A dynamic econometric model of the U.S. shrimp market

MISSING IMAGE

Material Information

Title:
A dynamic econometric model of the U.S. shrimp market
Uncontrolled:
Shrimp market
Physical Description:
ix, 158 leaves : ill. ; 28 cm.
Language:
English
Creator:
Lea, John Dale, 1947-
Publisher:
s.n.
Publication Date:

Subjects

Subjects / Keywords:
Shrimp industry -- Econometric models -- United States   ( lcsh )
Shrimp fisheries -- Economic aspects -- United States   ( lcsh )
Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
Genre:
bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
Statement of Responsibility:
by John Dale Lea.
General Note:
Typescript.
General Note:
Vita.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001079344
oclc - 19087114
notis - AFG4276
System ID:
AA00002144:00001

Full Text












A DYNAMIC ECONOMETRIC MODEL
OF
THE U.S. SHRIMP MARKET













By


JOHN


DALE


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


1988
















ACKNOWLEDGEMENTS


wish


to express


sincere


appreciation


to Dr.


Scott


Shonkwiler


diligent,


helpful,


cooperative


guidance


maj or


professor


during


the development


of this


dissertation,


two presentation


papers,


extra


Grant


proposal.


wish


express


appreciation


to Drs.


Maddala,


C. Cato


, R. L. Kilmer,


and T


. G.


Taylor


dedicating


time


serve


on my


advisory


committee


and for


their


helpful


comments


during


preparation


of the dissertation.


would


like


acknowledge


assistance


received


from


Drs.


John


Vondruska


and John


Poffenberger


the National


Marine


Fisheries


Service.


These


gentlemen


provided


most


of the data


used


in the study.


would


especially


like


thank


Roberts


of Louisiana


State


University


allowing


use,


misspecification


test


demonstrated


herein,


leadership.


simultaneous


Roberts


also


equation


provided


model


data


developed


used


under


to estimate


their


model.


Special


thanks


to Dr.


"Chuck"


Adams


very


tolerantly


allowed me


also

also


office


provided


goes


space


a great


to Dr. Jim


access


deal

Cato


to his library


of friendship.

and the Florida


My very

Sea Gran


and his

sincere

t Program


computer.


appreciation

and Dr. Max


Langham,


John


Gordon,


Larry


Libby


of the Food


and Resource


Economic


s Department


financial


suDDOrt


that


made


Ph.D.








Finally


would


like


thank


mother,


Mrs.


Luana


Lea;


mother-


father- in-law


Mrs.


Shattuck;


children,


Christopher,


Georgia,


and Margaret;


rest


extended


family


for their moral


support


during


this


unusual


adventure.


greatest


appreciation


goes


wife,


Marion,


unfaltering


love


support


through


these


four


years


of intense


study.


thank


for the


many


sacrifices


she has


made


to allow me


pursue


my goals.


could not


have


done


it without Marion.

















TABLE


OF CONTENTS


ACKNOWLEDGEMENTS . . ..... .... ....


LIST


OF TABLES .. a a .. a a a a a a a a *


CHAPTERS


INTRODUCTION.... .......


. . .. . . 1


An Introduction


Problem
Research


to the


Shrimp


Market


Statement.


. t . . .. 1
,. . ... 7
10


ectives


Research Approach.............
The Application of the Results


of This


Study


Scientific


Policy
view of


Merit...


Applications
the Remaini


* S t C. C


nf


Li


Chapters


* S S C C S C * t e C S C *
. . . . .
. ..Ug l .. .. ..


REVIEW


METHODOLOGICAL CONSIDERATIONS. .......e............. ......


Data


Constraints..


. .. .. . . .... 25


Some


Policy


The Adequacy


Implications of
of the Availabl


Inadequate


Data


Data


as Proxies


. .... 25


for the


Desired


Data...


.... 27


Empirical
Available


Evidence
Proxies..


Relating


to the Inadequacy


Implications


of Inadequate


Data


for Previous


Studies


Research Re
Theoretical


source
Constr


Constraints
aints.....


Policy


Implications


Implications


of Misspecification


for the Pr


esent


Effort


MISSPECIFICATION TEST . . ..... .... ....


Hausman


Test.


. a. a. . t. a a o I t 4 1


Pre


... 29


.......... ... 34


...... ..... ....... 35


Page


AB STRA CT .................................. ..... .... ..


OF LITERATURE .............. ..... ..... ....


tlll(~


I









Summary. ...... ..... . .. .... . . .

VECTOR AUTOREGRESSIVE MODELS................................


Vector


Autoregressive Theory


Estimation Procedures..........
Determining the Order of the M
Hosking's Test for White Noise
Estimating Relationships Among Va
Decomposition of the Parameter
Frequency Dimension Analysis..
Time Dimension Analysis.......


ESTIMATING


odel
* a a .


r


.


- -I


* t a a ft 4 4 9 ft a a a a a a a
*. a a. a a .. . t *. a p. .t


iaDies
Matrix


THE VAR MODEL... ... ........ ...................


action
acting


of Variables
the Order of


he VAR Model
VAR Model...


Testing the VAR Model....
Analyzing the VAR Model..
Frequency Domain Analysis


Time


Domain Analysis.....


RESPECIFYING THE


S IMULTANEOU S


EQUATION MODEL........... ......


Respecified Model . . . .. . .. . . 94
cussion of Analytical Results......................... 101
SEM Parameter Estimates .. ....... .... .. .... 101
Prediction Experiments .. . . .... .. . 107
Exogeneity of Imports . . .. .. . . 109
lity of the VAR Model .................. .... ... ....11 i


VIII


SUMMARY


AND CONCLUSIONS ..... ... .. ....... ...... ........


Econometric


Misspec
Reduced
Frequen
lytical
icy Imp


Techniques


.... .. .. .. .. .. .. ..... 115


ification Test..........
SForms. .. .. .. .. .....
cy and Time Domain Analy


Re
lic


suits...
ations..


*


Vector Autoregressive Model
Simultaneous Equation Model
The Benefits of This Approach
Concluding Remarks............


Pol:
Pol:
to S]


e .. ... . 11
. .. ... ... t.. 11
ses. ..... .....11
. ...... .. ... .... 11
S............ 11
icy Implications........ 11
icy Implications........ 12
EM Model Specification.. 12
. ... .... ...... ... .. 12


APPENDICES


SAS PROGRAM TO
THOMPSON ET AL.


CONDUCT THE MISSPECIFICATION TEST
MODEL. .. .. ....... .. ... ...


ON THE
a .a .a. ..a


PROGRAM TO ESTIMATE THE VAR MODEL AND ANALYZE ITS PARAMETER


-- d








SAS PROC


MATRIX


TO SELECT


THE ORDER


OF THE VAR model.........


AUTOCORRELATIONS


AMONG VARIABLES


IN THE VAR


VECTOR AND


ASSOCIATED


PREDICTION


Z-VALUES..


EXPERIMENT RESULTS


DATA


USED


IN THE


RESPECIFIED


OF THE


SHRIMP


MARKET...


REFERE NC S .. ... .. ... .. ... .. ... .. .. .. .. .. .. .. ..

BIOGRAPHICAL SKETCH.. .. ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .............
















LIST


OF TABLES


Table


Page


Comparing Restricted Reduced Form
with Unrestricted Reduced Form Pa


Parameter


rameter


Estimates


Estimates......


Tests


to Select


the Order


of the VAR Model..............


VAR Model


Restricted


Parameter


Estimates


t-Values...


Frequency


Relationships


of the VAR Model. .... ..........


Autocorrelations


3SLS


Parameter


Estimates


and Associated


t-Values........


Long Run Multipliers


of the Complete


Respecified SEM....


Prediction


eriment


3SLS


Parameter


Estimates


from


the Four


Equation


SEM.....


Long Run Multipliers


of the Four


Equation SEM...........


Elasticity


Flexibility


estimates


the Thompson


et al.


Respe


Model


cified


Compared
SEM. ...


with


Similar


Estimates


from


Figures


Page


Selected U.S


Shrimp


Market


in the VAR Model ... .. ..... .... .


Results...............


Data .... ..... .. .. .. .















Abstract


of Dissertation


of the University


of Florida


Presented


to the Graduate


in Partial


Fulfillment


School
of the


Requirements


for the Degree


of Doctor


of Philosophy


A DYNAMIC


THE U.S


ECONOMETRIC


SHRIMP


MODEL


MARKET


John Dale L(

April 1988


Chairman:
Department:


Scott


Food


Shonkwiler
d Resource


Economics


Recently


published


statements


relating


fragility


traditional


simultaneous


equation


econometric


models


cast


doubt


on the


specification


of existing models


therefore


on the


policies


implied


the models.

societal I


Concern


welfare


over


suggests


the impact


that


inappropriate p

specification


policiess


can have


models


that


might


likely


be relied


upon


for policy


development


should


be tested for


misspecification.


Since


the goal


of such


action


is the development


appropriate


policy


the objective


a specific


test


is either


to add


creditability


the existing


model


use


the information


obtained


from


test


an effort


to develop


a more


appropriately


specified model.


simultaneous


econometric


model


(SEM)


testing


respecification


process


demonstrated


here


includes


test








with


three


stage


least


squares


techniques.


misspecification


test


modification


test


suggested


Hausman.


Here


difference


between


unrestricted


restricted


reduced


forms


implied


the structural


model


provide


the data


for the


test.


These


data


also


provide


clues


sources


of misspecification


in the SEM


being


tested.


A vector


autoregressive


model


(VAR)


of the U.S. shrimp


market


estimated


part


effort


obtain


information


respecification


of the SEM.


Time


frequency


domain


analyses


model


provide


information


useful


policy


purposes;


however,


relatively


little


of the information


is useful


in respecifying


the SEM.


policy


implications


model


exis


ting


respecified


SEMs


are


discussed.


Also,


implications


existing


data


constraints


on attempts


to understand


the U.S.


shrimp


market


discussed.


Although


the existing


SEM was


found


to be misspecified,


its policy


implications


appear


accurate.


Analysis


model


indicated


that


shrimp


imports


lead


domestic


prices


short


term


domestic


prices


over


three


year


period.


This


implies


significant


amount


inertia


current


situation


of increasing


imports


decreasing


domestic


ices


that


has important


implications


for domestic


foreign


policy makers


investors.


are
















CHAPTER I
INTRODUCTION


An Introduction


to the U.S


. Shrimp


Market


The shrimp


fishery


is the most valuable


of U.S


fisheries


terms


exvesse


revenues


and in


terms


of the


value


of processed


products.


1985


U.S.


shrimp


fishermen


received


approximately


million


dollars


for their


products.


purposes


of comparison,


next


most


valuable


U.S.


fishery


1985


was


Pacific


salmon


fishery


with


landings


worth


approximately


million


dollars,


followed


American


lobster


fishery


with


landings


worth


approximately


115 million


dollars.


Comparing


shrimp


industry


with


other


food


industries


difficult


due to the impacts


it has


over


several


states;


however,


it IS


interesting


note


that


Florida


citrus


growers


received


over


million


dollars


for their


1983


orange


crop


(Mulkey


et al.).


The value


U.S.


processed


shrimp


products


1985


was


approximately


billion


dollars


represent


approximately


percent


total


value


of U


processed


fishery products


(USDCa,


USDCb).


addition


importance


national


economy,


domestic


shrimp


industry


a major


component


of the


economy


in coastal


communities


of the Gulf


and South Atlantic


regions


of the U.S.


Griffin


and Jones


estimated


the economic


impact


of the commercial


shrimp


catch


on the Texas


economy.


According


to their


analysis,


$1.00


output


one











supporting


directed


industries.


toward


substantial


the construction


portion


maintenance


this


support


of the fishing


fleet.


The Gulf


South


Atlantic


fleet


more


than


doubled


in size


from


about


6,600


boats


and vessels


in 1950


to about


14.000 in 1983


(Vondrus-


ka).


This


increase


in fleet


size


has occurred


while


total


landings


from


area


have


grown


less


than


percent:


Southern


landings


in 1960


were


pounds


was


149 million


in 1985


143 million


pounds,


(heads o

pounds.


142 million


>ff basis). T1

The average


pounds


average


for the f


1983


, and


183 million


for the 1950-83

ive-year period


period

ending


with


1985


was 165 million


pounds


(USDCa).


A major


reason


the fleet


been


able


to expand


in the


face


of such


meager


expansion


in landings


has been


the increasing


value


of the catch.


In real


terms


, the value


of the 1983


catch


, a year


of reduced


landings


, was 3


times


the value


of the 1950


catch


(Vondruska)


Shrimp


the Pacific


are


also


regions.


landed


In fact,


in northern


most


ports


of the reported


the New


England


increases


in total


landings


during


twenty year


period


between


1960


1980 were


due to increases


in these


areas


(Hu)


However


U.S.


landings


outside


the Gulf


South Atlantic


region


have


remained


fairly


unimportant


terms


value and


volume


of landings.


Over


the five


year period from


1980


to 1985


, landings


from


the northern


area


accounted


for less


than


percent


total


landings


(USDCa).


Additionally,


the shrimp


landed


in northern


ports


are a different


species


from


those


landed











warm


water


shrimp


landed


southern


ports


can


analyzed


separately


from


that


dealing with


the cold


water


shrimp


of the north.


Perhaps,


most


important


feature


of the U.S


shrimp


market


reliance


on imported


shrimp.


Since


early


1960s


imports


have


been


imports


maj or


of shrimp


source

have


shrimp


increased


consumed


dramatically,


U.S.


reaching


Since


a peak


1981


in 1983


when


they


represented


over


percent


of U.S.


supplies


(Prochaska


Keithly).


Imports


have


continued


increase


every


year


since


1983


however


the proportion


of total


U.S.


shrimp


supplies


accounted


for by


imported


shrimp


declined


increased


landings


approxi-


mately


percent


in 1986.


Figure


displays


the landings


imports


data


graphically.


Also displayed


are data


on the real


average monthly


wholesale


price


restaurants


26-30


other


count


eating


shrimp


places.


data


Because


expenditures


U.S.


Japan


major


world


markets


shrimp,


imports


into


U.S.


are


con-


sidered


to be influenced


the relationship


between


the value


of the


dollar


and Japanese


(Prochaska


Keithly).


worldwide


basis,


stocks


naturally


occurring


shrimp


thought


to be fully


exploited


(Rackowe).


During


past


decade,


1970-


world


have


shrimp


remained


catch


relatively


increased


stable


over


since


percent;


1977


however,


(Rackowe).


landings


Environmental


conditions


are


considered


the primary


cause


fluctuations


in land-


ings.


The annual


shrimp


crop


spends


a critical


stage


of its develop-


ment


estuarine


waters


where


rainfall


water


temperature


are


are


can



















ten million


pound


units


3-

2-

1-









3.7-


2.2-


-




1977 1982 1986

1-la




dollars


__

:


1977


1982


1986


Figure


elected


Monthly


Average


Real


Monthly


Shrimp


Shrimp


Market


Imports


Wholesale


Expenditures


Data


into


Price


source


the U.S.


26-30


in Eating


see Appendix
b) Monthly


Count


Places.;


Shrimp.;
d) Month


Lly




















billion


dollar


units


4.6-


3.6-



2.6-













2.0-


0.2-


1977 1982 1986

1-lc




ten million pound, heads-off units




, -

aL


1977


1982


1986


1-ld


Figure


.l--continued










While


U.S.


landings


have


remained


fairly


stable


since


the 1950s,


U.S. consumption


of shrimp


has grown significantly.


annual


average


rate


of increase


between


1950


1983


is 3.9


percent.


In 1983


, U.S.


consumption


was


times


1950


evel


(Vondruska).


capital


consumption,


however


increased


only


about


percent


year


over


the twenty year period,


1966-85.


The majority


of this


consumption,


proximately


percent


occurred


commercial


eating


establish-


ments

nmentl


, generally t

al or company


.ermed


"institutions


cafeterias.


" such


The fact


that


as restaurants


data


or gover-


on transactions


the institutional


major


setting have


impact


not


been


economic


collected


analysis


on a systematic


shrimp


basis


market.


Because


essential


data


demand


analysis


are


not


available,


attempts


to estimate


the retail


demand


for shrimp


in the U.S.


have


produced misleading


results.


essential


information


for estimating


the retail


demand


consumer


product


are


data


on the price


paid


consumer


quantities


institutional


purchased.


Given


setting


the preponderance


relevant


data


of transactions


calculating


in the


retail


demand


for shrimp


the related


elasticities


of demand


are data


from


transactions


institutions.


Unfortunately,


prices


shrimp


sold


through retail


outlets


such


as supermarkets


seafood markets


are the


only


data


available


which


relate


directly


transactions


with


final


consumers.


These


data


series


are not


complete


because


their


collection


discontinued


early


1980s.


available


data


was











movements


of shrimp


out of wholesale


warehouses.


An alternative


term


for this


movement


is "disappearances


from


cold


stora


Another


implication


of the large


proportion


of institutional


sales


that


shrimp


demand


is heavily


dependent


on the public


s demand


food


away


from


home.


