(NBR) model has been used in estimating import demands. ...... model can be written as follows (Liu, Kilmer and Lee (2007)) j j j ij i ij i i i i pdf ...... 9574 16132.
ESTIMATING IMPORT DEMAND FOR FRESH TOMATOES INTO THE UNITED STATES AND THE EUROPEAN UNION
By MOHAMMAD ALI
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 2007
1
© 2007 Mohammad Ali
2
To my parents, my wife Dr. Salina Parveen and my sons Sakib M. Adnan and Adib M. Adnan
3
ACKNOWLEDGMENTS I am very much grateful for the invaluable assistance, guidance and cooperation I received from my committee chair, Dr. Richard L. Kilmer. His motivation and perseverance kept me going when I had almost succumbed to complete frustration as I had to move to Delaware first and then to Maryland with my family just after my course work. Indeed, it is difficult to continue such a venture when someone is not on the spot. Moreover, I had to wait for complete dataset for the intended study period until January of 2007. The patience and flexibility he awarded to me with moral and financial support in the development of this dissertation were greatly appreciated. His knowledge and experience have been very beneficial to me over the years. I remain ever thankful for the time and trouble he took to meticulously review my work with helpful comments. I am also grateful to the members of my committee for their mentoring and support -both technical and theoretical. Dr. Ronald W. Ward helped me in manipulating data through mathematical programming that made the job easier and faster for me. Without his assistance, it would take much of my time and energy to get the data in working format. He also provided insights regarding the performance of the models used for my study and suggested some improvement to explain any kind of structural change that is not included directly in the model. I appreciate his enthusiasm for work which is very refreshing. Dr. Mark G. Brown offered considerable support in selecting the model for my study. He helped me look at some alternative models to check whether they fit better on the given data sets. Finally, my discussions with Dr. Thomas H. Spreen and Dr. Lawrence W. Kenny helped me shape this research within the realm of reality/practicality. A number of other individuals contributed directly or indirectly through their helpful comments and appreciation. I would like to recognize Dr. Ronald Jansen, United Nations, 4
Statistics Division and Gary Lucier, United States Department of Agriculture, Economic Research Service for their input and clarifications on different aspects of the data used in this research. I thank Carlos E. Jauregui (a doctoral candidate and friend in the same department) for helping me out whenever I got stuck with the computer programming of my model and Carol Fountain for her assistance in formatting my dissertation. I also thank the staff and members at the department as well as at the UF Library for their overall assistance. Now I would like to acknowledge some Bangladeshi friends and families for their contributions. My friends Dr. Abu M. Khan (Sayem) and Dr. Murshed M. Chowdhury supported me with accommodations (during their stay at the University of Florida (UF)) whenever I came to Gainesville for a short time to work on my dissertation. After that, I started getting board and lodging with transportation from our family friends Dr. Khandker A. Muttalib and Dr. Jaha A. Hamida (husband and wife and both working in the Physics department) until I am thoroughly done with my dissertation. I would like to express my extreme gratitude to them. I would also like to thank all my Bangladeshi Sunday volleyball partners and their families for their support and encouragement. I would like to express my endless thanks and gratitude to my family members and other relatives and well-wishers for their love, support and encouragement throughout my lifelong educational endeavors. It is my wife who encouraged and supported me both emotionally and financially to make this milestone possible. I thankfully appreciate her and my two sons Sakib and Adib for their patience, understanding, and moral support through all these years of studies. Finally, I would like to express my appreciation to the International Agricultural Trade and Policy Center (IATPC) at the University of Florida and its Director Dr. John J. VanSickle for partially funding this research project.
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TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES...........................................................................................................................8 LIST OF FIGURES .........................................................................................................................9 ABSTRACT...................................................................................................................................10 CHAPTER 1
INTRODUCTION ..................................................................................................................12 Problematic Situation..............................................................................................................13 Problem Statement..................................................................................................................14 Objectives ...............................................................................................................................14 Chapter Summary ...................................................................................................................14
2
BACKGROUND ....................................................................................................................16 U.S. Tomatoes ........................................................................................................................16 EU Tomatoes ..........................................................................................................................18 Data.........................................................................................................................................20
3
LITERATURE REVIEW .......................................................................................................26 Armington Trade Model .........................................................................................................26 Differential Approach and the Rotterdam Models .................................................................28 Demand System and Functional Formulation ........................................................................32 Production Approach and Utility Approach ...........................................................................33 Import Demand and the Producer Theory ..............................................................................37 Inverse Demand Analysis .......................................................................................................44 Differential Production Approach ..........................................................................................47 Summary of Literature Review ..............................................................................................51
4
THEORETICAL AND EMPIRICAL MODEL .....................................................................53 Theoretical Models .................................................................................................................53 Empirical Models....................................................................................................................60 Data Section............................................................................................................................61
5
EMPIRICAL RESULTS ........................................................................................................65 Results for U.S. Tomato Import Demand Analysis................................................................65 Descriptive Statistics .......................................................................................................65
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Model Results..................................................................................................................65 Summary for U.S. Analysis ....................................................................................................71 Results for EU-15 Tomato Import Demand Analysis ............................................................71 Descriptive Statistics .......................................................................................................72 Model Results..................................................................................................................72 Summary for EU-15 Analysis ................................................................................................79 6
CONCLUSIONS ....................................................................................................................96 Observations ...........................................................................................................................96 Summary.................................................................................................................................96 Conclusions.............................................................................................................................98 Implications ............................................................................................................................99
APPENDIX A
COMPUTER PRINTOUTS FOR U.S. ANALYSIS............................................................100
B
COMPUTER PRINTOUTS FOR EU-15 ANALYSIS ........................................................117
C
SUPERFLUOUS MATERIAL.............................................................................................140
LIST OF REFERENCES.............................................................................................................152 BIOGRAPHICAL SKETCH .......................................................................................................158
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LIST OF TABLES Table
page
2-1
Production of tomatoes ......................................................................................................22
2-2
U.S. exports and imports of fresh and processed tomatoes compared to World ...............22
2-3
U.S. fresh tomato exports to the EU ..................................................................................23
2-4
U.S. fresh tomato imports from the EU .............................................................................23
2-5
EU’s tomato exports compared with the U.S. and World (total tomatoes) .......................24
2-6
EU’s tomato imports compared with the U.S. and World (total tomatoes).......................24
2-7
EU’s tomato production compared with the U.S. and World (total tomatoes)..................25
5-1
Import cost shares, quantity shares, and average prices by country of origin for U.S. .....80
5-2
Test results for the production differential AIDS, CBS, Rotterdam and NBR models with first-order autocorrelation imposed for U.S. import demand analysis ......................80
5-3
Coefficient estimates of the production NBR model for the U.S. .....................................81
5-4
Demand parameter estimates and conditional elasticity of the production NBR model for the U.S..........................................................................................................................81
5-5
Divisia elasticities over time for the U.S. analysis ............................................................82
5-6
Conditional own-price elasticities over time for the U.S. analysis....................................83
5-7
Import cost shares, quantity shares, and average prices by country of origin for EU15........................................................................................................................................87
5-8
Test results for model selection for EU-15 analysis. .........................................................87
5-9
Coefficient estimates of the production NBR model for EU-15........................................88
5-10
Demand parameter and conditional elasticity estimates of the production NBR model for EU-15 ...........................................................................................................................89
5-11
Divisia elasticities over time for EU-15 analysis...............................................................90
5-12
Conditional own-price elasticities over time for EU-15 analysis ......................................91
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LIST OF FIGURES Figure
page
5-1
Impact of structural change on U.S. demand for Canadian and Dominican Republic fresh tomatoes. ...................................................................................................................84
5-2
Impact of structural change on U.S. demand for Mexican and EU-15 fresh tomatoes. ....85
5-3
Impact of structural change on U.S. demand for ROW fresh tomatoes. ...........................86
5-4
Impact of structural change on EU-15 demand for Albanian and Bulgarian fresh tomatoes .............................................................................................................................92
5-5
Impact of structural change on EU-15 demand for Israeli and Morocco fresh tomatoes.. ...........................................................................................................................93
5-6
Impact of structural change on EU-15 demand for Romanian and Turkish fresh tomatoes. ............................................................................................................................94
5-7
Impact of structural change on EU-15 demand for ROW fresh tomatoes.........................95
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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 ESTIMATING IMPORT DEMAND FOR FRESH TOMATOES INTO THE UNITED STATES AND THE EUROPEAN UNION By Mohammad Ali August 2007 Chair: Richard L. Kilmer Major: Food and Resource Economics Continuous talks and negotiations initiated by the World Trade Organization (WTO), in recent years, on globalization and trade liberalization have made international trade a key issue for all nations as it has expanded the global markets with enhanced competitiveness. There exist both opportunities and costs as it expands exports on one hand and poses threats of competition from importers on the other. Agriculture being the major player in international trade has to cope with this changing trend of the global market situation. The European Union (EU-15) being more and more open should be of especial interest to the growers, traders and policy makers of all nations including the United States (U.S.). This is a research project for the analysis of import demand for fresh tomatoes into the U.S. and the EU-15 for the assessment and evaluation of competitiveness to enable the specialty crop industry to compete successfully. The sources of data for this research are the United Nations Statistics Division- Commodity Trade Statistics Database website, Food and Agriculture Organization Statistics Database website and other websites maintained by the United States Department of Agriculture (USDA). Data for the period 1963-2005 have been used in this research. A differential production approach has been used for estimating import demand for fresh tomatoes. Imports are considered as inputs to importing firms. The mode used in this research is 10
derived from the basic principle of the theory of firm whereby the firm maximizes profit by determining a level of output and minimizing the cost of producing that level of output. The cost minimization stage is applied to get conditional factor demand equations in the estimation process. The differential production version of the Netherlands National Bureau of Research (NBR) specification is estimated by the iterative seemingly unrelated regression (SUR) method using the well known least square procedure (LSQ) in Time Series Processor (TSP). Results show that Mexico is the prominent supplier of fresh tomatoes in the U.S. import market facing no close competitor. Canada and EU-15 compete with each other for the U.S. import market whereby Canada is losing its relative share and EU-15 is gaining its relative share. For the EU-15 import demand for fresh tomatoes, Morocco is the major supplier with no close competitor. Israel and Rest of the World (ROW) are competing with each other in the EU-15 import market. Albania, Bulgaria and ROW are losing their relative share in the EU-15 import market with an indication of some kind of structural changes. Mexico and Morocco have significant influence and control over the U.S. and the EU-15 import markets. It is necessary for other participants to figure out the secrets and follow them to be competitive with these major players in their respective markets. Otherwise, the implications would be significant on both markets if there are some diseases or calamities in Mexico and Morocco.
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CHAPTER 1 INTRODUCTION Globalization, in a modern world, has emerged as a blessing for both developed and developing countries. With globalization comes trade liberalization that reduces barriers to international trade. According to the World Trade Organization (WTO), elimination of trade barriers can result in annual welfare gains for the world ranging from US $250 billion to US $620 billion. Trade liberalization can also help alleviate poverty by contributing to a more efficient resource allocation and raising productivity. Thus, free trade can contribute to higher wages and standard of living. So, it can be said that trade liberalization and poverty reduction/income growth go hand in hand (WTO, 2002). In the field of agriculture, increased globalization has both potential benefits and costs for the United States (U.S.). In some cases, there will be opportunities to expand U.S. exports and in others, there will be a threat of facing competition from importers with lower prices. The overall effects on the U.S. may further be complicated by high income elasticities of demand. For example, many of the specialty crops may have relatively higher income elasticities of demand in the U.S. than other field crops. Hence, income growth will definitely have a positive effect on the U.S. demand for those specialty crops; however, this may or may not neutralize the impact of increased competition as well as the effect of potentially lower prices. Thus, the globalization of markets along with the emphasis on international trade has increased interest on the competitiveness of the U.S. in global markets (Institute of Food and Agricultural Sciences (IFAS), 2002). U.S. farm cash receipts are valued at more than $241 billion and Florida is the tenth leading state in this respect with $6.84 billion in farm cash receipts as of 2004. Florida is also the fifth leading state in crop production with $5.36 billion in cash receipts (National Agricultural
12
Statistics Service (NASS), 2006). Agriculture accounts for more than 314,000 jobs in the state of Florida (IFAS, 2002). The U.S. is also one of the world’s leading importers and exporters of fruits, vegetables and nuts. The specialty crops are very important for Florida. The three leading specialty crops in terms of value are greenhouse/nursery at $1.63 billion, oranges at $980 million and tomatoes at $501 million (NASS, 2006). The specialty crops are important for feeding the nation as well as the world. So, it is very important to look at the future of this industry both domestically and globally The International Agricultural Trade and Policy Center (IATPC) at the University of Florida (UF) is entrusted with the responsibility to focus on research and education that will help the industry understand the implications of trade and policy related issues. The Center has been established to help growers, industry leaders and policy makers in understanding various impacts of all these issues on the future of the industry (IATPC website). The proposed project looks at the import demand for fresh tomatoes into the U.S and the European Union (EU). Problematic Situation The World Trade Organization (WTO), in recent times, is continuously initiating talks on agricultural trade aimed at trade liberalization. Consequently, the globalization of markets places enhanced emphasis on international trade and competitiveness among suppliers. It has become a necessary venture for the producers/processors to gain a larger share of world agricultural exports. The specialty crop sector also needs to keep pace with this trend of potentiality. One way of doing so is to provide firms with the necessary information on global markets. Therefore, demand studies for individual countries are needed for the specialty crop sector in order to enable the sector to strategically plan to expand exports. Thus, the analysis of import demand for tomatoes into the most potential markets like the EU is necessary for the U.S. specialty crop
13
industry for the assessment and evaluation of competitiveness that will enable the industry to compete successfully in an increasingly growing domestic and global markets. Problem Statement What is the state of competition among the suppliers for imported tomatoes into the United States and the European Union? Objectives The broad objective of this research is to estimate import demand for tomatoes into the United States and the European Union and utilize estimated parameters in order to measure the sensitivity of demand for tomatoes to changes in own price, prices of substitutes and quantity of imports, and thereby look at competitiveness among suppliers. The specific objectives include 1) To look at international trade in tomatoes imported into the United States and the European Union. 2) To review different demand models including import demand models. 3) To develop a model to estimate import demands for fresh tomatoes into the United States and the European Union. 4) To determine the extent of competition among the suppliers of fresh tomato imports into the United States and the European Union. 5) To look at if there is any structural influence on the import demand for fresh tomatoes. Chapter Summary Data on fresh tomato imports for this study have been obtained from the United Nations’ database. A differential production version of the Netherlands National Bureau of Research (NBR) model has been used in estimating import demands. In Chapter 2 a background for this study has been provided. Chapter 3 discusses a detailed literature review that is helpful for the study. Then the theoretical and empirical models are discussed in Chapter 4 that also includes the
14
data section in detail. Chapter 5 provides a discussion on empirical results. The concluding Chapter 6 includes observations, summary, conclusions, and implications and recommendations.
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CHAPTER 2 BACKGROUND U.S. Tomatoes The United States is one of the world’s largest producers of tomatoes. It is second in rank, just behind China (Economic and Research Services (ERS)-United States Department of Agriculture (USDA) website). Imports of tomatoes have also risen significantly since 1994. The industry has been growing rapidly over last few decades. In terms of U.S. farm cash receipts, the U.S. fresh and processed tomatoes are second only to potatoes among all vegetables in value. Tomatoes accounted for $2.06 billion in farm cash receipts in 2004 (NASS, 2006), which is 12 percent of all vegetable and melon receipts. In terms of 2002 harvested acreage of tomatoes, the five top states are California, Florida, Ohio, Indiana, and Michigan (ERS-USDA, 2003). However, the leading producers of fresh market tomatoes were Florida (39 percent), California (31 percent), Ohio (7 percent), Virginia (4 percent), and North Carolina (2.4 percent) in 2002. On the other hand, the top processing tomato producing states were California (95.4 percent), Indiana (1.7 percent), Ohio (1.7 percent), Michigan (0.7 percent), and Pensylvania (0.2 percent). The average annual per capita consumption of fresh and processed tomatoes rose by 18 percent during the 1990’s compared to the 1980’s, amounting to 91 pounds on a fresh-weight basis in 1999, with processed tomatoes accounting for about 80 percent (ERS-USDA, 2003). The total domestic utilization of fresh market tomatoes in 2002 was 5.2 billion pounds (18.4 pounds per person) while that of processed tomatoes totaled to 19.9 billion pounds (69.2 pounds per person). The fresh market data provided above excludes domestic greenhouse or hydroponic tomatoes that might add one more pound to fresh per capita consumption if included. Mexico and Canada are the major suppliers of fresh market tomatoes to the U.S. while Canada is the leading export market for U.S. fresh and processed tomatoes (ERS-USDA website).
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With respect to tomato exports and imports, about 7 percent of the U.S. fresh market tomato supply is exported. The top U.S. export markets in 2001 were Canada (78.6 percent), Mexico (13.9 percent), Belgium (4.09 percent), Japan (1.38 percent), and France (0.67 percent) (U.S. Trade Statistics website). For processed tomatoes, about 5 percent of the tomato product supply was exported during the 1990’s. The top U.S. export markets for processed tomatoes in 2001 were Canada (48.61 percent), Mexico (11.47 percent), Japan (8.88 percent), United Kingdom (4.67 percent) and South Korea (4 percent) (U.S. Trade Statistics website). Now, as for imported tomatoes, it is important to observe that more fresh tomatoes are imported than processed tomatoes. In 2000, fresh tomato imports accounted for about 32 percent of domestic consumption, which is down from 36 percent in 1998, but more than 19 percent in 1990 (ERS-USDA website). The U.S. normally imports most fresh tomatoes during the period when domestic supply is low, i.e., late fall to early spring. In 2001, Mexico supplied 82.47 percent of the value of fresh tomato imports followed by Canada (12.8 percent), the Netherlands (3.55 percent) and Israel (0.45 percent) (U.S. Trade Statistics website). As a net importer, the United States imported 36% of total fresh tomato consumption and exported about 9% of total domestic production in 2002 (ERS-USDA, 2003). In the case of processed tomatoes, imports accounted for 4 percent of domestic consumption during the 1990’s, which is down from 7 percent in the 1980’s (ERS-USDA website). In 2001, Canada accounted for 40 percent of the imported processed tomatoes followed by Italy (27.16 percent), Mexico (14.91 percent), Dominican Republic (5.32 percent), China (3.84), and Israel (2.75 percent) (ERS-USDA website). The importance of the U.S. tomato industry will be clear from the tables at the end of this chapter. Table 2-1 shows the U.S. tomato production including Florida’s share compared with the world’s total production. Florida
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production is mainly for the fresh market and it constitutes around 40% of U.S. fresh tomatoes. Table 2-2 shows the U.S. exports and imports of tomatoes compared with the world exports and imports. For the period 1991-2005, U.S. exports varied from 148,297 to 188,173 metric tons whereas imports varied from 360,770 to 951,785 metric tons. EU Tomatoes The Common Agriculture Policy (CAP) of 1962 has laid the foundation for creating the European Union (EU) through which Europe has taken a strong protective stance of its agricultural markets. This is especially true for products like dairy, fresh fruits and vegetables including tomatoes that are vulnerable to foreign competition as a result of domestic prices that are higher than the world price levels. In fact, European consumers pay almost twice the competitive world price for most of its agricultural products (Adams and Kilmer, 2003). In other words, European producers receive almost twice the world price for many agricultural products due to domestic farm programs. Thus, agricultural subsidies accounted for almost half of the EU’s total budget in 2000 (US $40 billion on agriculture) (ERS-USDA website). The domestic policies for citrus and tomatoes include export refunds, product withdrawals from the market, intervention thresholds, and direct producer aids. Recent EU General Agreement on Trade and Tariff (GATT) and later the World Trade Organization (WTO) membership has forced some changes to CAP, resulting in less domestic support for European agricultural markets. Consequently, the EU, once called “Fortress Europe” is now becoming more and more accessible to the world agricultural producers including the U.S. producers (Adams and Kilmer, 2003). For example, the EU is now the third largest regional export market for US agricultural products with imports of $6.4 billion in 2001 (Adams and Kilmer, 2003). The EU was a net exporter to the U.S. with a surplus of Eur 2.63 billion in 2001 while the U.S. was a net importer from the EU with a deficit of Eur 5.65 billion. The values for 18
2000 were Eur 2.63 billion and Eur 5.51 billion respectively with an exchange rate of Eur 1= US $1.12 (European Communities (EC) (2202)). Although the level of EU support for agriculture is decreasing, it is still relatively high compared to the U.S. and rest of the world. However, the recent changes have signaled a clear trend away from market-distorting actions and toward direct payments to producers. In general, the intention of the EU is to enhance European agricultural competitiveness by setting product intervention as “a real safety net measure, allowing EU producers to respond to market signals while protecting them from extreme price fluctuations,” and promoting market oriented, sustainable agriculture by finishing the transition from product support to producer support, introducing a “decoupled system of payments per farm” which are supposedly not connected to production (Adams and Kilmer, 2003). In fact, the EU wishes to allow flexibility in production, but at the same time it also wants to guarantee income stability to producers. During the last 10 years, the EU has reduced price supports but increased direct payments to tomato, dairy and citrus producers in order to compensate them for such reductions (Adams and Kilmer, 2003). After the successful negotiation of the 1993 Uruguay Round of GATT, the EU has been progressing towards liberalization of agricultural markets including citrus, tomatoes and dairy, moving from market-distorting support to less market-distorting regulation. Consistent with this market liberalization trend in Europe, the EU has made major changes to common market organization for tomatoes in 2000 that were less market distorting. So, there exists more market flexibility after 2000, a lesser amount of product can be removed from the market and supports for the export of tomatoes have also declined (Adams and Kilmer, 2003). As of 1998, the EU imports 4 percent of world tomato production and exports 7 percent of world tomato production. In fact, very little of the world’s fresh tomato production is exported fresh. The leading tomato
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producers for processing in 1999/2000 were the U.S. (11.6 million tons vs. 8.5 million tons in 1998/99), the EU (9.1 million tons vs. 8.0 million tons) and Turkey (1.8 million tons vs. 1.7 million tons) (Adams and Kilmer, 2003). Therefore, the importance of the EU cannot be ignored in terms of production, consumption and trade of tomatoes. The members of the EU-15 are Austria, Belgium, Denmark, Finland, France, Germany, Great Britain, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain, and Sweden. The export and import position of the EU in tomato trade can be visualized from Table 2-3 and Table 2-4. The tables show that U.S. fresh tomato export and import trade with the EU is important even though there are some up and down swings from year to year. They also depict that EU’s role in world’s export and import trade in tomatoes as well as production is quite significant (Table 2-5, Table 2-6 and Table 2-7). As the World Trade Organization (WTO) is constantly debating on agricultural trade with a vision towards trade liberalization and/or globalization of markets, emphasis on international trade and competitiveness among suppliers has become a striking issue in order to ensure a larger share of world agricultural exports. The specialty crop sector like tomatoes also needs to keep pace with this potential trend. Therefore, the study of import demand for tomatoes into the most potential markets like the EU is very much necessary and justified for the U.S. specialty crop industry in order to compete successfully through the assessment and evaluation of competitiveness in an increasingly growing domestic and global markets. Data The data on imports of fresh tomatoes have been used for 43 years i.e., for the period 19632005. The source of data is mainly the United Nations (U.N.) Statistics Division-Commodity Trade Statistics Database (UN-COMTRADE) website. The International Agricultural Trade and Policy Center (IATPC) at the University of Florida has made arrangements for data availability. 20
Other sources of data are online websites maintained by the USDA and the U.N. Food and Agriculture Organization (FAO) Statistics (UN-FAOSTAT) website. The required data are collected and manipulated to fit in the model to be used for this research. The data are in both volumes and values from which price/cost data can easily be calculated by dividing the value of imports by the volume of imports.
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Table 2-1. Production of tomatoes Year
U.S. Productiona (1,000 cwt)
Florida Productiona (1,000 cwt)
World Productiona (1,000 cwt)
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003b 2004b 2005b
240,905 251,448 214,582 230,196 268,181 259,798 261,780 232,242 220,668 293,455 254,830 220,501 270,438 232,000 283,700 243,500
15,240 16,170 20,858 17,160 16,995 15,035 14,484 13,720 13,952 15,820 15,760 14,908 14,400 14,190 15,120 15,540
1,677,225 1,670,099 1,645,031 1,710,874 1,825,395 1,911,961 2,048,519 1,968,839 2,116,780 2,352,832 2,367,172 2,316,384 2,380,374 2,564,700 2,713,800 2,727,800
a
U.S. Fresh Tomato Production (1,000 cwt) 33,800 33,988 39,033 36,663 37,387 34,098 33,634 32,777 32,628 36,735 37,665 35,527 37,302 35,578 38,346 39,462
Florida Fresh Tomato Production (1,000 cwt) 15,240 16,170 20,858 17,160 16,995 15,035 14,484 13,720 13,952 15,820 15,760 14,908 14,400 14,190 15,120 15,540
Total tomatoes include fresh and processed Source: National Agricultural Statistics Service, U.S. Department of Agriculture, ERS-USDA website: http://www.ers.usda.gov/Briefing/Tomatoes.and bhttp://www.nass.usda.gov/index.asp. b Also derived from data supplied by FAOSTAT (06/20/06), Food and Agriculture Organization, United Nations. . Note: 1 metric ton = 2,205 pounds and 1 cwt. = 100 pounds. Table 2-2. U.S. exports and imports of fresh and processed tomatoes compared to World Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002a 2003a 2004a 2005a
U.S. Exports (Metric Tons) 157,311 148,297 171,292 169,142 169,891 155,951 161,279 179,093 158,955 170,873 208,564 205,486 182,286 180,713 212,280 188,173
World Exports (Metric Tons) 2,390,374 2,437,142 2,477,245 2,951,351 3,231,714 3,452,170 3,356,339 3,752,235 3,973,383 3,975,530 3,786,645 4,235,422 4,272,195 4,526,953 4,843,480 4,894,498
U.S. Imports (Metric Tons) 360,995 360,770 196,027 418,395 396,040 620,944 737,150 742,464 847,320 740,656 730,063 823,541 860,098 939,257 931,970 951,785
World Imports (Metric Tons) 2,407,976 2,438,764 2,791,387 2,973,351 2,949,429 3,101,528 3,444,013 3,629,123 3,681,147 3,579,430 3,621,868 3,918,901 4,120,920 4,362,962 4,649,342 4,684,459
Source: National Agricultural Statistics Service, U.S. Department of Agriculture plus ERSUSDA and Bureau of the Census, U.S. Department of Commerce. aAlso Food and Agriculture Organization, United Nations. UN-FAOSTAT website. Note: 1 metric ton=1.102 short tons=2,205 pounds and 1 short ton=2000 pounds=0.907 metric tons.
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Table 2-3. U.S. fresh tomato exports to the EU Countries Austria BelgiumLuxembourg Denmark Finland France Germany Great Britain Greece Ireland Italy Netherlands Portugal Spain Sweden Total EU-15 EU-25 EU-27
Values in 1,000 Dollars 1995 1996 1997 1998 0 0 0 0 44 2,737 3,811 3,729 0 0 44 261 415 0 0 8 109 0 0 0 881 881 881
0 0 0 0 522 0 0 0 0 0 44 0 3,303 3,303 3,303
0 0 0 348 1,962 0 0 0 1,573 0 131 0 7,825 7,825 7,825
0 0 87 223 2,496 0 0 0 803 55 179 0 7,572 7,572 7,572
1999
2000
0 5,689
0 8,706
2001 0 5,978
0 0 44 541 1,896
0 0 792 0 2,193 0 0 0 497 209 305 0 12,702 12,702 12,702
0 0 975 24 75 0 0 94 0 39 29 0 7,214 7,214 7,214
51 0 1,163 476 155 0 10,015 10,015 10,015
2002a 0 6,372
2003a 0 3,461
2004a 0 2,845
2005a 0 399
0 0 0 0 1,087 0 0 0 1,355 0 0 0 8,814 8,814 8,814
0 0 208 0 703 0 0 0 4,144 0 0 22 8,538 8,538 8,538
0 0 3 5 659 0 0 3 2,549 0 0 0 6,064 6,064 6,064
0 0 0 7 0 0 0 0 705 0 0 0 1,111 1,111 1,111
Source: Department of Commerce, U.S. Census Bureau, Foreign Trade Statistics and aU.S. Trade Statistics website. Table2-4. U.S. fresh tomato imports from the EU Countries Austria BelgiumLuxembourg Denmark Finland France Germany Great Britain Greece Ireland Italy Netherlands Portugal Spain Sweden Total EU-15 EU-25 EU-27
Values in 1,000 Dollars 1995 1996 1997
1998
1999
2000
2001
2002a
2003a
2004a
2005a
0 2,766
0 4,114
0 5,097
0 5,555
0 3,292
0 2,056
0 1,102
0 1,389
0 2,046
0 3,997
0 2,139
0 0 0 4 0 0 0 0 21,131 0 1,982 0 25,883 25,883 25,883
0 0 0 0 23 0 0 0 42,646 0 3,879 0 50,662 50,662 50,662
6 0 0 18 15 0 0 23 52,909 0 7,829 0 65,897 65,897 65,897
17 0 160 0 11 0 0 3 64,487 0 10,894 0 81,127 81,127 81,127
40 0 231 0 0 0 0 0 57,171 0 10,711 5 71,450 71,450 71,450
0 0 0 0 6 0 0 0 46,392 0 10,698 0 59,152 59,152 59,152
0 0 0 0 0 0 0 9 51,027 0 9,709 0 61,847 61,847 61,847
0 0 0 0 0 0 0 13 45,630 0 13,710 0 60,742 60,758 60,758
0 0 0 0 0 0 0 0 33,908 0 7,025 9 42,988 43,051 43,051
0 0 0 0 0 0 0 0 27,721 0 6,001 0 37,719 37,732 37,732
0 0 0 0 0 0 0 4 16,065 0 820 0 19,028 19,053 19,053
Source: Department of Commerce, U.S. Census Bureau, Foreign Trade Statistics and aU.S. Trade Statistics website.
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Table 2-5. EU’s tomato exports compared with the U.S. and World (total tomatoes) Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002a 2003a 2004a 2005a
EU’s Exports (In Metric Tons) 1,187,299 1,296,414 1,425,689 1,571,570 1,897,143 1,838,367 1,778,314 1,950,304 1,805,104 1,982,756 1,800,303 2,051,591 1,992,242 2,089,092 2,254,156 2,207,576
U.S. Exports (In Metric Tons) 157,311 148,297 171,292 169,142 169,891 155,951 161,279 179,093 158,955 170,873 208,564 205,486 182,286 180,713 212,280 188,173
World Exports (In Metric Tons) 2,390,374 2,437,142 2,477,245 2,951,351 3,231,714 3,452,170 3,356,339 3,752,235 3,973,383 3,975,530 3,786,645 4,235,422 4,272,195 4,526,953 4,843,480 4,894,498
Source: U.S. Tomato Statistics, Economic Research Service (ERS), USDA and aFood & Agriculture Organization, United Nations. UN-FAOSTAT website. Table2-6. EU’s tomato imports compared with the U.S. and World (total tomatoes) Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002a 2003a 2004a 2005a
EU’s Imports (In Metric Tons) 1,307,863 1,401,731 1,495,584 1,576,035 1,632,286 1,577,282 1,735,146 1,807,677 1,726,751 1,743,478 1,806,436 1,919,086 1,928,620 2,068,209 2,155,020 2,124,053
U.S. Imports (In Metric Tons) 360,995 360,770 196,027 418,395 396,040 620,944 737,150 742,464 847,320 740,656 730,063 823,541 860,098 939,257 931,970 951,785
World Imports (In Metric Tons) 2,407,976 2,438,764 2,791,387 2,973,351 2,949,429 3,101,528 3,444,013 3,629,123 3,681,147 3,579,430 3,621,868 3,918,901 4,120,920 4,362,962 4,649,342 4,684,459
Source: U.S. Tomato Statistics, Economic Research Service (ERS), USDA and aFood & Agriculture Organization, United Nations. UN-FAOSTAT website.
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Table 2-7. EU’s tomato production compared with the U.S. and World (total tomatoes) Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003a 2004a 2005a
EU’s Production (In 1,000 cwt.) 298,035 298,680 279,777 280,862 299,553 286,962 324,208 303,232 326,787 361,113 358,844 332,034 346,133 333,250 379,494 373,221
U.S. Production (In 1,000 cwt.) 240,899 251,452 214,510 230,184 268,192 259,792 261,777 232,235 220,660 293,453 254,830 220,501 270,438 232,000 283,700 243,500
World Production (In 1,000 cwt.) 1,677,225 1,670,099 1,645,031 1,710,874 1,825,395 1,911,961 2,048,519 1,968,839 2,116,780 2,352,832 2,367,172 2,316,384 2,380,374 2,564,700 2,713,800 2,727,800
Source: U.S. Tomato Statistics, Economic Research Service (ERS), USDA. aAlso derived from data supplied by FAOSTAT (06/20/06), Food and Agriculture Organization, United Nations. Note: 1 metric ton = 2,205 pounds and 1 cwt. = 100 pounds.
