on the comovement of commodity prices
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7/21/2019 On the Comovement of Commodity Prices
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Agricultural Applied Economics Association
On the Comovement of Commodity PricesAuthor(s): Chunrong Ai, Arjun Chatrath and Frank SongSource: American Journal of Agricultural Economics, Vol. 88, No. 3 (Aug., 2006), pp. 574-588Published by: Oxford University Presson behalf of the Agricultural & Applied Economics
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7/21/2019 On the Comovement of Commodity Prices
2/16
ON
THE
COMOVEMENTOF COMMODITY
PRICES
CHUNRONG
AI,
ARJUN
CHATRATH,
AND
FRANK
SONG
We
present
strong
evidence
against
the excess-comovement
hypothesis-that
the
prices
of commodi-
ties move together beyond what can be explained by fundamentals. Prior studies employ broad macro-
economic indicators to
explain
common
price
movements,
and
potentially
correlated
fundamentals
are not controlled for. We use
inventory
and harvest data to fit a
partial equilibrium
model that more
effectively
captures
the variation
in
individual
prices.
The
model
explains
the
majority
of the comove-
ments
among
commodities
with
high
price
correlation,
and
all of the comovements
among
those with
marginal
price
correlation.
Common movements
in
supply
factors
appear
to
play
an
important
role in
the observed
comovements
in
commodity
prices.
Key
words:
commodity prices,
comovement,
herding.
Pindyck and Rotemberg (1990) find that prices
of
seemingly
unrelated commodities move to-
gether,
even after
controlling
for
macroeco-
nomic indicators such as
inflation,
industrial
production
(IP),
and interest rates. The au-
thors
regress
the
price
changes
of
seemingly
unrelated commodities
(wheat,
cotton,
copper,
gold,
crude,
lumber,
and
cocoa)
on
some
im-
portant
macroeconomic indicators and
find the
regression
residuals to be
highly
correlated.
Their
finding, subsequently
well
known as the
"excess
comovement
hypothesis"
(henceforth
ECH),
calls into
question
the
rationality
of
commodity
markets and flies in
the
face of
the
competitive
model of
price
formation. For in-
stance,
Pindyck
and
Rotemberg (1990) (PR)
suggest
that the excess comovements
may
be due
to
herding-where
traders
alternately
buy
or sell different
commodities at the same
time,
with little economic
justification.
The ex-
cess
comovement
of
prices
could
impede
the
decision-making
abilities of
hedgers
and fore-
casters,
who base their
decisions
on
fundamen-
tals,and could imply that countries exporting a
portfolio
of
seemingly
unrelated commodities
enjoy only
limited
diversification of revenues.
Since
PR,
several researchers have revis-
ited the ECH
employing
a
variety
of
data
and
test
procedures. Notably,
Deb, Trivedi,
and
Varangis (1996)
document that the PR
results are sensitive to the neglected structural
changes
in
prices
(in
the
1970s),
and to the con-
trols
for conditional
heteroskedasticity
in the
price
data.
The authors
suggest
that the
inap-
propriate
assumption
of
normality
in the PR
regression
residuals
cause
the false
appearance
of
excess
comovements.
Other researchers
have also
shown the PR
evidence to be
sen-
sitive
to methods. Palaskas
and
Varagis
(1991)
employ
cointegration
analysis
to show that
ex-
cess comovements
are
the
exception
rather
than the
rule in
twenty-one
pairs
of
monthly
and annual
prices.
Malliaris and Urritia
(1996)
employ
cointegration
analysis
to
reject
the
long-term
independence
of six
commodity
fu-
tures
price
series.
Cashin,
McDermott,
and
Scott
(1999) employ
a
nonparametric
mea-
sure of
comovement,
concordance,
suggested
by Pagan
(1999)
and find
little evidence of
syn-
chronocity
in the
turning points
in
prices
of
seven commodities
over the
PR
sample period.
Taken
together
these studies
seem to
suggest
that ECH
is the artifact of
econometric model-
ing, and if the right econometric model could
be
discovered,
the evidence
of excess comove-
ments
would
disappear.
Thus,
the research
on ECH
has focused
more on the
nature
of the
comovements,
rather
than the causes
themselves.1
For
example,
none of
the stud-
ies
explain
the
poor
explanatory powers
of
the macroeconomic
indicators
or
explore
the
Chunrong
Ai is associate
professor,
Department
of
Economics,
University
f Florida ndSchoolof
Economics,
Hvazhang
Univer-
sity
of
Scienceand
Technology,
hina.
Arjun
Chatrath
s
associate
professor,
chool
of
Business,
University
f
Portland. rank
Song
is associateprofessor,Schoolof EconomicsandFinance,Hong
Kong
University.
The
authorswish to thankthe two
anonymous
eviewers
or
theiruseful
comments nd
suggestions.Remaining
rrorsare our
own.
1
For
nstance,Deb,
Trevedi,
nd
Varangis1996)provide
esults
fromGARCHmodelsand note thatonly upon"controlling"or
the covariance
rocess
f
price hanges
oesthe covariancen stan-
dardized
esidualsendto
dissipate.Arguably,
ucha
specification
captures
he
symptoms
f the
underlying
ovariance
n
prices,
nd
not the fundamental
auses hemselves.
Amer. J.
Agr.
Econ.
88(3) (August
2006):
574-588
Copyright
2006
American
Agricultural
Economics
Association
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7/21/2019 On the Comovement of Commodity Prices
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Ai, Chatrath,
and
Song
Comovement
of
Commodity
Prices 575
possibility
that observed
comovements are
caused
by
fundamentals
beyond
these indica-
tors.
Intuitively,
it
is unreasonable
to
expect
that broad economic
indicators
employed
in
PR
will
capture
or reflect
all or even the ma-
jority of the supply or demand conditions in
individual commodities.
Moreover,
it is
likely
that such indicators will
reflect demand condi-
tions better for some
commodities than others.
For
instance,
IP
may
be more
closely
re-
lated to the
consumption
demand
for
lumber
or
copper
than for oats
or
barley.2
In
fact,
there is
much
evidence
that macroindicators
explain very
little
of
the variation
in
com-
modity prices.
Studies on
the macroeconomic
risk-premiums
in
commodity
prices, including
Park,
Wei,
and Frecka
(1988),
Bessembinder
and Chan (1992), Bailey and Chan (1993),
and
Bjornson
and Carter
(1997)
find PR-like
models to
perform very
poorly.
For
instance,
the
largest adjusted
R-squared
statistic in
Bjornson
and
Carter
(1997)
is
only
3.3%. In
contrast,
there
is
evidence that fundamental
factors such as the
weather have a
relatively
large
impact
on
individual
commodity price
behavior
(for
instance,
Roll
1984;
Brunner
1998;
Deaton and
Laroque 2003).
It is
worth
noting
that PR's inference that
price comovements may be driven by specu-
lative
herders
can also
be
challenged by
the
literature.
Given
that
commodity
price
co-
movements
appear
to
persist during periods
of booms and
busts,
their
inference would
seem to
imply
that
speculators play
a ma-
jor
role in
the behavior of
commodity prices.
