Price dynamics in the U.S. shrimp market


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Price dynamics in the U.S. shrimp market
Shrimp market
Physical Description:
xi, 206 leaves : ill. ; 28 cm.
Adams, Charles M
Publication Date:


Subjects / Keywords:
Shrimps -- Marketing -- United States   ( lcsh )
Shrimp fisheries   ( lcsh )
Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
bibliography   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph. D.)--University of Florida, 1984.
Bibliography: leaves 198-205.
Statement of Responsibility:
by Charles M. Adams.
General Note:
General Note:

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University of Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 000479801
oclc - 11977124
notis - ACP7304
sobekcm - AA00004887_00001
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Full Text







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To Mom and Dad

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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.



ACKNOWLEDGEMENTS...................................................... iii

LIST OF TABLES..................................................... vii

LIST OF FIGURES........................ ......................... ix

ABSTRACT............................. ..... .........o.. ......*... x


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 Determination-Causality................ 60
Granger Method..................................******* 61
Sims Method..................................... *..... 62
Haugh-Pierce Method........... ........................ 63
Dynamic Regression Methods................................ 65
Filter Models.................**........**********....... 66


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
Ex-vessel Price Models..... ........******............. 87
Margin Models.................. .......................... 90
Structural Margins........................ ......******* 90
Reduced and Final Form Margins............*..........* 92


Monthly Price Data...........................-..* 94
Haugh-Pierce Test.......... ...*.....*.......*********** 94
The 31-40 size class........... .. ............-....-. 96
The 21-25 size class..........................-....-. 98
Impulse response functions for both size classes..... 98
The Granger Test.................**.............****** 102
The 31-40 size class................. .....-.... *. cc 102
The 21-25 size class................................. 105
Sims Test......................***..............****** 107
The 31-40 size class............... ..** ... ** ....*** 107
The 21-25 size class.......................-......... 109
Quarterly Price Data................... ....*****.***** 109
Haugh-Pierce Test...................................... 110
The 31-40 size class...............**....... ...****** 111
The 21-25 size class...... ..e......* ......********** 111
Impulse response functions for both size classes..... 114
Granger Test...........*......*.......-**************** 116
The 31-40 size class*...................*****........ 116
The 21-25 size class.........*... ...**************** 118
Sims Test.............................. .....********* 120
The 31-40 size class............. ce....-........* .... 120
The 21-25 size class................ ...************* 120
Summary of Monthly and Quarterly Causality Results........ 122


Monthly Data.............................................* 124
The 31-40 Size Class.......*............... ....********** 125
Retail structural estimates............*.*...e......e 125
Wholesale structural estimates........****....... ..*** 127
Ex-vessel structural estimates...*...**************** 130
The 21-25 Size Class................... .......****** 132
Retail structural estimates .........* ...... ** ......* 132


Quarterly Data............................................ 134
The 31-40 Size Class................................... 135
Retail structural estimates............. ............. 135
Wholesale structural estimates....................... 137
Ex-vessel structural estimates....................... 140
Reduced and final form estimates..................... 142
Margin estimates.................. .................. 145
The 21-25 Size Class................................... 148
Retail structural estimates.......................... 148
Wholesale structural estimates..... .................. 151
Ex-vessel 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



B FINAL MODEL SPECIFICATIONS............................. .... 187

MODELS...................********************************* 192

D REDUCED FORM ESTIMATES....... ....... ......................... 196

IREFERENCES................**************************************** 198

BIOGRAPHICAL SKETCH......................... ..... ...........-... 206


Table Page

1 Haugh-Pierce (H-P) Causality Tests on Monthly Ex-vessel,
Wholesale, and Retail Prices for the 31-40 Size Class
Using ARIMA Filtered Data................................ 97

2 Haugh-Pierce (H-P) Causality Tests on Monthly Ex-vessel,
Wholesale, and Retail Prices for the 21-25 Size Class
Using ARIMA Filtered Data................................. 99

3 Granger Causality Tests on Monthly Ex-vessel, Wholesale,
and Retail Prices for the 31-40 Size Class Using First
Differenced Data................................**************** 103

4 Granger Causality Tests on Monthly Ex-vessel, Wholesale,
and Retail Prices for the 21-25 Size Class Using First
Differenced Data............... ............. .......*..... 106

5 Sims Causality Tests on Monthly Ex-vessel, Wholesale, and
Retail Prices for the 31-40 and 21-25 Size Classes Using
ARIMA Filtered Data....................**.......-...-..-** 108

