Citation
Price dynamics in the U.S. shrimp market

Material Information

Title:
Price dynamics in the U.S. shrimp market
Added title page title:
Shrimp market
Creator:
Adams, Charles M
Adams, Charles M., 1907-1990
Publication Date:
Language:
English
Physical Description:
xi, 206 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Causality ( jstor )
Imports ( jstor )
Market prices ( jstor )
Null hypothesis ( jstor )
Prices ( jstor )
Retail prices ( jstor )
Shrimp ( jstor )
Supply ( jstor )
Wholesale prices ( jstor )
Wholesale trade ( jstor )
Dissertations, Academic -- Food and Resource Economics -- UF
Food and Resource Economics thesis Ph. D
Shrimp fisheries ( lcsh )
Shrimps -- Marketing -- United States ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

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

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
030532376 ( ALEPH )
11977124 ( OCLC )
ACP7304 ( NOTIS )
AA00004887_00001 ( sobekcm )

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Full Text













PRICE DYNAMICS IN THE
U.S. SHRIMP MARKET










By



CHARLES M. ADAMS


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY



UNIVERSITY OF FLORIDA


1984


't
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- -^*^*-._____________________________________________________________________ -.... ^*^-jfc^...




PRICE DYNAMICS IN THE
U.S. SHRIMP MARKET
By
CHARLES M. ADAMS
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1984


To Mom and Dad


ACKNOWLEDGMENTS
I wish to express sincere appreciation to Dr. Fred J. Prochaska and
Dr. Tom H. Spreen for taking time to critique the many drafts of this
manuscript. Their guidance and friendship were invaluable. Thanks go
to Dr. Jim C. Cato, Dr. W. Steve Otwell and Dr. Gary F. Fairchild for
dedicating time to serve as counsel on the advisory committee. Special
thanks go to Fred, Jim, and the Florida Sea Grant Program for the
financial support provided throughout my stay as a graduate student.
This dissertation would be long in coming if not for someone to
decipher and type the initial scribbling. In that sense, Frankie
Thomas, with her patience, understanding and keen eyesight, was abso
lutely indispensable. Thanks also go to my fellow students, to whom I
am grateful for their aid and comaraderie.
However, my greatest appreciation goes to Sherry, Sam and ???,
whose love and patience provided the motivation needed to complete my
graduate studies.
iii


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
LIST OF TABLES vii
LIST OF FIGURES ix
ABSTRACT x
CHAPTER
I INTRODUCTION 1
Overview of Industry ... 4
Resource and Harvesting 4
General Industry Trends 6
Industry Issues.. 17
Problem Statement 20
Objectives 23
II THEORETICAL CONSIDERATIONS 25
Vertical Structure 25
Causal Direction of Price Determination in the
Vertical Market 41
Price Spreads Between Market Levels 44
Price Transmission 48
III EMPIRICAL METHODS 50
Time Series Analysis 51
Univariate Time Series 52 .
Autoregressive (AR) Process 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
iv


Dynamic Shock Model 67
Dynamic Regression Transfer Function 68
General Regression Methods 69
IV EMPIRICAL MODELS 74
Introduction 74
Implicit Models 74
Symmetric and Asymmetric Models 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
V EMPIRICAL RESULTSCAUSALITY ANALYSIS 94
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 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 Ill
The 21-25 size class Ill
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.. 120
The 21-25 size class.. 120
Summary of Monthly and Quarterly Causality Results 122
VI EMPIRICAL RESULTSPRICE AND MARGIN MODELS 124
Monthly Data 124
The 31-40 Size Class 125
Retail structural estimates 125
Wholesale structural estimates 127
Ex-vessel structural estimates 130
The 21-25 Size Class 132
Retail structural estimates 132
v


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 Asymmetry Analysis.... 162
Factors of Price Determination 164
Margin Analysis 168
Methodological Conclusions 169
Policy Implications.......... 170
Suggestions for Future Research 173
APPENDICES
A DERIVATION OF IMPULSE RESPONSE FUNCTIONS 178
B FINAL MODEL SPECIFICATIONS 187
C GRANGER TESTS USING DATA FILTERED BY USING ARIMA
MODELS 192
D REDUCED FORM ESTIMATES 196
REFERENCES 198
BIOGRAPHICAL SKETCH 206
vi


LIST OF TABLES
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
vii


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 (M1^) and the Wholesale/Ex-vessel (M^)
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
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 (Wt), and Ex-vessel (Pt) Models Before and
After Inclusion of a Lagged Dependent Variable 189
C.l 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.l Reduced Form Estimates and Flexibilities for Quar
terly Price Models at the Retail (Rt), Wholesale
(Wfc), and Ex-vessel (Pfc) 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 Class 197
viii


LIST OF FIGURES
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 System
with Equilibrium Prices pr, pw, and p in Time Period t.... 29
4 Graphical Representation of a Vertical Market System
with Supply and Demand Given Implicitly at Four Market
Levels and the Corresponding Equilibrium Prices, pr,
pw, p and pP in Time Period 35
5 Graphical Representation of a Vertical Market System
Characterized by Inelastic Supply with Demand Given
Implicitly at Four Market Levels 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 System 76
ix


Abstract of Dissertation Presented to the Graduate School of the
University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PRICE DYNAMICS IN THE
U.S. SHRIMP MARKET
By
Charles M. Adams
December 1984
Chairman: Frederick J. Prochaska
Major Department: 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 raw-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
x


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, cwn and other size landings
and imports of cwn-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 maricultural shrimp will have a greater relative price
impact on the 31-40 size class.
xi


CHAPTER I
INTRODUCTION
Management of the domestic shrimp fishery in the United States has
proven to be a considerable task. The goal of effective implementation
of policy has resulted in the organization of a complex management
structure and the allocation of substantial sums of research dollars to
be directed toward current research needs.
The passage of the Magnuson Fishery Conservation Management Act PL
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 systemfrom producer to consumer.
The impetus for this expression of increased need of control over
the fishery and its market system has been that the shrimp industry has
been growing in volume, value, and complexity. As the standard of
living has increased in the U.S., the demand for luxury goods, such as
shrimp, has increased. The consumption of fish and shellfish products
has increased steadily over the past two decades (U.S. Dept, of
1


2
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 capita 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.


3
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


4
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,


5
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,


6
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


7
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 capita. Both total and per capita 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 capita. This can be contrasted to per capita consumption of
all fishery products in the U.S. which had a continual upward trend from
10.3 pounds in 1960 to 12.3 pounds in 1982 (U.S. Dept, of Commerce(b),
1983).
Consumption of individual shrimp product forms has been changing.
In 1960, 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 capita 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 capita basis.


8
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 capita 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,


9
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


10
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


11
$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.


Figure 1. Trends in Quarterly Prices for 31-40 Count Raw-Headless Shrimp for Retail,
Wholesale, and Ex-vessel Market Levels.


Figure 2
Trends in Quarterly Prices for 21-25 Count Raw-Headless Shrimp for Retail,
Wholesale, and F.x-vessel Market Levels.
YEARS


14
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 and
wholesale/ex-vessel (M^) margins for the 31-40 size class exhibited a
slight upward trend. The margins M 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 M1^ increasing from $0.41 to
$0.81, while increased from $0.18 to $0.36. Average values during
this period for M and 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 M for both size classes varied consider
ably, while Mwp exhibited a stable upward trend. The margins and
Mwp averaged $0.75 and $0.46, respectively, for the 31-40 size class,
while and averaged $1.04 and $0.51 for the 21-25 size class.


15
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 M during this period. This large margin was maintained
for nearly three years, being relinquished only in the last quarter of
1982. The margins M1* and were both very erratic during this
period. The retail/wholesale margin averaged $2.46, compared to an
average of $0.57 for the 31-40 size class. The margins M1"** and
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


16
compared to a much smaller but Increasing 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


17
20 percent in some cases, significantly above prime rate. The last few
years, as a result, have exhibited an increasing number of foreclo
sures. Some producers have been forced to suspend fishing or retrofit
their vessel for alternative species, such as swordfish, shark, snapper,
or grouper. Processors are also experiencing increased costs as labor,
energy, and transportation costs climb. Creditors are becoming less
willing to advance new loans or extensions on existing mortgages at a
time when it is becoming increasingly necessary to obtain conversion
financing or loan extensions.
Industry Issues
In recent attempts to stabilize the economic conditions in the
domestic shrimp industry, several policy strategies are particularly
noteworthy. The unsuccessful 1981 Breaux Bill (HR4041) was introduced
as the "American Shrimp Industry Development Act." The purpose of this
legislation was to provide shrimp producers a means by which to estab
lish financing and implement a coordinated program of research, producer
and consumer education, and market promotion in an attempt to "improve,
maintain, and develop markets" for domestic shrimp products. The major
provisions of the bill addressed the establishment of a tariff or quota
system, establishment of regional market boards, and creating a compre
hensive data reporting network. Federal opponents argued that most
goals of the bill, with the exception of the marketing boards, were
clearly within easy reach of the current management process.
The controversial Texas closure has generated varying results.
Normally, the offshore Texas season is closed from June until mid July,
out to nine fathoms. This leaves a large portion of the FCZ, which


18
extends out to 200 miles, open to shrimping. However, beginning in
1981, the entire FCZ was closed to shrimping except out to four fathoms
with a 25 foot trawl. This represents an attempt to protect small
shrimp and increase the average size shrimp caught, thereby increasing
prices and gross revenues to the producer. The results in 1981 signal
led a successful year with Texas landings and value up. However, the
1982 and 1983 closure brought just the opposite results. Texas pro
ducers questioned the uncertainty of the closure, especially since no
fishing in the FCZ coupled with the possibility of minimum effect from
the closure would be disastrous. Louisiana producers argued that Texas
shrimpers would encroach on their traditional grounds during the clo
sure. In addition, Louisiana processors argued that a supply glut may
hit the market with less than efficient means to deal with the excess
supply.
In general, the U.S. shrimp industry has exhibited decreasing catch
per unit effort, increasing variability in producer price, and increas
ing costs of production. In addition, producers particularly have made
a case that they are experiencing reduced profits. Though there appears
to be no quick fix, several policy measures to address these problems
exist, each with its own set of advantages and disadvantages. In an
attempt to stabilize prices at a higher level, imposition of a tariff or
quota system has been suggested. Theoretically, in the presence of
import restrictions, prices should adjust to a higher level, with domes
tic supplies being more dependent on U.S. producers. However, the
erratic nature of U.S. production may have the effect of increasing
price volatility. In addition, lack of political endorsement, the
questionable impact on processor cost structure and reduced supplies to


19
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
Asia


20
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
vital.
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


21
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 MFCMA.
The shrimp industry is the most valuable domestic fishery in dock-
side dollars in the United States. This particular industry has recent
ly exhibited considerable price volatility and instability throughout
the market system. A host of factors have contributed to this state of
flux, such as fluctuating demand, tight world and domestic supplies,
changing market structure, increasing dependence on imports, increasing
costs of production, and fluctuating domestic economic conditions.
Changing market conditions appear to have left the producer bearing the
brunt of an array of economic symptoms. The symptoms which are being
expressed by producers, such as relatively depressed dockside prices and
reduced revenues, have motivated interest in several management policies
to help bolster demand for domestic products and, thus, act as price
supports (i.e., import tariff, import quota, limited entry, and promo
tional programs). In addition, the apparent concentrated nature of the
shrimp wholesale/processing market level (less than 20 firms control
approximately 90 percent of total U.S. output) may provide for some
market power in terms of gathering and assessing market information.
This may provide for a competitive advantage over firms in their own
market level and also provide an informational advantage over firms in
adjacent market levels. The recognition of the possible oligopolistic


22
nature of the wholesale/processing sector may provide insights into the
price determination process at each market level. In addition to pos
sible monoposonistic pricing, the concentrated nature of the processing
sector may result in price leads and lags in the market place, with the
market level possessing more timely and accurate information acting as a
price leader. The market level with the information edge may be able to
exploit this position in the price determination process to gain greater
profits relative to adjacent market levels. The existence of this
phenomenon is at least implied by recent legislation calling for aid in
establishing cooperatives and market orders in the producer sector.
Before the economic appropriateness of a tariff, quota, or limited
entry program can be accurately assessed, an understanding of price
dynamics is vital. This knowledge will provide a more clear view of how
these policies will impact the various market levels.
Studies done to date concerning the U.S. shrimp market system have
provided some insight into the mechanism of the structural components of
the system in an effort to understand market price fluctuations (Doll,
1972; Hopkins et al., 1980; Thompson and Roberts, 1982; Gillespie et
al., 1969; Prochaska and Keithly, 1983). Previous research has provided
a partial understanding of how imports, domestic business and economic
factors, and biological elements impact the pricing system. Limited
explanatory power has resulted. More importantly, contradicting model
specifications in terms of the direction of price determination are
evident in some of the previous major studies. No formal research has
been undertaken to employ current methodology regarding price causality
in the U.S. shrimp market system. In addition, no formal research has
been carried out regarding the presence or absence of asymmetric price


23
response, speed and magnitude of price adjustment between market levels,
and the determinants of prices and marketing margins. Further research
must be performed to provide insights into the sensitivity of price
transmission in a time (speed of adjustment), space (region of market),
and form (size and degree of processing) framework. Policy makers need
to understand the dynamics of price determination and transmission in
the market and the impact to producers, processors, retailers, and
consumers that increased control over prices in the market may pro
duce. A more fundamental knowledge of price linkages would provide
further understanding of how market levels interact and relate given
stimuli internal and external to the market system.
Objectives
The purpose of the research is to investigate and model the dyna
mics of price transmission between the producer, wholesale, and retail
levels of the U.S. shrimp market system on a size class basis for raw-
headless shrimp. This will be accomplished by developing an econometric
model of the prices and marketing margins. Primary emphasis is placed
on examining the dynamics of price for each market level and price
transmission between market levels. Insights, are developed into the
nature of the price adjustment process between market levels. Speci
fically, the objectives of the research are
(1) to determine the univariate time series characteristics of the
price series for each market level (producer, wholesale, and
retail) by size class (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
system,


24
(3) to examine speed of price adjustment between market levels for
each size class,
(4) to determine if price adjustment between market levels is sym
metric or asymmetric for each size class, and
(5) to identify major determinants of price and test hypotheses
regarding price relationships between market levels.


CHAPTER II
THEORETICAL CONSIDERATIONS
This chapter provides a brief discussion of the competitive market,
with emphasis given to the vertical structure. The dynamic properties
of price, such as the direction of price determination and lead/lag
relationships are discussed to provide an understanding of how actual
markets may depart from the static competitive model. Specifically,
causality between market levels in a vertical market system, the nature
of price spreads, and the importance of the mechanics of price transmis
sion between levels in a vertical market system is stressed. Thus, this
section provides a motivation for the modelling approach.
Vertical Structure
Bain (1964) discusses the market system as a means by which natural
resources, productive facilities, and labor forces are developed and
assembled to determine what and how much is to be produced and how the
goods and services are to be distributed to users. Cochrane (1957)
defines a market as a sphere or space where the forces of demand and
supply interact to determine or modify price as the ownership of some
quantity of goods or services is transferred with certain physical and
institutional arrangements in evidence. In a perfectly competitive
sense, many buyers and sellers come together to negotiate regarding a
homogenous product with perfect information, no rivalry, and with free
dom to enter or leave the market. As Kohls and Uhl (1980) argue,
25


26
arbitrage would result in an instantaneously determined unique equili
brium price for any quantity of goods representing a given time, loca
tion, and product form. Price formulation is a static process in this
setting (Heien, 1980).
When using the above concept of the market, one can visualize a
benchmark case where a single equilibrium market price is established at
which the quantities offered for sale by producers exactly equals the
quantities demanded by purchasers. The situation would only be true in
the simplest of markets where the original producers and final consumers
are involved in a direct arbitrage. Most agricultural commodity markets
are far more complex. In most markets, initial producers and final
consumers are separated by a complex vertical network of intermediate
processors, handlers, wholesalers, brokers, and marketing agents, each
exhibiting its own input demand and output supply. In this sense,
initial producers and final consumers do not face one another directly;
rather market signals must pass through the market system whether the
signal originates from the final consumer, initial producer, or inter
mediate agent. Often, consumer demand is not for the primary product
but for the primary product plus the utility derived from additional
characteristics added through processing and the necessary marketing
services. Thus, consumer demand is a direct demand for a final good
such as breaded shrimp, as opposed to a 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


27
D. = f(P, Y)
where P Is a vector of prices P^,...,Pj and Y is income. Each is
assumed to be a demand function homogenous of degree zero in prices and
income and monotonically decreasing in price (Deaton and Muellbauer,
1980). The market (consumer) demand, or "primary" demand for the market
then is the horizontal summation, of individual consumer demands D^.
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).


28
The intersection of primary producer supply and the final consumer
demand is of no real importance in a market where the product must 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 R^,
W^, and F^, respectively. Primary supply at producer level, derived
supply at wholesale level, and derived supply at retail level, are
represented by F8, W8, and R8, 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


29
Figure 3. Graphical Representation of a Vertical Market System with
Equilibrium Prices pr, pw, and pf in Time Period t.


30
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
m
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


31
and lags in pricing associated with disequilibrium are consistent with
perfect competition in the short run. Thus, issues regarding the dyna
mics of price transmission (lead/lag structures) become important when
addressing pricing efficiency on a timeliness and accuracy basis for the
short run movement in prices (Sporeleder and Chavas, 1979). As such, a
dynamic rather than a static approach may be more appropriate when
examining the transmission of prices between producer, wholesale, and
retail levels in the market place when using weekly or monthly rather
than quarterly or annual data. The price transmission model presented
below relates to Figure 3.
The retail (primary) demand for the final product is given by
(1) Rd = f(Pr; V)
where Rd is quantity demanded at retail by consumers, pr is retail
price, and V is a set of exogenous factors which affects consumer
demand, such as income. The retail (derived) supply for the finished
product is given as
(2) RS f(Pr, pw; 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)


32
The supply relationship at the wholesale/processor level is derived from
the producer level in equivalent units. This supply is given as
(4) WS = f(pW, pf; Y)
where p^ 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(pf; Z)
where Z is a set of exogenous factors affecting production, such as
weather.
When the market is assumed to be in equilibrium, i.e., Rd =* Rs,
= Ws, 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 f(pw; V,X)
(8) pW f(pr, pf; X,Y)
(9) pf f(pw; Y,Z)
which are fully simultaneous in prices. In Gardner's static competitive
model, these reduced form expressions for price are assumed to adjust
instantly to changes in raw product supply, supply functions of market
ing services, or retail food demand. In addition, Gardner suggests that
simple markup rules in pricing at each market level are not adequate


33
enough to accurately model price determination processes. Heien, how
ever, advocates the viability of markup pricing rules with a model
incorporating short run disequilibrium such that f Rs, Ws, and
f Fs. 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


34
signals, stability implies that the market will eventually equilibrate
to the static equilibrium point through some lag recursive adjustment
process (Silberberg, 1978). A stable market then will result in long
run and static adjustment tending to produce the same equilibrium point.
Ward (1982) suggests that increased concentration at one market level
may provide that level with a competitive edge in assessing market
information. This advantage effectively allows that market level to
react before other market levels and establish a pricing lead. Miller
(1980) attributes the lead/lag pricing structure to increased use of
formula pricing, demise of terminal markets, and general structural
changes in the market.
An attempt to directly estimate and interpret a set of reduced form
expressions, such as represented by equations 7, 8, and 9, will be
frustrated in that the signs of the parameter estimates will be ambigu
ous. This is due to the parameter estimate being unspecified as to
whether the representative shock originated from a supply or demand
shift (Chiang, 1974). In this sense, the above expressions for prices
pr, pw, and pf 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


35
PRICE t
w
P
Q
QUANTITY t
Figure 4. Graphical Representation of a Vertical Market System with
Supply and Demand Given Implicitly at Four Market Levels
and the Corresponding Equilibrium Prices pr, pw, px, and
pP in Time Period t.


36
domestic shrimp market where most shrimp produced domestically are off
loaded by a fish house (first handler) and sold to a wholesaler and/or
processor. The first handler for imported product is normally a bro
ker. The domestic and imported product is then processed under retail
or processor brand name and sold to the retail market.
The consumer's demand for retail product is given as
(10) q£ = f(pr, D)
C r
where QD is quantity demanded, p 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
(11) Q| = f(pr, pW, cr)
R w
where Qs is quantity supplied, p 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) Q* = f(pr, pW, cr)
R R
where 0.D is quantity demanded, which is the same function as for Qg.
R R
The similarity between Qs and QD is valid in terms of the theory of the
R R
firm as Qq represents the input demand of a retail firm and Qg 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).


37
The wholesaler-processor's supply of product to retail firms is
given as
/ION £/ f w w\
(13) Qs = f(p p c )
W f
where Qg 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
,,,x -.W t w w.
(14) QD = f(p P c )
W W W
where QD is quantity demanded. The expressions Qg 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) Qg = f(pf, pP, cf)
F
where Qg 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
duct from producers is given as
(16) QP = f(pf, pp, cf)


38
F
where Qq is the quantity demanded and which is given in terms of the
F
same variables as Qg.
The producers supply of raw product to first handlers is given as
(17) Qg = f(pP, X)
D
where Qs is the quantity supplied and X is a set of exogenous supply
shifters, such as weather.
By assuming that inventories remain relatively stable over time,
the quantity supplied at each market level is determined by the equili
brium quantity determined in the raw product market. Given that the
supply of raw shrimp product is determined in the shortrun primarily by
environmental conditions affecting the domestic production and by world
market conditions affecting the supply of imports offered to domestic
brokers, the supply of raw product to each market level is relatively
price inelastic (Doll, 1972; Hopkins et al., 1980; Grant and Griffin,
1979). Conceptualizing the market in this manner, and not addressing
the issue of inventories in any further detail, a set of price dependent
demand expressions depicted in Figure 5 are given as
(18)
Pr
= f(Q ,
D)
D
D
(19)
PW
= f(pr,
cr,
QD)
(20)
Pf
II
Hi
/-s
*
cw,
w
V
(21)
PP
= f(pf,
cf,
F
qd)
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
kas been shown to be appropriate for agricultural products. Houck
(1966, page 225) states that "although individuals make quantity


39
Figure 5. Graphical Representation of a Vertical Market System
Characterized by Inelastic Supply with Demand Given
Implicitly at Four Market Levels and the Corresponding
Equilibrium Prices pr, pw, p^, and pP in Time Period t.


40
decisions based on given prices, market supplies of many agricultural
products are so fixed in the short-run that prices must 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 estimatesan improvement over
reduced form estimates.
Expressions (18) through (21) are restrictive in the sense that
price determination is recursive from retail to raw product markets.
Certain structural attributes of the market and alternative pricing
policies of marketing agents may dictate a different price determination
process; i.e., upward recursive, a pricing locus or node at an intermed
iate market level, or simultaneity. Thus, a more general expression of
equations (18) through (21) with supply at each market level assumed
exogenous would be
(22) pr
(23) pw
(24) pf
(25) pP f(pf, cf,
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


41
process is characterized by instantaneous interdependent (simultaneous)
price shifts in a static competitive manner or whether unidirectional
relationships exist in a fully downward, fully upward, or an intermed
iate nodal form may very well be a theoretical question which requires
empirical support.
Causal Direction of Price Determination in the Vertical Market
In attempting to estimate equations 22 through 25, the model must
be specified in either seemingly unrelated, recursive, block recursive,
or fully simultaneous form. In doing so, restrictive implicit assump
tions (maintained hypotheses) regarding the direction of price determi
nation (causal) structure of the price series are imposed. A more
general representation of the structural price equations could be given
as
(26) pr = f (Mjj Qp, D)
(27) pw = f (M2; cr, Q*)
(28) pf f (M3; cW, Q¡J)
(29) pp f (M4; cf, qJ)
where 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 M^. 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


42
306) provides three motivations for determining the causal nature of the
relations of an economic system:
(1) Policy implications of any relation depend critically upon
whether the relation holds in one or more directions,
(2) Methods which are not designed to recognize the directional
nature of relations will often lead to acceptance of a rela
tion as 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


43
a theoretical basis for questioning the finding of unidirec
tional causality from producer to consumer prices also
exists. Derived demand analysis specifically yields a model
of price causality from the consumer price level to the
producer price index. This analysis has gone surprisingly
unnoticed and untested. Consider supply costs and the deter
mination of the cost of production. The producer pays the
opportunity cost of resource or the services of resources in
order to acquire input. The opportunity costs of resources
reflect the demand for input between competing uses. It is
the demand for final goods and services that generates the
opportunity costs of resources and intermediate materials.
This suggests causality from consumer prices to producer
prices (page 380).
Heien (1980), on the other hand, suggests that the competitive
market dictates the direction of causality from producer to consumer
through markup pricing rules. Bishop (1979) reiterates this confusion
over the direction of causality by stating
Some assume that changes in prices at the farm level lead to
changes in the wholesale and/or retail prices. Others assume
that because of the nature of the food processing industry,
no strong relationship exists between producer and retail
food prices (page 1).
Van Dijk (1978) points out that the theory of price formation in
the vertical market system does not provide an unambiguous indication of
the 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


44
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 must 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


45
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., pw pf in Figure 3. In an actual market setting, the spread
between two prices would typically consist of wages, transportation
costs, interest, processing, charges for marketing or handling services,
and profit markup necessary to provide for an acceptable rate of return.
In a competitive model, excess profit is dissipated to zero, or normal
profit.
The price found at the primary demand level (retail) or a derived
demand level above the producer level consists of two components (1)
producer related components and (2) processing and/or marketing related
costs. As pointed out by Fisher (1981) and Friedman (1962) this margin
concept operates under the assumption of fixed proportions in processing
and marketing which implies elasticity of substitution (a) between all
goods and marketing/processing inputs equal to zero. Recent studies by
Gardner (1975), Fisher (1981), and Heien (1980) have produced more
general models where a j4 0. In addition, dynamic lead/lag price spread
adjustment has been investigated through use of inventory disequilibrium
models (McCallum, 1974).


46
Gardner identifies the major determinants of the price spreads as
farm product supply, the supply functions of marketing services, and
retail food demand. For example, given a perfectly elastic supply for
marketing services, a shift in demand for marketing services would
result in no changes in the margin, as suppliers of marketing services
would be price takers. However, a less than perfectly elastic supply
function would result in a changing margin as prices of services
increase commensurate with increases in demand for services. Tomek 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


47
elasticities of demand and supply at each market level. The question of
who bears the margin shift is particularly important to trade policy.
As Fisher (1981) points out, for most agricultural products, the major
adjustments which result from a shift in marketing margins will be borne
by producer prices. Thus, producers have a strong economic motive for
establishing some influence over cost efficiencies in the processing
level of the market system.
The price formulation policy to be used at each market level is
dependent on a number of factors including firm policy and objectives,
i.e., following the leader pricing, staying abreast of competition, or
short run profit maximization (Dalrymple, 1961). George and King (1971)
discuss other forms such as average cost, experimental, or intuitive
pricing methods. Griffith (1975) and van Dijk (1978) discuss at great
length the phenomenon of price leveling and its causes and consequences.
These forms of pricing behavior are referred to as nonsystematic. On
the other hand, systematic pricing methods are evident when the margin
is determined by an absolute markup and/or percentage markup. These
markups may be either constant or variable as quantity changes. Studies
by Waugh (1964), Beck and Mather (1976), Etheridge (1975), Prochaska
(1978) and Bockstael (1977) have addressed these two margin compon
ents. Shepherd (1955), Rojko (1957), and Gardner (1975) suggest that
most margins are a combination of the two components. However, Dahl and
Hammond (1977) and Dalrymple (1961) assert that wholesalers typically
use constant percentage markups while retailers use a constant absolute
markup


48
Price Transmission
One characteristic of a competitive market is that prices are
transmitted efficiently through the vertical market system. Brorsen
(1983) points out that efficient price transmission can be thought of as
exhibiting a minimum of lags and distortions. This is important as
price serves as the market signal that relates changing demand and
supply conditions between consumers and producers. In this sense,
Sporleder and Chavas (1979) point out that pricing efficiency implies
optimal resource allocation, minimum cost levels, and efficient distri
bution. In addition, the major elements of pricing efficiency are given
as timelines (rapidity of transmission) and accuracy (reliability) of
price signals.
The competitive vertical market system in a static sense is defined
as having instantaneous price adjustment. However, most real world
markets are characterized by lead/lag and other forms of distortion as
prices gravitate toward some long run equilibrium. Price adjustment may
be initiated by a causal (lead) market level which results in prices in
adjacent market levels reacting, possibly asymmetrically, through some
distributed lag structure.
There have been a number of reasons offered as to how a lead posi
tion in the price transmission process is established. Ward (1982) and
Ngenge (1982) imply a relationship between assimilation of market infor
mation and causality. Gupta and Mueller (1981) provide support for this
contention by testing hypotheses of lead/lag structure in terms of
market concentration and information. The major hypothesis is that
concentrated market levels may have an advantage in assimilating market


49
information, which may in turn allow the more informed market level to
lead other market levels in price formulation. On the other hand, Heien
(1980) proposed that nonsystematic markup pricing rules were being
utilized by retailers to take advantage of price signals originating
from wholesalers and processors. Markup pricing rules would, in this
case, put the retailer in a lag position. Thus, market structure and
information availability may play an important role in the determination
of lead/lag relationships which characterize the price transmission
process between market levels.
The speed and extent with which price changes are passed to adja
cent market levels may not be equivalent for price increases or
decreases. Thus, the market may be characterized by asymmetry in price
transmission. At the retail/wholesale interface, this asymmetry may be
a function of (1) the cost of changing prices on current inventories,
(2) the need to move certain product types quickly, or (3) simply the
reluctance of retailers to relinquish a price peak once it is estab
lished. In addition, the desire to maintain most efficient use of
capacity may result in retail price rigidity as wholesale prices vary.
At the wholesale/producer interface, this asymmetry may not be as evi
dent since atomistic producers are hypothesized to be price takers.
However, if there exists monopsonistic pricing tendencies at the whole
sale/producer level, wholesale price increases may not be passed to
producers as strongly as price decreases.


