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Journal ArticleDOI

Whither Armington Trade Models

01 May 1990-American Journal of Agricultural Economics (Oxford University Press)-Vol. 72, Iss: 2, pp 455-467

AbstractThe Armington trade model distinguishes commodities by country of origin, and import demand is determined in a separable two-step procedure. This framework has been applied to numerous international agricultural markets with the objective of modeling import demand. In addition, computable general equilibrium (CGE) models commonly employ the Armington formulation in the trade linkage equations. The purpose of this paper is to test the Armington assumptions of homotheticity and separability with data from the international cotton and wheat markets. Both parametric and nonparametric tests were performed, and the empirical results reject the Armington assumptions. This has important implications for international trade modeling and CGE modeling.

Summary (2 min read)

WHITHER ARMINGTON TRADE MODELS?

  • Elasticities of import demand are .u~ed commogly to estimate the effects of trade ~arriers and to examine trade policy options.
  • The ease of use and flexibility are two reasons why ' the Armington model has been applied so often to international agricultural markets.
  • First, nonparametric methods (from Varian 1982 Varian , 1983 ) are used to test (a) whether the data are consistent with a stable system of well-behaved import demand equations and (b) whether Armington restrictions hold.

Two-Stage Theoretical Models

  • In general, a two-stage budgeting procedure assumes that consumers allocate their total expenditures in two stages (Deaton and Muellbauer, 1980b) .
  • Weak separability imposes restrictions on consumer behavior#.
  • A price change of a commodity in one group affects _the de.mand for_a commodity in another group only through the group income effect.
  • In the second stage (equation (3)), given the total amount imported, the importer decides how much to import from each supplier.
  • Thus, the Armington framework implies that in the second stage (within-.

Nonparametric Tests

  • The nonparametric approach to demand an 9 lysis uses the results of revealed preference analysis to derive algebraic conditions on demand functions (Varian 1983) .
  • The authors can al_so test for the compatibility of data with the existence of a utility function that is homothetic, separable, or both homothetic and separable (as is implied by the Armington model) . .
  • Second, for data sets that satisfy GARP the authors can proceed to test compatibility of the ~ata with restrictions on the utility function.
  • For the other four wheat _importers and the other four cotton importers separability was rejected for one or more of the source countries.
  • Finally, because all of the data violate I:IARP, the test for homothetic separability is redundant.

Armington Estimates

  • This ,model is homogeneous of degree zero in all prices and total expenditure.
  • It is not possible in general to impose the theoretical restrictions of symmetry and adding up (e.g. see Deat~n and Muellbauer, 1980b) .
  • In four of the cases, separability, homothetic separability, and the Armington model were rejected in all ten cases.
  • The full Armington restrictions were rejected in all-ten cases when the models were corrected for first order autocorrelation as well as in the OLS estimation.

AIDS Model Estimates

  • In an AIDS specification (Deaton and Muellbauer 1980a, 1980b) of import demand, the budget sha!e of imports from sourc~ i is given by: (10) The aggregate price deflator in (9) can be approximated by Stone's index from equation ( 6).8.
  • Thus, for each import source the authors estimated an AIDS excluding it a~d then tested whether its price had any influence on the included import shares,9 Initially they test this restriction alone without any separability restrictions on sources of imports within the group.
  • For Japan the restriction is rejected for both wheat and cotton in the full model including all sources.
  • Consider Tables 5 and 6 which summarize results for all countries.

Synthesis of Results

  • Table 7 summarizes the results from the three alternative approaches to testing Armington ~e$trictions on import demand equations for cotton and wheat, A"+" indicates the restriction is not rejected while a "-" indicates the restriction is rejected.
  • Separability was rejected iri 8 of 10 countries using the nonparametric approach, all 10 countries using the double-log model, and in 9 of 10 countries using the AIDS mod~!.
  • These necessary conditions are relatively weak restrictions compared to the Armington separability restrictions.
  • On this criterion the results are quite unequivocal.
  • _With all three approaches and in each country the Armington restrictions were _ _ comprehensively rejected.

Implications

  • . Armington model estimates are commonly used in counterfactual policy simulations.
  • In such contexts, the acid test might not be whether the Armington restrictions are rejected by the data but, rather, whether the resulting elasticity estimates are significantly biased.
  • _We can P!Ovide a partial answer to this :question.the authors.the authors.
  • When the omitted prices are p~ices of substitutes (posit_ive cross-elasticities), the own-price parameter estimate will be positively biased so that the own-price elasticities will be underestimated (i.e. less negative).
  • 10 This argument is relatively straightforward in the context of the double-log model about which the authors have already expressed their reservations.

