AN ANALYSIS OF MONTHLY WHEAT, FLOUR, AND BREAD PRICES
IN A STRUCTURAL AND TIME SERIES FRAMEWORK
by
RUSSELL ELI TRONSTAD
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Applied Economics
MONTANA STATE UNIVERSITY
Bozeman, Montana
June 1985
i i
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of a thesis submitted by
Russell Eli Tronstad
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for submission to the College of Graduate Studies.
Date
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Approved tar the Major Department
Date
Head, Major Department
Approved tor the Col lege of Graduate Studies
Date
Graduate Dean
i ii
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iv
ACKNOWLEDGMENTS
would
graduate
like to extend my sincerest thanks to the chairman of
committee,
Dr.
John
Marsh,
for
his
unlimited
guidance, and support during my work on this thesis.
to thank the other members of my committee,
Frank,
and professors Drs.
insights
and
helpful
my
patience,
I would also 1 ike
Drs. Gail Cramer, and Mike
Oscar Burt and Jeffrey LaFrance, for their
cirticisms on the
preliminary
draft
of
this
thesis.
Special
classmates
career.
appreciation
for
their
is expressed to my
support and
patience
roommates,
family,
throughout
my
and
academic
v
TABLE OF CONTENTS
Page
APPROVAL ................ , , , ................ , . , ....... , ..... , .. , . .
ii
STATEMENT OF PERMISSION TO USE ...................................
iii
ACKNOWLEDGMENTS ......... , .............. , ...... , , . . . . . . . . . . . . . . . . .
iv
TABLE OF CONTENTS ............................. , .... , ......... , . . .
v
LIST OF TABLES...................................................
vii
LIST OF FIGURES .................................................. viii
ABSTRACT .. ' ... ' ...................................... '''
I I . ' •.•. '
i;'{
Chapter
1
2
3
4
INTRODUCTION •.. , ....... , ................................ .
Statement of the Problem ............................ ..
Objectives ........................................... .
Procedures ........................................... .
Literature Review .................................... .
3
3
4
MODEL DEVELOPMENT ............................. , ......... .
7
Terminal Wheat Markets................................
Kansas City Flour Market..............................
Retail Bread Market...................................
8
12
14
ECONOMETRIC THEORY, ..... , ............................... .
16
Distributed Lags......................................
Stochastic and Nonstochastic Difference Equations.....
Recursive Systems ..... , .......... , .. ,, ... , ....... ,....
Time Series...........................................
16
22
23
24
EMPIRICAL RESUlTS ....................................... .
27
Terminal Wheat Markets .... , ............ ,.,, ... ,., ... ,.
Kansas City Flour Market.. .. .. .. .. .. .. .. . .. .. .. .. .. .. .
Retai 1 Bread Market...................................
Multivariate ARIMA Equations..........................
Structural vs. Multivariate ARIMA.....................
27
33
39
41
45
vi
TABLE OF CONTENTS-Continued
Pe:ge
5
SUMMARY AND CONCLUSIONS, .. , , , , , , , , , , , ••.•.• , . , ...• , , , , , , .
51
LITERATURE CITED •. ,,,,,,, ... ,,,,.,,,,,,.,,,,,,,.,,,,,,,.,,,,,,,,,
56
APPEND I X, . , , , , . , .. , , . , , , , , , , , , , , , , , , , , , , , . , , , , .. , , , .. , . , . , , , , . , . .
59
vii
LIST OF TABLES
Page
Tables
1.
2.
3.
4.
5.
6.
Statistical Results of Kansas City Hard Red Winter
Wheat, Minneapolis Dark Northern Spring Wheat, and
Portland Soft White Wheat Price Equations................
34
Estimates of Price Flexibilities for Kansas City Hard
Red Winter Wheat, Minneapolis Dark Northern Spring, and
Portland Soft White Wheat Price Equations................
36
Statistical Results of Kansas City Flour and U.S. Bread
Price Equations ....... ,..................................
42
Estimates of Price Flexiblllties for Kansas City Flour
Price and Retail Bread Price Equations ................ ,..
44
Statistical Results for the ARIMA models of Wheat, Flour,
and Bread Prices.........................................
48
Comparison of the Root Mean Square Errors of the
Structural and ARIMA Wheat, Flour, and Bread Price
Equations................................................
50
Appendix Table
7.
Original Data Used in the K.C. HRW, Minn. DNS, Port. sww,
K.C. Flour, and Retail Bread Price Equations ........... :.