6 Haugh-Pierce (H-P) Causality Tests on Quarterly Ex-vessel,
Wholesale, and Retail Prices for the 31-40 Size Class
Using ARIMA Filtered Data.......**.......**................ 112

7 Haugh-Pierce (H-P) Causality Tests on Quarterly Ex-vessel,
Wholesale, and Retail Prices for the 21-25 Size Class
Using ARIMA Filtered Data.................................. 113

8 Granger (H-P) Causality Tests on Quarterly Ex-vessel,
Wholesale, and Retail Prices for the 31-40 Size Class
Using First Differenced Data.................*..*..****.... 117

9 Granger (H-P) Causality Tests on Quarterly Ex-vessel,
Wholesale, and Retail Prices for the 21-25 Size Class
Using First Differenced Data................***............ 119

10 Sims Causality Tests on Quarterly Ex-vessel, Wholesale,
and Retail Prices for the 31-40 and 21-25 Size Classes
Using ARIMA Filtered Data.................................. 121


_~~ ii i

11 Summary of Monthly and Quarterly Causality Tests Using
Ex-vessel (E), Wholesale (W), and Retail (R) Price Data
by Size Class........................................... 123

12 Final Form Coefficients and Flexibility Estimates for
the Retail, Wholesale and Ex-vessel Price Models for the
31-40 Size Class........................................... 144

13 Final Form Margin Estimates and Flexibilities for the
Retail/Wholesale (Mrw) and the Wholesale/Ex-vessel (MwP)
Margins for the 31-40 Size Class........................... 146

14 Final Form Coefficients and Flexibility Estimates for
the Retail, Wholesale and Ex-vessel Price Models for the
21-25 Size Class........................................... 156

15 Final Form Margin Estimates and Flexibilities for
the Retail/Wholesale (Mrw) and the Wholesale/Ex-vessel
(MwP) Margins for the 21-25 Size Class.................... 159

B Ljung-Box Chi-Square Tests for White Noise on the
Residuals of the Monthly and Quarterly Retail (Rt),
Wholesale (W ), and Ex-vessel (Pt) Models Before and
After Inclusion of a Lagged Dependent Variable............. 189

C.1 Granger Causality Tests on Monthly Ex-vessel, Whole-
sale, and Retail Prices for the 31-40 Size Class
Using Data Filtered by an ARIMA Model...................... 192

C.2 Granger Causality Tests on Monthly Ex-vessel, Whole-
sale, and Retail Prices for the 21-25 Size Class
Using Data Filtered by an ARIMA Model...................... 193

C.3 Granger Causality Tests on Quarterly Wholesale and
Retail Prices for the 21-25 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 Ex-vessel (Pt) Market Levels for the
31-40 Size Class.........................*................. 196

D.2 Reduced Form Estimates and Flexibilities for Quar-
terly Price Models at the Retail (Rt), Wholesale
(Wt), and Ex-vessel (Pt) Market Levels for the
21-25 Size Clase...........................*............... 197



Figure Page

1 Trends in Quarterly Prices for 31-40 Count Raw Head-
less Shrimp for Retail, Wholesale, and Ex-Vessel
Market Levels. ..... ............ ...................... 12

2 Trends in Quarterly Prices for 21-25 Count Raw Head-
less Shrimp for Retail, Wholesale, and Ex-Vessel
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

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 rau-headless shrimp of the

31-40 and 21-25 size classes.

The presence of Granger causality was assessed between adjacent market

levels by using the Haugh-Pierce, 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 ex-vessel market levels were estimated. Expressions for

marketing margins were derived.

Monthly prices for both size classes in general exhibited unidirectional

causality from ex-vessel to wholesale to retail price. Unidirectional causality

did not characterize the ex-vessel/wholesale relationship for the 21-25 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 ex-vessel 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 21-25 size class, while beginning stocks, own and other size landings

and imports of own-size shrimp had a larger negative impact on price for the 31-

40 size class than for the 21-25 size class. Changes in beginning stocks and

landings and imports of own-size 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 21-25 size class than for the 31-40 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 31-40 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 31-40 size class.




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

94-265 (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 system-from 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

non-adjacent 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 long-run 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

estuarine-dependent 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,


respectively. The major species in the Pacific fishery are cold water,

non-estuarine-dependent 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 year-to-year fluctuation existed. The

total commercial landings in the U.S. in 1982 were 175.9 million pounds

heads-off. 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),


Consumption of individual shrimp product forms has been changing.

