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A linear-quadratic dynamic game approach to estimating power in the banana export market

Deodhar, Satish Y., Ph.D.

The Ohio State University, 1994

Copyright ©1994 by Deodhar, Satish Y. All rights reserved.

UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106

A LINEAR-QUADRATIC DYNAMIC GAME APPROACH

TO ESTIMATING MARKET POWER IN

THE BANANA EXPORT MARKET

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree Doctor of Philosophy in the Graduate

School of The Ohio State University

By

Satish Y. Deodhar, M.A.

*****

The Ohio State University 1994

Dissertation Committee: Approved By

Prof. Ian Sheldon

Prof. Dennis Henderson

Prof. Mario Miranda iviser Department of Agricultural Prof. Stanley Thompson and Rural Sociology Copyright by Satish Y. Deodhar 1994 flïï I

3?4^lltM - =h1(cy^ { ^ ^ o ^ o 3 ® )

"Economics is the most important", says Kautilya. For, both the spiritual good and material well-being depend on it.

Arthaéàstra - Kautilya (circa 320 B.C.) TO MY PARENTS

1 1 ACKNOWLEDGEMENTS

I would like to express my sincere appreciation and

gratitude to Prof. Ian Sheldon for his constant encouragement and guidance. As my "Guru", he has served in many roles, as a mentor, teacher, guide and a counselor. Gratitude is also owed to Prof. Mario Miranda and Prof. Dennis Henderson for their useful suggestions and insights. I am specially thankful to Prof. Perloff of the University of California, Berkeley, some of whose original computer programs have been used in this study.

Thanks go to all the members of my supporting cast. Suggestions of Prof. Jones for the static model, Peter Voros's help in mainframe computing, and Jim Dayton's frequent help in my imperfect word-processing is acknowledged. Credit must also go to fellow graduate students, who from time to time provided valuable information, and offered suggestions. Finally, I wish to thank my family, who had to endure the best and the worst in me. My parents, sister and brother-in- law were a source of constant support throughout my graduate program. To my lovely wife, Deepali, I offer sincere thanks for her unshakable faith in me, and her willingness to share with me the vicissitudes of my research endeavor.

iii VITA

1985 ...... B.A. (Econ), Gokhalé Institute of Politics and Economics, Puné, India.

1986-88 ...... Sub-Broker, Momsha Financial Consultancy Services, Puné, India.

1989 ...... M.A., Dept, of Economics, The Ohio State University, Columbus, OH.

1988-92 ...... Graduate Teaching Associate, Dept. of Economics, The Ohio State University, Columbus, OH.

1992-94 ...... Graduate Research Associate, Dept. of , The Ohio State University, Columbus, OH.

PUBLICATIONS

Deodhar, S. and Sheldon, I. (1994) "Is Foreign (Im)Perfectly Competitive?: An Analysis of the German Market for Banana Imports," Working Paper # ESO - 2154, The Ohio State University, Columbus: OH.

Deodhar, S. and Sheldon, I. (1994) "Estimation of Dynamic Oligopolistic Interaction: The Case of the Banana Export Market," Paper accepted for the Southern Economic Association Conference, November 1994, Orlando: FL.

FIELDS OF STUDY

Major Field: Agricultural Economics and Rural Sociology _Studies in International Agricultural Trade Minor Fields: , Labor Economics

IV TABLE OF CONTENTS

DEDICATION ...... il

ACKNOWLEDGEMENTS ...... ill

VITA ...... iv

LIST OF TABLES ...... vii

LIST OF FIGURES ...... viii

CHAPTER PAGE

I. INTRODUCTION ...... 1

1.1. Traditional Trade Theories ...... 1 1.2. The New Trade Theories ...... 3 1.3. Estimation of Market Power Using Dynamic Games ...... 5 1.4. Plan of Dissertation ...... 7

II. SYNTHESIS OF AND INTERNATIONAL TRADE ...... 10

2.1. Origin of the NTTs ...... 10 2.2. Domestic Markets and Foreign 13 2.3. Intra-Industry Trade ...... 19 2.4. Trade Policy Issues ...... 32 2.5. The Litmus Test ...... 39

III. STATIC MODELS OF MARKET POWER ESTIMATION .... 41

3.1. Traditional Approach ...... 41 3.2. Modern Approach ...... 45 3.3. Summing Up ...... 62 IV. DYNAMIC MODELS OF MARKET POWER ESTIMATION ... 65

4.1. Conjectural Variations Approach ...... 65 4.2. and ...... 72 4.3. Dyneunic Games Approach...... 86 4.4. Retrospection...... 100

V. THE BANANA EXPORT MARKET ...... 103

5.1. Historical Background ...... 103 5.2. Structure of the Banana Industry ...... 106 5.3. Motivation for the S t u d y ...... 108 5.4. Methodology ...... 112

VI. EMPIRICAL PROCEDURE ...... 115

6.1. Data Description and Sources ...... 115 6.2. The Static Model ...... 117 6.3. The Dynamic Model ...... 125

VII. CONCLUDING DISCUSSION ...... 142

7.1. Inference and Policy Implications ..... 142 7.2. Limitations and Future Direction ...... 149

APPENDICES

A. Data ...... 152 B. Restrictions Obtained From the Open-Loop First Order Condition ...... 154 C. Restrictions Obtained From the Feedback First Order Condition ...... 158 D. Solving the Restrictions to Obtain Values of V and Ô ...... 161 E. Glossary ...... 163

BIBLIOGRAPHY ...... 165

VI LIST OF TABLES

TABLE PAGE

3.1. Estimates of Lerner's (L) ...... 63

6.1. Description of Variables ...... 118

6.2. Estimation of the Static Model ...... 121

6.3. Bootstrapping of the Static Model ...... 123

6.4. Banana Export Adjustment (Markov) Equation ... 131

6.5. Classical Estimates of Dynamic Model...... 133

6.6. Bootstrapping Dynamic Model ...... 135

6.7. The of V ...... 136

6.8. Hypothesis Testing for Bootstrapped V & Ô .... 141

V l l LIST OF FIGURES

FIGURES PAGE

2.1. Import competition and domestic pricing... .. 15

2.2. Competitive export market and domestic pricing 17

2.3. Intra-industry trade ...... 24

2.4. Production Pattern of a MNC at home and abroad 29

2.5. VERs and the resultant Nash & mixed equilibria ...... 38

3.1. Parallel shift of the demand c u r v e .... 50

3.2. Rotation of the ...... 52

4.1. Cournot-Nash and Collusive payoffs ...... 77

4.2. Closed-loop and open-loop strategies ...... 84

4.3. Static and dynamic reaction functions ...... 92

6.1. Distribution of X ...... 124

6.2. Flowchart of the dynamic model ...... 126

6.3 Distribution of Vs ...... 138

6.4. Distribution of 6s ...... 139

6.5. Convergence of and Vf ...... 140

viix CHAPTER I

INTRODUCTION

1.1 Traditional Trade Theories

The notion that societies benefit from exchange of and services is a very old one. Smith (1776) wrote in The

Wealth of Nations, that the division of labor which reduces unit cost of production, is a consequence of a certain propensity in human nature; the propensity to truck, barter and exchange one thing for another. He advocated the concept of which meant that a country will specialize in the production and export of those goods in which it incurs lower compared to the other country.

Four decades later, Ricardo (1817) expanded his idea and proposed a theory that explained the reason for and pattern of trade between any two nations. In his treatment, trade occurs due to differences in technology between two nations and each one specializes in the production and export of good that it produces at lower opportunity cost under autarky. His important contention was that, even if a country has absolute advantage in producing each good (i.e. has lower opportunity cost for each good compared to the other country), trade can

1 2

occur and benefit both, as long as the opportunity costs of

producing different goods differ within the country. He

described this concept as the principle of comparative

advantage.

In Ricardo's analysis, labor is the only factor of

production and thus, comparative advantage arises solely due to international differences in labor productivity. However,

in practice, trade is also likely to be influenced by differences in countries' resources other than labor. A realistic view of trade then, must consider other factors of production such as land, capital and natural resources. The economics profession had to wait for more than a century, until Heckscher and Ohlin (1933) developed a theory which addressed this concern. In their model, there are two countries, two goods and two factors of production. Goods can be traded freely across countries but factors are assumed to be immobile internationally. The two important theorems of the Heckscher-Ohlin (HO) model state that a country will produce and export that commodity which uses its abundant factor more intensively, and that owners of a country's abundant factor gain from trade, but owners of its scarce factor lose. The former theorem implies that the greater the differences between the factor endowments of the two countries, the greater will be the volume of trade between them. This suggests that the volume of trade between the developed and developing countries should be very large and 3 the structure of trade will be of an inter-industry nature.

The latter theorem suggests that as the two countries are joined together in trade, there will be some winners and some losers among the owners of factors of production in both the countries. This implies that there are income distribution effects of trade which may create a conflict of between the owners of different factors of production.

However, the emerging pattern of world trade since the end of World War II has been at odds with both the predictions of the HO theory and the earlier Ricardian theory. Trade among the western industrial countries increased rapidly after the war even though they had comparable factor endowments.

The creation of a common market in the European Community (EC) did not pose income redistribution problems nearly as severe as those predicted by the HO theory. Moreover, intra­ community trade was characterized by the exchange of similar but differentiated products, i.e. intra-industry trade, a feature which was never envisioned by the traditional theories. In spite of these contradictions, traditional trade theory survived largely because of a lack of any alternative theory challenging it.

1.2 The New Trade Theories

In their effort to search for explanations for these stylized facts, trade theorists returned to Smith's idea that the division of labor lowers unit cost of production and that 4 division of labor is limited by the extent of the market. If it is possible to reap internal , then extension of the market by opening up trade will benefit all the countries party to it. Economies of scale will be realized by countries specializing in production and export of some goods and they will import remaining goods. Though trade theorists had informally expressed such a view, they could neither develop this idea in the framework of the traditional trade theories nor could they build new models that would yield implications consistent with the changing trade pattern.

This impasse was broken during the late 1970s and early

1980s when trade theorists started using models of imperfect competition developed by researchers in the field of industrial organization. Krugman (1979), Lancaster (1980) and

Dixit and Norman (1980), amongst others, published papers and books which show that scale economies can lead to arbitrary specialization in production and export in a monopolistically competitive . In an another paper, Brander and Krugman (1983) showed that if markets are oligopolistic in structure, trade could occur, even if there was no comparative advantage, and that two-way trade between identical products was equally possible.

This literature then, set the stage for the development of a new positive trade theory. The new theories, however, not only explain the observed structure of trade, but also provide a normative rationale for interventionist trade 5 policies. In particular, an influential paper by Brander and

Spencer (1985) showed that in oligopolistic markets, government policies such as an export subsidy could improve the performance of domestic firms and the economy. These normative aspects of the new theories have disturbed the academic community since they have far reaching implications for trade policy. Of course, these formulations have been received with a variety of well-merited criticisms, and certainly, it is the new positive trade theory that has been better received than the normative one. To put it in Helpman and Krugman's (1989, p;2) words, "Although the positive theory of trade under imperfect competition has now reached a certain maturity and acceptance, the same cannot be said of the theory of trade policy under imperfect competition."

Though a general theory of trade under imperfect competition has not been developed yet, trade theorists have written prolifically in this literature, which is now known collectively as the New Trade Theories (NTTs). A brief review of this literature is presented in chapter II.

1.3 Estimation of Market Power Using Dynamic Games

If the pattern of trade between countries and the desirability (if any) of government policies depends on the market structure of export industries, then knowing the type of market structure in the relevant industries becomes all- important. The field of industrial organization is rich both in theoretical analysis and empirical testing of imperfectly 6

competitive structures of domestic markets. Most of the

studies in this literature focus on estimating the degree of market power in a domestic market, i.e. the percentage markup

of over . Its varies, depending on the type of market structure which can lie anywhere between and . The majority of such

studies have used static models and a few have ventured into dynamic ones. However, limited attention has been paid to similar studies on export industries. A detailed review of this literature is presented in chapters III and IV.

Studies of the estimation of market structure in export industries need to incorporate two essential features. First, game-theoretic analysis is used as a tool to capture the strategic behavior of firms. This is necessary because, with imperfect competition, firms do not take price or output as given and realize that their actions, as well as the actions of their rivals, affect the market outcomes. This leads to a variety of strategic interactions among firms. Second, a dynamic approach to modelling export markets is essential since no market lasts only for one period. Demand in one period depends on the quantities demanded in the previous periods. Firm strategies certainly depend on their own and their rivals' past actions, and there are costs in adjusting production from one period to the next. Plantation industries for example, have long lags in production, and there are substantial adjustment costs in training, storage and capital 7 accumulation. Except for Karp and Perloff's (1989, 1993a) studies of the rice and coffee export market respectively, no serious attempt has been made in this regard.

1.4 Plan of Dissertation

In this dissertation, I have undertaken a study to estimate the degree of market imperfection, that uses a dynamic-games approach. This research concentrates on one of the most important agricultural export industries, namely the banana export industry. In particular, I have estimated the degree of market imperfection in the German market for banana imports. As reported by Read (1994), the slightly mundane image of bananas is belied by world trade in bananas that exceeds 5 billion US dollars per year, making it only second to coffee as a major traded agricultural commodity. A cursory look at the industry indicates that the banana export market is oligopolistic in structure. Indeed, the banana market worldwide is dominated by a few multinationals. Hallam and

McCorriston (1992) show that Chiquita, Dole and Del Monte account for a seventy-percent share of the world market. Read

(1986) points out that multinationals have vertically integrated themselves by engaging in production and shipping of bananas.

For the purpose of the present study, I have selected the

German market for banana imports for three reasons. First, just like the world market for bananas, the German market for 8 bananas is also dominated by three large firms (Chiquita, Dole and Noboa). Second, up until June 1993, Germany was the only country in the EC that allowed free access to banana imports.

Therefore, it was the ideal candidate to measure the degree of market power in a distortion-free market. Third, with the implementation of the common policy on banana imports by the

EC, it is the German market that has been hit the hardest in terms of effective quota restrictions. Further, knowing the degree of market imperfection is very crucial to the evaluation of the welfare changes caused by the new policy.

The subsequent chapters V and VII discuss this issue in more detail.

To summarize, the present empirical research aims at broadening our understanding of the structure and working of export markets in general, and of the banana export market in particular, in the context of the recently developed literature on the NTTs. In my research pursuit, I have accomplished the following:

Reviewed and interrelated literature on the new trade theories and static & dynamic game-theoretic approaches to estimating the degree of market power.

Estimated the degree of market power in the German market for banana imports using a static model.

Estimated the degree of market power using dynamic-game theoretic estimation procedures.

Compared and contrasted the static and dynamic estimation procedures and their results. Explored the possibilities for refining the existing estimation procedures, and extending the analysis to other industries.

The format of the presentation of my dissertation research is as follows: The synthesis of industrial organization and international trade that led to the development of NTTs is discussed in Chapter II. This will bring out the importance of market imperfections in influencing trade patterns and policy formulations.

Literature on the estimation of degree of market power using static and dynamic models is reviewed in Chapters III and IV respectively. Chapter V discusses the salient features of the banana market, the motivation for selecting the German market for banana imports, and the methodology followed. Data sources, and the detailed empirical procedure for the static and dynamic models are explained in Chapter VI. The data and derivation of restrictions that complement Chapter VI are included in the Appendices. Finally, Chapter VII interprets the results, derives conclusions and gives future direction to this kind of study. CHAPTER II

SYNTHESIS OF INDUSTRIAL ORGANIZATION AND INTERNATIONAL TRADE

2.1 Origin of the NTTs

The field of industrial organization (10) can be broadly defined as the branch of micro-economics concerned with the nature and behavior of firms operating in noncompetitive markets. More specifically, it deals with the positive and normative implications of the nature of competition and exercise of market power. It also examines the role of government regulatory and antitrust policies in improving market performance. As an applied field, industrial organization has traditionally been empirical in its approach and it has relied mostly on partial-equilibrium, closed- economy models. It is only recently that it has been subjected to intense theoretical scrutiny.

The field of international trade, on the other hand, has utilized the general-equilibrium competitive model with limited attention paid to empirical testing. It attempts, or rather, has attempted to answer questions relating to the pattern and composition of trade as well as to the overall level of trade; i.e. who what with whom and how much?

10 11

It also addresses questions relating to the

and the reasons for and effects of protection. The

traditional explanation of trade patterns, based on the

Ricardian or Heckscher-Ohlin (HO) type models, has typically

assumed constant , homogeneous products,

perfect competition, internationally immobile factors of

production and nations that differ either in terms of technology or factor endowments. These differences, in turn,

result in comparative advantage as the cornerstone of

international trade. The gains from trade are expected to be

larger, the greater the underlying differences among the nations and goods involved in international exchange.

This conventional approach has proved to be inadequate in two respects. First, though it is true that theorizing involves abstracting from reality by making certain assumptions, the assumptions made in the HO theory are too many and too restrictive. Leamer (1984, p:ll) suggests, "It takes neither great observational skill nor keen inquisitiveness to make one question the six assumptions^ and make one wonder whether the results hold up if these assumptions

1. Leamer illustrates the following six classes of assumptions:

Dimensionality. The number of goods n, and the number of factors of production m are equal to 2. n = m = 2. Mobility. Factors of production move costlessly within a country and are immobile between countries. However, goods move costlessly between countries and there are no other impediments to trade. Competition. Goods and the factor markets clear competitively, i.e. economic agents act as if they could buy or sell unlimited quantities at the prevailing market .

(Footnote continues on the next page.) 12 are relaxed." Second, even if the assumptions were true, the implications of the HO theory fail to account for several empirical regularities that have characterized world trade during the last two decades. It cannot explain aspects such as the phenomena of intra-industry trade, foreign direct and imperfect pass-through of exchange rate movements.

On the other hand, the traditional 10 literature has been criticized too, at times, as being mere descriptive statistics, since it did not consider any optimization techniques and/or any strategic interaction between firms.

The early studies in this literature also failed to capture effects of foreign competition on domestic market structure.

However, the New Industrial Organization (NIO) literature has begun using optimization techniques, and static and dynamic approaches to modelling oligopoly. Moreover, it has employed a set of tools in the form of non- to analyze the strategic behavior of firms thought to be pervasive under imperfect competition. Concurrently, trade analysts are increasingly aware of the intra-industry pattern of trade which implies an arbitrary nature of the

(Footnote continued from the previous page.)

Technology. Technology exhibits constant returns to scale, diminishing marginal product, and is costlessly available to all the countries. Factor Endowment Similarity. Variability of factor endowment ratios among countries is less than the variability of factor input intensities across industries. Demand Similarity. Individuals consume as if each were maximizing an identical homothetic function. 13

location of production facilities. However, these arbitrary

location decisions are of particular interest to policymakers

responsible for the well-being of residents of individual

political units. All this results in a new policy behavior in which strategic considerations assume paramount importance.

Therefore, trade analysts have been quick to adopt the

strategic analyses of the NIO as a substitute for the neoclassical framework. Thus, the New Trade Theories (NTTs)

are beginning to develop as a theoretical hybrid, where

strategic behavior, developed in the NIO literature, is being applied to the problem of interactions among firms based in different nations. Though considerable progress has been made during the last two decades, what exists is a series of very stylized special models rather than a general theory of wider applicability. The following review shows how each of the two fields has increasingly employed the theoretical tools of the other. The review focusses on the literature that includes; role of imports and exports in disciplining the domestic market; explanation of trade patterns using product differentiation and imperfect competition; and the policy implications of imperfect competition in trade models.

2.2 Domestic Markets and Foreign Competition

Early studies in the traditional 10 literature were mainly concerned with searching for variables that seemed to influence industry profitability. These studies made an 14 effort to establish a causal relationship between industry profitability and variables such as industry concentration ratios and . An exhaustive survey of this type of study is found in Schmalensee (1989a)^. An implicit assumption that was present in most of these studies was that of autarky. However, with a sharp increase in trade among nations after World War II, it was felt that international linkages could affect competition in domestic markets.

Jacquemin (1982) illustrates that, for a monopolist facing a perfectly elastic supply of imports (an implicit, small country assumption), the effectiveness of imports depends on domestic cost. In Figure 2.1, with marginal cost

MCi, and a world price of P„, the monopolist has to adopt competitive behavior and produce oq^ (q^q^ imported) output at the world market price P„. If marginal cost is MCg, the monopolist cannot charge his/her maximizing autarkic price, which is more than P„. Only when the marginal cost is as low as MC3, can the monopolist charge his/her monopoly price. Jacquemin obtains similar results for an oligopoly model.

A survey by Lyons (1979) of twenty three cross-sectional econometric studies, which related prices, and profitability

Schmalensee explains that, prior to the work of Bain (1951), most empirical research involved detailed case studies of particular industries. Bain's inter-industry approach shifted the research interest from industry studies to cross-section studies. These studies generally found that, while scale economies and product differentiation of existing sellers constituted barriers to entry in a market, high seller concentration facilitated among firms, both leading to higher profits. 15

w

DomesMc Demand

Figure 2.1

Import competition and domestic pricing. 16 to various measures of foreign competition, supported the hypothesis that imports restricted the ability of firms to raise prices above marginal cost. Pugel's (1980) study similarly confirmed the negative relation between domestic price-cost margins and the ratio of imports to domestic sales.

A recent study by De Ghellinck, Geroski and Jacquemin (1988) also shows that import variables are significant and trade has a large, but not an overpowering effect on domestic profitability. There are many studies like this that use reduced-form equations to assess the impact of imports.

However, it must be noted that these studies suffer from lack of statistical/theoretical rigor since, in many cases, dependent and independent variables are correlated.

