Thre Essays on Antidumping Duties and Risk Factors
Affecting International Seafood Trade
by
Dengjun Zhang
A disertation submited to the Graduate Faculty of
Auburn University
in partial fulfilment of the
requirements for the Degree of
Doctor of Philosophy
Auburn, Alabama
December 12, 2011
Keywords: Antidumping duties, exchange rate risk, price risk, demand system, cointegration
Copyright 2011 by Dengjun Zhang
Approved by
Henry Kinnucan, Chair, Profesor of Agricultural Economics and Rural Sociology
Henry Thompson, Profesor of Agricultural Economics and Rural Sociology
Norbert Wilson, Asociate Profesor of Agricultural Economics and Rural Sociology
Andrew Muhamad, United States Department of Agriculture
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ii
Abstract
This disertation includes three esays to addres influences of the antidumping policy,
price risk, and exchange risk in the US seafood import market. In the first chapter, I atempt to
evaluate the efect of trade diversion on the efectivenes of antidumping duties. Antidumping
duties can have the unintended consequence of increasing imports from countries not named
in the dispute. Previous research suggests ?trade diversion? significantly undermines the
efectivenes of antidumping duties. However, domestic consumers could reduce their losses,
as they can substitute out of the dutied good and into both the domestic good and the non
dutied good, which is, as might be expected, les expensive than the domestic good. Testing
these propositions using the 2003 antidumping duty imposed by the United States on catfish
imports from Vietnam, I find that the tradediversion efect was significant in the sense that
the quasirents of US producers enjoyed from the antidumping duty were reduced. The impact
on consumer welfare was modest due to the great loss generated from the higher price of the
dutiedgood. An implication for public policy of the empirical results is that, in terms of the
national welfare gain, it is optimal to lower the tarif rate when the amount of trade diversion
is large.
The second chapter examines the impact of the export price risk and exchangerisk on
the import demand. An extended Rotterdam model reveals that risk factors take efect on
marginal utility via ?adjusting? prices. This coincides with viewpoints in trade literature that
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riskaverse importers atach a risk premium as an extra markup to cover the cost of exchange
risk (Balg and Metcalf, Bergin) and/or price risk (Wolak and Kolstad). The derived model
further demonstrates that the trade efects of risk factors depend on ownprice elasticities and
substitutability betwen products within the same group. The modified specification makes
testing restrictions on the efects of the risk variables plausible, resulting in a reduction in the
parameter space. By further decomposing import price risk into export price risk and
exchangerate risk, the empirical model is applied to the US salmon import market. The
results support the hypothesis that importers are sensitive to price and exchangerate risks but
reject the proposition that those two risk factors exert an identical efect on import demand.
The third chapter focuses on the diference betwen the dynamic and static
specification for an import demand system inclusive of the price risk factor. I build risk
factors into an Almost Ideal Demand System (AIDS) where the price risk may play a role by
influencing baseline imports or import responsivenes to price. The riskaugmented AIDS
model tests causality betwen price risk and trade. A multivariate GARCH approach estimates
the conditional variances of prices. Nonstationarities in the data and endogeneity of price and
price volatility are taken into acount with Johansen?s approach and a Vector Error Correction
Model (VECM). The empirical results uncover a substantial role of risk factors in the US
codfish import market. China?s import share (CIF) increased 18% from 2004 to 2005, while
Canada lost 9%. Holding other factors constant, high fluctuation of Canada?s price would
reduce its share by 69%, and raise China?s share almost two times. China?s relatively stable
price further diminishes Canada?s share by 4% and increases China?s share by 9%.
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Acknowledgments
I would like to thank my advisor and commite chair, Dr. Henry Kinnucan, for initiating
me to do research from an economic perspective. This is one of the most important principles I
have learnt in Auburn and has been contributed substantialy to each chapter of my disertation.
Other appreciation goes to Dr. Henry Thompson, Dr. Andrew Muhamad, and Dr. Norbert
Wilson for their profesional comments. Special thanks to Dr. Hyeongwoo Kim for his
econometric help. I also want to expres my appreciation to Dr. Valentina Hartarska and Dr.
Diane Hite for their excelent teaching and research guidance.
Finaly, I owe my parents, my wife Jenny, and my son Andy a big debt of gratitude and
appreciation for their love, support, and patient in these years. In this period, with litle help from
me, Andy learnt to speak the Norwegian language fluently and speak English at least as well as
me. Your growing gives me the motivation to concentrate on my studies every day, because it is
the only way I can shorten the time of separation so that I can be reunited with you and Mum.
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Table of Contents
Abstract ........................................................................................................................................... ii
Acknowledgments .......................................................................................................................... iv
List of Tables ................................................................................................................................ vii
List of Figures ................................................................................................................................ ix
Chapter I. Antidumping Duties and Trade Diversion: An Armington Procedure .......................... 1
1.1 Introduction ................................................................................................................. 2
1.2 Model ........................................................................................................................... 5
Tarif PasThrough Elasticity (PTE) ............................................................... 6
TradeDiversion Efect ..................................................................................... 9
1.3 Parameterization ........................................................................................................ 11
1.4 Simulated Tarif PasThrough Elasticities (PTE) .................................................... 13
1.5 Welfare Analysis ....................................................................................................... 15
Distribution efects .......................................................................................... 17
Sensitivity Analysis ........................................................................................ 19
Tarif Rate and Trade Diversion ..................................................................... 21
1.6 Concluding Comments .............................................................................................. 22
Chapter II. Import Demand under Price and ExchangeRate Uncertainties ................................. 25
2.1 Introduction ............................................................................................................... 26
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2.2 Theoretical Model ..................................................................................................... 29
2.3 Model Specifications and Data .................................................................................. 35
2.4 Measurement of Uncertainty ..................................................................................... 37
2.5 Regresion Results .................................................................................................... 38
Model selection and Hypothesis tests ............................................................. 39
Price and Expenditure Elasticities .................................................................. 41
Volatility Elasticities ....................................................................................... 43
2.6 Conclusions ............................................................................................................... 44
Chapter III. A RiskAugmented Cointegrating Import Demand System ..................................... 46
3.1 Introduction ............................................................................................................... 47
3.2 Background ............................................................................................................... 49
3.3 The Theoretical Model .............................................................................................. 52
3.4 Empirical Model and Data ........................................................................................ 54
3.5 Price Volatility .......................................................................................................... 56
3.6 Econometric Procedure ............................................................................................. 58
3.7 Regresion Results .................................................................................................... 60
3.8 Summary and Implications ........................................................................................ 64
References ..................................................................................................................................... 66
Appendix 1: Tables and Figures for Chapter I .............................................................................. 74
Appendix 2: Tables and Figures for Chapter II ............................................................................ 82
Appendix 3: Tables and Figures for Chapter III ........................................................................... 93
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List of Tables
Table 1.1 Prices, Quantities, and Market Shares for Domestic and Imported Frozen Catfish
Filets, United States, 1999  2010 ........................................................................... 75
Table 1.2 Simulated Duty Pasthrough Elasticities
a
............................................................... 76
Table 1.3 Distributional Efects of a 35% Catfish Antidumping Duty Under Alternative
Asumptions About the Market Share of the NonDutied Good ............................. 77
Table 1.4 Sensitivity of Welfare Efects of the Catfish Antidumping Duty to the Armington
Elasticity (!) and Import Supply Elasticities (" = "
2
= "
3
)
a
...................................... 78
Table 1.5 Sensitivity of TradeDiversion Efects to Antidumping Duty Rates
a
...................... 79
Table 2.1 US Salmon Imports and Market Shares by Sources .................................................83
Table 2.2 GM Estimates of U.S. Import Demand System for Salmon, Rotterdam Model
Inclusive Import Price Risk, 19952008 Monthly Data (1 = Chile, 2 = Canada, 3.
Norway, 4 = United Kingdom, 5 = ROW) .............................................................. 84
Table 2.3 Tests of Theoretical Restrictions ............................................................................. 85
Table 2.4 GM Estimates of U.S. Import Demand System for Salmon, Rotterdam Model
19952008 Monthly Data (1 = Chile, 2 = Canada, 3 = Norway, 4 = United
Kingdom, 5 = ROW) ............................................................................................... 86
Table 2.5 Conditional Demand Elasticities (1 = Chile, 2 = Canada, 3 = Norway, 4 = United
Kingdom, 5 = ROW) ............................................................................................... 87
Table 2.6 Conditional Demand Elasticities (1 = Chile, 2 = Canada, 3 = Norway, 4 = United
Kingdom, 5 = ROW) (cont) ..................................................................................... 88
Table 3.1 US Cod Imports, Expenditure Shares, Prices by Sources .........................................94
Table 3.2 Johansen Cointegration Test Results ....................................................................... 95
Table 3.3 VECM Estimates of US Import Demand System for Codfish, AIDS Model, 1989 
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2010 Monthly Data (1 = Canada, 2 = China, 3 = Iceland, 4 = ROW) ..................... 96
Table 3.4 Derived Demand Elasticities (1 = Canada, 2 = China, 3 = Iceland, 4 = ROW) ...... 97
Table 3.A1 ARCH Test for Price (1 = Canada, 2 = China, 3 = Iceland) ...................................100
Table 3.A2 MGARCH Estimates of Conditional Variance of Price (1 = Canada, 2 = China, 3 =
Iceland) .................................................................................................................. 101
Table 3.A3 Unit Root Tests (1 = Canada, 2 = China, 3 = Iceland, 4 = ROW) ......................... 102
Table 3.A4 SUR Estimates of US Import Demand System for Cod, AIDS Model, 19892010
Monthly Data (1 = Canada, 2 = China, 3 = Iceland, 4 = ROW) ............................ 103
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ix
List of Figures
Figure 1.1 Welfare Analysis of an Antidumping Duty ............................................................. 80
Figure 2.1 Import US Dollar Prices of Salmon by Sources .......................................................89
Figure 2.2 Conditional Variance Estimates of Import Prices (in US dollar): January 1995 
December 2008 ........................................................................................................ 90
Figure 2.3 Conditional Variance Estimate of Export Prices (in Foreign Currency): January
1995  December 2008 ............................................................................................. 91
Figure 2.4 Conditional Variance Estimate of Bilateral Exchange Rate: January 1995 
December 2008 ........................................................................................................ 92
Figure 3.1 MGARCH Estimated Conditional Price Volatility .................................................98
Figure 3.A1 US Import Cod Prices by Sources ............................................................................99
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Chapter I. Antidumping Duties and Trade Diversion: An Armington Procedure
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1.1 Introduction
An antidumping (AD) duty aims to asist domestic producers by raising price in the home
market. Blonigen (2003) reports that AD cases worldwide increased from only a few in the
1970s to 2,200 in the 1990s. In the United States, calculated dumping margins betwen 1980 and
2000 rose from 15% to over 63%, and the probability of an afirmative ruling rose from 45% to
over 60% (Blonigen 2006). Durling and Prusa (2006 p. 676) note that the range of products
subjected to AD has been expanded, with measures frequently targeting agricultural products.
Frequent enhancements of AD measures induce extensive disputes about the validity of this
policy, which spurs persistent interest in the international trade literature. The most common
consensus is that the targeted tarif is a priori ineficacy due to: (i) a large import demand
elasticity (Kinnucan 2003, Kinnucan and Myrland 2006), (ii) the les competitive import
competing industry (Chang and Gayle 2006), and (iii) the tradediversion effect (Prusa 2001,
Galaway et al. 1999). Hencefore, the AD duty wil induce the nontargeted foreign suppliers to
increase their shipments. The tradediversion efect on AD duties is the primary focus of this
paper.
The standard result in the economics literature is that trade diversion undermines the
efectivenes of AD duties. However, as noted by Carter and GalantTrant (2010), most of the
studies relate to industrial products, and there are good reasons to expect a diferent outcome for
agricultural products. Unlike industrial products, agricultural products tend to be perishable, are
produced seasonaly, and must met stringent quality and food safety standards before they can
be admited for importation. These factors, coupled with weak control over production and
export decisions due to the biological and atomistic nature of agricultural production, constrain
the extent to which nontargeted countries can fil the gap in the domestic market left by a
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particular antidumping action. Indeed, in their empirical investigation Carter and Galant (2010,
p. 119) find ?a relatively smal amount of trade diversion for agricultural products, and this efect
does not extend beyond the year in which the case was initiated.?
Although economists find litle justification for AD duties because of the losses to
consumers and downstream industries in the importing countries, the policy persists, filings have
multiplied, and rulings have become more protectionist. Irwin (2005) reports that import
competing firms in the United States are increasingly turning to AD duties as an ?easy? means to
gain protection. A likely explanation is that the government distributes the revenue gained from
AD duties to domestic producers aleging harm.
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Therefore, the national welfare can be used to
assess efectivenes of AD duties, which should also be influenced by trade diversion.
Furthermore, part of what domestic producers gain is matched by the los to domestic
consumers. Trade diversion should benefit US consumers if the price of the nondutied good is
les expensive than the price of the protected good.
The purpose of this research is to determine the efects of trade diversion on the
efectivenes of the antidumping duty that was imposed by the United States on catfish imports
from Vietnam (US Department of Commerce 2003, 2009). The ?Catfish War? generated national
media atention, with articles appearing in The New York Times, The Wall Stret Journal, The
Christian Science Monitor, and The Economist discussing the policy and ethical dilemmas posed
by the dispute.
2
For the purposes of this paper, catfish is a useful case study in that the trade
diversion isue is clearly indicated in the data (table 1). Specificaly, prior to the implementation
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In the US, the Continued Dumping and Subsidy Ofset Act, comonly known as the ?Byrd
Amendment? (se Chang and Gayle 2006), was enacted by the US Congres in 2000 to provide for the
distribution of antidumping duty revenues to petitioners. It was repealed in 2006, with a phaseout period
for duty distribution.
2
The WSJ article entitled ?Catfish Case Mudies Waters for Bush ?Fast Track?? apeared 13 July 201.
For citations of the remaining articles and a god discusion of the isues involved, se Coleman (205,
pp. 68).
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of antidumping duties ranged from 37% to 64% in 2003 US producers, in esence, owned the
domestic market with a market share of 0.84. One year after the antidumping duty went into
efect, China entered the US market, and within four years, saw its market share increase from
0.01 to 0.17. Although by 2008 Vietnam had reestablished itself as an important competitor
with a market share of 0.18, it sems clear that without the entry of China: a) the quasirents US
producers enjoyed from the antidumping duty would have been higher, and b) the ability of the
duty to protect US producers? market share would have been greater. Examining these
hypotheses, I find that the entry of China did indeed undermine duty efectivenes. But the
degree of the tradediversion efect is primarily limited by the domestic industry?s dominant
market share. This ?home bias? in an Armington (1969) framework implies an atenuated pas
through elasticity and weak crossprice efects for the domestic product.
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Previous research on the pasthrough elasticity shows that the Armington substitution
elasticity (!) plays an important role in the extent to which a tarifinduced increase in the price
of an imported good wil raise the price of the protected good (Warr 2008). However, no study to
our knowledge investigates the relationship betwen the market share, the pasthrough
elasticity, and tradediversion efects. Thus, as a byproduct of our analysis, I fil a gap in the
literature relative to a key elasticity used to evaluate trade policy. A key finding is that the pas
through elasticity is inversely related to the market share of domestic producers. This ?home
bias? means a smal market share of imports. I will further ilustrate that the smaler market share
of imports, the les important tradediversion efects are apt to be.
We begin with the presentation of the structural model. Analytical expresions for the
pasthrough elasticity and the tradediversion efect are then derived. The welfare efects of the
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According to Whaley and Xin (209, p. 309), home bias is comonly defined in the literature as ?an
Armington preference for domestic over comparable foreign products in a trade model where gods are
heterogeneous across countries, a definition I adopt in this study.
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catfish antidumping duty are then measured, with special atention to tradediversion efects. The
paper concludes with a summary of the key findings.
1.2 Model
Consider a country that imports two products, Q
2
and Q
3
, diferentiated by source origin. The
imported products compete with a home good, Q
1
. The three goods are weakly separable from al
other goods in the home market, and consumers alocate income in acordance with the two
stage budgeting hypothesis. The home country imposes an antidumping duty on Q
2
defined as
follows:
(1)
!
P
2
=
where T is the duty expresed in ?iceberg? or proportionate form,
2
~
P is price inclusive of the
duty, hereafter ?demand price?, and
2
Pis price exclusive of the duty, hereafter ?supply price.?
Prices for the three goods are determined under competitive conditions.
Given these asumptions, an isue is the efect of the duty on the price of the domestic
good when the presence of the nondutied good, Q
3
, is taken into acount. To determine that, let
the demand and supply equations for the three goods be defined as follows:
(2) ? (4)
**
33
*
22
*
11
*
~
XPPPQ
iiiii
!""" +++= 3,2,1=i
(5) ? (7)
**
iii
PQ != 3,2,1=i
where the asterisk denotes proportionate change. Thus, for example, X* is the proportional
change in X where(
12
+
!
QP
3
)is total expenditure on the three goods by domestic
consumers. In this model, the "
ij
are conditional price elasticities of demand; the #
i
are
conditional expenditure elasticities; and the $
i
are price elasticities of supply. The demand curves
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are downward sloping ("
ii
< 0); the supply curves are nondecreasing ($
i
# 0); the goods are non
inferior (#
i
# 0) and substitute for one another in consumption ("
ij
> 0 for i $ j).
An increase in the duty shifts the supply curve for the dutied good to the left. To se this,
write equation (1) in proportionate change form:
(8)
!
P
2
*
=+T
*
.
Substituting equation (8) into equation (6) yields the taxburdened supply curve:
(6%) Q
2
*
!
2
*
.
Holding constant the demand price, a 1% increase in the AD shifts the supply curve for the
dutied good to the left from the initial market equilibrium point by an amount equal in
proportionate terms to the dutied good?s supply elasticity.
Equation (6) shows that an increase in the duty has opposite efects on the demand and
supply prices. Thus, for example, if the supply of the dutied good is perfectly inelastic ("
2
= 0),
foreign producers bear the full incidence andP
2
*
=!T. In this instance, the duty is inefective, as
it has no efect on prices in the domestic market. Thus, a necesary condition for the duty to be
efective is that "
2
> 0, an isue to which I shal return.
Equations (2)  (8) contain seven endogenous variables (P
1
*
,
23
,
!
*
Q
1
,
23
*
) and two
exogenous variables (
*
X
and T). Exogenous variables that afect demand and supply other than
consumer expenditure and the duty are suppresed.
