on the comovement of commodity prices

7/21/2019 On the Comovement of Commodity Prices

1/16

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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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


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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3/16

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.




4/16

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.




5/16

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.




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.




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.




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.




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.




10/16

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


(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




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




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




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.




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.




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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