In 1960, raw-headless 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, raw-headless, breaded, and

canned capturing 46.1, 35.1, 12.1, and 6.7 percent of total consumption,

respectively. On a per capital consumption basis, raw-headless and

peeled/deveined product forms demonstrated the more noticeable increases

during the last two decades. Consumption of raw-headless and peeled/de-

veined shrimp increased from .69 and .24 pounds, respectively, in 1960

to .92 and .60 pounds in 1980. During this period, raw-headless 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

non-traditional 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 semi-processed form,

most enter as unpeeled, raw-headless 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 31-35 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 ex-vessel 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


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 ex-vessel 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 raw-headless shrimp at the ex-vessel, wholesale, and

retail levels for the 31-40 (retail prices represent only the 36-42 size

class) and 21-25 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.




-L-- a





w -



cm l


m Lca


| I1




t 0

.s / u a


S 0

Yd o; d h ( '- 4
p: .4

Prices were relatively stable from 1968 to 1972, particularly for

the 31-40 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/ex-vessel (MP) margins for the 31-40 size class exhibited a

slight upward trend. The margins Mrw and Mwp had average values of

$0.50 and $0.21, respectively. The 21-25 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 ex-vessel share of retail dollar remained constant for both

size classes, with an average wholesale and ex-vessel share of retail

dollar at 71.5 and 58.8 percent, respectively, for the 31-40 size class,

and 69.0 and 58.6 percent, respectively, for the 21-25 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 31-40 size class,

while Mr and MEF averaged $1.04 and $0.51 for the 21-25 size class.

Wholesale and ex-vessel share of retail dollars increased slightly

during the period, with an average wholesale and ex-vessel share of

retail dollar of 76.7 and 62.8 percent, respectively, for the 31-40 size

class, and 75.3 and 63.9, respectively for the 21-25 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 ex-vessel prices

fell to a four-year 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 pre-1970 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 31-40 size class. The margins Mr and MwP

averaged $2.77 and $0.78 for the 21-25 size class. During this same

period, wholesale and ex-vessel share of retail dollar fell to 63.0 and

54.1 percent, respectively, for the 31-40 size class, and 66.0 and 56.5,

respectively, for the 21-25 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 31-40 and 21-25 size classes, respectively. This can be



compared to a much smaller but increasing MWP which averaged $0.81 and

$1.03 for the 31-40 and 21-25 size class, respectively. As retail price

remained rigid to advancing wholesale and ex-vessel prices, the whole-

sale and ex-vessel share of the retail dollars increased to an average

of 73.1 and 62.1 percent, respectively, for the 31-40 size class, and

74.7 and 63.4 percent, respectively for the 21-25 size class.

Prices at all market levels have trended up since 1968 but major

breaks in prices, particularly at wholesale and ex-vessel 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 --- -- -- -- --'- .--- --


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


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 full-time producer's complaint

of an increasing number of part-time 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

year-to-year 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


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 tariff-free 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


Problem Statement

The Magnuson Fisheries Conservation Management Act (MFCMA) of 1976

(PL 94-265) 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


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


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.


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 (31-40 and 21-25 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


(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.


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,



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 raw-headless 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 profit-maximizing 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).


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, sub-markets may be defined, each with its own






Graphical Representation of a Vertical Market System with
Equilibrium Prices pr, pW, and pf in Time Period t.



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 retail-farm 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


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


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


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 non-existent, 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


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/wholesaler-proces-

sor, wholesaler-processor/first handler, and first handler/producer.

These market level interfaces are particularly characteristic for the



- -- --~
- m -n -m a









f(p f,p ,cW)


f(pf ,pP,cf)

f(pf ,p ,c)


QF_= f(pPpfc)


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.


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)
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, )
where QS is quantity supplied, pw is wholesaler-processor 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 )
where QD is quantity demanded, which is the same function as for QS.
The similarity between QS and QD is valid in terms of the theory of the
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 wholesaler-processor'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 wholesaler-processors to the first handlers or fish house owner,

and cw is prices for marketing inputs utilized by wholesaler-processors

in transforming the product as received from the first handler to the

product purchased by retail firms. The wholesaler-processor firm's

demand for product from first handlers is given as

(14) QD M f(pf, pw cW)
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 wholesaler-processor firm.

The first handlers supply of product to wholesaler-processors is

given as

(15) Q = f(pf p 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

(pack-out) or sold on an average size per pound (box-weight) 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)

~_____~ _


where QD is the quantity demanded and which is given in terms of the
same variables as QS"

The producers supply of raw product to first handlers is given as

(17) f(pP, X)
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 short-run 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
(18) pr = f(Q D)
(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, first-handler, 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




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)


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-----


decisions based on given prices, market supplies of many agricultural

products are so fixed in the short-run 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 non-price 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 estimates-an 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
(22) pr f(pW, q, D)

(23) pW f(pr pf, cr, )
(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


(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


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 non-directional 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 non-directional, 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


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 short-run 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

"short-run" 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 macro-level 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


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--


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



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.