Jacquemin (1982) illustrates that, unlike imports, the influence of exports on domestic competition is less straightforward. An extreme situation is one where a domestic monopolist is confronted with a perfectly elastic demand for exports. Consider Figure 2.2. It can be demonstrated that export activity constrains the monopolist to behave competitively, as long as (s)he is not allowed to discriminate between domestic and foreign markets, and, if there are non­ decreasing marginal costs. Given the world price P„ and the marginal cost MCj, the monopolist will charge pj, and sell oq^ in the domestic market and q^q^ in the foreign market, if (s)he is not allowed to discriminate. This is analogous to the competitive situation. If the monopolist is allowed to 17

î

MC

MR Oomesfic Demand

Figure 2.2

Competitive export market and domestic pricing. 18

discriminate, (s)he will sell only oq^ at a price P„ in the

domestic market and export q^q^ at price p'„. However, for the marginal cost MC;, the non-discriminating monopolist has a choice. Either (s)he can produce competitive output oq^ and export q^q^, or (s)he might not export at all, producing only the monopolistic output oq^ for the domestic market. The choice depends on the relative magnitude of the producer's surplus under those two situations (comparison of areas A and

B). In another paper, Davies and McGuinness (1982) show that under conditions of uncertainty, a domestic monopolist not only adopts price discrimination but dumps output in foreign markets at a price lower than marginal cost.

Given the theoretical alternatives above, it is not surprising that empirical studies do not support any of them equivocally. Studies by Pagoulatos and Sorensen (1976);

Caves, Porter and Spence (1980); Neuman, Bobel and Haid (1979) show that exports reduce industrial profitability. However,

Geroski's (1981) research on industries in the U.K. shows a very significant positive effect of the rate of exports on the profit margin and a negative effect from the rate of imports.

In summary, the above discussion shows that the 10 literature has made use of trade variables to assess its effect on domestic competition. In their analysis of domestic oligopoly markets, however, these studies assume foreign markets to be competitive, when in reality they may be characterized by imperfect competition. Further, these 19 studies do not focus on assessing the effects of foreign competition on the structure and pattern of imports and exports for a country. Nevertheless, the 10 literature has certainly established the fact that international trade acts as a catalyst in disciplining competition in domestic markets.

The synthesis of 10 and trade however, is not a one way endeavor. Researchers in the field of international trade have extensively borrowed from 10 concepts. The following survey illustrates how effectively the trade literature has utilized 10 concepts.

2.3 Intra-Industry Trade

Recently, a new view of trade, christened as intra­ industry trade, which explains the existence of trade in similar goods has emerged as a complement to the HO theory.

Several models have been developed, for example Krugman

(1980), Lancaster (1980), Helpman (1981), Shaked and Sutton

(1984), where product differentiation and economies of scale become critical in explaining trade in similar goods. Of particular interest is a composite model of intra-industry trade developed by Helpman and Krugman (1985) that captures the common elements of the special models mentioned above.

They follow an integrated economy approach, where an integrated economy is a description of what the world economy would look like if factors of production were perfectly mobile. They then 'carve up' the integrated economy into separate countries 20

and analyze the conditions under which it can be reproduced

through trade. They have constructed a two-sector, two-factor

model of this integrated economy. Manufactures (X), which

consist of many differentiated products are produced in one

sector, and widget (Y), a homogeneous good, is produced in the

other. The two factors of production are labor and capital.

The widget sector is characterized by constant returns to

scale. The unit cost of production is given by Cy(w^,w^),

where w^ is the rate and w^ is the rental rate on capital.

Given constant returns to scale, this unit cost is both the

average and the marginal cost of production. Competition in

the widget sector brings about marginal cost pricing. The pricing condition is given by;

1 = Cy(WL,Wj , (1) where the widget price is set to unity by considering widgets as the numeraire good.

In the manufacturing sector, every variety is produced with the same increasing returns to scale technology. Assuming free entry and exit of firms, the number of firms n is determined endogenously with each firm producing a different variety. The pricing strategy of each firm is characterized by equality of price and :

p = C(Wi,,Wk,X), (2) where x is the output level of a single representative firm^.

3. This is achieved due to Chamberlinian-type (1933) . In equilibrium, 71 is determined such that profits are driven down to zero, and no further entry occurs. 21

All firms being symmetric, they end up producing the same level of output. Defining a measure of economies of scale

0 (Wi,,Wk,x ) as the ratio of average cost to marginal cost and a measure of monopoly power R(p,n) as the ratio of price to marginal revenue, and noting that, in equilibrium, marginal revenue is equal to marginal cost, they also derive the condition:

R(p,n) = 0 (Wi,,Wk,x ) (3)

This condition implies that, in equilibrium, the degree of economies of scale must equal the degree of monopoly power.

In perfect competition, these measures will equal 1, since both the average and marginal values of the cost and revenue function are equal in equilibrium. In imperfectly competitive markets, these measures will assume a value greater than 1, since average values of the cost and revenue function will be higher than the marginal values.

In the factor market, demand for factor i per unit of output in the widget sector is given by:

aix(Wi,,WK) 5 dCy(WL,WK)/dWi, i = L,K (4) and the demand for factor i per unit of output of the differentiated product is given by:

ai%(WL,Wx,x) 5 dc(WL,WK,x)/dWi, i = L,K (5) where c(.) is the average cost of producing a differentiated product. Using these representations of the factor demands, two market clearing conditions are illustrated: 22

aLy(WL,WK)T + ai.x(WL,WK,x)? = i: (6)

aKï(Wi,,WK)T + aKx(Wi,,WK,x)X = T , (7 )

where X is the size of the labor force, % is the capital

stock and ? and T are the output levels of the manufacturing

and widget sectors respectively. The total output in the

manufacturing sector is given by;

"X = n x . (8)

In the commodity market, due to Walras's law, it is

sufficient to specify market clearing conditions for only one market. Helpman and Krugman assume homothetic preferences, so

that the share of spending allocated to a particular commodity

is a function of commodity prices and the number of varieties

available. Taking Oy(p,n) as the share of spending allocated

to widgets, the condition for clearing of the widget market can be shown to be:

o,(p,n) = T / ( T + pxn). (9)

This expression shows that share of widget in spending is

equal to its share in gross domestic product.

In the integrated market, the raison d’être for the production of differentiated goods is that demand for variety

of products emerges at the aggregate level. This demand for variety at the aggregate level is embedded in the nature of consumer preferences. In Krugman's (1980) study, consumers prefer variety in consumption. The preferences are such that, ceteris paribus, consuming less of every variety but consuming more 23

numbers of goods increases the level of utility. Thus,

individual wishes of buying all the varieties results in

for variety. However, one does not need love

for variety at the micro level to generate a macro demand for

variety. Lancaster (1980) proposed the idea that every

individual may desire only one variety, and provided that

individual tastes and preferences are different, a demand for

variety of products will emerge at the aggregate level.

Helpman and Krugman incorporate both these ideas into their

analysis.

The above discussion, and equations (l)-(3) and (6)-(9),

completely describe the integrated economy. These seven

equations can be solved for seven unknowns - two factor prices, price and output level of a differentiated product,

output level of the widget sector and the manufacturing

sector, and the number of varieties/firms. This integrated economy is depicted in a box diagram as shown in Figure 2.3.

This diagram describes the intersectoral allocation of labor

and capital in the integrated equilibrium. The vectors OQ and

OQ' describe employment in the manufacturing and widget sector

respectively. The vector 00* describes aggregate employment which equals . OQ is drawn steeper than OQ' because it

is assumed that the manufacturing sector is relatively more capital intensive than the widget sector. Output can also be measured in terms of these vectors, where OQ = % and OQ' = T. 24

L* 0*

K*

0

figure 2.3 ^"‘«-industry Trade, 25

This integrated economy is divided between two nations,

a home country and a foreign country, by assigning 0 and 0* as

their respective origins. Labor and capital is allocated

between the two countries by considering an endowment point E.

By drawing a parallelogram between 0 and E, points and Py

are obtained. These are the output points, where OP^ = X, OPy

= Y and P%Q = X*, PyQ' = Y*. The home country produces n = X/x varieties of the differentiated product and the foreign

country produces n* = X*/x varieties, where n + n* = n = "X/x.

Similar equilibria can be demonstrated for any endowment configuration that lies in the parallelogram OQO'Q' that

replicates aggregate output, employment and the factor prices

of the integrated equilibrium. The parallelogram OQO'Q' is described as the factor price equalization set.

To identify the trade pattern, a factor price line BB' with the slope w^/w^ is drawn through E. The intersection of this line with the diagonal occurs at the consumption point C, where OC represents the gross domestic product of the home country and 0*C represents the gross domestic product of the

foreign country. Since every country spends the same proportion on widget and manufactured goods, and since all income is spent, the consumption pattern is shown by constructing a parallelogram between 0 and C. The vector 00% equals home consumption of manufactured goods and OCy equals home consumption of widget. 26

Comparing the production points (Py,??) and the

consumption points (Cx/C?) shows that in this equilibrium the

home country imports widgets and is a exporter of

manufactured products. Of course, the opposite is true for

the foreign country. The capital rich home country is a net

exporter of manufactured products that are capital-intensive,

and an importer of widgets. On the other hand, the relatively

labor rich foreign country exports labor-intensive widgets,

and is a net importer of manufactured products. More

importantly, this HO type trade pattern is also complemented

by intra-industry trade in the manufactured products, where

countries consume n varieties produced in the home country and

n* varieties produced in the foreign country.

The model presented above is a major breakthrough in

trade theory. While maintaining the HO trade pattern that is

determined by the cross-country differences in the relative

factor endowments, it also explains the existence of trade in

differentiated products that has become a common feature in many industries. Thus, the coexistence of inter-industry and

intra-industry trade is supported by this model.

Yet another feature of these kinds of models is that they

also offer explanations for the existence of multinational

corporations. Irrespective of whether or not the trade pattern is inter-industry or intra-industry, foreign

affiliations through actions such as licensing and foreign direct investment (FDI) are often preferred to trade, when 27

there are institutional barriers such as tariffs and quotas.

However, trade economists are intrigued by the fact that

foreign affiliations of firms occur, in spite of there being

no barriers to trade among nations. While a fully developed

theory of multinational corporations (MNCs) is not yet

available, several studies have examined different aspects of

multinational involvement.

Helpman (1984) and Helpman and Krugman (1985) try to

explain this phenomenon by invoking the intra-industry trade

model that was discussed earlier. While maintaining the basic

structure of that model, they incorporate into it, firm

specific inputs such as management, and product-

specific research that are highly specialized. They clump

them together under the name - headquarter services. Given

this, they show that MNCs emerge as a response to the

tendencies of factor rewards to differ across countries due to

the differences in the relative factor endowments.

In the manufacturing sector, they consider the cost

function for a manufactured good as:

C(Wi,,Wk,x ) = mini CP(Wi,, Wk, h, x) + C«(Wl, W^, h)] . (10)

The first term on the RHS shows the cost required to produce

X units of a differentiated product where h units of

headquarter services (H) are used. The second term shows the minimum cost required in order to produce h units of

headquarter services. CP(.) and C“ are assumed to exhibit

increasing returns to scale. In a monopolistically 28 competitive world with free entry, price equals average cost in equilibrium.

Factor price equalization takes place if factor endowment ratios of the two countries are not very different. This is the standard neoclassical result, where endowment point E is within the employment vector parallelogram OQO*Q', as shown in figure 2.3 earlier. If the endowment point lies outside this parallelogram, then factor price equalization does not take place. Helpman and Krugman analyze this situation to explain the existence of MNCs. They consider headquarter services as an output produced by a home firm and exported to its subsidiary abroad. It is assumed that the home firm sets up a subsidiary abroad instead of executing an arms' length contract with a foreign firm; i.e the process of internalization* is taken for granted.

In Figure 2.4, the employment vector OQ can be decomposed into the headquarter vector CD and a differentiated product employment vector DQ. Production of H is considered to be the most capital intensive. Now, L and K get used in three production processes in the home country. In standard neoclassical theory, if E lies outside the parallelogram, then the price of capital remains lower in the home country than

4. Firms may become multinational because they possess some ownership advantage such as a patent, or comparative advantage may necessitate a particular location of production, or executing a contract between a licensor and licensee is very difficult. The last case may arise when exchanging information between the two agents is very difficult. A firm may avoid this problem by internalizing the production activity abroad. McCulloch (1984), Buckley and Casson (1976), Casson (1979) and Rugman (1980) deal with this issue. 29

L*

0* 4

K*

0

Figure 2.4

Production pattern of a MNC at home and abroad. 30

that in the foreign country (the home country being capital

abundant). The Helpman-Krugman model implies that the home

firm tries to take advantage of this lower price of capital

and produces headquarter services which are very capital

intensive. This in turn drives the price of capital up.

Thus, the wedge between the prices of factors of production is

closed by production of headquarter services at home. This

production of H is then exported to the home firm's subsidiary

abroad. Figure 2.4 shows the net result of all this. The

home country imports widgets (Y) and is a net exporter of

differentiated product (X). It also exports headquarter

services (H) and produces X in the foreign country to the

extent of the employment vector E-E„. The important point is

the following: Due to differences in the endowments, factor

price equalization does not take place and the home firm takes

advantage of this by producing headquarter services and

exporting them to its subsidiary abroad. However, as mentioned earlier, by assuming that the home firm will set up

a subsidiary in the foreign country,the process of

internalization is taken for granted in this model.

Instead of establishing a subsidiary abroad, a home firm

can very well execute an arms' length contract with a firm in

a foreign country to produce the good in question. Ethier

(1986) has addressed this question by endogenizing the

internalization decision. In his two-country model, whether or not a firm will have a FDI depends on the nature of 31 information asymmetry between firms in two different countries. The information asymmetry in turn, is caused by the uncertainty about the outcome of the research activity that a firm undertakes. His model implies that if the variance between the research outcomes is very large, then sufficiently similar factor endowments will cause the home manufacturing firm to undertake direct investment. While this model tries to endogenize the issue of the FDIs, it contradicts what Helpman and Krugman have to say about the relation between factor endowments and the FDIs.

Apart from the two models discussed above, there are a few more models of FDI and licensing that incorporate industrial organization type analysis. In Horstmann and

Markusen's (1987) analysis, FDI results from the existence of some firm-specific asset that has a public-good characteristic. They assume a firm's reputation for quality as the firm specific asset. A licensor who wishes to transfer this asset to a licensee overseas, cannot monitor the licensee costlessly. In their view, MNCs see FDI as an attractive alternative which can avoid the problem of loss of reputation due to cheating by a licensee. A different view of FDI and licensing is taken by Sheldon and Henderson (1992) who treat licensing of branded food products as the outcome of strategic interaction between firms, where markets are imperfectly competitive. Product licensing is seen as a means of 32 circumventing non-institutional barriers to entry into a foreign market.

2.4 Trade Policy Issues

Applications of industrial organization to trade theory have not been limited only to positive analysis. The normative aspects of trade policy are also increasingly encroaching the industrial organization field. With development of the NTTs, it is being realized that the policy prescriptions of neoclassical trade theory need not be valid any more. Research is now underway that evaluates trade liberalization policies, and particularly, the role of government intervention in the context of the NTTs.

Trade liberalization policy has the potential to create additional welfare gains to an economy, in the presence of imperfect competition, due to a number of reasons. It reduces imperfectly competitive price distortions by forcing every domestic firm to compete against new foreign rivals. It gets rid of wasteful duplication of fixed costs by forcing exit of excessive firms that drive up average costs. With freer trade, there is also a reduction in transfer of excess profits to foreign patent holders. Finally, consumers stand to benefit from trade liberalization if it leads to availability of more varieties of differentiated products. These aspects have been simply ignored in the literature on evaluating the liberalization of agricultural markets, and have only recently 33 been incorporated into trade liberalization of other markets

(Brown, 1992).

In empirical studies, calibration methods, partial- equilibrium models and general-equilibrium models have been used to assess these effects. Rodrik's (1988) work on developing countries with small numbers of firms, shows that there are large welfare gains due to liberalization. His results show that the welfare effects are larger with free entry and collusion in the base period. Smith and Venables

(1988) study the effects of the European Community's (EC) prospective completion of its internal market. Their estimates show that the EC's welfare rises by two percent with the completion of the internal market. In their study, gains are realized due to both economies of scale and . Dixit's (1988) study on the US automobile industry is unique in assuming only imperfectly competitive behavior and not increasing returns to scale. He shows that, in the presence of an optimal pro-competition policy, there are only small remaining imperfectly competitive gains to be captured

(0.1% to 0.03% of 1% of consumption). Studies on free trade between Canada and the US by Cox & Harris (1986), and Markusen

& Wigle (1987), use numerical general equilibrium models that merge product differentiation, oligopolistic interactions and scale economies. Richardson (1989) concludes in his review article that, as a rule, trade liberalization leads to gains, which might be two or three times larger than those estimated 34 under perfect competition. However, it can cause significant adjustment pressure most heavily on workers and firms. Some

(Greenaway & Miller, 1986) have argued though that with product differentiation, adjustment cost are lower as it is easier to switch production lines to other varieties.

Although, generally imperfect competition may generate gains under trade liberalization, it is possible that the gains may not be passed on fully if there is imperfect competition. Often, changes in exchange rates are not fully passed on to import prices. Studies by Dornbusch (1987) and

Krugman (1987) show that the cause of this imperfect pass­ through® is the presence of imperfections in export markets.

A similar phenomenon could occur domestically, where liberalization induced price reductions in the input sector may not be passed on to final consumers, in a vertical production chain characterized by the presence of imperfectly competitive distribution and sectors*.

Probably the most controversial result of the NTTs has been to show that the so-called 'strategic trade' policy may

5. The relationship between changes in the exchange rate and its effect on import prices is termed as pass-through. Krugman defined a similar concept: pricing to market (PTM), where PTM occurs if an exporter either holds his/her domestic export price constant or raises (lowers) it for an importer who has realized a domestic currency appreciation (depreciation).

6. In a recent paper, McCorriston and Sheldon (1993b) show that, for the recently proposed changes to the EC banana regime, actual welfare gains in the U.K. turn out to be only 88% of the perfectly competitive situation. This difference is attributed to the existence of imperfections in the food processing, distribution and retail sector. 35 lead to outcomes superior to free trade. In the presence of market imperfections, government policy can alter the terms of competition to favor domestic over foreign firms and shift the excess returns due to monopolistic markets from foreign to domestic firms. This literature began with the publication of several papers by Brander and Spencer (1983, 1985), who showed that, in principle, government policies such as export subsidies can serve the same purpose as building up excess capacity to deter entry, a subject matter of industrial organization. This means that government policies can serve the strategic purpose of altering the subsequent incentives of firms, acting as a deterrent to foreign competitors.

In their model, Brander and Spencer (1985) consider a in which a foreign and home firm produce a homogeneous good for a third market. Neither firm produces for its domestic market. Home welfare is the firm's profits net of government revenue. They model firm rivalry as a Cournot game. The free trade equilibrium will be the where each firm maximizes its profits, taking as given, its rival's output. If the home government gives a per unit subsidy, the marginal cost of the home firm drops. This allows the home firm to precommit to produce more and make more profits. Thus, an optimum subsidy can have the effect of making the home firm act like a Stackelberg leader.

Brander and Spencer's model, however, suffers from some limitations. For example, Eaton and Grossman (1986) assert in 36

their study that the type of policy distortion that the

government should use depends on the nature of strategic

competition. If firms in the Brander-Spencer framework play

a Bertrand game, then they show that the appropriate policy is

an export tax. Of course, the analysis becomes complicated

when more firms are introduced and firms are allowed to sell

goods in their own markets. Dixit and Grossman (1986) and

Grossman (1988) point out that this model ignores the general

equilibrium implications of an export subsidy policy. An

export subsidy may result in expansion of the targeted sector

but it will bid up the prices of domestic resources to other

sectors. These sectors may lose in the process and thus, a

nation may not benefit overall.

There have been other studies, where instead of

considering indirect policies such as taxes and subsidies,

governments may use direct policies such as voluntary export

restraints (VERs). These studies concentrate on strategic

import policies. Digby etal. (1988) show that in a quantity-

setting Cournot game, a ratio quota will have more anti­

competitive effect than a tariff. Hwang and Mai (1988)

consider a duopoly model where a quota on a foreign firm

effectively imposes Cournot behavior on the home firm. Their

results show that if the home firm was initially playing more

(less) competitively than Cournot, then a quota will make the market less (more) competitive. 37

Harris (1985) and Krishna (1989) have considered the

effects of quantitative restraints when firms play Bertrand

strategies. Krishna's paper is a seminal one which shows that quotas set even at the free trade level can facilitate anti­ competitive behavior. She considers an oligopolistic market with one home firm and one foreign firm. Using the standard profit maximization rule, a unique Nash equilibrium exists in the free trade situation, as depicted in Figure 2.5 by the configuration (P", p”). P” is the equilibrium price of the home firm and p" is the equilibrium price of the foreign firm.

Their reaction functions are B(p) and b(P) respectively. She further sets a restraint R, on the foreign firm at the free trade level depicted by the Pp line. As a result, the new reaction curve of the foreign firm becomes kinked as shown by mnl5(P,R). (P“, p”) is the price configuration where an iso­ profit curve of the home firm is tangent to the reaction curve of the foreign firm. The other combination that gives the same level of profits is (P^, p) .

