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PRICE DYNAMICS IN THE U.S. SHRIMP MARKET By CHARLES M. ADAMS 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 1984 't '(? * ^A'^ ^ ^^y * * *^ 4 .*^ s *.'^*^'i  ^*^*._____________________________________________________________________ .... ^*^jfc^... To Mom and Dad LC~_, .L'YIY1YC ACKNOWLEDGMENTS I wish to express sincere appreciation to Dr. Fred J. Prochaska and Dr. Tom H. Spreen for taking time to critique the many drafts of this manuscript. Their guidance and friendship were invaluable. Thanks go to Dr. Jim C. Cato, Dr. W. Steve Otwell and Dr. Gary F. Fairchild for dedicating time to serve as counsel on the advisory committee. Special thanks go to Fred, Jim, and the Florida Sea Grant Program for the financial support provided throughout my stay as a graduate student. This dissertation would be long in coming if not for someone to decipher and type the initial scribbling. In that sense, Frankie Thomas, with her patience, understanding and keen eyesight, was abso lutely indispensable. Thanks also go to my fellow students, to whom I am grateful for their aid and comaraderie. However, my greatest appreciation goes to Sherry, Sam and ???. whose love and patience provided the motivation needed to complete my graduate studies. TABLE OF CONTENTS Page ACKNOWLEDGEMENTS...................................................... iii LIST OF TABLES..................................................... vii LIST OF FIGURES........................ ......................... ix ABSTRACT............................. ..... .........o.. ......*... x CHAPTER I INTRODUCTION................................................. 1 Overview of Industry........... ...****************** 4 Resource and Harvesting................................ 4 General Industry Trends................................ 6 Industry Issues... *******************************. 17 Problem Statement........* ....... ............... ...... 20 Objectives.............***************************************** 23 II THEORETICAL CONSIDERATIONS.................. .............. 25 Vertical Structure. **..............******................. 25 Causal Direction of Price Determination in the Vertical Market......................... ................ 41 Price Spreads Between Market Levels.....................** 44 Price Transmission......****...................... .****.** 48 III EMPIRICAL METODS.. ................... ............. .. 50 Time Series Analysis........... ..................... 51 Univariate Time Series...................* ...*.....****. 52. Autoregressive (AR) Process..........*;..........*6* .** 54 Moving Average (MA) Process............................ 55 Integrated Autoregressive Moving Average (ARIMA) Process**.........*................*.................. 56 Identification and Estimation of an ARIMA Model........ 57 Direction of Price DeterminationCausality................ 60 Granger Method..................................******* 61 Sims Method..................................... *..... 62 HaughPierce Method........... ........................ 63 Dynamic Regression Methods................................ 65 Filter Models.................**........**********....... 66 01W9.1 Dynamic Shock Model...................*................ 67 Dynamic Regression Transfer Function................... 68 General Regression Methods................. ...*******... 69 IV EMPIRICAL MODELS....... ..................... .............. 74 Introduction......................************************ 74 Implicit Models........................................... 74 Symmetric and Asyametric Modelse........*e....* ........... 77 Data ................. ...* .....*..********************* 79 Statistical Models............................ .. ........ 81 Retail Price Models.................................. 82 Wholesale Price Models.......................**........ 84 Exvessel Price Models..... ........******............. 87 Margin Models.................. .......................... 90 Structural Margins........................ ......******* 90 Reduced and Final Form Margins............*..........* 92 V EMPIRICAL RESULTSCAUSALITY ANALYSIS................. ..... 94 Monthly Price Data.............................*....ec... 94 HaughPierce Test.......... ...*.....*.......*********** 94 The 3140 size class........... .. ................. 96 The 2125 size class............................... 98 Impulse response functions for both size classes..... 98 The Granger Test.................**.............****** 102 The 3140 size class................. ......... *. cc 102 The 2125 size class................................. 105 Sims Test......................***..............****** 107 The 3140 size class............... ..** ... ** ....*** 107 The 2125 size class................................ 109 Quarterly Price Data................... ....*****.***** 109 HaughPierce Test...................................... 110 The 3140 size class...............**....... ...****** 111 The 2125 size class...... ..e......* ......********** 111 Impulse response functions for both size classes..... 114 Granger Test...........*......*.......**************** 116 The 3140 size class*...................*****........ 116 The 2125 size class.........*... ...**************** 118 Sims Test.............................. .....********* 120 The 3140 size class............. ce............* .... 120 The 2125 size class................ ...************* 120 Summary of Monthly and Quarterly Causality Results........ 122 VI EMPIRICAL RESULTSPRICE AND MARGIN MODELS...... ........... 124 Monthly Data.............................................* 124 The 3140 Size Class.......*............... ....********** 125 Retail structural estimates............*.*...e......e 125 Wholesale structural estimates........****....... ..*** 127 Exvessel structural estimates...*...**************** 130 The 2125 Size Class................... .......****** 132 Retail structural estimates .........* ...... ** ......* 132 r Quarterly Data............................................ 134 The 3140 Size Class................................... 135 Retail structural estimates............. ............. 135 Wholesale structural estimates....................... 137 Exvessel structural estimates....................... 140 Reduced and final form estimates..................... 142 Margin estimates.................. .................. 145 The 2125 Size Class................................... 148 Retail structural estimates.......................... 148 Wholesale structural estimates..... .................. 151 Exvessel structural estimates....................... 153 Reduced and final form estimates..................... 155 Margin estimates.......... .*...*..********.......... 157 VII SUMMARY AND CONCLUSIONS...................................... 161 Analysis of Price Determination........................... 162 Causality and Asymaetry Analysis....................... 162 Factors of Price Determination......................... 164 Margin Analysis**.....**..............**...............** 168 Methodological Conclusions........*........ ..*........... 169 Policy Implications.............************************** 170 Suggestions for Future Research........................... 173 APPENDICES A DERIVATION OF IMPULSE RESPONSE FUNCTIONS..................... 178 B FINAL MODEL SPECIFICATIONS............................. .... 187 C GRANGER TESTS USING DATA FILTERED BY USING ARIMA MODELS...................********************************* 192 D REDUCED FORM ESTIMATES....... ....... ......................... 196 IREFERENCES................**************************************** 198 BIOGRAPHICAL SKETCH......................... ..... .............. 206 LIST OF TABLES Table Page 1 HaughPierce (HP) Causality Tests on Monthly Exvessel, Wholesale, and Retail Prices for the 3140 Size Class Using ARIMA Filtered Data................................ 97 2 HaughPierce (HP) Causality Tests on Monthly Exvessel, Wholesale, and Retail Prices for the 2125 Size Class Using ARIMA Filtered Data................................. 99 3 Granger Causality Tests on Monthly Exvessel, Wholesale, and Retail Prices for the 3140 Size Class Using First Differenced Data................................**************** 103 4 Granger Causality Tests on Monthly Exvessel, Wholesale, and Retail Prices for the 2125 Size Class Using First Differenced Data............... ............. .......*..... 106 5 Sims Causality Tests on Monthly Exvessel, Wholesale, and Retail Prices for the 3140 and 2125 Size Classes Using ARIMA Filtered Data....................**............** 108 6 HaughPierce (HP) Causality Tests on Quarterly Exvessel, Wholesale, and Retail Prices for the 3140 Size Class Using ARIMA Filtered Data.......**.......**................ 112 7 HaughPierce (HP) Causality Tests on Quarterly Exvessel, Wholesale, and Retail Prices for the 2125 Size Class Using ARIMA Filtered Data.................................. 113 8 Granger (HP) Causality Tests on Quarterly Exvessel, Wholesale, and Retail Prices for the 3140 Size Class Using First Differenced Data.................*..*..****.... 117 9 Granger (HP) Causality Tests on Quarterly Exvessel, Wholesale, and Retail Prices for the 2125 Size Class Using First Differenced Data................***............ 119 10 Sims Causality Tests on Quarterly Exvessel, Wholesale, and Retail Prices for the 3140 and 2125 Size Classes Using ARIMA Filtered Data.................................. 121 vii _~~ ii i 11 Summary of Monthly and Quarterly Causality Tests Using Exvessel (E), Wholesale (W), and Retail (R) Price Data by Size Class........................................... 123 12 Final Form Coefficients and Flexibility Estimates for the Retail, Wholesale and Exvessel Price Models for the 3140 Size Class........................................... 144 13 Final Form Margin Estimates and Flexibilities for the Retail/Wholesale (Mrw) and the Wholesale/Exvessel (MwP) Margins for the 3140 Size Class........................... 146 14 Final Form Coefficients and Flexibility Estimates for the Retail, Wholesale and Exvessel Price Models for the 2125 Size Class........................................... 156 15 Final Form Margin Estimates and Flexibilities for the Retail/Wholesale (Mrw) and the Wholesale/Exvessel (MwP) Margins for the 2125 Size Class.................... 159 B LjungBox ChiSquare Tests for White Noise on the Residuals of the Monthly and Quarterly Retail (Rt), Wholesale (W ), and Exvessel (Pt) Models Before and After Inclusion of a Lagged Dependent Variable............. 189 C.1 Granger Causality Tests on Monthly Exvessel, Whole sale, and Retail Prices for the 3140 Size Class Using Data Filtered by an ARIMA Model...................... 192 C.2 Granger Causality Tests on Monthly Exvessel, Whole sale, and Retail Prices for the 2125 Size Class Using Data Filtered by an ARIMA Model...................... 193 C.3 Granger Causality Tests on Quarterly Wholesale and Retail Prices for the 2125 Size Using Data Filtered by an ARIMA Model.......................................... 194 D.1 Reduced Form Estimates and Flexibilities for Quar terly Price Models at the Retail (Rt), Wholesale (Wt), and Exvessel (Pt) Market Levels for the 3140 Size Class.........................*................. 196 D.2 Reduced Form Estimates and Flexibilities for Quar terly Price Models at the Retail (Rt), Wholesale (Wt), and Exvessel (Pt) Market Levels for the 2125 Size Clase...........................*............... 197 viii LIST OF FIGURES Figure Page 1 Trends in Quarterly Prices for 3140 Count Raw Head less Shrimp for Retail, Wholesale, and ExVessel Market Levels. ..... ............ ...................... 12 2 Trends in Quarterly Prices for 2125 Count Raw Head less Shrimp for Retail, Wholesale, and ExVessel Market Levels ................*****.........**..*******. 13 3 Graphical Representation of a Vertical Market Systea with Equilibrium Prices pr, p, and p' in Time Period t.... 29 4 Graphical Representation of a Vertical Market System with Supply and Demand Given Implicitly at Four Market Level and the Corresponding Equilibrium Prices, pr pe, p and pP in Time Period t............................ 35 5 Graphical Representation of a Vertical Market System Characterized by Inelastic Supply with Demand Given Implicitly at Four Market Levpls and the Corresponding Equilibrium Prices, pr, pW p and pP in Time Period t.... 39 6 Market Channel Schematic Representation for the U.S. Shrimp Market Syste......................................** 76 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 PRICE DYNAMICS IN THE U.S. SHRIMP MARKET By Charles M. Adame December 1984 Chairman: Frederick J. Prochaska Major Departaent: Food and Resource Economics Previous research regarding the dynamics of price determination in the domestic shrimp market is lacking. Understanding the mechanism of price determination in a dynamic setting is imperative to formulating effective policy and assessing price impacts at each market level. This study examines the monthly and quarterly price determination process for rauheadless shrimp of the 3140 and 2125 size classes. The presence of Granger causality was assessed between adjacent market levels by using the HaughPierce, Sims, and Granger tests. Distributed lag structures were identified between adjacent market levels that embody the empirically determined lead/lag relationship. Price dependent demands at the retail, wholesale, and exvessel market levels were estimated. Expressions for marketing margins were derived. Monthly prices for both size classes in general exhibited unidirectional causality from exvessel to wholesale to retail price. Unidirectional causality did not characterize the exvessel/wholesale relationship for the 2125 size class. Quarterly prices for both size classes were interdependent among market ____ levels, with no unidirectional causality evident. The prices for the larger size class shrimp adjusted slower to changes in the lagged causal price than did the prices for the smaller shrimp. Wholesale and exvessel prices were found to be more closely related than retail and wholesale prices for both size classes. Monthly prices were dependent on current and lagged causal price, however, lagged causal price was not an important determinant of quarterly price. Price response between market levels for both size classes was found to be symmetric. Income, prices of competing meat products, and imports of other size classes of shrimp were not important determinants of price for either size class. Changes in total retail supply had a relative larger impact on the price for the 2125 size class, while beginning stocks, own and other size landings and imports of ownsize shrimp had a larger negative impact on price for the 31 40 size class than for the 2125 size class. Changes in beginning stocks and landings and imports of ownsize shrimp were the most import determinants of price at each market level. Changes in the marketing cost index had a larger impact on prices for the 2125 size class than for the 3140 size class. Marketing margins were negatively related to changes in quantity variables and positively related to changes in marketing costs. Income and the price index for competing meat products were not important determinants of marketing margins. Prices for the 3140 size class are more affected by quantity changes, particularly at the retail level. Thus, policy measures which alter the quantity or size distribution of shrimp through import quotas, tariffs, or seasonal restrictions, will have a greater price impact on the smaller shrimp. Increased supplies of agricultural shrimp will have a greater relative price impact on the 3140 size class. xi __ CHAPTER I INTRODUCTION Management of the domestic shrimp fishery in the United States has proven to be a considerable task. The goal of effective implementation of policy has resulted in the organization of a complex management structure and the allocation of substantial sums of research dollars to be directed toward current research needs. The passage of the Magnuson Fishery Conservation Management Act PL 94265 (MFCMA) in 1976 dictated an increased need and provided further direction for the investigation of mechanisms and functions of seafood markets. A number of studies have been carried out concerning the various species of fish and shellfish in the seafood industry. The majority of these studies, when touching on economic issues, have rarely extended past the dockside market (Schuler, 1983). This appears to be due to a major emphasis being placed on management of physical resources. A few species, such as shrimp, have garnered an increasing level of research funds to be utilized toward a more complete analysis of the marketing systemfrom producer to consumer. The impetus for this expression of increased need of control over the fishery and its market system has been that the shrimp industry has been growing in volume, value, and complexity. As the standard of living has increased in the U.S., the demand for luxury goods, such as shrimp, has increased. The consumption of fish and shellfish products has increased steadily over the past two decades (U.S. Dept. of Commerce(b), 1983). The Food and Agricultural Organization of the United Nations predicts fish and shellfish consumption will probably increase through 1990 at a rate of growth greater than that for pork, beef, vegetables, cereals, and milk (Office of Technology Assessment, 1977). In particular, per capital consumption of shrimp products (edible meat weight) increased almost 50 percent from 1.08 pounds in 1960 to 1.52 pounds in 1982 (U.S. Dept. of Commerce(b), 1983). As a result of increased demand, the value of shrimp products has exhibited a commen surate increase. The increased complexity of the industry has mani fested itself in terms of increased awareness of biological and producer (effort) relationships, an increasingly more intricate domestic market system, and growing interdependence with