Con cl us ions

  • This paper tested the assumptions of the Armington trade model in the context of the international cotton-and wheat markets.
  • The Armington model is comprehensively rejected wit~ data from ,.the five leading importing countries for each good, using thre~ alternative testing approaches.
  • By analogy doubt is raised as to whether the Armington restrictions are appropriate for other goods and in other applications such as CGE modeling.
  • In order to make consumer models tractable these separability assumptions are frequently made.
  • "\Yhile this does not lead to biased p~rameter estimates, it might lead to biased standard errors and biased test results.

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Commerce
__
Mathematical models
Alston, Julian
M.
Whither Armington trade models?
1989
# 6506
WHITHER
ARMINGTON
TRADE MODELS?
Julian M./Alston, c;.olin A. Carter,
~chard
Green,
and
Daniel Pick
. UNIVERSITY
OF
CALIFORNIA
.
[I/\
,,,r:
SEP
19
1989
Agricultural
Et;onomtcs
LibrarJ
Julian Alston is
an
Assistant Professor
and
Colin
Carter
and
Richard Green are
Professors, all
in
the
Department
of Agricultural Economics
of
the University of
California, Davis. Daniel Pick is
an
economist in the Economic Research Service,
USDA. Senior
authorship
is
not
assigned. The
authors
are grateful for research
assistance from Jeff Karrenbroc}<
and
Dave Vidaver. Helpful comments
were.
received from Jim Chalfant,
Nancy
Cotfrel, John Freebairn
and
Mike Wohlgenant.
Giannini
·Foundation
Paper
No.
\
.-
')
/1
,
r:.
.~·,·
n~~
t...-,

'.
ABSTRACT
The
Armington
trade
model
distinguishes commodities
by
country
of origin
_and
impo~t
demand
is determined
in
a separable two-step procedure. This
framework
has
been
applied
to
numerous
international agricultural markets
with
the objective
of
~odeling
import
demand.
In
addition, computable general
- -
·-
.
equilibrium (CGE) models commonly
employ
the
Armington
formulation
in
the
trade
linkage equatiops.
The
purpose
of this
paper
is to test the
4rmington
assumptions of
homotheticity
and
separability
with
data
from the international cotton
and
wheat
markets. Both' parametric
and
nonparametric tests
were
performed
and
the
e~pirical
resµlts reject the Armingto~ assumptions. This
has
important
implications for international trade.modeling
an~
CGE modellng.'
Key Words: Armington, separability, homotheticity, nonparametric tests, wheat,
: .
and
cotton.

WHITHER
ARMINGTON
TRADE MODELS?
The
responsiveness
of
import
demand
to
international
price changes is
an
,
important
topic
in
applied
international agricultural
trade
research. Elasticities
of
import
demand
are
.u~ed
commogly
to estimate the effects of
trade
~arriers
and
to
examine
trade
policy options. There
was
renewed
!nterest
in
the topic
during
the
1985
debate
over
the
U.S.
Food
Security Act.
In
fact, the, price responsiveness
of
import
'!emand
for U.S. agricultural sales
became
the single
most
important
issue
in
the
policy
debate
(Thompson, 1988). Ultimately, the U.S.
government
decided
that
_the
import
demand
for U.S. agric~ltural exports (such as cotton
and
wheat)
was
price
responsive; Foreign
import
deman_d elasticities
in
excess of
unity
were
then
used
to
justify
lowering
U.S.
loan
rates-(i.e., floor prices) as a
means
of
attempting
to
regain
market
shares
in
the
international
markets
(FAPRI; Myers).
Empirical estimates of
import
demand
e!asticities are
predicated
on
the
specification
chosen
for the
trade·model.
A
number
of
different
model
specifications
have
appeared
in
the literature
and
these
are
well
documented
in
two
separate
surveys
by
Sarris (1981)
and
Thompson
(1981).
The
Armington
model
is
one
specification
which
has
been
very
popular.
It
is a disaggregate
model
which
-
distinguishes
commodities
by
country
of origin
with
import
demc,;1.nd
being
determined
in
a
separable
two-step procedure.
The
Armington
approach
permits
the calculation of cross-price elasticities
between
imports
from all sources
using
. estimates of the aggregate price elasticity
o~
demand
for imports, a single elasticity of
substitution
and
trade
shares. The ease of use
and
flexibility
are
two
reasons
why
'
the
Armington
model
has
been
applied
so often to international agricultural
markets.
Of_
course,
another
important
reason is
that
the
Armington
model
often
gives results
which
are
judged
to
be
successful because of
both
plausible
parameter