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CHAPTER 3 LITERATURE REVIEW In order to formulate a model to analyze the import demands for tomatoes into the European Union (EU) and the United States (U.S.), it is necessary to look at the literature on import demand estimation. The theory of demand has occupied a vast area in the field of economics covering consumer theory as well as the theory of the firm. Globalization of markets has increased the emphasis on international trade and on the competitiveness among exporters. So, import demand analysis is a vital point in determining the competitiveness in international trade. Armington Trade Model International trade flows are classified on three characteristics such as the kind of merchandise, the country (region) of origin or the seller, and the country (region) of demand or the buyer. The assumption frequently used in theories of demand is that merchandise of one kind supplied by one country is a perfect substitute for merchandise of the same kind supplied by any other country indicating infinite elasticities of substitution and constant price ratios. But, in reality there are lags in buyers’ responses as well as some other imperfections in their behaviors that should not be overlooked. So, it is preferable to recognize that any feasible world model of demand would find few, if any, merchandise with perfect substitutability. Bearing this in mind, Armington (1969) has presented a general theory of demand for products not only distinguished by kinds, but also distinguished by place of production. In his paper, a distinction has been made between goods and products in the sense that goods are distinguished only by their kinds whereas products are distinguished both by their kinds and place of production. Products are differentiated from the buyers’ viewpoint according to the area of the suppliers’ residence and they are assumed to be imperfect substitutes in demand. If there are 5 goods and 20 supply
26
regions, then the number of products distinguished will be 100. The geographic area not only serves as a basis for distinguishing products by origin, but also as a basis for identifying sources of demand. Now the problem in Armington’s (1969) model is to simplify the product demand functions systematically for practical use in estimation and forecasting. Beginning with the general Hicksian model, imposition of a sequence of more restrictive assumptions leads to a highly simplified specification of the product demand function that reveals the relationships between demand, income and prices. The basic modification to the Hicksian model is the assumption of independence, meaning that the buyers’ preferences for any given kind of product are independent of their purchases of any other kind of product. With this assumption of independence, it is possible, in principle, to measure the quantity of each good demanded by each country. There are demands for different groups of competing products and each of these demands can be considered to be a market and suppliers from different countries could be expected to compete in that market. Thus, the demand for a particular product can be expressed as a function of the size of the market for that product and the relative prices of competing products. Another assumption in Armington’s (1969) analysis is that the market share of each country is unaffected by changes in the size of the market as long as the relative prices remain unchanged. This additional assumption implies that the size of the market is a function of money income and the prices of different goods. Combining this with the earlier product demand function, the demand for any product can be expressed as a function of money income, the price of each good, and the price of that product relative to all other products in the same market. So, the approach used in his study assumes that (a) elasticities of substitution between competing
27
products in any market are constant irrespective of market shares, and (b) elasticity of substitution between any two products competing in a particular market is the same as the elasticity of substitution between any two other products competing in the same market. Hence, a specific type of relationship between the demand for a product, the size of the corresponding market and the relative prices has been suggested by these assumptions. The price parameter in this relation is the elasticity of substitution in that market. Analysis of changes in demand for any product is possible by differentiating the demand functions. The change in demand for any product will depend on the growth of the market and on the change in the product’s market share in that market collectively. The change in market share of a particular product will depend on the change in its price relative to the average change in prices of all other products in that market. The change in growth of the market depends on the change in income and income elasticity of demand for the respective good. Thus, this study emphasizes on the relevancy of demand theory to the research in some areas of trade analysis as well as forecasting. Differential Approach and the Rotterdam Models Seale et al. (1992) showed a Rotterdam application to international trade with a differential approach. A Rotterdam import allocation model is used to estimate a geographic import demand system for U.S. fresh apples in four importing markets –Canada, Hong Kong, Singapore and United Kingdom. The differential approach is widely used in estimating consumer demand systems, but in case of estimating import demand, it is used less frequently. Three of such studies are Theil and Clements (1987), Clements and Theil (1978) and Lee, Seale and Jierwiriyapant (1990). Theil and Clements (1978) estimated derived import demands for four aggregate import groups using the differential approach in production theory. Clements and Theil (1978) used the same approach and estimated import demands for 13 individual as well as four groups of countries for three broad categories such as food, raw materials and manufactures with the 28
assumption of homothetic technology. Following Barnett (1979), Lee, Seale and Jierwiriyapant (1990) used the differential approach in utility maximization in order to estimate Japanese import demands for five kinds of fresh fruits and the geographic import demands for citrus juice. In all of the above studies, the Rotterdam model has been used for estimation purpose. The study by Seale et al. (1992) estimated geographic import demands using the Rotterdam model. They treated each of the importing countries as an individual consumer, following Mountain (1988) who showed that the Rotterdam model like other popular flexible functional models is at least a second-order approximation of the underlying demand system. In this study, multistage budgeting has been utilized where an importing country first allocates total income (expenditures) between domestic and imported goods. Then, the total expenditure on imports is allocated among various imported goods and finally, depending on the expenditure for an import, it is allocated among different suppliers of each good. This is a method like the utility tree approach (Barten 1977) and can easily accommodate the differential approach to the utility maximization and is useful for estimating demands for disaggregated imports. Preferences for imports are based on block-wise dependence that enables estimation of geographic import demand subsystems independent of the import demands for all other goods. The conditional import demand system is derived through the differential approach and then parameterized as per a Rotterdam specification. The Rotterdam parameterization is attractive in this case, because it permits nested testing for restrictions on homogeneity, symmetry, homotheticity and separability (preferences being additive). The Seale’s (1992) study calculated expenditure and price elasticities from estimated parameters using both the Rotterdam absolute price model (Rotterdam A.P.) and the Rotterdam preference independence model (Rotterdam P.I.). The elasticities thus calculated, measure the
29
impacts on import shares among fresh apple suppliers as expenditures on total apple imports change and as the prices of imported apples from various geographic locations change. They also used Working’s (1943) model for calculating income elasticities of demand for fresh imported apples as a group and by sources of supply. Lee et al. (1994) have discussed the choice of model in consumer behavior analysis in Taiwan. Numerous specifications of a demand system in consumer demand analysis have evolved through time. These include linear and quadratic expenditure systems, translog models, the Working model, the Rotterdam model and the Almost Ideal Demand System (AIDS). Among all of them, two systems have become popular in agricultural economics, the Rotterdam model and the AIDS. However, the underlying assumptions for these two systems have different implications. The marginal expenditure shares and the Slutsky terms are taken to be constants in the Rotterdam model whereas they are considered to be functions of budget shares in AIDS. In order to choose an appropriate demand system, statistical tests are conducted when the underlying competing systems are nested (Amemiya, p.142). On the other hand, when the systems are not nested, an alternative testing procedure is needed. Deaton (1978) conducted a non-nested testing procedure in order to compare competing demand systems with the same dependent variables that are not applicable in comparing Rotterdam and AIDS, as the dependent variables are different. However, Barten (1993) explained that the Rotterdam and the AIDS are special cases of a more general demand system and also nested within that system. So, he suggested pair-wise and higher-order testing procedures to choose the best fitted system. Thus, the Lee et al. (1994) looked into how prices and income influenced Taiwanese consumer demand for the period 1970-89 and how the elasticities of demand evolved through time. They examined four different versions of the demand system indicated by Barten (1993) such as the
30
Rotterdam, a differential version of the AIDS, the Dutch Central Bureau of Statistics (CBS) system and the Netherlands National Bureau of Research (NBR) system. Then, a general model nesting all these four systems has been developed in order to facilitate choosing the best fitted one. The differential approach has been used by many other researchers. Rossi (1984) has made use of this approach in the theory of multiproduct firm in order to analyze input demand and output supply in Italian agriculture. In case of multiproduct and multifactor production structure, the firm’s technology is usually described by a production, cost or profit function. The approximation process may be in variable space comprising prices, quantities, or price-quantity ratio like in the case of classical translog specification. On the other hand, it may be in parameter space as in the case of so-called differential approach. Since the technology of a firm is basically unknown, the differential approach has an advantage in the sense that it does not specify any particular form, but can accommodate different technologies not being bias to any particular form. In this study, he actually followed Laitinen and Theil (1978, 1980) in estimating the parameters of aggregate multiproduct technologies using differential approach. He extended the works of Laitinen and Theil in case of short-run with fixed factors of production and then considered the dynamic adjustments along with the variables to model the role of weather in agriculture. Laitinen and Theil (1978) considered the demand and supply of the multiproduct firm without the usual specializing assumptions of input-output separability or constant elasticities of substitution or scale. They estimated a system of input demand equations under the condition of cost minimization and a system of output supply equations under the condition of profit
31
maximization. The prices are described in terms of substitution and complementary relation among inputs and among outputs in the demand and supply equations. Demand System and Functional Formulation Barten (1977) has reviewed the work done on the formulation and estimation of complete systems of consumer demand functions and delineated the related problems and issues that are of both theoretical and empirical in nature. From the theoretical consideration, constraints are imposed on such systems to deal with empirical problems like lack of sufficient data. There are various alternative approaches to deal with the issue and it is yet to make a clear-cut choice. Continuous research is going on concerning the problems of specifying and estimating such systems. The present review emphasizes the nature of the approach, its possibilities and limitations. It is basically an empirical approach since it aims at the formulation of the system that is to be estimated using actual data. Barten (1993) also discussed the choice of functional form in consumer allocation models, which are based on microeconomic theory of consumer demand. Allocation models are concerned with optimal allocation of given means for different alternatives, or as its dual, the minimal use of these means to achieve a given set of objectives. These models are formulated not only for consumer demand analysis, but also for demand for inputs in production, and composition of imports by origin of supply. Four basic approaches to arrive at demand equations, satisfying required properties, have been described. The first one is from a functionally specified, increasing and quasi-concave utility function like u = u(q1, …….qn) that is maximized subject to a budget constraint Σi piqi = m. Then the first order conditions are solved to get quantities as a function of prices and income. The parameters of the utility function become the constants of the demand equations. An example of this approach is the linear expenditure system (L.E.S.) that
32
can be seen in Deaton (1975). The second approach starts from a functionally specified indirect utility function like u* = u * (m, p1 , ......, p n ) and using Roy’s identity rule, one can obtain an estimable demand equation such as
⎛ ∂u * ∂u * ⎞ ⎟⎟ . qi = − (m / pi )⎜⎜ / ⎝ ∂ ln pi ∂ ln m ⎠
(3-1)
Example of this approach can be stated as the Indirect Translog Utility Function used by Christensen et al. (1975). Barten’s (1993) third approach is based on a specified expenditure function expressed in terms of utility and prices like e = e(u, p1 , ......., p n ) . Now, applying Shephard’s lemma (i.e., wi = ∂ ln e ∂ ln p j ) provides Hicksian demand as
qi = hi (u, p1 , ........, p n )
(3-2)
from where u can be eliminated by using an expenditure function in order to express it in terms of m and p. A good example of this type of specification is the Almost Ideal Demand System (AIDS) by Deaton and Muellbauer (1980). The fourth approach is related with some kind of double-logarithmic specification. Many earlier empirical demand studies used a doublelogarithmic specification with constant elasticities and they seem to work well empirically, but are not sufficiently adequate to explain theoretical restrictions. For example, the constant elasticity restriction requires a constant budget share. So, researchers working with a doublelogarithmic system started imposing theoretical restrictions on the estimation process in order to make it statistically efficient. Theil (1965) started such a double-logarithmic specification. Production Approach and Utility Approach Davis and Jensen (1994) discussed the supremacy of the production theory approach over the utility approach in import demand estimation. They pointed out the drawbacks of the two-
33
stage utility maximization approach that has been widely applied in estimating agricultural commodity import demand systems and elasticities, suggesting an alternative two-stage profit maximization approach that can overcome those limitations, but still retains the advantages. Since the nature of most imported commodities are inputs in the production process, the use of a utility-based demand system in estimating import demands will have conceptual as well as empirical disadvantages. The conceptual disadvantage of the two-stage utility maximization approach arises from the fact that most imported agricultural commodities are inputs, and not final goods entering consumers’ utility function. This conceptual misspecification of an import demand system has other empirical disadvantages. First, it is believed by most agricultural economists that aggregation under utility-based import demand models (i.e., defining the firststage utility aggregates) is a difficult job to form a consensus. In most utility-based models, the procedure is to pick a commodity and assume that it is weakly separable from all other goods that should have been included in the utility function for logical consistency. Thus, this unique condition of separability is not actually an intuitive one and the choice of first-stage aggregates becomes confusing and debatable. Secondly, since most of the models are a conditional demand system, the estimated elasticities are also conditional elasticities. The problem with these conditional elasticities is that they do not explain all of the price effects captured by the unconditional elasticities and hence, the use of conditional elasticities may lead to biased and erroneous inferences and policy recommendations. Thirdly, the unconditional elasticities obtained from such a misapplied utility-based import demand system are not structural estimates, rather they are reduced form estimates and the regressors used are incorrect. Under the above circumstances, Davis and Jensen (1994) prescribed an appealing alternative conceptual approach that satisfies the criterion such as (a) defining the first-stage
34
aggregates and thereby the estimation of unconditional elasticities easily and more intuitively, (b) making structural parameter estimation (derived demand) possible, and (c) retaining the advantages of two-stage utility maximization procedure. This approach is to model the import demand estimation in a two-stage, multiproduct, profit maximization framework under production theory. As soon as the producer theory is applied, the conceptual problem of treating imports as separate final goods is overcome and as a result, the parameters estimated thereon will be structural. Again, as a two-stage method, it will also retain all the advantages of the two-stage utility maximization procedure. Moreover, specifying the first-stage aggregates is more intuitive in a producer theory model of profit maximization than in a consumer theory model of utility maximization. Hence, the estimation of unconditional elasticities becomes less questionable and/or debatable. The presentation, being the integrated efforts of various authors (Blackorby, Primont, Russell (BPR) (1978); Bliss (1975); Chambers (1988); Fuss (1977); Lau (1972) and Yuhn (1991)), has been given in the following ways. First Stage In Davis and Jensen (1994) the transformation function of the multiproduct industry is assumed to be well behaved, intertemporally separable, and homothetically separable in input partition In and can be represented by F (q1,……,qm, X1,……., Xn) = 0. Here, q and X are outputs and aggregate inputs respectively. The aggregate input Xi is defined as Xi = Xi ( xi1,……,xin ), and i = 1,….,.n where, the xij’s are disaggregate inputs. Assuming perfect competition to prevail, profit maximization may occur in two stages that will be consistent with single-stage optimization (Bliss, chapter 7, property 3). The first-stage for a profit maximization problem solves the objective function ∏( p, W ) = max [ pq ' − WX ' : F (q, X ) ∈ T ] q, x
35
(3-3)
where, p and q are 1 × m vectors of output prices and quantities respectively, X and W are 1 × n vectors of aggregated input quantities and price indices respectively. Wi is defined as a linearly homogeneous aggregator function in the form of Wi = Wi ( wi1…….win ) and it is dual to the Xi. The wij is the factor price corresponding to a disaggregated input xij and T represents the technology set of the industry. From the above aggregate profit function ϑ( p,W), the output supplies and input demands can be derived by applying Hotelling’s (1932) lemma, which will be ∂∏ = ql = ql ( p, W ), ∂p l
−
∂∏ = X i = X i ( p, W ), ∂Wi
l = 1,…….., m,
(3-4)
i = 1,……….n
(3-5)
which are homogeneous of degree zero in p and W according to Euler’s theorem. Second Stage Following Davis and Jensen (1994) as the transformation function is assumed to be homothetically separable in the In partition, the sufficient conditions for two-stage optimization are satisfied (Blackorby et al., 1978) and the conditional demands are derivable from Hotelling’s (1932) lemma by differentiating the aggregate profit function with respect to the disaggregated input price wij.
−
∂∏ = xij , ∂ wij
i = 1,……..,n; and j = 1,…….., Ji.
(3-6)
In duality theory, there are two equivalent explanations for an optimal level of xij because, theoretically the second stage of the two-stage profit maximization problem can be expressed in two equivalent ways. Even though these two forms are the same as those of the two-stage utility maximization approach, their solutions to the second stage problem differ empirically. One of
36
the two forms is to minimize the cost of acquiring a predetermined level of aggregated input such as
⎡ Ji ⎤ Ci (wi , X i ) = min ⎢∑ wij xij : X i = X i ( xi1 , .......xin )⎥, i = 1,…..…,n xij ⎣ j =1 ⎦
(3-7)
which can be solved for xhij = xij(wi, Xi). Here, Ci(wi, Xi) is the cost function, wi is the vector of prices, xhij is the Hicksian conditional input demand function since it is conditional on predetermined aggregate input level (Xi) from the first stage. The Hicksian input demand function is homogeneous of degree zero in wi by Euler’s theorem. Following duality theory, the alternative form of the above minimization problem will be Ji ⎡ ⎤ X i (wi , C i ) = max ⎢ X i = X i xi1 ,....., xiJ i : C i = ∑ wij xij ⎥, i = 1,…, n j =1 xij ⎣ ⎦
(
)
(3-8)
giving a solution for xmij = xij(wi, Ci). The Xi(wi,Ci) part of the Equation 3-8 represents the indirect production function which can be considered as analogous to indirect utility function of the utility maximization problem. By Euler’s theorem the solution, xmij = xij(wi, Ci) is homogeneous of degree zero in wi and Ci and this is the conditional Marshallian input demand function that is conditional on the predetermined expenditure level Ci. So, solving Equation 3-7 and (3-8) we can get Hicksian demand and Marshallian demand respectively and they will be equivalent at the optimal point according to Chambers (1982) and Davis and Kruse (1993). Therefore, it is possible to calculate the conditional and unconditional elasticies and their relationship by applying the two-stage profit maximization approach to import demand analysis. Import Demand and the Producer Theory Burgess (1974a) explained the theory of import demand in a general equilibrium model. The traditional general equilibrium model of international trade treated imports as final goods with a perfect domestic substitute. So, the elasticity of demand for imports depends on domestic 37
supply and demand responses influenced by society’s preferences, and the transformation function indicating factor endowment and technology. But, this theoretical framework normally collapses when estimation of the elasticity of import demand is sought. In fact, some favorable functional forms have been chosen for facilitating estimation of the parameters of interest. Hence, the logarithm of the quantity of imports is considered as a linear function of the logarithm of income and the logarithm of the ratio of import price to a price index of all domestic goods. Thus, the parameters are to measure the income elasticity and price elasticity of imports. But, without imposing an arbitrary separability restriction on the consumer’s choice between domestic and imported goods, it is not possible to derive this estimating equation just from an explicit model of rational behavior. In Burgess (1974a), few attempts have subsequently been taken to develop a theory of import demand from the microeconomic standpoint whereby restrictions have been imposed on the underlying analytical structure. These restrictions need to be empirically justified rather than assumed a priori. So, imports are regarded as final goods entering into the consumers’ utility function directly with no perfect domestic substitute. One such framework is developed by Gregory (1971) and it assumes that a constant elasticity of substitution (CES) functional form can represent society’s preferences. Thus, the logarithm of the ratio of imports to domestic goods is a linear function of the logarithm of the ratio of their prices. This model has an advantage in the sense that the estimating equation gives an estimate of the elasticity of substitution between imports and domestic goods and the estimate of own price elasticity can readily be obtained from there. But, its major disadvantages are (1) the maintained hypothesis of separability between imports and all domestic goods indicating that the partial elasticities of substitution between imports and all other domestic goods are equal, and (2) ignorance of the fact that international
38
trade occurs in bulk as intermediary goods requiring further processing before reaching consumers. So, Burgess (1974a) developed a model of import demand without having these two major difficulties. Moreover, he explicitly incorporates the theory of import demand into a general equilibrium framework. The primary concern in this area has been to look at the responsiveness of import demand to changes in price and income in a partial equilibrium framework for predicting balance of payment consequences. But, in this general equilibrium framework of import demand , the balance of payments adjustment process prevails and the primary concern becomes the effect of changes in import prices, due to tariff policy, on the returns to primary factors as well as on income distribution. He agrees that most of the imported goods require further processing before delivery as a final product. The processing may be of complete transformation, or it may simply involve storing, handling, transportation, distribution and other marketing activities. These processing activities require domestic capital and labor. So, it is a policy question to address how tariff policy changes the domestic price of imports and how this will affect the competitive returns to the primary factors and also the distribution of income. An assumption of this production theory model is that imports are purchased by firms trying to minimize the cost of delivering a single product to the final consumer. Since a multifactor generalization of the Cobb-Douglas and CES functional forms are not flexible enough for analyzing issues in this respect, the transcendental logarithmic functional form developed by Christensen, Jorgenson and Lau (1973) has been used. It permits the Allen-Uzawa partial elasticities of substitution between factors to differ and it does not impose any arbitrary separability restrictions a priori. Thus, it enables the researcher to test the hypothesis about the effects of tariff policy on real income and distribution of income.
39
Following a cost minimization approach, Burgess (1974b) estimated import demand equations with a three-input, and two-output technology model. Imports are taken as an additional input along with the primary inputs of labor and capital, and a joint cost function is assumed to express technology. Now the producing unit combines labor and capital with the imported materials in order to minimize the cost of production of a specified bundle of consumption goods and investment goods. Technology, therefore, consists of two outputs, two primary inputs and imported materials. The transcendental logarithmic joint cost function used in this analysis is competent enough to test the maintained hypotheses of most of the previous studies. The partial derivative of the joint cost function with respect to the price of an input gives the cost minimizing level of that input demanded. This logarithmic derivation with respect to factor prices will yield the cost shares. In the same way, the partial derivative of the joint cost function with respect to output gives the marginal cost of the respective output and under the condition of a perfectly competitive situation, the marginal costs equal output prices. So, the logarithmic derivation with respect to output will provide an expression for revenue share. Burgess (1974b) assumed a maintained hypothesis of constant returns to scale technology and estimated the cost function using cost share and revenue share equations derived from the logarithmic derivation of the joint cost function. It found convincing results against the traditionally maintained hypothesis that technology is separable between inputs and outputs. Changes in output composition significantly influence the optimum input mix at any given set of factor prices. Therefore, the optimum level of input mix depends not only on factor prices, but also on the composition of final demands. According to the study results, changes in composition of output in favor of consumption goods will increase the demand for labor, but decrease the demands for capital and imports. The study also rejected the traditionally maintained hypothesis
40
of separability between inputs and outputs since it has been found that when labor and capital, and also labor and imports are substitutes, capital and imports are complements. This indicates that any measure that reduces the price of capital will enhance the demands for imports that will eventually have adverse effects on the country’s balance of payments. Diewert and Morrison (1989) used a producer theory approach to generate export supply and import demand functions. The approach uses an economy-wide gross national product (GNP) function or a restricted profit function with exports as outputs and imports as inputs. This kind of approach in modeling trade functions using a production theory framework was introduced by Kohli (1978). Unlike the traditional approach, imports are considered to be intermediate inputs into the producing sector on one hand, and exports are regarded as nondomestic outputs produced by the nation’s private production sector. This approach has an advantage over the traditional approach in the sense that one can model only the private production sector of the economy, ignoring the complexities of modeling the consumer sector. Duality theory can be applied in order to derive the producer supply and demand functions conveniently based on the consistency with profit maximizing behavior. Diewert and Morrison’s (1989) model of producer behavior is based on the short run competitive profit maximization motive, holding capital as fixed. Producers take the wage rate as fixed and can hire as much labor as required at the going wage rate. So, the profit maximizing firms, operating under conditions of perfect competition, actually face the domestic and international price vectors and a vector of domestic primary factor stock, and they in fact, make the domestic as well as foreign demand and supply decisions. The technology is represented by a production possibility set from which a well-defined profit function or restricted profit function can be obtained. Since the translog restricted profit function implemented by Kohli (1978)
41
frequently fails to maintain theoretical curvature conditions, a special case of the Biquadratic Restricted Profit Function defined by Diewert and Wales (1987) has been used in this study. Kohli (1978) has modeled the substitution possibilities between Canadian imports, exports and domestic inputs or outputs with a similar approach followed by Burgess (1974a, 1974b) in regard to the treatment of imports. In the study, imports are considered to be inputs like labor and capital, and exports are considered to be an output of technology. Output consists of investment goods and consumption goods. The technology represented by a restricted profit function having labor and capital fixed in the short run, and prices of imports, exports, consumption goods and investment goods as exogenous, is somewhat similar to Samuelson’s (1953-4, 1958) GNP function. The import demand and export supply functions, along with the supply equations for consumption goods and investment goods and also the inverse demand functions of domestic factors are simultaneously derived from this GNP function. In the estimation process the symmetry and homogeneity restrictions are assumed to hold. The procedure can estimate import and export functions without assuming that outputs and domestic inputs can be aggregated, and at the same time it can focus on the substitution possibilities inherent in the production technology. Truett and Truett (1998) investigated the Korean demand for imports and the impacts of trade liberalization on domestic factor inputs using a translog cost function using a production theory approach. They also regarded imports as productive inputs. The advantage of looking at imports as factors of production is that the impact of changes in import prices (due to tariff and/or other trade restrictive policies) on domestic input demands, domestic output prices and on the quantity of imports demanded, can be observed for appropriate decision making. Of course, the impact will depend on whether the imports have a complementary relationship or substitute
42
relationship with domestic inputs. The model used by them assumes that aggregate output consists of two types of goods - consumption goods and investment goods whereas the inputs are classified into three types - labor, capital and imports. In the early studies where imports were treated as final goods, the demand for imports was taken to be a function of national income, the price of imports, and the price of domestic goods, with some exchange rate adjustments (Houthakker and Magee (1969) is an example). However, the idea of imports as a productive factor, as mentioned earlier, was subsequently adopted by Burgess (1974b, p.225). The importance of treating imports as a productive factor is that if they are a substitute for or have a complementary relationship with one or more domestic inputs, then trade policy may affect domestic factor income and its distribution. For example, when there is a substitute relationship between imports and domestic inputs, any reduction in import restriction will decrease the demand for domestic inputs in the short run. But, if they have a complementary relationship, the reduction in trade restriction will have positive impact on the demand for domestic inputs. In the Truett and Truett (1998) study, it is assumed that imports are combined with domestic inputs (labor and capital) by the producer having an objective of minimizing cost of producing a bundle of goods to be sold domestically or abroad. They used a translog cost function with its corresponding input share and revenue share equations and estimated the cross price elasticities of demand between different pairs of inputs and also the direct price elasticities of demand for them. The question of separability of outputs (i.e., consumption goods and investment goods) has been investigated to look at whether Korea’s demand for imports is affected by the composition of outputs or not.
43
Trutt and Truett (1998) followed the Zellner–efficient method (ZEF) (Zellner, 1962) in estimating the cost function, cost share and revenue share equations by iterating on the estimated covariance matrix until convergence is reached. It could be argued that both prices and quantities may be considered as endogenous and it is more appropriate to use an iterative three-stage least square method (I3SLS) with some instrumental variables. The procedure has a problem in selecting the instrument variable since there is no straightforward method of doing so and thus it becomes somewhat arbitrary. As a result, the estimates may be too sensitive to the instrumental variables chosen. This is the limitation of cost function approach. However, the results of this procedure are found to be similar to those of the maximum likelihood method in various studies. Truett and Truett (1998) focuses its attention on the hypothesis of input-output separability. This means that the marginal rate of transformation between various products is independent of the composition of inputs and the marginal rate of substitution between factor pairs is independent of the composition of outputs. So, a sufficient condition for this is that all the interacting terms are zero. It suggests that whenever there exists an input-output separability, changes in output mix will not affect the cost minimizing input mix. The study also gives estimates of different elasticities of interest such as direct and cross price elasticities of demand for inputs as well as the inverse price elasticities of output supply and the elasticity of input prices in response to output prices etc. The elasticities are expressed in estimated parameters and cost and revenue shares. Inverse Demand Analysis Huang (1988) has provided a framework for estimating a complete price dependent demand system i.e., an inverse demand system. An inverse demand system is one where prices are functions of quantities demanded and income. It is as important as the quantity dependent demand system. It explains price variations as functions of quantity variations and it has 44
analogous properties like the regular demand system. Agricultural economists (i.e., Fox, Houck, Waugh) have long before recognized that lags between production decision and commodities marketed may predetermine quantities with some price adjustments for market clearing. Therefore, quantities rather than prices are more appropriate instrumental or control variables for analysis of many types of agricultural policies and problems. An inverse demand system is also theoretically justified in the classical demand theory framework. It is indicated by Hicks (1956, p.83) that the Marshallian demand has two functions such as (1) it shows the amounts consumers will take at given prices, and (2) it shows the prices at which consumers will buy given quantities. Hence, the second function, “quantity into price” implies the inverse demand system. Applications of inverse demand systems are found in Huang (1983, 1988), Barten and Bettendorf (1989), and Moschini and Vissa (1992). From empirical standpoint, inverse demand and regular demand systems are not equivalent. In order to avoid statistical inconsistencies, the right-hand side variables in such systems should be ones not controlled by the decision maker. Usually, the consumer in most industrialized economies is a price taker and quantity adjuster for most goods and services purchased. In this case, a regular demand system is indicated. However, for certain other goods like fresh fruits and vegetables, fresh fish etc., supply is very inelastic in the short-run and the producers are eventually price takers. Price taking producers and price taking consumers are linked by a group of traders who select a price that is expected to clear the market. This means, for fixed quantities the wholesale traders practically offer prices that are low enough to induce consumers to buy the entire available quantities. Hence, the traders set prices as a function of quantities whereby causality goes from quantity to price. In such cases, inverse demand systems are indicated.
45
Huang (1988) develops an inverse demand system and applies it to estimate price flexibilities for thirteen U.S. aggregate food groups and one non-food sector for 1947 through 1983. The demand system is estimated using a constraint maximum likelihood method. The concept of distance function and its related substitution effect and scale flexibilities are used. The system explores the interdependent nature of food price variations in response to changes in quantity. The price flexibilities indicate the change in commodity price needed to induce consumers to absorb a marginal increase in the quantity of that commodity or others. The estimated scale flexibilities provide the response of a commodity price to a proportionate change in the quantity of all goods. They also give an important linkage between compensated and uncompensated flexibilities. In order to understand an inverse demand system, one may illustrate the price effects of a marginal change in quantities demanded considering Anderson’s (1980) suggestion that the “scale slope” of quantities demanded plays the same role as the income slope in ordinary demand system. Moschini and Vissa (1992) also presented an inverse demand system that can be estimated in a linear form. They explained how to derive an inverse demand system that resembles one of the most commonly used demand systems in applied demand analysis, i.e., the Almost Ideal Demand System (AIDS) of Deaton and Muellbauer (1980) having its popularity for the availability of an approximate linear version. So, they named their system as the Linear Inverse Demand System (LIDS). In deriving an inverse demand system, one can start either from a direct utility function and exploit Wold’s identity yielding ordinary inverse demand system, or alternatively start from a distance (transformation) function and exploit Shephard’s theorem yielding compensated inverse demand system. They derived the system (LIDS) from a distance
46
function and showed that it has good approximation properties compared with inverse translog demand system (ITL) and nonlinear inverse demand system (NLIDS). Barten and Bettendorf (1989) used inverse demand system for price formulation of fish explaining why people pay for different types of fish the recorded prices. Gorman (1959) first established fish as a respectable, interesting and challenging subject in demand analysis. He started with the proposition that the price of fish depends in part on a function of its quantity consumed and income, and in part on the shadow prices of fundamental characteristics shared by all types of fish. Following Gorman, they related the price of each type of fish to its quantity demanded and to total real expenditure on fish. Their study refers to eight major types of fresh sea fish landed at Belgian fishery port. They assumed a weak separability of the total commodity bundle into these types of fish on one hand and other types on the other hand. So, only the quantities of these fish and their prices matter. They also assumed that collective consumer behavior for fresh sea fish could be interpreted as that of the rational representative consumer. Therefore, they expressed market demand by a system of Marshallian demand functions and deduced the inverse demand system. For the estimation purpose, they estimated a Rotterdam variant of inverse demand system. Differential Production Approach Washington and Kilmer (2002a, b) used a differential production approach to estimate import demand of whey with a comparison to Rotterdam model. The application of production theory to international trade is not a new concept. Previous studies using a production theory approach to international trade include Burgess (1974a) and (1974b), Kohli (1978) Diewert and Morrison (1989), and Truett and Truett (1998). Each of these studies recognized that most goods in international trade require further processing before final delivery to consumers. Even though a traded product is not physically altered, activities such as handling, storing, repackaging, 47
transportation, insurance, and retailing occur. Thus, a significant amount of domestic value is added when the final product reaches the consumer. Therefore, it seems more appropriate to view imported products as inputs rather than as final goods even if goods are not physically transformed. The production approach views imports as intermediary goods (inputs) and not as final goods entering the consumer’s utility function. Most of the imports arrive in a country in bulk and consumers rarely buy commodities in bulk or directly from exporting countries. Following the methodology of Laitinen and Theil (1978) and Theil (1980a, b), the model is derived from the differential approach to the theory of the firm where firms maximize profit in a two-stage procedure, i.e., in the first stage, determining the profit maximizing level of output to produce and in the second stage minimizing the cost of producing that profit maximizing level of output. According to Laitinen and Theil, and Davis and Jensen (1994), this procedure is consistent with a one-step or direct profit maximization procedure. The first stage provides the output supply equation and in the second stage, the conditional factor demand system is obtained. From the results of both stages, a system of unconditional derived demand equations is derived. The advantages of the production theory approach over the utility approach to import demand estimation have been discussed by Davis and Jensen (1994), Kohli (1991) and Washington and Kilmer (2002a, b). The striking points are the facts that (a) most imported agricultural commodities are inputs and not final goods, (b) specifying the first stage aggregates is more intuitive when using the production theory approach, (c) it is easier and more intuitive to estimate unconditional elasticities using production theory, (d) the estimated parameters using production theory will be structural parameters, and (e) viewing imports as intermediate goods not only has its merits in correctness, but it also leads to substantial simplifications theoretically.
48
For example, the demand for imports can be derived from production theory and there is no need to model final demand and as such it can avoid the difficulties that arise when we aggregate over individual consumers. Washington and Kilmer (2002a, b) articulated the system of equations for estimating such import demand in the following manner. In fact, the objective of a competitive firm in the first stage is to identify the profit-maximizing level of output by equating marginal cost with marginal revenue. This procedure yields the differential output supply equation N
d (log Q * ) = ϕ d (log p * ) + ∑ π j d (log w j )
(3-9)
j =1
where Q*, p* and wj represent the output, output price and the price of inputs respectively; ϕ and
π are the price elasticity of supply and the elasticity of supply with respect to input prices respectively. N is the total number of inputs used in production. In the second stage, the firm minimizes its input costs/expenditure. Here, the differential factor demand model is derived that will be used to estimate the system of source specific derived demand equations. This is specified as (Washington and Kilmer (2002a,b)) n
f i d (log x i ) = θ i* d (log X ) + ∑ π ij* d (log w j )
(3-10)
j =1
where f i is the factor share of imported good x from source country i in total input cost; xi and wi represent the quantity and price of inputs which include the price of each imported good from n
source country i; d (log X ) = ∑ f it d (log x t ) where d (log X ) is the Divisia volume input i =1
index; θ *i is the mean share of the ith input in the marginal cost of the firm; π *ij is the conditional
49
price coefficient between the ith and jth importing sources or inputs; n is the number of inputs in the system, n ∈ N. It is important to mention that the differential factor demand model is required to meet the following parameter restrictions in order for the model to conform to theoretical considerations:
∑π
* ij
= 0 (homogeneity), and
j
π ij* = π *ji (symmetry). The second stage procedure results in the conditional own price/cross price elasticity d (log x i ) π ij = = , d (log w j ) f i *
c ε xw
(3-11)
and the conditional Divisia volume input elasticity,
ε xX =
d (log xi ) θ i* = . d (log X ) f i
(3-12)
Using the relationship between the Divisia volume input index and output,
d (log X ) = γ d (log Q * ) , Equation 3-9 can be substituted into Equation 3-10 to yield the unconditional derived demand system (Washington and Kilmer (2002a,b)) n
n
j =1
j =1
f i d (log xi ) = θ i*γ [ϕ d (log p * ) + ∑ π j d (log w j )] + ∑ π ij* d (log w j ) .