CHAPTER III
EMPIRICAL METHODS
The study of price dynamics in a vertical market setting necessi
tates the investigation of the dynamic properties of price over time.
This entails, first, the identification of the stochastic properties of
the price series of concern in a 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.
50


51
Time Series Analysis
The objective of the time series analysis is to describe the under
lying stochastic process that produces the original price series. These
results can then be used to test hypotheses regarding the series of
interest or forecast future values. A distinction regarding the result
ing model is that the parameters determined are referred to in the
literature as being "mechanically" derived, often considered devoid of
theoretical economic content (Zellner, 1979). However, recent studies
have supported the contention that time series models, in fact, are
consistent with structural economic models (Anderson et al., 1983). In
addition, the dynamic adjustment properties of price series data as
revealed by time series analysis will allow testing of hypotheses orig
inally motivated by the theory.
There exists two principal time series approaches: time domain
(time series) analysis and frequency domain (spectral) analysis. The
two are theoretically equivalent (Granger and Newbold, 1977). As Ngenge
(1982) states, a result in one domain always has its equivalent result
in the other domain. The spectral approach is particularly useful if
the price series is suspected of being characterized by significant
periodicity and if the nature of these periodic components are unknown.
Price data for shrimp in the U.S. have empirically been found to not
contain an identifiable cyclical component (Thompson and Roberts, 1983).
Rather, periodicity is restricted to seasonal influences. Thus, the
spectral approach would be inappropriate. This study primarily uses the
more appropriate 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).


52
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 (x^,...,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(x^,...,xt) that assigns probabili
ties to the possible combinations of normally distributed x^, il,...,t.
Unfortunately, except for very small t, the probability functions of the
outcomes (xj,...,xt) are not completely known. However, it is possible
to generate a model that captures most of the underlying stochastic
properties and, thus, the random behavior of the series.
Each time series possesses a unique characteristicthe autocorre
lation function. This function, which is independent of the unit of
measurement, indicates whether the process moves in the same or opposite
direction through time. In other words, the autocorrelation function
provides a measure of how much interdependence (memory) there is between
data points in a given time series. The autocorrelation function is
given as
9x(U
Y,a>


53
where L is the number of lags, 9 (L) is the autocorrelation, Y-(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
Vl> W Et(*t E
where t 0,1,2,...T. The variance is given as
Yx(0) COV(xt, xt+0) COV(xt, xt) =* VAR(xt)
Thus, 9x(L) is defined as the autocorrelation at lag L.
The very strict assumption of stationarity of a time series implies
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 < 9X(L) < 1 for L > 0. In addition,
a time series characterized by
10, where L 0
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 differenced one or more times
to obtain stationarity. The number of differences taken, d, is known as
the order of homogeneity. A differenced series wt ig gven aa


54
* (i-e)dxt
where 3 represents the difference operator where 3wt = wt-l* ^ random
walk process given as
*t xt-i + 5
is homogenous of order one (first differenced). In fact, Xj. 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
cess of order p such that xt is expressed as a weighted average of past
observations lagged p periods with a random disturbance on the end
P
*t Ei ^t-i + R + t 0,I,2,...,T
where <(> is the weight on each lagged xt, is the random disturbance, p
is some maximum lag, and R is a constant term associated with the series
mean and drift (R>0 when drift is present). Assuming R=0, this may also
be written in backshift notation as
(1 $jB ... 4>pBP)xt £t
*(B)xt Ct
where 4>( 8) = (l^i & *pBI>) and can be viewed as a polynomial of order
p in lag operator B. The left-hand factor $( 3) acts as a filter on the
time series x resulting in a white noise process Pindyck and Rubin-
feld (1981) state that a necessary condition that x is stationary
requires that the autoregressive process of order p be characterized by


55
P
2 . < 1
i-1 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 9X(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 x^. is a weighted average of random disturbances lagged back q
periods. This series xt can be denoted as
xt .Yj 5t-j+ s
where is the weight on each lagged disturbance q is the maximum
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
Z 0? < -
i-1
However, this is only a necessary condition. Rewriting xt in backshift
notation and letting S=0 yields
WB)5t


56
The invertibility condition requires that
3_1(B)xt £t
where 8*(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=l) 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
0x(L) -
-8. + 8, 8T ., + ... 8 T 8
ii 1 L+l q-L q
1 3 2
1 + 87 + 87 + ... + B
1 2 q
, L
1,
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 $(8) and 8(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


57
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 d q
I *.(1-B) x R + EU. ,
i=0 1 t_1 j=0 1
%
For d0, this can be expressed as
Xt *lVl Vt-2 Vt-p E + 5t \\-l \ Vl '
In backshift notation, this is written as
(l jB ^B2 ... xBP)xt R + (l ^B B2B2 ... -
Finally, the above expressions, in differenced form, appear as
4>(B) xt = R + 8(BKt
where <(>(B) and B(B) are converging invertible polynomials in the lag
operator B. Since xfc has been differenced (is now homogeneous station
ary), the process can be modeled using an AR of order p and an MA of
order q. Thus, is an integrated (I) ARMA, or an ARIMA (p,d,q) pro
cess.
Identification and Estimation of an ARIMA Model
The discussion above has shown that a homogenous nonstationary time
series can be described as an ARIMA process of order p, d, and q.
However, the correct specification of an ARIMA process necessitates
selecting the proper values of p, d, and q to accurately describe the
underlying stochastic process that generated the original time series.
This task is accomplished by examining the autocorrelation function and
partial autocorrelation function of the time series.


58
Identification of an ARIMA model begins with determining the degree
of homogeneity in the time series. If the autocorrelative function
9X(L) of the original data does not dampen quickly to zero, the data
must be differenced d times until a stationary series results. This
decision is made by visually observing 9X(L) after each differencing to
see if 9X(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 9X(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 ~
9 (L) Z 9 9 (L i), L l,...,j,
x 1*1 J1 x
which are known as the Yule-Walker equations (Pindyck and Rubinfeld,
1981). The partial autocorrelation of order 3 (jj) for an AR(p) is
zero for j>l. 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.


59
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
5t 4>CB) 81CB)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
. ¡ h-*
r,
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 (Box and Pierce,
1970) given as
Q
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


60
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 R^ 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 misspecification 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 X^ 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 Xfc 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 X^. or causes Yt
when using past information on Xt and Yt
(2) Bi-directional feedback Yt causes Xt and Xfc causes Y^,
(3) Instantaneous causality Yt causes Xt where
current X is better predicted by including current Y, or


61
Xj. 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 Xfc and Y^. 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 X^ and Yt involves the estimation via
ordinary least squares of a four-equation regression model given as
A.l
n
1
A.2 X E a X + u
t j., J t-3 t
3-1 Tt + + t
n
E
i-1
2
B-2 V-i 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.l and A.2 to see if the c^ are different from zero. The F statistic
with q and T-t degrees of freedom is defined as


62
(ESS ESS )/(q)
F r u
q,T-t (ESSu)/(T-t)
where t is the number of parameters estimated in the unrestricted 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.l and A.2 is significant then
the null hypothesis is rejected, suggesting that Y causes X. A test of
the d^ 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.l and B.l 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(utug) = 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.
Sims 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
In this case,
- jLVm <
X ib.Y + e
c J-0 J C-J *
a test
of the hypothesis that X does not cause Y is


63
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 (-1>j >-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 = ^
F(B) Yfc 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)
uv
E(at-k-vt>
[E(ut)2E(t)2 ]1/2


64
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
1 /2
zero mean and standard deviation of T where T is the total number
of observations. Each rA(k) can be individually tested for signi
ficance where
r AA(k) > 2T1/2
uv
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) ruy(k) 0 for some k>0 implies X causes Y,
(2) ruv(k) 0 for some k<0 implies Y causes X,
(3) ruv(0) 0 implies instantaneous causality,
(4) ruv(k) 0 for some kX) and some k<0 implies feedback,
(5) ruv(k) 0 for all k<0 implies Y does not cause X,
(6) ruv(k) 0 for some kX) and ruv(k) 0 for all k<0 implies
unidirectional causality from X to Y,
(7) ruv(k) 0 fr and ruv(k) 0 implies X and Y are
related only instantaneously, and
(8) ruv(k) = 0 for all k implies X and Y are independent.
This study adopts the definitions of instantaneous and unidirec
tional causality and feedback as shown above. These notions of causal
inference from residual cross correlations have been utilized by several
recent studies (Bessler and Schrader, 1980a; Bessler and Schrader,
1980b; Miller, 1980; Shonkwiler and Spreen, 1982; Spreen and Shonkwiler,


65
1981). Haugh and Pierce suggest that the absence of unidirectional
causality from X to Y can be tested using
m
T Z [
k=l
r
uv
(k)]2 > X2U)
m
where m (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 J [',;;<*>i2 < 4 k=-m
The chi-square distributed statistic T E[r^(k)j 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 analysisthe transfer functionprovides a comprehensive
model of the dynamic relationship between time series; e.g., two price
series. In particular, the development of a bivariate transfer function
in terms of prices in adjacent market levels utilizes the time series
ARIMA filters for each series and the causal relationship between the
innovations of each series to construct a distributed lag or impulse


66
response model which embodies the dynamic nature of the relationship
exhibited by the two time series.
Haugh and Box (1977) outline the dynamic regression procedure as a
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 u^ and vt are obtained which can be
represented by
0(B)Xt = ut


67
where 0(B) and (B) are invertible polynomials in the lag operator B.
The terms ufc and vfc represent the white noise processes (innovations)
obtained from of X and Y, respectively. The polynomials 9(3) and ( S)
may be viewed as filters which are identified and estimated by using the
Box-Jenkins approach. The sample cross correlations between ut and vt
{r^(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. Xfc leads Yt, Haugh and
Box (1977) show that it is possible to express Yt as a distributed lag
on X^. as
Yt S(B)Xt + at
where 5(B) is some polynomial of Xt and afc is an error process. The
weights on the terms of the polynomial 5(B) are referred to as the
impulse response parameters. These parameters characterize the response
of Yt to changes in the "input" Xfc, net of the "masking effect" of the
stationary white noise process at. To identify the order of the poly
nomial 5(B) connecting Yt and X^., 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(k) f where k is the order of lag,
to arrive at a dynamic shock model given as
v V(B)u + Y(B)a
t t t


68
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,u8) 0, for
every t*s, then each parameter coefficient in V(B) is simply the bivari
ate regression coefficient relating vt to u^^ given as
V, ^ rAA(k)
k a uv
ut
where crv and o are the standard error of the innovation series and k
t t
is the lag of the residual cross correlation.
Dynamic Regression Transfer Function
Given that the parameter coefficients of V(B) have been identified
and the order of the polynomial is known, the original filter expres
sions
9(B)Xt ut
are substituted into the dynamic shock model (Haugh and Box,,1977) to
give
and isolating Yt yields the impulse response or transfer function
Yt (B)"1V(B)9(B)Xt + 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 S(B)Xt + X(B)at


69
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( 8), the parameters of 5(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
misspecification.
Once the transfer function relating X and Y has been identified,
the lead/lag structure; e.g., current and/or lagged prices, are included
in a more complete explanatory model of the market. The regression
methods that are employed to estimate the econometric model of prices
are discussed below.
General Regression Methods
The analysis of time series properties, causality tests, and deri
vation of the transfer function provides a set of expressions in terms
of endogenous and lagged endogenous variables. These expressions evolve
into a more comprehensive model when they are augmented with additional
exogenous variables whose presence is dictated by theory and knowledge
of the market. This study strives to generate such models describing
price at each of three market levels.


70
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.


71
A system of g expressions in terms of g endogenous and k predeter
mined variables can be written in matrix notation for each observation
as
IT + BX = E
t t t
where Y is a gxl vector of endogenous variables, X is a kxl vector of
predetermined variable, T 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 = -r1BXt + r_iEt or
Yt irXt + V
where ir is a gxk matrix of derived reduced form estimates and V is a gxl
vector of disturbances. The elements of ir, 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 ir 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


72
The reduced form matrix ir can be partitioned into submatrices such
that
Yt do + + D2Xt + 5t
where Yt is a g*l vector of endogenous variables, Yt_^ is a g*l vector
of endogenous variables lagged one period, Xt is a kxl vector of the
exogenous variables, dg is a vector of constant terms, Dj^ is a g*g
matrix of derived reduced form estimates for the lagged endogenous
variables, D2 is a g>4c matrix of derived reduced form estimates for the
exogenous variables, and is a g*l vector of disturbances. The ele
ments in Dj and 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 Yfc lagged one period and substi
tuted back into Yt gives
Repeating this procedure s times yields
However, note that if
lim D = 0,
S -H
then
lim E D*
S-H i**0
- (I-D^-1.
Then by dropping the time subscript, Y can be written as
Y = D + XX + E


73
where D (I Dj) *dg
X = (I D1)"1D2, and
E (I Dx )_1 5
A
The elements of D, X, and E are referred to as the final form estimates
of the model.


CHAPTER IV
EMPIRICAL MODELS
Introduction
The theoretical economic model of a system of price dependent
demands for the major market levels in the domestic shrimp marketing
system was developed in Chapter II. The empirical form of the model is
presented in this chapter. Initially, the price dependent demands are
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^; Q¡¡, D)
(31) pw f2(M2; cr, Qp)
(32) pf f3(M3; cW, qJ)
(33) pp f4(M4; cf, QJ)
74


75
where pr, pw, p^, and pp represent prices received by retailers, whole
salers, first handlers, and producers, respectively. 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, Qq, Qp,
Qq, and are the quantities offered by retailers, wholesalers, first
handlers, and producers, respectively, and cr, cw, and c^ 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, pw, p^, 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 II is 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


76
Figure 6. Market Channel Schematic Representation for the U.S
Shrimp Market System.


77
represented by equations (30) through (33) could be estimated. Price
data is not available to describe the transaction between the first
handlers and the wholesaler/processor (region B is Figure 6). Thus,
only expressions (30), (31), and (33) are modeled on a monthly and
quarterly basis for two size classes of 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
price.
Symmetric and Asymmetric Models
Price models often hypothesize that increases and decreases in
price at one level are passed on equally to adjacent levels (Helen,
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


78
(1) Rt % + ai wt + 5t
when Rt is retail price, Wt is wholesale price, and 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) Rfc WIt + WDt + 5t, t 1,...,N
where
t \l0 (Vi Vh> DIt-i
mt DI
1, Vi> Vi-1
t-i
{
otherwise
DD
t-i
i. Vi< "t-i-i
0, otherwise
where WIt and WDt represent cumulative wholesale price increases and
decreases, respectively. Thus, testing the significance of and 02 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 WQ + WIt + WDt (Identity)
where Wq equals for t-0. Substituting for WIt gives


79
Rt 0
+ (Wt WQ- WDt) + a2 WDt + ^
which yields
Rt = a* + aj Wt + a* WDt + ^
where ag = (cq ajW0) and = (<*2 al) A test of significance of
(2 Oj) provides a direct test of asymmetry. Recall that measures
the reaction of Rt when Wt increases and measures the reaction of Rt
when Wt decreases. The significance of can be measured via the
estimate by writing
2 "
*
- a.
+ a,
2 2 "I
and var(c*2) var(a£ + oj) varCaj) + varCa^) + 2 Cov(alf a£),
The t-statistic would then be written as
(<*2 + op -0
/VAR (o2)
*
2 +
Var Oj + Var a2 + 2 Cov (a^, <*2)
whereof is the estimate of c^. If in the event that is found to be
insignificant, the test of significance on the coefficient (Xj reverts to
a symmetric test of retail price response to increases or decreases in
wholesale price. Expressions for pr, pw, and pP can now be written in
explicit form.
Data
The estimation of time series properties and analysis of causal
relationships of prices for shell-on, fresh-frozen, raw-headless shrimp
(hence forth referred to simply as raw-headless) at retail, wholesale,


80
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 classesthe 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


81
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 (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 found in each model and discusses the variables
which are given to be predetermined. A discussion of the final


82
specification of each model is given in Appendix B. Excluding
consideration of the prices found in 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
NR
Rt c£ + S [Mj] + aj RDYt + a* TCFF^. + a* CPIt + ^
where Rt retail (non-institutional) price in time period t (Shellfish
Market Review, NMFS)
= aggregate real disposable income in billions of dollars (base
year 1972)(Bureau of Economic Analysis),
TCFFt Business Statistics! 1982, total retail supply (disappear
ances from wholesale market) of all sizes rawheadless shrimp
in millions of pounds (Shellfish Market Review, NMFS),
CPIt consumer price index for meat and poultry products, deseason-
alized with 1972 100 (CPI Detailed Report, Bureau of Labor
Statistics),
NR number of current and lagged endogenous and exogenous prices
found in m£ for each size class model, where i refers to size
class,
and o£ and g£ are the coefficients to be estimated, with the superscript
r referring to the retail model. Each is associated with a current


83
r R R
or lagged exogenous or endogenous price contained in M^. M3 and M2
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 rawheadless shrimp in
the Baltimore, Maryland area as reported by the National Marine
Fisheries Service (NMFS). The model was specified as a function of
quantities moving through the retail market and parameters which may
capture shifts in retail demand income and prices of competing meat
products. As income increases, demand for shrimp should increase,
thereby bidding up the price of shrimp. Similarly, as the price of
competing products increases consumers may consume more shrimp products,
also bidding up the price of shrimp. In this sense and 03 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, oJj is anticipated to have a negative sign.
The presence of 8£ 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 8? are anticipated to be positive, reflecting a direct positive
relationship between contemporaneous and lagged price movements at the
wholesale and retail level.


84
The specification of the model is the same for monthly or quarterly
data. The prices found in m£ 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 m£,
RDYt, and CPIt 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-headles3
shrimp is given as
and for 21-25 count raw-headless shrimp is given as
. NW ,
= b" + Z 8" [Mp + b BSFFt + b" 0l£ + b" I21t + bj TMCI^. + C2
i-1 4
where
WJ? wholesale price for 31-40 size class (Shellfish Market
Review. NMFS),
* 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),


85
Olj? 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,
0l£ 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,
13lt = imports of raw-headless shrimp of 31-40 size class at
selected ports of entry in millions of pounds (NMFS unpub
lished files),
12lt 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 M^ for each size class model, where i refers to size
class,
and o£, 6^, b, and are the coefficients to be estimated. Each 6^
and ^ is associated with a current or lagged endogenous or exogenous
price contained in Mj and M?[, 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


86
spread (costs incurred by the retailers). The quantity variable Qq
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^, a£, a^, b^, bj, and b^ are anticipated to be
negative in sign. The parameter 0It and I31t for the 31-40 size class
model and 0It and I21t 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 a£ and b£ are anticipated to be negative in sign.
Depending on whether the price determination process is character
ized by upward causality, downward causality, or simultaneity, the 8^'s
and d^'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 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 TMCIj. and for all prices found in the


87
corresponding M^. The parameters 0l£, 0l£, I31t, and I21t 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
and for 21-25 count raw-headless shrimp is given as
P
b + E
U i-1
[M^J + b^OL^ + b^ L21t + b* TMCI^ + ^
where
pj? ex-vessel price for the 31-40 size class (Shellfish Market
Review, NMFS),
2
Pt ex-vessel price for the 21-25 size class (Shellfish Market
Review, NMFS),
O
0L£ total domestic landings for all sizes of shrimp excluding the
31-40 size class landings in millions of pounds (Shellfish
Market Review, NMFS),
O
0L£ 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
files),


88
L21fc landings of shrimp in the 21-25 size class in the Gulf and
South Atlantic in millions of pounds (NMFS unpublished
files),
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 M? for each size class model, where i refers to size
class,
P p p p p
and o^, <5^, b^, and 8^ are the coefficients to be estimated. Each 6^
and 8^ is associated with a current or lagged endogenous or exogenous
P P
price contained in M3 and M2, 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 Qq 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, 0Lt and L31t for the 31-40 size class and 0Lt and L21t for


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PAGE 220

81,9(56,7< 2) )/25,'$


PRICE DYNAMICS IN THE
U.S. SHRIMP MARKET
By
CHARLES M. ADAMS
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1984

To Mom and Dad

ACKNOWLEDGMENTS
I wish to express sincere appreciation to Dr. Fred J. Prochaska and
Dr. Tom H. Spreen for taking time to critique the many drafts of this
manuscript. Their guidance and friendship were invaluable. Thanks go
to Dr. Jim C. Cato, Dr. W. Steve Otwell and Dr. Gary F. Fairchild for
dedicating time to serve as counsel on the advisory committee. Special
thanks go to Fred, Jim, and the Florida Sea Grant Program for the
financial support provided throughout my stay as a graduate student.
This dissertation would be long in coming if not for someone to
decipher and type the initial scribbling. In that sense, Frankie
Thomas, with her patience, understanding and keen eyesight, was abso¬
lutely indispensable. Thanks also go to my fellow students, to whom I
am grateful for their aid and comaraderie.
However, my greatest appreciation goes to Sherry, Sam and ???,
whose love and patience provided the motivation needed to complete my
graduate studies.
iii

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ill
LIST OF TABLES vii
LIST OF FIGURES ix
ABSTRACT x
CHAPTER
I INTRODUCTION 1
Overview of Industry ... 4
Resource and Harvesting . 4
General Industry Trends 6
Industry Issues.. 17
Problem Statement 20
Objectives 23
II THEORETICAL CONSIDERATIONS 25
Vertical Structure 25
Causal Direction of Price Determination in the
Vertical Market 41
Price Spreads Between Market Levels 44
Price Transmission 48
III EMPIRICAL METHODS 50
Time Series Analysis 51
Univariate Time Series 52 .
Autoregressive (AR) Process 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
iv

Dynamic Shock Model 67
Dynamic Regression Transfer Function 68
General Regression Methods 69
IV EMPIRICAL MODELS 74
Introduction 74
Implicit Models 74
Symmetric and Asymmetric Models 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
V EMPIRICAL RESULTS—CAUSALITY ANALYSIS 94
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 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 Ill
The 21-25 size class Ill
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.. 120
The 21-25 size class.. 120
Summary of Monthly and Quarterly Causality Results 122
VI EMPIRICAL RESULTS—PRICE AND MARGIN MODELS 124
Monthly Data 124
The 31-40 Size Class 125
Retail structural estimates 125
Wholesale structural estimates 127
Ex-vessel structural estimates 130
The 21-25 Size Class 132
Retail structural estimates 132
v

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 Asymmetry Analysis.... 162
Factors of Price Determination 164
Margin Analysis 168
Methodological Conclusions 169
Policy Implications 170
Suggestions for Future Research 173
APPENDICES
A DERIVATION OF IMPULSE RESPONSE FUNCTIONS 178
B FINAL MODEL SPECIFICATIONS 187
C GRANGER TESTS USING DATA FILTERED BY USING ARIMA
MODELS 192
D REDUCED FORM ESTIMATES 196
REFERENCES 198
BIOGRAPHICAL SKETCH 206
vi

LIST OF TABLES
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
vii

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 (M1^) 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
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 (Wt), and Ex-vessel (Pt) Models Before and
After Inclusion of a Lagged Dependent Variable 189
C.l 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.l Reduced Form Estimates and Flexibilities for Quar¬
terly Price Models at the Retail (Rt), Wholesale
(Wt), and Ex-vessel (Pfc) 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 Class 197
viii

LIST OF FIGURES
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 System
with Equilibrium Prices pr, pw, and p in Time Period t.... 29
4 Graphical Representation of a Vertical Market System
with Supply and Demand Given Implicitly at Four Market
Levels and the Corresponding Equilibrium Prices, pr,
pw, p , and pP in Time Period 35
5 Graphical Representation of a Vertical Market System
Characterized by Inelastic Supply with Demand Given
Implicitly at Four Market Levels 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 System 76
ix

Abstract of Dissertation Presented to the Graduate School of the
University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
PRICE DYNAMICS IN THE
U.S. SHRIMP MARKET
By
Charles M. Adams
December 1984
Chairman: Frederick J. Prochaska
Major Department: 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 raw-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
x

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, cwn and other size landings
and imports of cwn-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 maricultural shrimp will have a greater relative price
impact on the 31-40 size class.
xi

CHAPTER I
INTRODUCTION
Management of the domestic shrimp fishery in the United States has
proven to be a considerable task. The goal of effective implementation
of policy has resulted in the organization of a complex management
structure and the allocation of substantial sums of research dollars to
be directed toward current research needs.
The passage of the Magnuson Fishery Conservation Management Act PL
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
1

2
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 capita 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.

3
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

4
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,

5
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,

6
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

7
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 capita. Both total and per capita 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 capita. This can be contrasted to per capita consumption of
all fishery products in the U.S. which had a continual upward trend from
10.3 pounds in 1960 to 12.3 pounds in 1982 (U.S. Dept, of Commerce(b),
1983).
Consumption of individual shrimp product forms has been changing.
In 1960, 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 capita 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 capita basis.

8
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 capita 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,

9
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

10
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

11
$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.

Figure 1. Trends in Quarterly Prices for 31-40 Count Raw-Headless Shrimp for Retail,
Wholesale, and Ex-vessel Market Levels.

Figure 2
Trends in Quarterly Prices for 21-25 Count Raw-Headless Shrimp for Retail,
Wholesale, and F.x-vessel Market Levels.
YEARS

14
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 and
wholesale/ex-vessel (M^) margins for the 31-40 size class exhibited a
slight upward trend. The margins Mâ„¢ 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 M1^ increasing from $0.41 to
$0.81, while increased from $0.18 to $0.36. Average values during
this period for M™ and 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 M™ for both size classes varied consider¬
ably, while Mwp exhibited a stable upward trend. The margins and
Mwp averaged $0.75 and $0.46, respectively, for the 31-40 size class,
while and averaged $1.04 and $0.51 for the 21-25 size class.