If the foreign firm charges a price greater than p, then the home firm can maximize its profits by staying on its reaction curve B(p). However, if the foreign firm charges a price less than p, then the home firm can charge P“ and ensure profits at least equal to a Stackelberg leader’. As there is a discontinuity in the reaction curve of the home firm at

7. This assumes a rule. Given the fixity of R, lower prices will create an excess demand. The lucky customers will make arbitrage profits by reselling, and prices will once again increase. 38

bIP b(P.R) n = v

F(p,R) B(p,R)

Figure 2.5

VERs and the resultant Nash & mixed-strategy equilibria. 39 price p, a unique, mixed strategy equilibrium occurs where the foreign firm charges price p and the home firm randomizes over the prices P“ and P^. It is clear from Figure 2.5 that profits of both the firms increase after a VER is imposed. In fact, the home firm makes profits of a Stackelberg leader.

Krishna's paper shows that VERs affect the market not because they are set at the restrictive levels but because they impede the ability of firms to compete effectively. A government then, would like to impose such VERs only if the gains to the domestic producers by way of higher profits outweigh the losses to the domestic consumers due to higher prices.

The literature on strategic trade policy discussed above, shows that it is important to know the nature of game that firms play before any policy prescription is made. In strategic export policy, whether an export subsidy or an export tax is to be used as a policy instrument depends on the type of game being played among firms. Similarly, in strategic import policies, if alternative policy instruments such as quotas are used, they affect the very nature of the game being played among firms.

2.5 The Litmus Test

It can be concluded from the survey discussed above, that a fruitful synthesis of 10 and trade has surfaced in the form of the NTTs. Moreover, it can be affirmatively said that it is the field of international trade that has successfully 40

turned the synthesis to its advantage. The NTTs seem to

provide a refreshing alternative to the HO theory, where

existence of MNCs and intra-industry trade complements the

traditional inter-industry trade. These theories not only

give explanations for present day trade patterns but also

offer new insights for trade policy that could be radically

different from the established Laissez-Faire principle.

The development of the NTTs has sufficiently proven the

importance of imperfectly competitive market structures. In

fact, existence of imperfectly competitive market structures

is a prerequisite for the validity of the NTTs and their policy implications. It becomes imperative then, that empirical studies be carried out to estimate the degree of market imperfection in international markets. This is achieved by estimating a market power parameter which reflects the degree of market imperfection. Surely, the future scope for NTTs rests on this, and an empirical estimation of market power is its litmus test. Having established the importance of actually estimating market power, I turn next to the literature on how to conduct such an estimation. CHAPTER III

STATIC MODELS OF MARKET POWER ESTIMATION

3.1 Traditional Approach

It was the pioneering work of Mason (1939, 1949) and Bain

(1951) that led to the development of the Structure-Conduct-

Performance Paradigm (SCPP). This paradigm paid significant attention to the oligopolistic nature of markets and industries. According to the SCPP, market structure^ determines conduct^, and conduct yields market performance^.

Studies in this field have generally found that measures of either firm or industry profitability are strongly linked with market structure. A typical, stylized SCPP regression has the form:

Hi = /(CRi, BEi,..), (1) where i denotes the industry. Hi denotes some measure of firm or industry profitability and / is a linear function of

Market structure includes number of firms in a market, their degree of product differentiation, their cost structure, degree of vertical integration etc.

Conduct refers to pricing behavior, investment, , research and development etc.

Performance includes ratio of price to marginal cost, product variety, profits, efficiency etc.

41 42 explanatory variables such as CR^, the concentration ratio^

and BEif barriers to entry®. Regressions of these sort have been run on cross-sectional data for large samples of

industries. Weiss (1974) has discussed 46 such studies and

Gilbert (1984) has found 45 studies of the US banking industry alone.

The main benefit of SCPP studies is that they have made cross-industry comparisons which help in explaining the role of entry barriers. Most modern studies do not conduct such analysis. Schmalensee (1989a) contends that inter-industry studies have uncovered robust empirical regularities that are useful in developing theories. Recently, Schmalensee (1989b) undertook a study which uses the SCPP approach. He considered twelve different measures of profitability that are not highly correlated. His findings show that all the measures move counter-cyclically, whereas changes in the profitability- concentration relationship are pro-cyclical. In an another study, Domowitz, Hubbard and Petersen (1987) used panel data to study behavior of prices and margins in involved in repeated games. Their findings show that industries with high price-cost margins show cyclical price behavior.

4. The concentration ratio is a proxy for the degree of non­ competitiveness of an industry, measuring the share of a market taken by the largest n firms.

5. These are the variables that measure the difficulty of entering an industry. 43

However, there are some obvious drawbacks of this type of analysis. SCPP assumes that the relationship between performance measures and concentration is the same across all industries. This need not be true and can create biases.

Though the above representative regression shows a statistical relationship between structure and performance, the links between such variables cannot be interpreted as causal relationships but mere correlations. Variables on the right- hand side are not exogenous. In fact, structure, conduct and performance variables are simultaneously determined. For example, high short-run profits may induce entry and thereby lower concentration. Clarke and Davies (1982) show that even though Cowling and Waterson's (1976) model predicts a positive relation between profits and concentration, these variables are jointly determined by underlying cost and demand conditions. Thus, using ordinary least squares to regress a measure of performance on market structure variables is ad hoc.

Most industrial organization economists agree that the appropriate measure of the degree of market power is the gap between price (P) and marginal cost (MC), i.e. the ability of a firm to raise price above marginal cost. A unitless measure of it is :

L = (P - MC)/P, (2) which is called Lerner's measure. A researcher can directly measure this if (s)he has adequate data. Unfortunately, researchers rarely have such detailed information about 44 marginal cost. As a result, substitutes such as measures of profits, rates of return, market value of assets and price- cost margins are used in SCPP analysis. However, these substitutes have their limitations. The price-cost margin introduced by Collins and Preston (1968, 1969) is based on average variable cost and not marginal cost. Except for competitive firms in long-run equilibrium, average (variable) cost is not a good approximation of marginal cost. Tobin's q, defined as the ratio of the market value of a firm to the replacement cost of its tangible assets, should, on average, equal 1 under competitive conditions. But if intangible assets are large and still ignored, then Tobin's q could exceed 1 even in the absence of market power. Lastly, most measures of profits and rates of return use accounting as opposed to economic definitions of cost, employ arbitrary depreciation rules, and do not treat the cost of advertising and research & development reasonably. Fisher and McGowan

(1983) indicate that the time profile of the benefits derived from , depreciation methods used, and the growth rate of the firms differ among firms, so the comparison of accounting rates of return is misleading. Further, inferring the economic rate of return from accounting rates of return is very difficult since one does not have information about the past and the future values of the variables mentioned above. 45

3.2 M o d e m Approach

The new empirical industrial organization (NEIO) has been

motivated by some dissatisfaction over these issues. Survey

articles by Bresnahan (1989) and Perloff (1992) show that in

the last two decades, relatively complete structural

econometric models based on formal profit-maximizing theories

have been used to examine market power. Extensive use of the

latest computing techniques is another feature of these

studies. These studies have turned their attention away from

inter-industry comparisons and concentrate on a single

industry. Bresnahan and Schmalensee (1987) have aptly

described this new literature as ' The Empirical Renaissance in Industrial

Economics. ’

While SCPP takes price-cost margins to be observable, in

the NEIO, they are to be estimated using structural models.

In these models, aggregate or firm level data are used to

estimate a parameter X, that reflects the markup of price over marginal cost. Following Perloff (1992), a simple model can

be described as below. Given the inverse industry demand

function for a homogeneous product:

P = P(Q,Z)f (3) where Z is a vector of other variables such as income and the price of substitutes, industry revenue is given by:

R = P(Q,Z)Q. (4)

The effective marginal revenue will be given by the equation:

MR{X) = P + XPçQ, (5) 46

where Pç a dP/dQ. If there is only one firm in the industry

that acts like a monopoly, X = 1 and effective MR(1) is the

usual MR measure, (P + P^Q). If firms in the industry act

like price takers, then X = 0 and the effective MR(0) equals

price.

If the aggregate marginal cost curve facing the industry

is MC(Q,W), where W is a vector of various exogenous factors

that influence the cost, the (possibly) noncompetitive

equilibrium condition is given by;

MR(X) a P + XPqQ = MC(Q,W). (6)

By estimating the market demand equation, one can obtain an

estimate of the slope of the demand curve, Pg. Based on that

estimate, and the estimate of the equilibrium condition

equation, one can, if everything is identified, obtain an

estimate of the parameter X.

If the equilibrium condition above is rearranged as:

P - MC = -XPqQ, (7)

dividing both sides by P gives us Lerner's measure:

L s (P - MC)/P = -XPqQ/P = X/ji (8) where |x is the price of the market demand. Thus,

X® can be interpreted as an index of market power.

Let us now turn to empirical studies conducted to

estimate market power. This literature has grown in several

6. It can also be interpreted as the Herfindahl-Hirschman Index (HHI). Ottosen (1990) shows that Lerner's measure for an industry can be derived by considering market shares of firms. It is given by: L = HHI/|i = Z ( gj ) /p, , HHI being the squared sum of the market shares Si of individual firms. 47 different directions. This variety reflects not only the differences in the availability of data but also in the institutional details of the industries. These various approaches are discussed below.

3.2.1 Comparative Statics in Demand:

The comparative statics models with market power have a particular role for examining changes in the slope of the demand curve. If the exogenous variables affecting demand can rotate the demand curve around a given point, say the industry equilibrium point, then it will have no effect under perfect competition. Under perfect competition, intersect at the same point before and after the rotation, and thus, price and quantity remain the same before and after.

Under oligopoly or monopoly, however, changes in the elasticity of demand shift the perceived marginal revenue of firms and comparative statics will have different predictions as compared to perfect competition.

This approach becomes clear in a recent paper by Buschena and Perloff (1991) who have estimated market power exercised by the Philippines in the coconut oil export market. The

Philippine coconut oil export industry became concentrated in the 1970s due to the imposition of a levy on the sale of copra

(dried coconut meat), and the formation of a centralized

Philippine Coconut Authority (PCA) which controlled export 48

operations. In Buschena and Perloff's model, the world's

market demand curve is:

Q = ao + a^P +

P is the price, Z^ is a subset of Z that enters the equation

as a cross product with the price and e is the random error

term. The fringe export supply equation of the other minor

exporters is given by:

Qf = Po + PiP + + £2/ (10) where X is a vector of exogenous variables. The residual

demand facing the Philippines is the difference between the

above two equations,i.e. Qa = Q - Qf/ and is given by:

Qd = Ô0 + (0i + ôjZJP + Ô,Z + Ô,X + (Gi - 6,). (11)

Marginal cost MC, is a function of residual demand and

exogenous variables (W) that affect MC. It is given by:

MC = <})o + (j)iQa + (|)2W. (12)

Given all this, the degree of market power can be estimated by using the first-order condition for profit maximization:

P = *0 + 4iQd + 2W - XQd/(ôi + Ô2ZJ + S3, (13) where X is the market power parameter. If X = 0, the

Philippines behaves competitively and if X = 1, it uses all

its potential market power. The intermediate cases lie between 0 and 1. Based on an asymptotic t-test, Buschena and

Perloff could not reject the hypothesis that the Philippines acted as a price taker (X = 0) prior to the imposition of taxes and formation of PCA (1973). However, after the 49 creation of PCA, the estimate of market power increased to

0.578.

Before we proceed further, it is necessary to understand the importance of the interaction term PZ^ in the market demand function. Whether or not X is identified depends on the functional forms of the equations. Virtually any functional form for the demand curve leads to identification except the two most commonly used forms, linear and log- linear. If one wants to use a linear specification, one must add an interaction term that creates some nonlinearity and allows the demand curve to rotate’. X can be estimated then, because changes in exogenous variables (Z) cause the demand curve to rotate through the interaction term PZ^ which helps in tracing out the MC curve. The linear and the log-linear forms are separable in all the variables which leads to a parallel shift of the demand curve and so identification of X is not possible.

The need for the demand curve to rotate is illustrated in

Figure 3.1. Initially, we observe the market equilibrium El.

The researcher can estimate the demand curve Dj and the marginal revenue curve MR^ but does not directly observe costs. The observed equilibrium is consistent with a competitive industry structure, where the equilibrium is determined by the intersection of MC^ and D^. It is also

7. The systematic presentation of this idea was originally made by Bresnahan (1982). 50

$

MC

MC

\ MRMR

Q

Figure 3.1

Parallel shift of the demand curve. 51 consistent with the cartelized market structure, where is determined by the intersection of MCg and MRi ( as indicated by the hollow circle).

If tt3 = 0 (ie. Ô2 = 0), and Z increases by Az, the intercept of the residual demand curve shifts up by Ô3AZ, as shown for the new residual demand curve Dj. The new equilibrium E;, is still consistent with either of the two marginal cost curves. Thus, we cannot determine from this shift in Z if the industry is competitive or oligopolistic.

In contrast, if 0^ 0, a shift in Z allows us to determine the market structure. In Figure 3.2, when Z (also

Zi) increases, the new residual demand curve D3, rotates around the original equilibrium. As shown, if the industry is competitive and the marginal cost curve is MCj,, the equilibrium associated with D3 remains E^; whereas, if the industry is oligopolistic or cartelized, and the marginal cost curve is MC„, the new equilibrium is E3.

Just and Chern (1980) used comparative statics analysis to test whether or not the US tomato processing industry exercises market power in buying tomatoes from atomistic farmers. Since they considered the case of , it is the supply elasticity and not the demand elasticity that undergoes a shift. This of course does not affect the logic of the argument. It is the buying side which has the market power and the crucial exogenous variable that changes the elasticity of supply is the harvesting technology. In their 52

$

MC

W

MC

MR MR

Q

Figure 3.2

Rotation of the demand curve. 53 study, Just and Chern showed that the tomato processing industry was oligopsonistic.

3.2.2 Comparative Statics in Cost:

Comparative statics demand analysis is possible, only if data on equilibrium price and quantities is available. An alternative comparative statics analysis was proposed by

Panzar and Rosse (1977, 1987) which uses data on revenue and factor prices. The Panzar and Rosse (PR) approach involves estimating the reduced-form revenue function of the form:

Rit = R(Wit, Zit^ Yt/ params, et) (14) where i and t are firm and time subscripts respectively, W represents factor prices, Z represents variables that shift cost, Y represents variables that shift demand, params are the parameters of the reduced-form equation and e is the error term. The PR statistic is given by:

PR = /R(-)f (15) where R* is the vector of derivatives of the revenue function with respect to inputs and <,> represents the inner product.

The PR statistic has a clear economic interpretation. It represents the sum of the elasticities of the reduced-form revenue with respect to all factor prices. Thus, it gives the percentage change in the revenues that would follow from a one percent increase in all the factor prices. If a market is perfectly competitive then this statistic is unity, and, if it is a monopoly, then it assumes a value less than zero. Panzar 54

and Rosse applied their analysis to newspaper firms in local

media markets. They were able to reject the hypothesis that

newspapers are in their local markets. Shaffer

(1982) applied the PR analysis to a cross-section of banking

firms in New York State in 1979. His findings rejected both

the hypothesis of perfect competition and of monopoly.

Sullivan (1985) has extended the PR analysis to comparative

statics of market price and quantity in factor prices. His

results for the cigarette industry indicate at least a moderately high level of competition and allow for the

rejection of the perfect cartel model.

3.2.3 Econometric Estimation of MC;

Yet another approach attempts to estimate MC econometrically from cost data or from factor demand data.

This approach uses the methods of cost and factor demand

function estimation using flexible functional forms. It relies heavily on the economic theory of cost as a dual to production. The pioneering work in this area was done by

Gollop and Roberts (1979) and Appelbaum (1979, 1982). The key to their approach is to note that MC is the derivative of the total cost function with respect to quantity and that the factor demand equations are the derivatives of total cost with respect to factor prices. Then they estimate the demand equation, the supply relation and append to that system the estimation of factor demand equations. This substantially 55

increases the precision with which MC can be estimated since there will be cross-equation restrictions between factor

demand equations and the supply relations. Appelbaum used a

Cobb-Douglas function to specify the industry demand, and a

generalized Leontief function to specify cost. His results

show that the US rubber and textile industries are characterized by competitive behavior, and machinery and tobacco industries are characterized by significant oligopolistic behavior. Another approach to using factor demand information has recently been introduced by Hall

(1986). He presumes that MC could be directly observable by the conceptual experiment of changing quantity produced, holding everything else constant, and measuring by how much expenditures on inputs changed. He works with data on the rates of change of output and of the labor input. His contention is that changes in the labor input alone can reveal

MC. Under the assumption of constant returns, the wage rate times the change in labor demand, divided by labor's share in cost should give incremental cost which is an empirical estimation of MC. However, in the short run, the MC curve of interest is the short-run marginal cost curve which is not flat and AIC turns out to be a very poor proxy for it.

3.2.4 Supply Shocks :

There could be some markets where measures of market power may vary substantially from period to period. This 56

could be true of markets in which conduct of cartels is not

constant over time. There must be something in the data that

can explain this behavior. Porter (1983) addresses this issue

in the study of the US railroad industry, which is one of the

earliest industries that has been examined to assess market

power. In his study of the railroad cartel of the 1880s,

Porter uses industry-level data. He considers a constant

elasticity demand function of the form:

log Pt = ôo + ôilog Qt + ôjLt + Edt/ (16) where t indicates time period, P^ is the price of the grain

shipped, Qt is the quantity of grains in tons, is the demand-side, exogenous dummy variable taking a value equal to

1 if the Great Lakes were open to navigation and is the error term. The total cost function takes the form:

^it “ 6I(Qit, ^itr Zit, r. Soit)/ (17) where, is the vector of factor prices paid by firm i, are the other variables that shift cost, F are unknown parameters and Edt is the error term. The functional form for the marginal cost (MC) follows from (17):

MC = Ci(. ). (18)

Outside the perfectly competitive model, firms do not have supply curves. Instead, price-quantity setting follows a general supply relation:

“ 6!^(Qit, Zit/ r, Ecit) “ ®l(Qt/ Yt, Ô, Ejjt ) * (19) Here, Dj represents the partial derivative of a generic demand function D. As discussed before, under monopoly, X will take 57 the value 1 and under perfect competition it will be equal to zero. Given the specific functional forms, the supply relations in his study are given by:

log Pt = To + a“ + r^log Qt + Si> + Edt (20) and log Pt = l^ + a* + of + r^log Qt + Si> + Edt (21) with probability Jt and (1-m) respectively. Here, Jt represents the probability of successful collusion. a“ is a transformation of the conduct parameter in periods of successful collusion and a*’ measures the change in conduct when collusion breaks down. Shifts in an average firm's marginal cost are captured by a series of dummies St, which enter the inner product <.>. Porter estimates the parameters of these two equations and the switch probability Jt by using the switching regression® estimation procedure. The estimates are consistent with collusive behavior; approximately as anticompetitive as that implied by the Cournot model. Values indicate that the price is raised about 40 percent by successful collusion in the industry.

3.2.5 Comparative Statics in Industry Structure:

The methods of identification of the degree of market power described so far consider a particular industry and

The switching regression method is used when data can be divided into two or more subsets, which are believed to have different identifiable parameters. Dummy variables, and maximum likelihood estimation method is used to estimate the period when the parameter regime switches, and the probabilities of the switching. Important references are found in Judge gf a/. (1988). 58 assume the market structure as given. This assumption is not at odds with reality since substantial time-series changes in industry structure are rare events. However, methods based on cross-sections of similar markets cast some new light on the relationship between market structure and market power. These studies use price or a price index as the dependent variable, the goal of the investigation being, to know how concentration affects prices. Cotterill (1986) conducted such a study for retail food items sold by supermarkets in the local Vermont market. An aggregate price index, based on 121 product prices during August 1981 was used as a dependent variable. Analysis showed that the prices were significantly higher in the more concentrated markets. Similar studies have been undertaken for other geographically local markets such as gasoline suppliers (Marvel; 1978), cement (Roller and Weiss; 1986).

Their interpretation, that high concentration also means higher price-cost margins, is hard to defend. When markets are very large, more firms fit in it and markets appears to be less concentrated. But this need not necessarily imply that there will be lower prices or lower mark-up.

3.2.6 Market Power in Product-Differentiated Industries;

In the short run, the stock of products offered by firms and the attributes of these products is fixed. Thus, the measurement question is how much market power firms have due to existing product differentiation. Of course, compared to 59 a homogeneous product industry, the measurement problem is severe in a differentiated product industry. Even under the assumption of constant elasticity and symmetry, an N-product industry has N own-price elasticities, N income elasticities and N(N-l)/2 cross-price elasticities. On the cost side, the fact that firms produce multiple products suggests the existence of economies of scope.

The most common technique for apparently product- differentiated industries is to assume that the products in the industry are fairly close substitutes and use an index of several product prices as the observable price. This treatment is found in Gollop and Roberts (1979), Appelbaum

(1982), and Geroski (1983) to name a few. However, this method may result in the attribution of market power to noncompetitive conduct when in fact the source of the market power is differentiated products. Different economists have used different procedures to reduce the complexity of the estimation from its full size. The work of McFadden (1982) and others used nested logit models where there is prior information about groupings of products, such as when industry sources emphasize the existence of distinct product segments within which competition is more direct. A parallel literature, in the theory of spatial product differentiation, has concentrated on the relationship between heterogeneity in consumers' tastes and the demand curves facing differentiated oligopolists. These models emphasize the localization of 60 competition as a way to reduce the number of demand parameters. Empirical examples of this approach can be found in Bresnahan (1981, 1987).