Tarif PasThrough Elasticity (PTE)
Warr states (2008, p. 499) ?The manner in which the landed price of imports afects domestic
prices is central to trade policy analysis.? The tarif pasthrough elasticity (PTE) when an AD is
used to raise the import price may be defined as follows:
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(9)
P
1
*
T
=
!
2
"
#
$
%
&
*
where the first term in parenthesis indicates the price pasthrough elasticity and the second term
indicates duty incidence. In Warr?s analysis the supply of the imported good is asumed to be
perfectly elastic ($
2
= &), which implies the full incidence of the duty is borne by domestic
consumers, i.e.,
!
P
*
T=1. Here I relax that asumption and add tradediversion efects to
develop a more complete expresion for the PTE.
The PTE when third party efects are considered are (se appendix for derivation):
4
(10)
P
1
*
!
"
#
$
%
&
N=3
21
(!
3
'")+
132
(11)
!
2
*
T
"
#
$
%
&
N=3
2
(
1
)
313
)
(12)
P
3
*
!
"
#
$
%
&
N=
23
(!
1
'")+
123
where
231231321321333122122231131112332333222111
)()()())()(( !!!!!!!"!!!"!!!"!!!"!"!" ###########=$
, and
equation (11) is trade incidence borne by domestic consumers.
After presuming a downwardsloping demand curve and an upwardsloping supply curve
for each product in the market, I can justify the common denominator (') in (10)  (12) is
positive. Noted in the Armington framework, any pair of products in the group is a gross
substitute ("
ij
> 0 for i $ j); I can further observe each numerator in (10)  (12) with a positive
sign as wel. This indicates that the AD duty imposed on the subject country should increase
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PTE in general means the tarif pasthrough elasticity of the domestic god?s price. In order to
elaborate the relative price movements, I also calculate the PTE of the dutied god?s domestic price and
the nondutied good?s price. Except stated otherwise, in the paper, PTE only refers to price transmission
betwen tariff and the price of the protected good.
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domestic prices of the protected good, the dutied product, and the notdutied good. An increase
in the price of the dutied product is induced by an inward supply shift, whereas a rise in the
prices of the protected and nondutied products is induced by upward demand shifts.
In order to demonstrate the tarif pasthrough proces, equation (10) is restated as
follows:
(13)
P
1
*
T
!
"
#
$
%
&
N=3
12
("
3
'!)+
132
$
%
&
!
P
*
T
"
#
N=3
where the first term is price pasthrough elasticity, which is primarily determined by
substitution betwen goods from diferent sources. In (10) or (13), the supply elasticity of the
dutied good is a critical determinant of duty efectivenes. For example, if the supply of the
dutied good is perfectly inelastic ( 0
2
=! ), as might be true in a shortrun situation, the entire
incidence of the duty is borne by producers in the exporting country and the protected good?s
PTE = 0. This is true regardles of the size of the price pasthrough elasticity (the first term in
equation (13)) and whether tradediversion efects are considered. Alternatively, if supply of the
dutied good is perfectly elastic, equation (13) is reduced to:
(14)
P
1
*
T
!
"
#
$
%
&
2
='
N3
12
(!
3
")+
12
33
The corresponding expresion when tradediversion efects are ignored is:
(15)
P
1
*
!
"
#
$
%
&
2
='
N
12
(
Equations (14) and (15) represent the maximal efect of the duty on the price of the protected
good. Equation (15) is identical in form to the PE derived by Warr (2008, p. 500, equation (6)).
That this elasticity has an upper limit of one can be sen by imposing homogeneity to yield:
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(16)
P
1
*
T
!
"
#
$
%
&
2
='
N
12
+#
.
In this instance, the PTE increases as the protected good becomes a closer substitute for
the dutied good (larger "
12
), as the supply of the protected good becomes les price elastic
(smaler $
1
), and as the demand of the protected good becomes les expenditure elastic (smaler
#
1
).
TradeDiversion Efect
An analytical expresion for the tradediversion efect (TDE) can be obtained by subtracting
equation (14) from equation (15) to yield:
(17)
( )
( )
3113333111111
12311113213
))(()(
)(
!!!"!"!"
!!!"!!
####
+##
=TDE .
Equation (17) is the TDE when domestic consumers bear the full incidence of the duty and thus
represents the maximal efect. With this caveat in mind, the TDE is negative in sign, which
means ignoring the TDE wil cause the duty?s efect on domestic price to be overstated. The
degree of overstatement increases as: i) the protected good becomes a closer substitute for the
nondutied good (larger "
13
), ii) the nondutied good becomes a closer substitute for the dutied
good (larger "
32
), and iii) the supply of the nondutied good becomes les price elastic (smaler
$
3
). If $
3
= &, the duty has no efect on the price of the nondutied good and TDE = 0. Thus, the
extent to which the presence of a third good undermines the efectivenes of an AD depends on
substitution efects, but also on supply conditions in the market for the nondutied good. If
consumers respond to the duty by switching to the nondutied good to a greater extent than to the
protected good ("
32
> "
12
), as might be expected if the nondutied good is les expensive than the
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10
protected good (P
3
< P
1
), the atenuation of the PTE caused by the TDE could be empiricaly
important.
In the Armington model, consumer preferences are asumed to be homothetic, indicating
trade paterns changes only with relative price movements. Since an AD duty increases the
domestic price of each good in the group, the magnitudes of the growth rate should ilustrate
redistribution of shares among suppliers, and consequently reveal the mechanisms of the trade
diversion efect. The diferences betwen PTE are given by:
(18)
!
P
2
*
T
"
#
$
%
&
N=3
'
1
*
=3
!
2
(
1
'"
12
)(!
3
+"
13
('
32
)
(19)
3
*
!
"
#
$
%
&
N=
1
*
=3
2
3
(
113
)
231
!
3
)(
(20)
!
P
2
*
T
"
#
$
%
&
N=3
'
*
=3
!
2
(
1
'")!
332
)+"
1
(
3
'
12
)
For equation (18), the increase of the domestic price of the dutied good is greater than the
growth of the price of the protected good, on the sufficient conditions that (1) "
11
 > "
12
 which is
not a particularly onerous condition and (2) the nondutied good is a closer substitute to the
protected good than to the dutied good, i.e. "
31
> "
32
(as shown later, it is always true in the
Armington model given the US produces dominate the market). Considering the formula of
demand elasticities, equation (19) can be simplified to equal
!
2
3
(
1
"), indicating the growth
of the nondutied good price is les than the growth of the protected good price if $
1
< $
3
.
Although signs of (18) and (19) depend on the reasonable preconditions, I can tel the sign of
(20) is unequivocaly positive, indicating an improved comparative advantage of the nondutied
good compared to the dutied good. In general, implementation of an AD duty wil make the
!
11
relative price movements favor both the protected good and the nondutied good over the dutied
good, resulting in trade diversion.
1.3 Parameterization
To ases the importance of the tradediversion efect for the catfish AD, I need to set parameters
in the structural model. For this purpose, I first follow Warr (2008) and restrict demand
elasticities to conform to the ?Armington asumption? (Armington 1969). In the Armington?s
framework, imports from diferent sources and domestic production are asumed to be
imperfectly substitutable. The expenditure of a particular group is alocated to diferent suppliers
based on relative price movements. This implies the demand elasticities matrix is as follows:
(21)
!
!
!
"
#
$
$
$
%
&
''++
+''+
++''
=
!
!
!
"
#
$
$
$
%
&
=
())()(
)(())(
)()(()
)))
)))
)))
)1()()(
)()1()(
)()()1(
3321
3221
3211
333231
232221
131211
SSSS
SSSS
SSSS
!
where " = 1 is the price elasticity of demand for the three goods combined, and ! > 1 is the
Armington substitution elasticity. With the maintained hypothesis that the three goods form a
weakly separable group, the conditional budget shares sum to one. One advantage of the
Armington framework is that the number of parameters to derive the 9 demand elasticity is
reduced to three, i.e., !, S
1
, and S
2
, noting that S
1
= 1  S
2
 S
3
.
Muhamad et al. (2010, p. 437) estimate the (longrun) ownprice elasticity of demand
for US catfish to be
?
1
=.4. The sample period of the data used in Muhamad et al. is from
January 1993 to December 2007. Substituting this value and S
1
= 0.83 (mean value for 1999
2007 in our sample, close to the period employed in Muhamad et al.) into the expresion for
"
11
in equation (21), and solving for the substitution elasticity, yield
?
!=37. Considering the
decline in S
1
during the data period, our ?bestbet? estimate is 2.5. However, to gauge the
!
12
sensitivity of results to substitutability betwen products in the same group, I also conduct
alternative estimates of
?
!=1.5
and
?
.
Although the lower bound is outside the typical range
(from 2 to 5) for Armington elasticity asumed in applied equilibrium models (Warr 2008), it is
used to give the simulation results full play.
Muhamad et al. (2010, p. 437) estimate the longrun supply elasticity for domestic
catfish to be 1.05. So, I set the ?bestbet? value for
?
!
1
=. Since Muhamad et al. did not
estimate supply elasticities for imported catfish, I set
2
and
?
!
3
to 2, the value used in
Kinnucan?s (2003, p. 216) analysis. Also, to gauge the sensitivity of the results to import supply
response, I conducted additional simulations with
?
!
2
and
3
set alternatively to 4 and infinity.
As discussed before, the final determination of the AD measure was isued against the
targeted catfish in 2003, and this AD case remained in efect in 2009. Acordingly, I set three
baseline values from the data sample subperiods: 200204, 200507, and 200810. When
simulating, market shares, prices and quantities are mean values in each subperiod:
In 200204, on average, US catfish producer dominated the domestic market with a
market share of 0.83, and China owned a mere share (S
3
= 0.01). After the implementation of the
AD, China saw its market share rise to 0.11 at the expense of US producers in 200507; however,
Vietnam only lost 0.03 shares. In 200810, Vietnam reestablished itself as an important supplier
with a market share of 0.26, whereas China only gained a growth of 0.03. A comparison of
!
!
!
"
!
#
"
!
"
"
"
#
#
!
#
"
#
#
200220042.47 1.46 1.45 311 632 0.83 0.17 0.01
200520072.84 1.54 1.69 32763470.75 0.14 0.11
200820102.94 1.55 1.76 291127670.60 0.26 0.14
$%&'()*+,)./0123 45678&89)*:&02)01;3 <6%=(8)>?6%(
Year
!
13
simulating results with the baseline values from those subperiods should shed light on the trade
diversion efect.
Given " = 1 and the ?bestbet? value of
?
!=2.50, the demand elasticities matrices
(equation (21)) corresponding to the three sets of baseline market shares are:
(22) N=
1.260.5.1
4
..2.49
!
"
#
$
%
&
(200204: S
1
= 0.83, S
2
= 0.17, S
3
= 0.01)
(23)
1.380..16
.2..34
!
"
#
$
%
&
(200507: S
1
= 0.75, S
2
= 0.14, S
3
= 0.11)
(24) N=
1.60.9.21
..3.
!
"
#
$
%
&
(200810: S
1
= 0.60, S
2
= 0.26, S
3
= 0.14)
The most important elements in matrix (22)  (24) are "
12
and "
13
, as these elasticities are primary
determinants of tarif pasthrough elasticities and tradediversion efects (se equations (10) and
(17)). Since neither elasticity is very large in relation to the ownprice elasticity "
11
, I suggest
that: a) the duty may not be very efective at raising the price of the domestic good, and b) trade
diversion efects may not be very important.
1.4 Simulated Tariff PassThrough Elasticities (PTE)
In order to simulate tarif pasthrough elasticities (PTE), I build up scenarios using market
shares from 200204, 200507, and 200810, respectively. Armington elasticity (
?
!) is set
alternatively to 2 (?bestbet? value), 4, and 6; the supply elasticity vector is !" = (1.1, 2.0, 2.0),
our ?bestbet? estimates of these parameters.
!
14
Results suggest the AD duty does not substantialy afect the price of the protected good
(table 2). For the considered parameter values, the PTE of the protected good (P
1
*
/T) ranges
from 0.019 to 0.13. This suggests that if all imports from Vietnam were asesed at 63.88%, the
highest AD margin calculated by the US Department of Commerce (2003, 2009), the price of
domestic catfish would rise by at most 8.3% (0.13 ( 63.88%). This estimate assumes Armington
elasticity is 5 (the upper limit) in the scenario with S
3
= 0.14. In the scenarios with S
3
= 0.01 and
S
3
= 0.11, the maximum increase of the domestic catfish price is 5.6% and 4.7%, respectively.
The level of trade diversion can be evaluated by a comparison of the simulated tarif
pasthrough elasticities. In each case, the PTE of the domestic catfish and the nondutied catfish
are much smaler than the corresponding PTE of Vietnam?s catfish. As an example, in 200204,
for
?
!=2.5
(?bestbet? value), the domestic price of Vietnam?s catfish increases by 49%;
however, the prices of the protected catfish and China?s catfish only increase by 5.2% and 4.1%,
respectively. Actualy in each case, the PTE of China?s catfish is even smaler than the PTE of
the protected catfish, although the diferences are not substantialy significant. Changes in the
relative prices imply that the market share extracted from Vietnam?s producers due to the AD
policy is shared by the US and China, noting in the Armington framework, relative market shares
are asociated with relative prices through Armington elasticity.
5
The upshot is that, the market
share and quasirents US producers enjoyed from the AD policy would have been greater
without the entry of China. On the other hand, for US consumers, switching from the domestic
catfish to China?s catfish should increase their benefits, considering the domesticaly produced
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
5
Our simulated results show that the market share of the nonnamed country is increased by 0.03% in the
200204 scenario, 0.5% in the 200507 scenario, and 1.2% in the 200810 scenario. Taking the initial
market share of the nondutied good into acount (0.01, 0.11, and 0.14, respectively), this confirmed a
positive relationship betwen the initial market share and the degre of trade diversion.
!
15
catfish is generaly more expensive than China?s catfish (table 1). Next, I evaluate the
magnitudes of the welfare efects of trade diversion for al parties in the market.
1.5 Welfare Analysis
The implications of tradediversion efects from a welfare perspective are evaluated in a partial
equilibrium seting using figure 1 as a guide. Consistent with the structural model, the diagrams
depict a situation where the three goods are substitutes in consumption, but independent in
production. That is, the technologies used to produce the domestic and imported goods are
independent, and any specialized factors used to produce the three goods (e.g., catfish fed) are
perfectly elasticaly supplied to each country. The later asumption is necesary for welfare
efects to have significance in the sense that they can be traced to an identifiable group (e.g.,
domestic producers, se Thurman 1993).
The AD shifts the supply curve for the dutied good up from S to S% in panel B by an
amount equal to the perunit duty, i.e., the ad valorem duty multiplied by the price of the dutied
good in the preduty equilibrium. After the three markets have adjusted fully to the supply shift,
the market price of the dutied good increases from P
2
to P
2
?, and the supply price of the dutied
good decreases from P
2
to P
S
. The full welfare efect is measured in the market for the dutied
good (Just, Heuth, and Schmitz 2004, pp. 32226). Specificaly, the hatched area betwen the
price lines P
2
to P
S
and behind the supply curve S, labeled %PS
2
in panel B, represents the
welfare loss to producers of the dutied good. The hatched area betwen the price lines P
2
to P
2
?
and behind the equilibrium or ?total? demand curve D
T
, labeled %CS* in Panel B, represents the
welfare efect of the supply shift on the remaining parties afected by the duty. Specificaly,
%CS* = %CS
1
+ %CS
2
+ %CS
3
+ %PS
1
+ %PS
3
represents the welfare loss to domestic consumers
!
16
as a result of the higher prices they must pay for domestic and imported catfish following
imposition of the duty. Since the duty raises the market price of al three goods, producers of the
domestic and nondutied imported goods enjoy a welfare gain equal to the shaded areas labeled
%PS
1
and %PS
3
, respectively, in panels A and C.
Since a paralel upward shift in a supply curve always decreases consumer surplus, %CS*
< 0, which implies that consumer losses outweigh producer gains. However, the duty provides
tax revenue, which, depending on duty incidence, may be sufficient to compensate consumers
and yield a net welfare gain for the US.
With the maintained hypothesis that supply and demand shifts are paralel, the welfare
efects of the catfish duty may be approximated using the following formulas:
(25) ( ) 3,2,15.01
**
=+=! iQPQPPS
iiiii
(US and foreign producer impacts)
(26) ( )
*
2
*
222
5.01
~
* QPQPCS +!=" (?Consumer? impact in dutied market)
(27)
31
* PSPSCSCS !"!"!=! (US consumer impact)
(28) ( )( )
*
2
*
2
*
222
1
~
QPPQPTR +!=" (US treasury impact)
The P
i
Q
i
represents the value of the ith product in the initial equilibrium. Numerical values for
the asterisked variables in equations (25)  (28) were computed by simulating the model
(equations (2) ? (8)) for a 35% increase in the duty. In January 2009, the US Department of
Commerce ruled that catfish duties imposed in 2003 would remain in place (Martin 2009). The
de minimis weightedaverage antidumping margin in both the 2003 and 2009 USDC rulings is
36.84% (US Department of Commerce 2003, 2009). Thus, seting T
*
=0.35 provides a
conservative estimate of welfare impact.
!
17
Distribution efects
Our first set of simulations focuses on the welfare implications of trade diversion for al parties
(distribution efects). I chose the 200810 baseline values for prices and quantities. Simulations
were run with the market share for the nondutied good (S
3
) alternatively to be 0.07, 0.14 (mean
value for 200810), and 0.28 to miic the observed range in this parameter over the 200210
period. Although the later value is outside the range for S
3
reported in table 1, it is used to give
trade diversion full play. Acordingly, the market share of the protected good (S
1
) is alternatively
set to be 0.67, 0.60, and 0.46, since the market share of the dutied good (S
2
) is held constant at
0.26 (mean value for 200810). In each instance, the demand elasticities matrix is adjusted as
required to ensure that demand elasticities are consistent with theory. Other parameters are set to
be their ?bestbet? values, the domestic supply elasticity
?
!
1
=., the import supply elasticities
?
!=(
2
,
3
), and Armington elasticity
?
!=2.5.
The simulating results are reported in table 3. Focusing first on the case where S
3
= 0.14,
results indicate the largest beneficiary of the duty is the US treasury, which gains $29.2 milion.