15
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 Mâ„¢ during this period. This large margin was maintained
for nearly three years, being relinquished only in the last quarter of
1982. The margins M1* and were both very erratic during this
period. The retail/wholesale margin averaged $2.46, compared to an
average of $0.57 for the 31-40 size class. The margins M1"** and
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

16
compared to a much smaller but Increasing 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

17
20 percent in some cases, significantly above prime rate. The last few
years, as a result, have exhibited an increasing number of foreclo¬
sures. Some producers have been forced to suspend fishing or retrofit
their vessel for alternative species, such as swordfish, shark, snapper,
or grouper. Processors are also experiencing increased costs as labor,
energy, and transportation costs climb. Creditors are becoming less
willing to advance new loans or extensions on existing mortgages at a
time when it is becoming increasingly necessary to obtain conversion
financing or loan extensions.
Industry Issues
In recent attempts to stabilize the economic conditions in the
domestic shrimp industry, several policy strategies are particularly
noteworthy. The unsuccessful 1981 Breaux Bill (HR4041) was introduced
as the "American Shrimp Industry Development Act." The purpose of this
legislation was to provide shrimp producers a means by which to estab¬
lish financing and implement a coordinated program of research, producer
and consumer education, and market promotion in an attempt to "improve,
maintain, and develop markets" for domestic shrimp products. The major
provisions of the bill addressed the establishment of a tariff or quota
system, establishment of regional market boards, and creating a compre¬
hensive data reporting network. Federal opponents argued that most
goals of the bill, with the exception of the marketing boards, were
clearly within easy reach of the current management process.
The controversial Texas closure has generated varying results.
Normally, the offshore Texas season is closed from June until mid July,
out to nine fathoms. This leaves a large portion of the FCZ, which

18
extends out to 200 miles, open to shrimping. However, beginning in
1981, the entire FCZ was closed to shrimping except out to four fathoms
with a 25 foot trawl. This represents an attempt to protect small
shrimp and increase the average size shrimp caught, thereby increasing
prices and gross revenues to the producer. The results in 1981 signal¬
led a successful year with Texas landings and value up. However, the
1982 and 1983 closure brought just the opposite results. Texas pro¬
ducers questioned the uncertainty of the closure, especially since no
fishing in the FCZ coupled with the possibility of minimum effect from
the closure would be disastrous. Louisiana producers argued that Texas
shrimpers would encroach on their traditional grounds during the clo¬
sure. In addition, Louisiana processors argued that a supply glut may
hit the market with less than efficient means to deal with the excess
supply.
In general, the U.S. shrimp industry has exhibited decreasing catch
per unit effort, increasing variability in producer price, and increas¬
ing costs of production. In addition, producers particularly have made
a case that they are experiencing reduced profits. Though there appears
to be no quick fix, several policy measures to address these problems
exist, each with its own set of advantages and disadvantages. In an
attempt to stabilize prices at a higher level, imposition of a tariff or
quota system has been suggested. Theoretically, in the presence of
import restrictions, prices should adjust to a higher level, with domes¬
tic supplies being more dependent on U.S. producers. However, the
erratic nature of U.S. production may have the effect of increasing
price volatility. In addition, lack of political endorsement, the
questionable impact on processor cost structure and reduced supplies to

19
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
Asia

20
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
vital.
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

21
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 MFCMA.
The shrimp industry is the most valuable domestic fishery in dock-
side dollars in the United States. This particular industry has recent¬
ly exhibited considerable price volatility and instability throughout
the market system. A host of factors have contributed to this state of
flux, such as fluctuating demand, tight world and domestic supplies,
changing market structure, increasing dependence on imports, increasing
costs of production, and fluctuating domestic economic conditions.
Changing market conditions appear to have left the producer bearing the
brunt of an array of economic symptoms. The symptoms which are being
expressed by producers, such as relatively depressed dockside prices and
reduced revenues, have motivated interest in several management policies
to help bolster demand for domestic products and, thus, act as price
supports (i.e., import tariff, import quota, limited entry, and promo¬
tional programs). In addition, the apparent concentrated nature of the
shrimp wholesale/processing market level (less than 20 firms control
approximately 90 percent of total U.S. output) may provide for some
market power in terms of gathering and assessing market information.
This may provide for a competitive advantage over firms in their own
market level and also provide an informational advantage over firms in
adjacent market levels. The recognition of the possible oligopolistic

22
nature of the wholesale/processing sector may provide insights into the
price determination process at each market level. In addition to pos¬
sible monoposonistic pricing, the concentrated nature of the processing
sector may result in price leads and lags in the market place, with the
market level possessing more timely and accurate information acting as a
price leader. The market level with the information edge may be able to
exploit this position in the price determination process to gain greater
profits relative to adjacent market levels. The existence of this
phenomenon is at least implied by recent legislation calling for aid in
establishing cooperatives and market orders in the producer sector.
Before the economic appropriateness of a tariff, quota, or limited
entry program can be accurately assessed, an understanding of price
dynamics is vital. This knowledge will provide a more clear view of how
these policies will impact the various market levels.
Studies done to date concerning the U.S. shrimp market system have
provided some insight into the mechanism of the structural components of
the system in an effort to understand market price fluctuations (Doll,
1972; Hopkins et al., 1980; Thompson and Roberts, 1982; Gillespie et
al., 1969; Prochaska and Keithly, 1983). Previous research has provided
a partial understanding of how imports, domestic business and economic
factors, and biological elements impact the pricing system. Limited
explanatory power has resulted. More importantly, contradicting model
specifications in terms of the direction of price determination are
evident in some of the previous major studies. No formal research has
been undertaken to employ current methodology regarding price causality
in the U.S. shrimp market system. In addition, no formal research has
been carried out regarding the presence or absence of asymmetric price

23
response, speed and magnitude of price adjustment between market levels,
and the determinants of prices and marketing margins. Further research
must be performed to provide insights into the sensitivity of price
transmission in a time (speed of adjustment), space (region of market),
and form (size and degree of processing) framework. Policy makers need
to understand the dynamics of price determination and transmission in
the market and the impact to producers, processors, retailers, and
consumers that increased control over prices in the market may pro¬
duce. A more fundamental knowledge of price linkages would provide
further understanding of how market levels interact and relate given
stimuli internal and external to the market system.
Objectives
The purpose of the research is to investigate and model the dyna¬
mics of price transmission between the producer, wholesale, and retail
levels of the U.S. shrimp market system on a size class basis for raw-
headless shrimp. This will be accomplished by developing an econometric
model of the prices and marketing margins. Primary emphasis is placed
on examining the dynamics of price for each market level and price
transmission between market levels. Insights, are developed into the
nature of the price adjustment process between market levels. Speci¬
fically, the objectives of the research are
(1) to determine the univariate time series characteristics of the
price series for each market level (producer, wholesale, and
retail) by size class (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
system,

24
(3) to examine speed of price adjustment between market levels for
each size class,
(4) to determine if price adjustment between market levels is sym¬
metric or asymmetric for each size class, and
(5) to identify major determinants of price and test hypotheses
regarding price relationships between market levels.

CHAPTER II
THEORETICAL CONSIDERATIONS
This chapter provides a brief discussion of the competitive market,
with emphasis given to the vertical structure. The dynamic properties
of price, such as the direction of price determination and lead/lag
relationships are discussed to provide an understanding of how actual
markets may depart from the static competitive model. Specifically,
causality between market levels in a vertical market system, the nature
of price spreads, and the importance of the mechanics of price transmis¬
sion between levels in a vertical market system is stressed. Thus, this
section provides a motivation for the modelling approach.
Vertical Structure
Bain (1964) discusses the market system as a means by which natural
resources, productive facilities, and labor forces are developed and
assembled to determine what and how much is to be produced and how the
goods and services are to be distributed to users. Cochrane (1957)
defines a market as a sphere or space where the forces of demand and
supply interact to determine or modify price as the ownership of some
quantity of goods or services is transferred with certain physical and
institutional arrangements in evidence. In a perfectly competitive
sense, many buyers and sellers come together to negotiate regarding a
homogenous product with perfect information, no rivalry, and with free¬
dom to enter or leave the market. As Kohls and Uhl (1980) argue,
25

26
arbitrage would result in an instantaneously determined unique equili¬
brium price for any quantity of goods representing a given time, loca¬
tion, and product form. Price formulation is a static process in this
setting (Heien, 1980).
When using the above concept of the market, one can visualize a
benchmark case where a single equilibrium market price is established at
which the quantities offered for sale by producers exactly equals the
quantities demanded by purchasers. The situation would only be true in
the simplest of markets where the original producers and final consumers
are involved in a direct arbitrage. Most agricultural commodity markets
are far more complex. In most markets, initial producers and final
consumers are separated by a complex vertical network of intermediate
processors, handlers, wholesalers, brokers, and marketing agents, each
exhibiting its own input demand and output supply. In this sense,
initial producers and final consumers do not face one another directly;
rather market signals must pass through the market system whether the
signal originates from the final consumer, initial producer, or inter¬
mediate agent. Often, consumer demand is not for the primary product
but for the primary product plus the utility derived from additional
characteristics added through processing and the necessary marketing
services. Thus, consumer demand is a direct demand for a final good
such as breaded shrimp, as opposed to a 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

27
D. =â–  f(P, Y)
where P Is a vector of prices P^,...,Pj and Y is income. Each is
assumed to be a demand function homogenous of degree zero in prices and
income and monotonically decreasing in price (Deaton and Muellbauer,
1980). The market (consumer) demand, or "primary" demand for the market
then is the horizontal summation, of individual consumer demands D^.
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).

28
The intersection of primary producer supply and the final consumer
demand is of no real importance in a market where the product must 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 R^,
W^, and F^, respectively. Primary supply at producer level, derived
supply at wholesale level, and derived supply at retail level, are
represented by F8, W8, and R8, 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

29
Figure 3. Graphical Representation of a Vertical Market System with
Equilibrium Prices pr, pw, and pf in Time Period t.

30
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
0
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

31
and lags in pricing associated with disequilibrium are consistent with
perfect competition in the short run. Thus, issues regarding the dyna¬
mics of price transmission (lead/lag structures) become important when
addressing pricing efficiency on a timeliness and accuracy basis for the
short run movement in prices (Sporeleder and Chavas, 1979). As such, a
dynamic rather than a static approach may be more appropriate when
examining the transmission of prices between producer, wholesale, and
retail levels in the market place when using weekly or monthly rather
than quarterly or annual data. The price transmission model presented
below relates to Figure 3.
The retail (primary) demand for the final product is given by
(1) Rd = f(Pr; V)
where Rd is quantity demanded at retail by consumers, pr is retail
price, and V is a set of exogenous factors which affects consumer
demand, such as income. The retail (derived) supply for the finished
product is given as
(2) RS - f(Pr, pw; 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 =â–  f(pr, pW; X)

32
The supply relationship at the wholesale/processor level is derived from
the producer level in equivalent units. This supply is given as
(4) WS =» f(pW, pf; Y)
where p^ 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 =â–  f(pf; Z)
where Z is a set of exogenous factors affecting production, such as
weather.
When the market is assumed to be in equilibrium, i.e., Rd =* Rs,
= Ws, 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 - f(pw; V,X)
(8) pW - f(pr, pf; X,Y)
(9) pf - f(pw; Y,Z)
which are fully simultaneous in prices. In Gardner's static competitive
model, these reduced form expressions for price are assumed to adjust
instantly to changes in raw product supply, supply functions of market¬
ing services, or retail food demand. In addition, Gardner suggests that
simple markup rules in pricing at each market level are not adequate

33
enough to accurately model price determination processes. Heien, how¬
ever, advocates the viability of markup pricing rules with a model
incorporating short run disequilibrium such that f Rs, ¿ Ws, and
f Fs. 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

34
signals, stability implies that the market will eventually equilibrate
to the static equilibrium point through some lag recursive adjustment
process (Silberberg, 1978). A stable market then will result in long
run and static adjustment tending to produce the same equilibrium point.
Ward (1982) suggests that increased concentration at one market level
may provide that level with a competitive edge in assessing market
information. This advantage effectively allows that market level to
react before other market levels and establish a pricing lead. Miller
(1980) attributes the lead/lag pricing structure to increased use of
formula pricing, demise of terminal markets, and general structural
changes in the market.
An attempt to directly estimate and interpret a set of reduced form
expressions, such as represented by equations 7, 8, and 9, will be
frustrated in that the signs of the parameter estimates will be ambigu¬
ous. This is due to the parameter estimate being unspecified as to
whether the representative shock originated from a supply or demand
shift (Chiang, 1974). In this sense, the above expressions for prices
pr, pw, and pf 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

35
PRICE t
w
P
Q
QUANTITY t
Figure 4. Graphical Representation of a Vertical Market System with
Supply and Demand Given Implicitly at Four Market Levels
and the Corresponding Equilibrium Prices pr, pw, px, and
pP in Time Period t.

36
domestic shrimp market where most shrimp produced domestically are off¬
loaded by a fish house (first handler) and sold to a wholesaler and/or
processor. The first handler for imported product is normally a bro¬
ker. The domestic and imported product is then processed under retail
or processor brand name and sold to the retail market.
The consumer's demand for retail product is given as
(10) q£ = f(pr, D)
C r
where QD is quantity demanded, p 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
(11) Q* = f(pr, pW, cr)
R w
where Qs is quantity supplied, p 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) Q* = f(pr, pW, cr)
R R
where 0.D is quantity demanded, which is the same function as for Qg.
R R
The similarity between Qs and QD is valid in terms of the theory of the
R R
firm as Qq represents the input demand of a retail firm and Qg 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).

37
The wholesaler-processor's supply of product to retail firms is
given as
/lO\ £/ f w w\
(13) Qs = f(p , p , c )
W f
where Qg 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
,1/x -.W f w w.
(14) QD = f(p , P , c )
W W W
where QD is quantity demanded. The expressions Qg 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) Qg = f(pf, pP, cf)
F
where Qg 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¬
duct from producers is given as
(16) = f(pf, pp, cf)

38
F
where Qq is the quantity demanded and which is given in terms of the
F
same variables as Qg.
The producers supply of raw product to first handlers is given as
(17) Qg = f(pP, X)
D
where Qs is the quantity supplied and X is a set of exogenous supply
shifters, such as weather.
By assuming that inventories remain relatively stable over time,
the quantity supplied at each market level is determined by the equili¬
brium quantity determined in the raw product market. Given that the
supply of raw shrimp product is determined in the 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)
D
D
(19)
PW
= f(pr,
cr,
QD)
(20)
Pf
= f(pW,
cw,
w
V
(21)
PP
= f(pf,
cf,
F
qd)
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
kas been shown to be appropriate for agricultural products. Houck
(1966, page 225) states that "although individuals make quantity

39
Figure 5. Graphical Representation of a Vertical Market System
Characterized by Inelastic Supply with Demand Given
Implicitly at Four Market Levels and the Corresponding
Equilibrium Prices pr, pw, p^, and pP in Time Period t.

40
decisions based on given prices, market supplies of many agricultural
products are so fixed in the short-run that prices must 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
(23) pw
(24) pf
(25) pP - f(pf, cf,
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

41
process is characterized by instantaneous interdependent (simultaneous)
price shifts in a static competitive manner or whether unidirectional
relationships exist in a fully downward, fully upward, or an intermed¬
iate nodal form may very well be a theoretical question which requires
empirical support.
Causal Direction of Price Determination in the Vertical Market
In attempting to estimate equations 22 through 25, the model must
be specified in either seemingly unrelated, recursive, block recursive,
or fully simultaneous form. In doing so, restrictive implicit assump¬
tions (maintained hypotheses) regarding the direction of price determi¬
nation (causal) structure of the price series are imposed. A more
general representation of the structural price equations could be given
as
(26) pr = f (Mjj Qp, D)
(27) pw = f (M2; cr, Q*)
(28) pf - f (M3; cW, Q¡J)
(29) pp - f (M4; cf, qJ)
where 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 M^. 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

42
306) provides three motivations for determining the causal nature of the
relations of an economic system:
(1) Policy implications of any relation depend critically upon
whether the relation holds in one or more directions,
(2) Methods which are not designed to recognize the directional
nature of relations will often lead to acceptance of a rela¬
tion as 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

43
a theoretical basis for questioning the finding of unidirec¬
tional causality from producer to consumer prices also
exists. Derived demand analysis specifically yields a model
of price causality from the consumer price level to the
producer price index. This analysis has gone surprisingly
unnoticed and untested. Consider supply costs and the deter¬
mination of the cost of production. The producer pays the
opportunity cost of resource or the services of resources in
order to acquire input. The opportunity costs of resources
reflect the demand for input between competing uses. It is
the demand for final goods and services that generates the
opportunity costs of resources and intermediate materials.
This suggests causality from consumer prices to producer
prices (page 380).
Heien (1980), on the other hand, suggests that the competitive
market dictates the direction of causality from producer to consumer
through markup pricing rules. Bishop (1979) reiterates this confusion
over the direction of causality by stating
Some assume that changes in prices at the farm level lead to
changes in the wholesale and/or retail prices. Others assume
that because of the nature of the food processing industry,
no strong relationship exists between producer and retail
food prices (page 1).
Van Dijk (1978) points out that the theory of price formation in
the vertical market system does not provide an unambiguous indication of
the 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

44
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 must 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

45
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., pw - pf in Figure 3. In an actual market setting, the spread
between two prices would typically consist of wages, transportation
costs, interest, processing, charges for marketing or handling services,
and profit markup necessary to provide for an acceptable rate of return.
In a competitive model, excess profit is dissipated to zero, or normal
profit.
The price found at the primary demand level (retail) or a derived
demand level above the producer level consists of two components— (1)
producer related components and (2) processing and/or marketing related
costs. As pointed out by Fisher (1981) and Friedman (1962) this margin
concept operates under the assumption of fixed proportions in processing
and marketing which implies elasticity of substitution (a) between all
goods and marketing/processing inputs equal to zero. Recent studies by
Gardner (1975), Fisher (1981), and Heien (1980) have produced more
general models where a j4 0. In addition, dynamic lead/lag price spread
adjustment has been investigated through use of inventory disequilibrium
models (McCallum, 1974).

46
Gardner identifies the major determinants of the price spreads as
farm product supply, the supply functions of marketing services, and
retail food demand. For example, given a perfectly elastic supply for
marketing services, a shift in demand for marketing services would
result in no changes in the margin, as suppliers of marketing services
would be price takers. However, a less than perfectly elastic supply
function would result in a changing margin as prices of services
increase commensurate with increases in demand for services. Tomek 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

47
elasticities of demand and supply at each market level. The question of
who bears the margin shift is particularly important to trade policy.
As Fisher (1981) points out, for most agricultural products, the major
adjustments which result from a shift in marketing margins will be borne
by producer prices. Thus, producers have a strong economic motive for
establishing some influence over cost efficiencies in the processing
level of the market system.
The price formulation policy to be used at each market level is
dependent on a number of factors including firm policy and objectives,
i.e., following the leader pricing, staying abreast of competition, or
short run profit maximization (Dalrymple, 1961). George and King (1971)
discuss other forms such as average cost, experimental, or intuitive
pricing methods. Griffith (1975) and van Dijk (1978) discuss at great
length the phenomenon of price leveling and its causes and consequences.
These forms of pricing behavior are referred to as nonsystematic. On
the other hand, systematic pricing methods are evident when the margin
is determined by an absolute markup and/or percentage markup. These
markups may be either constant or variable as quantity changes. Studies
by Waugh (1964), Beck and Mather (1976), Etheridge (1975), Prochaska
(1978) and Bockstael (1977) have addressed these two margin compon¬
ents. Shepherd (1955), Rojko (1957), and Gardner (1975) suggest that
most margins are a combination of the two components. However, Dahl and
Hammond (1977) and Dalrymple (1961) assert that wholesalers typically
use constant percentage markups while retailers use a constant absolute
markup

48
Price Transmission
One characteristic of a competitive market is that prices are
transmitted efficiently through the vertical market system. Brorsen
(1983) points out that efficient price transmission can be thought of as
exhibiting a minimum of lags and distortions. This is important as
price serves as the market signal that relates changing demand and
supply conditions between consumers and producers. In this sense,
Sporleder and Chavas (1979) point out that pricing efficiency implies
optimal resource allocation, minimum cost levels, and efficient distri¬
bution. In addition, the major elements of pricing efficiency are given
as timelines (rapidity of transmission) and accuracy (reliability) of
price signals.
The competitive vertical market system in a static sense is defined
as having instantaneous price adjustment. However, most real world
markets are characterized by lead/lag and other forms of distortion as
prices gravitate toward some long run equilibrium. Price adjustment may
be initiated by a causal (lead) market level which results in prices in
adjacent market levels reacting, possibly asymmetrically, through some
distributed lag structure.
There have been a number of reasons offered as to how a lead posi¬
tion in the price transmission process is established. Ward (1982) and
Ngenge (1982) imply a relationship between assimilation of market infor¬
mation and causality. Gupta and Mueller (1981) provide support for this
contention by testing hypotheses of lead/lag structure in terms of
market concentration and information. The major hypothesis is that
concentrated market levels may have an advantage in assimilating market

49
information, which may in turn allow the more informed market level to
lead other market levels in price formulation. On the other hand, Heien
(1980) proposed that nonsystematic markup pricing rules were being
utilized by retailers to take advantage of price signals originating
from wholesalers and processors. Markup pricing rules would, in this
case, put the retailer in a lag position. Thus, market structure and
information availability may play an important role in the determination
of lead/lag relationships which characterize the price transmission
process between market levels.
The speed and extent with which price changes are passed to adja¬
cent market levels may not be equivalent for price increases or
decreases. Thus, the market may be characterized by asymmetry in price
transmission. At the retail/wholesale interface, this asymmetry may be
a function of (1) the cost of changing prices on current inventories,
(2) the need to move certain product types quickly, or (3) simply the
reluctance of retailers to relinquish a price peak once it is estab¬
lished. In addition, the desire to maintain most efficient use of
capacity may result in retail price rigidity as wholesale prices vary.
At the wholesale/producer interface, this asymmetry may not be as evi¬
dent since atomistic producers are hypothesized to be price takers.
However, if there exists monopsonistic pricing tendencies at the whole¬
sale/producer level, wholesale price increases may not be passed to
producers as strongly as price decreases.

CHAPTER III
EMPIRICAL METHODS
The study of price dynamics in a vertical market setting necessi¬
tates the investigation of the dynamic properties of price over time.
This entails, first, the identification of the stochastic properties of
the price series of concern in a 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.
50

51
Time Series Analysis
The objective of the time series analysis is to describe the under¬
lying stochastic process that produces the original price series. These
results can then be used to test hypotheses regarding the series of
interest or forecast future values. A distinction regarding the result¬
ing model is that the parameters determined are referred to in the
literature as being "mechanically" derived, often considered devoid of
theoretical economic content (Zellner, 1979). However, recent studies
have supported the contention that time series models, in fact, are
consistent with structural economic models (Anderson et al., 1983). In
addition, the dynamic adjustment properties of price series data as
revealed by time series analysis will allow testing of hypotheses orig¬
inally motivated by the theory.
There exists two principal time series approaches: time domain
(time series) analysis and frequency domain (spectral) analysis. The
two are theoretically equivalent (Granger and Newbold, 1977). As Ngenge
(1982) states, a result in one domain always has its equivalent result
in the other domain. The spectral approach is particularly useful if
the price series is suspected of being characterized by significant
periodicity and if the nature of these periodic components are unknown.
Price data for shrimp in the U.S. have empirically been found to not
contain an identifiable cyclical component (Thompson and Roberts, 1983).
Rather, periodicity is restricted to seasonal influences. Thus, the
spectral approach would be inappropriate. This study primarily uses the
more appropriate 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).

52
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 (x^,...,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(x^,...,xt) that assigns probabili¬
ties to the possible combinations of normally distributed x^, i=*l,...,t.
Unfortunately, except for very small t, the probability functions of the
outcomes (xj,...,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
9x(U
Y„a>

53
where L is the number of lags, 0_(L) is the autocorrelation, Y-(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
Vl> â–  C0V(ltf W - Et(*t - E
where t * 0,1,2,...T. The variance is given as
Yx(0) - COV(xt, xt+0) - COV(xt, xt) =* VAR(xt)
Thus, 0x(L) is defined as the autocorrelation at lag L.
The very strict assumption of stationarity of a time series implies
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 < 0X(L) < 1 for L > 0. In addition,
a time series characterized by
10, where L * 0
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 differenced one or more times
to obtain stationarity. The number of differences taken, d, is known as
the order of homogeneity. A differenced series wt ig g¿ven aa

54
* (i-e)dxt
where 3 represents the difference operator where 3wt = wt-l* ^ random
walk process given as
â–  xt-i + 5
is homogenous of order one (first differenced). In fact, Xj. 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¬
cess of order p such that xt is expressed as a weighted average of past
observations lagged p periods with a random disturbance on the end
P
*t " Ei ^t-i + R + t “ 0,I,2,...,T
where <(> is the weight on each lagged xt, is the random disturbance, p
is some maximum lag, and R is a constant term associated with the series
mean and drift (R>0 when drift is present). Assuming R=0, this may also
be written in backshift notation as
(1 - ♦jB - ... - *(B)xt - Ct
where p in lag operator B. The left-hand factor ( 8) acts as a filter on the
time series x resulting in a white noise process Pindyck and Rubin-
feld (1981) state that a necessary condition that x is stationary
requires that the autoregressive process of order p be characterized by

55
P
2 ♦. < 1
i-1 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 9X(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 x^. is a weighted average of random disturbances lagged back q
periods. This series xt can be denoted as
xt * .Yj 5t-j+ s
where is the weight on each lagged disturbance , q is the maximum
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
Z 6? < -
i-1
However, this is only a necessary condition. Rewriting xt in backshift
notation and letting S=0 yields
’ WB)5t

56
The invertibility condition requires that
3_1(B)xt -
where 8”*(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=l) 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
0x(L) -
-8. + 8, 8T ., + ... B T 8
ii 1 L+l q-L q
1 3 2
1 2 q
, L
1,
»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 $(8) and 8(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

57
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 d q
I K(l-B) x - R + 18.5. .
i-0 1 1 j=o 1
%
For d®0, this can be expressed as
Xt ’ *lVl ‘ Vt-2 ' — ' Vt-p " E + 5t ' \\-l ' \ Vl ' — ' 6,S<^
In backshift notation, this is written as
(l - - «^B2 - ... - xBP)xt - R + (l - BjB - B2B2 - ... - BqBq)Ct
Finally, the above expressions, in differenced form, appear as
<(.(B) xt = R + 8(BKt
where 4>(B) and 3(B) are converging invertible polynomials in the lag
operator B. Since xfc has been differenced (is now homogeneous station¬
ary), the process can be modeled using an AR of order p and an MA of
order q. Thus, is an integrated (I) ARMA, or an ARIMA (p,d,q) pro¬
cess.
Identification and Estimation of an ARIMA Model
The discussion above has shown that a homogenous nonstationary time
series can be described as an ARIMA process of order p, d, and q.
However, the correct specification of an ARIMA process necessitates
selecting the proper values of p, d, and q to accurately describe the
underlying stochastic process that generated the original time series.
This task is accomplished by examining the autocorrelation function and
partial autocorrelation function of the time series.

58
Identification of an ARIMA model begins with determining the degree
of homogeneity in the time series. If the autocorrelative function
9X(L) of the original data does not dampen quickly to zero, the data
must be differenced d times until a stationary series results. This
decision is made by visually observing 9X(L) after each differencing to
see if 9X(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 9X(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 ~
9 (L) - Z 9 9 (L - i), L - l,...,j,
x 1*1 J1 x
which are known as the Yule-Walker equations (Pindyck and Rubinfeld,
1981). The partial autocorrelation of order 3 (»jj) for an AR(p) is
zero for j>l. 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.

59
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
5t - 4>CB) 8“1CB)xfc
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
. ¡ 5t-k
r, =*
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 (Box and Pierce,
1970) given as
Q »
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.

