similar to joint-venturing because of access to
the plant-specific input. However, the adaptation of the acquirer's existing management

system to the acquired's system may be very costly. Moreover, acquisitions or mergers

\

°Recent models on the problem of cooperation between two partners within a joint venture can be found
in Darrough and Stoughton (1989) and Chan and Hoy (1991).

58

require much more capital investment so they are more risky. Capital involvement and
uncertain matters are neglected in order to simplify the model. Only a fixed labor
requirement, R, is assumed to exist from the acquisition of a local firm.

Moreover, since cultural differences increase the difficulty for foreign investors, it is
assumed that there is extra labor usage of C for any foreign firm adapting to the local
environment. Therefore, if a firm S sets up a new plant in country H, the plant has to use
extra labor of C units in addition to the total cost of a high-cost-plant in country S. If the
firm acquires a plant in the host country, the extra labor usage is C+R. If the firm joins
with a local firm to run a plant, the extra labor need is C+J. It is clear that a firm S
prefers setting up new plants in country H rather than acquiring or joint-venturing if the
local plant has no advantage over the investing firm. That is, a firm S will not acquire

or act as a partner for any high-cost-plant which has no local advantage.

Proposition 3.1: A necessary condition for the appearance of FDI is A > A'+ C.
Proof:

When a firm S decides whether to set up a plant in country H or not, it has to
compare its gains from advanced technology with the costs from adaptation to the local
market. A subsidiary plant (high-cost—plant) of a firm S in country H has the total cost
(A‘+C+thh)w while a high-cost-plant of a firm H has the total cost (A +thh)w when
the outputs of both plants are the same. If A > A°+C, a firm S can run a high-cost-plant
in country H in a lower cost than the local high-cost-plants. It is obvious that firms S will

invest in country H. Then all the high-cost-plants in country H are operated by firms S

59

while firms H can only retain, at most, low-cost—plants. If A<A'+C, firms S cannot
compete with the local firms in production in the host country. Firms S have no incentive
to invest in country H at all. Since at most, only one means of investment is possible, no
FDI appears in this case.

It should be noted that if A =A'+C, a firm S has no disadvantage in operating a high-
cost-plant in country H as the local high—cost-plants. However, since the profit of each
existing high-cost—plant is zero, one more plant will only lead to negative profits,
consequently, firms S do not have any interest in investing in country H. Therefore, the
condition of a firm S becoming a multinational enterprise is A > A'+C instead of

A2A'+C. C]

From the proof above, it is immediate to have a lemma:
Lemma 3.1: If A > A'+ C, all the high-cost—plants in country H are operated by firms

S.

When a firm S becomes a multinational enterprise, there is further consideration about
how to invest. Assume that an owner of plant-specific input prefers not to transfer his or
her ownership unless he or she has a higher income. Also assume that an owner does not
want to change his or her status as an entrepreneur unless he or she can earn more
income. However, if an entrepreneur has the same income to remain as an owner or to
become a worker, he or she prefers the status quo. The following propositions summarize

the decisions of firms H and firms S on whether forming joint-ventures or not.

60

Let 1r' and It” be the profits of a joint venture and a wholly—owned subsidiary
transformed from acquisition respectively; It' denotes the profit of a firm H. We have

some propositions below.

Proposition 3.2: If A > A'+ C, the necessary condition for a firm S forming a joint
venture with a firm H is n" 2 Max[1t"',w].
Proof:

As a firm is assumed to maximize its own profit, it chooses a kind of investment
which provides the greatest profit rate. If the multinational firm can earn more profits
from acquisition, i.e. 1:” > 112’ , acquisition will be preferred to joint-venturing. If the wage
rate is higher than the joint venture, i.e. w > it’, the joint venture cannot provide sufficient
remunerations to the entrepreneur H. Joint venturing is preferred if 1H > 11"” and 1c’ > w.
If 1c’=1tR'=w, an entrepreneur H still prefer joint-venturing as they can maintain the
operation of a plant if all the profit from the joint venture goes to the entrepreneur. So
the necessary condition for a firm S forming a joint venture with a firm H is n’ 2

Max[1tR',w]. El

Proposition 3.3: If A>A’+C, a firm H will be out of business if 1t'<w or

< F+A+l

B
A'+C

(3.24)

unless a firm S is willing to cooperate with it.

61

Proof:
When A>A'+C, according to Proposition 3.1, firms S invade country H and all
high-cost-plants are controlled by firms S. Firms H retain only at most low-cost—plants.

Suppose a firm H runs the business under its whole control, it has the profit as:

n’ = pg,’ — (A +B,x,’)w — Fw , (3.25)
where the superscript I denotes the equilibrium state under the invasion of firms S. The
profit of a high-cost-plant in country H, on the other hand, is equal to zero due to free

entry of firms S:

u," = 11,11; - (A'+C+B,x,,’)w = o .
The prices of all varieties have the same forms as in a closed economy ((3.11a) and
(3.11b)) with only a (possible) difference in wage rates due to constant price elasticities

of demand and the same marginal costs. But the equilibrium outputs are different:

 

 

1: 6 A.+C
x’ 1-6 B, p
and
1_ 6 A‘i'C
xh -
1-6 3,.

Substituting the equilibrium price function (3.11a) and the above equilibrium output of

x,1 into (3.25), it follows that the profit rate of a firm H is:

62

11’ = [p(A‘+c) — (F+A)]w. (3.25')
The entrepreneurs H prefer to be workers if 1t‘< w. From (3.25 '), we have the condition

that no firms H are willing to stay in the market unless firms H and firms S join together:

< F+A+l
A‘+C .

 

D (3.24)

C]

It is interesting to note that if A'+C is smaller or F+A+l is larger, [3 is more likely
to be smaller than (F +A+1)/(A'+C). This means that when the fixed costs of the
foreigners are relatively smaller, the local advantage of the local firms becomes less
favorable and then the profit rate of an entrepreneur H is more likely to be lower than
the wage rate. However, if a firm S offers to join with a firm H by providing the latter
a share at least the same as the wage rate, the firm H will stay in the market by forming

a joint venture with the foreign partner; otherwise, the firm H will leave the market.

Proposition 3.4: If A > A'+C and B < (F+A+ l)/ (A'+ C) (i.e. 1t‘ < w), the conditions
for a firm S forming a joint venture with a firm H are F+A>A'+C+J (or Ir'ZW)
and R2J+1 (or 19211:”).
Proof:

This proposition follows Proposition 3.2 and Proposition 3.3. The parameters are
derived in the following paragraphs.

When a firm S has the advantage over its foreign counterparts, in addition to setting

up high-cost—plants, it considers whether it is profitable to operate a low-cost-plant in the

63

host country through acquisition or by joint-venturing. If a firm S acquires a local firm,

the profit of that low-cost-plant is:

“R0 =p'xll __ (A¢+C+R+Brxll)w ,

or by using the equilibrium price (3.11a) and the value of x], we have:

n“=I1A'+C)Is - (A‘+C+R)]W. (3°26)
where the superscript R' denotes the equilibrium state under acquisition behaviors.
Though the marginal cost B. is obtained by buying a low-cost-plant, the fixed cost is
(A'+C+R)w as the adaptation is costly. An entrepreneur H is willing to sell his or her
firm at any positive price as he or she is planning to close the firm. This is logical since
under the assumption that all individuals desire higher income and no one cares about
each other's income, other things being constant, the entrepreneur H prefers a positive
income by selling his assets rather than letting the firm stand idle without any revenue.

Therefore, a firm S can take over a firm H if n‘°>0. From (3.26), it becomes:

>.A_.LC;R=1+ R

A'+C A‘+C_

(3 (3.27)

 

If (3.27) is fulfilled, it is possible for a firm S to acquire a firm H.

On the other hand, a joint venture has the profit rate as:

11" = pg] - (A‘+C+J+B,x,’)w ,

0f

64

n1 = [(A’+C)p - (A'+C+J+B,x,’)]w, (3.28)
by using (3.11a) and the equilibrium value, x}. The superscript J means the equilibrium
state under joint-venturing. As the joint venture can share the firm-specific knowledge
from the parent S and the plant-specific input from parent H, A' is included in the
production function and PW (the firm-specific cost) is saved. Since an entrepreneur H
maintains his or her position only if the earning is not less than w, the firm S has the
incentive to form a joint venture if the profit rate of a low-cost-plant is at least the same
as the wage rate: n’Zw. From (3.28), this means:

A‘+C+J+l =1+ J+1

(32
A‘+C A‘+C_

(3.29)

 

 

Equation (3.29) is the necessary condition that a firm S is willing to form a joint venture
with a firm H.

Because firms S compete with each other in searching for partners in joint ventures
or targets for acquisition, the profits will totally go to the firms H (or the former firms
H whatever case is applied). From the viewpoint of firms H (or former firms H), the
highest bid is desirable. A joint venture is preferred over acquisition if n’ > It” and then.
If both (3.27) and (3.29) stand, comparing (3.26) and (3.28), we have the condition: a
joint venture is preferred if R > J +1 and then (3.29) holds. Reminding that when 1t’ =1t'",
a joint venture is formed as an entrepreneur prefers to retain operation in a plant.
Combining (3.24), the conditions of joint-venturing are (F +A) > (A'+C +J) and R21 +1.

The intuition is obvious that when the fixed cost of a firm H (with only one plant) is

65

higher than the fixed cost of a joint venture, and the cost of acquisition is higher than the
cooperation cost of joint-venturing plus the wage rate, a firm S will form a joint venture

with a firm H. U

Similarly, acquisition is preferred if tt’ < 1:” and then B > [1 +R/(A‘+C)] and
R<J+ 1. Combining with (3.24), we have the conditions (F +A+ 1) > (A'+C+R) and
R < J + l. Low-cost-plants in country H will close down if neither [32[1+(J+1)/(A'+C)]
nor B > [1 +R/(A'+C)] holds.

On the other hand, the following propositions describe the conditions that firms H can

survive in the market under the invasion of firms S.

Proposition 3.5: If A > A'+ C, a firm H may stay in the market to have its low-cost-
plant under its total control if it'.>.w or

2 F+A+l
A‘+C

5 (3.30)

unless the firm H is willing to sell all the assets to a firm S or to form a joint venture
with a firm S.
Proof:

(3.30) is simply the reverse of (3.24) and the opposite explanation to Proposition 3.2
is applied here. One point to be noted is that if B=[(F+A+ l)/(A'+C)], the profit rate
of a firm H is equal to the wage rate. Then in this case, firms H stay in the market as

acquisition or joint-venturing is not attractive enough. El

66
Proposition 3.6: If A>A'+C and BZ(F+A+1)/(A'+C) (i.e. 1t'2w), the necessary

conditions for a firm S forming a joint venture with firm H is F+A> A’+C+J (or
1r'>1t') and RZJ (or 192w).
Proof:

If acquisition is preferred to joint-venturing, (3.26) is the total cost of the acquired
low-cost-plant. If joint-venturing is preferred, the total cost of the joint venture is equal
to (3.28).

If a firm S is able to acquire a low-cost-plant from a firm H, the acquirer has to pay
a compensation to the acquired more than the income of the latter. That is, 1t“°>1t‘.

Using this restriction by comparing (3.25') and (3.26), we have:

[(A'+C)l3 - (A'+C+R)]W > [(A'+C)B ‘(F+A)]W-

After simplifying, it becomes:

F+A >A‘+C+R. (3°31)
For a joint venture to be formed, the profit of the joint venture has to be greater than
the low-cost-plant operated by firm H alone so that the income of an entrepreneur H can
be covered by the earnings of the joint venture. From (3.25') and (3.28), this restriction

implies:

[(A’+C)B - (A‘+C+J)]W > [(A‘+C)13-(F+A)lw .

And after simplifying, we have:

67

. F+A >A‘+C+J. (3-32)
Comparing the costs, joint-venturing is preferred to acquisition if R>J. The
entrepreneurs H prefers joint-venturing even if R=J. In summary, the conditions for

preferring joint-venturing are F+A>A‘+C+J and RZJ. Cl

Similarly, acquisition is possible if F+A> A'+C+R and R<J. If neither
F+A> A'+C+J nor F+A > A‘+C+R holds, firms H maintain complete control over
their low-cost—plants.

The different cases of the possible forms of ownership in country H can be
summarized in Table 3.1. It is helpful to follow the table by explaining the notations
intuitively. The fixed cost of a firm-H-plant is denoted by A while A‘+C denotes the
fixed cost of a firm-S-plant in country H. If A is smaller than A'+C, it means that the
technological advantages of firms S do not compensate for the cost of adaptation in
country H. No firms S can compete with firms H and case (5) includes the situations that
no FDI occurs. Conversely, for cases (1) to (4), the technological advantage of a firm S
can compensate for the cost of adaption in country H, FDI is possible and all high-cost-
plants in country H are operated by firms S.

B reflects the importance of local knowledge (B=(Bh/B,)°"“°’> 1). The larger is B,
the more important is local knowledge, and vice versa. (F +A+ 1) is related to the firm—
specific cost and the total fixed cost of the low-cost-plant of a firm H plus the wage rate.
The wage rate is the opportunity cost of an entrepreneur (i.e. "1" in the total fixed labor

requirement, F+A+ 1) and then it should be counted. (F+A+1)/(A'+C) compares the

68

costs of a firm H (only operating a low-cost—plant) and the fixed costs of a firm S's high-
cost-plant. The larger is (F+A+1)/(A'+C), the greater is the advantage of a firm S over
a firm H, and vice versa. If B< (F +A+1)/(A'+C), it means that the local knowledge
is not as important as the technological advantage and then firms H may be driven out
of the market.

1 +R/(A'+C) (=(A'+C +R)/(A'+C)) refers to the comparison between the minimum
costs of a acquired low-cost—plant and a new-establishing plant of firm S (low cost) in
country H. The bigger is 1+R/(A'+C), the less the advantage of acquisition over a
newly set-up plant of a firm S. If BS[1+R/(A'+C)], the gain from the local knowledge
is not greater than the extra cost of acquisition (and vice versa) and then acquisition is not
justified.

1+(J+ l)/(A'+C) (=(A'+C+J+ l)/(A'+C)) refers to the comparison between the
minimum costs of a firm S from a joint venture and the cost of a high—cost-plant newly
set up by the firm S in country H. The opportunity cost of an entrepreneur H is taken
into account and then "1” is included in the numerator. The larger is 1+(J+1)/(A'+C),
the less the advantage of joint-venturing over a new set-up plant of a firm S. If
B < [1 +(J + 1)/(A'+C)], the gain from the local knowledge is smaller than the minimum
extra cost paid by firm S for the joint-venturing. No joint ventures will be formed in this
case.

For case (1), FDI is possible. However, the local knowledge is not as important as
the technological knowledge (i.e. B<(F+A+ l)/(A‘+C)) and the advantage of getting

local knowledge cannot compensate for either acquisition or joint-venturing. Firms S will

69

only set up high-cost-plants in country H.

A’+C+R is the fixed cost of an acquired plant and A‘+C+J is the fixed cost of a
joint venture. If F+A>A'+C+R, the total fixed costs of a firm H (operating only a
low-cost-plant) are larger than the minimum fixed costs of an acquired firm and then
acquisition is possible and vice versa. Analogously, if F+A > A’+C+J, the total fixed
costs of a firm H are larger than the minimum fixed costs of a joint venture and then
joint-venturing is possible, and vice versa.

For case (4), the local knowledge is more important (i.e. B.>.(F+A+1)/(A'+C)) and
the total fixed costs of a firm H are lower than either the minimum cooperation costs or
the minimum acquisition costs (i.e. F +ASA'+C +R and F+ASA'+C+J), firms S retain
low-cost—plants alone. Both foreign firms and local firms operate their own wholly-owned
firms.

Even if the local knowledge is more important than the technological advantage (i.e.
B2(F+A+1)/(A'+C)), if the minimum fixed costs of an acquired plant are smaller than
the total fixed costs of a firm H (i.e. F+A >A'+C+R) and the adaptation cost of that
acquired plant is lower than the cooperation cost of a joint venture (i.e. R < J), acquisition
is possible. This is the second part of case (2).

Although the local knowledge is not as important as the technical advantage of firms
S (i.e. B < (F+A+1)/(A'+C)), if the benefit from the local knowledge is larger than the
extra cost from acquisition (i.e. B > [1+R/(A'+C)] and accordingly, (F+A+ l)
> (A'+C+R)) and the adaption cost is lower than that of joint-venturing plus the wage

rate (i.e. R<J+1), acquisition is possible. This is the first part of case (2).

70

Table 3.1: The Summary of Forms of Ownership in Country H

 

Ownership forms in Country H

 

 

 

 

 

 

 

 

 

 

A > A' + C, Foreign wholly-owned subsidiaries
B < [(F + A + 1)/(A' + C)] , (high-cost-plants only)
BS[1+R/(A‘+C)] &

B < [l +(J+1)/(A'+C)]

(2) A > A' + C, Foreign wholly-owned subsidiaries
B < [(F + A + 1)/(A‘+C)] , (high-cost- and low-cost—plants)
F+A>A‘+C+R & R<J+1
A > A‘ + C, Foreign wholly-owned subsidiaries
B.>.[(F+A+1)/(A'+C)], (high-cost- and low-cost-plants)
F+A> A'+C+R & R<J

(3) A > A‘ +C, Foreign wholly-owned subsidiaries,
B < [(F + A + 1)/(A' + C)] , international joint ventures
F+A>A‘+C+J & 132J+1
A > A' +C, Foreign wholly-owned subsidiaries,
B2[(F+A+1)/(A'+C)], international joint ventures
F+A > A’+C+J & R2]

(4) A > A' + C, Foreign wholly-owned subsidiaries,
B.>_[(F +A + 1)/(A' +C)] , domestic wholly-owned firms
F + ASA. + C + R &

F + ASA. + C +1

(5) A.<_A'+ C Domestic wholly—owned firms (both

high-cost-plants and low—cost-plants)

 

 

71

 

_i __I Foreign
B Lx+c\ _ ’rt‘J—n

Domestic
hhol 1y-
Cured

    

\
TE=W

.- “mint—A—Au—“u

     

i Foreign molly-001nm!

 

 

o 1' / A'+C 11'+c+J-F A

Foreign molly—cured
:1 Domestic “rally—Outed

 

 

 

Figure 3.3: An Example of the distribution of Ownership Forms in Country H with

R>J+l>F-C+1>l and F+1>J>F

72
Similarly, when the local knowledge is more important than the technological

advantage (i.e. B2(F+A+1)/(A'+C)), if the minimum fixed costs of a joint venture are
smaller (i.e. F+A > A'+C+R) and joint—venturing derives costs not larger than
acquisition (i.e. R21), a joint venture may be formed. This is the second part of case (3).