Thus,


disposable


income


is expected


to be


a key


determinant


of shrimp


demand


(Rackowe).


Problem


Statement


With


world


shrimp


catch


levels


near


their


expected


maximum


with


reasonable


expectations


that


the demand


for shrimp


will


continue


strengthen,


a scenario


that


includes


rising


shr imp


prices


increased


congestion


U.S.


shrimping


grounds


not


unreasonable.


However,


during


early


1980s,


technology


of shrimp


production


substantially


transformed


perfection


commercial-scale


shrimp


mariculture


that


ostensibly


independent


critical


inputs


from


the natural


environment.


Accordingly,


limits


production


shrimp


have


been


expanded


from


that


a natural


production


system


to that


of controlled


production


systems


similar


those


used


to produce


swine


or poultry.


Shrimp


are


now


being


reared


from


breeding


stock


maturity


highlands


Colorado


(Brannon,


1986).


use


this


technology


under


more


favorable


biolo


ical


economic


conditions


existing


outside


implies


that


limits


production


are


those


imposed


public


domestic


shrimp


policy


fishery


market.


are immediately


ramifications


obvious.


was











the marginal


value


(price)


received


foreign


producers


is just


equal


their


marginal


cost


of production


and distribution.


To the


extent


that


maricultured


shrimp


are


less


costly


to produce


than


domestically


captured


shrimp


in the absence


of sufficient


shifts


in U.S


demand


for shrimp,


these


increased


supplies


will


have


a depressing


effect


the prices


U.S.


producers


receive


for shrimp.


Because


U.S.


shrimp


fishery


considered


fully


developed


possibly


over-capitalized,


purely


competitive


industry,


decrease


shrimp


prices


can


expected


force


some


U.S.


fishermen


out of business.


Policy


makers


be called


upon


to devise


programs


that


will


assist U.S.


citizens


adjust


these


changing


conditions.


These


policies


should


be based


on accurate


predictions


the likely


change s


that will


occur


in the U.S. shrimp market


due to the


changed


volume


imported


shrimp.


Recent


studies


of the U.S.


shrimp


sector


have


contributed


substan-


tially


to the understanding


of the industry.


However,


the development


complete


mathematical


models


of the industry


useful


for predicting


price


changes


been


severely


hampered


absence


required


data


capture


series


many


limitations


of the complexities


previous


modeling


of the market.


techniques


absence


of ideal


data


series


have


resulted


erroneous


conclusions


about


such


policy


variables


price


elasticity


demand


income


elasticity


of demand.


purpose


of this


paper


to focus


attention


on this


deficiency


its implications.











disequilibrium


in product


or factor markets,


and pricing


dynamics.


suggested


method


treating


such


complexities


vector


autore-


gressive


specification


(Sims).


Thus,


a second


purpose


this


paper


investigate


utility


of the


vector


autoregressive


specification


in understanding


the U.S. shrimp


market.


difficulty


of modelling


complex


behavioral


relationships


economic


process


such


a market


have


resulted


misspecification


of economic


models


of the U.S.


shrimp


market.


Indeed


economic


model


misspecification


appears


"more


likely


rule


rather


has been


vary


than


the exception"


cited


between


as a major


studies


(Judge


reason model


(Prochaska


al. ,


854)


results


and Keithly,


Misspecification


policy


implications


Adams,


These


considerations


have


important


implications


since


policies


based


misspecified models


be inappropriate.


concern


impacts


which


policy


can


have


societal


welfare


suggests


that


responsible


action


take


test


specification


models


that


might


likely


relied


policy


purposes.


goal


such


action


the development


appropriate


policy.


objective


creditability


existing


a specific


test


model


either


utilize


information


contained


in the model


and the information


obtained


from


a test


of its


specification


an effort


to develop


a more


accurately


specified model


for policy making


purposes.


Technological


development


in the production


of shrimp


has allowed











dislocation


highly


competitive


U.S.


production


subsector


substantial


changes


in the U.S.


marketing


subsector.


Because


policies


developed


address


this


situation


will


quite


likely


based


existing


econometric


models


the U.S.


shrimp


market


an appropriate


subject


demonstration


econometric


model


testing


respecification


procedure


briefly


described above.


Research


Objectives


The major


goal


of this


research


to develop


use in policy


making,


a more


complete


understanding


underlying


behavioral


relationships


demonstrate


U.S.


econometric


shrimp


market.


techniques,


secondary


viz. ,


goal


vector


autoreg-


ressive


model


simultaneous


equation


model


cification


test,


that


prove


useful


additions


analytical


process


understanding markets


in general.


The primary


objective


research


to develop


a dynamic,


econometric


model


U.S.


shrimp


market


which


can


judged


being


properly


specified


specification


criteria


to be discussed


study.


accomplishing


this


objective,


identified


deficiencies


of previous


models


will


be addressed.


vector


autoreg-


ressive


specification


market


will


investigated


usefulness


in understanding


relations


between


variables


of inter-


, for

fulness


usefulness

suggesting


predicting


alterations


instrument,


structural


econometric


model


which


treat


complex


behavioral


relationships


addressed











lack


of ideal


data


will


be addressed


recognizing


that


existing


data


appropriate


estimating


retail


level


relationships.


Instead,


data


will


be used


to estimate


relation-


ships


at the wholesale


market


level


which


generated


the data.


primary


specification


objective

an existing


will


be accomplished


econometric


model


first


testing


the market.


Next


vector


autoregressive


model


of the market


will


be specified,


estimated,


analyzed.


The information


gained


from


these


analyses


will


be used


to specify


a dynamic


structural


econometric


model.


The model


will


then


tested


for misspecification,


forecast


performance


will


compared


with


vector


autore


gressive


model.


Finally,


policy


implications


of the analyses


The specific


objectives


will


of this


be discussed.


study


are


test


system-wide


econometric model


of the U.S.


specification


shrimp


existing


market;


to construct


a vector


autoregressive


model


the U.S.


shrimp


market;


to determine


point


estimates


for the temporal


relation-


ships between

landings, and


wholesale


import


shrimp


shrimp


prices,


U.S.


quantities,


shrimp


construct


confidence


intervals


to specify


test


for these


estimates.


the specification


a traditional


econometric


model,


using


the results


from


objectives











discuss


policy


implications


models


other


information


developed.


Research Approach


Testing


specification


an existing


structural


model


of the


U.S.


shrimp market


should


provide


an initial


base


of information


useful


further


analysis.


A specification


test


based


on Hausman' s


1978


work


developed


applied.


The difference


between


estimated


parameters


of the restricted


unrestricted


reduced


forms


implied


structural


ference


model


between


provide


two


the basic


reduced


forms


data


also


test.


provides


dif-


information


possible


sources


of misspecification.


Similarly,


the specification


the shrimp


market


vector


autoregres


sive form


contributes


additional


information


that


is useful


in respecifying


the traditional


simultaneous


econometric model


(SEM).


The specification of


vector


autoregressive


(VAR)


model


will


based


policy


knowledge


makers,


U.S.


economic


shrimp


theory.


industry,


likely


degree


concerns


lags


used


spec


ifying


the VAR


are selected


a process


of increasing


the number


of lags


employed


until


tests


of the hypothesis


that


parameters


the additional


set of lagged


variables


in the


system


are equal


zero


cannot


be rejected


(Nickelsburg).


This


test


is executed


in the


context


of least


squares


estimation


procedures


s since,


in this


case


where


each


equation


system


contains


identical


regressors


, least


squares


estimation


is equivalent


to maximum


likelihood


estimation


(conditional











number


of lags


specified


will


be the


same


for each


equation,


protesting


will


be limited


to system-wide


specification.


Once


order


been


selected,


the model


will


reestimated


a restricted


form


reflecting


theoretical


judgement


relating


the exogeneity


of the variables


in the endogenous


system.


The model


will


then


be subjected


a diagnostic


test


to determine


distributional


characteristics


error


terms


system.


vector


variables


associated


structure


have


been


selected


appropriately,


error


terms


should


random


processes.


The degree


to which


they


approach


this


definition


will


be tested


using


Hosking's


portmanteau


statistic


(Hosking).


hypothesis


serially


correlated


residuals


cannot


rej ected


addition


variables


to the model


or some


transformation


of existing variables


be indicated.


Once


vector


autoregressive


system


been


specified,


relationships


among variables


of interest will


be obtained


decompos-


parameter matrix


system,


using


analyses


in the frequency


time


domains.


Confidence


intervals


for these


estimated


relation-


ships


will


be constructed


numerical


differentiation.


implications


vector


autoregressive


model,


along


with


information


gained


from


testing


specification


existing


structural


model


will


be used


in specifying


a dynamic


structural


model


(herein


called


"respecified"


model


distinguish


from


previously


existing


model


of Thompson


al. ,


which


referred











structural


model.


Finally,


structural


vector


autoregressive


models


will


be compared


and the implications


for policy


discussed.


The Application


of the Results


of This


Studv


Scientific


Merit


scientific


merit


of this study


arises


from


the demonstration


a model


the econometric


extent


specification


model


use of this


ied econometric


models


test


development

procedure

and more


can


procedure


results


appropriate


easily


of other


more

police


adopted


analysts.


as part


To the

specif-


general


will


benefit.


Additional


scientific


merit


practical


utility


derives


from


the demonstration,


as a part


of the testing


respecifi-


cation


process,


a vector


autoregressive


specification


phenomenon


under


study.


Policy


Applications


Potential


users


investors,


of the results


foreign


of this


governments,


study


domestic


include

state


domestic


federal


fishery


regulatory


agencies


domestic


international


trade


regulatory


agency


ies.


The policy


issues


that


can


be addressed


using


the results


of this


study


include


the advisability


a program


to assist


the U.S. shrimp


production


sector


adjust


projected,


continued


decrease


real


(adjusted


inflation)


shrimp


prices


possible,


con-


comitant


reduction


in operating


shrimping


vess


The results


of the


vector


autoregressive


analysis


should


be helpful


in understanding


which


appropriately

y, society in


foreign











Such


understanding


should


helpful


development


appropriate


policy.


For example,


given


the impact


of increased


shrimp


supplies


shrimp


prices


indication


delay


industry' s


response


price


changes,


domestic


foreign


investors


need


to adjust


their


estimates


of expected


prices


used


in analyzing


investments


in additional


productive


capacity.


The domestic


marketing


sector


should


find


these


results


helpful


in forming


expectations


of the


likely


increase


in shrimp


supply


in planning


investments


to market


the increase.


Preview


of the Remaining:


Chapters


The following


chapter


reviews


the literature


relating


to existing


studies


using


the shrimp


existing


market.


data


The third


estimate


chapter


retail


addresses


level


the problem


relationships


discusses


other


methodological


considerations.


fourth


fifth


chapters


discuss


the methodology


used


in applying


the misspecification


test


in specifying


vector


autoregressive


model


in analyze


dynamic


relationships


among


the variables


VAR.


The sixth


chapter


discusses


estimation


results.


seventh


chapter


discusses


the reestimation


of the structural


economet-


ric model

existing


and

and


its estimated

the respecified


parameters.

SEM results


The final

discusses


chapter


compares


the policy


implica-


tions


models


discusses


benefits


demonstrated


approach


development


appropriately


specified


simultaneous


equation models.
















CHAPTER


REVIEW


OF LITERATURE


A highly


valued


industry


allotted


a corresponding


degree


interest


collection


from


public


of data


officials.


that


makes


This


econometric


interest


analysis


often


results


possible.


Accord-


ingly,


the U.S.


shrimp


industry


has been


the subject


a substantial


amount


analysis.


Naturally,


one


would


expect


progression


methodologies


employed


over


years


to reflect


developments


economic


theory,


in statistics,


in computing


capability


that


have


generally


expect


proceeded


that


their


analysts


application


conducting


in applied


new


studies


economics.


have


One would


attempted


employ


most


advanced


techniques


at their


disposal


in their


attempt


common


body


of knowledge.


This


process


tended


increase


this


stock


of knowledge,


although


perhaps


not


uniformly


over


time.


Twenty


years


ago,


most


econometric


models


developed


to analyze


demand


shrimp


were


single-equation


functions.


Nash


catalogued


"best


specimen"


demand


functions


selected,


from


those


available


1968


a panel


marine


economists.


demand


functions


selected


shrimp


were


generally


linear,


single


equation


models


estimated


with


least


squares


techniques.


Three


seven


selected


equations


related


the wholesale


market


level


two related


the P.xvpAsl


market


lpvsl nnd


twn to the rstsil


1 eVP 1


The nrie


L. I











from


-.78


to +.38


with


four


out of the six ranging


from


-.29


-.46.


retail


price


elasticity


estimates


were


+.38


-.28.


Thus,


none


of the selected models


estimated


shrimp


demand


to be price


elastic


at the selected market


level.


The income


elasticity


estimates


were


in the elastic


range


.e.


, greater


than


one


ranged


from


.329 (Nash


and Bell,


22-26).


next


phase


of model


development


appears


to have


been


that


multi-equation


models.


example,


Timmer;


Gillespie


Doll


Batie;


Hopkins


et al.


Having


been


published


in the American


Journal


of Agricultural


Economics,


the study


Doll


perhaps,


most


widely


known


this


group.


discussing


five-equation


simultaneous


equation model


based


on annual


data,


Doll


first


deals


with


the maj or


data


problem


confronting


variables


all researchers


theoretically


in this a:

specified


rea:


the lack


model.


Doll


briefly


describes


what


variables


an ideal


model


would


contain


and then


states:


realities


"However,


when


available


ideal


data,


some


model


was


compromises


confronted


became


with


necessary"


432).


One of those


compromises


involves


imports


as a source


of shrimp


the U.S.


market.


Although


Doll


recognizes


that


foreign


suppliers


have


a choice


of marketing


areas


that


some


U.S.


importers


on forward


contracts,


Doll


forced


treat


imports


an exogenous


variable,


lack


of data.


For a similar


reason,


Doll


enters


domestic


landings


shrimp


into


model


exogenous


variable.


Doll


two


al.;











compromises


lend


credence


to the


statement


Sims


that


analysts


often


define


a variable


as exogenous


because


serious


effort


to model


variable


would


take


the researcher


too far afield from his


main


area


interest.


Another


compromise


recursive


nature


model.


Doll


does


not


attempt


to justify


this


specification.


Continuing with


the results


reported by


Doll,


he shows


that,


as of


1968


domestic


landings


were


single


largest


source


price


variation


the U.S.


shrimp


industry.


Increases


in U.S.


disposable


income


kept


a constant upward


pressure


on shrimp


prices


that


would


have


increased


prices


cents


pound


year.


However


increased


import


levels


resulted


an average


annual


decrease


in prices


of .05


cents


per pound


that


partially


offset


the price


increases


due to income


growth.


Doll


reports,


with


some


caveats


confidence


estimates


income


elasticity


of shrimp


retail


level


to be


1.12


estimated


own


price


demand


elasticity


at the retail


level


-.63.


Doll


notes


that


although


consumption


shrimp


individuals


would


be expected


to be


more


responsive


to retail


price,


such


a result


might


be obscured


in analyses,


such


as his,


which


have


data


majority


market


transactions


involving


final


consumers.


The institutional


demand for


shrimp


comprises


an important part


the final


market,


cost


of preparation


other


services


would
food.


to changes


important


Consumption


in price


under
alone


determinant


these


the price


conditions


. (Doll,


would


not


the prepared
be responsive


p. 435)


not











interest


have


attempted


to model


those


variables


that


previously


been


through


recognized


some


as being


compromise.


endogenous


Also


, the


were


dynamic


treated


relationships


as exogenous


between


variables


are


given


some


recognition


through


use


of lagged


vari-


ables.


Timmer


incorporates


import


supply


function


while


still


regarding

a domestic


Gulf


domestic

supply


of Mexico


landings

function


water


as exogenous.


Batie


1958


temperatures


successfully


period


to capture


using


biological


estimated


index


fluctua-


tions


in shrimp


populations.


Both


Hopkins


et al.


Thompson


et al.


model


domestic


landings


and imports.


Hopkins


develop


annual


model


of domestic


supply


function


of wholesale


prices


of shrimp


lagged


one year,


Gulf


South


Atlantic


landings


shrimp


lagged


one


year,


index


vessel


operating


costs


lagged


one year


average


monthly


Mississippi


River


discharge


for February


through


April.


Import


supply


is modeled


as a


function


of U.S.


exvessel


price


lagged


one year


imports


lagged


year.


Price


dependent


demand


the wholesale


level


is modeled


as a


function


Although


beginning


Hopkins


stocks,


imports,


expected


landings


inverse


relationship


shrimp.


between


quantity


supplied


and price


, they


found


a positive


relationship


between


imports


unexpected


U.S.


positive


wholesale


sign


price.


reflect


authors


a supply


explained


response


that


general


market


conditions.


contradicts


harvester


The authors

rs' complaint


also

that


commented

imports


that

have


the positive


a depressant


sign


effect


one











Beginning


stocks


of shrimp


were


found


to have


the largest


direct


impact


(negative


expected)


wholesale


prices.