60
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 R^ 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 misspecification 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 Xfc 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 X^. or causes Yt
when using past information on Xt and Yt
(2) Bi-directional feedback — Yt causes Xt and Xfc causes Y^,
(3) Instantaneous causality — Yt causes Xt where
current X is better predicted by including current Y, or

61
Xj. 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 Xfc and Y^ 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 X^ and Yt involves the estimation via
ordinary least squares of a four-equation regression model given as
A.l
n
1
j-1 i-1
A.2 X - E a X + u
t ¡ml j *-) t
B'1 Tt" + + vt
n
E
i-1
2
B-2 - ¿V-i * 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.l and A.2 to see if the c^ are different from zero. The F statistic
with q and T-t degrees of freedom is defined as

62
(ESS - ESS )/(q)
F =, r u
q,T-t (ESSu)/(T-t)
where t is the number of parameters estimated in the unrestricted 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.l and A.2 is significant then
the null hypothesis is rejected, suggesting that Y causes X. A test of
the d^ 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.l and B.l 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(utug) = E(vtvs) â–  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.
Sims 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
2 Vt-3 + •*
X - ib.Y + e
c J-0 J C-J *
In this case,
a test
of the hypothesis that X does not cause Y is

63
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 (-1>j >-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 =» ^
F(B) Yfc - 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)
uv
E(at-k-vt>
[E(ut)2E(»t)2 ]1/2

64
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-*/2, where T is the total number
of observations. Each r¿A(k) can be individually tested for signi¬
ficance where
r AA(k) > 2T”1/2
uv
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) ruy(k) * 0 for some k>0 implies X causes Y,
(2) ruv(k) * 0 for some k<0 implies Y causes X,
(3) ruv(0) * 0 implies instantaneous causality,
(4) ruv(k) * 0 for some kX) and some k<0 implies feedback,
(5) ruv(k) “ 0 for all k<0 implies Y does not cause X,
(6) ruv(k) » 0 for some kX) and ruv(k) - 0 for all k<0 implies
unidirectional causality from X to Y,
(7) ruv(k) * 0 for and ruv(k) * 0 implies X and Y are
related only instantaneously, and
(8) ruv(k) = 0 for all k implies X and Y are independent.
This study adopts the definitions of instantaneous and unidirec¬
tional causality and feedback as shown above. These notions of causal
inference from residual cross correlations have been utilized by several
recent studies (Bessler and Schrader, 1980a; Bessler and Schrader,
1980b; Miller, 1980; Shonkwiler and Spreen, 1982; Spreen and Shonkwiler,

65
1981). Haugh and Pierce suggest that the absence of unidirectional
causality from X to Y can be tested using
m
T Z [
k=l
r
uv
(k)]2 > X2U)
m
where m (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
* J tc]2 < 4+1 (°>
k=-m
The chi-square distributed statistic T E[r^(k)j 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

66
response model which embodies the dynamic nature of the relationship
exhibited by the two time series.
Haugh and Box (1977) outline the dynamic regression procedure as a
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 u^ and vt are obtained which can be
represented by
0(B)Xt = ut

67
where 0(B) and (B) are invertible polynomials in the lag operator B.
The terms ufc and represent the white noise processes (innovations)
obtained from of X and Y, respectively. The polynomials 9(3) and ( S)
may be viewed as filters which are identified and estimated by using the
Box-Jenkins approach. The sample cross correlations between ut and vt
{r^(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. Xfc leads Yt, Haugh and
Box (1977) show that it is possible to express Yt as a distributed lag
on X^. as
Yt - S(B)Xt + at
where 5(B) is some polynomial of Xt and afc is an error process. The
weights on the terms of the polynomial 5(B) are referred to as the
impulse response parameters. These parameters characterize the response
of Yt to changes in the "input" Xfc, net of the "masking effect" of the
stationary white noise process at. To identify the order of the poly¬
nomial 5(B) connecting Yt and X^., 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¿¿(k) f where k is the order of lag,
to arrive at a dynamic shock model given as
v - V(B)u + Y(B)a
t t t

68
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,u8) â–  0, for
every t*s, then each parameter coefficient in V(B) is simply the bivari¬
ate regression coefficient relating vt to u^^ given as
V, - —^ rAA(k)
k a uv
ut
where crv and o are the standard error of the innovation series and k
t t
is the lag of the residual cross correlation.
Dynamic Regression Transfer Function
Given that the parameter coefficients of V(B) have been identified
and the order of the polynomial is known, the original filter expres¬
sions
9(B)Xt - ut
are substituted into the dynamic shock model (Haugh and Box,,1977) to
give
and isolating Yt yields the impulse response or transfer function
Yt - ♦(B)"1V(B)9(B)Xt + 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
Y - S(B)X + X(B)a
t t t

69
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( 8), the parameters of 5(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
misspecification.
Once the transfer function relating X and Y has been identified,
the lead/lag structure; e.g., current and/or lagged prices, are included
in a more complete explanatory model of the market. The regression
methods that are employed to estimate the econometric model of prices
are discussed below.
General Regression Methods
The analysis of time series properties, causality tests, and deri¬
vation of the transfer function provides a set of expressions in terms
of endogenous and lagged endogenous variables. These expressions evolve
into a more comprehensive model when they are augmented with additional
exogenous variables whose presence is dictated by theory and knowledge
of the market. This study strives to generate such models describing
price at each of three market levels.

70
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.

71
A system of g expressions in terms of g endogenous and k predeter¬
mined variables can be written in matrix notation for each observation
as
IT + BX = E
t t t
where Y is a gxl vector of endogenous variables, X is a kxl vector of
predetermined variable, T 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"1BXt + r_iEt or
Yt - irXt + V
where ir is a gxk matrix of derived reduced form estimates and V is a gxl
vector of disturbances. The elements of ir, 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 ir 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

72
The reduced form matrix ir can be partitioned into submatrices such
that
Yt - do + + D2Xt + 5t
where Yt is a g*l vector of endogenous variables, Yt_^ is a g*l vector
of endogenous variables lagged one period, Xt is a kxl vector of the
exogenous variables, dg is a vector of constant terms, Dj^ is a g*g
matrix of derived reduced form estimates for the lagged endogenous
variables, D2 is a g>4c matrix of derived reduced form estimates for the
exogenous variables, and is a g*l vector of disturbances. The ele¬
ments in Dj and 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
Repeating this procedure s times yields
However, note that if
lim D® = 0,
S -M»
then
lim E D*
S-H» i**0
- (I-D^-1.
Then by dropping the time subscript, Y can be written as
Y = D + XX + E

73
where D » (I - Dj) *dg
X = (I - D1)"1D2, and
E - (I - Dx j”1 5
A
The elements of D, X, and E are referred to as the final form estimates
of the model.

CHAPTER IV
EMPIRICAL MODELS
Introduction
The theoretical economic model of a system of price dependent
demands for the major market levels in the domestic shrimp marketing
system was developed in Chapter II. The empirical form of the model is
presented in this chapter. Initially, the price dependent demands are
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^; Q¡¡, D)
(31) pw * f2(M2; cr, Qp)
(32) pf - f3(M3; cW, qJ)
(33) pp « f4(M4; cf, QJ)
74

75
where pr, pw, p^, and pp represent prices received by retailers, whole¬
salers, first handlers, and producers, respectively. 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, Qq, Qp,
Qq, and are the quantities offered by retailers, wholesalers, first
handlers, and producers, respectively, and cr, cw, and c^ 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, pw, p^, 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 II is 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

76
Figure 6. Market Channel Schematic Representation for the U.S
Shrimp Market System.

77
represented by equations (30) through (33) could be estimated. Price
data is not available to describe the transaction between the first
handlers and the wholesaler/processor (region B is Figure 6). Thus,
only expressions (30), (31), and (33) are modeled on a monthly and
quarterly basis for two size classes of 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
price.
Symmetric and Asymmetric Models
Price models often hypothesize that increases and decreases in
price at one level are passed on equally to adjacent levels (Helen,
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

78
(1) Rt * % + ai wt + 5t
when Rt is retail price, Wt is wholesale price, and 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) Rfc - + ctj WIt + WDt + 5t, t - 1,...,N
where
“t \l0 (Vi - Vh> DIt-i
mt (Vi - Vi-I* DDt-i
DI
Vi> Vi-1
t-i
{
otherwise
DD
t-i
i. Vi< "t-i-i
0, otherwise
where WIt and WDt represent cumulative wholesale price increases and
decreases, respectively. Thus, testing the significance of and 02 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 - WQ + WIt + WDt (Identity)
where Wq equals for t~0. Substituting for WIt gives

79
R
t " °0 + °1 (Wt " W0 ‘ WDt) + °2 TOt + ?t
which yields
Rt = a* + aj Wt + a* WDt + €t
where « (eg - ajWg) and aJ-Co^-ap. A test of significance of
(c^ “ ap provides a direct test of asymmetry. Recall that measures
the reaction of Rt when increases and measures the reaction of R^.
when Wt decreases. The significance of can be measured via the
estimate by writing
°2 " °2
*
- a.
+ a,
°2 " “2 T "I
£ A A
and varCo^) » var(a2 + up “ var(ap + var(c^) + 2 CovCuj, c^).
The t-statistic would then be written as
(«2 + ~°
/VAR (u2)
a2 + °1
Var + Var a2 + 2 Cov (a^, ap
wherec^ is the estimate of c^. If in the event that is found to be
insignificant, the test of significance on the coefficient aj reverts to
a symmetric test of retail price response to increases or decreases in
wholesale price. Expressions for pr, pw, and pP can now be written in
explicit form.
Data
The estimation of time series properties and analysis of causal
relationships of prices for shell-on, fresh-frozen, raw-headless shrimp
(hence forth referred to simply as raw-headless) at retail, wholesale,

80
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

81
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 (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 found in each model and discusses the variables
which are given to be predetermined. A discussion of the final

82
specification of each model is given in Appendix B. Excluding
consideration of the prices found in 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
NR
Rt - c£ + E [Mj] + aj RDYt + a* TCFF^. + a* CPIt + ^
where Rt * retail (non-institutional) price in time period t (Shellfish
Market Review, NMFS)
m 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 â–  consumer price index for meat and poultry products, deseason-
alized with 1972 - 100 (CPI Detailed Report, Bureau of Labor
Statistics),
NR » number of current and lagged endogenous and exogenous prices
found in m£ for each size class model, where i refers to size
class,
and o£ and g£ are the coefficients to be estimated, with the superscript
r referring to the retail model. Each is associated with a current

83
r R R
or lagged exogenous or endogenous price contained in M^. M3 and M2
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 and 03 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, oJj is anticipated to have a negative sign.
The presence of 8£ 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 8? are anticipated to be positive, reflecting a direct positive
relationship between contemporaneous and lagged price movements at the
wholesale and retail level.

84
The specification of the model is the same for monthly or quarterly
data. The prices found in m£ 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 m£,
RDYt, and CPIt 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-headles3
shrimp is given as
and for 21-25 count raw-headless shrimp is given as
. NW ,
=■ b" + Z 8" [Mp + b” BSFFt + b" 0l£ + b" I21t + bj TMCI^. + C2
i-1 4
where
WJ? - wholesale price for 31-40 size class (Shellfish Market
Review. NMFS),
* 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),

85
Olj? â–  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,
0l£ * 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,
13lt = imports of raw-headless shrimp of 31-40 size class at
selected ports of entry in millions of pounds (NMFS unpub¬
lished files),
12lt - 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 M^ for each size class model, where i refers to size
class,
and o£, 6^, b¿, and 0^ are the coefficients to be estimated. Each 6^
and 0* is associated with a current or lagged endogenous or exogenous
price contained in MÍj and M?[, 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

86
spread (costs incurred by the retailers). The quantity variable Qq
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^, a£, a^, b^, bíj, and b^ are anticipated to be
negative in sign. The parameter 0It and I31t for the 31-40 size class
model and 0It and I21t 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 a£ and b£ are anticipated to be negative in sign.
Depending on whether the price determination process is character¬
ized by upward causality, downward causality, or simultaneity, the 3^'s
and d^'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 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 TMCIj. and for all prices found in the

87
*\ r\
corresponding M^. The parameters 01^, 0l£, I31t, and I21t 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
and for 21-25 count raw-headless shrimp is given as
P ®
b + E
U i-1
[M^J + b^OL^ + b^ L21t + b* TMCI^ + ^
where
pj? * ex-vessel price for the 31-40 size class (Shellfish Market
Review, NMFS),
2
Pt - ex-vessel price for the 21-25 size class (Shellfish Market
Review, NMFS),
O
0L£ - total domestic landings for all sizes of shrimp excluding the
31-40 size class landings in millions of pounds (Shellfish
Market Review, NMFS),
o
0L£ * 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
files),

88
L21fc - landings of shrimp in the 21-25 size class in the Gulf and
South Atlantic in millions of pounds (NMFS unpublished
files),
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 M? for each size class model, where i refers to size
class,
P P P P P
and o^, 6^, b^, and 8^ are the coefficients to be estimated. Each 6^
and 8^ is associated with a current or lagged endogenous or exogenous
P P
price contained in M3 and M2, 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 Qq 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, 0Lt and L31t for the 31-40 size class and 0Lt and L21t for

89
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 ot^, a|, bp, bp are expected to have a negative sign.
The parameter TMCIt 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 TMCIr. Thus, the coefficients bp and OgP are
hypothesized to be negative in sign.
The prices which are found in each 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 and 8^ 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

90
quarterly data have been redefined such that TMCIt and the prices which
may appear in each represent simple three-month averages of the
monthly data. The parameters OL^, OL^, L31t, and L21t represent three-
month totals of the monthly data.
Margin Models
Estimation of the monthly and quarterly price dependent demand
models provides a set of structural coefficients for each model. These
estimated coefficients can be utilized to derive a system of expressions
describing the price spreads (margins) between adjacent market levels
for each size class. Exact specification of these margin models is
conditional on the lead/lag structures identified by the causality
analysis. The interpretation of the derived estimates for prices in the
margin models strictly depends on the nature of price determination and
the identification of the causal market level(s). Non-price parameter
estimates in the margin models will vary in sign depending on which
prices are identified as exogenous or endogenous in the structural
models. In addition, the derivation of the margin estimates is condi¬
tional on whether structural, reduced form, or final form estimates are
utilized. A brief discussion of margins follows derived from structural
and reduced or final form estimates.
Structural Margins
This discussion of margin models assumes symmetric price response,
no price lags, and recursive price determination arbitrarily stated to
be upward between wholesale and retail prices. Given these conditions,
the margin between wholesale and retail price can be written simply as

91
Mt " ° + 0t Wt
and by definition
M = R - W
t t t
where Mt, Rr> and Wt, are margin, retail price, and wholesale price at
time t, respectively. Since wholesale price is the causal price, retail
price can be written in structural form as
=» a + bW^
Then by substitution
* a + bWfc -
M - a + 0Wt
where a = a and 8 « b-1. The terms a and 8 are the absolute and per¬
centage components of the margin, respectively (George and King, 1971).
If the retail price is assumed to be the causal price, then wholesale
price can be written in structural form as
Wt â–  a + bRj.
Then by substitution
Mt - Rt - (a + bRfc)
Mt =â–  a + 8 Rt
where a = -a and 8 = 1 - b. Thus, the interpretation of the absolute
component (a) and the percentage component of price (8) depend on the
direction of price determination between the adjacent market levels.
These margin expressions are in terms of price. The structural
price models to be estimated also contain non-price parameters.

92
Depending on the direction of price determination as revealed in the
causality analysis, the coefficient estimates associated with these non¬
price parameters may vary in sign but possess the same absolute value
relative to the structural coefficient estimate. For a non-price
coefficient b^ in either the retail or wholesale structural model, a
recursive upward price causality relationship between adjacent retail
and wholesale market levels produces a corresponding coefficient in the
margin model with the same sign and absolute value as b^ found in the
retail model. Alternatively, for a coefficient b^ in either the retail
or wholesale structural model, a recursive downward price causality
relationship between adjacent market levels produces a corresponding
coefficient in the margin model with the same sign and absolute value as
b^ found in the retail model. Alternatively, for a coefficient b^ in
either the retail or wholesale structural model, a recursive downward
price causality relationship between adjacent market levels produces a
corresponding coefficient in the margin model with the opposite sign and
same absolute value as b^ as found in the wholesale model. Given this
method of derivation, the margins obtained from recursive structural
estimates allow inferences to be made about the effects on the margin
due to changes in exogenous variables from only one side of the
margin. This is due to the margin being expressed in terms of only the
causal price.
Reduced and Final Form Margins
Margin models can be derived from the reduced or final form coeffi¬
cient estimates of the structural price models. If the structural
models are recursive or simultaneous and do not contain lagged prices,

93
margin models are derived from the reduced form estimates. In the
presence of lagged endogenous prices, final form estimates are utilized
to obtain the margin models. In any case, the reduced or final form
margin expressions are not functions of current endogenous price para¬
meters. Only exogenous non-price parameters will appear in the reduced
or final form margin expressions (lagged prices may appear in the
reduced forms). Thus, the procedure for obtaining structural margin
models Is not applicable for the reduced and final form margin models.
Given that the retail/wholesale price spread is defined as mEw -
Rt ” Wt anc* t*ie wh°lesale/ex'"ve88el pric® spread is defined as Wt -
Pt, a structural margin allows for change In exogenous variables
through a single price—the causal price. Alternatively, the reduced or
final form margin model allows for change In exogenous variables through
both prices. The coefficients in the reduced or final form margins
models are simply the difference between the respective parameter esti¬
mates in the reduced or final forms for retail, wholesale, or ex-vessel
price, which are expressed in terms of the same set of exogenous vari¬
ables. Therefore, the sign and absolute value of the coefficient esti¬
mates in the reduced or final form margin model depend on the relative
magnitude of the respective reduced or final form coefficient estimates.
Thus, there are two forms of margin expressions - margins obtained
from structural estimates and margins obtained from reduced or final
form estimates. The structural margins allow inferences to be made
regarding change in non-price variables from only one side of the mar¬
gin, whereas, the reduced and final form margins examine changes from
both sides of the margin

CHAPTER V
EMPIRICAL RESULTS—CAUSALITY ANALYSIS
The causal relationships between prices at three market levels were
investigated using Haugh-Pierce, Granger, and Sims techniques for two
size classes of shrimp. The Haugh-Pierce test was employed to test
hypotheses regarding unidirectional and instantaneous causality, whereas
the Granger and Sims tests were utilized to test hypotheses regarding
strictly unidirectional causality. Monthly and quarterly time series
data over the years 1968-1981 and 1972-1981, respectively, were exam¬
ined. The findings are presented by estimation procedure utilized for
the 31-40 and 21-25 size classes on a monthly and quarterly basis. The
results are summarized to highlight contrasts and similarities between
the two size classes.
Monthly Price Data
Haugh-Pierce Test
The Haugh-Pierce procedure provides a means by which the data can
suggest the lead/lag relationship that exists between the two series of
data. This is accomplished by analyzing the cross correlations between
current and lagged observations in white noise residual series to detect
instantaneous and unidirectional causality under the null hypothesis
that the series are independent. Further, the Haugh-Pierce procedure
provides the necessary information to construct dynamic shock models and
impulse response functions that allow explicit specification of a
94

95
distributed lag model that relates the two price series once the causal
relationship has been identified. This specification ability is not
provided by the Granger or Sims approach and is necessary to specify a
complete econometric model of price dependent demands.
The Haugh-Pierce procedure requires that each price series for both
size classes be reduced to a white noise process. The estimated time
series ARIMA filter models that were necessary to transform the price
series for the 31-40 size class into approximately white noise processes
were found to be
(1—B)(l -.390B + ,135B3)E - e. , B-P x?o“17.44 and a -.149
(.072) (.073) C C L e
(1-B)(1 - .466B + .093B2)W. - w. , B-P xío^20*88 and a -.129
(.078) (.079) C
(1—B)(1 - .352B - .276B8 + .235B9)R - r , B-P x?s=-20.69 and a -.199
(.075) (.069) (.079) r
where Et, Wt, and Rt are ex-vessel, wholesale, and retail price, respec¬
tively, et, wt, and rt are the corresponding white noise residuals, B-P
refers to the Box-Pierce chi-square statistic, a is the standard devia¬
tion associated with each white noise residual series, and the values in
parentheses are standard errors of the estimates. The ARIMA models that
were necessary to transform the price series for the 21-25 size class
into approximately white noise processes were found to be
(1—B)(1 - .239B + .098B3 + .115B5)E_ - e_ , B-P x,^1^.21 and a -.205
(.076) (.080) (.089) * C 17
(1—B)(1 - .281B + .113B3)W - w , B-P x?Q~14-40 and 0 "*217
(.076) (.077) C I8
(1—B)(1 - .1944B)R = r , B-P x?-,=9.98 and a -.215
(.077) C C 17 r

96
where the terms are defined as for the models pertaining to the 31-40
size class. The calculated Box-Pierce statistics for both size classes
support the hypotheses that the residual series are white noise at the
.05 level. The above filter models are integrated (homogeneous degree
one) autoregressive with no moving average component. The Sims “univer¬
sal filter" given as (1-.75B)^ (Bishop, 1979) was applied to each series
but did not transform the series into white noise. A lag of twelve
periods was used on all tests at the monthly level. Empirical research
on price movement in the shrimp market has not shown statistically
significant periodicity other than seasonal fluctuations (Thompson and
Roberts, 1982). Therefore, a full year was assumed sufficient to cap¬
ture all pertinent price responses. The number of observations used for
each causality test differed slightly due to the lag structure of the
ARIMA models used to filter the corresponding price series.
The 31-40 size class
The Haugh-Pierce tests for causality between the residual series of
ex-vessel and wholesale prices indicated that unidirectional causality
exists such that ex-vessel price causes (leads) wholesale price (Test I
in Table 1). The Haugh-Pierce statistic relevant to the null hypothesis
that ex-vessel does not cause wholesale price was larger than the tabu¬
lated critical chi-square value at 12 degrees of freedom and, thus, the
null hypothesis Is rejected at the .05 percent level. However, the null
hypothesis that wholesale does not cause ex-vessel price was not
rejected. Thus, unidirectional causality exists such that ex-vessel
causes wholesale price. A lag of one period was significant. The
current cross correlations were significant for both lead/lag alterna¬
tives in Test I, indicating instantaneous causality exists such that
current ex-vessel causes current wholesale prices, and vice versa.

97
Table 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.
Series 1 â–  Prewhitened Ex-vessel Prices
Series 2 = Prewhitened Wholesale Prices
Series 3 = Prewhitened Retail Prices
TEST I
(N =* 162)‘
TEST II
(N = 158)
a
Lag (k) in
Causal
Series j
Cross Correlations {r^Ck)}
(a) r2,1(k> rl,2^k^
Cross Correlations {r^(
A A
(a) r3j2(k) (b) r2ji
0
.752*
.753*
.186*
.186*
1
.291*
-.051
.360*
.087
2
-.080
-.100
.092
-.005
3
.068
.058
.011
.011
4
-.026
.054
.175*
.045
5
-.036
-.015
-.028
-.051
6
-.076
-.003
.074
.155
7
.063
.043
-.072
-.026
8
.005
.050
.001
-.092
9
.045
.079
.091
-.043
10 .
.051
-.075
-.038
.005
11
-.115
-.048
-.015
-.089
12
-.057
-.027
.049
.050
TEST Is
(a) Null Hypothesis: ex-vessel does not cause wholesale price%
H-P xi2 " 21.16**
(b) Null Hypothesis: wholesale does not cause ex-vessel price,
H-P xf2 " 6.40***
TEST II:
(a) Null Hypothesis: wholesale does not cause retail price,
H-P x?2 “ 30.18**
(b) Null Hypothesis: retail does not cause wholesale price,
H-P xi2 â–  9.32***
®N is the effective number of observations for cross correlation.
*Greater than two standard errors (s), where s ■ N“^^.
**Reject null hypothesis at the .05 level.
***Fail to reject null hypothesis at the .10 level.

98
The tests for causality between the price series at wholesale and
retail market levels indicated that wholesale price leads retail (Test
11 in Table 1). Significant lags exist at one, four, and nine periods.
The insignificant current cross correlations indicated that no instan¬
taneous causality exists between retail and wholesale prices.
The 21-25 size class
The Haugh-Pierce test was applied to ex-vessel and wholesale prices
for 21-25 count price data (Test I in Table 2). The null hypothesis
that wholesale does not cause ex-vessel price was not rejected. The
null hypothesis that ex-vessel does not cause wholesale price was also
not rejected at the .05 level. Thus, unidirectional causality was found
not to exist between ex-vessel and wholesale prices when lags of up to
12 periods were examined. A lag of one period was significant. How¬
ever, the significant current cross correlation relative to both tests
suggested instantaneous causality exists such that ex-vessel and whole¬
sale price are instantaneously related only.
The test for causal direction between wholesale and retail price
series indicated that unidirectional causality exists only such that
wholesale causes retail price at the .05 level (Test II in Table 2).
Lags of one and two periods were significant. The insignificant current
cross correlation suggested that no instantaneous causality exists
between wholesale and retail price series.
Impulse response functions for both size classes
The residual cross correlations generated by the Haugh-Pierce test
provide necessary information to be used in the specification of the
exact nature of the lead/lag relationships suggested by the causality

99
Table 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.
Series 1 - Prewhitened Ex-vessel Prices
Series 2 = Prewhitened Wholesale Prices
Series 3 = Prewhitened Retail Prices
TEST I
(N =* 162)a
TEST II
(N =* 166)a
Lag (k) in
Causal
Series j
Cross Correlations (r^Ck)}
(a) r2}1(k) (b) r1>2(k)
Cross Correlations {r^
(a) r3>2(k) (b) r2>
0
.836*
.836*
.100
.100
1
.167*
-.037
.227*
.130
2
.005
.041
.389*
.059
3
-.010
-.063
.129
.061
4
.033
.020
.017
.014
5
-.026
.012
.022
-.080
6
-.027
-.044
.106
-.027
7
-.065
.087
.090
-.073
8
.017
-.064
-.027
-.078
9
-.038
-.012
.004
-.143
10
.100
.101
.040
-.081
11
-.069
-.141
.114
-.074
12
-.182*
-.128
.081
-.064
TEST I:
(a) Null Hypothesis: ex-vessel does not cause wholesale price,
H-P xf2 - 13.61***
(b) Null Hypothesis: wholesale does not cause ex-vessel price,
H-P Xi2 ” &.40***
TEST II:
(a) Null Hypothesis: wholesale does not cause retail price,
H-P X|2 " 44.02**
(b) Null Hypothesis: retail does not cause wholesale price,
H-P X12 * 13.10***
aN is the effective number of observations for cross correlation.
♦Greater than two standard errors (s), where s = N-1^.
♦♦Reject null hypothesis at the .05 level.
***Fail to reject null hypothesis at the .10 level.

100
test. The cross correlations are utilized in constructing the impulse
response functions or distributed lag expressions which are the neces¬
sary next step in operationalizing the causality results. These distri¬
buted lag expressions are utilized in the final specification of the
econometric model of prices. For the sake of simplicity and expediency,
the following discussion will center on only two price series for the
31-40 size class.
The Haugh-Pierce causality tests produced a set of residual cross
correlations between ex-vessel and wholesale 31-40 price series (Test I
in Table 1). The significance patterns in the estimated residual cross
correlations and the indicated causal direction suggested a dynamic
shock model written in backshift notation as
wt * (Ag - l1B)et + (1 - (fr^a,.
where Ag and Aj are impulse response weights at zero and one lags, et
and wt are the white noise residuals for the prewhitened ex-vessel and
wholesale price series, respectively, and at is some white noise process
written in first-order polynomial form in terms of $. The parameter
estimates of Aq and A^ are given as
A
\> =
a
c —
^ a
.129
.149
(.752) - .651
e
A
X1 "
a
( —
a
)r2,l^
.129
.149
(.291) - .252
The dynamic shock model can then be rewritten as
wt - (.651 - ,252B)et + (1 - «f^Bja,.
The ARIMA filter models for ex-vessel and wholesale price series are

101
(1-B)(1 - .390B + .135B3)Et - et
(1—B)(l - .466B + .093B2)Wt - wt
where Efc and are ex-vessel and wholesale price, respectively. Sub¬
stituting the above ARIMA expressions for et and wt into the dynamic
shock model yields the expression
(1-B)(1 - .466B + .093B2)Wfc = (.651 - .252B)(1-B)(1 - .390B
+ ,135B3)Et + (1 - B)at
which is the impulse response function. By carrying out the indicated
multiplication and division, the above expression reduces to
Wt - (.651 - .203B - .058B2 + .078B3 + .006B4 - .006B5 - .015B6
- .013B7 - .002B8 - .001B9 - .00lB10)Et + 9(B)at
where 9(B) is some polynomial on the error term a^. By dropping all
terms that are small relative to the leading parameters (less than .1),
Wt can be expressed in a more parsimonious form as
Wt * (.651 - .203B)Et + 9(B)at
Thus, the Haugh-Pierce causality results and the impulse response func¬
tion derivation suggested that current wholesale price be expressed as
some function of current ex-vessel price and ex-vessel price lagged one
period. Therefore, the final specification of the price dependent
demand expression at the wholesale level for 31-40 size class raw-
headless shrimp contains current ex-vessel price of 31-40 size product
and ex-vessel price lagged one period. The derivation of the monthly
impulse response functions for the 31-40 size class retail/wholesale and
21-25 size class retail/wholesale market level interfaces are presented

102
in Appendix A. The final parsimonious forms, however, are given for the
31-40 size class as
(i) - (.246 - .504B - .204B4)Wt + 01(B)vt
and for the 21-25 size class as
(ii) Rj. - (.099 - .235B - .371B2)Wt + 02(B)ut
where Rt and Wt are retail and wholesale price, respectively, 0^(B) and
02(B) are polynomials on the error terms vfc and u^, respectively.
The Granger Test
The Granger procedure allows the testing for the presence of uni¬
directional causality utilizing stationary time series data. The anal¬
ysis provides insight into the lag relationships linking prices between
adjacent market levels. The following analysis utilized first differ¬
enced and ARIMA filtered price series representing each size class at
the ex-vessel/wholesale and wholesale/retail market level interfaces.
Lags of twelve months were also used for the Granger tests.
The 31-40 size class
The Granger test for causality was applied to the prices for the
31-40 size class. The prices were first differenced (pt-pt_^) to trans¬
form them to an approximate stationary series. Unidirectional causality
was found to exist such that ex-vessel causes wholesale price (Table
3). In addition, the null hypothesis of no unidirectional causality
from wholesale to ex-vessel price was not rejected. These findings
indicated the ex-vessel price was causing wholesale price. Note that
the Box-Pierce statistic for each first differenced series was greater
2
than the critical x value, indicating that the first differenced data

103
Table 3: Granger Causality Tests on Monthly Ex-vessel, Wholesale, and
Retail Prices for the 31-40 Size Class Using First Differenced
Data.3
A. NULL HYPOTHESIS: wholesale does not cause ex-vessel price
0 Unidirectional Test: F^2 ¡21 = 1»52**
B. NULL HYPOTHESIS: ex-vessel does not cause wholesale price
0 Unidirectional Test: F^2 ¡21 * 3.73*
C. NULL HYPOTHESIS: retail does not cause wholesale price
° Unidirectional Test: F12 ¡30 " 1.22**
D. NULL HYPOTHESIS: wholesale does not cause retail price
0 Unidirectional Test: F¡2 ¡30 = 4.12*
aFirst differenced data for ex-vessel, wholesale, and retail prices have
residual Box-Pierce statistics of 53.29, 69.75, and 50.43,
respectively. These should be compared to a tabulated critical chi-
square value at 20 degrees of freedom of 31.14 at the .05 level.
♦Reject null hypothesis at the .01 level.
**Fail to reject null hypothesis at the .10 level.