While there is some
indication that
specula-
tive
behavior,
particularly
in futures
markets,
may
result
in
increased
volatility,
the
weight
of the evidence is
that
speculation
has either
an
ambiguous-
or
dampening impact
on
the
variation in
commodity prices (for
instance,
see Chari and
Jagannathan
1990;
Netz
1995;
Zulauf and Irwin
1998;
Carter
1999;
Chatrath
and
Song
1999;
Irwin
and Holt
2004).
In
sum-
mary,
PR
may
be
premature
in
concluding
that
their
findings
of
persisting
comovements are
"excessive,"
and
implying
that
herding
may
be the
prominent
cause for the comovements.
Consequently,
further
empirical
work in this
small literature
on
the relatedness of
commod-
ity
prices
is
warranted.
The
primary
objective
of this article
is to ex-
amine
the extent
to which the observed co-
movements
in the
prices
of commodities
can
be
explained
by
the relatedness
of their funda-
mentals.
Specifically,
we reexamine
the ECH
employing commodity-specific data such as
production
and
inventories,
in
conjunction
of
the traditional
macroeconomic
indicators,
to
more
completely
control for the relatedness
in
the
demand
and
supply
of the commodi-
ties. The main
focus of our
investigation
is
on five
commodities-wheat,
corn, oats,
soy-
beans,
and
barley,
for which
fairly
detailed
commodity-fundamental
information
is avail-
able. With the
exception
of
wheat,
these com-
modities
are
different from those
studied in
PR.
However,
as demonstrated
shortly,
these
seemingly unrelated commodities exhibit sim-
ilar
amplitude
of
comovement,
that
is,
they
have
"excess
comovement,"
as
defined
in PR.
The
commodity specific (market-level)
data
that are
employed
in this
study
allow
us to
make
improvements
on the tests
for
price
comovements
in two
ways.
First,
the
market-
level variables
allow us to test for
excess co-
movements
while
maintaining
a low reliance
on
presumptions
vis-d-vis the relatedness of
the commodities.
In
contrast,
PR
presuppose
the fundamentals for commodities such as
wheat,
cotton,
and
cocoa are
unrelated
beyond
the
general
economic
cycles.3
Second,
the data
allow us to
develop relatively
direct
proxies
of
demand/supply
conditions as are
required
for
effective
testing
of excess comovements.
These
data also allow
us to make inferences
on the
relative roles
of
supply
and demand
factors
in
the observed
correlations
in
commodity prices.
The relative
contributions of
supply
and de-
mand have
been studied with
respect
to indi-
vidual
commodity price
behavior
(for instance,
Myers
and
Runge 1985),
but not
in the context
of
commodity
comovements.
The
findings
in this article are
summarized
as follows.
(i)
The
correlation
of
commodity
prices
remained
high
for the
latter
half of the
twentieth
century. (ii)
The macro
indicators
such as
IP and
gross
domestic
product
(GDP)
fail to
explain
these
correlations,
consistent
with PR.
(iii)
The market-level indicators
such
as
inventory
and harvest
size,
in
conjunction
with the macro
indicators,
explain
a
strikingly
2
For instance, in PR, the macro indicators
and their lagged val-
ues
explain
less than 10% of the variation in
four
of the
eight
commodity prices
studied. The indicators were most successful in
explaining
the variation
in
gold
and crude
price changes
(adjusted-
R2 of
0.24 and
0.21),
and least
successful for cotton and wheat
(0.05
and
0.06).
3
Similarly,
the
filter
employed
for unrelated
commodities
in
Deb, Trivedi,
and
Varangis (1996)
is that
they
are
neither
jointly
produced
nor
jointly
consumed.
By
their
metric,
sugar
is unre-
lated to coffee or
cocoa,
and lumber and oil are
unrelated to
each
other and to nine
other
commodities,
including,
wheat,
copper,
and
cotton.
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7/21/2019 On the Comovement of Commodity Prices
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576
August
2006
Amer. J. Agr.
Econ.
large
portion
of
price
movements,
and ex-
plain
the
majority
of
correlations in commod-
ity prices. (iv) Supply
factors
appear
to
play
a
relatively large
role in
the observed correla-
tions,
at least
for
commodity
pairings
such as
wheat and oats, and soybeans and corn.
In the next section
we
develop
a
partial equi-
librium model
(Equilibrium Model),
which
will
accommodate the market-level and
macro
data. The Data section
describes the
price
and
fundamentals data
employed
in the
study.
The
Empirical
Results
section
begins by presenting
correlation results for
prices
and fundamental
factors. The main results
are then
presented
to
compare
the "Macro Model" similar
to
PR,
and our
"Equilibrium
Model,"
one that ac-
commodates the
market-level data. The com-
parison of these two frameworks is broadened
to
twenty
other
commodities,
agricultural,
and
otherwise.
Finally,
an
examination into the rel-
ative role of
supply
factors
in
the observed
comovements is
undertaken. The final section
summarizes the
findings.
Empirical mplementation
Let
pi
and
p1
represent
the
log price
histories
of two
commodities,
i
and
j,
and
X
a matrix of
macroeconomic indicators such as GDP and
interest
rates.
The PR
method
of
testing
for
pair-wise
excess-comovements is based on the
residuals
(ut)
from the
regressions
(1)
pi,t
=
biXt
+
ui,
Pj,t
=
bjXt
+
Uj,t
where b is a vector of
sensitivities and
u, is
the
regression
error
term.
Typically,
irst differ-
enced
prices
and economic
indicators
are em-
ployed.
In
the interest of
exposition,
we deal
in the
level series for now. In
PR,
the
ECH
is
supported
if
p
{uit,
ui,
t}
>
0.4
It
is clear that
commodity-specific
factors,
such
as inventories
or
production
are not
considered in
(1),
mainly
because commodities i
and
j
are
presumed
en-
tirely
unrelated in their
fundamentals. We refer
to
(1)
as the Macro model.
Now consider a framework
where individual
prices
are
determined in
equilibrium.
Because
total
supply
for
a nontraded
commodity
with
a
single
harvest season is inelastic
at
t,
the
de-
mand
function can
always
be
estimated
from
data.
Let the
inverse demand function be
given
by
(2)
pt
=
f(D,,
Xt)
+
Et
where
Dt
is the
consumption
at
t,
and
Et
is the
unexplained portion
of the current
price,
and
f
is the
function to
be
estimated.
Prices are influ-
enced
by quantity
demanded
and the
general
economic
conditions. Thus
the macro variables
(X,)
are
modeled as demand shifters.
Let
zt represent
the harvest size and
It
the
inventories for a
commodity
at time t. The
mar-
ket clears
at
Dt
+
I,
=
total
supply,
st
=
zt
+
(1
-
8)It-1,
where
8
is the per period deterio-
ration rate of
inventories. From
(2)
we have
(3)
pt
=
f(st-It,
Xt)
+
Et-.