2
estimates
and
statistical
significance:
The
Armington
approach
has
been
applied
to
modeling
agricultural
trade
by
Abbott
and
Paarlberg; Babula;
Figueroa
and
Webb;
Grennes,
Johnson
and
Thursby;
Johnson,
Grennes,
and
Thursby;
Penson
and
Babula; Sarris-(1983);·
and
Suryana.
In
addition,
it
has
been
accepted
as
the
,
appr6priate
way
in
which
to
model
trade
flows
~n
a
computable
general
eq_uilibriu~
(GGE)
model
(de·Melo
·and Robinson, 1981
and
198_5)
and
has
been
used
extensively
in
CGE
models
of
international
trade
in
agricultural
products
(e.g.,
Adelman
and
Robinson).
The
Armington
model
assumes
that
import
demands
are
homothetic
and
separable
amo~g
import
sources.
Thus,
within
a
market,
trade
patterns
change
only
with
relative
price
changes
and
the
elasticities
of
substitution
between
all
pairs
of
products
(e.g.,
between
United
States
and
Canadian
wheat)
are
idEntical
and
constant.
These
are
strong
restric~ons on.
demand.
In
this
paper
we
t~st these
restrictio"ns
using
data
from
the
internaHonal
cotton
and
wheat
markets.
Three
approaches
are
used
in
our
empirical
work.
All
three
approaches
test
restrictions
on
a
country's
system
of
import
demand
equations
for a
product
(cotton
or
wheat)
from
different
sources.
The
maintained
hypothesis
is
that
imports
of
the
product
from
different
countries
comprise
a
weakly
separable
group
so
that
we
are
considering
restrictions
on
the
seco_nd
stage
of
a
two-stage
budgeting
process.
First,
nonparametric
methods
(from Varian 1982, 1983)
are
used
to test (a)
whether
the
data
are
consistent
with
a
stable
system
of
well-behaved
import
demand
equations
and
(b)
whether
Armington
restrictions
hold.
The
appeal
of
this
approach
is
that
it
provides
a
complete
test
of
the
hypothesis
in
question
with
no
.additional
ass,umptions
concerning
functional
form
(Varian 1983,
p.
100).
The
principal
drawback
is
the
unknown
power
of
the tests
and
the
possibility of false
rejections
due
to
measurement
error
(Varian 1985,
Chalfant
and
Alston)
..
Second,
the
Armington
model
is
estimated
and
tested
as a
nested
model
defined
by
a
set
of
parametric
restrictions
on
a
double-log
import
demand
model
. ,
..

' .
'
3
incorporating
the
complete
set
of
relative prices. This
provides
a direct test of the
Armington
model
but
the
drawback
is that
we
are
testing against
an
alternative that
can~ot
be
fully compatible
with
the
adding-up
restrictions from
demand
theory
,
unless preferences
are
restricted to
be
homothetic
(e.g.,
see Deaton
and
Muellbauer
1980b,
pp'.·
17-1~).
Our
third
approach
follows Winters.
The
Almost
Ideal
Demand
System (AIDS)
of
Deaton
and
Muellbauer
(1980a) is
used
to estimate the para~,ete~s of the
import
demand
equations
and
Arming~~n !estrictions ar~ tested parametrically. As
with
the
nonparametric
approach,
this
approach
tests necessary conditions for
Armington
restrictions to
hold
in
a
model
in
which
other
theoretical restrictions
(symmetry
and
a,dding
up)
can
be:
imposed;
it
does
not
test the complete
set
of
restrictions
(including
functional
for~~
·for
demand)
that
make
up
the
Armington
model. This
approach
avoids the drawbacks of the
nonparametric
approach
(unknown
power)
and
that
of'the
direct
approach
with
the
ad
hoc double-log model.
,.
However,
it
does involve the imposition
of
the AIDS functional
form
to
be
tested as
a joint
hypothesis
with
the
Armington
restrictions.
That
is,
it
tests
whether
import
demand
equations
are
separable
and
homothetic
under
the
maintained
hypothesis
that
they
are
of
the AIDS form.
The
three
approaches
are
complementary.
The
alternate
methods
yield
different results
on
particular restrictions
but
we
find that all three app~oaches
comprehensively
reject the
Arminston
model. In
every
country
each
approach
rejects the restrictions
implied
by
the necessary conditions that the
demand
equations
are
both
homothetic
and
separable. Thus,
we
conclude
that
the
Armington
trade
model
is
inappropriate
for cotton
and
wheat.