Another method is to aggregate similar products until there are only a few elasticities to be estimated. Gelfand and Spiller (1987) use data on banking firms competing to make loans of a great many different types. They aggregate the loans until only two types are left and investigate the demand elasticities in the resulting two-by-two system. Similar works are done by Suslow (1986) and Slade (1987). A third approach to the problem of multiple products has been taken by

Baker and Bresnahan (1983, 1985). In their approach, the problem of estimating all of the cross-elasticities of demand is avoided by estimating only the interesting summary statistics of the demand for a product. To estimate the market power associated with a particular product, it is unnecessary to estimate all of the effects of all of the other products' prices in the market. Instead, only the total effect of competition from other products is considered.

Suppose, a seller of a particular variety faces demand given by:

Pi = D(Qi, P2,...,Pn, Y, Ô), (22) where P2,...,P„ are the prices of products of competing varieties in the market, Y is income and Ô is the set of demand equation parameters. A supply relation very similar to that in equation (19) can be derived for the variety in 61 question. Similar supply relations exist for the other (n-1) varieties too. The (n-1) supply relations and the (n-1) demand equations for the other varieties can be solved for the prices and quantities of those (n-1) varieties. Finally, the demand equation for the variety in question can be estimated in the form:

Pi = D(Qi, P^(.),...,?„(.), Y, Ô), (23) where, all other prices are substituted out in terms of exogenous variables. In this process, enormous information is lost by substituting out the prices of all other varieties; however, without this method it will be impossible to estimate all of the elements of Ô from equation (22).

3.2.7 Nonparametric Methods :

A number of studies also use nonparametric methods of testing for market power. The advantage of such methods is that they are not subject to the specification bias associated with the choice of a functional foinn, and they require less data. In Panzar and Posse's (1987) study, reduced-form revenue functions are estimated first, and then some restrictions on these functions are tested which depend on the type of market structure. As referred to earlier in their analysis, the sum of factor price elasticities of a firm's reduced-form revenue equation must be nonpositive for a monopolist, less than or equal to one in a symmetric

Chamberlinian equilibrium and equal to one in a long-run 62 competitive equilibrium. However, this much information is not enough to actually estimate the degree of market power.

Ashenfelter and Sullivan (1987) use a revealed approach to the cigarette market. The changes in the excise taxes are used to identify the market structure by allowing us to assess firms' reactions to the exogenous variations in the marginal cost. Rather than estimating a market structure parameter, they obtain a bound on the market structure parameter. Hall (1988) examines the relationship between changes in inputs and outputs. He concludes that because the cyclical variations in labor inputs are small relative to the cyclical changes in output, U.S. industries have marginal costs well below price. The main drawbacks of these models are that many times one must maintain the assumption of constant returns to scale and one may have to ignore the stochastic nature of the underlying problem.

3.3 Summing Up

There have been many more empirical studies than one can illustrate here, using different methods of estimation. Of course, the parametric and nonparametric approaches have key advantages over the SCPP approach. They are based on formal maximizing models so that the hypotheses can be directly tested. They use exogenous variables to explain variations in market structure rather than endogenous variables such as concentration ratios and advertising. In Table 3.1, the 63 estimated price-cost margins (Lerner's index, L) from several such NEIO are reproduced. They show that a great deal of market power exists in some of these markets. Despite the fact that so many studies are conducted, very few have paid attention to export markets. Therefore, in the context of the present research, it is worthwhile to estimate the degree of market power in the banana export market using a static structural model.

Table 3.1

Estimates of Lerner's index (L)

Author Industry L Appelbaum (1982) Rubber 0.049“ Appelbaum (1982) Textile 0.072“ Appelbaum (1982) Elec. Machinery 0.198“ Appelbaum (1982) Tobacco 0.648“ Azzam, Pagoulatos (1991) Meat packing 0.46 Bresnahan (1981) Automobiles 0.1/0.34b Lopez (1984) Food processing 0.504 Porter (1983) Railroads 0.40 Roberts (1984) Coffee roasting 0.055/0.025“ Schroeter (1988) Beef packing 0.079/0.036'* Schroeter, Azzam (1990) Beef 0.553 Pork 0.477 Slade (1987) Retail gasoline 0.10 Suslow (1986) Aluminum 0.59

“At sample midpoint. “Varies by type of car. “Largest & second largest firm, respectively. “^Figures for 1951 & 1983 respectively.

However, all these models fail to take into account the multi-period existence of any market. Almost all real world markets last for many periods. Moreover, multi-period 64 considerations seem to reduce the competitiveness of oligopoly markets even further. The game theory literature shows that cooperation among firms is likely in multi-period markets®.

Using static models is inappropriate since firms^ in setting strategies, take previous behavior into account, and since there are substantial adjustment costs in changing production from one period to the another. Many agricultural commodities are characterized by substantial gestation periods between planting and harvesting. Dynamic models, on the other hand, stand a better chance of explaining the workings of domestic or export markets characterized by oligopolistic behavior.

This issue and the review of dynamic models is taken up next.

9. Possibilities of punishment for deviating from cooperation exist in a multi-period setting. The relevant literature on game theory is discussed in the next chapter. CHAPTER IV

DYNAMIC MODELS OF MARKET POWER ESTIMATION

4.1 Conjectural Variations Approach

Samuels on (1948, p:352) wrote, "The geometric progression of the

Malthus population theories and the concern of the classical economists with the

approach toward a stationary state remind us that dynamic analysis is not new in

economics." Researchers in the field of industrial organization

too have been aware of the dynamic inter-dependence of

economic agents in oligopolistic markets. While the

traditional 10 literature has made an effort to incorporate

dynamic features into static oligopoly models, the NEIO

literature has employed dynamic game-theoretic models to estimate the degree of market imperfections. Before I proceed to review the latter, a brief description of the former is presented here.

In an oligopoly market, actions taken by a firm in one period affect the actions taken by other firms in subsequent periods, which also affect the profits of all the firms.

Therefore, a firm in an oligopolistic market has to form a belief about the likely response of other firms to its

65 66 actions. It then decides its profit maximizing action, taking into account these conjectures. This belief of a firm about its rivals' response to a change in its own decision variable was first introduced by Bowley (1924)^. The approach is illustrated here using the Cournot^ duopoly model. The notation followed is similar to that of

Varian (1987). Let firm 1 expect firm 2 to produce y t units of output. If firm 1 produces y^ units of output, the total output it expects to be sold in the market is Y = yi + yf.

The market price that this quantity will yield is p(Y) = p(yi

+ yf). The profit maximization problem of firm 1 is then;

max: p(Y)yi - Ci(yi); w.r.t. y^, (1) where Ci(yi) is the total cost function. The profit maximizing output must satisfy the condition:

p(Y) + d p d r yi=WC,(y,), (2) ~3Ÿ~3ÿl where MC^(.) is marginal cost. If one considers the expressions for the derivatives as discrete changes then one can express change in Y as: dY = dy^ + dyf and hence.

d r (3)

1. Though the credit of introducing this concept goes to Bowley, it was Frisch (1933) who phrased this concept as 'conjectural variations'.

2. Cournot (1838) first introduced the problem of oligopoly interdependence in a static model. In his model firms decide the profit maximizing output assuming that other firms do not change their output. Bowley (1924) and Stackelberg (1934) generalized his concept. 67

In equilibrium, will be and hence, equation (2) can be written as;

The term dy^/dyi in the above equation is nothing but the conjectural variations term. This tells us how firm 1 conjectures firm 2 will vary its output when firm 1 makes a small change in output. Let us name this term as v. If the firms are symmetric, i.e. they have identical costs and produce the same level of output, then equation (4) can further be generalized for n firms as:

1 + (n-l)v' Y = MC, (5 ) n where, n is the number of firms. Consider this equation and recall equation (6) from chapter III, which is used to estimate the market power parameter These two are identical equations, where X = [1 + (n-l)v]/n. It has been noted before that X ranges from 0 (competitive market) to 1

(collusive behavior). Given the relation between X and v above, the corresponding values for v range from -1 to 1 for duopoly models, v = -1 represents , where firms adjust their quantities so that total quantity produced, and therefore the price, is conjectured to be constant. When

V = 1, firms behave collusively. Each firm acts as if it can affect the total output, and therefore the price, but not its own market share. It can also be verified that for the 68

intermediate case, where firms have Cournot conjectures, i.e.

V = 0, the corresponding value of X is 0.5. Therefore,

estimating the conjectural variations parameter v reduces to

estimating the market power parameter X as described in

chapter III.

For the Cournot model, one can derive the reaction

function for firm 1, which shows the profit maximizing output

of firm 1 as a function of output chosen by firm 2. Suppose

at time t the firms are producing outputs { y ‘, y ^ }which are

not equilibrium outputs. Firm I's choice in period t+1 will

be given by:

y r = fi(y/). (6)

Similarly, firm 2's reaction function can be expressed as:

yV" = f2(ya)- (7)

This means that every time a firm gives its , it

assumes output of the rival firm to be fixed at the previous period output level. This process continues until the outputs

satisfy the condition Yi ~ ^1(72) and y^ = fzfyi).

The Cournot model discussed above is only one of the models developed in the static oligopoly framework.

Stackelberg's model assumes one firm to be a leader and the other to be the follower in which the leader has an advantage of taking action first. The Bertrand (1883) model is similar to Cournot but the conjectural variations are expressed in terms of prices and not quantities of output. However, all 69 these models that incorporate conjectural variations can be criticized for a number of reasons.

Tirole (1988) contends that a static model is, by definition, a model in which firms cannot react to one another and thus any conjecture about one's opponents' reaction that differs from no reaction is irrational. Friedman (1983) argues that these models ignore the fact that firms are willing to make trades between present and future profits and that firms will be maximizing discounted profits. These ideas can only be incorporated in a dynamic model. Fellner (1949) argues that conjectural variations are ad hoc in nature and turn out to be right for the wrong reasons. For example, in

Cournot equilibrium, each firm's beliefs about the constancy of the level of the other firms' actions are confirmed; however, reaction functions do not have a zero slope, indicating that firms do alter their production plans in response to actions taken by other firms. Thus, conjectural variations are inconsistent with reaction curves.

However, it must be emphasized here that the criticism of inconsistency is not directed at the comparative statics involved in arriving at the equilibrium. The comparative statics in oligopoly models, as described in equations ( 6 ) and

(7), are similar to the cobweb dynamics routinely employed in static competitive models. The argument for inconsistency is directed at the fact that conjectures formed by firms do not square with the underlying comparative statics. 70

Several attempts have been made by Friedman (1977),

Laitner (1980), Bresnahan (1981), Kamien and Schwartz (1983) and others to remove this inconsistency. These studies try to find the class of demand and cost functions for which conjectural variations about rivals' rates of response coincide with the actual rates of response, at least at the equilibrium. Among the cases that Bresnahan studies, he shows that Bertrand conjectures are consistent under an assumption of constant marginal cost. In this case, conjectural variations and the slope of the reaction functions, both turn out to be -1. This means that in equilibrium, firms are correct not only about the levels of one another's reaction functions, but also about the expectations of the rate of change. He further shows that Cournot conjectures become consistent, only as the slope of marginal cost curve changes from horizontal to vertical. But again, analysis in this literature is carried out within a static framework. Friedman

(1983) states that this literature would have seemed a valuable development had there not been considerable progress in economics (oligopoly included) in analyzing dynamic models.

Recently, Klemperer and Meyer (1989) have argued that the literature on consistent conjectures equilibria relies implicitly on firms' being uncertain, even in equilibrium, about their rivals' behavior, and this uncertainty is neither explained nor explicitly modeled. As a result the justification for the consistency condition is unclear. 71

Secondly, in all the studies, firms are projected as choosing either price or quantity as a strategic variable. In a world with exogenous uncertainty about, say, market demand, a firm may not want to commit to either of these simple types of

strategy. In their model, before a is realized, each firm commits to a function specifying the quantity it will produce as a function of its price. Hence, firms choose their supply functions as their strategic variables to maximize expected profits, given the supply functions chosen by other firms. The equilibrium is consistent in the sense that any price-output pair on a supply function is ex post optimal. The supply functions under uncertainty are positively sloped, and are distinct from the vertical supply functions that are exogenously imposed on firms in the Cournot model, and from the horizontal supply relations exogenously imposed in the Bertrand model. Klemperer and Meyer recommend using the empirical approach of Bresnahan (1982) and Lau

(1982) for testing the predictions of their model. However,

Klemperer and Meyer limit their analysis to the domain of static framework, and do not incorporate any dynamics in their model.

Many studies have been undertaken that use dynamic models to estimate the degree of market power. These studies are developed in a game-theoretic framework. Game theory, which models the interaction of two or more agents with conflicting objectives, provides a useful method for analyzing imperfectly 72 competitive markets. Therefore, it is necessary to review the concepts, terminology and relevance of game theory to oligopoly markets. Discussion of dynamic models will follow immediately after that.

4.2 Game Theory and Oligopoly

The theory of games is suggested to some extent by parlor games such as and bridge. Friedman (1983) illustrates two distinct features of these games. First, in a parlor game played for , the total amount won by all winners combined equals the total amount lost by all losers. In terms of game theory, this is described as a constant sum game. Second, these games are games involving a strategy. In Solitaire/Patience, a player plays a game against nature where there is no other conscious decision-maker whose actions depend on what the player does. However, in a game of chess, while choosing what action is to be taken, a player tries to guess how his/her opponent will react to the various actions (s)he might take.

In technical terms, the persons (n of them) playing the game are called players, the actions that they take at each turn/period are defined as moves and the amounts won or lost by them are called payoffs. The complete listing of moves for each conceivable situation that a player may face in the course of the game is called the strategy of the player.

Further, games are called cooperative or noncooperative depending on 73

whether or not rules of the game allow players to form a

coalition or a binding agreement.

For perfect competition (where n-»oo) and monopoly (where

n = 1), circumstances are analogous to those of the solitaire

player. In perfect competition, the behavior of one firm or

consumer has no effect on any other and so a competitive

market can be viewed as a model of many intertwined games

against nature. Similarly in monopoly, consumers do not guess

what the monopolist would do before choosing their actions.

As for the monopolist, for any price that (s)he chooses,

demand is predictable given the market demand schedule.

An oligopoly in comparison, is definitely interpretable

as a game in which the firms are the players, the choices of

prices or the quantities produced by firms are their

strategies, and the profits that they make are their payoffs.

Since the sum total of the profits made by all firms is not

zero or a constant, oligopoly can be described as a variable sum game. Moreover, in an industry which is unregulated and where

antitrust legislation rules out legally binding agreements

among firms, oligopoly can be considered as a noncooperative

game. It must be emphasized however, that economists are not

interested in uncooperative behavior of firms. Rather, they

are interested in explaining how cooperation can emerge from

self-interested firm behavior within a given set of rules. To

sum up in game-theoretic terminology, oligopoly can be defined

as a n-player, variable sum, noncooperative game. 74

Having established oligopoly as a game, oligopoly equilibrium can also be explained in terms of game theory. An important equilibrium concept applied in noncooperative game theory is the Nash (1951) equilibrium. The formal description of a game and the Nash equilibrium is as follows;

A game is described by three sets:

1. The set of players, N = {1,2,...,n} who are rational decision makers whose behavior is being studied.

2. Each player, iS N , has a strategy set from which (s)he must choose some particular strategy s^. A strategy combination is a selection of one strategy for each player and is denoted by, s = (Si,...,Sn) where s is a member of the Cartesian product set denoted by S = Sjj.

3. Each player i has a scalar-valued payoff function, Pi(s), whose value depends on the strategies of all the players. The vector of payoffs is given by P(s) =

Playing this game amounts to all players choosing a strategy simultaneously. This leads to the question of what strategies the players are expected to adopt. This question is addressed in the concept, the Nash equilibrium:

s* is a Nash equilibrium if s' E S and Fi(S ) & Pi ( Si ! ... f Si-i , S^, Siti f ... f Sn ) for any s_. E and for i = 1,..., n.

This means that s* is a Nash equilibrium if each si is available to the player to choose, and if it is impossible that any single player can obtain a higher payoff through the use of a different strategy, given the strategy choices of the other n-1 players. 75

Following the definition of Nash equilibrium above, the equilibrium in the Cournot oligopoly model can be shown to be nothing but a Nash equilibrium. This can be illustrated by a simple example. Consider a Cournot duopoly model where market demand is given by p(Y) = a - bY, where Y = y% + y^.

For convenience, let marginal cost be zero for both firms.

The profit function for firm 1 is;

Y2 ) = [a - bY]yi. (8)

Taking the derivative w.r.t. y^ gives the first order condition:

a - byz - 2byi = 0. (9)

This gives the reaction function for firm 1 as:

yi = [a - by;]/2b. (10)

Since the two firms are symmetric, firm 2 has a similar form of reaction function:

yz = [a - byj/2b. (11)

The intersection of the two reaction functions gives the

Cournot equilibrium. At the equilibrium, each firm's profits are maximized given the output level of the other firm. To recall the earlier discussion, the conjectural variation is zero in this model. Solving (10) and (11) gives the equilibrium quantities:

Yi = Yz = a/3b. (12) The profits of both the firms are jt„ = a^/9b each (here n stands for Cournot-Nash). 76

Now, this problem can be cast into a game theoretic framework. In this game, the strategies of the two players involve selecting y^, the optimal level of output. The strategy set for each player is [0, a/b] since any output more than a/b gives a negative price. The payoff function for these firms is their profit function. The Nash equilibrium can then be expressed for firm 1 as follows;

%(a/3b, a/3b) & %i(yi, a/3b). (13)

This means that given the strategy of firm 2 (of choosing output a/3b), firm 1 cannot increase its payoff by choosing any other output level.

However, it is important to note that the Cournot-Nash equilibrium is not Pareto optimal and Cournot equilibrium is not the only oligopoly equilibrium. Figure 4.1 shows a variety of single period payoffs that are possible under different assumptions. Point N indicates the Nash solution that was discussed before. The origin 0 indicates the

Competitive solution where price p = marginal cost = 0. The two firms in question may even collude to maximize joint monopoly profits and share the profits such that payoffs are more than the Nash solution. In our earlier example, the two firms may collude to maximize joint profit:

• 3x(Y) = [a - bY]Y. (14)

The first order condition is, a - 2bY = 0 which implies that total output Y = a/2b. The total profit due to collusion is jtn, = a^/4b which is larger than the sum of profits of the two 77

Firm 2

7Tm

7T. n

■7T 7T n m Firm 1

Figure 4.1

Cournot-Nash and Collusive payoffs. 78

firms in Nash equilibrium situation. This monopoly profit can

be shared in any fashion on the line segment e-f such that

their profits are larger than the Cournot-Nash case. In fact,

Figure 4.1 indicates that a point anywhere in the shaded

regionis a Pareto improvement over the Cournot-Nash

equilibrium. However, such collusive behavior is possible

only in an infinite period . In a single period

game, there is an incentive for an individual firm to cheat.

A firm would increase its output to make extra profits since

there is no mechanism for other firm to punish such a conduct

in later periods. If both firms realize this, then the only

outcome that is realistic is the Cournot-Nash outcome. In

this case, the behavior of firms is similar in structure to

the celebrated prisoners’ dilemma^ game. The same logic also

applies to a finite period repeated game. If there is no

future after the terminal period, there is no way that a firm can punish other firms by increasing output in the next period. Thus Nash equilibrium will prevail in the terminal period. If firms are going to play Cournot-Nash in the terminal period, they are not going to try a coalition in the penultimate period for similar reasons. By backward

Two prisoners awaiting a trial are held in separate cells. Each is offered the following deal: If one testifies against (finks) the other, (s)he is released, gets a reward and the other is sent to jail, provided the other does not fink. When neither finks, they are released. If both fink, both are sent to jail but they get their reward. The prisoners could set themselves free by both deciding not to fink; however, self interest leads to a Pareto- inefficient outcome where both fink. 79

induction, there will never be a coalition in any of the previous periods. This is referred to as the chain-store paradox

(Selten, 1978), where equilibrium is characterized by repetition of the single period Nash equilibrium.

Consider an infinite period repeated Cournot game against this background. Let both firms adopt the strategy of producing half the monopoly quantity as long as the other side does likewise and revert to the Cournot quantities in the face of any deviation. As long as the discounted present value of half the monopoly profits exceeds the best one can get from a deviation in a single period plus the Cournot profits thereafter, there can be an equilibrium in which firms collude. The preceding discussion is one facet of the result, known as the Folk Theorem. While Friedman (1971) asserts this

Folk Theorem for a Cournot game, it can be described for a

Bertrand game as follows;

For an infinitely repeated, complete information game in prices, any combination of profits ( jti,..., jtn ) such that 0 and s ( the monopoly profits) is a per-period equilibrium payoff for discount rate sufficiently close to 1.

Thus, any outcome from collusive to the competitive, can be enforceable through Nash threats. Precisely what outcome emerges in a market can be found out by estimating the market power parameter X.

Of the multiplicity of equilibria that are possible, which one will occur depends on a player's ability to effectively threaten other players for not being cooperative. 80

The effectiveness of the threat in turn depends on the

discount factor, length of the game, and the credibility of

the threat. A very low discount factor implies that profits

in future periods are worth substantially less than profits in

the current period. Therefore, punishments in future periods

become less effective. It has already been shown that finite

period games cannot sustain collusive equilibria. Further, if

the threats are not credible, in the sense that fiinns do not

believe that a firm will actually inflict the punishment in

the future, collusive outcomes are not likely to emerge.

The above arguments indicate that the possibility of

occurrence of collusive outcomes in dynamic games requires

some refinement of the Nash equilibrium. One widely used

refinement is the concept of Perfect equilibrium (Selten, 1965);

A perfect equilibrium is a Nash equilibrium that does not involve noncredible threats by requiring that the players ' behavior be optimal even in situations that are not reached on the equilibrium path".