(3-13)
Now, dividing through Equation 3-13 by f i and using Equations 3-11 and 3-12, one can get the unconditional derived demand elasticities, the elasticity of input demand with respect to output price
ε xp =
d (log x i ) d (log p * )
= γε xX ϕ ,
(3-14)
and the unconditional own price/cross price elasticity of input demand
50
ε xw =
d (log x i ) c = γ ε xX π j + ε xw . d (log w j )
(3-15)
Lastly, the unconditional elasticity of derived demand with respect to the price of an input contained in N but not in n can be found as
ε xw =
d (log xi ) = γ ε xX π j . d (log w j )
(3-16)
Summary of Literature Review
It has been seen that Consumer Demand system deals with the allocation of a given total budget over a set of commodities taking into account the effects of price variation. This is used as a tool by the demand analyst to describe and predict empirical consumer behavior. The demand system is derived from the theory of utility maximization. The differential approach to consumer theory as proposed by Barten (1964) and Theil (1965) is an approximation of these demand equations. Regarding the functional specification, four alternative approaches have been derived, with well-known demand systems as an illustration. These are the Barten (1964) and Theil's (1965) the Rotterdam model, Deaton and Muellbauer's (1980) the Almost Ideal Demand System (AIDS) model, Keller and Van Driel’s (1985) the Dutch Central Bureau of Statistics (CBS) model, and Neves’s (1994) AIDS income-variant the Netherlands National Bureau of Research (NBR) model. Consumer demand allocation models have widely been used in import demand studies by various researchers such as Lee, Seale, and Jierwiriyapant (1990), Seale, Sparks, and Buxton (1992), Lee, Brown, and Seale (1992), and Satyanarayana, Wilson, and Johnson (1999) and many more. In these studies, imports are considered to be final goods entering directly into the consumer’s utility function. Even though Satyanarayana, Wilson, and Johnson (1999) use a consumer demand theory model, they recognize that production theory could be used to estimate
51
the derived demand for malt; however, critical data was not available. As the nature of international trade is such that traded goods are either used in production processes or go through a number of domestic channels before reaching the consumer, the production processes and domestic channels generate some value added to the product by the time it reaches the final consumer. Therefore, it is more appropriate to view imported goods as inputs even if no transformation takes place (Kohli, 1978; Diewert & Morrison, 1989, and Truett and Truett, 1998). The other advantage of using an input demand model in import demand studies is related to how traded goods are typically reported. Most traded commodities are typically reported in bulk quantities and values at dockside. In fact, consumers almost never purchase commodities in such quantities or at the port/dockside. So, with the assumption that importing decisions are made by a profit-maximizing or cost-minimizing firm is more consistent with the way how trade data is typically reported (Washington and Kilmer, 2002a, b). This study intends to use Laitinen (1980) and Theil’s (1980a, b) differential input demand model along with three other input demand models which are the firm’s version of the AIDS, CBS and NBR on the consumer side. Of course, the ultimate choice of model specification has to be made depending on empirical grounds.
52
CHAPTER 4 THEORETICAL AND EMPIRICAL MODEL In this study, a production theory approach has been followed in estimating import demand for tomatoes into the United States and the European Union. Liu, Kilmer and Lee (2007) have a similar study on import demand with an emphasis on choice of appropriate functional forms. The procedure and models used by them have been followed in this study. This study uses Laitinen (1980) and Theil’s (1980 a, b) differential input demand model (Rotterdam) along with three additional input demand models which are the firm’s version of the AIDS, CBS and NBR on the consumer side. The choice of appropriate model amongst different specifications for the input demand allocation models ultimately depends on empirical grounds. This study examines the empirical performance of four similar input demand allocation models in an econometric analysis of the import market for tomatoes into the U.S. and the EU. The synthetic model developed by Barten (1993) has been used to compare the empirical results of these four models. In case of EU import market analysis the Synthetic model itself has been tried as a fifth model. Hence, the theoretical models for this study comprise the differential input demand model and the firm’s version of the AIDS model, CBS model, NBR model and Barten’s (1993) synthetic model. Theoretical Models
Differential Input Demand Model The differential input demand model (Laitinen (1980); Theil, (1980 a, b)) is based on the firm’s version of the fundamental matrix equation of consumer demand. The approach begins with the traditional production optimization problem of choosing a bundle of inputs that will Min C = ∑ pi x i
(4-1)
Subject to z = h(x )
53
where, C is total cost; pi and xi are the price and quantity for the i th input; z is output which is held constant; and x is a vector of n input quantities. The first order conditions are solved for the input demand equations xi = xi ( p1..... pn , z ) . The derivation of the differential input demand model (Laitinen (1980); Theil (1980 a, b)) is an approximation of this set of input demand equations resulting in the differential input demand system as represented by
f i d ln xi = θ i d ln X − ∑ π ij d ln p j
(4-2)
j
where f i = pi xi / C is the share of total cost from input i ; d ln xi is the change in the i th input;
θ i = ∂ ( pi xi / ∂z ) /(∂C / ∂z ) is ith input’s share in marginal cost, d ln X = ∑ f i d ln xi is the Divisia i
volume index; and π ij is the Slutsky coefficient. Equation 4-2 is the i th differential demand th
equation of the firm and it indicates that changes in the decision to purchase the i input depend upon the changes in the total amount of inputs obtained and changes in input prices. Given the data with sufficient variability in input prices and quantities, variables can be constructed for f i d ln xi , d ln X and d ln p j and the coefficients for θ i and π ij can be estimated.
The restrictions on the above input demand Equation 4-2 are adding-up:
∑θ
i
= 1,
i
homogeneity:
∑π
ij
= 0,
(4-3)
i
∑π
ij
= 0,
(4-4)
j
and Slutsky symmetry: π ij = π ji ,
(4-5)
and the condition for curvature is ( x ′π x) ≥ 0 . Equation 4-2 also results in own price and cross compensated price elasticities
54
ε xp =
π ij d ln xi =− d ln p j fi
(4-6)
and the Divisia volume elasticity
ε xX =
d ln xi θ i = . d ln X fi
(4-7)
The Production AIDS model Unlike the consumer AIDS model having expenditure as a function of utility and prices for a consumer as in Deaton and Muellbauer (1980), the production AIDS model has cost specified as a function of output and prices of inputs for a firm as (Liu, Kilmer and Lee(2007))
ln c(p, z ) = (1 − z ) ln a (p ) + z ln b(p ) where ln a(p ) = a 0 + ∑ a j ln p j + j
(4-8)
1 ∑∑ γ ij* ln pi ln p j 2 i j
β
and ln b(p ) = ln a(p ) + β 0 Π p j j ; j
c is the total cost, p is a vector of n input prices , and z is output that is held constant. When
there is no production, z = 0 and Equation 4-8 becomes ln c(p, z ) = ln a (p )
(4-9)
which is the firm’s fixed cost. The consumer AIDS model in differential form (Barten, 1993) can be written as follows to represent the production AIDS model (Liu, Kilmer and Lee (2007)) df i = β i d ln X + ∑ γ ij d ln p j .
(4-10)
j
This model is similar to the differential input demand model (Equation 4-2) on the right-hand side; however, the dependent variables are different on the left-hand side. The production AIDS
55
model explains the change in input i’s share (marginal share) of total cost, while the differential input demand model concerns with the change in input quantity. Following Lee, Brown, and Seale's (1994) version of the consumer AIDS model, the production AIDS model can be formulated as (Liu, Kilmer and Lee (2007)) f i d ln xi = ( β i + f i )d ln X − ∑ (γ ij − f i Δ ij + f i f j ) d ln p j
(4-11)
j
where Δ ij is Kronecher's delta equal to unity if i = j and zero otherwise. It can be noticed that the AIDS model (Equation 4-11) and the differential input demand (Equation 4-2) have the same dependent variable. Hence, this will allow the use of Barten's (1993) synthetic model to empirically test for the appropriate functional form. The restrictions on the production AIDS model are adding-up:
∑β
i
= 0,
i
homogeneity:
∑γ
ij
∑γ
ij
= 0,
(4-12)
i
= 0,
(4-13)
j
and Slutsky symmetry: γ ij = γ ji .
(4-14)
Also, the curvature condition is ( x ′π x) ≥ 0 where the π matrix is composed of the elements
π ij = γ ij − f i Δ ij + f i f j . Equation 4-11 results in the own price and cross compensated price elasticities to be
ε xp =
γ ij − f i Δ ij + f i f j d ln xi =− d ln p j fi
(4-15)
and the Divisia volume elasticity as
ε xX =
d ln xi β i + f i = . d ln X fi
(416)
56
The Production CBS Model Keller and van Driel (1985) developed the Dutch Central Bureau of Statistics (CBS) consumer demand model based on Working’s Engel model. The production CBS model in differential form is written as (Liu, Kilmer and Lee (2007)) f i (d ln xi − d ln X ) = β i d ln X − ∑ π ij d ln p j .
(4-17)
j
Following Lee, Brown, and Seale's (1994) version of the consumer CBS model and rearranging Equation 4-17, the production CBS model can be formulated as (Liu, Kilmer and Lee (2007)) f i d ln xi = ( β i + f i )d ln X − ∑ π ij d ln p j
(4-18)
j
which is another representation of the production CBS model and with this formulation, Barten's (1993) synthetic model can be used to empirically test for the appropriate functional form. This model has the production AIDS model’s volume coefficients β i (Equation 4-11) and the differential input demand model’s price coefficients π ij (Equation 4-2). It shares the adding-up, homogeneity and symmetry conditions with these two models. The constraints on the production CBS model are adding-up:
∑β
i
= 1,
i
homogeneity:
∑π
ij
∑π
ij
=0,
(4-19)
i
= 0,
(4-20)
j
and Slutsky symmetry: π ij = π ji .
(4-21)
Equation 4-18 also results in the own price and cross compensated price elasticities
ε xp =
π ij d ln xi =− d ln p j fi
(4-22)
57
and the Divisia volume elasticity
ε xX =
d ln xi β i + f i . = d ln X fi
(4-23)
The Production NBR Model Neves (1994) developed the consumer NBR as a consumer allocation model. On the producer side, the production NBR model written in differential form is (Liu, Kilmer and Lee (2007)) df i + f i d ln X = θ i d ln X − ∑ γ ij d ln p j .
(4-24)
j
Following Lee, Brown, and Seale's (1994) version of the consumer NBR model, the differential production NBR model has been written as (Liu, Kilmer and Lee (2007)) f i d ln xi = θ i d ln X − ∑ (γ ij − f i Δ ij + f i f j ) d ln p j .
(4-25)
j
This model has the volume coefficient θi as in the differential input demand model (Equation 42) and the price coefficients γ ij as in the production AIDS model (Equation 4-11). The constraints are adding-up:
∑θ
= 1,
i
i
homogeneity:
∑γ
ij
= 0,
(4-26)
i
∑γ
ij
= 0,
(4-27)
j
and Slutsky symmetry: γ ij = γ ji .
(4-28)
The curvature condition is ( x ′π x) ≥ 0 where the elements of the π matrix are
π ij = γ ij − f i Δ ij + f i f j . Equation 4-25 results in the own price and cross compensated price elasticities as
58
ε xp =
γ ij − Δ ij f i + f i f j d ln xi =− d ln p j fi
(4-29)
and the Divisia volume elasticity as
ε xX =
d ln xi θ i = . d ln X fi
(4-30)
The Synthetic Input Demand Model A synthetic model that contains all of the four input demand models was developed by Barten (1993). This synthetic system is employed to assess and compare the empirical performance of each of the four conditional demand systems. Following Lee, Brown, and Seale's (1994) version of Barten’s (1993) synthetic model, Barten's synthetic production model can be written as follows (Liu, Kilmer and Lee (2007)) f i d ln xi = (d i + δ 1 f i ) d ln X − ∑ (eij − δ 2 f i (Δ ij − f j )) d ln p j
(4-31)
j
where d i = δ 1 β i + (1 − δ 1 )θ i and eij = δ 2 γ ij + (1 − δ 2 )π ij . It is good to notice that Equation 4-31 becomes the differential input demand model when δ 1 = δ 2 =0, the production CBS model when δ 1 =1 and δ 2 =0, the production AIDS model when δ 1 = δ 2 =1, and the production NBR model when δ 1 =0 and δ 2 =1. The demand restrictions on Equation 4-31 are adding-up:
∑d
i
= 1 − δ 1 and
∑e
ij
= 0,
(4-32)
i
i
∑e
= 0,
(4-33)
Slutsky symmetry: eij = e ji ,
(4-34)
homogeneity:
ij
j
and the curvature condition is ( x ′π x) ≥ 0 when the elements of the π matrix are defined as
π ij = eij − δ 2 f i (Δ ij − f j ) .
59
Equation 4-31 also results in own-price and compensated cross-price elasticities as
ε xp =
eij − δ 2 f i (Δ ij − f j ) d ln xi =− d ln p j fi
(4-35)
and the Divisia volume elasticity as
ε xx =
d ln xi d i + δ 1 f i . = d ln X fi
(4-36) Empirical Models
In order to obtain estimable forms of the five demand systems, all variables must have dates attached. The standard practice of replacing the cost shares by their two-period moving average (Barten, 1993) has been followed as −
f it = ( f it + f it −1 ) / 2 .
(4-37)
This study uses annual data and the log differentials are measured as annual differences of the logarithmic value for time t and t-1. The differential input demand model (Equation 4-2) is transformed into f it Dxit = θ i DX t − ∑ π ij Dp jt + ε it
(4-38)
j
n
−
where Dxit = ln xit − ln xit −1 , DX t = ∑ f it Dxit , Dp jt = ln p jt − ln p jt −1 , ε it is the error term, and i =1
θ i and π ij are parameters to be estimated. The production AIDS model (Equation 4-11) is transformed into −
−
f it Dxit = ( β i + f it ) DX t − ∑ (γ ij − f it Δ ij + f it f jt ) Dp jt + ε it j
where β it and γ it are the parameters to be estimated. The production CBS model (Equation 4-18) is transformed into
60
(4-39)
−
−
f it Dxit = ( β i + f it ) DX t − ∑ π it Dp jt + ε it
(4-40)
j
where β it and π ij are the parameters to be estimated. The production NBR model (Equation 4-25) is transformed into −
f it Dxit = θ i DX t − ∑ (γ ij − f it Δ ij + f it f jt ) Dp jt + ε it
(4-41)
j
and θ i and γ ij are the parameters to be estimated. Barten's (1993) synthetic demand model (Equation 4-31) is transformed into −
−
−
f it Dxit = (d i + δ 1 f it ) DX t − ∑ (eij − δ 2 f it (Δ ij − f jt )) Dp jt + ε it
(4-42)
j
where d i , δ1 , δ 2 ,and eij are the parameters to be estimated. Data Section
The tomato data has been collected from various sources. Some of them are published and some of them are on-line websites. The main source for tomato import data is the United Nations (U.N.) Statistics Division–Commodity Trade Statistics Database (UN-COMTRADE) website. The International Agricultural Trade and Policy Center (IATPC) at the University of Florida has made necessary arrangements for the availability of this data. The U.S. tomato data are collected mostly from the website maintained by the USDA. Some data are also collected from the U.N. Food and Agriculture Organization (FAO) Statistics (UN-FAOSTAT) website. The data set for this research have been completed for the period 1963 – 2005. In doing so, the U.N. commodity specification SITC Rev.1 with commodity code 0544 for fresh tomatoes has been used. At present the EU has 27 members. This study is confined to EU–15. Because data for 12 new members (Cyprus, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Malta, Poland, Slovakia and Slovenia officially included on May 1, 2004, and Bulgaria and Romania included
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on January 1, 2007) are not available for the entire period under consideration. Therefore, they are not included in this research as part of the EU dataset. Hence, the EU means EU-15 in this study. In order to get the EU member country’s data as well as that of the EU as a whole, data for tomato imports has been collected from 1963-2005 irrespective of the country’s inclusion in the EU. The data on the value (in U.S. dollar) of imports include cost, insurance and freight. The price data have been derived by dividing the values by quantity (in kilograms) imported. For a continuous time series data for the period under research (1963-2005), a few steps have been taken. First, since Belgium and Luxembourg were Customs Union until 1998, data for Belgium and Luxembourg have been added together for the years from 1999 through 2005 to represent a continuous series for Belgium and Luxembourg. Second, the Federal Republic of Germany (FRG) data for 1963-1990 has been added to Germany data for 1991-2005 to make the Germany data series a continuous one. Third, the data for the United States of America (USA) has been constituted by adding USA before 1981 (with code 841) data to USA (code 842) data for 1981 through 2005. As the Customs area of the United States (U.S.) also includes the territory of U.S. Virgin Islands, the trade data of U.S. Virgin Islands before 1981 was also included in the USA data. Moreover, most of their trade occurred within the EU member countries. In this study, intra-trade among the EU members has been subtracted from total import trade figure of each member in order for arriving at the actual trade involvement of them with the outside world. Then, all the EU member countries’ trades have been added together to get EU import trade data. All these manipulations have been done through a mathematical programming in TSP (Time Series Processor) software. Thus, two sets of working data have been created – one for the EU-
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15 as a whole with different participating partner countries and rest of the world (ROW) and the other for the U.S. with different participating partner countries and ROW. In selecting separate participating partner countries in the working dataset, their shares in total import trade during the period under study have been taken into consideration. For EU-15, about 95% of import trade has been covered by separate partners and remaining trade has been placed under ROW. It should be mentioned here that Bulgaria and Romania are in the list of separate partners according to their contribution shares even though subsequently they have become EU members. In the same way, about 99.5% of total U.S. import trade is covered by separate partners and remaining goes to ROW. Thus, for the U.S. import the partner/source countries are Mexico, Canada, EU-15, Dominican Republic and ROW and those for the EU-15 are Morocco, Romania, Bulgaria, Israel, Albania, Turkey, USA and ROW. The U.S. is kept as a separate partner in the working dataset for particular interest even if its share in EU-15 import is very small (only 0.12%). All programs relating above mentioned data manipulation are provided in Appendix C. However, in the working dataset as created there remain some zeros in quantity and value columns for a few partner countries for few years indicating no import taking place during those years. In order to deal with this situation, the zero quantity is replaced by 1 being a small number compared to millions as Wooldridge (2000) indicated a similar procedure. For the corresponding number in the value column that ultimately is transformed into price (since price = value/quantity), a separate regression procedure is followed. Theoretically, corresponding to very low quantity, price should be very high. Keeping this in mind, an ordinary least square (OLS) regression is done on price with quantity and time trend (years) as independent variables along with a constant term. Then, zero value (price) is replaced by the highest price for the country of
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origin in question plus twice the standard deviation of the dependent variable plus inflation as the coefficient of the trend (years) variable with appropriate adjustment. The price regression models for the U.S. and the EU-15 are provided in Appendix A and Appendix B respectively.
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CHAPTER 5 EMPIRICAL RESULTS Results for U.S. Tomato Import Demand Analysis
The U.S. import demand analysis has been performed on the data set with four separate partners and ROW. The extent of their involvement and the empirical results are discussed below. Descriptive Statistics
Table 5-1 shows the cost share, quantity share and the average prices of imports from the five sources of origin for 1964, the sample mean, and 2005. The largest cost share was for the import of tomatoes from Mexico and the lowest was for imports from the Dominican Republic. The cost share for imports from Mexico actually decreased from 98.78% in 1964 to 72.70% in 2005 whereas the decrease for imports from ROW was from 0.38% in 1964 to 0.25% in 2005. During the same period the cost share for imports from Canada, EU-15 and Dominican Republic increased from 0.79% to 24.40%, from 0.0% to 2,52% and from 0.05% to 0.13% respectively. The average prices for imports from Mexico and Dominican Republic are the same, but the average import price for EU-15 tomatoes is higher than other countries and increased over time. Model Results
For the U.S. import demand analysis, the differential production version of all the five models i.e., AIDS, CBS, NBR, differential input demand (DID) and Synthetic were estimated with first order autocorrelation AR(1), homogeneity and symmetry imposed. As all of these models satisfy adding-up conditions, only four equations have been estimated excluding the ROW equation as indicated in Barten (1969). The parameters for the omitted equation are established from the estimates of other equations using the adding-up conditions. The models were estimated by the iterative seemingly unrelated regression (SUR) method that is performed
65
using the well known least square procedure (LSQ) in the Time Series Processor (TSP) (Hall and Cummins, 1998). All models are found to have significant autocorrelation based on t-statistics (Table 5-2). A likelihood ratio test is done comparing the log likelihood values of the first four models to that of the Synthetic model in order to choose an appropriate model for the given data. Table 5-2 shows the test result whereby the NBR model qualifies as a model to be used. So, only results from the production NBR as corrected for autocorrelation (TSP website) have been reported for further discussion. The model has been provided in Appendix A. The coefficient estimates (γij) for production NBR (Equation 4-25), the demand parameters θi and πij and the conditional demand elasticity estimates (Equation 4-29 and Equation 4-30) calculated at sample mean cost share are shown in Table 5-3 and Table 5-4. The property of the Slutsky matrix to be positive semi-definite one is validated as all the eigen values are positive except one which is zero. The eigen values for the production NBR Slutsky matrix are 1.20646D-17, 0.000940, 0.008208, 0.038217, and 0.10139. This is an indication that the import firms are operating optimally. Divisia Elasticities: The Divisia import volume elasticities for Canada, Dominican
Republic, Mexico, EU-15 and ROW are 0.172136, 0.173076, 1.06388, 1.24252 and -1.68288 respectively (Table 5-4). The Divisia import elasticities for Mexico, EU-15 and ROW are significant and more than unity in absolute value terms whereas those for Canada and Dominican Republic are not significant and less than unity. This means that if total imports of tomatoes into the U.S. increases by 1%, other things remaining the same, imports from Canada or Dominican Republic would not change and imports from Mexico and EU-15 would increase by more than 1%; however, the import from ROW (with a negative Divisia import elasticity) would cause a decline by more than 1%. The reason for this may be the trivial share of ROW (only 0.37%) in
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the U.S. total tomato import. So, when there is an increased volume of imports into the U.S., the prominent partners with larger shares capture the opportunity and the insignificant players aggregated in ROW loose their market share in competition. Conditional Own-Price Elasticities: The conditional own-price elasticities for Canada,
Dominican Republic, Mexico, EU-15 and ROW are -0.804941, -0.736886, -0.081015, -0.878641 and -0.520927 respectively. All of them are statistically significant but inelastic. These conditional elasticities indicate that the U.S. import demand for tomatoes from Mexico is the most inelastic meaning the least responsive to price change followed by ROW. The import demand for EU-15, Canada and the Dominican Republic tomatoes are more elastic, but still inelastic. Among them the EU-15 has the least inelastic demand and the most responsive to price change. This means that with a change in price the U.S. import demand for EU-15 tomatoes would change the most. For example, with a 1% decrease in an import price (ceterius paribus), the increases in the U.S. import demand for tomatoes would be 0.88% for EU-15 tomatoes; 0.80% for Canadian tomatoes, 0.74% for Dominican Republic tomatoes, 0.52% for ROW. The responsiveness of the U.S. import quantity would be almost the same (i.e., almost “no change”) for Mexican tomatoes if their prices change. Conditional Cross-Price Elasticities: It is noticeable from Table 5-4 that among the
conditional cross-price demand parameters fourteen (7 pairs) are statistically significant and different from zero. They are between (1) Canada and Mexico, (2) Canada and EU-15, (3) Dominican Republic and Mexico, (4) Dominican Republic and EU-15, (5) Dominican Republic and ROW, (6) Mexico and EU-15, and (7) Mexico and ROW. All of these conditional crossprice elasticity estimates are positive (implying input substitutes) except one involving ROW, i.e., between Dominican Republic and ROW. Results indicate that (1) if price of Mexican
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tomatoes increases by 1%, the U.S. import demand for Canadian tomatoes will increase by 0.76%. On the other hand, if the price of Canadian tomatoes increases by 1%, the U.S. import demand for Mexican tomatoes will increase by 0.04% only. (2) If the price of EU-15 tomatoes is increased by 1%, the U.S. import demand for Canadian tomatoes would increase by 0.10%; however, if Canadian tomato price is increased by 1%, import demand for EU-15 tomato would increase by 0.12%. (3) A 1% price increase in Mexican tomatoes will cause a 1.20% increase in the U.S. import demand for Dominican Republic tomatoes whereas a 1% increase in the price of Dominican Republic tomatoes will have 0.003% impact on the import demand for Mexican tomatoes. (4) If the price of EU-15 tomatoes is increased by 1%, import demand for Dominican Republic tomatoes would increase by 0.27%; on the other hand, if price of Dominican Republic tomatoes is increased by 1%, the import demand for EU-15 tomatoes would increase by 0.02%. (5) The conditional cross-price elasticities between Dominican Republic and ROW are negative indicating complementary relation which is not expected. Most of the conditional cross-price elasticities related to ROW are negative. The conditional cross-price elasticities show that if the price of ROW tomatoes increases by 1%, the U.S. import demand for Dominican Republic tomatoes would decline by 0.80% and if price of Dominican Republic tomatoes increases by 1%, the import demand for ROW tomatoes would decline by 0.17%. (6) The conditional cross-price elasticities between Mexico and EU-15 show that if the price of EU-15 tomatoes is increased by 1%, the U.S. import demand for Mexican tomatoes would increase by 0.03%, but if the price of Mexican tomatoes is increased by 1%, the import demand for EU-15 tomatoes would increase by 0.73%. (7) Finally, the conditional cross-price elasticities suggest that if the price of ROW increases by 1%, the U.S. import demand for Mexican tomatoes would increase by only 0.01%;
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on the contrary, if the price of Mexican tomatoes increases by 1%, the import demand for ROW tomatoes would increase by 0.92%. The Divisia volume elasticities and the conditional own-price elasticities for the U.S. analysis are calculated from 1995 to 2005 and the results are presented in Table 5-5 and Table 56 respectively. Even though there is no variable in the model directly related to any sort of structural change, it is to some extent accounted for through potential changes in the Divisia volume index coefficient that enters directly in elasticity calculation. If the Divisia volume elasticity and the conditional own-price elasticity change over time, this indicates that structural change is occurring recognizing that the precise nature of this structural change is not known. Therefore, these two elasticities are calculated over a period of 11 years with an initial sample size of 32 years (1964-1995) and each time adding one more year forward with a block of 32 years and subtracting the first year from the previous block. In the top part of both the Tables 5-5 and 5-6, elasticities are calculated letting both estimated parameters (numerator θi and πij) and mean factor cost shares (denominator MFi) change along with the sample; but in the bottom part of the tables, the denominator (MFi) is held constant at the initial sample block for the years 1964 to 1995 (2,33). The model for this simulation is provided in Appendix A. In the top part of both the tables elasticities show changes over time, but these changes may be due to structural influences (θi and πij) or mean cost share influences (MFi) or both. On the other hand, in the bottom part of Tables 5-5 and 5-6, the changes are due to (θi and πij) representing the structural changes more precisely. Thus, Table 5-5 (bottom part) shows that Divisia elasticities for Canada increase for a while and then decline, implying that Canada ultimately is losing shares of any increases in the U.S. imports. The Dominican Republic has a difficulty in capturing the U.S. import market. The
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Divisia elasticities for the Dominican Republic show that this country is having increasing problems keeping its share of any increases in the U.S. imports of fresh tomatoes. Mexico holds a more or less stable position with little evidence of structural adjustments; EU-15 has a little improvement in capturing the U.S. import market; and the ROW has some insignificant mixed impact of gaining and losing. Table 5-6 (bottom part) shows the conditional own-price elasticity changes over time as a result of structural influences. The U.S. imports from Canada indicate some variation in price sensitiveness due to structural adjustments; the Dominican Republic is becoming more price sensitive; Mexico is becoming less price sensitive although it was already highly insensitive to price changes; EU-15 is highly sensitive to price changes and getting slightly more sensitive; and the ROW is, in fact, less sensitive to price changes. Conditional price elasticities do not always behave as one might expect when underlying structural changes are occurring. For example, conditional own-price elasticities in the U.S. import demand analysis for Canadian fresh tomatoes for the years 2003, 2004 and 2005 are not of the right sign (positive instead of negative). So, it seems more appropriate to look at the change in the share of each partner country when the total import volume changes over time in order for getting some idea about structural change. Moreover, import volume is an important variable in the model. Thus, the shares of each participating country have been calculated over the same period (i.e., 1995-2005) with the U.S. total import increases of 10%, 15%, 20%, 25%, and 30% using the Divisia elasticities at the bottom part of Table 5-5. The variations/ fluctuations in each partner’s market share of the U.S. import market over the time are the result of structural change since the underlying variable values are kept fixed in the simulations. These are shown in Figure 5-1 through Figure 5-3 and the related data are given in Appendix C.
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Figure 5-1 shows the situations for Canada and Dominican Republic. Canada is losing its relative shares of the growth in the U.S. import over time, but the losses are numerically quite small. Dominican Republic was stable for a while at the beginning of the period and then lost a small portion of its share in the U.S. import market and sustained the loss for the rest of the period under consideration. For the most part the share changes were extremely small. In Figure 5-2, Mexico holds a very stable share in the U.S. fresh tomato import market throughout the entire period with a little increase in its share toward the ending years. The case of EU-15 is interesting because the shares have generally risen over the study period, as seen in the left portion of Figure 5-2. Finally, Figure 5-3 indicates that the ROW is steadily losing its small share of the U.S. import market for fresh tomatoes, but not by a magnitude leading to any particular concern. Summary for U.S. Analysis
From the above discussion and the conditional price elasticities in Table 5-4, it is clear that the U.S. import demand for Mexican tomatoes is the most stable one meaning that it does not change much with the change in its own price or the changes in other partners’ prices. It implies that the U.S. consumers prefer Mexican tomatoes. In other words, Mexico faces no close competitors in the U.S. import market for fresh tomatoes. Results show that there is almost a sharp competition between Canada and EU-15 while the Dominican Republic is not competitive with EU-15. The market shares of different partners do not vary much indicating very little structural change reflected through the estimated parameters measured across time. Results for EU-15 Tomato Import Demand Analysis
The EU-15 analysis was ultimately done with a data set created for six partner countries and the ROW. The empirical data status and model results are described below in detail.
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Descriptive Statistics
The cost shares, quantity shares and the average prices of imports from all the seven sources of origin for 1964, sample mean and 2005 are displayed in Table 5-7. Among the separate countries, the largest import cost share was for the imports from Morocco and the smallest was for imports from Turkey. ROW ranked second in terms of cost share. The cost share for the imports from Morocco decreased from 84.12% in 1964 to 63.94% in 2005 and the import cost shares for the imports from Albania, Bulgaria and Romania also decreased during the same time period. On the other hand, import cost shares for the imports from Israel, Turkey and ROW showed considerable increase during that time. The average prices for the imports from Bulgaria and Romania are almost the same and those for Albania, Morocco, Turkey and ROW are similar. Model Results
In order to analyze EU-15 import demand, all of the five differential production models were estimated in the same way as they were estimated for the U.S. import demand analysis. The AIDS and CBS were estimated with first order autocorrelation (AR1) whereas the other three models had no significant autocorrelation (Table 5-8). Symmetry and homogeneity conditions were imposed in all of them. The likelihood ratio (LR) test (Table 5-8) shows that DID would be the most appropriate model followed by the CBS model. So, DID was applied to estimate the conditional demand parameters and demand elasticity estimates (Equation 4-6 and Equation 4-7). But, four out of eight conditional own-price elasticities were of the wrong sign (not negative) which is clearly unacceptable according to economic theory. Also the signs of the eigen values of the Slutsky matrix were not correct. The first three eigen values came out negative instead of positive.
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Different trials were given with different years and with a different number of participating partner countries even though in the original working data there were eight participating partners including the ROW. However, all the conditional own-price elasticities were not found to be negative. Then the CBS model was tried, but the results were of the same kind. So, with the given data neither the DID nor CBS was working. Therefore, as a second choice the AIDS and NBR were applied. For these two models all the conditional own-price demand elasticities are found to be negative except the one related to the U.S. Finally, given that the U.S. import share is very small (0.12%), the U.S. data were merged with ROW making seven partner countries involved in EU-15 imports of fresh tomatoes. At this stage, the AIDS, NBR and the Synthetic model itself were estimated and all the own-price demand coefficients were found to be negative. However, they were not statistically significant in the Synthetic model; but they were all significant except one related to the ROW in both AIDS and NBR. These two models are almost equally likely for estimation purposes in case of the given data. Of course, DID and CBS were also estimated again with seven partner countries, but no fruitful results were found. The production NBR model has been selected between them on the grounds that it generates the larger likelihood value, it has a closer LR test statistics for acceptance (Table 5-8), eigen values are either zero or positive except one which is –0.0065308 , and conditional own-price elasticities are negative while most of the conditional cross price elasticities are positive (Table 5-10). However, the data is not rich enough to give theoretically precise results. Therefore, the estimates found will likely deviate from the correct estimates; however, the estimates are an approximation of the correct estimates and will be interpreted. The model is provided in Appendix B.