59
v Ill
LIST OF FIGURES
Figures
Page
1.
Koyck geometric 1ags . . , .... , , , ......................... .
19
2.
Pascal dlstrubutlon .•...................•....•...•......
20
ix
ABSTRACT
Wheat, flour, and bread prices fluctuate at all levels of the
market.
Accurate forecasts of these prices are valuable to buyers and
sellers
that trade in the cash and futures markets.
Rational
distributed lag models of monthly prices from June 1977 to May 1984 for
Kansas City No. 1 Hard Red Winter Wheat, Minneapolis Dark Northern
Spring Wheat, Portland No. 1 Soft White Wheat, Kansas City flour, and
retail bread prices are made to evaluate the economic or structural
factors influencing price.
Multivariate
autoregressive-integratedmoving average error (ARIMA) models are also used to compare with the
structural models price forecasting ability.
Rational lags are
estimated using a nonlinear least squares algorithm, incorporating the
specification of nonstochastic difference equations so that
the
disturbance process is divorced from the systematic portion of the
difference equations.
Certain economic factors are found to be significant in Influencing
the prices of wheat, flour, and bread. Partial derivatives and price
flexibilities are calculated to estimate the short, intermediate, and
long-run adjustments of prices in the structural models.
In the
structural models total wheat stocks are the most Influential variable
in determining wheat prices and the price of wheat was most influential
in the flour price equation.
Flour price is highly significant in
influencing retail bread price, with the secular effects of income
increasing
over time.
The price forecasting abilities of the
structural and ARIMA are found to be relatively close when co~paring
the
Root Mean Square Errors and the adjusted coefficients
of
determination.
1
CHAPTER 1
INTRODUCTION
United
States wheat production and marketing Is highly
with the international grain market.
wheat
production
is
Currently the U.S. share of world
about 14 percent and its share
exports is about 43 percent.
Integrated
of
world
wheat
In general,
U.S. wheat is used for food,
feed, and seed, as well as
exports, with
changes in stocks accounting
for the net disappearance.
For the marketing years of June 1977 to May
1984,
24
about 61 percent of U.S. wheat disappearance was exported; about
percent was used for human consumption;
for
seed;
feeding.
and
about
However,
about 4.5 percent was used
7 percent was used for
livestock
and
poultry
there has been a relatively rapid increase In wheat
fed during the last two years of that period. 1
The
the
process. in which wheat moves Into human
consumption
wheat first being stored (public and private storage),
into flour,
Usually
Involves
processing
and then further processsed Into an edible retail product.
these
retail
products fall Into the
general
categories
of
cereal products and bakery products. Considering these marketing stages
of wheat,
consists
the final demand for the end product (i.e. cereal and bread)
of the demand
for the farm based component (wheat) plus
the
U.S. Department of Agriculture.
Economic Research Service.
Wheat
Outlook and Situation, Statistical Bulletins WS-247-273, Washington
D.C. Government Printing Office. 1981-1983.
2
demand
for
the
services
component
(i.e.
storage,
processing
and
dis t r i but 1on) .
The market structure of the U.S.
and
initial
market.
marketing levels illustrates an example of a
competitive
with the farmers being a price taker since
individual demand is Infinitely elastic.
of
production
Specifically, there are numerous local elevators buying wheat
many producers,
from
wheat Industry at the
Local elevators are
each
composed
many farmer owned cooperatives that handle most of the trade to the
terminal
elevators.
selling
The
to foreign buyers,
concentration
ratio
terminal elevators,
which do most
are relatively few in number so
Increases
from the farm level
to
of
the
that
the
the
terminal
1eve 1 .
Statement of the Problem
complexity
The
of
the U.S.
wheat market makes It
difficult
predict certain variables in wheat production and marketing.
to
This is a
particular problem In predicting wheat prices since they are subJect to
economic,
technical,
institutional, and random factors ln the market.
However, If some of the important variables that Influence price can be
identified
and
used
to form an efficient
price
forecasting
model,
buyers and sellers in the market would be able to predict price changes
that could improve upon marketing strategies.
Models of annual
wheat
prices are more common than either quarterly or monthly models, but the
annual
models are more useful for yearly production decisions than for
marketing
have
a current year's crop.
Short term changes in
wheat
more of an Influence on producer marketing decisions.