, beginning


stocks


are a function


of imports,


most


of which


enter


the U.S


during


last


quarter


year


(Hopkins


al. ,


also


valuable


equation


note


that


primarily


researchers


a time


trend


found


with


that


lagged


import


imports


supply


playing


dominant


role


in the


determination


current


imports.


As for elas-


ticities,


Hopkins


report


income


elasticity


of 1


price


elasticity


-.27.


Thompson


et al.


model


domestic


landings


as a function


of fishing


effort,

average


average precipitation

atmospheric temperature


in coastal

in coastal


Louisiana

Louisiana


lagged

lagged


two months,

two months,


quarterly


dummy


variables.


Fishing


effort


a function


current


price


exvessel


esel


price


fuel,


shrimp,


seasonal


current


dummy


quantity


landed,


variables.


import


quantity


variable


is modeled


as a function


the wholesale


price


shrimp


lagged


two months,


rate


of exchange


between


U.S.


dollars


the Japanese


lagged


two months,


and seasonal


dummy variables.


Thompson


suggest


that


studies


the U.S.


shrimp


market


using


data


collected


prior


to recent


structural


changes


in the market


be dated and,


therefore,


estimate


a simultaneous


system model


using


monthly


data


from


September


1974


through


December


1983.


authors


recognize


difficulty


estimating


retail


demand


shrimp


when


the existing


data


relate


to the wholesale


level.


It is difficult


own











In discussing


their


demand


equation,


they


apparently


consider


retail


demand


function


because


they


mention


that


"economic


theory


suggests


that


prices


substitute


complementary


products


included


equation


Equation


their


consumption


equation.


They


also


mention


the results


of adding


the price


index


processed


meat


explanatory


variable


equation.


reported


version


their


model


these


variables


were


included


because


authors


found


variables


to be


insignificant


trial


runs.


attempted


inclusion


of the processed


meat


variable


could


interpreted


imply


they


consider


equation


representative


derived


wholesale-level


demand,


processed


meat


could


con-


sidered


input


a shrimp


product.


This


consideration


seems


unlikely


, impling


that


they


consider


the equation


to be representative


of retail


demand.


appears


that


Thompson


. have


attempted


estimate


retail


demand


using wholesale-level


data


Thompson


estimate


price


elasticity


their


demand


function


elasticity


to be


inelastic


of demand


that


-.11.


contradicts


They


obtain


that


most


an estimate


other


of income


research.


Thompson


et al.


estimate


is in the inelastic


range


, viz


-.42


which


indicative


an inferior


good.


The authors


explain


this


discrepancy


noting


that


the elasticities


from


previous


research


were


calculated


from


models


estimated


with


data


from


the late


1950s


to early


1970s:


period


when


shrimp


consumption


was increasing.


A portion
dur inp the


of the


II


ri od


correlation


I


-tl rn


II -


between


nrPvi nijjq


consumption


stiidi sP


dca1t


wi th


income
pnn bP


i


|











period


would


elasticity


annual


data


of demand


more


demand.


from


1960


shrimp


closely


approximate


A recent
through 1980
of 0.73. T


study by
found an


actual


Hu (1
income


estimated


L983)


income
using


elasticity


elasticity


less


than


one can


probably


be attributed


to the inclusion


several


years


determinant


of data


after


expenditures


the early
at retail


1970'


eating


With


income


establishments


70-80


site


percent


use


: shrimp
income I


consumption
iv overstate


occurring
the size


these


elasticity


(Thompson et


Thompson


estimate


actually


elasticity


consumption


Thus


given


the comparisc


a change

in between


in expenditures


estimates


retail


is difficult.


eating


places.


expenditures


variable


alternative


is used


definition


a proxy


income


for the variable


authors.


is possible.


Since


However,


no quantity


data


accompany


the expenditures


data,


it is impossible


to determine


changes


expenditures


are


result


changes


in quantity


sold,


changes in p

If the major


proxy


rice,


chang


for income


or some

;e had i


combination


,een


is plausible.


of changes


in quantity,


If the major


in quantity


use of


change


expenditure


had been


price.

s as a


in price,


use of expenditures


as a proxy


for price


becomes


plausible.


Under


alternative


interpretation


that


retail


expenditures


eating


aces


be considered


a proxy


output


price,


the Thompson


et al.


model


might


be expected


to predict


price


elasticity


rather


than


income


elasticity.


In this


case,


Thompson


et al.


estimate


is consistent


with


the majority


of estimates


of price


elasticity.


most


recent


innovation


in shrimp


market


modeling


efforts


utilization


causality


measures


Adams


assist


n specifying


S, p.











be included


test


in the


hypotheses


price determination

dynamic properties


model and

regarding

i between

of price d


then


use these


lead/lag


interfacin

[eterminatii


stochastic


structures

g market

on and the


characteristics


and the direction

levels. Finally,


structural


attributes


market,


suggested


theory,


are


incorporated


into


econometric


model


describing


price


at each market


level.


Specifically,


causality


tests


are


used


specify


a model


based


on monthly


data


a recursive


form


while


a simultaneous


form


dictated


for a model


based


on quarterly


data.


Theoretical


considera-


tions


determined


what


nonprice


variables,


such


income,


quantities,


and consumer


price


index,


would


enter


each


of the structural


equations.


These


nonprice


variables


enter


the equations


an unlagged


or current


form.


The causality


testing


procedures,


their


related


impulse


response


functions,

variables


and

and


certain

their


diagnostic


specific


checks


degree


dictate

lag e


which


nter


price


structural


equations.


Adams'


s results


relating


income


elasticity


support


those


Thompson


et al.:


Real


disposable


income


was


found


not


a significant


determinant


of monthly


quarterly


prices


either


size


ass.


This finding


reflects


the fact


that


real


disposable


income


over


changes
e time


very
period


little


on a monthly


the analysis.


or quarterly


Previous


basis


monthly


quarterly


analyses


corroborate


insignificance


income


while


studies


using


annual


data


typically


find


income


significant.


(Adams,


165)


The price


flexibilities


of demand


derived


from


final


form


coeffi-


cient'


n a


re ouite


inelastic


less


than


. i .e .


for both


size


classes


. -2


4m


I











general,


most


variables


anticipated


relationship


with


dependent


variable


of their


related


, price


dependent


demand


equations.


However,


termed:


there


was


all other


one


exce


imports.


ption


This


involving


variable


one


category


a positive


imports


relationship


with


the dependent variable


of both


size


classes


of shrimp


under


study.


Adams


found


that


beginning


inventories


a larger


effect


both


classes


landings.


shrimp


This


prices


effect


than


does


is in accord


class


with


of imports


the findings


or domestic


of Hopkins


et al.


Also


in accord


with


Hopkins


et al .,


Adams


found


that


total


imports


shrimp ar

quarterly


e positively


models,


related


not


to price.


a significant


Income,

determinax


in Adams's

It of price


monthly


dependent


demand.
















CHAPTER


METHODOLOGICAL


CONSIDERATIONS


Economists


strive


develop


their


models


on strong


theoretical


foundations;


resource


however,


constraints,


limitations


availability


economic


of data


theory,


can


often


research


lead


model


misspecifications


chapter will


discuss


which


reduce


the implications


utility


of these


three


model.


constraints


This


on the


present


past


efforts


to better


understand


the U.S.


shrimp


market.


Data


Constraints


maj or


data


constraint,


mentioned


above


lack


information


on quantities


and prices


of shrimp


sold


to final


consumers


through


institutional


markets.


Although


approximately


percent


U.S.


shrimp


consumption


occurs


these


commercial


eating


places


price


quantity


data


these


transactions


are


systematically


collected.


a result,


researchers


are forced


use available


data


from


sales


retail


outlets,


which


accounts


only


percent


shrimp


consumption,


represent


the primary


market


data


(Adams,


Thompson


et al.,


12).


Alternatively,


analysts


chose


estimate


retail


level


relationships


using


prices


quantities


from


the wholesale


level.


Some


Policy


Implications


of Inadequate


Data


Neither


these


two


approaches


appropriate


data


used


are not


adeauate


nroxi es


for the desired


data .


If the data


. say











data,


then


relationships


found


more


accurately


describe


wholesale


level


rather


than


the retail


level.


Using


wholesale


level


relationships


development


lieu


of policy


can


lead


desired


retail


to inappropriate


relationships


policies.


an example,


consider


a situation


in which


an industry


characterized


constant


returns


scale


fixed


proportions.


Layard


Walters'


s (p.


260-276)


illustration


Marshall'


s rules


relating


to the influences


governing


the price


elasticity


of demand


a factor


proportion


of production


production


helpful


function


this


perfect


context.


competition


Given


in the


fixed-


factor


market,


Layard and


Walters


show that


the price


elasticity


of demand


a factor


produced


equal


times


share


elasticity


cost


demand


product


final


being


product.


Mathematically,


= yV?


, where


e is


the price


elasticity


of demand


for the factor,


, shrimp


v is


the share


of the factor


in the


cost


of the final


product;


is the


price


elasticity


of demand


for the final


product,


e.g.


a shrimp


entree


a restaurant.


absence


adequate


data


on the


retail


market,


the above


relationship


elasticity


price


might


of demand


elasticity


used


for the final


of demand


obtain


indication


product.


for the final


As long


product


price


as v <


is elastic


Thi


quite


likely


case


relating


shrimp


final


products


can


, the











Obviously,


the shrimp


a shrimp


dish


is less


than


percent


of the


related


food


cost.


Thus,


34-41


percent


represent


upper


bound


proportion


restaurant


sales


accounted


for by


shrimp.


Thus,


long


greater


the wholesale

in absolute


level


value,


price


than


elasticity


percent


of demand foi

(approximately)


shrimp


that


the retail


level


price


elasticity


of demand


for shrimp


products


elastic.


implication


that


demand


shrimp


elastic


consistent


with


findings


most


previous


studies


shr imp


market.


However


such


a possibility


provides


some


explanation


for the


contra-intuitive


results


those


previous


studies.


Recall


comments


Doll,


quoted


literature


review,


that


one


would


expect


consumers


to be responsive


to retail


price.


The Adeauacv


of the Available


Data


as Proxies


for the Desired


Data


Since


required


data


exist,


attempts


estimate


retail


demand


for shrimp


associated


elasticities


must


rely


proxies


for the desired


data.


Thus,


the veracity


of such


estimates


be addressed


through


a consideration


of the suitability


of the existing


data


as appropriate


proxies


for the desired


data.


Attention


is focused


retail


food


market


shrimp


prices


(retail


prices)


proxies


desired


unavailable


prices


of shrimp


institu-


tions


(institutional


prices).


argument


that


retail


prices


are not


good


proxies


for the institutional


prices


is based


on a consideration


probable


production


processes


associated


with


products


not


use


can











retail


outlets


home


consumption


shrimp


purchased


in institu-


tions


for immediate


consumption are


two distinct


products.


A difference


in production


processes


argues


against


the existence


a high


degree


the analysis


of correlation


of Gardner,


assume


between

that t


two product


:he production


prices.

I process


Following

es in the


two markets


can be


represented by


the following production functions


= f(s


and I


= f(s


where


R and


are


the quantities


produced


in the retail


institu-


tional


markets


, s is the input


of shrimp


into


processes


, and a


are bundles


of marketing


inputs


specific


to their


associated


proces-


ses.


Gardner


shows


ratio


a retail


level


price


a farm


level


price


can


change


differentially


according


source


shock


the market.


example


, Gardner


derives


the elasticity


the retail/farm


price


ratio


with


respect


a shift


in demand


for the


retail


product


Epr/pf = NrSb(es


-eb)/D


where


N is the price


the relative


share


elasticity


input


of demand for


b in the price


the retail pi

of the retail


:oduct


product,


elasticities


supply


inputs,


function


of N


the elasticity


of substitution


between


two inputs.


Now,


for the price


in the retail


market


, to be highly


corre-


lated with


the price


in the institutional market,


Epr/Ps


= NrSa(es


ea)/D


will


highly


correlated


with


Epi/Ps


NiSb(es


-eb)/D,


This


are


Ses,


, Pr











that


elasticities


of substitution


between


two


inputs


different


in the


two processes.


elasticity


substitution


between


two


inputs


retail


market


much


closer


zero


see


Heien)


than


institutional


market


where


institutional


operator


have


con-


siderable


control


over


composition


final


product.


retail


market


operator


is relatively


more


restricted


in the


types


amounts


of marketing


demonstrates


that


; services

markup pr


can


ricing


to the shrimp


behavior


it sells.


predictable


Heien

food


retailers.


Conversely,


nature


of the institutional


product


allows


to be combined


with


a wider


range


of variable


inputs


such


as other


food


ingredients


labor


than


can


the retail


product.


This


implies


that


If the retail


product


the institutional


product


in fact


two distinct


products


can


be assumed


that


, Ni.


Thus,


shown


that


products


are


different,


appears


improbable


that


their


prices


are


highly


correlated


are


therefore


not good


proxies,


one for the other.


Empirical


Evidence


Relating


to the Inadequacy


of Available


Proxies


Some


empirical


evidence


exists


which


lends


credence


to the notion


that


two


products


are distinct.


Nash,


in a study


of purchasing


patterns


fresh


frozen


seafood,


found


that


income


a more


pronounced


effect


on consumption


of seafood


away


from


home


than


it had


on at-home


consumption.


of the head


of the household


was also


found


have


a significant


effect


on away-from-home


seafood


consump-


are


can


are











institutions,


are different.


Assuming


both


groups


have


access


to both


products,


the finding


of the product


forms


tha

can


they


imply


tend

that


consume


either


two product


one or the other


forms


represent


distinct


products.


Given


a difference


consuming


groups


difference


products,


plausible


assume


that


one


demand


relationship may


not be an adequate


representative


of the other.


Keithly,


in a study


of the socioeconomic


determinants


at home


seafood


consumption,


found


that


expenditures


on meals


consumed


away


from


home


were


negatively


related


to home


consumption


of total


seafood


product


forms


with


exception


shellfish


which


insignificant,


positive


parameter.


Assuming


that


some


increase


away


from


home


food


expenditures


are for seafood,


this


finding


imply


that


seafood consumed at


home


seafood


consumed


away


from home


are substitute


products.


Evidence


a more


general


nature


that


food


for home


consumption


food


consumed


away


from


home


represent


distinct


products


found


in the work of Mincer.


Mincer


demonstrated


that


estimated


income


elasticities


for a variety


commodities


will


tend


to be biased


if the


opportunity


cost


time


is omitted.


Evidence


a similar


vein


found


work


in the


suggests


works


that


of Hiemstra


the income


Eklund


elasticity


in that


of expenditures


of Burk.


for food


Their


away


from


home


considerably


higher


perhaps


twice


high


elasticity


home


food


consumption


expenditures


(Prochaska


Schrimper).


Apparently


addition


preparation


services











Implications


of Inadequate


Data


for Previous


Studies


further


implication


use


wholesale


level


data


proxy


for retail


data


involves


the prices


complements


or substitutes


expected


to be included


in a


demand


function.


Several


previous


authors


have


noted


their


inability


(see


Thompson


et al.,


to demonstrate


significant


effects


complementary


substitute


products


demand


for shrimp.


lack


correct


data


series


explain


these


empirical


problems.


proper


explanatory


variables


use


input


demand


function


are


prices


inputs


outputs


(McFadden,


theory


of retail


demand


holds


that


retail


demand


a function


of the


price


product,


income,


prices


other


products


(complements


or substitutes).


An attempt


to identify


complementary


substitution effects

are estimating to be


implies

a retail


analysts


demand


consider


function.


function


If the existing


they

data,


e.g.,


U.S.


correct


shrimp


data,


this


consumption


fact


data,


explain


are


not


adequate


the expected


proxies


relationships


are not obtained.


indicate


that


previous


attempts


to estimate


retail


demand


shrimp


attempts


estimate


wholesale


level


derived


demand


which


include


theoretically


correct


explanatory variables


should be


viewed


with


caution.


An example


an attempt


estimate


retail


level


demand


work


Doll,


used


retail


food


outlet


price


data


U.S.


shrimp


consumption


(which


wholesale


level


data)


explain











effect


consumer


price


index


meat,


poultry,


fish


demand


equation


which


employed


wholesale


prices


standard


wholesale


level


consumption


figures.


Since


consumer


price


index


should,


theoretically


an argument


in a


retail


level


demand equation


while


demand


other


two


equation,


variables


should


not


belong


remarkable


wholesale


that


level


consumer


derived


price


index variable


was


found


to be insignificant.


A similar


problem


was


noted


Thompson


et al.,


included


producers

stitutes


tion,


price

in their


employed


index


for processed


(apparent)


wholesale


estimation


level


meat


a price


of retail


prices


level


wholesale


for shrimp


shrimp


level


sub-


consump-


consump-


tion


analysis.


the wholesale


level


data


are not


adequate


proxies


for retail


or institutional


level


data,


their


use


in a demand


estimation


process


would


only


appropriate


estimation


derived


demand.


fact


that


complementary


substitute


retail


level


products


are


considered


appropriate


arguments


derived


demand


functions


explain


previous


authors


have


experienced


problems


demonstrating


complementary


substitution


effects


in their


demand equations.


light


these


considerations,


appears


unlikely


that


retail


market price


of shrimp


is an adequate


proxy


for the institution-


al market


products


price


with


because


relatively


two product


distinct


forms


markets


are probably


production


two distinct


technologies.