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The estimates for the coefficients (γij) of production NBR (Equation 4-25), the demand parameters θi and πij and the demand elasticity estimates (Equation 4-29 and Equation 4-30) as calculated at sample mean cost shares are shown in Table 5-9 and Table 5-10. The property that the Slutsky matrix be positive semi-definite is not validated as all the eigen values are positive or zero except one that is -0.0065308. The eigen values for the production NBR Slutsky matrix are 0.0065308, 9.47247D-18, 0.021110, 0.026703, 0.043189, 0.071218 and 0.13542. The 0.0065308 eigen value is problematic, but is very close to zero. Divisia Elasticities: The Divisia import volume elasticities for Albania, Bulgaria, Israel,
Morocco, Romania, Turkey and ROW are -1.08036, 0.58081, 0.33524, 1.09925, 0.18365, 0.74704, and 2.44395 respectively. The Divisia import volume elasticities for Albania and Morocco are statistically significant and more than unity in absolute value terms. The Divisia import volume elasticity for ROW is also more than unity, but not statistically significant. All other Divisia import elasticities are insignificant and less than unity. This means that if total tomato import into the EU-15 is increased by 1%, other things being equal, the import from Albania (with negative volume elasticity) would decrease by 1.08% and imports from Bulgaria, Israel, Morocco, Romania, Turkey and ROW would increase by 0%, 0%, 1.10%, 0%, 0% and0% respectively. So, in terms of import volume increase, Morocco captures the opportunity as a prominent partner. Conditional Own-Price Elasticities: The conditional own-price elasticities for Albania,
Bulgaria, Israel, Morocco, Romania, Turkey and ROW are -1.07609, -0.72700, -0.83100, 0.13009, -0.65609, -0.96215, and -0.89697 respectively (Table 5-10). All of them are statistically significant except the one associated with ROW. These conditional elasticities show that EU-15 import demand for Albanian tomatoes is elastic and the others are inelastic even though the
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import demand for Turkish tomatoes is almost unitary elastic. Among the partners, the inelasticity is the most (i.e., the least responsive to price change) for the import demand for tomatoes from Morocco. Conditional own-price elasticities indicate that for a 1% decrease in the import prices, ceterius paribus, the increases in EU-15 import demand for tomatoes would be 1.08% for Albanian tomatoes, 0.73% for Bulgarian tomatoes, 0.83% for Israeli an tomatoes, 0.13% for Morocco tomatoes, 0.66% for Romanian tomatoes, 0.96% for Turkish tomatoes, and 0.90% for ROW tomatoes. So, EU-15 import quantity from Albania would increase the most followed by Turkey, ROW, Israel, Bulgaria and Romania if their prices decrease. The import quantity from Morocco would not change much with the change in price. Conditional Cross-Price Elasticities: Among the conditional cross-price demand
parameters, only five were statistically significant (different from zero). They are between (1) Albania and Morocco, (2) Bulgaria and Morocco, (3) Bulgaria and ROW, (4) Morocco and Turkey, and (5) Turkey and ROW (Table 5-10). All of the corresponding conditional cross-price elasticities are positive (input substitute relation) excepting the ones related to ROW, which indicate a complementary relationship. (1) The conditional cross-price elasticity estimates between Albania and Morocco are significant indicating that if the price of Morocco tomatoes is increased by 1%, the EU-15 import demand for Albanian tomatoes would increase by 0.64%; on the other hand, if the price of Albanian tomatoes increases by 1%, the EU-15 demand for Morocco tomatoes would not change much (only increases by 0.02%). (2) The conditional crossprice elasticity between Bulgaria and Morocco is significant, but the same between Morocco and Bulgaria is not. These conditional elasticities show that if the price of Morocco tomatoes is increased by 1%, the EU-15 import demand for Bulgarian tomatoes would increase by almost 1% whereas if the price of Bulgarian tomatoes is increased by 1%, the demand for Morocco
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tomato would not change. (3) The conditional cross-price elasticities between Bulgaria and ROW are significant and negative (input complement). If the price of ROW tomatoes increases by 1%, the import demand for Bulgarian tomatoes would decrease by 0.54%, but when the price of Bulgarian tomatoes is increased by 1%, the import demand for ROW tomatoes would decrease by 0.38% (4) The conditional cross-price elasticities between Morocco and Turkey are also significant and positive. If the price of Turkish tomatoes is increased by 1%, the EU-15 demand for Morocco tomato would increase by 0.03%; on the other hand, if the price of Morocco tomatoes is increased by 1%, the EU-15 demand from Turkey would increase by 1.27% (elasticity is more than unity). (5) The conditional cross-price elasticies between Turkey and ROW show complementary relations. It means a 1% increase in the price of ROW tomatoes would result 0.85% reduction in the EU-15 import demand for Turkish tomatoes whereas a 1% increase in the price of Turkish tomatoes would result 0.29% reduction in import demand for ROW tomatoes. (6) The conditional cross-price elasticities between Israel and ROW are significant and positive that means a 1% increase in ROW tomato price would increase EU-15 import demand for Israeli tomato by 0.74% whereas a 1% increase in the price of Israeli tomatoes would increase EU-15 import demand for ROW tomatoes by 0.64%. (7) The conditional cross-price elasticities between Romania and Turkey are also significant indicating that if the price of Turkish tomatoes is increased by 1%, the EU-15 demand for Romanian tomatoes would increase by 0.09%; on the contrary, if the price of Romanian tomatoes is increased by 1%, the import demand for Turkish tomatoes would increase by 0.36%. In the same way as the U.S. analysis, the Divisia volume elasticities and the conditional own-price elasticities for the EU-15 analysis are calculated from 1995 to 2005 and the results are presented in Table 5-11 and Table 5-12 respectively. Even though there is no variable in the
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model related directly to any sort of structural change, underlying structural change could be accounted for in the Divisia volume index coefficient and in the elasticities. Similarly, conditional own-price elasticities are derived from the own-price coefficients that could change over time. Therefore, these two elasticities are calculated over a period of 11 years with an initial sample size of 32 years (1964-1995) and then for each adjustment period one year forward is added and the earliest year among the 32 years is dropped. This way the sample size is kept fixed. In the top parts of both the Tables 5-11 and 5-12, elasticities are calculated letting both estimated parameters (numerator θi and πij) and mean factor cost shares (denominator MFi) change along with the sample; but in the bottom part the denominator (MFi) is held constant at the initial sample block for the years 1964 to 1995 (2,33) and the resulting changes are only attributable to changes in the parameters θi and πij representing the structural impacts. The model for the above simulation is provided in Appendix B. Table 5-11 shows the changes in the Divisia volume elasticities over time. The top part of the table indicates that these changes may be structural or due to changes in mean cost shares or both. The bottom part explains the changes as a result of changes in the parameters, thus capturing potential structural change more precisely. The table indicates that Albania is losing in the EU-15 import volume in anyway even if the loss is not as bad as it was at the beginning. Bulgaria has some loss and gain in between with an ultimate loss at the end; Israel shows some losses in the middle of the period under consideration but gains at the end while Morocco has a somewhat stable position indicating very little structural impact; Romania has some ups and downs in the EU-15 import volume; Turkey was gaining at the beginning with a sudden drop in between and again gaining a little toward the end of the period; and the ROW is somehow experiencing steady loss in the EU-15 import volume until the end of the period.
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Table 5-12 (bottom part) tells the same story about structural impact in terms of own-price sensitiveness. Albania is getting less price sensitive while Bulgaria is getting more price sensitive; Israel is becoming less price sensitive; Morocco is becoming less price sensitive during the more recent years; and Romania is becoming more price sensitive while Turkey is getting less price sensitive. The ROW has mixed impacts even though it becomes less price sensitive near the end of the study period. As conditional price elasticities do not always behave the way they theoretically should ( as in case of conditional own-price elasticities for the EU-15 import demand for Israeli tomatoes for the years 2003, 2004 and 2005), it is better to look at the changes in shares of each partner country when the total import volume changes over time in order to explain the impact of structural changes. So, the shares of each participating country have been calculated over the same period (i.e., 1995-2005) with the EU-15 total import increases of 10%, 15%, 20%, 25%, and 30% using the Divisia elasticities at the bottom part of Table 5-11. The variations/ fluctuations in each partner’s market share of the EU-15 import market over the time are actually the result of structural changes. These are shown in Figure 5-4 through Figure 5-7 and the related data are provided in Appendix C. In Figure 5-4, the stories for Albania and Bulgaria are almost the same. Both experience losses (Albania having negative Divisia elasticities) in relative shares of the growth in the EU-15 imports over time. Even if the losses in share toward the end period are not as bad as the earlier years, they are, in any case, going to lose EU-15 import market share unless they do something to reverse the situation. Figure 5-5 explains the impact of some structural influence on Israel’s market share in EU-15 tomato import market. Although at the beginning it experienced little stability and losses, it really picked up increasing shares toward the ending part of the period as a
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result of some structural impact. On the other hand, Morocco has a stable and steady growth (with a slight decrease at the end) in its market share in EU-15 fresh tomato import market, but showing little sign of structural influence. In Figure 5-6, Romania’s situation is somewhat stable with little loss and gain over time. So, structural factor may not be in effect for this variation in its share in EU-15 import market. Turkey faced some stability and a little growth in market share at the beginning and then a sharp drop that may be due to structural adjustment even though toward the end of the period there appears to be some recovery. Finally, Figure 5-7 shows that from a stable situation ROW started experiencing a sharp drop in market share until the terminal year of the time period when it picked up some gain again. This kind of disruption reflects potential structural changes. Summary for EU-15 Analysis
The above discussion and Table 5-10 summarize that the EU-15 import demand for Morocco tomatoes is the most stable one. It means, the import quantity from Morocco does not change much with the change in its own price or the prices of the other partner countries. This implies that Morocco faces no close competitors and it is a prominent partner with the EU-15. However, there exists some competition between Israel and ROW. As the EU-15 import market grows over time, Albania is going to lose its share under any situation; Bulgaria’s position is somehow stable even though losing its share; Israel was losing initially, but toward the recent time it is picking up its share; and Morocco’s case is more stable showing no indication of structural effect. Turkey shows a stable condition at the beginning and then some drops and pick ups, but towards the end period it is gaining its share.
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Table 5-1. Import cost shares, quantity shares, and average prices by country of origin for U.S. Year
Canada
Dom. Rep.
1964 Average
0.79% 4.48% (7.51) 24.40%
2005 1964 Average 2005 1964 Average 2005 1964 Average 2005 1964 Average 2005
0.05% 0.22% (0.27) 0.13%
Mexico EU-15 Annual Cost Share 98.78% 0% 90.59% 3.67% (12.31) (5.21) 72.70% 2.52%
ROW 0.38% 1.04% (1.10) 0.25%
$219,358 39,753,000 (78,152,300) 274,699,840
$13,291 436,666 (724,383) 1,449,620
Annual Cost in U.S. Dollars $27,354,888 $2.20833 271,616,000 25,298,800 (228,486,000) (41,842,800) 818,552,896 28,333,600
$105,323 5,254,056 (7,347,914) 2,857,037
0.50% 2.95% (4.87) 14.88%
0.17% 0.31% (0.41) 0.09%
Annual Quantity Share 98.76% 0% 95.18% 1.20% (6.12) (1.78) 84.20% 0.78%
0.57% 0.36% (0.35) 0.05%
562,125 23,049,400 (43,161,800) 141,642,032
189,476 1,066,709 (1,740,665) 856,968
Annual Quantity in Kilograms 111,638,936 1 398,402,000 8,394,931 (198,047,000) (13,874,400) 801,408,192 7,396,764
648,311 1,604,506 (1,523,853) 482,476
$0.39 1.02 (0.52) 1.94
$0.07 0.59 (0.50) 1.69
Annual Average Price (U.S. Dollar/Kilogram) $0.25 $2.21 $0.16 0.59 2.17 2.05 (0.27) (1.19) (1.93) 1.02 3.83 5.92
Table 5-2. Test results for the production differential AIDS, CBS, Rotterdam and NBR models with first-order autocorrelation imposed for U.S. import demand analysis Model
Rho
t-statistics
P value
Log Likelihood
LR=2(Lsn-Lmodl)a
AIDS
0.410442
5.63482
0.000
593.24964
24.98326
CBS
0.345709
4.59926
0.000
567.39256
76.69742
NBR
0.493086
7.11773
0.000
604.56978
2.34298
DID
0.431854
6.02729
0.000
571.26802
68.9465
Synthetic
0.48838
6.91896
0.000
605.74127b
The table value for χ = 5.99 at α = .05 level and 9.21 at α = .01 level. bThe estimates for δ1 and δ2 are -0.207467 and 1.14440 with standard errors 0.163098 and 0.100646 respectively.
a
2 2
80
Table 5-3. Coefficient estimates of the production NBR model for the U.S. Equation
θi
Canada
.007711 (.009057)a .000384 (.001200) .963753** (.015325) .045628** (.009426) -.017475** (.004185)
Dom. Rep. Mexico EU-15 ROW a
γ ij Canada
Dom.Rep.
Mexico
EU-15
ROW
.006731 (.413064)
.000069 (.000643) .000578 (.000545)
-.006387 (.004580) .000646 (.000671) .011868 (.006770)
.002778* (.001516) .000508** (.000218) -.006322** (.002633) .003108* (.001694)
-.003190* (.001767) -.001801** (.000608) .000196 (.005445) -.000071 (.001694) .004867** (.001535)
Numbers in parentheses are asymptotic standard errors estimated using the Delta method. **Statistically different from zero at α = 0.05 level. *Statistically different from zero at α = 0.10 level.
Table 5-4. Demand parameter estimates and conditional elasticity of the production NBR model for the U.S. Equation
θi
Canada
Dom. Rep.
Canada
.007711 (.009057)b .000384 (.001200) .963753** (.015325) .045628** (.009426) -.017475** (.004185)
-.036056** (.004131)
.000168 (.000643) -.001633** (.000545)
Dom. Rep. Mexico EU-15 ROW
Equation Canada Dom. Rep. Mexico EU-15 ROW a
Divisia Elasticity .172136 (.202191)b .173076 (.541235) 1.06388** (.016917) 1.24252** (.256675) -1.68288** (.402980)
-πija Mexico
.034190** (.004580) .002654** (.000672) -.073390** (.006770)
EU-15
ROW
.004423** (.001516) .000589** (.000218) .026944** (.002633) -.032265** (.001694)
-.002725 (.001767) -.001778** (.000525) .009603** (.001949) .000310 (.000727) -.005409** (.0015363)
Conditional price elasticityc Canada
Dom. Rep.
Mexico
EU-15
ROW
-.804941** (.092216) .075999 (.290059) .037742** (.005056) .120434** (.041271) -.262448 (.170118)
.003761 (.014353) -.736886** (.245827) .002930** (.000741) .016050** (.005926) -.171249** (.050587)
.763289** (.102247) 1.19724** (.302747) -.081015** (.007474) .733718** (.071706) .924778** (.187730)
.098733** (.033835) .265896** (.098172) .029743** (.002907) -.878641** (.046123) .029847 (.069991)
-.060841 (.039437) -.802252** (.236985) .010601** (.002152) .008440 (.019792) -.520927** (.147788)
The eigen values for the Slutsky matrix are 1.20646D-17, 0.00093948, 0.0082077, 0.038217 and 0.10139. bNumbers in parentheses are asymptotic standard errors. Standard errors were estimated using the delta method. cEstimated at sample mean cost shares. **Statistically different from zero at α = 0.05 level. *Statistically different from zero at α = 0.10 level.
81
Table5-5. Divisia elasticities over time for the U.S. analysis Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Divisia elasticities (Ei )a with both parameter and mean change Canada Dom. Rep. Mexico EU-15 0.453614 0.272034 1.000443 3.554495 0.404887 0.244738 1.004255 2.892485 0.302610 0.240887 1.012297 2.248715 0.337869 0.165349 1.022119 1.737735 0.275252 0.175672 1.028195 1.534845 0.325307 0.174524 1.038350 1.321553 0.251374 0.156900 1.049991 1.207141 0.139138 0.127674 1.063852 1.161990 0.111075 0.115558 1.076720 1.074732 0.088835 0.135994 1.088653 1.023946 0.008797 0.220775 1.103784 1.022021
ROW -2.46572 -2.38155 -2.28929 -2.13422 -1.80969 -1.74041 -1.62653 -1.66412 -1.59095 -1.52566 -1.58419
Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Divisia elasticities (Ei m)b with parameter change but mean fixed at sample 2,33 Canada Dom. Rep Mexico EU-15 0.453614 0.272034 1.000443 3.554495 0.46222 0.244212 0.999473 3.631007 0.415626 0.238535 1.000634 3.591645 0.589547 0.162676 1.001227 3.470977 0.625145 0.171781 0.996715 3.671049 0.982030 0.168225 0.994714 3.641943 0.977150 0.148069 0.993505 3.720346 0.654073 0.118138 0.995146 3.909508 0.611752 0.104625 0.996742 3.830233 0.566848 0.119939 0.997732 3.783115 0.064474 0.192196 1.001609 3.870090
ROW -2.46572 -2.46810 -2.50041 -2.52384 -2.32388 -2.38393 -2.34837 -2.53007 -2.55266 -2.55990 -2.71122
Ei (1+j), (32+j) = θ i (1+j), (32+j) / MFi (1+j), (32+j) where j = 1, 2, …………11 and θ i is estimated parameter and MFi is calculated from data. b Ei m(1+j), (32+j) = θ i (1+j), (32+j) / MFi (2,33) where j = 1, 2, …………11 and θ i is estimated parameter and MFi is calculated from data. a
82
Table 5-6. Conditional own-price elasticities over time for the U.S. analysis Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Conditional own-price elasticities (Eii)a with both parameter and mean change Canada Dom. Rep. Mexico EU-15 -0.82696 -0.54947 -0.02043 -0.74888 -0.89775 -0.69700 -0.02642 -0.76510 -0.98687 -0.78031 -0.03434 -0.79223 -0.79147 -0.77489 -0.04130 -0.83624 -0.80862 -0.80959 -0.05118 -0.85197 -0.69272 -0.74529 -0.05758 -0.86696 -0.72265 -0.85646 -0.06747 -0.87083 -0.76935 -0.90842 -0.07703 -0.88850 -0.77081 -0.93193 -0.08552 -0.89734 -0.79078 -0.86940 -0.09113 -0.88896 -0.78010 -0.86068 -0.09682 -0.89557
Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Conditional own-price elasticities (Eiim)b with parameter change but mean fixed at sample 2,33 Canada Dom. Rep. Mexico EU-15 ROW -0.82696 -0.54947 -0.02043 -0.74888 -0.47103 -0.88563 -0.69764 -0.02185 -0.71244 -0.50910 -0.98887 -0.78240 -0.02327 -0.68783 -0.52097 -0.65205 -0.77844 -0.02169 -0.71085 -0.45608 -0.59770 -0.81368 -0.02181 -0.70585 -0.49080 -0.13554 -0.75429 -0.01745 -0.71706 -0.34083 -0.03170 -0.86423 -0.01619 -0.70975 -0.26450 -0.07995 -0.91485 -0.01552 -0.75583 -0.29811 0.03398 -0.93785 -0.01484 -0.78265 -0.32343 0.02589 -0.88419 -0.01194 -0.75031 -0.31126 0.20133 -0.87803 -0.00933 -0.77383 -0.34936
ROW -0.47103 -0.52577 -0.56006 -0.53747 -0.59960 -0.51387 -0.48483 -0.53174 -0.57082 -0.58124 -0.61120
Eii (1+j), (32+j) = πij (1+j), (32+j)/MFi (1+j), (32+j) where j= 1, 2, ………….11 and πij is the estimated parameter and MFi is calculated from data. bEiim(1+j), (32+j) = πij (1+j), (32+j)/MFi (2,33) where j = 1, 2, ………….11 and πij is the estimated parameter and MFi is calculated from data.
a
83
Canada share of US import market
0.0054
0.0054
0.0052
0.0052
0.0050
0.0050 0.0048
0.0048
0.0046
0.0046
0.0044
0.0044
0.0042 10
0.0042 15
2004
20
2002 2000 Structural change associated with the elasticities
25 1998
30
1996
Percentage increase in total US imports
A
1994
Dominican Republic share of US import market
0.0041
0.0041
0.0040
0.0040
0.0039
0.0039
0.0038
0.0038 0.0037
0.0037
0.0036
0.0036
0.0035 10
0.0035 2004
15 20
2002 2000
Structural change associated with the elasticities
25 1998
30
1996 1994
Percentage increase in total US imports
B
Figure 5-1. Impact of structural change on U.S. demand for Canadian and Dominican Republic fresh tomatoes. (A) Canadian tomatoes (B) Dominican Republic tomatoes.
84
Mexico share of US import market
0.9820 0.9818 0.9816 0.9814 0.9812 0.9810 0.9808 0.9806 0.9804 0.9802 0.9800 10
0.9820 0.9818 0.9816 0.9814 0.9812 0.9810 0.9808 0.9806 0.9804 0.9802 0.9800 15
2004
20
2002 2000 Structural change associated with the elasticities
25 1998
30
1996
Percentage increase in total US imports
A
1994
EU-15 share of US import market
0.0090
0.0090
0.0085
0.0085
0.0080
0.0080 0.0075
0.0075
0.0070
0.0070
0.0065 10
0.0065
15
2004
20
2002 2000 Structural change associated with the elasticities
25 1998
30
1996 1994
Percentage increase in total US imports
B
Figure 5-2. Impact of structural change on U.S. demand for Mexican and EU-15 fresh tomatoes. (A) Mexican tomatoes (B) EU-15 tomatoes.
85
Rest of the World share of US import market
0.0022 0.0020 0.0018
0.0022 0.0020 0.0018
0.0016 0.0014 0.0012 0.0010 0.0008 0.0006 0.0004 10
0.0016 0.0014 0.0012 0.0010 0.0008 0.0006 0.0004 15
2004
20
2002 2000 Structural change associated with the elasticities
25 1998
30
1996
Percentage increase in total US imports
1994
Figure 5-3. Impact of structural change on U.S. demand for ROW fresh tomatoes.
86
Table 5-7. Import cost shares, quantity shares, and average prices by country of origin for EU-15 Year
Albania
Bulgaria
1964 Average
0.13% 2.16% (2.56) 0%
4.88% 3.61% (2.84) 0.01%
Israel Morocco Annual Cost Share 0% 84.12% 4.36% 76.36% (4.82) (6.53) 12.44% 63.94%
$48,038 2,017,004 (2,341,134) 3.03
$1,840,474 2,911,697 (2,319,369) 20,624
0.37% 3.10% (3.70) 0%
2005 1964 Average 2005 1964 Average 2005 1964 Average 2005 1964 Average 2005
Romania
Turkey
ROW
3.61% 6.73% (6.10) 0.01%
0% 1.74% (2.58) 6.43%
7.26% 5.04% (3.34) 17.17%
Annual Cost in U.S. Dollars $1,262 $31,730,108 7,888,280 9,241,680 (1,073,390) (4,802,280) 44,735,840 229945104
$1,361,401 5,643,429 (5,380,099) 35,735
$1.06 3,526,344 (6,423,904) 23,119,076
$2,739,627 7,098,639 (1,056,850) 61,743,611
8.18% 4.97% (3.81) 0.01%
Annual Quantity Share 0% 76.21% 2.81% 72.66% (2.64) (10.39) 7.60% 70.05%
6.83% 10.04% (8.53) 0.01%
0% 1.70% (2.49) 5.93%
8.41% 4.72% (3.74) 16.40%
572,000 4,484,032 (4,616,481) 1
12,660,747 8,258,625 (6,620,936) 19,526
Annual Quantity in Kilograms 3,312 118,009,256 10,570,330 5,537,090 131,722,000 17,382,800 (6,407,523) (39,308,500) (17,403,900) 25,201,496 232,239,648 37,440
1 3,599,705 (6,157,144) 19,664,766
13,023,064 9,515,378 (10,678,700) 54,367,024
$0.08 0.77 (0.86) 3.03
$0.15 0.55 (0.41) 1.06
Annual Average Price (U.S. $/Kg) $0.38 $0.27 $0.13 1.04 0.69 0.54 (0.46) (0.25) (0.38) 1.78 0.99 0.95
$1.06 0.80 (0.35) 1.18
$0.21 0.78 (0.37) 1.14
Table 5-8. Test results for model selection for EU-15 analysis. Model
Rho
t-statistics
P value
Log Likelihood
LR=2(Lsn-Lmodl)
AIDS
-0.13526
-2.00077
0.045
685.31208
31.38804
CBS
-0.12500
-1.85916
0.063
695.98166
10.04888
NBR
-0.09441
-1.39541
0.163
688.35849
25.29522
DID
-0.06767
-1.00291
0.316
700.27111
1.46998
0.233
b
Synthetic
-0.08094
-1.19275
701.0061
The table value for χ = 5.99 at α = .05 level and 9.21 at α = .01 level. bThe estimates for δ1 and δ2 are 0.308207 and -0.030456 with standard errors 0.190839 and 0.127050 respectively. a
2 2
87
Table 5-9. Coefficient estimates of the production NBR model for EU-15 Equation
θi
Albania
-.02328** (.01092)a .02098 (.01544) .01462 (.02276) .83943 (.07548) .01236 (.03242) .01299 (.02177) .12291 (.05040)
Bulgaria Israel Morocco Romania Turkey ROW a
γ ij
Albania -.00210 (.00277)
Bulgaria .00062 (.00278) .00856 (.00536)
Israel .00331 (.00311) .00175 (.00429) .00547 (.00725)
Morocco -.00259 (.00757) .00843 (.01073) -.04045** (.01416) .08116 (.05321)
Romania .00045 (.00395) .00021 (.00555) -.00011 (.00722) -.04160** (.02001) .01862 (.01371)
Turkey -.00016 (.00116) .00162 (.00164) -.00007 (.00235) .00880 (.00767) .00511 (.00338) .00036 (.00246)
ROW .00048 (.00640) -.02118** (.00947) .03011 (.01184) -.01375 (.04528) .01733 (.01362) -.01565** (.00246) .00265 (.03178)
Numbers in parentheses are asymptotic standard errors computed with the Delta method. **Statistically different from zero at α = 0.05 level. *Statistically different from zero at α = 0.10 level.
88
Table 5-10. Demand parameter and conditional elasticity estimates of the production NBR model for EU-15 Equation
θi
Albania
-.02338** (.01092)b .02098 (.01544) .01462 (.02276) .83943 (.07548) .01236 (.03242) .01299 (.02177) .12291 (.05040)
Bulgaria Israel Morocco Romania Turkey ROW Equation
Divisia Elasticityc
Albania
-1.08036** ( 50684)b .58081 (.42734) .33524 (.52193) 1.09925** (.09884) .18365 (.48165) .74704 (1.25201) 2.44395 (1.00028)
Bulgaria Israel Morocco Romania Turkey ROW a
- π ij
Albania -.02319** (.00277)
Bulgaria .00140 (.00278) -.02626** (.00536)
Israel .00425 (.00311) .00332 (.00429) -.03624** (.00725)
a
Morocco .01387* (.00757) .03601** (.01073) -.00715 (.01416) -.09934* (.05321)
Romania .00190 (.00395) .00264 (.00555) .00282 (.00722) .009811 (.02003) -.04417** ( .01371)
Turkey .00021 (.00116) .00225 (.00164) .00069 (.00235) .02207** (.00767) .00628 (.00338) -.01673** (.00246)
ROW .00157 (.00640) -.01936** (..00920) .03231 (.01102) .02473 (.03619) .02072 (.01457) -.01477** (.00520) -.04519 (.03178)
Turkey .00988 (.05375) .06219 (.04549) .01576 (.05398) .02891** (.01004) .09330* (.05022) -.96215** (.14129) -.29323** (.10313)
ROW .07273 (.29696) -.53590** (.25477) .74090** (.25270) .03238 (.04740) .30774 (.21643) -.84985** (.29890) -.89697 (.63084)
Conditional price elasticityc Albania -1.07609** (.12843) .03871 (.07702) .09734 (.07125) .01816* (.00992) .02820 (.05872) .01225 (.06662) .03110 (.12701)
Bulgaria .06489 (.12911) -.72700** (.14849) .07619 (.09829) .04716 (.01405) .03922 (.08240) .12921 (.09451) -.38420** (18265)
Israel .19701 (.14419) .09199 (.11867) -.83100** (.16614) -.00936 (.01854) .04190 (.10726) .03954 (.13542) .64131** (.21873)
Morocco .64348* (.35142) .99692** (.29696) -.16388 (.32458) -.13009* (.06968) .14573 (.29751) 1.26971** (.44111) .49079 (.71836)
Romania .08811 (.18345) .07309 (.15358) .06469 (.16557) .01285 (.02623) -.65609** (.20370) .36129* (.19446) .41120 (.28919)
The eigen values for the Slutsky matrix are -0.0065308, 9.47247D-18, 0.021110, 0.026703, 0.043189, 0.071218 and 0.13542. bNumbers in parentheses are asymptotic standard errors and were estimated using the delta method. cEstimated at sample mean cost shares. **Statistically different from zero at α = 0.05 level. *Statistically different from zero at α = 0.10 level.
89
Table 5-11. Divisia elasticities over time for EU-15 analysis Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Divisia elasticities (Ei ) with both parameter and mean change Albania Bulgaria Israel Morocco Romania -1.47386 0.61053 0.19870 1.15429 0.02082 -1.34877 0.37179 0.19081 1.15992 0.05682 -1.31760 0.47812 0.02233 1.17049 -0.08559 -1.22725 0.45224 -0.11496 1.16672 0.11012 -1.43440 0.37988 -0.21824 1.20907 0.23150 -1.25003 0.66127 -0.24613 1.20233 0.45997 -1.27236 0.90023 0.12357 1.20443 0.38382 -1.03652 0.81050 0.19538 1.29244 0.01685 -1.14369 0.68212 0.47961 1.25276 0.10092 -1.20686 0.76306 0.52833 1.26734 0.10415 -1.16712 0.77719 0.78517 1.13938 0.17902
Turkey 1.80311 1.76605 1.85061 1.50872 1.98134 0.66449 0.27793 -0.18537 0.60706 0.21202 0.48810
ROW 2.49313 2.55665 2.63550 2.47556 1.66476 1.32249 1.02599 -0.03721 0.02162 -0.22080 1.52012
Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Divisia elasticities Ei M parameter change but mean fixed at sample 2,33 Albania Bulgaria Israel Morocco Romania Turkey -1.47386 0.61053 0.19870 1.15429 0.02082 1.80311 -1.34721 0.35930 0.21725 1.16156 0.05617 1.91003 -1.31264 0.44402 0.03010 1.17133 -0.08321 2.12307 -1.21739 0.40056 -0.18171 1.16698 0.10477 1.76848 -1.41599 0.31833 -0.39158 1.21030 0.21533 2.39415 -1.22543 0.51199 -0.49715 1.20444 0.41229 0.90753 -1.23698 0.64172 0.27876 1.20766 0.32508 0.44179 -0.99987 0.53954 0.47998 1.30145 0.01339 -0.33920 -1.09474 0.42501 1.26150 1.26548 0.07390 1.34488 -1.14249 0.44667 1.49365 1.28141 0.06871 0.55217 -1.08704 0.42910 2.38274 1.15126 0.10583 1.40678
ROW 2.49313 2.45700 2.49529 2.33258 1.54427 1.23111 0.96850 -0.03349 0.01896 -0.19863 1.45360
Ei (1+j), (32+j) = θ i (1+j), (32+j) / MFi (1+j), (32+j) where j = 1, 2, …………11 and θ i is estimated parameter and MFi is calculated from data. b Ei m(1+j), (32+j) = θ i (1+j), (32+j) / MFi (2,33) where j = 1, 2, …………11 and θ i is estimated parameter and MFi is calculated from data. a
90
Table 5-12. Conditional own-price elasticities over time for EU-15 analysis Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Conditional own-price elasticities (Eii)a with both parameter and mean change Albania Bulgaria Israel Morocco Romania Turkey -1.33563 -0.02298 -0.87042 -0.14148 0.03344 -1.03718 -1.34502 -0.57405 -0.99189 -0.11948 -0.05058 -1.04681 -1.27132 -0.73028 -0.95801 -0.10879 -0.19846 -1.05458 -1.28189 -0.73225 -0.92933 -0.11400 -0.33547 -1.03818 -1.32045 -0.74338 -1.00634 -0.15487 -0.57981 -0.96492 -1.29714 -0.82131 -0.88734 -0.18874 -0.64474 -0.82970 -1.27507 -0.84578 -0.83289 -0.20691 -0.71041 -0.85740 -1.18356 -0.81415 -0.76029 -0.14355 -0.66842 -0.86986 -1.06549 -0.79684 -0.54959 -0.08599 -0.64424 -0.95343 -1.06675 -0.81324 -0.43974 -0.08052 -0.62588 -0.84424 -1.07429 -0.79961 -0.38157 -0.05384 -0.60391 -0.82246
Year 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Conditional own-price elasticities (Eii m)b with parameter change but mean fixed at sample 2,33 Albania Bulgaria Israel Morocco Romania Turkey ROW -1.33563 -0.02298 -0.87042 -0.14148 0.03344 -1.03718 -1.59637 -1.34455 -0.58523 -0.99633 -0.12040 -0.05944 -1.05196 -1.40270 -1.27009 -0.74302 -0.95876 -0.10924 -0.21590 -1.06512 -2.34216 -1.27917 -0.75266 -0.91645 -0.11414 -0.35938 -1.04772 -2.24060 -1.31562 -0.77087 -1.05308 -0.15557 -0.59727 -0.96125 -1.62209 -1.29019 -0.84270 -0.83031 -0.19001 -0.66422 -0.77426 -1.57816 -1.26587 -0.86681 -0.69987 -0.20890 -0.72978 -0.78541 -1.89479 -1.17511 -0.84995 -0.50572 -0.14830 -0.70395 -0.78046 -1.20374 -1.06032 -0.84448 0.07348 -0.09234 -0.69854 -0.92776 -1.10966 -1.06026 -0.85959 0.45255 -0.08741 -0.70333 -0.64011 -1.07722 -1.06545 -0.85648 0.72246 -0.06003 -0.70843 -0.54614 -0.50506
ROW -1.59637 -1.42251 -2.42236 -2.32185 -1.67719 -1.62733 -1.95294 -1.23559 -1.13652 -1.09511 -0.48632
Eii (1+j), (32+j) = πij (1+j), (32+j)/MFi (1+j), (32+j) where j = 1, 2, ………….11 and πij is the estimated parameter and MFi is calculated from data. bEiim(1+j), (32+j) = πij (1+j), (32+j)/MFi (2,33) where j = 1, 2, ………….11 and πij is the estimated parameter and MFi is calculated from data.
a
91
Albania share of EU-15 import market
0.2200
0.2200
0.2000
0.2000
0.1800
0.1800 0.1600
0.1600
0.1400
0.1400
0.1200
0.1200
0.1000 10
0.1000 2004
15 20
2002 2000
Structural change associated with the elasticities
25 1998
30
1996
Percentage increase in total EU-15 imports
A
1994
Bulgaria share of EU-15 import market
0.0480
0.0480
0.0470
0.0470
0.0460
0.0460 0.0450
0.0450
0.0440
0.0440
0.0430
0.0430
0.0420
0.0420
0.0410 10
0.0410 15
2004
20
2002 2000 Structural change associated with the elasticities
25 1998
30
1996 1994
Percentage increase in total EU-15 imports
B
Figure 5-4. Impact of structural change on EU-15 demand for Albanian and Bulgarian fresh tomatoes. (A) Albanian tomatoes (B) Bulgarian tomatoes.
92
Israel share of EU-15 import market
0.0150
0.0150
0.0140
0.0140
0.0130
0.0130
0.0120
0.0120 0.0110
0.0110
0.0100
0.0100
0.0090
0.0090
0.0080 0.0070 10
0.0080 0.0070 15
2004
20
2002 2000 Structural change associated with the elasticities
25 1998
30
1996
Percentage increase in total EU-15 imports
A
1994
Morocco share of EU-15 import market
0.5700
0.5700
0.5650
0.5650
0.5600
0.5600 0.5550
0.5550
0.5500
0.5500
0.5450
0.5450
0.5400
0.5400
0.5350 10
0.5350 15
2004
20
2002 2000 Structural change associated with the elasticities
25 1998
30
1996
Percentage increase in total EU-15 imports
B 1994
Figure 5-5. Impact of structural change on EU-15 demand for Israeli and Morocco fresh tomatoes. (A) Israeli tomatoes (B) Morocco tomatoes.