world markets. For the formu lation and implementation of effective fishery management and, especial ly, trade policy, the understanding of market functions and dynamics must keep pace with growth and change in the market system. In accordance with this need, some research efforts have been directed toward understanding and detailing the U.S. shrimp market system. The National Marine Fisheries Service has maintained a base of production and market data on the shrimp industry. Significant gains in understanding the shrimp industry have resulted. However, this study proposes that there exists a significant absence of knowledge in the area of price formulation; particularly in terms of price dynamics and the behavior of price margins throughout the different levels of the market system. Even less effort has been directed toward examining these relationships on a product form and size basis for shrimp as the product moves through the marketing system. In addition, the direction of price determination in the market has never been formally tested. This has relegated the specification of the nature of the pricing system in most empirical studies, in terms of being either simultaneous or recursive, to simply a matter of precedence or guesswork. The lack of understanding in these causal relationships has been borne out by publi cation of contradictory model formulations and empirical results. The marketing system for shrimp is an intricate mechanism. Before the finished product reaches the consumer at the restaurant, fresh fish market, or retail grocery store, the shrimp product may pass through various combinations of handlers. The path taken is related to the origin, form, and destination of the shrimp product. With the primary supply at the producer (or importer) level and primary demand at the consumer level, a maze of derived demand and supply relationships exist, each generating respective prices. These prices are a function of the market for marketing services and imputs employed at each stage of processing and determine the gross margin which exists between the respective market levels. The responsiveness of these prices to exogen ous and endogenous change in the market place is directly related to how quickly and at what magnitude changes in profit and costs are passed between the various market levels. Structural differences between levels in the market system and informational advantages from one level to another may play a major role in the efficient transmission of prices between market levels. Understanding how the market levels interface and how efficiently the respective price linkages adjust, in terms of speed and magnitude, is of utmost importance if policy is to reach its goal of formulating effective measures in the market system. Partici pants throughout the market system will benefit through further under standing of the price linkage system. Knowledge of how the margins adjust between market levels will allow each level to observe and react to market signals more efficiently. This will be especially true for nonadjacent market levels. Increased understanding of the efficiency and dynamics of the U.S. shrimp market system should provide for a greater chance of achieving the longrun goals established by the MFCMA. The possibility of formu lating effective policy and the realization of benefits to all levels of the market, from consumer to producer, would surely be increased if the aspects of basic market functions are more thoroughly understood. Such understanding of the dynamic properties of price determination would be invaluable to achieving more efficient fishery management policy formu lation as dictated by the MFCMA and motivated by current economic prob lems in the industry. Overview of Industry Resource and Harvesting The U.S. shrimp industry is the single most valuable component of the nation's fishing industry, when measured in terms of dockside value of commercial landings. There are four major shrimp producing areas in the U.S.: Gulf of Mexico, Pacific Northwest, South Atlantic, and New England, in order of landings volume. The Gulf reported 74.0 percent of total commercial landings in 1982 (U.S. Dept. of Commerce(b), 1983). The primary species sought in the Gulf and South Atlantic are warm water estuarinedependent species of the family Penaeidae, specifically, white shrimp (Penaeus setiferus), brown shrimp (P. aztecus), and pink shrimp (P. duorarum). The major regions of production for brown, white, and pink shrimp in order of importance are Texas, Louisiana, and Florida, 'LLI respectively. The major species in the Pacific fishery are cold water, nonestuarinedependent shrimp of the family Pandalidae. These shrimp are typically smaller than the Gulf species and are marketed differently (U.S. International Trade Commission, 1976). The major production periods for Gulf shrimp are June and July for browns and September and October for whites and pinks. The primary method for taking shrimp is a twin otter trawl which is pulled along the bottom in up to 40 fathoms of water. A smaller per centage of the catch is taken by deep water trawls in the Pacific and stationary butterfly nets which are fished at the mouth of the estuaries in Louisiana as shrimp move from the estuaries to the Gulf. Hu (1983) estimates there are approximately 27,000 people who depend on harvesting shrimp on a full or part time basis in the U.S. The majority of these are in the Gulf of Mexico where fleet size was estimated to be 10,060 boats and vessels in 1980 (Prochaska and Cato, 1981). Boats are defined as craft less than five net tons and vessels are craft five net tons and over. The number of vessels increased from 2,600 in 1961 to 4,585 in 1980, an increase of 76 percent. The number of vessels increased 24 percent from 1976 to 1980. The number of boats increased 2,987 in 1961 to 5,475 in 1980, an increase of 52 percent. The number of boats increased 19 percent from 1976 to 1980. Since 1980, the extended jurisdiction by Mexico over coastal waters out to 200 miles from its own coastline has displaced a number of U.S. craft from the rich Campeche grounds, a traditional fishing area for U.S. shrimpers. These craft have moved from Mexican waters to U.S. coastal waters, which extend 200 miles from the coastline since the enactment of extended jurisdiction by the U.S. in 1976. This area,  ~/~ f ~ which extends from the state water boundary out to 200 miles from shore, is known as the Fishery Conservation Zone (FCZ). This displacement of craft from the Campeche grounds to the FCZ is believed to have had a significant effect on the domestic industry (Fishing Gazette, 1981). Fleets that depended on the revenues generated by fishing the Campeche grounds (estimated at $35 million in 1979) have had to begin fishing operations in the FCZ. An estimated 600 shrimp vessels were displaced by the Mexico closure. As the craft entered the FCZ fishery, landings per craft trended downward, while total landings exhibited no apparent trend (U.S. Dept. of Commerce(b), various years). Competition among domestic producers has increased as relatively stable domestic stocks within the FCZ are being fished by an increasing number of vessels. In general, as the number of vessels and boats has increased, average landings, catch per unit of effort, and gross revenues per craft have been declining. Environmental conditions appear to have a greater impact on total catch than does effort, but effort appears more signifi cant with respect to catch per unit effort. General Industry Trends Total commercial domestic shrimp landings in the U.S. have been relatively constant since the early 1950's. The fishery in the U.S. can be considered a mature fishery. A slight upward trend existed from 1961 to 1970 (average annual increase of 5.8 percent). Between 1970 and 1982, there appeared to be no apparent trend (1.3 average annual percent change); however, considerable yeartoyear fluctuation existed. The total commercial landings in the U.S. in 1982 were 175.9 million pounds headsoff. This was a significant decrease from 218.0 million pounds in 1981 and represented only a 19.0 percent increase in landings since 1960 (U.S. Dept. of Commerce(d), various years). The record year was 1977 when a domestic catch of 288 million pounds was reported. While U.S. landings have apparently reached a plateau, alluding to the attainment of maximum sustainable yield in the fishery resource, U.S. consumption has surpassed U.S. production. Consumption of all forms of shrimp products in 1982 was 399.6 million pounds and 1.52 pounds edible meat weight per capital. Both total and per capital con sumption trended up between 1960 and 1970, with a plateau being reached and maintained during the 1970's. A maximum was reached in 1977 at 1.56 pounds per capital. This can be contrasted to per capital consumption of all fishery products in the U.S. which had a continual upward trend from 10.3 pounds in 1960 to 12.3 pounds in 1982 (U.S. Dept. of Commerce(b), 1983). Consumption of individual shrimp product forms has been changing. In 1960, rawheadless shrimp represented the largest share of total consumption of the four major forms of shrimp products at 47.8 percent with peeled, breaded, and canned shrimp representing 25.2, 8.0, and 9.0 percent of total consumption, respectively (Hu, 1983). By 1980, this ordering had changed with peeled/deveined, rawheadless, breaded, and canned capturing 46.1, 35.1, 12.1, and 6.7 percent of total consumption, respectively. On a per capital consumption basis, rawheadless and peeled/deveined product forms demonstrated the more noticeable increases during the last two decades. Consumption of rawheadless and peeled/de veined shrimp increased from .69 and .24 pounds, respectively, in 1960 to .92 and .60 pounds in 1980. During this period, rawheadless shrimp remained the most important product form on a per capital basis. However, peeled/deveined shrimp overtook breaded shrimp as the second most important product form consumed. Breaded and canned forms remained relatively constant on a per capital basis over this time period. With domestic landings falling short of consumption, imports have played a critical role in maintaining supply in the shrimp industry for many years. Imports have exceeded domestic landings since 1961, except for the years 1971, 1977, and 1978. Between 1960 and 1982, imports more than doubled. The major exporters of shrimp to the U.S. are Mexico, Ecuador, Panama, and India, in order of volume (Suazo, 1983). As with domestic landings, imports apparently reached a plateau in 1970, with an average annual increase of only 1.0 percent between 1970 and 1981 (U.S. Dept. of Commerce(d), various years). The total volume of imports increased from 122.5 million pounds in 1960 to 247.2 million pounds in 1970, an average annual percentage increase of 7.5 percent. Imports increased to 320 million pounds in 1982, an average annual percentage increase from 1970 of only 3.1 percent. The total 1982 imports, how ever, represented a 24 percent increase from 1981. Preliminary esti mates put the level of 1983 imports even higher at 421 million pounds. Ecuador has become increasingly important in the import market due to that country's increased production of maricultured shrimp. Thus, imports are increasing, possibly due in large part to shrimp produced in nontraditional fashion. The U.S. has long been the major market for world shrimp supplies, with Japan running second. However, Japan's use of world shrimp products exceeded that of the U.S. in 1979 and 1981, increasing the degree of competition for stable world supplies. Imports have been suggested to have a depressant effect on producer prices. As the domestic market comes to rely more heavily on imports, producers have become increasingly more concerned about the price effect and substitutability relationships that imports have with the domestic product. Mexican imports, the major source of imports into the U.S., enter the country tariff free. These imports compete favorably in the domestic shrimp processing market with domestic produced shrimp. Though some imports do enter the U.S. in a processed or semiprocessed form, most enter as unpeeled, rawheadless shrimp, making them an excellent substitute for the same domestic product (Hu, 1983). Increased imports of maricultured shrimp may have a varied effect on the domestic market. Shrimp grown in controlled production systems are to a degree isolated from seasonal climactic changes which greatly affect natural produc tion. Thus, cultured shrimp may be available year round, possibly reducing seasonalities in price. In addition, cultured shrimp imports will consist of very few size classes. Ecuador, for example, is produc ing primarily 3135 count shrimp (Mock, 1982). Thus, markets for speci fic size classes may be impacted disproportionately. In an attempt to place a general upward pressure on exvessel prices, domestic producers have suggested initiating a tariff or quota system on imported shrimp products. Both policies have been shown empirically to have the effect of reducing the level of imports, thereby raising domestic prices (Prochaska and Keithly, 1983). Processed shrimp products were valued at $1.1 billion in 1982, 24.5 percent of total value of all processed fishery products in the U.S. The impact of import restrictions through the use of a tariff or quota would have the effect of reducing the supplies available for processing and marketing. This reduction may have the effect of increasing the cost per unit processed as economies of size in processing are lost in R the short run. This would no doubt vary depending on the volume and form of product marketed (breaded, peeled and deveined, or canned). For example, breaded shrimp producers are more dependent on imports than producers of peeled or canned products. A reduction in imports may initially have a greater impact on the cost of producing breaded shrimp than other forms (Prochaska, 1983). The actual cost effect on prices at other market levels would further depend on how much of the cost is passed on to retail in the form of high prices, absorbed in the proces sor profit margin, or passed down to producers in the form of lower ex vessel prices, if indeed, the processor has the ability to do so. The dockside value of commercial U.S. shrimp production and the value of imports have also exhibited considerable change since 1960. Total value of the domestic commercial catch increased from $66.9 mil lion in 1960 to $509.1 million in 1982, which represents nearly a seven fold increase. From 1960 to 1970, the value of landings increased on an average annual percentage basis of 8.0 percent. Between 1970 and 1982, the annual rate increased to 13.4 percent. However, quantity landed exhibited only a 3.3 average annual percent increase between 1960 and 1982 (U.S. Dept. of Commerce(b), various years). Total domestic produc tion and imports have remained relatively stable during the last four years, with imports showing a significant increase only in the last two years. Import value, on the other hand, has continued to increase since 1960. From 1960 to 1970, the value of imports increased from $36.4 million to $200.0 million in 1970, an average annual percentage increase of 13.9 percent. The value of imports continued to increase to $980.2 million dollars in 1982, an average annual increase of 16.4 percent. Preliminary estimates indicate that the 1983 value of shrimp imports was $1,223 million. The rapidly increasing value of imports and domestic production reflects the tight market for domestic as well as import supplies in the last decade. The divergence between value and volume of landings is further highlighted by the 574 percent increase in the average exvessel price for all size classes per pound over the same period. This price increased only 86 percent between 1960 and 1974, but increased by 170 percent between 1975 and 1982. The demand for shrimp products, and thus, consumer price, has been shown to be strongly related to disposable income on an annual basis (Doll, 1972; Hopkins, et al., 1980). Real disposable income in 1972 dollars in the United States increased 481 percent from $504 billion in 1961 to $1,060 billion in 1982 (U.S. Dept. of Commerce(a), 1983). Total retail and institutional expenditures for all shrimp products in the United States, excluding export revenues, was estimated to be approxi mately $3.8 billion in 1980 (Hu, 1983). In contrast, total expenditures for shrimp products was still less than $1 billion in 1975. Institu tional (restaurant) sales accounted for 81 percent of the market in 1980, with 19 percent going to retail sales (food stores and retail grocery). The institutional share has remained at least 70 percent since 1960 (Hu, 1983). Prices for rawheadless shrimp at the exvessel, wholesale, and retail levels for the 3140 (retail prices represent only the 3642 size class) and 2125 size classes (tail count per pound) generally trended upward between 1968 and 1983 (Figures 1 and 2). During this 16 year period, however, prices, margins, and shares endured distinct periods of escalation, depression, and wide variability. 1_ 12 S, L a 0 In a IS O II w  CO I0 V4 cm l 0* m Lca Li.  