Further


, it


appears


that


previous


efforts


to estimate


the retail


level











information


on the prices


and actual


quantities


of shrimp


sold


through


institutions,


seems


appropriate


consider


estimate


retail


demand


for shrimp


associated


elasticities


as being


only


rough


approximations


actual


values.


Furthermore,


with


discontinuance


collection


retail


prices


probable


difficulty


(given


of imputir

diverse


a price


for shrimp


technology)


appears


in the institutional


that


market


calculation


retail


demand


estimates


shrimp


U.S.


become


virtually


impossible.


Thus


the model


developed here


will


focus


on the wholesale


market


level.


Research


Resource


Constraints


practical


limits


imposed


research


project


resource


con-


straints


can


also


lead


expediencies


that


cause


mis specification.


example,


variables


that


could


be considered


endogenous


have


been


entered


into


economic


models


as exogenous


variables


due to inadequate


information


available


to the analyst


Thompson


et al.)


as Sims


observed,


"because


seriously


explaining


them


would


require


extensive


modeling


effort


areas


away


from


the main


interests


of the


model


builders"


Theoretical


Constraints


increasing


understanding


complexities


economic


processes


, reflected


in the work


of Muth


(1960


, 1961)


Nerlove


(1967)


Lucas;


Pierce;


increased


economists


appreciation


difficulty


properly


specifying


many


economic


models


, 6).











prescribe


econometric


propel


model


r number

(Nerlove,


of lags

1972).


or leads of

Attempts


! variables


in a


account


dynamic

c known


complex


ities


have


created additional


problems.


For example,


Sims


notes


including


that


create

critique


econometrics


expectations


identification


standard


text


variables


problems.

econometric


econometric


Perhaps


models


Judge


most


model


disconcerting


contained


authors


recent


note


"that


possibilities


model


misspecification


are


numerous


false


statistical


models


are most


likely


the rule


rather


than


the exception"


(Judge


et al.,


p. 854).


Policy


Implications


of Missoecification


These


critiques


have


significant


relevance


in the


present


context


relating


the economic


impact


of increasing


shrimp


imports


likelihood


development


that


existing


policy


econometric


address


this


models


will


situation.


be used


Policies


based


misspecified


models


be inappropriate.


For example


the advisabil-


placing


some


restriction


on the flow


of shrimp


into


the U.S.


linked


to the demand


for shrimp.


Some


economists,


e.g.,


Prochaska


Keithly


, suggest


the income


elasticity


of shrimp


demand


is high


enough


that,


when


combined


with


reasonable


growth


rate


in U.S.


disposable


income


the expected


growth


rate


aquacultured


shrimp


supplies,


barrier


will


nece


ssary


to prevent


a decline


in the level


of real


shrimp


prices.


implications


research


other


economists


are


that


trade











indicating


that


shrimp


can


considered


inferior


good.


Coupled


with


price


inelasticity


increased


supply,


an income


elasticity


the inelastic


prevent


range


a decline


implies

in shrimp


that


barriers


prices,


since


to entry

growth


in income


cessary

cannot


expected


to shift


demand


sufficiently


to offset


the depressive


effects


on price


of increased


supplies.


Implications


for the Present


Effort


To the


extent


that


these


contradictory


implications


are the result


of misspecification


of the


econometric


models


used,


a test


system-


wide specification

policy formation.


may

Given


be useful


in selecting


the potential


adverse


a model

impacts


as the basis of

of inappropriate


policy,


appears


cation


appropriate


model


used


encourage


policy


the testing


development.


of the specifi-


Finally,


development


more


accurate


models


of the shrimp


market


is to proceed


from


the base


of existing


knowledge


contributed


current


models,


would


helpful


some


analysis


an existing


model


would


reveal


those


portions


model


most


appropriate


inclusion


into


respecification.


Thus,


appears


that


effort


develop


a more


accurate


understanding


economic


process,


such


operation


market


should


begin


with


such


a review


existing


work


proceed


with


investigation


the value


newer


techniques


existing


knowledge


stock


can


knowledge


then


be used


subject.


in an attempt


newly


to respecify


acquired


traditional










model


development


believe


that


follows


testing


the suggestion


implications


of Zellner


structural


Palm


assumptions


transfer


functions


and,


add,


final


equations


important


element


in the


process


of iterating


in on a model


that


is reasonably


accord with


the information


in the sample


data.


An obvious


next


step


in the evolution


of shrimp


market


models


generalize


the dynamic


model


used


Adams


allowing


all right-


hand


side


variables


to enter


the model


in appropriate


degrees


of lag.


For example,


lagged


quantities


have


a significant


effect


on current


quantities


and,


thereby,


current


price.


This


relationship


seems


especially


relevant


since


such


a large


portion


of shrimp


flow


through


institutions.


Institutions


can


expected


have


established


capacity


to market


an expected


quantity


a given


product


that


fluctuate


around


some


trend.


trend


can


seen


the result


the adj us tment


process


followed


individual


firms


as they


respond


changes


in their


operating


environment.


One method


of capturing


the influence


of this


adj us tment


process


a variable


interest


lags


variable


predicting


equations


as Adams


does.


However


such


a procedure


inadequate.


assumes,


method


explicitly


modelling


implicitly,


partial


a theory


adjustment


of expectation


processes


formation


(see


Gould).


As Maccin i


has pointed


out,


schemes


that


relate


expected


variables


solely


past


values


the variable


being


forecast


have


been


widely


criticized


because


they


assume


that


the firm


"ignores











business


data,


Maccini


found


that


firms


tend


to utilize


"economi-


cally


rational"


expectations


making


forecasts.


"Economically


rational"


implies


that


firm


depends


on other


relevant


variables


such


as shifts


government


policy


or other


exogenous


changes


in the


economic


environment,


addition


lags


variable


being


predicted,


form


expectations.


These


expectations


turn,


affect


adjustment


rates.


level


a single


industry,


such


addressed


this


study,


notion


"economically


rational"


expectations


imply


that


lags


of variables


other


than


the endogenous


variable


be useful


explaining


endogenous


variable


a given


equation.


Obvious


candidates


are


lags


of variables


that


appear


in unlagged


form.


Thus,


this


study


seeks


expand


previous


efforts


allowing


more


generous


expression


of lagged


variables


in what


should


be considered


respecification


of existing models


of the U.S


shrimp


industry.


Given


acknowledged


difficulties


faced


in the specification


traditional


econometric


model,


possible


that


an alternative,


data-based


approach


to model


specification may


a useful


addition


specification


process.


particular,


initial


vector


auto-


regressive


specification


(VAR)


the economic


phenomenon


under


study


useful


since,


argued


Sims,


can accommodate


above


mentioned


modeling


complexities


considerable


extent.


Additionally,


since


a VAR


model


can


seen


unrestricted


reduced


form


a generalized


econometric


model,


parameter


es-











large


extent,


this


feature


of the VAR model


frees


the analysis


from


constraint


particular


theory


relating


the operation


economic


phenomena


under


study


and allows


the sample


data


to speak for


themselves.


suggestion


employ


such


data-based


techniques


current


interest


in such


techniques


derive


additional


impetus


from


apparent


exceeded


economic


ques


fact


advances


theory.


also


that


advances


obtaining


current


be encouraged


computational


successful


interest


empirical


in data-based


a recognition


among


capability


models


modeling


economists


have


based


techni-


that


formulation,


identification


estimation


dynamic


econometric


models


must


approached


substantially


new


different


ways


(Sargent,


216).


This


study


seeks


follow


spirit


this


search


an integrated


approach


to economic


model


development


attempt


understand


more


fully


operation


U.S.


shrimp


market.















CHAPTER


MISSPECIFICATION TEST


The value


an econometric


model


estimated


with


two stage


least


squares


(2SLS)


three


stage


least


squares


(3SLS)


procedures


contingent


on a number


of conditions


(Theil,


511-513)


two of which


being


that


structural


equations


are


correctly


specified


linear

handle


parameters


nonlinearities,


such


variables.

estimates


Although


exhibit


methods

reduced


exist

level


efficiency,


when


compared


to maximum


likelihood


estimators,


unless


specification


linear


variables.


Proper


specification


par-


ticularly


important


a 3SLS


analysis


since


misspecification


single


equation


transmitted


or "spread"


across


the entire


system


the 3SLS


process


(Judge


et al.,


617)


Unfortunately,


the probability


of the


correct


specification


being


used


appears


to be quite


low.


An additional


factor


in support


of this


belief


that


misspecification


tests


of econometric


models


have


been

could,


widely

in the


used.

e past,


This

have


failure


been


examine


due to the lack


system-wide


necessary


specification

y statistical


software


computing


power.


Thus,


it is probable


that


the results


a test


specification


existing


econometric


model


will


indicate


the model


is misspecified.


Note


that


term


"misspecifica-


tion"


appropriate


since


test


used


here


searches


ways


which the


existing


specification


inadequate


rather


than


searching


are


__











purpose


of testing


an existing model


of the U.S.


shrimp market


present


time


to demonstrate


a specification


test


procedure


that


can


more


widely


applied


to understand


strengths


weaknesses


of the existing model


so that


this


knowledge


can


be included


in a


respecification


of the model.


analyzing


tests


existing


be impractical.


econometric


For example,


model


without


some


detailed


specification


knowledge


exis


ting


data


resources


impossible


question


particular


regressors.


Thus


, in


following


analysis


list


endogenous


predetermined variables


not questioned,


implying


that


the results


of the analysis


are contingent


on the validity


of the list


selected


the original


analysts.


Additionally,


the functional


form


of the existing


model


must


be taken


as given,


since


alteration


original


specification


would


constitute


a respecification


model.


Thus,


the principle


source


of testable


misspecification,


once


list


of endogenous


and predetermined


variables


functional


form


have


been


selected,


set of


exclusion


restrictions


placed


on the


model'


parameters


the analysts.


set of exclusion


restrictions


placed


on the structural


model


will


imply


restrictions


derived


or restricted


reduced


form


the structural


model.


The veracity


of these analyst-imposed


restric-


tions


can


tested


comparing


the restricted


reduced


form


with


unrestricted


reduced


form


of the


same


model.


Because


the unrestricted


reduced


form


system


equations


with


identical,


predetermined


use











values


consistent


with


population


parameter


values


(Schmidt,


78).


Since


unrestricted


reduced


form


not


influenced


exclusion


restrictions,


consistency


of the reduced


form


estimates


will


not be dependent


on the model


specification.


This


result


is not


without


some


cost,


as Dhrymes


127)


has shown


that


the unrestricted


reduced


form


estimators


are


asymptotically


inefficient


in comparison


with


3SLS


reduced


form


estimators


developed


from


a correctly


specified


econometric


model.


The problem


associated


with


the 3SLS


estimator


that


structural


parameter


estimates,


thus,


their


derived


reduced


form


representation,


will


inconsistent


structural


equations


are misspecified


(Challen


and Hagger


134).


Hausman


Test


The relationships


between


the restricted


unrestricted


reduced


form


estimators


motivate


use of the Hausman


test


(Hausman)


in the


present


analysis.


test


is based


on the existence


two estimators


a vector


statistics,


viz. ,


vector


parameter


values


simultaneous


equation


system's


reduced


form.


Under


the null


hypothesis


no misspecification


of the model,


one of


the estimators,


here,


restricted


reduced


form


parameter


estimates


derived


from


3SLS


estimation


structural


parameters


, is


asymptotically


consistent


efficient.


Under


alternative


hypothesis,


this


estimator


biased


inconsistent.


second


estimator,


here


the OLS estimate


unrestricted


reduced


form,


consistent


comparatively










misspecified,


two estimators


will


be dissimilar


in value.


Thus,


the difference


between


two provides


the data


for the specification


test.


Vec(7o)


- Vec(r3)


difference


between


estimates


o being


the unrestricted


reduced


form


estimator


while


is the restricted


reduced


form


estimator.


symbol


"Vec(


implies


vectorization


the matrix


within


parentheses


(see


Judge


al., p. 949)

Vec(iro) and


Denote


Vec(73)


parameter


covariance


Then


matrices


a Hausman


associated


specification


with

test


stati


stic


m = q'


(var(q))-l


where


var(q)


- n3


the variance


This


test


statistic


distributed


as chi-square


with


grees


of freedom


equal


the number


elements


Note


that


if the


system


contains


identitie


only


the reduced


form


parameters


the behavioral


equations


would


be used


since


including


identities would cause


and 0o


to be singular.


The covariance


of the restricted


reduced


form parameter


estimates


is obtained


a basis


through


discussion,


a procedure


assume


outlined


Schmidt


the simultaneous


236-239).


equation


model


the form


(4.1)


YF +XA


where


Y and v


are t


x g matrices


of endogenous variables


and structural


disturbances,


X is


x k matrix


of predetermined variables,


parameter


matrices


are


respectively.


implied,


+ v


= o0


= Zp + v











Note


the restricted


reduced


form


parameter


estimates


are functions


structural


parameters,


i.e.,


-AF"1


Thus,


following


result


established


the reduced


form


estimates


can


385)


be obtained


variance/covariance


matrix


from


(4.3)


Var(ir3)


= a~83/a8.'.


B'r3/8a


where


is the variance/covariance


matrix


the structural


parameter


estimates


(the


elements


derived


3SLS


procedures.


Schmidt


provides


a practical


derivation


of equation


(4.3)


(4.4)


Var(73)


= DW


where,


D=-(r-1)'


W is


a block


diagonal


matrix with


, i= 1


, given


The matrices


are the


and ki


endogenous


and predetermined


regr


essors


appearing


in the ith


equation.


In practice


columns


the estimated


reduced


form


parameter


matrix


are


used


first


columns


since


plim(X'X)X'Yi


converges


vector


population


parameter


values


associated


with


endogenous


variables


equation.


remainder


With


submatrix


auxiliary


regression


predetermined


variables


appearing


equation


complete


regres


sor matrix.


variance


unrestricted


reduced


form


Var(7o),


obtained


from


a seemingly


unrelated


(SUR)


estimation


of the


unres


tric-


ted reduced


form.


This


procedure


allows


the cross-equation


covariances


to enter


test.


The variance/covariance


matrix


of the SUR


parameter


estimates


can


be represented


W' D'


Wi=plim(X'X)-1X'(YiXi)











where


e X)


2 is the


error


covariance


matrix


from


the OLS


estimation


the unrestricted


reduced


form parameters,


i.e.


(Y-X(X'X)


-1X'Y)


Y-X(X'X)


-X'Y)


The Structural


Model


structural


model


seven


equation,


simultaneous


equation


model


U.S.


shrimp


industry


based


monthly


data


(Thompson,


Roberts,


Pawlyk).


This


model


was briefly


discussed


in the preced-


chapter.


The data


for reestimating


the model


were


kindly


provided


Dr. Kenneth


predetermined


equation


Roberts.


seven


over-identified


Counting


endogenous


with


the intercept,


there


variables


total


are fourteen


model.


number


Each


of over-identifying


restrictions


being


fifty.


The endogenous


variables


in the model


Consumption
warehouses)


(disappearances


thousands


from wholesale


of pounds


Wholesale


price


26-30


count


frozen


shrimp,


York


($/lb.


Exve


ssel


Mexico


price


($/lb.)

month


of 26-30
thousands


cold


count


shrimp,


of pounds,


storage


Northern Gulf


lagged one


(stocks),


month


thousands


pounds


Imports,


thousands


of pounds


Landings
pounds


from


U.S.


Gulf


of Mexico


ports


thousands


Fishing


effort,


number


fishing


trips


Gulf


shrimpers.


The predetermined


variables


in the model


Wholesale


price,


lagged


one month


are


are











month


cold


storage


holdings


(stocks),


lagged


month


Currency


exchange


rate


between


U.S.


Japan


(yen/dollar)


lagged


two months


Unadjusted


retail


sales


in eating


places


Prime


rate


of interest


on short-term,


business


loans


Diesel


fuel


price


(dollars/gallon)


Avera


ge precipitation


in coastal


Louisiana,


inches


lagged


two months


Avera


ge atmospheric


temperature


coastal


Louisiana


(degrees


Fahrenheit)


lagged


two months


Quarterly


dummy variable


for second,


third,


and fourth


quarter


of the


year


(j=2


,3,4)


Error


terms


(g=l,


,3,4,5


All equations
form as


are linear


in the


parameters


are shown


in functional


= f(Pw


= f(Sl


Pel,Q


, Q4


= f(L,

= f(S1


= f(Pw2


Pwl, Q2


, p4)


, Q2


= f(PR2


, Q2


, Q4,


= f(Pe


p7).


authors


provide


very


little


theoretical


justification


of the


model


specification


, in general,


not specifically


identify


behavior


being


modeled


each


equation.


Thus


difficult


provide m


iuch


more


information


re arding


he rationale ol


their


model


one


.











In discussing


their


specification,


the authors


note


that


economic


theory


suggests


that


prices


substitute


complementary


products


be included


in their


first


equation.


