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GLOBAL COMPETITION FOR THE JAPANESE FRUIT JUICE MARKET By SHIFERAW TESFAYE FELEKE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2006 Copyright 2006 By Shiferaw Tesfaye Feleke This document is dedicated to my mom ACKNOWLEDGMENTS Writer William Arthur Ward once said, "Feeling gratitude and not expressing it is like wrapping a present and not giving it." I couldn't agree more. My first, and most sincere, acknowledgment must go to the chairman of my supervisory committee, Dr. Richard L Kilmer. I would like to express my deepest gratitude and sincere appreciation to him for his meticulous review of the manuscript, guidance, encouragement and patience to successfully complete my study. I gratefully acknowledge and thank him for everything he did throughout my program. I was very fortunate to work closely with him. Our frequent interactions were very invaluable learning experiences. I am also very grateful to Dr. Jonq Lee for introducing me the differential demand systems and TSP program and helping me understand the basics and analytics of differential demand systems that provide the basis of this study. I sincerely thank him for his patience in reviewing, providing me with invaluable comments and suggestions from the very beginning of proposal preparation up until the completion of this dissertation. Many thanks must also go to the other members of my supervisory committee, Drs. Ronald Ward, James Stems and Lawrence Kenny, for providing me with constructive comments and suggestions. I would like to thank them all for their support and guidance. I am also grateful to Dr. Mark Brown for his assistance with the data analysis. I am grateful to the Food and Resource Economics Department of the University of Florida for affording me the opportunity of research assistantship to pursue my studies in the department for the last six years. Special thanks must go to the department chair, Dr. Thomas Spreen, graduate coordinator Dr. Jeffery Burkhardt, and graduate program assistant Jessica Herman. I am very appreciative of the support I received from Dr. Spreen and Jessica Herman. I am also thankful to my officemate Katherine Finn for every help she offered me during the preparation of this dissertation and for being a nice officemate. I would also like to thank my friends and classmates Marco, Angel, Lurleen, Joy, Mariana and Maria. Special thanks go to Lurleen for being an important force of motivation. Our frequent interactions have been the source of learning. I am indebted to my fellow friends Seleshi, Worku, Abiy, Dr. Getachew, Dr. Ayalew, Dr. Tesfaye, Saba Haile Selasie, Saba Ataro and Measho for their support, encouragement and friendship. My final, and most heartfelt, acknowledgment must go to my father Tesfaye, my sister Firehiwot, my wife Genet and my daughter Biruktawit. I dedicate this dissertation to my mother Yeshi who passed away a couple of years ago. TABLE OF CONTENTS page A C K N O W L E D G M E N T S ................................................................................................. iv LIST OF TABLES .............. .......... .. ....... ........... ....... ix L IST O F F IG U R E S .... ...... ................................................ .. .. ..... .............. xii A B S T R A C T .............................................. ..........................................x iii 1 IN TR OD U CTION ............................................... .. ......................... .. B ack g rou n d ...................................... .............................. .... ......... ...... . O objectives ................................................................. ........ .......... 4 H ypotheses ................................................ 5 O u tlin e ............................................................................ . 7 2 GLOBAL PRODUCTION, TRADE AND CONSUMPTION OF FRUIT................9 G lobal Fruit P reduction ... ..... ... ... ......... .......... ......... ..................... 9 The Production of Oranges, Lemons and Limes, and Grapefruits and Pomelos 12 The Production of Grapes, Apples, and Pineapples ..........................................16 Global Fruit Trade .................................... .. .......... .. ............19 G lobal Fruit Consum ption .......................................................... ............... 21 3 TH EORETICAL M OD ELS ............................................... ............................ 24 D em and A pproaches............. ........................................................ ... ...... 24 Production A pproach............................................................ ............... 25 Consum er D em and A approach ........................................ ......... ............... 28 U utility M axim ization ........................................ .... ....... ..... ...... 29 The Rotterdam M odel .................. ............................ ........ .................. 32 B lock Independence ........................ .. ...................... .. ...... .... ..... ...... 36 B lockw ise D ependence ............................................. ............................. 39 Uniform Substitute Hypothesis ....................................... ....................... 42 Uniform substitute given block independence ..........................................42 Uniform substitute given blockwise dependence.......................................45 4 EMPIRICAL MODELS AND ESTIMATION PROCEDURES ...............................48 E m pirical M models ............... ........... .................... .................... 4 8 The Relative Price Version of the Rotterdam Model ........................................48 The Absolute Price Version of the Rotterdam Model .......................................52 Block Independent Nonuniform SubstituteRotterdam Model........................54 Blockwise Dependent Nonuniform SubstituteRotterdam Model....................56 Block Independent Uniform SubstituteRotterdam Model ..............................60 Blockwise Dependent Uniform SubstituteRotterdam Model.........................63 Data Sources ............ .......... ..................... 66 A n alytical M eth od s........... .......................................................................... ............... 67 5 RESULTS AND DISCU SSION ........................................... .......................... 69 D descriptive R results .......... ........ ... ........ ........ ............ ...... .............. 69 Test for Firstorder A utocorrelation ........................................ ....................... 70 H ypothesis Testing for M odel Selection .......................................... ............... .... 72 Block Independence and Uniform Substitute Hypothesis................................72 Blockwise Dependence and Uniform Substitute Hypothesis...........................74 The relative Price Version of the Rotterdam Model.................................................76 P aram eter E stim ates ................................................................ ....................7 7 Expenditure Elasticities ................................ .................. .......... ..... 82 Ownprice Elasticities ......................... .... .... ... ............... 88 C rossprice E lasticities ............................................... ............................. 90 6 MARKET STRUCTURES AND STRATEGY OPTIONS ......................................97 M ark et Structu res................ .. .. .... .... ........ .. ..... ... .. .................... 97 Block Independence (Direct) with Nonuniform Substitution..........................97 Block Independence (Direct) with Uniform Substitution ..................................98 Blockwise Dependence with Nonuniform Substitution.............................. 98 Blockwise dependence with Uniform Substitution............... ................... 100 Parameter and Elasticity Estimates in Five Market Structures .......................101 Param eter estim ates ........................................................ ............. 102 Expenditure elasticities ........................................ ......................... 104 P rice elasticities....... ............................................. ...... ...... ... ......... 106 M market Strategy O ptions................................................. .............................. 109 7 SUMMARY, CONCLUSIONS AND IMPLICATIONS ............... ..................110 Sum m ary and C onclu sions ............................................................ ..................... 110 Im plications ........... ......................................... ........... ... ..... ....... 114 APPENDIX A PRICE COEFFICIENTS OF FRUIT JUICES IN JAPAN...................................118 B PRICE ELASTICITES OF FRUIT JUICES IN JAPAN ............. ...............124 C PARAMETER ESTIMATES OF ROTTERDAM MODEL UNDER DIFFERENT SEPARABILITY A S SUM PTION S ........................................................................136 D PRICE ELASTICITIES OF FRUIT JUICES IN JAPAN IN DIFFERENT M ARKET STRU CTURES ............................................................. ............ .142 E TWOSTAGE ROTTERDAM MODEL ..............................166 F PARAMETER ESTIAMTES OF FRUIT JUCIES IN A TWOSTAGE R O T TE R D A M M O D E L ........................................ ...........................................180 LIST OF REFEREN CES ........................................................... .. ............... 187 BIOGRAPHICAL SKETCH ............................................................. ............... 192 LIST OF TABLES Table page 2.1 Global citrus production, area harvested and yield per hectare, 2005 ...................10 2.2 Global production of oranges, grapefruit and pommels, and lemons and limes in 2 0 0 5 ............................................................................................... 12 2.3 Global production of apples, grapes, and pineapples, 2005.................................16 2.4 Fruit juice imports to Japan by country of origin..................................................22 2.5 Per capital consumption of fruits in industrialized and developing countries ..........23 4.1 Codes for countries exporting fruit juice to Japan .............................. ...............50 5.1 Fruit juice quantity and price logchanges, and expenditure shares, Japan, D ecember 1995 to M ay 2005 ............................................................................70 5.2 Test for firstorder autocorrelation..................................................71 5.3 H hypothesis testing for m odel selection ........................................ .....................74 5.4 Marginal expenditure shares of imported fruit juices in Japan ..............................77 5.5 Parameter estimates of cross prices of fruit juices in Japan .............. ...............80 5.6 Parameter estimates of own prices of fruit juices in Japan ................................82 5.7 Expenditure elasticity estimates of fruit juices in Japan .............. ......................84 5.8 Own price elasticities of fruit juices in Japan........................... .... ............... 89 5.9 Crossprice elasticity estimates of substitutes ......................................................94 5.10 Crossprice elasticity estimates of complements .............................................. 96 6.1 Importance of country of origin in five market structures ................................... 101 6.2 Relative price coefficients of fruit juices in five market structures ....................... 104 6.3 Expenditure elasticity estimates of fruit juices in Japan in five market structures 105 6.4 Uncompensated own price elasticity estimates of fruit juices in Japan ............... 107 6.5 Compensated own price elasticity estimates of fruit juices in Japan ..................... 108 6.6 Market strategies by market structures ..................................... ...............109 Ai Relative price coefficients of fruit juices in Japan .............................................. 118 A2 Slutsky price coefficients of fruit juices in Japan ...........................121 Bl Uncompensated price elasticities of fruit juices in Japan..................................... 124 B2 Compensated price elasticities of fruit juices in Japan ......................................... 130 C.1 Marginal value shares of fruit juices in a block independent Rotterdam model....136 C.2 Relative price coefficients of fruit juices in a block independent Rotterdam m odel .................................... ................... ............... ........... 136 C.3 Marginal value shares of fruit juices in a block independent uniformsubstitute R otterdam m odel ............................................. ... .... ................. 137 C.4 Marginal value shares of fruit juices in a blockwise dependent Rotterdam m odel .................................... ................... ............... ........... 138 C.5 Constant of proportionality of fruit juice groups in a in blockwise dependent R otterdam m odel ............................................. ... .... ................. 138 C.6 Withingroup relative price coefficients of fruit juices in a blockwise dependent R otterdam ............................................................... ... .... ......... 138 C.7 Marginal value shares of fruit juices in a blockwise dependent uniform substitute R otterdam m odel ......................................................... .......... ..... 139 C.8 Constant of proportionality of fruit juice groups in a blockwise dependent uniformsubstituteRotterdam model ........... ..................................140 C.9 Withingroup relative price coefficients of blockwise dependent uniform substitute R otterdam m odel ......................................................... .......... ..... 140 F.1 Marginal value shares of fruit juices in a twostage block independent R otterdam m odel ............................................. ... .... .................. 180 F.2 Relative price coefficients of fruit juices in a twostage block independent R otterdam m odel ............................................. ... .... ........... ....... 181 F.3 Marginal value shares of fruit juices in a twostage block independent uniform substituteR otterdam m odel e........................................... .......................... 182 F.4 Marginal value shares of fruit juices in a twostage blockwise dependent R otterdam m odel ............................................. ... .... .................. 183 F.5 Relative price coefficients of fruit juices in a twostage blockwise dependent R otterdam m odel ............................................. ... .... .................. 184 F.6 Marginal value shares of fruit juices in a twostage blockwise dependent uniformsub stituteRotterdam model ........... ..... .............. ............... 185 F.7 Relative price coefficients of fruit juices in a twostage blockwise dependent uniformsub stituteRotterdam model ........... ..... .............. ............... 186 LIST OF FIGURES Figure page 2.1 Citrus productions (MT) of major producers, 19612005.............. ................. 11 2.2 Orange productions (MT) of major producers, 19612005.............. ...................13 2.3 Lemon and lime production (MT) of the top four producers, 19612005 ..............14 2.4 Grapefruit and pomelos production (MT) in the U.S. and China, 19612005 .........15 2.5 Grape productions (MT) of the top three countries, 19612005 ............................17 2.6 Apple productions (M T) in the U.S. and China...................................................18 2.7 Pineapple productions (MT) of major producers, 19612005................................19 3.1 A tw o stage profit m axim ization .............. ..................... ........... ... ............ 26 3.2 A twostage utility maximization......... ..... ............................. ... ............ 