Equation
(3)
is
a
partial equilibrium
formula-
tion that
considers the effects
of both current
and
expected
demand and
supply
conditions.5
Note
that the variable
(st
-
It)
generally
repre-
sents
the
commodity
specific
variables
missing
in
(1).
In the
theory
of
commodity prices,
inven-
tories
are
endogenous (for
instance,
Williams
and
Wright
1991;
Deaton and
Laroque
1992;
Chambers
and
Bailey
1996),
and the above
demand
function alone cannot
explain
price
behavior
unless
inventory
is
explained.
How-
ever,
the
objective
of this article
is not to model
inventory per
se. Our
objective
is to estimate
the demand function
employing
the
observed
supply
and
inventories,
and
analyze
the extent
to which these
variables
explain
the common
movements
in
commodity prices.
The advan-
tage of not modeling inventories is that we do
not have
to
deal
with the
econometric
issue
relating
to
the
nonnegativity
constraint
for in-
ventories.
In
this
respect,
note that
equation
(3)
holds whether or not the
nonnegativity
con-
straint is
binding.
The
disadvantage
of course
is that we
cannot
explain
common
movements
in
inventories (if
any)
across commodities.
Be-
cause
inventory
is
not
explicitly
modeled,
our
4 Note
that
zero
correlation
between the error term in
(1)
will
not
represent
absolute evidence of a lack of excess comovement
as
long
as all
factors
have not
been
controlled for.
It
is
possible
that further controls will reveal an
underlying relationship
that is
not
evident
in
the
residuals in
(2). Naturally,
the more
compre-
hensive the
controls,
the less the
chance
of
reaching
an
erroneous
conclusion.
5
Large
commodity price
movements have
been associated
with
both demand and supply shocks. For instance, Gilbert (1989) ar-
gues
that the dollar's
appreciation
in the
early
1980s
magnified
the
debt
obligations
of
developing
countries
and induced an increase
in the
supply
of
commodities,
which resulted
in the decline
in real
dollar
prices
(also
see Deaton and Miller
1996).
Dornbusch
(1985)
argues
that an
appreciation
of the
dollar
reduces
the demand
in
the rest
of the
world,
and results
in
a decline
in the
commodity's
real
market-clearing price
in U.S. dollars.
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7/21/2019 On the Comovement of Commodity Prices
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Ai,
Chatrath,
and
Song
Comovement
of Commodity
Prices
577
study
may
be considered a
partial equilibrium
analysis.
To estimate
equation
(3),
we
must:
(i)
model
the functional form
off(.),
and
(ii)
address
the
endogeneity
of the
inventory
variable.
Since
our objective is to identify the sources and not
the
manner of
comovement,
we
do not want
our
analysis
to be
impacted by
the
misspeci-
fication of the functional form.
To
avoid mis-
specification
error,
we
adopt
the
flexible model
(4)
Pt
=
to
+
ai,1(st
-
It)
+
'
-
+
al,n(st
-
I,)m
+
O2,1(St
-
It)Xt
+
"- "
+
Z2,n(St
-
t)kXt
+
-3Xo
+
X
where the orders of m and k are determined by
the data
through
a
cross-validation
approach
that is
common
in
the
nonparametric
litera-
ture
(e.g.,
Ai and Chen
2003).
The
endogene-
ity
of the
inventory
variable will
be addressed
by
an instrumental variable
approach
with
1,
St,
s$,...S"+l,
stXt,
s2Xt,...sk+ltX
as
instru-
ments. As with
equation (1), equation
(4) may
be estimated with the
variables in their levels
or
in their first differenced
forms. For
expo-
sition,
(4)
will be
referred
as
the
Equilibrium
model. A comparison of the explanatory pow-
ers of the
Equilibrium
model
and the tradi-
tional Macro model will
indicate the
degree
to
which
prior
studies on excess
comovements
suffer from
biases
resulting
from
missing
vari-
ables. Similar indications
may
be
gleaned
from
a
comparison
of
the
pair-wise
correlation
of
the
residuals from
the alternate
models.
Data and
Empirical
Results
Data
The
majority
of the
empirical
tests in this
study
are conducted on
quarterly
data for five
commodities-wheat
(all),
barley
(all),
corn
(for grain),
oats,
and
soybeans,
from
January
1957 to
September
2002.
The
study spans
beyond
the
sample
intervals in PR
(1960-
85),
and
Deb, Trevidi,
and
Varangis
(1960-85
and
1974-92).
Our attention
is
mainly
on the
five commodities since
detailed and
lengthy
market-specific
data are
unavailable for other
important commodities, such as cotton or lum-
ber.
Quarterly sampling
of
prices
is
employed
since
commodity-specific
data
(production,
in-
ventories,
etc.)
are
sparse
for finer intervals.
It
may
be
argued
that the
quarterly sampling
makes the
rejection
of excess
comovements
more
stringent:
it
is
well documented that the
correlations
in
price changes
tend to be
smaller
in
higher
frequency
data
(for
instance,
see
PR).
The data
on
U.S.
prices,
inventories
(on-
farm,
off-farm,
total),
harvest
size,
yield
per
acre,
and
planted
acres for the
five commodi-
ties are obtained from the U.S. Department
of
Agriculture.6
These commodities
have well
known sources of
supply,
namely
carried-over
inventories
and harvest. We
do not
directly
control for
government
stockholdings.
How-
ever,
we
do
indirectly
assess
the extent to
which such
stockholdings
have
altered the
nature
of
commodity
comovements
by
com-
paring
our results
from the
full
sample
with
that
of the
post-1972 sample,
over
which
gov-
ernment
stockholdings
of
commodities are
known to have become
pervasive
(for
instance,
Westcott, and Hoffman 1999; Goodwin,
Schnepf,
and
Dohlman
2005).
With the
ex-
ception
of
oats,
there
are no
(or very
minor)
U.S.
imports
of
these
commodities.
We do not
differentiate between
net
exports
and domes-
tic
disappearance.
The macroeconomic
indica-
tors
employed
in the
paper
are
IP,
the
(GDP),
consumer
price
index
(CPI),
three-month
sec-
ondary
market
Treasury
bill
yield
(r),
and the
broad
dollar index
(FXR).
These
data are ob-
tained from the
Federal
Reserve Bank
data
files. Pindyck and Rotemberg (1990) also em-
ploy
the S&P 500 Stock
index but
do not find
a
significant impact
on
commodity
prices.
Finally,
our
study
also
employs price
histo-
ries of
twenty
other
commodities.
These data
are obtained from
the files of the
International
Monetary
Fund and
are detailed
in the
Ap-
pendix.
While
good
fundamental
data are not
available
for these
commodities,
their
price
histories
allow us to comment
on the
gener-
ality
of our main
findings.
In that
respect,
it is
noteworthy that the twenty-five commodities
in this
study
include
four commodities
studied
in
Pindyck
and
Rotemberg
(1990)-namely
wheat, cotton,
copper,
and
cocoa.
Quarterly
prices
(beginning
for
March,
June,
September,
and
December)
for the
twenty
five commodi-
ties are obtained
by
averaging
over
monthly
prices.7
Commodity
Correlations
We
begin
our
empirical
analysis
by
examin-
ing correlation patterns across five agricultural
6
For
oats, inventory
data
are
incomplete
between
1986
and 1989.
