CAN
1
_.
'0
O·
G I ULTURAL ECO OMICr.
'1); LID ARY
J~~~6 '1989
~
Staff Pap-ers
DEPARTMENT OF
AGRICULTURAL ECONOMIC.§ ,
!yniversity of Kentucky • CoUege of Agriculture
Lexington 40546
October 1988
DElWfD STUILITY rol HlATS:
In AlOTHIR APPROACH
RI\OZ&\ h.luAGen
and
Barry if. Bobst.
Paper prosentlld At tbe .eting of the SOuthern baionel rood Demand
Reaearch Teobnical Coslttee f K1nneapoU.• t October 3-.lf, 1988
statt Papera are ~~bli8b.d without toraal review. Vieva expressed are tho••
ot tbe author' aDd do not ~rloct the views ot the Un1veralty of Kentuck)" tbe
Agricultural Experilllent Station, or the Cooperative Extenaion Service ..
DEMAND STABILITY FOR KEAts: YET ANOTItER APPROACH
by
Reza Najar%4deh and Barry V. RobBt
The agricultural economics literature is being lnundatedwlth
demand
meat
hypothesis.
studies
concerned with
the
structural
stability
The question 18 whether consumer demand for meat. h ..
shifted in recent years in favor of white
~ats
(poultry and fish)
at the expense of red meats (beef. veal, pork, and lamb)? Just this
year at
l~a.t
three papers have been published on the subject and
have come down on different sides of it.
Evidence in favor of
structural stability has been presented by Chalfont and Alston.
Papers indicating different aspects of structural change hAve
appeared from Eales and Unnevehr and from Dahlgran.
Many. If not
most, of the pre·198a studies are cited in these papers.
The
reviews show that respectable economists with respectable studies
have come down on both sides of this issue.
We hope our efforts
will be regarded a$ aqual1y respectable.
Whether they welcome us or not, our results place um in the
structural stability camp.
by
a
different
Furthermore, we come to our conclusions
train of reasoning concerning
stability of meat demand.
the structural
In fact, our original goal was not the
structural issue so much as it was to extend the Box-Cox functional
form analysis conducted by Chang from the composite commodlcy "meat"
to a jo1nt analysis of its constituents.
In doing so we us6d a
different data set from a different time period and used a maximum
likelihood criterion function somewhat different from the one Chang
ueed to det.rains
vnat
functionsl form
b~~t
fit his a®at deBand
However, our results lndicated " f'.metlonal font that wu
data.
••••ntially the
8 . . &S
Chan,'..
Reproducibility of experiments 1.
a hallaark of the natural seiencllla. To be considered valid, result.
lIWIt
be reproducible by
OthOE'lI.
Stability of un4erlylng phenoMnA
1s •• lcloa at iS8\14 in the natural Klenc•• , where.s it i. precis.,ly
the 1.s. hero.
Cb.ul&' •••• to
POl.'
WI
this reason, the congruence of our re.ulu with
to be
-.
atrona evidence of structural at&bility in
th. demand for Deata,
CIuma's
study
Chang uaed the lox-Cox nexible functional form to aMly:e per
capita . a t dtaund on armual data for 1935·1974, excluding the 1942-
1947 val.' years.
Hia model .pecified rod ..at (baef. v ••l, pork.
laJab, and 8Utton) .s
&
functJ.on of the deflated retail price index
of red &eats and deflated per capita income .. follows:
Where the exponentiation notation is, for any variable X,
(2)
X{k) ....
(Xk - l)/k.
The likelihood function asaociate with this modal 1.
where
82 1~
the e.timated regression variance for the ROdel
liven value of k.
a
An iterative regression procedure vas used to
auimize the l1kelihoocl function.
obtained when k - -0.84.
Th. CUrrent Study
4t
The lUXi9!W!1 of thla function 11&8
The current gtudy applie. the
Box~Cox
flexible fora approach
to the analysis of joint dea.ndG for ••veral ..ats.
the object is to <Ii. aggregate Cbang'iI analy.1s.
Essentially.
The analyst. deals
with jOint. qu.rterly demands for four seats: beef, pork. chicken,
The aod$l 1••at_ted on quarterly data for the 1964-
and turkey.
84 period. Full re.ults are pre••nted in Najarzadeh' 8 dis.ertation.
Tho "8W1ption underlying joint .stiMation ia that d.euncl for
. .au is govern.d by a branch of a weakly ••tt~z:able utility function
.
.
who.. fOIill, though not directly •• t1llable. deterain.. the
characteristic exponent k in the demand equations that derive from
thi. utility function branch.
Det.raining the likelihood function
maxiaIz1ng value of k. therefore, provides an eaplrical estimate of
the functional form of the deeand equations which best confora to
the underlying utIlity function.
Tbis argument
lIU
uaed by Gerkina
and 84y.s in their analysb of housing demand.
.
An adaptation of
the single··equation likelihood function used
1n previous studies was 116cesaary to aceoUlJlOdate our 1N1tlple·
product approach.