27 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy GLOBAL COMPETITION FOR THE JAPANESE FRUIT JUICE MAREKT By Shiferaw Tesfaye Feleke August 2006 Chair: Richard L. Kilmer Major Department: Food and Resource Economics This study identifies the market structure of fruit juices imported into Japan within the context of a consumer demand theory using three different versions of the Rotterdam model (the block independent uniform substituteRotterdam model, the block wise dependent uniform substituteRotterdam model, and the relative price version of the Rotterdam model). The models were formulated under the hypotheses of block independence/blockwise dependence among products that belong to different product groups and uniform substitute among products that belong to the same product group. They were estimated for six different kinds of fruit juices (orange, grapefruit, other citrus, apple, pineapple and grape juices imported from 18 countries) on monthly per capital data over the period December, 1995, to May, 2005, using the nonlinear least squares (LSQ) in the Time Series Processor (TSP) program. Statistical tests select the relative price version of the Rotterdam demand model as explaining the allocation decisions better compared with the other versions and identify a market structure which involves both direct and indirect competition based on the country of origin. The results have important implications for countries exporting fruit juices to Japan for identifying marketing strategies such as price reduction, product promotion, market integration, as well as export supply decisions in light of the expansion and contraction of the Japanese market for imported fruit juices because of the change in income. CHAPTER 1 INTRODUCTION Japan, with the second largest economy in the world and a population of about 127 million, imports agricultural products worth over $30 billion each year (USDA). The U.S. is the leading agricultural supplier accounting for nearly onethird of Japan's total agricultural imports, though this share has declined slightly since the mid1990s. China and the EU15 are the nextlargest suppliers, each with over 12% of Japan's agricultural imports (USDA). This study focuses on a portion of Japan's imports which include orange, grapefruit, other citrus, apple, pineapple and grape juices. Orange, grapefruit, apple and grape juices account for 86% of fruit juice imports on a value basis (JETRO). The leading exporters of orange and grapefruit juices to Japan are Brazil and the U.S., respectively. The U.S. is also a leading exporter of grape and apple juices while Thailand and Israel are the leading exporters of pineapple and other citrus juices, respectively. Background Following the deregulation of imports of apple, grapefruit, and pineapple juices as of April 1990 and that of orange juice as of April 1992, the import penetration ratio (the fraction of income spent on imports or the increase in the extent of consumption of imports) of processed fruits into Japan has increased (JETRO). Furthermore, Japan is undergoing a profound change as a result of its aging population. Japan's statistical agency has measured a decline in population growth that is about to become an absolute decline, and population shrank for the first time in 2006 and will gradually fall for a number of years thereafter. The impact of this demographic change on the demand for fruit in Japan is an empirical question, since either the aging affluent consumers may increase consumption of fruits to stay healthy or demand may decrease with the absolute decrease in population size. In either case, the increase of import penetration in the face of an aging population and declining population growth will lead to an increased competition among exporters. The purpose of this study is to assess the competitiveness of the world's largest exporters of fruit juice into Japan through the analysis of market structure. The analysis of market structure in marketing is concerned with identifying closely competing brands of the same product (Clements and Selvanathan, 1988). Consumption theory is amenable to the analysis of market structure in international markets through demand analysis. The approach involves the analysis of the change in marginal utilities of a certain product due to a change in consumption of a closely related product. The decrease in marginal utility of one product with an increased consumption of another product implies that the products are substitutes and are thus in a competitive market structure. Otherwise, they are not substitutes (i.e., complements or independent) and are thus in a noncompetitive market structure. Substitute products can be uniform1 (close) or nonuniform. If two products are uniform substitutes, priceoriented marketing strategies and/or generic product promotion are recommended because consumers are not influenced by the country of origin of such products. If two products are nonuniform substitutes, consumers are influenced by the country of origin and thus exporters can exercise a monopolistic power over their respective products. In this case, a nonprice 1 The change in the marginal utility of a dollar spent on product i is the same as that of another dollar spent on product j . marketing strategy (e.g., product promotion) and/or price reduction is recommended to increase market share. Be it uniform or nonuniform, the decision to use a particular marketing strategy depends on the price elasticity of demand for the product in question. Under a situation in which a product is a uniform substitute but price inelastic, the decision to reduce price is not advised because total revenue is reduced when price is decreased. However, the response of demand to changes in price may be higher under the uniform substitute relationship than under the nonuniform substitute relationship. This implies that both the nature of substitution (uniform/nonuniform) and the magnitude of substitution elasticitiess) are important in international trade since they have different implications to exporters for marketing strategies such as market promotion, product differentiation as well as a product supply plan (expansion or contraction of supply). Most empirical studies have pursued the estimation of conditional demand functions in isolation without testing for the nature of substitution within a product group, and the nature and magnitude of substitution between product groups. However, conditional demand parameters thus estimated are rarely of interest for policy analysts because the appropriateness of marketing strategy depends on the relationship between products within the same product group and across different product groups. If, for example, the relationship between products within the same product group is uniform, the appropriate marketing strategy is price reduction because consumers view those products as homogenous. If, however, the products in the group are nonuniform, product promotion is recommended because consumers can pay a different price since they view them as differentiated products. Furthermore, since the optimal allocation of expenditure to products in any one partition may depend on prices of products outside that group in a uniform or nonuniform fashion, the failure to consider the nature and magnitude of substitution between products in different products groups may misguide marketing strategists. For example, the effect of a change in price of Chinese apple juice on the demand for Brazilian may be the same as that on the demand for Florida orange juice. The marketing strategy that is appropriate for this situation is different from the situation in which the effect of a change in the price of Chinese apple juice on the demand for Brazilian orange juice is different from that on the demand for Florida orange juice. To be useful for policy applications in terms of designing an effective marketing strategy, the demand for fruit juices in this study is estimated under different scenarios of market structures consistent with consumer's preference structure. Objectives The objectives of this study are the following. (1) To characterize the trend and pattern of the world fruit production, trade and consumption. (2) To identify the market structure of fruit juices imported into Japan by estimating a differential consumer demand system. (3) To assess the competitiveness of the world's largest exporters of fruit juice into Japan. (4) To simulate the impact of changes in population growth on the growth rate of demand for fruit juices by country of origin. In order to identify the market structure of fruit juices in Japan, two hypotheses are tested. These are block independence/uniform substitute and blockwise dependence/uniform substitute hypotheses. Hypotheses Block Independence/Uniform Substitute Hypothesis The hypothesis of block independence/uniform substitute states that there is no change in marginal utility of a dollar spent on a product in one product group caused by an extra dollar spent on another product in another product group. But, the change in the marginal utility of a dollar spent on a product in one product group caused by an extra dollar spent on another product in the same product group is the same for all pairs of products in that group. This hypothesis represents the market structure of block independent (direct competition) with uniform substitution such that a change in the price of a product in one group (e.g. orange juice group) does not affect the demand for another product in another group (e.g. apple juice group). But, the change in the price of a product in one group (e.g. orange juice group) uniformly affects the demand for another product in the same group. The failure to reject the null hypothesis implies that exporters of one fruit juice group don't have to worry about the change in price of products that belong to other juice groups because competition occurs only between products of the same product group or the same products differentiated by country of origin. Furthermore, exporters of products that belong to the same product group can only compete by reducing price (i.e. use a priceoriented marketing strategy and/or generic product promotion) because under such circumstances consumers are not influenced by the country of origin of the product, since they perceive products from different countries as homogenous. Brand promotion is not recommended because brand promotion for a uniform substitute product is technically a generic promotion. For example, if Florida orange juice is a uniform substitute to Brazilian orange juice, promoting Florida orange juice may rather help raise the sales of Brazilian orange juice. In summary, if two products are uniform, only a slight decrease in price makes a big difference in sales, implying that the market of uniform substitute products is very competitive. This may lead firms to merge so that they will be able to exercise a monopolistic power. Blockwise Dependence/Uniform Substitute Hypothesis The hypothesis of blockwise dependence/uniform substitute hypothesis states that the change in the marginal utility of a dollar spent on a product in one product group caused by an extra dollar spent on another product which belongs to a different product group is the same for all pairs of products that belong to the two product groups. Also, the change in the marginal utility of a dollar spent on a product in one product group caused by an extra dollar spent on another product in the same product group is the same for all pairs of products in that group. This hypothesis represents the market structure of blockwise dependent with uniform substitution such that a change in the price of a product in one group (e.g. orange juice group) affects the demand for another product in another group (e.g. apple juice group) in a similar fashion. Furthermore, the change in the price of a product in one group (e.g. orange juice group) uniformly affects the demand for another product in the same group. The failure to reject the null hypothesis implies that exporters of one fruit juice group need to watch the change in price of products in other juice groups because competition occurs between products of different product groups. Since the competition between products in different groups occurs in a similar fashion, a slight change in price of one product in one group will significantly affect the demand for products in other groups. Furthermore, exporters of products that belong to the same product group can only compete by reducing price because under such circumstances consumers are not influenced by the country of origin of the product, since they perceive products from different countries and product groups as homogenous. In summary, if two products are uniform within and across product groups, only a slight decrease in price makes a big difference in sales, implying that the exporters of products that belong to different product groups is very competitive. Hence, exporters of products that belong to different product groups should pay close attention to the price behavior of either product because only a slight change in price of one juice group significantly affects the sales of another juice group. Based on results of the test of the above hypothesis, the study will identify the market structure of Japan's fruit juice market. This will allow analyzing the competitiveness of countries exporting fruit juices to Japan, and drawing implications in terms of marketing strategies. Results will be useful for providing a structure for marketing research on closely related products and identifying marketing strategies involving price reduction, product differentiation and market promotion. Outline The dissertation is organized as follows. Chapter 2 presents the global fruit production, trade and consumption. In this chapter, the trend, pattern and quantity of production, trade and consumption of major players are investigated. Chapter 3 presents the theoretical section in which the common approaches in import demand analysis and the different demand models are reviewed. The chapter also derives the different versions of the Rotterdam model used for empirical estimation and tests the hypothesis presented in chapter 1. Chapter 4 presents the empirical model and the estimation procedure. This chapter includes (1) the systems of equations that are empirically applied to statistical data (2) the procedures that need to be followed to estimate the models (3) the source of data and analytical methods. Chapter 5 presents the results and discussion. This chapter discusses (1) the model that best describes the import data of fruit juices (2) the expenditure and price elasticities estimated from the selected model (3) results of simulation about the effect of the decline in population growth on the growth of demand for fruit juices. Chapter 6 presents different market structure scenarios and compares the results of these different market structures with the results of chapter 5. Finally, chapter 7 summaries the results and draws conclusions. Based on the conclusions, implications are drawn. CHAPTER 2 GLOBAL PRODUCTION, TRADE AND CONSUMPTION OF FRUIT This chapter presents a description of global fruit production, trade and consumption. Both citrus and noncitrus fruits are included. The citrus fruits include orange, grapefruit, and lemons and limes while the noncitrus fruits include apples, grapes and pineapples. Data for this report come mainly from the website maintained by the Food and Agricultural Organization (FAO). Global Fruit Production Citrus (Citrus L.) is one of the world's most important fruit crops commercially grown primarily between the latitudes 400N to 400S (University of Pretoria). According to the University of Pretoria, Yunnan province in southcentral China may be the center of origin due to the diversity of species found, and the network of rivers in this area which could have provided "on route dispersal" to the south. From there, they slowly spread to northern Africa mainly through migration and trade. Citrus spread throughout Europe during the MiddleAges and were then brought to the Americas by Spanish explorers. Worldwide trade of citrus fruits didn't appear until the 1800s and trade in orange juice developed as late as 1940. Citrus production in Florida dates back to the colonization of the state by the Spaniards in the 15th century (Spreen et al. 2006). Today, the major types of edible citrus include citron, sour orange, sweet orange, lime, lemon, shaddock pomeloss), grapefruit, mandarin, and kumquat. The world's largest producers of citrus fruits are Brazil, China, U.S. and Mexico whose combined production accounted for half of the world's total in 2005. During the same year, Brazil's production accounted for the highest proportion (19%) followed by that of China (15%), U.S. (10%) and Mexico (6%) of the world's total (Table 2.1). In terms of area, China, Brazil, Nigeria and Mexico rank first, second, third, and fourth, respectively, accounting for about 23%, 12% and 10% and 7% of the global citrus area harvested in 2005, respectively. During the same year, the world's highest yield per ha was obtained in Turkey, Syria, S. Korea and U.S., each producing about 26 Mt per hectare. The productivity of citrus in China as measured by yield per ha is one of the lowest in the world (FAO, 2005). Table 2.1 Global citrus production, area harvested and yield per hectare, 2005 Country Production(MT) % Yield (MT/Ha) Area (ha) % Brazil 20,142,100 19 Turkey 26.7 China 1,714,300 23 China 16,019,500 15 Syria 26.3 Brazil 930,379 12 U.S. 10,317,200 10 S. Korea 26.2 Nigeria 730,000 10 Mexico 6,475,411 6 U.S. 26.0 Mexico 523,505 7 Spain 4,867,300 5 Guatemala 24.7 U.S. 397,080 5 India 4,750,000 5 Palestine 24.5 India 264,500 3 Italy 3,836,793 4 Israel 23.7 Spain 240,759 3 Iran 3,825,000 4 Cyprus 23.2 Iran 232,500 3 Nigeria 3,250,000 3 Australia 22.8 Pakistan 185,400 2 Egypt 2,797,600 3 Italy 22.5 Italy 170,338 2 Total 78,801,620 74 Total 5,388,761 70 World 105,431,984 100 World 13.9 World 7,605,363 100 (Source: FAO, 2005) During the last four decades, global citrus production showed a period of sustained growth, primarily due to expansion of cultivation (Figure 2.1). Over the same period, the world citrus production increased more than four fold from 24,999,430 Mt to 105,431,984 Mt, growing at an average annual rate of 1.5 % (Figure 2.1). The rate of growth could have been higher, were it not for the occurrence of freezes in Florida in the 1980s. Both bearing tree numbers and production declined by 40% between 1975 and 1986 as freezes destroyed a large portion of the industry in Lake, Orange, and Pasco counties of the state of Florida (Spreen, et al. 2006). However, the increase in prices caused by the slowed production in Florida stimulated the development of new plantings (Spreen et al.). Given the lag between price signals and output changes, an increase in production occurred in the 1990s and 2000s (Figure 2.1). Until the early 1980s during which freezes devastated the Florida citrus production, the U.S. was the world's largest producer of citrus. During the decade of the 1980s, Brazil became the largest citrus producer in the world and the first, and almost exclusive, orange juice exporting country (UNCTAD). Brazil's citrus production grew at an average rate of 4.5% over the last four decades while that of the U.S. grew at 0.6%. < ... 