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 non-economic sense and, secondly, the

incorporation of these underlying stochastic properties in an explana-

tory economic model-in 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,. :< .


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 Box-Jenkins time domain approach, due to the nature of

the data, access to and familiarity with established software and the

relative ease of Box-Jenkins 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, i-1,.*.,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 characteristic-the 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 non-station-

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=- (1-B) x

where 0 represents the difference operator where O&t = wt-1 A random

walk process given as

xt xt-1 +

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
xt E ixt-i + R + t, t 0,1,2,...,T
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 R-0, 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 left-hand 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


Z i< 1
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
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


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 (q-1) 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 "' q-Lq 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

non-zero 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 non-stationary. 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(1-B) xt-i R + Z
1-0 j0 j1=0

For d-0, this can be expressed as

xt xt-1- 2xt-2 t-p 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-


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 Yule-Walker 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 Box-Jenkins 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 Yule-Walker 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)8-1()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 k-k
rk 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

Q TE rk
k-1 k

for the first K residual autocorrelations. The Q statistic is dis-

tributed as chi square with K-p-q 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 Determination-Causality

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) Bi-directional 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


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 four-equation regression model given as

n n
A. X = Eat- + c1Yt-i + ut
j=1 i-1
n 2
A.2 X = ZEaX +
t j t-j t
n n 1

where n is the maximum number of lags used To test the null hypothesis

that Y does not cause X, an F-test is performed using the residuals from
A. and A.2 to see if the are different from zero The F statistic

with q and T-t degrees of freedom is defined as
Jt1 iit

B.2 Y bY +Ev
t it- t

where n is the maximum number of lags used. To test the null hypothesis

that Y does not cause X, an F-test 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 T-t degrees of freedom is defined as

(ESSr ESS )/(q)
q,T-t (ESS )/(T-t)
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

X- E aY +e
Xt a jYt-j + et
n 2
EbY +
Xt EjbJ t-j t
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 F-test

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).

Haugh-Pierce 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

r (k) (ut-k
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 T-1/2, where T is the total number

of observations. Each r^v(k) can be individually tested for signi-

ficance where

ruv^^(k) > 2T-1/2

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,


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)

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

T E [r^^(k) 2 < X2
k--m uv

The chi-square distributed statistic T E [r(k) ]2 will hereafter be

referred to as the Haugh-Pierce 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 Haugh-Pierce 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 analysis-the transfer function-provides 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


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

two-step 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 Box-Jenkins 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

Box-Jenkins 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 chi-square 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 ut-k given as

V m--rAA(k)
k a Uv
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-


e(B)Xt ut

+(B)Yt vt

are substituted into the dynamic shock model (Haugh and Box,, 1977) to


#(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, non-linear 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


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


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 -r-1BX + 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


Yt do + DYt-.1 + D2Xt +Et

where Yt is a gxl vector of endogenous variables, Yt-1 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 D2Xt-1 + 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 1-0

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


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.



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

re-introduced 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)


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 fresh-frozen, raw-headless 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


------------------ -----------~-------------------- -------------------------

Foreign Shrimp Domestic Shrimp
SProduction I Production -

Figure 6. Market Channel Schematic Representation for the U.S
Shrimp Market System.

I ___ ___



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 fresh-frozen, raw-headless

shrimp product. Supply models were not estimated due to the assumption

that supply of raw product is exogenous and inelastic with respect to


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 Wolffram-form price equation

(Young, 1980) would allow for asymmetric price response and is given as

(2) Rt o + i WIt + WDt + W t, t ,...,N

WIt -= (w wt-i-) It-i

WDt M E (Wt-i Wt-i-1) DDt-i

.t i t-i "t-i-1

0, otherwise

D 1, Wt-i Wt-i-1
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 t-0. Substituting for WIt gives

- -.~---


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 t-statistic 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.


The estimation of time series properties and analysis of causal

relationships of prices for shell-on, fresh-frozen, raw-headless shrimp

(hence forth referred to simply as raw-headless) at retail, wholesale,

and ex-vessel market levels was accomplished for the years 1968-1981.