93
Romania share of EU-15 import market
0.1000
0.1000
0.0950
0.0950
0.0900
0.0900 0.0850
0.0850
0.0800
0.0800
0.0750 10
0.0750
2004
15 20
2002 2000
Structural change associated with the elasticities
25 1998
30
1996
Percentage increase in total EU-15 imports
A
1994
Turkey share of EU-15 import market
0.0080
0.0080
0.0075
0.0075
0.0070
0.0070
0.0065
0.0065
0.0060
0.0060 0.0055
0.0055
0.0050
0.0050
0.0045 0.0040 10
0.0045 0.0040 2004
15 20
2002 2000
Structural change associated with the elasticities
25 1998
30
1996
Percentage increase in total EU-15 imports
B 1994
Figure 5-6. Impact of structural change on EU-15 demand for Romanian and Turkish fresh tomatoes. (A) Romanian tomatoes (B) Turkish tomatoes.
94
Rest-of-the World share of EU-15 import market
0.0450
0.0450
0.0400
0.0400
0.0350
0.0350 0.0300
0.0300
0.0250
0.0250
0.0200 10
0.0200
2004
15 20
2002 2000
Structural change associated with the elasticities
25 1998
30
1996
Percentage increase in total EU-15 imports
1994
Figure 5-7. Impact of structural change on EU-15 demand for ROW fresh tomatoes
95
CHAPTER 6 CONCLUSIONS Observations
In order to have a good demand analysis empirical data is very important. The empirical data used in this research do not behave equally well for the U.S. import demand analysis and the EU-15 analysis. In case of the U.S., the results are as per expectation according to economic theory from the appropriate model at first instance (NBR as qualified by LR test). However, the scenario is not the same for the EU-15 import demand analysis. The empirical data was not giving a theoretically convinced results from the model that seemed appropriate by the LR test (the DID). So, a different specification of model had to be chosen (NBR), as a second line of choice, in order to analyze the given data set with a little manipulation (merging the U.S. data with ROW). Hence, it is the data, not always the models that cause problems in generating theoretically acceptable results. Summary
Divisia volume elasticities show that when the U.S. total import volume is increased by 1%, fresh tomato imports from each of Mexico and the EU-15 would increase by more than 1%, but imports from ROW would decrease by more than 1%. Conditional own-price elasticities indicate that the U.S. demands for fresh tomatoes from all of the five sources under study are inelastic. Inelasticity is the most for the demand for Mexican tomatoes (-0.08) and the least for EU-15 tomatoes (-0.88). Among the significant conditional cross-price elasticities only the ones between Dominican Republic and ROW and vice versa are negative indicating a complementary relation. All others (six pairs) show a substitute relationship as expected. The conditional crossprice elasticities suggest that the U.S. demand for Mexican tomatoes remains almost the same when other countries individually change their price in either direction. On the other hand, when
96
Mexico increases/decreases its price by (say) 1%, the increase/decrease in quantity of import from Canada, Dominican Republic, EU-15 and ROW would be 0.76%, 1.20%, 0.73%, and 0.92% respectively. So, Mexico is competitive with others, but others are not competitive with Mexico. Conditional cross-price elasticities also show that Canada and EU-15 are competitive with one another (0.10 against 0.12). None of these source specific import demands seem to be influenced by structural changes even as Canada is gradually losing its market share while EU15 is gaining its share. For EU-15 import demand, the only two significant (and more than unity) Divisia volume elasticities indicate that with a 1% increase in total import volume EU-15 demand for Morocco fresh tomatoes would increase by more than 1%, but the import demand for Albanian tomatoes would decrease by more than 1%. All of the conditional own-price elasticities are significant except the one related to ROW. Only the conditional own-price elasticity of the demand for Albanian tomatoes is elastic (-1.08). Among the conditional inelastic demands, Morocco has the most inelasticity (-0.13) and Turkey has the least inelasticity (almost unitary elastic). Of thirteen significant conditional cross-price elasticities, four relating Bulgaria, Turkey and ROW show a complementary relationship; others show a substitute relationship. The conditional cross-price elasticities suggest that Morocco is competitive with others, but others are not competitive with Morocco. If Morocco increases its price by 1%, Eu-15 import demand for Albanian tomatoes increases by 0.64%, demand for Bulgarian tomatoes increases by 1% and that for Turkey increases by 1.27%, but if others increase their price individually by 1%, demand for Morocco tomatoes almost does not change. Conditional cross-price elasticities also show some competition between Israel and ROW. There exists some structural influence on import demands for fresh tomatoes into the EU-15 especially for Albania, Israel, Turkey and ROW.
97
Conclusions
Given the continuous changes in international as well as domestic trade policies and trade liberalization/globalization, the potentiality of exporting countries/producers to achieve a larger share in international trade is of greater interest. It has been found that for the U.S. import demand of fresh tomatoes the prominent supplier is Mexico facing no close competitor. Canada and EU-15 compete closely with each other for the U.S. imports of fresh tomatoes. Hence, the two products seem to be homogeneous. On the other hand, Mexican fresh tomatoes have heterogeneous characteristics compared with other partners’. The U.S. consumers have either some preferential tastes for Mexican tomatoes, or Mexico has some especial strategies, technologies and product qualities that make it a prominent one in the U.S. import market. Canada is losing its share in the U.S. imports while EU-15 is gaining. However, no significant symptom of structural change impact has been found in case of the U.S. import market for fresh tomatoes. Similarly, for the EU-15 import demand for fresh tomatoes Morocco is the major supplier with no close competitor. Israel and ROW are somehow competing with each other for EU-15 imports indicating some homogeneous tendency in their products. However, Morocco seems to enjoy some preferential treatment in the EU-15 fresh tomato import market that characterizes its product as heterogeneous to others’. Albania, Bulgaria and ROW are losing their share in EU-15 imports. Some structural impacts have been found with respect to EU-15 import demand for tomatoes from Albania, Bulgaria, Israel, Turkey and ROW. One interesting finding is that some small exporters like Israel and Turkey are increasingly penetrating into the EU-15 import market in recent years.
98
Implications
As the U.S. fresh tomato import market is dominated by Mexico and it has no competitor, it is necessary for the other countries to figure out some measures that will make their competition with Mexico closer in order to get a larger share in the U.S. import market. Canada also needs to look into its overall situation and find out the causes of losing share of the U.S. fresh tomato import market to the EU-15 In the same way, Morocco holds the dominating position in the EU-15 import market and other partners except Bulgaria and Romania (have become EU members subsequently) have to do something that will make them closer competitors to Morocco. Albania’s losing situation is very delicate and needs immediate attention. Israel and Turkey should explore further to keep on increasing their market shares. Since the main suppliers for the U.S. and EU-15 fresh tomato markets are Mexico and Morocco respectively, in case of any calamities, diseases or disruption in their supply, there could be significant impacts on these two markets. Unless other countries succeed in becoming more competitive with these two prominent suppliers, the U.S. and the EU-15 import markets will remain at some risk. Thus, the import demand analysis of this research will help the participating countries determine the level of competitiveness among other competitors and then make appropriate decision thereby to ensure their own gains from trade. It is also expected to help the policy makers to undertake changes/adjustments in policies and implement them effectively.
99
APPENDIX A COMPUTER PRINTOUTS FOR U.S. ANALYSIS The Model to deal with zero quantity and price for U.S. Analysis. OPTIONS MEMORY=1500 Double; ?US#01 Price Calculation Model; TITLE 'TOMATO IMPORTS TO THE US';
? To replace Zero price for U.S. Import Analysis;
smpl 1 43; LOAD ZYRS ZIMP V1 Q1 V2 Q2 V3 Q3 V4 Q4 V5 Q5; 1963 902 189750 730125 2481 21320 20705768 108846184 13928 65690 13565 94217 1964 902 219358 562125 13291 189476 27354888 111638936 0 0 105323 648311 1965 902 298959 733875 33276 188640 29424864 120410128 0 0 167763 668557 1966 902 241757 562312 9319 50292 52008580 162705440 703 6875 57697 231001 1967 902 306522 803312 41735 379875 42585292 164302752 123059 306330 23536 126579 1968 902 222304 575562 75850 508062 46973296 175722128 12883 47249 45275 197879 1969 902 216389 400250 144332 916687 68018008 202410752 17355 30914 32468 194149 1970 902 560946 977250 121233 797875 94966856 290759360 2768 17812 180445 796919 1971 902 393364 505250 203117 1523625 84131328 258677808 55205 104367 34202 163878 1972 902 245434 409687 220130 1345187 88150080 264119568 0 0 129604 313238 1973 902 143427 467187 169100 834375 115137936 339795200 12065 18312 139288 484990 1974 902 90716 135582 219628 1049062 64070732 267888560 11595 52601 135977 1137011 1975 902 111149 247117 375471 1656500 64131552 253600880 0 0 126452 1748431 1976 902 151567 233824 258069 1036375 72428816 294192576 9574 16132 89110 874245 1977 902 159007 288937 632044 1977812 149405840 356244928 0 0 160421 674755 1978 902 302144 523625 376993 894437 161319616 369276320 0 0 128911 236786 1979 902 263748 468312 324980 835062 153871376 322163936 0 0 53016 89746 1980 902 240082 380875 254595 586750 131475112 294612672 1363 3062 28456 50561 1981 902 331663 448187 554520 1126937 237938496 236592128 52344 58011 268097 312113 1982 902 369382 563750 117345 352375 173374416 267219568 88818 136482 632151 534929 1983 902 616082 788625 243863 780500 226757760 331736864 145836 71248 1384907 601291 1984 902 959659 1086062 392689 1111375 171133120 369494048 2079176 1028974 1814396 1075765 1985 902 748704 766812 829172 2122750 168479888 380314432 3612847 1590097 1933597 1223189 1986 902 1298959 1261125 4040176 9988785 327903168 430983424 3628705 1705323 1156736 1081471 1987 902 2107219 1930875 2212019 5768554 160881840 406785376 3911491 1579579 1266919 1024096 1988 902 2573120 2117875 1203746 2862687 152356480 362726880 3674326 1624760 3513976 1160022 1989 902 2888215 2327812 477349 1266562 224163760 385940928 5684585 2677385 3466587 1489777 1990 902 3345576 3075187 1019288 1404125 390824864 352312128 3181770 1305635 3820630 2897837 1991 902 4560436 2672000 467383 418250 269461472 353543872 8658034 3027499 5897411 1109323 1992 902 5664522 5213699 618499 559437 141482016 183116320 8592061 2916249 10776134 4222087 1993 902 6490505 4733488 328571 326875 325450048 400494304 25714519 9677932 8478949 3162569 1994 902 10479733 7673394 15237 16117 335774656 376031680 31977654 10490708 7133936 1827493 1995 902 17997856 11655089 39438 43191 434508160 593079616 45101016 14822351 4221050 1343177 1996 902 38849532 21769264 94680 100296 613726272 685677632 88867703 27270029 10402293 2332987 1997 902 61045808 37504200 53591 49441 549398080 660608640 119103389 41025640 17126556 3275951 1998 902 102889656 61728728 40701 28812 600902720 734053120 144522212 46619633 24440423 4889259 1999 902 121800280 79553504 2398 1687 517601728 615063808 123059860 41901303 18251894 4135634 2000 902 163877088 101390248 10665 14687 438421792 589954432 101363658 34695648 14394573 4008089 2001 902 169921584 105680184 0 0 517007488 679187072 99481702 34809782 14115626 3864210 2002 902 175542448 100499128 2290 2875 582243072 724015808 91658917 30983318 19301177 4595575 2003 902 234794400 130153808 11978 21011 794276800 784988032 63798848 19163022 23735958 4930831 2004 902 261605248 133565936 641605 807375 789782848 779020288 56011543 15406065 18641380 3172048 2005 902 274699840 141642032 1449620 856968 818552896 801408192 28333599 7396764 2857037 482476 ? V: value in US dollars; Q: quantity in kilograms; ? 1: Canada ? 2: Dominican Republic ? 3: Mexico ? 4: European Union-15 ? 5: Rest of the World ? 902: United States as Importer; select q2>0; P2=V2/Q2; olsq P2 C Q2 ZYRS; select q4>0;
100
P4=V4/Q4; olsq P4 C Q4 ZYRS; SMPL 1, 43; Q2=1*(Q2=0)+Q2*(Q2>0); Q4=1*(Q4=0)+Q4*(Q4>0); Print Q2 P2 Q4 P4; END;
The United States NBR Import Demand Model. OPTIONS MEMORY=1500 Double; ? US_02NBR-SELECTEDNEW2007-V2 Models for US Import Analysis with EU-15; TITLE 'TOMATO IMPORTS TO THE US'; ? For Cost Share, Quantity Share and Average Price calculation; ? NBR Final Model with AR1 plus Homogeneity and Symmetry imposed (Automatic Rho selection); smpl 1 43; LOAD ZYRS ZIMP V1 V5 Q5; 1963 902 189750 13565 94217 1964 902 219358 105323 648311 1965 902 298959 0 167763 668557 1966 902 241757 57697 231001 1967 902 306522 23536 126579 1968 902 222304 45275 197879 1969 902 216389 32468 194149 1970 902 560946 180445 796919 1971 902 393364 34202 163878 1972 902 245434 129604 313238 1973 902 143427 139288 484990 1974 902 90716 135977 1137011 1975 902 111149 126452 1748431 1976 902 151567 89110 874245 1977 902 159007 0 160421 674755 1978 902 302144 128911 236786 1979 902 263748 53016 89746 1980 902 240082 28456 50561 1981 902 331663 268097 312113 1982 902 369382 632151 534929 1983 902 616082 1384907 601291
Q1
V2
Q2
730125
2481
21320
20705768
108846184
13928
65690
562125
13291
189476
27354888
111638936
0
0
733875
33276
188640
29424864
120410128
0
562312
9319
50292
52008580
162705440
703
6875
803312
41735
379875
42585292
164302752
123059
306330
575562
75850
508062
46973296
175722128
12883
47249
400250
144332
916687
68018008
202410752
17355
30914
977250
121233
797875
94966856
290759360
2768
17812
505250
203117
1523625
84131328
258677808
55205
104367
409687
220130
1345187
88150080
264119568
0
0
467187
169100
834375
115137936
339795200
12065
18312
135582
219628
1049062
64070732
267888560
11595
52601
247117
375471
1656500
64131552
253600880
0
0
233824
258069
1036375
72428816
294192576
9574
16132
288937
632044
1977812
149405840
356244928
0
523625
376993
894437
161319616
369276320
0
0
468312
324980
835062
153871376
322163936
0
0
380875
254595
586750
131475112
294612672
1363
3062
448187
554520
1126937
237938496
236592128
52344
58011
563750
117345
352375
173374416
267219568
88818
136482
788625
243863
780500
226757760
331736864
145836
71248
101
V3
Q3
V4
Q4
1984 902 959659 1814396 1075765 1985 902 748704 1933597 1223189 1986 902 1298959 1156736 1081471 1987 902 2107219 1266919 1024096 1988 902 2573120 3513976 1160022 1989 902 2888215 3466587 1489777 1990 902 3345576 3820630 2897837 1991 902 4560436 5897411 1109323 1992 902 5664522 10776134 4222087 1993 902 6490505 8478949 3162569 1994 902 10479733 7133936 1827493 1995 902 17997856 4221050 1343177 1996 902 38849532 10402293 2332987 1997 902 61045808 17126556 3275951 1998 902 102889656 24440423 4889259 1999 902 121800280 18251894 4135634 2000 902 163877088 14394573 4008089 2001 902 169921584 14115626 3864210 2002 902 175542448 19301177 4595575 2003 902 234794400 23735958 4930831 2004 902 261605248 18641380 3172048 2005 902 274699840 2857037 482476 ? ? ? ? ? ? ?
1086062
392689
1111375
171133120
369494048
2079176
1028974
766812
829172
2122750
168479888
380314432
3612847
1590097
1261125
4040176
9988785
327903168
430983424
3628705
1705323
1930875
2212019
5768554
160881840
406785376
3911491
1579579
2117875
1203746
2862687
152356480
362726880
3674326
1624760
2327812
477349
1266562
224163760
385940928
5684585
2677385
3075187
1019288
1404125
390824864
352312128
3181770
1305635
2672000
467383
418250
269461472
353543872
8658034
3027499
5213699
618499
559437
141482016
183116320
8592061
2916249
4733488
328571
326875
325450048
400494304
25714519
9677932
7673394
15237
16117
335774656
376031680
31977654
10490708
11655089
39438
43191
434508160
593079616
45101016
14822351
21769264
94680
100296
613726272
685677632
88867703
27270029
37504200
53591
49441
549398080
660608640
119103389
41025640
61728728
40701
28812
600902720
734053120
144522212
46619633
79553504
2398
1687
517601728
615063808
123059860
41901303
101390248
10665
14687
438421792
589954432
101363658
34695648
105680184
0
0
517007488
679187072
99481702
34809782
100499128
2290
2875
582243072
724015808
91658917
30983318
130153808
11978
21011
794276800
784988032
63798848
19163022
133565936
641605
807375
789782848
779020288
56011543
15406065
141642032
1449620
856968
818552896
801408192
28333599
7396764
V: value in US dollars; Q: quantity in kilograms; 1: Canada 2: Dominican Republic 3: Mexico 4: European Union-15 5: Rest of the World 902: United States as Importer;
? Eliminating zero values in Q; Q2=1*(Q2=0)+Q2*(Q2>0); Q4=1*(Q4=0)+Q4*(Q4>0); PRINT ZYRS Q2 Q4; ? Eliminating Pi=0;
?? [Following Highest Price + Twice Std.Dev. + Inflation];
SELECT ZYRS=2001; V2=2.40887; SELECT ZYRS=1964; V4=2.20833; SELECT ZYRS=1965; V4=2.30727; SELECT ZYRS=1972; V4=2.99985;
102
SELECT ZYRS=1975; V4=3.29667; SELECT ZYRS=1977; V4=3.49455; SELECT ZYRS=1978; V4=3.59349; SELECT ZYRS=1979; V4=3.69243; ?To find out Average and Annual Costs for making Table; smpl 2, 43; msd v1-v5; smpl 2,2; msd v1-v5; print v1-v5; smpl 43,43; msd v1-v5; print v1-v5; ? To find Average and Annual Import Quantity (kg) for making Table; smpl 2,43; msd q1-q5; smpl 2,2; msd q1-q5; print q1-q5; smpl 43,43; msd q1-q5; print q1-q5; ? End of Calculation for Table; SMPL 1, 43; ? Defining Total Cost(S); S=v1+v2+V3+V4+v5; ? Calculating prices (Pi) P1=v1/Q1; P2=v2/Q2;P3=v3/Q3;P4=v4/Q4; P5=v5/Q5; PRINT ZYRS Q1 P1 Q2 P2 Q3 P3 Q4 P4 Q5 P5; ? To find Average and Annual Price (US $/Kg) for making Table; smpl 2,43; msd p1-p5; smpl 2,2; msd p1-p5; print p1-p5; smpl 43,43; msd p1-p5; print p1-p5; ? End of Calculation for Table; SMPL 1,43; ? CALCULATION OF FACTOR COST SHARES (Fi=PRICE*QUANTITY/TOTAL COST) F1=v1/S; F2=v2/S; F3=v3/S; F4=v4/S; F5=v5/S; ? LOGGING ALL PRICES AND QUANTITIES(LPi,LQi) LP1=LOG(P1); LP2=LOG(P2); LP3=LOG(P3); LP4=LOG(P4); LP5=LOG(P5); LQ1=LOG(Q1);LQ2=LOG(Q2); LQ3=LOG(Q3);LQ4=LOG(Q4); LQ5=LOG(Q5); smpl 2 43;
103
? CALCULATION TWO PERIOD MEAN OF FACTOR SHARES( Fi1) F11=(F1+F1(-1))/2; F21=(F2+F2(-1))/2; F31=(F3+F3(-1))/2; F41=(F4+F4(-1))/2; F51=(F5+F5(-1))/2; ? Calculation of Total Quantity for finding Shares; T=q1+q2+q3+q4+q5; ? Calculation of Quantity Shares for making Table; k1=Q1/T; k2=Q2/T; k3=Q3/T; k4=Q4/T; k5=Q5/T; msd k1-k5; smpl 2,2; msd k1-k5; smpl 43,43; msd k1-k5; ? End of Quantity Share Calculation; SMPL 2,43; ? CALCULATION: CHANGE IN LOGGED PRICES(DPi) DP1=LP1-LP1(-1); DP2=LP2-LP2(-1); DP3=LP3-LP3(-1); DP4=LP4-LP4(-1); DP5=LP5-LP5(-1); ? CALCULATION:CHANGE IN LOGGED QUANTITY(DQi) DQ1=LQ1-LQ1(-1); DQ2=LQ2-LQ2(-1); DQ3=LQ3-LQ3(-1); DQ4=LQ4-LQ4(-1); DQ5=LQ5-LQ5(-1); ? DEPENDENT VARIABLE fi*Dq and SUMMATION INDEX(FDQi) FDQ1=F11*DQ1; FDQ2=F21*DQ2; FDQ3=F31*DQ3; FDQ4=F41*DQ4; FDQ5=F51*DQ5; DQ=FDQ1+FDQ2+FDQ3+FDQ4+FDQ5; ?Fi*DP and SUMMATION INDEX(DP) FDP1=F11*DP1; FDP2=F21*DP2; FDP3=F31*DP3; FDP4=F41*DP4; FDP5=F51*DP5;
DP=FDP1+FDP2+FDP3+FDP4+FDP5; SMPL 2, 43; ? DIFFEREENTIAL NBR MODEL WITH AR1 PLUS HOMOGENEITY AND SYMMETRY; trend obs; d1 = (obs=1); frml res1 FDQ1-(A1*DQ+B11*DP1+B12*DP2+B13*DP3+B14*DP4+(-B11-B12-B13-B14)*DP5-F11*(DP1-DP)); frml eq1 [d1*res1*sqrt(1-rho**2) + (1-d1)*(res1 - rho*res1(-1))]* (1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res2 FDQ2-(A2*DQ+B12*DP1+B22*DP2+B23*DP3+B24*DP4+(-B12-B22-B23-B24)*DP5-F21*(DP2-DP)); frml eq2 [d1*res2*sqrt(1-rho**2) + (1-d1)*(res2 - rho*res2(-1))]* (1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res3 FDQ3-(A3*DQ+B13*DP1+B23*DP2+B33*DP3+B34*DP4+(-B13-B23-B33-B34)*DP5-F31*(DP3-DP)); frml eq3 [d1*res3*sqrt(1-rho**2) + (1-d1)*(res3 - rho*res3(-1))]* (1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res4 FDQ4-(A4*DQ+B14*DP1+B24*DP2+B34*DP3+B44*DP4+(-B14-B24-B34-B44)*DP5-F41*(DP4-DP)); frml eq4 [d1*res4*sqrt(1-rho**2) + (1-d1)*(res4 - rho*res4(-1))]* (1-rho**2)**(-1/(2*@nob)); ? mark significant variables with STARS;
104
REGOPT (STARS,STAR1=.10,STAR2=.05) T; PARAM A1 0 A2 0 A3 0 A4 0 B11 0 B12 0 B13 0 B14 0 B22 0 B23 0 B24 0 B33 0 B34 0 B44 0 rho 0; eqsub eq1 res1;eqsub eq2 res2;eqsub eq3 res3;eqsub eq4 res4; lsq(nodropmiss,tol=1e-7,maxit=1000) eq1 eq2 eq3 eq4; COPY @LOGL LU; LU1=LU; SMPL 2, 43; ? Elasticities; MSD F11 F21 F31 F41 F51; ?================= MEAN FACTOR SHARES SET MF1=@MEAN(1); SET MF2=@MEAN(2); SET MF3=@MEAN(3); SET MF4=@MEAN(4); SET MF5=@MEAN(5); PRINT MF1-MF5; SMPL 2,2; MSD F1 F2 F3 F4 F5; ?================= MEAN FACTOR SHARES SET FF1=@MEAN(1); SET FF2=@MEAN(2); SET FF3=@MEAN(3); SET FF4=@MEAN(4); SET FF5=@MEAN(5); PRINT FF1-FF5; SMPL 43,43; MSD F1 F2 F3 F4 F5; ?================= MEAN FACTOR SHARES SET FL1=@MEAN(1); SET FL2=@MEAN(2); SET FL3=@MEAN(3); SET FL4=@MEAN(4); SET FL5=@MEAN(5); PRINT FL1-FL5; SMPL 2, 43; SET B15=-B11-B12-B13-B14; SET B21=B12; SET B25=-B21-B22-B23-B24; SET B31=B13; SET B32=B23; SET B35=-B31-B32-B33-B34; SET B41=B14; SET B42=B24; SET B43=B34;
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SET B45=-B41-B42-B43-B44; SET B55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24)-(-B13-B23-B33-B34)-(-B14-B24-B34-B44)); SET A5=1-A1-A2-A3-A4; ? Calculate the standard errors for ROW frml row1 A5=1-A1-A2-A3-A4; frml row2 B15=-B11-B12-B13-B14; frml row3 B25=-B21-B22-B23-B24; frml row4 B35=-B31-B32-B33-B34; frml row5 B45=-B41-B42-B43-B44; frml row6 B55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24)-(-B13-B23-B33-B34)-(-B14-B24-B34-B44)); frml row7 B21=B12; frml row8 B31=B13; frml row9 B32=B23; frml row10 B41=B14; frml row11 B42=B24; frml row12 B43=B34; analyz row1-row12; ?? Calculate Eigenvalues SET SET SET SET SET
B51=B15; B52=B25; B53=B35; B54=B45; B55=B55;
? Tranform r to Pie SET SET SET SET SET
D11=(B11-MF1+MF1*MF1); D12=(B12+MF1*MF2); D13=(B13+MF1*MF3); D14=(B14+MF1*MF4); D15=(-B11-B12-B13-B14+MF1*MF5);
SET SET SET SET SET
D21=(B12+MF2*MF1); D22=(B22-MF2+MF2*MF2); D23=(B23+MF2*MF3); D24=(B24+MF2*MF4); D25=(-B12-B22-B23-B24+MF2*MF5);
SET SET SET SET SET
D31=(B13+MF3*MF1); D32=(B23+MF3*MF2); D33=(B33-MF3+MF3*MF3); D34=(B34+MF3*MF4); D35=(-B13-B23-B33-B34+MF3*MF5);
SET SET SET SET SET
D41=(B14+MF4*MF1); D42=(B24+MF4*MF2); D43=(B34+MF4*MF3); D44=(B44-MF4+MF4*MF4); D45=(-B14-B24-B34-B44+MF4*MF5);
SET D51=(-B11-B12-B13-B14+MF5*MF1); SET D52=(-B12-B22-B23-B24+MF5*MF2); SET D53=(-B13-B23-B33-B34+MF5*MF3); SET D54=(-B14-B24-B34-B44+MF5*MF4); SET D55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24)-(-B13-B23-B33-B34)-(-B14-B24-B34-B44)-MF5+MF5*MF5); ? Create each row five; MMAKE(VERT) MMAKE(VERT) MMAKE(VERT)
E1 D11-D15; E2 D21-D25; E3 D31-D35;
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MMAKE(VERT) MMAKE(VERT)
E4 D41-D45; E5 D51-D55;
? Creates square matrix MMAKE E E1-E5; ? Calculate Eigenvalues of E MAT EV = EIGVAL(E); Print E EV; ? Creates standard errors for pi ij's where the pi ij's are D11, D12, etc frml frml frml frml frml
pi1 pi2 pi3 pi4 pi5
d11=(B11-MF1+MF1*MF1); d12=(B12+MF1*MF2); d13=(B13+MF1*MF3); d14=(B14+MF1*MF4); d15=(-B11-B12-B13-B14+MF1*MF5);
frml frml frml frml frml
pi6 d21=(B12+MF2*MF1); pi7 d22=(B22-MF2+MF2*MF2); pi8 d23=(B23+MF2*MF3); pi9 d24=(B24+MF2*MF4); pi10 d25=(-B12-B22-B23-B24+MF2*MF5);
frml frml frml frml frml
pi11 pi12 pi13 pi14 pi15
d31=(B13+MF3*MF1); d32=(B23+MF3*MF2); d33=(B33-MF3+MF3*MF3); d34=(B34+MF3*MF4); d35=(-B13-B23-B33-B34+MF3*MF5);
frml frml frml frml frml
pi16 pi17 pi18 pi19 pi20
d41=(B14+MF4*MF1); d42=(B24+MF4*MF2); d43=(B34+MF4*MF3); d44=(B44-MF4+MF4*MF4); d45=(-B14-B24-B34-B44+MF4*MF5);
frml frml frml frml frml
pi21 pi22 pi23 pi24 pi25
d51=(-B11-B12-B13-B14+MF5*MF1); d52=(-B12-B22-B23-B24+MF5*MF2); d53=(-B13-B23-B33-B34+MF5*MF3); d54=(-B14-B24-B34-B44+MF5*MF4); d55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24) -(-B13-B23-B33-B34)-(-B14-B24-B34-B44)-MF5+MF5*MF5);