7 ." .., :r ..,r .: .., ~." .., .: .., ~." 2 ,000,0 00 world ,,  Brazil 10o,O ,O0  China "*t Mexico : *,.: .. .... U.S. 80,000,000 < 60',OO( O.. / S / 1961 1965 190 1973 977.1981 1.985,119 19.93A997 2001 .2405 / Figure 2.1 Citrus productions (MT) of major producers, 19612005 Over the last few years, the Chinese citrus production experienced a fast growth (over 3%) over the last few decades (particularly in the 1990s) mainly due to the expansion of cultivation, thus emerging as the second largest producer of citrus fruits in the early 2000s (Figure 2.1). the early 2000s (Figure 2.1). The Production of Oranges, Lemons and Limes, and Grapefruits and Pomelos Oranges. The major citrus fruits are oranges, lemons and limes, and grapefruit and pommels, whose combined production accounted for 55% of the world's total citrus in 2005 (FAO, 2005). Among citrus fruits, orange is the most important fruit, accounting for about 43 percent of the world's citrus production in 2005. The world's largest producers of oranges are Brazil and U.S, whose combined production in 2005 was 44% of the world's total orange production with Brazil alone accounting for 30% of the world production. The U.S. produced 14 percent of the world production in 2005 (Table 2.2). The top ten countries produced 76 percent of the world production in 2005. Table 2.2 Global production of oranges, grapefruit and pommels, and lemons and limes in 2005 Oranges I Grapefruit and Pommels I Lemons & Limes Country Production % Country production % country production % Metric tons Brazil 17,804,600 30 U.S. 914,440 25 Mexico 1,824,890 15 U.S. 8,266,270 14 China 443,000 12 India 1,420,000 11 Mexico 3,969,810 7 Mexico 257,711 7 Argentina 1,300,000 10 India 3,100,000 5 Israel 250,000 7 Iran 1,100,000 9 Italy 2,533,535 4 Cuba 226,000 6 Brazil 1,000,000 8 China 2,412,000 4 S. Africa 212,348 6 U.S. 745,500 6 Spain 2,149,900 4 Argentina 170,000 5 Spain 734,300 6 Iran 1,900,,000 3 Turkey 150,000 4 China 634,500 5 Egypt 1,789,000 3 India 142,000 4 Italy 609,435 5 Indonesia 1,311,703 2 Tunisia 72,000 2 Turkey 600,000 5 Total 45,236,818 76 Total 2,837,499 77 Total 9,968,625 79 World 59,858,474 100 World 3,667,862 100 World 12,554,879 100 (Source: FAO, 2005) From 1961 to 2005, global orange production increased almost four fold from 15,946,492 Mt to 59,858,474 Mt, growing at an average annual rate of 1.4 % (FAO. 2005). Most of the growth was accounted for by developing countries, primarily in South America but also in Asia and to a lesser extent in Africa. In South America, the volume of production expanded considerably in Brazil and Mexico (Figure 2.2). In Asia, production expanded significantly in China, India and Pakistan and Iran. Orange production in China, Brazil and Mexico increased at an average annual rate of 4.3%, 2.7% and 1.4%, respectively over the same period (FAO, 2005). Spreen and Brown (1995) noted that freezes in Florida in the 1980s provided a major impetus to the expansion of orange production in Brazil. The average orange production of Brazil and Mexico in the 1990s was 50 percent and 60 percent larger than the average production in the 1980s, respectively (FAO, 2005). Brazil  China  Mexico SU.S. Figure 2.2 Orange productions (MT) of major producers, 19612005 Lemons and limes. Lemons and limes are the second most important citrus crops accounting for about 9 percent of the global citrus production in 2005. Like the case with oranges, there has been a significant increase in production of lemons and limes through expansion of cultivation. Over the last four decades, the global lemon and lime production increased more than five fold from 2,625,865 MT in 1961 to 12,554,879MTt in 2005, growing at the average rate of 1.6% per annum (FAO, 2005). Most of the growth was accounted for by Mexico, India and Argentina (Figure 2.3). 2,000,000 Argentina m India 1,800,000 Mexco 1,600,000 o U.S. 1,400,000 1,200,000 1,000,000 800,000 600,000 400,000  200,000 1961 1966 1971 1976 1981 1986 1991 1996 2001 Figure 2.3 Lemon and lime production (MT) of the top four producers, 19612005 The world's largest producers of lemons and limes are Mexico, India and Argentina whose production in 2005 was 15%, 11% and 10% of the world production, respectively. Other major producers of lemons and limes include Spain, China, Italy and Turkey, each accounting for about 5 percent of the world's total in 2005 (Table 2.2). The top ten countries produced about 80 percent of the world's total in 2005. Until the mid1980s, the U.S. was the world's largest producer of lemons and limes (Figure 2.3). Between the mid1980s and mid1990s, the U.S. production slowed while that of Mexico continued to rise particularly in the mid1990s during which it emerged to be the world's largest producer of lemons and limes. Over the last four decades, Mexico's production grew at an average annual rate of 2.3% while that of U.S. grew at 0.4%. In 2005, U.S. produced 6% of the world's total, which is way below the production of Mexico, India, Argentina, Iran and Brazil (Table 2.2). Over the same period, India and Argentina also increased their production and emerged as the second and third largest producers of lemons and limes, respectively (Table 2.2). India and Argentina increased their production at an average annual rate of 1.4 and 2.8%, respectively. Grapefruit and pommels. Grapefruit and pommels are the third most important citrus crops, accounting for about 3.5% of the world citrus production. Over the last four decades, the global grapefruit and pommels production increased by 73% from 2,120,896 MT in 1961 to 3,667,862 MT in 2005, growing at average rate of 0.8% per annum (Figure 2.4). 3,000,000  China  U. S. 2,500,000 2,000,000 1,500,000 1,000,000 500,000 1961 1966 1971 1976 1981 1986 1991 1996 2001 Figure 2.4 Grapefruit and pomelos production (MT) in the U.S. and China, 19612005 The growth rate of grapefruit and pomelos production over the last four decades was modest compared to the growth rate of other citrus fruits. This is due to the slow growth of grapefruit production in the U.S. On average, grapefruit and pomelos production in the U.S. grew at 0.2% per annum. Over the same period, China's production grew at a 3.8%. U.S. is the world's largest producer with 25% of the world's total (Table 2.2). China is the second largest producer with 12 percent of the world's total. Mexico and Israel are also important producers, each producing about 7% of the world's total. The top ten countries produced 77 percent of the world production in 2005 (Table 2.2). The Production of Grapes, Apples, and Pineapples Grapes. Among noncitrus fruits, grapes are the most important noncitrus fruit in terms of production. The maj or producers of grapes are Italy, France and the U.S. whose production in 2005 accounted for 14%, 10% and 10%, respectively (Table 2.3). China and Spain are also important producers of grapes, each accounting for about 9 percent. The top ten countries produced about 71 percent of the world's total in 2005. Table 2.3 Global production of apples, grapes, and pineapples, 2005 Apples Grapes Pineapples Country production % Country production % Country production % Metric tons China 25,006,500 39 Italy 9,256,814 14 Thailand 2,050,000 13 U.S. 4,254,290 7 France 6,787,000 10 Philippine 1,800,000 11 Turkey 2,550,000 4 U.S. 6,414,610 10 China 1,460,000 9 Iran 2,400,000 4 Spain 5,879,800 9 Brazil 1,418,420 9 Italy 2,194,875 3 China 5,698,000 9 India 1,300,000 8 France 2,123,000 3 Turkey 3,650,000 5 Nigeria 889,000 6 Poland 2,050,000 3 Iran 2,800,000 4 C. Rica 725,224 5 Russia 2,050,000 3 Argentina 2,365,000 4 Mexico 720,900 5 Germany 1,600,000 3 Chile 2,250,000 3 Indonesia 673,065 4 India 1,470,000 2 Australia 1,834,000 3 Kenya 600,000 4 Total 45,698,665 72 Total 46,935,224 71 Total 11,636,609 73 World 63,488,907 100 World 66,533,393 100 World 15,886,647 10 0 (Source: FAO, 2005) The production of grapes in the U.S. has been growing steadily, while that in Italy and France appears to be declining since the mid1990s (Figure 2.5). Unlike the case with citrus fruits, the increase in global grape production is modest. It increased by a little more than 50% over the last four decades, growing at an average rate of 0.2% per annum (FAO, 2005). This is due to the decline of production in the two major producing 17 countries (France and Italy) whose production declined at an average rate of 0.4% and 0.2%, respectively. 14,000,00  France t Italy 12,000,000 U.S. 10,000,000 8,ox,oo@. 8,000,01PT 6,000,000  4,000,000  2,000,000 . ,D t t(  t 0 00 oo '0   i o O Oi ; ( (^ ( 0 0 ;0 S*CD CD Figure 2.5 Grape productions (MT) of the top three countries, 19612005 Apples. Apples are the second most important noncitrus fruits. Over the last four decades, the world apple production increased nearly four fold from 17,053,651 MT in 1961 to 63,488,907 MT in 2005, growing at an average rate of 1.2% per annum. The world's largest producers of apples are China and the U.S. China produced 39% of the world's total in 2005. U.S. production accounts for 7% of the world's total (Table 2.3). Until the early 1990, the U.S. was the largest producer of apples (Figure 2.6). Since then, China has become the world's largest producer of apples. On average, China's apple production grew at the rate of 4.7% per annum while that of the U.S grew at 0.7% per annum over the last four decades. The growth of apple production in China is explained by an increase in area expansion. 30,000,000 China U. S. 25,000,00.0 20,000,000 15,000,000 10,000,000 5,000,000 0g 1961 1966 1971 1976 1981 1986 1991 1996 2001 Figure 2.6 Apple productions (MT) in the U.S. and China Pineapples. Pineapples are the third most important noncitrus fruit. Over the last four decades, the global pineapple production increased almost four fold from 3,831,437 MT to 15,886,647 MT at an average rate of 1.4% per annum. Until the early 1980s, U.S. was the world's largest producer of pineapples (Figure 2.7). Since then, its production has declined so that it is not in the list of the top 10 producing countries (Table 2.3). Over the last four decades, the U.S. production declined at an annual rate of 1.3 percent per annum (FAO, 2005). Currently, the world's largest producers of pineapple are Thailand, and the Philippines, accounting for 13% and 11% of the world's total, respectively (Table 2.3). They increased their production over the last four decades at 2.8% and 2.5% per annum, respectively. China and Brazil have also emerged as the third and fourth largest producers, each producing about 9% of the world's total. The top ten countries produced 73 percent of the world's total in 2005. 4,000,000  Brazil China 3,500,000  Philippines 3,000,000  Thailand ( U. S. 2,500,000 2,000,000 1,500,000 1,000,000 500,000 0 1961 1965 1969 1973 1977 1981 1985 1989 1993 1997 2001 2005 Figure 2.7 Pineapple productions (MT) of major producers, 19612005 Global Fruit Trade International trade in fruits and vegetables has expanded more rapidly than trade in other agricultural commodities, especially since the 1980s (Huang, 2004). This is attributed to rising incomes, falling transportation costs, improved technology, and evolving international agreements. Citrus fruits rank first in international fruit trade in terms of value (UNCTAD). As a result of trade liberalization and technological advances in fruit transport and storage, the citrus fruit industry is becoming more global in scope. The major players in the global trade of fruits and vegetables are the E.U, the North American Free Trade Agreement (NAFTA) countries, China and Japan. Exports of fresh citrus fruits represent roughly 10% of total citrus fruit production (UNCTAD). The international trade on fruits and vegetables is dominated by processed forms. According to UNCTAD, international trade in citrus juice only started to increase in the 1940s, after World War II, when citrus processing technologies were invented and developed. The advent of frozen concentrated orange juice (FCOJ) after World War II provided a new impetus for the citrus industry (Spreen et al. 2006). Citrus fruit processing accounts for approximately one third of total citrus fruit production. More than 80% of it is orange processing, mostly for orange juice production. The major feature of the world market for orange juice is the geographical concentration of production. There are only two main players: the State of Florida in the U.S. and the State of Sao Paulo in Brazil. Production of orange juice between these two players account for over 80% of world orange juice production (Spreen et al. 2006). The major difference between them is that Brazil exports 99 percent of its production while 90 percent of Florida's production is consumed domestically and only 10 percent is exported (UNCTAD). The citrus industry in Florida currently faces two major challenges (citrus canker and citrus greening) and increasing urbanization in the state, which has resulted in increasing land values (Spreen et al. 2006). Nonetheless, the Florida citrus industry will continue to be an important supplier of citrus products to both the U.S. and world market. International trade in orange juice takes place in the form of frozen concentrated orange juice (FCOJ), in order to reduce the volume used, so that storage and transportation costs are lower. Spreen et al. (2006) notes that FCOJ provided a means to (1) store orange juice from the harvest season into other time periods, (2) provided a way to produce a product with a consistent taste, and (3) offered new modes of transport and new retail package alternatives to the consumer. The E.U. is the largest importer of orange juice, accounting for over 80% of the world orange juice imports (UNCTAD). The other major importers of orange juice are Canada and Japan. Most of imports by the E.U. and Japan come from Brazil. Brazil's exports of orange juice to Japan account for over 70% of Japan's total import of orange juice (Table 2.4). In North America, the U.S. and Canada consume orange juice mainly from Florida, while a small quantity of imports comes from Brazil. The U.S. is the leading exporter of apple juice, grapefruit juice and grape juice to Japan. Thailand and Israel are the leading exporters of pineapple juice and other citrus, respectively. The U.S. share of grapefruit import is significant. However, the slow growth rate of grapefruit production in U.S. implies that the U.S. is unlikely to continue as a dominant supplier of grapefruit juice. The same is true with apple juice since the apple production growth rate in U.S. is slower relative to other countries such as China. Currently, the U.S. is a dominant supplier of apple juice to the Japanese market, followed by China and Austria. With regard to grape juice, the U.S. is still the dominant supplier and is expected to dominant the market since its production has been growing while that of France and Italy, which are the world's largest producers, has been declining. Global Fruit Consumption Higher income, urbanization, demographic shifts, improved transportation, and consumer perceptions regarding quality and safety are changing global food consumption patterns (Huang, 2004). Diet diversification and increasing demand for better quality products have increased imports of highvalue and processed food products in developed countries. Fruits are mainly consumed in industrialized countries, not only because consumers in these countries have high income levels but also because they have increasing concerns about healthy eating. However, the growth of per capital consumption of fruits in these countries seems to be stagnating. Over the period 1980 to 2003, the per capital consumption of citrus fruits (oranges, grapefruit and lemons and limes) in these countries grew at an average rate of one percent per annum. Table 2.4 Fruit juice imports to Japan by country of origin product Exporter % Orange juice Brazil 72.4 U.S. 23.7 Australia 1.4 Apple juice U.S. 22.4 China 18.9 Austria 18.6 Grapefruit juice U.S. 87.1 Israel 9.6 Australia 2.4 Grape juice U.S. 46.9 Brazil 14.1 Argentina 11.7 Pineapple juice Thailand 42.4 USA 28.6 The Philippines 27.6 Other citrus juice Israel 40.5 Italy 21.8 Argentina 13.9 (JETRO) Among 26 industrialized countries, the U.S. and Canada are the largest consumers of orange and mandarins followed by the EU. In fact, some E.U. countries such as Ireland, the Netherlands and Greece consume more oranges than do the U.S. and Canada on a per capital basis. The average per capital consumption of oranges and Mandarins in industrialized countries over the period 1990 to 2003 is 29 kilograms while that of grapefruit and lemons and limes is 3.0 and 3.6 kilograms, respectively (Table 2.5). Japan's consumption of both citrus (except grapefruit) and noncitrus fruits is small compared to other industrialized countries. The average annual per capital consumption of oranges and apples in Japan over the period 1980 to 2003 is about 14 and 12 kilograms, respectively, while those of grapes and grapefruit are 2.8 and 2.5 kilograms, respectively (Table 2.5). Table 2.5 Per capital consumption of fruits in industrialized and developing countries Developing Industrialized Fruits countries Countries E.U. Canada Japan U.S. Orange and mandarins 8.00 29.23 27.52 46.28 13.80 39.87 Grapefruit 0.32 2.91 2.17 4.05 2.49 4.12 Lemons and limes 1.25 3.59 3.78 2.60 0.84 5.26 Apples 4.67 20.3 24.82 18.82 11.58 21.02 Grapes 2.20 7.60 8.67 10.19 2.79 8.18 Pineapples 