Although domestic producers gain $8.1 milion, this comes at the expense of domestic
consumers, who lose $28.3 milion. Adding together these efects yields a net gain to the
domestic economy of $9.0 milion. A gain occurs because import supply is sufficiently upward
sloping to permit the US to act as a monopsonist and price discriminate against foreign suppliers
via the imposition of a tarif (Enke 1944). Specificaly, for the considered parameter values,
domestic consumers bear 51% of the duty, which means 49% of the US treasury gain comes
from Vietnam producers. Vietnam producers lose $18.1 milion, while China producers gain $1.5
milion, for a net welfare loss to al afected parties of $7.7 milion. The upshot is that the AD did
more to punish foreign producers than to reward domestic producers, a common result in the AD
!
18
literature for farm products (e.g., Asche 2001; Brester et al. 2002; Kinnucan 2003; Kinnucan and
Myrland 2006).
Turning to tradediversion efects, rent disipation asociated with trade diversion
increases with the market size of the dutied good, but the increase is modest. An increase in the
market share of the nondutied good from 0.07 to 0.14 causes the domestic producer surplus to
decline by 12%. The corresponding decline is 33%, when the market share of the nondutied
good is increased by 4 times from 0.07 to 0.28. Thus, for the considered parameter values, trade
diversion has a moderate efect on rent disipation. Trade diversion has an even les important
effect on consumer surplus. When the market share of the nondutied good increases from 0.07
to 0.28, consumers? loss is dwindled by a mere 3.2%, too smal to mater. Although domestic
consumers switch to the les expensive China?s catfish when the domestic price of the protected
good rises, their benefits from the switch are diluted by the huge loss from the rising price of the
dutiedgood due to an inward supply shift. This is consistent with the simulated tarif pas
through elasticities (PTE). As shown in table 2, in each scenario, the PTE of the protected good
is much greater than the corresponding PTE of the protected good and the nondutied good in
magnitude.
Linking producer surplus to consumer surplus, I calculate the value of the redistribution
eficiency of the AD duty, defined as the ratio of domestic producers? gain to domestic
consumers? loss (in absolute value). Litle of the lost quasirent rebounds to the benefit of
domestic consumers, noting that the redistribution eficiency is reduced from 0.32 to 0.22 when
S
3
is increased from 0.07 to 0.28. The upshot is that, for the considered parameter values, the
tradediversion efects are confined largely to domestic producer impacts, and even then they are
!
19
les important than other factors that afect duty eficacy, namely substitution efects and import
supply elasticities, as shown in our following set of simulations.
Sensitivity Analysis
The foregoing results are based on the ?bestbet? values of Armington elasticity and the import
supply elasticities. To gauge the sensitivity of results to the elasticity of substitution, I set
?
!
alternatively to 1.5, 2.5 (?bestbet? value) and 5, and the import supply elasticities =(
2
,
3
)
alternatively to 2 (?bestbet? value), 4 and &. In these simulations, market shares are set to their
average values for 200810 (S = (0.62, 0.24, 0.14)), the domestic supply elasticity to its ?best
bet? value
?
!
1
=.. The demand elasticity matrices corresponding to the diferent Armington
elasticities are:
(29) N=
.20.3.7
1
...4
!
"
#
$
%
&
(! = 1.5)
(30) =
.60.39.2
1
...
!
"
#
$
%
&
(! = 2.5)
(31) N=
2.6.05.6
39
.1.4.
!
"
#
$
%
&
(! = 5.0)
Results suggest Armington elasticity and import supply elasticities are pivotal in
determining both the size of the welfare impacts and their distributional consequences (table 4).
An increase in Armington elasticity (
?
!) has more substantial effects on US producers than on
other parties. In the instance where =
2
,
3
), the US producer surplus is increased 1.3
!
20
times when
?
! is raised from 1.5 to 2.5. The corresponding price increase fals to 67% when
?
!
is increased from 2 to 5. Import supply elasticities also have a substantial impact on producer
surplus. Using
?
!=(
2
,
3
)as the standard of comparison, if import supply is perfectly elastic,
the benefits of the duty for domestic producers are overstated by a factor of 1.6 (= $5.85 milion /
$3.56 milion) when
?
1.5, and by a factor of 2.2 (= $30.3 milion / $13.5 milion) when
?
!=5. Thus, the erroneous treatment of import prices as exogenous causes a significant upward
bias in the estimated gain to domestic producers, and this bias increases as the goods become
closer substitutes.
6
Turning to distributional impacts, the national welfare gain from the duty converts to a
loss for an import supply elasticity as smal as 4.0. If
?
!=, the national welfare gain from a
35% duty is betwen $10.5 milion and $25.5 milion, with the later estimate corresponding to
the upper limit of the substitution elasticity (
?
5). When
?
!, domestic consumers bear the
full brunt of the duty, with losses ranging from $39.8 milion to $49.3 milion. Above al, if
import supplies are perfectly elastic, the duty in esence represents a transfer from domestic
consumers to domestic producers and the US Treasury, and the incidence of the duty is shifted
entirely to the US consumers, indicating a null efect of AD on the welfare of foreign producers.
For the redistributive eficiency of the duty (domestic producer gain / domestic consumer loss), it
increases as import supplies become more price elastic, and as the goods become closer
substitutes. For the considered parameter values, this ratio never exceds 0.61 (= $30.3 milion /
$49.3 milion); for ?bestbet? parameter values, the ratio is 0.29 (= $8.11 milion / $28.3
milion).
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
6
The study by War (208) treats import price as exogenous when developing an analytical expresion
for the pasthrough elasticity, while the study by Muhamad et al. (2010) treats import price as
exogenous when evaluating the welfare impact of the catfish duty.
!
21
Tarif Rate and Trade Diversion
Since trade diversion makes the AD policy les efective in terms of producer surplus, net
national welfare, and redistribution eficiency, a low tarif rate (i.e. AD margin) may be proposed
to reduce trade diversion because it limits the benefits for the nonnamed countries to increase
their exports to the US.
7
But, on the other hand, a low tarif rate would directly reduce the
revenue gain for the government and reduce the extent to which the price of the protected good
rises, provided that the tarif pasthrough elasticity is constant. To examine the correlation
betwen the tarif rate and trade diversion, I recomputed the welfare distribution with alternative
AD rates. After implementing in 2003, the rate of the AD duty against Vietnam?s catfish ranges
from 37% to 64%. Thus, I set the tarif rate with alternative 15%, 35%, 50%, and 70%, where
50% is equal to the inverse of the ?bestbet? import supply elasticity. The supply elasticities and
the Armington elasticity are set to their ?bestbet? values
?
!=(1.,2) and
?
!=2 to permit
isolation of the marketshare efect. Prices and quantities are mean values for 200810. The
market share of the nondutied good is increased from 0.07 to 0.28 in three steps.
Results indicate producer surplus and consumer surplus (in absolute value) are increasing
functions of the tarif rate (table 5). When the tarif rate is increased, consumers? loss from the
increasing price of the dutied good overwhelms the positive efects of the demand outward shift
of the protected good and the nondutied good. In the instance where S
3
= 0.14, using T* = 35%
as the benchmark, if the tarif rate is increased to 50%, gains to domestic producers and the US
treasury are improved by $3.6 milion and $3.1 milion, respectively; however, the loss for
domestic consumers is also increased by $ 9.9 milion, resulting in a decline in net national
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
"
!Konings, et al. (201) relate the lower amount of import diversion in Europe to lower duty levels, which
limit the benefits of protection for the nonnamed countries.
!
22
welfare (%W
us
). If the tarif rate is raised to 70%, the huge negative efect on domestic consumers
results in a negative net national welfare.
Finaly, I focus on the national welfare gain to justify tradediversion efects on the tarif
rate. In each scenario, the national welfare gain (%W
us
in table 5) is not a monotonic function of
the tarif rate. In the instance where S
3
= 0.14, the national welfare is raised by 35% when the
tarif rate is increased from 15% to 35%, but it is reduced by 13% when the tarif rate keeps
rising to 50%. Moreover, the national welfare becomes negative when the tarif rate is set at
70%. The simulated results further demonstrate the tarif rate of 35% sems to be the ?optimal
tariff? in each case. In the cases with T* = 35%, the national gain is $9.7 million when S
3
= 0.7,
$9.0 milion when S
3
= 0.14, and $7.5 milion when S
3
= 0.28. The negative relationship betwen
the maximal national welfare and the market share of the nondutied good coincides with the
previous findings that the tradediversion effect has a stronger consequence of dwindling the
domestic producer surplus than increasing consumer surplus. In the instance with T* = 70%, the
national welfare loss is $3.5 million when S
2
= 0.7, and $8.4 million when S
2
= 0.28. This implies
that the breakeven point of the tariff rate at which %W
us
= 0 is negatively related to the extent of
trade diversion. In other words, the greater trade diversion, the faster the national welfare
converges to zero when the tarif rate is growing. The upshot is that the tarif rate tends to be
lower when the extent of trade diversion is greater in order to obtain an ?optimal? gain in
national welfare or avoid a nil or negative welfare efect.
1.6 Concluding Comments
Despite the tarif rate as high as 64%, the antidumping duty the United States imposed in 2003
on catfish imports from Vietnam failed to prevent a precipitous decline in domestic industry
!
23
market share (from 84% in 2003 to 58% in 2010). It is tempting to ascribe AD inefectivenes to
the entry of China as a new foreign competitor in 2004, as consumers substitute out of the dutied
good and into both the domestic good and the nondutied good. This switch may also reduce the
loss to consumers, considering that the nondutied good is generaly les expensive than the
protected good. Study results suggest trade diversion is an epiphenomenon. Specificaly, China?s
ability to capture 28% of the domestic market following AD implementation is estimated to have
eroded the quasirents that domestic producers received by at most 33%. On the contrary, trade
diversion cannot reduce consumers? loss substantialy since the pasthrough elasticity (PTE) of
the dutied good (related to a supply shift) is much greater than the PTE of the protected good and
the nondutied good (related to demand shifts). The simulated duty incidence suggests, for the
considered parameter values, about one half of the duty appeared as a rise in the US price of the
dutied product.
Further, the extent to which trade diversion influences the efectivenes of an AD duty
depends on the market share of the domestic good. In an Armington framework, a dominant
market share for the domestic good, or ?home bias,? means that the crossprice elasticities of the
protected good tend to be smal. As an example, in 2005 when US producers enjoyed a market
share of 0.83, the crossprice elasticities in question consistent with an Armington elasticity of
2.5 are "
12
= 0.20 and "
13
= 0.06.
8
Even in 2010 when US producers still dominated the market
but with a smaler share of 0.58, the corresponding crossprice elasticities are "
12
= 0.87 and "
13
= 0.15. This indicates: (i) the efect of an AD on the price of the protected good (tarif pas
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
8
The complete demand elasticity matrices coresponding to the 205 and 2010 market shares given in
table 1are N
205
=
1.6.20.6
3
...4
!
"
#
$
%
&
and N
201
=
..87.
463
...
!
"
#
$
%
&
. It may be noted that the
"
12
element in N
2005
matrices is close to Muhamad et al.?s (2010, p. 437) estimate of this parameter
(0.18), even though in their study Armington restrictions were not imposed.
!
24
through elasticity, i.e. equation (10)) wil tend to be smal, and (ii) the atenuation of the tarif
pasthrough elasticity of the domestic good caused by trade diversion is tiny (equation (17)).
Moreover, the tradediversion efect on demand for the protected good is even weak, leading a
modest efect of trade diversion on both price and volume of the protected good.
The implications of these results would sem to be straightforward. First, in terms of net
national welfare, the higher the extent of trade diversion, the smaler the tarif rate, ceteris
paribus. A high tarif rate punishes domestic consumers more, since the tarif incidence is borne
by the domestic consumers and the targeted foreign suppliers, given an upward sloping import
supply curve. The sideefect of a large tarif rate is to exaggerate import diversion, which has a
primarily negative efect on domestic producers? welfare. On the other hand, trade diversion has
little consequence of reducing consumers? loss. This implies that a tarif rate beyond some limit
may reduce the net national welfare. Second, the inverse relationship betwen domestic industry
market share and the tarif pasthrough elasticity of the protected good indicates that an industry
with a large market share at duty inception can expect to be disappointed in that quasirents wil
be modest. To the extent the protected industry?s market share continues to decline after AD
implementation (as was the case for catfish), removal of the AD wil induce larger economic
consequences than its insertion. This asymmetry may help to explain the tendency for ADs to
remain in place long after the initial petition was filed (Bown 2007).
!
25
Chapter II. Import Demand under Price and ExchangeRate Uncertainties
!
26
2.1 Introduction
In a study of price uncertainty, Wolak and Kolstad (1991) point out that fluctuations in exchange
rates might be one of the several inherent risk sources in actual import prices. In terms of
exchange risk, while some studies argue for a negative efect on agricultural trade (e.g. Anderson
and Garcia 1989; Cho, Sheldon, and McCorriston 2002; Wang and Barret 2007; and Kandilov
2008), others advocate a positive relationship (se Langley, Giugale, Meyers, and Halahan
2000; Awokuse and Yuan 2005). More recently, by employing panel data, Erdema, Nazlioglub,
and Erdemc (2010) argue that the increased variability of exchange leads to more reduction in
imports of agricultural goods than in exports in Turkey. Two implications can be generated from
the previous research. First, the agricultural industry is more sensitive to risk factors in that
agricultural goods are typicaly traded with flexible pricing strategies, and they are les storable
than manufactured products (Wang and Barret). Second, since the trade efect of the exchange
uncertainty is asociated with properties of the market, the impact of exchange risk should be
evaluated in the context of disaggregate data (McKenzie 1999). But, disaggregate agricultural
trade markets, in most cases, are perfectly competitive, indicating that the import price risk may
reflect al information like the exchangerate risk. If the exchangerate risk completely pases
through into the import price risk, the trade efect of the export price risk and the exchangerate
risk should be equal. One purpose of the present paper is to test the equivalence of the exchange
risk efect and the export price risk efect.
Compared to exchangerate risk, price risk has received les atention in the literature on
agricultural trade. When studying the exchangerate risk, Klasen (2004) claims that price is
predictable due to contract constraints. Although such a viewpoint is appropriate for industrial
goods, it is not applicable for agricultural trade where product diferentiation is weak and firms
!
27
are more numerous (Carter and GunningTrant 2011). A search of the literature results in only
two studies that test the impact of price risk on agricultural trade flows: Seo (2001) and
Muhamad (2011), which are extended from Wolak and Kolstad (1991). Taking Chinese wheat
imports market as an example, Seo investigates the relationship among the expected price, the
systematic risk of price, and monopolistic power of the exporters. Muhamad develops a
diferential demand system by incorporating import price uncertainty and finds evidence that the
UK carnation importing firms are more responsive to price risk than to the expected price.
In the research of either agricultural trade or nonagricultural trade, even les atention
has been given to the diferences betwen influences of exchange risk and price risk in trade
flows. Ignoring the diferences betwen price risk efect and exchange risk may also lead to
conflicting empirical evidence on the trade efect of exchange risk. The diferential efects of
price and the exchange rate on trade may contribute to nonequivalence of efects of exchange
risk and price risk. Two notable exceptions of which I am aware discuss and evaluate the
relationship betwen price risk and exchange risk. Cushman (1983) states that uncertain price as
wel as exchange rate leads to percentage changes in real exchange rate, implying uncertainty in
real exchange rate should be included in the trade models. Cushman?s specification is more
applicable for aggregate trade rather than disaggregate commodities that are of interest in the
present paper. Kawai and Zilcha (1986) explicitly take exchange rate and commodityprice
uncertainties into acount when examining the optimum behavior of a riskaverse international
trader; however, they do not develop an empirical analysis.
The inconclusive research results on exchange volatility may be also partly atributed to
the flaws of its microeconomic foundation since the normaly employed import demand equation
in the previous literature is not derived from a utility function or is based on a too restrictive
!
28
utility function. As De Grauwe (1988) ilustrated, the positive trade efect of exchange risk is
plausible given a general utility function underlying the import demand equation. Given a
sufficient concave utility function facing importers, an increase in exchange risk might cause
firms to raise import demand in order to avoid the worst possible outcome.
The main purpose of this research is to examine whether price and exchange volatilities
have detectable efects on import demand by applying a demand system upon the utility theory.
This question is of interest because the optimaldecision of importers should distinguish the
impacts of price risk and exchange risk owing their diferent properties and diferent
availabilities of hedging instruments. In addition, the linkage betwen risk impact and price
efect needs to be revealed theoreticaly in order to analyze the empirical results. Few empirical
studies combine export price risk and exchange risk, although previous research has extensively
explored the trade efect of the exchange risk with ambiguous results. The US salmon import
market is taken as an empirical case because salmon is one of the major seafoods imported by
the US, and the export earning is a crucial instrument for one of the major suppliers, Chile, to
restore balance of payments.
The main contribution of the present research is to distinguish exchange risk from price
risk in a diferential demand system and to examine impacts of those uncertainties on import
demand. Implications of the research are an alternative method to handle diferent sources of
uncertainty in the demand system and a complementary explanation based on the underlying
utility function.
This study is structured as follows. I start with the theoretical framework followed by
model specifications and data. After estimating the variances of price and exchange rate, I
!
29
describe the regresion results for the US salmon imports demand system. The paper concludes
with brief remarks and implications.
2.2 Theoretical Model
The import demands for a particular good is derived from Armington?s (1969) method, which
asumes consumers employ a multistage budgeting procedure for alocating expenditure among
competing sources. First, total expenditure is alocated over broad groups of goods based on a
weakly separable utility function or a utility tree framework. Second, expenditure on this
particular good is then alocated betwen the domestic and imported varieties. Finaly,
expenditure on imports of this particular good is divided among various source countries. A
complete demand system built upon a utility function can reveal determinants of trade patern
adequately.
9
This demand system can further demonstrate the degree of market power that is
contingent on the substitutability of goods from diferent sources (Galaway, Blonigen and Flym
1999 p. 217). As Seo (2001) noted, the research of Wolak and Kolstad (1991) is limited to only
homogenous goods, causing an omision of the supplier?s influence on price risk owing product
diferentiation.
The Rotterdam odel, which is derived from an implicit utility function, has been widely
used to demonstrate the agricultural trade patern (e.g. Seale, Sparks, and Buxton 1992;
Washington and Kilmer 2002; Muhamad 2009, 2011). Among them, Muhamad (2011) is the
first study applying the Rotterdam model to examine the trade efect of risk variables. Diferent
from Muhamad (2011), in the present research, I justify theoreticaly that uncertainty factors
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9
The conditional demand systems can be derived from either the consumer demand theory or production
theory. As Washington and Kilmer (202) point out, there are no empirical differences in estimates of
conditional elasticities between consumers demand theory and production theory.
!