I1 ,,,,,, 13 ,4 W W r t 0 4bft .s / u a o. co* S 0 Yd o; d h ( ' 4 p: .4 'a I. Prices were relatively stable from 1968 to 1972, particularly for the 3140 size class. This reflects a period characterized by relative ly stable real disposable income and uniform levels of domestic produc tion and imports. During this period the retail/wholesale (Mrw) and wholesale/exvessel (MP) margins for the 3140 size class exhibited a slight upward trend. The margins Mrw and Mwp had average values of $0.50 and $0.21, respectively. The 2125 size class exhibited the same moderate upward trend in margins with M"w increasing from $0.41 to $0.81, while M"w increased from $0.18 to $0.36. Average values during this period for Mrw and MwP were $0.70 and $0.24, respectively. Whole sale and exvessel share of retail dollar remained constant for both size classes, with an average wholesale and exvessel share of retail dollar at 71.5 and 58.8 percent, respectively, for the 3140 size class, and 69.0 and 58.6 percent, respectively, for the 2125 size class. Prices for both size classes increased drastically and became much more volatile during the period from 1973 to 1978. Prices rose through 1973 and peaked in early 1974 as real disposable income increased and 1973 supplies were low. However, prices declined during 1974 as a real income declined. Domestic production remained low in 1974 but imports reached a record amount. Prices climbed again from 1975 to 1976. Record domestic production and imports in 1977 signalled a drastic decline in prices. However, prices climbed steadily throughout 1978 as total supplies fell off and real disposable income steadily increased. During this seven year period Mrw for both size classes varied consider ably, while MwP exhibited a stable upward trend. The margins Mrw and MRP averaged $0.75 and $0.46, respectively, for the 3140 size class, while Mr and MEF averaged $1.04 and $0.51 for the 2125 size class. Wholesale and exvessel share of retail dollars increased slightly during the period, with an average wholesale and exvessel share of retail dollar of 76.7 and 62.8 percent, respectively, for the 3140 size class, and 75.3 and 63.9, respectively for the 2125 size class. The three year period from 1979 through 1981 witnessed rapidly escalating margins between retail and wholesale prices for both size classes, which were maintained even as wholesale and exvessel prices fell to a fouryear low in 1981. Thus, in contrast to previous years, retail prices did not closely follow movements in wholesale and ex vessel prices. Prices peaked in 1979 as domestic production reached a low equal to pre1970 levels. In addition, real disposable income advanced steadily in 1979. In 1980 and 1981, total supplies of shrimp increased and prices continued to fall. However, retail prices for both size classes fell by a lesser amount in 1979 through 1981, resulting in a very large Mrw during this period. This large margin was maintained for nearly three years, being relinquished only in the last quarter of 1982. The margins M"w and MwP were both very erratic during this period. The retail/wholesale margin averaged $2.46, compared to an average MwP of $0.57 for the 3140 size class. The margins Mr and MwP averaged $2.77 and $0.78 for the 2125 size class. During this same period, wholesale and exvessel share of retail dollar fell to 63.0 and 54.1 percent, respectively, for the 3140 size class, and 66.0 and 56.5, respectively, for the 2125 size class. Prices at all three market levels resumed following one another more closely during the years 1982 and 1983. The margins stabilized during this period. The retail/wholesale margin averaged $2.00 and $2.28 for the 3140 and 2125 size classes, respectively. This can be j_ 16 compared to a much smaller but increasing MWP which averaged $0.81 and $1.03 for the 3140 and 2125 size class, respectively. As retail price remained rigid to advancing wholesale and exvessel prices, the whole sale and exvessel share of the retail dollars increased to an average of 73.1 and 62.1 percent, respectively, for the 3140 size class, and 74.7 and 63.4 percent, respectively for the 2125 size class. Prices at all market levels have trended up since 1968 but major breaks in prices, particularly at wholesale and exvessel levels, occur red in 1974, 1977, and 1979. These periods were characterized by slack ened demand brought on by reduction or fluctuations in real disposable income. When the economy is in a state of flux due to recessionary conditions, consumer real disposable income also fluctuates. As a result, demand for shrimp products and, thus, shrimp prices, are equally unstable (Prochaska and Cato, 1981). Record production in 1977 helped offset the low prices. During these periods vessel costs were increas ing, further tightening the cost/price squeeze. The inflationary spiral which began in the early 1970's placed increased pressure on the profit margins of producers and processors. Fuel is now the major single cost component for shrimp vessels, accounting for 60 to 70 percent of the variable costs of a fishing trip. The high fuel requirements for the larger offshore boats placed many operators in financial jeopardy as diesel fuel exceeded a dollar per gallon. As a result, federal assis tance in the form of fuel subsidies has been unsuccessfully solicited by vessel owners. The dramatic price recovery in 1978 and 1979 was negated to a great extent in real terms as costs skyrocketed during the same period. Interest rates on vessel loans, often a floating percentage through a Production Credit Association or local institution, exceeded ^; fvyw     ' .  17 20 percent in some cases, significantly above prime rate. The last few years, as a result, have exhibited an increasing number of foreclo sures. Some producers have been forced to suspend fishing or retrofit their vessel for alternative species, such as swordfish, shark, snapper, or grouper. Processors are also experiencing increased costs as labor, energy, and transportation costs, climb. Creditors are becoming less willing to advance new loans or extensions on existing mortgages at a time when it is becoming increasingly necessary to obtain conversion financing or loan extensions. Industry Issues In recent attempts to stabilize the economic conditions in the domestic shrimp industry, several policy strategies are particularly noteworthy. The unsuccessful 1981 Breaux Bill (HR4041) was introduced as the "American Shrimp Industry Development Act." The purpose of this legislation was to provide shrimp producers a means by which to estab lish financing and implement a coordinated program of research, producer and consumer education, and market promotion in an attempt to "improve, maintain, and develop markets" for domestic shrimp products. The major provisions of the bill addressed the establishment of a tariff or quota system, establishment of regional market boards, and creating a compre hensive data reporting network. Federal opponents argued that most goals of the bill, with the exception of the marketing boards, were clearly within easy reach of the current management process. The controversial Texas closure has generated varying results. Normally, the offshore Texas season is closed from June until mid July, out to nine fathoms. This leaves a large portion of the FCZ, which extends out to 200 miles, open to shrimping. However, beginning in 1981, the entire FCZ was closed to shrimping except out to four fathoms with a 25 foot trawl. This represents an attempt to protect small shrimp and increase the average size shrimp caught, thereby increasing prices and gross revenues to the producer. The results in 1981 signal led a successful year with Texas landings and value up. However, the 1982 and 1983 closure brought just the opposite results. Texas pro ducers questioned the uncertainty of the closure, especially since no fishing in the FCZ coupled with the possibility of minimum effect from the closure would be disastrous. Louisiana producers argued that Texas shrimpers would encroach on their traditional grounds during the clo sure. In addition, Louisiana processors argued that a supply glut may hit the market with less than efficient means to deal with the excess supply. In general, the U.S. shrimp industry has exhibited decreasing catch per unit effort, increasing variability in producer price, and increas ing costs of production. In addition, producers particularly have made a case that they are experiencing reduced profits. Though there appears to be no quick fix, several policy measures to address these problems exist, each with its own set of advantages and disadvantages. In an attempt to stabilize prices at a higher level, imposition of a tariff or quota system has been suggested. Theoretically, in the presence of import restrictions, prices should adjust to a higher level, with domes tic supplies being more dependent on U.S. producers. However, the erratic nature of U.S. production may have the effect of increasing price volatility. In addition, lack of political endorsement, the questionable impact on processor cost structure and reduced supplies to consumers, make this alternative a less than unanimous choice. A limited entry program, where the number of domestic producers is main tained at a lower than current level, has been suggested as a means by which production and profit per craft could be increased. This alterna tive provides a possible solution to the fulltime producer's complaint of an increasing number of parttime producers. However, limited entry poses questions such as by how much should the existing fleet be reduced, which craft are to be eliminated, who bares the burden of costs of enforcement, and how will displaced capital be utilized? The latter issue is particularly noteworthy due to the degree of capital immobility in the shrimp fishery. Thus, each of these "solutions" brings with it a complement of issues to be dealt with, with no certain answers. In summary, the U.S. shrimp industry has experienced a period of reduced growth beginning in the 1960's and extending through the 1970's. The industry has been characterized by volatility in recent years. Domestic production, imports and consumption demonstrated steady upward trends until the early 1970's. At that time, the trend disappeared and volatility set in. Thus, between 1970 and 1982, there appears to be .little trend in supplies and consumption, but an increasing level of yeartoyear variability. Prices and value, on the other hand, have maintained a fairly steady upward trend, but exhibited volatility in recent years. This trend may hold if world supplies reach a maximum and disposable income continues to increase. In addition, the increasing importance of Japan in the world shrimp market will provide for increased competition for limited supplies, causing further upward pressure on prices. Future supplies may be augmented, however, through the controlled production of maricultured shrimp in South America and Asia. The U.S. shrimp industry, particularly the more important Gulf industry, is in a period of adaptation and transition. Recently, pro ducers and processors have had to face rising fuel prices, increasing interest rates, growing levels of tarifffree imports, increased compe tition for domestic stocks, and a generally slackened economic situation on a national level. This has resulted in a number of vessels to either suspend fishing operations entirely or retrofit to seek stocks of alter native species. More widespread change can be expected as the industry adopts new harvesting, processing, and marketing techniques in order to become more profitable. Ultimately, the impact of this change is re flected in th price paid and received in the producer, wholesaler processor, and retail markets. Understanding how these impacts are transmitted through the pricing system and their order of magnitude is of crucial importance to management and trade policy formulation. Before the impact of the change can be fully understood, an understand ing of how prices and margins are determined in the market place is vital. Problem Statement The Magnuson Fisheries Conservation Management Act (MFCMA) of 1976 (PL 94265) has charged policy makers with the efficient management of the U.S. seafood industry, including the shrimp fisheries through the use of regional fisheries management plans. To accomplish this task, directives must be oriented toward biological, social, and economic issues. Consideration of one without the other may lead to invalid conclusions and inefficient policies. Developers of management plans are required to trace impacts of proposed legislation throughout the market system. Imperative to the economic component of a given management plan is the understanding of the structure, conduct, and performance of seafood market systems. This includes an understanding of the dynamics of price formulation in terms of the time, space, and form characteristics at each level of the seafood market. A better understanding of the existing shrimp marketing system is necessary for the obtainment of the overall objective of the MFCHA. The shrimp industry is the most valuable domestic fishery in dock side dollars in the United States. This particular industry has recent ly exhibited considerable price volatility and instability throughout the market system. A host of factors have contributed to this state of flux, such as fluctuating demand, tight world and domestic supplies, changing market structure, increasing dependence on imports, increasing costs of production, and fluctuating domestic economic conditions. Changing market conditions appear to have left the producer bearing the brunt of an array of economic symptoms. The symptoms which are being expressed by producers, such as relatively depressed dockside prices and reduced revenues, have motivated interest in several management policies to help bolster demand for domestic products and, thus, act as price supports (i.e., import tariff, import quota, limited entry, and promo tional programs). In addition, the apparent concentrated nature of the shrimp wholesale/processing market level (less than 20 firms control approximately 90 percent of total U.S. output) may provide for some market power in terms of gathering and assessing market information. This may provide for a competitive advantage over firms in their own market level and also provide an informational advantage over firms in adjacent market levels. The recognition of the possible oligopolistic 22 nature of the wholesale/processing sector may provide insights into the price determination process at each market level. In addition to pos sible monoposonistic pricing, the concentrated nature of the processing sector may result in price leads and lags in the market place, with the market level possessing more timely and accurate information acting as a price leader. The market level with the information edge may be able to exploit this position in the price determination process to gain greater profits relative to adjacent market levels. The existence of this phenomenon is at least implied by recent legislation calling for aid in establishing cooperatives and market orders in the producer sector. Before the economic appropriateness of a tariff, quota, or limited entry program can be accurately assessed, an understanding of price dynamics is vital. This knowledge will provide a more clear view of how these policies will impact the various market levels. Studies done to date concerning the U.S. shrimp market system have provided some insight into the mechanism of the structural components of the system in an effort to understand market price fluctuations (Doll, 1972; Hopkins et al., 1980; Thompson and Roberts, 1982; Gillespie et al., 1969; Prochaska and Keithly, 1983). Previous research has provided a partial understanding of how imports, domestic business and economic factors, and biological elements impact the pricing system. Limited explanatory power has resulted. More importantly, contradicting model specifications in terms of the direction of price determination are evident in some of the previous major studies. No formal research has been undertaken to employ current methodology regarding price causality in the U.S. shrimp market system. In addition, no formal research has been carried out regarding the presence or absence of asymmetric price *7" response, speed and magnitude of price adjustment between market levels, and the determinants of prices and marketing margins. Further research must be performed to provide insights into the sensitivity of price transmission in a time (speed of adjustment), space (region of market), and form (size and degree of processing) framework. Policy makers need to understand the dynamics of price determination and transmission in the market and the impact to producers, processors, retailers, and consumers that increased control over prices in the market may pro duce. A more fundamental knowledge of price linkages would provide further understanding of how market levels interact and relate given stimuli internal and external to the market system. Objectives The purpose of the research is to investigate and model the dyna mics of price transmission between the producer, wholesale, and retail levels of the U.S. shrimp market system on a size class basis for raw headless shrimp. This will be accomplished by developing an econometric model of the prices and marketing margins. Primary emphasis is placed on examining the dynamics of price for each market level and price transmission between market levels. Insights, are developed into the nature of the price adjustment process between market levels. Speci fically, the objectives of the research are (1) to determine the univariate time series characteristics of the price series for each market level (producer, wholesale, and retail) by size class (3140 and 2125 count shrimp), (2) to identify the direction of price determination between adjacent market levels for the producer, wholesaler, and retail markets for each size class of shrimp in the market system, 24 (3) to examine speed of price adjustment between market levels for each size class, (4) to determine if price adjustment between market levels is sym metric or asymmetric for each size class, and (5) to identify major determinants of price and test hypotheses regarding price relationships between market levels. CHAPTER II THEORETICAL CONSIDERATIONS This chapter provides a brief discussion of the competitive market, with emphasis given to the vertical structure. The dynamic properties of price, such as the direction of price determination and lead/lag relationships are discussed to provide an understanding of how actual markets may depart from the static