All tests for oats
(including
bivariate
correlations)
are conducted
with
this
gap
in
data.
7
Similar results are
obtained
when
employing prices
rather
than
average prices.
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7/21/2019 On the Comovement of Commodity Prices
6/16
578
August
2006
Amer.
J. Agr.
Econ.
Table
1.
Correlation
in
Production
Variables
Wheat
Barley
Corn Oats
Soybeans
A.
Changes
n
yield
Wheat 1
0.535
0.227
0.521
0.201
Barley
0.537 1
0.431 0.541 0.224
Corn 0.227 0.430 1 0.589 0.828
Oats
0.522 0.543 0.589
1 0.539
Soybeans
0.197 0.218
0.827 0.536 1
B.
Changes
n
planted
acres
Wheat 1
-0.174 0.412
-0.401
-0.055
Barley
-0.178 1
0.226 0.253 0.142
Corn
0.407
0.225
1 -0.649
0.179
Oats
-0.425 0.225
-0.633
1
-0.260
Soybeans
-0.034 0.137
0.178
-0.277
1
Note:
Pearsonian correlation
coefficients are
reported
for
changes
in
yield
per
acre
and
planted
acres
sampled
annually
for five commodities
from 1957
through
2002. Coefficients
above the
diagonal
relate to the de-trended
changes.
commodities. Our discussion
of
significance
levels for
a
bivariate correlation
coefficient r
is based on
the statistic t
=
r/n
-
2//1 -
which is
asymptotically
t-distributed
with
n
-
2
degrees
of
freedom,
where n is the sam-
ple
size.
For
the full
sample,
this
implies
that
absolute
correlation
coefficients of about 0.12
and 0.19
are
significant
at the 10%
and 1%
levels,
respectively.
For
price changes
and
their
regression
residuals,
we also
compute Spear-
man Rank correlations. Commodity prices are
characterized
by frequent price
jumps
so that
the
price
changes
are
typically
fat
tailed. The
Spearman
correlations
employ
the difference
in
the
ranking
of a
variable,
so
that
they
are
relatively
immune to extreme outliers.
Table
1
reports
the
cross-commodity
cor-
relations of
some
production
related funda-
mentals.
It
is
apparent
that
the
yield per
acre is
closely
related with correlation
ranging
from
about
0.20 for
wheat-soybean
to 0.83 for
soybeans-corn. One can expect yield changes
to be
positively
related because trends in
pro-
duction
technologies
are often
related across
commodities.
However,
other factors
(such
as
the
weather)
seem
to
be at
play.
Specifically,
the
correlations remain
high
for
detrended
changes
in
yield (coefficients
presented
above
the
diagonal).
On the
other
hand,
the
correla-
tion
coefficient for
planted
acres
ranges
from
a
very negative
-0.63
(corn, oats)
to a
highly
positive
0.41
(wheat,
corn).8
These
patterns
continue
to be
supported
for the
detrended
data.
Table
2
(Panel
A) reports
the correlation co-
efficients for the actual
supply
of the commod-
ity.
The
coefficients for
changes
in
supply
are
strikingly
high
for
some
of the
pairings,
close
to 0.90 or above for
wheat-barley, oats-barley,
and
soybeans-corn.
Very
negative
coefficients
are noted for the other
pairings.
These
pat-
terns
persist
for the detrended
data.
Similarly
wide-ranging
correlations are seen for
changes
in inventories
(Panel B).
The coefficients for
changes
in
disappearance
are relatively mod-
est,
with the
exception
of
pairings
of
wheat,
oats,
and
barley, possibly
reflecting
their com-
plementarities (Panel
C).9
We find the corre-
lations
in
table
1
and 2 are
little-changed
when
the data are restricted to the
post-1972 period
(these
results are not
reported
in
the interest
of
brevity).
Table
3
reports
the correlation
of
quarterly
log price changes
for the five
commodities over
the PR
sample
and the full
sample.
As the cor-
relation coefficients are fairly similar across
these
samples
(as
well
as the
post-1972
sam-
ple),
we limit our discussion to
the results over
the
longer
interval. The
relationship
between
the
commodity prices ranges
from the
very
high
to the
comparatively
low. The
pair-wise
correlation of
price
changes
is between 0.20
(wheat-soybeans)
and
0.64
(wheat-barley).
All correlation
coefficients
are
significant
at
the 1% level. The
highest
coefficients are
seen
for the
pairings involving
corn
and the small-
est for those with soybeans. Rank correlations,
discussed
shortly, provide
similar indications.
8
It should be
noted that
the relationship between
prices and
planted
acres is
likely
influenced
by
government
programs
such as
acreage
control.
9 We
assume the
deterioration
rate
(8)
to
be
minor and
drop
it
from our framework.
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7/21/2019 On the Comovement of Commodity Prices
7/16
Ai,
Chatrath,
and
Song
Comovement
of
Commodity
Prices 579
Table 2.
Relatedness
in
Supply, Disappearance,
and Inventories
Wheat
Barley
Corn Oats
Soybeans
A.
Changes
n
supply
Wheat
1
0.946
-0.460
0.733 -0.440
Barley
0.946
1 -0.426
0.887
-0.396
Corn -0.459 -0.426 1 -0.306 0.976
Oats
0.732
0.887
-0.306 1 -0.265
Soybeans
-0.440 -0.400 0.977 -0.265
1
B.
Changes
n
Inventories
Wheat 1
0.912
-0.285
0.717
-0.246
Barley
0.913
1 -0.250
0.887
-0.205
Corn
-0.286 -0.250 1 -0.147 0.941
Oats
0.717 0.888 -0.146 1 -0.100
Soybeans
-0.246 -0.202
0.940 -0.095
1
C.
Changes
n
disappearance
Wheat
1
0.723 0.119 0.535
-0.055
Barley 0.723 1 0.165 0.741 -0.078
Corn
0.119 0.165 1 -0.059
0.438
Oats
0.535 0.740 -0.050 1
-0.137
Soybeans
-0.055 -0.078
0.437
-0.137
1
Note:
Pearsonian correlation
coefficients
are
reported
for
changes
in
quarterly
supply, disappearance,
and inventories
for five
commodities
from
Q1/1957 through
Q4/2002.
Coefficients
above the
diagonal
relate to the de-trended
changes.
Table 3.
Correlation
of
Changes
in
Prices
Wheat
Barley
Corn Oats
Soybeans
A. PR
sample
1960-1985
Wheat 1 0.697 0.474 0.514 0.151
Barley
0.705
1 0.646 0.793
0.389
Corn
0.490 0.660
1
0.557
0.588
Oats
0.527
0.800
0.573
1
0.389
Soybeans
0.163
0.398
0.595
0.400
1
B. Full
sample
1957-2002
Wheat
1
0.638
0.462
0.543
0.198
Barley
0.640 1 0.522 0.581
0.370
Corn
0.470
0.533
1
0.532
0.583
Oats
0.544
0.582 0.536 1
0.377
Soybeans
0.201
0.375
0.589
0.378
1
Note:
Pearsonian correlation coefficients
are
reported
for
changes
in
log prices
below the
diagonal,
and
changes
in
log
real
prices
above
the
diagonal.