30
take efect through marginal utilities, and the efect depends on price efects and substitutability
betwen goods.
Taking volatility components into acount, the extended general Rotterdam odel can be
derived from the following utility maximization problem:
(1)
!"#
!!
u = u(q, v)
s.t. p?q = y
where u is the utility to be maximized, q is a vector of imports from diferent source countries, p
is the corresponding import price vector, v is a vector of risk variables, and y is the conditional
expenditure on the imported goods of interest.
The first order conditions of the utility maximization problem are:
(2) !
!!
!
!!
= y
(3) &p
i
+ u
i
= 0 i = 1, 2, ?, n.
where u
i
=
!!
!!
!
is marginal utility, & is the Langrage multiplier.
For the maximization problem with the conditional budget constraint, a negative definite
bordered Hesian matrix is the necesary and sufficient condition, implying the matrix
(4) U =
!!
!
!
!
!
!"
is negative definite. Here, u
ij
=
!!
!
!!
!
.
From the equations (2) and (3), the efects of price (p
j
) on the ith product (q
i
) and
expenditure (y) are therefore given by:
(5) q
ij
=!
!!!
!!!
!
!"
!
!!
(6) q
iy
= !
!"
!
!!
!
31
where U
ij
and U
i
are cofactors of the matrix U, U is determinant of this matrix. Here q
ij
(=
!!
!
!!
!
)
is paralel to the Slutsky equation in Phlips (1983, p. 49). I further denote !
!"
!
=
!
!"
!!
, which is a
measure of Hicksian complementary or substituting efect (Tintner 1952).
In the spirit of Tintner (1952), which is recently applied in Brown and Le (2010), the
impact of a volatility variable (v
j
) is revealed in the demand system by diferentiating the first
order equations with respect to one risk variable to yield:
(7)
!!
!
!
!
!
!"
.
!
!
!
!
!
!!
!
=
!
!
!!
!
where !
!
denotes
!!
!!
!
, !
!!
!
=
!!
!
!!
!
represents the efect of volatility on marginal utility of the ith
product, and !
!!
!
is the efect of the volatility j on the ith product.
Next, from (7), I solve !
!!
!
:
(8) !
!!
!
=  !
!"
!!
!
!!
!
!!
!
Considering the equation !
!"
!
=
!
!"
!!
, equation (8) can be restated as
(9) !
!!
!
= 
!
!
!
!!!
!
!"
!
!
!!
!
After obtaining the results of efects of the exogenous variables (p, y, and v) on the
demand for the ith good, I derive the extended Rotterdam odel by using a diferential approach
(Theil 1977, 1980). First, the import demand equations are solutions to (2) and (3).
(10) q
i
= q
i
(y, p, v)
By diferentiating both sides of (10) and relating the parameters to (5), (6) and (9), I
obtain the extended Rotterdam model in the form:
(11) !
!
!!"!
!
=!
!
!!"! + !
!"
!!!"!
!
!
!!
!
!"
!!!"!
!
!
!!
!
32
where Q =
!
!
!
!!"!
!
!
!!!
is real expenditure, w
i
=
!
!!
!
, '
i
=w
i
A
i
= p
i
!"
!
!!
, (
ij
=w
i
!
!
!
=
!
!!
!
!
!"
!"
!!
, and
)
ik
= !
!"
!
!!
!
!!
!
. Here A
i
is expenditure elasticity, !
!"
!
is Hicksian price elasticity, and !
!!
!
is
elasticity of marginal utility of the jth product with respect to v
k
. The estimated coeficients can
be explicitly converted into the corresponding elasticities.
Indicated by )
ik
= !
!"
!
!!
!
!!
!
, the net effect of the volatility depends on its impact on
the marginal utility of each product in the group, which is further weighted by the corresponding
price efect. This is consistent with what De Grauwe (1988) points out: the exchange volatility
afects import demand through the consumer?s marginal utility for the good, and the direction of
this efect depends on the curvature of the underlying utility function. For example, in the likely
case where the ownrisk (v
i
) only afects the ith good ()
ii
=!
!!
!
!!
!
) or the ownrisk efect
dominates the sign of the reduced efect of the volatility, the direction of the volatility?s impact
depends solely on the efect of the ith volatility on the marginal utility of the ith good (!
!!
!
), as
the sign of !
!!
is a priori negative. For example, the trade efect of volatility is positive when
!
!!
!
> 0 due to sufficiently riskaverse behavior of importers, i.e. a more concave utility function.
The opposite is true if !
!!
!
< 0. Hence, whether volatility exerts a positive or negative efect on
trade volume depends on the direction of its efect on marginal utility. This caveat needs to be
borne in mind when interpreting the empirical results.
In (11), coeficients of the risk variables are in reduced form. In order to further
demonstrate how volatility factors afect the market, with simple manipulation, I restate equation
(11) as follows:
(12) !
!
!!"!
!
= !
!
!!"! + !
!"
!!!"!
!
!
!
!!!!
!
!
!!
!!"!
!
!
33
where the parameters of volatility are expresed in structural forms. This expresion reflects that
change in the jth ?efective? price is the actual price change minus the summation of changes in
marginal utility of the relevant jth product as a result of changes in al volatility variables in the
demand system. If changes in kth volatility decrease (increase) marginal utility of the jth good,
demand for the ith good would be more (les) sensitive to changes in the kth price given the ith
good and the jth good are substitutable (complementary) to each other.
10
In terms of uncertainty
in international trade, Balg and Metcalf (2010) and Bergin (2004) posit a riskaverse firm would
atach a risk premium as an extra markup to cover the costs of exchangerate fluctuations; Wolak
and Kolstad (1991) postulate that inputprice risk premium is the percentage above the current
expected market price a firm would pay for riskles input supply.
When implementing (12) to the empirical research of agricultural trade, I decompose the
import price risk into export price risk and exchange risk to obtain the following theoretical
model:
(13) !
!
!!"!
!
= !
!
!!"! + !
!"
!!!"!
!
!
!!
!
!"
!
!!
!!!"!!
!
!
 !
!
!!!"
!"#!!
!
!
where !!
!
stands for risk of the export price measured in exporting country?s currency, and
!!
!
represents the exchange risk.
The underlying utility function with the budget constrain represented by equation (1)
indicates the general restrictions on the demand system, namely:
11
(14) !
!
!
!!!
= 0 (homogeneity)
(15) (
ij
= (
ji
(symmetry)
(16) !
!
!
!!
!, !
!"
!
!!!
= 0 (addingup)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
10
The interpretation of the risk factor exerting its role through changes in ?efective prices? is identical to
that in the advertisingaugmented trade model (e.g. Dufy 195)
11
Coeficients of risk factors satisfy the adingup restrictions through the price efects. Se Brown and
Lee (202) for more detail.
!
34
Besides the general constraints, other specific restrictions can be placed on the efects of
the risk variables upon the econometric tests against the unrestricted model A represented by
equation (13). This results in a reduction of the parameter spaces and eficiency of regresion
results. Duffy (1987) asumes no cross efect of preference variables, implying the following
specific restrictions:
(R1) !
!"
= 0 for j $ k (zero crossprice risk efect)
(R1?) !
!"
= 0 for j $ l (zero crossexchange risk efect)
If Duffy?s restriction (R1) cannot be rejected, a stronger restriction (Theil 1980) that
ownrisk efects are identical can be further tested (for elaboration, I suppose there are 5 price
risk variables and 4 exchange volatility variables in the demand system):
(R2) !
!!
= !
!!
= !
!!
= !
!!
= !
!!
!= (constant ownrisk efect)
(R2?) !
!!
= !
!!
= !
!!
= !
!!
= (constant ownrisk efect)
Given R1 and R2 cannot be rejected, one main concern in the present paper is the
equivalency of ownprice risk and exchange ownrisk efect:
(R3) ! = (equivalency of price risk and exchange risk efects)
Lastly, I test the hypothesis of risk neutrality
(R4) ! = 0 (pricerisk neutrality)
(R4?) = 0 (exchangerisk neutrality)
If R4 is rejected, the conventional Rotterdam model exclusive of risk factors is preferred.
Diferent from the general restrictions that, as common treatment in the literature, can be
imposed in the regresion to be consistent with the demand theory, the specific restrictions (R1
R4) are imposed only if they are compatible with the data.
The above specific hypotheses are summarized as follows
!
35
Models for testing
Model symbol Restrictions
Model A Equation (13) with homogeneity and symmetry constraints
imposed
Model B Zero crossrisk efect (R1 and/or R1?)
Model C A constant ownrisk efect (R2 and/or R2?)
Model D Equivalency of price risk and exchange risk efects (R3)
Model E Risk neutrality, i.e. conventional demand system (R4)
2.3 Model Specifications and Data
The forgone theoretical model is proposed to highlight the efects of export price risk and
exchange risk on the US import demand for salmon, which can be diferentiated by sources.
Since the introduction of salmon aquaculture in the early 1980s, the international salmon
trade is growing with Chile, Canada, Norway, and the UK being the main suppliers. Among
importers, the US has traditionaly been the world?s major market for salmon. Currently, Atlantic
salmon is the second most imported seafood product in the US only after shrimp. Chile and
Canada were the leading countries exporting farmed Atlantic salmon to the US throughout the
past twenty years. In 1995, America imported salmon at the value of $277 milion, of which
about 42% came from Chile and 49% from Canada (se table 1). The US salmon import surged
almost 4.6 times from 1995 to 2008; however, the market was stil highly concentrated with
more than 85% of total imports from Chile and Canada. During the sample period, the prices of
salmon from diferent sources had diferent levels of volatility despite the stable relative price
ratios (se figure 1). Subsequently, the trade efect of the importers? atitudes to price risk
deserves more atention. Taking Chile as an example, the great fluctuation of price and exchange
!
36
rate did not reduce its dominant position in this market (se table 1), implying the importers
might not be sensitive to the volatility of Chile?s salmon price.
In this study, US salmon import data on value (CIF in US dollar) and quantity (kilogram)
are from the US International Trade Commision (USITC) where import salmon is represented
by 52 HTSUS10 codes acording to diferent species and forms of salmon. Among them
Atlantic salmon (fresh, frozen, filet fresh, and filet frozen) represented by 11 HTSUS10 codes
consistently acounted for about 85% of total imports during the sample period. The data period
is from January 1995 to December 2008, totaly 156 observation.
12
Data on exchangerates are
obtained from the US Department of Agriculture ? Economic Research Service (ERS).
The demand system for US import salmon contains five equations distinguished by
import sources, namely Chile, Canada, Norway, the UK, and the rest of the world (ROW) that is
an aggregation of farmed Atlantic salmon imported from countries not specified. For a particular
supplier, the monthly import price is obtained by dividing the total import (CIF) value in the US
dollar by quantity (kilogram). For ROW, the monthly aggregate value and quantity are used to
calculate the import price. Dividing the import price (in the US dollar) by the corresponding
monthly average exchange rate (foreign currency per US dollar) yields the export price in foreign
currency. After creating the import price and export price, the variances of prices (and exchange
rates) can be estimated. Since the US dollar is used as the representative currency for ROW, only
the export price risk is measured for ROW. Subsequently, upon the theoretical model represented
by equation (13), the empirical model estimated is
(17) !
!!
!!"#!
!!
= *
i
+!
!
!!"!
!
+!
!
!!
!"
!!!"!
!!
! !
!"
!
!!
!!!"!!
!!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
12
The sample period is ended in 208 in order to avoid structural changes in the US salmon import
market induced by the 208 economic recesion and the outbreaks of infectious salmon anemia (ISA) that
has been released since later 207 (see Asche, Hansen, and Tveteras 2009).
!
37
 !
!
!!!"
!!!"!!
!!
! +$
i,t.
where i denotes suppliers (Chile = 1, Canada = 2, Norway = 3, the UK = 4, and ROW = 5), t
stands for the time subscript (monthly), w
i
is budget share, q
i
represents import volume, p
i
is
import price (in US dollar), !!
!
stands for variance of export price (!
!
, in foreign currency),
!!
!
represents variance of the real exchangerate !!
!
, and $
i
is the i.i.d. error term. The
intercept a
i
is included in each demand equation to acount for autonomous shifts in demand due
to taste change or other trendlike phenomena. Following Theil (1980), changes in real
expenditure are replaced with a Divisia volume index (!!!"!
!
= !
!!
!
!!
!!"!
!!
), and finite
logarithmic changes are employed to replace infinitesimal changes in the theoretical model.
However, the variables are 12month diferenced in order to acount for seasonality in demand
(Le 1988) and also to save the degree of freedom. Hence, 'lnx
t
= lnx
t
 lnx
t12
) dlnx
t
. Similarly,
!
!!
is the arithmetic mean of the expenditure share of the ith good in t12 and t.
2.4 Measurement of Uncertainty
The generalized autoregresive conditional heteroskedasticity (GARCH) model is employed to
measure the price and exchangerate volatilities. The GARCH method can fully reveal the
characteristics of timeseries data (Kandilov 2008) and can explicitly test whether the movement
in the conditional variance of price or exchange rate over time is statisticaly significant
(Patichis 2003). Those advantages lend the GARCH method to wide applications in the
agricultural trade literature (for example, Wang and Barret 2007; Kandilov 2008; and Erdema,
Nazlioglub, and Erdemc 2010).
!
38
For a typical AR(1)ARCH(1,1) model in which the residuals are from a AR(1) proces,
the volatility is obtained by jointly estimating the following equations:
13
(18) AR(1): E
i,t
= *
0
+ *
1
E
i,t1
+ +
i,t
(19) GARCH(1, 1) V(E
i
)
t
= ,
0
+ ,
1
!
!! !
!
+ ,
2
V(E
i
)
t1
+ 
i,t
where, E
i
is the diferential logarithm price or bilateral exchangerate variable, V(E
i
) represents
the conditional volatility, and +
i,t
and ,
i,t
are error terms of AR(1) and GARCH (1,1) proceses,
respectively. For the GARCH(1,1) proces to be welldefined, restrictions on the estimated
coeficients include 
0
> 0, 
1
+ 
2
< 1, and  
1
 < 1.
Price and exchange variance estimates by country are depicted in figure 24. For each
major supplier, the import price is more volatile than the corresponding export price. The
exchangerate variances sem to track each other reasonably wel. On the other hand, the
exchange rates in general fluctuate les than either export prices or import prices. This renders
equivalence of the export price risk and the exchangerate risk efects suspect. For Chile and
Canada, which succesfully captured the lion?s share of the US salmon imports, their prices and
exchange rates were no les volatile than those of other suppliers.
2.5 Regresion Results
The demand system of the US salmon import market contains five equations distinguished by
exporting sources: Chile, Canada, Norway, the UK, and ROW. In estimation, one equation
(ROW) is dropped from the system to avoid singularity. The relevant coeficients can be
recovered on the basis of demand constraints. The preliminary estimation using the Semingly
Unrelated Regresion (SUR) indicated the evidence of firstorder autocorrelation in some
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
13
As Patichis (203) points out, the order of the AR proces has litle impact on the GARCH models.
!
39
equations. Acordingly, the General Method of Moments (GM) approach was employed to
produce the NeweyWest estimator in order to correct autocorrelation as wel as
heteroskedasticity.
Model selection and Hypothesis tests
For purposes of comparison, the Rotterdam model inclusive of the import price risk variables is
first estimated, and the results are displayed in table 2.
14
The results in general reflect that the
diferentialbased demand system is compatible with the data at a satisfactory level in that al 5
estimated expenditure coeficients and 4 ownprice coeficients are significant and have the
correct signs in agreement with the demand theory. In the case of Chile, the major supplier, the
ownprice efect is negative but not significant. Most crossprice efects are significant with a
positive or negative sign. The negative crossprice elasticities betwen Chilean and Canadian
salmon indicate those two varieties are complementary to each other. This contradicts the fact
that there were opposite trends of market shares for Chile and Canada during the sample period.
For variance estimates, in the cases of Chile, Canada, and Norway, coeficients of the export
price volatilities are significantly diferent from zero, ranging from 0.6 to 1.3. However, the
insignificant ownprice efect in Chile?s equation and the unexpected substitutability betwen
Chilean salmon and Canadian salmon render the estimated import price variance efects suspect.
This leads us to the estimation of the extended Rotterdam model, where the import price risk is
decomposed into the export price risk and the exchange risk.
Before turning to the empirical results of the extended Rotterdam model, specific
restrictions of the demand system are justified by a comparison of models with diferent
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
14
The general demand restrictions and Dufy?s restriction (zero crosrisk efects) are imposed when
estimating the model.
!
40
economic hypotheses.
15
Acording to the likelihood ratio (LR) test results (table 3), I fail to
reject Model C against Model B where the Duffy?s restriction is imposed, indicating the support
of Theil?s hypothesis, i.e. a constant exchange risk efect. The results may relate to the common
properties of data generating proceses for exchange rates, as demonstrated in figure 4. Rejection
of Model C? against Model B (pvalue = 0.03) indicates diferent responses of marginal utility to
changes in export price risk due to diferential price signals. The information related to price
should be more available for imports from major suppliers. This is further evidenced by the
testing results of the hypothesis that efects of price variances for major suppliers (i.e. Chile,
Canada, and Norway) are identical (pvalue = 0.23). Consequently, the hypothesis of a constant
export price variance efect is treated as a maintained hypothesis in the present paper. Next, I test
the equivalence of import price risk and exchange risk efects by testing Model D against Model
C where restrictions of a constant export price risk efect and a constant exchange risk efect are
imposed. The LR test results show Model D is rejected with a pvalue = 0.023. Subsequently, the
conventional Rotterdam model exclusive of risk factors (Model E) is tested against Model C.
Model E is firmly rejected (p < 0.0001), indicating: (1) importers are not risk neutral, reflecting
risk factors should explain the observed salmon trade patern in addition to traditional variables
like relative prices, and (2) the empirical results from the conventional Rotterdam odel may be
misleading due to mispecification. Acording to the above test results, the remaining discussion
wil rely on estimates of Model D and the results are reported in table 4, where regresion results
of the conventional Rotterdam model (Model E) are also listed to highlight the diferences.
Estimates of Model D are overal satisfactory in that al marginal share estimates ('
i
) are
significantly positive and al ownprice coeficients (
ii
) are negative and significant. Chile and
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
15
I start from Model B due to the parameterizing problem. Following Phlips (1983, p55), al models have
homogeneity and symmetry imposed though both properties are rejected in preliminary tests.
!
41
Canada?s regresion results have the best explanatory powers with R
2
equaling 0.48 and 0.55,
respectively. With respect to expenditure and price efects, the estimated coeficients of Model D
are substantialy diferent from the counterparts of the conventional Rotterdam model (Model E).