However,


their


prelimi-


nary

index


tests


to identify


for processed


substitution


meat


were


effects


unsuccessful


using

and t


the producers


therefore


' price


the variable


was not


included


in the model.


Also,


citing


the inability


of previous


researchers


to demonstrate


significant


complementarity


or substitution


effects


the authors


did not


include


ices


of potential


substitute


or complementary products.


Thompson


et al.


describe


the second


equation


in their


model


as a


price


level


exvessel


equation,


prices


noting


motivates


that


this


the inclusion


designation


current


assures


that


lagged


wholesale


exves


sel prices


move


together.


dependence


of exvessel


prices


on market


conditions


wholesale


level


treated


including


current


lagged


wholesale


price


exvessel


price


equation.


Noting


that


the United


States


Japan


are the major


competitors


world


supplies


shrimp,


authors


include


rate


exchange


between


the Japanese


yen and


the U.S. dollar


in the equation


explaining


imports


of shrimp


into


the U.S.


The equation


explaining


landings


of shrimp


reflects


influence


of environmental


factors


on the annual


shrimp


crop/population.


quantity
harvest


landed


is dependent


extent


on the


fishing


amount


of shrimp


effort


available


exerted


industry.


account


pink
life


Three


for 98


shrimp
cycle.


cies


percent


are estuary
Growth r


of annual


dependent


:ates


shrimp
Gulf


during


(brown,
landings.


during
this


the early


time


white,
Brown,


stages
l be


will


and pink)
white, and


of their
adversely


r


r


-- w


I











Louisiana
wetlands.


was


used


Data


reflect


precipitation


salinity


were


used


levels


instead


Louisiana
salinity


levels
monthly


because


basis


latter


Average


were


atmospheric


consistently


temperature


available


was used


instead


water


available


temperature in
in a consistent


estuaries


timely


fashion.


latter
Shrimp


was


landings


follow


typically
and July


a seasonal


low from


pattern
January


reflecting


from


through


spring


year


April


season


year.
id high
brown


Landings


in May,
shrimp


are


June,


gradual
season


dummy


decline


for white


variables


in landings


shrimp


which


after


July


reaches


are included


is interrupted


a peak


equation


in October.
to reflect


the fall
Quarter-
seasonal -


in landings


(Thompson


et al.


, p.


authors


note


that


treat


production


response


industry


adequately


it is


necessary


to include


the equation


explaining


effort


expended


harvesting


shrimp.


number


shrimping


trips


made


industry


vessels


selected


proxy


effort.


authors


explain


that


the existence


of externalities


in the


shrimp


shrimp


fishery


landed.


increased


"Hence,


effort


or may


equations


not


were


increase


included


amount


to describe


'behavior'


industry


terms


landings


effort,


respec-


tively"


(Thompson


et al.,


Hausman


Test


Results


Discussion


The structural


model


was estimated


3SLS.


The results


were


total


agreement


with


those


published


Thompson


uncertainty


regarding


exact


form


several


exogenous


variables.


However,


since


same


data


were


used


to construct


both


the restricted


the unrestricted


reduced


forms


and their


assoc


iated variances,


this


discrepancy


will


affect


test


results.


Following


steps


outlined


previous


section,


Hausman's


statistic


not


was











the critical


value


for a chi-square


variable


with


98 degrees


of freedom


confidence


level,


null


hypothesis


that


model


correctly


specified


is rejected.


itself,


Hausman


test


result


limited


value


in dis-


covering


possible


causes


for the rejection


of the null


hypothesis


possibly


finding


avenues


improving


specification


econometric


model.


Some


desired


information


can


obtained


from


a consideration


two


sets


parameter


estimates.


facilitate


the comparison


of the 3SLS


reduced


form


parameters


from


restricted


model


with


the OLS


parameters


estimates


from


the unrestric-


ted reduced form,


Table


presents


both


sets


parameters


along with


the t-values


for each


parameter.


A large


difference


between


estimated


parameter values


coupled


with


an indication


parameter


significance


as shown


the associated


values


greater


than


two signals


a possible


source


of model


misspecifi-


cation.


obvious


example


fuel


price


variable


which


designated


letter


In six


seven


equations


the OLS


estimate


is much


larger


in absolute


value


than


the 3SLS


estimate.


consistency


of plausible


signs


on the fuel 1


price


variables


consis-


tent


indication


significance


across


seven


equations


argues


inclusion


of the


fuel


price


variable


more


than


equation


a respecification


of the model.


Apparently,


this


variable


reflect


the fact


that


changes


in fuel


ces


have


impacts


at all


market


levels.


Further,


appears


that


fuel


a substantial


effect


one














Table


Comparing Restricted Reduced Form Parameter Estimates
with Unrestricted Reduced Form Parameter Estimates


Description of Symbols
Symbol Description


Symbol


Description


Restricted Reduced Form
Unrestricted Reduced Form
Constant
Second Quarter Dunmy Variable
Third Quarter Dunmiy Variable
Fourth Quarter Dunny Variable
Expenditures in Eating Places
Interest Rate


Fuel Pric
Exvessel
Cold Stor
Wholesale
Wholesale
Yen/Dolla
Precipita
Temperatu


e Index
Price Lagged One Period
age Lagged One Period
Price Lagged One Perio
Price Lagged Two Perio
r Rate Lagged Two Perio
tion Lagged Two Periods
re Lagged Two Periods


APPARENT CONSUMPTION EQUATI
Parameters
RRF URF
Cn 15931.17 -21872.27
02 2406.30 -463.02


6777.
6666.
1.
21.
-3.
-793.
0.
-56.
277.
2.
-1.
1.


-12234.
-1757.
0.
-817.
779.
69.
54.
217.


ON
t-Values
t-RRF t-URF
9.59 -2.12
1.81 -0.32
4.98 -1.62
5.04 -0.08
6.03 6.69
0,94 -0.21
-0.42 -2.08
-1.15 -0.63
1.00 0.31
-0.48 -0.34
1.13 0.46
1.07 3.57
-0.54 0.34
0.59 2.99


EXVESSEL PRICE EQUATION
Parameters
RRF URF
Cn 1.87 2.00
Q2 -0.16 -0.09
Q3 -0.36 -0.17
Q4 -0.10 -0.00
E 0.00 -0.00
R -0.05 -0.04
F 0.01 0.79
Pel 1.03 0.79
S1 -0.00 -0.00
Pwl 0.12 0.14
Pw2 -0.36 -0.05
EX2 -0.00 -0.00
PR2 0.00 0.01
T2 -0.00 -0.00


t-
t-RRF
2.88
-1.32
-2.37
-0.72
2.28
-2.74
0.44
3.70
-2.37
0.57
-2.50
-1.90
0.61
-0.67


Values
t-

4
-1
-1
-0
-1
-3
2
6
-3
1
-0
-3
1
-0


LANDINGS EQUATION
Parameters
RRF URF
Cn -20957.91 -25404.
Q2 3776.62 4210.
Q3 1841.08 -3395.
Q4 -2206.48 -3913.
E 0.08 2.
R -20.70 161.
F -1038.65 -11318.
Pel 457.52 -2687.


t-Values
t-RRF t-UJRF
-3.47 -2.84
1.86 3.34
0.57 -1.73
-0.82 -2.26
0.71 3.21
-0.72 0.72
-0.58 -2.22
0.73 -1.12
-0.76 -0.62
0.45 0.16
-n 70 A c


WHOLESALE PRICE EQUATION
Parameters
RRF URF
Cn 2.13 2.60
Q2 -0.16 -0.10
Q3 -0.41 -0.18
Q4 -0.14 -0.00
E 0.00 -0.00
R -0.03 -0.02
F 0.00 0.79
Pel 1.17 0.44
S1 -0.00 -0.00
Pwl 0.08 0.51
'D,.I -n t.i -n n


t-Values
t-RRF
3.14
-1.22
-2.74
-1.00
2.48
-1.76
0.44
5.83
-2.36
0.53
-4, -Tl


d
ds
ds












Table


Continued:


COLD STORAGE EQUATION
Parameters
RRF URF
Cn -27353.80 -25497.
Q2 502.80 -431.
Q3 -2067.62 -1120.
Q4 -80.54 541.
E -1.34 -0.
R -31.73 134.
F -829.51 -4942.
Pel 927.49 1650.
S1 0.97 0.
Pwl 83.37 115.
Pw2 1425.36 177.
EX2 11.32 13.
PR2 -266.06 -215.
T2 389.93 330.


t-Values
t-RRF t-URF
-5.08 -2.99
0.30 -0.36
-0.78 -0.60
-0.04 0.33
-4.15 -0.51
-1.06 0.63
-0.58 -1.02
1.32 0.72
57.07 25.37
0.50 0.06
3.42 0.13
1.55 0.82
-1.38 -1.64
4.66 5.52


IMPORTS EQUATION
Parameters
RRF URF
Cn 7584.98 -16969
Q2 -958.78 -3334
Q3 1462.16 -4874
Q4 7483.64 3546
E 0.00 3
R 0.00 -233
F 0.00 -8162
Pel 0.00 1382
S1 0.00 0
Pwl 0.00 -1386
Pw2 2046.29 924
EX2 16.25 68
PR2 0.00 56
T2 0.00 86


t-Values
t-RRF t-URF
2.47 -1.92
-0.84 -2.67
1.27 -2.50
6.64 2.07
0.00 4.79
0.00 -1.05
0.00 -1.62
0.00 0.58
0.00 0.04
0.00 -0.67
6.58 0.64
1.78 4.11
0.00 0.41
0.00 1.39


FISHING TRIPS EQ
Parameters
RRF
Cn -58747.00 -
Q2 13132.00
Q3 -3093.84 -
Q4 -8091.91
E 0.38


NATION


URF
47905.
15391.
11584.
-9508.
0.
388.
-3481.
337.


t-Va
t-RRF
-3.45
2.09
-0.34
-1.00
0.88
-0.91
-0.67
0.94
-0.94
0.49
-0.91
-0.86
-1.36
4.06


associated


point


that


since


structural


model


only


permits


fuel


price


to enter


trips


equation,


appears


that


this


variable' s


effect


not


communicated


rest


restricted


reduced


form


equations.


This


suggests


that


trips


equation


is not











The explanatory


weakness


of the


trips


equation


be due to problems


inherent


in the trips


variable.


For example,


a proxy


the trips


fishing


variable,


effort,


included


in the structural


inappropriate


this


model


task.


Shrimpers


take


same


number


trips


time


period,


but adjust


amount


fishing


time


trip


on the


basis


fuel


shrimp


prices.


Thus,


the number


of trips


they


make


not be


very


powerful


in explaining


fishing


effort.


These


considerations


argue


for dropping


trips


equation


from


a respecification


of the model


adding


fuel


variable


in several


of the other


equations.


Another

differences


"expenditures


variable


between


eating


associated


restricted


places,


with

d and


" E.


significant parameter

unrestricted reduced


Since


the OLS


estimate


forms


estimates


parameter


are


often


larger


than


those


estimated


3SLS


estimator


be argued


that


the econometric


specification


results


impact


especially

econometric


apparent


expenditures


important

model's


consumption


being


considering


estimation


on imports.


underestimated.


policy

impact


This


implications


expenditures


The unrestricted model


suggests


that


expenditures


have


a much


larger


impact


on landings


as well


on consumption


positive


Thompson


on imports


side,


than


appears


decision


suggested


the unrestricted


exclude


expenditures


econometric


model


from


model.


supports


wholesale


price,


exvessel


price


cold


storage


equations.











be used


calculate


an income


elasticity


of demand


shrimp.


their


article,


Thompson


calculated


elasticity


demand


related


retail


expenditures


inelastic


range


(.42


percent).


However


if the unrestricted


model


correct


in indicating


that


econometric


model


substantially


underestimates


the impact


expenditures


consumption,


then


possible


that


income


elasticity


demand


for shrimp


is in the elastic


range.


As shown


Table


4.1,


the unrestricted


reduced


form parameter


estimate


on expendi-


ture


three


times


larger


than


the restricted


reduced


form


estimate.


This

into


difference

the elastic


in value

range.


enough


The policy


to boost


implications


estimated


elasticity


one estimate


versus


the other


are substantially


different.


The results


relating


to the Yen/Dollar


exchange


rate


variable


also


merit


discussion.


The unrestricted model


indicates


that


this


variable


should


added


apparent


consumption


equation.


In agreement


with


model


indicates


specified


exchange


Thompson


rate


variable


should


unrestricted


not


model


included


wholesale


tion


price


equation


of the t-values


or the exvessel


listed


in Table


price


indicates


equation.


that


An examina-


the two models


largely


not


completely


agreement


regarding


the restrictions


placed on


the model


the analysts.


final


point


relation


between


reduced


form


Hausman


test


developed


here


structural


test


Hausman


presents


in his


paper.


This


latter


test


compares


Vec(f3)


Vec(8 2)


where


these


are


al.,











the off diagonal


elements


of the


error


covariance


matrix


are near


zero.


Additionally,


there


no guarantee


that


of the elements


of $2


consistent


if the over-identifying


restrictions


are incorrect.


test


this


type,


i.e.,


comparing


Vec( 3)


Vec( 2)


Thompson


model.


results


indicate


that


the hypothesis


proper

cancer


specification


level.


cannot


The inconsistency


rejected

of the t


conventional


wo tests


an obvious


signifi-

subj ect


for further


research.


Although


specification


test


results


relating


the existing


SEM indicate


that


the null


hypothesis


no misspecification


could


rejected,


analysis


reduced


form


parameter


values


generally


supported,


with


some


notable


exceptions,


original


analysts'


theoretical


decisions


regarding which


variables


to include


a given


equation.


in the existing


These

4 may


results

not be


may

very


indicate

serious.


that


the misspecification


Indeed


, a comparison


policy


implications


existing


model


with


those


respecified model


to be discussed


in Chapters


and VII


suggests


that


policy


implications


existing


model


are


robust


misspecification.


However,


results


indicate


that


several


variables


should


disagreement


with


be added


to the model


the theorists'


in various


parameter


locations,


restrictions.


indicating


These


results


should


be useful


in respecifying


the structural


model.


are


was


run


Summary















CHAPTER


VECTOR AUTOREGRESSIVE MODELS


primary


purpose


this


study


better


understand


relationships


among


relevant


economic


variables


associated


with


U.S.


shrimp


market t


for policy making


purposes.


Typically


the approach


to this


metric


problem


model


SEM).


sought


within


However,


context


several


a simultaneous


reasons,


econo-


including


analysts'


among


incomplete


the variables


understanding


of interest,


time


the resulting


related


simultaneous


relationships


models


are


misspecified.


This


study


hypothesizes


that


the analysts


understanding


of the economic


phenomena


under


study


the analysts'


later


specifi-


cation


a related


can


be improved


the knowledge


gained


from


specification


analysis


a vector


autoregress


(VAR)


specification


of the subject.


Vector


Autoreeressive


Theory


Understanding


the reasoning


for selecting


the VAR


approach


begins


with


standard


explanation


that


the simultaneous


econometric


model


expressed


part


(the


complete


system


contain


trend


component:


see Judge


et al.,


P. 686)


of a multivariate,


autoregressive


moving


average


time


series


(ARMA)


model


. Quenouille,


1957


Theil


Boot,


1962


Zellner


Palm,


1974;


Wallis


, 1977


or Anderson


al. ,


1983).


A general


dynamic


simultaneous


equation


model


(SEM)


be written


can


can











A(L)Zt


+ B(L)Xt


= C(L)et


D(L)Xt


= F(L)vt,


where


F(L)


a vector


are matrices


of endogenous


of polynomials


variables


, A(L)


in the non-negative


D(L),


powers


of the


operator


are


vectors


a vector


of random


exogenous


serially


variables,


uncorrelated


errors


where,

assumed


have


zero


mean


constant


variances.


system


combined


to form


the single


ARMA model


(5.2)


G(L)


H(L)pt


where


G(L)


H(L)


are


appropriately


restricted


matrices


having


nonzero


is the


elements


vector


A(L)


, B(L)


containing


C(L)


both


and Xt.


respectively


In general,


J(L)


= JO


+ J1L


+ J2L2


+ J3L3


where


= A,


etc.


H(L)


invertible,


ARMA


model


can


expressed


purely


autoregressive


form


(5.3)


A(L)


where


A(L)


been


redefined


A(L)


G(L)


Then,


autoregressive


form


in (


5.3)


can be written


a generalized,


restric-


reduced


form


= A(L)Yt-_


where


A(L)


has again


been


appropriately


redefined.


The equation


system


(5.4)


is restricted


such


that


the Xt


subvector


of Yt


is exogenous.


If these


restrictions


are not imposed


the unrestricted


reduced


form


can


= #t,


ted,


, B(L),


C(L),


D(L),


F(L),


=(H(L))-1











known


vector


autoregressive


systems.


Thus,


system


unrestricted


reduced


form


some


unknown structural


system


equa-


tions;


alternatively


the VAR


model


is consistent


with


many


different


structural


models.