competitive model. Specifically, causality between market levels in a vertical market system, the nature of price spreads, and the importance of the mechanics of price transmis sion between levels in a vertical market system is stressed. Thus, this section provides a motivation for the modelling approach. Vertical Structure Bain (1964) discusses the market system as a means by which natural resources, productive facilities, and labor forces are developed and assembled to determine what and how much is to be produced and how the goods and services are to be distributed to users. Cochrane (1957) defines a market as a sphere or space where the forces of demand and supply interact to determine or modify price as the ownership of some quantity of goods or services is transferred with certain physical and institutional arrangements in evidence. In a perfectly competitive sense, many buyers and sellers come together to negotiate regarding a homogenous product with perfect information, no rivalry, and with free dom to enter or leave the market. As Kohls and Uhl (1980) argue, `i 26 arbitrage would result in an instantaneously determined unique equili brium price for any quantity of goods representing a given time, loca tion, and product form. Price formulation is a static process in this setting (Heien, 1980). When using the above concept of the market, one can visualize a benchmark case where a single equilibrium market price is established at which the quantities offered for sale by producers exactly equals the quantities demanded by purchasers. The situation would only be true in the simplest of markets where the original producers and final consumers are involved in a direct arbitrage. Most agricultural commodity markets are far more complex. In most markets, initial producers and final consumers are separated by a complex vertical network of intermediate processors, handlers, wholesalers, brokers, and marketing agents, each exhibiting its own input demand and output supply. In this sense, initial producers and final consumers do not face one another directly; rather market signals must pass through the market system whether the signal originates from the final consumer, initial producer, or inter mediate agent. Often, consumer demand is not for the primary product but for the primary product plus the utility derived from additional characteristics added through processing and the necessary marketing services. Thus, consumer demand is a direct demand for a final good such as breaded shrimp, as opposed to a rawheadless shrimp. The demand for the primary product is derived from the demand for the final good. The Marshallian consumer demand for a final good is simply the. quantity demanded by an individual (i) consumer over a given set of prices and a fixed income level (ceteris paribus) given as _ / i Di f(P, Y) where P is a vector of prices P1,p.,P and Y is income. Each Di is assumed to be a demand function homogenous of degree zero in prices and income and monotonically decreasing in price (Deaton and Huellbauer, 1980). The market (consumer) demand, or "primary" demand for the market then is the horizontal summation, of individual consumer demands Di. Demand exhibited by wholesalers, processors, and producers is derived demand. The demand is for the original good to be used as an input in a higher level in the market system. In other words, producers face the demand for their product by processors, who will in turn uti lize the product as input. The demand by an individual processor for the input is given as the value of marginal product (marginal product of input multiplied by the market price of the processed good). In a strict sense, this is only true when one input is utilized. When more than one input is utilized in the production of the processed good, substitution, output, and profitmaximizing effects must be considered (Gould and Ferguson, 1980). Similarly, when summing individual proces sor's value of marginal product functions to arrive at the market demand, a possible change in market price of the processed good from simultaneous expansion or contraction of all processors must be consi dered. Thus, the derived market demand for the processor level is not simply the horizontal summation over all processors of their value of marginal products for the input. Similarly, the supply faced by the market levels is derived supply. These supply relationships are derived from the primary supply of the producer and are best defined as the supply of intermediate goods (i.e. processor output). 28 The intersection of primary producer supply and the final consumer demand is of no real importance in a market where the product aust go through some transformation or processing to final form.' The price resulting from such an equilibrium would suggest that processing and marketing services are rendered at zero cost. Thus, market equilibrium is actually determined through the simultaneous equating of the supply and demand for the initial product plus marketing services. For most actual markets, there may be several levels, each representing different stages of processing or handling. At each level within the vertical market, a representative equilibrium price exists which represents the equating of the derived or primary supply and demand at that level and reflects value added through processing and marketing services up to that level in the market system. Representation of a conceptual model of vertical markets is pro vided in Figure 3. Primary demand at the retail, derived demand at wholesale, and derived demand at producer level, are represented by Rd, Wd, and Fd, respectively. Primary supply at producer level, derived supply at wholesale level, and derived supply at retail level, are represented by F8, Ws, and R0, respectively. Retail, wholesale, and producer level prices which result from the solution of the six demand and supply equations representing the three market levels are denoted by pr pW, and p respectively. Note that an equivalent quantity of good Q is being traced through the market system, making adjustments for processing inputs and product loss at each stage of processing. In actual markets there may be several stages of processing. In addition, alternate channels may exist depending on the ultimate form and market of the raw good. Thus, submarkets may be defined, each with its own  PRICE pr P QUANTITY t Graphical Representation of a Vertical Market System with Equilibrium Prices pr, pW, and pf in Time Period t. FS Rd Figure 3. ~~ ,.\, 29 ,  I  price which reflects equilibrium between two adjacent submarkets; i.e., producer and first handler, first handler and processor, processor and wholesaler, wholesaler and retailer, and retailer and consumer. As Bressler and King (1978)'point out in a competitive framework, all of these stages and prices are interdependent and determined simultaneously in a single market context with multiple prices. Therefore, vertical market equilibrium prices dictate the simultaneous equating of supply and demand for goods and services across the various market levels. Bressler and King, however, do not discuss the possibility that alter native market organization or the time frame of analysis may warrant the price determination process to be viewed more appropriately as a recur sive lead/lag process, rather than simultaneous. Gardner (1975) presents a basic theoretical methodology for the determination of retail and farm price. This competitive model is an extension of the Allen (1938) and Hicks (1957) one product two input model and provides a means by which quantifiable predictions can be made regarding the impact that changes in demand and supply of food products would have on the retailfarm price ratio and the farmer's share of retail food expenditure. The model is developed in a static equilibrium framework. Gardner's static approach implies shifts in supply and demand would result in instantaneous shifts in price with no concern given to the time path of adjustment. In relaxing the static setting Heien (1980) develops a price determination model that allows for dis equilibrium in the retail, wholesale and farm market levels. In parti cular, Heien argues that as the time period of analysis becomes shorter, the dynamics of prices (i.e. speed and magnitude of adjustment, asym metry, and causality) become important. Watson (1963) notes that leads 31 and lags in pricing associated with disequilibrium are consistent with perfect competition in the short run. Thus, issues regarding the dyna mics of price transmission (lead/lag structures) become important when addressing pricing efficiency on a timeliness and accuracy basis for the short run movement in prices (Sporeleder and Chavas, 1979). As such, a dynamic rather than a static approach may be more appropriate when examining the transmission of prices between producer, wholesale, and retail levels in the market place when using weekly or monthly rather than quarterly or annual data. The price transmission model presented below relates to Figure 3. The retail (primary) demand for the final product is given by (1) Rd f(pr; V) where Rd is quantity demanded at retail by consumers, pr is retail price, and V is a set of exogenous factors which affects consumer demand, such as income. The retail (derived) supply for the finished product is given as (2) s f(pr, p; X) where pW is wholesale price of the processed product and X is a set of exogenous factors such as the cost for marketing services. The wholesale/processor level in the model is characterized by derived relationships of the demand and supply sides of the market. The wholesale demand is a derived factor demand from the retail level for the wholesale/processor component of the final good. This relationship is given as __ (3) Wd f(pr. pW; X) The supply relationship at the wholesale/processor level is derived from the producer level in equivalent units. This supply is given as (4) W = f(pW, pf; Y) where pf is producer price and Y consists of other wholesale costs, such as storage. The producer demand, which is derived from the wholesale demand for producer output, is given as (5) Fd f(pW, pf; Y) The primary supply as an aggregate of producer output is given as (6) Fs f(p; Z) where Z is a set of exogenous factors affecting production, such as weather. When the market is assumed to be in equilibrium, i.e., Rd Rs, Wd = W, and Fd = FS, partial reduced form expressions for retail, whole sale, and producer prices can be obtained from solving 1 and 2, 3 and 4, and 5 and 6, respectively, yielding (7) pr fCp; V,X) (8) pw f(pr, pf; X,Y) (8) pw = (9) pf = f(p ; Y,Z) which are fully simultaneous in prices. In Gardner's static competitive model, these reduced form expressions for price are assumed to adjust instantly to changes in raw product supply, supply functions of market ing services, or retail food demand. In addition, Gardner suggests that simple markup rules in pricing at each market level are not adequate 33 enough to accurately model price determination processes. Heien, how ever, advocates the viability of markup pricing rules with a model incorporating short run disequilibrium such that Rd s Rs, Wd s Ws, and Fd 0 Fp. In this situation the time path of price adjustment becomes important as time inherently becomes one of the exogenous factors in price determination. Heien further suggests that price changes are passed unidirectionally upward through the pricing system via a markup policy at each market level, which he shows is consistent with firm optimization behavior. Thus, a lead/lag price determination relation ship between market levels may arise. In the Gardner model, the direc tion of causality, which may ultimately be an empirical question, is indeterminate, or assumed nonexistent, due to the implied simultaneous specification. Given the presence of highly competitive markets, auc tions, and the increased use of computerized marketing techniques, rapid and simultaneous adjustment of prices to changes in supply and demand may be valid. However, in less competitive and less organized markets, such as those for many seafood products, the notion of short run dis equilibrium and the possibility of prices needing time to equilibrate warrants the investigation of the resulting dynamic properties of price transmission and causal direction as prices move between equilibrium points among market levels in a lead/lag fashion. Disequilibrium is particularly of interest in markets where price supports and production control exist. Though most seafood markets (shrimp being no exception) are not as yet subject to these management policy measures, Bockstael (1982) has applied disequilibrium models to various domestic seafood markets with some success. In markets where disequilibrium is a result of erroneous or delayed informational 34 signals, stability implies that the market will eventually equilibrate to the static equilibrium point through some lag recursive adjustment process (Silberberg, 1978). A stable market then will result in long run and static adjustment tending to produce the same equilibrium point. Ward (1982) suggests that increased concentration at one market level may provide that level with a competitive edge in assessing market information. This advantage effectively allows that market level to react before other market levels and establish a pricing lead. Miller (1980) attributes the lead/lag pricing structure to increased use of formula pricing, demise of terminal markets, and general structural changes in the market. An attempt to directly estimate and interpret a set of reduced form expressions, such as represented by equations 7, 8, and 9, will be frustrated in that the signs of the parameter estimates will be ambigu ous. This is due to the parameter estimate being unspecified as to whether the representative shock originated from a supply or demand shift (Chiang, 1974). In this sense, the above expressions for prices pr pW, and p are not sufficient for testing hypotheses regarding lead/lag relationships and determinants of prices and margins. A more appropriate strategy for a study of price determination would be to conceptualize a model that will yield structural price expressions at each market level that are directly estimable. A conceptual model of a vertical market system for shrimp products is given in Figure 4. This market system has four linkage points of adjacent market levels: consumer/retailer, retailer/wholesalerproces sor, wholesalerprocessor/first handler, and first handler/producer. These market level interfaces are particularly characteristic for the 35 PRICEt   ~  m n m a   R= S QC= D = 0 P Qs= f(pr,pw,cr) f(pr,D) f(p f,p ,cW) f(pr,pw,cr) f(pf ,pP,cf) f(pf ,p ,c) f(pP,X) QF_= f(pPpfc) Q QUANTITY t Graphical Representation of a Vertical Market System with Supply and Demand Given Implicitly at Four Market Levels and the Corresponding Equilibrium Prices pr, pW, pf, and pP in Time Period t. Figure 4. 36 domestic shrimp market where most shrimp produced domestically are off loaded by a fish house (first handler) and sold to a wholesaler and/or processor. The first handler for imported product is normally a bro ker. The domestic and imported product is then processed under retail or processor brand name and sold to the retail market. The consumer's demand for retail product is given as (10) QD f(pr, D) C where QD is quantity demanded, pr is retail price paid by the consumer, and D is a set of demand shifters which would represent income, price of substitutes, etc. The retailer's supply of retail product to consumers is given as SR r w r (11) QS f(p p, c, ) R where QS is quantity supplied, pw is wholesalerprocessor price or price of retail input paid to the wholesaler, and cr is prices for marketing inputs utilized by the retailer in transforming the product to a shelf ready product. The retailer demand for product from the wholesaler processor is given as (12) QD f(pr p c ) R R where QD is quantity demanded, which is the same function as for QS. R R The similarity between QS and QD is valid in terms of the theory of the R R firm as QD represents the input demand of a retail firm and QS repre sents the output supply of a retail firm. These two relationships will be functions of the same variables; i.e. input and output prices, under profit maximizing behavior (Silberberg, 1978). The wholesalerprocessor's supply of product to retail firms is given as (13) QS M f(p p W cw) W f where QS is quantity supplied, p is first handler price or the price paid by wholesalerprocessors to the first handlers or fish house owner, and cw is prices for marketing inputs utilized by wholesalerprocessors in transforming the product as received from the first handler to the product purchased by retail firms. The wholesalerprocessor firm's demand for product from first handlers is given as (14) QD M f(pf, pw cW) W W W w w w where QD is quantity demanded. The expressions QS and QD are functions of the same variables, and represent supply and demand, respectively, for a wholesalerprocessor firm. The first handlers supply of product to wholesalerprocessors is given as (15) Q = f(pf p f) F where QS is quantity supplied, pP is the price paid by the unloading or fish house to the boat, and cf which is the price of marketing services used by the fish house. The actual price per pound for the catch may vary, depending on whether the shrimp is sold after being sorted by size (packout) or sold on an average size per pound (boxweight) basis .