They
prices
also
3
haVe
important
implications for the flour
and
Previous studies dealing with the wheat,
dealt
more
with
time
bread
flour,
series analysis and have
markets.
and bread markets
not
considered
interrelationship of these markets in a structural framework.
that
provides
coefficients
the
estimates
may
of
structural
parameters
the
A study
and
response
be more useful In understanding the relationship
wheat and processing markets,
by measuring Impacts
of
of
exogenous
shocks to the wheat and wheat products Industries.
Objectives
Three major objectives are addressed in this research.
is
objective
distributed
bread
to
develop
a
monthly
econometric
lags for terminal wheat prices,
price.
The
The
model
first
based
flour price,
and
on
retail
terminal wheat prices include Kansas City Hard
Red
Winter (HRW), Minneapolis Dark Northern Spring (DNS), and Portland Soft
White
Wheat (SWW).
price
Is
dynamic
a U.S.
Flour price Is a Kansas City quotation and
average.
interrelationships
The second objective is
of
these markets
by
to
bread
analyze
calculating
the
short,
intermediate, and long term price flexibillties, and to Interpret their
meanings.
The
multivariate
third
objective
Is
to
estimate
ARIMA model for each price series,
an
alternative
and to compare
their
predictive performances with those of the structural model.
Procedures
The
using
structural
a
nonlinear
parameters for the first objective
least
squares
algorithm
which
are
estimated
incorporates
4
nonstochastic
difference equations and a
autoregressive/moving
average
error
dynamic
model is based on prior knowledge of the industry and economic
theory.
The short, intermediate, and long term price flexibilities are
based
on
structure.
joint
The specification of the variables
the distributed lags of the structural
equations,
estimated by a mathematical algorithm using a recursion
ARIMA
models
are
estimated
by the
accounting for trend and seasonality.
performances
of
the
Box-Jenkins
the
and
are
formula.
integrated
The
method,
Finally, the relative predictive
structural and ARIMA models
are
calculated Root Mean Square Errors of forecast (RMSE).
period by period
in
evaluated
via
Predictions are
for a sample of twelve months.
Literature Review
No
previous
dynamic
work,
known to the author,
model that interlinks the wheat,
has estimated a
flour,
and
bread
monthly
markets.
Most
of the work completed in this area involves using structural
time
series methods to forecast farm wheat
pric~s
and
in either annyal
or
quarterly periods.
A Kansas study conducted by Kahlon (1961)
the
wheat
competitive
by
primarily
investigated
and complementary nature of the different classes
comparing
their respective price
and
consumption
ratios.
Least-square regression lines were fitted to log price ratios of
(the
dependent
variable)
for the interwar period (1929-1938) and the
(1946-1957).
substitutes
variable) and log consumption ratios (the
Kahlon
for
of
wheat
independent
postwar
period
concluded that hard winter and spring wheats were
each other and that all wheat
price
movements
were
5
positively correlated.
hard
wheats
However,
his results showed that the soft and
were not statistically significant as
oeing
competitive
products ..
Wang
various
(1962) estimated structural parameters for price functions of
classes of wheat in the
u.s ..
An annual model
data
from 1929-1957 was hypothesized and the
were
estimated
by ordinary least squares.
Incorporating
regression
coefficients
Domestic wheat
price
was
estimated as a function of the adjusted supplies of each class of wheat
and
per
capita
disposable Income.
Results showed that at
least
89
percent of the variation in domestic wheat prices could be explained by
these
variables,
with
the adjusted supply of wheat
being
the
more
significant variable.
Vannerson (1969) estimated monthly U.S.
data
and
an annual wheat price model.
wheat prices using postwar
Parameters
estimated
annual model were incorporated in the monthly model.
included
the
in
the
The monthly model
effects of government support price and
loan
programs,
stocks of wheat remaining in commercial holdings, exports of
and
whe~t,
domestic food and feed consumption. The monthly model was determined to
be
useful
for
Inventory
control
of
wheat
stocks,
although
some
autocorrelation was felt to be present In the error structure.
A study by Barr (1973) estimated annual average farm price of wheat
from
1964-1972
by
stocks on July 1.
fifth
power
variables
so
using a ratio of normal food usa to
total
ending
The ratio of food use to stocks was specified to the
that
existed.
a
curvilinear
relationship
between
The results showed that average wheat
the
price
two
rose
sharply when total ending stocks were less than 600 million bushels.