These


considerations


argue


in favor


of using


VAR specification


of the economic


phenomena


under


study


because


specification


minimizes


exposure


the recognized


dangers


analyst


observe


induced


relation


specification


to univariate


errors.


times


As Anderson


series


et al.


estimation:


250)


"the


time


series


analyst


not


constrained


particular


theory


during


identification and estimation


of the model


second


argument


use


specification


arises


directly


ted.


from


Note


the generalized


that


nature


generalized


of the VAR


reduced


system


form


just


equation


demonstra-


system


equations


have


identical


regressors


long


restrictions


imposed.


Thus,


the system in


can


be consistently


estimated


using


ordinary


least


squares


without


being


concerned


about


the existence


simultaneous


equations


bias.


Furthermore,


estimating


each


equation


separately


using


ordinary


least


squares


produces


asymptotically


consistent


estimates


because


the right-hand side


variables


are the


same


every


equation.


From


a practical


point


of view,


then,


models


are easy


to estimate


because


efficient


consistent


estimates


produced


without


using system estimation procedures


(Hakkio


and Morris,


10).


More


important,


however


are


implications


this


consistency


estimation


desired


population


parameter


use


are


can










SEM,


then


the estimates


of properly


specified


model


are consistent


with


the information


in the data


sample


therefore,


consistent


with


underlying,


but unspecified


SEM.


Thus,


model


provides


practical


method


obtaining


consistent


estimates


population


parameters


use in the prediction and


control


of economic


phenomena,


while


minimizing


exposure


specification


errors


made


in a limited


information


environment.


Some


preliminary


evidence


relating


to the robustness


to misspeci-


fiction


models


versus


SEM models


been


presented


Hakkio


and Morris


(1984,


Their


results


indicate


that


point


estimates


from


a VAR


model


are more


robust


to model


misspecification


than


point


estimates

estimates


from

from


a structural

a structural


model.


model


However,


are more


they


efficient


found

than


that

those


point

from a


model


except


when


model


badly


misspecified.


Hakkio


Morris


speculate


that


specification


more


robust


because


a less


restrictive


system of


equations


than


is the SEM.


additional


attraction


specification


that


parameter


matrix,


the matrix,


A(L)


, in equation


system


contains


information


on the relationships


between


the variables


included


in the


vector


This


information


can


quite


useful


prediction


purposes


can also


provide


guidance


in policy


matters.


Thus,


specification


several


characteristics


which


recommend


in applied


work.


Estimation


Procedures


use










above,


this


results


least


squares


parameter


estimates


coinciding


with


the maximum


likelihood estimates.


Once


exogenous


endogen-


ous variables


to be included


in the model


are selected,


the specifica-


tion


the model


is completed


deciding


where


the variables


enter


model.


model


composed


three


parts


exogenous


variables,


endogenous


variables,


error


vector.


exogenous


variables


will


include


the intercept,


the indicator


or dummy


variables,


trend


exogenous


system


variable,


of endogenous


other


variables.


variable


Such


judged


a model


represented


(5.5)


= bt


+ A(L)Yt


where


s a


vector


of the endogenous


variables


a vector


composed


the indicator variables


the trend and


intercept variables,


the selected exogenous


variables.


Determining


the Order


of the Model


A complication ar


ises


in selecting


the order


of the autoregressive


portion


of the model.


This


selection


accomplished


sequentially


adding


lags


of the


vector


to the model


testing whether


the added


variables


have


estimated


parameters


that


are


significantly


different


from zero.


Several


tests


of the null


hypothesis


that


parameters


of the


added


variables


are


not


significantly


different


from


zero


are


avail-


able.


Nickelsburg


studied


the small-sample


properties


of six criteria


using


Monte


Carlo


techniques


found


none


to be


clearly


superior


can










several


criteria


base


decision


combined


information.


Accordingly,


four


criteria


were


selected


for calculation.


The criteria


Akaike


s AIC


criterion,


Schwartz


s SC


criterion,


likelihood


ratio


statistic


(LR),


and Sims


modified


likelihood


ratio


test


(SMLR).


The criteria


are represe


nted


AIC(j)


j)/t


SC(j)


= In j

= In i2j


Int)/t,


LR(j


-m)=-


t(lnI


-lnlSm


SMLR(j-m)


t-((k*m)+s


)(lnlZj


-lnlEm


where


is the error variance/covariance


matrix


of the test version


the model


having j


included


lags


of the dependant variable


vector,


k is


the dimension


test


of the


version


vector


model,


m are the number


s is


of lags


number


in the


exogenous


regressors


in the


two criteria


tem (Sims


select


The decision


the model


of order


rule


that minimizes


for the first


the value


of the criterion.


The last


two criteria


are distributed


asymptotically


as chi-square


with


degrees


of freedom


equal


the number


of restric-


tions


placed


on the restricted


model


k2(m-j).


Thus


the decision


rule


test,


pairwise


models


increasing


order


select


the model


with


the largest


not rejected


as insignificant.


purpose


adding


lags


dependent


variable


until


error


process


becomes


white


noise


remove


influence


past


values


variable


present


value.


This


process


accordance


with


the notion


that


a major


portion


of the variation


are


+ (k










is also


required


in Chow'


technique


, discussed below,


of analyzing


lead/lag


relationships


among


variables


the endogenous


system.


The variation


remaining


error


process


after


pre-whitening


will


a combination


of random


variation


the variation


caused


other


variables


. Greenberg


Webster,


153).


Thus,


analyz-


residuals


of pre-whitened


time


series


influence


of other


variables


on a variable


interest .can


be detected.


technique


employed


here


analogous


to the pre-whitening


processes


employed


well-known


causality


testing


procedures


however,


instead


pre-


whitening


each


time


series


individually


vector


time


series


variables


are treated


simultaneously.


Hoskina


s Test


for White


Noise


Testing


a white


noise


error


process


context


multivariate


system


accomplished


using


Hosking


s (p.


605)


multi-


variate


portmanteau


statistic


tr(Cr'Co


= Zr=1 ..


-1CrCo


where


n is the number


of observations


, tr is the


trace


operator,


are the estimated


autocovariance


matrices


of the


vector


of endogen-


variables


zero


levels,


respectively


s=o(nl/


Note


that


s=o(nl/2)


implies


that


s is


at most


of order n1/


(Greenberg


Webster,


313).


portmanteau


statistic


dis-


tribute


as chi-square


with


k2(s-p)


degrees


of freedom,


where


k is the


dimension


endogenous


vector


order


process.


ous











Estimating


Relationships


Among


Variables


Once


the VAR


model


has been


estimated,


the information


concerning


the relationships


two


alternative


parameter matrix


among


the variables


techniques.


of the simultaneous


in the model


technique


system


involves


to discover


can be obtained


decomposing


the trigonomet-


c functions


implied


its characteristic


roots.


The other


detects


relationships


between


two


variables


considering


correlations


between


variables


various


distances


time,


i.e.


various


levels.


These


two


techniques


are


also


known


analyses


frequency


dimension


and in the


time


dimension,


respectively.


techniques


will


be discussed


sequentially.


Decomposition


of the Parameter


Matrix


exogenous


variables


in section


of the model


at (


can be


dropped


since


they


are hypothesized


to have


no simultaneous


relation-


ship


with


endogenous


variables


simultaneous


system.


generalized


model


becomes


equivalent


model


(5.4)


which


can


rewritten


without


the lag


operator


= AlYt-1


+ A2Yt-2


*+* YAmYt-m


+ Ut.


adding


an appropriate


identity


for m-i of the m lags


this


system


can be rewritten


S Am

* a O
0

0


Yt-4


two











redefining


vector


names,


system


can


be written


as a first-


order


system with


the more


compact


matrix


form


= AYt-1


+ Ut.


Here


are


vectors,


being


number


variables


in each


vector


and m being


the number


of lags


and A


is the


km x km matrix


parameters.


Since


error


vector


would have


been


shown


insignificantly


different


from


a vector


zeros


estimation


testing


phase


discussed


above,


can


now


set equal


zero


the equation


system


in (


becomes


a homogeneous


, linear


system


of difference


equations


of the form,


= AYt-1.


The solution


to such


a system


is Yt


= AtY0.


Assuming


quickly


moment


appreciate


that


characterizes


are scalars


time


one can


path


following


relations


can


seen


if I

if I


the solution

the solution


path

path


is explosive

is damped


the solution


oscillates


the solution path


is monotonic.


case


a multivariate


system,


in which


regain


their

path


matrix

of Yt.


designations,


course,


the matrix


eliciting


A again


the desired


characterize

information


time


is somewhat


more


complicated


under


these


more


interesting


circumstances.


Chow


(chpt.


shows


this


is accomplished


utilizing


the characteris-


roots


characteristic


vectors


of matrix A.











Freauency


Dimension Analysis


A characteristic


root


of A is


a scalar,


that


satisfies


A- II=


With


A being


a square


matrix


of dimension


where


p=km,


roots


will


be obtained.


Associated


with


each


characteristic


root,


characteristic


vector,


which


satisfies


Aibi.


Writing


this


equation


in expanded


form


yields


A(bI


, bp)


= (Albl,


, bp)


Denoting


matrix


, *bp)


whose


columns


characteristic


with


vectors


the characteristic


A and


roots


setting


equal


represented


to the diagonal


along


its main


matrix


diagon-


system


of characteristic


roots


vectors


can


be written AB =


equivalently


= BDB-1


This


implies


the solution,


= AtYo


be written


= BDtB-lYo.


simplify


some


mathematical


computations


involved


deriving


this


solution,


Chow,


introduces


the canonical


variables,


with


vector


form


representation:


B-1Yt


= BZt.


Using


the expressions


= BDB-


, Zt-l


= AYt_1,


redefined


B-1(BDB


DZt-1.


solution


to Z


t = DZt


is Zt


= DtZ0.


Thus,


the solution


for Yt


can be


expressed


terms


canonical


variables


BDtZo.


solution


for individual


elements


of Yt


is given


= B;P iZlnti)


*1


nto)


+ + B (Z*n t


are


can


can


, pbp)


= (bI


= B-Ytl


-1)Yt-l


v -^ *


/


f r^


* Y


*n










indicated.


Further


analysis


these


complex


numbers


can


reveal


information


concerning


the related variable's


cycle


frequency


phase


shift


(lead or


A complex


lag)


root,


relationship


with


is defined


other variables


as A


in the


= a + bi where


system.

-1)1/2


a and


are real


numbers.


term,


complex,


arises


from


the fact


that


the complex


root


is composed


a real


part,


and an


imaginary part,


being


imaginary


number.


complex


number,


represented


on a


Cartesian


plane


with


imaginary values mapped


along


vertical


axis


real


numbers


along


the horizontal


axis.


The length


a ray


from


complex


the origin


number,


to the point

d is called


(a,b)


the absolute


the modulus


value


Using


plane


trigonometry,


modulus


calculated


, cosO


or a


cos8


sine


where


is the angle


between


modulus


horizontal


axis.


Using


these


results


complex


characteristic


root


can be


expressed


as A


=a +bi


(cos0


*sinO)


Xlei0


The relation,


= cos8


*sin0


used here


explained by


Chiang


. 518-520).


Returning


the solution


an individual


time


series


variable


given


above


in equation


consider


the contribution


a pair


of complex


conjugate


roots,


say,


would


make


the time


path


of Yit


Note


that


cost


*sin t)


De Moivre'


theorem


(Chiang,


522).


Thus


t(cos~t +


i sin t)


= Rtei


t(coset


- i'sin0t)


= Rte


-i0t


can


(a2+b2)1/2











pairs


complex


conjugates


such


that


BIZ10


then


B1(ZIOXtl)


from


equation


can


repre


sented by


SRtei e


+ SR


-ist = SRt(


-ilt)


= SRt


cos( +0t)

SRtei e it


+ isin(#+Bt)


+ SRte


cos(4+Ot)


-it


sin(+Bt)


SRtcos(t+Ot).


Thus


the contribution


a pair


of complex


conjugates


a cosine


function


time


multiplied


a factor,


As with


the previous


discussion


relating


to the characterization


a solution


a univari-


ate system,


this time path


will


be damped


or explosive


depending on


value


of R


Note


that


the complete


solution


of Yt


is the


sum of the various


individual


contributions


as shown


equation


involve


additional


pairs


complex


roots


singular,


real


roots.


studying


the expression,


2SRtcos (+Bt)


one can


understand


relationship


between


various


time


series


(variables


interest)


determined.


Note


that


if 2SRt


= 0,


equation


would


simple


cosine


function


time


that


would


repeat


itself


every


time


Ot became


some


multiple


of 27r.


For example,


cost


when


etc.


More


generally


cost


when


27r+k,


47+k,


etc.


Dividing


both


sides


of this


last


expression


reveals


that


cost


will


have


same


value


when


= k/O,


2r-+k/6


4ir+k/9


every


= 2Ir/O


time


units.


Thus


, the time


length


the cycle


is 2r/8,


where


is measured


in radians.


Equivalently,


one cycle


is completed


2/eO


time


units.


frequency


function


number


can


, 2ir,


= k,


B2Z20


e-ie










because


there


will


a frequency


corresponding


to each


pair


of complex


roots


in the solution


of Yt-


nonzero,


the value


of cos(*+0t)


will


be shifted forward or


backward


according


value


For example


, assume


one


time


series


obeyed


the function


cos(Ot)


at frequency,


a second


time


series


have


followed cos(+Bt)


the value


at the


one when


same


while


frequency;


the second


the first


series


series


would


would


have


value


one when


= -/e0.


second


series


arrives


at or becomes


one before


the first


series.


Equivalently,


the second series


leads


first

series


time

lags


series


time


the second


units.


time


Stated


units.


Thus,


differently


is the phase


first

shift


in number


time


units


function,


cos(4+et),


indicates


leading


relationship


with


cost


if $


is positive


or a lagged relation-


ship


if


is negative.


If both


time


series


have


nonzero


the lag


or lead


relationship


between


two,


at a


given


frequency,


is given by


r(sr)ij


= abs(ji'-j)/8r.


Conventional


usage


is that


if Oi>ej,


series


leads


series


r(sr)ij


time


units


at frequency,


However


, when


r(sr)ij


is subtracted from


a complete


cycle


lead-lag


relationship


reversed.


This


result


reflects


cyclical


nature


underlying


trigonometric


functions


implies


that


causal


hypotheses


take


form,


leads


Yj t,


form,


leads


appropriate


conclusion


relating


lead-lag


relationship


depends


results


If


, 2n/6,











summary,


contribution


a pair


complex


roots


time


path


solution


a times


series


variable


can


obtained


calculating


an expression


of the form,


2SRtcos(4+Ot).


The expression,


2SRt


will


define


the amplitude


of the function,


e.g., the magnitude


the swings


above


below


trend


line.


The function


will


tend


converge


trend


line


if R<1


tend


to explode


diverge

length


from

(will


trend


complete


line


a full


if R>1.

cycle)


The

in 2/0B


function


time


will


units


have


which


ia cycle

implies a


cycle frequency


of 9/2w.


The phase


of the cycle


will


be defined


time


distance


between


two


series


will


defined


r(6r)ij


abs( i


Finally,


lead-lag


relationship


between


two series


establish


ed on


the basis


of hypothesis


testing.


The estimated dynamic


properties


of the various


series


in the VAR,


as determined


parameters


of equation


(5.7),


are functions


of the


parameters


submatrices,


, from


equation


Thus,


variances


of the dynamic


parameters


are related


to the variances


of the


parameters


matrices.


385)


shown


that


if Y


f(X)


then


the variance


of Y is var(Y)


(BY/aX)


' cov(X)


*(aY/aX).


present


case


, the phase


angles


frequency


angles


are functions


elements


matrix


equation


i.e. ,


they


function


parameter


estimates.


Thus,


variances


estimated


angles


and frequencies


can


be found


using


s result.


example


the variance


of the frequency


angle


var(9)


= (80/aA)


*cov(A)


*ae/aA,


out


are


-4j)/ r.











differentiation,


i.e.,


adding


a small


value


to individual


elements


dividing


change


change


individual


parameter


estimate.


The variances


of the frequency


angles


can


be employed


in testing


hypotheses


that


individual


frequency


angles


are not


significantly


different


from


zero.


Assuming


the frequency


angle


values


are normally


distributed,


z statistics,


where


= (6-0)/a


and a


- the


square


root


the variance


of the frequency


angle,


can


be calculated


used


in the


hypothesis


tests.


Since


these


tests


are


valid


only


sample


stati


stics


are normally


distributed,


a test


of the normality


assumption


should be


conducted


prior


to testing.


Time


Dimension Analysis


A second


method


of determining


the relationships


among


variables


of interest


to analyze


the variables


of interest


are correlated


over


time.


This


procedure


is facilitated


considering


group


variables


interest


vector.


correlations


can


then


calculated


autocorrelations,


i.e.,


correlation


variable


with


sequentially


higher


ordered


lags


of itself.


Using matrix algebra,


result


will


a series


matrices


whose


elements


will


covariance

variables


relationships

of interest arn


among


variables


e the variables


interest.


in the endogenous


Here


vector


of the


vector


autoregressive model.


autocorrelation


matrices


were


calculated


following


procedure


outlined


Chow


49-54).