2.01 3.61 1.97 2.61 1.43 7.01 (Source: FAO, 2005) Japan's domestic supply of pineapples is heavily dependent on imports. In 2003, 95% of the domestic supply of pineapples came from imports (FAO, 2005). Japan is also heavily dependent on imports for its supply of lemons and limes. In terms of apples and grapes, the significance of imports has been increasing since the last decade during which the deregulation was in effect. CHAPTER 3 THEORETICAL MODELS Demand Approaches Approaches common in the literature of import demand analysis involve use of consumer demand theory and production theory. The consumer demand approach treats imports as final products that directly enter a consumer's utility function (Schmitz, A. and Seale, J. 2002) while the production theory treats imports as inputs (Washington and Kilmer, 2002). The first approach enables the derivation of the traditional consumer demand and labor supply functions from utility maximization, while the second approach enables the derivation of derived/input demand and output supply functions from profit maximization or cost minimization. The fact that output supply functions are derived in the production approach while labor supply functions are derived in the consumer demand approach marks one major difference between the two approaches. Another major difference between the two approaches is that the parameter estimates of unconditional consumer demand and unconditional input demand are different. However, similar parameter estimates can be obtained for the conditional consumer demand and derived demand for inputs. Furthermore, under the assumption of the constant percentage of retail price type of marketing margin, the demand for any given quantity of product is equally elastic (or inelastic) with respect to price at all market levels (Goodwin, 1994). This implies that conflicts of interest between the producer level and subsequent market levels are reduced. The constant percentage of retail price marketing margin is fairly typical for products for which the marketing process involves fixed investments and substantial economies of scale (Goodwin, 1994, pp. 292). Production Approach In the production approach, two allocation decisions, one involving outputs and another involving inputs, are made. These two decisions can be made successively or simultaneously through a twostep profit maximization or onestep or direct profit maximization procedure yielding a system of output supply and input demand functions (Washington, 2000). They are made successively in such a way that given output and input prices, first the output manager decides on the quantity of output, and knowing the quantity of output planned to be produced, the input manger decides on the quantity of inputs required to produce the planned output. The simultaneous decisions are made by one manager such that the input and output decisions are not independent of each other. In this case, since the input demand and output supply functions are not independent of each other and that their error terms are correlated (Laitinen, 1980), the input demand function can not be estimated independently of the output supply function and vice versa. Once the output supply and conditional input demand are estimated, the unconditional demand parameters can be derived from the parameter estimates of the two functions (Washington and Kilmer, 2002). The input allocation decisions that involve the use of conditional input demand functions can be implemented in stages/hierarchies (Theil, 1980b). That is, total expenditure is first allocated over broader groups of inputs and then group expenditures are allocated over individual inputs within each group. The twostage input allocation decision of the production approach is comparable to the twostage utility maximization of consumer demand approach (Figure 3.2). The consumer demand approach can yield a system of group consumer demand and conditional demand functions from which the parameter estimates of the unconditional demand function can be derived. As noted earlier, the unconditional demand parameters thus estimated are not the same as those derived from the system of output supply and conditional demand functions generated in the production approach discussed earlier. However, the parameter estimates of the input demand function (P ), group demand function (P2) and conditional input demand (P3) in Figure 3.1 are the same as that of the corresponding functions in Figure 3.2. That is, the parameter estimates of the input demand function (P ) are the same as that of the unconditional consumer demand (Cl); the parameter estimates of the group input demand functions (P2) are the same as that of the group consumer demand functions (C2); and that the parameter estimates of the conditional input demand functions (P3) conditional consumer demand functions (C3) in Figure 3.2. 2Stage profit maximization Output supply function Input demand function (P 1) I Group input demand function Conditional input demand (P2) function (P3) Figure 3.1 A two stage profit maximization Figure 3.2 A twostage utility maximization Although the two approaches provide the same empirical estimates with regard to the conditional demand, and that the demand for any given quantity of product is equally elastic (or inelastic) with respect to price at all market levels under the assumption of the constant percentage of retail price type of marketing margin (Goodwin, 1994), the production approach does not seem to lend itself to a theoretically consistent investigation of demand relationships among narrowly defined import products because of their independence. It may be realistic for broadly defined groups of imported products. For example, Theil (1980b) applied the production approach to broad imported products such as food, crude materials, semimanufactures, finished manufactures under the assumption of input independence. However, when it comes to narrowlydefined products such as fruit juices, it does not seem conceptually defensible and practical to apply the production approach simply because the importing firm's production function of an imported fruit juice is independent of other imported juices. Let the production function of a narrowlydefined import product such as orange juice be given by (3.1) h = h(hl(xl ),...,+hg (xgl ,.,+h, (xm)) where hg is a production function of each import product or input; xg is the import product or input. The groups run from 1 tom ; the number of inputs in each group is only one to indicate that each import is a unique input that produces a unique output; the number of inputs in group g is n The total number of products isn, +...+ nm. Equation (3.1) implies that the elasticity of output with respect to each input is independent of all other inputs; hence, all cross effects are zero. Let h (.) represents the production function of, say, Florida orange juice. This function does not have the orange juices of other countries as inputs because each individual input yields its own unique output. Hence, the constrained cost minimization procedure will not yield a demand function that consists of the prices of other orange juices. As a result, theoretically we can't investigate the relationship between Florida orange juice and other juices. The presence of input independence in the production function precludes us from investigating the substitution between imports of orange juice from different countries and competition among exporting countries. Consumer Demand Approach The present study chooses the consumer approach over the production approach since it allows investigating the nature of demand relationship among imported products and competition among different exporters. Consumption theory is amenable to analyze the market structure of commodities in fruit juice market. The theory involves the analysis of the change in marginal utilities of a certain product due to a change in consumption of a closely related product. The changes in marginal utilities are related to the price substitution terms of demand functions. Starting with a traditional utility function that is assumed to be well behaved (twice differentiable, increasing in its arguments, strict concavity), we can derive the Marshallian demand functions. They satisfy the properties of adding up, symmetry of the cross price derivatives, homogeneous of degree zero in prices and expenditure, and negative semidefiniteness in compensated price responses. Utility Maximization The maximization of a utility function u(q) subject to a budget constraint m = p'q is set up in a constrained optimization problem using the Lagrange method as (3.2). L(q,A)= u(q)+ A(m p'q) where q is the vector of consumption products; A is the Lagrange multiplier which can be interpreted as the marginal utility of income; m is total expenditure; p is the vector of prices. The first order conditions are (3.2.1) L(q ) (q) p = 0 9q and (3.2.2) mL(qA) p' q = 0 . The first order conditions imply that the marginal rate of substitution should equal the price ratio at the optimum, which in turn implies that the internal rate of trade should equal the external or market rate of trade. That is, a consumer will adjust purchases of products until their willingness to trade one for the other just matches the rate at which they can be traded in the marketplace, as given by the ratio of prices. From the first order conditions, we derive the demand functions for all products i and the marginal utility of income function as (3.3) q, = f (m,p) and (3.4) A= A(m,p). The choice of a functional form is at the interface of economic theory and the data. In other words, the functional form should satisfy the economic proprieties and fit to a statistical data satisfactorily. Two steps are followed in demand specification (Fousekis and Revell, 2000). First, behavioral assumptions are imposed which lead to a cost or to an indirect utility function. Second, a functional form is selected. Parsimony and flexibility are desirable properties considered in the selection of functional forms. The most common and parsimonious demand model, which dominated the import demand literature in the past, was the Armington trade model. The application of the Armington model to trade data dates back to the late 1970s and became popular in the 1980s and 1990s (Grennes et al. 1977, Sarris, 1981; Sarris, 1983; Abbot and Paarberg, 1986; Babula, 1987; Alston et al. 1990; Duffy et al. 1990; Haniotis, 1990). However, the Armington trade model came to be increasingly criticized on both conceptual and empirical grounds. The hypothesis of separability and homotheticity may not be supported by import data (Alston, et al. 1990). Traditional methods of implementing the Armington trade model result in theoretically and statistically inconsistent parameter estimates (Davis and Kruse, 1993). Consequently, systemwide demand models such as the Rotterdam model and the Almost Ideal Demand Systems have come to be popular in the contemporary import demand literature (Clements and Theil, 1978, Lee et al. 1990; Seale et al. 1992; Zhang et al. 1994; Yang and Koo, 1994; Schmitz and Wahl, 1998; Fabiosa and Ukhova, 2000; Soshnin et al. 1999; Schmitz and Seale, 2002; Washington and Kilmer, 2002). The choice among different systemwide demand specifications (e.g., the Rotterdam model versus AIDS model) is based on statistical tests (Brown et al. 1994). Economic theory does not suggest a criterion to choose ex ante between demand models. Barten (1993) demonstrates that the Rotterdam and AIDS models are special cases of a general demand model so that nested tests can be applied to choose either the Rotterdam or AIDS model or the hybrid of these two models (Central Statistical Bureau (CBS) and National Bureau of Research (NBR)). In the field of consumer demand analysis, the issue of selecting among competing functional forms has been addressed in a number of recent studies (Eales et al. 1997; Lee et al. 1994, Barten; 1993.; Schmitz and Seale, 2002; Weatherspoon and Seale, 1995). They have demonstrated that a family of competing systems can be generated through alternative parameterizations of Theil's differential system (Theil 1980). However, separability is an issue in estimating systemwide models (Seale, 1996). The AIDS model is not globally separable and only becomes separable locally under stringent conditions (Lee et al. 1994). This will render multistage demand estimation difficult. However, it is not uncommon to find the application of the AIDS model in a twostage budgeting framework (Heien and Pick, 1991; Soshnin, et al. 1999). In these two studies, the AIDS model was used for both the first and second stages. Other studies have specified a twostage demand system by applying the LES model for the first stage and the AIDS model for the second stage (Fan, et al. 1995; Han and Wahl, 1998; Michalek and Keyzer, 1992; Ma and Rae, 2003). Gao et al. (1996) specified a twostage demand by applying the extension of the AIDS model for the first stage and Generalized Linear Expenditure System for the second stage. The Rotterdam model, which is globally separable, has been applied in several studies to specify a twostage demand system. These include Duffy (1986); Clements and Johnson (1983), Clements and Selvanathan (1988), Brown and Lee (1997), Xao et al. (1998); E. Selvanathan and A Selvanatha (2004). All of these studies have used the Rotterdam model for both the first and second stage in a block independent framework for different applications, mostly of advertising. The present study prefers to use the Rotterdam model because of its global separability. Unlike the previous studies which have applied the Rotterdam model, the present study tests different separability hypotheses. The hypotheses will be discussed in the next sections. The Rotterdam Model Following Theil (1980a, 1980b), the Rotterdam model is derived from the maximization of a general utility function or total differentiation of a general demand function. Totally differentiating (3.3) yields (3.5) dq, = dm + lp,. am J\ P j Expressing (3.5) in log form (dlog q, = dq /q, ) yields (3.6) q,d(logq)= a (m)d(logm)+ i q d(logp) am J1,l where d(log q, )is the log change in quantity demanded of product i and d(log p ) is the log change in price of product j. Based on Barten's Fundamental matrix, the total substitution effects cq, in (3.6) can be decomposed into specific and general substitution terms as (37) aq, Au A aq, aqj aq, (3.7) = Au q pj aA/m am am am where u' is the (i, j)h element of U 1 the inverse of the Hessian; Au' is the specific substitution effect, which shows that the corresponding component depends upon the specific relation, in terms of u' between i and j. In other words, the utility obtained a aq, aqqj from product i is a function of the consumption level of products ; is OA/ I m am 9m the general substitution effect, which shows that all products are competing for the q, consumer's budget, and q, is the income effect of the price change dp on the am demand for the ith product. Therefore, the total substitution effect of a price change can be expressed as the sum of the substitution effect A' and income 9A/m am am m effect am q and is known as the Slutsky equation. The component Au of aq, /ap@ is the effect on q, of a change in pj when the change is accompanied by an income change so that the marginal utility of income remains unchanged. Substituting (3.7) into (3.6) and multiplying both sides by p, /m, we find w,(dlogq,)=p, q' d(logm)+ am (3.8) N Ppp A aq, aq, aq, n m 1 M aAamm amam m where w, is the expenditure share of product i defined as w, = p q m Multiplying out the second terms of the righthand expression of (3.8) yields w,(dlogq)= p (dlogm)+ pup jP (logpj) (3.9)m j A _q, q "d(log pj) N a" q d(logp). am AI am ahn m m m a J The first term of the righthand side expression of (3.9) is the marginal value share defined as cq, (3.9.1) 0, =p, dm The second term of the righthand side expression of (3.9) is the relative price coefficient v, defined as (3.9.2) v A = p p, p. m The third terms of the right handside expression of (3.9) can be rearranged to yield the general substitution effect as Np,p, A Sq, aq, Zq, A am' a /q a a d(log pj ppj p lo p ( ) m A/1am am d m Sm m Am Jm (3.9.3) N O= 00j d(log p) J1 where m = q, which is the reciprocal of the income elasticity of the marginal utility of income A . The fourth terms of the right handside expression of (3.9) can be rearranged to yield the income effect of a price change as (3.9.4) P q, d(log )p (logp ) = 0, w dlogp). I gm dm ma m m Substituting (3.9.1) through (3.9.4) and rearranging them yields (3.10) wd(logq,)= d(logm) w jd(logq) + vd(log p) 0, d(logp) . J =1 ) J=1 J=1 Rearranging (3.10) and using the constraint that the sum of the relative price N coefficients is proportional to the marginal value share Y v, = 00,, we find the relative J1 price version of the Rotterdam model (3.11) and the absolute price version of the Rotterdam model (3.12) as (3.11) w,d(logq,)= Od(logQ)+ vd logP . N (3.12) w,d(logq,)=O,d(logQ)+ r d (log p). J1 where d(log Q) = d(logm) w d(logq,)\ is the real income term; r, = v, 0,0j are the Slutsky price coefficients; (logP) = ,d(og p,) is the Frisch price index. J1 In order to identify the market structure underlying the importation of fruit juices into Japan, four different versions of the Rotterdam model are derived from the relative price version of the Rotterdam Model under different hypotheses. The hypotheses which represent different market structures are block independence, blockwise dependence, and uniform substitutes. The block independence and blockwise dependence hypotheses are applied to products that belong to different product groups while the uniform hypothesis is applied to products within the same product group. The models derived under these hypotheses in this study are block independent nonuniform substituteRotterdam model, block independent uniformsubstitute Rotterdam model, blockwise dependent nonuniform substituteRotterdam model and blockwise dependent uniform substituteRotterdam model. Block Independence Block independence is a special case of strong separability where one can group commodities into different blocks depending on some tangible criterion. Separability is a relative concept whose frame of reference is some partition of a product set into mutually exclusive and exhaustive subsets. Blundell and Robin (2000) indicate that the idea behind separability in consumer preferences is the existence of "natural" groupings of related commodities that reflect the budgeting decisions consistent with the true preference ordering of the representative consumer. Otherwise, empirical estimates of structural demand parameters are invalid. The usefulness of separability depends on the ability to classify products into groups which are empirically valid (Barten, 1977). The grouping of commodities into blocks is of paramount significance from a statistical point of view since it increases the degrees of freedom. However, the blocking 37 has to be theoretically consistent and empirically plausible. Suppose that we have G < N blocks or groups denoted as S,,..., SG such that each product belongs to exactly one group, the consumer's preferences under block independence is represented by the sum of G subutility functions, each involving the quantities of only one group given as (3.13) u= u u(q ,...,qn ,...,+ug(qg,...,qg ,...,+um(q i,...,q n)) where ug is a subutility function; qg is a subvector of q which consists of the q, s that fall underSg(g = 1,...,G). The groups run from 1 tom; the number of commodities in group 1 is n,; the number of commodities in group g is ng. The total number of products is n, +...