6
Arzac
supply
(1979)
with
data
stabilization
variables
estimated an annual structural model of
from 1947-1975.
the
U.S.
grain
to
market.
evaluate
a
endogenous
Included In the model were domestic consumption,
commercial
domestic supply, and the market price of wheat.
government stocks,
weather,
for
was
wheat
The
inventories,
policy
The purpose
U.S.
and
Exports,
support prices, diversion rates, disposable income,
a time trend were treated as exogenous
variables.
The
most influential variables were the market and support prices of wheat,
an
index of weather conditions,
and trend in the domestic
supply
of
wheat.
A study by Westcott,
U.S.
Hull, and Green (1984) estimated an aggregate
wheat price model by using three classes of wheat stocks,
wheat
price,
and quarterly binary seasonal variables.
lagged
The following
three wheat stocks were considered: (1) total wheat stocks (al 1 private
and
government
Credit
wheat In storage);
Corporation
(2) total
stocks
less
owned
reserve
(FOR) in storage (SFONE); and (3) SFONE less CCC wheat on loan
(~FTWO).
Hyperbolic
curves
ratio
variables,
years
1971-1981
The
(CCC) wheat in storage less farmer
Commodity
relating
quarterly wheat prices
for a given lagged price,
SFTWO for 1982-1983 was .278,
Indicated
that
the
stocks-to-use
were constructed for
and then were used to predict prices
mean absolute error of prediction for
to
total
for
stocks,
turning points In wheat prices.
1982-1983.
SFONE,
and
.261, and .246 respectively. The results
less aggregated wheat stocks (SFONE
compared to total wheat stocks,
the
and
SFTWO),
were slightly better at predicting the
7
CHAPTER 2
MODEl DEVELOPMENT
This
chapter presents the theoretical and practical framework
tor
the
equations.
The
nature
of
the
interrelationships between the market levels and the specification
and
modeling
wheat,
is
framework
essentially
justification
It
is
by
the
and
hypothesized
twofold;
modal
describing
the
wheat,
that
the
flour,
monthly
price
interrelationships
and bread markets are of a
recursive
That is, wheat prices at the terminal markets are established
economic
forces specific to that level and then feed forward
The flour and bread market
flour and bread markets.
further
bread price
of the Individual variables at each level of the market.
between the U.S.
nature.
flour,
into
prices
are
determined by economic variables specific to their industries.
Such a framework is hypothesized since, on such a short-term basjs, the
concentration
Importance
of
of
economic
power
at the
terminal
markets
the international market may reduce the effect
domestic flour and bread trades on wheat prices.
and
the
of
the
However, if the time
period were expanded to quarterly or annual observations, more feedback
would be expected from the flour and bread markets,
representing
more
of a jointly dependent relationship among prices.
Since
that
the model is formulated on a monthly
determine
distributed
wheat,
lags.
flour,
Such
and
dynamics
basis,
bread prices are
indicate that
the
variables
specified
a
change
with
in
an
8
economic
variable spreads its effect (on price) over
periods
(discussion in Chapter 3).
may
delayed
be
adjustments
in
several
monthly
This seems reasonable since there
the
markets
due
to
formation
of
expectations, and institutional and technical constraints.
Terminal Wheat Markets
The
first
Terminal
price level considered is the
wheat
prices are defined for Kansas City,
Minneapolis, Dark Northern Spring;
Each
Spring.
relation,
wheat
and
all
price
prices
determined random variables.
set
terminal
wheat
market.
Hard Red
Winter;
and Portland, Soft White Winter and
equation is treated
as
a
together are considered a set
are
relatively
technology.
good
of
form
jointly
Consequently, each equation has a common
of independent variables since it is believed that
wheats
reduced
substitutes
with
the
the
different
present
milling
However, it is not hypothesized that the magnitude of each
independent variable will be the same in each wheat market.
In
general,
seasonality,
estimated
each class of wheat is considered to be a function of
wheat
wheat
exports,
production.
feedgrain
exports,
Specifically,
the
wheat
stocks,
equation
for
and
the
terminal market price of the rth class of wheat is:
PWHrt
= f
1 [D,OEXFGt-j•OEXWHt-j•Kt-j•PRODt-j•E(PWHrlt-i•£rtl
r=1,2,3,
j=O,I, ... ,k
(1 l
k~p
where
PWH 1 = Price of No. 1 Kansas City Hard Red Winter Wheat ($/bu.).
PWH 2 =Price of Minneapolis Dark Northern Spring Wheat ($/bu.).