Hean expenditure weights were used to weight the
likelihood function, as follow.:
where
Wi -
expenditure weight for the lth
•552
weight. were
Pork:
.309
Chicken:
.109
Turkey:
.030.
3
~at.
These
e~p.nditur•
Per capita demand functions were specified as functioN of
deflated prices. deflated per capita disposable inca.... and "easonal
dummies with the firat quarter deleted.
These functions had the
following general form:
(5)
~
for the ith meat.
Quantities, prices, and
~,
...
lnco~
are
exponentiated by & common value of k for all meats.
An iterative
estimation process was used. in which the regression DIOdel in
equation (5) was estimated for alternative values of k to determine
the value which maximized the likelihood function in equation (4).
Estimation precision vas carried to 2 decimal places in k.
The
l1ke1ihood-maxiaizing value for k was found to be ·0.91 for the
four-meat model over the 1964-84 sample period.
e.timat~s
of the demand aodel parameters at k
- ·0.91 are shown in Table 1.
Slutsky-constrained estimates vere
UnconStrained
also obtained. but are not shown here.
A test of the restrictions
could not reject the hypothesis that the data were consistent with
the existence of the Slutsky conditions.
The
nonlinear data transformation makes it difficult to
interpret coeff1cients directly. so elasticity measures are even
more useful than usual.
Elasticities computed at sample means are
shown in Table 2 for all parameters with t-ratios exceeding +/- 1.0.
All owu prlce coefficients meet thh criterion, although the t-ratio
N
for turkey price 1s quite low.
Ineome
4
e~astlcitie8
are le88 than
unitary for beef and pork, 4na more than unitary fQr chicken and
turkey.
Cross-price elasticities are positive in all but one case and,
except for that case, indicate plausible competitive relationships.
Cross-price elasticities for beef price in the pork. chicken, and
Cross -price elasticities
turkey deJlUlnd function. are positive.
between beef and pork are nearly the SaDe, indicating approxiaata
.,,-.etry between these _ate.
Crosu-p:dce
red seats and the poultry meats are
~t
~.la.tlcitie.
symmetrical.
between the
Chicken and
turkey dell4nds are affected by beef prices. while beef delllWld
appears to be respoNlive only to turkey prices. Neither chicken nor
turkey are responsive to pork prices, but pork demand responds to
turkey prIces.
These cross-price relationships of beef and pork
demand with turkey price is consistent with riSing competition of
processed turkey products vith processed red Hat products. No such
convenient explanation exists for the relationships of beef and pork
demand with chicken price.
Beef deil4nd is indicated to be
independent of chicken price, and pork demand Is shown to be weakly
comple_ntary.
The seasonal demand shifters seea reasonable.
The weak
seasonality of beef demand and the increase in chicken demand in the
spring and sUIIl1JI.er qua.rters are borne out by simple inspection of the
data. LikeWise, the strong fourth quarter shifts in demand for pork
and turkey are as one would expect.
The Structural Stability Issue
Similarity of this estimate of the likelibood function·
5
maximizing funetional form with Chang's previous work has already
been .entioned, but some issues about the preBent &stimates must be
answered in order for this comparison to be taken serIously. First,
1s the aodel ignoring a structural change in deaand from red meats
to poultry taking plece during the study period?
Second, doe. the
rather poor fit for beef dema.nd suggest mis!Specification of th.
DIOde!?
Theae issues are examined by aean.
o~
analy.1. of goodne •• -
of-fit of the model over sequential subperiods.
are obtained for
each of 15 sequential
subperiods beginning with
Predicted values
7-year
(28
quarter)
and ending with 19;8-84.
1964~10
Mean
square errors are calculated for each subper10d and compared. Since
comparative values rather than absolute numbers are important here,
Table 3 displays these goodness-of-fit result. as rankings of the
mean square errors.
hnkings are in descending order, with the
highest aean square errors ranked number one.
Ideally.
these
rBnkings should appear in no particular order. indicating no change
in the model's predictive capability over the sample period.
Inspection of the mean square error rankings for beef indicate
a clustering of ranks rather than a random ordering.
A sequence of
rising mean square errors occurs from the 1967-73 period through
1971-77.
They decline after 1971, and in fact the model seems to
fit best as it moves into the 19808.
These results do not suggest
any deterioration of the model' 8 predictive abUity during the
sample period, but they do mirror the economic disturbances of the
early 19708.
The rankings for pork appear to be the most randomly ordered
6
of any of the meats.
No ••qu0nce. or ether orderings ere apparent.
If the chicken deund function has a
improve in
pr~dict:ive
tr~nd.
it seou to be to
capability over the swaple period.
The three
poorest fits Appear 1n the first three subperiods.
Turkey.
on the other hand.
structural change.
display. ela.sie syaptou of
Tho poore.t fits occur in the early and late
.ubperiods, and the beat fits are clustered in the aiddle, when.
presumably, dependent and independent
their 8aurple Mans.
v.ri~bl&.
vere
clos.st to
This pattern indicate. a structural chanao 1.
occurring that 1. not accounted for by the model'. specification.