In model D, both the constant export price risk efect and the constant exchangerate risk
efect are significant and are negative in sign, implying the US salmon importers are in general
riskaverse. The magnitude of the exchange risk coeficient is 2 times the magnitude of the
export price risk coeficient (0.13 vs. 0.07). This indicates that the marginal utility of the
imported salmon is more responsive to the exchange risk than to export price risk. Compared to
the export price risk, the exchange risk is far beyond the control of the agricultural traders. The
estimated coeficients of variances of the export price risk and the exchange risk are substantialy
smaler than the estimated import price risk efects in the alternative Rotterdam odel. Because
in the Rotterdam model the statistical significance of parameters have les economic meaning
than elasticities, the remaining discussion wil focus on conditional expenditure elasticities,
Hicksian price elasticities, and risk elasticities, which are estimated at the means of budget shares
(table 5).
Price and Expenditure Elasticities
For Chile, Canada, and Norway, the expenditure elasticities are close to one, in the range
betwen 0.98 and 1.16, suggesting consumer preferences for salmon from these sources are
homothetic. When consumer preferences are homothetic, the market share only responds to
changes in the relative price. This further implies that price and price risk play a crucial role in
this market. On the other hand, imports from runnersup in this market (i.e. the UK and ROW)
are les sensitive to changes in the total import expenditure. For example, a onepercentage
growth in the conditional expenditure would improve imports from UK and ROW by 0.4% and
!
42
0.2%, respectively. The uneven distribution of benefits from the rising expenditure can explain
the stable market share of Chile in 19952008 (table 1).
The estimated ownprice elasticities in the range betwen 0.3 in Chile and 2.4 in
Norway indicate that importers respond diferently to changes in prices of salmon from diferent
sources. The import demand is les sensitive to changes in major suppliers? prices and is more
sensitive to changes in other suppliers? prices. Considering aggregate data on frozen and fresh
salmon were employed in the regresion, those findings are somewhat in acordance with the
previous research. Xie, Kinnucan, and Myrland (2009) estimate the world demand for fresh
salmon is slightly elastic at 1.03 and for frozen salmon at 0.37. The greatest ownprice elasticity
for Norway (2.4) is not unexpected, because fresh salmon acounted for a great proportion of
imports from Norway during the data period.
In most cases, the crossprice elasticities are significant and positive, suggesting
competition betwen any pairs of salmon in the group of interest. The only exception is salmon
from Norway and the UK, where the negative crossprice elasticities indicate complementary
relations betwen these two goods. Import demand for Chile and Canada are les sensitive to
prices of salmon from other suppliers. For example, a onepercentage increase in the price of
Norway?s salmon would raise imports from Chile by 0.12% and raise imports from Canada by
0.29%. On the contrary, import demand for salmon from the runnersup is more sensitive to
changes in prices of salmon from the major suppliers. Taking Norway as an example, a one
percentage increase in prices of Chile and Canada?s salmon would improve imports from
Norway by 1.4% and 2.2%, respectively. These findings are consistent with the properties of the
market where Chile and Canada jointly had the lion?s share of the market throughout the sample
period.
!
43
Volatility Elasticities
The estimates of uncertainty variables are central to this research. Since I cannot reject the
Theil?s restriction that either the price risk or the exchange risk takes a role in the marginal utility
via ?adjusted? price with a negative constant, the strength of the response in demand for the ith
salmon with respect to changes in the risk factor of the jth salmon solely depends upon
substitutability betwen the these two varieties. For example, in Canada?s equation, an increase
in variance of Chile?s salmon price would expand Chile?s ?adjusted? price, which consequently
efects the demand for Canada?s salmon to some extend, depending on the magnitude of import
demand elasticity of Canada?s salmon with respect to Chile?s price.
Uncertainty from the owncurrency realignments exerts a significantly negative efect on
imports from Chile (0.04), Canada (0.08), Norway (0.32), and the UK (0.11). These results
are compatible with the findings in Wang and Barret (2007) and Kandilov (2008). Thus, the
estimate results reject De Grauwe?s hypothesis (1988) that an increase in the exchange risk
would cause firms to import more in order to avoid the worst possible outcome. Compared to
exchange risks, export price risks have les substantial impacts on the trade flows. The variances
of the ownprice have negative efects in al cases, with the derived elasticities ranging from 
0.02 in Chile and 0.18 in Norway. With regard to the export price risk elasticities, the diferent
response of the import demand is likely to be explained by market shares, transportation costs,
and availability of information. This is evidenced by a greater tolerance for the price volatilities
of salmon from Chile and Canada, which are major suppliers in this market, and at the same
time, have a shorter distance to the US than any other suppliers, including Norway and the UK.
Diferent from ownrisk elasticities, which have consistently negative signs, the cross
risk efects are ambiguous, depending on substitutability betwen products. Demand for salmon
!
44
from Chile is les significantly influenced by the price volatilities of Canada?s salmon and
Norway?s salmon, with a modest magnitude of 0.005 and 0.009, respectively. Demand for
Canada?s salmon is more sensitive to Chile?s price volatility than the response of Chile?s salmon
demand to Canada?s price volatility (0.008 vs. 0.005). The same conclusion can be made on the
comparison of exchangerate volatility elasticities. The diferent responses to risk factors may be
correlated with changes in the market where Chile gained an 11% increase of shares from 1995
to 2008, and Canada lost 13%.
Two arguments further shed light on trade efects of the risk variables. First, demand
elasticities with respect to risk factors are generaly smal in absolute values, since the impacts of
risk variables are weighted by price efects, which are, in most cases, are not strong. Second, the
substantial diference betwen export price risk and exchangerate risk may explain why, in
some cases, the Rotterdam model inclusive of the import price risk failed to capture significant
efects of ownprice variance.
2.6 Conclusions
Analogous to the treatment of preference variables in the literature (Brown and Le 2002, 2010),
I augmented risk factors into the Rotterdam model in which risk factors afect marginal utilities
via ?adjusted prices?. This methodology is appealing since it is commonly recognized that risk
averse firms are supposed to add a proportional markup on the realized or expected prices. When
the extended Rotterdam odel inclusive of risk factors is employed to evaluate the trade patern,
one hypothesis deserved more atention: the equivalence of export price risk and exchange risk
efects. In the literature, few endeavors have been made to examine the combined efect of
exportprice risk and exchange risk, especialy regarding agricultural trade where trade
participators are presumed to be more riskaverse.
!
45
The empirical evidence given above appears to sustain the conjecture that export price
risk and exchange risk take significant efect on the US import demand for farmed Atlantic
salmon, although they difer from each other. The diference betwen efects of export price risk
and exchange risk may be asociated with abilities of importers to control the uncertainty in the
market. Despite being significant in most cases, the elasticities of price risk and exchange risk
are tiny. This can be explained by price inelastic demand curves and weak substitutability
betwen products from diferent source countries since, theoreticaly, risk factors take efect on
trade flows by changing marginal utility, which is further weighted by price efects. Those
findings are consistent with the features of the US farmed salmon import market, where the two
largest suppliers (Chile and Canada) acounted for about 85% of the total salmon throughout the
sample period, although their prices and exchangerates had a great degree of fluctuation. In
general, relative price advantages, availability of substitutes, and consumer preferences are likely
to be the main factors resulting in the observed trade patern.
!
46
Chapter II. A RiskAugmented Cointegrating Import Demand System
!
47
3.1 Introduction
The main purpose of this paper is to examine the role of price risk in the alocation of import
expenditures across exporting sources by taking the US codfish market as an empirical
application. The agricultural industry is more sensitive to price risk in that agricultural goods are
les storable than manufactured products and are traded with flexible prices (Wang and Barret
2007), and agricultural product diferentiation is weak and firms are more numerous (Carter and
GunningTrant 2010). Trade data from the US International Trade Commite (USITC) reveals
that China replaced Canada as the major supplier of cod to the US after 2004. In addition to the
traditional variables like relative prices, I want to evaluate the extent to which the import price
risk can explain the observed trade patern.
In the research of agricultural trade, litle atention has been paid to the influence of price
uncertainty in trade flows. Seo (2001) and Muhamad (2011) are two exceptions. Taking
Chinese wheat imports market as an example, Seo investigates the relationship betwen the
expected price, the systematic risk of price, and monopolistic power of the exporters.
Muhamad develops a diferential demand system inclusive of import price uncertainty and
finds the evidence that the UK carnation importing firms are, for the most part, riskaverse. In a
study of price uncertainty, Wolak and Kolstad (1991) point out that fluctuations in exchange
rates might be one of the inherent risk sources in actual import prices. The significant
relationship betwen exchange rate risk and import demand for agricultural commodities is
verified in Langley et al. (2000); Cho, Sheldon, and McCorriston (2002); and Kandilov (2008).
Considering the numerous trade firms, the US codfish market can be presumed to be reasonably
competitive, indicating that the import price expresed in US dollars should contain al the
relevant information such as exchange volatility.
!
48
In the above trade literature, few studies are based on a complete demand system with the
exception of Muhamad (2011). This lack of atention to demand interrelationships may cause
biased empirical results. As Alesie and Kapteyn (1991 p. 404) state, ?One obvious omited
factor in microstudies is the interdependence of preferences.? In a welintegrated international
market like codfish, the trade impact of the price risk of a product from a particular country can
be offset by the price risk of other similar goods through a substitute or complementary efects.
Moreover, the systemwide approach to demand system facilitates the joint testing of theoretical
restrictions due to the underlying utility function (Duffy 1987), and evaluating the preference
variable like the price risk that is the main concern in the present paper.
Diferent from Muhamad (2011), where a diferential approach in line with the
Rotterdam demand model is applied, in the present paper I build risk factors into the Almost
Ideal Demand System (AIDS) of Deaton and Muelbauer (1980). The extended AIDS model
inclusive of risk factors can distinguish the ?competitive efect? and ?baseline efect? of price
risks, which is important to demonstrate the risk preference of importers, as I wil se later.
Another diference of the present paper compared with Muhamad (2011) is that I acount for
the stationarity of data generating proces when estimating the empirical model.
On the basis of a great deal of compeling reasons and evidence from previous research,
the price terms may be endogenous in the typical demand system for agricultural goods.
Furthermore, the price volatility can also be deemed to be jointly determined with prices and
expenditure shares, considering contracts betwen importers and leading suppliers can strongly
stabilize the price. Therefore, in the present paper, the empirical model is estimated by applying
a cointegratingbased Vector Error Correction Model (VECM) approach, in which the
?normalization? of the demand equation provides a useful framework to alow for endogeneity of
!
49
either price or volatility. Duffy (2003) investigates the advantages of cointegrating longrun
estimates compared to static equilibrium estimates from other regresion methods like the
Semingly Unrelated Regresion (SUR). As Reziti and Ozanne (1999) state, the cointegration
technique can further improve the estimation of the theoretical model with regard to the adjusting
mechanism of the market. This view is cited and echoed by Granger (1999, p. 16):
?The clasical approach to constructing a model starts with a sound, internaly
consistent, economic theory which provides a tight specification for the empirical model.
This model is then estimated and interpreted. Unfortunately, this strategy towards
modeling has not always proved to be a succesful one. Models produced in this way
often do not fit the data in various important directions. As one pair of applied
economists put it, ?a recurring problem in empirical studies of consumer and producer
behavior is that the regularity properties implied by microeconomic theory have more
often than not been rejected? (Rezili and Ozanne (1997)), who then go on to say ?such
rejection means that empirical work loses a good deal of its theoretical credibility.? They
point out that a major problem is ?the failure of static equilibrium theory to acount for
dynamic aspects of static equilibrium theory to acount for dynamic aspects of consumer
and producer behavior? and show how the introduction of dynamics into an equilibrium
model, by use of a stricture known as an errorcorrecting model, leads to clear
improvements.?
In what follows, the US codfish import market is briefly overviewed. Next, I discuss the
theoretical framework. Afterwards, the empirical models are established upon the theory,
followed by the measurement of price volatility and estimation methods. The later includes
estimation results and analysis. The final section consists of summary and implications.
3.2 Background
The US codfish import market is selected to implement the empirical study. For the last 20 years,
this market has been relatively concentrated with Canada, China, and Iceland as the major
!
50
suppliers; however, expenditure shares alocated by US importers to the main suppliers varied
dramaticaly over recent decades. Canada and Iceland have historicaly been the largest exporters
to the US, but since 2004 China has dominated this market. At the same time, the total (CIF)
value of codfish import reduced by 45 percent in the period from 1989 to 2010. The huge
variation in this market makes the codfish an insightful case to the role of price risk in addition to
traditional determinants (expenditure and prices) in the observed trade patern. Further, the
suppliers include a developing country (China) and a developed country (Canada) that have
diferent exchange rate regimes and diferent transportation costs, leading to diferent
movements of prices. Kandilov (2008) claims that trade efects of exchange volatility are
remarkably larger on agricultural exports from the developing countries than from the developed
countries.
Codfish, or cod, is a species of deepsea fish common to the North Pacific Ocean and
North Atlantic Ocean. Acording to USITC, from 1989 to 2010, the US has imported codfish
from 80 countries, among which the leading countries include Canada, China, and Iceland. On
average, the annual imports (CIF) of codfish from those countries acount for about 70% of total
codfish imports. In the USITC database, there are 25 HTS10 codes for codfish responding to
diferent species and forms. Among them filet frozen, filet fresh, fresh, frozen, and dried
codfish represented by 8 HTS10 codes consistently acounts for about 90 percent of total
imports. For the top suppliers, Canada has dominated dried codfish during the sample period.
Canada and Iceland shared the fresh cod market, and China explored and controlled the filet
frozen codfish market where other top suppliers have not substantialy entered. In this paper, the
major species and forms of codfish are aggregated to construct the demand system upon a two
stage budgeting proces.
!
51
Over the last twenty years, US codfish import volumes have experienced dramatic
changes. In total, the US imported 474 milion US dollars value of codfish in 1989; however, the
total value sharply declined to 262 milion US dollars in 2010. This sharp decline happened in
the early years of the period, and the variation of total imports has become relatively weak since
1994. The low fluctuation of total imports does not suggest a stable market share for individual
suppliers. As shown in table 1, imports of codfish from China grew faster after 1999, resulting in
China?s dominant role in this market since 2004. Betwen 19891999, on average, the annual
CIF value of Canadian codfish acounted for 41% of the total codfish imports and Chinese
codfish only 2.6%. However, in the period of 20002010, the positions for these two countries
were reversed in the market (17% vs. 44%).
The observed trade patern can be explained by changes in importers? budget and relative
prices (table 1, figure A1). The four price series have a decidedly upward movement and sem to
track each other reasonably wel. However, the price of China?s cod increased a leser degree
with a comparison of prices of Canada and Iceland?s cod. Figure A1 further implies an
interesting fact that there is a negative relationship betwen expenditure share and variation of
price. Before 2004 when Canada dominated the codfish market, the movement of its price was
weak; however, Canada?s price fluctuated strongly when its expenditure share was decreasing
after 2004. For China, the degree of price variations has become significantly smaler since
China was changing from a runnerup to a leader in this market after 2004. Two implications can
be generated from this observation. First, the variance of price may be one of the determinants to
explain the trade patern. Second, expenditure share and movement of price might jointly
determine each other, indicating the plausibility of applying the cointegrating technique in the
empirical analysis.
!
52
3.3 The Theoretical Model
Wolak and Kolstad (1991) postulate that an inputprice risk premium (or cost of risk) is the
percentage above the current expected market price a firm would pay for riskles input supply. In
terms of elements of price risk like exchange fluctuations, Balg and Metcalf (2010) and Bergin
(2004) posit a riskaverse firm would atach a risk premium as an extra markup to cover the costs
of uncertainty. Therefore, a change in price risk would influence the ?efective? price of the good
(?competitive efect?). On the other hand, riskaverse importers are perceived to define a
baseline plan due to maintenance of cooperation and diversification. The baseline expenditure
patern can be modified by the information about price risk (?baseline efect?), though it might
be independent of price. For a riskaverse firm, the competitive efect of risk is expected to be
negative, but the baseline efect may be positive or negative depending on the firm?s atitudes to
risk. If the firm is sufficiently riskaverse, the positive baseline efect may be greater than the
negative competitive efect and dominates the sign of combined efect of price risk. As De
Grauwe (1988) postulates, it is likely that an increase in price risk might cause firms to import
more to avoid the worst possible outcome. Starting from a traditional AIDS model, I demonstrate
how to incorporate the competitive efect and the baseline efect of price risk into this demand
system.
Following Deaton and Muelbauer (1980), the importer?s expenditure function is first
defined in the form:
(1) log c(u, p) = a(p) + u b(p)
where c(
.
) is a cost (expenditure) function, u is the utility function, p is a vector of price, and
(2) a(p) = logP = a
0
+ !!"#!
!
+ !! !
!"
!
!"#!!!"#!
!!!
!
53
(3) b(p) = !!
!
!
.
where a
0
, a
k
, !, !, and !
!"
!
are parameters.
Applying Shephard?s lema and defining !
!"
!!!!
!"
!
!
!"
!
!, the general AIDS
demand system with the expenditure share (w
i
) as the dependent variable can be derived from
specification (1)  (3),
(4) w
i
= a
i
+ )
i
log (x/P) + !
!"!
!"#!
!!
where a
i
can be explained as the baseline portion of imports from the ith country, and x is the
total expenditure.
Riskaverse importers should take the risk components (v) into acount when alocating
expenditure across suppliers to maximize utility or minimize expenditure. First, the competitive
efect of risk factors implies that the utility function can be modified by incorporating
multiplicative scaling factors.
(5) u = u(q*)
where !
!
!
= q
i
m
i
and m
i
is a scaling factor. As common in the literature on preference variables in
consumption literature (for example, Duffy 1995), m
i
is endogenized by asuming that it varies
with the level of price volatility of the ith product in a constant elasticity formulation, i.e. m
i
=
!
!
!
!
where 
i
is negative and is greater than unity in absolute value if importers are riskaverse.
Since the budget constraint for importers is not efected by importers? atitudes to price risk, I
can define an ?efective price? (or ?adjusted price?) as !
!
!
= p
i
/m
i
, indicating the expenditure
function can be specified as
(6) c(u, p, v) = c(u, p*)
Acordingly, (1) can be restated as:
(7) log c(u, p*) = a(p*) + u b(p*),
!
54
where p* is a vector with the components like !
!
!
.