PWH 3 =Price of No. 1 Portland Soft White Wheat ($/bu.).
9
K
= Beginning
stocks of government and private wheat storage,
(all classes of wheat (million bushels)J. 1
QEXFG = Quantity of U.S. feed grain exports,
oats, and barley (mil. metric tons)).
(corn, sorghum,
QEXWH =Quantity of U.S. wheat exports (all classes of
(thousand bushels)).
wheat
= United
PROD
States Department of Agriculture (U.S.D.A.) monthly
projected harvest (crop year from March to August
(mil. metric tons)).
D =Seasonal binary variables specific to eleven months with
the month of January omitted.
E
= Expectation
the
operator.
rth wheat price.
Refers to the lagged expectation of
• = Random disturbance term with mean zero, constant variance,
and serial independence.
All
The
prices are deflated by the Consumer Price Index (1967 =
sample
period for the variables is based on monthly
data from June of 1977 through May of 1984.
specified
time
100).
series
The reduced form mode 1 is
as a set of difference equations (with the justification
of
the lagged expectation of the dependent variables given in Chapter
3).
Difference
the
necessary
equations are specified since,
information
in small samples,
al.l
to explain wheat prices cannot be contained
in
the specified set of independent variables.
Over the sample period,
the
total
disappearance
wheat exports averaged about 44 percent of
of
U.S.
wheat
supplies.
Consequently,
inclusion of this variable in the structural equations is crucial.
quantity
of
wheat
exported
each
month
reflects
factors
such
1 Since only quarterly stock figures are published by the U.S.D.A.,
the remaining months were linearly interpolated from the quarterly
figures.
The
as
10
International relations,
and
general
difficult
foreign
exchange rates, ocean freight rates, tariffs,
affairs.
to quantify,
Since some
If not Impossible,
of
these
variables
are
the export variable itself
would tend to proxy the sum of these effects.
Monthly
measure
exports
of feedgrains were also Included as
an
Indirect
of the substitution relationship between wheat and feedgralns.
Generally, corn is the key component in the feedgraln market with other
feedgrains
reacting to economic changes in the
consumption of corn,
that of wheat.
relative
Thus,
to
barley,
corn
market.
Usually
and sorghum in livestock feeding exceeds
Nevertheless, in periods when feedgrain prices increase
wheat
prices,
utilization of wheat as
feed
increases.
changes in fsedgrain exports would be expected to influence
the
level of wheat price.
Wheat stocks are assumed to have a strong Influence on wheat prices
since
they measure the net balance that occurs between production
disappearance.
because
of
Thus,
for
example,
and
if wheat stocks are building
an increase in production and/or a decrease in wheat
up
use,
economic logic implies that wheat prices would reflect these changes.
After
completion
expectation
of
expectations
future
of a wheat harvest for a given
next year's crop production
Is
crop
year,
important.
the
Producer
play an important role here since anticipated changes
wheat production will have an Impact on current
wheat
In
prices.
For example, if next season's crop production is projected to increase,
less
grain will probably be stored and more marketed.
figures
beginning
used
of
are a forecast of total U.S.
March unti 1
the harvest has
The
production
wheat production from
been
completed.
the
After
I
I
11
completion
U.S.
of harvest,
wheat
production.
the U.S.D.A.
figures are estimates of
Such .projections
usually
actual
reflect
weather
conditions as well as government farm programs which are implemented or
will be enacted.
The
binary variables are specified to account for monthly seasonal
wheat prices over the course of a crop
patterns
in
seasonal
variables
may
capture other factors
in
casting doubt on their meaning and interpretation.
usua 11 y
making
an
the
year.
the
At
times,
model,
However,
thus,
this
is
inherent risk with seasonal time series data (Sims
197 4)'
binary method legitimate for the purposes of
study.
this
The expected signs or the partial derivatives in equation ( 1 )
the a priori relationships among the variables.
a
a
PWHr
OEXFG
< 0
a
a
PWHr
OEXWH
< 0
a
a
They are given as:
PWHr
K
a PWHr
a
indicate
PROD
< 0
(2 )
< 0
( 3)
Ceteris paribus, an increase (decrease) in the quantity demanded of
a
commodity decreases (Increases) its price.
of
a
substitute increases (decreases),
decreases
the price of
the
(increases) and consequently reduces (increases)
through the demand response process.
monthly
If the quantity
changes
in
d~manded
substitute
own
price
Therefore it is hypothesized that
export quantities of wheat
and
feedgrains
will
display a negative relationship with wheat prices. Stocks and the
production
that
of wheat represent supply variables,
thus,
it is expected
changes in thelr levels would demonstrate a negative
with wheat prices.
correlation
12
Kansas City Flour Market
In
the monthly model,
the price of wheat Interacts with the flour
market and Is thus one of the factors responsible for determining flour
price.