(Nichols and Johnston, 1979). The first handler's demand for raw pro dact from producers is given as ,: (16) QD f(pf p cf) ~_____~ _  F where QD is the quantity demanded and which is given in terms of the F same variables as QS" The producers supply of raw product to first handlers is given as (17) f(pP, X) D where QS is the quantity supplied and X is a set of exogenous supply shifters, such as weather. By assuming that inventories remain relatively stable over time, the quantity supplied at each market level is determined by the equili brium quantity determined in the raw product market. Given that the supply of raw shrimp product is determined in the shortrun primarily by environmental conditions affecting the domestic production and by world market conditions affecting the supply of imports offered to domestic brokers, the supply of raw product to each market level is relatively price inelastic (Doll, 1972; Hopkins et al., 1980; Grant and Griffin, 1979). Conceptualizing the market in this manner, and not addressing the issue of inventories in any further detail, a set of price dependent demand expressions depicted in Figure 5 are given as C (18) pr = f(Q D) D R (19) pW = f(pr, cr, QD) (20) pf f(pW, c, QD) (21) pP f(pf, cf, Q) which can be derived for the retail, wholesale, firsthandler, and raw product market, respectively. Prices are now dependent on quantity (supply) at each market level. Normalizing demand expressions on price has been shown to be appropriate for agricultural products. Houck (1966, page 225) states that "although individuals make quantity 196 Bak PRICE t p PW Figure 5.  a _ " .  a _ pr = f(QD,D) pW= f(prcr.r R P p f f (p ,c,Q ) pP= f(pf,cf,Q) Q QUANTITY t Graphical Representation of a Vertical Market System Characterized by Inelastic Supply with Demand Given Implicitly at Four Market Levels and the Corresponding Equilibrium Prices prT pw pf, and pP in Time Period t. __ ~__L ~ , 1 40 decisions based on given prices, market supplies of many agricultural products are so fixed in the shortrun that prices mast bear the entire adjustment burden." This argument for estimating price flexibilities applies to many seafood products, particularly to shrimp, as supplies are often determined by nonprice factors and can be considered exogen ous. Thus, a set of structural price dependent demand expressions, with an exogenous inelastic supply, can be derived that lend themselves to unambiguous interpretation of parameter estimatesan improvement over reduced form estimates. Expressions (18) through (21) are restrictive in the sense that price determination is recursive from retail to raw product markets. Certain structural attributes of the market and alternative pricing policies of marketing agents may dictate a different price determination process; i.e., upward recursive, a pricing locus or node at an intermed iate market level, or simultaneity. Thus, a more general expression of equations (18) through (21) with supply at each market level assumed exogenous would be C (22) pr f(pW, q, D) (23) pW f(pr pf, cr, ) W (24) pf f(pW, pP, c, QD) (25) pP f(pf, cf, QD) However, properly specifying which prices are endogenous, lagged endo genous, or exogenous relative to the price expression representing a given market level may not be possible based on a priori knowledge of the market. Thus, whether the vertical market price determination process is characterized by instantaneous interdependent (simultaneous) price shifts in a static competitive manner or whether unidirectional relationships exist in a fully downward, fully upward, or an intermed iate nodal form may very well be a theoretical question which requires empirical support. Causal Direction of Price Determination in the Vertical Market In attempting to estimate equations 22 through 25, the model must be specified in either seemingly unrelated, recursive, block recursive, or fully simultaneous form. In doing so, restrictive implicit assump tions (maintained hypotheses) regarding the direction of price determi nation (causal) structure of the price series are imposed. A more general representation of the structural price equations could be given as (26) pr f (M1; Q D D) (27) p f (M2; cr, rQ) (28) pf f (M3; cw Q ) (29) pP f (M4; cf QD) where Mi represents a set of prices consisting of subsets of endogenous, lagged endogenous, and exogenous prices. Testing for the causal rela tionships between prices provides for the identification of the subsets of each Mi. Though economic theory suggests the structural specifica tions of the model, a priori information may not be detailed enough to suggest the exact specification of leads, lags, and other dynamic com ponents, thus leading to model misspecification. Orcutt (1952, page  u t s 42 306) provides three motivations for determining the causal nature of the relations of an economic system: (1) Policy implications of any relation depend critically upon whether the relation holds in one or more directions, (2) Methods which are not designed to recognize the directional nature of relations will often lead to acceptance of a rela tion as nondirectional when on the basis of available data, only a more restricted causal relation is justified, and (3) If we do not use techniques adapted to finding causal, as contrasted to nondirectional, relations, we may fail to find relations which actually exist and which could be found on the basis of available data. If there exists a strong causal structure that is not embodied in the structural specification of an explanatory model, the possibility of biased and inconsistent parameter estimates exists. Bishop (1979, page 2) states that "given the potentially serious problem with simultaneous equations bias when a simultaneous system is estimated by a single equation method, it is important to ascertain the causal structure." This is no less true when modelling in a dynamic lead/lag framework. Sims (1972, page 540) notes that "most efficient estimation techniques for distributive lags are invalid unless causality is unidirectional" in the Granger sense. Thus, testing the implicit causal assumptions on which most single equations or systems regressions are based is of vital importance. Strotz and Wold (1960) emphasize that this is particularly true when dealing with explanatory rather than descriptive "curve fit ting" models. The direction of causality as dictated by the theory is a debate able topic. Colclough and Lange (1982) express a theoretical basis for questioning the direction of causality. They state that 43 a theoretical basis for questioning the finding of unidirec tional causality from producer to consumer prices also exists. Derived demand analysis specifically yields a model of price causality from the consumer price level to the producer price index. This analysis has gone surprisingly unnoticed and untested. Consider supply costs and the deter mination of the cost of production. The producer pays the opportunity cost of resource or the services of resources in order to acquire input. The opportunity costs of resources reflect the demand for input between competing uses. It is the demand for final goods and services that generates the opportunity costs of resources and intermediate materials. This suggests causality from consumer prices to producer prices (page 380). Heien (1980), on the other hand, suggests that the competitive market dictates the direction of causality from producer to consumer through markup pricing rules. Bishop (1979) reiterates this confusion over the direction of causality by stating Some assume that changes in prices at the farm level lead to changes in the wholesale and/or retail prices. Others assume that because of the nature of the food processing industry, no strong relationship exists between producer and retail food prices (page 1). Van Dijk (1978) points out that the theory of price formation in the vertical market system does not provide an unambiguous indication of the shortrun cause and effect nature of prices. When retail prices lead producer prices, derived demand would appear to be manifesting itself in the market place. Alternatively, when producer prices lead retail prices, an adaptive pricing or markup policy may be evident. Van Dijk suggests that this scheme is not clear cut in that derived demand may result in producer to retail price movements if producers are anti cipating future demand conditions. Causality is often referred to as a time related phenomenon and its presence (in a unidirectional sense) implies recursiveness (Van Dijk, 1978). Thus, the sampling interval of the data relative to the changes in the "lead" and "lag" variables may obscure the identification of a recursive structure. An apparent interdependent instantaneous change, or simultaneity, may be an appropriate inference if the sampling inter val exceeds the time lapse of response between lead and lag variables. In this sense, daily, monthly, quarterly, or annual data may suggest different price determination processes. This information, however, would be no less helpful in correctly specifying a "long run" versus a "shortrun" model. There have been numerous studies investigating the direction of causality in agricultural markets (Bessler and Schrader, 1980a; Miller, 1980; Ward, 1982; Ngenge, 1982; Grant, Ngenge, Brorsen and Chavas, 1983; Spreen and Shonkwiler, 1981; Van Dijk, 1978). Additional studies have analyzed markets at the macrolevel using price indices (Silver and Wallace, 1980; Sims, 1972; Colclough and Lange, 1982). However, no studies have been done to test the direction of price causality between vertical market levels in the seafood market of the U.S. Before a model for the U.S. shrimp market, such as that represented by equations (26) through (29), can be specified and estimated to address the issue of the dynamics of price determination, the causal properties of the price determination process mast be identified. Price Spreads Between Market Levels Tomek and Robinson (1972) point out that a price spread or market ing margin may be defined alternatively as (1) the difference in price ultimately paid by the consumer for the final product and price received by the producer for the raw goods or (2) the price or cost of the col lection of processing inputs and marketing services added to the raw product. Both can be viewed as the price response to some markup rule which is a function of the supply and demand for the marketing input. A price spread then is the difference between the price associated with two market demands adjacent or otherwise, relative to an equivalent quantity of goods. Retail margins would be the difference between the price paid by the retailer to the wholesaler and the price received by the retailer from the consumer, i.e., pr pW in Figure 3. Wholesale margins would be the difference between the price paid by the wholesaler to the producer and price received by the wholesaler from the retailer, i.e., py f in Figure 3. In an actual market setting, the spread between two prices would typically consist of wages, transportation costs, interest, processing, charges for marketing or handling services, and profit markup necessary to provide for an acceptable rate of return. In a competitive model, excess profit is dissipated to zero, or normal profit. The price found at the primary demand level (retail) or a derived demand level above the producer level consists of two components (1) producer related components and (2) processing and/or marketing related costs. As pointed out by Fisher (1981) and Friedman (1962) this margin concept operates under the assumption of fixed proportions in processing and marketing which implies elasticity of substitution (a) between all goods and marketing/processing inputs equal to zero. Recent studies by Gardner (1975), Fisher (1981), and Heien (1980) have produced more general models where a # 0. In addition, dynamic lead/lag price spread adjustment has been investigated through use of inventory disequilibrium models (McCallum, 1974). r 'i 46 Gardner identifies the major determinants of the price spreads as farm product supply, the supply functions of marketing services, and retail food demand. For example, given a perfectly elastic supply for marketing services, a shift in demand for marketing services would result in no changes in the margin, as suppliers of marketing services would be price takers. However, a less than perfectly elastic supply function would result in a changing margin as prices of services increase commensurate with increases in demand for services. Tomsk and Robinson (1972) argue that derived demand and supply curves shift as the cost of existing marketing services increase or as the supply of market ing services shift. Each of these factors will have an impact on the margin at given quantities as demand at different market levels converge or diverge. Alternatively, the demands may be parallel to each other, which implies that marketing costs, and thus margins, do not change over the range of quantities marketed. Shifts in product prices at a given market level are, in an effi cient competitive setting, fully and immediately reflected in prices at higher market levels. Thus, a competitive model will show no relation ship between margin changes and shifts in raw or processed prices (McClements, 1972). Given this mechanism, market signals are passed through the vertical system instantaneously and without distortion allowing market participants at each level to make rational decisions. In addition, competition dictates that the costs of marketing services just exhaust the margin between two demands. Changes in costs of marketing services are reflected in an equal change in the margin (Van Dijk, 1978). How this change is distributed between the interfac ing market levels (incidence) is a function of the relative price elasticities of demand and supply at each market level. The question of who bears the margin shift is particularly important to trade policy. As Fisher (1981) points out, for most agricultural products, the major adjustments which result from a shift in marketing margins will be borne by producer prices. Thus, producers have a strong economic motive for establishing some influence over cost efficiencies in the processing level of the market system. The price formulation policy to be used at each market level is dependent on a number of factors including firm policy and objectives, i.e., following the leader pricing, staying abreast of competition, or short run profit maximization (Dalrymple, 1961). George and King (1971) discuss other forms such as average cost, experimental, or intuitive pricing methods. Griffith (1975) and van Dijk (1978) discuss at great length the phenomenon of price leveling and its causes and consequences. These forms of pricing behavior are referred to as nonsystematic. On the other hand, systematic pricing methods are evident when the margin is determined by an absolute markup and/or percentage markup. These markups may be either constant or variable as quantity changes. Studies by Waugh (1964), Beck and Mather (1976), Etheridge (1975), Prochaska (1978) and Bockstael (1977) have addressed these two margin compon ents. Shepherd (1955), Rojko (1957), and Gardner (1975) suggest that most margins are a combination of the two components. However, Dahl and Hammond (1977) and Dalrymple (1961) assert that wholesalers typically use constant percentage markups while retailers use a constant absolute markup. 48 Price Transmission One characteristic of a competitive market is that prices are transmitted efficiently through the vertical market system. Brorsen (1983) points out that efficient price transmission can be thought of as exhibiting a minimum of lags and distortions. This is important as price serves as the market signal that relates changing demand and supply conditions between consumers and producers. In this sense, Sporleder and Chavas (1979) point out that pricing efficiency implies optimal resource allocation, minimum cost levels, and efficient distri bution. In addition, the major elements of pricing efficiency are given as timelines (rapidity of transmission) and accuracy (reliability) of price signals. The competitive vertical market system in a static sense is defined as having instantaneous price adjustment. However, most real world markets are characterized by lead/lag and other forms of distortion as prices gravitate toward some long run equilibrium. Price adjustment may be initiated by a causal (lead) market level which results in prices in adjacent market levels reacting, possibly asymmetrically, through some distributed lag structure. There have been a number of reasons offered as to how a lead posi tion in the price transmission process is established. Ward (1982) and Ngenge (1982) imply a relationship between assimilation of market infor mation and causality. Gupta and Mueller (1981) provide support for this contention by testing hypotheses of lead/lag structure in terms of market concentration and information. The major hypothesis is that concentrated market levels may have an advantage in assimilating market ~i . i T' ~C '~ information, which may in turn allow the more informed market level to lead other market levels in price formulation. On the other hand, Heien (1980) proposed that nonsystematic markup pricing rules were being utilized by retailers to take advantage of price signals originating from wholesalers and processors. Markup pricing rules would, in this case, put the retailer in a lag position. Thus, market structure and information availability may play an important role in the determination of lead/lag relationships which characterize the price transmission process between market levels. The speed and extent with which price changes are passed to adja cent market levels may not be equivalent for price increases or decreases. Thus, the market may be characterized by asymmetry in price transmission. At the retail/wholesale interface, this asymmetry may be a function of (1) the cost of changing prices on current inventories, (2) the need to move certain product types quickly, or (3) simply the reluctance of retailers to relinquish a price peak once it is estab lished. In addition, the desire to maintain most efficient use of capacity may result in retail price rigidity as wholesale prices vary. At the wholesale/producer interface, this asymmetry may not be as evi dent since atomistic producers are hypothesized to be price takers. However, if there exists monopsonistic pricing tendencies at the whole sale/producer level, wholesale price increases may not be passed to producers as strongly as price decreases. CHAPTER III EMPIRICAL METHODS The study of price dynamics in a vertical market setting necessi tates the investigation of the dynamic properties of price over time. This entails, first, the identification of the stochastic properties of the price series of concern in a noneconomic sense and, secondly, the incorporation of these underlying stochastic properties in an explana tory economic modelin order to test hypotheses regarding price deter mination processes. To accomplish the stated objectives of this study, price determination models must embody both economic theory and the empirically determined stochastic processes. The analysis is initially concerned with making inferences regard ing the stochastic properties characterizing observed price data through the use of time series methods. These stochastic characteristics are utilized to test hypotheses regarding lead/lag structures and the direc tion of price determination (causality) between interfacing market levels. Finally, the dynamic properties of price determination and the structural attributes of the market as suggested by theory are incor porated into an econometric model describing price at each market level. The analytical procedure outlined here will employ time series and regression (ordinary, two stage, and three stage least squares) methods. 