For example, if firm 1 threatens to punish firm 2 in future periods for producing too much in the current period, the threat is credible only if the punishment (i.e. a move not on the equilibrium path) is in firm I's best interest in the

future period. A similar concept, called subgame perfect

4. This definition; however, does not allow for uncertainty. Once uncertainty is involved, equilibrium concepts need to incorporate probability distributions over the actions available, and beliefs about what state a player has already reached. These concepts are captured in (Kreps and Wilson, 1982) and 'trembling-hand' perfect equilibrium (Selten, 1975). 81 equilibrium, stems out of this. A subgame perfect equilibrium is a set of strategies for each player such that in any subgame the strategies form a Nash equilibrium. Here, a subgame is a subset of an original game that itself can be regarded as a game.

The single period repeated games that have been considered so far, are able to support collusive behavior, however, they are inappropriate where firms incur substantial adjustment costs in production, storage, and where there is learning over time. Even demand in one period depends on the quantities sold in the past. In short, there is always an intertemporal dependence among economic variables. This requires an oligopoly market to be modeled as a single dynamic game rather than as repeated single period games.

In the study of oligopoly markets that are modeled as dynamic games, two important equilibrium concepts are used.

One is open-loop Nash equilibrium and the other, closed-loop Nash equilibrium. These concepts are borrowed from optimal control theory which often distinguishes between open-loop and closed- loop solutions to optimal control problems. In an open-loop equilibrium, controls (i.e. moves made by a firm that constitute its strategy), are a function of time and the initial state. The open-loop strategy space is defined as below; 82

= [Xi(y(0),t)| Xi(y(0),t) is a continuous function of time t , V t & 0 ], where Xi(.) is the control variable (e.g. rate of change of output) of the i^** firm, y(0) is the initial state (e.g. the initial output). Since moves are independent of the current state of the system, and a firm is committed to a preannounced plan not anticipating any response, this equilibrium is not subgame perfect. However, it does resemble the static Cournot equilibrium.

In contrast, in a closed-loop equilibrium, players design their optimal policies as decision rules dependent on the current state of the game. The closed-loop strategy space is defined as:

5 “ = [Xi(y(t) ,t) I Xi(y(t) ,t) is a piecewise continuous function of time t a 0, and Lipschitz®- continuous w. r. t. y(t) = (yi(t),... ,y„(t) ) ].

Since state variables at time t summarize the latest available information about the system at time t, and since firms take the mechanism for determining future behavior as given, closed-loop strategies can be referred to as Markov strategies and a closed-loop equilibrium can be considered a subgame perfect equilibrium.

At this stage, I introduce an example from Starr and Ho

(1969) which illustrates the two concepts. Consider Figure

4.2 (a). In a two-player game, each player has two possible

5. with respect to the state variable, the Lipschitz condition states that, there exists a non-negative constant K; such that; \f(t,y) - f{t,y) I & K ||y-y||, V t e [tg,T] ; y , y e R”. 83

moves labeled, 0 and 1. At each stage, both players choose a

move simultaneously. The possible resulting pair of moves in

stage t = 0 are: 0,0; 0,1; 1,0; and 1,1 which lead to three

possible states: x = 0, x = 1 and x = 2. Associated with each

pair of moves are the transition costs, c^ and Cj shown in

circles in Figure 4.2 (a). The objective of each player is to minimize transition costs in reaching t = 2 .

Closed-loop strategies : At t = 1 there are three possible states. At state x = 2, the situation for the two players is depicted in Figure 4.2 (b). Only the pair 0,0 has the Nash property. The corresponding costs are 2,2. If

X = 1, the pair is 1,1 and costs are 0,3 as shown in Figure

4.2 (c). Figure 4.2 (d) shows that for x = 0, the Nash pair of moves is 1,0 with associated costs 4,1.

In stage t = 0, it is assumed that players play Nash moves in t = 1, and therefore the circled Nash costs of the stage, t = 1 are added to the cost of transition at t = 0.

Now, players play Nash moves at t = 0, taking into account that they play Nash moves in the subsequent period too. The resulting situation is depicted in Figure 4.2 (e). Both players incur cost; 4,4, the Nash pair of moves in t = 0 is

0,1 and the trajectory of states is x = 2 and x = 2 in stages t = 1,2 respectively. Thus, the closed-loop strategy for player 1 is 0,0 and for player 2 is 1,0. 84

(a)

X*0

t'O PLAYER 2 t- 2 0 1 0 1.3 * * 2 PLAYER I (b) 1 4,1 0 ,2 t - l

PLAYER 2 0 1 0 2.2 3,1 *•1 PLAYER< (c) 1 2,4

PLAYER 2 0 1

0 9,2 2,3 (d) PLAYER I 1 © 1,4 PLAYER 2 0 1 0 2.3 PLAYER I (e) 1 3.2 3,3

PLAYER 2 0 0 0 1 10 II- 0 0 4,4 3,3 IT VASH CLOSED-LOOP PLAYER I 01 4,6 2,3 6 ,3 2,4 10 4,3 1.4 7,2 8,1 11 0 ,3 7,4 9,3 NASH OPEN-LOOP

(f )

Figure 4.2

Closed-loop and open-loop strategies. 85

Open-loop strategy; In the open loop strategy, players consider the costs corresponding to alternative time paths of moves without regard to whether or not moves in t = 1 are rational given the state that is reached in t = 1. Costs for each pair of open-loop sequence are tabulated in Figure 4.2

(f). Strategy 1,1 for player 1 and strategy 0,0 for player 2

is the only equilibrium solution here. This gives rise to cost 3,2 respectively. The state trajectory in this case is

X = 0 and x = 0 in stages t = 1, 2 respectively.

The reason for this divergence of solutions in the two

strategy schemes is that in the open-loop strategy, moves are not subgame perfect. For example, in Figure 4.2 ( f ), the strategies 0,0 for player 1 and 0,0 for player 2 are not subgame perfect. If in stage t = 0, both players choose move

0, the state x = 1 is reached. However, having reached this stage, it is not optimal for players to choose the move 0 again in stage t = 1. The optimal move for both players is 1 as evident from Figure 4.2 (c).

On the basis of the subgame perfection criterion then, the closed-loop equilibria are certainly more appropriate than the open-loop equilibria. A number of dynamic oligopoly models test which concept resembles the actual behavior of

firms. Some of them in particular, also parameterize this oligopoly behavior into an index known as dynamic conjectural variations. As explained in the earlier section, this is 86

tantamount to estimating the degree of market power in a

dynamic setting.

4.3 Dynamic Games Approach

The use of dynamic game-theoretic models to estimate the

degree of market imperfection is a recent development. While

some of the studies have constructed theoretical models that

determine the sign of the dynamic conjectural variations

parameter, others have estimated it empirically using dynamic

programming techniques.

The term dynamic conjectural variations was first used by

Riordan (1985) which he related to the equilibrium behavior of

firms in a homogeneous-good Cournot oligopoly model that lasts

for two periods. In his model, there are n symmetric firms, each having a constant unit cost of production c, up to an exogenous capacity of k. The inverse market demand function is given by:

n Pt = - Y , 1 a^ and a; are randomly determined by the following moving average process :

= 8, (16)

32 = pa^ + (1-p )E2, (17) where 0 ^ p ^ 1 and and Sj are i.i.d. random variables. In period t, a% is observed only after that period's quantity 87

decisions are made. Firms do not observe a^ and output

decisions of the rivals. The only thing they observe is the

market price. Hence, firms are imperfectly informed about the

market environment.

The strategy of firm i is the specification of an output

in period 1, gi and specifying output in period 2 as a

function of period 1 price, i.e. g i = (^2 (Pi) • A symmetric

equilibrium is defined by a strategy that maximizes the

discounted expected profits of each neutral firm, given

that its rivals are following that strategy. That is,

[gif olipj] solves the following;

max: F[ (p^ - c)g^ + ô(P; - c)02(pj], (18)

s.t. Pi = - (n - l)gr - (19)

P2 = ^2 - (n - l)02(Pi) - o,(Pi) , (20) where Ô is the discount rate. After solving this problem

analytically, Riordan derives the dynamic conjectural

variations parameter as: do;(p,) jp. _ p

That is, in equilibrium, each firm believes that a one-unit

increase in its first-period output would lead each rival firm

to decrease its second-period output by p/(n + 1). This

belief about rival firms turns out to be correct because all

firms are assumed to follow an equilibrium strategy. The 88 purpose of this parameter is: A firm perceives that an

increase in its output will lower the current market-clearing price, which will cause rival firms to think that the demand curve has shifted down, and hence induce them to lower their outputs in the future.

The negative sign of the parameter indicates that firm behavior is less than Cournot. If the value of p is zero,

i.e. if firms can learn nothing about the demand curve from the past, then the solution is identical to the static Cournot model. However, as p gets larger, firms draw stronger inferences about the current demand curve from the past prices. Consequently, a firm is better able to influence

future outputs of rivals by manipulating the current-period price. All firms then, perceive an incentive to expand output, which results in a more competitive market in period

1. An aggregate parameter of conjectural variations is given by p(n - l)/(n + 1) which increases in absolute value, as the number of firms increases. As n gets large, market behavior becomes more and more competitive.

Riordan derives a similar result for an extension of this model to the infinite horizon case. The one-period negative dynamic conjectural variations effect holds good at each period, and output is uniformly greater than the Cournot levels. Riordan's negative dynamic conjectural variations model, then, drives home the idea that market behavior is competitive due to imperfect information about the demand 89 conditions. One way in which firms might become informed about demand conditions is by observing rivals' previous output decisions. This implies that in a homogeneous oligopoly, the exchange of quantity information by rival firms may prove to be potentially anticompetitive.

In a recent paper, Dockner (1992) proved important theorems that provide a link between the static and dynamic concepts of Nash equilibrium, and the static and dynamic concepts of conjectural variations. He has constructed an infinite horizon, homogeneous good duopoly model where firms incur adjustment costs when changing production®. Introducing adjustment costs makes this model what Friedman (1977) calls a time dependent or structurally linked dynamic game.

In his duopoly model, the inverse demand function is given by p(Q(t)), where p(.) is the price at time t and Q(t)

= qi(t) + qz(t) is the industry output at time t. The cost function is given by Ci(qi(t)), i = 1,2. Production adjustment costs are given by Ai(Xi(t)), where Xi(t) s qi(t) is the rate of change of output for firm i at time t. Given this, firms choose their production plans over an infinite period so as to maximize the discounted stream of profits: maxn? = |e-^‘[p(0(t))g.(t) -CJg^(t)) -A,(x,(t))] dt, (22)

Studies by Fershtman and Kainien (1987), Reynolds (1987), Maskin and Tirole (1987), and Driskill and McCafferty (1989) also incorporate production adjustment costs; however, the theorems in Dockner's paper are generalized to include nonlinear demand and variation in costs across firms. 90

subject to initial condition qi(0) = q^o and r > 0, the discount rate’. Problem (22) then constitutes a two-person, variable-sum differentiable game with the levels of output qi(t) as the state variables, and the rates of change of output as the control variables. Assuming that there exists an open-loop and closed-loop equilibrium for the general problem presented above, Dockner proves two important theorems®. They are as follows: A. The steady state open-loop equilibrium of the dynamic game (22) coincides with the Cournot equilibrium of the corresponding static game.

B. Any steady state closed-loop equilibrium of the dynamic game (22) can be viewed as a conjectural variations equilibrium of the corresponding static game.

Having proved the above results, Dockner considers specific

functional forms for the demand and the cost functions.

Assuming linear demand and quadratic costs, he proves the

uniqueness of the closed-loop equilibrium and derives the dynamic conjectural variations parameter too. The linear demand functions takes the form:

P(Q) = a - (qi +qj). (23)

Quadratic asymmetric production costs are given by:

CiiQi) = (24) where a, b, c^ (i=l,2) are constants, a - Ci > 0 and quadratic production adjustment cost is given by:

7. Many times, the discount rate r used in the present value formulations is expressed in the form p = l/(l+r), where p is referred to as the discount factor.

8. General existence results for differential games are found in Fershtman and Muller (1984) and Mehlmann (1988). 91

A,(x,) = ^ xl. (25)

With these specifications, the dynamic problem (22) becomes an

asymmetric linear-quadratic differential game. This

generalizes the game discussed by Driskill and McCafferty

(1989) that allows only for symmetric technologies across

firms. Confining attention to the linear-quadratic game

structure, he proves one more theorem, namely;

C. There exists a unique, globally and asymptotically stable perfect equilibrium within the class of linear closed-loop (subgame perfect) strategies.

The derivations of his model also lead to the following linear decision rules (reaction curves):

qi(t) = Xi(t) = + ôg^(t) +ag^(t)], ixj. (26)

From this decision rule, theorem B, and the proof of theorem

C, Dockner proves an important theorem:

D. The steady state closed-loop (subgame perfect) equilibrium of the dynamic game (22) coincides with a conjectural variations equilibrium of the corresponding static game with constant conjectures equal to % = ^ .

Here parameters a and ô are negative, which is a consequence of the stability condition of the Nash equilibrium. It implies the downward sloping nature of the reaction curves. Therefore, the dynamic conjectural variations parameter %, turn out to be negative. Dockner explains the steady state closed-loop equilibrium using a phase diagram. In Figure 4.3, the dark lines correspond to 92

q 2

q' 2 q 2

q q q

Dynamic Reaction Functions

Cournot Reaction Functions

q * Closed-Loop Steady State Equilibrium

q. Cournot Equilibrium

Figure 4.3

Static and dynamic reaction functions. 93 equation (26) which shows the dynamic reaction curves, and the light lines that lie inside are the static reaction curves.

Since the closed-loop conjectural variations are negative, and the static conjectural variations are zero, obviously, the closed-loop equilibrium is more competitive than the static

Cournot equilibrium. Therefore, the equilibrium quantities for the closed-loop equilibrium are larger than that of the

Cournot equilibrium. The intersection of the dynamic reaction functions corresponds to the steady state equilibrium that is globally and asymptotically stable. The arrows in the phase diagram show that for some initial condition, the output path for both firms converges to the steady state.

It is easily verified that as the discount rate r or the adjustment costs increase in value, the absolute value of % decreases. In the limit, as r » or k -> oo, the dynamic conjecture converges to the Cournot conjecture, i.e. % -* 0.

As r becomes very large, it means that firms are myopic; therefore, they are interested only in a one shot game.

Similarly, with very high adjustment costs, rivals are less likely to react aggressively. In the limit, a firm can safely assume that rivals will not change their output in response to a change in its output. Thus, with high r or k, dynamic conjectures approach the Cournot conjecture.

The theoretical studies presented above show that conjectural variations under dynamic settings will be negative and are bounded by Cournot behavior. However, Dockner's 94 result seems to rest on the fact that he imposes the Cournot-

Nash equilibrium concept in his model. Therefore, in his model, conjectural variations are bounded above by zero. This result however, does not square with the implications of the

Folk Theorem. As shown earlier, outcomes ranging from Cournot to collusive are a distinct possibility in the spirit of the

Folk Theorem. Within a group of oligopolistic industries, the nature of market imperfections differ substantially; therefore, verifying the theoretical results empirically in different oligopolistic industries becomes necessary. Karp and Perloff (1989, 1993a) have conducted such studies for the rice export market and coffee export market respectively.

Another study is by Roberts and Samuelson (1988) which deals with conjectures in advertizing decisions of firms in the US cigarette industry®.

Karp and Perloff employ a linear-quadratic model with respect to the rice and coffee export markets. In an oligopolistic market of n+1 firms, the linear demand curve is given by;

P t = a(t) - = a(t) - bQ^, (27) where p^ is the price in period t, q^t is the output of i'="' firm

Roberts and Samuelson develop a dynamic model of advertizing decisions by oligopolistic firms. In their model, the future advertizing reactions of rivals to the current advertizing decisions of a firm, as perceived by that firm, are defined as the dynamic conjectural variations. The empirical study of domestic cigarette manufacturing industry for the period 1971-1982 shows that firms do take into account the actions of their rivals in making advertising decisions. 95

in period t, 0% is the total exports of all firms. Each firm

incurs a constant marginal cost and a quadratic adjustment cost, (Yi + 0 .50iUit)Uit/ where Ô is the cost of adjustment parameter and u^,= q % ^ qit-i* Given this demand and cost

structure, they invoke the now familiar equilibrium concepts;

open-loop Nash equilibrium and closed-loop Nash equilibrium.

Assuming a discount factor p, in an open-loop Nash equilibrium strategy regime, firm i maximizes the discounted stream of profits given by;

(Pt - - (Yi + . (28)

In this dynamic setting, a firm maximizes discounted profits given the entire output path of other firms. Considering the corresponding matrix notation of equation (28) and taking first-order conditions, they show that the open-loop equilibrium satisfies the following condition:

K ,v, = - G)(I - ^G)]'e^à, (29) where is a matrix with zeros everywhere except that all elements of the i^^ row and column are b other than the (i,i) element, which is 2b. The dynamic conjectural variations parameter is given by v^, which is defined as dUj/dUi. G is a

(n+1) X (n+1) matrix that emerges from the first order conditions and establishes a linear relationship between q^ and qt_i. The elements of the column vector e^ are all zeros except the i^** element, which is 1. Equation (29) can then be solved for v^ and ô provided one has estimated the matrix G. 96

Karp and Perloff estimate the following adjustment equation to

recover the matrix G:

qt = g(t) + Gqt_i. (30)

The elements of the matrix K^ require the value of b,

which is obtained by estimating the demand function as given

in equation (27). Different methods have been used to

estimate equation (30). One is the classical unrestricted

estimation that uses Zellner's (1962) seemingly unrelated

equations (SURE) method. However, it is very difficult to

incorporate certain inequality constraints in the SURE method

that are important for the above dynamic system. For the

estimated system to make sense, the following three properties

are essential:

1. The system is stable, i.e. -1 < g^ + ng; < 1 and -1 < gi - < 1.

2. The market structure lies between collusion and price taking, i.e. 1 > v = f(G) > -1.

3. The adjustment parameter is positive, i.e. Ô = f(G, b) > 0

Such inequality constraints are imposed using Bayesian techniques. Geweke (1986) developed a method using Monte

Carlo numerical integration to impose inequality restrictions in a normal linear regression model. Bayesian techniques, however, assume that the error terms are normally distributed.

This assumption can be relaxed by using a bootstrapping approach.

The estimation procedure for the closed-loop model is similar; estimates of the demand parameter b, and the matrix 97

G are recovered from equations (27) and (30) respectively.

Values of Vi and Ô are found out by solving an equation similar to equation (29). Of course, as is illustrated now, the basic approach under the closed-loop Nash equilibrium strategy regime is quite different.

Under the open-loop equilibrium concept, firms decide the optimal output path at the start of the game and do not revise their moves contingent on what the other firms might do in each period. However, this assumption is too naive, and it is necessary to consider a closed-loop strategy, where the optimal output choices of a firm depend on time and the current state of the system. Therefore, Karp and Perloff apply the value function method of dynamic programming to derive the equilibrium conditions. If the value of the present and discounted future profits of firm i can be expressed as Ji(qt_if v), given the state of the quantity choices q^.i, and the market power parameter v, then firm i's dynamic programming profit maximization problem can be written in the following way;

= max (Pt - ~ (Yi + + pJi(gt,v) . (31)

Without matrix notation, the first order condition for firm i is shown as: dJi(gt,v) £jj^(gt,v) ■ Pt = 0i + (l+v)bg_-t + Yi + OiUit - P (32) "âgit ■

Karp and Perloff show that the corresponding condition for the 98

static model contains only the first two terms on the right

hand side. The above expression can be given a meaningful

economic interpretation. After rearranging the terms, it

means that in equilibrium, the sum of marginal cost and the

marginal adjustment cost must equal the sum of marginal

revenue and the discounted shadow value of a unit of export.

Converting this equation into matrix form, and taking first

order conditions, they show that the closed-loop equilibrium

satisfies the following condition:

[Kj + + (e,el + pXJÔJv, = [G']'^e,ôi = ylà,. (33)

As before, Ki is derived from the estimated demand equation

and G is derived from estimating the adjustment equation (30).

The rest of the terms are expressed in terms of the estimated

parameters of the model. Once again the values of v^ and

are extracted from this equation.

Karp and Perloff use this methodology to estimate the

degree of imperfection in the rice export market and the

coffee export market. There are reasons to believe that these

markets are oligopolistic in nature. The rice export market

is dominated by three countries; China, Pakistan and Thailand which account for half of all world exports, and their

respective exporting agencies control the supplies. Almost

93% of the total imports are affected by non-tariff barriers,

and there are high transactions costs such as brokerage fees

etc. Therefore, in their view, the rice market is a good candidate to test for market imperfection, where the rice 99 export market is treated as a triopoly with other exporting countries acting as fringe suppliers. The coffee export market too is similarly dominated by two countries, Brazil and

Columbia. The use of a dynamic model is prompted here also by the fact that there is a lag of 2 to 5 years between planting and the first harvest for coffee, and that both nations maintain substantial stockpiles. These features lead to nonlinear adjustment cost in production and storage. This is precisely the reason why the quadratic cost of adjustment term is included in the objective functions described above.