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Cites background from "Whither Armington Trade Models"

  • ...For example, Winters (1984), and Alston et al. (1990) argue that the functional form is too restrictive and that the nonhomothetic, AIDS specification is preferable....

    [...]

  • ...This specification was first proposed by Paul Armington in 1969 and has since become known as the "Armington approach" to modeling import demand....

    [...]

  • ...This specification was first proposed by Paul Armington in 1969 and has since become known as the "Armington approach" to modeling import demand. However, it has been widely criticized in the literature. For example, Winters (1984), and Alston et al....

    [...]


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References
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Posted Content
Abstract: Ever since Richard Stone (1954) first estimated a system of demand equations derived explicitly from consumer theory, there has been a continuing search for alternative specifications and functional forms. Many models have been proposed, but perhaps the most important in current use, apart from the original linear expenditure system, are the Rotterdam model (see Henri Theil, 1965, 1976; Anton Barten) and the translog model (see Laurits Christensen, Dale Jorgenson, and Lawrence Lau; Jorgenson and Lau). Both of these models have been extensively estimated and have, in addition, been used to test the homogeneity and symmetry restrictions of demand theory. In this paper, we propose and estimate a new model which is of comparable generality to the Rotterdam and translog models but which has considerable advantages over both. Our model, which we call the Almost Ideal Demand System (AIDS), gives an arbitrary first-order approximation to any demand system; it satisfies the axioms of choice exactly; it aggregates perfectly over consumers without invoking parallel linear Engel curves; it has a functional form which is consistent with known household-budget data; it is simple to estimate, largely avoiding the need for non-linear estimation; and it can be used to test the restrictions of homogeneity and symmetry through linear restrictions on fixed parameters. Although many of these desirable properties are possessed by one or other of the Rotterdam or translog models, neither possesses all of them simultaneously. In Section I of the paper, we discuss the theoretical specification of the AIDS and justify the claims in the previous paragraph. In Section II, the model is estimated on postwar British data and we use our results to test the homogeneity and symmetry restrictions. Our results are consistent with earlier findings in that both sets of restrictions are decisively rejected. We also find that imposition of homogeneity generates positive serial correlation in the errors of those equations which reject the restrictions most strongly; this suggests that the now standard rejection of homogeneity in demand analysis may be due to insufficient attention to the dynamic aspects of consumer behavior. Finally, in Section III, we offer a summary and conclusions. We believe that the results of this paper suggest that the AIDS is to be recommended as a vehicle for testing, extending, and improving conventional demand analysis. This does not imply that the system, particularly in its simple static form, is to be regarded as a fully satisfactory explanation of consumers' behavior. Indeed, by proposing a demand system which is superior to its predecessors, we hope to be able to reveal more clearly the problems and potential solutions associated with the usual approach.