3,. :< . 51 Time Series Analysis The objective of the time series analysis is to describe the under lying stochastic process that produces the original price series. These results can then be used to test hypotheses regarding the series of interest or forecast future values. A distinction regarding the result ing model is that the parameters determined are referred to in the literature as being "mechanically" derived, often considered devoid of theoretical economic content (Zellner, 1979). However, recent studies have supported the contention that time series models, in fact, are consistent with structural economic models (Anderson et al., 1983). In addition, the dynamic adjustment properties of price series data as revealed by time series analysis will allow testing of hypotheses orig inally motivated by the theory. There exists two principal time series approaches: time domain (time series) analysis and frequency domain (spectral) analysis. The two are theoretically equivalent (Granger and Newbold, 1977). As Ngenge (1982) states, a result in one domain always has its equivalent result in the other domain. The spectral approach is particularly useful if the price series is suspected of being characterized by significant periodicity and if the nature of these periodic components are unknown. Price data for shrimp in the U.S. have empirically been found to not contain an identifiable cyclical component (Thompson and Roberts, 1983). Rather, periodicity is restricted to seasonal influences. Thus, the spectral approach would be inappropriate. This study primarily uses the more appropriate BoxJenkins time domain approach, due to the nature of the data, access to and familiarity with established software and the relative ease of BoxJenkins estimation (Box and Jenkins, 1976). The two fundamental steps in time series analysis are (1) identifi cation of the appropriate model and (2) estimation of parameters. The following discussions outline these two steps. Univariate Time Series An observed time series (xl,...,xt) may be considered a realization of some theoretical stochastic process (Granger and Newbold, 1977). In a general sense, the observed time series is selected from a finite set of jointly distributed random variables, such that there exists some probability distribution function P(x1,...,xt) that assigns. probabili ties to the possible combinations of normally distributed xi, i1,.*.,t. Unfortunately, except for very small t, the probability functions of the outcomes (x1,...,xt) are not completely known. However, it is possible to generate a model that captures most of the underlying stochastic properties and, thus, the random behavior of the series. Each time series possesses a unique characteristicthe autocorre lation function. This function, which is independent of the unit of measurement, indicates whether the process moves in the same or opposite direction through time. In other words, the autocorrelation function provides a measure of how much interdependence (memory) there is between data points in a given time series. The autocorrelation function is given as y (L) 0 (L) =  x Yx(O) xm m where L is the number of lags, 8,(L) is the autocorrelation, Yx(L) is the covariance between xt and xt+L, and Yx(0) is the variance of the stochastic process under the assumption of stationarity. The covariance of the series is given as (L) COV(xt, xt+L) E[(xt E (xt))(xt+L E(xt+))] where t 0,1,2,...T. The variance is given as yX(0) COV(xt, xt+0) COV(xt, xt) VAR(xt Thus, ex(L) is defined as the autocorrelation at lag L. The very strict assumption of stationarity of a time series mlplies that Yx(L) and Yx(0) are the same for all values of t. In fact, sta tionarity implies that the joint and conditional probability functions are invariant with respect to time. In particular, a stationary time series will be characterized by 1 < 8x(L) < 1 for L > 0. In addition, a time series characterized by 0, where L 0 0 (L)  1, L 0 is called a white noise process. A white noise process is not autocor related and, thus, exhibits no interdependency (the series is serially uncorrelated). White noise is that part of a time series that cannot be explained by its own past. As Pindyck and Rubinfeld (1981) note, most time series encountered in economic studies are not white noise processes and are nonstation ary. However, these series can usually be difference one or more times to obtain stationarity. The number of differences taken, d, is known as the order of homogeneity. A difference series wt is given as  i  "'  S= (1B) x where 0 represents the difference operator where O&t = wt1 A random walk process given as xt xt1 + is homogenous of order one (first differenced. In fact, xt is station ary and white noise. If a series is white noise, it is also stationary, but the converse is not necessarily true. Autoregressive (AR) Process Many time series can be described as being an autoregressive pro ceas of order p such that xt is expressed as a weighted average of past observations lagged p periods with a random disturbance on the end P xt E ixti + R + t, t 0,1,2,...,T i=1 where # is the weight on each lagged xt, Ft is the random disturbance, p is some maximum lag, and R is a constant term associated with the series mean and drift (R)> when drift is present). Assuming R0, this may also be written in backshift notation as. (1 1B ... p B t #(B)xt t where #(B) (1#i1O...* OP) and can be viewed as a polynomial of order p in lag operator B. The lefthand factor #( ) acts as a filter on the tim series x resulting in a white noise process 9(e Pindyck and Rubin feld (1981) state that a necessary condition that x is stationary requires that the autoregressive process of order p be characterized by 55 P Z i< 1 il The sufficient condition is that roots of the characteristic equation #(B) 0 lie outside the unit circle. In addition, Fuller (1976) shows that when a time series is a stationary autoregressive process, the autocorrelation function 8x(L) is a monotonically declining function of L that decays exponentially to zero. An autoregressive process possesses infinite memory where the current value of xt depends on all past values. Moving Average (MA) Process Some time series can be defined as a moving average of order q where xt is a weighted average of random disturbances lagged back q periods. This series xt can be denoted as q xt j t + S where Oj is the weight on each lagged disturbance tj, q is the meaimm lag, and S is the mean of the process. Here we assume (as in the case of autoregressive model) that the random disturbance is generated by a white noise process. Thus, the mean S is invariant with t. In addi tion, by assuming stationarity, a moving average is characterized by q "e2<* i1 However, this is only a necessary condition. Rewriting xt in backshift notation and letting SIO yields xt 0(B) The invertibility condition requires that 8 (B)xt t where 1 (B) must converge and the roots of the characteristic equation 8(B) be outside the unit circle. A moving average process of order one (q1) has a memory of only one period. In general, a moving average process of order q has a memory of exactly q periods and the autocorrelation function is given by A I1 +1 "' qLq q L 1,,q (L) 1 + + 2 + + x 1 2 q 0 (truncated) L < q Thus, the autocorrelation function for a moving average process has q nonzero values and is zero for lags greater than q. This can be con trasted to the exponentially decaying lags for an autoregressive pro cess. There exists a relationship between moving average and autore gressive processes such that a finite order moving average process can be expressed as an infinite order autoregressive process. The converse is also true. In other words, an autoregressive process can be inverted into a pure moving average process and vice versa. This requires that certain invertibility conditions are met. In particular, the roots of the characteristic equations +(B) and B(B) must again all be outside the unit circle (Nelson, 1973). Integrated Autoregressive Moving Average (ARIMA) Process Many time series encountered are neither characterized by a pure moving average or pure autoregressive process. In addition, these time series are often nonstationary. Thus, time series such as these are combinations of the above processes with a degree of homogeneity greater than zero. An ARIMA process of order (p,d,q), where p, d, and q are the order of the AR, difference, and MA components respectively, is given as P q ZE L(1B) xti R + Z 10 j0 j1=0 For d0, this can be expressed as xt xt1 2xt2 tp R + Ft 1 l q  In backshift notation, this is written as (1 1B B2 . )xt R + (1 BB B2 .. 0qBq)t Finally, the above expressions, in difference form, appear as (B) xt R + (B)t where #(B) and B(B) are converging invertible polynomials in the lag operator B. Since xt has been difference (is now homogeneous station ary), the process can be modeled using an AR of order p and an MA of order q. Thus, xt is an integrated (I) ARMA, or an ARIMA (p,d,q) pro cess. Identification and Estimation of an ARIMA Model The discussion above has shown that a homogenous nonstationary'time series can be described as an ARIMA process of order p, d, and q. However, the correct specification of an ARIMA process necessitates selecting the proper values of p, d, and q to accurately describe the underlying stochastic process that generated the original time series. This task is accomplished by examining the autocorrelation function and partial autocorrelation function of the time series. Identification of an ARIMA model begins with determining the degree of homogeneity in the time series. If the autocorrelative function 8,(L) of the original data does not dampen quickly to zero, the data must be difference d times until a stationary series results. This decision is made by visually observing 0x(L) after each differencing to see if 0,(L) dampens quickly. After determining the degree of homoge neity, the order of the autoregressive and moving average components must be specified. For the autoregressive component, this is done by examining Ox(L) for oscillations. Examining the partial autocorrela tions of the series provides a more definite estimation of the correct value of x. The partial autocorrelation function is derived from a set of linear equations given as J  (L) E e 6 (L i), L = ...,j, x i 1i x which are known as the YuleWalker equations (Pindyck and Rubinfeld, 1981). The partial autocorrelation of order j (ejj) for an AR(p) is zero for j>1. Spikes in the partial autocorrelation function are indi cative of significant autoregressive terms (p), whereas spikes in the autocorrelation function are indicative of significant moving average terms (q). Once the ARIMA model has been specified as to the order of p, d, and q, the parameters are estimated. The BoxJenkins estimation tech nique utilized in this study is discussed in detail by Nelson (1973). The procedure is of an iterative nature, requiring initial approxima tions of parameter estimates. These initial parameter values can be determined through solutions of the YuleWalker equations. After the ARIMA model has been identified and estimated, the model should be checked to determine if the specification is correct. The residuals (innovations) of an estimated ARIMA model are given as A #B)81()xt If the model has been correctly specified, the residuals are white noise; i.e., the residuals are not dependent on their own past. Thus, the sample autocorrelation function of the residuals (rt) given as A k kk rk t t would be approximately zero for lags (k) greater than zero. If the model is correctly specified, the residual autocorrelations are indepen dent, normally distributed random variables with mean zero and variance 1/T, where T is the number of observations (Pindyck and Rubinfeld, 1981). A test is then performed using the statistic Q (Bar and Pierce, 1970) given as KA2 Q TE rk k1 k for the first K residual autocorrelations. The Q statistic is dis tributed as chi square with Kpq degrees of freedom. If Q is greater than the tabulated critical value, the hypothesis that the residuals are white noise is rejected. In this case, an alternative ARIMA model is selected and the procedure repeated. Direction of Price DeterminationCausality The empirical model must be properly specified with respect to the appropriate cause and effect relationship as suggested by knowledge of the market and as dictated by the theory. Correct specification is vital to obtaining valid parameter estimates. Misspecification is trivial only if R2 is equal to one (Pindyck and Rubinfeld, 1981). However, theory can only suggest the nature of the cause and effect relationship. Often necessary a priori information is not available to properly specify the direction of causality; e.g., between prices, in the market place, thus avoiding aisspecification and providing consis tent and efficient parameter estimates. A causality relationship between two time series of data, Y and X, can be defined in the Granger sense (Granger, 1969, page 428) where "Yt is causing Xt if we are better able to predict Xt using all available information, than if the information apart from Yt had been used." The rather cumbersome restriction of using all available information can be avoided as Shonkwiler and Spreen (1982) suggest by saying Yt causes Xt when Yt can improve the predictions of Xt compared to the prediction of Xt taking into account the past history of Xt alone. In this sense, Granger (1969) and Bishop (1979) give four basic definitions of interde pendency of a bivariate series as (1) Unidirectional causality Yt causes Xt or t causes Yt when using past information on Xt and Yt (2) Bidirectional feedback Yt causes Xt and Xt causes Yt, (3) Instantaneous causality Yt causes Xt where current X is better predicted by including current Y, or 61 Xt causes Yt where current Y is better predicts by including current X, and (4) No causality. Pierce (1977) discusses other causal patterns and these will be men tioned later. Each time series Xt and t is assumed stationary. Though the above definitions are not in testable form, definition (1) implies a recursive relationship between Xt and Yt, while (3) implies simul taneity. The "strength" of causality and the existence of a lead/lag relationship lose any meaning if (2) exists (Bishop, 1979). Testable forms of these definitions regarding the null hypothesis of no causality are given below. Granger Method The Granger test for unidirectional and instantaneous causality between two stationary time series Xt and Yt involves the estimation via ordinary least squares of a fourequation regression model given as n n A. X = Eat + c1Yti + ut j=1 i1 n 2 A.2 X = ZEaX + t j tj t ji1 n n 1 where n is the maximum number of lags used To test the null hypothesis that Y does not cause X, an Ftest is performed using the residuals from A. and A.2 to see if the are different from zero The F statistic with q and Tt degrees of freedom is defined as Jt1 iit 2 B.2 Y bY +Ev t it t ji1 where n is the maximum number of lags used. To test the null hypothesis that Y does not cause X, an Ftest is performed using the residuals from A.1 and A.2 to see if the ci are different from zero. The F statistic with q and Tt degrees of freedom is defined as (ESSr ESS )/(q) q,Tt (ESS )/(Tt) where t is the number of parameters estimated in the unrestricted model (A),where t is the number of parameters estimated in the restricted model (A.1), q is the number of parameters estimated in the restricted model (A.2), T is total number of observations, and ESSr and ESSu are error sums of squares for the restricted and unrestricted model, respectively. If the F statistic for A.1 and A.2 is significant then the null hypothesis is rejected, suggesting that Y causes X. A test of the di can be performed testing causality in the opposite direction to support this result (Colclough and Lange, 1982) or check for the existence of feedback. To check for either instantaneous or unidirectional causality, the index i in equations A.1 and B.1 is initialized to zero. The present study, however, will use the Granger method to test hypotheses regarding strictly unidirectional causality. These tests assume the error terms are uncorrelated white noise, such that E(utus) E(vtvs) 0 for s*t, for every t and s. Rejecting the null hypothesis that Y does not cause X suggests that X should be specified as some function of lagged Y. Sins Method Another method of testing for unidirectional causality has been proposed by Sims (1972) where the test involves