However.
the ujor component of the change appear. to
~
in
seasonalIty rather than in the economic variable relationship•.
Seasonal variation in turkey -consumption is declining over tiae, but
this is not taken into account in tho current specification.
Year ..
to-year changes in quantities deaanded ••em to be vell accounted for
by the price and income components of the specification.
Concluding Remarks
It is well-known that it i5 difficult to validate a structural
specificatlon on the same data set uaed to estimate ita parameters.
For this reason, our conclu.ion that the structure of meat demand
1. stable, with the exception of seasonality in turkey, may not be
wholly persuasive.
That is why the agreement with Chang's results
sre so interesting.
If one accepts the argument that the functional
fom of demand equations reflects the form of their underlying
utility function (which 11 done routinely in the clUe of linear
expenditure functions). then the inference of preference stability
7
follow. fro. the apparent atabillty of functional fora.
8
Chalfont, J. A., and J. M. Alston.
"Accounting for
Chana..
in
T•• tell." Jouma1qf I'QUtlcal !1;llDOJU. 96 (April 1988) :391-340.
ChanS. H. S. "FUnctional Forms and the De.and for Meat." Royi•• of
i&onomlcs And StAtiltie •• 59(Auguat 1977):355-359.
Dahlsran, R. A.
"Changing Meat Derund Structure in the United
State.: Evidence froll a Price Flexibility Analys! •• "
Barm
Central JQYmAl of Agricultynl Economics. 10(July 1988) :165-
176.
lal•• , J. S.. and L. J. Unnevehr. "Deund for Beaf and Chicken
Products:
Separab:Uity
Structural
and
Change. "
_"iCAU
JRurnAl of Asriculty[al iQonOlicl' 70(August 1988):521-532.
Ger'klng, S. D. , and W. J. Bayes. "The lole of Functional Form in
Estimating Elaaticitt•• of Housing Expenditure•• "
Southern
Icggpmic JourDA1. 47(1980):287-302.
Najarzadeb. ReZ4. "Functional Foma and Deund.e for Different Type.
of
Keats
in
the
United
States. 1t
Unpublished
Dissertation. University of Kentucky, 1981.
9
Ph.D.
~ ~ff1ct.nt
UccOlP8trd.DMl
Tab10 1.
Ie ..
"'~' 91
btlutela at
for hef t Pork, Chlekeft, &1.lCl 'l'urby.
Pork
Ie.f.
Chlcbn
'luray
--1305."
liltercept
-71.00
.. 61.2'
..'2:U.05
IMf Price
.. 1.81
(-5.40)
1.12
(3.03)
1.70
(2.74)
25.69
(1.78)
0.29
.. 0.04
(·0.01)
0.54
·3.26
(2.71)
(-14.7)
. (0. 'U).
0.03
(0.18)
.. 0.23
(·1.50)
.. 1.61
.. 2.56
(¥6.30)
(-0.44)
hrk Prlc.
Cblcbn Price
0.56
1.07
.. 0.11
(2.99)
(5.13)
(-0031)
.. 10.56
(-1.32)
66.27
(6.82)
57.99
(5.39)
210.91
(11.8)
l1i6.8l
(2.85)
Turkey hiea
lccOlH
quartet' 2
-0.0003
(-0.34)
Quutsr 3
0.0018
(1.95)
Qu,artlltll;'
4
0.0007
Is
Likelihood-Value
-r-r4t1~.
.. 0.0031
(·3.15)
-0.0045
(~4.4S)
(O.72)
0.003'
(3.18)
0."
0.S7
21.469
are in parenthos4e.
10
0.0109
(6.58)
0.0128
0.1554
(4.07)
0.4444
(7.65)
(11.6)
-0.0001
( .. 0.47)
(11.6)
0.96
0.11
0.6868
Tabl. 2.
hie.
am
lneoae Ilutlclty IiIt:tuto. at
Sapt. . . . .
leef
Pork
Chicken
Turkey
leef Price
... 49
.23
.24
.94
hrk Pric.
.19
...13'
-..
-.11
....52
._ ..
...
-.74
Cb1cJr,eD
mc.
Turkey hie.
.29
.42
IDCoae
. 70
.46
11
1.16 ...,.. ,.
~
1.69
Table 3.
Ranks of Prediction Error Mean Squares for Beof. Pork.
Chicken. and Turkey Demand in Fifteen Subs ample Periods.
Pork
Chicken
Turkey
10
8
1
1
1965-71
9
9
2
2
3
1966-72
7
15
3
5
4
1967·73
5
13
8
8
5
1968-74
4
11
5
10
6
1969-75
)
6
4
13
7
1970-76
2
4
14
12
8
1971·77
1
7
9
15
9
1972·78
6
5
13
14
10
1973-79
8
1
12
11
11
1974-80
11
3
7
9
12
1975·81
13
10
6
7
13
1976~82
14
14
15
6
14
1977-83
15
12
10
4
15
1978-84
12
2
11
3
Period
Years
1
1964-10
2
Beef
12
... ",eo
..,
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