For the cases that the local knowledge is less important (i.e. B < (F+A+1)/(A‘+C)),
if the ratio of the cost of a joint venture to a newly established firm-S-plant (high-cost-
plant) is smaller than the gain from the local knowledge, B2[1+(J+1)/(A'+C)] (or
accordingly, (F+A) > (A'+C +J)) and joint-venturing costs plus the wage rate are not as
high as acquisition costs (i.e. R2J+1), even if the local knowledge is not as important
as the technological advantage, joint ventures will be formed. This is the first part of case
(3).

It is not possible to cover all cases in a 2—dimensional diagram, but it may be helpful
to illustrate an example. Figure 3.3 is the example of R>J + 1 >F-C+ 1 >1 and
F+1>J> F. The first constraint means that joint-venturing is preferred to acquisition
(i.e. R>J + 1). It also refers to the fact that the extra costs of a joint venture are larger
than the total fixed costs of a firm H (i.e. J+C+1>F+1). Moreover, the example
assumes that F-C > 0, so that the firm-specific cost is larger than the culture-adaptation-
cost. Since joint-venturing is preferred to acquisition, the diagram includes only the cases
in which low-cost-plants are wholly-owned or transferred to joint ventures. No acquisition
appears in this example. The second constraint means that the cost of cooperation is
higher than the firm—specific cost but lower than the firm-specific cost plus the

Opportunity costs of an entrepreneur H (i.e. the wage rate).

73
The diagram shows the relationship between B and A. Going up along the vertical line

(i.e. B is larger), the local knowledge becomes more important and then firms H are
more likely to operate low-cost—plants more efficiently than firms S operating high-cost—
plants. While going to the right along the horizontal line (i.e. A is larger), the
technological advantage of firms S are larger (as A’ is assumed fixed and then is further
smaller than A) and then firms S are more likely to operate high-cost-plants more
efficiently than firms H operating high—cost-plants. It is clear that on the whole, FDI is
more likely if moving to rightward; joint-venturing is more likely if moving upward.

Since the technology of country S is more advanced than country H, A’ is smaller than
A, which is assumed at the beginning of this chapter. The feasible values therefore are
only on the right hand side of the vertical line A=A'.

If ASA'+C, no FDI can enter country H. So left of the vertical line of A=A'+C and
right of A=A' is an area of only exporting and then all plants in country H are wholly
owned by the local firms. On the right hand side of A =A‘+C, the foreign firms are able
to invest in country H.

The line 1t‘=w (or B=[(F+A+1)/(A'+C)], corresponding to (3.24)) is upward
sloping as it is positively related to A. It is denoted as 1t‘=w since this line represents that
the profit of a firm H is equal to the wage rate. Below the line (i.e. It‘< w) but right of
line A =A‘+C, the domestic firms leave the market unless firms S cooperate with them.
Above the line nl=w (i.e. It‘> w), firms H survive under foreign entries.

The line 1r‘=w (or B=[1+(J+1)/(A’+C)], corresponding to (3.29)) is horizontal as

it is independent from A. Along the line, the profit of a joint venture is equal to the wage

74

rate, the opportunity cost of an entrepreneur H. Below the line (i.e. It’ < w) but right of
line A=A'+C, the investing firms will only set up high-cost-plants since the profit of a
joint venture cannot compensate for the opportunity cost of an entrepreneur H. Thus, for
the area below the horizontal line, the joint ventures are not profitable and so the area
represents all foreign wholly-owned high-cost-plants only.

Above the line It’ =w (i.e. 1t’ > w), joint venturing is possible. Though firms H cannot
survive below line 1t‘=w, firms S find it valuable to cooperate with local low-cost-plants
for the area above line n’=w but below n‘=w. Thus the area between the two lines
includes foreign wholly-owned subsidiaries (high-cost-plants) and joint ventures.

The line 1t’=1t‘ (or F+A=A'+C+J) is vertical as it is not dependent on B. The
vertical line is on the right hand side of line A=A'+C because J >F in this example
(recall that J+1 > F-C+1). On the right hand side of the vertical line 1t’=1c‘(i.e. 1t’ > n'),
the joint ventures are more efficient even if there are extra costs of cooperation and
cultural adaptation. For the area above line 1t‘=w, firms H can survive. However, firms
S are able to pay the entrepreneurs H even more than what firms H can earn themselves
and then joint-venturing is possible. The area right of the vertical line 1t’ =1t‘ but above
line n‘=w includes both foreign wholly-owned subsidiaries (high-cost—plants) and joint
ventures.

On the other hand, on the left hand side of 1t’ =1t' (i.e. It’ <1t') but right of A=A'+C,
the joint ventures are not as efficient as firms H in operating low-cost-plants and joint
ventures do not appear. We already know earlier that above the line 1t’ =w, the domestic

firms can survive under foreign entries. It follows that the area between the two vertical

75
lines ( i.e. A=A°+C and rt’=1t‘) but above line n‘=w includes both foreign wholly-

owned subsidiaries (high-cost-plants only) and domestic wholly-owned firms (each firm
H operates only one low-cost-plant).

The intersecting point of the upward sloping 1t‘=w and A=A' ((F+A'+1)/(A'+C),
point a) is below the intersecting point of 1t’ =w and A=A’ ((1+(J+1)/(A’+C), point b)
as J +C>F+1 from the second constraint of this example. It can be seen that as this
example considered is F—C+ 1 > 1, both intersecting points with A=A' are above B: 1.

Recall that It is the autarky profit rate of a firm H. From the restriction for ensuring
1:2w in the autarky economy, we have to add the comparison between (3.16) and w
(1t=(1t,-Fw)2w) in the diagram. To reorganize the inequality, it becomes:

F+1
B-l,

 

A2

The curve 1t=w (i.e. A =[(F+1)/(B—1)]) is downward sloping as A is negatively related
to B (but not linearly). Since Bh> B,, it must be B> 1. So the curve 1t=w has the lower
bound of B=1. On the other hand, A=0 is the left bound of the curve as A must not be
negative. All the feasible values must be higher than the curve. The intersecting point of
1t=w cutting A=A' is (F+A'+ l)/A' (point e) and the intersecting point cutting the line
A=A'+C is (F+A'+1)/(A'+C) (point (1) which is below the intersecting points of both
lines n‘=w and n’=w cutting at A=A‘+C.

There is also an additional restriction to ensure that M>N.10 We assume that L is

very large compared to all other variables; subsequently this upper bound is far above.

 

"The restriction corresponds to condition (28) of the working paper.

76

The restriction is not shown for simplification.

3.6 Coexistence Of International Joint Ventures And Foreign Wholly-Owned
Subsidiaries In The Host Country

As the main interest of this thesis is comparing international joint ventures and foreign
wholly-owned subsidiaries, we concentrate on case (3) in Table 3.1.“ From Figure 3.3
which is a case in which joint-venturing is more efficient than acquisition, it can be
noticed that coexistence of foreign wholly-owned subsidiaries and international joint
ventures is at the right upper corner. This means that if A is larger (especially compared
with A') or B is larger, other things being equal, the possibility of the appearance of both
international joint ventures and foreign wholly—owned subsidiaries is higher. The reason
is simple: if the technology gap between the two countries is larger (the difference
between A and A' is larger) and the value of local knowledge is higher (B is larger), the
foreign firms find it easier to invade country H. However, the gain of local knowledge
is also larger. It is, therefore, more likely for firms S to operate their wholly-owned high-
cost—plants in addition to cooperating with firms H in operating low-cost—plants.

It can be shown that the price elasticity of any variety is the same as a closed
economy. The prices and outputs can be found from the assumption of profit
maximization and utility maximization and the fact of equal demand functions and same

marginal costs for all varieties. The price and output of each variety are as follows:

 

"The other cases are described in the working paper.

77

 

 

 

 

B B B B
J h J J I J J‘ In J‘ J‘ _ I J‘
= _w —' —w = —W - —w
P]. 6 ’ P1 9 , P1. 6 ’ P1 6 ’
6 A ’ +0 6 A ‘ +C
th - xi] - p
1 -6 B, 1 -6 B,
6 A ‘ 6 A "
x J ___ x" =
" 1-6 B, ’ 1-6 B, p
where the superscript J denotes the equilibrium value under joint ventures.
The full employment condition in country H becomes:
N M"
L = Z (A‘ +C+J+B,x,) + Z (A ‘ +C+thj)
i=1 j=N+l (3.33)

where M’ is the equilibrium number of varieties of good X produced in country H. It
implies that the low-cost-plants are joint ventures with each firm H providing lower
marginal cost (B0. But a firm S provides firm-specific knowledge and then the fixed cost
of a low-cost-plant is A'+C. In addition to the cooperation cost J, the total fixed cost of
a joint venture is A'+C+J. The high-cost-plants are wholly-owned by firms S, so the
local knowledge is absent (then the marginal cost of each plant is B.) while the fixed cost
is A'+C.

Substituting the value of x,J and x,’ into (3.33) and using a simple calculation, the

number of varieties is:

78

J = (1 -6)(L-NJ)
A’+C

M

 

+ GNU-B)

Since under FDI all plants are more efficient than those in a closed economy, M’ should

be greater than MA (MA means the number of varieties produced in a closed economy).

3.7 Extensions And Discussions
(a) Internalization

The model assumes implicitly that a firm can expand to any size. However, when a
firm gets bigger, the management problem becomes more complicated, and then it may
be inefficient for a firm exceeding a certain size. If the firm-specific cost is set as a
positive function to the number of plants operated, the internalization matters can be

included in horizontal integration.

(1)) TWO-way FDI
The model only allows one-way FDI, facing the same difficulty as the K-M-H model.

However, if the model includes two sectors so that one country has the technology
advantage on one sector and the other country has the advantage on the other sector, two-
way FDI is possible. The extension can explain the cross-investment between two
developed countries as long as the countries do not have equal technology levels in all

production processes.

79

T ost

All foreign subsidiaries have been assumed to produce varieties different from the
source country. This may be the main characteristic different from the K-M-H model due
to the different assumptions of the transferability of the firm-specific knowledge. One
reason is that the increasing returns to scale lead to higher efficiency in producing the
same variety in only one place. But it is possible to include a case such that a similar
variety is produced in both countries. If the transport cost is included so that exporting

may not be worthwhile, the same variety can be produced in both countries.

(fdlfiThree Forms of Ownership in the Host Coungy

Different production costs of the same products in a country may be the critical

 

assumption for the result of coexistence of foreign wholly-owned subsidiaries and joint
ventures within an industry. It has been assumed that there are only two kinds of plants
different in production costs in a country. The result is that at most two forms of
ownership can appear in the host country at the same time (as listed in Table 3.1). It is
logical to extend the model to include three types of plants with different production
costs. The conjecture is that in such an extension, three forms of ownership can coexist
in a host country: foreign wholly-owned subsidiaries, domestic wholly-owned subsidiaries

and international joint ventures.

(e) Collusion

A rather strict assumption is that all the firms in the same country cannot cooperate

80

together to become a monopoly or to form a cartel. If the firms combine together to form
a monopoly, in addition to the saving of firm-specific costs, the monopoly power can
make each owner earn more, and then there is an incentive for the firms to merge. One
possible reason to prevent such a monopoly is that the cooperation cost between any two
firms is higher than the firm-specific cost. A cartel may not be efficient as: the free-rider
problem is an obstacle and the anti-trust law is another explanation for no cartels arising.
Moreover, if the punishment of the other firms is so inefficiently that it does not cause
a firm to lose enough from cheating within a cartel, collusion will not be successful.

Therefore, the assumption of no cooperation between local firms may have some grounds.

3.8 Concluding Remarks

This chapter combines the analysis of the recent trade literature about applying
increasing returns in trade models and the FDI literature on emphasizing transaction costs
for multinational enterprises to elaborate the decision of a multinational enterprise to set
up wholly-owned subsidiaries or joint ventures in a deve10ping country. A multinational
enterprise (or a potential multinational enterprise) will choose the entry mode in a foreign
country based on the extent of gains from advanced technology compared to the costs of
investment in a foreign country.

Forming a joint venture is a choice as long as the cooperation cost can be covered by
the joint contribution from the parent firms. It has been shown that even if there are no
impediments of trade and no taxes imposed, both international joint ventures and foreign

wholly-owned enterprises can coexist in a developing country if the market is large

81

enough to support two types of plants in the developing country and the cooperation cost
can be covered. The other possibilities are totally foreign subsidiaries, totally domestic
firms, coexistence of domestic wholly-owned firms and foreign wholly—owned
subsidiaries.

In this model of differentiated products, the critical assumption is that the local
knowledge is not transferable so there are only a limited number of varieties produced
at a lower cost. The implication is that when foreign wholly-owned subsidiaries and
international joint ventures coexist in an industry, the production functions within the
industry are not homogeneous.

Although the basic model seems limited by strict assumptions, extensions can be
applied to expand the explanatory power. One limitation of this chapter is that only one-
way FDI is allowed. However, two-way FDI may be extended in a two-sector model in
which one country has the technological advantage in one sector, and the other country
has the advantage in another sector. In conjecture, a two-way interindustry FDI results
though it is still not certain in two-way intra-industry FDI which may require a more
complicated market structure.

Although this chapter focuses on the investment from a developed country in a
developing country, the results can be applied to the FDI between two developed
countries. This is because in the real world, no two developed countries have the same
technology levels in all industries. One country may have the technological advantage in
industry A while the other has the advantage in industry B. An example is the automobile

industries of the United States and Japan which both are developed countries. There has

82

been evidence that the cost of a Japanese car was lower than the same class of an
American car.12 In fact Japanese automobile firms set up both wholly-owned subsidiaries
and joint ventures in the United States. The entry modes are similar to those in this
chapter. However, the Japanese investment in the automobile industry may be mainly due
to the jump—over of trade impediments. Whether the theory of this chapter applies to these
facts remains inconclusive. Some research may be done in this direction.

When the firms have greater marketing power and they carry out strategic behaviors,
for example, the results will not be so clear-cut. Moreover, this chapter is only based on
the static analysis. The learning process and technology growth problems are ignored in
the static situation. The learning and growth matters are very important in the decision
making of a multinational enterprise and so the results will be much more complicated
under a dynamic process. Further investigation of dynamic analysis and strategic

behaviors is the next job in perfecting the research direction.

 

”Dixit (1988) shows some estimated costs of the Japanese cars and American cars in the early 19805.

Chapter 4

Welfare Analysis Of Foreign Direct
Investment Under Spillover Effects

4.1 Introduction

This chapter uses a very simple model to look into the welfare effects of the host
country when FDI leads to technological imitation. The conclusion is not single direction:
FDI may or may not be beneficial to the host country but the indications for the welfare
effects can be seen from the imitation rate, the technological gaps and preferences.

Technology and management skills may spill over to sectors without foreign
investment because the management skills are usually common to many industries and
better technology can raise efficiency of the whole society. Therefore, there are positive
extemalities on interindustry spillovers apart from the more direct intra-industry spillover
effects. Not only are the intra-industry spillovers positive when tested empirically‘, but
there is also evidence of beneficial interindustry spillovers2 in the real world.

The developing countries usually find it difficult to catch up with the developed
country. The requirement of better education of workers and the existence of cultural

differences, for example, may slow down the learning process. Also the technology

 

IFor example, there are empirical works of Blomstrt'im and Persson (1983), Globerman (1979), Jaffe
(1986), Levin and Reiss (1988), and Spence (1984).

zsee Bernstein (1988), Bernstein and Nadiri (1988), Scherer (1984) and Schmookler (1966).

83

34

transfer is costly3 or the transfer is imperfect to the host country.‘

This paper assumes that both intra-industry spillovers and interindustry spillovers are
possible. The technology transfer is reflected by lowering the costs of the host country.
But technology transfer is not perfect, so the host country cannot lower the cost to the
level of the source country. It is further assumed that the spillover effects appear
exogenously for simplification.

The basic set-up in this chapter is different from chapter 3. A monopoly may arise in
the investing sector so that local profits are lost to the foreigners. On the other side,
however, efficiencies of local industries are raised by FDI. Even the non-investing sector
has improved productivity due to interindustry spillover effects. It is hard to say whether
FDI is good for the host country or not.

A policy evaluation in this model is that governmental intervention in FDI may be
justified because intervention may increase the domestic welfare. Furthermore, compared
to a complete ban of FDI, minimum local ownership requirements - all foreign firms
operating locally must at least include a certain share of local ownership, which is

common in developing countries - should be a better policy.

4.2 The Model
A two-country two-sector model is used instead of the two-country one-sector model

in the previous chapter. Country S is still the developed country, and it is also the source

 

3Teece(l977) concludes that there are costs in transferring technology.

‘Imitation is assumed perfect in some literature. One example is Segerstrom (1991).

85

country. Country H is the host country. It is also assumed that both countries have the
same size and the same endowment, particularly both have labor forces of size L units
of labor. The two sectors are called sector X and sector Y. Labor is the only physical
input used in producing good X and good Y. Good X is tradable while good Y is non-
tradable and is consumed only by the people in the respective country.‘ Moreover, FDI
is only possible in sector X. Both goods are homogeneous rather than differentiated.
However, sector Y is perfectly competitive while sector X is occupied by one domestic
firm or one foreign firm or both. The only forms of FDI are establishment of a foreign
wholly-owned subsidiary or setting up of an international joint venture. All consumers are
the laborers who earn their own income, and the number of consumers is equal to the
number of workers. The profit(s) earned by the firm(s) in sector X is(are) distributed
equally to all individuals with the same nationality.

The reason why good Y is non-tradable and the production is isolated from FDI is
owing to controlling the effects of interindustry spillovers. Moreover, the algebra

complexities can be reduced for cleaner results by concentrating FDI on only 1 sector.

Comm H
At first, country H is considered. The production of good X is determined by the

number of workers, the technology and management inputs (i.e. the firm-specific assets)
and the local knowledge. Let X be the amount of output of good X in country H. As

before, a minimum amount of the firm-specific inputs, F, is sufficient for any level of

 

5600d Y may be referred to certain local services so that basically the foreigners do not consume the
services and trading is not possible.

86

output of good X within a firm. The production of firm—specific assets is subject to
constant returns to scale and furthermore, each unit of the firm-specific assets is produced
by 1 unit of labor, i.e. F=LF where LF is the total labor required in producing firm-
specific inputs.