analyz pi1-pi25; ? Elasticities ? Divisia Input Index FRML EL1 E1=A1/MF1; FRML EL2 E2=A2/MF2; FRML EL3 E3=A3/MF3; FRML EL4 E4=A4/MF4; FRML EL5 E5=(1-A1-A2-A3-A4)/MF5; ? Divisia Input Index WITH FIRST F FRML EL6 EF1=A1/FF1; FRML EL7 EF2=A2/FF2; FRML EL8 EF3=A3/FF3; FRML EL9 EF4=A4/FF4; FRML EL10 EF5=(1-A1-A2-A3-A4)/FF5; ? Divisia FRML EL11 FRML EL12 FRML EL13 FRML EL14 FRML EL15
Input Index WITH LAST F EL1=A1/FL1; EL2=A2/FL2; EL3=A3/FL3; EL4=A4/FL4; EL5=(1-A1-A2-A3-A4)/FL5;
? Compensated price elasticities
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FRML FRML FRML FRML FRML
EP16 EP17 EP18 EP19 EP20
E11=(B11-MF1+MF1*MF1)/MF1; E12=(B12+MF1*MF2)/MF1; E13=(B13+MF1*MF3)/MF1; E14=(B14+MF1*MF4)/MF1; E15=(-B11-B12-B13-B14+MF1*MF5)/MF1;
FRML FRML FRML FRML FRML
EP21 EP22 EP23 EP24 EP25
E21=(B12+MF2*MF1)/MF2; E22=(B22-MF2+MF2*MF2)/MF2; E23=(B23+MF2*MF3)/MF2; E24=(B24+MF2*MF4)/MF2; E25=(-B12-B22-B23-B24+MF2*MF5)/MF2;
FRML FRML FRML FRML FRML
EP26 EP27 EP28 EP29 EP30
E31=(B13+MF3*MF1)/MF3; E32=(B23+MF3*MF2)/MF3; E33=(B33-MF3+MF3*MF3)/MF3; E34=(B34+MF3*MF4)/MF3; E35=(-B13-B23-B33-B34+MF3*MF5)/MF3;
FRML FRML FRML FRML FRML
EP31 EP32 EP33 EP34 EP35
E41=(B14+MF4*MF1)/MF4; E42=(B24+MF4*MF2)/MF4; E43=(B34+MF4*MF3)/MF4; E44=(B44-MF4+MF4*MF4)/MF4; E45=(-B14-B24-B34-B44+MF4*MF5)/MF4;
FRML EP36 E51=(-B11-B12-B13-B14+MF5*MF1)/MF5; FRML EP37 E52=(-B12-B22-B23-B24+MF5*MF2)/MF5; FRML EP38 E53=(-B13-B23-B33-B34+MF5*MF3)/MF5; FRML EP39 E54=(-B14-B24-B34-B44+MF5*MF4)/MF5; FRML EP40 E55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24)-(-B13-B23-B33-B34)-(-B14-B24-B34-B44)MF5+MF5*MF5)/MF5; ANALYZ EL1-EL15; ANALYZ EP16-EP40; PRINT; smpl 2,2; print LU; ?mark significant variables with STARS; REGOPT (STARS,STAR1=.10,STAR2=.05,) T; END;
US NBR Simulation Model OPTIONS MEMORY=1400 Double; ? US_02NBR-SELECTEDNEW2007-RECWW Models for US Import Analysis; TITLE 'TOMATO IMPORTS TO THE US'; ? For Elasticity Trend over 11 years & Calculating Mean Quantity for sample 2,33; ? NBR Final Model with AR1 plus Homogeneity and Symmetry imposed (Automatic Rho selection); smpl 1 43; LOAD ZYRS ZIMP 1963 902 1964 902 1965 902 1966 902 1967 902 1968 902 1969 902 1970 902 1971 902 1972 902 1973 902 1974 902 1975 902 1976 902
V1 Q1 V2 Q2 V3 Q3 V4 Q4 189750 730125 2481 21320 20705768 108846184 219358 562125 13291 189476 27354888 111638936 298959 733875 33276 188640 29424864 120410128 241757 562312 9319 50292 52008580 162705440 306522 803312 41735 379875 42585292 164302752 222304 575562 75850 508062 46973296 175722128 216389 400250 144332 916687 68018008 202410752 560946 977250 121233 797875 94966856 290759360 393364 505250 203117 1523625 84131328 258677808 245434 409687 220130 1345187 88150080 264119568 143427 467187 169100 834375 115137936 339795200 90716 135582 219628 1049062 64070732 267888560 111149 247117 375471 1656500 64131552 253600880 151567 233824 258069 1036375 72428816 294192576
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V5 Q5; 13928 65690 13565 94217 0 0 105323 648311 0 0 167763 668557 703 6875 57697 231001 123059 306330 23536 126579 12883 47249 45275 197879 17355 30914 32468 194149 2768 17812 180445 796919 55205 104367 34202 163878 0 0 129604 313238 12065 18312 139288 484990 11595 52601 135977 1137011 0 0 126452 1748431 9574 16132 89110 874245
1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902 902
159007 288937 632044 1977812 149405840 356244928 0 0 160421 674755 302144 523625 376993 894437 161319616 369276320 0 0 128911 236786 263748 468312 324980 835062 153871376 322163936 0 0 53016 89746 240082 380875 254595 586750 131475112 294612672 1363 3062 28456 50561 331663 448187 554520 1126937 237938496 236592128 52344 58011 268097 312113 369382 563750 117345 352375 173374416 267219568 88818 136482 632151 534929 616082 788625 243863 780500 226757760 331736864 145836 71248 1384907 601291 959659 1086062 392689 1111375 171133120 369494048 2079176 1028974 1814396 1075765 748704 766812 829172 2122750 168479888 380314432 3612847 1590097 1933597 1223189 1298959 1261125 4040176 9988785 327903168 430983424 3628705 1705323 1156736 1081471 2107219 1930875 2212019 5768554 160881840 406785376 3911491 1579579 1266919 1024096 2573120 2117875 1203746 2862687 152356480 362726880 3674326 1624760 3513976 1160022 2888215 2327812 477349 1266562 224163760 385940928 5684585 2677385 3466587 1489777 3345576 3075187 1019288 1404125 390824864 352312128 3181770 1305635 3820630 2897837 4560436 2672000 467383 418250 269461472 353543872 8658034 3027499 5897411 1109323 5664522 5213699 618499 559437 141482016 183116320 8592061 2916249 10776134 4222087 6490505 4733488 328571 326875 325450048 400494304 25714519 9677932 8478949 3162569 10479733 7673394 15237 16117 335774656 376031680 31977654 10490708 7133936 1827493 17997856 11655089 39438 43191 434508160 593079616 45101016 14822351 4221050 1343177 38849532 21769264 94680 100296 613726272 685677632 88867703 27270029 10402293 2332987 61045808 37504200 53591 49441 549398080 660608640 119103389 41025640 17126556 3275951 102889656 61728728 40701 28812 600902720 734053120 144522212 46619633 24440423 4889259 121800280 79553504 2398 1687 517601728 615063808 123059860 41901303 18251894 4135634 163877088 101390248 10665 14687 438421792 589954432 101363658 34695648 14394573 4008089 169921584 105680184 0 0 517007488 679187072 99481702 34809782 14115626 3864210 175542448 100499128 2290 2875 582243072 724015808 91658917 30983318 19301177 4595575 234794400 130153808 11978 21011 794276800 784988032 63798848 19163022 23735958 4930831 261605248 133565936 641605 807375 789782848 779020288 56011543 15406065 18641380 3172048 274699840 141642032 1449620 856968 818552896 801408192 28333599 7396764 2857037 482476
? V: value in US dollars; Q: quantity in kilograms; ? 1: Canada ? 2: Dominican Republic ? 3: Mexico ? 4: European Union-15 ? 5: Rest of the World ? 902: United States as Importer; ? Eliminating zero values in Q; Q2=1*(Q2=0)+Q2*(Q2>0); Q4=1*(Q4=0)+Q4*(Q4>0); PRINT ZYRS Q2 Q4; ? Eliminating Pi=0; ?? [Following Highest Price + Twice Std.Dev. + Inflation]; SELECT ZYRS=2001; V2=2.40887; SELECT ZYRS=1964; V4=2.20833; SELECT ZYRS=1965; V4=2.30727; SELECT ZYRS=1972; V4=2.99985; SELECT ZYRS=1975; V4=3.29667; SELECT ZYRS=1977; V4=3.49455; SELECT ZYRS=1978; V4=3.59349; SELECT ZYRS=1979; V4=3.69243; ?To find out Average and Annual Costs for making Table; smpl 2, 43; msd v1-v5;
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smpl 2,2; msd v1-v5; print v1-v5; smpl 43,43; msd v1-v5; print v1-v5; ? To find Average and Annual Import Quantity (kg) for making Table; smpl 2,43; msd q1-q5; smpl 2,2; msd q1-q5; print q1-q5; smpl 43,43; msd q1-q5; print q1-q5; ? End of Calculation for Table; SMPL 1, 43; ? Defining Total Cost(S); S=v1+v2+V3+V4+v5; ? Calculating prices (Pi) P1=v1/Q1; P2=v2/Q2;P3=v3/Q3;P4=v4/Q4; P5=v5/Q5; PRINT ZYRS Q1 P1 Q2 P2 Q3 P3 Q4 P4 Q5 P5; ? To find Average and Annual Price (US $/Kg) for making Table; smpl 2,43; msd p1-p5; smpl 2,2; msd p1-p5; print p1-p5; smpl 43,43; msd p1-p5; print p1-p5; ? End of Calculation for Table; SMPL 1,43; ? CALCULATION OF FACTOR COST SHARES (Fi=PRICE*QUANTITY/TOTAL COST) F1=v1/S; F2=v2/S; F3=v3/S; F4=v4/S; F5=v5/S; ? LOGGING ALL PRICES AND QUANTITIES(LPi,LQi) LP1=LOG(P1); LP2=LOG(P2); LP3=LOG(P3); LP4=LOG(P4); LP5=LOG(P5); LQ1=LOG(Q1);LQ2=LOG(Q2); LQ3=LOG(Q3);LQ4=LOG(Q4); LQ5=LOG(Q5); smpl 2 43; ? CALCULATION TWO PERIOD MEAN OF FACTOR SHARES( Fi1) F11=(F1+F1(-1))/2; F21=(F2+F2(-1))/2; F31=(F3+F3(-1))/2; F41=(F4+F4(-1))/2; F51=(F5+F5(-1))/2; ? Calculation of Total Quantity for finding Shares; T=q1+q2+q3+q4+q5; ? Calculation of Quantity Shares for making Table; k1=Q1/T; k2=Q2/T; k3=Q3/T; k4=Q4/T; k5=Q5/T; msd k1-k5;
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smpl 2,2; msd k1-k5; smpl 43,43; msd k1-k5; ? End of Quantity Share Calculation; ? Calculation of Mean Quantity for Structural Change; smpl 2,33; msd q1-q5; msd T; SMPL 2,43; ? CALCULATION: CHANGE IN LOGGED PRICES(DPi) DP1=LP1-LP1(-1); DP2=LP2-LP2(-1); DP3=LP3-LP3(-1); DP4=LP4-LP4(-1); DP5=LP5-LP5(-1); ? CALCULATION:CHANGE IN LOGGED QUANTITY(DQi) DQ1=LQ1-LQ1(-1); DQ2=LQ2-LQ2(-1); DQ3=LQ3-LQ3(-1); DQ4=LQ4-LQ4(-1); DQ5=LQ5-LQ5(-1); ? DEPENDENT VARIABLE fi*Dq and SUMMATION INDEX(FDQi) FDQ1=F11*DQ1; FDQ2=F21*DQ2; FDQ3=F31*DQ3; FDQ4=F41*DQ4; FDQ5=F51*DQ5; DQ=FDQ1+FDQ2+FDQ3+FDQ4+FDQ5; ?Fi*DP and SUMMATION INDEX(DP) FDP1=F11*DP1; FDP2=F21*DP2; FDP3=F31*DP3; FDP4=F41*DP4; FDP5=F51*DP5; DP=FDP1+FDP2+FDP3+FDP4+FDP5; proc zzzz; ? DIFFEREENTIAL NBR MODEL WITH AR1 PLUS HOMOGENEITY AND SYMMETRY; trend obs; d1 = (obs=1); frml res1 FDQ1-(A1*DQ+B11*DP1+B12*DP2+B13*DP3+B14*DP4+(-B11-B12-B13-B14)*DP5-F11*(DP1-DP)); frml eq1 [d1*res1*sqrt(1-rho**2) + (1-d1)*(res1 - rho*res1(-1))]* (1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res2 FDQ2-(A2*DQ+B12*DP1+B22*DP2+B23*DP3+B24*DP4+(-B12-B22-B23-B24)*DP5-F21*(DP2-DP)); frml eq2 [d1*res2*sqrt(1-rho**2) + (1-d1)*(res2 - rho*res2(-1))]* (1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res3 FDQ3-(A3*DQ+B13*DP1+B23*DP2+B33*DP3+B34*DP4+(-B13-B23-B33-B34)*DP5-F31*(DP3-DP)); frml eq3 [d1*res3*sqrt(1-rho**2) + (1-d1)*(res3 - rho*res3(-1))]* (1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res4 FDQ4-(A4*DQ+B14*DP1+B24*DP2+B34*DP3+B44*DP4+(-B14-B24-B34-B44)*DP5-F41*(DP4-DP)); frml eq4 [d1*res4*sqrt(1-rho**2) + (1-d1)*(res4 - rho*res4(-1))]* (1-rho**2)**(-1/(2*@nob)); ? mark significant variables with STARS;
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REGOPT (STARS,STAR1=.10,STAR2=.05) T; PARAM A1 0 A2 0 A3 0 A4 0 B11 0 B12 0 B13 0 B14 0 B22 0 B23 0 B24 0 B33 0 B34 0 B44 0 rho 0; eqsub eq1 res1;eqsub eq2 res2;eqsub eq3 res3;eqsub eq4 res4; lsq(nodropmiss,tol=1e-7,maxit=1000) eq1 eq2 eq3 eq4; COPY @LOGL LU; LU1=LU; SMPL NR1,NR2; ? Elasticities; MSD F11 F21 F31 F41 F51; ?================= MEAN FACTOR SHARES SET MF1=@MEAN(1); SET MF2=@MEAN(2); SET MF3=@MEAN(3); SET MF4=@MEAN(4); SET MF5=@MEAN(5); PRINT MF1-MF5; SMPL NR1,NR1; MSD F1 F2 F3 F4 F5; ?================= MEAN FACTOR SHARES SET FF1=@MEAN(1); SET FF2=@MEAN(2); SET FF3=@MEAN(3); SET FF4=@MEAN(4); SET FF5=@MEAN(5); PRINT FF1-FF5; SMPL NR2,NR2; MSD F1 F2 F3 F4 F5; ?================= MEAN FACTOR SHARES SET FL1=@MEAN(1); SET FL2=@MEAN(2); SET FL3=@MEAN(3); SET FL4=@MEAN(4); SET FL5=@MEAN(5); PRINT FL1-FL5; SMPL NR1,NR2; SET B15=-B11-B12-B13-B14; SET B21=B12; SET B25=-B21-B22-B23-B24; SET B31=B13; SET B32=B23; SET B35=-B31-B32-B33-B34; SET B41=B14; SET B42=B24; SET B43=B34;
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SET B45=-B41-B42-B43-B44; SET B55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24)-(-B13-B23-B33-B34)-(-B14-B24-B34-B44)); SET A5=1-A1-A2-A3-A4; ? Calculate the standard errors for ROW frml row1 A5=1-A1-A2-A3-A4; frml row2 B15=-B11-B12-B13-B14; frml row3 B25=-B21-B22-B23-B24; frml row4 B35=-B31-B32-B33-B34; frml row5 B45=-B41-B42-B43-B44; frml row6 B55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24)-(-B13-B23-B33-B34)-(-B14-B24-B34-B44)); frml row7 B21=B12; frml row8 B31=B13; frml row9 B32=B23; frml row10 B41=B14; frml row11 B42=B24; frml row12 B43=B34; analyz row1-row12; ?? Calculate Eigenvalues SET B51=B15; SET B52=B25; SET B53=B35; SET B54=B45; SET B55=B55; ? Tranform r to Pie SET D11=(B11-MF1+MF1*MF1); SET D12=(B12+MF1*MF2); SET D13=(B13+MF1*MF3); SET D14=(B14+MF1*MF4); SET D15=(-B11-B12-B13-B14+MF1*MF5); SET D21=(B12+MF2*MF1); SET D22=(B22-MF2+MF2*MF2); SET D23=(B23+MF2*MF3); SET D24=(B24+MF2*MF4); SET D25=(-B12-B22-B23-B24+MF2*MF5); SET D31=(B13+MF3*MF1); SET D32=(B23+MF3*MF2); SET D33=(B33-MF3+MF3*MF3); SET D34=(B34+MF3*MF4); SET D35=(-B13-B23-B33-B34+MF3*MF5); SET D41=(B14+MF4*MF1); SET D42=(B24+MF4*MF2); SET D43=(B34+MF4*MF3); SET D44=(B44-MF4+MF4*MF4); SET D45=(-B14-B24-B34-B44+MF4*MF5); SET D51=(-B11-B12-B13-B14+MF5*MF1); SET D52=(-B12-B22-B23-B24+MF5*MF2); SET D53=(-B13-B23-B33-B34+MF5*MF3); SET D54=(-B14-B24-B34-B44+MF5*MF4); SET D55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24)-(-B13-B23-B33-B34)-(-B14-B24-B34-B44)-MF5+MF5*MF5); ? Create each row five; MMAKE(VERT) E1 D11-D15; MMAKE(VERT) E2 D21-D25;
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MMAKE(VERT) E3 D31-D35; MMAKE(VERT) E4 D41-D45; MMAKE(VERT) E5 D51-D55; ? Creates square matrix MMAKE E E1-E5; ? Calculate Eigenvalues of E MAT EV = EIGVAL(E); Print E EV; ? Creates standard errors for pi ij's where the pi ij's are D11, D12, etc frml pi1 d11=(B11-MF1+MF1*MF1); frml pi2 d12=(B12+MF1*MF2); frml pi3 d13=(B13+MF1*MF3); frml pi4 d14=(B14+MF1*MF4); frml pi5 d15=(-B11-B12-B13-B14+MF1*MF5); frml pi6 d21=(B12+MF2*MF1); frml pi7 d22=(B22-MF2+MF2*MF2); frml pi8 d23=(B23+MF2*MF3); frml pi9 d24=(B24+MF2*MF4); frml pi10 d25=(-B12-B22-B23-B24+MF2*MF5); frml pi11 d31=(B13+MF3*MF1); frml pi12 d32=(B23+MF3*MF2); frml pi13 d33=(B33-MF3+MF3*MF3); frml pi14 d34=(B34+MF3*MF4); frml pi15 d35=(-B13-B23-B33-B34+MF3*MF5); frml pi16 d41=(B14+MF4*MF1); frml pi17 d42=(B24+MF4*MF2); frml pi18 d43=(B34+MF4*MF3); frml pi19 d44=(B44-MF4+MF4*MF4); frml pi20 d45=(-B14-B24-B34-B44+MF4*MF5); frml pi21 d51=(-B11-B12-B13-B14+MF5*MF1); frml pi22 d52=(-B12-B22-B23-B24+MF5*MF2); frml pi23 d53=(-B13-B23-B33-B34+MF5*MF3); frml pi24 d54=(-B14-B24-B34-B44+MF5*MF4); frml pi25 d55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24) -(-B13-B23-B33-B34)-(-B14-B24-B34-B44)-MF5+MF5*MF5); analyz pi1-pi25; ? Elasticities ? Divisia Input Index FRML EL1 E1=A1/MF1; FRML EL1M E1M=A1/MMF1; FRML EL2 E1=A2/MF2; FRML EL2M E2M=A2/MMF2; FRML EL3 E3=A3/MF3; FRML EL3M E3M=A3/MMF3; FRML EL4 E4=A4/MF4; FRML EL4M E4M=A4/MMF4; FRML EL5 E5=(1-A1-A2-A3-A4)/MF5; FRML EL5M E5M=(1-A1-A2-A3-A4)/MMF5; ? Divisia Input Index WITH FIRST F FRML EL6 EF1=A1/FF1; FRML EL6M EF1M=A1/MFF1; FRML EL7 EF2=A2/FF2; FRML EL7M EF2M=A2/MFF2; FRML EL8 EF3=A3/FF3; FRML EL8M EF3M=A3/MFF3; FRML EL9 EF4=A4/FF4; FRML EL9M EF4M=A4/MFF4; FRML EL10 EF5=(1-A1-A2-A3-A4)/FF5; FRML EL10M EF5M=(1-A1-A2-A3-A4)/MFF5; ? Divisia Input Index WITH LAST F FRML EL11 EL1=A1/FL1; FRML EL11M EL1M=A1/MFL1; FRML EL12 EL2=A2/FL2; FRML EL12M EL2M=A2/MFL2; FRML EL13 EL3=A3/FL3; FRML EL13M EL3M=A3/MFL3; FRML EL14 EL4=A4/FL4; FRML EL14M EL4M=A4/MFL4;
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FRML EL15 EL5=(1-A1-A2-A3-A4)/FL5; FRML EL15M EL5M=(1-A1-A2-A3-A4)/MFL5; ? Compensated price elasticities FRML EP16 E11=(B11-MF1+MF1*MF1)/MF1; FRML EP16M E11M=(B11-MMF1+MMF1*MMF1)/MMF1; FRML EP17 E12=(B12+MF1*MF2)/MF1; FRML EP17M E12M=(B12+MMF1*MMF2)/MMF1; FRML EP18 E13=(B13+MF1*MF3)/MF1; FRML EP18M E13M=(B13+MMF1*MMF3)/MMF1; FRML EP19 E14=(B14+MF1*MF4)/MF1; FRML EP19M E14M=(B14+MMF1*MMF4)/MMF1; FRML EP20 E15=(-B11-B12-B13-B14+MF1*MF5)/MF1; FRML EP20M E15M=(-B11-B12-B13-B14+MMF1*MMF5)/MMF1; FRML EP21 E21=(B12+MF2*MF1)/MF2; FRML EP21M E21M=(B12+MMF2*MMF1)/MMF2; FRML EP22 E22=(B22-MF2+MF2*MF2)/MF2; FRML EP22M E22M=(B22-MMF2+MMF2*MMF2)/MMF2; FRML EP23 E23=(B23+MF2*MF3)/MF2; FRML EP23M E23M=(B23+MMF2*MMF3)/MMF2; FRML EP24 E24=(B24+MF2*MF4)/MF2; FRML EP24M E24M=(B24+MMF2*MMF4)/MMF2; FRML EP25 E25=(-B12-B22-B23-B24+MF2*MF5)/MF2; FRML EP25M E25M=(-B12-B22-B23-B24+MMF2*MMF5)/MMF2; FRML EP26 E31=(B13+MF3*MF1)/MF3; FRML EP26M E31M=(B13+MMF3*MMF1)/MMF3; FRML EP27 E32=(B23+MF3*MF2)/MF3; FRML EP27M E32M=(B23+MMF3*MMF2)/MMF3; FRML EP28 E33=(B33-MF3+MF3*MF3)/MF3; FRML EP28M E33M=(B33-MMF3+MMF3*MMF3)/MMF3; FRML EP29 E34=(B34+MF3*MF4)/MF3; FRML EP29M E34M=(B34+MMF3*MMF4)/MMF3; FRML EP30 E35=(-B13-B23-B33-B34+MF3*MF5)/MF3; FRML EP30M E35M=(-B13-B23-B33-B34+MMF3*MMF5)/MMF3; FRML EP31 E41=(B14+MF4*MF1)/MF4; FRML EP31M E41M=(B14+MMF4*MMF1)/MMF4; FRML EP32 E42=(B24+MF4*MF2)/MF4; FRML EP32M E42M=(B24+MMF4*MMF2)/MMF4; FRML EP33 E43=(B34+MF4*MF3)/MF4; FRML EP33M E43M=(B34+MMF4*MMF3)/MMF4; FRML EP34 E44=(B44-MF4+MF4*MF4)/MF4; FRML EP34M E44M=(B44-MMF4+MMF4*MMF4)/MMF4; FRML EP35 E45=(-B14-B24-B34-B44+MF4*MF5)/MF4; FRML EP35M E45M=(-B14-B24-B34-B44+MMF4*MMF5)/MMF4; FRML EP36 E51=(-B11-B12-B13-B14+MF5*MF1)/MF5; FRML EP36M E51M=(-B11-B12-B13-B14+MMF5*MMF1)/MMF5; FRML EP37 E52=(-B12-B22-B23-B24+MF5*MF2)/MF5; FRML EP37M E52M=(-B12-B22-B23-B24+MMF5*MMF2)/MMF5; FRML EP38 E53=(-B13-B23-B33-B34+MF5*MF3)/MF5; FRML EP38M E53M=(-B13-B23-B33-B34+MMF5*MMF3)/MMF5; FRML EP39 E54=(-B14-B24-B34-B44+MF5*MF4)/MF5; FRML EP39M E54M=(-B14-B24-B34-B44+MMF5*MMF4)/MMF5; FRML EP40 E55=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24)-(-B13-B23-B33-B34)-(-B14-B24-B34-B44)-MF5+MF5*MF5)/MF5; FRML EP40M E55M=(-(-B11-B12-B13-B14)-(-B12-B22-B23-B24)-(-B13-B23-B33-B34)-(-B14-B24-B34-B44)-MMF5+MMF5*MMF5)/MMF5; ANALYZ EL1-EL5, EL1M-EL5M; MMAKE ELCOEF @COEFA; ANALYZ EP16-EP40, EP16M-EP40M; MMAKE EPCOEF @COEFA; MMAKE(VERTICAL) MBM ELCOEF EPCOEF; MMAKE MBETA MBETA MBM; ?smpl 2,2; ?print LU; ?mark significant variables with STARS; ?REGOPT (STARS,STAR1=.10,STAR2=.05,) T; endproc zzzz; MFORM(TYPE=GEN,NROW=60,NCOL=1) MBETA=0; SMPL 2, 33; MSD F11 F21 F31 F41 F51; ?================= MEAN FACTOR SHARES SET MMF1=@MEAN(1); SET MMF2=@MEAN(2); SET MMF3=@MEAN(3); SET MMF4=@MEAN(4); SET MMF5=@MEAN(5); SMPL 2,2; MSD F1 F2 F3 F4 F5; ?================= MEAN FACTOR SHARES SET MFF1=@MEAN(1); SET MFF2=@MEAN(2);
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SET MFF3=@MEAN(3); SET MFF4=@MEAN(4); SET MFF5=@MEAN(5); SMPL 33,33; MSD F1 F2 F3 F4 F5; ?================= MEAN FACTOR SHARES SET MFL1=@MEAN(1); SET MFL2=@MEAN(2); SET MFL3=@MEAN(3); SET MFL4=@MEAN(4); SET MFL5=@MEAN(5); DO J=1 TO 11; SET NR1=1+J; SET NR2=32+J; SMPL NR1,NR2; ZZZZ; ENDDO; WRITE(FORMAT=EXCEL,FILE='U:\TOMATORESEARCH\USNEWANALYSIS\ELEPELAS-RECWW.XLS') MBETA; END;
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APPENDIX B COMPUTER PRINTOUTS FOR EU-15 ANALYSIS The Model to deal with zero quantity and price for EU-15 Analysis OPTIONS MEMORY=1500 signif=5 DOUBLE; TITLE 'TOMATO IMPORTS TO THE EU';
? EU15#01Price Calculation Model; ? To replace zero Price for EU-15 Import Analysis;
SMPL 1 43; ?READ(FORMAT=EXCEL,FILE='U:\TomatoResearch\TSPWORKS2006\EUAnalysis\EUonly.xls'); LOAD ZYRS ZIMP V1 Q1 V2 Q2 V3 Q3 V4 Q4 V5 Q5 V6 Q6 V7 Q7 V8 Q8; 1963 901 31653 451074 1773563 16782212 18133 40123 26567148 122325848 1004321 9072714 7000 72000 3240 12187 3376225 19971241 1964 901 48038 572000 1840474 12660747 1262 3312 31730108 118009256 1361401 10570330 0 0 2419 6437 2737208 13016627 1965 901 118653 1108312 2220545 15148287 5152 5562 27267956 125699712 1928476 15228634 0 0 17404 53152 1795230 12036480 1966 901 187269 1748000 2856091 13152661 85829 107862 36479432 108006936 2691155 19047720 1000 12812 11245 21812 2539638 10580398 1967 901 207999 2220125 3753435 18649844 46886 118310 36637392 122262104 2789153 18614500 0 0 69348 154932 2665245 13813254 1968 901 310461 2266000 4405008 19895024 26510 101198 27803468 97863480 5120585 33277424 0 0 74419 93022 1488195 7481394 1969 901 368538 2496687 3916124 14940986 32359 99740 36980408 129603024 7855349 34033604 0 0 128959 220245 3636690 12882177 1970 901 457730 2397937 4464447 15889571 40904 68278 38635412 133623216 9460210 42568288 3115 40398 260188 308561 11442442 37441791 1971 901 469036 2752398 4245967 16817272 64882 136795 44930860 129688160 14373836 59700256 0 0 284716 335143 4986064 14826093 1972 901 962086 4625350 4017254 16139896 35034 42506 45938032 118869120 15097659 63092032 1550 1875 284469 401349 7784385 19256671 1973 901 1594265 4437519 4893273 14262623 36545 29147 77101920 170786640 19292240 54257208 0 0 657057 745654 976072 1966077 1974 901 1797788 5708053 5692533 15417826 216473 219126 65580600 138533712 15978113 43303736 6326 42800 108407 82604 1433878 2602306 1975 901 3158736 7143835 7033987 15033790 731299 1000174 99121944 137464352 15771246 39263124 33343 187800 41024 42096 1391526 2230043 1976 901 2968861 7003612 5147297 12926526 1831054 3315306 75478176 106260064 13685706 37747484 4957 17625 196696 132987 2215727 4062108 1977 901 3472400 9189788 7425601 15885014 2325006 4158786 82794408 115851376 9554171 25682334 1000 1687 53600 51748 2066804 3061723 1978 901 2963215 6163585 7430996 14492037 2309641 3208973 85231920 104367608 9191896 21285690 37511 104073 200784 202229 2231462 2797116 1979 901 4026272 6798812 7907311 16267033 2373524 2974927 93011048 104508152 9071943 19847036 44832 82886 196614 141842 1673201 1711795 1980 901 6052384 10362511 4767464 11321398 2157749 1940617 87930720 91080208 11919843 23267114 102946 122824 867395 513303 2614841 2395847 1981 901 5573419 10825753 4173807 10542792 1422141 1240105 74939560 89919392 6717752 15562404 115808 164500 246247 303185 2178646 2958982 1982 901 6942520 16861542 2793814 7765386 1335471 1713708 50565584 66672692 6240809 14409339 89026 207127 39146 36069 1739339 3025668 1983 901 5955306 13127198 3990447 10570612 635025 665686 48541384 67457464 7539437 20009412 74331 144311 69812 82299 1714422 3349194 1984 901 4628415 11485112 2225929 6696144 1818868 2723827 49903220 82007208 8647271 24582260 410328 781058 73121 98443 1755933 3507856 1985 901 3714979 9679074 2804760 8574710 1519295 2329586 56146208 91701904 4742369 15723088 140775 329186 66289 88741 1109962 2356596 1986 901 4428861 9652574 2080354 5348562 2521897 2659235 68524448 96462176 4144346 11844698 670611 1127182 84403 88221 1740140 2880545 1987 901 4756993 9699476 2978113 6105456 2280814 2929812 87123544 97076016 5764089 12027178 2554835 3132693 141317 109611 2877196 3757298 1988 901 5344652 8643190 2402380 4767624 4903546 3937171 76347792 84892376 6708963 14960272 2264643 2524775 349851 243009 4564090 5078631 1989 901 4125968 6758386 2317410 5286987 3193985 3638453 71171816 97750632 7488692 16598397 2450896 3062926 1633335 864997 3588237 4834089
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1990 901 7360551 11020187 3029963 5708198 10650899 8021161 130990440 110714248 2765811 5380596 5190490 4332286 1125452 702779 6934463 5863059 1991 901 1869942 2294788 5032627 8084701 8374074 6277594 145453872 140390832 3665304 6377014 5308010 5725206 2509599 1876646 5001624 4620865 1992 901 404674 585339 3651196 5088920 6577894 5570072 139864960 141403616 3295008 5192788 6377826 7713368 391317 410689 5869919 5966114 1993 901 116900 270875 1710821 2183913 5634468 5223672 143160640 177926880 2223115 3715382 3718712 4547761 188735 224006 4278326 4454055 1994 901 43000 47199 357690 560199 5986108 5533320 120315416 160862048 1217387 2056625 4114383 5180666 155184 156425 3399291 3484049 1995 901 0 0 29111 43369 11579928 6364214 147584576 146905040 125053 151773 2661260 2334571 308488 239044 5825043 4559700 1996 901 24187 11375 183522 69726 17264544 9271430 148078032 157396080 230793 297000 4508979 3476803 38016 20788 5271388 3221124 1997 901 0 0 15124 21386 20697980 10657880 104872824 154990608 38161 46226 1020557 927674 82651 103135 7566921 5781611 1998 901 0 0 22636 30788 22782924 12299150 147687616 186837792 29637 48398 905471 869349 92865 72220 7331996 5544938 1999 901 0 0 60193 71125 22791080 14885635 141139536 206332992 0 0 2285333 2621314 205003 163351 5596276 5080246 2000 901 10448 18000 54910 66112 23066744 16460790 117918632 149369664 0 0 10910094 11328141 39582 24734 12195800 10873083 2001 901 16528 57300 9909 16625 21346768 17480612 108504040 185144192 22387 33500 6927946 9118854 10763 9212 10767377 11338870 2002 901 61870 101898 37526 55663 21751194 14590805 170802208 181180384 4604 3625 16571994 18724980 21009 14917 12378914 12102489 2003 901 22075 26453 206498 198835 24412648 16800316 136954944 182067392 43642 46710 26240464 25322332 21415 17437 29699618 29466621 2004 901 150833 169081 84115 84338 31703530 18551426 172314848 192159904 190675 188753 19238032 17210976 12976 6761 27974391 29547420 2005 901 0 0 20624 19526 44735840 25201496 229945104 232239648 35735 37440 23119076 19664766 43605 31100 61700006 54335924 ? 1: Albania ? 2: Bulgaria ? 3: Israel ? 4: Morocco ? 5: Romania ? 6: Turkey ? 7: United States ? 8: Rest of the World; ?901 EU-15 as importer; select q1>0; P1=V1/Q1; olsq P1 C Q1 ZYRS; select q5>0; P5=V5/Q5; olsq P5 C Q5 ZYRS; select q6>0; P6=V6/Q6; olsq P6 C Q6 ZYRS; SMPL 1, 43; Q1=1*(Q1=0)+Q1*(Q1>0); Q5=1*(Q5=0)+Q5*(Q5>0); Q6=1*(Q6=0)+Q6*(Q6>0); Print Q1 P1 Q5 P5 Q6 P6; END; The EU-15 NBR Import Demand Model. OPTIONS MEMORY=1500 Double; Import Analysis Without USA ; TITLE 'TOMATO IMPORTS TO THE US'; calculation;
? EU15_02NBR-NEW2007-FINAL SELECTED-V2 Models for EU ? For Cost Share, Quantity Share and Average Price
118