104
Is not white noise at the .05 percent level. Thus, due to the presence
of serial dependence, the possibility of spurious results exists.
The Granger test was repeated for data transformed by an appro¬
priate ARIMA filter (Appendix C). The ARIMA filter models necessary to
transform the two series into approximately white noise residuals were
the same as those used in the Haugh-Pierce tests. The resulting Box-
Pierce statistics indicated that the residuals for filtered ex-vessel
and wholesale data, et and wt, respectively, are white noise at the .05
level. Unidirectional causality was again found to exist only such that
ex-vessel causes wholesale price. Thus for the ex-vessel/wholesale test
the results using first differenced data are identical to the results
using data filtered by an ARIMA model. However, the latter approach
reduces the chances of spurious regression.
The same tests were applied to the wholesale and retail price
series (Table 3). First differencing did not transform the price series
into white noise. However, the use of the ARIMA filters utilized in the
Haugh-Pierce test did transform the price series into white noise pro¬
cesses. The results were invariant relative to first differencing
(Table 3) or filtering by an ARIMA model (Appendix B). In both cases
the tests supported the null hypotheses that retail does not cause
wholesale price in a unidirectional sense and rejects the null hypo¬
theses that wholesale does not cause retail price. Thus, it appears
there was significant unidirectional causality between wholesale and
retail market levels such that wholesale causes retail price. In this
case, retail prices would be most appropriately specified as some func¬
tion of lagged wholesale price.

105
The 21-25 size class
The results of the Granger test for causality between ex-vessel and
wholesale monthly prices using first differenced data for 21-25 size
class are presented in Table 4. Two null hypotheses tested are that
wholesale price does not cause ex-vessel price and ex-vessel price does
not cause wholesale price. Each null hypothesis was tested for the
absence of unidirectional causality. The test finds no evidence of
unidirectional causality from wholesale to ex-vessel price. Thus,
expressing ex-vessel price as some function of lagged wholesale price
was not supported. Note, however, that first differencing did not
transform the wholesale series into a white noise process. The second
null hypothesis, however, was rejected at the .01 level for unidirec¬
tional causality such that ex-vessel causes wholesale price. Thus, the
causal relationship between the two series was such that wholesale price
should be specified as some function of lagged ex-vessel price.
Since first differencing did not transform the wholesale price
series into a white noise process, the test was repeated using ex-vessel
and wholesale price data filtered by an appropriate ARIMA model (Appen¬
dix C). The ARIMA models utilized to transform the ex-vessel and whole¬
sale price series into white noise were the same as those discussed for
the Haugh-Pierce test. Box-Pierce statistics indicate that the resi¬
duals for ex-vessel and wholesale data, et and wt, respectively, are
white noise at the .05 level. The results using the filtered data,
however, were invariant to the results using first differenced data.
The Granger test was also used to analyze the causal relationship
between wholesale and retail prices. The test was applied to first
differenced data (Table 3) and data filtered by appropriate ARIMA models

106
Table 4: Granger Causality Tests on Monthly Ex-vessel, Wholesale, and
Retail Prices for the 21-25 Size Class Using First Differenced
Data.3
A. NULL HYPOTHESIS: wholesale does not cause ex-vessel price
° Unidirectional Test: 130 = 1.04**
B. NULL HYPOTHESIS: ex-vessel does not cause wholesale price
0 Unidirectional Test: F^ 130 = 2.86*
C. NULL HYPOTHESIS: retail does not cause wholesale price
0 Unidirectional Test: F^£ 130 = 1»30**
D. NULL HYPOTHESIS: wholesale does not cause retail price
0 Unidirectional Test: F^ 130 * 3.38**
aFirst differenced data for ex-vessel, wholesale, and retail prices have
residual Box-Pierce statistics of 30.47, 32.64, and 21.09,
respectively. These should be compared to a tabulated critical chi-
square value at 20 degrees of freedom of 31.14 at the .05 level.
♦Reject null hypothesis at the .01 level.
**Fail to reject null hypothesis at the .10 level.

107
(Appendix C). The ARIMA filter that was utilized to transform the
retail price series into a white noise was the same as that used in the
Haugh-Pierce test. The Box-Pierce statistic for both first-differenced
and ARIMA filtered retail data indicates that the residuals are white
noise. The tests for unidirectional causality for both the first dif¬
ferenced and filtered data indicated that the null hypothesis suggesting
retail does not cause wholesale price was not rejected. However, the
null hypothesis that wholesale does not cause retail price was rejected
at the .01 level. These findings suggest that retail price be expressed
as some function of lagged wholesale price. As with the ex-vessel and
wholesale market levels, the results were invariant with respect to the
filtering procedure.
Sims Test
The Sims procedure offers a second alternative test for unidirec¬
tional causality between adjacent market levels. Additionally, the Sims
procedure requires the use of data that has been transformed to a white
noise process. The same ARIMA filter models that were utilized for the
Haugh-Pierce procedure are utilized for the Sims test. Recall that the
filters did an adequate job of transforming all of the original series
into white noise processes based on the Box-Pierce statistics. The Sims
test also utilized twelve lags.
The 31-40 size class
The Sims causality test indicated that the unidirectional causality
exists such that ex-vessel causes wholesale price and wholesale causes
retail price (Table 5). The null hypotheses of no causality in the
opposite direction were not rejected at the .10 level. This finding

Table 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.
31-40 Size Class
21-25 Size Class
A.NULL HYPOTHESIS: wholesale does not cause
ex-vessel price
A.NULL HYPOTHESIS: wholesale does not cause
ex-vessel price
° Unidirectional Test: jq9 ** 0.79**
° Unidirectional Test: F^ H3 * 2.47*
B.NULL HYPOTHESIS: ex-vessel does not cause
wholesale price
B.NULL HYPOTHESIS: ex-vessel does not cause
wholesale price
° Unidirectional Test: Fu 1Q9 “ 3.03*
° Unidirectional Test: F^ 113 “ 4.05*
C.NULL HYPOTHESIS: retail does not cause
wholesale price
C.NULL HYPOTHESIS: retail does not cause
wholesale price
0 Unidirectional Test: Fjj =* 0.86**
0 Unidirectional Test: F^ 113 “ 0.86**
D.NULL HYPOTHESIS: wholesale does not cause
retail price
D.NULL HYPOTHESIS: wholesale does not cause
retail price
0 Unidirectional Test: Fjj ^q9 = 3.78*
0 Unidirectional Test: F^ = 4.73*
♦Reject null hypothesis at the .01 level.
**Fail to reject null hypothesis at the .10 level
108

109
suggested that the causal relationship between ex-vessel and wholesale
prices is recursive upward. Thus, wholesale prices should be expressed
as some lagged function of ex-vessel prices. Similarly, the causal
relationship between wholesale and retail prices was found to be recur¬
sive upward. Retail prices would be appropriately specified as some
function of lagged wholesale price.
The 21-25 size class
The causal relationship between ex-vessel, wholesale, and retail
price series using the Sims test indicated the presence of feedback
between ex-vessel and wholesale prices (Table 5). The null hypotheses
stating that ex-vessel does not cause wholesale price and wholesale does
not cause ex-vessel price were both rejected at the .01 level. Thus,
feedback is present between ex-vessel and wholesale prices. The null
hypothesis of no unidirectional causality from retail to wholesale price
was not rejected, whereas the null hypothesis of no unidirectional
causality from wholesale to retail price was rejected at the .01 level.
Thus, the causal relationship between wholesale and retail price is
unidirectional such that wholesale causes retail price.
Quarterly Price Data
The Haugh-Pierce, Granger, and Sims tests for causality were also
applied to quarterly data. This analysis was performed to gain insights
into how the process of price determination between the three market
levels evolves as the observational time period is increased from a one-
month to a three-month interval.

110
Haugh-Pierce Test
The Haugh-Pierce test for instantaneous and unidirectional causal¬
ity utilized quarterly data filtered by appropriate ARIMA models. The
ARIMA filter models necessary to transform the original quarterly price
data for the 31-40 size class into approximate white noise processes are
given in terms of the backshift operator B as
(1 —B)(1 - .161B3 + .409B6)E. - e. , B-P xfo-l^OS and cr -.305
(.147) (.155)
(1—B)(1 - . 165B + .344B6)W - w,. , B-P x?q“13.01 and a -.279
(.143) (.150) C w
(1-B)(1 -.417B)R - r. , B-P X?q”13.00 and a-.341
(.125) C
where Et and Wt, and Rfc are ex-vessel, wholesale, and retail prices,
respectively, et, wt, and rt are the corresponding white noise resi¬
duals, B-P refers to the Box-Pierce chi-square statistic, a is the
standard deviation associated with each white noise residual series, and
the values in parentheses are standard errors of the estimates. The
ARIMA filter models necessary to transform the original quarterly price
data for the 21-25 size class into approximate white noise processes are
given in terms of the backshift operator as
(1—B)( 1 - .169B2 + .203B4 + ,425B6)E. - e. , B-P x?7-12.72 and a-.349
(.151) (.161) (.169) C C *
(1-B)(1 + .259B4 + .334B6)W - w , B-P x?s=8.34 and a -.385
(.161) (.166) C C 10 w
(1-B)(1 - .460B + .154B5)R - r.. , B-P X?q=,8.24 and a -.322
(.127) (.130)

Ill
where the terms are defined as for the models pertaining to the 31-40
size class. The calculated Box-Pierce statistics for both size classes
supported the hypothesis that the residual series are white noise pro¬
cesses at the .05 level. The quarterly filter models are integrated
(homogeneous degree one) autoregressive with no moving average compon¬
ent. A lag of six quarters (1.5 years) was considered sufficient to
capture all pertinent price response. Price responses between market
levels lagged beyond 1.5 years were considered unlikely. This results
from the need to market fresh frozen shrimp quickly, due to a relatively
short shelf life.
The 31-40 size class
The null hypotheses of no unidirectional causality were not
rejected at a minimum .10 level in all cases (Table 6). Thus, unidirec¬
tional causality was not present. The virtual absence of any signifi¬
cant lagged residual cross correlation terms (k>0) further illustrates
the lack of a unidirectional causal relationship between the prices.
However, the highly significant zero lag (k=0) cross correlation term
indicated the presence of instantaneous causality (in the Pierce defini¬
tion) such that ex-vessel, wholesale, and retail prices are instan¬
taneously related only.
The 21-25 size class
The findings for the 21-25 size class prices were the same as for
the 31-40 size class prices (Table 7). Failure to reject the null
hypotheses of no unidirectional causality at the .10 level for both the
ex-vessel/wholesale and wholesale/retail relationships indicated that
unidirectional causality in either direction does not exist. The

112
Table 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.
Series 1 =
Series 2 «
Series 3 *
Prewhitened Ex-vessel Prices
Prewhitened Wholesale Prices
Prewhitened Retail Prices
TEST
I
TEST
II
(N - 49)a
(N =
49)a
Lag (k) in
A
Cross Correlations (r..(k)}
A
Cross Correlations {r..(k)
Causal
A
A
A
A
Series j
(a) r2>1(k)
(b) r1>2(k)
(a) r3j2(k)
(b) r2>3(k
0
.912*
.912*
.618*
.618*
1
.059
-.058
.248
-.033
2
-.075
-.030
-.097
.050
3
.022
-.082
.119
-.107
4
-.158
-.163
-.052
-.123
5
-.211
-.148
-.319*
-.207
6
-.001
.049
-.128
.029
TEST Is
(a) Null Hypothesis: ex-vessel does not cause wholesale price,
H-P X6 - 3.87**
(b) Null Hypothesis: wholesale does not cause ex-vessel price,
H-P x| = 3.40**
TEST II:
(a) Null Hypothesis: wholesale does not cause retail price,
H-P - 10.09**
(b) Null Hypothesis: retail does not cause wholesale price,
H-P X6 â–  3.63**
aN is the effective number of observations for cross correlation.
♦Greater than two standard errors (s), where s = N-*^.
**Fail to reject null hypothesis at .10 level.

113
Table 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.
Series
1 â–  Prewhitened Ex-vessel Prices
Series
2 â–  Prewhitened Wholesale Prices
Series
3 = Prewhitened Retail Prices
TEST I
TEST II
(N - 49)a
(N - 49)a
A
Lag (k) in Cross Correlations {r^(k)}
Causal A A
Series j (a) r2>1(k) (b) r1>2(k)
A
Cross Correlations (r^Ck)}
(a) r3>2(k) (b) r2>3(k)
0
.934* .934*
.469* .469*
1
.152 -.044
.127 .208
2
-.186 -.032
-.066 -.049
3
-.084 -.049
-.152 -.133
4
-.060 -.104
.055 .011
5
-.066 “-.166
-.096 -.238
6
-.124 -.003
-.114 .080
TEST I:
(a)
Null Hypothesis: ex-vessel does not
cause wholesale price,
H-P X6 â–  4.31**
(b)
Null Hypothesis: wholesale does not
cause ex-vessel price,
H-P x| â–  2.16**
TEST II:
(a)
Null Hypothesis: wholesale does not
H-P “ 3.33**
cause retail price,
(b)
Null Hypothesis: retail does not cause wholesale price,
H-P X6 - 4.07**
®N is the effective number of observations for cross correlation.
♦Greater than two standard errors (s), where s * N-^^.
**Fail to reject null hypothesis at .10 level.

114
absence of any significant residual cross correlations further illus¬
trates this finding. As with the analysis with the 31-40 size class
prices, the zero lag residual cross correlations are significant, indi¬
cating the presence of instantaneous causality in the Pierce defini¬
tion. Notice that zero lag cross correlations for the 21-25 size class
are roughly the same size at the ex-vessel/wholesale relationship but
smaller at the retail/wholesale relationship than for the 31-40 size
class data, suggesting in general a stronger instantaneous relationship
for the prices of the smaller shrimp product.
Impulse response functions for both size classes
The residual cross-correlations generated by the Haugh-Pierce test
were used to construct a set of impulse response functions which capture
the lead/lag properties that exist for the ex-vessel/wholesale and
wholesale/retail quarterly price relationships for each size class. The
definition and derivation of these expressions have been discussed for
the monthly price analysis and will not be repeated. The stepwise
process of deriving these expressions for the quarterly data is pre¬
sented in Appendix A. Thus, only the resulting final parsimonious
expressions, written in terms of the backshift operator B, will be
discussed in this section.
The Haugh-Pierce analysis indicated that the ex-vessel/wholesale
and wholesale/retail price relationships were characterized by instan¬
taneous causality running both directions. In addition, no unidirec¬
tional causality was found. Therefore, these price series are related
in a fully simultaneous, rather than recursive, nature. To accommodate
this characteristic, two impulse response functions were specified for

115
the ex-vessel/wholesale and wholesale/retail relationship for each size
class.
The parsimonious form of the two impulse functions corresponding to
the ex-vessel/wholesale relationship for the 31-40 size class are given
as
Wt - (.834)Et + ^(B)aJ
Et - (.998 - .165B)Wt + <(>2(B)a2
with the impulse response functions representing the wholesale/retail
price relationship given as
Wt - (.505 - .128B)Rt + 4»3(B)a^
Rj. - (.757 - ,113B)Wt + where B is the backshift operator, Rj. is retail price, Wt is wholesale
price, Et is ex-vessel price, and ^ is some polynomial expression of
the white noise error term a£.
The impulse response functions for the same two price relationships
as above, except for the 21-25 size class, and written in parsimonious
form are shown as
Wt - (1.03 - .141B + ,406b2)Et + ^(BjaJ
Et - (.847 - .143B2)Wt + 2(B)a2
and
Wt - (.560 - .506B + .114B2)Rt + 3(B)a£
Rt - (.393 + ,181B)Wt + where the variables are defined as for the 31-40 size class expressions.
The exact lead/lag structure of the interdependent price relation¬
ships are unveiled in the impulse response functions. Note that the lag

116
structure is very short for the 31-40 size class price series, requiring
a lag of at most only one period. However, the impulse response
functions for the 21-25 size class prices require lags of up to two
quarters. Price shocks appear to take longer to work through the system
for the larger sized shrimp.
The impulse response functions are incorporated into a quarterly
model of price at the ex-vessel, wholesale, and retail levels of the
market. These impulse response expressions provide a means by which the
lead/lag properties of prices between adjacent market levels may be
embodied in a more complete econometric model.
Granger Test
The Granger test was applied to ex-vessel, wholesale, and retail
prices for both size classes. The test was applied to price series
transformed into approximate white noise processes by first differ¬
encing. A total of six lags were specified for the Granger tests.
The 31-40 size class
The Granger causality test applied to first differenced data indi¬
cated that the causal relationships between ex-vessel and wholesale and
retail prices is not unidirectional (Table 8). All null hypotheses
regarding the absence of strictly unidirectional causality were not
rejected, thus no unidirectional causality in either direction is indi¬
cated. Note that first differencing the original series transformed the
series into white noise, as indicated by the given Box-Pierce statistics
at the .05 level. The same test was applied to first differenced whole¬
sale and retail price series (Table 8). The null hypotheses regarding
the absence of strictly unidirectional causality were not rejected at

117
Table 8: Granger Causality Tests on Quarterly Ex-vessel, Wholesale, and
Retail Prices for the 31-40 Size Class Using First Differenced
Data.3
A. NULL HYPOTHESIS: wholesale does not cause ex-vessel price
0 Unidirectional Test: Fg 20 = 0.69*
B. NULL HYPOTHESIS: ex-vessel does not cause wholesale price
0 Unidirectional Test: Fg 20 “ 1»34*
C. NULL HYPOTHESIS: retail does not cause wholesale price
0 Unidirectional Test: Fg 20 " 0.34*
D. NULL HYPOTHESIS: wholesale does not cause retail price
0 Unidirectional Test: Fg 20 “ 1»05*
aFirst differenced ex-vessel, wholesale, and retail price data for the
31-40 size class have Box-Pierce statistics of 24.13, 21.14, and 29.64,
respectively. These should be compared against a tabulated critical
chi-square value at 20 degrees of freedom of 31.14 at the .05 level.
*Fail to reject null hypothesis at the .10 level.

118
the .10 level. The derived Box-Pierce statistics indicated that the
first differenced series were approximately white noise. Thus, the
absence of unidirectional causality characterized the first differenced
quarterly 31-40 size class data.
The 21-25 size class
The Granger test on first differenced ex-vessel and wholesale
prices indicated that both null hypotheses regarding the absence of
unidirectional causality were not rejected (Table 9). The first differ¬
encing of the quarterly ex-vessel and wholesale price series did an
adequate job of transforming the series into white noise processes, as
indicated by the Box-Pierce statistics. Thus, unidirectional causality
between ex-vessel and wholesale prices for the 21-25 count class was not
found.
Testing the causal relationship between retail and wholesale prices
using first differenced data indicated that no causal relationship
exists (Table 9). Both hypotheses of no unidirectional causality were
not rejected at both the .05 level. However, the Box-Pierce statistic
for the first differenced retail price data indicated that the hypothe¬
sis that the residuals are white noise was not supported at the .05
level. Thus, as a check for robustness, the Granger test was also
performed on the wholesale/retail relationship using ARIMA filtered data
(Appendix B). The approximate ARIMA filter necessary to transform the
original retail price series into white noise was the same as that used
in the Haugh-Pierce test. The resulting Box-Pierce statistic shows that
the residuals are approximately white noise when compared to a tabulated
Xjg value of 28.9 at the .05 level. Both hypotheses regarding the

119
Table 9: Granger Causality Tests on Quarterly Ex-vessel, Wholesale, and
Retail Prices for the 21-25 Size Class Using First Differenced
Data.3
A. NULL HYPOTHESIS: wholesale does not cause ex-vessel price
0 Unidirectional Test: 20 ** 0»62*
B. NULL HYPOTHESIS: ex-vessel does not cause wholesale price
0 Unidirectional Test: Fg 20 " 1»05*
C. NULL HYPOTHESIS: retail does not cause wholesale price
0 Unidirectional Test: Fg 20 " 1»23*
D. NULL HYPOTHESIS: wholesale does not cause retail price
0 Unidirectional Test: F^ 20 "
aFirst differenced ex-vessel, wholesale, and retail price data for the
21-25 size class have Box-Pierce statistics of 21.04, 15.88, and 33.90,
respectively. These should be compared against a tabulated critical
chi-square value at 20 degrees of freedom of 31.14 at the .05 level.
*Fail to reject null hypothesis at the .10 level.

120
absence of unidirectional causality were not rejected at the .10 level.
Thus, the findings were identical when either first differenced or ARIMA
filtered data were utilized.
Sims Test
The Sims test for causality was applied to ex-vessel/wholesale and
retail/wholesale price relationships using data prewhitened by ARIMA
filters. The same filters as those used in the quarterly Haugh-Pierce
test were used for the Sims test. A total of six lags were used for the
Sims test.
The 31-40 size class
The ex-vessel/wholesale and wholesale/retail price relationships
were examined for the absence of unidirectional causality (Table 10).
Four null hypotheses of no causality were tested and all were not
rejected at the .10 level. Thus, no unidirectional causal patterns were
detected using the Sims test on prewhitened data.
The 21-25 size class
The ex-vessel/wholesale and wholesale/retail price relationships
were examined for the absence of unidirectional causality (Table 10).
As with the prewhitened prices representing the smaller size class of
shrimp, unidirectional causality was found to be absent at the .10
level. Thus, all four null hypotheses of no causality could not be
rejected

Table 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.
31-40 Size Class
21-25 Size Class
A.
NULL HYPOTHESIS: wholesale does not cause
ex-vessel price
A.
NULL HYPOTHESIS: wholesale does not cause
ex-vessel price
° Unidirectional Test: F^ g ■ 0.30*
0 Unidirectional Test: Fg g ** 0.33*
B.
NULL HYPOTHESIS: ex-vessel does not cause
wholesale price
B.
NULL HYPOTHESIS: ex-vessel does not cause
wholesale price
° Unidirectional Test: F^ g “ 0.50*
0 Unidirectional Test: Fg g = 0.26*
C.
NULL HYPOTHESIS: retail does not cause
wholesale price
C.
NULL HYPOTHESIS: retail does not cause
wholesale price
0 Unidirectional Test: F5 3 “ 0.98*
0 Unidirectional Test: Fg 3 “ 0.35*
D.
NULL HYPOTHESIS: wholesale does not cause
retail price
D.
NULL HYPOTHESIS: wholesale does not cause
retail price
0 Unidirectional Test: F5 3 “ 0.57*
0 Unidirectional Test: Fg g = 1.87*
*Fail to reject null hypothesis at the .10 level.
121

122
Summary of Monthly and Quarterly Causality Results
The findings of the Granger, Sims, and Haugh-Pierce procedures on
the monthly data for both size classes suggested in general that upward
unidirectional causality exists between the three market levels such
that ex-vessel causes wholesale price and wholesale causes retail price.
An exception to this generalization is the relationship implied by the
findings for the Sims and Haugh-Pierce test on the ex-vessel/ wholesale
price interface for the 21-25 size class, where the Haugh-Pierce test
found no unidirectional causality and the Sims test found feedback. The
Haugh-Pierce test indicated instantaneous causality exists that between
ex-vessel and wholesale prices for both size classes, however, instan¬
taneous causality was found between the wholesale and retail prices only
for the 31-40 size class. The same set of tests using quarterly data
for both size classes found no evidence of unidirectional causality
between the price series representing any two adjacent market levels.
The Haugh-Pierce test suggested that ex-vessel, wholesale, and retail
prices are instantaneously related only. These monthly and quarterly
causality results are summarized in Table 11.
These findings indicate that the price determination process is
recursive from ex-vessel to retail market levels on a monthly basis and
simultaneous on a quarterly basis. Thus, the monthly price determina¬
tion process may be dominated by changes in supplies, with not enough
time being allowed for retail factors to play an important part in
determining prices. However, the quarterly time period allows enough
time for feedback of market signals to occur between retail, wholesale,
and ex-vessel market levels, resulting in an interdependent process of
price determination

123
Table 11: Summary of Monthly and Quarterly Causality Tests Using Ex¬
vessel (E), Wholesale (W), and Retail (R) Price Data by Size
Class*
Test3
M«i1 1
Haugh-Pierce
Granger
Sims
Hypothesis*5
31-40
21-25
31-40 21-25
31-40
21-25
(Monthly Data)
E<-/—>W
R
R
E -f->W
R
F
R R
R
R
W -/—>E
F
F
F F
F
R
W<-/->R
R
F
W -f->R
R
R
R R
R
R
R -/—>W
F
F
F F
F
F
(Quarterly Data)
E<-/—>W
R
R
E -7t->W
F
F
F F
F
F
W —>E
F
F
F F
F
F
W<-T^—>R
R
R
W -f->R
F
F
F F
F
F
R -/—>W
F
F
F F
F
F
aReject (R) and
fail to
reject (F)
the null hypothesis
•
^No unidirectional causality indicated by -/->, which reads "does not
cause", and no instantaneous causality indicated by <—**->•

CHAPTER VI
EMPIRICAL RESULTS—PRICE AND MARGIN MODELS
Price dependent monthly and quarterly demand equations were esti¬
mated using ordinary least squares and three stage least squares
methods. The variables found in each expression were dictated by the
theoretical model presented in Chapter II and the impluse response
functions derived from the causality analysis presented in Chapter V.
However, certain lagged price variables were either included or elimi¬
nated based on a set of diagnostic checks and pretesting procedures,
both of which are discussed in Appendix B. The criteria determining
whether single equation or systems estimation methods were used are also
presented in Appendix B.
As with the causality tests, monthly and quarterly data were used
for both the 31-40 and 21-25 size classes. The monthly and quarterly
models utilized data for the years 1972 through 1981. Estimates of the
monthly models by size class are presented first, followed by quarterly
model estimates.
Monthly Data
The structural models of monthly retail, wholesale, and ex—vessel
demand were estimated using ordinary least squares methods. This method
is justified given the generally recursive nature of the price deter¬
mination process as indicated by the monthly causality analysis. A
major hypothesis to be tested with the monthly models was the existence
124

125
of asymmetrical price response between market levels. At present,
methods to test these hypotheses require recursive expressions. The
recursive structure of the retail, wholesale, and ex-vessel demand for
the 31-40 size class lend themselves well to testing for asymmetry. For
the 21-25 size class, however, only the wholesale/retail market inter¬
face was characterized by recursivity, while the ex-vessel/wholesale
market interface was characterized by simultaneity. Therefore, in order
to perform the test of asymmetry, only the retail demand expression was
estimated for the 21-25 size class. Discussion emphasizes estimates
that were significant at least at the .25 level.
The 31-40 Size Class
Price models for retail, wholesale, and ex-vessel market levels are
presented. Given that the causal direction for monthly prices is up¬
ward, only the retail and wholesale price models are presented in asym¬
metric form.
Retail structural estimates
Empirical estimates of the parameters and corresponding standard
errors for the retail price model are given as
R =â–  1.023 + .907 R . + .329 W - .111 W . - .105 W , + .042 FW
L (.920) (.040)1 t_1 (.117)1 C (.136) t_A (.063)2 c (.044)
+ .00086 RDY + .0036 TCFF + .0020 CPI
(.0013) t (.0037) 1 (.0017)3 C
where the values in parentheses are standard errors and the subscripts
1,2, and 3 refer to significance at the .01, .10 and .25 level of confi-
9
dence. The model explained approximately 99 percent (R * .9893) of the
monthly variation in retail price. Four of the nine estimated coeffi¬
cients were statistically significant at the .25 level or greater.