Figure
1
traces the
CPI-deflated
prices
of
the five commodities
and
demonstrates the
relatively
weaker
relationship
for the
price
of
soybeans (the
uppermost
series),
which
tends
to
be more volatile. As is
borne out
by
all
the
series,
the
interval
1972-74 witnessed a
sharp
rise in
prices,
followed
by
a
compara-
bly sharp
fall
between 1975
and 1977. The co-
movements in the
price
series are
especially
high over 1972-77. Deb, Trivedi,and Varangis
(1996)
also
note the structural
instability
of
commodities in
the
early
1970s.
High
degrees
of
relatedness
across the five
commodities
per-
sist
through
the 1970s and
1980s,
when
govern-
ment
stockholdings
started to become
more
pervasive,
and
beyond
the end of
the
PR
sample (1985),
even as
commodity
prices
and
price-volatility appear
to settle down.
Performance
of
the Macro
and
Equilibrium
Models
Table
4
reports
the results from
the
Macro
model,
where
differenced
log
CPI-deflated
prices are regressed on contemporaneous and
lagged
values of three macro
indicators and
two sets of
{1, 0}
dummies aimed at
controlling
for the oil-crisis
period.
The macro
variables
are: the differenced real
GDP,
differenced
dol-
lar
index,
and
(as
in
PR)
level
interest
rate.
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7/21/2019 On the Comovement of Commodity Prices
8/16
580
August
2006
Amer.
J.
Agr.
Econ.
6
4
0
L i
ii
i
i
1957
1962 1967 1972 1977
1982 1987 1992
1997 2002
---
Wheat
-
Barley
- -
Corn
- -
Oats
.
Soybeans
Figure
1.
Quarterly
eal
prices
of
five commodities
Q1/1957-
Q3/2002
Table 4. OLS
Results of Model with Macro
Indicators
Wheat
Barley
Corn
Oats
Soybeans
GDP
0.001
(0.21)
-0.001
(-0.33)
0.001
(0.69)
-0.001
(-0.35)
0.002
(1.01)
GDP(-1)
-0.001
(-0.07)
-0.001
(-0.35)
-0.002
(-1.31)
-0.002
(-0.79)
-0.001
(-0.69)
R
0.054
(0.80)
0.042
(0.81)
0.113
(1.63)
0.033
(0.48)
0.129
(1.74)
R(-1)
-0.058
(-0.83)
-0.056
(-1.05)
-0.128
(-1.80)
-0.044
(-0.62)
-0.180
(-2.36)
F
0.042
(0.68)
0.006
(0.13)
0.054
(0.85)
0.068
(1.07)
-0.051
(-0.76)
F(-1) -0.115 (-1.83) -0.069 (-1.41) -0.035 (-0.54) -0.029 (-0.45) 0.030(0.44)
D71-74
0.630
(3.28)
0.650
(4.38)
0.522
(2.66)
0.504
(2.55)
0.520
(2.48)
D75-77
-0.644
(-3.16)
-0.571
(-3.63)
-0.493
(-2.38)
-0.443
(-2.12)
-0.338
(-1.52)
Adj.
R2
0.069 0.108
0.053
0.016 0.055
DW
1.950 1.957
1.829
1.925
1.787
Note:
The
dependent
variable is the
change
in the
log
of real
prices.
GDP is
changes
in
real
GDP,
R is level
one-year
interest
rates,
F
is
the
change
in the
dollar
index. D71-74 takes
the
value of
1
if
the
quarter
falls
between 1971
and
1974,
and zero otherwise.
D75-77
takes the value
of
1
if the
quarter
falls between
1975
and
1977.
Coefficients
displayed
are x
10.
Figures
in
parenthesis
are
t-statistics.
The
sample
covers
Q1/1957-Q4/2002.
The macro
indicators
explain relatively
little
of the
variance
of the
price changes.
The ad-
justed R-squared ranges from less than 0.02
for oats to 0.11
for
barley.
Moreover,
only
the
two dummies
(for
the 1972-74 and 1975-77
intervals)
stand out
as
statistically significant.
As in the PR
study,
none of the macro indica-
tors is
consistently
important,
at
least in
this
specification.
Other
variables,
such as
lagged
values of the
dependent
variable, IP,
alternate
interest
rates,
and narrower
foreign
exchange
indexes,
failed to
improve
the
performance
of
the model.
Prior to the estimation of (4), the vari-
ables
Dt
=
(st
-
It)
and
st
are de-
seasoned
by
regressing
them on a constant and
three
quarterly
dummies
(Q2,
Q3, Q4).10
To estimate the
Equilibrium
model
(4),
we
must
first determine
the order of m and
k. Once the order of m and k are deter-
mined,
we then
estimate the model
using
two
stage
least
squares (2SLS)
estimation
since
inventory
is
endogenous.
The
2SLS
es-
timation
uses
1,
s,, s
,...,s
s,
X,,
sX,,...,
sfX,
as instrumental variables for
D,,..., D,
DXt,...,
DXt.
The order
of m and k are de-
termined
through
a trade-off between overfit-
ting
the
model
and
obtaining improvements
to its
explanatory
power.
We
employ
a cross-
validation
approach
that involves
selecting
the order of m and k that minimize a cri-
terion akin
to
the sum of
square
errors
between the
fitted and
refitted
dependent
vari-
able
(see
Ai and
Chen
2003). Specifically,
10An alternate estimation that does not
employ,
the seasonal
filters
produced only
slightly higher adjusted
R statistics.
By
conducting
these
alternate
regressions
we
assess
that the role of
seasonality per
se in
commodity
comovements is
relatively
modest.
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7/21/2019 On the Comovement of Commodity Prices
9/16
Ai, Chatrath,
nd
Song
Comovement
f Commodity
rices
581
Table 5. Predictive
Powers
of
Macro-indicators nd Fundamentals
Wheat
Barley
Corn Oats
Soybeans
A.
Change og
real
prices
1. Macro
model 0.069
0.108 0.053
0.016 0.055
2.
Equil
model
0.437
0.416 0.542
0.440
0.308
B. Level real
prices
1. Macro
model 0.580
0.719 0.656
0.661 0.598
2.
Equil
model
0.895
0.912 0.903
0.873
0.864
Note:
The
figures
are
adjusted
R2 from
the estimation of two
specifications.
The first is the
OLS
estimation of the Macro model
(1);
the
second
is the
2SLS
estimation
of
the
Equilibrium
model
(4).
The
sample
covers
Q1/1957-Q4/2002.
we
regress
Pt,
Dt,
.
.
,
D,
DXt
. .
,
DX,
re-
spectively
on the
instruments
1,
st,
s2,...,s
,
X,,
stXt, ...
,stXt
to obtain the fitted
val-
ues
t,
Dt
...,
DB, DtXt
..
,kXt.