Assuming the discount factor p = 0.95, the classical,

SURE estimates of the conjectural variations for the coffee market were as following; v° = -0.84 and vj = -0.80, where superscripts refer to open-loop and closed-loop equilibria and subscript refers to classical estimates. These values are very close to the competitive level -1, the hypothesis that they could not reject. For rice, these estimates were v° = -0.37 and v° = -0.32, which again are close to the competitive level of -1/2. As explained in section 4.1, the competitive conjectural variations are given by the formula, -

1/n, where n is the number of firms. Here n = 2. Among the

Bayesian inequality constrained estimates, the median estimates based on absolute loss function are closer to the classical estimates. The open-loop and closed-loop estimates are -0.76 and -0.73 respectively for coffee, and are -0.35 and

-0.30 respectively for rice. The corresponding estimates 100

using the bootstrapping method are quite high too. The median

estimates based on thie absolute loss function are -0.86 and

-0.81 for coffee, and -0.40 and -0.35 for rice.

The simulation results based on these conjectural

variations estimates show that the steady-state output levels

in the closed-loop model are higher than those in the open-

loop model. Of course, the simulations also show that the

output level is a decreasing function of the conjectural

variations parameter in both the models; however, for a given

level of conjectural variation, steady state output levels are

higher for the closed-loop model than the open-loop model.

This difference is highest at a value close to 0.8. In

absolute terms however, this difference is very small. It is

only in the extreme cases of price-taking and collusive

behavior that the two have the same steady-state output

levels.

4.4 Retrospection

The review of literature has now reached the frontiers of research involved in modelling and estimating the degree of market imperfection in oligopolistic industries. Certainly, the research has come a long way since classical economists thought about the stationary state and Bowley introduced the conjectural variations concept. The conjectural variation concept was later refined by the idea of consistency in conjectures. Along the way, the theory of games offered a new 101

perspective of looking at oligopolistic markets. In

particular, the Folk Theorem opened up the possibility of

(im)perfect collusion among firms within the framework of

noncooperative game theory. At the same time, developments in

dynamic programming and numerical methods enhanced the scope

of game theory to incorporate structural dependency of firms.

Dynamic models can now be estimated that incorporate

production adjustment costs, and strategic interaction among

firms that characterize the oligopolistic industries.

The developments noted above leave many aspects

unfinished. Dockner's paper theoretically shows that the

steady-state open-loop equilibrium concept is the dynamic analog of the static Cournot equilibrium. He also shows that the limiting value of closed-loop conjectural variations is the Cournot conjectures for a linear-quadratic game. However, this result might be due to the fact that he imposes the

Cournot-Nash equilibrium concept on the model. Karp and

Perloff on the other hand, present an empirical model that nests collusive outcomes having positive conjectural variations to competitive outcomes that correspond to negative conjectures. Despite apparent oligopolistic features present in the rice and coffee export markets, their results show that these export markets are closer to price-taking behavior.

The proof of the pudding is in the eating. It is a worthwhile exercise to test the conclusions of Dockner. An industry might be selected to ascertain whether or not the 102 open-loop conjectural variations parameter corresponds to its

static counterpart. Both a static and an open-loop dynamic model can be estimated for this purpose. A circumstantially evident oligopoly market might be chosen to estimate a closed-

loop conjectural variations parameter using the linear- quadratic game. This would help knowing, whether the conjectural variations parameter turns out to be positive, contrary to Dockner's proposition. If it does, it will also confirm that the linear quadratic model presented by Karp and

Perloff does nest collusive outcomes. How critical the positive value of conjectural variations is to trade policies and New Trade Theories has already been discussed. In order to conduct such analysis, I have selected the German market for banana imports. The reasons behind the choice of the market, and how I propose to estimate the conjectural variations parameter for that market are discussed in the following chapter. CHAPTER V

THE BANANA EXPORT MARKET

5.1 Historical Background

Banana trade dates back to the mid-nineteenth century, when bananas were exported from the Caribbean islands to the southern coast of the United states. Trade, at that time, was highly irregular and risky due to uncertain supplies and perishability of the fruit, and the hazardous voyages of the ships. Later, due to an increase in US demand, export- oriented production was undertaken on the Central American mainland. Between 1870 and 1899, 114 banana companies were established in the US, however, only twenty-two lasted until the end of the century.

At the turn of the century there were three major companies: United Fruit Co. (UFCo), Cuyamel Fruit Co. and the

Standard Fruit Co. The UFCo was the largest among the three.

Its activities covered shipping, marketing and production of bananas. It was a truly vertically integrated banana multinational company (MNC) which enjoyed economies of scale.

It absorbed a number of smaller companies through share exchange and cash payments. In 1929, it bought the Cuyamel

103 104

Fruit Co. In the 1930s Sigatoka and Panama diseases presented a major threat to the banana companies. This prompted them to make heavy investments in piping and/or aerial spraying, for the application of a newly discovered pesticide, Bordeaux

Mixture. Fighting Panama disease meant flooding and fallowing the plantations. This was very costly too.

To overcome these problems, and fight UFCo effectively, the Standard Fruit Co. started planting disease resistant

Cavendish bananas. It further developed the revolutionary boxing technique to ship the bananas. This not only lowered shipping costs, but also improved the quality of the delivered bananas. Boxing techniques further helped UFCo to differentiate their bananas from the bananas of other companies. In the late 1940s, it introduced the 'Chiquita' banana, and advertised it extensively. UFCo also introduced adhesive labels that were applied to three fingers of each hand of bananas. The Standard Fruit Co. followed suit and branded its banana as 'Cabana', which later changed the name to 'Dole', after the company's acquisition by Castle & Cooke in 1968.

In an effort to diversify into new lines, a significant entry in the banana export market was made by the Del Monte

Corporation, a large multinational fruit and vegetable processor. In the early 1970s it began commercial operations in the Philippines and in Costa Rica. It acquired plantations from United Brands (The new name of UFCo.) in Guatemala. In 105 another development. Central American countries, led by

Panama, Honduras and Costa Rica, formed a Union of Banana

Exporting Countries (UPEB in Spanish). This union motivated the formation of an intergovernmental banana company,

Comunbana^. However, its activities have been limited to small-scale operations.

Looking back at the evolution of the banana trade over the last hundred years; it is certain that it has witnessed significant changes. The idea of shipping bananas from the

Caribbean to the US itself was a novel thing in the mid­ nineteenth century. The development of disease resistant varieties, boxing technique, and product differentiation by the banana companies are some of the major changes in this market. Of course, the improvement in refrigeration facilities has also contributed significantly to the banana trade. However, one feature of this market has remained strikingly permanent. The world market for bananas is dominated by a few MNCs. Except for the early years of formation of this market, there have been two or three firms that have dominated the market throughout. I turn now to address this issue.

The formation of UPEB and Comunbana was the outcome of the 'Banana War'. In March 1974, Panama, Honduras and Costa Rica unilaterally declared the imposition of a banana export tax of $1 per box. MNCs protested and eventually settled the matter by accepting an export tax that was less that $1 per box. Central American nations, however, felt the need to maintain higher prices and gain greater industry control by creating a united front against the MNCs. The end result was the formation of UPEB and Comunbana. 106

5.2 Structure of the Banana industry

The structure of the banana industry is, to a large extent, the legacy of its past. UFCo, the dominant firm in the first half of the century, is still dominant in the form of United Brands, selling Chiquita bananas. Though now owned by Castle & Cooke, the Standard Fruit co. is still its major competitor, selling under the brand name. Dole. Only the entry of Del Monte is a recent phenomenon. Even though bananas have free access to the US, figures for the year 1983 show that these three MNCs shared 87 percent of the total US market (World Banana Economy, 1983). Hallam and McCorriston

(1992) report that in 1990, these three firms accounted for 70 percent of the world market and 66 percent of the European

Community (EC) market. Even in the individual EC nations, markets are highly concentrated. While in Germany; Noboa,

Chiquita and Dole account for 72 percent of the market share,

75 percent of the supplies to the U.K. were accounted by the firms Geest and Fyffes (McCorriston and Sheldon, 1993b), which supply bananas from the African-Caribbean-Pacific (ACP) countries. In the spirit of the SCPP approach then, the export market for bananas is definitely oligopolistic in structure.

Market structure is also reflected in the pattern of production and costs. A look at the production and cost pattern too seems to reflect oligopolistic tendencies of this market. A report by UNCTAD (1978) showed that in 1971, out of 107 the average retail price, the gross return to domestic producers in the exporting countries was only 11.5 percent, the rest being captured by foreign enterprises that are involved in shipping, insurance, ripening and retailing.

Again, many of these activities are controlled by the MNCs.

The banana plant is a giant herb^; it has an underground stem

(rhizome) from which roots and leaves grow; the mass of leaves forming a compact cylinder above ground is called the pseudostem. The rhizome produces a number of suckers which are capable of producing successive crops. After harvesting a bunch, the pseudostem is cut down and another sucker from the rhizome that has been allowed to grow takes its place. It generally takes one year to 15 months before the plant is ready for another harvest. Thus, there is a gestation period of about a year and a quarter in the production process. This cycle continues for 5 to 20 years for a single plant, after which replanting is desirable.

On large commercial plantations, production is highly capital intensive. Capital investment is necessary for automatic cable conveyors, piping and/or aerial spraying of chemicals and boxing. As a result, the unit costs of production vary inversely with the plantation size. Bananas are an extremely perishable commodity. Once bananas are harvested, only 21 days are available before they become

The description of banana plant presented here is borrowed from a comprehensive study on the banana industry by Arthur e/a/. (1968). 108

unusable. Therefore, during those 21 days, bananas need

proper ventilation, refrigeration and careful shipping, all of

which is costly.

The above characteristics of the world banana export

market indicate that there are only a few firms that dominate

the world market. Second, economies of scale seem to play a

role in the production process. Third, the gestation period

of production lasting for about 15 months suggests a

possibility that costs of adjustment in production could be

very high. And fourth, there are high storage costs in terms

of refrigeration of bananas. Undoubtedly, these are the

features of a potentially oligopolistic market. However,

these descriptive features must be incorporated into a

theoretical model that will measure the degree of market

imperfection in this market. Therefore, a natural extension

of this is to apply a dynamic oligopoly model that estimates the conjectural variations parameter for this market.

5.3 Motivation for the Study

I have chosen the German market for banana imports for estimating the degree of market imperfection. As mentioned above, one reason for the estimation of degree of market imperfection in this market would be to verify whether or not the banana market behaves imperfectly as suggested by the stylized facts of this market. It would be a pure 109 intellectual exercise in itself. However, there are other important motivations for this study.

First, estimation of the degree of market imperfection in the banana export market will bring us a step closer to ascertaining the validity of the New Trade Theories (NTTs).

Their explanations of the complementarity of inter-industry and intra-industry trade, existence of MNCs, pricing-to-market behavior, and the possibility of newer sets of trade policies rest on the assumption that export markets are imperfectly competitive. Second, the results of this study will affect the way in which effects of trade reforms are being measured in the banana export market. This is very important because trade in bananas is very significant. Certainly, the mundane image of bananas is belied by the world trade in bananas that exceeded 5 billion US dollars in 1991. Among importing regions, the EC and the US are the two largest importers. Up until June 1993, the EC member nations have applied a range of restrictions on Banana imports. While Germany allowed free entry of bananas, the 'BeNeLux' countries applied a 20 percent tariff on all imports, and others allowed preferential access to banana imports from their former colonies, namely the

African, Caribbean and Pacific (ACP) countries. Therefore, there was wide disparity in prices in European countries. As reported in McCorriston and Sheldon (1993a), if the 1987 retail price of banana in Germany is indexed to 100, the price of bananas in Italy turned out to be 211. 110

However, since 1 July 1993, the EC has announced its new common policy on banana imports. Under the new scheme, an import quota of 2 million tonnes, with a levy equivalent to a

20 percent tariff rate is imposed on the non-preferential banana exporting countries (the Dollar countries). However, any additional imports from these countries are faced with a prohibitive tariff rate of 177 percent^. Numerous studies have appeared in the literature that analyze the options available to the EC, and the corresponding gains and losses to different parties involved in it\. However, these studies ignore an important feature - the market structure of the world banana export industry. All the studies have implicitly assumed that market structure is perfectly competitive. Under perfectly competitive markets, the effects of a quota are considered equivalent to the effects of a tariff. If the market structure is in fact oligopolistic, then the effects of the new banana regime might be quite different. It has already been noted in earlier chapters that the effects of a tariff and quota are not necessarily equivalent under oligopoly, since the latter affects the firms' behavior itself. Indeed, recent work by Hallam and McCorriston (1992),

3. The actual policy is much more complicated than this. Apart from the quota on Dollar countries, preferential access to the former colonies of the importing countries is still maintained. A detailed explanation of the policy can be found in Read (1994).

4. As reported in McCorriston and Sheldon (1993a), these include Borrell and Cuthbertson (1991), Borrell and Yang (1990,1992), Fitzpatrick and Associates (1990), Hallam and McCorriston (1992) and Matthews (1992). Ill and McCorriston and Sheldon (1993b) also implies that by assuming perfect competition welfare studies are likely to over-estimate the welfare effects following trade policy changes. Thus, estimating the degree of market imperfection in the banana export market is very critical to this issue.

Finally, estimation of the degree of market power is important to businessmen and governments from a legal point of view. An anti-trust suit was lodged against UFCo by the US

Justice department in 1954, for violating the 1890 Sherman

Anti-trust Act and the Wilson Tariff Act (Read, 1986). The suit alleged that the company had monopolized the banana industry by restricting the international trade in bananas.

More recently, the EC Commission gave a ruling against the

United Brands for misusing its dominant market position in the

EC banana market. A fresh Commission enquiry, again involving

United brands, began in 1990 (McCorriston and Sheldon, 1993b).

In such anti-trust cases, professional opinion can be sought from economists. Based on the studies that estimate the degree of market power, economists can testify, whether or not the industry/firms is/are monopolistic in structure.

Having described the motivation for this study, it is easy to understand why the German market for banana imports is chosen for the study. First, as mentioned above, just like the global market for bananas, the German market for bananas too is dominated by three large multinationals (Chiquita, Dole and Noboa). Second, up until June 1993, among the EC member 112 countries, only Germany had a free access to banana imports.

Therefore, it is an ideal market for testing whether or not markets can be imperfectly competitive in structure, in spite of the absence of any tariff and non-tariff barriers. Third, with the implementation of the common policy on banana imports by the EC, it is the German market that has been hit the hardest in terms of effective quota restrictions. This was inevitable because, unlike other EC countries such as the U.K. and France, Germany never allowed preferential access to ACP bananas. Again, as mentioned earlier, knowing the degree of imperfection in the German market is critical to the evaluation of the welfare changes caused by the recent common policy on banana imports. The specific implications to the

German market, based on the results of this research are discussed in the final chapter.

5.4 Methodology

It must be admitted at the outset that the conjectural variations approach that I have used to estimate the degree of market power is subject to some well merited criticism.

Prescribing games that correspond to a particular value of conjectural variations is extremely difficult. To that extent, one might consider conjectural variations as being ad hoc in nature. However, it must be noted that their values are determined endogenously in the model. They give yardstick values that correspond to many familiar cases such as perfect 113 competition, collusion and Cournot-Nash. Treated as an ordinal measure, the intermediate values capture the idea of varying degrees of competition. Finally, in the absence of any alternative method that measures the degree of market imperfection, conjectural variations approach is the best possible method®.

In the remaining chapters, therefore, I discuss in detail, the empirical procedure followed to estimate the conjectural variations parameter, comparisons of the various methods used, and conclusions and future direction to this kind of study. The following methodology was followed in the remaining chapters;

Estimation of the degree of market power in the German market for banana imports using a static model that acts as a benchmark study. For this purpose, I have used a static structural model on the lines of Bresnahan (1982) approach. This involved an econometric estimation of the demand functions and the first order conditions.

Estimation of the degree of market power using a linear- quadratic dynamic model with open-loop strategies.

Use of the same linear-quadratic framework with feedback strategies. While the quadratic adjustment equations

5. Dixit (1986, p;107) wrote, dynamic models that are equally versatile, and usable in applications, seem far off. In the meantime, the static conjectural variations model will go on being used, and it seems worthwhile to provide a unified treatment of it." Karp and Perloff (1991, p;2) opined: "The index is designed to describe rather than explain the market outcome. A given mark-up may be consistent with a number of different games..." 114

captured the production adjustment and storage costs, the state contingent export choices captured the strategic interaction among the banana MNCs.

Based on the estimates of the conjectural variations parameter derived from the three methods, inferences are made about the degree of imperfection in the banana export market.

The static model and the open-loop dynamic model are compared, and the equivalence of the two approaches is verified.

The open-loop and feedback estimation results are compared, and their divergence from the corresponding results of Karp and Perloff is discussed.

Attention is given to the ways in which techniques in this study can be improved and/or replaced by some other more appropriate method of estimation.

Possibility of extending the analysis to other markets is explored. CHAPTER VI

EMPIRICAL PROCEDURE

6.1 Data Description and Sources

Earlier chapters of the thesis have specified the purpose of the present research, the choice of the export market, and the selection of theoretical models. This chapter describes the empirical procedure used to estimate the degree of market power enjoyed by multinational firms in exporting bananas to the Federal Republic of Germany. First, data requirements, data sources, and the definition of variables used in the empirical analysis are discussed. This is followed by a discussion of the execution of static and dynamic models of oligopoly, and the results from using both procedures.

The static model of oligopoly requires the estimation of

German import demand for bananas at the retail level, and the estimation of the first order profit maximization condition for the banana supplying multinational firms. For this purpose, annual data on aggregate quantities of bananas imported into Germany, retail prices, and import prices^ were

1. Import price refers to f.o.r. price charged by importers to wholesalers at Hamburg port.

115 116

collected for the period 1970-1992 from the Food and

Agriculture Organization (FAC) publications: World Banana

Economy (1983) and Banana Statistics (1992). Exogenous

demographic variables were collected from Warnes (1993), and

the International Labo(u)r Office (ILO) publication: From

Pyramid to Pillar (1989) = . Other exogenous variables used for

the static model are a time trend and squared time trend. A

consumer price index, used for deflating the nominal

variables, was collected from the International Monetary Fund

(IMF) publications: International Financial Statistics (1994),

and International Financial Statistics Yearbook (1992)^.

The dynamic model also requires estimation of the demand

function. The relevant data requirements are, therefore, the

same as for the static model. In addition, the dynamic model

requires estimation of a system of Markov equations, where banana exports of multinational firms are regressed on the

lagged values of their own exports to Germany and the lagged values of exports of other multinational firms. Quantities of

bananas exported to Germany by the individual multinational

firms were not available directly; however, market shares of multinational firms in the German banana market were available

for a certain number of years. These market shares were

2. Total population figures were available for every year; however, population data for age 65-and-above, was reported as a percentage of total population every five years. Other values were interpolated.

3. The base year for the consumer price index is 1985; i.e. CPl85=100. 117 collected from the magazine. International Fruit World (1988), and FAO publications: World Banana Economy (1983) and The

World Banana Economy (1986). A complete set of data for the above mentioned variables is presented in Appendix A. Table

6.1 gives definitions of the relevant variables.

6.2 The Static Model

In order to estimate the static model, I have followed an approach similar to that of Bresnahan (1982). The intention here is to find an industry-wide, average parameter of market power, using a standard structural econometric method. As discussed earlier in Chapter III, the market power parameter is constrained theoretically to lie between 0 and 1; 0 indicating perfectly competitive behavior, and 1 indicating perfectly collusive behavior. If there are n firms in the market, and if they behave in a Cournot-Nash fashion this parameter assumes the value 1/n.

6.2.1 Model Description:

A linear demand function was specified for the German banana market that takes the following form:

Qt = Oo + OjPt + agZt + «3? + a^TT + G;. (1)

Qt represents the total quantity of bananas imported annually into Germany over the period 1970-1992. Pt represents the real retail price of bananas; is the German population aged

65-and-above, and T and TT are the trend variables. 118

Table 6.1

Description of Variables

Variable Description Pt Real Retail Price of Bananas in German Market: DM/tonne®.

Qt Total Quantity of Bananas Imported into Germany: thousand-tonne/year.

qit Quantity Imported into Germany by Bonita; thousand-tonne/year.

qzt Quantity Imported into Germany by Chiquita; thousand-tonne/year.

q,t Quantity Imported into Germany by Dole ; thousand-tonne/year.

qt Column vector of & qat*

qit-i One Year Lagged Quantity Imported into Germany by Bonita.

q2t-i One Year Lagged Quantity Imported into Germany by Chiquita.

qst-i One Year Lagged Quantity Imported into Germany by Dole.

qt-i Column vector of qit_i/ qat-i & qat-i- T Time Trend = 1, 2, ....

TT Squared Time Trend = 1, 4,

Wt Real Import Price of Bananas in German Market ; DM/tonne

Zt German Population: Age 65 & above.

“a metric ton. 1 metric ton = 1000 kg = approx. 2200 Ib = 5 5 cartons of 40 lbs net. 119

Conspicuously absent explanatory variables are the prices of substitute fruits, income and the total population of Germany.

As reported in the publication: Banana

Handbook (1985), the cross-price elasticity of demand for bananas with respect to other fruits is very low, in fact, it is 0 in Germany. Huang (1993) in his study of the US demand for food, estimated the cross price elasticity of bananas with respect to the price of oranges to be -0.08. Thus, the choice of bananas in consumption is a matter of customer preference, and they do not accept other fruits as ready substitutes. The income measures too did not affect banana consumption in

Germany. The World Bank publication also reports that banana consumption is responsive to income only in countries where per capita GNP is less than $1500 per year. In countries like

Germany, which exhibit a very high per capita income, banana consumption has reached saturation level with respect to income variations. Also, the size of the German population has been constant over the time period under consideration.