The cost function of good X is similar to that in Chapter 3: it is subject to increasing
returns to scale while the marginal product is constant. As before, A is the coefficient of
the fixed cost and B, and BI] denote the coefficients of the marginal cost with or without
local knowledge respectively. However, as good X is homogeneous in this model, only
one plant is necessary and the plant must obtain local knowledge. If no good X is
produced, it is assumed that no fixed cost is necessary. Thus, the labor required in a plant

(LP, excluding the production of firm-specific assets) is:
LP = A + BIX , X > O 9
= O , X = 0 .

Adding LP and LP together, the total labor required in sector X (Lx) is equal to the

employment of the monopoly (firm H):

LX=F+A+B,X, X>0,
(4.1)

=0, X=0.

Under the assumption of perfect mobility of labor where all the workers are identical,

the wage rate, w, is the same for all workers. The total cost of the monopoly becomes:

TCx = x” = (F+A+B,X)w , X > 0 ,

=0, X=0.

87

The production of good Y, unlike good X, is under constant returns to scale, and then

the labor required is:

a=cy, am

where C is a constant; Ly is the labor used in sector Y.
Due to the fact that labor is perfectly mobile, the society is fully employed and so
L=Lx+Ly. The production of good Y and good X is restricted by the full employment

condition. Using (4.1) and (4.2), Good Y has the following relationship with good X:

L-(F+A +B,X)
Y = if x > o,

C
' (4.3)
L

— iX=0.
C f

 

The price of good Y is equal to the constant multiplied by the wage rate (average cost).

To take, good Y as the numeraire, we have:

1 = Cw . (4.4)

It is assumed that the utility of an individual j is in form of a Cobb-Douglas function

as follows:

01' = cgcfll-a o < a < 1 , (4.5)
where c,,- is the consumption of good X and cyj is the consumption of good Y by the
individual j.

The monopoly in sector X is owned by all the consumers who have equal shares in

88

the firm, but the decision making of the firm is independent from the shareholders.6
Therefore, the income of a typical consumer includes both wages and the share of profits.
As each individual owns 1 unit of labor, w is the wage income each worker earns. Let

P be the price of X. The total profit functions are:

IIx = PX-(F+A+B,X)w , if X > 0 ,

(4.6)
= 0 , if X = O .

Each consumer, i.e. each shareholder, has the share of profits:

II

n = .35

L e

As all individuals are identical, the income of every consumer is:
II = w + 1: .
Then each individual has the following income constraint:
W+1t z Pcfi’rcfl. . (4.7)

goungy S

The main difference between the two countries is that the technology level in
producing either good is higher in country 8. It is assumed that only the marginal product

(of either good) is higher in country 8. All the other factors such as endowments and

 

“This assumption may not be reasonable as a rational person will try to affect the decisions of the firm
to maximize one's own utility. The assumption of the independent decision making is useful in projecting
the decision making in the real world. A more reasonable assumption may be the division of ownership
of the firm from the laborers. However, it will only provide the same intuition results but with more
complicated algebras.

89

consumer preferences are equal in the two countries. The different variables are
represented in asterisks. In sector X, the employment and the total cost functions (X' > O)

are:

Lx‘ = F+A +B,‘X‘ ,

Tc; = L§w‘ , where B,’ < B, .
But it should be noted that in the absence of local knowledge, the marginal product of
country S may or may not be higher than the marginal product of country H which has
the local knowledge, i.e. B, may or may not be larger than Bh'. This means that the local
knowledge may be efficient enough to cover the disadvantage in the technology level. As
the marginal costs are different in the two countries, the variables (in physical terms or
money terms) in sector X are different from country H.

The labor employed and the price of good Y are:

L; = C‘Y’,

P; =C’w’, where C‘<C.

Py' is the price of good Y in country S. Since the prices of good Y in both countries may
not be the same, PY' may not be equal to 1. This is not important for the autarky
condition, but in open economies, the prices of good Y in both countries should be
compared as the firms in sector X evaluate the profit rates in terms of the price of good
Y in their own countries. We will see the importance in Proposition 4.4.

For the demand side, the utility function of a typical individual is:

90

j‘ = w el-a
U Cd cyj .

The profit functions and income of a consumer (X‘>O) are:

E
II

PX‘X‘ - (F+A +B,'X‘)w‘ ,

4.3 Closed Economies

At first, we look into the closed economy of country H. It is assumed that all identical
consumers maximize their utility functions, and the firms maximize the profits. From the
demand side, consumer j maximizes his utility (equation (4.5)) subject to the income

constraint (equation (4.7)). We can write it down as below:

, j__. a l—a
Max U eve”

Subject to W+1t 2 chi+cfi .
Since no saving is allowed in this static situation, all incomes are exchanged for the goods
and then the inequality can be taken to be equality within the income constraint. It is
assumed that in equilibrium, both goods supplied are positive. Let 71. be the Lagrange
Multiplier, then from the first order condition (with respect to the consumption of good)
and the total amount of all individual consumption on good X, the price of good X has

the relationship as:

91

l-
p = 3.. X ‘ (4.8a)
A X
And the price of good Y has the relationship as:
I
1 = 1:1 .5 (4.311)
A Y
Combining (4.8a) and (4.8b), the inverse demand function can be expressed as:
p = _E_ I - (4.9)
l - a X
Since the decision of the monopoly is independent from the shareholders, the profit
maximization condition is reached by having the marginal revenue (MR) equal to the
marginal cost (MC). Using the first order condition of the first derivative of the total
profit (4.6) with respective to X, we have:

P(1-l) = 3,11»
8

where e is the elasticity of demand for good X. It is well-known that the elasticity of

good X, e, is equal to: e=1/(1-01). Then the profit maximizing price is:

P = _ (4.10)

From (4.4), the wage rate becomes:

=— 4.11
w C ( )

and then we can get the profit maximizing price as:

92

BI

_ (4.10')
«C .

I" =
Substituting (4.9) into (4.10'), we can get good X in terms of good Y (Y>0):

2
X=°‘

— Y (4.12)
1 - a

silo

Using the full employment condition, we have:

L=LX+LY

_ 2
4.1.3.11“
l-a

Therefore we can solve the equilibrium quantity of good Y as:

l-a L-(F+A)

 

A _
Y - l-a+a2 C (4.13)
Substituting (4.13) into (4.12), we have equilibrium good X as:
2 _
X" = a L (F+A) (4.14)

 

l-a+a2 B,

where the superscript A represents the equilibrium level in the autarky economy.

From (4.6) and (4.14), the total equilibrium profit (x>O) is as below:

114 ___ a(l-a)L-(F+A)
(l-a+a2)C

 

(4.15)

And we have the equilibrium national income as:

93

L-(F+A)

I" = II"+Lw =
(l-a+a2)C.

 

By assuming that no individual's utility function is affected by others, the social welfare
function is the sum of all consumers. Since all individuals are identical, and the social
welfare function is assumed to be additive with each one has equal weight, the welfare

is equal to L multiplied by a typical individual's utility function:

UA = Lc A‘c A” = xA'YA”

 

 

x y

a 4.1

= a2_C_ l-a L-(F+A) ( 6)
l—aB, 1-a+¢2 C

The equilibrium condition of country H can be shown in Figure 4.1. (4.3) is the
production possibility frontier. From that equation, Y=L/C if X=0 and X=[L-
(F+A)]/B, if Y =0. The production possibility frontier is line PP except at point a which
is broken. This is because if production of good X is zero, the production of good Y is
L/C (point b) instead of [L-(F+A)]/C (point a). It is derived from (4.3) that PP can be
represented by the equation B,X +CY=L—(F+A), X>0 and Y20.

The price ratio is equal to the wage consumption (the consumption financed by wage
income only) between sector X and sector Y. Suppose that the price ratio, P, is higher
than the wage consumption ratio of good X on good Y. This means that firm H finds it
profitable to hire more workers to produce good X, and then P will be lowered. The
reverse is true if P is lower than the wage distribution ratio. In equilibrium, P is equal

to the wage distribution ratio; therefore, W, the wage constraint, has a slope of -P‘.

94

 

 

 

 

 

Y
b
I. //
c
L-F-A p ,1
C \i
a \1
YA ' C
\ I UA
\ I
)1
U P
A \ X
0 X L-F-A
Bl

 

 

 

Figure 4.1: Equilibrium Condition of Country H in a Closed Economy

95
As noted above, X =[L-(F+A)]/B, if Y=0. From the total profit (4.6) and the price-

wage relation (4.10), we can get the ratio of the total wage income to the total income

for distributing good X when Y=0. The relationship is:

Lw _ aL
___... _ _—
IIX+Lw L-(F+A)

where Lw is the total wage income. Therefore, the distribution of good X to wage

income when Y=0 is:

Lw x=£

11,, +Lw B,

 

Accordingly, for W, X =cIL/B, when Y =0. On the other hand, when X =0, no profits
are earned and so all good Y is distributed to the wage income. It is easily seen that the
other intercept of W is Y=L/C when X=O from (4.3). W can be represented by an
equation B.X+aCY=aL. W is steeper than PP as the slope of PP is —B,/C while the
slope of W is equal to -B,/OIC (recall that 0<a<1).

Intuitively, existence of profits in sector X but not in sector Y explains the different
slopes. If more resources (i.e. labor) are used in sector X, the proportion of wages to
national income is lower as more profits are taken by the monopoly. Conversely, if more
labor is hired in sector Y, the proportion of wages is higher. If no good X is produced,
all national income comprises only wages; then on the Y-axis, WW must touch point b.
If all products produced are good X, the difference between the national income and total
wages is the largest as shown on the horizontal line.

The income constraint is the sum of the incomes of all individuals, i.e. the income

96

constraint is equal to L multiplied by 1". The income constraint, II, also has the slope of -
P", parallel to W. This is because in equilibrium, each individual has the share of
profit of TIA/L in addition to the wage rate. Each individual takes the profit share as
exogenous wealth. The difference between II and W is ITA horizontally, so 11 is parallel
to W.

From both assumptions of full employment and maximization of utility, the social
welfare function, U", must touch PP curve. On the other hand, since the consumers
distribute their consumptions of both goods depending on the price ratio, the slope of the
utility curve is equal to the slope of the price ratio, i.e. UA is tangent to 11. Therefore,
U" is tangent to II by cutting PP at point c. It can be seen that the efficiency of
production is not maximized. This is because good X is not produced at the most efficient
point (PatMC) and then the economy cannot reach the first best position though all the
resources are used.

The situations in the closed economy of country S are similar to those in country H
with the appropriate asterisks added to the equations. Since the technology level is higher
in country S, the production level (and then the consumption level) of either good is
higher than country H. It is obvious by comparing B, and B,', or C and C'. A similar

diagram (not shown) as Figure 4.1 can be used for country S.

4.4 One-Sided Investment From The Developed Country To The Developing
Country

In the world with one tradable good with the same endowments in both countries and

97

immobile labor across countries, if a monopoly is operating in either country, it is
possible to trade between the countries7. For the sake of isolating the welfare effects of
the developing country under FDI, it is assumed that trade is banned between the
countries, and country S even prohibits any foreign investment. The only way for the two
countries to have contacts is through investments from country S to country H. Therefore,
country S must be the source country while country H is the host country.8 It is also
assumed that only the sector-X-firm in country 8 (firm S) has the incentive to invest in
country H. A rationale for no firms investing in sector Y may be due to the fact that the
costs generated from investing to sector Y are too high and then the firms are discouraged
to invest in that sector.

In addition to the advantage of advanced technology, firm S can save the costs of
management and technology (F is saved) in operating one more plant abroad. The
problem is that firm S loses the advantage of local knowledge in the foreign country, and
then the fixed cost of the foreign subsidiary will be higher (the coefficient of the variable

cost is Bh' instead of B,’).

 

7Brander (1981) provides a model to explain the intra-industry trade in a homogeneous good. He proves
that when there is increasing retums to scale under Cournot competition, a low cost firm may not drive
out a high cost firm.

“The assumptions may seem too artificial, but the assumptions can be further justified by taking
transport costs into consideration. If transport costs are higher than the investment costs (e. g. the loss of
advantage of local knowledge), a firm will substitute exports by direct production in the foreign country.
In this case, it is not necessary to maintain trade.

It is also possible to justify one-sided investments. If the loss of the local knowledge advantage is too
large for the high-cost firm but the loss of local knowledge advantage can be covered by the low-cost firm,
only one-sided FDI appears.

To make the model be simpler, the above non-trade one—sided investment situation is taken for granted.
This extreme case can be used to evaluate the effect of FDI on the host country in a most unfavorable
situation. If the host country is better off in this case, it is suggested that FDI be welcomed. However, if
the host country loses, FDI should be treated more cautiously though it does not suggest that FDI must be
evil to the host country in general cases.

98
If a wholly-owned subsidiary is established, the labor hired by a subsidiary S (the

subsidiary of firm 8) in country H is LxS=A+B,,‘Xs. Forming a joint venture with the
local firm Can reduce the marginal costs by utilizing the local knowledge of the local
firm. As discussed in Chapter 3, cooperation costs arise within the joint venture. Firm
S thus compares the effects from both the positive side and the negative side to decide
whether to set up a wholly-owned subsidiary, to cooperate with the local firm to form a
joint-venture, or simply to cancel the investment plan. It is assumed that an extra cost,

J, results from joint-venturing. That is, for a joint venture, the labor hired becomes:

L; = A +J+B,'X",
where LxJ is the labor hired by the joint venture and X’ is the output of the joint venture.

Though acquisition is a possible behavior, we will not analyze this kind of activity in
this chapter by concentrating attention on comparing a newly established wholly-owned
subsidiary and a joint venture. To justify this simplification, we can assume that the
takeover cost is too high for a firm to buy out an existing plant.

Under the effects of FDI, country H not only improves the efficiency in sector X
where the technology is directly transferred but also raises the efficiency of sector Y due
to the spillover effects. However, the imitation or the technology transfer is not perfect,
so the production cost is reduced to a level between the original cost and the lowest level
in country S. For simplification but not loss of generality, the technology transfer rate is
assumed to be the same for both sectors. The rate is y, 0<y<1. The percentage of

reduction in the marginal cost of sector X (1,) and the average cost of sector Y (5,) are:

 

 

Sector X:
t; = “31'3” 0 < ‘x < 1'31
B, ’ B, ’
Sector Y: .
b = M O < b < C-C
y C y

The equations above guarantee that the technology level in country H may not be higher
than country S. If the cost gap is larger, the learning speed is faster under the same value
of y. The technology transfer is only possible under FDI since there is no other way for
country H to contact country S. This is not a critical assumption. Even if there is
technology transfer without FDI, as long as the transfer rate is lower than that of FDI,
the basic result is applied. What is really important is the assumption of faster transfer
rate under FDI9. This assumption is reasonable as FDI allows the local people to have
better chance to learn the advanced technology or management skills.

By adopting technology transfers, if firm H (the sector-X-firm based in county H)
survives under competition, the labor hired by the local firm in sector X becomes:

L? = F + A + [(1-c,)B,]x"
(4.17)

= F + A + 111-1)B,+vB{Ix”.

where the superscript H denotes the labor used or output produced by firm H. If there

is FDI, the labor hired in sector Y is:

 

s’It is assumed that the technology transfer is free from any cost. There are discussions about the costs
of transferring technology. One example is Wang and Blomstrt'im (1992).

100

Ly = [(1-5,)C1Y (4.18)
= [(1-Y)C+YC‘1Y.

The entry mode of firm S depends on three considerations: the first is whether or not
the total cost of the subsidiary with the loss of advantage of local knowledge is higher
than the total cost of firm H (under technology transfer); the second is that is it profitable
for firm S to cooperate with the local firm; the third is what the strategies of the two

firms are. In this model, the strategy is assumed to be Cournot-Nash Competition.

Cournot—Nash Equilibrium
Suppose that firm S enters country H to set up a wholly-owned subsidiary and firm
H competes with the foreign challenger independently. Thus there are two firms operating

in the host country. Let
Bt = (1 -rx)B,

=(1-Y)B, + 731'.

and
C, = (l —b,)C

= (l-y)C + yC’ .

Good Y in country H remains to be the numeraire. Firm H maximizes its profits by

selling products X“, i.e.

Max 11” = PX” - (F+A +B,X”)w . (4.19)

101

From the first order condition of the profit with respect to X", we have:

P(1--l—] = aw (4.20)
"a ,

where 1],, is the price elasticity facing firm H.

Similarly, the foreign subsidiary, subsidiary S, maximizes the profits in country H.
The profits earned will be used to purchase good X in country H and then the purchased
good X will be sent back to country S. It is assumed that the consumers in country S take
the amount of good X coming abroad as exogenous and then the price elasticity of good
X remains 8 (both in home and abroad). Leth be the sales of good X by subsidiary S,

the profit maximization of subsidiary S is:

Max 11‘ = sz — (A +B,,‘Xs)w . (4.21)
Subsidiary S saves the costs of producing firm-specific assets but the, local advantage is
lost by investing in country S. From the first derivative of 11s with respect to XS, the

following equilibrium point can be reached:
P(l -—1—] = B;w (4.22)

where n, is the price elasticity facing subsidiary S.

Let 6,, and as be the market shares of firm H and subsidiary S respectively. It is clear
that oH+os=1. Let X1 be the total sales (or total demand) of good X in country H, i.e.
X‘=X"+Xs. Then the relationship between the price elasticity and the market share of

firm H is:

102

 

 

a_x'
,, = -QLHL = 5" 313$
H 6P x” ax’ x'x”
ax"
= ——8_
0H (4.23)

since by Cournot conjecture, BXIIBX"= 1.10
Similar to firm H, the relationship between the price elasticity of firm F and the

market share can be written as:

n, = 3— (4.24)
as

Substituting (4.23) into (4.20) and (4.24) into (4.22) respectively and using the fact

that 8: l/(l-oc), the price of X can be written in two different ways:

 

Btw
P = (4.25a)
l-o,+ona
or
p = _L (4.25b)
l - as + as a

Combining (4.25a) and (4.25b) together, we have:

 

"’I'he duopoly equilibrium follows the derivation in Markusen (1981).

103

O
B,, = l-os+asu

 

Bt l-o,,+o,,a .