126
The significance of the parameter estimate representing retail
price lagged one period (Rt_^) indicates that factors which cause a one
cent change in retail price (Rt) have a further effect in the same
direction of .91 cents in the following period. Thus, virtually the
full impact of a change in retail price in a given period is passed on
to retail price in the next period. The lagged retail price variable
was included to account for first order serial correlation in the error
terms for the retail price equation. Given that decision variables such
as real disposable income (RDYt) and the price index for competing meat
products (CPIt) are very stable across months, price in the previous
periods may be a very important decision variable for developing expec¬
tations needed to establish price in the current period. The signifi¬
cant parameter estimate for Rt_^ supports this logic. The inclusion of
the lagged dependent variable reduced the errors to white noise (Appen¬
dix Table B).
The absence of asymmetric responses of current retail price to
changes in current wholesale price is indicated by the insignificant
parameter estimated for falling current wholesale price (FWt). The
insignificance of the asymmetric parameter estimate causes the parameter
estimate on the current wholesale price variable (W£) to be interpreted
as a symmetric test on current wholesale price (FWfc). The insignifi¬
cance of the asymmetric parameter estimate causes the parameter estimate
on the current wholesale price variable (Wt) to be interpreted as a
symmetric test on current wholesale price. The estimate for Wt was
significant and indicates that as current wholesale price changes by one
cent current retail price changes by .33 cents in the same direction.
The estimates for the parameters of wholesale price lagged one and four

127
periods (Wt_j and Wt_^) are symmetric tests. A one cent change in
wholesale price was found to change retail price in the opposite direc¬
tion by .11 cents four periods in the future, as indicated by the sign¬
ificant estimate at the .10 level for the Wt_^ parameter. The estimate
for Wt-1 was insignificant.
The more traditional shifters of primary demand, such as real
disposable income, total retail supply (TCFFt) and price of competing
meat products were generally found to not have a large impact on retail
price. A one unit change in the substitute price index, which was
proxied by the consumer price index for meat and poultry, caused retail
price to change in the same direction by .2 cents, as indicated by the
estimate on the parameter CPIt which was significant at the .25 level.
However, this weak significance may simply be due to correlation over
time between the retail price for shrimp and the retail price for other
meat products. Just how sensitive the consumption of meat and poultry
is to changes in the price of shrimp products is questionable, particu¬
larly when the per capita consumption of read meat and poultry of 203.5
pounds for 1982 is compared to the consumption in edible meat weight of
all shrimp products of 1.53 pounds in 1982 (Food Consumption Prices, and
Expenditures 1962-1982, 1983; Fisheries of the United States, 1983).
The parameter estimates for real disposable income and total retail
supply were found to be insignificant.
Wholesale structural estimates
Empirical estimates of the parameters and corresponding standard
errors for the wholesale price model are given as

128
W - .289 + .687 W , + .709 P - .372 P - .024 FP
t (. 139) 2 (.059^'1 (.0451)t"A (.0711>t"i (.030) C
- .0016 BSFF + .0167 131 - .0020 01 - .0008 TMCI
(.0007)L t (.0221) 1 (.0026) C (.0011) C
where the values in parentheses are standard errors and the subscripts 1
and 2 refer to significance at the .01 and .05 level of confidence. The
2
model explained approximately 99 percent (R â–  .9937) of the monthly
variation in wholesale price. Five of the nine estimated coefficients
were statistically significant at the .05 level or greater.
The significance of the estimated parameter representing wholesale
price lagged one percent (Wt_j) indicates (as did the analogous estimate
in the retail price expression) that factors which cause a change in
wholesale price (Wfc) have an effect on wholesale price in the next
period. Specifically a one cent change in wholesale price causes whole¬
sale price in the next period to change in the same direction by -.69
cents. This is indicated by the estimate of the parameter being
significant at the .05 level. In addition, the lagged dependent vari¬
able was included due to the presence of first order serially correlated
errors. With the inclusion of this lagged dependent variable, the
residuals reduced to an approximate white noise process (Appendix Table
B).
Asymmetry was found not to characterize the price response rela¬
tionship between current ex-vessel (Pt) and current wholesale prices.
This is indicated by the estimate of current falling ex-vessel price
being insignificant (null hypothesis of zero value not rejected using a
one-tailed test). Thus, the estimate on current ex-vessel price reverts
to a test of symmetric price response between ex-vessel and wholesale
prices, which was found to be significant at the .05 level. This

129
estimate shows that a one cent change in ex-vessel price causes current
wholesale price to change by .71 cents in the same direction. This
represents an elasticity of price transmission derived at the means
between ex-vessel and wholesale price of .60. Thus, current wholesale
and ex-vessel price appear to follow one another closely. This rela¬
tionship was not found to characterize current wholesale and retail
prices.
Increases in the beginning inventories of all raw-headless shrimp
(BSFFt) had a significant impact on current wholesale price.
Specifically, a one million pound increase in the level of beginning
inventories decreases wholesale price by .16 cents. This estimate
contrasts to values found by Doll (.82) on an annual basis and Thompson
and Roberts (.52) on a monthly basis. An annual study by Hopkins et al.
found beginning inventories had no significant effects on wholesale
price.
The parameter estimates corresponding to imports of own-size
product (I31t) and imports of all other sizes of shrimp (0It) were found
to be not significantly different from zero. This finding is
corroborated somewhat by annual studies done by Hopkins et al. and Doll
on the response of wholesale price to changes in the level of total
imports. Thompson and Roberts, however, did find a significant inverse
relationship between imports and wholesale price.
Wholesale price did not possess a significant relationship with
marketing costs, as indicated by the insignificant coefficient estimate
for the index of marketing costs represented by TMCIt. The variable
TMCIt served as a proxy for costs of marketing and processing shrimp
products incurred at the wholesale level. However, this index was

130
actually defined as an index for intermediate costs in the processing of
more traditional agricultural commodities and may be a relatively poor
proxy for cost incurred in seafood wholesaling and processing. The
disaggregated components of TMCIt were also tested, such that parameters
for individual indexes could be estimated for labor, packaging and
transportation costs. These estimates for component indexes were also
found to be insignificant, possibly due to a high degree of multico¬
linearity between the individual series of data for each index.
Ex-vessel structural estimates
Empirical estimates of the parameter and corresponding standard
errors for the ex-vessel price model are given as
P = .131 + .935 P , - .0084 OL - .016 L31 + .0008 TMCI
C (.065)2 C.030)^"1 (.003)2 C (.011)3 C (.0005) C
where the values in parentheses are standard errors and the subscripts
1, 2, and 3 refer to significance at the .01, .05, and .20 level of
confidence. The model explained approximately 96 percent (R =.9642) of
the monthly variation in ex-vessel price. Four of the five estimates
were statistically significant at the .20 level of confidence or
greater.
The significant parameter estimate for ex-vessel price lagged one
period (Pt_j) indicates that the factors which cause current ex-vessel
(Pj.) price to change by one cent, result in ex-vessel price in the next
period to be further affected in the same direction by .94 cents. Thus,
virtually the full impact of a current ex-vessel price change is passed
on to ex-vessel price in the next period. As with the retail and
wholesale price equation, the lagged dependent variable was included due

131
to the presence of first order serially correlated errors. However,
t
inclusion of the lagged dependent variable did not remove the serial
correlation from the error terms.
Ex-vessel price was significantly affected by quantity landed, both
in terms of own-size landings and total landings of other sizes of
shrimp. The estimated coefficient for total landings of all other sizes
of shrimp (0Lfc) indicates that as these landings increase by one million
pounds ex-vessel price will decrease by .84 cents. This value contrasts
to similarly defined estimates by Doll (.32 cents) and Thompson and
Roberts (.56 cents). The estimated coefficient for own-size landings
(L31t) Indicates that as landings of only 31-40 count shrimp Increases
by one million pounds, ex-vessel price decreases by 1.6 cents. However,
ex-vessel price for the 31-40 size class appears to be more sensitive to
total landings of all other sized shrimp than to landings of shrimp in
the 31-40 size class. This is illustrated by the price flexibilities
derived at the means for the parameters 0Lt and L31t of .036 and .013,
respectively. The parameter estimate for the marketing cost index TMCIt
was found to have a small standard error relative to the estimated
coefficient, but possessed the wrong sign. Input costs of processing
raw product were hypothesized to have an inverse relationship with the
demand for raw product. Thus, on the basis of a one-tailed test, the
estimate was found to be insignificant. As with the wholesale model,
the costs of intermediate goods and services used in manufacturing food
products had no significant impact on the determination of price.

132
The 21-25 Size Class
Only the price model for the retail market level is estimated.
This was because the retail/wholesale market level interface was recur¬
sive. The wholesale/ex-vessel market level interface was characterized
by simultaneity. This limitation on the models presented is warranted
due to the necessity of performing the asymmetry test, which does not
lend itself to non-recursive methods.
Retail structural estimates
Empirical estimates of the parameters and corresponding standard
errors for the retail price model are given as
R - .342 + .851 R + .066 W + .210 W - .105 W
C (.952) (.039)^ (.085) t (.127) * (.088) t~¿
- .027 FW - .0007 RDY - .0069 TCFF + .0029 CPI
(.035) C (.0013) t (.0042)2 C (.0016)2 t
where the values in parentheses are standard errors and the subscripts 1
and 2 denote significance at the .01 and .10 level of confidence. The
2
model explained approximately 99 (R -.9897) percent of the variation in
retail price. Four of the eleven estimates were statistically
significant at the .25 level or greater.
The significant positive parameter estimate for retail price lagged
one period (R^j) again indicates that factors which affect current
retail price (R£) have a further impact on price in the next period.
Specifically, a one cent change in retail price causes a .85 cent change
in retail price in the following period. The lagged dependent variable
was included to account for first order serial correlation in the error
terms. The inclusion of this term reduced the error terms to white
noise

133
The response relationship between retail and wholesale prices is
characterized by symmetry. The parameter estimate for current falling
wholesale price is insignificant, indicating that symmetry exists.
Given that the coefficient estimate for current wholesale price is
insignificant, the coefficient estimate for current wholesale price (Wt)
is tested for significance under the assumption of symmetric response of
retail price to increasing or decreasing wholesale price. Current
wholesale price was found to not have a significant impact on the deter¬
mination of current retail price. Wholesale price lagged one period
(Wt_^) had a significant impact on current retail price. A one cent
change in wholesale price was found to change retail price in the next
period by .21 cents in the same direction. However, a change in
wholesale price by one cent was shown to not cause a significant change
in retail price two periods later.
The primary demand shifters included in the 21-25 size class model,
such as real disposable income (RDYt), retail supply (TCFFt), and price
index of competing meat products (CPIt), were found to be somewhat more
important in determining current retail price than for the 31-40 size
size class model. The retail supply of all size classes of raw-headless
shrimp and the proxy for the substitute price of other meats were both
significant at the .10 level of confidence. A one million pound change
in the retail supply will cause a .7 cent change in current retail price
in the opposite direction. The sign is as that expected if the TCFFt is
interpreted as capturing a supply effect. A one unit change in the
consumer price index for meat and poultry causes a significant .3 cent
change in retail price in the same direction. This suggests that as the
price of meats and poultry increases, shrimp appears to be substituted

134
for these two products, thus increasing the demand for shrimp and
eventually bidding up the price for shrimp products. Due to the
relatively small percentage share that shrimp accounts for in the per
capita consumption of meat, poultry, and fish, however, the measured
impact may be simply the correlation over time between the prices of
shrimp and other meat products. The parameter estimate for real
disposable income was not found to be statistically significant. Thus,
real income has little effect on the determination of retail price of
either size class on a monthly basis. This is verified by simply
observing the data over the time period of the analysis (1972-1981)—
prices have fluctuated as real disposable income remained relatively
stable* Finally, the constant term was also found to be insignificant.
Quarterly Data
Structural expressions for quarterly retail, wholesale, and ex¬
vessel demand are estimated using the three stage least squares
method. This approach is warranted due to (1) the simultaneous nature
of the price relationships found in the causality results for the quar¬
terly data and (2) the presence of significant contemporaneous cross
correlation of the residuals from two stage least squares analysis of
the simultaneous system. Once the structural estimates of the coeffi¬
cients are obtained, derived reduced form parameters are calculated. In
addition, the presence of lagged dependent variables in the reduced form
expressions necessitates the derivation of the final form estimates of
the parameters. These final form estimates are then used to construct
margin expressions in terms of the full set of exogenous variables of
the structural model. Final form expressions are computed for both 31-

135
40 and 21-25 size class shrimp.. The results are discussed by size class
in terms of initial structural, reduced form and final form estimates
and final form margin estimates. Tests for asymmetry were not performed
due to the simultaneous nature of the quarterly models and the fact that
asymmetry tests require recursiveness.
As pointed out by Christ (1966) and Kmenta (1971), conventional
tests of statistical significance; i.e. t-statistics, are not valid for
most simultaneous estimation procedures. This is particularly true for
small sample studies such as the present study. Thus, the discussion of
the findings from the quarterly analysis emphasizes all estimates
possessing the anticipated sign, regardless of the relative sizes of a
given parameter estimate and the corresponding standard error as found
in the initial structural estimation. In the analysis of quarterly
data, the structural estimates represent only partial effects; i.e., the
impact of a predetermined variable only on the level, or structure, in
the market for which it has a direct effect. The reduced and final form
estimates provide, in addition, the indirect effects on the other market
levels.
The 31-40 Size Class
Price models for retail, wholesale, and ex-vessel market levels are
presented, in terms of the structural, reduced form, and final form
2
parameter estimates. The structural model had a system R of .9660.
Final form expressions for retail/wholesale and wholesale/ex-vessel
margins are also discussed.
Retail structural estimates
Empirical estimates of the parameters and corresponding standard
errors for the retail price model are given as

136
R = .370 + .556 W + .629 R - .0024 RDY + .0023 TCFF + .0094 CPI
t (1.021) (.108) C (.060) t_1 (.0016) C (.0044) C (.0036) C
where the values in parentheses are standard errors. Four of the six
estimated coefficients possess the anticipated sign.
The parameter estimate for current wholesale price (Wt) indicates
that as current wholesale price changes by one cent, retail price (Rfc)
changes by .56 cents in the same direction. This corresponds to an
elasticity of price transmission at the means between current wholesale
and retail price of .39. Thus, current retail price is inelastic to
changes in current wholesale price. A one cent change in retail price
was shown to have a further effect on retail price in the next period.
This is apparent when considering the coefficient associated with Rt_j,
which was included due to the error terms being first order serially
correlated. The coefficient estimates for retail price lagged one
period (Rt_p indicate that factors which cause retail price to change
by one cent caused retail price to experience further change in the same
direction of .63 cents in the next period. This "carry-over" effect
represents an elasticity of price transmission between lagged and
current retail price of .62. The cumulative impact of the current and
lagged price will be evident in the final form analysis which is
discussed later.
The primary demand shifters income (RDYt), retail supply (TCFFt),
and price of competing meat products (CPIt) were, as in the monthly
models for the 31-40 size class, not as a group very important deter¬
minants of retail price. The estimated coefficient for the variable
CPIt indicated that a one unit change in the consumer price index for
meat and poultry will result in a .94 cent change in retail price of

137
shrimp as shrimp is a substitute for relatively higher priced substi¬
tutes. This estimate, however, may simply be capturing the positive
correlation over time between the prices of raw-headless shrimp and
competing meat products. The estimated coefficient on the income
parameter RDYt has the wrong sign and is, thus, insignificant. In
addition, the estimated coefficient on the supply variable TCFFt was
expected to have a negative sign, Indicating that as the quantity
supplied changes, retail price should change in the opposite
direction. The estimated coefficient, however, has a positive sign.
This same finding of insignificance was found for the monthly retail
model.
Wholesale structural estimates
The empirical estimates of the parameters and the corresponding
standard errors for the wholesale price model are given below as
W = .247 - .051 R + 1.110 P + .041 R - .0011 BSFF
t (.173) (.137) t (.093) C (.093) t-1 (.0015)
+ .0001 01 - .0036 131 + .00033 TMCI
(.0016) C (.0129) C (.00081)
where the values in parentheses are the standard errors. Seven of the
eight estimated coefficients possess the anticipated sign.
Current wholesale price was shown to be very sensitive to changes
in current ex-vessel price (Pfc). The estimated coefficient for ex¬
vessel price shows that as ex—vessel price increases by one cent, whole¬
sale price increases by 1.1 cents. This translates into an elasticity
of price transmission at the means between current ex-vessel and whole¬
sale price of .932. An elasticity of price transmission less than one
in describing the response of wholesale price to an ex-vessel price

138
seems plausible. The cost of the raw product, of course, represents a
smaller percentage of the wholesale price than of the ex-vessel price,
due to value added through processing and wholesaling. A percentage
change in the raw product price should result in a smaller percentage
change in total price at the wholesale than at the ex-vessel level.
However, given that the product form under scrutiny is raw-headless
shrimp, which actually requires little further processing, the per¬
centage change in wholesale given a change in ex-vessel price should be
close to 1.0. In addition, price differences attributable to time and
space dimensions are largely represented by the cost of holding
inventory and transportation, which represent a relatively small
percentage of wholesale price (Penn, 1980; Hu, 1983).
Retail price lagged one period (Rt_p had a small positive impact
on current wholesale price. Specifically, a one cent change in retail
price will have a .04 cent change in the same direction in wholesale in
the next period. The positive estimate may be describing the positive
effect on the derived demand for wholesale product given changes in the
demand at the retail level in the previous period. Current retail price
appears to have an insignificant impact on current wholesale price as
indicated by the negative coefficient estimate for the retail price
parameter and the relatively large standard error. However, a positive
relationship between current retail and wholesale price was expected.
This finding, coupled with the relationship between retail and wholesale
prices as shown in the quarterly retail model, suggests that retail
price is more sensitive to changes in wholesale price than wholesale
price is to changes in retail price.

139
The estimated coefficients for the quantity variables given as
beginning inventories of raw-headless shrimp (BSFFt) and imports of raw-
headless shrimp of the 31-40 size class (1311) have the expected sign
although the level of statistical significance is questionable due to
large standard errors. A one million pound change in beginning inven¬
tories will change wholesale price in the opposite direction by .11
cents. The estimate may be describing the relationship between inven¬
tories and wholesale price where inventories which are built up dispro¬
portionately during the first and fourth quarters due to imports are
released into the market system. A one million pound change in own-size
imports (131c) results in wholesale price changing in the opposite
direction by .36 cents. Wholesale price is more sensitive to changes in
beginning inventories of raw-headless shrimp than changes in imports of
31-40 count shrimp. This is indicated by the flexibilities of -.022 and
-.004, computed at the means of wholesale price to changes in beginning
stocks and own-size imports, respectively. The estimated coefficient
for total imports of all other size classes of raw-headless shrimp (0It)
did not have the anticipated sign. A positive relationship between
other size imports and wholesale price for a given size class may have
two possible explanations. First, as price of other size classes
increases, the quantity supplied of other size classes may increase.
Secondly, over the last ten years, imports and prices have increased
simultaneously, because of relatively large demand increases concurrent
with positive supply shifts.
Wholesale price is positively related to costs of intermediate
goods and services. Specifically, a one unit change in the index of
these processing and wholesaling costs results in a wholesale price

140
change in the same direction of .03 cents. A flexibility estimate of
.02 suggests wholesale prices are not highly dependent on changes in
marketing costs. This low estimate may reflect the inappropriateness of
using an aggregate cost index for processing and wholesaling general
agricultural commodities in estimating the response of prices for raw-
headless shrimp to changes in marketing costs. In addition, the
quarterly time period, as may be true for the monthly data, may not be a
long enough sampling interval over the time period of the analysis to
detect significant changes in general input cost levels.
Ex-vessel structural estimates
Empirical estimates of the parameters and the corresponding
standard errors for the ex-vessel price model are given as
P - -.129 + .906 W - .00011 OL - .0027 L31 - .00025 TMCI
C (.075) (.033) (.00097) (.0024) C (.00055) t
where the values in parentheses are standard errors. All estimates have
the expected sign.
Ex-vessel price was found to be very sensitive to changes in whole¬
sale price. The estimated coefficient for Wt indicates that a one cent
change in current wholesale price will result in a .91 cent change in
current ex-vessel price. This corresponds to a flexibility estimated at
the means of 1.08. Thus, ex-vessel price is slightly flexible to
changes in wholesale price. Given the estimate for Pt in the wholesale
model, ex-vessel and wholesale price are major determinants of each
other in a given quarter. Market conditions in the producer/first
handler and wholesale market are not only important to own price deter¬
mination, but also important to price determination in the adjacent

141
market. This relationship is not nearly as strong between retail and
wholesale market levels.
The coefficient estimates for own-size landings (L31t> and total
landings of all other size classes (0Lt) are shown to be inversely
related to ex-vessel price. A one million pound change in landings of
31-40 count shrimp results in current ex-vessel price changing in the
opposite direction by .2 cents. A one million pound change in total
landings of other-size shrimp causes ex-vessel price to change in the
opposite direction by .01 cents. These structural estimates for own-
size and other size landings correspond to flexibility estimates of
-.007 and -.003, respectively. Thus, ex-vessel price is very inflexible
to quantity landed. However, ex-vessel price is more sensitive to own-
size landings than to total landings of other size classes.
Ex-vessel price was found to be inversely related to the costs of
intermediate goods and services in the wholesaling and processing
sector. The estimated coefficient for the parameter TMCIt indicated
that as the index that represents these cost changes by one unit, ex¬
vessel price changes in the opposite direction by .03 cents. If these
costs more nearly represent costs incurred at the wholesale level,
theory would suggest that, as costs Increase, derived supply (wholesaler
supply to retailer) would shift up and derived demand (wholesale demand
for producer raw product) would shift down, thereby causing wholesale
prices to increase and producer (ex-vessel) prices to decrease (Tomek
and Robinson, 1972). The findings for the 31-40 size class wholesale
and ex-vessel price models regarding the TMCIt variable lend support to
the theory. These findings, however, are questionable due to the
relatively large standard error associated with the parameter

142
estimate. In addition, TMCIt is at best only a proxy for the cost of
inputs associated with wholesaling and processing raw-headless shrimp.
Reduced and final form estimates
The reduced form and final form coefficient and price flexiblity
estimates corresponding to the structural coefficient estimates for the
retail, wholesale, and ex-vessel price models were derived. The reduced
and final form estimates of the structural system describe each jointly
determined variable in terms of all predetermined variables. This
differs from the structural equations in that each structural equation
attempts to describe a specific part of the system being modeled in a
ceteris paribus fashion, while also taking into account all of the
interdependencies among the jointly determined variables. In addition,
structural estimates are only derived for varibles directly involved in
the part of the system represented by a given equation. Structural
estimates and reduced and final form estimates are measures of change in
the jointly determined variable given a change in a predetermined vari¬
able. The structural estimate, however, assumes all other predetermined
variables are constant in the current time period (partial effect),
while reduced and final form estimates represent an equilibrium after
all variables have been allowed to change. When lagged dependent varia¬
bles are present, the reduced form estimates are essentially an inter¬
mediate result, since effects of the lagged variables have not been
allowed enough time to work through the system. In this case, final
form estimates would be more appropriate for analysis. Lagged
endogenous variables (prices) exist in this study. Thus, the reduced
forms are presented only in Appendix D. The following discussion is
oriented toward the final form estimates.

143
The final form coefficients found in Table 12 provide the long-run
impact of changes in the full set of predetermined variables on each
jointly determined variable. The term "long-run” implies that enough
time has elapsed such that the effects of all lagged variables have been
taken into account. For the model representing the 31-40 size class,
only a lag of one quarter was necessary. The values are of the same
sign, but generally larger than the reduced form estimates, reflecting
the cumulative effect of the lagged terra which is incorporated in the
estimate. In addition, the flexibility estimates are relatively larger
than the reduced form flexibilities.
The retail final form estimates are larger than either the whole¬
sale or ex-vessel estimates. The latter of the two are very close in
value which reflects the close dependency between the ex-vessel and
wholesale market levels found in the initial structural model. Excep¬
tions are the estimate for RDYt, TCFFt, and CPIt. The estimates for
RDYt and CPIt, however, are insignificant based on the sign. The flexi¬
bility estimates are generally larger for the ex-vessel level than for
either retail or wholesale levels. With the exception of TCFFt, how¬
ever, the flexibility estimates are close in value. Flexibility esti¬
mates are not computed for CPIt and TMCIfc since these variables are
already expressed in terms of percentages. The signs on the final form
estimates are generally the same as found at the structural level, with
the exception of TCFFt and CPIt. In the longer-run, TCFFt appears to
pick up the impact of retail supply.

Table 12: Final Form Coefficients and Flexibility Estimates for the Retail, Wholesale and Ex-vessel
Price Models for the 31-40 Size Class.
Jointly Predetermined Variables
Determined
Variables
RDYt
TCFFt
CPIt
BSFFt
0It
I21t
0Lt
L21t
TMCIt
Rt
.0039a
-.0038
.0151
-.1770
.0211
-.5803
-.0178
-.4829
.0086
(.8750)b
(-.0780)
(-2.493)
(.2970) i
(-.4600)
(-.1410) i
(-.6850)
Wt
.0069
-.0067
-.0270
-.1180
.0140
-.3866
-.0119
-.3219
.0157
(2.2070)
(-.1970)
(-2.3680)
(.2810) i
(-.4370)
(-.1340) i
(-.6500)
Pt
-.0063
-.0060
-.0245
-.1069
.0127
-.3503
-.0108
-.2942
.0048
(2.4010)
(-.2110)
(-2.5570)
(.3040) i
(-.4720)
(-.1450) i
(-.7090)
aEstiraated final form coefficient.
^Estimated flexibility derived at the means.
144

145
Margin estimates
The margin expressions representing retail/wholesale and whole¬
sale/ex-vessel price spreads were derived from the final form estimates
for each market level (Table 13). The values in parentheses are the
derived flexibility estimates. Note that flexibilities are not shown
for CPIt and TMCIt since these terms are already percentage values.
Each estimate for the quarterly margins was obtained by subtracting the
corresponding estimates predetermined variable from each price model.
The indicated margin flexibilities were derived at the means after the
estimates were obtained. The estimated coefficients of the margin
expression were generally of the same sign found for the corresponding
parameter estimates in the final form expressions. The estimates for
the retail/wholesale margin were typically larger than for the
wholesale/ex-vessel margin, which reflects the increasingly larger
marketing cost at the retail level. In addition, the margin flexibility
estimates derived are larger for the retail/wholesale margin than for
the wholesale/ex-vesel margin. This finding supports the structural,
reduced form, and final form analysis regarding basic relationships
between the three market levels. For example, retail and wholesale
price have been shown to be relatively unresponsive to changes in each
other as shown in the monthly and quarterly price analysis. Thus,
changes in retail price are not fully passed to wholesale price, and
vice versa. This relationship does not characterize wholesale and ex¬
vessel market levels. The retail/wholesale margin, therefore, could be
expected to be relatively more flexible to changes in market conditions
as compared to the wholesale/ex-vessel margin.