Second, the baseline efect means price risk takes efect on the baseline expenditure
shares, which can be performed via adjusting the price index since the baseline imports are
originaly related to this index (Duffy 1995). Consequently, decomposing price risk efect into
the competitive efect and the baseline efect indicates an updated price index:
(8) log P* = a
0
+ !!"#!
!
!
!
+ !
!"
!"#!
!
!
!
!"#!
!!
+ !! !
!"
!
!"#!
!
!
!!"#!
!
!
!!
Hence, replacing equation (1) and (2) with (6) and (7) results in the riskaugmented AIDS
demand system in the form:
(9) w
i
= a
i
+ !
!"!"
!"#!
!"
+ )
i
log (x/P*) + !
!"
!!"#!
!
!!"#!
!!
Rearranging terms in (9) yields the theoretical model:
(10) w
i
= a
i
+ )
i
log (x/P*) + !
!"
!"#!
!!
+ !
!"!"
!"#!
!
where !
!"
(=!
!"
!!
!"
!) is the combined efect of price risk. For riskaverse importers, the
competitive efect of ownrisk is negative since !
!
is negative and !
!!
is also negative due to the
law of demand. Considering 
i
 >1, if '
ii
. 0, the parameter of ownrisk in equation (10), i.e.!
!!
,
should be greater than the ownprice efect (!
!!
) in absolute value. Therefore, the baseline efect
is positive as long as the estimated !
!!
is bigger than &
ii
in absolute value. The opposite is true if
!
!!
is smaler than &
ii
in absolute value. For cross efects, the sign of !
!"
(i $ j) depends on
substitutability betwen goods i and j, indicating an undetermined sign of the crossrisk efect.
3.4 Empirical Model and Data
The empirical model of the US codfish import demand is specified by incorporating an error
term into (10) to obtain:
(11) w
i,t
= a
i
+ )
i
log (x
t
/!
!
!
) + !
!"
!!"#!
!!
!
!!
+! !
!"
!
!!
!"#!!
!!
+ u
i,t
!
55
where i represents supplier (Canada = 1, China = 2, Iceland = 3, and ROW = 4); t stands for the
time subscript (monthly); u
i
is an i.i.d. error term; and P*, as a common in the literature (e.g.
Duffy 2003), is measured in the Stone form:
(12) log!
!
!
= !
!!
!
!!
!"#!p
j,t
.
Al other terms and variables are as previously defined.
Only price volatilities of cod from the top 3 suppliers, i.e. Canada, China, and Iceland,
are taken into acount in the demand system. Except for the major suppliers, there were lots of
runnersup in the US codfish market, so the fluctuation of the price of ROW was smoothed
during the sample period, as confirmed in figure A1. Furthermore, as discussed in the later
sector, the statistical test rejected the existence of a conditional volatility of the ROW price.
To satisfy properties of the demand system, namely homogeneity, symmetry, and adding
up, the following restrictions are imposed:
(13) !
!"
!
!!!
= 0 (homogeneity)
(14) #
ij
= #
ji
(symmetry)
(15) !
!
!
!!
! , !
!
!
!!
= !
!"
!
!!!
= !
!"
!
!!
= 0 (addingup)
After estimating the demand system represented by (11), the estimate parameters can be
used to derive the Marshalian elasticities
(16) !
!"
!
= )
i
/ !
!
(income elasticity)
(17) E
ii
= 1 + /
ii
/ !
!
 )
i
(ownprice elasticity)
(18) E
ij
= /
ij
/ !
!
 ()
i
!
!
!) / !
!
(crossprice elasticity)
(19) !
!"
!
= 0
ij
/ !
!
(pricerisk elasticity)
where !
!
is the expenditure share of commodity i in the base year ( to be discussed in detail).
!
56
Monthly cod import data from January 1989 to December 2010 are employed to estimate
the riskaugmented AIDS model represented by (11). The data are from the US International
Trade Commite (USITC) and the US National Marine Fishery Sources (NMFS). Import values
are in the US dollar on a costinsurancefreight (CIF) basis and import quantities are measured in
unit of kilograms, resulting in the unit of prices in US$ per kilogram (dividing value by quantity
for each month). For a particular month, expenditure share of the ith country (w
i
) is calculated by
dividing import value for country i by total import value in this month. Further, price and
expenditure time series are normalized to one (with respect to the base year 2004) in order to
minimize the estimating problems due to the Stone Index approximation (Pashardes 1993,
Moschini 1995).
3.5 Price Volatility
Before estimating the import demand system, the moments of import price distribution must be
estimated. The methods of measuring risk have evolved over time, and they can fal roughly into
two categories: the unconditional volatility represented by the moving standard deviation and the
conditional volatility represented by the generalized autoregresive conditional
heteroskedasticity method (GARCH). While a clearly dominant method has not yet emerged in
the empirical research (BahmaniOskooee and Hegerty 2007), the conditional volatility has
become more popular after the advent of cointegrating analysis because: (i) the GARCH model
acounts wel for the heavy tails of the distribution of the original variable (Kandilov 2008); (ii)
this method alows for timevarying conditional variance (i.e. volatility clustering) in the original
variable (Wang and Barret 2007); and (iii) the GARCH model can test whether the movement in
the conditional variance of a variable over time is statisticaly significant or not. These
!
57
advantages have led GARCHtype models to be very eficient in evaluating price uncertainty
(Rezitis and Stavropoulos 2011). Given the correlation betwen Canada?s price, China?s price,
and Iceland?s price, the MultivariateGARCH method (MGARCH) rather than the univariate
GARCH method is applied in the present paper.
One condition for the implement of the GARCHtype model is the existence of an ARCH
efect in the price dynamics. I first test the individual and joint ARCH efects of the three codfish
import prices by applying the Lagrange Multiplier (LM) method.
16
The sample value is larger
than the LM critical value at the 5% level of significance for each individual test and the joint
test (Table A1). Thus, the MGARCH method is employed in the present paper to obtain the
proxy for price risk.
The MGARCH model is expanded from the univariate GARCH approach by acounting
for the conditional correlation betwen innovations from diferent price data generating
proceses. In the paper, I focus on uncertainty in the prices of cod from Canada, China, and
Iceland, indicating a 3dimensional vector GARCH (1,1) proces such that
(20) V
t
= a
0
+ A !
!!
!!
+ B V
t1
where V
t
is a vector (3(1) of conditional price variance, !
!!
!!
is a vector (3(1) of the squared
error terms from mean regresions, and others are parameters to be estimated. Given diferent
asumptions of the conditional correlations, there are many types of MGARCH specification in
the literature. In the present paper, I apply the DCCGARCH model of Robert Engle (2002)
since it presumes timevarying conditional correlations, and is les restrictive.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
#$
!For an individual ARCH test, I first regres one price variable on its lags to obtain the residual.
Then I regres residual on m lags, and ases joint significance of coeficients of lag variables. If
the coeficients are diferent from zero based on LM test then the null of conditional
homoscedasticity can be rejected.
!
58
Figure 1 presents the estimated conditional variance for each price series by applying the
DCCGARCH approach (table A2). Canada and China?s prices had high degrees of variation
throughout the period. Consistent with the patern of price movements reflected in figure 1,
Canada?s price became more volatile in the later period; however, China?s price had more
fluctuation in the early period. For Iceland, except for several extreme observations, the price
volatility had a considerably low degree of fluctuation. Extreme observations also emerged in the
estimated Canadian and Chinese price variances. In order to avoid distortion impacts of extreme
observations when justifying the impact of price volatility, I compute the mean values of price
volatility variables for 20002002 when China?s share began to rise and for 20082010 when
China finaly dominated the market. By a comparison of those two periods, Canada?s price
volatility increased as high as 5.7 times, and Iceland?s price volatility increased 7.4 times. On the
contrary, China?s price volatility reduced by 70%. Intuitively, price uncertainty could be one of
the crucial determinants explaining the cod trade patern during the sample period.
3.6 Econometric Procedure
In a multivariate time series context, the first step is to test the stationarity of each variable.
Properties of the data series generating proceses dictate the methods to verify a common
stochastic trend among the data series. Given the existence of cointegration among variables, the
longrun relation betwen variables can be estimated by applying the Vector Error Correction
Model (VECM). If any linear combination of these variables fails to result in common stochastic
trends, the SUR estimates of the demand system ay be appropriate after transforming variables
to be stationary acording to the properties of the data generating proceses.
!
59
Prior to the cointegration test, the stationarity properties of variables are evaluated by
implementing the Augmented Dickey Fuller (ADF) test. The order of augmentation in the ADF
test is determined by the Akaike Information Criterion (AIC). If the null hypothesis cannot be
rejected, I can conclude that the data series is integrated of order one, I(1). The outcomes of the
ADF test suggest (table A3), at the conventional percent level, the null hypothesis cannot be
rejected for almost al variables, indicating most variables included in the models are integrated
of order one.
After evaluating the stationarity of each variable, atempts are made to test for the
presence of common stochastic trends among the variables. As most variables included in the
demand system are I(1), the Johansen procedure is implemented to test for cointegration in the
import demand expresion. This method is based on an unrestricted vector autoregresive
regresion (VAR) approach, and hence al variables incorporated in the model are asumed to be
endogenous. The test results produced from the Johansen trace and eigenvalue tests are reported
in table 2. Both the trace test and the eigenvalue test indicate five cointegration relationships
betwen variables in the demand system, which contradicts the expected ranks of three
cointegration spaces upon the demand theory. With a further inspection of the test results, the
sample values of the null hypothesis r = 5 in the eigenvalue test and the null hypotheses r = 5 and
r = 4 in the trace test are only marginaly larger than the critical value at the 5% level. On
balance, therefore, the predictions from the theoretical framework and the moderate support from
the econometric test results ensure the three cointegrating relationships betwen variables in the
demand system.
Since the Johansen test, which is based on an unrestricted VAR approach, just confirms
the cointegrating space, economic constraints need to be imposed on VAR to obtain the
!
60
identified longrun relationship. At the same time, the shortrun adjusting mechanism is
controlled by an error correction proces. Thus, the VECM approach is employed to estimate the
demand system represented by equation (11). Subsequently, I restate the demand system in a
VCEM form:
17
(21) 'Y
t
= *)`Y
t1
+ .
1
%Y
t1
+ ? + .
p
%Y
tg
+ ?D
t
+ U
t
where Y
t
is a 11(1 vector of al variables in the demand system, i.e. w
1,t
, w
2,t
, w
3,t
, log(x
t
/!
!
!
*),
logp
1,t
, logp
2,t
, logp
3,t
, logp
4,t
logv(p
1,t
), logv(p
2,t
),
and logv(p
3,t
); D
t
is a vector of dummy variables
utilized to control seasonal adjustments in the trade patern; g represents the number of lags for
the first diference variables. Here, * is the loading matrix (11(3), matrix ) (11(3) has the long
run coeficients, .
i
(11(11) is short run parameters matrix, and ? is a matrix of coeficients of
dummy variables. As usual, U
t
is a vector of error term.
Considering the existence of three cointegrating relationships in the unrestricted VAR
model, I need 3(3 = 9 constraints to identify each demand equation (Iootty, Pinto Jr, and Ebeling
2009). Hence, besides three normalizing constraints, three homogeneity constraints and three
symmetry constraints are imposed on VECM when estimating the longrun economic demand
relationship.
3.7 Regresion Results
Table 3 reports the estimated longrun coeficients ()?s) of the US codfish import demand
system expresed in the VECM specification, i.e. equation (21). For the purpose of comparison,
the SUR estimates of the static demand system are also regresed (Table A4). The VECM
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
#"
!The Akaike criterion proposed a lag order of 3 while the Schwarz information criterion and
HannanQuinn criterion proposed a lag order of 1, so the lag order of 1 is chosen in order to
avoid unstable estimate results after considering 11 variables in the system.
!
61
estimated coeficients are more significant and larger in magnitude when compared to the SUR
estimates. Moreover, there is strong evidence of autocorrelation in the residues of SUR
regresion. Therefore, the remaining discussion wil rely on the regresion results from VECM.
The regresion results overal are satisfactory in that most of the estimated parameters are
statisticaly significant. Consistent with the trade theory, the estimated coeficients of ownprice
are significant with negative signs for al countries, suggesting that an improvement in
competitivenes (a lower relative price) yields an increase in expenditure share. The 3 ownrisk
efects, in the range betwen 0.11 and 0.18, are significantly negative, implying the competitive
efect dominates the sign of the risk factor. What is an interesting finding is that, in each case,
the coeficient of ownprice is greater than the corresponding coeficient of ownrisk, indicating,
as discussed in the previous sector, the baseline efect of the price risk is positive. Both positive
and negative coeficients of crossrisk factors are captured in the regresion, and 9 out of the 12
cross efects are substantialy diferent from zero. Moreover, when the crossprice efect is
positive (negative), the corresponding crossrisk efect is also positive (negative). Given a
positive expenditure efect, the positive crossprice efect indicates the two goods are substitutes
for each other. Thus, a rise in the fluctuation of one good?s price would decrease its marginal
utility and consequently improve the marginal utility of its substitute, leading to a positive efect
of the crossprice variance, and vice versa for complementary goods.
Considering the lack of economic meaning of the estimated coeficients in the demand
system, I derive expenditure elasticities (!
!
!
), price elasticities (E
ij
), and volatility elasticities
(!
!"
!
) by employing suppliers? expenditure shares in the base year, 2004. The estimated
elasticities are displayed in Table 4.
!
62
Imports from Canada, China, and Iceland are more sensitive to changes in total imports.
For example a onepercentage increase in the conditional expenditure would increase imports
from Canada and China by 2.0% and 4.5%, respectively. The expenditure elasticity of Iceland?s
cod is negative (!
!
!
= 4.5), suggesting that imports from Iceland would increase when the total
expenditure decreases. Since 1995, when China entered into the US codfish market substantialy
(expenditure share > 1), the total expenditure has kept a rising trend until 2008. Hence, China?s
dominating market role is first due to changes in import expenditure of codfish.
In general, US codfish demand is strongly sensitive to changes in price. China?s codfish
has the greatest price elasticity (E
22
= 11.7), followed by Iceland (E
33
= 8.5), and Canada (E
11
=
3.9). This suggests, taking China as an example, a onepercentage decrease in China?s price
would increase cod imports from China by 11.7%, holding other determinants constant. Cross
price elasticities reflect the patern commonly found in trade literature. Most of the offdiagonal
elements are positive, implying gross substitutes betwen cod from diferent sources. A one
percentage increase in Canada and Iceland?s prices would raise imports from China by 1.1% and
6.0%, respectively. On the other hand, a onepercentage increase in China?s price only benefits
Canada by a 2.5% increase of import volume, and a onepercentage increase in Iceland?s price
would further drop Canada?s imports by 0.96%.
Turning to price volatility elasticities (!
!"
!
), the main concern in the present paper, al
ownrisk elasticities are statisticaly significant with expected negative signs. This means the
competitive efect of the risk factor dominates the sign of the risk factor, though the baseline
efect of the risk factor is positive. For example, a 1% increase in Canada?s price volatility is
estimated to decrease the import demand for Canada?s cod by 0.51%, given the other variables
are constant. For Iceland, a 1% increase in price volatility should reduce import demand for
!
63
Iceland?s cod by 0.85%. The US importers are les sensitive to the fluctuation of China?s price,
considering the smalest ownrisk elasticity (!
!!
!
= 0.32). The ownrisk elasticities are much
smaler than the corresponding ownprice elasticities, 0.51 vs. 3.88 in the case of Canada, 0.32
vs. 11.7 in the case of China, and 0.85 vs. 8.52 in the case of Iceland. I further evaluate the
extent to which price and risk may have contributed to the rising market share of China at the
expense of Canada. During the sample period, the great annual growth rate of China?s share
happened in 2005. China?s share increased 18% from 2004 to 2005, while Canada lost 9%. In
2005, the price of Canada?s cod was increased by 0.59%, resulting in a 2.3% decrease of volume
of cod imported from Canada. For China, the price of cod was increased by 5.6%, shrinking
imports from China by 66%, ceteris paribus. Unlike changes in price, Canada?s price volatility
in 2005 was as large as 1.4 times of the magnitude in 2004. On the contrary, China?s price was
relatively stable as the magnitude of volatility decreased by 29% in 2005. Considering the
estimated ownrisk elasticities, the increased price volatility would reduce imports from Canada
by 69%; however, the declined volatility would increase demand for China?s cod by 9.3%, which
offset the negative efect of the rising price in the same year.
The import demand for codfish is also sensitive to the changes in the crossrisk factors. A
onepercentage increase in volatility of China?s cod price and Iceland?s cod price would increase
imports from Canada by 0.13% and 0.36%, respectively. Imports of China?s cod are only
sensitive to Canada?s price volatility (!
!"
!
= 1.28). Codfish from Iceland only responds
negatively to Canada?s price volatility, though the corresponding crossprice elasticity is not
significant. Taking the annual growth rates (20042005) of Canada and China? price volatilities
into account (136% and 29%, respectively), ceteris paribus, changes in Canada?s price volatility
would increase cod imports from China 1.7 times, which completely offset the negative efect of
!
64
the rising ownprice. In contrast, China?s relatively stable price would further reduce cod imports
from Canada by 3.9%.
Overal, the inclusion of risk factors in the demand system can adequately track the
observed trade patern. In the case of China, influences of the low volatility of ownprice and the
high volatility of crossprices offset the negative efect of the rising ownprice and contribute
substantialy to the rising trend of codfish imported from China during the sample period. By
way of comparison, for Canada, in spite of a low degree of changes in the annual average price,
the high fluctuation of price and the strong substitutability betwen Canada and China?s cod are
the main reasons explaining the downward trend of cod imports from Canada during the sample
period.
3.8 Summary and Implications
In the present paper, I developed a riskaugmented Almost Ideal Demand System (AIDS) model
to explore the extent to which risk factors explain the observed trade patern. In the extended
model, the risk efect on import demand is decomposed into the competitive efect and the
baseline efect. Taking nonstationarities in the data and endogeneity into acount, I employ a
cointegratingbased Vector Error Correction Model (VECM) approach to estimate the longrun
responses of imports to the changes in the one or several determinants.
The resulting model is utilized to the US codfish market and the estimate results of the
demand system inclusive of price volatility adequately revealed formulation of the observed
trade patern. First, the estimated VECM longrun responses of importers to expenditure, price,
and volatility are more significant and larger in magnitude when compared to the Semingly
Unrelated Regresion (SUR) estimates, implying the static model may understate the responses
!