Using the fact that oH+os= 1, after some rearrangement, the market shares are as

 

 

follows:
B-aB‘
0s :11 . f (4.26)
'“ Bt+B,, ’
and
B'- B
0,: 1 " °‘ . 14.27)
1'“ B,,'+B,

Sector Y is still perfectly competitive. As good Y is the numeraire, under the effects

of spillovers, we have the wage rate similar to (4.11):

I

W = (4.28)

1
Ca
where the superscript I denotes the equilibrium value under FDI. Accordingly, the

equilibrium price of good X in country H is:

B ‘ a
p1 = __L+_t (4.25')
(l+a)C,

From the consumption decisions of consumers, the inverse demand function of good X

(recalled that good Y is the numeraire) can be reached as (4.9). Substituting (4.25') into

104
(4.9), the following relationship between demand for good X and good Y of country H

consumers can be found:

Y! = 1"“ Bk +thg (4.29)
a(l+a) Ca

 

where XeH is the country-H-consumers' demand for good X.
Since the consumers use all income on consumption. The total income is equal to the

total expenditure on both good X and good Y in country H:

11”+w1. = PIX: +Y’ . (4.30)

Substituting the profit function (i.e. (4.19)) and (4.29) into (4.30), we have:

a «(Bi-«Bax, + a(l+a)(L-F-A)

Xe = (4.31)
B; +Bt B; +Bt

 

 

On the other hand, subsidiary S uses all the profits to exchange for good X in country

H. The total profit of subsidiary S is equal to the total expenditure on good X, i.e.:

HS = Plxg , (4.32)
where X08 is the country-S-demand for good X in country H. Substituting (4.21) and

(4.32), the relationship between X8 and XCs becomes:

= BraBixs _ (1+a)A

x‘
C
3,53, 3; +3, .

(4.33)

In equilibrium, the supply of good X is equal to the demand for good X, i.e.

105

x§+xf = xhx", (4.34)
since X'=XS+X". Substituting (4.31) and (4.33) into (4.34), the following relationship

between the quantities of producing good X by the subsidiary S and firm H becomes:

a(L-F-A)-A _ (B;+B,)-a(B;-aB,)X,
B; (l+a)B,,’

X S = (4.35)

 

 

Using the fact that XC“=<S,,XI and substituting (4.31) and (4.35) into it, we solve X“:

 

 

 

 

 

 

2
x" = °‘ (1”) (L-F-A) - 1+“ A (4.36)
(1+a2)(aB,-B;) (1+a2)(B,-aa;)
Substituting (4.35) into (4.36), we can solve XS:
3
XS = “1”” (L-F-A) + 1*“ —A (4.37)
(1+a2)(B,,'-aB,) (1+a2)(B,-a3;)
Substituting (4.31) into (4.36), we can solve Xe”:
a 1+0: B’-aB
x3: a(l+a) (L_F_A) _ ( )(1 .) A
(1+a2)(3,,‘+a,) (1+a2)(B,-a3;)(3;+3,)
(4.38)

XCS is solved by substituting (4.33) into (4.37):

106

 

 

«(1+a)(B,-aB;) (L_F_A)_ a(1+«u) A

X3 =
C (1 +a2)(B;-a3,)(a,,‘ +B,) (1+a2)(B,,‘ +B,)

Y‘ can be solved by substituting (4.29) into (4.38):

Y'-._1L(L-F-A)- (l-a)(B,,-aB,) A

_ (4.39)
(1+a2)C, (1 +a2)(a, -aB;)C,

 

(We can also get the results by using XS=63XI .)

One interesting point of the difference between Yl and X1 is that C, does not affect
any part of good X while YI is affected by all exogenous variables. The reason is that the
production of good Y is determined by the spillover effects so the equilibrium amount of
good Y is determined by B, in addition to the other variables. Conversely, XI need not

depend on C5.

Proposition 4.1: Firm H will be driven out of the market if l'l“<0, or

«’1. +F < (1 -¢)(B;+B.)
A «B; —Bt

 

 

unless a joint venture is set up.
Proof:

Firm H will not stay in the market if it makes negative profits under Cournot-Nash
competition. That is, if the Cournot-Nash equilibrium leads to losses, firm H will leave

the market and then oH=0. The condition for firm H to leave the market is IIH <0, i.e.:

107
P’x” < (F+A +3915)»: . (4.40)
Substituting (4.37) into inequality (4.40), we have the following condition:

.21.): < (l-a)(B;+B.)
A “8;-8

f

(4.41)

 

 

Proposition 4.2: Firm 8 is kept out from country H if 115.: 0, or

L-F < (“CNN-B.)
A Bt-aB;

 

unless a joint venture is formed.
Proof:

If firm H can maintain its monopoly status, this means that subsidiary S will make
negative profit under Cournot-Nash competition and then 03:0. The situation for firm

S staying outside the market of country H is TIS<0, i.e.:

P’Xs < (A +B,,'Xs)w . (4-42)
(4.42) shows that even if the investor sells all the outputs produced in the host country,
the costs of production in that country cannot be covered. Substituting (4.37) into

inequality (4.42), the following condition is obtained:

108

if < (1+a)(B; -B,)

(4.43)
A at " “B;

 

El
It is assumed in Cournot-Nash competition that the rivals do not cooperate with each
other, so we have the following result:
Proposition 4.3: If H520 and 11320, or both (4.41) and (4.43) do not hold, a duopoly

of a local firm and a foreign firm will appear in country H.

Under Cournot-Nash competition, if both firm H and subsidiary S operate in the
market, no joint ventures are formed as any kind of collusion is assumed to be excluded.
However, if a monopoly stays in the market, the incumbent considers whether or not to
c00perate with the potential rival for getting greater profits.

It is clear that appearance of a monopoly or duopolistic competition depends on all the
exogenous variables: the preference of good X (a), the imitation rate (7), the extent of
loss of local knowledge (Bf-Bf), the coefficients of the marginal costs with local

knowledge (B, and B,'), the fixed costs (F and A) and the size of the labor force (L).

Proposition 4.4: If 1'1“ < 0 or (4.41) holds, an international joint venture is formed in
country H if the quantity of good X purchased by firm S under a joint venture is

larger than that under a wholly-owned subsidiary, or:

109

 

Bi- 1'
J < [¢(l-¢)L-A]
Bi

otherwise, only a foreign wholly-owned subsidiary exists in country H.
Proof:

If subsidiary S can push firm H out of the market, it will decide whether or not to
accept firm H as a partner for contributing the local knowledge. Suppose that firm S
decides to run the business on its own. The consumers in country H retain only the
wages. A typical consumer (of country H) maximizes his utility level subject to the

budget constraint with only the wage rate on the left-hand side:

- l-a
Max U1 - (93)“ c)”.

. _ )9
Subject to w - Pei + c1, ,
where c,,-“’ is the consumption of good X by consumer j. It can be shown that the price
elasticity is also the standard 8. From the first order conditions of the utility

maximization condition, we can get the relationships of the prices in terms of good X and

good Y similar to (4.8a) and (4.8b). Then the inverse demand function is similar to (4.9):
P 0 = —— (4.44)

where the superscript 0 denotes the equilibrium values under the foreign monopoly. HC"0
is the country-H-consumers' demand for good X and Y0 is the total demand for good Y
(in country H).

On the other hand, from (4.22) and (4.24) and using the wage rate (equation (4.28)),

110

since 113:8 and as: 1, we have the equilibrium price as:

Bi
1: C,

P 0 = (4.45)

Since all the profit of subsidiary S is used to purchase good X in country H, we have:

1°0ng = 110 = POXO-(A +B;x0)w°,

where w°=w'. It can be simplified into:

x30 =(1—a)x0-£B’% (4.46)
II

On the other hand, combining (4.44) and (4.45), the total demand for good X in country

H has the following relationship with good Y:

2 C
xg°=—°‘ —‘Y°

(4.47)
l - a B;

All the country-H—consumers earn only wages and the wage incomes are used to exchange

for good X and good Y. We have:

wOL = P°x§°+Y0.

Therefore, Y0 is solved as:

o = (l—a)L
C6

Y (4.48)

Substituting (4.48) into (4.47), we can get the solution of X3“:

111

azL
31'

 

x30 = (4.49)

Using the fact that X°=XCS°+XCHo and substituting (4.46) and (4.49) into it, we solve

X0 as:

 

 

X0 = “f" (4.50)
Bk
Substituting (4.50) into (4.46), we have:
a 1 -a L-A
X50 = ( 3 (4.51)
Bk

Next we consider the situation in which a joint venture is formed. Suppose that all
profits are taken by firm S. This case is used to compare the total profit rate of a
potential joint venture with the profit rate of a wholly-owned subsidiary. Let the
superscript J denote the variables under a joint venture. The decision of the foreign-

dominated joint venture is:

Max 11’ = PJXJ-(A +J+B,’x’)w’ .
where the notations correspond to those used in the analysis above. The equilibrium price

is as follows:

a;
a C,

P"=

 

It is straight forward to get the equilibrium variables. The quantity of good Y is:

112

y, = (1-a)L
C6

the total local consumption of good X is:

 

x11! _ azL
C - t
B, ;
the total output of good X:
x] _ (ll/'24 “J
B,’

and the purchase of good X by firm S in country H is:

a(1-a)L-A-J

ng =
B,’

 

(4.52)

Since the profit of firm S will be distributed to the consumers in country S, the firm

cares about the profit of subsidiary S in term of PY' instead of P0 or PJ and so the

quantity of good X exchanged in country H are considered rather than the ”surface" profit

in terms of P0 or P’. Firm S will consider joining with firm H if and only if XCSJ

(equation (4.52)) is larger than XCso (equation (4.51)) if assuming that firm S avoiding

negotiation when the potential profit is not greater:

xg’ -XC‘° =

[a(1-a)L-A](B; -B,')-JB,' >

 

Bh'B,‘

To rearrange the order, we have the following condition for firm S willing to form a joint

113

venture:

Bi - Bf

J s [a(1-a)L-A]
31'

(4.53)

 

If (4.53) does not hold, firm S decides to operate the business on its own. El

Proposition 4.5: If l'ls<0 or (4.43) holds, an international joint venture is possible
if the profit of f‘um H under joint-venturing is greater than that under operating a

monopoly alone, or:

J < [¢(l-a)L-A] - %[¢(l -¢)L-F-—A]

otherwise, no FDI exists.
Proof:

The equilibrium values when firm H remains the monopoly are the same as those
under a closed economy. On the other hand, suppose that a joint venture is formed under
the dominance of firm H. It is more convenient to consider the case that all the profit is
kept by firm H. The maximum profit of the potential joint venture is compared with that

of a wholly-owned subsidiary H. The decision of a joint venture is:

Max 11” = PX” - (A +J+B,'X”)w ,

where the superscript D is used to identify the key variables under the local firm-

dominated joint venture. The equilibrium price is:

 

Then the output of good Y can be solved as:

YD = 1"“ L‘A‘J
1-¢+¢2 C5

 

and the total consumption of good X in country H is:

x”: «2 L-A-J
l-aHIt2 B,‘

 

The maximized profit becomes:

«(1 -a)L-A -J
(l-a+a2)C,

nD=

 

(4.54)

Firm H is willing to join firm S to form a joint venture if the following condition is

fulfilled by assuming that firm H prefers no change if a larger profit is not earned:

II”-II‘>0.

Comparing (4.54) and (4.15), a joint venture is possible if:

J < [a(l-a)L-A] - %[a(l-a)L—F—A] (4.55)

115
4.5 Evaluation Of The Host Country's Welfare Under FDI

Case 4. 1: Only a foreign wholly-owned subsidiary is set up

If the cooperation costs are very high so that firm S only makes a lower profit from
a joint venture, firm S will operate a subsidiary under its complete control. As good Y
in country H is only consumed by the citizens of the respective country, the investing
firm takes only good X from country H. The transfer of technology and management
from the headquarters to the subsidiary is a kind of invisible trade, but no money
exchange is involved.

The equilibrium demands for good X and good Y by country H have been shown in
(4.48) and (4.49) respectively. From the two equations, the social welfare function of

country H is:

no. 01-.
_ a2 CI) ‘
l-a B;

To determine whether the welfare of the host country is higher or lower, we can

(l-a)L

Ca (4-56)

 

 

directly compare U0 and U‘. Since we are only interested in the sign of UO-U", it is
equivalent to compare ano and an‘. Taking logarithms of (4.16) and (4.56), the

difference of the transformed values is:

111110-1111!A = 1n[(1 -a+a2)a,'c‘-'L]—1n[3;'c,1-“(L-F-A)] .

l 16
Though C, < C and (L-F-A) < L, it is not certain which one of B,‘ and B, is larger, and

furthermore, (l-a+ct2) > 1. The welfare may or may not be higher under the
displacement of domestic monopoly by foreign monopoly.

However, from the first derivatives shown in Appendix 4A, there are some indications
for the effects of different exogenous variables. If 'y is larger, B,’ is smaller, B, is
larger, C is larger, C' is smaller, F+A is larger or L is smaller, the possibility of
U">UA is higher. The reason is quite straight forward: if the imitation rate (i.e. y) is
higher, it means that the improvement in sector Y is more significant and then the loss
of profits to firm S is more likely to be covered; if the cost gap in sector Y, (i.e. C-C'
is larger), the improvement in good Y is larger and then it is more likely to be
compensated for the profit loss in sector X; if the production cost of the foreign investor
lowers a lot (B; is smaller or B, is larger), the overall rise in efficiency is higher, and
then the loss of profits is also more likely to be compensated for; if the fixed cost of
sector X (i.e. F +A) is higher, the saving of the cost due to FDI has more positive effects
on efficiency too; if the population (i.e. L) is smaller, the technological improvement per
capita can be used better. Let us assume that B,,'-B,'=B,,—B,, i.e. the advantage of local
knowledge is the same in both countries. An additional indication is that smaller B,‘-B,‘
makes U">UA more likely. That is, if the local knowledge is less important, the
possibility of improvement in welfare is higher.

The effects of 01 (the preference on good X) are more complicated. There is no simple
trend which we can see from the first derivative. However, if the spillover effect is

smaller, the benefit of the local knowledge is less important or the cost gap between the

117

two countries in sector X is bigger, the higher preference in good X is more likely to lead
to higher welfare. Conversely, if the spillover effect is larger, or the local knowledge is
more important, or the cost gap is smaller, then the higher preference in good Y is more
likely to lead to higher welfare. The reason is obvious: if the improvement is greater in
sector Y, the people preferring good Y are more likely to be better off as the spillover
effect is reflected in sector Y only (sector X is dominated by a foreign firm). On the
other hand, if the improvement in sector X is greater (i.e. the local knowledge is not so
important or the cost gap is huge), it benefits those preferring good X.

Comparing P0 and PA (the price in autarky economy, (4.10')), the difference is:

A = (B; -B,)C+y(C-C‘)B,
aC,

PO—P

 

The denominator and the second term of the numerator are positive, but the first term of
the numerator may be either positive or negative. The price of good X may or may not
be lower under the invasion of the foreign firm. If the local knowledge affects the costs
more (B,'-B,' is larger), the imitation of advanced technology is faster (7 is closer to 1)
or the cost gap(s) between the two countries is (are) closer (B,-B,‘ or C-C‘ is smaller),
the probability of P0 > P" is larger. Conversely, if (Bf-Bf) is smaller, 7 is closer to 0,

B,-B,' or C-C' is bigger, P0 is more probably lower than P".

118

 

 

 

 

 

 

 

 

 

 

Figure 4.2: An Example of Welfare Improvement in Country H with the
Displacement of the Domestic Monopoly by a Foreign Monopoly in

Sector X

119

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.3: An Example of Immiserizing Country H with the Displacement of the

Domestic Monopoly by a Foreign Monopoly in Sector X

120

If P°>P", due to the fact that the social utility function is convex to the origin,
Y0 > YA is the necessary condition while X°> X" is the sufficient condition for country
H to be better off under FDI. The intuition is that if the price of good X is higher, the
domestic consumption will shift to good Y. Therefore, for the whole country to be better
off the consumption of good Y must be greater. However, if the consumption of good X
is larger even if the price is higher, it implies that both goods are consumed more and
so country H must be better off. The reverse reason applies to the case of lower price of
good X. If P°<P", X°>XA is the necessary condition while Y">YA is the sufficient
condition for country H to be better off. If P°=PA, the consumption of both goods have
to be larger to make country H better off.

Figure 4.2 and Figure 4.3 show the example of P°< PA. Subsidiary 8 must be more
efficient than firm H as the marginal cost (even if there is a loss in local knowledge) is
lower. The production possibility frontier of country H shifts outward (from PP to P'P')
due to the spillovers and investments from country S. The x-intercept of P'P' is (L-A)/B,'
instead of (L-F-A)/B, (of PP). The new production possibility frontier is P'P' except at
the point that no good X is produced. The broken point is (L-A)/C5 at the vertical line.
The production of good Y when good X is zero is at point b' (L/C5) which must be
higher than point b (equal to UC, the autarky output of good Y by using all labor). The
equation of P'P' is B,’X+C5Y=L-A, Y20, X>0. It should be noted that P'P' may or
may not be parallel to PP as it depends on the values of B,'/C5 and B/C.

Figure 4.2 shows a case in which country H is better off in the open economy. The

social welfare function of country H is U0 which is tangent to the price ratio P° (IT) at

121
point c'. The summation of the country-H-demand for good X and country-S-demand for

good X (in country H) is marked at point d. It is possible that U0 is higher than the
autarky utility level U" (tangent to PP at point c) as shown in Figure 4.2.

From Figure 4.3, it is the case that country H is immiserizing from opening the
market to foreign investors when P°<P‘. It is shown as a case that Y°< YA (the
sufficient condition is not fulfilled) though X0 > X" (the necessary condition is fulfilled).
The social welfare U0 is lower than the autarky utility U‘.

The analysis of the cases of P0 > P" is straight forward; therefore, those cases are not
discussed. The major difference from Figures 4.2 and 4.3 is that the slope of P0 should
be steeper than P" rather than that shown in the graphs.

All the workers in country S can surely get more good X than a closed economy. By
assuming that firm F maximizes profits in its home country while taking good X taken
from country H as given, it is easily seen that the equilibrium price ratio and outputs are
the same as those under a closed economy; therefore, the total consumption of good X
is larger while the consumption of good Y remains the same. The welfare of country S

must be higher than that under the autarky economy.

Case 4. 2: A joint venture is established with jinn S possessing greater bargaining power.

The multinational corporation may cooperate with the local firm only if the profit
under complete control is not higher than that under a joint venture. Since the setting-up
of a joint venture will lead to higher efficiency in sector X (compared with the wholly-

owned subsidiary of firm S) while the transfer effects to sector Y remain the same, the

122

production possibility frontier of country H may shift out if the combination of technology
advantage of firm S and the advantage of local knowledge of firm H can cover the
c00peration costs.

Whether country H is better off or worse off under the open economy is similar to
case 4.1. However, since the original firm H may make some profits in this case, country

H is in a better position to improve the welfare.

Case 4. 3: Firm H remains as a monopoly in its own country

The same as a closed economy.