Table 13: Final Form Margin Estimates and Flexibilities for the Retail/Wholesale (Mâ„¢) and the
Wholesale/Ex-vessel (MWP) Margins for the 31-40 Size Class.
Predetermined
Variables
Margin
RDYt
TCFFt
CPIt
BSFFt
0It
I21t
0Lt
L21t
TMClt
Mâ„¢
-,0030a
(—2•259)b
.0029
(.200)
.0119
-.0590
(-2.788)
.0071
(.336)
-.1937
(-.515)
-.0059
(-.157)
-.1610
(-.766)
.0029
M«P
.0006
(1.192)
-.0007
(-.127)
-.0025
-.0111
(-1.384)
.0013
(.162)
-.0363
(-.255)
-.0011
(-.077)
-.0277
(-.348)
.0009
aFinal form margin estimate.
^Flexibility derived at the means.
146

147
The estimated coefficients for real disposable income (RDYt), total
retail supply (TCFFt), and price index of competing meat products (CPIt)
indicate that these variables have mixed impacts on the margins. Real
disposable income appears to be insignificant. This finding reflects
insignificant changes in disposable Income over the period analyzed.
Total retail supply and price index of competing meat products have a
positive impact on Mâ„¢ but a negative impact on Mwp. Attempts to draw
conclusive inferences from these inconsistent findings appears
questionable.
The coefficients for beginning inventories (BSFFt) and own-size
imports (I31t), which originally were found in the wholesale price
model, indicate that the margins are inversely related to beginning
inventories of raw-headless shrimp and imports of 31-40 size class raw-
headless shrimp. A one million pound increase in BSFFt and I31t results
in a 5.9 and 19.4 cent decrease, respectively, in M1^ and a 1.1 and 3.6
cent decrease, respectively, in M4^. However, each margin was found to
be more sensitive to change in beginning inventories than to imports of
the 31-40 size class, as the flexibilities indicate. Specifically, a
one percent increase in BSFFt decreased and by 2.79 and 1.38
percent respectively. This compares to a decrease of .52 and .26
percent in Mâ„¢ and M^, respectively, given a one percent increase in
I31t.
Landing of own-size shrimp (L31t) and total landings of all other
size shrimp (0Lt) were found to be inversely related and inflexible to
each margin. Specifically, a one million pound increase in other
landings and own-size landings was shown to decrease M1^ by .59 and
16.10 cents, respectively. The same change was shown to decrease MWP by

148
.11 and 2.77 cents, respectively. In addition, a one percent increase
in other-size and own-size landings decreases Mâ„¢ by .157 and .766
percent, respectively. The same changes would decrease by .077 and
.348 percent, respectively. The inverse relationship between the
quantity variables and both margins may suggest, as was found with the
monthly margin expressions, that economies of size in terms of quantity
handled may exist for retailers, wholesalers, and first-handlers. The
inverse price effect attributed to changes in quantities appears to have
a much larger Impact on the more volatile retail/wholesale margin.
Both margins were found to be positively related to increases in
intermediate food marketing costs (TMCIt). Specifically, a one unit
increase in TMCIt was found to increase Mâ„¢ and Mwp by .29 and .09
cents, respectively. Thus, the retail/wholesale margin was more sensi¬
tive than the wholesale/ex-vessel margins to changes in marketing costs.
The 21-25 Size Class
Price models for retail, wholesale, and ex-vessel market levels are
presented in terms of the initial structural, reduced form, and final
form parameter estimates. This is in contrast to the analysis of month¬
ly data where only the asymmetric retail price model was estimated. The
9
structural model had a weighted system R of .966. Final form margin
expressions are also discussed.
Retail structural estimates
The empirical estimates of the parameters and corresponding
standard errors for the retail price model are given as
R =â–  .145 + .477 W + .708 R - .00037 RDY - .0036 TCFF + .0020 CPI
(1.185) (.092) C (.056) t-1 (.0018) t (.0048) C (.0033) C

149
where the values in parentheses are the standard errors. All but one of
the coefficient estimates are of the anticipated sign.
Current retail price (Rc) was found to be positively related to
current wholesale price (Wt) and retail price lagged one period (Rt_^).
A one cent change in current wholesale price caused current retail price
to change in the same direction by .48 cents. This represents an
elasticity of price transmission of .34. Current retail price was thus
found to be inelastic to changes in current wholesale price. A one cent
change in retail price was shown to have a further positive effect on
retail price in the next period. As in the case of retail price
estimation for the 31-40 size - shrimp, Rt_^ was included to account for
first order serially correlated error terms in the retail model.
However, the coefficient for Rt_j can be interpreted such that factors
which cause a one cent change in retail price cause further change in
retail price in the next period of .71 cents. This lagged effect for
the 21-25 size class is slightly greater than the comparable value of
.63 found for the 31-40 size class. In terms of the elasticity of price
transmission between lagged and current retail price, a one percent
change in retail price has a .70 percent change in retail price next
period in the same direction.
Estimates for two of the three retail demand shifters included in
the retail demand model were of the anticipated sign. However, the
indicated impact on retail price was found to be small. A one million
pound change in total retail supply of raw-headless shrimp changes
retail price in the opposite direction by .36 cents. This represents a
flexibility estimate of -.058. This is in contrast to the insignifiance
found for the same variable in the 31-40 size class retail model. A one

150
unit change in the consumer price index for meat and poultry results in
retail price changing in the same direction by .20 cents. This
represents a price flexibility of .067. This coefficient may simply be
capturing the positive correlation over time between shrimp prices and
meat and poultry prices. Retail prices, however, appear to be very
inelastic to changes in supply and price of competing meat products.
The flexibility estimate for CPIt derived for the 21-25 size class was
much smaller than that derived for the 31-40 size class, which indicates
retail price for the 31-40 size class products is much more sensitive to
changes in the prices of competing meat products. This observation, of
course, assumes that indeed a substitution effect is being captured by
the parameter estimate for CPIt. This contrast in findings for the 21-
25 and 31-40 size classes suggests that the smaller shrimp are viewed as
less of a luxury item and compete with meat and poultry in a more direct
sense for consumer budget expenditures than do the larger, more
expensive 21-25 count shrimp. The estimated coefficient on the income
parameter RDYfc was found to be of the negative sign and thus assumed to
be insignificant. This same negative relationship was found with the
31-40 quarterly retail model. In addition, income was found to be
insignificant in the monthly retail price models. This suggests that a
monthly or quarterly sampling period is not of sufficient length over
the time period of the analysis to capture the relatively stable effect
of monthly and quarterly real disposable income on retail demand.
However, studies done by Doll (1972), Hopkins et al. (1980), and Cleary
(1969) have found real disposable income to be significant on an annual
basis

151
Wholesale structural estimates
The empirical parameter estimates and the corresponding standard
errors of the wholesale price model are given as
W =* .048 + .356 R + .798 P - .300 R + .146 W
C (.202) (.195) t (.131) C (.162) t-i (.052) t"1
- .0011 BSFF + .0008 01 - .0025 121 + .0015 TMCI
(.0019) C (.0019) C (.020) (.0010) C
where the values in parentheses are the standard errors. Seven of the
nine estimates have the anticipated sign.
Retail price was found to be a more important determinant of whole¬
sale price for the 21-25 size class than for the 31-40 size class. A
one cent change in retail price caused current wholesale price to change
in the same direction by .36 cents. This one cent change in retail
price was shown to not have a further significant effect on wholesale
price in the next period, as indicated by the negative estimated coeffi¬
cient of the parameter The estimated elasticity of price
transmission between current retail and current wholesale price was
found to be .502. Though inelastic, change in retail price was shown to
be much more important to the determination of wholesale price for the
21-25 size class product than for the 31-40 size class product.
Ex-vessel price was found to be an important determinant of whole¬
sale price. A one cent change in current ex-vessel price was found to
change current wholesale price by .80 cents in the same direction. This
elasticity of price transmission indicates that a one percent change in
ex-vessel price will change wholesale price in the same direction by .68
percent. Thus, ex-vessel price appears to have a larger impact on
wholesale price than does retail price.

152
Factors which affect current wholesale price were found to have an
additional positive impact on wholesale price in the next period.
Specifically, given that these factors have caused current wholesale
price to change by one cent, the estimated coefficient for Wt_^
indicates that a further change in wholesale price in the same direction
of .15 cents will follow in the next period. However, the carry-over
effect is relatively small. The elasticity of price transmission
between lagged and current wholesale price was estimated to be .145.
Wholesale price lagged one period (Wfc_^) was originally included due to
first order serially correlated errors found for the wholesale price
model.
Wholesale price was found to have a negative relationship with
beginning inventories of raw-headless product (BSFFt) and imports of
raw-headless product (12lt). A million pound change in beginning
inventories and imports of 21-25 size shrimp causes wholesale price to
change in the opposite direction by .11 and .25 cents, respectively.
Total imports of all other sizes of raw-headless shrimp (0It) had an
insignificant impact on the determination of wholesale price and the
wrong sign on the coefficient. This same result was found in the
wholesale model for the 31-40 size class and in the monthly analysis.
The parameter 0It may simply be capturing the positive correlation over
time between total imports and wholesale price. Wholesale price was
anticipated to have a negative relationship with total imports, such
that as the total amount of imports increased, wholesale price would be
bid down.
Wholesale price was shown to have a positive relationship with the
costs of intermediate goods and services in wholesaling and

153
processing. The estimated coefficient for the cost parameter TMCIt
indicated that a one unit change in the intermediate goods and services
index causes wholesale price to change by .15 cents in the same direc¬
tion. This estimate is much greater than the value of .03 found for the
31-40 size class. Thus, these costs appear to be of greater importance
to the wholesale price determination process for the larger size
shrimp. This finding may be partially explained by the differing lag
structure found in the wholesale price model for each size class. The
21-25 size class wholesale price model included wholesale price lagged
one period, whereas the 31-40 size class model did not. The variable
Wt-i was included due to the presence of first order serially correlated
error terms in the wholesale price model in the absence of Wt_^. The
significant estimated coefficient on the variable suggests that the
larger shrimp do not move through the market as fast as the smaller size
shrimp. The larger shrimp, therefore, may be held up in the inventory
longer and incur larger interest costs on a per pound basis. With
interest cost being a component of the aggregate cost index TMCIt,
wholesale prices may be more sensitive to changes in this cost of inven¬
tory due to a slower market turnover rate.
Ex-vessel structural estimates
The empirical parameter estimates and the corresponding standard
errors of the ex-vessel price model are given as
P = .120 + .861 W - .0011 OL - .0188 L21 - .00025 TMCI
t (.068) (.027) C (.0011) t (.0078) (.00057) C
where the values in parentheses are the standard errors. All five of
the estimated coefficients had the anticipated sign.

154
Ex-vessel price was shown to have a very strong positive relation¬
ship with wholesale price. A one cent change in current wholesale price
was found to cause ex-vessel price to change in the same direction by
.86 cents. This represents an elasticity of price transmission between
ex-vessel and wholesale price of 1.01. This finding is virtually iden¬
tical to the elasticity value found for the 31-40 size class. Thus, ex¬
vessel and wholesale prices follow one another very closely when the
causal shock originates from wholesale price. As indicated by the
smaller estimated coefficient and corresponding elasticity of price
transmission for ex-vessel price in the previously discussed wholesale
demand model, wholesale prices do not follow ex-vessel price changes as
closely.
Both landings of 21-25 size shrimp (L21t) and total landings of all
other size shrimp (0Lt) had the anticipated negative relationship with
ex-vessel price. A one million pound change in landings of 21-25 shrimp
changes ex-vessel price in the opposite direction by 1.88 cents.
Whereas a one million pound change in the total landings of all other
size classes of shrimp changed ex-vessel price in the opposite direction
by .11 cents. This latter effect is only weekly significant. The
percentage impact on ex-vessel price is almost twice as large for a
percentage change in own-size landings (-.021) as that for other size
landings (-.012).
Ex-vessel price was found to be inversely related to costs of
intermediate goods and services (TMCIj.) A one unit change in the index
for the costs of intermediary goods and services causes ex-vessel price
to change in the opposite direction by .03 cents. The price flexibility
estimate -.02 suggests that ex-vessel price, as was wholesale price, is

155
very inelastic to changes in these intermediate costs. The findings for
the 21-25 size class wholesale and ex-vessel prices regarding TMCIt are
in agreement with the findings of the 31-40 size class models.
Reduced and final form estimates
The reduced form and final form coefficients and price flexibility
estimates corresponding to the structural coefficient estimates for the
retail, wholesale, and ex-vessel price models were obtained. A review
discussion on the definition and general interpretation of reduced and
final form estimates was presented for the 31-40 size class analysis and
will not be repeated here. Due to the presence of lagged endogenous
variables in the retail and wholesale price expressions, the reduced
form estimates are intermediate and presented in Appendix D. The fol¬
lowing discussion will be oriented toward final form estimates.
The final form estimates indicate the long-run impact that each
predetermined variable has at the three market level (Table 14). As
with the 31-40 models, a lag of only one period was incorporated into
the final form estimates. Retail and wholesale price, however, were
both lagged a single quarter for the 21-25 models. The cumulative final
form estimates were larger in an absolute sense than the reduced form
estimates, reflecting the impact of these additional lag periods. In
addition, the final form coefficient estimates and flexibilities for the
retail level were found to be larger than the respective estimates at
wholesale or ex-vessel levels.
All quantity variables, with the exception of other size imports
(0It), have the expected negative sign. A one million pound increase in
landings of 21-25 count shrimp was shown to decrease retail, wholesale,

Table 14: Final Form Coefficients and Flexibility Estimates for the Retail, Wholesale and Ex-vessel
Price Models for the 21-25 Size Class.
Jointly Predetermined Variables
Determined
Variables
RDYt
TCFFt
CPIt
BSFFt
oit
I21t
0Lt
L21t
TMCIt
Rt
-.0028a
-.0274
.0152
-.0239
.0173
-.0542
-.0189
-.3247
.0273
1
(-.4920)b
(-.4410)
(-.2630)
(.1930) i
(-.0247) 1
(-.1250) l
(-.2200)
Wt
-.00094
-.0092
.0051
-.0145
.0106
-.0333
-.0116
-.1987
.0167
1
(-.2330)
(-.2090)
(-.2250)
(.1670) i
(-.0230) I
(-.1080) l
(-.1900)
Pt
-.00081
-.0079
.0044
-.0125
.0091
-.0286
-.0111
-.1900
.0141
f
(-.2360)
(-.2110)
(-.2280)
(.1690)
(-.0230) i
(-.1220) i
(-.2130)
aEstimated final form coefficient.
^Estimated flexibility derived at the means.
156

157
and ex-vessel price by 32.5, 19.9, and 19.0 cents, respectively. The
corresponding price flexibilities at the retail, wholesale and ex-vessel
levels were -.22, -.19, and -.21, respectively. In a relative sense
between predetermined variables, the price flexibility estimates for
own-size landings (L21t), beginning stocks (BSFFt), and retail supply
(TCFFt) indicated that these parameters have approximately the same
impact on price at all three levels. The retail flexibility is slightly
higher for the retail supply, indicating a greater sensitivity at the
retail level. The estimates for own-size imports (I21t), other-size
imports (0It) and landings of other-size shrimp (0Lt), indicate that
changes in these variables have a relatively smaller impact on prices at
each market level. A one-unit change in the marketing cost variable
TMCIt causes a change in the same direction in retail, wholesale, and
ex-vessel price of 2.7, 1.7, and 1.4 cents, respectively, which are
substantially larger than that estimated for the 31-40 size class. The
coefficient estimates at all market levels are positive for the CPIt
variable, indicating substitution between shrimp and competing meat
products. Note tha-t flexibilities are not estimated for CPIt and TMCIt
since these variables are already in percentage terms.
Margin estimates
The margin expressions representing retail/wholesale and whole¬
sale/ex-vessel price spreads were obtained from the final form estimates
for the three market levels. The methodology utilized for deriving the
coefficient estimates and flexibilities contained in these expressions
was the same as that employed in the 31-40 class analysis.

158
The coefficient estimates and margin flexibilities obtained for the
retail/wholesale margins were larger than for the wholesale/ex-vessel
margin (Table 15), as was found in the margin analysis for the 31-40
size class prices. This finding appears to result from retail
(wholesale) price being relatively unresponsive to changes in wholesale
(retail) price, while wholesale and ex-vessel prices follow each other
closely, thus allowing a more steady margin between ex-vessel and
wholesale price. The 31-40 size class prices were similar in this
respect. In addition, retail price is much more sensitive to changes in
the predetermined variables than are either wholesale or ex-vessel
prices. In fact, the latter two prices are approximately equal in terms
of flexibility to changes in each predetermined variable. These two
conditions combine to cause the margin between retail and wholesale
prices to be more sensitive to changes in the predetermined variables
than is the margin between wholesale and ex-vessel prices.
The retail/wholesale margin was found to be relatively sensitive to
»
changes in TCFFt. A one million pound increase in retail supply of raw-
headless shrimp of all sizes decreases the margin by 1.8 cents. This
estimate corresponds to a margin flexibility estimate of -1.01. This
estimate approximates unitary flexibility. In contrast, Mwp is not as
sensitive to changes in TCFFt. The same shift in TCFFt produced a -.13
cent change in Mwp. This coefficient corresponds to a margin
flexibility estimate of only -.199 percent. A one unit change in price
index for competing meat products (CPIt) changes Mâ„¢ and Mwp in the same
direction by 1.01 and .07 cents, respectively. Thus, the wholesale/ex¬
vessel margin is not as sensitive to shifts in factors which determine
retail demand. Real disposable income (RDYt) was found to be

Table 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.
Predetermined
Variables
Margin
RDTt
TCFFt
CPIt
BSFFt
0It
I21t
0Lt
L21t
TMCIt
Mâ„¢
-.00186a
(-1.121)b
-.0182
(-1.005)
.0101
-.0094
(-.355)
.0067
(.257)
-.0209
(-.035)
-.0073
(-.166)
-.1260
(-.293)
.0106
MWP
-.00013
(-.217)
-.0013
(-.199)
.0007
-.0020
(-.209)
.0015
(.159)
-.0047
(-.022)
-.0005
(-.031)
-.0087
(-.056)
.0026
aFinal form margin estimate.
^Flexibility derived at the means.
159

160
insignificant at the structural level and, thus, is insignificant in the
margin analysis.
Both margins were found to be inversely related to beginning stocks
(BSFFt), own-size imports (I21t), total other-size landings (0Lt), and
own-size landings (L21t). A one million pound increase in beginning
stocks was found to decrease Mwr and by .94 and .20 cents, respec¬
tively. In terms of margin flexibilities, a one percent increase in
beginning stocks will decrease Mwr and by .36 and .21 percent,
respectively. A one million pound increase in own-size imports was
shown to decrease M1^ and by 2.09 and .47 cents, respectively.
These estimates correspond to Mâ„¢ and flexibilities of -.035 and
-.022 percent. A one million pound increase in own-size landings
decreased Mrw and MWP by 12.6 and .87 cents, respectively. The
corresponding flexibilities for M1^ and are -.293 and -.056 percent,
respectively. Changes in other-size landings had an inverse relation¬
ship with the margins, though the impact was less than for changes in
the other quantity variables.
Both margins were found to be positively related to changes in
marketing costs. As TMCIt changes by one unit, M1^ and change by
1.06 and .26 cents, respectively, in the same direction. The 21-25 size
class margins were found to be more sensitive to changes in the inter¬
mediate marketing costs than were the 31-40 size class margins. Since
both size classes of shrimp are being analyzed as being raw-headless,
the observed disparity in sensitivity to changes in Intermediate
marketing costs is not due to differing product form. The response
differences are more likely due to the larger shrimp being held in
inventory longer and incurring increased storage costs, which are
embodied in the TMCIt parameter.

CHAPTER VII
SUMMARY AND CONCLUSIONS
The domestic shrimp industry is the most valuable commercial fish¬
ing industry in the United States. Domestic production, however, repre¬
sents less than half of the domestic consumption of shrimp products over
the last two decades. More recently, imports have represented over 70
percent of the market. Though prices have generally trended up over the
last ten years, producers of shrimp products have been experiencing
economic hard times brought on by fluctuating prices, increased costs of
production, over capitalization, and fully exploited stocks. In addi¬
tion, retailers, wholesalers, and processors have had to endure
increased costs of labor, energy, and cost of holding inventories, as
well as periods of general economic recession. In an attempt to counter
these undesirable market conditions, policy makers have suggested price
oriented measures such as market promotion, import control, and
increased producer market coordination as means by which to stabilize
and boost prices.
To fully understand the impact such policy measures will have on
price at each market level, an understanding of the dynamics of prices
in the shrimp market system is crucial. Previous research on the domes¬
tic shrimp market system has failed to focus on important aspects of
price dynamics, particularly the direction of price determination, the
nature of lead/lag relationships and the determinants of prices and
margins at various market levels on a size class basis. The purpose of
161

162
the present study was to fill this void in the basic understanding of
how prices and price spreads by size class of shrimp behave across
market levels.
Analysis of Price Determination
â– *
Causality and Asymmetry Analysis
Unidirectional causality in the absence of feedback such that ex¬
vessel causes wholesale price and wholesale causes retail price general¬
ly characterized the monthly data. An exception to this was the rela¬
tionship between ex-vessel and wholesale price for the 21-25 size class.
These findings suggest monthly price determination was unidirectional
from ex-vessel to wholesale price and wholesale to retail price. Unidi¬
rectional causality was not found to characterize quarterly prices for
either size class. The ama;usos found that quarterly ex-vessel, whole¬
sale, and retail prices are instantaneously related only.
The impulse response functions of the monthly and quarterly price
data suggested that the 21-25 size class prices are characterized by a
slower adjustment process than the 31-40 size class, with respect to
price changes at adjacent market levels. In addition, on a monthly
basis the retail/wholesale relationship for both size classes requires
more time to adjust.
Asymmetry was found not to characterize the retail/wholesale price
and wholesale/ex-vessel price relationships. Price movements between
market levels appear to be passed equally regardless of whether causal
prices are rising or falling.
The findings of the causality and asymmetry analysis indicate that
neither monthly nor quarterly price determination is dominated by the

163
wholesale market level—a finding contrary to some Industry allega¬
tions. The wholesale market level is more concentrated relative to the
retail and producer level (Hu, 1983). In this sense, the wholesale
market level is suspected to have acquired some power over buying and
selling functions and thereby may be exercising some control over the
pricing process. Acting as a price leader, wholesaler-processors may be
able to pass costs up via higher selling prices and pass costs down via
lower buying prices. In this capacity, the wholesaler-processor market
level would be acting as a causal node in the market place with the
other market levels in a lag position. Dominance by the wholesale level
in pricing is in general rejected given the upward and symmetric nature
of monthly price determination and the simultaneous nature of quarterly
price determination.
Though monthly prices are characterized as upward recursive from
the producer level, caution must be taken not to immediately suspect
that the producer (ex-vessel) level has omnipotent control over short
run price determination. On the contrary, vessel operators are in
general price takers with few market outlet alternatives for a highly
perishable product. This is particularly true when considering that
producer cooperatives are the exception rather than the rule. In addi¬
tion, other forms of market cooperation (market orders, agreements,
etc.) are virtually non-existent in the shrimp industry. Rather, the
effects of monthly supply shifts, which originate at the producer level
and are closely linked to shifts in the environmental conditions, tend
to dominate the primary and derived demand shifts which originate at the
upper market levels. Possibly, initial buyers of raw product are acting
on expectations of how the upper market levels will be reacting, thereby

164
establishing a lead position at the producer level. In addition, the
sampling interval may not be long enough for primary demand shifters to
exhibit a significant impact at lower market levels. This appears to be
particularly true on a monthly basis. The sampling interval of the
quarterly data appears to be long enough for price determination to
become less recursive and more interdependent in nature. Over quarters,
no one market level appears to dominate the price determination pro¬
cess. This may be due to primary demand shifters having enough time
within a quarter to enter into the decision making processes at lower
market levels.
Factors of Price Determination
The quarterly expressions for retail, wholesale, and ex-vessel
prices for both size classes were estimated using three-stage least
squares. Monthly expressions were estimated using ordinary least
squares. Given the findings from the causality analysis on quarterly
and monthly data, the price expressions were specified as simultaneous
and recursive, respectively, in price for both size classes.
Price linkages between wholesale and ex-vessel market levels were
found to be stronger than between retail and wholesale market levels, as
indicated by the derived elasticities of price transmission. Ex-vessel
(wholesale) price is a very important determinant of wholesale (ex¬
vessel) price, whereas wholesale price was a less important determinant
of retail price. The retail market, thus, appears to be more of an
isolated market. Wholesalers and producers appear to be very much
interdependent and closely linked when formulating price at the respec¬
tive market levels

165
Monthly prices at the retail, wholesale, and ex-vessel market
levels appear to be closely related to factors which affect own-market
level price in the previous period. Quarterly prices for either size
class do not consistently exhibit this characteristic. Quarterly prices
also have a shorter lag structure on causal price than monthly prices.
On a size class basis, quarterly prices for the larger shrimp require a
longer lag structure on causal price than do quarterly prices for the
smaller shrimp. These findings on a size class basis are consistent
with the monthly price models. The indicated lag structures suggest
that monthly and quarterly prices for the larger size shrimp require at
least one additional time period for current market information to be
incorporated into the price making process. The slower adjustment in
prices suggests the larger shrimp are being held in inventory longer,
with the smaller more versatile shrimp being pushed to the retail market
in a shorter period of time.
Real disposable income was found to not be a significant deter¬
minant of monthly or quarterly prices for either size class. This
finding reflects the fact that real disposable income changes very
little on a monthly or quarterly basis over the time period of the
analysis. Previous monthly and quarterly analyses corroborate the
Insignificance of income while studies using annual data typically find
income as significant. The price index for competing meat products was
found to have greater effect on quarterly prices for the smaller size
class, suggesting a greater degree of substitutability between the
smaller shrimp and other meats than for the larger shrimp. Monthly
estimates indicated little difference by size class.

166
In general, total supplies, beginning inventories, imports and
landings of raw-headless shrimp had the anticipated negative relation¬
ship with the respective price. An exception to this general finding
was the positive estimate for imports of all other sizes of shrimp.
Total supply of raw-headless shrimp on the retail market was found to
negatively impact prices for both size classes, with a larger impact on
the 21-25 size class. This was found to be true for the monthly and
quarterly estimates and the derived price flexibilities. In the absence
of significant cross effects, the inverse of the price flexibility
estimate represents the lower limit of the price elasticity. Therefore,
demand for the 21-25 size class shrimp appears to be more inelastic than
for the smaller 31-40 size count shrimp, which suggests that the smaller
shrimp substitutes with other size classes more easily. This conclu¬
sion, plus the greater substitutability of small shrimp with other meat
products, suggests a more isolated market for the larger shrimp.
Beginning inventories were found to have a negative impact on both
size classes, but a much larger unit and percentage impact on the prices
for the smaller shrimp. This suggests that as inventories increase,
prices of the smaller shrimp vary more, possibly through increased
promotional efforts to clear out unwanted stocks of small shrimp. As
was indicated in the monthly analysis for retail price, the smaller
shrimp appear to be a greater competitor with other meats for a share of
the consumer's budget than are the larger shrimp. Therefore, whole¬
salers may be more willing to adjust prices for the smaller shrimp to
reduce inventories during periods when stocks are building. This find¬
ing, coupled with the indicated shorter lag structure on the 31-40 size
class, suggests that wholesalers attempt to move the smaller shrimp

167
through the market at a faster pace than the larger shrimp. If smaller
shrimp are perceived as less of a luxury item than larger shrimp, whole¬
salers may be more able to market these smaller shrimp in food stores on
a larger scale than they could larger shrimp.
Imports of own-size shrimp were found to have a negative impact on
prices for both size classes, however, the impact is much larger for the
smaller size shrimp. The average volume of classified shrimp imports
from 1972 through 1982 in the 31-40 size class is 30 percent greater
than the amount imported for the 21-25 size class. However, on a rela¬
tive basis imports are more important to the 21-25 size class. Over the
same period an average 42 percent of the supply of 21-25 size class raw-
headless shrimp was imported, while only 36 percent of the supply of 31-
40 size class shrimp was imported. This relationship may be particular¬
ly important in the future since much of the shrimp produced in maricul-
ture systems will be in the 31-40 size class. Imports of all other size
classes of shrimp had a positive relationship with price for both size
classes, illustrating how demand and supply of imported product have
simultaneously increased over the period of the analysis. To separate
these effects, simultaneous estimation of both demand and supply func¬
tions is necessary, however, sufficient data for proper specification by
size class are not available.
Landings of own-size shrimp had a larger impact on prices of the
smaller size class of shrimp, both in terms of unit and percent changes.
Thus, prices for the smaller size shrimp are much more sensitive to
changes In own-size landings. This finding has particular relevance
when considering the impact of policy measures which seek to alter the
size distribution of shrimp taken (Texas Closure). Total landings of

168
all other size classes appear to have essentially the same impact on
both size classes.
The marketing cost index was found to have a positive impact on
quarterly prices at the retail, wholesale and ex-vessel level for each
size class. The monthly analysis found a positive impact at the whole¬
sale level and a negative impact at the ex-vessel level. This discre¬
pancy probably results from this index being a relatively poor represen¬
tation of processing and marketing costs for this classification of
seafood (raw-headless shrimp). The impact of changes in the marketing
cost index on the 21-25 size class was much larger than for the 31-40
size class, again suggesting that the larger shrimp are held in inven¬
tory longer, thereby incurring increased interest and other holding
costs.
Margin Analysis
Marketing margins were derived from the final form estimates as the
retail/wholesale (Mâ„¢) and wholesale/ex-vessel (M^P) price spreads for
each size class. Margins were inversely related to changes in quantity
variables, with the exception of imports of all other size classes.
These findings suggested possible economies of size in handling quanti¬
ties of shrimp. The Mâ„¢ was found to be much more flexibile to changes
in quantities than was MWP because retail and wholesale prices are not
as closely related as was the wholesale and ex-vessel prices. Both
margins for each size class were found to be especially sensitive to
change in own-size landings and imports. Changes in marketing costs had
a greater impact on both margins for the 21-25 size class product, with
a larger impact on the retail/wholesale margin. Total supply of shrimp

169
on the retail market had, in general, an inverse relationship with both
margins. However, changes in total retail supply had a small positive
relationship with Mâ„¢ for the 31-40 size class. Due to questionable
results for real disposable income and the index of prices for competing
meat products at the structural and final form stages of the analysis,
these parameters are interpreted as to have little impact on margins
over quarterly intervals.
Methodological Conclusions
The study provided some insight on methodological concerns regard¬
ing the appropriate specification of price dependent demands for raw-
headless shrimp on a monthly and quarterly basis. These findings on
direction and factors of price determination should provide some guid¬
ance for specifying models of additional size classes and for different
product forms when the data become available.
The findings of the monthly tests in general suggest an upward
recursive relationship between prices at the three market levels. Thus,
an appropriate specification for prices of both size classes would be
such that wholesale and retail prices are some distributed lag function
of ex-vessel and wholesale prices, respectively. An exception to this
is the relationship characterizing the ex-vessel and wholesale prices
for the larger size class. These prices appear to be simultaneously
related. The findings of the causality tests on quarterly prices at the
three market levels also Indicated an interdependent or simultaneous
specification would be most appropriate.
The inclusion of lagged own price was also found to be important,
even in a simultaneous setting. The tests for asymmetry indicated that

170
price dependent demands should be specified in symmetric form—at least
on a monthly basis*
Income was found not to be a significant determinant of price on a
monthly or quarterly basis* Thus, the use of price dependent demands
using monthly or quarterly data to address income related issues in the
market for a given product form and size class of shrimp (particularly
those analyzed in this study) may not be appropriate.
Total imports were found to be positively related to price. There¬
fore, addressing questions concerning the aggregate import market with
recursive or simultaneous price models only is not appropriate. A
morecomplete model of supply and demand appears necessary.
Policy Implications
One of the primary purposes of this study was to evaluate the
differential impacts of variables of concern on price at each market
level. Prior knowledge of these differential impacts is necessary for
the prediction of changes in a given price to a change in a specific
variable. This information is also vital to understanding changes in
price given a policy change which may indirectly effect the market at
more than one level.
The estimated price relationships suggest all market levels are
impacted by changes in policy measures. Impacts are nearly equal at the
wholesale and ex-vessel levels with considerably higher impacts at the
retail levels. Impacts at the retail market levels will likely take
longer to be fully realized.
No one market level appears to have sufficient market power to
acquire an unequal share of the costs and benefits of increased or

171
reduced trade. On a month to month basis, it appears that one market
level will lead another in determining prices. This probably is due to
factors other than market power, such as wide month-to-raonth variations
in landings, response time and time required for market information to
fully permeate the system. The latter criteria is suggested by the
recursive nature of monthly price changes compared to the simultaneous
nature of quarterly price movements. Although prices are simultaneously
determined on a quarterly basis, price increases from restrictive trade
policies can be passed on to higher market levels with proportionately
larger price increases. This is particularly true for the larger
shrimp. The symmetric nature of price changes found in the analysis
suggests price increases resulting form decreased imports will be sub¬
stantially larger at higher market levels. In addition, given the
weaker linkage between retail and wholesale prices than is found between
wholesale and ex-vessel prices for both size classes, policy measures
administered at the retail level (market promotional programs) may have
less of an impact on the total system than will policy measures admin¬
istered at the lower market levels, such as implementation of coopera¬
tives or market orders.
Although the direction of price impacts are generally the same for
the two size classes analyzed, there are some differences in terms of
the magnitude of the effects. The 31-40 count shrimp market appears to
be much more affected by changes in imports. This is particularly
troublesome considering that this market is already subject to wider
price responses than the 21-25 count shrimp market for comparable
changes in quantities in the domestic market. The 31-40 count shrimp
market will most likely be disproportionately impacted by new maricul-
ture production which is expected to produce shrimp of similar size.