65
of import to changes in expenditure, price, and volatility. On the basis of the VCEM regresion
results, it can be argued that in the long run, the price volatility exerts significant efects on
importers? strategic decision to alocate expenditure among diferent source suppliers. For
example, the low fluctuation of China?s price and the high fluctuation of the competing
suppliers? prices contributed substantialy to China?s rapid rise as a major supplier of codfish
imported to the US after 2004; whereas, there was a huge negative efect of the rising price on
cod imports from China due to the extremely elastic demand curve.
The policy implications of these results for agriculture trade would likely sem to be
straightforward. Exporting countries interested in a target market should atempt to stabilize the
price. However, as Wolak and Kolstad (1991) state, much of price uncertainty is induced by
factors, which are out of the control of suppliers. Furthermore, the negative relationship betwen
price uncertainty and expenditure share limits abilities of runnersup to reduce price uncertainty.
Consequently, perhaps a more reasonable implication is related to trade policy designing which,
in most cases, is esentialy based on price analysis. For example, regarding the antidumping
policy, the relationship betwen the antidumping duties and price risk is investigated in Blonigen
(2004), which is cited in Carter and GunningTrant (2011, p. 99) as follows: ?Substantial price
volatility in agricultural markets often leads to higher AD margins compared with those of
manufacturing, particularly when the product is highly perishable.?
!
66
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!
74
Appendix 1: Tables and Figures for Chapter I
!
75
Table 1.1 Prices, Quantities, and Market Shares for Domestic and Imported Frozen
Catfish Filets, United States, 19992010
a
1 = US, 2 = Vietnam, 3 = Rest of World (China mainly). Vietnam and ROW prices are measured by
dividing CIF value by quantity.
b
Year in which antidumping duties were imposed on imports from Vietnam.
Sources: Hanson and Sites (209), NOAH Fisheries (201), and USITC (201)
!
!
!
"
!
#
"
!
"
"
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#
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#
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!
76
Table 1.2 Simulated Duty Passthrough Elasticities
a
a
The suply elasticities set to "
1
= 1.1, "
2
= 2.0, and "
3
= 2.0
b
Computed using text equations (10)  (12) and (13).
Price
PasThrough
P
1
*/P
2
*
b
/ T*
b
P
1
* / T*
b
P
3
/ T*
b
! = 1.50.0380.5880.0220.017
! = 2.50.1060.4860.0520.041
! = 5.00.2400.3610.0870.076
! = 1.50.0330.5860.0190.014
! = 2.50.0920.4800.0440.035
! = 5.00.211 0.3500.0740.064
! = 1.50.0580.5970.0350.026
! = 2.50.1550.5070.0790.063
! = 5.00.3250.3990.1300.113
20022004 (S
3
= 0.01)
20052007 (S
3
= 0.11)
20082010 (S
3
= 0.14)
Duty PasThrough
Armington
Elasticity
23
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"9:2"$.'N2("/:.'2"O&'"(:2">*(02>";&&>"0/":2+>"1&=/(.=(".("!
5
"4"?@5CL"0(/"$2.="P.+*2"O&'"5??F8B?@"9:2"
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!
"4"?@BCL"0/"0(/"$2.="P.+*2"O&'"5??F8B?@"
"
"
!
77
Table 1.3 Distributional Effects of a 35% Catfish Antidumping Duty Under Alternative
Asumptions About the Market Share of the NonDutied Good
! !
!
"#
!
Tab
l
e
3. D
i
s
tr
i
b
u
ti
on
al
Effe
c
ts
of a 35%
C
atfi
s
h
A
n
ti
d
u
mp
i
n
g D
u
ty U
n
d
e
r
A
l
te
r
n
ati
ve
A
s
u
mp
ti
on
s
A
b
ou
t th
e
M
ar
k
e
t S
h
ar
e
of
th
e
N
on

D
u
ti
e
d
G
ood
a
Fo
r
de
t
a
i
l
s
,
s
e
t
e
xt
e
qua
t
i
ons
(
25)

(2
8
)
a
n
d
a
t
e
n
d
a
n
t
d
i
s
c
u
s
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o
n
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b
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c
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p
t
f
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a
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t
s
h
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r
e
s
,
o
t
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p
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r
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t
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r
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t
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l
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ar
k
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u
t
i
ed
g
o
d
i
s
h
el
d
co
n
s
t
an
t
at
S
2
=
0
.
2
6
, th
e
m
e
a
n
va
l
ue
f
or
2008

10.
T
he
m
i
ddl
e
va
lu
e
f
o
r
th
e
n
o
n

dut
i
e
d
good,
S
3
=
0
.
1
4
,
i
s
t
h
e
m
e
a
n
v
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l
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o
f
t
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r
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t
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r
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r
t
h
e
2
0
8

10
pe
r
i
od.
S
3
= 0.07
S
3
= 0.14
S
3
= 0.28
U
.S
. P
roduc
e
rs
!
PS
1
M
i
l
$
9.15
8.14
6.10
33.4
U
.S
. Cons
um
e
rs
!
CS
=
!
CS
1
+
!
CS
2
+
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CS
3
M
i
l
$
28.6
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3.16
U
.S
.
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re
a
s
ury
!
TR
M
i
l
$
29.2
29.2
29.1
0.19
T
ot
a
l
U
.S
. Im
pa
c
t
!
W
US
=
!
PS
1
+
!
CS
+
!
TR
M
i
l
$
9.69
8.96
7.48
22.8
V
i
e
t
na
m
P
roduc
e
rs
!
PS
2
M
i
l
$
18.1
18.1
18.2
0.28
Chi
na
P
roduc
e
rs
!
PS
3
M
i
l
$
0.77
1.51
3.00
289
T
ot
a
l
Im
pa
c
t
!
W
US
+
!
PS
2
+
!
P
S
2
M
i
l
$
7.66
7.67
7.69
0.36
Inc
i
de
nc
e
of D
ut
y:
U
.S
. Cons
um
e
rs
/
T
*
%/
100
0.508
0.507
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0.35
V
i
e
t
na
m
P
roduc
e
rs
P
2
* /
T
*
%/
100
0.492
0.493
0.494
0.36
Re
di
s
t
ri
but
i
on E
f
fi
c
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nc
y
!
PS
1
/
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1
0.32
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a
rke
t
S
ha
re
of N
onD
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d G
ood
b
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roup
F
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!
78
Table 1.4 Sensitivity of Welfare Effects of the Catfish Antidumping Duty to the Armington
Elasticity (#) and Import Suply Elasticities (! = !
2
= !
3
)
a
! !
!
"#
!
Tab
l
e
4.
S
e
n
s
i
ti
vi
ty
of
W
e
l
far
e
Effe
c
ts
of
th
e
C
atfi
s
h
A
n
ti
d
u
mp
i
n
g
D
u
ty
to
th
e
A
r
mi
n
gton
El
as
ti
c
i
ty
(
!
)
an
d
I
mp
or
t
S
u
p
l
y
El
as
ti
c
i
ti
e
s
(
"
=
"
2
=
"
3
)
a
a
Th
e
d
o
m
e
s
t
i
c
s
u
p
l
y
e
l
a
s
t
i
c
i
t
y
i
s
s
e
t
t
o
!
1
=
1
.
a
n
d
m
a
r
k
e
t
s
h
a
r
e
s
a
r
e
s
e
t
t
o
S
1
=
0
.
6
0
,
S
2
=
0
.
2
6
an
d
S
3
=
0
.
1
4
,
t
h
e
m
e
a
n
v
a
l
u
e
s
f
o
r
2
0
8

10.
b
?
Be
s
t

be
t
?
e
s
t
i
m
a
t
e
s
.
!
= 2
!
= 4
!
=
"
!
= 2
b
!
= 4
!
=
"
!
= 2
!
= 4
!
=
"
U
.S
. P
roduc
e
rs
3.56
4.42
5.85
8.1
1
10.6
15.2
13.5
18.7
30.3
U
.S
. Cons
um
e
rs
27.0
32.3
39.8
28.3
35.0
44.3
30.3
39.3
49.3
U
.S
.
T
re
a
s
ury
32.0
28.8
23.4
29.2
24.1
13.7
25.8
17.4
6.54
T
ot
a
l
U
.S
. Im
pa
c
t
8.50
0.89
10.5
8.94
0.37
15.4
8.96
3.20
25.5
V
i
e
t
na
m
P
roduc
e
rs
15.4
9.24
0.00
18.1
1
1.2
0.00
21.1
13.5
0.00
Chi
na
P
roduc
e
rs
0.62
0.49
0.00
1.53
1.40
0.00
2.80
3.1
1
0.00
T
ot
a
l
Im
pa
c
t
6.27
7.86
10.5
7.67
10.2
15.4
9.36
13.6
25.5
Inc
i
de
nc
e
of D
ut
y:
U
.S
. Cons
um
e
rs
0.60
0.75
1.00
0.51
0.67
1.00
0.40
0.56
1.00
V
i
e
t
na
m
P
roduc
e
rs
0.40
0.25
0.00
0.49
0.33
0.00
0.60
0.44
0.00
Re
di
s
t
ri
but
i
on E
f
fi
c
i
e
nc
y
0.13
0.14
0.15
0.29
0.30
0.34
0.45
0.48
0.61
#
= 1.5
#
= 2.5
#
= 5
G
roup
!
79
Table 1.5 Sensitivity of TradeDiversion Effects to Antidumping Duty Rates
a
! !
!
""
!
Tab
l
e
5
. S
e
n
s
i
ti
vi
ty of Tr
ad
e

D
i
ve
r
s
i
on
Effe
c
ts
to A
n
ti
d
u
mp
i
n
g D
u
ty R
ate
s
a
a
Th
e
s
u
p
l
y
e
l
a
s
t
i
c
i
t
i
e
s
s
e
t
t
o
!
1
=
1
.
,
!
2
=
!
3
=
2.
0,
an
d
"
=
2
.5
, a
ll ?
b
e
s
t

be
t
?
va
l
ue
s
.
b
Ma
r
k
e
t
s
h
a
r
e
o
f
t
h
e
d
u
t
i
e
d
g
o
d
i
s
h
e
l
d
c
o
n
s
t
a
n
t
a
t
S
2
=
0
.
2
6
,
th
e
m
e
a
n
v
a
lu
e
f
o
r
2
0
8

10.
T
* = 15%
T
* = 35%
T
* = 50%
T
* = 70%
T
* = 15%
T
* = 35%
T
* = 50%
T
* = 70%
T
* = 15%
T
* = 35%
T
* = 50%
T
* = 70%
U
.S
. P
roduc
e
rs
3.89
9.15
13.2
18.6
3.46
8.14
1
1.7
16.5
2.59
6.10
8.76
12.4
U
.S
. Cons
um
e
rs
13.2
28.6
38.6
49.8
13.1
28.3
38.2
49.2
12.8
27.7
37.3
48.0
U
.S
.
T
re
a
s
ury
16.3
29.2
32.3
27.7
16.3
29.2
32.3
27.6
16.2
29.1
32.2
27.5
T
ot
a
l
U
.S
. Im
pa
c
t
6.96
9.69
6.83
3.52
6.65
8.96
5.77
5.05
6.04
7.48
3.62
8.14
V
i
e
t
na
m
P
roduc
e
rs
8.69
18.12
23.58
28.71
8.70
18.1
23.6
28.7
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18.2
23.6
28.8
Chi
na
P
roduc
e
rs
0.33
0.77
1.1
1
1.58
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3.08
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3.00
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6.13
T
ot
a
l
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pa
c
t
1.41
7.66
15.6
30.7
1.41
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15.7
30.7
1.41
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15.7
30.8
Inc
i
de
nc
e
of D
ut
y:
U
.S
. Cons
um
e
rs
0.508
0.508
0.508
0.508
0.507
0.507
0.507
0.507
0.506
0.506
0.506
0.506
V
i
e
t
na
m
P
roduc
e
rs
0.492
0.492
0.492
0.492
0.493
0.493
0.493
0.493
0.494
0.494
0.494
0.494
Re
di
s
t
ri
but
i
on
E
f
fi
c
i
e
nc
y
0.29
0.32
0.34
0.37
0.26
0.29
0.31
0.34
0.20
0.22
0.23
0.26
S
3
= 0.07
b
S
3
= 0.14
b
S
3
= 0.28
b
G
roup
!
80
Figure 1.1 Welfare Analysis of an Antidumping Duty
!
!
!
"#!
Figure 1: Welfare Analysis of an Antidumping Duty
28
!
81
Apendix: Derivation of the PassThrough Elasticity
To derive the PTE, I first reduce the structural model (equations (2) ? (8)) to three equations by
solving for equilibrium in each market to yield:
(A1) 0
~
)(
*
313
*
212
*
1111
=!!! PPP """#
(A2)
2
+)
2
T
*
(A3) 0)(
~
*
3333
*
232
*
131
=!+!! PPP "#"" .
The equilibrium in matrix form is:
(A4)
(!
1
)
1213
"
2
()!"
2
3132
(
3
)
#
$
%
&
'
1
*
!
P
2
3
*
#
$
=
0
2
"%
&
'
T
*
Cramer?s rule is applied to equation (A4) to obtain the reducedform elasticitiesP
1
*
Tand
!
P
2
*
T (and
3
*
). Inserting these expresions into
(A5)
1
*
=
PT
*
!
2
"
#
$
%
&
!
2
gives the PTE when N = 3. The corresponding expresion when N = 2 is obtained by the seting
the structural elasticities in equations (A1) ? (A3) that have a 3 in the subscript to zero, and
repeating the above steps.
!
82
Appendix 2: Tables and Figures for Chapter II
!
83
Table 2.1 US Salmon Imports and Market Shares by Sources
Year
Total Imports Value Shares (%)
(mil. US $) Chile Canada Norway UK ROW
1995 277 42.1 49.0 5.5 1.9 1.5
1996 316 46.8 44.6 3.6 3.0 1.9
1997 428 43.2 50.1 2.5 2.1 2.1
1998 549 48.9 42.2 3.6 3.4 1.8
1999 689 40.5 39.0 9.6 7.0 3.9
2000 794 53.4 32.1 6.9 5.1 2.5
2001 879 51.4 39.8 4.7 3.1 1.0
2002 947 52.1 39.5 4.7 3.0 0.8
2003 1,072 58.7 28.3 5.2 6.3 1.5
2004 1,032 62.6 26.7 3.8 5.5 1.5
2005 1,184 62.1 29.2 3.3 3.8 1.6
2006 1,471 60.1 28.8 4.7 4.4 2.0
2007 1,579 58.9 26.5 5.6 6.4 2.7
2008 1,562 57.0 28.8 4.0 6.1 4.1
Average 52.7 36.0 4.8 4.4 2.1
Note: Data are obtained from USITC.
!
84
Table 2.2 GM Estimates of U.S. Import Demand System for Salmon, Rotterdam Model
Inclusive Import Price Risk, 19952008 Monthly Data (1 = Chile, 2 = Canada, 3. Norway, 4
= United Kingdom, 5 = ROW)
Variable Coef. Eq 1 Eq 2 Eq 3 Eq 4 Eq 5
Trend *
i
0.0021 0.0166
a
0.0019 0.0055
c
0.007
a
(0.063) (0.063) (0.019) (0.028) (0.015)
' ln Q '
i
0.5414
a
0.421
a
0.029
a
0.0187
c
0.010
a
(0.025) (0.0302) (0.0107) (0.0109) (0.08)
' ln p
1
(
i1
0.0072
(0.0158)
' ln p
2
(
i2
0.0313
b
0.179
a
(0.0142) (0.0304)
' ln p
3
(
i3
0.0016 0.102
a
0.0549
a
(0.07) (0.0168) (0.011)
' ln p
4
(
i4
0.0307
a
0.0559
a
0.028
a
0.047
a
(0.010) (0.01) (0.063) (0.071)
' ln p
5
(
i5
0.0062 0.0524
a
0.0208
a
0.0116
a
0.026
a
(0.05) (0.059) (0.045) (0.041) (0.035)
' ln v(p
1
) /
1
1.315
b
(0.515)
' ln v(p
2
) /
2
1.0135
a
(0.168)
' ln v(p
3
) /
3
0.616
a
(0.23)
' ln v(p
4
) /
4
0.165
(0.154)
' ln v(p
5
) /
5
0.180
(0.153)
Note: Numbers in parentheses are asymptotic standard erors.
a
indicates significance at the p < 0.01 level;
b
indicates significance at the p < 0.05 level;
c
indicates significance at the p < 0.10 level.
!
85
Table 2.3 Tests of Theoretical Restrictions
Model Against
Number of
Restrictions
LR Statistic pvalue
Model B
Model C Model B 4 10.75 0.029
Model C! Model B
3 3.96 0.265
Model D Model C 1 5.14 0.023
Model E Model C 2 55.10 <0.0001
Note: Model B restricts the crossefect of price and exchange risks are zero (Duffy?s
restriction). Model C and Model C! impose an identical nonzero efect of al ownprice risk and
an identical nonzero efect of al ownexchange risk (Theil?s restriction), respectively. Model D
imposes the equivalence of the nonzero ownprice and nonzero ownrisk efects. odel E
imposes the additional restriction that the identical nonzero efects of risk factor are equal to
zero. For each model, symmetry and homogeneity are imposed.
!
86
Table 2.4 GM Estimates of U.S. Import Demand System for Salmon, Rotterdam Model
19952008 Monthly Data (1 = Chile, 2 = Canada, 3 = Norway, 4 = United Kingdom, 5 =
ROW)
!
"#
!
Tab
l
e
4
.
G
M
Es
ti
mate
s
of U
.S
. I
mp
or
t D
e
man
d
S
ys
te
m for
S
al
mon
, R
otte
r
d
am M
od
e
l
1995

2008 M
on
th
l
y D
ata (1 =
C
h
i
l
e
, 2
=
C
an
ad
a, 3. N
or
w
ay
, 4 =
U
n
i
te
d
K
i
n
gd
om, 5 =
R
O
W
)
!
!
$%
&
'
(
!
)
!
*
+,

.
!
'/
0
%
1

!
0
1,
2
'
!
34
&
!
'
/2
.
34
5'
6
13
'
!
731
,
34
2
'8
9
!
!
$%
&
'
(
!
:
!
*+
,
.
%
;
!
1,
8
<
!
=
3
2
%
18
9
!
>3
1
,
3
?(
'
!
@%'
=
A
!
:B
!
C
!
:B
!
"
!
:B
!
D
!
:B
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E
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:B
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F
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C
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"
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!