Case 4. 4: A joint venture is formed under firm H 's domination

Though firm H can maintain as a monopoly, if the cooperation costs are not so high
that the joint venture earns more profits than the sole venture of firm H, it is possible for
the two firms to join together. The main difference from case 4.2 is that firm H has the
larger bargaining power, and then the profits earned by firm H are not less than autarky.
Therefore, in addition to the benefits from spillovers, country H must be better off while
country S may also improve its welfare by getting some profits (if any) from the joint

venture.

Case 4. 5: A duopoly occurs in the host country
If the difference between the cost functions of the two firms is not large, it is possible

for the two firms to coexist in the host country.

123
The welfare of country H comes out directly by using (4.39) and (4.40):

 

 

H3 be
U’ = XC l”
= a(l+a) C. l-a L-F—A_Bi-GB.A 457)
1"“ B,:+Bt 1+a2 Ca Bt-aB; C5 (.

 

 

As the sign of U'—UA is equal to the sign of an'-an", the difference in welfare can be

compared by using the logarithms of (4.16) and (4.57):

111111-1111!A =

«In

 

 

 

 

hugs Bl +111 l-a+a2_(_3_ PEI-“B: A
a CB;+B: 1+“2 C, Bt-aB;L'F'A

The sign is not certain so that it is not sure whether country H will be better off or worse
off. Even worse than case 4.1, there are no indications on the exogenous variables except
C and C'. The first derivatives with respect to various exogenous variables are shown in
Appendix 4B. The only indication we have is that the larger the cost gap is in sector Y
(i.e. C-C’), the larger is the likelihood of U) U". The intuition is that since no profits
in sector Y are taken by foreigners, all the efficiency improvement of sector Y is
reserved for country H.

Comparing the price ratio under duopolistic competition (4.25') with that of the

autarky (i.e. (4.10')), we have:

124

«C(YBI’ +B.‘)-[(1-1)C+(1 +a)YC’]B,
a(l+a)CC,

PI‘PA =

 

Since the first term of the numerator is positive while the second term is negative, Pl may
or may not be higher than PA.

Similar to the analysis in case 4.1, if P’>P“‘, Y‘> YA is the necessary condition for
country H to be better off while X‘ > XA is the sufficient condition. If P‘< P", X1 > X" is
the necessary condition for country H to be better off while Y‘> YA is the sufficient
condition. If P‘=P", in order for country H to be better off, consumption in both goods

must be larger.

4.6 Policy Of Minimum Ownership Requirements
Suppose country H restricts FDI by requiring that any firm operating in that country

must be at least 50% owned by the local owners.

Case 4.1: Only a foreign wholly-owned subsidiary is set up if there is no intervention
The foreign firm will set up a wholly—owned subsidiary if there are no government
restrictions. Restrictions on the local ownership may lower overall economic performance
of country H more than the free market since the mandatory joint—venturing may lead to
higher costs. Whether the country is better off or not depends on how much efficiency
is lost and how much the profit is shared by the local partner. Firm H has no threat to
be driven out of the market again as firm S cannot enter country H without firm H's

cooperation. As firm H will not cooperate with firm S if firm H cannot receive a share

125

at least the same as its monopolistic status, country H may not be worse than a closed
economy.

On the other hand, if firm 8 chooses not to invest in country H due to the high
cooperation costs, country H may lose the chance to improve its efficiency. If firm S does
not enter country H at all, the opportunity of the technology transfer is foregone.

So country H may or may not be as good as no restrictions though the policy

guarantees not worse than a closed economy.

Case 4. 2: A joint venture is established with firm S possessing greater bargaining power
if there is no government intervention

The multinational enterprise prefers to join with the local firm even if no restrictions
are imposed. Under the policy, firm S cannot enter country H without the c00peration
of firm H. Firm H will try to protect its own) benefits by asking for at least the profit rate
under a closed economy. The welfare of country H is likely to be higher since the local
firm gets potentially greater profits than within a closed economy. Moreover, imposing
restrictions is preferred to no restrictions as firm H stands on an upperhand position in

bargaining with the foreign investor.

Case 4. 3: Firm H remains as a monopoly in its own country
It is firm H who rejects the foreign partner by avoiding the high cooperation costs.

Therefore, the ownership restriction is not bound.

126

Case 4. 4: A joint-venture is formed under firm H 's domination
Again, the policy of minimum ownership requirement has no effects on the firm

behavior. Firm H has already had the greater bargaining power in joint-venturing.

Case 4. 5: A potential duopoly will occur if there is no intervention

If the firms are allowed to compete with each other, the firms will not cooperate with
one another. However, a duopoly does not exist as firm S is not allowed to operate its
business alone. As we have analyzed before, country H may or may not be better off
under the competition. The policy does not have any clear result on welfare. One certain
point is that since firm H has the stronger bargaining power in this new order, country
H may not be worse than the autarky economy.

The risk is that if the cooperation cost between the two firms is very high and firm
S is not willing to enter the market from the very beginning, country H may lose the

chance of technology transfer.

It is indicated that the policy of minimum local ownership requirements may be worse
than no intervention in case 4.1 and case 4.5 though it will not be worse than the autarky
economy. There are risks that the foreign investor may be banned from entering the host
country, and then the local enterprises may lose the chance to learn advanced skills.

If the foreign firm tends to cooperate with the local firm even if there is no
intervention, regulations can back up the local firm in getting a greater share under joint-

venturing. Therefore, the host country must be better off in case 4.2 under the policy.

127

If the local firm has strong competitive power to keep the foreign rival outside the
local market as in case 4.3 or to'bargain effectively (case 4.4), country H will be

indifferent to whether or not the policy is enforced.

4.7 Concluding Remarks

A model of two sectors is used in this chapter. Only the sector with increasing returns
to scale is allowed to have FDI. Moreover, FDI has been assumed to be one-sided: from
the advanced country to the developing country. The existence of cost gaps between the
two countries is assumed and so apart from the ownership of firm-specific knowledge,
the technology advantage calls for multinational enterprises.

If a subsidiary is set up by a multinational enterprise in a developing country, it can
be seen that the welfare of the host country may or may not be higher. In the case that
the foreign firm sets up a wholly-owned subsidiary in the host country, influences on
welfare can be seen from the exogenous variables. If the imitation rate of the host country
is higher, or the local knowledge is less important, or the cost gaps between the two
countries are larger, or the fixed cost is larger, FDI is more likely to increase the welfare
of the host country. Moreover, if the foreign firm raises the efficiency of one good higher
than the other good and if the people in that country are inclined to consume that
favorable good, the host country is also more likely to be better off.

The same imitation rate under joint-venturing has been assumed in the model.
Compared with the foreign monopolistic case, for the joint-venturing case, the host

country stands on a better position if the spillover effects are the same in both sectors,

128

although the welfare effect is still not certain.

For the duopoly case, the welfare effect is also not clear. The only indication is that
the larger the cost gap is in the non-traded sector, the higher is likelihood that welfare
will improve.

The government restriction of local ownership on FDI may or may not be justified.
If the multinational enterprise prefers sole-venturing (which is the case the government
aims to control), the welfare may be lower than when there are no restrictions on
ownership. This is because when cooperation between the investing firm and the local
firm is difficult, the investor will cancel the investment plan, and then the host country
may lose the chance of technology transfer. Even if the foreign investors stay in the local
market, efficiency is lower so country H may not be better than free foreign investments.
However, if the foreign investor prefers local partnership, the restriction strengthens the
bargaining power of the local partner and then the local welfare is higher provided that
the imitation rate under FDI is higher than that under absence of FDI.

One merit of the policy on minimum local ownership is that it guarantees that local
welfare is at least the same as a closed economy provided the local company has the
larger bargaining power with the foreign investor. The host country has the chance to
learn advanced technology while the loss of profits can be avoided. This policy is a better
strategy than total prohibition of FDI.

As no clear-cut welfare changes are concluded, whether FDI should be welcomed or
not is not easy to say simply by theories. Empirical tests such as the effects of FDI on

the growth rates will provide a better understanding of the welfare effects.

129
It should be pointed out that the analysis in this chapter should be treated more

carefully. For example, in the dynamic world, the strategies of the firms will be much
more complicated and the results may be different. Moreover, this chapter only includes
two countries. A third country may affect the investment decisions of a multinational
enterprise as the firm has more choices, and the competition is more severe in a world
with more countries. The assumption of equal rate of technology transfer for both a
wholly-owned subsidiary or a joint venture may be too simple. For example, if the
multinational enterprise is not willing to reveal its advanced technology to a joint venture,
joint-venturing may not be as attractive to the host country as suggested in this chapter.
Lastly, this chapter does not include factor transfers which are also important in the
welfare analysis. Therefore, this chapter can provide some indications to the government

policies on local ownership requirement but not conclusive.

Appendix 4A: The First Derivatives for Case 4.1

This appendix shows the first derivatives of exogenous variables on the difference
between an° and an‘.

Let Z°=an°-anA.

(4A.1)
azo C-C‘

_ = l—
67 ( a) C,

 

>0

The larger is y, the higher the probability of 2° >0. This predicts that the higher is the

imitation rate, the more likely is the welfare to be increased.

1 30
(4A.2)

 

 

= < 0
BB; B;
B,‘ has the negative effects on Z°.
(4A.3)
o
62_ = E. > 0
BB, B,

B, has the positive effects on Z°. If the advantage of local knowledge is the same in both
countries, i.e. B,'-B,'=B,,-B,, the smaller is the advantage of local knowledge, the
higher is the probability of 2° to be greater than 0. Moreover, if B,-B,' (the cost gap)
is bigger, the more possible is it for 2° to be positive.

(4A.4)

0 ' a
_a.z_.=(l—a)YC >0

ac cc,

 

larger C has a positive effect on Z°.

(4A.5)

332—0 = —(_1;Ql <0
60’ C,

The smaller is C', the more likely is Z°>0. Combining (4A.4) and (4A.5) together, if

131

the cost gap in sector Y (C-C') is larger, welfare is more likely to be improved.
(4A.6)

o
_63__ = 1 > 0

6(F +A)

The larger F+A is, the higher the probability that Z°>0.

(4A.7)

6Z0

1
6L '1: L-F-A

 

The larger is L, the more likely is Z°<0.

(4A.8)

 

The effects of 01 are not certain. However,

CB 0
"]>0 A «20.5 .. aai>0

cs; a

 

ifln

 

Since C5<C, this implies that B,>B,,'. Though it is still not certain what the effect is

when 0: <0.5, this indicates that the larger is B, over B,’ or the smaller is the difference

between C and C5, a larger 01 will lead to higher likelihood that Z°>O. That is, the

smaller is the cost gap, the more important is the local knowledge, or the slower is the

imitation rate in sector Y, higher preference in good X makes it more likely for welfare

to be improved.

132
On the other hand,

C6 Bl
cs;

0
]so A a<0.5 - fag—<0

 

and

This indicates that the smaller B, over B,‘ is or B, is smaller than B,‘, or the larger the
difference between C and C5 is, a smaller at will lead to better chance for Z1 to be

positive.

Appendix 4B: The First Derivatives for Case 4.5

Let Z'=an‘-an"; and

= (3,-aB,‘)(L-F—A)-(B,,‘—aB,)A .

(413.1)

6Z1 C'-C Bt-Bl‘ _ (L-F-A—aA)(B,-B,') + 81-31. C-C‘

__:a +

Y CI) 3,: +Bt A Bt - «B; C5

 

 

 

 

<0 >0 ? ? >0

It is not certain what the effect of changes of 7 on 2' is.

 

 

(413.2)
az’ = _ at _ a(L-F—A)+A + a
BB; B; +Bt A Bt ~aB;
< 0 7 ?

The effect of B,’ is also not certain.

133

 

(43.3)
a_z_l = E. .. “(1‘Y) + (l-y)(L-F-A+aA) _ 1-7
a I Bl B;+Bt A Bt-CB;
> 0 < O 1? ?

The change of B, also does not indicate certain results.

 

 

(411.4)
BZI = _ cry + y(L-F-A+aA) _ y
as; B;+B, A 3,113;
< o 7 ?

The change of B,‘ does not have certain indication either.

 

 

(413.5)
I e
E. = (1-a)YC > 0
6C CC,
The larger is C, the more likely is Z‘>0.
(43.6)
r
52 = -(1—a)—Y— < 0
ac: C5

The smaller is C', the more probably is Z‘>0. Therefore, if C-C' is larger, the host

country is more likely better off under duopolistic competition.

134

 

(43.7)
62' _ 3:93; _ 1

8L A L—F-A
7 < o

The change of L has no certain effects on Z‘.

 

 

 

 

 

 

(4B.8)

I B -
6i =,n 1mg, 1 + a 1 1 2a
6a a C 3,4,3; 1+1! l-t.z~I-t!2

> 0 > 0 < 0 ?
B; (L -F-A) —B,A 2,, + B,"

A 1+1):2 13,-“); '

? < 0 ?

The effects of 01 are uncertain.

Chapter 5

The Duration Times Of International
Joint Ventures And Foreign Wholly-
Owned Subsidiaries

5 .1 Introduction

A firm investing in a foreign country faces some difficulties since the environment is
different from the home country. Some examples of the difficulties include cultural
differences and different laws. A multinational firm can choose between setting up a new
plant, acquiring an existing local firm, forming a joint venture with a local firm,
licensing, or giving up the plan to enter a foreign market (maybe exporting to or no
participation in the foreign market at all).

A firm may prefer to control a subsidiary to avoid complications in decision-making
and the leakage of technological knowledge to the other firms. Negotiations with other
partners are time-consuming and thus reduce efficiency. The probability of the loss of the
technological advantage to other firms affects the profit rate in the future, so a firm tries
to avoid these possibilities. However, establishing new plants or acquiring an existing
plant may require a lot of investment. If the multinational firm is not familiar with a
foreign market, the firm has to bear risks when investing in a project. The multinational

firm may be able to reduce risks by cooperating with a foreign firm when entering the

135

136
foreign market. Furthermore, the local knowledge explained in Chapter 3 is also an

important factor in joint-venturing. After a plant is established in a certain location, the
plant will develop better knowledge in producing a good. This knowledge includes
information about the local markets (labor and product) and the connection to the local
enterprises which provide services to the plant. It is costly for late comers to acquire the
same knowledge; therefore, it is reasonable for a multinational firm to choose joint-
venturing as a form of entering a new market.

Generally speaking, the parent firms of a joint venture utilize each others' strengths.
Over time, as the parent firms learn more from each other, the benefit of the joint
venture decreases. Particularly, in the case of an international joint venture, the foreign
firm gets experience in the local market through a joint venture and the local firm learns
the advanced technology or management from the foreign partner. After accumulating the
knowledge from the partner(s), the marginal benefit of the joint venture to either partner
becomes smaller and smaller. On the other hand, although the parents will understand
each other better over time, the cooperation costs between different parents may remain
the same or fall slightly as each parent maximizes its own benefits which may be conflicts
to the partner(s); in addition, the diversified goals of the parents are not easily reconciled
or compromised. Eventually the benefit to one (or more) of the partners may be lower
than the cooperation cost, and, at this point, it is very easy for the joint venture to break
down even though it may still be profitable. On average, it is hypothesized that an
international joint venture has a shorter life span than a foreign wholly-owned subsidiary.

The main purpose of this chapter is to test whether joint ventures between foreign

137

countries and U.S. firms have shorter life spans than wholly-owned subsidiaries.

Though the discussions on the instability of joint ventures are not new topics, there
is no formal theory on this concept. Moreover, there have been only a few empirical
papers on the duration time (also called survival time) of joint ventures. Franko (1970)
is one of the pioneers in this area. Later, Kogut (1988) and Geringer and Hebert (1991)
also worked on the instability rates of joint ventures (i.e. the proportion of liquidation or
sellout to the number of joint ventures). These papers relied on questionnaires from the
managers of the related firms and emphasized what characteristics of a joint venture
would affect the instability rate.

The aforementioned papers take the instability of joint ventures for granted. Gomes-
Casseres (1987) was the first to compare the duration time of joint ventures and wholly-
owned subsidiaries of the MNEs. His data came from the Harvard Multinational
Enterprise Project which comprises a sample of about 5,000 subsidiaries of 180 large
U.S. MNEs. He compared the data of instability rates between international joint ventures
and U.S. wholly-owned subsidiaries up to 1975, and he found that though the liquidation
of joint ventures is not very different from wholly-owned subsidiaries, the sellout rate of
joint-ventures (to one of the partners or outsiders) is higher than wholly-owned
subsidiaries. On the whole, the instability rate of joint ventures is about 30% while that
of wholly-owned subsidiaries is only about 15%. The main reason should be due to the
higher sell-out rate rather than the liquidation rate.

Chowdhury (1992) extends the research to compare the performance of international

joint ventures and foreign wholly-owned subsidiaries. He broke down the instability rates

138

between joint ventures and wholly-owned subsidiaries into several periods instead of the
lump-sum data of Gomes-Casseres. His findings suggest that the average longevity of
both international joint ventures and wholly-owned subsidiaries had consistently declined
from 1951 to 1975. That is, the entry year of a U.S. affiliate in other countries does not
affect the instability rate a lot. It also shows that U.S. foreign wholly-owned subsidiaries
have lower instability rates.

Comes-Casseres and Chowdhury directly compare the instability rate up to 1975 and
conclude that joint ventures are more unstable. One problem of these two papers is that
the authors only describe the data instead of testing the instability rate among the different
kinds of affiliates. Though their work is appreciated enough, the evidence does not seem
very convincing. Moreover, the two papers only studied U.S. FDI. There has been no
work for FDI in the United States.

This chapter is based on more recent data (during the period between 1980 and 1991)
to compare the stability of international joint ventures and foreign wholly-owned
subsidiaries by using duration models to test the results rather than simply describing the
results. Furthermore, both data sets of U.S. FDI and FDI in the United States are used.
This approach can provide a better overall picture comparing the life spans of the joint
ventures and wholly-owned subsidiaries, and analyzing whether the longevity of joint

ventures associated with U.S. investment abroad or foreign investment in U.S. differ.

5.2 Sources and Data Collection

The records of the transactions of FDI in the United States and U.S. FDI are collected

139

from Mergers and Acquisitions which provides information about new transactions
between firms. However, the transactions include acquisitions or joint ventures only while
no new plants are recorded in that journal. The transactions covered in this chapter are
drawn from the Summer 1980 to Spring 1981 issues (4 issues included); the transactions
mainly started in 1980 though a few transactions became effective in late 1979.

The list in the journal includes not only FDI but also transactions between U.S. firms
in the United States, so not all records are relevant to the purposes of this chapter. Only
the transactions related to FDI in the United States and U.S. FDI are used. For joint
ventures, only the cooperation between a foreign firm and a U.S. firm in the United
States or the cooperation between a U.S. firm and a local firm in a foreign country are
counted.