Subtracting


the expectation











where


t-E(Y


Multiple


substitutions


into


equation


replacing


yields


(5.10)


= Ut


+ AU.t-.


+ A2Ut_2


+At 1Ut.


The autocovariance


matrix,


for r > 0


E(Y*


t-r)


= (Ut


+ AUt


+ A2Ut..


... +At-lUt)


(Ut-r


+ AUt-r-1


r-1Ut)


+ A2Ut-r-2


t-r)


= (ArUt-rUt


-r + Ar+lUt


-r-1Ut


-r-l


... + At-1U1Ut


-r-1


'A',t-r-l)


= Ar(V


+ AVA


+ A2VA


... + At-r-1VA't-r-


where


E(UtU


for t/s


Note


that


current


period


variance/covariance


matrix


(when


r=O)


the matrix


inside


paren-


theses


equation


Denote


variance/covariance


matrix


with


the symbol


practice


this


matrix


is determined by


setting


such


that


AnVAn'


negligible.


example


present


analysis


was set to 200.


autocovariance


matrices


relating


covariances


between


error


terms


separated


various


lengths


time


are obtained


through


equation


this


raising


sequentially,


the value


arranging


r and


the resulting


recalculating.


matrices


doing


in increasing


order


one can


observe


covariance


between


two times


series


changes


as one variable


is compared


to larger


lags


of another variable.


covariances


between


two


variables,


also


termed


cross-


covariances,


reveal


lead/lag


relationships


between


the variables.


example,


value


cross-covariance


between


two


variables


+At -


E(UtUs)=Vt











correlation


between


two


variables


obtained


dividing


cross-covariance


square


root


of the product


of the variances


two series.


The variances


of each


series


are found


along


the main


diagonal


of the variance/covariance


matrix


(where


r=0).


Understanding


significance


calculated


correlations


requires


measures


standard


errors


of the


correlations.


These


statistics


are


obtained


using


technique,


based


on Rao


result,


described earlier.


In this


case,


the variance/covariance


matrix


of the


autocorrelations,


var(O)


= (8a/aA)


'*cov(A)


*8a0/A,


where


cov(A)


variance/covariance


matrix


estimated


parameters.


value


, an/aA,


is estimated


numerical


differentia-


tion,


i.e.


, by


sequentially


adding a


small


value


to individual


elements


dividing


change


in n


change


individual


parameter


estimate.


practical


aspects


this


process


are


somewhat


complicated


however,


is possible


to provide


the basis


an understanding


process


with


a short


example.


Assume


a model


wherein


the number


estimated


variables


parameters


in the model


equals


equals


number


Thus,


autocorrelatioa


endogenous

n matrices


at each


are


symmetric


with


dimensions


Also,


assume


that


the variances


of autocorrelations


out to


a lag


are desired.


process


small


would


.000001)


to change


amount


value


and recalculate


one estimated


the autocovariances


parameter


out


a lag











numerical


derivatives


associated


with


change


a particular


parameter


estimate.


Because


there


are


parameter


estimates


there


will


be 50 matrices


of derivatives.


Next


matrices


of derivatives


must


sorted


so that


derivatives


associated


with


a given


order


are


same


matrix.


Next,


each


of these


11 rearranged matrices


with


dimensions


sorted


into


smaller


matrices


with


dimensions


50 by


that


contain


only


derivatives


associated


with


a particular


endogenous


variable


assumed


(recall


here).


that


Each


there


these


are


endogenous


55 rearranged


variables


matrices


model


are used


post


parameters


multiply


to obtain


variance/covariance


the variance/covariance


matrix


matrix


estimated


of the autocorrela-


tions


at each


order


of lag.


variances


of the correlations


between


a single


endogenous


variable


itself


the other


four


variables


each


order


of lag,


are


located


along


the main


diagonals


of the 55


resulting matrices.


vertically


Extracting


each


concatenating


of these


whole


group


diagonals


result


as a row vector


a 55


matrix


containing


11 submatrices.


Each


the 11 submatrices


contains


variances


autocovariances


between


five


endogenous


variables

Once


at orders


of lag


variance


from zero


matrix


to ten.


of the autocorrelations


is calculated


can be used


to test


the hypotheses


that


the estimated


autocorrelations


significantly


different


from


zero.


complication


arises


calculating


test


statistics


such


z-values,


where


(c-0)/a


are


are











normally


distributed.


They


lie within


the unit


circle.


Thus


appropriate


transformation


of the correlation values


is required before


hypothesis


tests


based


normal


distribution


can


used.


Assuming


transformed


autocorrelations


are


normally


distributed


implies


that


a z statistic


can


be calculated.


If the z statistic


greater


than


two,


hypothesis


on the


autocorrelation


value


rejected.


This


chapter


estimation,


discussed


the frequency


vector


time


domain


autoregressive


analyses


model,


for estimating


relations


chapter


between


provides


the endogenous


empirical


variables


applications


of the model.


of this


following


material.


can
















CHAPTER


ESTIMATING


VAR MODEL


Estimating


a vector


autoregressive


model


of the U.S.


shrimp market


entails


selection


variables


included


the model,


selection


order


the model,


testing


assure


that


residuals


discussed


model


sequence.


are


time


The chapter


independent.


concludes


These


with


steps


a section


will


discussing


the estimated


the endogenous


parameters


variables


of the


VAR


as revealed


model


through


the relationships


analyses


among


in the frequency


and time


dimensions.


Selection


of Variables


in the VAR Model


selection


vated


of variables


understanding


included


market


the model


probable


is moti-


effects


changes


important


variables


will


have


on market


participants.


additional


exvessel


selection


price


criterion


U.S.


shrimp


parsimony.


Of major


open-entry


concern


nature


shrimp

single

existing


fishing

price v

a data


industry.


ariable


U.S.


However


in the model

shrimp uti


wholes al

because


lization


price


was


it relates


chosen


most


importation.


directly


Further,


exvessel


prices


can


be derived


from


the wholesale


price


series


Imports


of shrimp


were


included


reflect


increasing


importance


this


variable


market.


Domestic


landings


are


added


other


source


of shrimp


supply


to the U.S


market.










End-of-the-month


cold


storage


holdings


shrimp


in U.S.


ware-


houses


were


behavior;


included


however,


they


primarily

y are also


capture


essential


effects


for calculating


inventory


an estimate


apparent


consumption.


Thus


the inclusion


cold


storage


holdings


obviates

estimate


need


apparent


to include a]

t consumption


parent

can be


consumption,


derived once


since an adequate

landings, imports,


and cold


storage


holdings


are estimated.


Another


maj or


force


in the market


thought


to be the Japanese-


yen/U


.S.-dollar


exchange


rate


(Thompson


et al.)


since


foreign suppliers


choose


either


these


two


markets


depending


relative


strengths


reflect


of the


a weakening


two currencies.


of the


An increase


relative


in the yen/$


to the dollar


ratio


thus


would


foreign


suppliers


will


find


sales


in the U.S.


relatively


more


attractive


than


sales


to Japanese


buyers.


Theoretical


considerations


suggest


the inclusion


of income


prices


substitute


commodities.


Following


Thompson


al.,


U.S.


aggregate


expenditures


in commercial


eating


places


is used


as a proxy


for an actual


income


variable


such


as U.S


aggregate


disposable


income.


"expenditures"


justified


because


approximately


U.S.


shrimp


consumption


occurs


a commercial


setting.


Prices


substitute


products


are included in


the model


dividing


the wholesale


price


of shrimp


expenditures


gross


national


product


implicit


price


deflator.


The price


deflator


can


be considered


an index


of all


other


input


prices


thus,


inclusion


brings


prices


use











rational


economic


agents


only


respond


changes


real


prices.


Completing


the list


of variables


in the model


are a trend


variable


eleven


(monthly)


indicator


or dummy


variables.


These


variables


were


included


to account


for temporal


persistence


and seasonal


effects.


Selecting


the Order


of the VAR Model


Once


specification


variables t<

of the model


o be included


completed


the model are

deciding where


selected


the variables


enter


ogenous


model.


variables


model


, the endogenous


composed


variables,


three


and the


parts


error vector.


exogenous


variables


will


include


intercept,


indicator


vari-


ables,


trend


variable,


other


variables


judged


exogenous


to the


system


of endogenous


variables.


In the present model,


the expenditures


variable


was


judged


to be


exogenous.


remaining


variables


(landings


, imports,


wholesale


price,


cold


storage


holdings,


the yen/$


ratio)


enter


the model


as endogenous


factors.


The model,


as shown


at 5


Chapter


can


be represented


t = bt


+ AY.t_


where


a vector


endogenous


variables


and b


a vector


composed


of the indicator


variables


the trend and


intercept variables,


the expenditures


variable.


Estimation


model


accomplished


using


ordinary


least


squares


techniques.


actual


calculations


were


made


a micro-


computer


using


program


displayed


in Appendix


program


written


matrix-based


programming


language


entitled


"Gauss


ex-










As described


in the previous


chapter,


this


selection


is accomplished by


sequentially


adding


lags


vector


model


testing


whether


added


variables


have


estimated


parameters


that


are


sig-


nificantly


different


from zero.


noted


the previous


chapter,


the criteria


selected


with


order


test


are


Akaike


criterion,


Schwartz'


s SC


cri-


terion,


likelihood


ratio


statistic


(LR),


Sims'


modified


likelihood


ratio


test


(SMLR).


decision


rule


first


criteria


to select


the model


of order


that


minimizes


the value


the criterion.


The last


two criteria


are distributed


asymptotically


chi-square


with


degrees


of freedom


equal


to the number


of restrictions


placed


restricted


model,


symbolized


k2(m-j).


Thus,


decision


select


rule


the model


test


with


, pairwise,


the largest


models


lag not


increasing


rejected


order


as insignificant.


Table


presents


results


of calculating


values


four


lagged


criteria


dependent


shrimp


vectors.


model


Note


over


that


increasing


AIC,


numbers


SMLR


added


criteria


indicate


the model


with


should be


selected.


The degrees


of freedom


between


rejecting


two


adjacent


the null


models


hypothesis


Thus


37.653


, the


critical


percent


value


confidence


level.


The SMLR


would


rej ect


all models


of order


higher


than


one until


twelfth


order.


The values


of the maximum


likelihood


ratio


test,


given


column


headed


with


indicate


the order


of the model


should


at least


eight;


however,


the other


three


criteria


suggest a


use










were


calculated


using


the PROC


MATRIX


procedure


of SAS


to operate


program


presented


in Appendix


Table


Tests


to Select


the Order


of the VAR Model*


SMLR


SMLR1


4.92
4.59
4.32


10.54
11.02
11.45
11.94
12.37
12.72
13.05
13.52


33.34
23.78
33.52
39.66
41.14
25.01
47.49
54.95
46.21
56.74
68.98
73.07
47.75


28.58
19.68
26.73
30.45
30.36
17.71
32.22
35.65
28.61
33.43
38.59
38.71
23.87


23.78
57.30
96.95
138.09
163.10
210.58
265.53
311.74
368.47
437.45
510.52
558.27


19.68
45.70
74.45
101.92
115.53
142.90
172.28
192.98
217.14
244.76
270.45
279.13


37.7
67.5
96.2
124.3
152.1
179.6
206.9
234.0
261.0
287.9
314.7
341.4


* The column heading symbols
L=Number of lags, LDS=the


covariance
criterion,
likelihood


model c
freedom
square
values


matrix,
LR=the


ratio
order


relating
value at
indicate


have


SC=Schwartz'


likelihood


criterion,


the following meanings
E the determinant of


s SC


ratio


criterion,


criterion,


LR1 and SMLR1=refer


2 and sequentially
to the LR1 and SMLR1


percent


circumstances


level


in which


high
tests
of


r


AIC=Akaike'


SMLR=Sim's


to tests


orders,


s, X2(.05)
confidence.


the null


error
s AIC


modified
between a


DF=degree of
is the Chi-
Underlined


hypothesis


can


rejected.


Sims


suggests


that


some


cases


advisable


inves-


tigate


significance


large


lags


endogenous


vector


include


those


lags


with


significant


parameters


while


dropping


inter-


mediate


lagged


variables


with


insignificant


parameters.


s pos-


sibility


can


be considered


using


the LR and


SMLR


criteria


the data


in column


LDS of Table


6.1.


Columns


LR1 and


SMLR1


give


the values


the LR and SMLR


criteria


when


a model


of order


two is


tested


against










between


a model


of order


two and


a model


of order


three.


Similarly,


the value


in column


on row eight.relates


a test


between models


order


two and eight.


Underlined


values


indicate


circumstances


in which


the hypothesis


zero


values


added


parameters


can


rej ected


level,


i.e.,


circumstances


in which


test


suggests


that


the model


choice


the higher


order


model.


Thus


the LR criteria


again


argues


for an higher


order model;


however,


the implications


of the other


three


criteria


an order


are in


higher


agreement


than


that


one.


the model 1


Thus


should


appears


not


be specified


inappropriate


with


to follow


Sims


s suggestion


include


"high"'


orders


lagged


dependent


vector


present


case.


fact


weight


evidence


indicates


model


should


first


order.


However,


con-


sideration


of Nickelburg'


finding


that


"underfitting


of models


quite


common"


.183)


the present model


is specified


as a second order


VAR model.


Testing


the VAR Model


After


reestimated


the order


of the VAR


in a restricted


form


model


that


been


reflects


selected


theoretical


the model


judgement


relating


the exogeneity


of the variables


in the endogenous


system.


In the


present


case


this


relates


to the yen/$


variable.


It is unlikely


that


the other


variables


in the


system,


with


the exception


trend


exchange


and

rate


intercept


since


variables


shrimp


have


market


significant


cannot


impact


considered


on the

a major











Incorporating


restrictions


such


into


non-sample


estimation


information


mentioned


parameters


model


necessitates


use


is the estimator


of the restricted


denoted


here


least

that i


squares


s obtained


estimator.


when


This


sum


squared


residuals


model.


are


minimized


subject


restrictions.


shown


various


texts,


including


Judge


472-473),


the generalized


least


squares


restricted


(GLSR)


estimator


the solution


to the minimization


problem


minimize


over


(y-Z3)


I)(y-Zfi)


subject


to Rfl=r,


where


vectorization


ordinary


least


squares


(OLS)


parameter


matrix,


the vectorization


of the OLS Y matrix,


is the


block


diagonal


matrix


with


matrices


predetermined


variables


associated


with


each


endogenous


variable


along


the main


diagonal,


I is


the OLS


error


covarinace


matrix,


and R is


a matrix


zeros


ones


appropriately


placed


to pick


out the individual


elements


of /3 subject


restrictions


vector


this


case,


r is


a column


vector


technique


zeros.

of forming


minimization


the Lagrangian


problem

solving


solved


the partial


through


derivatives


of the Lagrangian


for 0.


The result


= B +


(z'(-lI)Z)


(E-QIl)z)-1R


-l(r-Rf)


The approach


used


here


to first


estimate


fOLS


and then


calcu-


late


GLSR


expression


shown


above.


ordinary


least


squares


estimator


/OLS


'(E-


= (X


'X)-X'Y,










variables),


the expenditures


in eating


places


variable,


the first


second


endogenous


vector.


endogenous


vector


composed

storage


of five

holdings


variables


landings

yen/dollar


, imports


exchange


wholesale


ratio.


price,


cold


resulting


estimator,


fOLS,


a (24


x 5)


matrix


parameter


estimates.


getting


restrictions


that


only


intercept


trend


variable


have


a significant


influence


on the yen/dollar


ratio


implies


twenty


exclusion


restrictions


parameters


equation


explaining


fifth


the yen/dollar


column


ratio.


These


estimator.


parameters


Following


are


found


Bewley


these


restrictions


can


be represented


'(fOLS)R2


= G,


where


a (20


x 24)


matrix


composed


of null


identity


matrices


as follows


Z(8x14)


Z(12x2)


I(12)


I(4)


Z(4x5)


I(4)


Z(4x6)
Z(4x1)


Z(12x


where


Z(ixj)


implies


a null


matrix


with


dimensions,


I(4)


an identity


matrix


of dimension


x 4).


a (5


x 1)


vector


such


that R2


' and


G is


a (20


x 1)


null matrix.


Note


that


since


GLSR


estimator


employs


vectorization


timator


restrictions


must


transformed


erate


on a column


vector


rather


than


multi-column


matrix.


Bewley


demonstrates


this


process


showing


that


stacking


the columns


of RI


'(fOLS)R2


yields


the restrictions


employed


in the GLSR


estimator,


i.e.,


where


es-


= [0o


-= r,











Since


these


restrictions


operate


only


on the


parameters


yen/dollar


ratio


equation


they


are known


"within


equation"


restric-


tions.


Alternatively,


in the terminology


used


Bewley


82)


, they


"uniform


mixed


linear


constraints"


(UMLC).