? NBR Model with Homogeneity and Symmetry imposed without Rho (since Rho=-0.094410 with P value 0.163 & LU1=689.03834)& LU2=688.35849; smpl 1 43; ?READ(FORMAT=EXCEL,FILE='U:\TomatoResearch\TSPWORKS2006\EUAnalysis\EUonly.xls'); LOAD ZYRS ZIMP V1 Q1 V2 Q2 Q5 V6 Q6 V7 Q7 1963 901 31653 451074 1773563 16782212 9072714 7000 72000 3240 12187 1964 901 48038 572000 1840474 12660747 10570330 0 0 2419 6437 1965 901 118653 1108312 2220545 15148287 15228634 0 0 17404 53152 1966 901 187269 1748000 2856091 13152661 19047720 1000 12812 11245 21812 1967 901 207999 2220125 3753435 18649844 18614500 0 0 69348 154932 1968 901 310461 2266000 4405008 19895024 33277424 0 0 74419 93022 1969 901 368538 2496687 3916124 14940986 34033604 0 0 128959 220245 1970 901 457730 2397937 4464447 15889571 42568288 3115 40398 260188 308561 1971 901 469036 2752398 4245967 16817272 59700256 0 0 284716 335143 1972 901 962086 4625350 4017254 16139896 63092032 1550 1875 284469 401349 1973 901 1594265 4437519 4893273 14262623 54257208 0 0 657057 745654 1974 901 1797788 5708053 5692533 15417826 43303736 6326 42800 108407 82604 1975 901 3158736 7143835 7033987 15033790 39263124 33343 187800 41024 42096 1976 901 2968861 7003612 5147297 12926526 37747484 4957 17625 196696 132987 1977 901 3472400 9189788 7425601 15885014 25682334 1000 1687 53600 51748 1978 901 2963215 6163585 7430996 14492037 21285690 37511 104073 200784 202229 1979 901 4026272 6798812 7907311 16267033 19847036 44832 82886 196614 141842 1980 901 6052384 10362511 4767464 11321398 23267114 102946 122824 867395 513303 1981 901 5573419 10825753 4173807 10542792 15562404 115808 164500 246247 303185 1982 901 6942520 16861542 2793814 7765386 14409339 89026 207127 39146 36069 1983 901 5955306 13127198 3990447 10570612 20009412 74331 144311 69812 82299 1984 901 4628415 11485112 2225929 6696144 24582260 410328 781058 73121 98443 1985 901 3714979 9679074 2804760 8574710 15723088 140775 329186 66289 88741 1986 901 4428861 9652574 2080354 5348562 11844698 670611 1127182 84403 88221 1987 901 4756993 9699476 2978113 6105456 12027178 2554835 3132693 141317 109611 1988 901 5344652 8643190 2402380 4767624 14960272 2264643 2524775 349851 243009 1989 901 4125968 6758386 2317410 5286987 16598397 2450896 3062926 1633335 864997 1990 901 7360551 11020187 3029963 5708198 5380596 5190490 4332286 1125452 702779 1991 901 1869942 2294788 5032627 8084701 6377014 5308010 5725206 2509599 1876646 1992 901 404674 585339 3651196 5088920 5192788 6377826 7713368 391317 410689 1993 901 116900 270875 1710821 2183913 3715382 3718712 4547761 188735 224006
V3 V8 Q8; 18133 40123 3376225 19971241 1262 3312 2737208 13016627 5152 5562 1795230 12036480 85829 107862 2539638 10580398 46886 118310 2665245 13813254 26510 101198 1488195 7481394 32359 99740 3636690 12882177 40904 68278 11442442 37441791 64882 136795 4986064 14826093 35034 42506 7784385 19256671 36545 29147 976072 1966077 216473 219126 1433878 2602306 731299 1000174 1391526 2230043 1831054 3315306 2215727 4062108 2325006 4158786 2066804 3061723 2309641 3208973 2231462 2797116 2373524 2974927 1673201 1711795 2157749 1940617 2614841 2395847 1422141 1240105 2178646 2958982 1335471 1713708 1739339 3025668 635025 665686 1714422 3349194 1818868 2723827 1755933 3507856 1519295 2329586 1109962 2356596 2521897 2659235 1740140 2880545 2280814 2929812 2877196 3757298 4903546 3937171 4564090 5078631 3193985 3638453 3588237 4834089 10650899 8021161 6934463 5863059 8374074 6277594 5001624 4620865 6577894 5570072 5869919 5966114 5634468 5223672 4278326 4454055
119
Q3
V4
Q4
V5
26567148 122325848
1004321
31730108 118009256
1361401
27267956 125699712
1928476
36479432 108006936
2691155
36637392 122262104
2789153
27803468
97863480
5120585
36980408 129603024
7855349
38635412 133623216
9460210
44930860 129688160 14373836 45938032 118869120 15097659 77101920 170786640 19292240 65580600 138533712 15978113 99121944 137464352 15771246 75478176 106260064 13685706 82794408 115851376
9554171
85231920 104367608
9191896
93011048 104508152
9071943
87930720
91080208 11919843
74939560
89919392
6717752
50565584
66672692
6240809
48541384
67457464
7539437
49903220
82007208
8647271
56146208
91701904
4742369
68524448
96462176
4144346
87123544
97076016
5764089
76347792
84892376
6708963
71171816
97750632
7488692
130990440 110714248
2765811
145453872 140390832
3665304
139864960 141403616
3295008
143160640 177926880
2223115
1994 901 43000 47199 357690 560199 5986108 5533320 120315416 160862048 1217387 2056625 4114383 5180666 155184 156425 3399291 3484049 1995 901 0 0 29111 43369 11579928 6364214 147584576 146905040 125053 151773 2661260 2334571 308488 239044 5825043 4559700 1996 901 24187 11375 183522 69726 17264544 9271430 148078032 157396080 230793 297000 4508979 3476803 38016 20788 5271388 3221124 1997 901 0 0 15124 21386 20697980 10657880 104872824 154990608 38161 46226 1020557 927674 82651 103135 7566921 5781611 1998 901 0 0 22636 30788 22782924 12299150 147687616 186837792 29637 48398 905471 869349 92865 72220 7331996 5544938 1999 901 0 0 60193 71125 22791080 14885635 141139536 206332992 0 0 2285333 2621314 205003 163351 5596276 5080246 2000 901 10448 18000 54910 66112 23066744 16460790 117918632 149369664 0 0 10910094 11328141 39582 24734 12195800 10873083 2001 901 16528 57300 9909 16625 21346768 17480612 108504040 185144192 22387 33500 6927946 9118854 10763 9212 10767377 11338870 2002 901 61870 101898 37526 55663 21751194 14590805 170802208 181180384 4604 3625 16571994 18724980 21009 14917 12378914 12102489 2003 901 22075 26453 206498 198835 24412648 16800316 136954944 182067392 43642 46710 26240464 25322332 21415 17437 29699618 29466621 2004 901 150833 169081 84115 84338 31703530 18551426 172314848 192159904 190675 188753 19238032 17210976 12976 6761 27974391 29547420 2005 901 0 0 20624 19526 44735840 25201496 229945104 232239648 35735 37440 23119076 19664766 43605 31100 61700006 54335924 ? V: ? 1: ? 2: ? 3: ? 4: ? 5: ? 6: ? 7: ?901
value in (not million) US dollars; Q: quantity in (not million) kilograms; Albania Bulgaria Israel Morocco Romania Turkey United States:7 and Rest of the World:8; EU-15 as importer;
? Eliminating zero values in Q; Q1=1*(Q1=0)+Q1*(Q1>0); Q5=1*(Q5=0)+Q5*(Q5>0); Q6=1*(Q6=0)+Q6*(Q6>0); PRINT ZYRS Q1 Q5 Q6; ? Adding USA with ROW; v7=v7+v8; q7=q7+q8; print v7 q7; ? Eliminating Pi=0; ?? [Following highest price+twice the Std.Dev.+inflation]; SELECT ZYRS=1995; V1=2.82813; SELECT ZYRS=1997; V1=2.86838; SELECT ZYRS=1998; V1=2.88851; SELECT ZYRS=1999; V1=2.90863; SELECT ZYRS=2005; V1=3.02940; SELECT ZYRS=1999; V5=1.74572; SELECT ZYRS=2000; V5=1.76601; SELECT ZYRS=1964; V6=1.05760; SELECT ZYRS=1965; V6=1.08666; SELECT ZYRS=1967; V6=1.14477;
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SELECT ZYRS=1968; V6=1.17383; SELECT ZYRS=1969; V6=1.20289; SELECT ZYRS=1971; V6=1.26101; SELECT ZYRS=1973; V6=1.31912; ? To find out Average and Annual Costs for making Table; smpl 2,43; msd v1-v7; smpl 2,2; msd v1-v7; print v1-v7; smpl 43,43; msd v1-v7; print v1-v7; ? Calculation to find out Average and Annual Import Quantity (kg) for making Table; smpl 2,43; msd q1-q7; smpl 2,2; msd q1-q7; print q1-q7; smpl 43,43; msd q1-q7; print q1-q7; ? End of calculation for Table; SMPL 1,43; ? Defining Total Cost(S); S=V1+V2+V3+V4+V5+V6+V7; ? Calculating prices (Pi) P1=V1/Q1; P2=V2/Q2; P3=V3/Q3; P4=V4/Q4; P5=V5/Q5; P6=V6/Q6; P7=V7/Q7; PRINT ZYRS Q1 P1 Q2 P2 Q3 P3 Q4 P4 Q5 P5 Q6 P6 q7 p7; ? Calculation to find Average ans Annual Price (US$/Kg) for making Table; smpl 2,43; msd p1-p7; smpl 2,2; msd p1-p7; print p1-p7; smpl 43,43; msd p1-p7; ? End of Calculation for Table; SMPL 1,43; ? CALCULATION OF FACTOR COST SHARES (Fi=PRICE*QUANTITY/TOTAL COST) F1=V1/S; F2=V2/S; F3=V3/S; F4=V4/S; F5=V5/S; F6=V6/S; F7=V7/S; ? LOGGING ALL PRICES AND QUANTITIES(LPi,LQi) LP1=LOG(P1); LP2=LOG(P2); LP3=LOG(P3); LP4=LOG(P4); LP5=LOG(P5); LP6=LOG(P6); LP7=LOG(P7); LQ1=LOG(Q1); LQ2=LOG(Q2); LQ3=LOG(Q3); LQ4=LOG(Q4); LQ5=LOG(Q5); LQ6=LOG(Q6); LQ7=LOG(Q7);
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smpl 2 43; ? CALCULATION FOR TWO PERIOD MEAN OF FACTOR SHARES( Fi1) F11=(F1+F1(-1))/2; F21=(F2+F2(-1))/2; F31=(F3+F3(-1))/2; F41=(F4+F4(-1))/2; F51=(F5+F5(-1))/2; F61=(F6+F6(-1))/2; F71=(F7+F7(-1))/2; ? Calculation of Quantity Share for making Table; T=q1+q2+q3+q4+q5+q6+q7; k1=q1/T; k2=q2/T; k3=q3/T; k4=q4/T; k5=q5/T; k6=q6/T; k7=q7/T; msd k1-k7; smpl 2,2; msd k1-k7; smpl 43,43; msd k1-k7; ? End of Quantity Share calculation; SMPL 2,43; ? CALCULATION: CHANGE IN LOGGED PRICES(DPi) DP1=LP1-LP1(-1); DP2=LP2-LP2(-1); DP3=LP3-LP3(-1); DP4=LP4-LP4(-1); DP5=LP5-LP5(-1); DP6=LP6-LP6(-1); DP7=LP7-LP7(-1); ? CALCULATION:CHANGE IN LOGGED QUANTITY(DQi) DQ1=LQ1-LQ1(-1); DQ2=LQ2-LQ2(-1); DQ3=LQ3-LQ3(-1); DQ4=LQ4-LQ4(-1); DQ5=LQ5-LQ5(-1); DQ6=LQ6-LQ6(-1); DQ7=LQ7-LQ7(-1); ? DEPENDENT VARIABLE fi*Dq and SUMMATION INDEX(FDQi) FDQ1=F11*DQ1; FDQ2=F21*DQ2; FDQ3=F31*DQ3; FDQ4=F41*DQ4; FDQ5=F51*DQ5; FDQ6=F61*DQ6; FDQ7=F71*DQ7; DQ=FDQ1+FDQ2+FDQ3+FDQ4+FDQ5+FDQ6+FDQ7; ?Fi*DP and SUMMATION INDEX(DP)- NOT NEEDED FOR THIS MODEL; FDP1=F11*DP1; FDP2=F21*DP2; FDP3=F31*DP3; FDP4=F41*DP4; FDP5=F51*DP5; FDP6=F61*DP6; FDP7=F71*DP7; DP=FDP1+FDP2+FDP3+FDP4+FDP5+FDP6+FDP7; SMPL 2, 43; ? DIFFEREENTIAL NBR MODEL WITH AR1 PLUS HOMOGENEITY AND SYMMETRY; trend obs; d1 = (obs=1); frml res1 FDQ1=(A1*DQ+B11*DP1+B12*DP2+B13*DP3+B14*DP4+B15*DP5+B16*DP6+(-B11-B12-B13-B14-B15B16)*DP7-F11*(DP1-DP)); ?frml eq1 [d1*res1*sqrt(1-rho**2) + (1-d1)*(res1 - rho*res1(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res2 FDQ2=(A2*DQ+B12*DP1+B22*DP2+B23*DP3+B24*DP4+B25*DP5+B26*DP6+(-B12-B22-B23-B24-B25B26)*DP7-F21*(DP2-DP)); ?frml eq2 [d1*res2*sqrt(1-rho**2) + (1-d1)*(res2 - rho*res2(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res3 FDQ3=(A3*DQ+B13*DP1+B23*DP2+B33*DP3+B34*DP4+B35*DP5+B36*DP6+(-B13-B23-B33-B34-B35B36)*DP7-F31*(DP3-DP)); ?frml eq3 [d1*res3*sqrt(1-rho**2) + (1-d1)*(res3 - rho*res3(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res4 FDQ4=(A4*DQ+B14*DP1+B24*DP2+B34*DP3+B44*DP4+B45*DP5+B46*DP6+(-B14-B24-B34-B44-B45B46)*DP7-F41*(DP4-DP)); ?frml eq4 [d1*res4*sqrt(1-rho**2) + (1-d1)*(res4 - rho*res4(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs;
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d1 = (obs=1); frml res5 FDQ5=(A5*DQ+B15*DP1+B25*DP2+B35*DP3+B45*DP4+B55*DP5+B56*DP6+(-B15-B25-B35-B45-B55B56)*DP7-F51*(DP5-DP)); ?frml eq5 [d1*res5*sqrt(1-rho**2) + (1-d1)*(res5 - rho*res5(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res6 FDQ6=(A6*DQ+B16*DP1+B26*DP2+B36*DP3+B46*DP4+B56*DP5+B66*DP6+(-B16-B26-B36-B46-B56B66)*DP7-F61*(DP6-DP)); ?frml eq6 [d1*res6*sqrt(1-rho**2) + (1-d1)*(res6 - rho*res6(-1))]*(1-rho**2)**(-1/(2*@nob)); REGOPT (STARS,STAR1=.10,STAR2=.05) T; PARAM A1 0 A2 0 A3 0 A4 0 A5 0 A6 0 B11 0 B12 0 B13 0 B14 0 B15 0 B16 0 B22 0 B23 0 B24 0 B25 0 B26 0 B33 0 B34 0 B35 0 B36 0 B44 0 B45 0 B46 0 B55 0 B56 0 B66 0; ?rho 0; ?eqsub eq1 res1;?eqsub eq2 res2;?eqsub eq3 res3;?eqsub eq4 res4;?eqsub eq5 res5;?eqsub eq6 res6; ?lsq(nodropmiss,tol=1e-7,maxit=1000) eq1 eq2 eq3 eq4 eq5 eq6; lsq(nodropmiss,tol=1e-7,maxit=1000) res1 res2 res3 res4 res5 res6; COPY @LOGL LU; LU1=LU; SMPL 2, 43; ? Elasticities; MSD F11 F21 F31 F41 F51 F61 F71; ?================= MEAN FACTOR SHARES SET MF1=@MEAN(1); SET MF2=@MEAN(2); SET MF3=@MEAN(3); SET MF4=@MEAN(4); SET MF5=@MEAN(5); SET MF6=@MEAN(6); SET MF7=@MEAN(7); PRINT MF1-MF7; SMPL 2,2; MSD F1 F2 F3 F4 F5 F6 F7; ?================= MEAN FACTOR SHARES SET FF1=@MEAN(1); SET FF2=@MEAN(2); SET FF3=@MEAN(3); SET FF4=@MEAN(4); SET FF5=@MEAN(5); SET FF6=@MEAN(6); SET FF7=@MEAN(7); PRINT FF1-FF7; SMPL 43,43; MSD F1 F2 F3 F4 F5 F6 F7; ?================= MEAN FACTOR SHARES SET FL1=@MEAN(1); SET FL2=@MEAN(2); SET FL3=@MEAN(3); SET FL4=@MEAN(4); SET FL5=@MEAN(5);
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SET FL6=@MEAN(6); SET FL7=@MEAN(7); PRINT FL1-FL7; SMPL 2, 43; SET B17=-B11-B12-B13-B14-B15-B16; SET B21=B12; SET B27=-B21-B22-B23-B24-B25-B26; SET B31=B13; SET B32=B23; SET B37=-B31-B32-B33-B34-B35-B36; SET SET SET SET
B41=B14; B42=B24; B43=B34; B47=-B41-B42-B43-B44-B45-B46;
SET SET SET SET SET
B51=B15; B52=B25; B53=B35; B54=B45; B57=-B51-B52-B53-B54-B55-B56;
SET SET SET SET SET SET
B61=B16; B62=B26; B63=B36; B64=B46; B65=B56; B67=-B61-B62-B63-B64-B65-B66;
SET B77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)-(-B14B24-B34-B44-B45-B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)); SET A7=1-A1-A2-A3-A4-A5-A6; ? Calculate the standard errors for ROW frml row1 A7=1-A1-A2-A3-A4-A5-A6; frml row2 B17=-B11-B12-B13-B14-B15-B16; frml row3 B27=-B21-B22-B23-B24-B25-B26; frml row4 B37=-B31-B32-B33-B34-B35-B36; frml row5 B47=-B41-B42-B43-B44-B45-B46; frml row6 B57=-B51-B52-B53-B54-B55-B56; frml row7 B67=-B61-B62-B63-B64-B65-B66; frml row8 B77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)(-B14-B24-B34-B44-B45-B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)); frml frml frml frml frml frml frml frml frml frml frml frml frml frml frml
row9 B21=B12; row10 B31=B13; row11 B32=B23; row12 B41=B14; row13 B42=B24; row14 B43=B34; row15 B51=B15; row16 B52=B25; row17 B53=B35; row18 B54=B45; row19 B61=B16; row20 B62=B26; row21 B63=B36; row22 B64=B46; row23 B65=B56;
analyz row1-row23;
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?? Calculate Eigenvalues SET SET SET SET SET SET SET
B71=B17; B72=B27; B73=B37; B74=B47; B75=B57; B76=B67; B77=B77;
? Tranform r to Pie; SET SET SET SET SET SET SET
D11=(B11-MF1+MF1*MF1); D12=(B12+MF1*MF2); D13=(B13+MF1*MF3); D14=(B14+MF1*MF4); D15=(B15+MF1*MF5); D16=(B16+MF1*MF6); D17=(-B11-B12-B13-B14-B15-B16+MF1*MF7);
SET SET SET SET SET SET SET
D21=(B12+MF2*MF1); D22=(B22-MF2+MF2*MF2); D23=(B23+MF2*MF3); D24=(B24+MF2*MF4); D25=(B25+MF2*MF5); D26=(B26+MF2*MF6); D27=(-B12-B22-B23-B24-B25-B26+MF2*MF7);
SET SET SET SET SET SET SET
D31=(B13+MF3*MF1); D32=(B23+MF3*MF2); D33=(B33-MF3+MF3*MF3); D34=(B34+MF3*MF4); D35=(B35+MF3*MF5); D36=(B36+MF3*MF6); D37=(-B13-B23-B33-B34-B35-B36+MF3*MF7);
SET SET SET SET SET SET SET
D41=(B14+MF4*MF1); D42=(B24+MF4*MF2); D43=(B34+MF4*MF3); D44=(B44-MF4+MF4*MF4); D45=(B45+MF4*MF5); D46=(B46+MF4*MF6); D47=(-B14-B24-B34-B44-B45-B46+MF4*MF7);
SET SET SET SET SET SET SET
D51=(B15+MF5*MF1); D52=(B25+MF5*MF2); D53=(B35+MF5*MF3); D54=(B45+MF5*MF4); D55=(B55-MF5+MF5*MF5); D56=(B56+MF5*MF6); D57=(-B15-B25-B35-B45-B55-B56+MF5*MF7);
SET SET SET SET SET SET SET
D61=(B16+MF6*MF1); D62=(B26+MF6*MF2); D63=(B36+MF6*MF3); D64=(B46+MF6*MF4); D65=(B56+MF6*MF5); D66=(B66-MF6+MF6*MF6); D67=(-B16-B26-B36-B46-B56-B66+MF6*MF7);
SET D71=(-B11-B12-B13-B14-B15-B16+MF7*MF1); SET D72=(-B12-B22-B23-B24-B25-B26+MF7*MF2); SET D73=(-B13-B23-B33-B34-B35-B36+MF7*MF3); SET D74=(-B14-B24-B34-B44-B45-B46+MF7*MF4); SET D75=(-B15-B25-B35-B45-B55-B56+MF7*MF5); SET D76=(-B16-B26-B36-B46-B56-B66+MF7*MF6); SET D77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)-(-B14B24-B34-B44-B45-B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)-MF7+MF7*MF7); ? Create each row EIGHT;
125
MMAKE(VERT) MMAKE(VERT) MMAKE(VERT) MMAKE(VERT) MMAKE(VERT) MMAKE(VERT) MMAKE(VERT)
E1 E2 E3 E4 E5 E6 E7
D11-D17; D21-D27; D31-D37; D41-D47; D51-D57; D61-D67; D71-D77;
? Creates square matrix MMAKE E E1-E7; ? Calculate Eigenvalues of E MAT EV = EIGVAL(E); Print E EV; ? Creates standard errors for pi ij's where the pi ij's are D11, D12, etc; frml frml frml frml frml frml frml
pi1 pi2 pi3 pi4 pi5 pi6 pi7
D11=(B11-MF1+MF1*MF1); D12=(B12+MF1*MF2); D13=(B13+MF1*MF3); D14=(B14+MF1*MF4); D15=(B15+MF1*MF5); D16=(B16+MF1*MF6); D17=(-B11-B12-B13-B14-B15-B16+MF1*MF7);
frml frml frml frml frml frml frml
pi8 D21=(B12+MF2*MF1); pi9 D22=(B22-MF2+MF2*MF2); pi10 D23=(B23+MF2*MF3); pi11 D24=(B24+MF2*MF4); pi12 D25=(B25+MF2*MF5); pi13 D26=(B26+MF2*MF6); pi14 D27=(-B12-B22-B23-B24-B25-B26+MF2*MF7);
frml frml frml frml frml frml frml
pi15 pi16 pi17 pi18 pi19 pi20 pi21
D31=(B13+MF3*MF1); D32=(B23+MF3*MF2); D33=(B33-MF3+MF3*MF3); D34=(B34+MF3*MF4); D35=(B35+MF3*MF5); D36=(B36+MF3*MF6); D37=(-B13-B23-B33-B34-B35-B36+MF3*MF7);
frml frml frml frml frml frml frml
pi22 pi23 pi24 pi25 pi26 pi27 pi28
D41=(B14+MF4*MF1); D42=(B24+MF4*MF2); D43=(B34+MF4*MF3); D44=(B44-MF4+MF4*MF4); D45=(B45+MF4*MF5); D46=(B46+MF4*MF6); D47=(-B14-B24-B34-B44-B45-B46+MF4*MF7);
frml frml frml frml frml frml frml
pi29 pi30 pi31 pi32 pi33 pi34 pi35
D51=(B15+MF5*MF1); D52=(B25+MF5*MF2); D53=(B35+MF5*MF3); D54=(B45+MF5*MF4); D55=(B55-MF5+MF5*MF5); D56=(B56+MF5*MF6); D57=(-B15-B25-B35-B45-B55-B56+MF5*MF7);
frml frml frml frml frml frml frml
pi36 pi37 pi38 pi39 pi40 pi41 pi42
D61=(B16+MF6*MF1); D62=(B26+MF6*MF2); D63=(B36+MF6*MF3); D64=(B46+MF6*MF4); D65=(B56+MF6*MF5); D66=(B66-MF6+MF6*MF6); D67=(-B16-B26-B36-B46-B56-B66+MF6*MF7);
frml pi43 D71=(-B11-B12-B13-B14-B15-B16+MF7*MF1); frml pi44 D72=(-B12-B22-B23-B24-B25-B26+MF7*MF2); frml pi45 D73=(-B13-B23-B33-B34-B35-B36+MF7*MF3);
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frml pi46 D74=(-B14-B24-B34-B44-B45-B46+MF7*MF4); frml pi47 D75=(-B15-B25-B35-B45-B55-B56+MF7*MF5); frml pi48 D76=(-B16-B26-B36-B46-B56-B66+MF7*MF6); frml pi49 D77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)(-B14-B24-B34-B44-B45-B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)-MF7+MF7*MF7); analyz pi1-pi49; ? Elasticities ? Divisia Input Index FRML EL1 E1=A1/MF1; FRML EL2 E2=A2/MF2; FRML EL3 E3=A3/MF3; FRML EL4 E4=A4/MF4; FRML EL5 E5=A5/MF5; FRML EL6 E6=A6/MF6; FRML EL7 E7=(1-A1-A2-A3-A4-A5-A6)/MF7; ? Divisia Input Index WITH FIRST F FRML EL8 EF1=A1/FF1; FRML EL9 EF2=A2/FF2; FRML EL10 EF3=A3/FF3; FRML EL11 EF4=A4/FF4; FRML EL12 EF5=A5/FF5; FRML EL13 EF6=A6/FF6; FRML EL14 EF7=(1-A1-A2-A3-A4-A5-A6)/FF7; ? Divisia FRML EL15 FRML EL16 FRML EL17 FRML EL18 FRML EL19 FRML EL20 FRML EL21
Input Index WITH LAST F EL1=A1/FL1; EL2=A2/FL2; EL3=A3/FL3; EL4=A4/FL4; EL5=A5/FL5; EL6=A6/FL6; EL7=(1-A1-A2-A3-A4-A5-A6)/FL7;
? Compensated price elasticities FRML FRML FRML FRML FRML FRML FRML
EP11 EP12 EP13 EP14 EP15 EP16 EP17
E11=(B11-MF1+MF1*MF1)/MF1; E12=(B12+MF1*MF2)/MF1; E13=(B13+MF1*MF3)/MF1; E14=(B14+MF1*MF4)/MF1; E15=(B15+MF1*MF5)/MF1; E16=(B16+MF1*MF6)/MF1; E17=(-B11-B12-B13-B14-B15-B16+MF1*MF7)/MF1;
FRML FRML FRML FRML FRML FRML FRML
EP21 EP22 EP23 EP24 EP25 EP26 EP27
E21=(B12+MF2*MF1)/MF2; E22=(B22-MF2+MF2*MF2)/MF2; E23=(B23+MF2*MF3)/MF2; E24=(B24+MF2*MF4)/MF2; E25=(B25+MF2*MF5)/MF2; E26=(B26+MF2*MF6)/MF2; E27=(-B12-B22-B23-B24-B25-B26+MF2*MF7)/MF2;
FRML FRML FRML FRML FRML FRML FRML
EP31 EP32 EP33 EP34 EP35 EP36 EP37
E31=(B13+MF3*MF1)/MF3; E32=(B23+MF3*MF2)/MF3; E33=(B33-MF3+MF3*MF3)/MF3; E34=(B34+MF3*MF4)/MF3; E35=(B35+MF3*MF5)/MF3; E36=(B36+MF3*MF6)/MF3; E37=(-B13-B23-B33-B34-B35-B36+MF3*MF7)/MF3;
FRML FRML FRML FRML FRML FRML FRML
EP41 EP42 EP43 EP44 EP45 EP46 EP47
E41=(B14+MF4*MF1)/MF4; E42=(B24+MF4*MF2)/MF4; E43=(B34+MF4*MF3)/MF4; E44=(B44-MF4+MF4*MF4)/MF4; E45=(B45+MF4*MF5)/MF4; E46=(B46+MF4*MF6)/MF4; E47=(-B14-B24-B34-B44-B45-B46+MF4*MF7)/MF4;
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FRML FRML FRML FRML FRML FRML FRML
EP51 EP52 EP53 EP54 EP55 EP56 EP57
E51=(B15+MF5*MF1)/MF5; E52=(B25+MF5*MF2)/MF5; E53=(B35+MF5*MF3)/MF5; E54=(B45+MF5*MF4)/MF5; E55=(B55-MF5+MF5*MF5)/MF5; E56=(B56+MF5*MF6)/MF5; E57=(-B15-B25-B35-B45-B55-B56+MF5*MF7)/MF5;
FRML FRML FRML FRML FRML FRML FRML
EP61 EP62 EP63 EP64 EP65 EP66 EP67
E61=(B16+MF6*MF1)/MF6; E62=(B26+MF6*MF2)/MF6; E63=(B36+MF6*MF3)/MF6; E64=(B46+MF6*MF4)/MF6; E65=(B56+MF6*MF5)/MF6; E66=(B66-MF6+MF6*MF6)/MF6; E67=(-B16-B26-B36-B46-B56-B66+MF6*MF7)/MF6;
FRML EP71 E71=(-B11-B12-B13-B14-B15-B16+MF7*MF1)/MF7; FRML EP72 E72=(-B12-B22-B23-B24-B25-B26+MF7*MF2)/MF7; FRML EP73 E73=(-B13-B23-B33-B34-B35-B36+MF7*MF3)/MF7; FRML EP74 E74=(-B14-B24-B34-B44-B45-B46+MF7*MF4)/MF7; FRML EP75 E75=(-B15-B25-B35-B45-B55-B56+MF7*MF5)/MF7; FRML EP76 E76=(-B16-B26-B36-B46-B56-B66+MF7*MF6)/MF7; FRML EP77 E77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)(-B14-B24-B34-B44-B45-B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)-MF7+MF7*MF7)/MF7; ANALYZ ANALYZ ANALYZ ANALYZ ANALYZ ANALYZ ANALYZ ANALYZ
EL1-EL21; EP11-EP17; EP21-EP27; EP31-EP37; EP41-EP47; EP51-EP57; EP61-EP67; EP71-EP77;
PRINT; smpl 2,2; print LU; ?mark significant variables with STARS; REGOPT (STARS,STAR1=.10,STAR2=.05,) T; END;
EU-15 NBR Simulation Model OPTIONS MEMORY=1500 Double; ? EU15_02NBR-NEW2007SELECTED-RECW Models for EU Import Analysis without USA with all calculations; TITLE 'TOMATO IMPORTS TO THE US'; ? For Elasticity Trend over 11 years & Calculating Mean Quantity for sample 2,33; ? NBR Model with Homogeneity and Symmetry imposed without Rho (since Rho=-0.094410 with P value 0.163 & LU1=689.03834)& LU2=688.35849; smpl 1 43; ?READ(FORMAT=EXCEL,FILE='U:\TomatoResearch\TSPWORKS2006\EUAnalysis\EUonly.xls'); LOAD ZYRS ZIMP V1 Q1 V2 Q2 V3 Q3 V4 Q4 V5 Q5 V6 Q6 V7 Q7 V8 Q8; 1963 901 31653 451074 1773563 16782212 18133 40123 26567148 122325848 1004321 9072714 7000 72000 3240 12187 3376225 19971241 1964 901 48038 572000 1840474 12660747 1262 3312 31730108 118009256 1361401 10570330 0 0 2419 6437 2737208 13016627 1965 901 118653 1108312 2220545 15148287 5152 5562 27267956 125699712 1928476 15228634 0 0 17404 53152 1795230 12036480 1966 901 187269 1748000 2856091 13152661 85829 107862 36479432 108006936 2691155 19047720 1000 12812 11245 21812 2539638 10580398
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1967 901 207999 2220125 3753435 18649844 46886 118310 36637392 122262104 2789153 18614500 0 0 69348 154932 2665245 13813254 1968 901 310461 2266000 4405008 19895024 26510 101198 27803468 97863480 5120585 33277424 0 0 74419 93022 1488195 7481394 1969 901 368538 2496687 3916124 14940986 32359 99740 36980408 129603024 7855349 34033604 0 0 128959 220245 3636690 12882177 1970 901 457730 2397937 4464447 15889571 40904 68278 38635412 133623216 9460210 42568288 3115 40398 260188 308561 11442442 37441791 1971 901 469036 2752398 4245967 16817272 64882 136795 44930860 129688160 14373836 59700256 0 0 284716 335143 4986064 14826093 1972 901 962086 4625350 4017254 16139896 35034 42506 45938032 118869120 15097659 63092032 1550 1875 284469 401349 7784385 19256671 1973 901 1594265 4437519 4893273 14262623 36545 29147 77101920 170786640 19292240 54257208 0 0 657057 745654 976072 1966077 1974 901 1797788 5708053 5692533 15417826 216473 219126 65580600 138533712 15978113 43303736 6326 42800 108407 82604 1433878 2602306 1975 901 3158736 7143835 7033987 15033790 731299 1000174 99121944 137464352 15771246 39263124 33343 187800 41024 42096 1391526 2230043 1976 901 2968861 7003612 5147297 12926526 1831054 3315306 75478176 106260064 13685706 37747484 4957 17625 196696 132987 2215727 4062108 1977 901 3472400 9189788 7425601 15885014 2325006 4158786 82794408 115851376 9554171 25682334 1000 1687 53600 51748 2066804 3061723 1978 901 2963215 6163585 7430996 14492037 2309641 3208973 85231920 104367608 9191896 21285690 37511 104073 200784 202229 2231462 2797116 1979 901 4026272 6798812 7907311 16267033 2373524 2974927 93011048 104508152 9071943 19847036 44832 82886 196614 141842 1673201 1711795 1980 901 6052384 10362511 4767464 11321398 2157749 1940617 87930720 91080208 11919843 23267114 102946 122824 867395 513303 2614841 2395847 1981 901 5573419 10825753 4173807 10542792 1422141 1240105 74939560 89919392 6717752 15562404 115808 164500 246247 303185 2178646 2958982 1982 901 6942520 16861542 2793814 7765386 1335471 1713708 50565584 66672692 6240809 14409339 89026 207127 39146 36069 1739339 3025668 1983 901 5955306 13127198 3990447 10570612 635025 665686 48541384 67457464 7539437 20009412 74331 144311 69812 82299 1714422 3349194 1984 901 4628415 11485112 2225929 6696144 1818868 2723827 49903220 82007208 8647271 24582260 410328 781058 73121 98443 1755933 3507856 1985 901 3714979 9679074 2804760 8574710 1519295 2329586 56146208 91701904 4742369 15723088 140775 329186 66289 88741 1109962 2356596 1986 901 4428861 9652574 2080354 5348562 2521897 2659235 68524448 96462176 4144346 11844698 670611 1127182 84403 88221 1740140 2880545 1987 901 4756993 9699476 2978113 6105456 2280814 2929812 87123544 97076016 5764089 12027178 2554835 3132693 141317 109611 2877196 3757298 1988 901 5344652 8643190 2402380 4767624 4903546 3937171 76347792 84892376 6708963 14960272 2264643 2524775 349851 243009 4564090 5078631 1989 901 4125968 6758386 2317410 5286987 3193985 3638453 71171816 97750632 7488692 16598397 2450896 3062926 1633335 864997 3588237 4834089 1990 901 7360551 11020187 3029963 5708198 10650899 8021161 130990440 110714248 2765811 5380596 5190490 4332286 1125452 702779 6934463 5863059 1991 901 1869942 2294788 5032627 8084701 8374074 6277594 145453872 140390832 3665304 6377014 5308010 5725206 2509599 1876646 5001624 4620865 1992 901 404674 585339 3651196 5088920 6577894 5570072 139864960 141403616 3295008 5192788 6377826 7713368 391317 410689 5869919 5966114 1993 901 116900 270875 1710821 2183913 5634468 5223672 143160640 177926880 2223115 3715382 3718712 4547761 188735 224006 4278326 4454055 1994 901 43000 47199 357690 560199 5986108 5533320 120315416 160862048 1217387 2056625 4114383 5180666 155184 156425 3399291 3484049 1995 901 0 0 29111 43369 11579928 6364214 147584576 146905040 125053 151773 2661260 2334571 308488 239044 5825043 4559700 1996 901 24187 11375 183522 69726 17264544 9271430 148078032 157396080 230793 297000 4508979 3476803 38016 20788 5271388 3221124 1997 901 0 0 15124 21386 20697980 10657880 104872824 154990608 38161 46226 1020557 927674 82651 103135 7566921 5781611 1998 901 0 0 22636 30788 22782924 12299150 147687616 186837792 29637 48398 905471 869349 92865 72220 7331996 5544938 1999 901 0 0 60193 71125 22791080 14885635 141139536 206332992 0 0 2285333 2621314 205003 163351 5596276 5080246 2000 901 10448 18000 54910 66112 23066744 16460790 117918632 149369664 0 0 10910094 11328141 39582 24734 12195800 10873083 2001 901 16528 57300 9909 16625 21346768 17480612 108504040 185144192 22387 33500 6927946 9118854 10763 9212 10767377 11338870