One problem with the recorded transactions in Mergers and Acquisitions is that
"failure" cases of the partnerships are unreported. It is necessary to depend on other
sources in order to follow the life span of a wholly-owned subsidiary or a joint venture.
Moody '8 Manuals and Who Owns Whom are used to keep track of each transaction. The
former has better records of the firms but may not record the full list of the subsidiaries.
The latter includes a better list of the subsidiaries of MNEs but no changes in the
ownership of subsidiaries are recorded explicitly. Both of these sources are cross-
referenced to build the most complete data set possible. If a transaction from Mergers and
Acquisitions cannot be followed in Moody 's Manuals or Who Owns Whom, the case is
dropped from the data set.

The latest sources available were published in mid-1992, so the record of a subsidiary

140

or a joint venture is assumed to be up to December 31, 1991. If a case is still recorded
in the 1992 publications, it is taken to be a censored case up to that date. If there is a
case reported that the subsidiary _or the joint venture is terminated - it was sold out,
closed, or the status was changed from a joint venture to a wholly-owned subsidiary or
reverse - then the transaction is taken to have ended.

Assume that the change of the ownership of the whole parent firm is not due to the
performance of the targeted affiliate.l If a foreign parent firm investing in the United
States is acquired by another firm which is not based in the United States, the subsidiary
(or joint venture) is treated as still alive. If the parent itself is acquired by a firm based
in the United States, the subsidiary is taken as terminated. The rationale is that if the
parent firm is acquired by another foreign firm, there is no reason to believe the
acquisition is due to the affiliate while the affiliate is still a foreign affiliate in the United
States. More important, since the new parent firm and the original firm may be under
special negotiation which the outsiders cannot identify. It may not be appropriate to take
these cases as the termination of the targeted affiliates. If the foreign parent firm is
acquired by a U.S. firm, it is clear that the affiliate is no longer a foreign affiliate.
Although the acquisition is not due to the affiliate, it is ridiculous to count the affiliate
as a "foreign firm". Similarly, the same standard is applied to the U.S. firms investing
in other countries. That is, if a U.S. parent firm is acquired by a foreign firm, the
subsidiary (or joint venture) is treated as terminated. If a U.S. parent firm is acquired by

another U.S. firm and the subsidiary is not sold out, the affiliate is treated as survived.

 

lIt may not be a true situation; however, the reverse assumption that the change of ownership of the
whole parent firm is due to the performance of the targeted affiliate also has problems.

141

This standard of this paragraph may be controversial, but since there are only 13 cases
belonged to this situation, the results should not be much different no matter what is the
standard.

However, if a wholly-owned subsidiary or a joint venture is sold to another parent
firm, the subsidiary (or joint venture) is taken to be terminated. This is different from the
transaction of the whole parent firm since if only the subsidiary or the joint venture is
sold out, the management may be much different than the change of ownership of the
whole parent firm. A more important point is that if a affiliate is sold to another firm,
it means that the original parent should be beneficial from the new transaction. Though
the subsidiary itself is still alive, this means that the transaction is certainly a case of

instability.

5.3 The Proportional Hazards Model

Since the purpose of this chapter is to compare the duration time of international joint
ventures and wholly-owned subsidiaries, a duration model will be applied. In order to
include a variable to distinguish joint ventures from wholly—owned subsidiaries,
explanatory variables - at least a dummy variable indicating joint ventures or not - must
be included in the model; the proportional hazards model is a most convenient model to

use.2 The summary of proportional hazards model in this section mainly follows

 

2Cox (1972) was the first to present the proportional hazards model. It was originally based on strictly
continuous data. Kalbfleisch and Prentice (1973) extend the model to grouped data. Sometimes, the
precision of the measurement of data is not good: The data are not distributed along a continuous line, and
some data have the same length of duration time (the data are tied). In this case, grouped data appear.
Kalbfleisch and Prentice prove that the proportional hazards model is still valid in grouped data. As
duration models have become more well-known, some text books such as Kalbfleisch and Prentice (1980)

142
Kalbfleisch and Prentice (1980 Ch.l, Ch.4 and Ch.5) and Cox and Oakes (1984 Ch.2,

Ch.7) while Chung et al. (1991) is also a reference.

A duration model deals with modelling data in which each individual terminates the
targeted activities at a point of time when an event occurs. Such an event is usually
referred to as a failure though the event may not lead to the individual itself disappearing.
For example, a "failure" may be the performance of a certain task in a learning
experiment in psychology, or a change in residence in a demographic study, or promotion
of people in a business survey. A specific distribution of the duration time of the data is
usually assumed. If factors affecting the duration time of an event are tested, explanatory
variables are used. When explanatory variables are included in the model, matters
become more complicated; however, the proportional hazards model allows us to use a
simple method to test whether the duration time is affected by the variables. There are
various applications of the proportional hazards model in clinical and criminological
analyses. Some examples of the former include the studies of heart transplants3 and

medical treatment effects‘. The examples related to criminology are studies of duration

 

and Cox and Oakes (1984) provide good descriptions of the model. Chung et al. (1991) gives the most
updated summary of the duration models.

3Examples are Crowled and Hu (1977) and Lagakos (1980). Crowled and Hu use some independent
variables to test the lifetimes of the patients after heart transplants. The independent variables include
personal characteristics such as age and previous surgery history and the degree to which donor and
recipient (of the heart) are mismatched for tissue type. Lagakos further uses graphical analyses of the
relation between heart transplants and the independent variables. The graphs were drawn according to the
ranking of the residual scores which were calculated from the data.

4An example is Kay (1977 ) which compares Prednisone treatment and placebo tablets against cirrhosis
(a liver disease). The other independent variables include age, sex, daily alcohol consumption, the activity
of the cirrhosis and the absence/presence of ascites.

143

time of recidivism of ex—offenders after release from prisons5 and the effectiveness of
supervision after sentencing“. .

It is helpful to briefly explain the proportional hazards model. Suppose that we are
considering a homogeneous population of individuals each of which has a " failure time".
That is, we deal with the distribution of a non-negative random variable, T, which has

a distribution function:
FT(t) = Pr(T<t) ,
where t denotes time. It means that T refers to the "failure time”. The distribution

function FT(t) refers to the probability of the ”failure" up to T. The survivor function is:

S,(t) = 1-F,(t) = Pr(th) . (5.1)

The function reflects the probability of surviving at time t. In other words, at time t, an
individual with " failure time" T has the probability of ST(t) to "survive". Assuming that
T is continuous, the distribution has a probability density function which is equal to the

negative value of the differentiation of (5.1):

 

5 Barton and Tumbull (1981) study the factors affecting the ex-offender's postrelease performance. The
2 groups of male offenders from Cheshine and Somers correctional institutions are compared. The other
independent variables include age, drug use and monthly income. Schmidt and Witte (1988) use the data
of released people of the North Carolina Department of Correction to study recidivism. The independent
variables include age, time served in prison, previous incarceration, rule violations in prison, education,
race, sex, alcohol consumption, drug used. marital status, supervision methods and nature of crimes.
Chung et al. (1991) provides a survey on the quantitative literature of applying duration models to analyze
the time until recidivism.

6Rhodes (1986) compares two competing events: completing supervision without misconduct and being
removed from supervision because of misconduct. The other independent variables include age, sex, race,
marital status, education and prior criminal records.

144

f1“) = -S,’(t) = lim P'(tST<t+At)

at-°0° At

(5.2)

 

where at denotes the change in t. Accordingly, we may use another expression for the

survivor function:

5.1:) = ff.(u)du

A useful expression is the hazard function:

 

hr“) = lim Pr(tsT<t+At | tsT)

tit-'0' At

(5.3)

It means that given an individual with "failure time" T surviving up to time t, the hazard
function is the probability that the individual "fails" at t. In other words, if an individual
has survived up to the present period, the hazard function reflects the probability that the
individual "fails" at present. By the definition of conditional probability, we have (after
omitting the suffix T):

1(1) = £% . (5.4)

Substituting (5 .2) into the hazard function (5 .4), it becomes:

145

—S’(t) = _ dS(t)

 

h(t) =
S t S t dt
( ) ( ) (5.5)
= _ dlnS(t)
dt ,
by using the fact that
d—S(‘—) = dlnS(t)
S(t) .
Integrating (5.5) and using S(O)=1, we obtain:
3
S(t) = exp[-fh(u)du] (5.6)
0 e

The hazard model discussed so far does not allow explanatory variables. Cox (1972)

introduced a hazard rate with explanatory variables, namely:

h(t;x.fl) = h.(t)e"' . ‘57)
where B is a P X1 vector of unknown parameters and x is a matrix of variables describing
N individuals: [x,, x2, ..., x,, ...,xN] in which xi is a le vector, i=l,...N, and h,,(t) is
called a baseline hazard which is an unknown function giving the hazard function for the
conditions x =0.

The Risk Set R(t,) reflects that all the individuals "survive" at least up to time t,, so
R(t,) includes all the individuals which "fail" at ti and all the survivors at t,. The
conditional probability that individual i fails at ti given the Risk Set R(t,) (completing the

time at t,) is:

146

 

h(t, ; x,. b) = e’t"
(5.8)
X h(t,;x,.fl) X 12""
keflt) helm)

Because of the multiplicative assumption (5.7) which at time t h,,(t) is the same at both
the numerator and denominator, the baseline hazard function h,,(t) is cancelled. The
conditional probability (5.8) is convenient because it is not affected by the distribution of
the baseline hazard function, so the difficulty of determining the distribution is avoided.

Usually, the observed duration time of some individuals may be tied at the same point
(the data are grouped). That is, it may be observed that more than one individual has the
same duration time. Suppose that there are given J observations (t,,x,.,), j=l, ..., J,

m=1, ..., Mj, ..., M]; and

t,<t2<...<tJ.
The observations are tied so that at time t, the number of individuals is M,. The total
number of the individuals is 2’,=, M,, all of which have "failure" time up to t,.

If the sample is censored at tJ so that there are MJ+1 individuals surviving at t, which
is the last point of observation, the number of the total individuals is EMF, M,=N.
When the sample contains grouped data and is censored at the right side (i.e. all
individuals are observed from the beginning but not all individuals are observed
"failure”), the partial likelihood of the conditional probability functions of all the

individuals can be constructed as:

 

e11.
L " u 15 9)
.i'1 a," 1 °
2 e
(“‘1’ J ,
where
"I
41 E ‘1-

The partial likelihood is simple but the usual large-sample properties of maximum
likelihood estimates are applied: the estimates are consistent and asymptotically normally
distributed with asymptotic covariance matrix estimated consistently by the inverse of the
matrix of second partial derivatives of the log likelihood function.7 The maximum
likelihood can be found by using iterations. The details of the iteration method are in

Appendix 5A.

5.4 The Estimated Model

At first, the model used in this paper is based on the proportional hazards model
which has been discussed in the previous section. Since the main purpose is not the
distribution of the duration time of the affiliates but the effects of joint ventures or
subsidiaries on the instability rate, explanatory variables are used. In particular, the
explanatory variables which we used are represented by the vectors of x. x,'B of

individual i is as follows:

 

7Refer to the discussion of Cox (1975). Cox shows that the partial likelihood is simpler than the full
likelihood as for examples, only the parameters of interest are involved and the nuisance parameters are
excluded.

148

1113 = 1),th + BZSALES, + (3,111, + 3,0, + 3511110057111; + B,DEVELOP, ,
where 131. k= l,...,6, are the coefficients to be estimated. The variables include:

(1) JV, the dummy variable for firm types (1 =joint venture, 0=wholly-owned
subsidiary);

(2) SALES, the total sales (in term of millions USS) of the parent firm of the source
country (a proxy of the size of the investing firms). For a joint venture, only the total sale
of the investing firm (relative to the host country) is counted;

(3) HI and C1, the dummy variables for the form of integration (HI=1 if horizontal
integration, 0 if vertical integration or conglomerate integration; CI=1 if conglomerate
integration, 0 if vertical integration or horizontal integration). The forms of integration
can be divided in the following way: horizontal integration is denoted by HI=1 and
Cl=0; conglomerate integration is denoted by HI=0 and CI=1; and vertical integration
is represented by HI=0 and CI=O;

(4) INDUSTRY, the dummy variable of industrial classification of the investment (1
if service sector, 0 if manufacturing or mining sectors); and,

(5) DEVELOP, the dummy variable for controlling whether an investing firm is based
in a developing country or not (if the host country is the United States) or whether the
host country is a developing country or not (if the investing firm is based in the United

States). (1 if developing country, 0 if developed country.)8

 

”The developed countries include Australia, Belgium, Canada, Denmark, Federal Germany, Finland,
France, Japan, Ireland, Italy, Netherlands, New Zealand, Norway, Spain, Sweden, Switzerland and United
Kingdom. The developing countries include Brazil, China, Hong Kong, Hungry, Korea, Mexico, Monaco,
Philippines, Portugal, Sharjah, Saudi Arabia, Singapore, Venezuela and Yugoslavia.

149

Three regressions are run, one for each data set:
Sample (a): U.S. direct investment in other countries;
Sample (b): FDI in the United States;
Sample (0): Sum of the data sets (a) and (b).
For sample (c) above, an additional dummy variable is used to control for the possible
difference in samples (a) or (b): US=1 if U.S. FDI, 0 if FDI in the United States.

JV is the main variable we want to test in this model. Because the hypothesis is that
a joint venture is expected to be more unstable, the coefficient of JV, B,, should be
positive. That is, a positive JV coefficient implies a higher instability rate for joint
ventures and a positive relationship between earlier failure times and joint ventures as
opposed to wholly-owned subsidiaries.

SALES is the proxy for the size of an investing parent. Theoretically, the larger the
firm, the deeper the pocket and the higher risk it can bear. Thus a larger firm may allow
the subsidiary (or affiliated joint venture) to operate for a longer time, other things being
constant. Thus B, should be negative which implies that a larger parent tends to have
lower instability rates for subsidiaries or joint ventures. Though it may be predicted that
a larger firm prefers to control subsidiaries so that the parent firm's size may be
positively correlated with the choice of wholly-owned subsidiaries, there is no evidence
to support this prediction.9

Theoretically, the form of expansion (horiZontal, vertical or conglomerate integration)

 

9Blomstr6m and Zejan (1991) suggest the positive relationship between the choice of a wholly-owned
subsidiary and the size of a parent; however, the empirical results from their paper do not support this

prediction.

150

of a firm has no clear-cut relationship to the duration time. The form of expansion may
depend more on the location-specific advantage of a host country.10 Experience is also
important to a firm and then a firm tends to expand horizontally or vertically to deepen
its experience within an industry. Conglomerate integration is related to the investment
into a field in which the investing parent firm has less experience. If less experience is
positively correlated with less stability, then CI should have a positive relationship with
the instability rate. However, we have no good reasons to predict the duration time of
horizontal integration in contrast to vertical integration. Whether a firm chooses to expand
horizontally or vertically depends on the location-specific advantage and there are no
general rules about which one will lead to ”long-life" affiliates.

As a practical matter, it is difficult to identify the form of integration. A MNE usually
has many different kinds of businesses. For the purposes of this paper, we have devised
the following way to distinguish between different forms of integration. If the business
of the new subsidiary or the joint venture is similar to that of the parent firm, horizontal
integration is assumed; if the parent firm is operating a business which is upstream or
downstream of the subsidiary or the joint venture, it is taken as vertical integration;
otherwise, it is counted as conglomerate integration.

Next, we consider the variable DEVELOP. Sometimes, a firm based in a developed
country investing in a developing country may not be strictly concentrating on the profit

rate of the single project. It may treat the investment as a long term project for collecting

 

1“The concept of location-specific advantage is explained in section 2.1 of Chapter 2.

151

information about the foreign market." However, political conditions in developing
countries may be less stable, and this political instability may shorten the duration of a
subsidiary or a joint venture. Another matter is that the developing countries usually
prefer local participation in foreign investment projects, partly from the viewpoint of
political independence. A developing country may require foreign firms to have at least
a minimum share of local ownerships. Even if a developing country does not mandate
local ownership, a MNE may voluntarily find a local partner to avoid political problems
later. Thus, an investing firm will tend to set up joint ventures in a developing country
though it might prefer wholly-owned subsidiaries if there were no political considerations.
Therefore it is hypothesized that this variable is positively related to JV; given this, we
should check for the presence of multicollinearity before including it.

The dummy variable INDUSTRY is simply used to see whether the type of business
(service or manufacturing) affects the duration time. There is no clear-cut indication about

the sign of the coefficient.

 

11Of course, this factor may also be applied to a developed country. The difference is that a U.S. firm
(for example) is presumed to know a developed country much better than a developing country (c. g. the
legal system in a host developed country is closer to the source country), so that a U.S. firm should find
the profit rate in a developed-country-venture more important.

152

 

 

 

Group 0 Group 1
1—
i? _
5
(O
.D
O
L _—
C].
'6
.3.
Z
3
Ln _
O—
I I I I I
O 156
MONTHS

Kaplan—Meier Survival Curve

STETEL’:

 

 

 

Figure 5.1: The Kaplan-Meier Survivor Functions of Foreign Wholly-Owned

Subsidiaries (Group 0) and International Joint Ventures (Group 1)

153

One obvious variable which is likely to affect the duration time and which is missed
from this list is the profit rate of a subsidiary or a joint venture. It is clear that the profit
rate will be negatively correlated with the instability rate. Unfortunately, there are no
profit data on the individual subsidiaries from the sources mentioned in section 5.2. The
only data on net income (the total income minus taxes) available are the aggregate values
for parent firms. We do not include this variable in the model as we cannot distinguish
the profit rate from the other subsidiaries within a parent firm. Even if we could get the
data for individual subsidiaries, the matter of transfer pricing might make the data biased.

From the four issues between Summer 1980 and Spring 1981 of Mergers and
Acquisitions, there are 278 transactions which are related to the international joint
ventures or foreign subsidiaries; however, only 215 cases have the records of duration
time, 99 of which are FDI in the United States and 116 of which are U.S. direct
investment in other countries. The duration time variable for all subsidiaries or joint

ventures is in terms of months. The cases are summarized in Appendix 5B.

5.5 Results

At first, it may be helpful to compare the survivor functions of the foreign wholly-
owned subsidiaries and international joint ventures without consideration of other
explanatory variables. Sample (c) is divided into two parts: one includes joint ventures,
and the other includes wholly-owned subsidiaries. Using Kaplan-Meier survivor function
estimates for the two parts respectively, we can plot the two survivor functions in Figure

5.1. (A brief description of Kaplan-Meier is given in Appendix 5C.) It should be noted

154

that the sample is censored when the duration time is longer than or equal to 132 months.
So the survivor functions become flat after that point. The difference of the functions is
that the survival probability (i.e. the survivor function) of the international joint ventures
(denoted by group 1) are lower than that Of the foreign wholly—owned subsidiaries
(denoted by group O). Graphically it can be seen that, on the whole, joint ventures have
a smaller survivor function.