+ m. Under (3.13), the utility obtained from the products in group g is independent of 02u the utility of products in group h. That is = 0. However, for i and j in the same aq,8qj 02u group 0 That is, the consumption of an extra unit of product j has an effect Oq,Oqj on the utility of product i and vice versa. Formally, the hypothesis of block independence (H0) states that the change in the marginal utility of a dollar spent on the ith product (i e Sg )caused by an extra dollar spent on the jth product which belongs to a different group (j e Sh, g # h) equals zero. The alternative hypothesis states that the change in the marginal utility of a dollar spent on the ith product (i G Sg )caused by an extra dollar spent on the jth product which belongs to a different group (j e Sh,g g h) is different from zero. d2H Ho : 2,q q = O for i Sg and jeSh; g h, 82U HA: T( 0 Ofori Sg and j Sh; g h. Under this hypothesis, the Hessian (2 u/aq, 9q, )and its inverse (2 u/aq, qj )l becomes a block diagonal. The marginal utility of each product depends only on the quantities consumed of the products that belong to the same group (Theil, 1975). Following Theil (1975), the changes in the marginal utilities can be related to demand parameters as v, = Ap,u'p, where v, are the relative price coefficients. When m i and j belong to different product groups, v0 can be set equal to zero because u' equals zero under the assumption of block independence. This implies that the assumption of block independence represents a market structure whereby the change in the relative price of a product in one product group does not affect the demand for another product in another product group. For instance, under this market structure, we are hypothesizing that the change in the price of U.S. grapefruit juice does not affect the demand for Brazilian orange juice. Orange juice and grapefruit juices are in different product groups. Block independent nonuniform substituteRotterdam Model. Following Theil (1980a), the block independent nonuniform substituteRotterdam model can be derived from (3.11) by setting v, equal to zero for i and j that belong to different groups as (3.14) w,d(log q,)=O,d(logQ)+ _vd log . JES I 'P Since all v, with i and j in different groups vanished, the number of free parameters is obviously reduced. However, no product is a specific substitute or complement of any product that belongs to a different group. The demand equation of the ith product contains Ng relative prices when it belongs to set S. The number of free parameters depends on the number of blocks and the number of commodities in each block. Theil (1980) shows that with G blocks having N commodities in total and an equal number of commodities in each block, the number of free parameters is 0.5N(1+ N/G). Blockwise Dependence In the previous section, we have assumed that the consumer's utility function can be additively separated into group utility functions. A weaker assumption is that the consumer utility function u(q) equals some functions( ) rather than the sum of the group utility functions. (3.15) u = uu (q ,...,q ...,u (qG ,...,q g M., (q ,..., q ) Unlike the case with (3.13), the utility obtained from a product in one group under (3.15) is not independent of the consumption of another product in another group. That is, a2u for i and j in different groups,  + 0. Since we are dealing with products in each 9q, 9qj group on a blockwise basis, we are assuming that the effect of the consumption of an extra unit of product j j Sh ) on the marginal utility of product i (i e S; g # h) is the same for all pairs of products in the two product groups; i.e., this effect is independent of i and j. Formally, the hypothesis of blockwise dependence (Ho) states that the change in marginal utility of a dollar spent on the ith product (i e Sg)caused by an extra dollar spent on the jth product which belongs to a different group (j e Sh, g # h) equals some constantagh; i.e., this effect is independent of i and j and hence, the same for all pairs of products in the two product groups. For instance, in the orange and apple juice groups, an extra dollar spent on either U.S. orange juice or Brazilian orange juice in the orange juice group has the same effect on the marginal utility of a dollar spent on Chinese apple juice or Austrian apple juice in the apple juice group. The utility interaction of two products of different groups in a blockwise dependence framework is a matter of the groups rather than the individual products (Theil, 1980a). H,: 2 O(p q, )(pJ qJ)= agh for all i e g,j e h(g f h). HA: B2 u/(p, q, )(p J q a g for all i e g, j e h(g h) . Following Theil (1975), the changes in marginal utilities can be related to the relative price coefficients (vy ) as OM 2Un CU g 2 h M 02U A A (3.16) v' =qAOm 2 Ug 'uh m a2u A A A u, a uh g0({p,q,) Oqj )=A h C'u/IUg */iuh' where i Sg; je Sh; and g h. Equation (3.16) shows that the crossgroup term is the same for all pairs of products from different groups. Following Theil (1975) and Brown (1993), the relative price coefficients corresponding to (3.16) can be given as (3.17) v, = gh gh, O where vY is the relative price coefficient; ~gh is a factor of proportionality which is the same for all i e Sg andj e Sh ; 0, is the marginal expenditure share. This implies that the assumption of blockwise dependence represents a market structure whereby the change in the price of a product in one group would affect the demand for another product in another product group in the same fashion. In other words, the effect of a change in the price of a product in group A on the demand for another product in group B is the same for all pairs of products in the two groups. For instance, under this market structure, we are hypothesizing that the effect of a change in the price of U.S. orange juice on the demand for Israelis grapefruit juice is the same as that of Brazilian orange juice on the demand for U.S. grapefruit juice. Blockwise dependent nonuniform substituteRotterdam model. Following Theil (1980a), the blockwise dependent nonuniform substituteRotterdam model can be derived from (3.11) as (3.18) w,d(logq,)= O,d(logQ)+ s vjd log + 0, Vghd log P P h3g P where 6, is the marginal expenditure share; v, is the relative price coefficient, which applies for the products within a group; 0, is the conditional marginal expenditure share; Vgh is the group relative price coefficient defined as Vgh = Z v, where g h. itg jth Substituting equation (3.17) forv0 we can write the group price coefficient as Vgh = (~fghg where = Z6, and 0, = ZO are the 0, are the group marginal leg ]jh expenditure shares of group g and h, respectively. Uniform Substitute Hypothesis In the previous two sections, no restriction was imposed within the groups of commodities, but weak separability prevails between groups. Now, we impose a testable restriction (uniform hypothesis) on products within a given group. A group of closely related products are uniform substitutes when the cross effect of an additional dollar spent on one product on the marginal utility of another dollar spent on another product is the same for all pairs of products in the group (Brown, 1993). The uniform substitute hypothesis was initially proposed by Theil (1980a) to deal with the demand for closely related products such as different brands of a product. Since the same products that are imported from different countries can be treated like different brands of the same product, the application of this hypothesis to the same product differentiated by country of origin is relevant. We consider this hypothesis given block independence and blockwise dependence framework discussed earlier. In other words, we impose the uniform substitute hypothesis on (3.14) and (3.18). Uniform substitute given block independence Suppose that we have a product group S, that consists of the same product differentiated by country of origin of production. The consumer's preferences for a uniform product given block independence can be represented by the sum of G sub utility functions, each involving the quantities of only one group given as (3.19) u = uul(q ..., q ,...,+u, qg,...,qg ,...,+um(q ,..., qmn) Under (3.19), the utility that a consumer obtains from the products in one group is 02U independent of the utility of products in another group. That is, = 0 for i e Sg aq,8q, andj j Sh. However, for the ith and sth products in the same group, we are hypothesizing that the marginal utility of a dollar spent on the ith product (i e S, )caused by an extra dollar spent on the sth product which belongs to the same group (s e S ) is the same because i and s are the same products differentiated by country of origin of production. Theil (1980a) writes the submatrix of the Hessian of the utility function 0 in expenditure terms, multiplied by the scalar ..m/A as 011 k .. k [o1 _.nm 02U k 022 ... k A L (pqj)O(pqj) k k 0"" 1 where all the offdiagonal elements(O' = , i j) are equal to a positive constant k. Since O.m/A is negative, this type of preference structure implies that the marginal utility of a dollar spent on each product in Sg is affected negatively and by the same amount kAI/.m when an additional dollar is on any other product in the group. Thus, all products in S, are affected uniformly by the additional consumption of any other products in the group. Since we have betweengroup (block independence) in addition to the within group restrictions (uniform substitute), we have two null hypotheses. The block independence hypothesis has to do with the products between two product groups, and the uniform substitute has to do with products within the same group. Note that the uniform substitute hypothesis in this study is applied to the same product differentiated by country of origin. Formally, the null hypothesis of a uniform substitute relationship states that the marginal utility of a dollar spent on the ith product (i e S, )caused by an extra dollar spent on the sh product which belongs to the same group (s e Sg )equals some positive constant k except when i = s, i.e., this effect is independent of i and s and hence, the same for all pairs of products in the same group. 02U Ho =k fori, sSg. The block independence hypothesis states that the marginal utility of a dollar spent on the ith product (i e g) caused by an extra dollar spent on the jh product which belongs to a different group (j e h,g # h)equals zero. H : 7 2 = 0 for i S and je Sh; g h. 0(qp, q, )n\P 4 nh Combining the two null hypotheses corresponding to the uniform substitute and block independence, the new null hypothesis which corresponds to the uniform substitute hypothesis given block independence can be restated as H = k fori, s S ,; = 0 for i S and j Sh; 0(Pq(pqpq, )gqj g h. HA .: k fori, s e Sp = 0 for i e Sg and jESg; g h. Theil (1980a) derives the relative price coefficients of a block independent uniform substitute model as f ,o((1ko) v =# 7=I i 1 kO, (3.20) k0j v, = 0 I vj lkO ij where vj is the relative price coefficients; 0, is the marginal value share, k is a constant; 0, is the group marginal value share; q is the income flexibility. Block independent Uniform SubstituteRotterdam Model. Substituting the price substitution terms (3.20) in the block independent nonuniform substitute Rotterdam model (3.14), the block independent uniform substituteRotterdam model can be derived as (3.21) wd(logq,)= Od(logQ)+ 0(1kO) d( logP + k d log ' 1k P) k P where 0, is the unconditional marginal value share; q is the income flexibility; k is a constant; 0g is the group marginal value share; Uniform substitute given blockwise dependence The consumer's preferences for a uniform product given blockwise dependence can be represented by consumer utility function u(q) equals some function f( ) rather than the sum of the group utility functions. (3.22) u =u(u(q,,...,q ),...,u(qG, ..,q ),Gn M(qM,...,q1 M)). Under (3.24), the utility that a consumer obtains from the products in one group is not independent of the utility of products in another group. That is, for ith and jth 82 products in two different groups,  # 0. The consumption of product i has an tq,9 qj effect on that of product j and vice versa. For the ith and sth products in the same 82U group,  0. tq, Oq, Since we have betweengroup (blockwise dependence) and within group (uniform substitute) restrictions, we have two null hypotheses. The blockwise dependence hypothesis has to do with the products between product groups, and the uniform substitute has to with products within the same group. Formally, the null hypothesis of a uniform substitute relationship states that the marginal utility of a dollar spent on the ith product (i S )caused by an extra dollar spent on the sth product which belongs to the same group (S e Sg )equals some constant k, i.e., this effect is independent of i and s and hence, the same for all pairs of products in the same group. 82U Ho 2U (p,,=kfori,seS,;ig s. The blockwise dependence hypothesis states that the marginal utility of a dollar spent on the th product (i e Sg )caused by an extra dollar spent on the jth product which belongs to a different group (j e Sh,g g h) equals some constantagh. 82u H0* = pq,)(pj ( j agh for iSg and jiSh; gfh, Combining the two null hypotheses corresponding to the uniform substitute and blockwise dependence, the new null hypothesis which corresponds to the uniform substitute hypothesis given blockwise dependence can be restated as U2U 12U HO: .