172
The differing magnitude of price responses for the 31-40 and 21-25
count shrimp to changes in various causal factors is useful in assessing
the market impacts of other policy measures. One such policy measure is
the ban on shrimping in the Fisheries Conservation Zone off the coast of
Texas during a period in the summer season—otherwise known as the Texas
Closure. The goal of the closure is to increase the quantity of large
shrimp available for harvest in Texas and surrounding waters by protect¬
ing smaller juvenile shrimp early in the season. This is of particular
interest to this study in that one of the two size classes most affected
by the 1981. Texas Closure was the 31-40 size class (Klima, Baxter, and
Patella, 1982). Given that the predominant size count of shrimp caught
in Texas and Louisiana waters during the months immediately following
the closure are of the 31-40 size class, the market for the 31-40 count
shrimp may realize a larger impact due to policy measures, such as the
Texas Closure, that alter the size distribution harvested. Public
officials may want to reconsider this policy, especially when consider¬
ing this size class will most likely be affected by imports resulting
from expanded shrimp marlculture production.
The analysis has shown that prices at each market level are, in
general, inversely related to quantities. Further, the margin analysis
indicated an inverse relationship between quantity and margins, with
changes in quantity causing prices to change more at upper market
levels. Thus, restrictive trade policies would have the effect of
decreasing available supplies, increasing prices, and increasing the
price spread. The price spread is made up of profit and cost compon¬
ents. Under the assumption that the market is competitive, profits are
reduced to only normal rates of return. Changes in the price spread

173
will then be due to changes in the cost component. Assuming the market
for raw-headless shrimp is functioning competitively, the findings in
the margin analysis suggests that inefficiencies may arise in the whole¬
sale-processing sector as quantities are reduced; e.g. through an import
quota. Therefore, a reduction in imports may be initially beneficial to
producers but of questionable short-run benefit to wholesalers and
processors. In the longer run, inefficient firms may be eliminated,
resulting in a reduction in competition among the remaining more effici¬
ent firms. Reduced competition and higher prices may result in a grow¬
ing profit component.
Suggestions for Future Research
Proper identification of causal direction was vital to this study.
Similarly, the analysis of causality using the Granger, Sims and Haugh-
Pierce methods was dependent on the stationarity and white noise proper¬
ties of the time series of interest. Properly filtering these series is
a crucial step. However, as Fiege and Pearce (1979) have noted, the
causality tests are conditional on the specific ARIMA filters used. As
Pindyck and Rubinfeld (1981) point out, using the Box-Jenkins method of
identifying the ARIMA filter requires some subjectiveness when deciding
on the final specifications. Hsiao (1979) and Bessler and Schrader
(1980) point out that the Akaike (1970) autoregressive predictive error
criterion, which removes some of this subjectiveness from the estimation
of time series filters, may be a better procedure. Utilizing both
approaches in future studies would provide a check for robustness in
filter estimation. The possibility of utilizing an inappropriate filter
is particularly of concern when considering the importance of the filter

174
in the derivation of impulse response functions which provide exact
specification of the distributed lag relationship between the two time
series.
The empirical identification of a directional or "causal" relation¬
ship is by no means a definitive indication of a cause and effect rela¬
tionship between two variables. An empirical analysis of causality by
itself only allows for inferences regarding lead/lag structures which is
simply an additional piece of information regarding model specifica¬
tion. The assessment of a true causal linkage between two variables is
a theoretical question and is only supplemented by the empirical analy¬
sis. The causal findings of this study should be viewed in this sense.
The analysis could have benefitted from a more representative
sample of prices at all three market levels. Retail and wholesale price
represented only the Baltimore, Maryland and New York Fulton markets,
respectively. Though prices for shrimp of a given product form may
differ primarily by transportation cost between spatially separated
markets, a more spatially representative sample of price at the retail
and wholesale market levels might provide some conclusive findings
regarding strength of causality and length of the lag structure connect¬
ing prices in adjacent markets.
Retail price is not reported by NMFS for the 31-40 size class.
Prices for the 36-42 size were used instead. Similarly, prior to 1980,
ex-vessel price is reported by NMFS as a weighted average for domestic
landings in the Gulf of Mexico and South Atlantic. For the years 1980
and after, ex-vessel price is a weighted average for landings in the
Western Gulf only. This inconsistency in ex-vessel price is noteworthy
due to varying methods of establishing dockside price among ports in the

175
Gulf. Future causality studies would benefit from the use of price
series that are deflnitionally more consistent in terras of representa¬
tive regions and size class. In addition, studies of causality on a
regional basis would provide insight into the relative importance of
major ports and major market areas to the price determination process;
i.e., lead/lag relationship between prices among major ports and among
markets.
The retail market in this study represented the food-store or
grocery sales market, which represents only 20 to 30 percent of the
total retail sales for shrimp products. The preponderance of shrimp (70
to 80 percent) are consumed in restaurants and other institutional
outlets. Thus, the price analysis in this study pertains only to a very
restricted segment of the retail market. Unfortunately, data on the
institutional price of shrimp are not available.
An obvious extension to the portion of the study concerned with the
estimation of price dependent demands would be to consider additional
size classes and product forms. An unfortunate overriding constraint is
the paucity of published price and quantity data by size class and
product form (breaded shrimp, peeled/deveined, etc.), which is particu¬
larly noteworthy for quantity data. Monthly price and quantity data
documented over a sufficient length of time to do meaningful analyses
are restricted to a very few size classes and product forms. Landings
data by size class for the Gulf and South Atlantic by size class are
available, however, retail supply and beginning inventories by size
class are not available. The "unclassified" import category has
increased to approximately 50 percent of reported imports, providing for
increased unreliability in import data by size class. There also exists

176
a shortage of quantity data on alternative product forms at retail and
wholesale market levels. Inclusion of terms representing these data in
the price models would allow more complete analysis of substitution
between size classes and product forms. Further studies into the paths
that alternative size classes and product forms take from producer or
importer to consumer need to be undertaken.
Cost data for processing, wholesaling, and retailing of shrimp
products are also scarce. More representative cost data for seafood
processing and marketing, particularly disaggregated into individual
components (labor, energy, interest, transportation, etc.) are crucial
to the further understanding of the behavior of price spreads. Such
data on costs may be superior to the intermediate food marketing cost
index for general agricultural commodities published by the USDA, which
was used in the study.
A further improvement to the model developed in this study of the
determinants of prices and margins would be to include quantity Imported
as endogenous to the model. Including import price explicitly would
allow for additional inferences to be made specifically regarding the
important import market. With prices and quantity imported both
increasing over time, as has been the case in the last decade, a simul¬
taneous model of the import market may be appropriate.

APPENDIX A
DERIVATION OF IMPULSE RESPONSE FUNCTIONS

The terms to be included in the dynamic shock model relating two
adjacent market levels are determined by examining the Haugh-Pierce
residual cross-correlations for significance. Each term is estimated by
solving for the bivariate regression coefficient (X^) which is a
function of the standard deviation for each residual series and the
corresponding residual cross-correlation estimate at lag k. Once the
dynamic shock model is estimated, the respective ARIMA filter models are
substituted into the expression. The resulting expression is then
solved in terms of the "causal" (lagged) price. The resulting equation
is referred to as the impulse response function. The following
discussion details this procedure for each size class using monthly and
quarterly data.
Monthly Data
31-40 Size Class: Wt - f(Pt)
The implied dynamic shock model for the wholesale (Wfc)/ex-vessel
(Pt) price relationship is given as
(1) wt - (Aq - X1B)e(; + where wt and et are the residual series for wholesale and ex-vessel
price, respectively, X^ are the regression parameters to be estimated,
(B) is a polynomial in the lag operator B (which is unique to the white
noise disturbance associated with the dynamic shock model), and at is
178

179
the white noise disturbance associated with the dynamic shock model.
The parameters to be estimated are given as
A [r (0)]
0 a u we
e
H-T1 [%.«>]
where aw and ag are the standard deviations of the residual series for
A
wholesale and ex-vessel (lagged) price, respectively, and rwg(k) is the
estimated residual cross-correlation at lag k, where ex-vessel price is
the lagged price. Solving for each A^ gives
(2.1)
(2.2) X.
.129
.149
.129
1 .149
(.752) - .651
(.291) - .252
Therefore, the dynamic shock model is given as
(3) wt =» (.651 - .252 B)et + $(B)at
Replacing wt and et with the respective ARIMA filter models yields
(4) (1 - B)(l - .466B + .0928B2)wt = (.651 - .252B)(1 - B)(l - .3896B
+ ,1335B3)Pt + Performing the necessary operations to solve for wt in terms of Pt and
then simplifying yields
wt - (.651 - .203B - .058B2 + .078B3 + .006B4 - .006B5 - .005B6
- .003B7 - .002B8 - .001B9)Pt +
180
where * is the polynomial in the lag operator B resulting from the
solution process* Writing this in a more parsimonious form by dropping
all terms which are small relative to the leading parameters (less than
.1) yields
(5) Wt = (.651 - *203B)Pt + 4>'(B)at
Hereafter, only expressions (1) through (5) are given for the remaining
price relationships.
31-40 Size Class: R*. â–  F(Wt)
(1) rt - (X0 - XjB - 84B4)wt + where rt is the residual series for retail price.
172
(2.1) \) " Tl29 (*186) " *246
172
(2.2) \ “ Tl29 (,360) " ,476
172
(2.3) X4 = 7129 (*175) = *232
(3) rfc - (.246 - .476B - ,232Br)wt - <|>(B)at
(4) (1 - B)(1 - .3517B - .2759B8 + .2346B9)Rt - (.246 - .476B
- .232B4)(1 - B)(1 - .466B + .0928B2)wt + (5) R - (.246 - .504B - .240B4)Wt + 4>'(B)at
21-25 Size Class: Rt * f(Wt)
(1) rt - (XQ - XlB - X2B2 - X3B3)wt + (2.1) *o " Tllf (-100) = *099

181
(2.2) Xj - -j~- C.227) - .226
(2.3) ^2 " fiH (,389) = *388
?i s
(2.4) ^3 “ 75i§- (*129> = *128
(3) r - (.099 - .226B - .388B2 - ,128B3)wt + $(B)at
(4) (1 - B)(1 - .1944B)Rt - (.099 - .226B - .388B2
- .129B3)(1 - B)(1 - .2809B + .1127B3)Wt + <|>(B)at
(5) Rfc - (.099 - .235B) - .37lB2)Wt + 4>'(B)at
(The following discussion details the impulse response functions derived
for the ex-vessel/wholesale price relationship for the 21-25 size class
which were derived for - f(Pt) and Pt â–  f(Wt), due to indications of
simultaneity in the causality studies.)
21-25 Size Class: W =• f(Pt)
(1) wt - Oq - X1B)efc + ♦(B)a(;
?1 7
(2.1) *0 " T55F <*836> - .885
717
(2.2) X1 " 7205 (-167} “ *177
(3) w^_ * (.885 - .177B)et + $(B)at
(4) (1 - B)(1 - .2809B + .1127B3)Wt - (.885 - .117B)(1 - B)(l
- .2391B + .0979B3 + .ll45B5)Pfc + *,(B)a
(5) W - (.885 - . 140B + .099B5)Pt + '(B)at
21-25 Size Class: Pt â–  f(Wt)
et " (X0)wt + ♦^B^at
(1)

182
(2) \j =TÍI7 (*836) = *789
(3) et - (.789)wt + <|>(B)at
(4) (1 - B)(1 - .239B + .098B3 + .115B5)Pt =
(•789)(1 - B)(1 - .2809B + ,1127B3)Wt + (5) Pt = (.789)Wt + r(B)afc
Quarterly Data
31-40 Size Class: W - f(P )
(1) wt - XQet + <|»(B)at
(2) *0 “T3ÜT (*912) " *834
(3) wt =* (.834)et + ♦(B)at
(4) (1 - B)(1 - .1649B) + .3444B6)Wt -
(.834)(1 - B)(1 - .1607B3 + .4090B6)Pt + (B)at
(5) W - (.834 - .250B3 - .141B4 - .123B5)Pt + '(B)at
31-40 Size Class: Pt â–  f(Wt)
(1) et = XQwt + ij>(B)at
30 S
(2) x0 3 7279 (,912) " *998
(3) efc - (.998)wt + (4) (1 - B)Cl “ .1607B3 + .409B6)Pt =
(.998)(1 - B)(1 - .1649B + .3444B6)Wt + ♦(B)at
P - (.998 - .16SB)W + '(B)at
(5)

183
31-40 Size Class: Rt » f(Wt)
(1) rt - (\) + XiB)wt + ^B)at
•ja i
(2.1) \) " 737? (*618) = *757
•JA I
(2.2) Xj =» (.248) = .304
(3) rfc * (.757 + .304B)wt + (B)at
(4) (1 - B)(1 - .4l72B)Rt - (.757 - .304B)(1 - B)
+ .3444B6)Wt + <{>(B)at
(5) Rt - (.757 - . 113B + .263B6)Wt + +'(B)a
31-40 Size Class: Wt - f(Rt)
(1) wt " ^X0^rt + ^B^at
(2) *0 =TW (*618) " -505
(3) wt - (.505)rt + H*)at
(4) (1 - B)(1 - .1649B + ,3444B6)wt =â– 
(.505)(1 - B)(l - .4172B) + $(B)at
(5) wfc - (.505 - ,128B)rt + 21-25 Size Class: W - f(Pt)
(1) wt = (XQ - XjB - X2B2)et + KB)at
<2-i> - Tim- (-934> - i-o3°
<2-2> X1 “ T§Hf- (*X52> - -168
(2.3) \ - -jIHI (-.186) - -.205
(1 - .1649B

184
(3)
Wt
-
(1.03 - .168B + .205B )et
+ (B)at
(4)
(1
-
B)(1 + .259B4 + .334B6)Wt
+ (1.03 -
. 168B
+
• ,205B2)(1 - B)(1 + .169B2
+ .203B4
+ .425B6)Pfc + (5)
Wt
-
(1.03 - .141B + .406B2 + .
113B7)Pt 4
â–  <^,(B)at
21-25
Size
Class: Pt =- f(Wt)
(1)
et
(XQ)wt + (B)at
(2)
\>
-
:lut <-9M) -
(3)
et
-
(.847)wt + (4)
(1
-
B)(1 + .169B2 + .203B4 + .
425B6)Pt -
(
•847)(1 - B)(1 + .259B4 +
.334B6)Wt
+ (5)
Pt
-
(.847 - .143B2)Wt + 21-25
Size
Class: Rt » f(Wt)
(1)
rt
-
( \)>Wt + ^B*at
(2)
\)
-
.*3845 (‘469) - *393
(3)
rt
as
(.393)wt + (4)
(1
-
B)(1 - .460B + .154B5)Rt -
- (.393)(1
- B)(l + .259B4
■ .334B6)Wt + 4»(B)at
(5)
R
t
-
(.393 + .181B + ,119B4)Wt
+ ♦,(B)at
21-25
Size
Class: Wt - f(Rt)
wt « (Aq + \B)rt + *(B)at
(1)

185
(2.1) -7333J («469) - .560
(2.2) tHi! (,208) “ *248
(3) et - (.560 - .248B)rt + (B)at
(4) (1 - B)(1 + .2594B4 + .3342B6)Wt =
(.560 - .248B)(1 - B)(1 - .4596B + .1539B5)Rt + (B)at
Wt =* (.560 - .506B + .114B2)Rt + (5)

APPENDIX B
FINAL MODEL SPECIFICATIONS

The final specification of each model estimated is given in Chapter
VI. The non-price predetermined variables included in the final speci¬
fication of each model are as discussed in Chapter IV. The prices
(current and/or lagged) which are found in the Mj set of each price
model, however, were selected initially via the impulse response models
and statistical criteria. The models were initially estimated with the
full complement of current and/or lagged prices, as suggested by the
impulse response functions. Due to insignificance (monthly and quar¬
terly models) and difficulties encountered in obtaining final form
estimates (quarterly models) for lags greater than two, certain prices
were omitted from the final monthly and quarterly models estimated and
presented in Chapter VI. Thus, a form of pretesting was employed to
arrive at the Mj price set for each model.
Once the price models were specified, initial estimates were per¬
formed to check for serial correlation in the residuals. The total and
partial autocorrelation functions of each model were examined. In
addition, the null hypothesis of no serial dependence (white noise) was
tested for the residual series of each model using the Ljung and Box
(1978) statistic given as

188
where
n-k
1 atat-k
k-1
Z a?
k-1
where n is the number of observations in the series, k is the lag
length, m is the maximum lag, and at is the residual series. For vir¬
tually every series for which the null hypothesis was rejected, first
order autocorrelation was evident. Thus, the polynomial A(B) defined in
Chapter V is not simply equal to one. A number of methods are available
that correct for serial correlation. This study utilized both the
Cochran-Orcutt method and addition of a lagged dependent variable. The
inclusion of a dependent variable lagged one period, however, gave more
promising results, based on the resulting Ljung-Box statistic. The
results of the procedure for the monthly and quarterly data for both
size classes are given in Table B. Therefore, an additional lagged
endogenous price may occur in the of each price model due to statis¬
tical considerations.
The efficient estimation of systems of equations (this study
employed recursive and simultaneous systems) requires that the cross
correlation of error terms must be taken account. In particular, the
contemporaneous cross correlation among error texrms in a system of
models must theoretically be zero. Mehta and Swamy (1976), however,
suggest a less rigid criterion, e.g. that the contemporaneous cross
correlation between error terms be less than or equal to .30. When this
is not the case, single equation methods and 2SLS are no longer effi¬
cient. Instead, single equation and 2SLS methods should be replaced by
seemingly unrelated estimation and 3SLS methods, respectively (Pindyck

189
Table B: Ljung-Box Chi-Square Tests for White Noise on the Residuals of
the Monthly and Quarterly Retail (Rt), Wholesale (Wt), and
Ex-vessel (Pt) Models Before and After Inclusion of a Lagged
Dependent Variable.
Dependent
variable
31-40 Size
Class
21-25 Size
Class
Ba
Monthly
Ab
B
A
R
355.04*
24.05***
264.46*
5.22***
W
107.06*
26.04***
NEC
NE
P
499.47*
38.26*
NE
NE
R
73.70*
Quarterly
21.51***
65.29*
11.61***
W
12.57***
-
38.17*
26.84***
P
21.74***
-
31.02**
-
ry
aXig before inclusion of dependent variable lagged one period.
bX^g after inclusion of dependent variable lagged one period.
cNot estimated
♦Reject null hypothesis of no dependence at the .01 level
♦♦Reject null hypothesis of no dependence at the .025 level.
♦♦♦Fail to reject the null hypothesis of no dependence at the .05 level.

190
and Rubinfeld, 1981). This study found that the monthly models for both
size classes exhibited contemporaneous cross correlation of the error
terms well within the Mehta and Swamy efficiency range. Thus, single
equation methods were appropriate for the monthly models. However, the
contemporaneous cross correlation among error terms for the quarterly
simultaneous models was found to exceed the .30 value for both size
classes. Therefore, the quarterly models were estimated with 3SLS
methods

APPENDIX C
GRANGER TESTS USING DATA FILTERED
BY USING ARIMA MODELS

Table C.l: Granger Causality Tests on Monthly Ex-vessel, Wholesale, and
Retail Prices for the 31-40 Size Class Using Data Filtered
by an ARIMA Model.
A. NULL HYPOTHESIS: wholesale does not cause ex-vessel price
0 Unidirectional Test: 121 " 1.57**
B. NULL HYPOTHESIS: ex-vessel does not cause wholesale price
0 Unidirectional Test: F^ 121 “ ^«65*
C. NULL HYPOTHESIS: retail does not cause wholesale price
0 Unidirectional Test: Fj^ 121 * 0.96**
D. NULL HYPOTHESIS: wholesale does not cause retail price
0 Unidirectional Test: F^ 121 ” 3.91*
♦Reject null hypothesis at the .05 level.
**Fail to reject null hypothesis at the .10 level.
192

193
Table C.2: Granger Causality Tests on Monthly Ex-vessel, Wholesale, and
Retail Prices for the 21-25 Size Class Using Data Filtered
by an ARIMA Model.
A. NULL HYPOTHESIS: wholesale does not cause ex-vessel price
8 Unidirectional Test: 125 “ 0»87**
B. NULL HYPOTHESIS: ex-vessel does not cause wholesale price
8 Unidirectional Test: F^ 125 = 2.41*
C. NULL HYPOTHESIS: retail does not cause wholesale price
8 Unidirectional Test: F^ 125 “ 1.14**
D. NULL HYPOTHESIS: wholesale does not cause retail price
8 Unidirectional Test: F^ 125 = 3.27*
♦Reject null hypothesis at the .05 level.
**Fail to reject null hypothesis at the .10 level.

194
Table C.3: Granger Causality Tests on Quarterly Wholesale and Retail
Prices for the 21-25 Size Class Using Data Filtered by an
ARIMA Model.
A. NULL HYPOTHESIS: retail does not cause wholesale price
° Unidirectional Test: Fg = 1.18**
B. NULL HYPOTHESIS: wholesale does not cause retail price
° Unidirectional Test: F^ ^ m 0.65**
*Fail to reject null hypothesis at the .10 level.

APPENDIX D
REDUCED FORM ESTIMATES

Table D.l: Reduced Form Estimates and Flexibilities for Quarterly price Models at the Retail (Rfc), Wholesale
(Wt), and Ex-vessel (Pt) Market Levels for the 31-40 Size Class.
Endogenous
Variables
Predetermined Variables
®t-l
RDYt
TCFFt
CPIt
BSFFt
oit
1311
01^.
L31t
TMCIt
Rt
.848a
.00059
-.00057
-.0023
-.0269
.0032
-.0882
-.0027
-.0734
.0013
(.836)b
(.132)
(-.012)
(-.379)
(.045)
(-.071)
(-.021)
(-.104)
wt
.393
.00539
-.00516
-.0211
-.0485
.0057
-.1586
-.0048
-.1321
.0023
(.552)
(1.724)
(-.151)
(-.973)
(.114)
(-.181)
1
•
o
->
(-.266)
pt
.356
.00489
-.00468
-.0191
-.0439
.0052
-.1437
-.0045
-.1223
.0018
(.596)
(1.864)
(-.164)
(-1.050)
(.124)
(-.195)
(-.060)
(-.294)
aReduced form estimates.
^Flexibility estimates derived at the means.
I
196

Table D.2: Seduced Form Estimates and Flexibilities for Quarterly Price Models at the Retail (R^), Wholesale (Wt), and
Ex-vessel (Pt) Market Levels for the 21-25 Size Class.
Endogenous
Variables
Predetermined Variables
Vi
wt-l
RDYt
TCFFt
CPIt
BSFFt
oit
I31t
0L,.
L31t
-TMCIt
Rt-
.548a
.487
-.00081
-.0078
.0044
-.0037
.0027
-.0083
-.0029
-.0500
.0042
L
(.541)b
(.342)
(-.142)
(-.126)
(-.041)
(.030)
(-.004)
(-.019)
(-.033)
wt
-.335
1.020
-.00092
-.0090
.0050
-.0077
.0056
-.0175
-.0061
-.1048
.0088
(-.467)
(1.012)
(-.228)
(-.204)
(-.120)
(.088)
(-.012)
(-.057)
(-.099)
Pt
-.288
.878
-.00079
-.0077
.0043
-.0066
.0048
-.0150
-.0064
-.1091
.0073
(-.471)
(1.023)
(-.230)
(-.205)
(-.120)
(.089)
(-.012)
(-.070)
(-.121)
aReduced form estimates.
^Flexibility estimates derived at the means.
197

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Journal of

BIOGRAPHICAL SKETCH
Charles Marcus Adams was born to Odice ("Skeet”) and Ophelia Adams
on June 1, 1954, in Houston, Texas. He graduated from R.L. Turner High
School in Farmers Branch, Texas, in June, 1972. He received the
Bachelor of Science degree Cum Laude in wildlife and fisheries science
with a fisheries option from Texas A&M University in May, 1976. He also
received the Master of Science Degree in agricultural economics from
Texas A&M University in December of 1978. From 1978 through 1980, he
served as research associate in the Department of Agricultural Economics
at Texas A&M University. From 1972 through 1980, his skills as a duck
hunter par excellence were honed on the Brazos River bottom.
In September 1980, Chuck entered the Food and Resource Economics
Department at the University of Florida to pursue the Ph.D. with an
interest in marine economics. He served as graduate research assistant
until September, 1984, when he accepted the position of marine economics
specialist with the Florida Sea Grant program.
Chuck married the voluptuous former Sherry Annette Densmore, a
native of Buffalo, New York, in June, 1979. His permanent address is
5418 S.W. 80th Sfreet, Gainesville, Florida 32608.
206

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
Fred J. Hjrochaska, Chairman
Professor of Food and Resource
Economics
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
—"V
Thomas H. Spreen
Associate Professor of Food and
Resource Economics
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
James C. Cato
Professor of Food a^d Resource
Economics

I certify that I have read this study and that in ray opinion it
conforms to acceptable standards of scholarly presentation and is fully
adequate, in scope and quality, as a dissertation for the degree of
Doctor of Philosophy.
/
zl
W.''Steven Otwell
Associate Professor of Food Sciences
This dissertation was submitted to the Graduate Faculty of the
College of Agriculture and to the Graduate School, and was accepted as
partial fulfillment of the requirements for the degree of Doctor of
Philosophy.
December, 1984
Dean for Graduate Studies and Research

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UNIVERSITY OF FLORIDA
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