4,474 citations


Journal ArticleDOI
01 Mar 1969
Abstract: Cette A©tude offre un appui thA©orique A certaines pratiques de recherche selon lesquelles la variation d'un flux commercial particulier entre pays est considA©rA©e comme la rA©sultante de deux A©lA©ments: la modification qui se produirait si le pays fournisseur donnA© devait conserver sa part du marchA©, et l'A©cart entre les ventes effectives et celles qui s'effectueraient si sa part du marchA© demeurait constante. Ces pratiques comprennent la mA©thode de prA©vision des A©changes dans laquelle: 1) les prA©visions de l'expansion des divers marchA©s, combinA©es avec une matrice relative A la pA©riode courante, fournissent une matrice pour la pA©riode future A©tablie sur la base de parts du marchA© constantes; 2) cette matrice A©tablie sur la base de parts du marchA© constantes est modifiA©e pour tenir compte de facteurs censA©s engendrer des gains ou des pertes de parts. Dans la prA©sente A©tude, on fait valoir que l'analyse des modifications des flux commerciaux en deux A©lA©ments reprA©sentant, l'un des parts du marchA© constantes et l'autre des parts du marchA© modifiA©es, n'intA©resse pas seulement la comptabilitA©, mais qu'elle peut certainement Aatre rattachA©e purement et simplement A la thA©orie traditionnelle du comportement des consommateurs. On part de l'hypothA¨se que les produits sont diffA©renciA©s non seulement d'aprA¨s leur espA¨ce mais A©galement d'aprA¨s leur origine. Autrement dit, on suppose que des produits originaires de diffA©rents pays et offerts concurrement sur le mAame marchA© ne sont pas susceptibles de se remplacer parfaitement. Il est dA©montrA© ensuite qu'une spA©cialisation poussA©e et suffisamment rA©aliste de la fonction de bien-Aatre de Hicks permet d'obtenir des A©quations assez simples de la demande englobant les deux A©lA©ments mentionnA©s plus haut. Cette spA©cialisation se fonde sur l'hypothA¨se "d' indA©pendance" (telle qu'elle a A©tA© formulA©e par R. M. Solow, R. H. Strotz et d'autres) ainsi que sur celle selon laquelle les A©lasticitA©s du remplacement entre produits offerts concurremment sur un marchA© quelconque donnA© sont constantes et A©gales. /// Este estudio ofrece un apoyo teA³rico a ciertas prAicticas de investigaciA³n segAon las cuales a la variaciA³n en una corriente determinada de intercambio entre paA­ses se la considera como la suma de dos componentes: la variaciA³n que ocurrirA­a si un paA­s vendedor dado mantuviera su participaciA³n en el mercado, y la desviaciA³n de las ventas efectivas con respecto a las ventas que tendrA­an lugar de permanecer constantes las participaciones. Dichas prAicticas incluyen la previsiA³n de los intercambios, en la cual 1) los pronA³sticos del crecimiento en diversos mercados, junto con la matriz de un perA­odo de base, resultan en una matriz de participaciones constantes para el perA­odo futuro, y 2) se modifica esta matriz de participaciones constantes para tener en cuenta a los factores que se espere que produzcan pA©rdidas o ganancias en las participaciones. En este trabajo se mantiene que el anAilisis de las variaciones en las corrientes de intercambio comercial, separando el componente de participaciones constantes y el de ajuste de las participaciones, es mAis que una simple cuestiA³n de contabilidad, y en realidad se le puede ligar sencilla y rigurosamente a la teorA­a tradicional del comportamiento del consumidor. El punto de partida es el supuesto de que se establecen distinciones no solamente segAon la clase de los productos sino tambiA©n segAon el lugar de producciA³n de los mismos. Es decir, se supone que los productos de distintos paA­ses que compiten en el mismo mercado son sustitutos imperfectos. Se demuestra luego que una especializaciA³n eficaz y bastante realista de la funciA³n hicksiana del bienestar lleva a relaciones de demanda muy sencillas en las que se incluyen los componentes de la participaciA³n constante y del ajuste de las participaciones. Esta especializaciA³n exige el supuesto de "independencia" (que formularan R. M. Solow, R. H. Strotz, et al.) y el supuesto de que las elasticidades de sustituciA³n entre los productos que compiten en un mercado determinado son constantes e iguales.

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Book
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3,540 citations



Journal ArticleDOI
Abstract: In the literature, a variety of approaches have been used to calculate demand elasticities in almost ideal demand system (AIDS) models of demand. It is common to estimate the linear approximate almost ideal demand system (LA/AIDS) instead of the AIDS. When the LA/AIDS is estimated, all of the previously reported approaches to compute elasticities are theoretically incorrect. This paper presents correct formulas for LA/ AIDS elasticities and illustrates the potential errors from using incorrect computing The almost ideal demand system (AIDS) of Deaton and Muellbauer (1980a,b) has become popular in recent years (Anderson and Blundell; Blanciforti and Green 1983a,b; Blanciforti, Green, and King; Chalfant; Eales and Unnevehr; Fujii, Khaled, and Mak; Fulponi, Heien and Willett; Murray; Parsons; Ray). A variety of approaches to computing elasticities has been used, and some of the approaches may lead to significant errors. This paper clarifies the differences between alternative approaches to estimating demand elasticities in AIDS models.

569 citations