=U =k fori, seSG 0U agh for i Sg and S (Gq,)(pq) k f(orisJ jeSh; g h, 02U 12U HA (: .pq)(pqqj)#kfor i,seSg ;p,, agh for i eS and j Sh; g h. Seale (2003) derives the relative price coefficients for a blockwise dependent uniform substitute Rotterdam model as S Ogg (1 kO,jgg) 1kO, (3.23) k 1 kOg where vj is the relative price coefficients; 0 is the income flexibility; 08 is the conditional marginal value share, k is a constant; 9g is the group marginal value share. Blockwise dependent Uniform SubstituteRotterdam Model Substituting the price substitution terms (3.23) in the blockwiseRotterdam model (3.18), the blockwise dependent uniform substituteRotterdam model can be derived as I1 kOI (p wd(logq)=Od(logQ)+ 1 d logP + d logP + (3.24) 1 Sk,0 ) P IS1 P) O,'I Vgh dlog Phj h1g P ) The uniform substitute restriction results in a substantial reduction in the parameter space and can be useful for obtaining more precise parameter estimates and maintaining sufficient degrees of freedom (Brown, 1993). CHAPTER 4 EMPIRICAL MODELS AND ESTIMATION PROCEDURES Since the differential approach to consumption theory discussed in chapter 3 does not postulate constancy for the coefficients of its demand equations, we are not entitled yet to talk about empirical estimation. In this chapter, we discuss the ways in which the theoretical models in chapter 3 are parameterized so that they can be applied to statistical data. Since the nature of data forces us to work with finite rather than infinitesimal changes, we replace the infinitesimal changes by finite changes. Furthermore, we postulate that the coefficients are constant to make the models operational. Finally, estimation procedures are presented for the different versions of the Rotterdam model. Empirical Models The Relative Price Version of the Rotterdam Model Following Theil (1975), the relative price version of the Rotterdam model (3.11) can be written in finite changes as (4.1) ,dq,,t = 0dQ, + I v + J1 IdP, where, = (Mw +w,,, 12)/2 is the average expenditure share ;dq, = log(q,,/q,, 1,) is the finite change in quantity imported of product i; 0, is the marginal expenditure share of product i; dQ, = w,,dql, +... + wl,,dql,, is the finite change version of the Divisia price index (real income) ; vj is the relative (Frischdeflated) price coefficients; dpt, = log(pt /p,t 1) is the finite change in price of product j; dPt = Odpl +... + 018dpl,, is the finite change version of the Frisch price index; Note that the lower case p is for prices of individual products and the upper case P is for Divisia price indices. ,, is the demand disturbance, which is regarded as the random effect of all variables other than income and prices. It is assumed that it has zero expectation, that the variances and contemporaneous covariances are constant over time, and that all other covariances vanish as (4.2) =0 if s t The coefficients of (4.1) are subject to the addingup constraint = 1 and the symmetry constraint vJ = v, and negative definiteness of the matrix v, Furthermore, the sum of the relative price coefficients is proportional to the marginal expenditure 18 shares V, = SO,, where q is the income flexibility. J1 In this study, six fruit juice groups (orange, grapefruit, other citrus, apple, pineapple and grape juices) imported from 18 countries with three countries for each juice group are included (Table 4.1). In order to estimate (4.1), three steps are followed. First, one of the 18 demand equations is deleted in order to eliminate singularity. Second, the constraint on the price 18 18 coefficient vv, = 80, is imposed and third, the adding up constraint Ok = 1 is j=1 k=1 imposed on the income coefficients. Table 4.1 Codes for countries exporting fruit juice to Japan Exporting Quantity log Price log Budget Product country changes changes shares Code Orange juice U.S. dqi dpi wi 1 Brazil dq2 dp2 W2 2 ROW dq3 dp3 w3 3 Grapefruit juice U.S. dq4 dp4 w4 4 Israel dq5 dp5 W5 5 ROW dq6 dp6 w6 6 Apple juice U.S. dq7 dp7 w7 7 Austria dqs dps w8 8 ROW dq9 dp9 W9 9 Pineapple juice Thailand dqio dpio wlo 10 Philippines dq11 dpi1 wii 11 ROW dqi2 dpi2 w12 12 Grape juice U.S. dq13 dp13 w13 13 Argentina dq14 dp14 w14 14 ROW dq15 dp15 w15 15 Other citrus juice Italy dq16 dp16 w16 16 Israel dq17 dp17 w17 17 ROW dqis dpis wls 18 aROW means rest of the world 18 Imposing the constraint vi, 71= 60, on the price coefficients, we write the own 18 price coefficient v, in terms of the other price coefficients as v,, = 00, Yv, so that the price term of (4.1) becomes 00, 18 18 dP) + v, (dpj dP) , (dp, dP)+ v (dpJ dp,) (4.3) 17 Imposing the addingup constraint 01 = 1 6Ok on the income coefficients, the price substitution term of (4.3) becomes 17 18 (4.4) = 00, dp dp18 Z Ok(dpk dp18) + v, (dpj dp,). k=1 J# Substituting (4.4) into (4.1), we obtain (4.5) W,dq, = O,dq, +OA,(O)+zv, (dp, dp,)+E, J#i 17 whereA,(O) = dp, dp18 Ok(dpk dp1 8) . k=l Equation (4.1) is still not estimable unless conditions are imposed on the matrix of price coefficients in addition to symmetry and negative definiteness, such as preference independence and/or block independence (Theil, 1980a). As soon as there is one constraint on the price coefficients such as v12 = 0 (preference independence between product 1 and product 2) in addition to symmetry and negative definiteness, it is possible to estimate (4.1). The reason that (4.1) is still not estimable is that the income flexibility q is not identified because of its invariance under monotone transformation of the consumer's utility function (Theil, 1980) in which case there may not be unique demand functions. Equation (4.1) can be estimated using the following system of symmetry constrained equations. dq, = dQ + QA, (0)+v1(dp2 dp)+v13 (dp3 dp,) +... +v, 8(dp8 dp,) w2dq2 =2dQ + A2 (0)+ v(dp dp2)+ 23(dp3 dp2)+ + (dp1 dp2) T3dq3 03dQ + A3(O)+ v13 dp, dp3 )+3 (dp2 dp3)+ +v318 (dp8 d)3 S4dq4 = 04dQ + A4 (0) + v14 (dp1 dp4) + v24 (dp dp4 )+ + V418 (dp dp4) 5 dq = BdQO + A,(0)+ v,,dp, dp ,)+ v25dp2 dp5,)+ +v518(dp1 dp5) Sdq, =,6dQ + A, (0)+v,,dp, dp6 )+v26 dp, d)+...+v,,,18(dp, dp,) wAdq7 = 0,dQ + A7(0) +v7 (dp dp,) + 27dp2 dp,) +... + V71(dp dp7) w dq8 = 08d + (Q0) + v,, dp, dp,) + 2 d +...+ 0 ,, V81(dp, dp8) Wgdqg9 = dQ + A9 ()+19 (dp dp9 + V29 dp2 dp9) + 91 8 (dp8 dp9) w1Odq1, = O1dQ + A10 ()+v1o(dp1 dpO1)+v210(dp2 dp1O)+...+v118(dp18 dp1O) wdq, =,,dQ+A (O)+v,,, (dp, dp1,,)+v2,(dp2 dp1,,)+...+ v,111,(dp, dp,,) w12dq, =012dQ + (A12(0)+v112(dp dp12)+v22(dp2 dp12)+...+121(dp1 dp12) w,3dq,3 =013dQ + (A13(0)+v 113(dp, dp,13)+v213 (dp2 dp,13) +... +v1318 (dpS dp,13) wi, Jq1, = 014dQ + A(0) +v1 (dp, dp,14)+v214 (dp2 dp14)+...+v1418 (dp18 dp,14) w5,dq1, = ,,dQ + A5,(0)+ 1,(dp, dp,)+v215(dp dp,)+... + v51(dp, dp) 116d16 = 16dQ + A16(0)+v116(dp dp16) +216 (d dpl6)+*+ 618s(dpl dpl6) w17dq,, = 0,7dQ + (A17(0)+ v,17 (dp dp7) + 217 (dp dp17) +... +v171 (dp dp) The above system of equations provides the specific price substitution effect. The specific substitution effect accounts for the n price changes on the demand for the ith product (Theil, 1980). The specific substitution effect is one component of the effect of a change in price. In order to estimate the total price substitution effect, one needs to estimate the absolute price version of the Rotterdam model. The total substitution effect is the sum of the specific and general substitution effect. The general substitution effect is concerned with the competition of all products for an extra dollar of the consumer's income. The Absolute Price Version of the Rotterdam Model The absolute price version of the Rotterdam model (3.12) can be written in finite changes as N (4.7) wdq, = dQ + 7rdpJ +, J1 where vrj = v J b0, 0 The Slutsky price coefficients r, are symmetric negative semi definite of rank n n 1 and satisfy the homogeneity property Trj = 0. A major convenience of the absolute j=1 price version is its linearity in the parameters, thus implying that a leastsquare regression estimation yields best linear unbiased parameter estimates when (1) the explanatory variables take nonstochastic values; (2) the disturbances have zero means and a constant contemporaneous covariance matrix and are serially uncorrelated; and (3) the homogeneity condition and the Slutsky symmetry condition are ignored. A disadvantage of the absolute price version of the Rotterdam model is that the number of the Slutsky price coefficients r, grows rapidly when the number of commodities N increases. The number of free parameters in (4.7) is given by N + N2, where N is the number of commodities. Even after imposing the restrictions of adding up, homogeneity, and symmetry, the number of free parameters is reduced to0.5(N+ 2)(N ). The absolute price version of the Rotterdam model with symmetry and homogeneity imposed can be estimated using the following system of equations. w,dql = 01dQ + [T, (dp, dp8)+ ,12 (dp2 dp,8)+... + ,18 (dp7, dp,8)] (4.8) w2dq, =O dQ + [r,2(dp, dp,8)+ ,z22(dp2 dp,8)+...+,, .(dp7, dp,,)] w,3dq3 =03dQ + [7r (dp, dpd)+ c23 (dp p2 dp8))+ ...' +n d,,7 dp8 )] SW4dq4 Swdq5 = T6dq 6 wdq, = w9dq9 = w10dq 0 w1 dq 1 w12dq12 Twedq {W13dq13 W14dql4 W15dq15 SW16dq16 w17dq 17 0dQ + [l4 (dp,  0,dQ +[ [ dp,  06dQ + [1T6 dp1  0,dQ +[;0dp,  0,1dQ + [11, dp,  0gdQ + [T19 dp,  = +,dQ +T 10(dp, =01 dQ +[TII(dp, =0,12dQ+[T1Z(dp, =013dQ + [113, dp1 014dQ + [1T14 (1 = 015dQ + [115 (dp1 =016dQ + [IT16 (dp = 01dQ + ,17 (dp, 1)+.. + .7418( 17 dp18) p,) +...+ (dp,, 7 dp dp, 18 )++518 (417 18)] p,1 )+... + 7618 41, 1dp)1 p18)+...+ 718(dp4, dp ] ,18) +. + 1(dp1 dp18)] p18)+ + 91 1 (dp1 dp1) dPls)+" 2(dP2 IPls8)+:25(CdP2 d 1p)+) 27 (d2  dp18)+'7 (CdP2 d dp18 )+ (dpd dp,1 )+ : 1 (dp2  dp1 )+212 (d  dp18+7;T213(dp2 dp,,)+7 ,dp dp1)+, 4dp2 P 21 dp18)+z (dp2  dp18,) +z (dp  dp,8) +7 21 (dp2 Block Independent Nonuniform SubstituteRotterdam Model The block independent nonuniform substituteRotterdam model (3.14) can be written in finite changes as (4.9) wudq, = Od + Iv,, d +6, . The estimation procedure of (4.9) is similar to that of (4.1) presented earlier. In order to estimate (4.9), one of the 18 demand equations is deleted to eliminate singularity. Using the constraint v1, = 00,, we write the own price coefficient v,, in terms of t Vo so that the price term of (4.9) becomes j#1 d18) )+ +1018 (d17 dp18)+ ...+ 1118 (d17  dp18 +.. + ,. + 4(17 18 )+* +71318 (17  18)+ +.. +71j ( p17 dp18 )+ ...+ 1518 (d17 p18 )+. + 71618 ( 17  p,)+ +...,,(1p,, dp1)] dp18)] dp18)] d18)] dp18)] dp18)] dp18)] dp1)] the other price coefficients as v,, = 00, 00, dP) + v,(dp, dP). J^zlS, , (dp, dP) + vZv, (dp I^jeS, dp,). 18 Now, using the adding up constraint 01 = 1 Ok ,(4.10) becomes k=1 17 dp 18 Ok(dpk k=l dpl8) + v, d(p, jGSg Substituting (4.11) into (4.9) yields (4.12) w,dq, = O,dq, + 4,A, ()+ v, (dp dp,)+, Equation (4.9) can thus be estimated using the following symmetryconstrained system of equations. OdQ + A, (0)+ V12 (dp2, 02dQ + A2 (o0) + v12 (dp1  ,dQ + A,3 (0) + V13 (dp1 04dQ + #A (0) +v,, (dp, O4dQ +A4(0) v45(dp5 S5dQ + A, (0)+ v45 dp4 06dQ + A6 (o) + V46 (dp4 SOdQ + OA7 (0) + v,7 (dp, :0dQ +A, (0)+ v7(dp,7 S9dQ + A9 (0)+ v79 (dP7 dp ,) + V23(dp3 dp) dp4)+46(dp dp4) dp,)+ 56 (dp6 dp,) dp6)+ v56 (dp5 dp5) dp7) +v79(dp9 dp,) dp,)+ v89 (dp9 dp) dp9)+v89(dp8 dp9) (4.10) (4.11) 00, dp, dp,). Swdq, : wdqw Tw24dq 2 SWadq 6 {7dq7 w8 dq8 w9wdq9 w[dq,3 [9dq94 IV, (dp, Ji^ J Sw,,dq,, w1 ,dql , {W13dq13 S14dq14 w15 dq15 S16dq16 w117dq17 O10dQ+ Ao(0)+ v101,(dp,, 0,1dQ + ZA1 (0) + v10, (dp OB~dQ + A12 (0) + v10,1 (dp1 03dQ + A13 (0)+ ,v314 (dp14 014dQ + A14 (0) + v1314 (dp13 O15dQ + A15 (0) +v1315 (dp,3 016dQ + A16 (0)+v1617(dp17 ,17dQ+ A17(0)+Av1617 (dp16 Blockwise Dependent Nonuniform SubstituteRotterdam Model The blockwise dependent nonuniform substituteRotterdam model (3.18,) can be written in finite changes as dp j 01 6 dph (4.14) wdq, =,dQ + V + I Vs, + E dP Y ^ ^ dP 0 h J S, where v, is the specific price coefficients of products within in a group; Vgh is group relative price coefficients; dPh is the Frisch price index of a group, and E, is the error term. The estimation procedure of equation (4.14) is also similar to that of (4.1). In order to estimate (4.14), one of the 18 demand equations is deleted to eliminate singularity. Using the constraint that the sum of the price substitution terms is proportional to the marginal value share I V, + Y Vgh = 00,, we write the own price coefficient jGSg 0 h l J Sg dp,)+v1012(dp12 dp,)+ v1112 (d12 dp10)+v112 (dp 11 d13)+ V1315 415 d14)+ V1415 (15 dp15) + V1415 (d14 dp16)+1618 (d18 dp17)+ 718 (dp18 dpo) dp,,) *12) dp13) dp14) dp5) dp16) dp17) 01 6 v, in terms of the other price coefficients as v,, = 00, V, Vgh and JS hg substitute it in equation (4.14) so that the first price term of equation (4.14) which corresponds to the within group demand becomes (4.15) = o V Vg dp, dP)+ Zv,(dp, dP) (4.16) 0 d d6 01 6 V= Jd V (dp, dP) + v,((dp, dp, ) Substituting (4.16) into (4.14), we obtain j sg (4.17) s o Vy (dV@P dP)+ E, Equation (4.14) can thus be estimated using the following symmetryconstrained system of equations (equation 4.18). system of equations (equation 4.18). W dql = OdQ + o0, K + (V2 +V3 +... +V6) (dp, dP)+ v 1(dp2 dp)+ V3 (dp3 dp)+ 0 [v, (dP2 dP) + V (dP3 dP) +... + V(d d)] dq2 =0dQ+ 00 (V12 +V3 +...V16)(d2 dP)+ o u^ +o u + ua j v(dq d p) + 1 +2+ O) v12 (dp1 dp2)+ V23(dP3 dP2) 02 IV12 +Po2 d + V23 + P3 dp+ V d d yp2 01, +02 +0 ,dqz,=dQ+ 0 +0 V2 +V2+...+ dP)+ v13 (dp d3 ) + V23 (d dp3) 03 V1 [2(dP dP)+ V13(dP3 dP)+.. + V6(dP6 dP)] o, +2, +0 wi4, = 4,dQ+ !4 04 (V12 + V23 + +.V26) (dp4 dP)+ 1 04 + 5 + 068 V45 (dp5 dp4,)+ V46 (dp6 dp4)+ S 054 0 v12(dl dp)+23d3 d)+...+V26(dP6 dP) 04 +05 +03 T 5 =0d+ 0 05 (V12 + V2( 3 V V+...+ V26)dp dP)+ 1 04 +05 + 6 V45 (d4 dp)+ V(d s dp) + 05 [V12(dP dP) + 2(dP3 dP)+...+ V26(d dP)] 04 + 0, + 06 ) wdq, =06dQ+ 006 (V,2+V +...+V + )(dp6 dP)+ V46 (dP4 dP6) + V56 (dP 5 e6 ) + 06 [V (p dP) + V{ P( dP)+... + V(dP dP)] 0 4 +5 + 06 w dq, =0_dQ + (V, 7+V, 23 +...36 dP)+ 07s( +0s8+09 9 V78 (dP8 dP7) + V79 (dP9 dP7) + 07 [V, (dP, dP) +V (dP, dP) +... +V36 (dP6 dP)] dq + 0, + 09 wdq, =0dQ + 008 0 (V +V3 + ...+V36 d dP)+ 07 +08 +09  v78 (dp, dp,) + V89 (d9 dp,8) + 08 [V13 ( 09 ( +13 V23 +V36(dp9dp) wTdq9 = OdQ + V09 09 + O, + 09 +'3)(dp P)+ V,,9 (dp dp9)+ V9(dp, dp9) )+ 07. + + 0936 [0d +001 010 (V14 + _V24 _+_ + _V46) (dplo dP)_+ dq,9 =dQ + 0o9 V +V + + ...dP)+ lOll (dll d9) + V9(dP dp ) + 010 9 V14 (dp dP)+V2 (dP2 dP)+...+V36(dP6 dP) o +ol011 ++0 ,,.JLq,, = OldQ + 01 _ 10 (V +V24 +...+ (d dP)+ K 010 + [v( l + 02 VlOll(dPlo d+Pll)+ V2(dPl2 dPll) + 01 [V14(dP dP)+ V24(dP2 dP)+... +V46dP6 dP)] Ol1 + On + O12 2dq2 =01dQ+ (V4+V24 +...+V46) (dp dP)+ 0, + +ol + 1012 V01 ( d10 n 1) + V1112 ( d12 dn1) + v1012 (dp10 dp12)+V112 (dp11 dpl2)+ K010 V011 (dP dP) +V24dP2 dP)+...+ 46 dP6 dP)] 01. +oil + 012 w13dq13 = 03dQ +01+ 013 +15 + V25+ + +...+V) (dp3 dP)+ 1314(d14 )+J315(5 13)+ 013 14 [015 5(d4 dp+ V(dP2 d)+'...+ V5(d6 dP)] 013 + 014 + 0dP1+ w,,J, =0 ,,dQ+ 014 (V15 +V25 +...+ V56(dp dP)+ lq13 + 14dQ + 3 015 v1314(dP13 dP14)+V1415(dP15 dP4) [ 041 5 (d d)+25 (ddp)+...+V56(dP6 dP)] 013 +0 +01 wIdq1, = 0,dQ + 0 15 (5 V25 +.. + V56 (dp5 dP)+ L1q (013 + 014 + 015 V1315 (dP13 dP15) + V1415 (dP14 dP15)+ [ 013 4 15 ([v15i dP)+ V25(dP2 d)+...+ 6(dP6 dP) 013 +6014 + 1 w16dql6 =16dQ + 0016 016 +0 16 +V26 + + 56) dp16 dP)+ 1 016 +017 +018 V1617(dp17 dp16)+1618(d18 dp16+ 016 16(dP dP)+V26 dP dP)+...+V6(dP dP)] 7dq, = 017dQ+ 0017 01 +0+01 + 26 + +...+V56) (dp dP)+ 1 617(dp16 dp17 ) + 718 (dp18 dp ) + K016 +817 +818 Block Independent Uniform SubstituteRotterdam Model The block independent uniform substituteRotterdam model (3.21) can be written in finite changes as 8d (1kIo,) d , k @,p dp (4.20) wdq = ,dq + (k dP + d I' k k dP lk dP Equation (4.20) can be estimated using the following system of equations. 1, 1O k, 1 ) k] 8, 0, 01 j) (dp, dP) + (dP2 dP) + 1k,(0, +02 +03) 1kI(, + 02 +03 ) w,dq, = 0,dQ + _ k013 (dp3 dP) 1 k,(01,+0 + 03) _ 12 (dp, dP) + (dp2 dP) + 1 k, (, + 0, + 03 ) 1 k, (, + 0, + 0) wzdq2 = 0dQ + I k1( 0203) (dp, dP) 1k,1(0, +0 + 03,) k0103 (dp, dP) + (dp dP) + 1 k (0, +0, +03) 1 k(0, + 02 +03) 03 (1 k, 03) lq =k(O O2Od+ c/ ) 04(1 k204) d k20405  S'14 =04dQ+ k2(04+05+6) k20406 (dp6 dP) 1 k,(0, +0 +06) S k2 (dp dP) + 5 k (d5 dP) + Td5=1 k2 (04 +08 +06) 1k4 (04 + 8, + 06 20506 (dp6 dP) 1k (04 +05 +06) k,0, 0,( 1k 6,) k20406 (dp4 dP)+ k205 (dp dP) + 1 k2 (04+ 5 ) 1 k (04 +05 +) wdq, = ,dQ + ( 06 k 2 6 dp, dP) 1 k2 (04 + 85 6+ c) k 040 k 0 0 07 k30 (dp dP) + (dp dP) + 1 k3(07 +0,+0 ) 1 k (0 +0 +09) wdq6 = 67dQ + _ S(1 k8 0) k3009 (dp9 dP) 1k3(8 +0,+09) k3008 (p7 (dp, k3(07 +08 +09) k30809 (dp9 k ( +0 8 +09) k30709 (cp7 k, (07 +08 +09) 09 (1 k309) k3(O7 + 08 + 09) 0,(1k0+0) k4(01o + 11 + 012 k401001 (dp k4(010 + 011 + 012) k410(12 dp k4 +0111+ ) k4(010 +01 + 012) k4(10 +011 + 012) k4(010 +0112 0 ^(fo 7ft+f2)(d12 013(1 k5013)d) k5 (013 +014 +015) (d Pl k50130 (d dP) k5 (013 + 014 + 015 ) k51314 (d3 dP)  k5(013 +014 + 015) k5014015 ( ) k5(013 +014 (d dP) k,(8, +014 +1 08(1 k3o8) dP)+ (dp8 1k3(07 +08 +09) dP) dP)+ 30809 (dp8 1 k (07 +08 + 09) dP) d k4010011 ] dP) + (diI dP) + 1 k (010 +011 + 012)) dP) dP) + 8k1 (1 k411 ) (pl1 1 k4(o + 8Oil + 012) dP) P k4011012 ( dP)+ (dpl, 1 k4(0 + 1 +1 2)  dP) k501301 ( 1 k(0 + 014 + 01 ) + 014(1k5014) + (dp14 dP) + 1 k,(013+014 + 015) w 1 w ,/q, = 0dQ + { 1 = w9dq9 = 09dQ + () 1 ,,,Jiq,,, =01odQ + [ 1 w1dq,, = 01dQ + d = + w12dq1 = 012dQ + w13dq13 = 013dQ + w1q11 =014dQ 1 +  1 1 15dq15 = 15dQ + 0 16 = 16dQ + 1 16dq16 O16dQ+c/{ 1 k5013015 d13 ^) (dp, k,(013 +014 + 015) 8,0 15(1 k,5 015 ) (dp15 (dp,, k, (013 +014 + 015 8016 (1 k6 016) (dp16 k6(016 + 017 + 018) k6016018 (dp8  k6(016 + 017 + 018) dP) + k5014 15 (4 dP) + 1 k,(013+04 + 15) dP)  dP) + (01617, dP) + 1 k6 16 + 17 81  dP) k6 167 dP )+ 017 (1 k6 17) (dp17 17 (dpl6 dP) + (dp,, dP) + 1 k6 (16 + 17 18) 1k6(16 17 + 18) 17dq7 = 017dQ + k0101 k6 17 1 + 8 (dp,, dP) 1 k6 (,16 + 17+ 180 ) Blockwise Dependent Uniform SubstituteRotterdam Model The blockwise dependent uniform substituteRotterdam model (3.24) can be written in finite changes as (4.22) w,dq, = 0,dO+ Q+ 1 k,0 + Vgh dP k,, dP 1ke, dP hsg dP Equation (4.22) can be estimated using the following system of equations. 0,(1k,0,) kze0e, ^ k01(1 k01 (dp, dP) + kl0 (dP2 dP) + wdq1 =dQ(0+ + 03) 1 k, (012 +0 + 0 wldq, = 1,dO + # + k,003 (dp3 DP) 1 k,(01 +02 +03) 01 [V2(dP2 dP+VPPP)+ Vd3 dP)+...+V16(dP6 dP)] k10102 (dp dP) + 01 dp, dP)+ 1 k ((0, ++ 0 0 w2dq2 O2 dQ. + k1023 (003 [ 01 +2 [(dP2dP)+ 3(dP3 dP)+...+6(dP6 dP)] 9 + 0 + b3 k1013 (dpl dP) + k10 (dp2 dP)+ 1 k (0 + 02 + 03) 1 k,(0 + 02 + 03) wzdq, = dQ +< (1 k, _) 3dq3 3dQ3) (dp3 DP) 1 k1 (01 + 02 + 03) l02+03+0, K +01 o jV12(dP2 dP)+V13(dP3 dP)+...+ Vl(dP6dP)] S0(1 k204) d k204 dp 1dq(=0d +O24 05 ) 1k2(04 +05 +06) w4dq4 = 04dQ +D k20406 (dpp DP) 1k (04 +05 +06)+ 04 05 V12 (dRl dP) + V23(dP3 dP )+...+ V26( d) 8, +0, + 06 F k20405 ((1 dP) k )dP) dq5 1 (04 + 05 +06) 1k (04 +,05 +06) wdq, = 8,dQ +a> k20506 (dpDP) 1 k (04 + 05 + 06) 5 [V 1 2(d dP) + V23(dP, dP) +... +V26(dP6 dP 04+0 +5+06 k206 (dp dP)+ k200 (d) dP 1 k(04 +0, + 0) 1k (0+4 8 +06) wdq, = 6,d6 +0 k06 (dp6 DP) 1 k (04 + 0, + 06) 06 V2 (d dP) + 2 (dP2 dP)+... + V26(dP6 dP 8 (1 k30 dP k30 (d dPk)+ 7 =e + 1k07, 8 +0, + ) d k?(8 +0 +0) 09) w dk379 (dp9 DP) 1k3(7 + +09) 07 + [V13(dp dp) + V23 (P2 dP)+ ...+V36(dP6 dp) 0 + 8 +9 + j 7 I + k3078 ( dp dP) + (05(13 _p dP)+ 1 k3 (0,+0, + 09) 1 k3 (0 + 8 + 09) ,8d k3(389 (dp9 DP) 1k3(0,7 + 0,8 +0,9 08 V13 (dp dP)+ V (dP dP)+...+ (dP6 dP)] 07 +08 + 09 k3079 (dp, dP)+ 1 k (0 + 08 + 09) 1 wdq, =9,dQ + , 9 k1 k, 9dq9 309d+ ( (dp 9 DP) L1 k3 (O7 + + 9) 09 [V3 (dP dP() Vd+ V3 (dP I 0 ( 1 + 082 + 91) \ ..Ji/, =0 81dQ + 0 11 0 ( 1 k 4 0 1 0 1 2d 2 1 k4 (0 10 + + 012 ) 010 [V4 (dP1 dP) + V4 (dP2  0 1 0 + oil + i 1 k2089 dp, dP) + k3(07 +.08+09) dP  dP)+ + V3( dP6 dP) k401,0 2l(dp k4(010 + 81 + 012) dP )+... + V4(dP dP) + + dP)] k401l,, _l(1 11) _ S k4O 01 2 (dplo dP)+ (dp, dP)+ 1 k (1, + 4(01 + 012) 1 k4 (010 + 0i + 012) wndq,1 = 6,,dQ + + w1d1 Q + k400 + D,) in [V4 (dP dP)+V24(dP2 dP)+...