a system of two regres sion equations n X E aY +e Xt a jYtj + et jn n 2 EbY + Xt EjbJ tj t Jo In this case, a test of the hypothesis that X does not cause Y is _ I performed by testing if the coefficients on future Y are not significantly different from zero. This procedure involves an Ftest defined as for the Granger test which uses errors from both regressions, the second regression not including future (lead) Y (l>ji>n). The variables can be reversed and the test repeated to check for causality in the opposite direction or feedback. The series are assumed to be stationary with white noise error. Filtering the X and Y series may be necessary to achieve stationarity. If the residuals are not white noise, the causality tests are invalid (Granger and Newbold, 1977). HaughPierce Method The Haugh (1972) and Pierce (1977) method makes use of the tech niques of determining residual cross correlation to infer causality between two time series X and Y. Assume initially that two time series, Xt and Yt, can be represented by G(B) Xt u, F(B) Yt = vt where F(B) and G(B) are converging invertible polynomial filters in the lag operator B (backshift notation) and the innovations vt and ut being white noise processes which are uncorrelated with themselves. The cross correlation between the innovations at lag k is given as E(ut,)k r (k) (utk U [E(ut)2E(vt :)2 ]1/2 Since u and v are not observed, the estimated value of the innovations are utilized resulting in the sample cross correlations r(k), which Haugh has shown are asymptotically normal independently distributed with zero mean and standard deviation of T1/2, where T is the total number of observations. Each r^v(k) can be individually tested for signi ficance where ruv^^(k) > 2T1/2 implies a significant cross correlation. Pierce (1977) lists alter native conditions of significance found in residual cross correlations and the corresponding causality inference as (1) ruv(k) *0 for some k>0 implies X causes Y, (2) ruv(k) $ 0 for some k<0 implies Y causes X, (3) r.,(0) 0 implies instantaneous causality, (4) ruv(k) 0 for some k>0 and some k (5) ruv(k) = 0 for all k<0 implies Y does not cause X, (6) ruv(k) 0 for some )00 and ruv(k) = 0 for all k<0 implies unidirectional causality from X to Y, (7) ruv(k) 0 for all k 0 and ruv(k) # 0 implies X and Y are related only instantaneously, and (8) ruv(k) 0 for all k implies X and Y are independent. This study adopts the definitions of instantaneous and unidirec tional causality and feedback as shown above. These notions of causal inference from residual cross correlations have been utilized by several recent studies (Bessler and Schrader, 1980a; Bessler and Schrader, 1980b; Miller, 1980; Shonkwiler and Spreen, 1982; Spreen and Shonkwiler, 65 1981). Haugh and Pierce suggest that the absence of unidirectional causality from X to Y can be tested using T [r ^ (k)]2 > x(c) k= where a (degree of freedom) is the maximum lag period. If the expres sion is true, then we reject the null hypothesis that X does not cause Y. Similarly, the null hypothesis that X and Y are unrelated would not be rejected at the a level if and only if a T E [r^^(k) 2 < X2 km uv The chisquare distributed statistic T E [r(k) ]2 will hereafter be referred to as the HaughPierce statistic. The data are used to discern the nature of price determination complementing a priori knowledge of the market. These causality results provide a more definitive basis for model specification. This study proceeds with the HaughPierce notion of causality. Dynamic Regression Methods The dynamic regression approach is a technique which utilizes the underlying dynamic and causal properties of a time series. The final result of the analysisthe transfer functionprovides a comprehensive model of the dynamic relationship between time series; e.g., two price series. In particular, the development of a bivariate transfer function in terms of prices in adjacent market levels utilizes the time series ARIMA filters for each series and the causal relationship between the innovations of each series to construct a distributed lag or impulse _ I 66 response model which embodies the dynamic nature of the relationship exhibited by the two time series. Haugh and Box (1977) outline the dynamic regression procedure as a twostep process which identifies (1) the relationship between two series by characterizing the univariate models of each time series and (2) the relationship between the two univariate innovation series. The innovation series are each assumed a white noise process and are con sidered the "driving force" of the original series. Shonkwiler and Spreen (1982) provide a more detailed outline of the dynamic regression procedure, which would be to (1) identify and estimate univariate time series or filter models for each series of interest via BoxJenkins methodology, (2) use the innovation series of the filtered series to determine the properties of causality between the series via Haugh and Pierce notions of causality, (3) identify a "dynamic shock" model that expresses the relation ship between the innovation series given the causal pattern from (2) via Haugh and Box methodology, and (4) derive an "impulse response" or distributed lag model utiliz ing knowledge of the original univariate filter models and the dynamic shock models via Haugh and Box methodology. This final specification is referred to as the transfer function. Filter Models The filters are determined by applying time series methods to the original time series; e.g., Xt and Yt, as discussed earlier in this chapter. Stationary time series ut and vt are obtained which can be represented by e(B)Xt ut S(B)Yt vt __ where e(B) and +(B) are invertible polynomials in the lag operator B. The terms ut and vt represent the white noise processes (innovations) obtained from of X and Y, respectively. The polynomials 0(8) and #(8) may be viewed as filters which are identified and estimated by using the BoxJenkins approach. The sample cross correlations between ut and vt {ru(k)} provide a means by which the properties of interdependency (causality) between X and Y can be assessed. In addition, tests of unidirectional causality can be performed using the chisquare Haugh Pierce statistic. These inferences regarding the direction of price determination are vital for specification of the transfer function. Dynamic Shock Model Having determined a lead/lag structure; e.g. Xt leads Yt, Haugh and Box (1977) show that it is possible to express Yt as a distributed lag on Xt as Yt = 6(B)Xt + at where 6(B) is some polynomial of Xt and at is an error process. The weights on the terms of the polynomial 6(B) are referred to as the impulse response parameters. These parameters characterize the response of Yt to changes in the "input" X net of the "masking effect" of the stationary white noise process at. To identify the order of the poly nomial 6(B) connecting Yt and Xt, a model must first be identified that connects the innovations ut and vt. This procedure will make use of the sample residual cross correlations r^W(k), where k is the order of lag, to arrive at a dynamic shock model given as vt = V(B)ut + Y(B)at where vt and ut are the white noise processes of filtered Y and X series, respectively, at is the dynamic shock model error process, and V(B) and Y(B) are polynomials of the lag operator B. Since by defini tion ut and vt are orthogonal to themselves; e.g., COV(ut,us) 0, for every t*s, then each parameter coefficient in V(B) is simply the bivari ate regression coefficient relating vt to utk given as V V mrAA(k) k a Uv t vt where ot and ut are the standard error of the innovation series and k t t is the lag of the residual cross correlation. Dynamic Regression Transfer Function Given that the parameter coefficients of V(B) have been identified and the order of the polynomial is known, the original filter expres sions e(B)Xt ut +(B)Yt vt are substituted into the dynamic shock model (Haugh and Box,, 1977) to give #(B)Yt V(B)O(B)Xt + T(B)at and isolating Yt yields the impulse response or transfer function Yt = #(B) V(B)(B)Xt + #(B) Y(B)a Completing the necessary multiplication and division of the polynomials shown above, a distributed lag function emerges which expresses Yt as a function of current and/or lagged Xt and is expressed as Yt = (B)Xt + X(B)at These polynomials are of interest in that they explicitly show the lead/lag structure between time series X and Y as revealed by the data. Depending on the nature of X( ), the parameters of 6(B) and X(B) may be estimated using ordinary least squares, nonlinear least squares, or maximum likelihood techniques. The transfer function embodies the causal properties and lead/lag structure between X and Y and provides the basis from which to determine the speed and magnitude with which change in X is reflected in Y, given the specification above. In addition, the structural characteristics of the relationship between X and Y have been supported by giving the data a chance to "speak" of relationships that do or do not exist, comple menting expectations based on theory and minimizing the probability of misspecification. Once the transfer function relating X and Y has been identified, the lead/lag structure; e.g., current and/or lagged prices, are included in a more complete explanatory model of the market. The regression methods that are employed to estimate the econometric model of prices are discussed below. General Regression Methods The analysis of time series properties, causality tests, and deri vation of the transfer function provides a set of expressions in terms of endogenous and lagged endogenous variables. These expressions evolve into a more comprehensive model when they are augmented with additional exogenous variables whose presence is dictated by theory and knowledge of the market. This study strives to generate such models describing price at each of three market levels. The method of analysis that was utilized in estimating the proposed model is linear regression. The use of ordinary, two stage, or three stage least squares regression is conditional on the analysis of the direction of price determination and the error structures of the esti mated expressions. A detailed discussion of regression technique and methods can be found in Kmenta (1971) or Theil (1971). If the analysis of the direction of price determination infers recursiveness, single equation methods such as ordinary least squares (OLS) may be an appropriate tool for estimation. However, if simul taneity is implied, a simultaneous system estimation approach, such as two stage (2SLS) or three stage (3SLS) least squares, is required. Both methods provide insight into relationships which exist within the struc ture of the market system. The initial estimates obtained from single equation methods or systems methods are referred to as structural esti mates. These estimates for each equation relate a unique set of prede termined and endogenous variables to a given endogenous variable. Each equation describes a part of the structure of the market (Theil, 1971). The estimates obtained can provide further insights into the market through the derivation of reduced and final form parameter estimates. The reduced form of the model expresses each endogenous variable of the model in terms of only exogenous variables. A reduced form estimate provides a clearer interpretation of the relationships between endogen ous and predetermined variables since the impact of a predetermined variable on each endogenous variable has now been isolated. Further, Kmenta (1971) states that the reduced form shows explicitly how the endogenous variables are jointly dependent on the predetermined vari ables and the disturbances of the model.  ~V~  A system of g expressions in terms of g endogenous and k predeter mined variables can be written in matrix notation for each observation as rY + BX E t t t where Y is a gxl vector of endogenous variables, X is a kxl vector of predetermined variable, r is a gxg matrix of endogenous variable coeffi cients, B is a kxk matrix of predetermined variable coefficients, and E is a gxl vector of disturbance terms. Once the system of g equations has been estimated, it can be expressed in reduced form as Yt r1BX + rlEt or Yt IXt + V where v is a gxk matrix of derived reduced form estimates and V is a gxl vector of disturbances. The elements of w, which include exogenous and, possibly, lagged endogenous variable coefficients, are referred to as impact multipliers (Goldberger, 1964). The impact multiplier measures the immediate effect of a change in the predetermined variable on the endogenous variable after all interdependencies have been accounted for in the same time period. If the matrix t includes lagged endogenous variables, estimates can be derived that measure the total effect of changes that may take one or more time periods (suggested by the pre sence of lagged terms) to work through the market. These parameters are referred to as total multipliers and are derived from the final form of the matrix of reduced form estimates. Thus, in the presence of lagged endogenous variables, the reduced form estimates represent an inter mediate step. _ * The reduced form matrix w can be partitioned into submatrices such that Yt do + DYt.1 + D2Xt +Et where Yt is a gxl vector of endogenous variables, Yt1 is a gxl vector of endogenous variables lagged one period, Xt is a kxl vector of the exogenous variables, dO is a vector of constant terms, D1 is a gxg matrix of derived reduced form estimates for the lagged endogenous variables, D2 is a g*k matrix of derived reduced form estimates for the exogenous variables, and It is a gxl vector of disturbances. The ele ments in D1 and D2 are impact multipliers. For the sake of simplicity, no lagged exogenous variables are included in this discussion and the endogenous variables are only lagged one period. To obtain a final form expression for the system, Yt must be expressed in a form free of lagged endogenous variables. The expression Yt lagged one period and substi tuted back into Yt gives Yt (DldOdO) + DIYt + D D2Xt1 + D2t + D t +t Repeating this procedure s times yields a s 5 t E d + Dts + E D Xt + ED1 t 10 1 1 1 10 However, note that if lim DI 0, Si 1+ Then by dropping the te subscript, can be written as Then by dropping the time subscript, Yt can be written as Y D + XI + E 73 where D (I DY)1d X (I D1)D2, and E (I D1)1 The elements of D, X, and E are referred to as the final form estimates of the model. CHAPTER IV EMPIRICAL MODELS Introduction The theoretical economic model of a system of price dependent demands for the major market levels in the domestic shrimp marketing system was developed in Chapter II. The empirical form of the model is presented in this chapter. Initially, the price dependent demands are reintroduced in implicit form and allied with specific sectors of the domestic shrimp market system. A general discussion of the data uti lized by the analysis is given. Explicit asymmetric price dependent demand expressions, with specific data needs are discussed for three market levels on a monthly and quarterly basis. In addition, expres sions for the margin between levels are derived. Finally the estimation procedures are summarized. Implicit Models A general representation of the structural price equations devel oped in Chapter II are given implicitly as (30) pr f(M1; QD D) (31) p f2(M2; cr QR) (32) pf f3(M3; cw, Q) (33) pP f4(M; c QD) 75 where pr p9, pf, and pP represent prices received by retailers, whole salers, first handlers, and producers, respectively. Mi represents a set of input prices consisting of subsets of current and lagged endogen ous and exogenous prices, D is a set of retail demand shifters, %, (, QW, and are the quantities offered by retailers, wholesalers, first handlers, and producers, respectively, and cr, cw, and cf are costs associated with offering the product to consumers, retailers, and whole salers, respectively. Each price expression coincides with demand at a given market level of the domestic market system. An illustrative schematic of this system of market channels is presented in Figure 6. The schematic is divided into four sectors. Each sector represents a market level characterized by a given demand expression, with sector A, B, C, and D associated with demand pr, pV, pf, and pP, respectively. Thus, each demand represents the price determination process that exists in a given sector of the market system for freshfrozen, rawheadless shrimp product. The final specification of the price dependent demand model is constrained by available data. The objectives of this study require inferences to be made regarding price determination on a size class basis. Estimation of the full set of demand models represented by equations (10), (12), (14) and (16) given in Chapter IIi i impossible due to the lack of data by size class necessary to specify each demand expression (data will be discussed in detail later in this chapter). Thus, data availability placed restrictions on which of the expressions ~tar~~'  ~  Foreign Shrimp Domestic Shrimp SProduction I Production  Figure 6. Market Channel Schematic Representation for the U.S Shrimp Market System. I ___ ___ ., 77 represented by equations (30) through (33) could be estimated. Price data is not available to describe the transaction between the first handlers and the wholesaler/processor (region B is Figure 6). Thus, only expressions (30), (31), and (33) are modeled on a monthly and quarterly basis for two size classes of freshfrozen, rawheadless shrimp product. Supply models were not estimated due to the assumption that supply of raw product is exogenous and inelastic with respect to price. Symmetric and Asymmetric Models Price models often hypothesize that increases and decreases in price at one level are passed on equally to adjacent levels (Reien, 1980). The question here is not one of demand irreversibility, such as habit formation with a given good or its competitors. Rather, the question is one of asymmetry in price transmission between adjacent market levels. The possible reasons for asymmetric price response have been discussed in Chapter II. Once the direction of price causality between adjacent market levels has been determined, the question of asymmetry in price transmission can be addressed. Asymmetric tests are restricted to recursive models. The methodology for dealing with the inherent endogenous nature of asymmetric variables in a simultaneous framework is not developed in this study. Only if causality between the prices of adjacent market levels is found to be unidirectional will asymmetric models be tested. A price equation, assuming the direction of price causality is upward through the market system, may be given as (1) Rt MO + t wt + when Rt is retail price, Wt is wholesale price, and et is the error term. This simple model assumes symmetric retail price response to changes in wholesale price regardless of whether wholesale price increases or decreases. An alternative Wolfframform price equation (Young, 1980) would allow for asymmetric price response and is given as (2) Rt o + i WIt + WDt + W t, t ,...,N where t WIt = (w wti) Iti t WDt M E (Wti Wti1) DDti .t i ti "ti1 0, otherwise D 1, Wti Wti1 DD  O, otherwise where Wit and WDt represent cumulative wholesale price increases and decreases, respectively. Thus, testing the significance of al and a2 is a test of the significance of the effect of a wholesale price increase and decrease, respectively. Gollnick (1972) suggests a convenient rear rangement of equation (2) such that Wt = W W I + WDt (Identity) wit w W W "t where W0 equals Wt for t0. Substituting for WIt gives  .