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Commerce
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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.