Monthly and quarterly price models were estimated with data from 1972-

1982. The analyses were oriented toward two size classes-the 31-40 and

21-25 tails per pound ("count") sizes classes of shell-on, fresh-frozen,

raw-headless 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 31-40 size class. Retail

prices are given, however, for the 36-42 size classes. Though the 36-42

size class represents a smaller shrimp than the 31-40 size class, this

study circumvents this data inconsistency by assuming the prices for the

36-42 and 31-40 size classes are not significantly different. For the

sake of notational simplicity, the discussions henceforth will refer

only to the 31-40 and 21-25 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 three-month averages of the monthly data. To

obtain the quarterly price data, the monthly price series were simply

averaged over three-month periods for the years 1972 through 1981. An

attempt was made to use a weighted average for the ex-vessel series,

however, no significant gain was made relative to a three-month average

(the three-month 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 three-month 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 31-40

and 21-25 size class are identical relative to the predetermined

variables discussed below. All price models are over identified. Price

and quantity variables are in heads-off units.

Retail Price Models

The monthly retail price model for 36-42 and 21-25 count raw-head-

less shrimp is given as

Rt a E 0 [M ] + C RDt + TCFPt + a CPIt +

where Rt retail (non-institutional) 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 raw-headless 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


NR number of current and lagged endogenous and exogenous prices

found in Mf for each size class model, where i refers to size


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


or lagged exogenous or endogenous price contained in MI. M4 and

refer to a set of prices for the 36-42 and 21-25 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 raw-headless 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.


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 3-month averages of the monthly

data. The parameter TCFFt now represents a three-month total for retail

supply of all sizes of raw-headless 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 31-40 count raw-headless

shrimp is given as

W3 + 6 [M] + BSFFt + c 01 + 31 + MC +

and for 21-25 count raw-headless shrimp is given as

W b0 + 62 [M] + b b + b+ TMCI +t
i-i B bI21+ b hC +


W= wholesale price for 31-40 size class (Shellfish Market

Review NMFS),

W-= wholesale price for 21-25 size class (Shellfish Market

Review NMFS),

BSFFt beginning inventories of raw-headless shrimp in millions of

pounds (Shellfish Market Review, NMFS),


13 = total imports of raw-headless shrimp of all size classes

(Shellfish Market Review, NMFS), excluding the 31-40 size

class imports in millions of pounds,

012 = total imports of raw-headless shrimp of all size classes

(Shellfish Market Review, NMFS), excluding the 21-25 size

class imports in millions of pounds,

131t = imports of raw-headless shrimp of 31-40 size class at

selected ports of entry in millions of pounds (NMFS unpub-

lished files),

121t imports of raw-headless shrimp of 21-25 size class at

selected ports of entry in millions of-pounds (NMFS unpub-

lished files),

TMCIt = intermediate food marketing cost index, 1967-100 (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


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 ex-warehouse prices in the New York metropol-

itan area for boxed and branded raw-headless 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 31-40 size class

model and OZt and 121t for the 21-25 size class model were included in

an attempt to measure the relative impact of "own-size" and "other-size"

imports, respectively, on price for a given size class. Own-size

imports are expected to have a larger impact on price of a given size

shrimp than do other-size 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 ex-vessel 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 three-month intervals of the raw data.

Ex-vessel Price Models

The monthly ex-vessel price model for 31-40 count raw-headless

shrimp is given as

P E 3 ] + aP OL +2 L31t + + 3

and for 21-25 count raw-headless shrimp is given as

2 P NP P P 2 P P
Pt bo + E [M] + b2OLt + b2 L21t + b3 MCI +2
i=l 1


P3 ex-vessel price for the 31-40 size class (Shellfish Market

Review. NMFS),

P ex-vessel price for the 21-25 size class (Shellfish Market

Review. NMFS),

OL3 = total domestic landings for all sizes of shrimp excluding the

31-40 size class landings in millions of pounds (Shellfish

Market Review, IHFS),

O2 = total domestic landings of all sizes of shrimp excluding the

21-25 size class landings in millions of pounds (Shellfish

Market Review, NMFS),

L31t = landings of shrimp in the 31-40 size class in the Gulf and

South Atlantic in millions of pounds (NMFS unpublished


L21t landings of shrimp in the 21-25 size class in the Gulf and

South Atlantic in millions of pounds (NMFS unpublished


TMCIt = intermediate food marketing cost index, 1967-100 (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


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 ex-vessel 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 (pack-out or box-weight

price not specified). Prior to 1980, the ex-vessel 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.

Ex-vessel 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 31-40 size class and OLt and L21t for

the 21-25 size class. This disaggregation was done to measure the

relative impact of "own-size" and "other size" landings on ex-vessel

price for a given size class. Own-size landings are expected to have a

greater impact on the ex-vessel 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, ex-vessel 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 ex-vessel 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 ex-vessel price models described above represent the monthly

and quarterly specifications. The monthly data are as described. The

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