As we discussed in the previous section, some variables may be correlated with each
other, so before running the model we check for the presence of multicollinearity. From
Table 5.1, we can see that the correlations between the independent variables are not
close. The closest relationship is between JV and DEVELOP (0.4204) as expected since
developing countries usually require local participation in foreign subsidiaries,” thus we

need not worry about the problem of multicollinearity in the model.

Table 5.1: Correlations between the Independent Variables (Sample (c))

 

(individuals = 193)
| JV SALES HI (:1 INDUSTRY DEVELOP US

 

JV | 1.0000

SALES 1 0.0496 1.0000

HI 1 0.0246 0.1632 1.0000

or | 0.1737 0.0584 0.5584 1.0000

INDUSTRY | 0.0407 0.1092 0.1163 0.1208 1.0000

DEVELOP | 0.4204 0.0271 0.1238 0.1816 0.0002 1.0000

US 1 0.2832 0.1548 0.1230 0.1760 0.0075 0.3281 1.0000

 

 

12HI and C1 are also highly correlated. This is not a problem, however, because the 2 dummy
variables are combined to represent the forms of integration, and then vertical integration is zero in both
variables. The negative correlation is due to the lower proportion of vertical integration in the sample.

155

First, we run the model for U.S. direct investment in other countries (sample (a)), and

the results appear in Table 5.2.

Table 5.2: U.S. FDI (Sample (a))

 

Individuals =

chi2(6) = 17.44

Prob > chi2 = 0.0078
Log Likelihood = -265.10316

 

 

 

I Coefficients Std. Err. t P> |t|
JV | 1.24314 0.32027 3.881 0.000
SALES | -0.00006 0.00005 -l.261 0.210
HI | 0.17358 0.31787 0.546 0.586
CI I 0.94691 0.41359 2.289 0.024
INDUSTRY | -0.04732 0.27352 -0. 173 0.863
DEVELOP | -0.73246 0.34167 -2. 144 0.034

Note: t: Student-t test statistic

P> |t|: Significant level

 

From Table 5.2, it can be seen that the signs of the coefficients are generally
consistent with our predictions. The signs are positive for JV, HI and CI but negative for
SALES, INDUSTRY and DEVELOP. The chi-square test suggests that at least one
explanatory variable is significant. As the coefficient of JV is positive and highly
significant, it supports the theory that joint ventures are more unstable than wholly-owned
subsidiaries for U.S. direct investment in other countries. Another significant variable is
CI which also has a positive sign. It implies that conglomerate integration is more

unstable than horizontal integration or vertical integration. Though HI has a positive

156

coefficient too, it is not significant.

Apart from the fact that JV and C1 are significant, DEVELOP is also significant at
the 5% level. Its negative sign implies that the projects of U.S. FDI in developing
countries tend to be more stable, as predicted earlier. The degree of correlation found
between JV and DEVELOP suggests that U.S. firms are more likely to form joint
ventures in developing countries.

The coefficient on SALES is small and negative, and the coefficient on INDUSTRY
is also very small in absolute value; both variables are insignificant at the 5% level. Our
hypothesis that the size of a parent may be correlated with more stable affiliates is not
supported by the data.

Six observations of SALES are missing and then Table 5 .2 does not include the
complete data set. If only the significant variables (JV, CI and DEVELOP) are included
in the model, the results are similar.13

Next, we test the results of the sub-sample of FDI in the United States (sample (b)).
These results can be compared with sample (a) in order to find out whether the instability
of joint ventures is unique to U.S. affiliates or not. In sample (b), there is only 1 foreign
firm investing in the United States which is based in a developing country, so it is not
possible for us to test the effects of DEVELOP. The results appear in Table 5.3.

The signs of the coefficients are the same as the previous results: positive for JV, HI

and CI, negative for SALES and INDUSTRY. However, JV and C1 are not significant

 

”The coefficients of JV, CI and DEVELOP are 1.0516, 0.7405 and -0.6308 respectively. The t-values
for JV and C1 are 3.433 and 2.162 respectively while the probabilities greater than the absolute t-values
are 0.000 and 0.033 respectively. The t-value and probability for DEVELOP is -l.9l9 and 0.057
respectively. Though the significance levels are not as high as those in table 1, the results are similar.

157

and the absolute values of the coefficients are much smaller than in sample (a). The only
significant variable is INDUSTRY and the negative sign suggests that FDI in the United
States may last longer when it occurs in the service sector. One possible explanation is
that the United States has a comparative advantage in services, so only the stronger
foreign firms can compete in the United States and accordingly, the affiliates are last

longer. This may be an interesting topic for future research.

Table 5.3: FDI in the United States (Sample (b))

 

 

 

Individuals = 83
chi2(5) = 8.41
Prob > chi2 = 0.1351

Log Likelihood = -l76.32368

| Coefficients Std. Err. t P> |t|

IV | 0.32327 0.41874 0.772 0.442

SALES | -0.00001 0.00003 0418 0.677

HI I 0.29646 0.41222 0.719 0.474

CI | 0.52367 0.41539 1.261 0.211

INDUSTRY | -0.81511 0.38912 -2.095 0.039

 

Quite a few observations are missing for SALES. If we retain only the variables JV
and INDUSTRY and the model is re—estimated using the entire data set, we find that
although the significance level of JV is improved and the absolute value is larger, it is

still insignificant at the 5% (or 10%) level.“ One possible reason is that the sample only

 

"A total of 99 cases are used. The coefficient of JV is 0.4632 and the t-value is 1.326. The probability
greater than the absolute t—value is 0.188. For INDUSTRY, the coefficient is -0.6371 and the t-value is
-2. 110. The probability greater than the absolute t-value is 0.037.

158

includes 13 cases of international joint ventures in the United States, and then the
standard error may be larger. The group test (chi-square test) is not as good as sample
(b) and so it is possible that none Of the independent variables are significant.

Finally, we ran the model using the combined sample (sample (0)); the results are
Shown in Table 5.4. The signs of the coefficients are also the same as in the previous
estimations. Moreover, the chi-square test also suggests that at least one independent
variable is significant. The coefficients Of JV and CI are positive and significant while
that of DEVELOP is negative and insignificant at the 5% level. The Sign on the dummy
variable, US, distinguishing between FDI in the United States or U.S. direct investment
abroad is positive but not significant. Overall, international joint ventures appear to be
more unstable and conglomerate integration tends to have shorter duration time.
DEVELOP is negatively significant at the 10% level suggesting that FDI related to
developing countries tends to last longer, though the evidence is not very strong. None
of the other coefficients are significant, and then the results are not strong enough to
support the prediction of signs.

There are some data missing in Table 5.4 (also due to SALES). If we make use of all
the data by including only the significant variables, i.e. only JV and C1 are included in

the model, the absolute values of the coefficients are smaller but still significant.”

 

15215 cases are used. The coefficient and t-value of JV are 0.5787 and 2.961 respectively. The
probability greater than the absolute t—value is 0.003. The values of C1 are 0.5397 and 0.2101 respectively
and the probability is 0.011. Since all the data are used, and other variables are dropped, it is not
surprising to find slightly different values. The results still support the theory that joint ventures and
conglomerate plants are more unstable.

159
Table 5.4: Combined Data Set (Sample (c)) Results

 

 

 

Individuals = 193
chi2(7) = 18.95
Prob > chi2 - 0.0083

Log Likelihood = —516.97271

I Coefficients Std. Err. t P> ItI

JV I 0.83624 0.22786 3.670 0.000

SALES I -0.00002 0.00003 -0.604 0.546

HI I 0.25483 0.25131 1.014 0.312

CI I 0.67345 0.28695 2.347 0.020

INDUSTRY I -0.27374 0.21819 -1.255 0.211

DEVELOP | 0.57021 0.32020 -1.781 0.077

US I 0.13481 0.21431 0.629 0.530

 

5.6 Test of the Appropriation of the Proportional Hazards Model

It is not clear whether the proportional hazards model is appropriate or not. A simple
method can be used to check the adequacy of the model“, that is, whether the log-linear
assumption of the model (equation (5.7)) is appropriate or not.

From (5 .6), taking the exponential to both sides and applying the results to the

baseline hazard:

T
—fh,(t)dt = 3150(7) (5.10)
0

where S, is the baseline survivor function. Substitute (5.10) into the integration of (5.7),

 

l6Chung et al. (1991), pp.79-80.

160

it becomes:

T
[h(:;x,p)d: = -1ns,(7')e”' (5.11)
0

Let

T
v = -1nfh(t;x,p)dt (5.12)
0 .

Taking logarithm of (5.11) and then we have:

—v = ln{—ln[S,(T)]}+x’B

Given the survival time t according to the proportional hazards model, a transformation

of t is used:

2 = —ln{-ln[S,,(T)]} .

It is clear that v is the difference between 2 and x'B, and then

I. = x’ B +v
is a linear regression model.
Though we do not know the distribution of the baseline hazard function, it is possible
tO estimate the distribution of the ”residuals", v. It can be shown that v has the extreme-

value distribution with the distribution function F(v):

170’) = cxp[-cxp(-v)] . (5.13)

The general idea behind the extreme-value distribution is that if an individual with the

161

”failure" time at T has the survivor function S(T;x,B), then S(T;x,B) is assumed to be

uniformly distributed. From (5.12), we have:

T
v = -1nfh(1;x,p)d: = -ln{—ln[S(T;x,B)]}
0

The distribution of v is Obtained accordingly.” Since there are some data censored after
T>132, the ”residuals" are either censored or uncensored.
Once B and the baseline survivor function are estimated, we can calculate the

estimated "residuals" as

1), = -ln{-ln[S,(t,)]} - x,'I‘i . (5.14)
Comparing the distribution of the estimated "residuals" (5.14) with the extreme-value
distribution (i.e. 5.13), we can check the adequacy of the proportional hazards model.
It is convenient to use Kolomogorov-Smimov one-sample test to examine the
hypothesis that the actual distribution of the "residuals" is equal to the extreme-value
distribution. The basic idea is very simple: to find out the largest difference between the
actual and hypothesized distribution functions and then to determine whether it is
acceptable that the distributions are the same.“ Let

K. = SVPIF(9)-F(V)I

-ee<ee

 

1"This result is extended from the idea of Cox and Oakes (1984), pp.88-89.

18Please refer to Chapter 6 of Conover (1971).

162

If the null hypothesis is false, then estimates of F(v) , the distribution function of

‘7 will tend to near the true distribution instead Of F(v) and consequently K, is large;

so it is reasonable to believe that if K, is large, the null hypothesis is rejected.

For the sample (c), we find that the greatest positive value of the difference Kv is
0.0244 and the greatest negative value is 02938. The probability of accepting the null
hypothesis is 0.000. Therefore, using Kolomogorov-Smirnov test, we find the hypothesis
that the "residuals" have an extreme-value distribution is rejected, so the log-linear
assumption of the proportional hazards model is not appropriate. The similar results can

be got by testing the other samples.

5.7 Parametric Models

Although the log-linear assumption Of the survival time distribution in the proportional
hazards model is not appropriate in estimating the hazard function (or the survivor
function), the empirical results are still valuable. It is because our main interest is the
comparison between wholly-owned subsidiaries and international joint ventures rather than
the exact distribution of the "failure” time. Though the magnitude Of the estimated
coefficients of the explanatory variables is not unbiased, the significance levels may
probably be still useful. We use other models to estimate B's to check whether the results

are significantly different from proportional hazards model. The exponential distribution

163

and Weibull distribution are chosen for convenience. ‘9

Exponential Distribution

The exponential distribution20 has the density function:

f0) = 0f“,

and the survivor function as

S(t) = a“,
where it is required that 0>0. Its mean is 1/0 and its variance is 1/02. To allow

explanatory variables to enter into a survival model, a convenient choice is”:

l
— = cxp(x1'fl)

6 0

Clearly this implies 0=exp(-x,'B). Suppose that the sample consists of N cases of which
n have failed before the last observed period, so that N-(n+ l) are censored. Let the
Observed failure times for the affiliates be denoted ti (i= 1,2, . . . ,n), and the censored times

for the "survivors" after the last observed period be denoted t“, (i =n + 1,. . . ,N). Assuming

 

l"Proportional hazards model has an advantage over the two parametric models from the viewpoint that
the former does not depend on the exact hazard functions (of survivor functions) while the latter two
depend on the assumptions of the distributions. The parametric models are applied here to compare the
results of the proportional hazards model.

2"The exponential model follows Chung et al. (1991), pp.7l-73.
21A more obvious possibility to let 0 vary over Observations as a function Of explanatory variables is

(l/0)=x,'B which is in a linear regression; however, this is an inconvenient choice because 0 (and 1/0)
must be positive, and then restricting x,'B > 0 for all i is a bothersome set of restrictions to impose.

164

that the individual outcomes are independent from each other, the likelihood function

becomes:

a ll
L03) = IIOexM-Oq) I'I cxP(-0t.-‘)

i-l i=n+l

n II
= IIexp1-xi’mepr—cxp1-xi’tn.) n cxp[-exp(-x,'fi)t,‘] .

1"! Hut
The likelihood is then maximized and the estimates for B can be Obtained from the
iterative method.
Table 5 .5 shows the results of the whole sample (sample (0)) estimated under the

exponential model.

Table 5.5 Exponential Model - Combined Data (Sample (c))

 

 

 

Individuals = 193
Model chi2(7) = 18.090
Prob > chi2 = 0.0116

Log Likelihood = -213.442

| Coefficients Std. Err. t P> |tI

IV I -0.75182 0.22660 -3.318 0.001

SALES I 0.00002 0.00003 0.633 0.528

HI I -0.24633 0.25148 0980 0.329

CI I -0.65367 0.28688 -2.279 0.024

INDUSTRY | 0.24788 0.21737 1.140 0.256

DEVELOP I 0.48232 0.31753 1.519 0.130

US I -0.09642 0.21431 0450 0.653

constant I 5.55609 0.27577 20.148 0.000

 

A survivor function is decreasing as it reflects the survival ratio Of the data while a

165

hazard function is increasing. Since the likelihood is based on the survivor function rather
than the hazard function, the signs of the coefficients are expected to be opposite Of the
proportional hazards model. A positive coefficient means that an increase in the
corresponding element in the explanatory variables raises the mean time Of the duration
of an affiliate in foreign countries, and vice versa for a negative coefficient. As noted in
Table 5 .5, all the signs are Opposite to Table 5 .4 as expected. Particularly, the signs of
the coefficients Of JV and C1 are negative and significant, which support the conclusions
of the proportional hazards model. The chi-square test also support the fact that at least
one independent variable is significant. This indicates that joint venturing and
conglomerate integration tend to reduce the life span Of an affiliate.

Running the exponential model for sample (a) and sample (b), the signs of the
coefficients further support the proportional hazards model findings. The coefficients of
IV and C1 are also negative and significant at the 5% level for the sample of U.S. direct
investment in other countries (sample (a)) while the coefficient of DEVELOP is positive
but only significant at the 10% level. On the other hand, the sign of the coefficient of
INDUSTRY is positive and significant at the 5% level for the sample of FDI in the
United States (sample (b)). If only JV and INDUSTRY are included in sample (b),
INDUSTRY is significant at the 10% level. The foreign affiliates at the service sectors

in the U.S. also have a larger mean life span.

166

Weibull Distribution
The other parametric model that can be used is Weibull distribution”. let y =ln(t) and

the density function of y is:

y = 0"f(W) .
where w=(y-x'B)/O and O is the standard deviation of y. A Weibull regression model is

given by:

f(W) = “PW-e"),

The Weibull distribution is a generalization of the exponential. If 6: 1, the hazard rate
is constant and the Weibull distribution is the same as the exponential distribution. A
Weibull distribution has an increasing hazard rate if O>1 and a decreasing hazard rate
if O'< 1. Therefore, a Weibull distribution can avoid the restriction of an exponential
distribution where the hazard rate must be constant. However the Weibull distribution is
monotonic such that the hazard rate is increasing, decreasing or constant but it cannot be
increasing at first and then decreasing later or vice versa.

The likelihood function for a sample with censored data for case i, i=n+1,...,N, is:

 

2”The Weibull model follows Kalbfleisch and Prentice (1980), pp.54-55.

L(p,0) = H 0-11.691)
('1

I
:::l:[ (y'lcgqp
l-l

estimates.

Table 5.6: Weibull Model - Combined Data (Sample (c))

i-n+l

 

(J

 

167

N
H S(w,)

 

r r
yi'xt P -exp( ”1:1“

 

.fi {ml-411'f01.

where S(w) =l,.°°f(u)du. An iterative method is required to obtain the maximum likelihood

 

 

 

Individuals = 193
O = 0.614 Model chi2(6) = 21.089
Std Err(O) = 0.049 Prob > chi2 = 0.0036
Log Likelihood = -200.107
I Coefficients Std. Err. t P> ItI

JV I -0.54044 0.13918 -3.883 0.000

SALES | 0.00001 0.00002 0.781 0.436

HI I -0. 16149 0.15419 -1.047 0.296

Cl | -0.44423 0.17564 -2.529 0.012

INDUSTRY I 0. 17220 0. 13386 1.286 0.200

DEVELOP | 0.36592 0. 19667 1. 861 0.064

US | -0.08167 0.13142 0621 0.535

constant I 5.2628 0.16801 31.325 0.000

 

(standard errors conditional on O)

 

The results of the Weibull model for the overall sample (sample (c)) are shown in

Table 5.6. The signs of the coefficients should be the same as the exponential model (or

the opposite of the proportional hazards model). The results confirm this prediction. The

chi-square test suggests that at least one explanatory variable is significant. Furthermore,

168
IV and Clare also significant at the 5% level in which both JV and Clare negative. The

coefficient of DEVELOP is positive though it is only significant at 10% level. The
Weibull model suggests that joint ventures tend to terminate earlier and conglomerate
integration leads to a shorter duration time. U.S. firms investing in developing countries
or foreign firms in the U.S. based in developing countries have a larger mean of the
duration time although the evident is not very strong.

It can be checked that if only JV, CI and DEVELOP are included in the model, the
coefficients remain significant and have the same signs as in Table 5.6. If the models for
sample (a) and sample (b) are run, the results are also consistent with the proportional
hazards model: for sample (a) (U .S. investment abroad), JV, CI and DEVELOP are
significant and have the same signs as Table 5.6. For sample (b) (foreign investment in
the U.S.), INDUSTRY is positive and significant, i.e. foreign firms of services in the
U.S. on average have a longer duration time.