+V46(dP6 dP) 010 + Ol1 + 012) k401012 (dp, dP) + k40,0 (dpc, dP)+ 1 k4(010 +o +) 1 k4(o ( +0o1) + 12) W12dq2 = 012dQ + 012 4012) + 1 12 12 3 11 /k ) 1+ )(dp12 DP) 8 0 [14(ai dP)+ V24(dP2 P)+...+ 46(dP6 P)] 10 + ol + 012 013(1 k5013) (dp1 k4013014 d dP) 1q k5(013 +014 +015) 1 k5(03 +014 + 15) 13dq13 = 013dQ + 13 k 03 015 (dp15 DP) 1k,(013 +01 + +015) 013 [V1 (dP, dP)+ V25(dP dP)+... + V5(dP6 dP) 013 + 014 + 015 k5013014 (dp13 dP)+ 014(1k5014) (4 dP) 1k (013+14 + 015) 1k5(013+014 +015) w ,, 4k 1 = 0,dQ+p + D 5 13 15 (dp15 DP) 1 k5 (03 + 014 + 015) S015 [V15(dP dP) +V25(dP2 dP)+... + V56(dP6 dP)] 613 + 014 + 015 01(1 kk01 k(p0 )+ i(d7 dP) + 1 k (1+01 +0 + 08) 1 k6 (016 + 0 + 018) wl5dq, = 8,dQ+p + 6 016 0 18) (dp18 DP) 1 k, (8,0 + 8,0 + 0,1) 016 +01 P[V16(dP dP)+ V26 (dP2 dP)+ ... + V56(dP5 dP) 013 + 014 + 051 16 (1k60160) (d6 1P)+ 0 ( 1 (dp7 d+ 1((61,, +,, +P ,, d + W17dq17 = 071 + k6 (16 17 +018) 1 k6 (16 17 + 018) k601 18 (p DP) +1k6 16 + )17 + 18 ) 017 [V16 dP2 dP)+ V26 dP, dP)+... + V56(dP, dP)] 016 + 017 + 018) ( A,, dP)+ (d^ ^ dP) + 1 k (0,s +0, + 818) 1 ks(0,s +0, + 8+^) 17dq17 17 = d d + +  k6 (dp8 DP) 1 k_(0,s +0, + 8+^) V16, (dP, dP)+ V,, (dP3 dP)+... + V, (dP, dP)} 1^ si +6'^ +6'i + Data Sources The sources of data for this study are the Statistics Bureau of Japan and Japan's Ministry of Finance as well as the Food and Agricultural Organization. Monthly population data from December 1995 to May 2005 came from the web page t (http://www.stat.go.jp/english/data/jinsui/22.htm) maintained by the Statistics Bureau of Japan's Ministry of Internal Affairs and Communications. Import data came from the Trade Statistics of Japan that are published by the Ministry of Finance and the Customs under the provision of the Customs Law and the relevant international conventions. It is available on the web page http://www.customs.go.jp. The monthly imports and expenditures on imports of orange, grapefruit, other citrus, apple, pineapple and grape juices were obtained for the period December, 1995 to May, 2005. The values of imports are on a cost, insurance and freight (CIF) basis, which include costs of the product, insurance and transportation. Unit import values, which proxy commodity prices, were obtained by dividing import values by import quantities. Data on the production, consumption and trade of fruit juices came from the webpage http://faostat.fao.org/faostat/ maintained by the Food and Agricultural Organization. Analytical Methods The method used to estimate the model is the nonlinear least square (LSQ) in the Time Series Processor Program (TSP 4.5). This method is based on the entire system of equations, and estimates all parameters jointly. When estimating the system of demand equations, one of the equations has to be deleted or the covariance matrix will be singular. However, parameter estimates of the deleted equation can be recovered by reestimating the system with another equation in the system. Parameter estimates are invariant to the deleted equation when using maximum likelihood estimation (Barten, 1969). The LSQ command computes maximum likelihood estimates if it is specified with no instruments and more than one equation (Cummins, 1999). Since the parameter estimates in this study are generated from a system of demand equations without specifying instruments, they can be taken as maximum likelihood estimates. With 68 normally distributed disturbances (u,), the ML method has all the desirable asymptotical properties of Maximum Likelihood (ML) estimators and, therefore, is asymptotically efficient among all estimators (Greene, 2000). The likelihood ratio test is used to test for autocorrelation. CHAPTER 5 RESULTS AND DISCUSSION Descriptive Results Since Japan's deregulation of imports in the 1990s, the imports of fruit juices have increased with the exception of U.S. apple juice (Table 5.1). Over the period January, 1995 to May, 2005, the imports of U.S. apple juice has decreased by 17% while that of U.S. orange, grapefruit and grape juices increased by 4%, 12% and 5%, respectively. The highest increase was attained by the ROW grapefruit juice (51%) followed by the Chinese apple juice (31%) and the Israelis grapefruit fruit juice (26%). The analysis of import stability as measured by the coefficient of variation shows that the imports of fruit juices in Japan over the given period have exhibited a significant fluctuation. The fluctuation of imports varies from country to country. U.S. orange and grape juices have experienced the highest fluctuation among U.S. fruit juices. Over the same period, Japan's import price of all fruit juices has decreased (Table 5.1). On average, Japan's import price of U.S. orange, grapefruit, apple and grape juices has decreased by 12%, 10%, 7% and 6% per month over the period December, 1995 to May, 2005. Over the same period, apple juice imported from the rest of the world has witnessed the largest price decrease (13%). Among U.S. products, prices of orange and grapefruit juices are relatively more stable than those of the respective competitors' products. The prices of apples are less stable compared to their respective rival products. Except for Brazilian orange juice (25%) and the ROW apple juice (19%), the average expenditure share of fruit juices in Japan is below 10% (Table 5.1). Expenditure share of U.S. juices, expressed as a percentage of total fruit juice expenditure, ranges from 6% for apple juice to 8% for grapefruit juice. Table 5.1 Fruit juice quantity and price logchanges, and expenditure shares, Japan, December 1995 to May 2005 Imports Quantity logchanges Price logchanges Expenditure shares dq, = log(q,, /q,l,) dp, = log(p,,/p,,,_) (T,) Mean SD Mean SD Mean SD U.S. oranges 0.0410 0.6701 0.1155 0.2803 0.0724 0.0335 Brazilian. oranges 0.0982 0.9847 0.1033 0.2683 0.2542 0.0895 ROW oranges 0.0959 0.8876 0.0083 0.4210 0.0324 0.0205 U.S. grapefruits 0.1200 0.4909 0.0979 0.2907 0.0808 0.0302 Israelis grapefruits 0.2617 1.0503 0.0720 0.5821 0.0259 0.0168 ROW grapefruits 0.5078 1.3739 0.1149 0.8360 0.0111 0.0104 U.S. apples 0.1694 0.9249 0.0690 0.2847 0.0567 0.0422 Chinese apples 0.3176 0.6891 0.1405 0.2798 0.0727 0.0372 ROW apples 0.0760 0.4059 0.0946 0.1958 0.1652 0.0510 Thai pineapples 0.1549 1.0317 0.0572 0.3934 0.0109 0.0058 Philippines pineapples 0.1578 1.7814 0.0606 0.3713 0.0075 0.0037 ROW pineapples 0.1109 1.5452 0.0414 0.5171 0.0089 0.0062 U.S. grapes 0.0529 0.5942 0.0647 0.2890 0.0621 0.0249 Argentinean grapes 0.2792 1.1260 0.0969 0.3346 0.0091 0.0058 ROW grapes 0.1717 0.4728 0.0802 0.2584 0.0648 0.0235 Israelis other citrus 0.0861 0.6349 0.0924 0.3138 0.0220 0.0064 Italian other citrus 0.1756 0.7744 0.0902 0.2412 0.0172 0.0069 ROW other citrus 0.2032 0.8238 0.1031 0.5923 0.0250 0.0118 (Source: Study data) Test for Firstorder Autocorrelation A test for first order autocorrelation AR (1) was carried out for five different versions of the Rotterdam model. These are block independent nonuniform substitute Rotterdam model (4.9), blockwise dependent nonuniform substitute Rotterdam model (4.14), block independent uniform substitute Rotterdam model (4.20) and blockwise dependent uniform substitute Rotterdam model (4.22). The test was done considering each model with and without autocorrelation as the unrestricted and restricted model, respectively. The null hypothesis(H0 : p 0) was tested using the likelihood ratio test 2(L(O) L(O))~2[J] where 6 is a vector of restricted parameter given as LR estimates and 6 is a vector of parameter estimates associated with the unrestricted model. The restricted model is the one with first order serial correlation while the unrestricted model is the one without first order autocorrelation. Under the null hypothesis (H0), the LR has an asymptotic chisquare distribution with the degrees of freedom equal to the number of restrictions J. Since symmetry was imposed as part of the estimation procedure, the coefficient of autocorrelation was taken to be common across equations. The result of the test indicates that the null hypothesis of no autocorrelation was rejected in all of the models (Table 5.2), implying that the data is serially correlated. The value of p, which is common across equations in each system, ranges from 0.31 for (4.1) to 0.36 for (4.9), and is significantly different from zero (P<0.001). The Hildreth and Lu (1960) approach was used for the correction. Table 5.2: Test for firstorder autocorrelation Model Coefficient Log Likelihood 2(L( ) L( ))a value Equation (4.20) Rho= 0.00 4710.26 150.82*** Rho= 0.35 4785.67 Equation (4.9) Rho = 0.00 4716.24 147.32*** Rho = 0.36 4789.90 Equation (4.22) Rho = 0.00 4748.99 128.36*** Rho= 0.33 4813.17 Equation (4.14) Rho= 0.00 4757.74 136.70*** Rho= 0.35 4826.09 Equation (4.1) Rho = 0.00 4892.99 83.60*** Rho= 0.31 4934.79 a Twice the difference between the log likelihood value for the unconstrained model, L ) and the log likelihood value for the constrained model, L (o). *** The chisquare critical value is at the 1% significance level. Hypothesis Testing for Model Selection Following the correction for firstorder autocorrelation, the study tests two hypotheses (block independence/uniform substitute hypothesis and blockwise dependence/uniform substitute hypothesis) to select the model that best describes the import data of fruit juices in Japan. The hypotheses of block independence and block wise dependence have to do with the relationship between products that belong to two different product groups while that of the uniform substitute has to do with a relationship between products that belong to the same product group. Therefore, the block independence/uniform substitute hypotheses and blockwise dependence/uniform substitute hypothesis involve betweengroup (block independence or blockwise dependence) and withingroup (uniform substitute) relationships. Recall that the uniform substitute hypothesis is applied to the same product differentiated by country of production. The result of these tests enables us to select the model that best describes the import data of fruit juices in Japan. In light of these hypotheses, two restricted models were derived from the relative price version of the Rotterdam model (4.1). The restricted models are block independent uniform substituteRotterdam model (4.20), and block wise dependent uniform substituteRotterdam model (4.22). Since these two restricted versions (4.20) and (4.22) are nested in the unrestricted version (4.1), the likelihood ratio test is used. Block Independence and Uniform Substitute Hypothesis The hypothesis of block independence states that there is no specific cross price effect (v ) between any two products in any two different product groups. The uniform substitute hypothesis states that the specific cross price effect (v, )between any two products in the same product group is the same for all pairs of goods in that group. Combining the two null hypotheses, the null hypothesis of block independence and uniform substitute relationship can be restated as Ho: v, =O, i Sg j Sh and g h; v,, =k for anyi, s eSg. HA : v, 0, i eSg j Sh and g h; v,, k for any i, sSg. The test for the hypothesis of block independence and uniform substitution involves a comparison between the uniform substitute block independent Rotterdam model (4.20) and the relative price version of the Rotterdam model (4.1). Since (4.20) is a restricted function, we expect its likelihood value to be smaller than that of (4.1). The likelihood value of (4.20) is 4785.67 with 24 degrees of freedom while the value of(4.1) is 4934.79 with 171 degrees of freedom (Table 5.3). The value of the model chisquare is 298.24 which is greater than the critical chisquare value at 1% significance level. Therefore, we reject the null hypothesis, and conclude that there is competition between products that belong to different product groups since there is a change in marginal utility of a dollar spent on a product in one product group caused by an extra dollar spent on another product in another product group. For example, an extra dollar spent on U.S. orange juice, affects the marginal utility of another dollar spent on the Chinese apple juice j . Furthermore, the change in marginal utility of a dollar spent on a product caused by an extra dollar spent on another product is not the same for all pairs of products within the same group. The country of origin makes a difference in one's decision to buy a certain fruit juice. For example, the change in marginal utility of a dollar spent on the U.S. orange juice i, caused by an extra dollar spent on Brazilian orange juice r is not the same as that of the change in marginal utility of a dollar spent on the U.S. orange juice caused by an extra dollar spent on the ROW orange juice, s. This suggests that consumers decide to buy orange juice based on the country of origin. In summary, consumers are influenced by the country of origin when they choose between products that belong to the same group. Table 5.3 Hypothesis testing for model selection Model Log likelihood Free parameters 2(L() L()a value Equation (4.20) 4785.67 24 298.24*** Equation (4.22) 4813.17 39 243.24*** Equation (4.1) 4934.79 171 a Twice the difference between the log likelihood value for the unconstrained model, L (0 and the log likelihood value for the constrained model, L (). *** The chisquare critical value is at the 1% significance level. Blockwise Dependence and Uniform Substitute Hypothesis The hypothesis of blockwise dependence states that the specific cross price effect (v, ) between any two products in two different product groups is the same for all pairs of products in the two groups. The uniform substitute hypothesis states that the specific cross price effect (v,) between any two products in the same product is the same for all pairs of products within that group. Combining the two null hypotheses, the new null hypothesis which corresponds to the blockwise dependence uniform substitute relationship can be restated as Ho : vJ = agh, i E Sg j e Sh and g h; and v,, = k for any i,r e Sg HA : vY agh, i Sg j Sh and Sg Sh ; and v,, k for any i,r e Sg. The test for the hypothesis of blockwise dependence and uniform substitution involves a comparison between the blockwise uniform substituteRotterdam model (4.22) and the relative price version of the Rotterdam model (4.1). The likelihood value of (4.22) is 4813.17 with 39 degrees of freedom while the value of (4.1) is 4934.79 with 171 degrees of freedom (Table 5.3). The value of the model chisquare is 243.24 which is greater than the critical chisquare value at 1% probability level. Therefore, we reject the null hypothesis, and conclude that the competition between products in different groups is not the same for all pairs of products in the two groups the change in marginal utility of a dollar spent on a product in one product group caused by an extra dollar spent on another product in another product group is not the same for all pairs of products in the two groups. In other words, the competition between product i of group g and product j of group h is not the same as that of product i and product / of group h since the change in marginal utility of product i, caused by an extra dollar spent on product j is not the same as that of the change in marginal utility of a dollar spent on product i caused by an extra dollar spent on product 1. For example, an extra dollar spent on U.S. orange juice j, affects the marginal utility of another dollar spent on Thai pineapple juice differently than does it affect the marginal utility of a dollar spent on the Philippines pineapple juice. In other words, the effect of the change in price of U.S. orange juice on the demand for Thai pineapple juice is not the same as that of the effect on the demand for the Philippines pineapple juice. This implies that the country of origin of the pineapple juice makes a difference when a consumer decides to buy orange and pineapple juices. Furthermore, we can conclude that the change in marginal utility of a dollar spent on a product caused by an extra dollar spent on another product is not the same for all pairs of products within the same group. The country of origin makes a difference in one's decision to choose between products that belong to the same product group. For example, the change in marginal utility of a dollar spent on U.S. orange juice i, caused by an extra dollar spent on Brazilian orange juice r is not the same as that of the change in marginal utility of a dollar spent on U.S. orange juice i caused by an extra dollar spent on the ROW orange juice, s. This implies that consumers are influenced by the country of origin and thus decide to buy orange juice based on the country of origin. In summary, the country of origin is taken into account by consumers when they choose between products that belong to different product groups and also when they choose between products that belong to the same product group. Therefore, based on the results of the likelihood ratio test which rejected both restricted models (Table 5.3) the relative price version of the Rotterdam model (4.1) is chosen to best describe the import data of Japan's import of fruit juices. The relative Price Version of the Rotterdam Model Since the relative price version of the Rotterdam model does not have any restriction within or across the price coefficients, individual products are competing with each other based on the country of origin. In