87
Table 2.5 Conditional Demand Elasticities (1 = Chile, 2 = Canada, 3 = Norway, 4 = United
Kingdom, 5 = ROW)
Eqn
Expenditure
Elasticities
Hicksian Price Elasticities
E
i
y
*
1i
E
*
2i
E
*
3i
E
*
4i
E
*
5i
E
1
0.975
a
0.303
a
0.073
c
0.124
a
0.090
a
0.016
(0.03)
(0.063) (0.04) (0.036) (0.014) (0.012)
2
1.163
a
0.107
c
0.619
a
0.291
a
0.084
a
0.139
a
(0.063)
(0.059) (0.07) (0.04) (0.03) (0.018)
3
0.993
a
1.350
a
2.165
a
2.41
a
0.701
a
0.393
a
(0.18)
(0.395) (0.31) (0.25) (0.101) (0.082)
4
0.344
b
1.085
a
0.691
a
0.776
a
0.851
a
0.160
a
(0.182)
(0.165) (0.245) (0.11) (0.149) (0.068)
5
0.194
a
0.412
a
2.422
a
0.920
a
0.339
a
1.574
b
(0.234)
(0.302) (0.31) (0.191) (0.143) (0.124)
Note: Numbers in parentheses are asymptotic standard erors.
a
indicates significance at the p < 0.01 level;
b
indicates significance at the p < 0.05 level;
c
indicates significance at the p < 0.10 level.
!
88
Table 2.6 Conditional Demand Elasticities (1 = Chile, 2 = Canada, 3 = Norway, 4 = United
Kingdom, 5 = ROW) (cont)
! "#!
5. iti ti il, 2 = Cada, 3. N United
)
!
$%&!
$'()&*+,.)!
$/01,+2+,+)1!
!
3+241+0&!5.+2)!$/01,+2+,+)1!
!
E
i
y
!
!
*
1i
E !
*
2i
E !
*
3i
E !
*
4i
E !
*
5i
E !
!
6!
!"#$%
&
!
!
'!"(!(
)&
! !"!$(
*
! !"+,
)&
! !"!#!
)&
! !"!+.!
!
!
/!"!(0!
!
/!"!.(0! /!"!0! /!"!(.0! /!"!+0! /!"!+,0!
!
"!
+"+.(
)&
!
!
!"+!$
*
! '!".+#
)&
! !",#+
)&
! !"!1
)&
! !"+(#
)&
!
!
!
/!"!.(0!
!
/!"!%#0! /!"!$0! /!"!0! /!"!(0! /!"!+10!
!
7!
!"##(
)&
!
!
+"(%!
)&
! ,"+.%
)&
! ',"+
)&
! '!"$!+
)&
! '!"(#(
)&
!
!
!
/!"+10!
!
/!"(#%0! /!"(+0! /!",%0! /!"+!+0! /!"!1,0!
!
8!
!"(
2
!
!
+"!1%
)&
! !".#+
)&
! '!"$$.
)&
! '!"1%+
)&
! '!"+.!
)&
!
!
!
/!"+1,0!
!
/!"+.%0! /!",%0! /!"++0! /!"+#0! /!"!.10!
!
9!
!"+#
)&
!
!
!"+,
)&
! ,",,
)&
! '!"#,!
)&
! '!"((#
)&
! '+"%$
2
!
!
!
/!",(0!
!
/!"(!,0! /!"(+0! /!"+#+0! /!"+(0! /!"+,0!
!
:;,)).1!+&!(0.)&,?)1)1!0.)!01@=(,;,+2!1,0&*0.*!).;.1A!
0
!+&*+20,)1!1+B&+C+20&2)!0,!,?)!!D!EAE6!/)F)/G!
>
!
+&*+20,)1!1+B&+C+20&2)!0,!,?)!!D!EAE9!/)F)/G!
2
!+&*+20,)1!1+B&+C+20&2)!0,!,?)!!D!EA6E!/)F)/A! !
!
89
Figure 2.1 Import US Dollar Prices of Salmon by Sources
3
4
5
6
19951996199719992000200120032004200520072008
Import Price of Chile's Salmon
4.0
4.5
5.0
5.5
6.0
19951996199719992000200120032004200520072008
Import Price of Canada's Salmon
4
5
6
7
19951996199719992000200120032004200520072008
Import Price of Norway's Salmon
3
4
5
6
7
8
9
10
19951996199719992000200120032004200520072008
Import Price of the UK's Salmon
3
4
5
6
19951996199719992000200120032004200520072008
Import Price of the ROW's Salmon
!
90
Figure 2.2 Conditional Variance Estimates of Import Prices (in US dollar): January 1995 
December 2008
0.03
0.04
0.05
0.06
19951996199719992000200120032004200520072008
Volatility of Import Price of Chile's Salmon
0.04
0.05
0.06
0.07
19951996199719992000200120032004200520072008
Volatility of Import Price of Canada's Salmon
0.08
0.10
0.12
0.14
0.16
0.18
19951996199719992000200120032004200520072008
Volatility of Import Price of Norway's Salmon
0.10
0.15
0.20
0.25
0.30
0.35
19951996199719992000200120032004200520072008
Volatility of Import Price of the UK's Salmon
0.20
0.25
0.30
0.35
0.40
0.45
19951996199719992000200120032004200520072008
Volatility of Import Price of the ROW's Salmon
!
91
Figure 2.3 Conditional Variance Estimate of Export Prices (in Foreign Curency):
January 1995  December 2008
0.04
0.06
0.08
0.10
0.12
0.14
19951996199719992000200120032004200520072008
Volatility of Export Price of Chile's Salmon
0.05
0.10
0.15
0.20
0.25
19951996199719992000200120032004200520072008
Volatility of Export Price of Canada's Salmon
0.15
0.20
0.25
19951996199719992000200120032004200520072008
Volatility of Export Price of Norway's Salmon
0.10
0.15
0.20
0.25
0.30
0.35
19951996199719992000200120032004200520072008
Volatility of Export Price of the UK's Salmon
!
92
Figure 2.4 Conditional Variance Estimate of Bilateral Exchange Rate: January 1995 
December 2008
0.04
0.06
0.08
0.10
19951996199719992000200120032004200520072008
Conditional Variance of US?Chile Exchange
0.02
0.04
0.06
0.08
0.10
19951996199719992000200120032004200520072008
Conditional Variance of US?Canada Exchange
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
19951996199719992000200120032004200520072008
Conditional Variance of US?Norway Exchange
0.03
0.04
0.05
0.06
19951996199719992000200120032004200520072008
Conditional Variance of US?UK Exchange
!
93
Appendix 3: Tables and Figures for Chapter III
!
94
Table 3.1 US Cod Imports, Expenditure Shares, Prices by Sources
YEAR
Imports
(mil. US $)
Expenditure shares (%) Prices (US$ / Kilogram)
Canada China Iceland ROW Canada China Iceland ROW
1989 474
61.2 0.2 21.0 17.5
1.4 2.8 2.1 1.3
1990 501
68.9 0.4 15.3 15.4
1.3 2.0 1.6 1.4
1991 510
59.3 0.7 18.4 21.6
1.6 1.8 2.0 1.7
1992 375
49.5 1.6 21.2 27.6
1.5 1.5 1.8 1.6
1993 291
36.2 1.9 36.4 25.4
1.5 1.6 1.7 1.5
1994 262
26.2 1.0 37.0 35.7
1.4 1.9 1.7 1.5
1995 281
24.5 3.1 33.6 38.7
1.3 1.5 1.8 1.6
1996 255
32.9 3.0 37.1 27.0
1.3 1.8 1.7 1.6
1997 318
30.0 5.4 33.6 31.1
1.4 1.7 1.8 1.6
1998 313
30.1 3.6 35.4 31.0
1.5 1.5 2.1 1.9
1999 379
30.5 7.8 36.0 25.6
1.8 1.9 2.2 2.2
2000 355
29.6 13.8 30.3 26.2
1.8 2.2 2.2 2.1
2001 290
28.5 15.7 29.4 26.4
1.7 2.1 2.1 2.0
2002 337
24.3 20.0 26.2 29.5
1.7 2.3 2.2 2.0
2003 315
24.5 23.5 23.3 28.7
1.8 2.3 2.3 2.1
2004 325
21.0 33.1 20.7 25.2
1.9 2.3 2.3 2.2
2005 327
11.8 51.1 15.6 21.5
1.9 2.5 2.7 2.4
2006 349
9.5 61.0 13.6 16.0
2.1 2.9 3.0 2.5
2007 355
8.6 71.1 8.2 12.2
2.3 3.1 3.2 2.7
2008 332
9.7 70.7 6.1 13.5
2.5 3.4 3.0 2.8
2009 250
11.8 63.4 9.5 15.3
2.4 2.7 2.6 2.2
2010 262 10.6 64.1 10.0 15.3 2.2 2.3 2.8 2.4
Sources: USITC and value data are in CIF measure.
!
95
Table 3.2 Johansen Cointegration Test Results
Eigenvalue Method
Maximum Eigen Method
H
o
: H
a
: Eigenvalue
0.05
Critical
value
H
o
: H
a
:
MaxEigen
Statistic
0.05
Critical
value
r = 0 r = 1 545.6* 358.7
r = 0 r # 1 138.3* 79.23
r = 1 r = 2 407.2* 307.2
r . 1 r # 2 93.2* 73.47
r = 2 r = 3 314.0* 260.8
r . 2 r # 3 73.6* 67.77
r = 3 r = 4 240.3* 216.6
r . 3 r # 4 62.1* 61.59
r = 4 r = 5 178.2* 178.0
r . 4 r # 5 56.5* 55.81
r = 5 r = 6 121.6 141.7
r . 5 r # 6 46.2 49.97
r = 6 r = 7 75.4 108.6
r . 6 r # 7 30.3 43.62
r = 7 r = 8 45.0 81.25
r . 7 r # 8 20.5 37.83
r = 8 r = 9 24.5 56.28
r . 8 r # 9 15.9 31.56
r = 9 r = 10 8.56 35.46
r . 9 r # 10 6.79 24.97
r = 10 r = 11 1.77 17.8
r . 10 r # 11 1.77 17.80
*: significant at the 5% level. Critical values are from Pesaran, Shin, and Smith (2000)
!
96
Table 3.3 VECM Estimates of US Import Demand System for Codfish, AIDS Model, 1989
2010 Monthly Data (1 = Canada, 2 = China, 3 = Iceland, 4 = ROW)
Variable Eq 1 Eq 2 Eq 3 Eq 4
constant 0.321*** 0.090 0.503*** 0.267***
(0.045) (0.174) (0.121) (0.033)
log (x/P*)
0.212*** 1.168*** 1.151*** 0.229***
(0.068) (0.269) (0.186) (0.05)
log p
1
0.559*** 0.603*** 0.157 0.113***
(0.108) (0.086) (0.1) (0.058)
log p
2
0.603*** 3.134*** 2.229*** 0.303***
(0.086) (0.342) (0.237) (0.062)
log p
3
0.157 2.229*** 1.820*** 0.252***
(0.1) (0.237) (0.188) (0.057)
log p
4
0.113** 0.303*** 0.252*** 0.164***
(0.058) (0.067) (0.059) (0.048)
log v(p
1
) 0.106** 0.421*** 0.248*** 0.067***
(0.03) (0.117) (0.081) (0.021)
log v(p
2
)
0.028* 0.106* 0.062 0.016
(0.016) (0.061) (0.043) (0.012)
log v(p
3
)
0.075*** 0.149 0.178*** 0.047***
(0.025) (0.098) (0.068) (0.018)
Note: Numbers in parentheses are asymptotic standard erors. Single asterisk (*) indicates significance at the p <
0.10 level; double asterisk (**) indicates significance at the p < 0.05 level; triple asterisk (**) indicates significance
at the p < 0.01 level.
!
97
Table 3.4 Derived Demand Elasticities (1 = Canada, 2 = China, 3 = Iceland, 4 = ROW)
Note: Numbers in parentheses are standard erors computed via the Delta method. Note: Numbers in parentheses
are asymptotic standard errors. Single asterisk (*) indicates significance at the p < 0.10 level; double asterisk (*)
indicates significance at the p < 0.05 level; triple asterisk (**) indicates significance at the p < 0.01 level.
! "#!
Table 4. Derived Demand Elasticities (1 = Canada, 2 = China, 3 = Iceland, 4 = ROW)
Eqn
Expenditure
Elasticities
Marshalian Price Elasticities
Price Volatility Elasticities
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
!
1 2.01***
3.88*** 2.54*** 0.96** 0.29
0.51*** 0.13* 0.36***
(0.324)
(0.516) (0.412) (0.474) (0.274)
(0.141) (0.077) (0.121)
2 4.54***
1.08*** 11.67*** 6.01*** 0.03
1.28*** 0.32* 0.45
(0.814)
(0.262) (1.036) (0.717) (0.202)
(0.355) (0.186) (0.297)
3 4.48**
0.41 12.42*** 8.52*** 0.17
1.18*** 0.30* 0.85**
(0.886)
(0.474) (1.127) (0.897) (0.28)
(0.387) (0.202) (0.324)
4 0.08
0.64*** 1.51*** 0.82*** 1.43***
0.27*** 0.06 0.19***
(0.2)
(0.233) (0.248) (0.226) (0.192) (0.086) (0.047) (0.072)
Note: Numbers in parentheses are stanar errs c te ia te lta ethod. Note: Numbers in
parenthee are symptotic tndard erors.Singleasterisk (*)indicassignificanc at the p < 0.10 level;
double asterisk (**)indicatessgnificance at thep < 0.5 level;trple asterisk (**) indicates significance
at the p < 0.1 lvl.
!
98
Figure 3.1 MGARCH Estimated Conditional Price Volatility
0.00
0.02
0.04
0.06
0.08
19891991199319951997199920022004200620082010
Volatility of Pcan
0.0
0.1
0.2
0.3
0.4
0.5
19891991199319951997199920022004200620082010
Volatility of Pchn
0.00
0.05
0.10
0.15
0.20
19891991199319951997199920022004200620082010
Volatility of Pice
!
99
Figure 3.A1 US Import Cod Prices by Sources
1.5
2.0
2.5
3.0
19891991199319951997199920022004200620082010
Price of Canada's Cod
1.0
1.5
2.0
2.5
3.0
3.5
4.0
19891991199319951997199920022004200620082010
Price of China's Cod
1.5
2.0
2.5
3.0
3.5
4.0
19891991199319951997199920022004200620082010
Price of Iceland's Cod
2
4
6
8
19891991199319951997199920022004200620082010
Price of ROW's Cod
!
100
Table 3.A1 ARCH Test for Price (1 = Canada, 2 = China, 3 = Iceland)
ChiSquared DF P  value
' log p
1
59 16 <0.00001
' log p
2
56 16 <0.00001
' log p
3
75 16 <0.00001
Joint test 312 180 <0.00001
Note: (1) the null hypothesis is no ARCH efect; (2) the lag length is 16 in the univariate test, and 5 in the
multivariate test.
!
101
Table 3.A2 MGARCH Estimates of Conditional Variance of Price (1 = Canada, 2 =
China, 3 = Iceland)
a
i
A
i1
A
i2
A
i3
B
i1
B
i2
B
i3
Equation
1 0.0001 0.201 0.000002 0.00003 0.7739 0.000003 0.0302
(0.0002) (0.0292) (0.0591) (0.0693) (0.0503) (0.0212) (0.0886)
Equation
2 0.0001 0.00000001 0.1474 0.0001 0.000003 0.8546 1E10
(0.0648) (0.0704) (0.0003) (0.0158) (0.0212) (0.0009) (0.1432)
Equation
3 0.0002 0.0003 0.0001 0.333 0.0458 1E10 0.637
(0.001) (0.0011) (0.0158) (0.0228) (0.0003) (0.1432) (0.1984)
Note: Numbers in parentheses are standard erors computed.
!
102
Table 3.A3 Unit Root Tests (1 = Canada, 2 = China, 3 = Iceland, 4 = ROW)
Variable ADF
c
a
ADF
c,t
b
w
1
1.88 (5)
c
2.77 (5)
w
2
0.35 (8) 1.72 (8)
w
3
1.14 (8) 1.90 (8)
w
4
3.99 (2) 4.60 (2)
log (x/P*) 1.9 (7)
6.83 (1)
log p
1
0.86 (8) 2.58 (8)
log p
2
2.64 (6) 3.39 (6)
log p
3
1.28 (2) 3.64 (2)
log p
4
1.39 (5) 2.68 (5)
log v(p
1
) 2.25 (2) 2.93 (1)
log v(p
2
) 1.04 (1) 3.13 (1)
log v(p
3
) 3.61 (1) 3.90 (1)
Critical Value (5%) 2.87 3.42
a
ADF
c
test is in the form: 'Y
t
= 1
0
+ 1
1
Y
t1
+ !
!
!
!!
!
!!
+ e
t
;
b
ADF
c,t
test is in the form: 'Y
t
= 1
0
+ 1
1
t + 1
2
Y
t1
+ !
!
!
!!
!
!!
+ e
t
;
c
The number of laged diference terms in the test is given in bracket for each variable. The maximum order is 8.
!
103
Table 3.A4 SUR Estimates of US Import Demand System for Cod, AIDS Model, 19892010
Monthly Data (1 = Canada, 2 = China, 3 = Iceland, 4 = ROW)
Variable Eq 1 Eq 2 Eq 3 Eq 4
constant 0.279*** 0.212*** 0.251*** 0.258***
(0.018) (0.018) (0.014) (0.033)
log (x/P*)
0.321*** 0.237*** 0.041* 0.043*
(0.027) (0.027) (0.02) (0.018)
log p
1
0.093* 0.046* 0.016 0.031
(0.056) (0.027) (0.045) (0.025)
log p
2
0.046* 0.055* 0.017 0.008
(0.027) (0.029) (0.021) (0.02)
log p
3
0.016 0.017 0.021 0.054
(0.045) (0.021) (0.05) (0.036)
log p
4
0.031 0.008 0.054** 0.031
(0.025) (0.017) (0.02) (0.02)
log v(p
1
) 0.009 0.089*** 0.051*** 0.029***
(0.012) (0.012) (0.009) (0.008)
log v(p
2
)
0.027*** 0.094*** 0.037*** 0.030***
(0.007) (0.007) (0.005) (0.005)
log v(p
3
)
0.040*** 0.015 0.010 0.015*
(0.01) (0.01) (0.008) (0.007)
Note: Numbers in parentheses are asymptotic standard erors. Single asterisk (*) indicates significance at the p <
0.10 level; double asterisk (**) indicates significance at the p < 0.05 level; triple asterisk (**) indicates significance
at the p < 0.01 level. The estimated coeficients of dumy variables are supresed from the report.