However, the German population is aging over time, and, therefore, population in the age cohort 65-and-above is growing. Interestingly, a report by the Commission of the

European Communities (1976) states that bananas are regarded as a health food, and they are an important part of the diet of the sick and very old. This justifies the inclusion of the variable Zt in the demand equation. 120

Given the demand function, perceived marginal revenue is

given by the term;

MR; =I\ + XQt [dP^/dQJ. (2)

If firms demonstrate Bertrand behavior, the parameter X will

turn out to be 0; if they demonstrate collusive behavior, it

will turn out to be 1. X will take the value 1/n if firms

behave in a Cournot-Nash fashion. Marginal cost is assumed to

take the following functional form:

M C t = Yo + YiWt + Y z ? ' (3) where is the import price of bananas which is thought of as

a proxy for the cost of bananas. Decreases in marginal cost

due to technological advances in shipping, storage etc. get

captured in the trend variable T. However, marginal cost is

assumed to be constant with respect to output. It was noted

in an earlier chapter that this industry is characterized by

high fixed costs; therefore, given constant marginal cost it

has decreasing average cost. As long as marginal cost is

below average cost, the assumption of a constant marginal cost

of supplying an additional carton or additional tonne of

banana is justified.

The profit maximizing condition is given by the

condition: MR^ = MCf Substituting in for MR^ and MC^, and

rearranging terms, we get the following functional form:

Pt = Yo + YiWt + YzT + YaOt + Eg, (4) where Y3 = -X[dPt/dQt]. It is also evident from equation (1)

that [dPt/dQt] = l/Oi. Therefore, the market power parameter 121

is nothing but the product of two regression coefficients with

a negative sign:

X = -OiYa* (5)

6.2.2 Regressions and Bootstrapping:

Since equations ( 1 ) and ( 4 ) represent a simultaneous equations system with Pt and Qt being determined simultaneously, a two stage least squares estimation procedure was used to estimate the system^. A three stage least squares procedure was also employed; however, no improvement over the two stage least square method was observed. Table 6.2 presents the results of the estimation of these equations.

Table 6.2

Estimation of the Static Model.

Qt = 684 - 0.32Pt + 106Zt - 80T + 4.2TT (1') (1.11)* (-3.6) (1.80) (-11.4) (13.0)

R-square between observed and predicted = 0.95 Dl=0.77 < DW(23,4)=1.48 < D„=1.53 at 1% significance.

Pt = 502 + 1.38Wt - 21.2T + 0.91Qt (4') (1.34) (4.82) (-2.28) (3.4)

R-square between observed and predicted = 0.46 Dl=0.86 < DW,23,3)=1 • 35 < D„=1.4 at 1% significance.

'Figures in parenthesis refer to t ratios.

4. Instruments used were import price, population aged 65-and-above, time and time squared. The demand equation is exactly identified, and the first order condition over identified. 122

Though the Durbin-Watson ratios lie in the inconclusive range for rejecting the hypothesis of the existence of autocorrelation, it is also clear that they are very close to the upper bound where one can reject the hypothesis of the existence of autocorrelation. In the above regressions, a.^= -

0.32 and y3= 0.91, and both are statistically significant.

Therefore the market power parameter for this industry is X =

-(-0.32)(0.91) = 0.29. The German market for bananas is dominated by three firms that account for a market share of more than 75%. If the rest of the firms are treated as fringe suppliers, then this market can be described as an effective triopoly. In that case, the Cournot-Nash market power parameter (X=l/n) turns out to be 1/3. The estimated value of

0.29 is much closer to this number than to 0, the value of X that describes competitive behavior.

For the purposes of hypothesis testing, I conducted a bootstrap procedure (Efron; 1979) to estimate the standard error of the market power parameter. This procedure enables us to generate a distribution for the parameter in question, and to test its robustness. The test can also show the probability of that parameter lying outside the theoretical range.

The bootstrap procedure is a computer-intensive, nonparametric approach to statistical inference based on data resampling. It involves the regression errors for each observation; randomly sampling the normalized errors with 123 replacement; generating a new dependent variable by using the normalized, resampled errors, and, finally, regressing the newly created dependent variable on the explanatory variables®. For the present model, this procedure was performed 1000 times on both equations (1) and (4), and X was then calculated each time. Using these 1000 values of X, its mean and standard error is easily calculated, which helps conduct hypothesis testing. On the basis of this procedure,

I could reject the hypothesis of perfect competition and collusive behavior, but could not reject the hypothesis of

Cournot-Nash behavior. The results of the bootstrap procedure, and hypothesis testing are summarized below in

Table 6.3. Figure 6.1 too gives an idea of the distribution of X. It shows that values of X are concentrated around its mean value, as reported below.

Table 6.3

Bootstrapping* of the Static Model.

% of (X<0 or X>1) Mean value of X Std. Error 0.003 % 0.27248 0.13

Hypothesis Test Stat Remark Ho: X=0, Hi: X>0 2.1 Reject Ho at 5% & 2.5%. Hg: X=l, Hi: X<1 -5.6 Reject Ho at all levels. Hq:X=.33, Hi:Xx.S3 -0.7 Cannot reject Ho at any level.

*1000 iterations performed.

5. Judge ef aZ. (1988) give a good explanation of this procedure. 124

0.05 0.25 0.45 0.65 0.85 A

Figure 6.1

Distribution of X. 125

6.3 The Dynamic Model

There are three outstanding features of the dynamic model

that are ignored in the static model. First, the dynamic

model considers an objective function for firms that includes

not only present profits, but also discounted future profits.

Second, it incorporates the possibility of production

adjustment costs by including a quadratic cost of adjustment

term in the objective function. Third, game-theoretic,

strategic interaction among firms is captured in the first-

order, profit-maximizing conditions.

6.3.1 Summary of the Procedure:

Before I discuss the estimation procedure in detail, a

flowchart of the empirical procedure is provided in Figure

6 .2 :

First, a dynamic objective function (profit) is set up

for individual firms. The nature of the objective function

varies, depending on the assumed nature of firm behavior (i.e.

open-loop or feedback).

Then, profit maximizing first order conditions (f.o.c.)

are derived from this function. These f.o.c. contain two

important parameters : the slope (b) of the demand function,

and the lagged coefficient matrix (G) of the Markov equation, which is obtained by regressing exports of a firm on the

lagged values of its own exports and lagged values of exports

of other firms. 126

Estimate Demand Estimate Markov Function Equation

use use lagged demand coefficient di fferenti ate slope Matrix G

First Order Condi tion

solve simultaneous equati ons 1

Derive V and S

statistical test

Taylor Expansion Bootstrapping

»WW!H»1WIW6

Figure 6.2

Flowchart of the dynamic model. 127

These coefficients are recovered by estimating the demand function and the Markov equation. Values of these coefficients and an assumed value of the discount factor (P) are substituted into the f.o.c.

After some transformations, the f.o.c. can be expressed as a system of two simultaneous equations with two unknowns;

V, the conjectural variations parameter, and Ô, the cost of adjustment parameter. The simultaneous equations are then solved to obtain the values of V and Ô.

Finally, for the purpose of hypothesis testing, a standard error is calculated for V using the Taylor Expansion method. Another approach followed is to bootstrap V and Ô, and find out their mean and standard deviation.

6.3.2 The Objective Function and the F.O.C.:

The top three firms operating in the German market for banana imports are viewed as players engaged in a strategic game. The objective of each firm is to maximize the sum of present and discounted future profits. The exact form of the objective function, however, depends on the behavioral assumption made about the firms.

Open-loop Strategy: As explained in Chapter IV, if firms follow an open-loop strategy, they choose a time-path of the optimum quantities of exports at the beginning of the game, assuming the export path of other firms to be constant. The objective (profit) function of an individual firm over an 128

infinite time-horizon for this kind of behavior is assumed to take the following form:

- 8; - - (w^ + O.Sô^u^Ju^j , (6) where is the German retail price of bananas in period t ,

is the quantity of bananas exported to Germany by the i^*’ firm in period t, u^^ is the change in exports of firm i from period t-1 to period t , and p is the discount factor. The term (0i

+ 0.5())iqit)qit represents the quadratic production cost, and (%

+ 0.50iUit)Uit represents quadratic production adjustment cost.

The inverse demand function is assumed to take a linear

form:

Pt = a - bèg^t = a - jbQt • (7) i«l

Converting the objective function (6) into matrix form, and deriving the f.o.c. gives the following matrix equation (see appendix B ):

= [G-^I - G){I - ^G)]'e,à, . (8)

In deriving the matrix equation (8), no symmetry assumptions are made; however, for analytical tractability symmetry is introduced at this stage. That is, it is assumed that

Vjjj. = y V i, j; = Ô V i ; and G is symmetric such that elements G^^ = V i=j; G^^ = V ixj .

Feedback Strateav: Under the open-loop strategy concept, firms decide the optimal export path at the start of the game and do not revise their moves contingent on what the other 129 firms might do in subsequent periods. However, this assumption is too naive, and it is necessary to consider a subgame perfect feedback strategy, where optimal export choices depend not only on time but on the current state of the system. The value function method of dynamic programming is used to set up the dynamic objective function for this kind of firm behavior. If the value of the present and discounted future profits of firm i can be expressed as Ji(qt-i^Vi), then firm i's dynamic programming profit maximization problem can be written in the following way;

max[(Pt - 6i - (cu^ + + ^Ji{gt,V^)] .(9)

Converting this objective function into matrix form, and deriving the f.o.c. gives the following matrix equation (see

Appendix C ):

[K, + + (e,e', + pXJôj/y, = [G']-^e,ô, = . (10)

Again, no symmetry assumptions are required for deriving this condition; however, the symmetry requirements, considered for the open-loop case are introduced here too.

6.3.3 Demand Slope and Markov Equation:

As shown in Appendix B and Appendix C, matrix equations

(8) and (10) have two unknowns: V and Ô. The rest of the matrices in these equations are expressed in terms of the demand slope parameter: b, and the Markov process lagged 130 coefficient matrix: G. For example, matrix Ki is expressed in terms of the parameter b, matrix is expressed in terms of matrix G, and matrix is expressed both in terms of the parameter b and matrix G. Therefore, it is necessary to estimate the matrix G, and recover the parameter b for solving matrix equations (8) and (10).

The demand parameter b, is really the slope of the inverse demand function described in equation (7). In section

6 .2, the demand function for bananas has already been specified and estimated. The inverse of the slope of that demand function is used as the value of b. Appendix B and

Appendix C show that matrix G establishes a relationship between q^ and q^.i given by: q^ = Gq^.i. To recover the matrix

G, this relationship is estimated by using Zellner's (1962) seemingly unrelated equations (SURE) method. The model requires restricting the elements of the G matrix such that own lagged coefficients (g^) are the same for the three firms, and lagged coefficients of other firms (g%) are the same for the three firms. The F statistic for imposing these restrictions is 1.6, and the critical value for testing the restrictions, F (7,36) is 2.3 at the 5 percent significance level. Therefore, the restrictions cannot be rejected. Since the restriction could not be rejected, they were imposed, and then regression equations were estimated. Table 6.4 presents the results of the regression estimation. 131

Table 6.4

Banana Export Adjustment (Markov) Equation.

Bonita: q^^ Chiquita :qjt Dole: qst Time trend 2.43 3.85 2.36 (6.10)’ (5.20) (4.95) Own lagged exports 0.05376 0.85376 0.85376 (gi) (22.97) (22.97) (22.97) Lagged exports of -0.03485 -0.034Ô5 -0.03485 other firms (gj) (-3.22) (-3.22) (-3.22) R-square 0.97 0.83 0.51 Durbin-Watson 2.6 1.4 1.3 Durbin's h -1.53 1.15 1.47

'Figures in parenthesis refer to t ratios.

The Durbin-Watson test is not valid for the estimated equations since they have a lagged dependent variable as one of the explanatory variables. For this reason, Durbin's h test was performed. For all three equations, the test statistic is less than the critical value of ±1.645 at the 5 percent significance level. Therefore, the hypothesis that there is no first-order autocorrelation cannot be rejected.

Further, the coefficients g^ and g% do satisfy the required stability conditions, i.e.: (-1 < gi + ng^ < 1) and (-1 < g% - gj < 1). The above equations were regressed on 16 observations. While market share data were not available for some of the earlier years of 1970s, the last three years had to be excluded because of an unusual export trend generated by the possibility of the European Community (EC) announcing its common import policy for bananas. The EC was deliberating on setting common quotas and tariffs on banana imports by the end 132 of 1992. In the light of this, banana multinationals started exporting large amounts of bananas to Europe, expecting that fixing of quotas might be influenced by the amounts imported during most recent years. The excessive exports of bananas in the last few years then, did not reflect the strategic behavior of firms among themselves, but was the result of an anticipated exogenous policy change.

6.3.4 Solving for V and Ô:

Having estimated the symmetric G matrix, and the slope of the inverse demand function, and having assumed V^j = V, =

Ô, matrix equations (8) and (10) can now be solved for V and

Ô. Both matrix equations now represent a system of three equations with two unknowns. It can also be noted that the rank of the matrices in (8) and (10) is two, therefore, only the first two equations need to be solved simultaneously to recover the values of V and Ô (see Appendix D). It turns out that V in both the cases is a function of G alone, and Ô is a function of both b and G. For the open-loop case, a unique solution exists for V; however, for the feedback case, there are two solutions that emerge from solving a quadratic equation in V. One solution is close to the open-loop value, and the other is infeasible (V < -0.5 or V > 1). Therefore, only the feasible root is chosen as the solution.

The solutions to both the open-loop and feedback strategies satisfy the restrictions required by theory, i.e.; 133

-0.5 g V à 1 and ô > 0. No ready standard errors were

available for V, since V does not emerge directly from a

regression equation. However, standard errors were calculated

for V using the Taylor expansion method®. The results of this

procedure are summarized in Table 6.5. The subscripts of V:

o and f, refer to open-loop and feedback, and the superscript

c refers to classical estimates. These results are named the

classical estimates to distinguish them from the bootstrap

estimates that are discussed subsequently.

Table 6.5

Classical Estimates of Dynamic Model.

V: àt VS ... 0.08 0.187 o.io 0.191 (0.36)* - (0.33) -

Hypothesis Test Stat Remark H(,;V==-0.5, Hi:V:>-0.5 1.6 Cannot reject Hq at 5% or 1%. Ho:V:=0 , 0.22 Cannot reject Hq at any level. Ho:V^=l, Hi:V:-0.5 2.13 Reject Ho at 5% & 2.5%. Ho:V^=0, Hi:VS ;^0 0.6 Cannot reject Ho at any level. Ho:V^=l, Hi:V%

‘Figures in parenthesis are standard errors.

Table 6.5 shows that both the values of V are positive; however, the hypothesis of Cournot-Nash behavior cannot be re­ jected. The hypothesis of collusive behavior is rejected for

6. I benefitted from an e-mail discussion that I had with Professor Perloff on how to employ the Taylor expansion method to calculate standard error. Further, a copy of the original program written by Professor Perloff was made available to me by Professor Sheldon. 134 both types of firm behavior. Under the open-loop strategy assumption, the hypothesis of perfect competition cannot be rejected. Only in the case of feedback strategies, can the hypothesis of perfect competition be rejected.

6.3.5 Bootstrapping V and Ô ;

The bootstrapping method can be used as an alternative method for estimating V and Ô, and performing hypothesis testing. Section 6.2 has already explained the bootstrapping procedure. In the present context, this involves bootstrapping the Markov equation, and generating numerous values of g^ and g^. These values, in turn, are used to calculate V and ô. From the numerous values of V and Ô, their mean values and standard errors are calculated. However, the bootstrapping procedure that is followed here is a little different than the usual one reported in section 6 .2.

Freedman and Peters (1984) show that when lagged endogenous variables are used as explanatory variables, and there is no autocorrelation, one can bootstrap by resampling the rows of the original data. The Markov equation has lagged endogenous variables as explanatory variables, and Durbin's h test shows that there is no first-order autocorrelation. Therefore, bootstrapping was done by resampling the original data with replacement.

Table 6.6 gives the results of this procedure.

Resampling and regressing the data 1000 times with 135

replacement, the inequality restrictions on and gg, and V

and Ô are imposed, and constrained estimates of V and Ô are

derived. While estimates of V are a little lower than the

classical case, the relative position of open-loop and

Table 6.6

Bootstrapping* Dynamic Model.

Open-loop Feedback Mean values of V & ô Vg=0.06, 02=0.22 V|=0.17, 01=0.23 Standard error 0.33, 0.13 0.30, 0.18 Values Unstable 0.2% 0 .2% rejected Ô < 0 2 .8% 0 .0% because V < -0.5 2 .8% 2 .8% V > 1 8.7% 8.7%

*1000 iterations performed. Superscript B refers to Bootstrap estimate.

feedback V is maintained. The standard errors of V show a similar pattern. Similarly, values of Ô are higher than the classical case, and the relative position of open-loop and

feedback Ô is maintained. Standard errors of Ô are also calculated based on bootstrapping the Markov equations that generate multiple values of g^ and g^. However, Ô is a

function not only of g^ and but also of b, the demand slope. Thus, simultaneous bootstrapping of the b is also necessary. However, for the present analysis b is assumed to be given, and bootstrapping performed only on the Markov equation. Therefore, it would be correct to describe the standard errors of Ô as pseudo standard errors. 136

Having bootstrapped the values of V, it is an interesting exercise to look at how the V are distributed over the feasible range (Table 6.7 and Figure 6.3). The distribution of open-loop V has a thicker left tail while the distribution of feedback V has almost symmetric small tails. The concentration of values is in the interval (-0.25 < V < 0.5).

The percentage of V lying in this range is nearly 70 percent for the open-loop V, and nearly 79 percent for the feedback V.

Similarly, Figure 6.4 shows that the value of Ô is concentrated in the interval 0.1 to 0.3. The highest frequency being in the range 0.1 to 0.2.

As mentioned in Chapter IV, game-theoretic intuition would tells us that values of V must converge when markets are perfectly competitive or (perfectly) collusive, i.e. the

Table 6.7

The Distribution of V

Range Open-loop Feedback -0.5 £ V < -0.25 19.0% 5.7% -0.25 a V < 0.5 69.4% 78.5% 0.75 aval 4.0% 4.6%

values of and Vf must be the same at V = -0.5 and V = 1.

In a perfectly competitive market (where n-><») firms are mere price takers, and have no effect on the behavior of other firms or the market price. Therefore, open-loop and feedback behaviors collapse into one. Similarly, in the case of a 137

perfectly collusive or monopoly market, there is no strategic

interaction among firms since firms either form a cartel or

there is only one firm in the market. Therefore, once again,

open-loop and feedback behaviors collapse into one. In short,

in a perfectly competitive or monopolistic market structure,

firm(s) is/are playing a game against nature and not against

each other. This intuition then, can be verified by looking

at the bootstrapped values of V. In Figure 6.5, selected values of Vj, are plotted on the x-axis, and corresponding values of Vf (and too) are plotted on the on y-axis. The

figure shows that and Vf do converge to each other at the values -0.5 and 1, and for other values, Vf is higher than Vq.

Finally, I present the hypothesis tests conducted on the bootstrap estimates of V and Ô. In the classical case, under open-loop behavior, the hypothesis of perfect competition was not rejected. However, under feedback behavior, the hypothesis of perfect competition was rejected. For the bootstrap estimates, this hypothesis is rejected under both open-loop and feedback behavior. The hypothesis of collusive behavior is also rejected in both the cases. Only the hypothesis of Cournot-Nash behavior is not rejected. Calcu­ lation of the pseudo-standard error also allowed a test hypothesis on 6. For both behavioral assumptions, the hypothesis of 0=0 was rejected. This shows that, even though the absolute value of the parameter is small, it is statistically significant, and the cost of adjustment in 138

35 T

'0.375 -0.125 0.125 0.375 0.625 0.875

îVoBVf

Figure 6.3

Distribution of Vs. 139

50 ••

40 ■■

K 30 ■■

20 ■■

10 ■■

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95

IdoHdf

Figure 6.4

Distribution of ôs. 140

Ü i Vo J Vf

-0.4 •

- 0.6 - 0.5 - 0.25 0 0.25 0.5 0.75 1 Selected values of Vo

Figure 6.5

Convergence of and Vf. 141 production are important. The tests are summarized below in

Table 6 .8.

Table 6.8

Hypothesis Testing for Bootstrapped V & ô.

Hypothesis t-ratio Remark Ho:V“=-d.5, Hi:V“>-0.5 1.7 Reject Ho at 5%. Ho:V^=d, H^rVS^^O Ô.17 Cannot reject Ho. Ho:V^=l, Hi:V:0 1.74 Reject Ho at 5%. Ho:V$=-Ù.5, Hi:Vg>-0.5 2.2 Reject Ho at 5% & 2.5%. Hq:V^=Ô, Hi:V| xO 0.56 Cannot reject Ho. Ho:V^=l, Hi:V;0 1.76 Reject Ho at 5%.

In summary, the empirical procedure was conducted as: the estimation of a demand and Markov equation, setting up and differentiating the objective function, solving the first order condition for V and Ô, and finally, performing statistical tests on them. In the next chapter, I discuss whether or not the results of this chapter concur with the theoretical models, summarize, and provide future directions for this kind of study. CHAPTER VII

CONCLUDING DISCUSSION

7.1 Inferences and Policy Implications

The present study was based primarily on three objectives. First, by incorporating imperfect competition in their analysis, the New Trade Theories (NTTs) have dominated the field of during the last two decades. It seems important, therefore, to verify empirically the assumption of imperfect competition in international markets. Second, many studies have been carried out to assess the degree of market power in domestic markets, based on static models; however, as has been elaborated in Chapter IV, using dynamic models is perhaps more appropriate. Therefore, in this study, the aim has been to estimate, compare and contrast static and dynamic models of market imperfection for a given industry. Finally, estimation of the degree of market imperfection has important, real-world policy implications.