other words, it allows investigating the relationship between individual products based on the country of origin of the product. For example, we can investigate the relationship between apple juice from China and orange juice from U.S. Parameter Estimates Marginal expenditure shares Results indicate that the marginal expenditure shares are all positive except for those of the Israel's grapefruit juice and the ROW pineapple juice (Table 5.4). However, the coefficient of the Israelis grapefruit juice is not statistically significant. The largest share of the increase in marginal expenditure on imported fruit juices goes to Brazilian orange juice (70%) followed by that of the ROW apple juice (8%). This is consistent with the average expenditure shares since the Brazilian orange juice (25%) and the ROW apple juice (17%) have the first and second highest average expenditure shares (Table 5.1). Japanese imports of U.S. orange juice grapefruit and apple juice receive only 34% of the increase in marginal expenditures. Except for apple juice and grape juice, imports of fruit juices from ROW receive less than one percent of each dollar increase in expenditures. Table 5.4 Marginal expenditure shares of imported fruit juices in Japan Product Estimates SE UO.SO. oranges 0.0337*** 0.0100 Brazilian oranges 0.6997*** 0.0373 ROW oranges 0.0033 0.0058 UO.SO. grapefruits 0.0441*** 0.0078 Israelis grapefruits 0.0016 0.0059 ROW grapefruits 0.0051 0.0034 UO.SO. apples 0.04686*** 0.0124 Chinese apples 0.0473** 0.0092 ROW apples 0.0800*** 0.0159 Thai pineapples 0.0044* 0.0023 Philippine pO. apples 0.0024 0.0022 ROW pineapples 0.0073** 0.0036 UO.SO. grapes 0.0080 0.0076 Argentinean grapes 0.0017 0.0024 ROW grapes 0.0188*** 0.0066 Israelis other citrus 0.0045 0.0032 Italian other citrus 0.0019 0.0027 ROW other citrus 0.0064 0.0041 *** (**)* significance at 1%, 5% and 10% Price effects. Price effects are described here by both relative and Slutsky price coefficients. The Slutsky price coefficients n, can be derived from relative (Frisch deflated) price coefficients v, and marginal value shares O, using ,j = v, ,00 , where q is the coefficient of income flexibility. The Slutsky price coefficients (r, )are the sum of the specific v, and general substitution effects ( 00,Oj ). The Slutsky price coefficients n, measure the total substitution effect of a change in the jh price on the demand for the ith product or, equivalently, the effect of such a change when real income remains constant. The relative price coefficients measure the specific substitution effect which accounts for the n price changes on the demand for the ith product, or equivalently, the effect of such a change when the marginal utility of income remains constant. The general substitution effect( 00,Oj ), which serves as a deflator of the specific substitution effect by transforming the absolute prices into relative prices, accounts for the Frisch price index changes on the demand for the ith product. If the relative price coefficients v, and v,, are both positive, it means that an increase in the relative price of either product raises the demand for the other, and thus the two products are called specific substitutes. Similarly, if v and vj, are both negative, it means that an increase in the relative price (opportunity cost) of either product reduces the demand for the other, or thus the two products are called specific complements. The Hicks's definitions of net substitutes and net complements are based on the signs of n,. The sign of the parameter rn determines if products i and j are net complements r, < 0 or net substitutes r, > 0. In terms of the Slutsky equation, qj, /9p, = (qj, /9p,) q, (Sq, /1m), if the substitution term, (q, 1/p, ) > 0 for net (or Hicksian) substitutes, and (aq, /p, ) < 0 for net (or Hicksian) complements. While the Slutsky price coefficients provide the net substitution effects when real income remains constant, the relative price coefficients provide the same effects when the marginal utility of income remains unchanged. The concepts of net substitutes and complements focus solely on the substitution effects. The statistically significant relative and Slutsky cross price coefficients are presented in Table 5.5. Most of these products are substitutes. The difference between the coefficients of the relative and absolute price coefficients in terms of magnitude is small. This implies that the general substitution effect is small. The general substitution effect is concerned with the competition of all products for an extra dollar of the consumer's income. Contrary to expectation, the cross price effects of products that belong to the same group are not necessarily greater than the cross effects of products that belong to different product groups. For example, the cross price effect of U.S. grapefruit/ROW grapefruit juice is smaller than that of U.S. grapefruit /U.S apple juice. Furthermore, products that belong to the same product group are not necessarily substitutes. For example, U.S. apple/ROW apple that belong to the same product group are complements. Based on the cross price effects of substitute products, we can identify the market structure of fruit juice in Japan (Figure 5.6), showing that there are both direct and indirect competitions based on the country of origin. Recall that the direct competition refers to the competition between products within the same juice group (e.g., orange juice group) while the indirect competition refers to the competition between products in different juice groups (e.g., orange juice and apple juice). Except for grape juice, there is no direct competition in Japan's fruit juice market. The indirect competition appears to be more important than the direct competition in Japan's fruit juice market. Table 5.5: Parameter estimates of cross prices of fruit juices in Japan Products Relative price coefficients Slutsky coefficients U.S. orange/Brazilian orange U.S. orange/ROW grapefruit U.S. orange/U.S. apple U.S. orange/Philippines pineapple U.S. orange/Israelis citrus U.S. orange/ROW citrus Brazilian. orange/Chinese apple Brazilian orange/ROW apple Brazilian orange/ROW p. apple Brazilian orange/Israelis citrus ROW orange/U.S apple ROW orange/ROW apple ROW orange/Argentinean grape U.S. grapefruit/ROW grapefruit U.S. grapefruit/U.S. apple U.S. grapefruit/Thai. pineapple U.S. grapefruit/Philippines pineapple U.S. grapefruit/U.S. grape U.S. grapefruit/ROW grape Israelis grapefruit/Italian citrus ROW grapefruit/Italian citrus U.S. apple/ROW apple U.S. apple/Philippines pineapple U.S. apple/ROW pineapple U.S. apple/Argentinean grape U.S. apple/Israelis citrus U.S. apple/ROW citrus Chinese apple/ROW pineapple Chinese apple/U.S. grape ROW apple/Israelis citrus Philipp. pineapple/Argentinean grape Philipp. pineapple/ROW grape Philipp. pineapple/Israelis citrus ROW pineapple/Argentinean grape U.S. grape/Argentinean grape U.S. grape/ROW citrus *** (**)* significance at 1%, 5% and 10% Estimates 0.0395 0.0089** 0.0309** 0.0087** 0.0158** 0.0107** 0.0701*** 0.1769*** 0.0304*** 0.0076 0.0129** 0.0216** 0.0036* 0.0102*** 0.0230** 0.0188*** 0.0146*** 0.0161* 0.0194** 0.00467** 0.0043*** 0.0445** 0.00649** 0.0143*** 0.0177*** 0.0127*** 0.0097** 0.0066 0.0211** 0.0127* 0.0050*** 0.0069* 0.00477** 0.0055*** 0.0108** 0.0085** SE 0.0296 0.0040 0.0126 0.0044 0.0062 0.0052 0.0236 0.0402 0.0099 0.9335 0.6936 0.0103 0.0022 0.0030 0.0096 0.0035 0.0034 0.0091 0.0095 0.0020 0.0013 0.0178 0.0031 0.0046 0.0035 0.0045 0.0047 0.0043 0.0087 0.0080 0.0019 0.0039 0.0021 0.0017 0.0043 0.0039 Estimates 0.0822*** 0.0086** 0.0338*** 0.0088** 0.0155** 0.0103** 0.0101 0.0754** 0.0211** 0.0134* 0.0132* 0.0221** 0.0036* 0.0106*** 0.0267*** 0.0185*** 0.0144*** 0.0155* 0.0209** 0.0046** 0.0043*** 0.0377** 0.0066** 0.0149*** 0.0176*** 0.0123*** 0.0103** 0.0072* 0.0218** 0.0133* 0.0050*** 0.0070* 0.0047** 0.0054*** 0.0108** 0.0086** SE 0.0259 0.0040 0.0128 0.0044 0.0062 0.0052 0.0207 0.0354 0.0085 0.0080 0.0069 0.0102 0.0022 0.0030 0.0096 0.0035 0.0034 0.0091 0.0095 0.0020 0.0013 0.0176 0.0031 0.0046 0.0035 0.0045 0.0047 0.0042 0.0087 0.0079 0.0019 0.0039 0.0021 0.0017 0.0043 0.0039 Table 5.6 Market structure of fruit juices in Japan Country Brazil U.S. U.S. Orange Brazil Grapefruit U.S. Israel Israel I I I I I I Apple U.S. China SS Pineapples Thailan Philipp d ine Grapes I Other citrus U.S. Argenti Israel Italy na 4.4 14 441444 U.S. China Thailand I Philippin es 9* 11 Argentin a V 1 Israel a, I I Italy I Iss I I 4 1 4 4 4. 6 4 1 9 I 9 9 9. I 9 I SS SS S SS Product Orange Grapefruit Apple Pineapple grape Other citrus SS Italy SI SSI Results also indicate that the relative price coefficients and the Slutsky own price coefficients are all negative and significantly different from zero except for the ROW apple juice (Table 5.7). Contrary to expectation, the own price coefficient of the ROW apple juice is positive but not statistically significant. The negative signs are consistent with demand theory since they ensure the negativity of the own substitution effect. Table 5.7 Parameter estimates of own prices of fruit juices in Japan Juice Relative price Slutsky price coefficients (v,) coefficients (zn) Estimate SE Estimate SE U.S. oranges 0.1139*** 0.0222 0.1118*** 0.0224 Brazilian oranges 0.9667*** 0.1275 0.0791 0.0861 ROW oranges 0.0469*** 0.0053 0.0469*** 0.0053 U.S. grapefruits 0.0471*** 0.0131 0.0436*** 0.0131 Israelis grapefruits 0.0142*** 0.0045 0.0142*** 0.0045 ROW grapefruits 0.0079*** 0.0015 0.0078*** 0.0016 U.S. apples 0.0308* 0.0177 0.0268 0.0180 Chinese apples 0.0439*** 0.0135 0.0398*** 0.0134 ROW apples 0.0116 0.0383 0.0233 0.0371 Thai pineapples 0.0095*** 0.0021 0.0095*** 0.0021 Philippine pineapples 0.0231*** 0.0020 0.0231*** 0.0020 ROW pineapples 0.0057** 0.0027 0.0057** 0.0027 U.S. grapes 0.0523*** 0.0126 0.0522*** 0.0126 Argentinean grapes 0.0059 0.0038 0.0058 0.0038 ROW grapes 0.0409*** 0.0149 0.0402*** 0.0149 Israelis other citrus 0.0221*** 0.0042 0.0220*** 0.0042 Italian other citrus 0.0202*** 0.0044 0.0202*** 0.0044 ROW other citrus 0.0239*** 0.0026 0.0238*** 0.0026 *** (**)* significance at 1%, 5% and 10% Expenditure Elasticities The value of income flexibility is estimated to be =1.8126. The reciprocal of this coefficient, which is the value of the income elasticity of the marginal utility of income is 1/0= 0.5517. This estimate is consistent with the estimates of Frisch (1959) for the richest section of the population. According to Frisch (1959), a value of 1/0=0.7 is for the better off part of the population. Since Japanese consumers are among the richest in the world, a value of 1/0= 0.5517 obtained in this study is a reasonable estimate for Japan. The expenditure elasticities are calculated at the sample means of expenditure shares of the respective imported fruit juices using the equation 77 = 8, /w, where 0, is the marginal value share of product i and wj is the average value share of the same product. Expenditure elasticities of imported products are useful to provide guidance for marketing strategies and policy making in exporting countries. The estimates of the expenditure elasticities are positive except for those of the Israelis grapefruit juice and the ROW pineapple juice (Table 5.8). However, the expenditure elasticity of Israel's grapefruit juice is statistically insignificant while that of the ROW pineapple juice is statistically significant. Thus, we can conclude that the Israelis grapefruit juice is not an inferior product while that of the ROW pineapple juice is an inferior product. Among the 18 fruit juices, only the demand for Brazilian orange juice is expenditure elastic (2.7522). All four major fruit juices (orange, grapefruit, apple and grape juices) that the U.S. exports to Japan are expenditure inelastic, implying that there is less preference for the U.S. juices. The expenditure elasticities of U.S. exports range from 0.1302 for grape juice to 0.8252 for apple juice. The demand for these products exported by the rest of the world is also expenditure inelastic. The high expenditure elasticity of Brazilian orange juice and low expenditure elasticities of U.S. and the ROW products is not surprising given that Brazil's share of the total import expenditure is very high compared to that of other countries. The average expenditure share of Brazilian orange juice is 25% while that of U.S. ranges from 5% for apple juice to 8% for grapefruit juice (Table 5.1). The average expenditure share of fruit juices imported from the ROW is the smallest except for that of apple juice, which accounts for about 17% of the total import expenditure on imported fruit juices. The major exporting country of apple juice in the category of the ROW is Austria. Table 5.8 Expenditure elasticity estimates of fruit juices in Japan Product Estimate SE USA orange 0.4654*** 0.1390 Brazil orange 2.7525*** 0.1467 ROW orange 0.1047 0.1789 USA grapefruit 0.5463*** 0.0967 Israel grapefruit 0.0630 0.2300 ROW grapefruit 0.4603 0.3115 USA apple 0.8252*** 0.2189 Chinese apple 0.6504*** 0.1267 ROW apple 0.4842*** 0.0963 Thailand pineapple 0.4048* 0.2158 Philippines pineapple 0.3212 0.2954 ROW pineapple 0.8262** 0.4060 USA grape 0.1301 0.1226 Argentina grape 0.1921 0.2670 ROW grape 0.2912*** 0.1031 Israel other citrus 0.2065 0.1491 Italy other citrus 0.1153 0.1582 ROW other citrus 0.2578 0.1649 *** (**)* significance at 1%, 5% and 10% The high expenditure elasticity may imply that there is a strong preference for Brazilian orange juice, and that it is a luxury product. It also implies that as expenditures on imported fruit juice increases, consumers change their consumption of Brazilian orange juice more, in terms of percentage, than they change their consumption of the same juice imported from the U.S. or the rest of the world. Furthermore, these results have important implications for exporting countries in terms of making export decisions in light of the expansion and contraction of the Japanese market for imported fruit juices because of the change in expenditure. Under a situation where the Japanese market for imported fruit juices expands because of an increase in expenditure, Brazil will become much better off. This is because as the Japanese market for imported fruit juices expands because of increasing expenditure, Brazilian orange juice market share will increase more than proportionately. Other Exporters will not be as well off since they are expenditure inelastic. Given that Brazilian orange juice makes up the larger proportion of the total imports of fruit juices in Japan, a one percent increase in expenditure on imported fruit juices results in a far greater increase in actual imports; and, its market share would increase further upon the expansion of the Japanese market of imported fruit juices over time. However, under conditions in which the economy goes to recession, or expenditure growth slows down, Brazil will be worse off because, a given percentage decrease in expenditure on imported fruit juices results in a far greater decrease in actual imports; and its market share would decrease further upon the contraction of the market of imported fruit juices over time because of its larger expenditure elasticity. The fact that recession has been more frequent in Japan over the past few years requires Brazil to devise an effective export strategy which takes account of the performance of the economy. In addition to recession, the growth of population is another major factor anticipated to affect the demand for imported fruit juices in Japan as a result of its aging population. The population growth of Japan has turned negative in 2006 (Statistics Bureau of Japan). With per capital income growing at 2% per annum and assuming that it will remain constant until 2020, and population growth starting to take negative rate since 2006, the growth of demand for fruit juices imported into Japan is projected (Table 5.9). The growth of demand for fruit juice in Japan is positive except for that of Israelis grapefruit juice over the over the period 2006 through 2014. The demand for Israelis grapefruit is negative not only due to the population growth but also negative expenditure elasticity. Products which have positive expenditure elasticity will continue to grow at a declining rate regardless of the negative growth of population except for U.S. grape juice and Israelis and Italian other citrus juices. From the result of the simulation, it appears that grape and other citrus juice will be more affected than the other juices. The demand for Brazilian orange juices declined from 5.53% in 2005 when the growth of population was 0.3% to 5.49% in 2006 when the growth of population turned negative. It will continue to shrink over the period 2006 through 2020 while the demand for U.S. orange is projected to shrink at 1.12.9 to 0.66% over the same period. Among U.S. products, apple juice will grow at a higher rate (more than 1%) while grape juice will grow at the smallest rate (less than 0.25%). These simulations were made under the assumption that the growth of per capital income will remain constant at 2% per annum over the period 2006 through 2020. The increase in the growth of per capital income will offset the decrease in population growth so that the decline in the growth of demand may be checked. If income grows at more than 2%, demand may increase, though population growth slows down. The prospect of the growth of demand for fruit juices will depend on the growth of per capital income relative to the decline in growth of the population. If both move in the same direction, the decline of the growth rate of demand for fruit juices will be greater. 