~ 79: Rt 0 + a (wt WDt)+ 2 WDt + Ct which yields Rt + 1 Wt + "2 t + where a (C aL W0) and 42 (a2 al). A test of significance of (a2 o1) provides a direct test of asymmetry. Recall that ac measures the reaction of Rt when Wt increases and a2 measures the reaction of Rt when Wt decreases. The significance of a2 can be measured via the estimate E2 by writing 02 a2  and var(a2) var(a + al) var(al) + var(a4) + 2 Cov(ai, a4). The tstatistic would then be written as M (2 + a) 0 2 + t  NVAR (G2) Var a, + Var a2 + 2 Cov (ci 2) where is the estimate of a. If in the event that 4 is found to be insignificant, the test of significance on the coefficient a, reverts to a symmetric test of retail price response to increases or decreases in wholesale price. Expressions for pr pW, and pP can now be written in explicit form. Data The estimation of time series properties and analysis of causal relationships of prices for shellon, freshfrozen, rawheadless shrimp (hence forth referred to simply as rawheadless) at retail, wholesale, and exvessel market levels was accomplished for the years 19681981. Monthly and quarterly price models were estimated with data from 1972 1982. The analyses were oriented toward two size classesthe 3140 and 2125 tails per pound ("count") sizes classes of shellon, freshfrozen, rawheadless shrimp. The size class price and quantity data at each market level relate to these specific size class, with one exception. Retail price data are not reported for the 3140 size class. Retail prices are given, however, for the 3642 size classes. Though the 3642 size class represents a smaller shrimp than the 3140 size class, this study circumvents this data inconsistency by assuming the prices for the 3642 and 3140 size classes are not significantly different. For the sake of notational simplicity, the discussions henceforth will refer only to the 3140 and 2125 size classes. However, the reader should bear in mind the discrepancy at the retail. level. Monthly prices, aggregate beginning inventories, aggregate land ings, and aggregate import data were obtained from the Shellfish Market Review published by the National Marine Fisheries Service (NMFS). Monthly cost index data were obtained from the Agricultural Outlook published by the U.S.D.A. and unpublished U.S.D.A. files. Monthly income and consumer price index data were obtained from reports pub lished by the Bureau of Economic Analysis and the Bureau of Labor Sta tistics, respectively. Monthly landings and import data on a size class basis were obtained from unpublished NMFS data tapes. Though 168 month ly observations were available for the time series and causality analy sis, the estimation of price models were restricted to only 120 observa tions due to data limitations on monthly landings and import data by size class. The quarterly observations were constructed from the published secondary monthly data. Quarterly price, income, and index data were constructed as unweighted threemonth averages of the monthly data. To obtain the quarterly price data, the monthly price series were simply averaged over threemonth periods for the years 1972 through 1981. An attempt was made to use a weighted average for the exvessel series, however, no significant gain was made relative to a threemonth average (the threemonth average explained 99 percent of the variation in the weighted average). Because of this, and since no reliable quantity variable was available to properly weight the 'wholesale and retail levels, a simple threemonth average was used for all three quarterly price series. Quarterly consumption, landings, and import data were constructed as unweighted totals over the same three month intervals. Beginning inventories on a quarterly basis, however, represent inven tories at the beginning of the first month of each quarter. Statistical Models The exact specification of the monthly and quarterly price models is conditional on the outcome of the first and second objectives as outlined in Chapter I. The causality analysis will determine the direc tion of price determination and, thus, what prices make up the subsets of Mi (equations 30 through 33) found in each price model. The causality analysis must be completed before the system of price models can be specified in terms of current and lagged exogenous and endogenous prices. The following discussion of the price models ignores the specification of Mi found in each model and discusses the variables which are given to be predetermined. A discussion of the final specification of each model is given in Appendix B. Excluding consideration of the prices found in Mi for each model and the definition of certain quantity variables, the price models for the 3140 and 2125 size class are identical relative to the predetermined variables discussed below. All price models are over identified. Price and quantity variables are in headsoff units. Retail Price Models The monthly retail price model for 3642 and 2125 count rawhead less shrimp is given as MR Rt a E 0 [M ] + C RDt + TCFPt + a CPIt + where Rt retail (noninstitutional) price in time period t (Shellfish Market Review, NNFS) RDYt aggregate real disposable income in billions of dollars (base year 1972)(Bureau of Economic Analysis), TCFFt Business Statistics: 1982, total retail supply (disappear ances from wholesale market) of all sizes rawheadless shrimp in millions of pounds (Shellfish Market Review, NMFS), CPIt consumer price index for meat and poultry products, deseason alized with 1972 100 (CPI Detailed Report, Bureau of Labor Statistics), NR number of current and lagged endogenous and exogenous prices found in Mf for each size class model, where i refers to size class, and af and f are the coefficients to be estimated, with the superscript r referring to the retail model. Each O is associated with a current 83 or lagged exogenous or endogenous price contained in MI. M4 and refer to a set of prices for the 3642 and 2125 size class, respective ly. The model is the same for each size class, varying only by the dependent price. Thus, only one model is discussed. The retail price expression represents the demand by consumers for the retail product and corresponds to equation (30). The retail price data represents grocery and food store prices for rawheadless shrimp in the Baltimore, Maryland area as reported by the National Marine Fisheries Service (NMFS). The model was specified as a function of quantities moving through the retail market and parameters which may capture shifts in retail demand income and prices of competing meat products. As income increases, demand for shrimp should increase, thereby bidding up the price of shrimp. Similarly, as the price of competing products increases consumers may consume more shrimp products, also bidding up the price of shrimp. In this sense l and 3 are hypo thesized to have positive signs. The consumption, or retail supply, of shrimp product should be indirectly related to price. This assumption should hold true even though TCFFt is aggregate in nature and TCFFt may pick up some substitution effects between other size classes and a very specific size class. Thus, i is anticipated to have a negative sign. The presence of Sf associated with a wholesale price allows for a price determination process between retail and wholesale price which is characterized by recursivity or simultaneity. The signs on current and lagged i are anticipated to be positive, reflecting a direct positive relationship between contemporaneous and lagged price movements at the wholesale and retail level. 84 The specification of the model is the same for monthly or quarterly data. The prices found in MT for each size class may differ for monthly and quarterly data as the price determination process evolves over a longer sampling internal since the data has been condensed into three month quarters. In the quarterly model all price parameters in MH, RDYt, and CPI represent unweighted 3month averages of the monthly data. The parameter TCFFt now represents a threemonth total for retail supply of all sizes of rawheadless shrimp. The variables for monthly models are defined as above but represent the secondary data (monthly) as published by the various data reporting agencies. Wholesale Price Models The monthly wholesale price model for 3140 count rawheadless shrimp is given as W3 + 6 [M] + BSFFt + c 01 + 31 + MC + i=1 and for 2125 count rawheadless shrimp is given as NW W b0 + 62 [M] + b b + b+ TMCI +t ii B bI21+ b hC + where W= wholesale price for 3140 size class (Shellfish Market Review NMFS), W= wholesale price for 2125 size class (Shellfish Market Review NMFS), BSFFt beginning inventories of rawheadless shrimp in millions of pounds (Shellfish Market Review, NMFS), 85 13 = total imports of rawheadless shrimp of all size classes (Shellfish Market Review, NMFS), excluding the 3140 size class imports in millions of pounds, 012 = total imports of rawheadless shrimp of all size classes (Shellfish Market Review, NMFS), excluding the 2125 size class imports in millions of pounds, 131t = imports of rawheadless shrimp of 3140 size class at selected ports of entry in millions of pounds (NMFS unpub lished files), 121t imports of rawheadless shrimp of 2125 size class at selected ports of entry in millions ofpounds (NMFS unpub lished files), TMCIt = intermediate food marketing cost index, 1967100 (Agricul tural Outlook, USDA and unpublished USDA files), NW number of current and lagged endogenous and exogenous prices found in "I for each size class model, where i refers to size class, and 'j, i, and B0 are the coefficients to be estimated. Each e6 and f is associated with a current or lagged endogenous or exogenous price contained in M3 and IM, respectively. The wholesale price expression represents the demand by retailers for wholesale product, which corresponds to equation (31). The whole sale price data represents exwarehouse prices in the New York metropol itan area for boxed and branded rawheadless brown shrimp as reported by the NMFS for the New York Fulton Fish Market. Wholesale price was specified as a function of quantities moving through the wholesale market and costs (input prices) representing the retail/wholesale price spread (costs incurred by the retailers). The quantity variable found in expression (31) has been separated into component quantities inventories and imports. Wholesale price is assumed to be inversely related to the quantity demanded and moving through the wholesale level. Thus, the coefficients a', Z, b', b and bM are anticipated to be negative in sign. The parameter OIl and I31t for the 3140 size class model and OZt and 121t for the 2125 size class model were included in an attempt to measure the relative impact of "ownsize" and "othersize" imports, respectively, on price for a given size class. Ownsize imports are expected to have a larger impact on price of a given size shrimp than do othersize imports. The parameter TMCIt was included to capture the effect that chang ing costs have on the demand for wholesale product. This term repre sents the individual components of the total intermediate food marketing cost index. Costs of marketing and processing are hypothesized to have an inverse relationship with the demand for and, thus, price of the "raw" product at the lower adjacent market level. Therefore, the coef ficients aC and b4 are anticipated to be negative in sign. Depending on whether the price determination process is character ized by upward causality, downward causality, or siaultaneity, the 's and 6's may be associated with the retail and/or exvessel prices. As was the case with the retail expressions, the signs on current and lagged f1 and OF are anticipated to be positive. The discussion regarding monthly and quarterly. models for retail demand applies to the wholesale models as well. The monthly models use the data as reported. The quarterly models use an unweighted three month average for the parameter TMCIt and for all prices found in the __ _~ i_ corresponding M. The parameters 01i, 01i, I31t, and 121 represent totals over threemonth intervals of the raw data. Exvessel Price Models The monthly exvessel price model for 3140 count rawheadless shrimp is given as NP P E 3 ] + aP OL +2 L31t + + 3 and for 2125 count rawheadless shrimp is given as NP 2 P NP P P 2 P P Pt bo + E [M] + b2OLt + b2 L21t + b3 MCI +2 i=l 1 where P3 exvessel price for the 3140 size class (Shellfish Market Review. NMFS), P exvessel price for the 2125 size class (Shellfish Market Review. NMFS), OL3 = total domestic landings for all sizes of shrimp excluding the 3140 size class landings in millions of pounds (Shellfish Market Review, IHFS), O2 = total domestic landings of all sizes of shrimp excluding the 2125 size class landings in millions of pounds (Shellfish Market Review, NMFS), L31t = landings of shrimp in the 3140 size class in the Gulf and South Atlantic in millions of pounds (NMFS unpublished files), L21t landings of shrimp in the 2125 size class in the Gulf and South Atlantic in millions of pounds (NMFS unpublished files), TMCIt = intermediate food marketing cost index, 1967100 (Agricul tural Outlook, USDA and unpublished USDA files), NP number of current and lagged exogenous and exogenous prices found in MN for each size class model, where i refers to size class, and 4, 6 b, and are the coefficients to be estimated. Each and 0F is associated with a current or lagged endogenous or exogenous price contained in 13 and I, respectively. The exvessel price expression represents the demand by first handlers for raw product and corresponds to equation (33). The ex vessel price data represents a dockside price (packout or boxweight price not specified). Prior to 1980, the exvessel price represents a weighted average for all species of shrimp landed in the Gulf and South Atlantic. From 1980 to 1981 the price data as reported represents a weighted average for species landed in the Western Gulf only. There appeared to be no appreciable change in the magnitude and trend of the prices when this structural change in the data occurred. Exvessel price was specified as a function of the quantities offered to first handlers and costs incurred in the initial wholesale/processing stages. The quantity variable ? found in expres sion (33) has been separated into two component quantities landings of all sizes excluding the size class of interest and landings of only the size class of interest. The quantity landed was broken down into two components, OLt and L31t for the 3140 size class and OLt and L21t for the 2125 size class. This disaggregation was done to measure the relative impact of "ownsize" and "other size" landings on exvessel price for a given size class. Ownsize landings are expected to have a greater impact on the exvessel price of the corresponding size class. Though the quantity of shrimp brought to the unloading house is considered to depend primarily on environmental conditions, the price offered by the unloading house to the vessel operator for the shrimp is hypothesized to be inversely related to quantity landed. Thus, the coefficients ov, 4, bP, bp are expected to have a negative sign. The parameter TKCIt was included to measure the effect that chang ing wholesale and processing costs have on the dockside price that emerges from the first handler/producer transaction. Most shrimp landed are sold to a dockside fish house. The product is then sold and trucked to wholesalers or processors for packaging, branding, etc. Cost data for first handlers of the shrimp are not available. Therefore, the aggregate cost index was included as a proxy for the costs which may influence the demand by first handlers for raw product. Given that this cost index more nearly approximate costs at the wholesale/processor market levels, exvessel price is hypothesized to have an inverse rela tionship with changes in TMCIt. Thus, the coefficients bP and aP are hypothesized to be negative in sign. The prices which are found in each 4 depend on whether the price determination process between exvessel and wholesale price is char acterized by recursivity or simultaneity. The signs on current and lagged 4. and ?1 are hypothesized to be positive. The exvessel price models described above represent the monthly and quarterly specifications. The monthly data are as described. The _ __ __ 