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2002 901 61870 101898 37526 55663 21751194 14590805 170802208 181180384 4604 3625 16571994 18724980 21009 14917 12378914 12102489 2003 901 22075 26453 206498 198835 24412648 16800316 136954944 182067392 43642 46710 26240464 25322332 21415 17437 29699618 29466621 2004 901 150833 169081 84115 84338 31703530 18551426 172314848 192159904 190675 188753 19238032 17210976 12976 6761 27974391 29547420 2005 901 0 0 20624 19526 44735840 25201496 229945104 232239648 35735 37440 23119076 19664766 43605 31100 61700006 54335924 ? V: value in (not million) US dollars; Q: quantity in (not million) kilograms; ? 1: Albania ? 2: Bulgaria ? 3: Israel ? 4: Morocco ? 5: Romania ? 6: Turkey ? 7: United States:7 and Rest of the World:8; ?901 EU-15 as importer; ? Eliminating zero values in Q; Q1=1*(Q1=0)+Q1*(Q1>0); Q5=1*(Q5=0)+Q5*(Q5>0); Q6=1*(Q6=0)+Q6*(Q6>0); PRINT ZYRS Q1 Q5 Q6; ? Adding USA with ROW; v7=v7+v8; q7=q7+q8; print v7 q7; ? Eliminating Pi=0; ?? [Following highest price+twice the Std.Dev.+inflation]; SELECT ZYRS=1995; V1=2.82813; SELECT ZYRS=1997; V1=2.86838; SELECT ZYRS=1998; V1=2.88851; SELECT ZYRS=1999; V1=2.90863; SELECT ZYRS=2005; V1=3.02940; SELECT ZYRS=1999; V5=1.74572; SELECT ZYRS=2000; V5=1.76601; SELECT ZYRS=1964; V6=1.05760; SELECT ZYRS=1965; V6=1.08666; SELECT ZYRS=1967; V6=1.14477; SELECT ZYRS=1968; V6=1.17383; SELECT ZYRS=1969; V6=1.20289; SELECT ZYRS=1971; V6=1.26101; SELECT ZYRS=1973; V6=1.31912; ? To find out Average and Annual Costs for making Table; smpl 2,43; msd v1-v7; smpl 2,2; msd v1-v7;
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print v1-v7; smpl 43,43; msd v1-v7; print v1-v7; ? Calculation to find out Average and Annual Import Quantity (kg) for making Table; smpl 2,43; msd q1-q7; smpl 2,2; msd q1-q7; print q1-q7; smpl 43,43; msd q1-q7; print q1-q7; ? End of calculation for Table; SMPL 1,43; ? Defining Total Cost(S); S=V1+V2+V3+V4+V5+V6+V7; ? Calculating prices (Pi) P1=V1/Q1; P2=V2/Q2; P3=V3/Q3; P4=V4/Q4; P5=V5/Q5; P6=V6/Q6; P7=V7/Q7; PRINT ZYRS Q1 P1 Q2 P2 Q3 P3 Q4 P4 Q5 P5 Q6 P6 q7 p7; ? Calculation to find Average ans Annual Price (US$/Kg) for making Table; smpl 2,43; msd p1-p7; smpl 2,2; msd p1-p7; print p1-p7; smpl 43,43; msd p1-p7; ? End of Calculation for Table; SMPL 1,43; ? CALCULATION OF FACTOR COST SHARES (Fi=PRICE*QUANTITY/TOTAL COST) F1=V1/S; F2=V2/S; F3=V3/S; F4=V4/S; F5=V5/S; F6=V6/S; F7=V7/S; ? LOGGING ALL PRICES AND QUANTITIES(LPi,LQi) LP1=LOG(P1); LP2=LOG(P2); LP3=LOG(P3); LP4=LOG(P4); LP5=LOG(P5); LP6=LOG(P6); LP7=LOG(P7); LQ1=LOG(Q1); LQ2=LOG(Q2); LQ3=LOG(Q3); LQ4=LOG(Q4); LQ5=LOG(Q5); LQ6=LOG(Q6); LQ7=LOG(Q7); smpl 2 43; ? CALCULATION FOR TWO PERIOD MEAN OF FACTOR SHARES( Fi1) F11=(F1+F1(-1))/2; F21=(F2+F2(-1))/2; F31=(F3+F3(-1))/2; F41=(F4+F4(-1))/2; F51=(F5+F5(-1))/2; F61=(F6+F6(-1))/2; F71=(F7+F7(-1))/2; ? Calculation of Quantity Share for making Table; T=q1+q2+q3+q4+q5+q6+q7; k1=q1/T; k2=q2/T; k3=q3/T; k4=q4/T; k5=q5/T; k6=q6/T; k7=q7/T; msd k1-k7; smpl 2,2;
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msd k1-k7; smpl 43,43; msd k1-k7; ? End of Quantity Share calculation; smpl 2,33; msd q1-q7; msd T; SMPL 2,43; ? CALCULATION: CHANGE IN LOGGED PRICES(DPi) DP1=LP1-LP1(-1); DP2=LP2-LP2(-1); DP3=LP3-LP3(-1); DP4=LP4-LP4(-1); DP5=LP5-LP5(-1); DP6=LP6-LP6(-1); DP7=LP7-LP7(-1); ? CALCULATION:CHANGE IN LOGGED QUANTITY(DQi) DQ1=LQ1-LQ1(-1); DQ2=LQ2-LQ2(-1); DQ3=LQ3-LQ3(-1); DQ4=LQ4-LQ4(-1); DQ5=LQ5-LQ5(-1); DQ6=LQ6-LQ6(-1); DQ7=LQ7-LQ7(-1); ? DEPENDENT VARIABLE fi*Dq and SUMMATION INDEX(FDQi) FDQ1=F11*DQ1; FDQ2=F21*DQ2; FDQ3=F31*DQ3; FDQ4=F41*DQ4; FDQ5=F51*DQ5; FDQ6=F61*DQ6; FDQ7=F71*DQ7; DQ=FDQ1+FDQ2+FDQ3+FDQ4+FDQ5+FDQ6+FDQ7; ?Fi*DP and SUMMATION INDEX(DP)- NOT NEEDED FOR THIS MODEL; FDP1=F11*DP1; FDP2=F21*DP2; FDP3=F31*DP3; FDP4=F41*DP4; FDP5=F51*DP5; FDP6=F61*DP6; FDP7=F71*DP7; DP=FDP1+FDP2+FDP3+FDP4+FDP5+FDP6+FDP7; proc zzzz; ? DIFFEREENTIAL NBR MODEL WITH AR1 PLUS HOMOGENEITY AND SYMMETRY; trend obs; d1 = (obs=1); frml res1 FDQ1=(A1*DQ+B11*DP1+B12*DP2+B13*DP3+B14*DP4+B15*DP5+B16*DP6+(-B11-B12-B13-B14-B15-B16)*DP7-F11*(DP1DP)); ?frml eq1 [d1*res1*sqrt(1-rho**2) + (1-d1)*(res1 - rho*res1(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res2 FDQ2=(A2*DQ+B12*DP1+B22*DP2+B23*DP3+B24*DP4+B25*DP5+B26*DP6+(-B12-B22-B23-B24-B25-B26)*DP7-F21*(DP2DP)); ?frml eq2 [d1*res2*sqrt(1-rho**2) + (1-d1)*(res2 - rho*res2(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res3 FDQ3=(A3*DQ+B13*DP1+B23*DP2+B33*DP3+B34*DP4+B35*DP5+B36*DP6+(-B13-B23-B33-B34-B35-B36)*DP7-F31*(DP3DP)); ?frml eq3 [d1*res3*sqrt(1-rho**2) + (1-d1)*(res3 - rho*res3(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res4 FDQ4=(A4*DQ+B14*DP1+B24*DP2+B34*DP3+B44*DP4+B45*DP5+B46*DP6+(-B14-B24-B34-B44-B45-B46)*DP7-F41*(DP4DP)); ?frml eq4 [d1*res4*sqrt(1-rho**2) + (1-d1)*(res4 - rho*res4(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1); frml res5 FDQ5=(A5*DQ+B15*DP1+B25*DP2+B35*DP3+B45*DP4+B55*DP5+B56*DP6+(-B15-B25-B35-B45-B55-B56)*DP7-F51*(DP5DP)); ?frml eq5 [d1*res5*sqrt(1-rho**2) + (1-d1)*(res5 - rho*res5(-1))]*(1-rho**2)**(-1/(2*@nob)); trend obs; d1 = (obs=1);
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frml res6 FDQ6=(A6*DQ+B16*DP1+B26*DP2+B36*DP3+B46*DP4+B56*DP5+B66*DP6+(-B16-B26-B36-B46-B56-B66)*DP7-F61*(DP6DP)); ?frml eq6 [d1*res6*sqrt(1-rho**2) + (1-d1)*(res6 - rho*res6(-1))]*(1-rho**2)**(-1/(2*@nob)); REGOPT (STARS,STAR1=.10,STAR2=.05) T; PARAM A1 0 A2 0 A3 0 A4 0 A5 0 A6 0 B11 0 B12 0 B13 0 B14 0 B15 0 B16 0 B22 0 B23 0 B24 0 B25 0 B26 0 B33 0 B34 0 B35 0 B36 0 B44 0 B45 0 B46 0 B55 0 B56 0 B66 0; ?rho 0; ?eqsub eq1 res1;?eqsub eq2 res2;?eqsub eq3 res3;?eqsub eq4 res4;?eqsub eq5 res5;?eqsub eq6 res6; ?lsq(nodropmiss,tol=1e-7,maxit=1000) eq1 eq2 eq3 eq4 eq5 eq6; lsq(nodropmiss,tol=1e-7,maxit=1000) res1 res2 res3 res4 res5 res6; COPY @LOGL LU; LU1=LU; SMPL NR1, NR2; ? Elasticities; MSD F11 F21 F31 F41 F51 F61 F71; ?================= MEAN FACTOR SHARES SET MF1=@MEAN(1); SET MF2=@MEAN(2); SET MF3=@MEAN(3); SET MF4=@MEAN(4); SET MF5=@MEAN(5); SET MF6=@MEAN(6); SET MF7=@MEAN(7); PRINT MF1-MF7; SMPL NR1,NR1; MSD F1 F2 F3 F4 F5 F6 F7; ?================= MEAN FACTOR SHARES SET FF1=@MEAN(1); SET FF2=@MEAN(2); SET FF3=@MEAN(3); SET FF4=@MEAN(4); SET FF5=@MEAN(5); SET FF6=@MEAN(6); SET FF7=@MEAN(7); PRINT FF1-FF7; SMPL NR2,NR2; MSD F1 F2 F3 F4 F5 F6 F7; ?================= MEAN FACTOR SHARES SET FL1=@MEAN(1); SET FL2=@MEAN(2); SET FL3=@MEAN(3); SET FL4=@MEAN(4); SET FL5=@MEAN(5); SET FL6=@MEAN(6); SET FL7=@MEAN(7); PRINT FL1-FL7; SMPL NR1, NR2;
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SET B17=-B11-B12-B13-B14-B15-B16; SET B21=B12; SET B27=-B21-B22-B23-B24-B25-B26; SET B31=B13; SET B32=B23; SET B37=-B31-B32-B33-B34-B35-B36; SET B41=B14; SET B42=B24; SET B43=B34; SET B47=-B41-B42-B43-B44-B45-B46; SET B51=B15; SET B52=B25; SET B53=B35; SET B54=B45; SET B57=-B51-B52-B53-B54-B55-B56; SET B61=B16; SET B62=B26; SET B63=B36; SET B64=B46; SET B65=B56; SET B67=-B61-B62-B63-B64-B65-B66; SET B77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)-(-B14-B24-B34-B44-B45-B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)); SET A7=1-A1-A2-A3-A4-A5-A6; ? Calculate the standard errors for ROW frml row1 A7=1-A1-A2-A3-A4-A5-A6; frml row2 B17=-B11-B12-B13-B14-B15-B16; frml row3 B27=-B21-B22-B23-B24-B25-B26; frml row4 B37=-B31-B32-B33-B34-B35-B36; frml row5 B47=-B41-B42-B43-B44-B45-B46; frml row6 B57=-B51-B52-B53-B54-B55-B56; frml row7 B67=-B61-B62-B63-B64-B65-B66; frml row8 B77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)-(-B14-B24-B34-B44-B45B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)); frml row9 B21=B12; frml row10 B31=B13; frml row11 B32=B23; frml row12 B41=B14; frml row13 B42=B24; frml row14 B43=B34; frml row15 B51=B15; frml row16 B52=B25; frml row17 B53=B35; frml row18 B54=B45; frml row19 B61=B16; frml row20 B62=B26; frml row21 B63=B36; frml row22 B64=B46; frml row23 B65=B56; analyz row1-row23; ?? Calculate Eigenvalues SET B71=B17; SET B72=B27; SET B73=B37; SET B74=B47;
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SET B75=B57; SET B76=B67; SET B77=B77; ? Tranform r to Pie; SET D11=(B11-MF1+MF1*MF1); SET D12=(B12+MF1*MF2); SET D13=(B13+MF1*MF3); SET D14=(B14+MF1*MF4); SET D15=(B15+MF1*MF5); SET D16=(B16+MF1*MF6); SET D17=(-B11-B12-B13-B14-B15-B16+MF1*MF7); SET D21=(B12+MF2*MF1); SET D22=(B22-MF2+MF2*MF2); SET D23=(B23+MF2*MF3); SET D24=(B24+MF2*MF4); SET D25=(B25+MF2*MF5); SET D26=(B26+MF2*MF6); SET D27=(-B12-B22-B23-B24-B25-B26+MF2*MF7); SET D31=(B13+MF3*MF1); SET D32=(B23+MF3*MF2); SET D33=(B33-MF3+MF3*MF3); SET D34=(B34+MF3*MF4); SET D35=(B35+MF3*MF5); SET D36=(B36+MF3*MF6); SET D37=(-B13-B23-B33-B34-B35-B36+MF3*MF7); SET D41=(B14+MF4*MF1); SET D42=(B24+MF4*MF2); SET D43=(B34+MF4*MF3); SET D44=(B44-MF4+MF4*MF4); SET D45=(B45+MF4*MF5); SET D46=(B46+MF4*MF6); SET D47=(-B14-B24-B34-B44-B45-B46+MF4*MF7); SET D51=(B15+MF5*MF1); SET D52=(B25+MF5*MF2); SET D53=(B35+MF5*MF3); SET D54=(B45+MF5*MF4); SET D55=(B55-MF5+MF5*MF5); SET D56=(B56+MF5*MF6); SET D57=(-B15-B25-B35-B45-B55-B56+MF5*MF7); SET D61=(B16+MF6*MF1); SET D62=(B26+MF6*MF2); SET D63=(B36+MF6*MF3); SET D64=(B46+MF6*MF4); SET D65=(B56+MF6*MF5); SET D66=(B66-MF6+MF6*MF6); SET D67=(-B16-B26-B36-B46-B56-B66+MF6*MF7); SET D71=(-B11-B12-B13-B14-B15-B16+MF7*MF1); SET D72=(-B12-B22-B23-B24-B25-B26+MF7*MF2); SET D73=(-B13-B23-B33-B34-B35-B36+MF7*MF3); SET D74=(-B14-B24-B34-B44-B45-B46+MF7*MF4); SET D75=(-B15-B25-B35-B45-B55-B56+MF7*MF5); SET D76=(-B16-B26-B36-B46-B56-B66+MF7*MF6); SET D77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)-(-B14-B24-B34-B44-B45-B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)-MF7+MF7*MF7); ? Create each row EIGHT; MMAKE(VERT) MMAKE(VERT) MMAKE(VERT) MMAKE(VERT) MMAKE(VERT)
E1 D11-D17; E2 D21-D27; E3 D31-D37; E4 D41-D47; E5 D51-D57;
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MMAKE(VERT) E6 D61-D67; MMAKE(VERT) E7 D71-D77; ? Creates square matrix MMAKE E E1-E7; ? Calculate Eigenvalues of E MAT EV = EIGVAL(E); Print E EV; ? Creates standard errors for pi ij's where the pi ij's are D11, D12, etc; frml pi1 D11=(B11-MF1+MF1*MF1); frml pi2 D12=(B12+MF1*MF2); frml pi3 D13=(B13+MF1*MF3); frml pi4 D14=(B14+MF1*MF4); frml pi5 D15=(B15+MF1*MF5); frml pi6 D16=(B16+MF1*MF6); frml pi7 D17=(-B11-B12-B13-B14-B15-B16+MF1*MF7); frml pi8 D21=(B12+MF2*MF1); frml pi9 D22=(B22-MF2+MF2*MF2); frml pi10 D23=(B23+MF2*MF3); frml pi11 D24=(B24+MF2*MF4); frml pi12 D25=(B25+MF2*MF5); frml pi13 D26=(B26+MF2*MF6); frml pi14 D27=(-B12-B22-B23-B24-B25-B26+MF2*MF7); frml pi15 D31=(B13+MF3*MF1); frml pi16 D32=(B23+MF3*MF2); frml pi17 D33=(B33-MF3+MF3*MF3); frml pi18 D34=(B34+MF3*MF4); frml pi19 D35=(B35+MF3*MF5); frml pi20 D36=(B36+MF3*MF6); frml pi21 D37=(-B13-B23-B33-B34-B35-B36+MF3*MF7); frml pi22 D41=(B14+MF4*MF1); frml pi23 D42=(B24+MF4*MF2); frml pi24 D43=(B34+MF4*MF3); frml pi25 D44=(B44-MF4+MF4*MF4); frml pi26 D45=(B45+MF4*MF5); frml pi27 D46=(B46+MF4*MF6); frml pi28 D47=(-B14-B24-B34-B44-B45-B46+MF4*MF7); frml pi29 D51=(B15+MF5*MF1); frml pi30 D52=(B25+MF5*MF2); frml pi31 D53=(B35+MF5*MF3); frml pi32 D54=(B45+MF5*MF4); frml pi33 D55=(B55-MF5+MF5*MF5); frml pi34 D56=(B56+MF5*MF6); frml pi35 D57=(-B15-B25-B35-B45-B55-B56+MF5*MF7); frml pi36 D61=(B16+MF6*MF1); frml pi37 D62=(B26+MF6*MF2); frml pi38 D63=(B36+MF6*MF3); frml pi39 D64=(B46+MF6*MF4); frml pi40 D65=(B56+MF6*MF5); frml pi41 D66=(B66-MF6+MF6*MF6); frml pi42 D67=(-B16-B26-B36-B46-B56-B66+MF6*MF7); frml pi43 D71=(-B11-B12-B13-B14-B15-B16+MF7*MF1); frml pi44 D72=(-B12-B22-B23-B24-B25-B26+MF7*MF2); frml pi45 D73=(-B13-B23-B33-B34-B35-B36+MF7*MF3); frml pi46 D74=(-B14-B24-B34-B44-B45-B46+MF7*MF4); frml pi47 D75=(-B15-B25-B35-B45-B55-B56+MF7*MF5); frml pi48 D76=(-B16-B26-B36-B46-B56-B66+MF7*MF6); frml pi49 D77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)-(-B14-B24-B34-B44-B45B46)
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-(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)-MF7+MF7*MF7); analyz pi1-pi49; ? Elasticities ? Divisia Input Index ???????CHANGE WILL START HERE FOR RECURSIVE MODEL; FRML EL1 E1=A1/MF1; FRML EL1M E1M=A1/MMF1; FRML EL2 E2=A2/MF2; FRML EL2M E2M=A2/MMF2; FRML EL3 E3=A3/MF3; FRML EL3M E3M=A3/MMF3; FRML EL4 E4=A4/MF4; FRML EL4M E4M=A4/MMF4; FRML EL5 E5=A5/MF5; FRML EL5M E5M=A5/MMF5; FRML EL6 E6=A6/MF6; FRML EL6M E6M=A6/MMF6; FRML EL7 E7=(1-A1-A2-A3-A4-A5-A6)/MF7; FRML EL7M E7M=(1-A1-A2-A3-A4-A5-A6)/MMF7; ? Divisia Input Index WITH FIRST F FRML EL8 EF1=A1/FF1; FRML EL8M EF1M=A1/MFF1; FRML EL9 EF2=A2/FF2; FRML EL9M EF2M=A2/MFF2; FRML EL10 EF3=A3/FF3; FRML EL10M EF3M=A3/MFF3; FRML EL11 EF4=A4/FF4; FRML EL11M EF4M=A4/MFF4; FRML EL12 EF5=A5/FF5; FRML EL12M EF5M=A5/MFF5; FRML EL13 EF6=A6/FF6; FRML EL13M EF6M=A6/MFF6; FRML EL14 EF7=(1-A1-A2-A3-A4-A5-A6)/FF7; FRML EL14M EF7M=(1-A1-A2-A3-A4-A5-A6)/MFF7; ? Divisia Input Index WITH LAST F FRML EL15 EL1=A1/FL1; FRML EL15M EL1M=A1/MFL1; FRML EL16 EL2=A2/FL2; FRML EL16M EL2M=A2/MFL2; FRML EL17 EL3=A3/FL3; FRML EL17M EL3M=A3/MFL3; FRML EL18 EL4=A4/FL4; FRML EL18M EL4M=A4/MFL4; FRML EL19 EL5=A5/FL5; FRML EL19M EL5M=A5/MFL5; FRML EL20 EL6=A6/FL6; FRML EL20M EL6M=A6/MFL6; FRML EL21 EL7=(1-A1-A2-A3-A4-A5-A6)/FL7; FRML EL21M EL7M=(1-A1-A2-A3-A4-A5-A6)/MFL7; ? Compensated price elasticities FRML EP1 E11=(B11-MF1+MF1*MF1)/MF1; FRML EP1M E11M=(B11-MMF1+MMF1*MMF1)/MMF1; FRML EP2 E12=(B12+MF1*MF2)/MF1; FRML EP2M E12M=(B12+MMF1*MMF2)/MMF1; FRML EP3 E13=(B13+MF1*MF3)/MF1; FRML EP3M E13M=(B13+MMF1*MMF3)/MMF1; FRML EP4 E14=(B14+MF1*MF4)/MF1; FRML EP4M E14M=(B14+MMF1*MMF4)/MMF1; FRML EP5 E15=(B15+MF1*MF5)/MF1; FRML EP5M E15M=(B15+MMF1*MMF5)/MMF1; FRML EP6 E16=(B16+MF1*MF6)/MF1; FRML EP6M E16M=(B16+MMF1*MMF6)/MMF1; FRML EP7 E17=(-B11-B12-B13-B14-B15-B16+MF1*MF7)/MF1; FRML EP7M E17M=(-B11-B12-B13-B14-B15B16+MMF1*MMF7)/MMF1; FRML EP8 E21=(B12+MF2*MF1)/MF2; FRML EP8M E21M=(B12+MMF2*MMF1)/MMF2; FRML EP9 E22=(B22-MF2+MF2*MF2)/MF2; FRML EP9M E22M=(B22-MMF2+MMF2*MMF2)/MMF2; FRML EP10 E23=(B23+MF2*MF3)/MF2; FRML EP10M E23M=(B23+MMF2*MMF3)/MMF2; FRML EP11 E24=(B24+MF2*MF4)/MF2; FRML EP11M E24M=(B24+MMF2*MMF4)/MMF2; FRML EP12 E25=(B25+MF2*MF5)/MF2; FRML EP12M E25M=(B25+MMF2*MMF5)/MMF2; FRML EP13 E26=(B26+MF2*MF6)/MF2; FRML EP13M E26M=(B26+MMF2*MMF6)/MMF2; FRML EP14 E27=(-B12-B22-B23-B24-B25-B26+MF2*MF7)/MF2; FRML EP14M E27M=(-B12-B22-B23-B24-B25B26+MMF2*MMF7)/MMF2; FRML EP15 E31=(B13+MF3*MF1)/MF3; FRML EP15M E31M=(B13+MMF3*MMF1)/MMF3; FRML EP16 E32=(B23+MF3*MF2)/MF3; FRML EP16M E32M=(B23+MMF3*MMF2)/MMF3; FRML EP17 E33=(B33-MF3+MF3*MF3)/MF3; FRML EP17M E33M=(B33-MMF3+MMF3*MMF3)/MMF3; FRML EP18 E34=(B34+MF3*MF4)/MF3; FRML EP18M E34M=(B34+MMF3*MMF4)/MMF3; FRML EP19 E35=(B35+MF3*MF5)/MF3; FRML EP19M E35M=(B35+MMF3*MMF5)/MMF3; FRML EP20 E36=(B36+MF3*MF6)/MF3; FRML EP20M E36M=(B36+MMF3*MMF6)/MMF3; FRML EP21 E37=(-B13-B23-B33-B34-B35-B36+MF3*MF7)/MF3; FRML EP21M E37M=(-B13-B23-B33-B34-B35B36+MMF3*MMF7)/MMF3; FRML EP22 E41=(B14+MF4*MF1)/MF4; FRML EP22M E41M=(B14+MMF4*MMF1)/MMF4; FRML EP23 E42=(B24+MF4*MF2)/MF4; FRML EP23M E42M=(B24+MMF4*MMF2)/MMF4; FRML EP24 E43=(B34+MF4*MF3)/MF4; FRML EP24M E43M=(B34+MMF4*MMF3)/MMF4; FRML EP25 E44=(B44-MF4+MF4*MF4)/MF4; FRML EP25M E44M=(B44-MMF4+MMF4*MMF4)/MMF4; FRML EP26 E45=(B45+MF4*MF5)/MF4; FRML EP26M E45M=(B45+MMF4*MMF5)/MMF4; FRML EP27 E46=(B46+MF4*MF6)/MF4; FRML EP27M E46M=(B46+MMF4*MMF6)/MMF4; FRML EP28 E47=(-B14-B24-B34-B44-B45-B46+MF4*MF7)/MF4; FRML EP28M E47M=(-B14-B24-B34-B44-B45B46+MMF4*MMF7)/MMF4;
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FRML EP29 E51=(B15+MF5*MF1)/MF5; FRML EP29M E51M=(B15+MMF5*MMF1)/MMF5; FRML EP30 E52=(B25+MF5*MF2)/MF5; FRML EP30M E52M=(B25+MMF5*MMF2)/MMF5; FRML EP31 E53=(B35+MF5*MF3)/MF5; FRML EP31M E53M=(B35+MMF5*MMF3)/MMF5; FRML EP32 E54=(B45+MF5*MF4)/MF5; FRML EP32M E54M=(B45+MMF5*MMF4)/MMF5; FRML EP33 E55=(B55-MF5+MF5*MF5)/MF5; FRML EP33M E55M=(B55-MMF5+MMF5*MMF5)/MMF5; FRML EP34 E56=(B56+MF5*MF6)/MF5; FRML EP34M E56M=(B56+MMF5*MMF6)/MMF5; FRML EP35 E57=(-B15-B25-B35-B45-B55-B56+MF5*MF7)/MF5; FRML EP35M E57M=(-B15-B25-B35-B45-B55B56+MMF5*MMF7)/MMF5; FRML EP36 E61=(B16+MF6*MF1)/MF6; FRML EP36M E61M=(B16+MMF6*MMF1)/MMF6; FRML EP37 E62=(B26+MF6*MF2)/MF6; FRML EP37M E62M=(B26+MMF6*MMF2)/MMF6; FRML EP38 E63=(B36+MF6*MF3)/MF6; FRML EP38M E63M=(B36+MMF6*MMF3)/MMF6; FRML EP39 E64=(B46+MF6*MF4)/MF6; FRML EP39M E64M=(B46+MMF6*MMF4)/MMF6; FRML EP40 E65=(B56+MF6*MF5)/MF6; FRML EP40M E65M=(B56+MMF6*MMF5)/MMF6; FRML EP41 E66=(B66-MF6+MF6*MF6)/MF6; FRML EP41M E66M=(B66-MMF6+MMF6*MMF6)/MMF6; FRML EP42 E67=(-B16-B26-B36-B46-B56-B66+MF6*MF7)/MF6; FRML EP42M E67M=(-B16-B26-B36-B46-B56B66+MMF6*MMF7)/MMF6; FRML EP43 E71=(-B11-B12-B13-B14-B15-B16+MF7*MF1)/MF7; FRML EP43M E71M=(-B11-B12-B13-B14-B15B16+MMF7*MMF1)/MMF7; FRML EP44 E72=(-B12-B22-B23-B24-B25-B26+MF7*MF2)/MF7; FRML EP44M E72M=(-B12-B22-B23-B24-B25B26+MMF7*MMF2)/MMF7; FRML EP45 E73=(-B13-B23-B33-B34-B35-B36+MF7*MF3)/MF7; FRML EP45M E73M=(-B13-B23-B33-B34-B35B36+MMF7*MMF3)/MMF7; FRML EP46 E74=(-B14-B24-B34-B44-B45-B46+MF7*MF4)/MF7; FRML EP46M E74M=(-B14-B24-B34-B44-B45B46+MMF7*MMF4)/MMF7; FRML EP47 E75=(-B15-B25-B35-B45-B55-B56+MF7*MF5)/MF7; FRML EP47M E75M=(-B15-B25-B35-B45-B55B56+MMF7*MMF5)/MMF7; FRML EP48 E76=(-B16-B26-B36-B46-B56-B66+MF7*MF6)/MF7; FRML EP48M E76M=(-B16-B26-B36-B46-B56B66+MMF7*MMF6)/MMF7; FRML EP49 E77=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)-(-B14-B24-B34-B44-B45B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)-MF7+MF7*MF7)/MF7; FRML EP49M E77M=(-(-B11-B12-B13-B14-B15-B16)-(-B12-B22-B23-B24-B25-B26)-(-B13-B23-B33-B34-B35-B36)-(-B14-B24-B34-B44B45-B46) -(-B15-B25-B35-B45-B55-B56)-(-B16-B26-B36-B46-B56-B66)-MMF7+MMF7*MMF7)/MMF7; ANALYZ EL1-EL7, EL1M-EL7M; MMAKE ELCOEF @COEFA; ANALYZ EP1-EP49, EP1M-EP49M; MMAKE EPCOEF @COEFA; MMAKE(VERTICAL) MBM ELCOEF EPCOEF; MMAKE MBETA MBETA MBM; endproc zzzz; MFORM(TYPE=GEN,NROW=112,NCOL=1) MBETA=0; SMPL 2, 33; MSD F11 F21 F31 F41 F51 F61 F71; ?================= MEAN FACTOR SHARES SET MMF1=@MEAN(1); SET MMF2=@MEAN(2); SET MMF3=@MEAN(3); SET MMF4=@MEAN(4); SET MMF5=@MEAN(5); SET MMF6=@MEAN(6); SET MMF7=@MEAN(7); SMPL 2 2; MSD F1 F2 F3 F4 F5 F6 F7; ?================= MEAN FACTOR SHARES SET MFF1=@MEAN(1); SET MFF2=@MEAN(2); SET MFF3=@MEAN(3);
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SET MFF4=@MEAN(4); SET MFF5=@MEAN(5); SET MFF6=@MEAN(6); SET MFF7=@MEAN(7); SMPL 33,33; MSD F1 F2 F3 F4 F5 F6 F7; ?================= MEAN FACTOR SHARES SET MFL1=@MEAN(1); SET MFL2=@MEAN(2); SET MFL3=@MEAN(3); SET MFL4=@MEAN(4); SET MFL5=@MEAN(5); SET MFL6=@MEAN(6); SET MFL7=@MEAN(7); DO J=1 TO 11; SET NR1=1+J; SET NR2=32+J; SMPL NR1, NR2; ZZZZ; ENDDO; WRITE(FORMAT=EXCEL,FILE='U:\TOMATORESEARCH\EUNEWANALYSIS\ELEPELAS-RECW.XLS') MBETA; END;
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APPENDIX C SUPERFLUOUS MATERIAL Program Creating TLB Dataset for 1963-2005 (TOMDATA2005.TLB) OPTIONS MEMORY=500 LIMPRN=120 LINLIM=60; ?=====================================================================================; ? TOM2005#01.TSP - CREATING NEW TLB DATABASE WITH 2005 DATA INCLUDED WITH Q & V ; ?=====================================================================================; FREQ NONE; TITLE 'TOMATO EXPORTS TO AND FROM EEC THROUGH 2005'; ?IN 'H:\Zstudents\MohAli\TSP2007\DATA2005\TOMDATA2005'; OUT 'H:\Zstudents\MohAli\TSP2007\DATA2005\TOMDATA2005'; READ(FORMAT=EXCEL,FILE='H:\Zstudents\MohAli\TSP2007\DATA2005\TOMDATA2005.XLS'); DOC NUM 'COUNTER'; DOC YRS 'YEAR 1963-2005'; DOC IMP 'IMPORTING COUNTRY'; DOC EPX 'EXPORTING COUNTRY'; DOC COM 'TOMATOES = 544'; DOC V 'VALUE OF TOMATOES TRADED $US'; DOC Q 'QUANTITY OF TOMATOES TRADED (KG)'; DOC UNT 'UNIT=2 FOR KILOGRAMS'; OUT; ?PRINT @NOB; ?DBLIST 'H:\Zstudents\MohAli\TSP2007\DATA2005\TOMDATA2005'; END;
Program Creating Individual Country’s Value and Quantity (V. Q.) for EU-15 (TOMDATA2005_15.TLB) OPTIONS MEMORY=1500 signif=0; ? TOM2005#02.TSP; TITLE 'TOMATO EXPORTS TO AND FROM EEC 15 COUNTRIES'; IN 'H:\Zstudents\MohAli\TSP2007\DATA2005\TOMDATA2005'; SUPRES SMPL; ?==========================================================================; ? INITALIZING ALL PARTNER COUNTRIES TO ZERO; ?==========================================================================; ?==========================================================================; ? ALL IMPORTING AND EXPORTING COUNTRIES - USE EITHER ZIMPZ15 OR ZIMPZ27 ; ?==========================================================================; LIST ZIMPZ15 40 58 208 246 251 276 300 372 381 528 620 724 752 826 842; ? ORIGINAL 15 EEC COUNTRIES; LIST ZIMPZ27 40 58 208 246 251 276 300 372 381 528 620 724 752 826 842 100 196 203 233 348 428 440 470 616 642 703 705; ? ADDED 12 ADDITIONAL COUNTRIES; ?==========================================================================; ? IMPORTING COUNTRIES WITH NEW COUNTIRES ADDED ; ?==========================================================================; LIST ZEPXZ 0 8 12 20 24 28 31 32 36 40 44 50 51 52 56 58 68 70 76 80 84 86 90 92 96 100 104 108 120 124 129 132 136 140 144 152 156 166 170 180 188 191 192 196 200 203 204 208 212 214 218 222 226 230 231 232 233 234 246 251 266 270 275 276 288 292 296 300 304 308 312 320 324 332 340 344 348 352 360 364 372 376 381 384 388 392 400 404 408 410 414 418 422 428 430 434 440 442 446 450 454 458 462 466 470 474 478 480 484 492 496 498 500 504 508 516 520 524 528 530 532 533 536 554 558 562 566 579 583 584 586 591 604 608 616 620 624 638 642 643 646 658 659 678 682 686 690 694 699 702 703 704 705 706 710 711 716 717 724 732 736 740 752 757 760 764 768 780 784 788 792 796 800 804 807 810 818 826 834 837 838 839 842 849 854 858 860 862 879 882 887 890 891 894 899 900 568 798 112 174 178 184 795 762; ? EXPORTING COUNTRIES;
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?==========================================================================; ? THE NEW DATA IS CREATED AND THEN THE PROCEDURE IS TURNED OFF ?==========================================================================; DOT(VALUE=I) ZEPXZ; V.=0; Q.=0; print i; ENDDOT; ?==========================================================================; ? FOR EACH IMPORTER CREATE A V. AND Q. WITH THE PARTNER TRADE; ?==========================================================================; DOT(CHAR=#, VALUE=J) ZIMPZ15; ? 0; THEN; DO; V.%=V; Q.%=Q; ENDDO; ELSE; SET IDD=1; ENDDO; ENDDOT; ENDDOT; SELECT 1; DOT ZEPXZ; V.=V.; Q.=Q.; ENDDOT; ?==========================================================================; ? CREATING 901 AND 902 ; ?==========================================================================; SELECT 1; SET NRR=@NOB; PRINT NRR; DEU= (IMP^=842); ?1=EU 0=US; EU_US = (DEU=1)*901 + (DEU=0)*902; ? 901=EU CODE AND 902=NEW CODE FOR US; SET M=0; DO L=901 TO 902; DO K=1963 TO 2005; SET M=M+1; SMPL 1,NRR; SET NR2=NRR+M; DOT(CHAR=%, VALUE=I) ZEPXZ; SMPL 1,NRR; SELECT EU_US=L & YRS=K; MSD(NOPRINT) V. Q.; SMPL NR2,NR2; V.=@SUM(1); Q.=@SUM(2); YRS=K; IMP=L; UNT=2; COM=544; ENDDOT; ENDDO; ENDDO; PRINT NR2; SET NR3=NRR+1; print nr3 nr2; SMPL NR3, NR2; SMPL 1,NR2; OUT 'H:\Zstudents\MohAli\TSP2007\DATA2005\TOMDATA2005_15'; ?