We
then
apply ordinary least squares (OLS) to
P,
=
"lo
+
Ollb
+
???
+
-m
bm
+
21b)Xt
+
...
2kbkX
+
X'3
+
ut
with the
first observation
deleted. Then com-
pute
the fitted
value for observation 1 as
p
=
&10
+
&11Dib
...
+
&mDB
+&21BX1 +-
..
&2k
kX1+
X0f3.
Similarly, apply
OLS with the
ith
(i
=
2,...
,
N)
observation deleted and
then
com-
pute
fi.
The
optimal
m,
k
are
those
that mini-
mize the
criterion
(m, k)
=
z1
(p,
-
)2
Employing
the
approach
on the
differenced
model,
we find this
criterion
to
decline in the
order
to
at
least
m
=
8,
k
=
8
for
wheat, oats,
barley,
and
soybeans,
and
up
to m
=
6,
k
=
8
for corn. The
criterion
provides slightly
lower
orders
for
the level
series.
Thus,
our
selection
of
m
=
k=
6
represents
a
conservative
order of
polynomial.
As
before,
Xt
contains the
three
current and
lagged
macro indicators and the
two calendar
dummies.
The Macro and
Equi-
librium models were
estimated for the full sam-
ple,
for the
PR-sample,
and
for
the
post-1972
period.
The
results are similar so that
we
only
report
those
for
the
longer
interval.
Table
5
reports
the
R-squared
coefficients
from the
Equilibrium
and Macro
models
em-
ploying, alternately,
level- and
first-differenced
variables. It is readily apparent that the Equi-
librium
model far
outperforms
the
Macro
model in
explaining
price
behavior. For the
first differenced
specifications (Panel A),
the
R-squared
from
the
Equilibrium
model is be-
tween 0.30
and
0.50
larger
than from
the
Macro
model,
representing
between a fourfold and
a
twenty-sevenfold
increase in
explanatory
power.
For the
specifications
involving
vari-
ables
in
their
levels
(Panel
B),
the
R-squared
from the Macro model ranges from 0.58
(wheat)
to 0.72
(barley),
while that from the
Equilibrium
model
ranges
from 0.86
(soy-
beans)
to
0.91
(barley).
Figures
2
and
3
provide
a
graphic
compari-
son
of the
performance
of the Macro and
Equi-
librium models for the two commodities
for
which the
Equilibrium
model
performed
best
(worst),
that
is,
corn
(soybeans).11
It
is
evi-
dent
that
the
predicted
values from the
Macro
model
captures
little more
than the
general
trend in
real
prices:
in not one
of the com-
modities do the predicted values trace the turn-
ing points.
On the
other
hand,
the
predicted
values from the
Equilibrium
model
trace the
peaks
and
valleys remarkably
well
for
corn,
and
reasonably
so
for
soybeans.
To
summarize,
the Macro model is almost
entirely
ineffec-
tive
in
explaining
commodity price
behavior
while the
Equilibrium
model
explains
a sub-
stantial
amount of
price
variation.
As both
em-
ploy only
"fundamental"
variables,
it is clear
that the
latter
will
provide
a much better
op-
portunity to investigate the existence of excess
comovements.
Residual
Correlations
The residuals from
the
Macro
and the
Equi-
librium models
generally
do not
appear
to be
normal,
with
probability
plots
that
indicate
clustering
at the
tails.12
While
a
high
frequency
of outliers will
not
negate
the
correlation
re-
sults
per
se,
it
becomes
important
to
get
a
sense of their
influence on
the
results.
Thus,
n
The
graphic
fit of
wheat,
barley,
and oats
appears
closer to
corn
than
soybeans.
These
figures
are not
reported
in
the
interest
of
brevity.
12While the nonnormality appears stronger in the residuals from
the Macro model, the Jarque-Berra chi-square tests reject normal-
ity
in the residuals from both models.
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7/21/2019 On the Comovement of Commodity Prices
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582
August
2006
Amer.
J. Agr.
Econ.
(a)
0.4:;-\/>
o.6
:
i.
0'A.A
)\
..
0.2 .
0
1957
1962 1967 1972 1977 1982 1987 1992 1997
2002
(b)
3
2.5
2
1957
1962 1967 1972 1977 1982 1987 1992
1997 2002
P(Actual)
-
-
-
P(Macro)
P(Equil)
1.5
I1
Figure
2.
(a)
Real corn
prices:
actual versus
predicted
and
(b)
real
soybeans
prices:
actual versus
predicted
we
augment
the
Pearsonian
correlations with
Rank
correlations.
Table 6 reports the correlation coefficients
for the
change
in
log
real
prices (Panel A),
for
the
residuals from the
Macro model
(Panel
B)
and for
the
Equilibrium
Model
(Panel
C).
The Pearsonian
coefficients for the
Macro-
model residuals
range
from 0.13
to 0.58 and
the Rank
correlations
range
from
0.22
to
0.65. The
comparison
of the
correlation ma-
trices
in
Panels A and B
indicate that the
macrovariables
explain only
a
minority
of
the
correlation-even
among
the
comparatively
unrelated commodities
(for instance,
wheat
and
soybeans).
On the other
hand,
the corre-
lation coefficients for the
residuals from
the
Equilibrium
model
presented
in Panel C are
relatively
small-even for
the
highly
related
wheat and
barley,
and wheat
and oats
pairings.
The Pearsonian
coefficients
range
from -0.02
(barley-soybeans)
to 0.165
(wheat-oats),
sub-
stantially smaller than those in Panels A or
B. Similar
range
coefficients are observed
for
the Rank
correlations,
from -0.04
(barley-
soybeans)
to 0.15
(wheat-oats).
In
summary,
the
Equilibrium
model
appears
to
capture
the
fundamental
relationships
well
enough
to ex-
plain
the
majority
of the correlation in ob-
viously
related commodities. For less related
commodities,
for instance
the
wheat-soybeans
pairing,
there
appears
to be
no
residual corre-
lation,
in other
words,
no excess comovements.
To perform
a wider test
on
excess comove-
ments we examine the
correlations between
the five
agricultural
commodities studied thus
far,
and
a wider
group
of
commodities
repre-
senting
both
agriculture
and
manufacturing.
Table
7
reports
the Pearsonian correlations
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7/21/2019 On the Comovement of Commodity Prices
11/16
Ai,
Chatrath,
and
Song
Comovement
of Commodity
Prices 583
(a)
0.3
-00l"
1
%
...
...
-0.3
-0.5
1957 1962 1967
1972 1977 1982
1987
1992
1997
2002
(b)
0.6
0.4
SI
-0.2
-0.4
-0.6
1957 1962 1967 1972 1977 1982 1987 1992 1997
2002
S
Actual
- - -
Macro
Equil
Figure
3.
(a)
Change
in
log
real corn
prices:
actual
versus
predicted
and
(b)
changes
in
log
real
soybeans
prices:
actual
versus
predicted
between
residuals from the Macro
and
Equi-librium models for the five commodities and
the residuals from the
Macro model
for
the
twenty
other commodities. The Rank
correlations are
fairly
similar,
and
are not re-
ported.