In particular, it has been timely to conduct a study on the export market for bananas, in the light of the adoption of the common banana import regime by the European Community (EC).

142 143

The empirical study and its results, as reported in

Chapter VI, show that the objectives, as laid out above, were accomplished. Both the static and dynamic models reject the hypothesis that the German banana market is competitive, but do not reject the hypothesis that firms behave in Cournot-Nash fashion. In fact, the classical estimate of the dynamic conjectural variation of the feedback model is 0.2, which is beyond Cournot-Nash behavior. Thus, the present study does substantiate empirically, the presence of market imperfection in a particular export market. Therefore, in the case of bananas, the NTTs have passed the litmus test. It must be mentioned, however, that the original work of Karp and Perloff on the coffee and rice export markets showed those markets to be competitive. One reason for the divergence of our results may lie in the fact that they consider countries as the optimizing agents, and the present study focuses on firms as the optimizing agents. Coffee and rice exports of the producing countries are undertaken by government run federations or marketing boards that are not necessarily maximizing profits. The overriding considerations for these boards might be to maximize revenues or foreign exchange, and/or maintain high employment, that leads to more competitive outcomes. In perspective, therefore, the present study also brings out the differences in market outcome resulting from differences in firm objectives and behavior. 144

Another important aspect of this study was to check the validity of using a dynamic model. A dynamic model is recommended because two kinds of intertemporal interdependencies are present in a market. One is the dynamic production adjustment costs, and the other is the dynamic strategic interaction among the firms. The estimates of the adjustment parameter ô are positive in both the open-loop and feedback models. The bootstrap estimates, and the consequent calculation of the pseudo-standard errors for Ô enabled me to show that these estimates are significantly different from zero. Thus, the results support the existence of dynamic adjustment costs.

The Folk Theorem suggests that, in a dynamic setting, the strategic interaction of firms could lead to (im)perfectly collusive behavior. This implies that estimates of conjectural variations, modeled in a dynamic setting should turn out to be more collusive than one derived from a static model. The present study does substantiate this. The static model, unable to capture dynamic aspects, generates a value of the conjectural variations parameter (using both classical and bootstrap methods) which is lower than the Cournot-Nash value of 0.33. However, in the dynamic model, and especially in the feedback strategies, the value of the conjectural variations parameter clearly exceeds the Cournot-Nash value of 0, indicating that market is more imperfectly competitive than what it is thought to be using the static model. It implies 145

that the strategic interaction among firms in multi-period

markets is significant enough to affect market behavior.

This result supports the Karp and Perloff methodology,

where firm behavior, ranging from competition to collusion is

nested in the model. However, this result contradicts the

theoretical work of Dockner, as presented in Chapter IV.

Dockner's results indicate that conjectural variations will be

negative and bounded above by the Cournot behavior. This

excludes the possibility of (im)perfect collusion beyond the

Cournot-Nash outcome. This might be because Dockner imposes

the Cournot-Nash assumption in his model. Further, as

discussed before, both Dockner, and Karp and Perloff have

shown that the open-loop dynamic model is nothing but the

dynamic analog of the static model. Therefore, the results of

this study should show, in principle, the same degree of

market imperfection both in the open-loop and static model.

Results presented in Chapter VI, do show that, as compared to

the feedback model, the degree of market imperfection

indicated by the open-loop model is closer to the degree of

market imperfection indicated by the static model.

Finally, in terms of policy guidelines, the present

research has undermined the assumption in most empirical trade

analysis that the banana export market is perfectly

competitive. This has two major implications: First, recent work by McCorriston and Sheldon (1993b) has shown that the

degree of transmission of changes in tariffs depends on the 146 nature of strategic interaction between firms. Their simulation results show that only in case of Bertrand strategies (i.e. competitive market) pass-through of prices induced by a tariff policy will be complete. However, when markets demonstrate Cournot behavior, the degree of pass­ through will only be 66 percent of the competitive case.

Most of the welfare studies (see footnote 4, Chapter V) on the adoption of a common banana tariff by the EC assume markets to be perfectly competitive. However, doubts have been raised about the validity of this assumption^. Indeed, the study by

McCorriston and Sheldon, coupled with the results of the current research indicate that the assumption of perfect competition made in earlier welfare studies is wrong, and it could lead to grossly incorrect forecasts about welfare effects.

Certainly, the above analysis is relevant to the German market since a tariff of about 20 percent is imposed on the imports of bananas to Germany as a result of the implementation of the common policy on banana imports by the

EC. However, it would be naive to conclude the analysis at that. More importantly, the EC has imposed a levy equivalent to a tariff of about 177 percent on bananas imported from the

1. Hallam and McCorriston (1992) have mentioned in their report. Fair Trade in Bananas, "....Nevertheless, the key point is that ignoring industry and market structure is an important deficiency in agricultural trade policy analysis as it is typically carried out. Consequently, by assuming perfect competition such studies are likely to over-estimate the welfare effects following trade policy changes. indeed, one must go further. The perfectly competitive model in this case is quite misleading." 147

central american countries (dollar countries) that exceed 2

million tonnes per year. Prior to the new policy, Germany

alone used to buy about 1.35 million tonnes of bananas from

the dollar countries. This implies that the prohibitive

tariff of about 177 percent has, for all intents and purposes,

become a binding quota for Germany, and the original tariff of

about 20 percent is being used to extract any quota rents that

the firms might be accumulating in the process.

The effects of a tariff and quota are equivalent if the markets are perfectly competitive (Bhagwati; 1965, 1968), however, if the markets are imperfectly competitive in

structure, then this equivalence seems to vanish. While Fung

(1989) has shown that tariffs and quotas are equivalent if

firms play Cournot-Nash strategies, Hwang and Mai (1988) have shown that a quota affects firm behavior, and, therefore, can generate pro- or anti-competitive effects depending on the initial values of the conjectural variations parameter. For conjectures that are less (more) than Cournot, a quota will make the market less (more) competitive. In the special case where firms initially play Cournot strategies, the quota and tariff are equivalent since the quota does not affect firms' behavior.

Therefore, knowing that Germany faces an effective quota, the question of the pre-quota degree of market imperfection in the German banana market is important. A recent calibration study on the German market for banana imports by McCorriston 148 and Sheldon (1994) shows that the firms collectively behaved more competitively than Cournot. The simulated welfare losses to consumers and the profit gains to firms were much higher in the case of a 20 percent tariff-equivalent quota as compared to the effects of a 20 percent tariff. However, the calibrated estimates of conjectural variations are based on a single observation and no statistical significance can be attached to it.

In the present research, though the actual values of conjectural variations were a little different than the

Cournot-Nash outcome, the hypothesis of Cournot-Nash behavior was not rejected. Based on this result it can be said that the effect of the imposition of an effective quota will not be any different than the effect of imposition of an equivalent tariff. Further, firms were behaving in Cournot-Nash fashion before the implementation of the effective quota, and they will continue to do so even after the implementation of the quota. Thus the degree of imperfection in the German market for banana imports will remain as it is. If we make a prediction on the basis of the actual value of the classical feedback conjectural variations estimate (V = 0.2), the effect will be pro-competitive, albeit very small.

The new policy on banana imports was devised to fulfil conflicting objectives. In the light of the analysis presented above, it can be said that the policymakers of the

EC have tried to maintain preferential access to the ACP 149

countries and harmonize the European market for banana imports

without doing too much harm to the German market. Knowing the

nature of market imperfection, the German policymakers need

not be worried too much that quota will be used by MNCs as a

facilitating practice to hike the domestic prices, although

the restrictions, by definition will raise German consumer

prices. What they might be complaining about, however, is the

fact that the 20 percent tariff revenue meant for extracting

the quota rents is going to the EC and not to the German

exchequer. While the banana firms might not earn quota rents,

and the ACP countries will be content with the preferential

access to their bananas, policymakers from the central

american countries will be concerned about the employment

problem created by the effective quotas. Finally, even though

the new policy is only moderately harmful in general, GATT

authorities will certainly be concerned about the regressive

banana policy, since their objective is to eventually remove

the non-tariff and tariff barriers, in that order.

7.2 Limitations and Future Direction

The advantages of the model used for the present study

are overwhelming as compared to the previous studies, however,

there are a few limitations that must be taken into account.

While undertaking the empirical procedure, it was noticed that the value of V, the dynamic conjectural variations parameter,

is very sensitive to the g^ coefficient of the Markov 150

equation. In fact, in the bootstrap method, it was observed

that V lay outside the theoretically constrained range,

whenever the value of was positive. Although this happened

in less than 3 percent of the bootstrapped cases, this anomaly

needs some further investigation.

Another limitation, as discussed in Chapter V, is that

although the model nests competitive, Cournot and perfectly

collusive games, it cannot specify a specific game structure

for every value of V that lies within the theoretically constrained range. The Folk Theorem, which presents game- theorists with an embarrassing wealth of equilibria, makes this task extremely difficult. Therefore, estimating a conjectural variations parameter is a modest attempt to capture the degree of market power^.

The research conducted in this dissertation can be extended in two directions. First, this methodology can be applied to other industries that are potential targets for any policy reforms, so that information regarding the nature of market structure is incorporated in any welfare studies conducted on those markets. Second, numerical methods could be used to measure the degree of market imperfections, and that can handle complex formulations of demand and cost

2. Recently, Gasmi, Laffont and Vuong (1992) have done a study on the soft drink market duopoly. They do not use the conventional conjectural variations approach. They have formulated non-nested models of Cournot, stackelberg and collusive behavior in prices and advertizing. Using the likelihood ratio principle and goodness of fit, they selected a model which showed tacit collusion in advertizing between Pepsico and Coca-Cola. However, their analysis is carried out in a static framework. 151

functions, and the dynamic game-theoretic interactions among

firms. Generally, economic problems are cast in the context

of an analytically tractable mathematical model that gives

closed-form solutions. • This puts restrictions on the

complexity of functional forms that can be used in the model.

For example, in the present study, the linear-quadratic

formulation gives analytical solutions; however, if some other nonlinear functional forms were to be used, which, a priori, may be more desirable, analytical solutions are not necessarily guaranteed. Therefore, an alternative to this is to use computer intensive numerical methods which yield approximate solutions^. It is for this reason that the

National Science Foundation (1991, p:27) report on mentions, and I quote, "Currently there is no known general purpose algorithm for computing dynamic and game-theoretic equilibria. Most such equilibria are found analytically, .... We foresee that advanced computing (read numerical methods) will help make substantial inroads in this difficult area. "

3. Judd (1991) in his book. Numerical Methods in Economics, mentions that numerical solutions are not exact and will contain some error. However, careful methods can reduce the approximation error to the point where the benefit from flexible specifications justify the approach. Further, numerical methods do not prove the existence of an equilibrium. Any solution must be considered provisional until it can be shown that a solution exists. APPENDIX A

DATA

152 Y Pt Wt Qt q2t qst qit Zt 70 2751.98 1057.54 517.3 8.01

71 2358.49 1020.75 631.9 8.09

72 2277.28 983.90 669.0 8.14

73 2103.51 844.74 670.4 8.18

74 2140.63 985.94 589.1 259.204 100.147 76.583 8.19

75 2330.38 1076.70 552.4 248.580 88.384 66.288 8.84

76 2149.93 973.13 554.0 243.760 94.180 63.710 8.80

77 2207.08 994.55 583.6 250.948 105.048 64.196 8.78

78 1952.19 837.98 617.0 259.140 129.570 64.785 8.77

79 1964.29 855.87 603.3 247.353 144.792 60.330 8.79

80 2297.46 1077.39 533.6 240.120 112.056 69.368 8.86

81 2514.22 1176.34 522.9 224.847 104.580 73.206 8.88

82 2443.24 1151.35 505.9 217.537 101.180 75.885 8.87

83 2531.38 1360.88 495.3 205.549 94.107 79.248 8.90

84 2420.84 1331.97 619.1 247.640 111.438 105.247 8.86

85 2420.00 1340.00 654.1 255.099 117.738 118.719 8.84

86 2562.56 1210.21 702.3 273.897 126.414 127.467 8.85

87 2577.42 1160.84 747.6 284.088 134.568 144.287 8.86

88 2426.04 1055.23 817.8 318.942 139.026 144.342 9.46

89 2264.88 961.61 921.0 359.190 156.570 162.557 9.55

90 2532.71 1131.78 1160.9 9.74

91 2330.62 1001.81 1355.2 9.87

92 2463.08 738.49 1380.0 10.00 y represents year 19__ . and are expressed as DM/tonne. Zt in terms of millions. Rest are in terms of thousand tonnes. APPENDIX B

RESTRICTIONS OBTAINED FROM

THE OPEN-LOOP FIRST ORDER CONDITION

154 155

Converting the open-loop objective function for a representative fimn in the matrix form, and writing it in continuous time gives the following expression;

dt (1 ) where the discount factor p is written in terms of discount rate r; A = (a - 0i); e^ is the i^" unit vector; is the column vector of = b(eeî + 6^6 ') + (jjieiei; Ut is the column vector of Ui^; and = eie^ôi, where is the cost of adjustment parameter of the i^" firm. It is assumed that C0i=0 , which implies that adjustment costs are minimized when there is no adjustment. The explicit matrix forms for firm 1, in a triopoly market (n=3) are as below:

1 1 9it' 2jb+(j)_£ b b "it" Si = 0 f e = 1 / 9t = ?2t , Ki = b 0 0 / Ut = "zt , and 0 1 ?3t b 0 0 "at

0i 0 0 Si - 0 0 0 (2 ) 0 0 0

In deriving the first order conditions, attention is restricted to the quadratic part of the problem, since interest lies in imposing restrictions not on the intercept terms, but on the demand slope and the coefficients of the Markov equation^.

The Lagrangian for the i'^" firm is written as:

(3) where is a (n x 1) column vector. After differentiating the Lagrangian, the following equations emerge: (4)

-ViS^u^ + = 0 (5) Here is a (n x 1) column matrix with 1 in the i^*’ row and V^j

Derivations are borrowed from the original work by Karp and Perloff (1993b). I have attempted to simply them by writing the intermediate steps. 156

du,- in the row. The term V^j = 21, \f X j , and 1, V i = j ~Hüit For example, the vector for firm 1 looks as follows:

Vi = '12 (6 )

13

Now, it is assumed that is a linear function of q^; i.e., ^it = HitQtf for some (n x n) square matrix Hif Letting T -♦ <» so that Hit -, Hi, equation (5) becomes: -ViSiUt + = 0, i = l,...,n. (7)

= ViSiUt . Now simplify the R.H.S.

ViHj^q,. = ôjUjt «

v'iH.q, = 0,e

(E - S)q^ = -5gt_i .

9t = (-S - E)-^Sq,..^ .

Let (S - E)-^S = G . (11)

9t = Ggt.i . (12)

Substituting Hiqt for Xit in equation ( 4 ) one gets : --Pfi9t - = 0 . (13) Using (12) this is rewritten as: {-K, - H, + pH,G)gt = 0 . (14)

{-K. - Hi + pHiG) = 0 157

-(H_£ - PH^G) = .

- pG) = -K i .

Hi = -Kj( J - PG)-^ . (15) From the definition of G in (11), we know: S = (S - E)G . (16)

S — SG = —EG .

S{I - G)G-i = -E .

E = S(I - G-:) . (17) Pre-multiply both sides of (9) by ei to get: eiE = e 'iS (I - G-^) . (18)

v'iHi = ô^el(I - G-:) . (19) Now use equation (15) to write, -v 'iK iiJ - pG)-: = 0^el(I - G-^) .

-V'iHi = 6,ei [(I - G-:) (I - PG)] .

= -[(%- G-')(T - pG)]' Biài .

= [g -^(J - G) (I - pG)f e^ôj . (20) This is the equation (8 ) in Chapter VI. APPENDIX C

RESTRICTIONS OBTAINED FROM

THE FEEDBACK FIRST ORDER CONDITIONS

158 159

Converting all the variables into matrix form, the stationary dynamic programming problem can be written as:

= max (1 )

= max + Si + + gtS^g^.i - lg^-igigc_i (2 )

The first-order condition is:

-V1(JC, + s, + pH,)g, + v'iS.g,., = 0 . (3) Stacking such conditions for n firms to obtain: Sgt = ggt_i , (4: where the i^** row of E is VÎ (K^ + S^ + PHi), and the i^^ row of S is ô^eî. Equation (4) can be written in the form: g<: = Gg^.i , (5) where G = E"^S. Substituting equation ( 5 ) into ( 2 ) gives :

-j-gt-i-s^gt-ij

= max -^gi.iG'lK^ + gj + PH,)Gg„, + gi.^G'S^g^,, + • (6 )

= max -^g;.i[G'(jf, + g^ + PH,) - G'g, - g,G + g, gt-i (7)

H, = G'(h , + g, + pH,)G - G'g, - g,G + g, . (8) N o w vectorise equation (8) by performing the vec operation:

Vec H,= Vec [g'(JC, + g, + pH,)G - G'g, - g,G + g,] (9)

= Vec [g'(h, + g, + PH,)] - Vec [G'g,] - Vec [g,G] +Vec [g,] (10)

= (G' ® G')vec (h,+ g, + pH,) - ( I ® G') 7 e c(g,)

- (G' 0 I) Vec(g,) + Vec (g,) . (11)

[Vec H, - p ( G' 0 G' ) 7ec H,] = 160

(G' ® G')Vec{K^) + {{G' ® G') - { 1 0 G') - {G' 0 I) + j ) y e c ( g j (12)

[j - P(G' ® G')]vec Hi =

{G'0G')Vec{Ki) + i{G'0G')-{I0G')-{G'0I)+l) àiVec{eie'i)\ (1 3)

Vec = [j - P(G/ ® G')]"'[(G' G') Vec(JCj] +

[l-p(G'®G')r Vec{eie'i)ài (14) Equation (14) can be expressed in short as; V e c Hi = (ûi + X iôi ^ (15) where o)i is the first term of RHS of (14), and x^ is the second term except ôi* Here, Vec Hi, o)i and Xi are all (n^ x 1) column vectors. Therefore, equation (7) can be converted back in the form of (n X n) vectors by using inverse-vec(torization) operation. It then assumes the form: Hi = Wi + Xi ài ^ (16) where Wi, Xi are the transformed forms of cüi and Xi having the dimension, (n x n).

Now, once again, consider equations (4) and (5). We know from these equations: EG = S. Take the i^"' row of EG = S, i.e. v'iiK i + Si + pSi)G = ôiel . (17) Now, Substitute the value of Hi from equation (16) into equation (17): v'ilKi + Si + P(Wi + %iôi)]G = ôiel . (18)

vl[jCi + pWi + (6iel + pXi)ôjG = Ôiel .

G'[jCi + pWi + {eiS'i + PXi)ôjVi = 6iôi .

[Ki + pWi + (Biel + pXi)ôjVi = G'-'e^ôi . (19) This is the equation (10) in chapter VI. APPENDIX D

SOLVING THE RESTRICTIONS

TO OBTAIN VALUES OF V AND Ô

161 162

D.l. Solving the open-loop model for V and ô.

The restriction derived in Appendix B is the following:

= [g - ^ I - G) (J - PG)f e,0, . (1) Imposing the symmetry conditions, and expanding the matrices, we get (assuming n=3):

2 b b b 1 Ô

b 0 0 V - 2(3 X 3) 0 (2 ) b 0 0 V 0 where Z is a symmetric matrix, and <|)i is assumed to be 0, which implies that marginal cost is constant. The matrices are multiplied to obtain two equations:

Zj^iô (3) 2bV = Zi,i0 (4) b Ô = (5) ^2,1 ' and V = (6 ) 2%:. ' •

D.2. Solving the feedback model for V and Ô.

The restriction derived in Appendix C is the following:

[k, + + (e,ei + pXJôjV, = G'-^e,à, a y A - (7) Under the assumption of symmetry, the rank of the matrices in the above equations is two, and we need to look only at the first two equations. Define matrix A^ and so that bA^ s + pWi and B^ s e^eî + px^. The i^“ and j^’' equation is: b(A,, + y E Ajj) + (B,, + y E b,^)ô = y,,ô , (8) and b(A„i + V E + ^8,^ + V E , (9) where A^j, B^j and y^ are elements of A^, B^ and y^. Solving the second equation gives Ô as a linear function of b and a nonlinear function of V. Substituting the value of Ô into the first equation gives a quadratic in V that is independent of b. Of the two roots of V, one is closer to the open-loop solution, and the other falls outside the theoretical range. Therefore, we pick up the feasible root. Here, V is a function of p and G, and ô is a function of b, p and G. APPENDIX E

GLOSSARY

163 164

ACP African-Caribbean-Pacific (countries).

EC European Community.

FAO Food and Agriculture Organization.

PDI Foreign Direct Investment.

GATT General Agreement on Tariff and Trade.

HO Heckscher-Ohlin (theory).

ILO International Labo(u)r Office.

IMF International Monetary Fund.

10 Industrial Organization.

MNCS Multinational Corporations.

NEIO New Empirical Industrial Organization.

NIO New Industrial Organization.

NTTS New Trade Theories.

PGA Philippines Coconut Authority.

PTM Pricing to Market.

SCPP Structure-Conduct-Performance Paradigm.

UFCO United Fruit Company.

UNCTAD United Nations Conference on Trade and Development.

UPEB Union de Paises Exportadores de Banano. BIBLIOGRAPHY

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