This


convenient


since


Bewley


102-103)


shows


that


under


special


case


that


restrictions


placed


on a model


are UMLC,


the generalized


least


square


restricted


estimator


equivalent


to the maximum


likelihood


estimator,


which


implies


that


the restrictions


placed


on the model


the UMLC


be tested


with


the maximum


likelihood


test.


Recall


that


the log


of the likelihood


function


for a multivariate,


normally


distributed


variable


= -n/21og(2ir)


- n/21og|I


- l/2(y-Zf)'n-l(y-Z/3),


where


a block


diagonal


matrix


with


matrices


predetermined


variables


along


its main


diagonal,


is the vectorization


of the matrix


of dependent


variables


is the determinant


of the


error


covariance


matrix


number


observations.


Since


term,


Zp)'n-1(y-Zfi),


a scalar


likelihood


function


pressed


as L


- n/21og[l


where


c is


a constant.


Thus


, maximizing


likelihood


an observed


sample


equivalent


to minimizing


determinant


of the


error


covariance


matrix


of the


system.


Testing


the veracity


of the restrictions


amounts


to comparing


maximum


likelihood


values


two


systems:


one with


restrictions


without.


two


values


are


significantly


different,


parameters


of the restricted


variables


are assumed


to be significantly


are


can


can


ex-


one










model


divided


likelihood


value


the unrestricted


model.


Symbolically,


the likelihood ratio


= L(G*)/L(3).


times


natural


this


ratio


distributed


with


degrees


of freedom


equal


the number


of restrictions


placed


on the


restricted model.


Thus,


-21nA


= -21n[L(p*)/L(/3)


c-n/


inln*


-(c-n/21njn|)


= n [lnl0*


- lnill],


where


the symbols


remain


as described


immediately


above.


restrictions


placed


VAR,


viz,


that


neither


price,


landings,


imports,


cold


storage


holdings


, expenditures


eating


places,


nor


are assumed


the monthly


to be


dummy


correct.


variables


affect


calculated


the yen/dollar


likelihood


ratio


ratio,


value


of 26.06 is


not


large


enough


to reject


the hypothesis


that


parame-


ter values


these


variables,


yen/dollar


equation,


are


zero


given


twenty


grees


of freedom.


Once


restricted


form


model


been


estimated,


residual


vector


Hoskings


tested


portmanteau


as being

statistic


essentially

discussed


a random


Chapt<


process

er III.


using

The


portmanteau statistic


is distributed


as chi-square


with


k2(s-p)


degrees


of freedom,


where


dimension


of the endogenous


vector,


s was


selected


to be


order


process.


present


case,


statistic


was


calculated


466.36


with


grees


of freedom


Thus


, the null


hypothesis


that


error


process











Analvzine


the VAR Model


Table


6.2 displays


parameter


estimates


of the restricted


form


of the


vector


autoregressive


model.


The t-values


give


some


indication


proper


first


while,


order


of each


this


endogenous


model.


endogenous


typically


variable.


variable


case


The t-values


Note


that


a high


with


associated


with


in all


associated


cases,


t-value;


second


each


the first


second


lags


each


endogenous


variable


are


underlined


table.


expected,


variables


most


are


parameters


insignificantly


different


other


from


lagged


zero.


endogenous


noteworthy


to note


that


those


trend


parameters


with


high


t-values


have


signs


that


might


be expected.


trend


imports


has been


positive


while


trend


in price


cold


storage


have


been


slightly negative.


Concern

import v


over


variables


imports


impact


of imports


in the price


equation.


Note


equati


that


on price

on and o


since


focuses


in the price


t-values


attention


variables

on these


variables


nificant.


are


low,


However,


results


these


since


frequency


relationships


are


relationships


domain


analysis


not


statistically


appear


discussed


sig-


support


below,


some


value


to mention


following


points.


Both


sets


parameters


indicate


a negative


relationship


between


first


order


predetermined


variable


dependent


variable.


Both


sets


parameters


also


indicate


a positive


relationship


between


second


order


of the predetermined


variable


the dependent variable.

















CO)N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00
NC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

43 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


I I I I I I I I I I I I I I I
o ooo o o oo o o o o










0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


00 000000000000000
*I I I I I I I


0000N

0 0 0 0 (0
00000(
.00004
0 0 0 0 1

1


S0 0 0 0 0
A o o o -
S0 00 0 0


00 0 0


0 ID N .

rC) rI CO U

N C N N
MMOR
* *
.4 *4 0 *4
I I



OD 0 >
CD (D r^ 0


(00O0> 0) Nsa SN N Un 4 N 4 4 4 0a 0n 4 *4
o 4 o r C. m a me


r .* S A O 4 p .
0) CI 0 O 4t O4 0
I I I I I I


0 CO .-4 CQ


*4 rl4 0O .4
S.4 *
0 M4*- NC


(D NO C0 3 f O n NIA S inN C (C 0 r 3
ON N (O f- o t l cn o0 ) 0 Cn CD Ct BO C r O m4 nC


o00 coC 0) om o N co ) r N t C ND O 0o
Pfl 0I fiP 004' NC') 0) C 0004 (J ON COON r40
* p p P P( P P 5 5 p( p a p p 5 5


.-I 00 0
*4 I


D IOA 04 OO -O N 0O O0OOO N OO
SI I I 1 I I I


NO *4 C NOOl N 4 0 )
r U U C ) N a) U C oo
CC c0 m' in gb g, .4 *4 (' 40


j ICD


'-4 fO CD O N 000 c c


mfN M 4O00 ON 04 N* 00 O


NN 0 C0


* a a a
r- NM 0 0)


u1 0) N

oo rr o
S0no


*O
OD r 4


*1 0


oo in o co r^ UD r^ -tf nD csi ro so o cM Ot rT C
NA N O4M N* 4 (o N e N.o o oo ooo o
N oC o n0- 0) N C0 NN e 4 o ooo 04o 0
O O O O ON ON N Nl OOC O O4 0 C' 000 O 00
S0 000 00 0f0 .4 000 N 00000 00

*4 000000000000000000 00000


* R
SN S
4''4A

0 -N
0 0


1D0 0 00)0 0 0)
* Co o N) C Co vI 04 .*
.j430 (D U1N CnC


) NON ONO N) C
roJ or f^ on CT r( r- r-I ( l
o o ON IS. ro NO O


ON COO 0O) O OO 0O 0


ow to
*4 4 NC
0 I P



0 CO


0 r* N r' N 0
NC c N OSN C
a N 4r 0 0O C
S0) o oN (o (


S 0 o* N


0o (D NOND OOQ M


I I I


IAN 0)0 *4 40Ii


O m 00 0 Na NcM 0 0 0 ) 0


ID (CD G 0 ) (C 4 0


0 0 0 D D ( 0


rN t Om o 0o) 4 *4 0o 4 C ) ^


o 00 C o CON 00


000000
I I I


7% *-n W C r CM C' ) M oo
r4 N0) *Co0o oA *o o
.43 4 r- r. N (0D rNO r' 4 4 *4 iU, Or- c
'*0 0)4 (0 *o Nt 0)o 0D N


4 *4 O r0 C- N 4 IA 0


I I I


F0 )0 4 D 0.


. 0


0 0


I I I I I I


0n r4 C tOn oc vPt p N w in


N N (00 0 0 VI 4! MN r* r 4 4.


< *4 Q r


(0 o


. N r. N 0I O *4 (- M) 0U fO 3


i a0 a S S S i-n o p ra P o

0 OI CM 0 C t P 0 1 5 t I
S t 1 I f t t t I


SC0 N IN


S0 0


0ON


000000
I


St .n q


O *


- r- V *W V- l I UJ F- UJ UU I-. I


0 0


S00
* *
00


a .


*


II Ei f











importer


decided


on a particular


level


import


purchases.


month


later,


when


the changed


level


of imports


begin


arriving,


it has


effect


prices.


one


instance,


results


have


captured


demand


response


the other


instance,


a supply


response.


Thus,


one might


conclude


that


within


the period


one month


imports


have


inverse


relationship


with


price


but,


over


a two month


period,


imports


have


a positive


relationship


with


price.


final


note


relating


stability


of the VAR


model


is of


value.


Since


explosive


time


series


are


atypical


economic


perience,


it is generally


believed


that


economic


processes


are stable.


Thus


an acceptable


model


an economic


process


should


also


exhibit


stability.


present,


case,


i.e.,


context


of the model


presented


that


in equation


roots


6.1;


necessary


eigenvalues


conditions


parameter


for stability


matrix


are


lagged


endogenous


variables


are less


than


one in absolute


value.


As shown


following


section,


the estimated


model


meets


these


necessary


conditions

Frequency


for stability.

Domain Analysis


Following


process


outlined


in Chapter


the large


A matrix


equation


was


decomposed


determine


frequency-determined


relationships

autoregressive


among the variables

system. The actual


in the dependent


calculations


vector


were


of the


carried


vector


out using


Gauss


program


detailed


Appendix


Table


presents


results


of these


calculations.


Three


frequencies


were


revealed,


having


ex-











degree


of confidence


one might


place


on these


estimates.


Accordingly,


appears


that


the 2


month


cycle


the three


year


cycle


have


some


validity.


basis


this


information


one


might


then


consider


the lead/lag


relationships


associated


with


each


of these


three


frequencies.


Table


Frequency


Relationships


of the VAR


Cycle


Lengths


t-Values

Phase-shift


2.31
7.34


Months
36.54


56.59


Values


Landings
Imports
Price


Storage


-17.69


-4.89


15.83
-13.09
-14.65


Lead-Lag Relationships Associated with


the 2


.31 Month


Cycle*


Imports


Landings
+0.67
-1.64


Months
Imports


Price


Price


Storage


Lead-Lag Relationships


+2.23
-0.08


+1.62
-0.69

Associated with


+1.56
-0.75


+0.95 +1.70
-1.36 -0.61

the 36.54 Month Cycle*
Months


Imports


Landings
+12.07


Imports


Price


Price


-24.47
+13.68
-22.86


-34.92


. Storage +23.74
* -12.80


-24.86


-26.48


*Column variables


*Underlining


Lead


indicates


(+) or Lag (-) Row Variables
the lead-lag relationship of


choice.











that


two possibilities


are given


for each


pair


of variables:


either


leads


or B


leads


For example,


the figures


on rows


nine


ten of


table


indicate


that


landings


either


lead


imports


.67 months


imports


1.64 months.


Since


the analysis


only


captures


a segment


of continuous


time


, it


is impossible


leading.


to determine


This


from


impossibility


the phase-shift value


easily


which


understood


variable


picturing


segment


a graph


two sine


waves.


If the


waves


are out of phase,


cannot


determine,


from


information


contained


graph,


which


of the


waves


leading.


only


information


contained


in the


graph


and in the frequency


analy


sis presented


here


is the time


distance


phase-shift


distance


separating


cycles


two


variables.


Recall


that


absence


additional


information


concerning


the relationship


between


two variables,


the designation


of the leading


variable


among


a given


pair


arbitrarily


set by


the convention


selecting


variable


with


the highest


positive


phase-shift


value


leading


variable.


However,


designated


lead/lag


relationship


between


two


variables


can


reversed


subtracting


the phase-shift


time


separating


two series


from a


complete


cycle.


Given


studied,


some

may


knowled


that


process


designation


generating


leading


data


variable


being

need


not be arbitrary.


For example,


given


time


between


ordering


shipment


shrimp


from


a foreign


seller


importation


shrimp


, it


is unlikely


that


price


is leading


imports


less


than


one


one











Table


6.3.


It is interesting


to note


that


this


short-term


relationship


between


wholesale


price


imports


appears


supported


information


from


three-year


cycle


on row


of Table


6.3.


Note


also,


from


data


captured


in the three-year


cycle


rows


18 and


plausibility


asserting


that


imports


lead


price


in the short-term and


price


Table


leads


6.3,


imports


price


leads


the medium


imports


term.


indicated


medium-term


on row


approximately


three


years.


A consideration


of the data


on the relationship


between


price


storage


argues


for concluding


that


price


leads


storage


approximately


two months.


return


product.


Thus,


to storage


short-term


operations


storage


is related


fluctuations


to the price


would


not


expected


affect


price,


rather,


that


short-term


price


fluctuations


would


affect


storage


levels.


Similar


considerations


indicate


that


landings


storage


lead


leads


wholesale


imports


price


1.35


months


months.


in the short-term and


meanings


that


most


other

cases


lead-lag

in which


relationship

a reasonable


data


are somewhat


argument


can


more


be made


obscure.


select


In those


either


relational


possibilities,


relationship


choice


indicated


Table


underlining


appropriate


value


rows


nine


through


twenty-one.


Time


Domain Analysis


Following


relationships


process


among


discussed


the variables


Chapter


in the endogenous


III,


vector


lead-lag


of the VAR











demonstrated


in Chapter


III,


the autocorrelation matrix


relating


to the


vector


of variables


in the VAR model


(6.2)


= Ar(V


+ AVA


+ A2VA2'


.. + At-r-lVA't-r-1)


where


r is


the lag


or time


distance


between


two variables,


Vt-s=E(UtUs)


and A


the parameter matrix


of the VAR.


autocovariance


matrices


relating


covariances


between


error


terms


separated


various


lengths


of time


are obtained


through


equation


this


sequentially,


raising


value


arranging


r and


the resulting


recalculating.


matrices


doing


in increasing


order,


changes


one can


observe


as one variable


covariance


is compared


between


to larger


lags


two times


of another


series


variable.


The covariances


or cross-covariances


between


two variables


reveal


lead/lag


variables

covariance


relationships,


(Chow,

between


averaged


52).


over


example


two variables


all frequencies,


value


at r=2, suggestion


be highest


between


cross-

g that


Yjt-2


are most


highly


related,


or that


Yjt-2


leads


time


periods


Note


that


these


time


dimensional


relationships


are of


general


domain


nature


analysis


while


relationships


are specific


discovered


to the identified


frequency


frequencies.


Thus,


frequency


denominated relationships


be expected


to be


more


accurate


than


the time


denominated


relationships.


The correlation


cross-covariance


between


square


two variables


root


is obtained


the product


dividing


of the variances


two series.


The variances


of each


series


are found


along


the main


two











Appendix


D presents


sequence


autocovariance


matrices


time


series


variables


endogenous


system


model


under


study


here.


Table


.4 provides


a summary


the information


Appendix D.


Table 6.4


Autocorrelations in the VAR Model


Maximum Correlation Value (r) Between Column Variable and Row Variable, Associated
t-Value (t) and Lag (L) at which the Maximum Correlation Occurs


Landings


Imports


Price


Storage


Yen/Dollar Rate


Landings
Imports


Price


Storage


Yen/S Rate


0.11


-0.14
-0.27
0.35
-0.02


-1.37
-1.86
2.91
-0.12


-0.30


1.00


-2.66 10


0.28 2.03


0.25


1.51 0


-0.20 -1.36


0.29 2.42 0
-0.21 -1.50 5


-0.56


0.43


-3.04


-0.04 -0.23


0.03


2.15


-0.41 -1.91


2.48


-0.33 -1.71


-0.10 -0.64


a autocorrelation
b continuously in


a single


creasing


variable


cross-correlation


general


, the


results


time


domain


analysis


provides


support


support


for the


broadly


defined


relationships


among


variables


estimated


often not


frequency


in agreement


analysis;


regarding specific


however


details


two


analyses


are


of the relationships.


For example,


the data


frequency


in Table


analysis.


6.4 indicate


However,


that

time


imports

domain


lead


price


analysis


indi-


cates


that


imports


lead


price


ten months


rather


than


the 1.


55 months


indicated by


the frequency


analysis.


similarly,


both analyses


indicate


that


landings


lead


wholesale


price;


but,


time


domain


analysis


indicates


the time-distance


separating


two variables


is five months


rather


than


the 2.2 months


suggested


the frequency


domain


analysis.











indicates


that,


medium-term,


imports


lead


storage


approximately


twelve


months.


The time


dimension


analysis


estimates


time


distance


between


these


two variables


to be five


months.


some


cases


the results


of the


two types


of analysis


appear


agreement.


example


, both


time


frequency


domain


analysis


indicate


that


price


leads


storage


approximately nine


or ten


months.


results


two


analyses


are


also


reasonably


close


concerning


frequency


relationship


analysis


between


indicates


the yen/dollar


a leadership


ratio


role


and imports.


the yen/dollar


ratio


approximately


seven


months.


time


domain


analysis


indi-


cates


time


distance


between


two


variables


to be four


months;


however,


cross-correlation


function


between


two


variables


sharply


peaked


four


month


lag.


fact,


difference


between


the cross-correlation


value


at the four


month


interval


and the


seven


month


interval


amounts


to only


four


percent


correlation


value


at the four


month


interval


(see


Appendix


In those


incidence


where


results


time


domain


analysis


frequency


:requenc

based


domain


results.


differ,


a knowledge


For example,


in the


of the market


case


favors


of the relationship


between


imports


wholesale


price,


frequency


analysis


result,


that


imports


lead


price


1.55


months,


appears


more


plausible


than


the alternative


that


imports


lead


price


ten months.


Given


that


supplies


shrimp


are


regularly


added


storage


during


spring,


summer,


fall


harvest


seasons


during


winter


not


new