The
log
real
price
changes (reported
in
the first
column)
for
wheat,
barley,
corn, oats,
and
soybeans
are correlated
most
positively
to the
following
commodities: raw material in-
dex
(range
0.15-0.24),
cotton
(0.16-0.28),
co-
conut
(0.07-0.21), sugar-US
(0.09-0.19),
and
sugar-I
(0.07-0.22).
The
correlation coeffi-
cients of the residuals from the Macro model
(reported
in the second column
for each com-
modity)
are not
substantially
reduced.
They
range
from
raw
material index
(0.15-0.23),
cotton
(0.14-0.26),
coconut
(0.04-0.19),
sugar-
US
(0.05-0.13),
and
sugar-I (0.04-0.16).
On
the other
hand,
the correlation
coefficients
from the
Equilibrium
model
(third
column
for each
of the five
commodities)
are sub-
stantially
smaller
for these commodities.
They
range
from raw
material
(-0.03
to
0.06),
cotton
(0.01-0.08),
coconut
(-0.00
to
0.06),
sugar-US
(-0.00
to
0.05),
and
sugar-I
(-0.01
to
0.06).
Importantly,
the
relationship
between
wheat
and
cotton,
that
is found to
persist
in
Pindyck
and
Rotemberg (1990),
disappears
when em-
ploying
the
Equilibrium
model. Once
more,
the
Equilibrium
model
appears
to
explain
the
comovements that the Macro
model does
not
A Test
of
Confirmation
and
a Note
on the Role
of Supply
The correlations of the
residuals from the
Macro and
Equilibrium
models that have
been
presented
thus far
suggest
that
the
supply
and
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7/21/2019 On the Comovement of Commodity Prices
12/16
584
August
2006 Amer.J.
Agr.
Econ.
Table6.
Correlation
of
Residuals rom Macroand
Equilibrium
Models
Wheat
Barley
Corn Oats
Soybeans
A.
Changes
n
log
real
prices
Wheat
1 0.561 0.384 0.569
0.258
Barley
0.638
1 0.471 0.534 0.340
Corn 0.462 0.522 1 0.469 0.652
Oats
0.543 0.581 0.532
1 0.309
Soybeans
0.198 0.370 0.583 0.377
1
B.
Residuals rom
macromodel
Wheat 1 0.532 0.321 0.541 0.219
Barley
0.584 1 0.429 0.507
0.321
Corn
0.408
0.463 1 0.452 0.650
Oats
0.496 0.545 0.506
1 0.336
Soybeans
0.132
0.301 0.558 0.329
1
C.Residuals rom
equilibrium
model
Wheat
1 0.133 0.144 0.152
0.044
Barley 0.156 1 0.010 0.066 -0.039
Corn
0.118 0.052
1
0.043
0.100
Oats
0.165 0.097
0.012 1 0.127
Soybeans
0.031 -0.019 0.079 0.096
1
Note:
Statistics
below and
above the
diagonal
are,
respectively,
Pearsonian coefficients
and
Spearman
Rank coefficients.
The
sample
covers
Q1/1957-Q4/2002.
inventory
variables
(along
with the
macro indi-
cators)
explain
the
majority
of
common move-
ments
in
commodity prices.
Two
important
questions
remain to
be reconciled:
First,
to
what extent does
the difference in
the esti-
mation
techniques
play
a
role
in the
results?
As described
above,
the
Macro model is es-
timated with a linear
specification
while the
Equilibrium
model is
implemented
using
2SLS
and a
sixth order
polynomial.
Second,
to what
degree
are the
commodity
comovements
a re-
sult
of
supply
factors?
Economists have
gained
an
increasing appreciation
for the
importance
of
supply
shocks as
sources of fluctuations in
aggregate
economic
performance
in
general,
and the distribution
of
price changes
in
parti-
cular (for instance, see Myers and Runge 1985;
Balke and
Wynne
1996).
The
relative role of
supply
factors in
commodity
price
comove-
ments remains to be
addressed.
We
address the first
question
on the role of
estimation
technique
via a more careful com-
parison
of
the
empirical
results from
the Macro
and
Equilibrium
frameworks.
We
do this
by
respecifying
the
empirical
framework of the
Macro model to more
closely
match
that
of
the
Equilibrium
model.
We estimate the model
(5)
pt
=
o
+
oX1t
+
. .
.
+
anXt
+ Et
using
OLS,
with
a
sixth-order
polynomial
on
the
contemporaneous
and
lagged
macroeco-
nomic
indicators.
We examine the
extent to
which this
specification
improves
the
explana-
tory power
over
the more traditional
specifica-
tion Macro
model,
and the
extent to which
this
specification
affects
residual correlations. We
find that the
explanatory power
of the Macro
model is little
changed
for
corn, oats,
and
soybeans
with
R-square
coefficients of
0.023,
0.025,
and
0.005
for the differenced series.
For
wheat and
barley,
the
polynomial
model
per-
formed
better,
with
R-squared
coefficients
of
0.172
and
0.161,
respectively,
which
represent
improvements
of 0.10 and 0.05 over
the linear
model
(from
table
4).
However,
the
polyno-
mial
fit for
the
Macro model did not
provide
a
noteworthy
change
in
residual
correlations
for
any
of
the
pairings
using
either Pearsonian
or Rank correlations. Thus, it appears that it
is
mainly
the
inputs
of the
two
models,
rather
than their
econometric
implementation
that
cause the
disparity
in the
results of residual
correlations.
We
address
the second
question-on
the relative role of
supply
in
commodity
comovements
by integrating
out the
inventory,
a demand variable. Note that
we can
always
write
(6) pt =
E{f
(st
-
It,
Xt)
I
t, Xt}+
u
=
g(s,, X,)
+
ut
where
ut
=
Et
+
(f(Dt,
Xt)
-
g(st,
Xt).
Thus,
the
relative role of
supply
can be assessed
by
com-
paring
the fit of
equation (6)
with that
of the
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7/21/2019 On the Comovement of Commodity Prices
13/16
Table 7.
Relatively
Unrelated Commodities: Correlation of
Residuals from the Macro and
Equilibrium
Wheat
Barley
Corn
AP
c(Macro) e(Equil)
AP
e(Macro) e(Equil)
AP
?(Macro) c(Equil)
AP
?(
Materials
Nickel 0.002 -0.012 0.008 -0.057
-0.082 0.042 0.055 0.037 -0.057 -0.060
-0
Copper
-0.018 -0.062 -0.138 0.050
0.014 -0.056 -0.015 -0.062 -0.104
0.031
TSP
0.150 0.015 -0.049
0.136
-0.046 -0.002
0.133
0.028 -0.001
0.088 -0.