To use the Kolomogorov-Smimov test, both the exponential distribution and the
Weibull distribution are rejected; therefore, all three models used in this chapter are not
appropriate to describe the hazard function. However as the signs are consistent in the
three models, it is suggested that joint ventures should have a shorter duration time than
the wholly-owned subsidiaries. Although the true distribution of the survivor function is
unknown, it is reasonable to believe that the average duration time of joint ventures is

shorter than that of the wholly-owned subsidiaries.

1 69
5 .8 Concluding Remarks

The hypothesis in this chapter is that international joint ventures should have shorter
duration times than wholly-owned subsidiaries. The c00peration costs between partners
of a joint venture remain stable over time as it is assumed that the conflicts between
different firms are not easy to solve. However, the benefits from the joint venture
decrease as the partners gather more and more knowledge from the other partner over
time. After applying different models (the proportional hazards model, the exponential
model and the Weibull model) to compare new international joint ventures and foreign
acquisitions between the end of 1979 and the end of 1991, the hypothesis is not rejected
with a sample of U.S. direct investment in other countries. This result is consistent to
previous studies; however, the evidence on the relative stability of foreign wholly-owned
subsidiaries compared with international joint ventures in the United States is not strong
enough to support this theory. A possible reason is that there is a lack of data in
international joint ventures in the United States and then the standard error is larger.

We also found, for the U.S. direct investment abroad, conglomerate integration tends
to have a shorter duration time. This may be due to the fact that under conglomerate
integration, parent firms tend to have less experience in the new business of the affiliates,
and it is easier for such affiliates to fail. However, it should be cautious that FDI in the
United States does not support this prediction.

The results also suggest that U.S. subsidiaries or joint ventures in developing countries
have, on average, longer duration times than those in developed countries. This may be

due to a higher ratio of joint ventures in developing countries; also U.S. firms may

170

tolerate poorer performance of affiliates in developing countries since long run profit may
be more important in such cases. As there is only one case of a firm based in a
developing country with an investment in the U.S., the results between U.S. investment
abroad and foreign investment in the United States cannot be compared.

A result for the sub-sample of FDI in the United States is that the foreign affiliates in
the service sectors have longer duration time in the United States. The reason is not clear
and further research on this matter should be done before any conclusion can be made.

For the overall sample, the results suggest that instability among joint ventures and
conglomerate integration is larger. While it cannot tell us that the two sub-samples
perform differently (the dummy variable US is not significant at the 5% level), we can
say that the prediction of instability of joint ventures is not contradicted by the results.
We cannot conclude, however, that joint ventures are less stable irrespective of whether
they are associated with U.S. investment abroad or foreign investment in the U.S. since
our evidence on FDI in the United States is rather limited.

The results of this study should be taken cautiously as the true distribution of the
survivor function is unknown. However, as we do not care about the distribution of the
duration time, the problem is not very big. After running different models, we have
similar results from all the tests, At least we can say that the observations are consistent
with the predictions of shorter duration time of joint ventures when compared to wholly-
owned subsidiaries for U.S. FDI.

A limitation in the sample is that the change of ownership of a subsidiary or a joint

venture is not distinguished from "real failure". That is, the reason for the termination

171

of an affiliate is not included in the data set. We cannot distinguish between the shut-
down of a plant and the sale. As our main interest is the overall instability rate of
international joint ventures instead of the types of termination, so this problem should not

be important to our results.

Appendix 5A: Maximum Likelihood of the Proportional Hazards Model
The maximum likelihood of the proportional hazards model can be solved by using

Newton-Raphson method. Taking logarithm of the likelihood function (5.9), we have:

1 J
I
logL = 12.1: q] B - 12.; Mjlogzj (5A.1)
where
z = ex“
tent)

The first derivative of (5A.1) with respect to I5 is:

J J M
j-l j-l Z;

 

where

 

y = 2 ‘xt’xt
tell!)
And the second derivative is:
M
azlogL -—-—’ lyijI-vj (5A.3)
apap' z I.j

where

_ ' :1! I
v] - E e xkxk
tent!)
By using the results of the first and second derivatives (equations (5A.2) and (5A.3)),

the Newton-Raphson method can be used to obtain the maximum likelihood of B after

n + 1 iterations:

" aiogL

g - 110.35.
a... a. I a,” .

63.661

 

The initial values of a, Bo» can be any values though the usual choices are OLS

estimates or zeros. We adopt the values of a 1 when a 1 is consistent to B .
3+ .+ I

173

Appendix 5B: Summary of the Data Set

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MONTHS‘ 0150* IV 111 Ct mommy DEVELOP us
1 I 134 o o 4399 o o 1 o o
. 2 s7 1 o 903 o 1 o o o
H 3 s3 1 1 1973 1 o o 1 1
4 ' 137 o o 2185 o 1 o o o
, 5 63 1 1 1 o o o o
I 6 133 o o 230 o o 1 o 1
L 7 29 1 o 318 1 o 1 o o
s 56 1 o o o o o 0
II 9 74 1 o 726 o 1 o o 1
110 102 1 o 1692 1 o o o o
11 112 1 1 2115 o 1 o o o
12 133 o o 420 1 o o o 1
13 156 o o 111 1 o 1 o 1
14 45 1 o 1 o 1 o o
15 136' o 1 522 o o o 1 1
16 104 1 1 233 o 1 1 1 1
17 76 1 1 72 o o 1 o 1
1s 71 1 o 3013 o 1 1 o 1
19 139 o o 749 o o 1 o o
20 69 1 0 179615 0 o 1 o o
21 135 o o 5000 1 o 1 o o
22 141 o o 6754 1 o 1 o o
23 72 1 o 104 1 o 1 o 1
24 37 1 1 476 o 1 1 o o
25 ‘ 71 1 1 554 1 o o 1 1
26 4s 1 o 1122 o o 1 o 1
27 2t- 1 o 4392 1 o o o o
23 57 1 o 700 1 o o o o
29 125 1 0 1s 1 o o 1 1
30 131 1 o 263 1 o o o 1

 

 

 

 

 

 

 

 

 

 

 

174

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MONTHS‘ DIEDh IV SALES‘ 1‘" C1 INDUSTRY DEVELOP US
(111. USS)

31 137 0 0 193 0 1 0 0 0
32 89 1 1 409 l 0 1 0 1
33 107 1 0 8935 0 1 0 0 l
34 143 O 0 84 1 0 0 0 1
35 81 l 0 6561 1 0 0 0 0
36 125 1 1 6474 0 0 1 1 l
37 143 0 1 819 1 0 1 0 0
38 133 0 0 420 1 0 0 O 1
39 56 1 1 4515 1 0 0 1 1
40 139 0 0 1434 0 1 0 0 1
41 142 0 0 1 1 10 0 1 0 0 0
42 123 1 0 . 0 0 1 0 0
43 142 0 1 6622 1 0 0 1 1
44 135 0 1 1792 1 0 1 1 1
45 143 0 0 4599 0 0 0 0 1
46 128 1 0 494 0 0 0 0 0
47 1 l4 1 0 898 1 0 0 0 1
48 63 1 0 1583 0 1 0 0 0
49 147 0 0 13835 0 1 0 0 0
50 139 0 0 1051 0 1 1 0 0
51 142 0 1 3145 1 0 0 1 1
52 135 0 0 7997 0 1 0 0 1
53 141 0 1 190 0 0 1 1 1
54 109 1 0 10772 0 0 0 0 1
55 1 16 1 1 10 0 1 0 0 0
56 140 0 0 531 1 0 1 0 1
57 143 O 0 509 1 0 1 0 1
58 133 0 0 420 1 0 0 0 1
59 135 0 0 2501 1 0 0 0 0
60 48 1 0 3294 1 0 1 0 0
61 64 1 0 109 1 0 0 0 1
62 133 0 1 1771 1 0 0 1 1

 

 

 

 

 

 

 

 

 

 

 

 

175

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CASE MONTHS' DIED‘ JV SALES‘ HI C1 INDUmY DEVELOP US
(m. 085)
63 50 1 1 3145 0 0 0 0 1
64 22 1 0 1023 0 1 0 0 0
65 21 1 0 880 0 1 1 0 1
66 134 0 0 134 1 0 0 0 1
67 131 l 0 263 1 O 0 0 1
68 132 0 0 1022 0 0 0 0 1
69 139 0 0 1898 0 1 1 0 0
70 133 0 0 386 0 0 0 0 1
H 71 66 1 0 221 1 0 1 0 1
H 72 141 0 0 2134 0 0 0 0 0
H 73 132 0 0 3911 1 0 1 0 0
I 74 135 0 0 1883 l 0 0 0 1
75 24 1 0 354 1 0 0 0 1
76 142 0 0 21513 0 0 0 0 0
ll 77 134 0 0 77 1 0 0 0 1
78 133 0 0 420 1 0 0 0 1
79 136 0 0 931 1 0 1 1 0 1
80 107 1 0 1 144 1 0 1 0 1
81 132 0 1 50791 1 0 0 1 1
82 132 0 0 447 1 0 0 0 0
83 133 0 0 224 1 0 1 0 0
84 141 0 0 1390 1 0 1 0 0
85 141 0 0 3548 0 0 0 0 1
86 142 0 0 366 1 0 0 0 1
87 107 1 0 1 144 1 0 1 0 1
88 69 1 1 1042 1 0 1 0 1
89 132 0 0 2096 1 0 1 0 0
90 60 1 0 76m 1 0 0 0 0
91 74 1 1 6631 1 1 0 0 1 1
92 82 1 0 330 1 0 0 0 0
93 134 0 1 805 1 0 0 0 1
94 135 0 0 1 100 0 0 0 0 0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C_T MONTHS‘ DIED" SALES‘ C1 INDUSTRY DEVELOP US
(m. 083)
95 137 0 56 0 0 1 1
96 30 1 294 1 0 0 0
97 125 1 f 18 O 0 1 l
98 89 1 1452 0 0 0 l
99 138 0 1500 0 1 0 0
100 74 1 1419 0 0 0 0
101 61 1 295 0 0 1 1
102 135 0 62 0 0 0 0
103 141 0 298 1 0 0 1
104 68 1 328 0 0 0 0
105 76 1 610 0 1 0 0
106 144 0 751 0 0 0 0
107 72 1 881 l 0 0 0
108 102 l 1 0 0 0
109 143 0 586 0 0 0 1
110 24 1 848 0 1 1 1
111 133 0 32 0 1 0 0
112 59 1 562 0 0 0 1
113 138 0 21513 0 0 0 0
114 118 1 934 0 0 0 0
115 70 1 469 0 1 0 1
116 137 0 898 0 0 1 1
117 17 1 21483 0 0 0 0
118 76 1 216 1 0 0 0
119 41 1 116 0 0 0 1
120 73 1 6006 1 0 0 0
121 112 1 667 0 0 0 0
122 30 1 5029 0 0 0 0
123 141 0 270 0 1 0 0
124 143 0 7869 0 1 1 1
125 45 1 1052 0 1 0 0
126 143 0 492 0 0 0 0

 

 

 

177

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.' c.4513 MONTHS' 131121)" sw HI c1 mpumv DEVELOP us

___-_I (m. 1183) __ _
127 I 135 o 203 1 o 1 1 o
128 34 1 264 1 o o o o
129 46 1 8392 o o o o 1
130 132 o 700 1 o o o o
131 134 o 2405 o o 1 o 1
132 24 1 1012 1 o o o 1
133 138 o 100 1 o o o 1
134 144 o 1 o 1 o o
135 138 o 185 o o 1 o o
136 43 1 4667 o 1 o o 1
137 62 1 104 1 o 1 o 1
138 103 1 3662 o o o 1 1
139 92 1 439 o o o o o
140 59 1 496 o o o o 1
141 48 1 5333 o 1 o o o
142 70 1 3393 o 1 o o 1
143 65 1 12739 0 o o o o
144 23 1 2693 o 1 o o o
145 102 1 194 1 o 1 o o
146 134 o 382 1 o 1 o 1
147 137 o 525 o o o o 1
148 88 1 738 1 o o 0 1
149 48 1 176 o o o o 1
150 20 1 1 o o o o
151 132 0 12572 0 o o o 1
152 68 1 1 o o o o
153 27 1 1946 1 o o o 1
154 100 1 1 o 1 o o
155 91 1 o 1 1 o o
156 102 1 14926 0 1 o o o
157 19 1 2717 o 0 o 1 1
158 58 1 1683 1 o 0 1 1

 

 

 

 

 

 

 

 

 

 

 

178

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

._ ____~fi ,
.I MONTHS' DIED‘ SALES' 1n (:1 INDUSTRY DEVELOP us
'_ 4__________ (m‘ "‘Lw __
n 134 0 1324 o 1 0 0 0
I 160 55 1 4170 1 o 0 o 1
161 102 1 2500 0 1 o 0 0
I 162 71 1 268 1 0 0 0 1
1 163 40 1 1323 1 0 0 0 1
I 164 141 o 2164 1 0 1 0 0
165 98 1 o 1 1 o o
i 166 141 0 0 o 0 0 0
II 167 124 1 6474 1 0 1 1 1
|L168 142 0 2829 1 o 0 1 1
II 169 90 1 1082 0 1 o 0 1
II 170 58 1 1 0 o 0 0
171 133 0 420 1 o 0 0 1
172 133 0 420 1 0 o 1 1
173 69 1 544 1 0 o o 1
I 174 28 1 34737 1 0 0 1 1
175 140 0 84350 1 0 1 1 1
176 136 0 241 o o 1 o o
177 I 60 1 1908 1 0 o 1 1
178 135 0 7082 1 0 o o o
179 53 1 503 0 1 0 0 1
180 134 0 457 1 o 1 1 1
181 45 1 0 0 o 0 0
182 I 33 1 23 1 0 o 0 o
183 ‘ 98 1 824 1 o 1 o 1
184 65 1 19 o o o o 1
185 45 1 397 o 1 1 0 o
186 141 0 521 o 1 o 0 1
187 66 1 4241 1 0 1 o 1
188 143 0 4085 1 0 1 o 1
189 27 1 951 o 1 o o o
190 64 1 59 1 o 1 o 1

 

 

 

 

 

 

 

 

 

 

 

179

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MONTHS‘ DIBD" JV SALES‘ HI CI INDUSTRY DEVELOP US
(m. USS)
144 0 0 5238 0 0 0 0 0
140 0 0 . 0 0 0 0 1
71 l 0 141 0 0 0 0 0
140 0 0 104 1 0 1 0 1
13 1 0 33 0 1 0 0 1
140 0 0 2957 l O O 0 0
143 0 0 221 0 0 0 0 0
113 1 l 2100 0 0 l O 0
20 1 O 4392 1 0 0 0 0
137 0 0 . 1 0 1 0 O
78 1 0 l 143 0 1 0 0 0
136 0 0 175 0 0 0 0 l
134 0 0 166 0 0 0 0 l
45 1 0 4159 0 0 1 O 0
156 0 O 7428 1 0 0 0 1
104 l 1 297 0 0 0 1 1
133 0 1 3185 1 0 0 0 0
42 1 0 5338 0 1 1 0 1
79 1 0 420 l 0 0 0 0
141 0 1 . 1 0 0 0 1
l 12 1 0 89 1 0 1 0 l
68 1 0 166 1 0 1 0 1
92 1 0 1 158 0 1 0 0 1
135 0 0 2184 0 1 0 0 0
44 1 1 1501 0 0 O 0 1
Note: a: MONTHS: Dependent variable. The duration time of the subsidiary or joint venture in term of months up to Dec. 31 ,
1991;

b: DIED: It denotes whether the plant 'failed' at Dec. 31, 1991 or not. DIED=lz failed; DIED=0z survived.
c: If the datum is missed for SALES, "." is put in the item.

180
Appendix 5C: Kaplan-Meier Estimates

The summary here follows Kalbfleisch and Prentice (1980, pp.6—13) and Cox and
Oakes (1984, pp.48-50). If T is a discrete random variable taking observations at tl < t2 <

. <tJ with
f(t,) = P<T=t,). j = 1. .1.
then the survivor function is:

J
sm=2flm
11112:

= Zfltpmtj-t) ,
where H(x) is the Heaviside function:

H(x) 0 x<0

l, 120.

The hazard at t,- is defined as the conditional probability of " failure" at t:

hj =P(T=tj I T25.)

: fig)

50,-)

j = 1,2, ,J

 

where S(tj) = f(t,-) + f(tj+,) + . . . + f(t,) . Corresponding to (5 .5) , the survivor function is given

by:

 

181

S(t)= H (1 ‘J-h)
.flfi“

To have T>t it is necessary and sufficient to survive all points before t. Letf

terms of the h, f,- may be written in the form:

f1 =hi, f2 414015,
' fj = (l-h1)(l-h2)...(l—hj_l)h , ,
f, = (l-h,)(1-h2)...(l-h1_l)h1 .
The constraints of ijO and ijSI imply that OShjSI.

An estimate of the survivor function is analogous to (5C.1):

S(t)= II(1- 49,-),

flfl“

(5C.1)

=f(tj). In

(5C.2)

where 1;] are the maximum likelihood estimators of the hi. The likelihood from N

individuals, of which n are uncensored (the failure times are observed) and N-n are

censored (the individuals survive at the last observed time, t,):

L= Hflfi S(t)

i-l i=u+l

where the two products are taken over uncensored and censored individuals respectively.

The log likelihood is:

182

3 IV
lnL = Z 1nf,+ Z lnS(t,.)

i=1 i=n+!

where the the conventions from the summations are similar. Since the sample is discrete
so that individuals are grouped into I +1 observations in which Mi, j=1,...,J are

uncensored and MJ+1 are censored. From (5C.1) above, we have:

15' ‘ ”13(9) = thJ(1’hj) ,

 

S(tj) = MJ,1(l-h1) . L

The total log likelihood is then:

J - J+1
1111. = 2 [Mjlnhj+(z Mk-Mj)1n(l 45)]
jal k1] .
Let
1*!
N} = 2: MI: s
H

which is the number of individuals at risk at a time t5. The maximum likelihood estimators

are the solutions of:

 

em = _{lLNj-M, = 0
ah} I 1-h,

that is,

183

R

fi.=_

J

'4‘

The corresponding estimates of the survivor functions are:

.1
S(t) = {IF-£51] (5C.3)
11'1" J .

Any term in the product which has Mj=0 can be omitted without affecting (5C.3).

S(t) is a function of the data only.

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