Rubber 0.158 0.177
-0.070 0.084
0.094 0.046 0.092
0.101 0.091 0.100
Raw-material 0.177
0.182
-0.032 0.151
0.154
0.024
0.186 0.209 0.052 0.178
Beverages/sugar
Sugar (I)
0.160
0.113
0.038 0.217
0.164 -0.007 0.073 0.036 0.032
0.137
Sugar (US)
0.124
0.072 0.046 0.192
0.133
-0.004
0.087
0.049 0.040
0.155
Coffee
(0)
-0.018
0.027
-0.038 -0.124
-0.087 -0.035
-0.042
-0.005
-0.026
0.036
Coffee
(R)
-0.017 0.023 -0.001 -0.061
-0.029 -0.065 -0.098 -0.066 -0.016
-0.040 -0.
Cocoa -0.001 -0.012 0.015 -0.101 -0.127 0.039 0.031 0.015 -0.036 -0.110 -0.
Edible oils
Palm 0.146
0.122
0.019
0.099
0.062 0.012
0.181
0.146
0.026
0.108
Groundnut
0.039 0.012 -0.009 0.028
-0.006
0.024
0.156 0.122 0.029
-0.017
-0.
Coconut
0.160 0.136 -0.002 0.072
0.038 0.041 0.193 0.163 0.020
0.137
Meats/hides
Hides
-0.033
-0.047 -0.007
0.040 0.048
-0.069
0.110
0.116
0.021
-0.010
Lamb
0.091 0.071 0.036 0.155
0.136 0.091 0.060 0.081 0.116
0.093
Beef
0.095 0.072 -0.095 0.170
0.168 0.043 0.239 0.214 0.052
0.102
Miscellaneous
Rice
0.116 0.071 -0.018 0.018
-0.049 0.032 0.145 0.105 0.045
-0.048
-0.
Cotton
0.160
0.140 0.022
0.198
0.182
0.026
0.282 0.263 0.052
0.171
Banana -0.001 0.004 0.013 0.107 0.127 0.008 0.083 0.102 0.056 0.209
Fishmeal
0.123 0.121 0.061 0.102
0.095 0.058 0.058 0.038
-0.053 -0.010 -0.
Note: AP is the
change
in
log
of
real
prices,
E(Macro)
is
the residual from
the
OLS estimation with controls
for
Macroeconomic
indicators,
and
E(Equil)
is the
residuals fr
Pearsonian correlations.
The
sample
covers
Q1/1957-04/2002.
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7/21/2019 On the Comovement of Commodity Prices
14/16
586
August
2006 Amer.
J.
Agr.
Econ.
Table 8.
The Role of
Supply
in
Commodity
Comovements
Wheat
Barley
Corn Oats
Soybeans
A.
Adjusted
R2
0.618 0.427
0.510 0.535 0.348
B.
Correlation f residuals
Wheat 1 0.074 0.016 -0.042 0.036
Barley
0.055
1 0.142 0.093
0.016
Corn
0.109 0.151
1 0.091 0.146
Oats
-0.022 0.114
0.097 1 0.061
Soybeans
0.048 0.010 0.161 0.085
1
Note:
The results are
from the OLS estimation of the
supply-model
[equation
(6)J.
Correlations
below the
diagonal
are Pearsonian
correlations and
above the
diagonal
are Rank
correlations for the OLS residuals.
The
sample
covers
Q1/1957-Q4/2002.
Macro
model,
and more
importantly,
the
Equilibrium
model.13 To
avoid
possible
misspecification error in the functional form,
we
adopt
the
same functional form for
g(.)
as
was
employed
to
implement
the
Equilibrium
model:
g(st,
Xt)
=
o0
+
aOl,lSt
+
-? -
+
atl,nS't
+
O2,1sXt
+-
"
"
+
-2,nskXt
+
o3Xt.
Equation (6)
is
estimated
employing
OLS
with
s,
dea-
sonalized
as it
was in the estimation of
the
Equilibrium
model.
Table 8
reports
the
regression adjusted
R-squareds
from
(6),
our
"Supply"
model. In
the interest of
brevity,
we
present
results
only
for first
differenced
series over the full
sam-
ple, since results from level series and those for
the PR
sample
and
post-1972
sample produced
comparable
results.
While our intention
is not
to
compare
the
goodness
of fit
across the
2SLS
(Equilibrium)
and OLS
(Supply) estimations,
it
is
worth
noting
that the
Supply
model
es-
timations
produced adjusted R-squared
coef-
ficients that are
relatively
high,
ranging
from
0.35 for
soybeans,
to 0.62 for wheat.
More
direct
evidence
of the role of
supply
in the
commodity price
comovements is
provided
by
the residualcorrelations. These compare favor-
ably
to the
Equilibrium
model for which
the re-
sults
were
earlier
reported
(table
6,
Panel
C).
For
instance,
the
correlation
coefficients for
pairings
involving
wheat are
consistently
lower
in
the
Supply
model,
using
either
Pearsonian or
Rank
correlations.
Importantly, only
a
few
cor-
relation coefficients in
table 8 are
statistically
significant,
suggesting
that
supply-side
funda-
mental
factors
(along
with
the
macrovariables)
may
be
sufficient in
explaining
the
majority
of
the comovements in commodity prices. Thus,
while
the
incomplete
controls for fundamental
factors
(for
instance,
we
only
consider
the U.S.
market)
do
not allow us to
comprehensively
distinguish between the impact of demand and
supply
in the observed
comovements,
the evi-
dence
suggests
that the
supply
factors
play
the
larger
role.
Conclusion
This
study
addresses
the
important question
of
whether
the observed correlation
in the
prices
of commodities
is
"excessive,"
as described
by
Pindyck
and
Rotemberg (1990).
Our
findings
suggest that the comovements are not exces-
sive. We show that much of
the comovements
come from common tendencies in demand and
supply
factors. We fit a
partial equilibrium
model that controls for
commodity-factor
cor-
relations
ignored
in
Pindyck
and
Rotemberg
(1990).
This
empirical
model
explains
the ma-
jority
of the comovements
among
commodi-
ties with
high
price
correlation,
and all of the
comovements
among
those that are
marginally
correlated.
How does
the evidence
in
this article
help
our
understanding
of
commodity price
behav-
ior?
Foremost,
our
findings provide,
in our es-
timation,
the most
convincing
evidence
against
the ECH
for commodities.
Further,
the success
of the
empirical
model that
employs
commod-
ity supply
data
suggests
that
commodity
funda-
mentals
are
related more
closely
than
assumed
in
Pindyk
and
Rotemberg.
In
particular,
the
supply
side factors
appear
to
play
a
large
role
in the observed
price
comovements.
Our re-
sults also
show that the fundamental
factors
explain a large portion of the variability in in-
dividual
commodity prices
and
price
changes,
raising
doubts
on the
role of
speculation per
se
in
causing
the
large
price
movements
com-
monly
observed
in
commodity
markets.
Over-
all,
the results reaffirm
the notion that
price
s3
A caveat in this
framework is that the X variables may repre-
sent commodity demand, so that we are not fully controlling for
demand effects.
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7/21/2019 On the Comovement of Commodity Prices
15/16
Ai, Chatrath,
nd
Song
Comovement
f Commodity
rices
587
movements are not a
sufficient statistic for un-
derstanding commodity
markets or
developing
a
commodity price
model.
[Received
September
2004;
accepted September2005.]
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