It is recognized that consumer demand represents primary demand
at the retail level,
with the demand for flour and wheat being derived
demands
Robinson 1972).
(Tomek
and
However,
In this
study
It
is
hypothesized that one month is not a sufficient time period for changes
in the flour market to significantly impact terminal prices, but rather
the reverse occurs.
In addition, other economic variables specific to
the flour market level are important.
The following equation specifies
the determinants of Kansas City flour price:
j =0' 1 ' ... 'k
1=1
,2, ... ,p
k::;p
where
PKCF =Price of Kansas City Flour ($/cwt. ),
PWH 1 =Price of No. 1 Kansas City Hard Red Winter Wheat ($/bu, ).
DISP =Disposable Income per capita ($/thousand people).
QFLM =Quantity
peop 1e).
of flour milled per
capita
(mil.
cwtlthousand
W =Wage Index of flour mill workers (1967 = 100)
D =Seasonal binary variables specific to eleven months with the month of
January omitted.
E = Expectation operator. Refers to the lagged expectation of
flour price.
€
All
= Random disturbance term with mean zero, constant variance,
and serial Independence.
price and income variables are deflated by the CPI (1967=100).
13
The
contemporaneous
recursively
of
K.C.
HRW enters
the
flour
equation
as an exogenous variable because It is believed that on
monthly basis,
wheat
price
a
the world wheat market Is the primary influence on K.C.
(rather than the K.C.
wheat price jointly determined
with
the
expected signs of the partial derivatives in equation (41
are
K.C. flour price).
The
given as:
a
a
PKCF
PWH 1
> 0
a
a
PKCF
DINC
>
a
PKCF
il QFLM
a PKCF
a w
0
< 0
(5)
< 0
( 6)
Flour is made with wheat as the major raw material resource.
and
Bread
related products made from flour are a relatively smal 1 portion of
consumer expenditures,
therefore the consumption of these products
fairly constant and not highly price responsive.
is
The milling Industry
is a fairly competitive industry so that we would expect the profits in
the
industry
concepts
to
be
in mind,
yielding a normal rate
of
return.
With
it appea.rs logical that the price of flour wi 11
highly influenced by the price of wheat rather than the price of
(in a monthly time framework).
(decrease)
these
in the price of K.C.
be
bread
Such reasoning implies that an increase
HRW wheat would result In an increase
(decrease) in the price of K.C. flour.
Per capita quantity of flour mil led would be expected to display
negative relationship with the price of K.C.
paribus,
market
with
additional
That is, ceteris
supplies of flour would only be sold to
users at lower prices.
respect
flour.
domestic
The partial derivative of flour
to income is expected to oe positive,
a
however,
price
not
of
14
great
The
magnitude.
reasoning
that
positive sign is consistent
with
flour (and particularly its end products)
theoretical
are
normal
goods.
The flour mill wage is used as a proxy for the processing margin in
flour
production.
the raw product.
Such marketing costs affect the derived demand
For example,
for
if there were an increase in the flour
mill wage the result would be a decrease in the derived demand on wheat
The
prices.
extent of its reduction would depend upon
the
relative
elasticities of supply and demand for wheat (Tomek and Robinson 1972).
Retail Bread Market
The
logic
specification of the retail price of bread is based on similar
used
in
The
modeling the flour market.
retai 1
bread
price
equation is given as:
where
PBR =Retail price of bread (cents/lb.),
PKCF
= Price
of K.C. flour ($/cwt.).
DINC =Disposable income per capita ($/thousand people).
PPOT = Indexed price of potatoes (1967
D
= 100).
= Seasonal binary variables specific to eleven months with
the month of January omitted.
E
= Expectation
E
= Random
operator.
of the'price of bread.
Refers to the lagged expectation
disturbance term with mean zero, constant variance,
and serial independence.
15
The
expected signs of the partial derivatives In equation (7)
are
given as:
All
a
a
PBR
PKCF
> 0
a
a
PBR
DINC
> 0
price
a
a
PBR > 0
PPOT
(8)
( 9)
and income variables are deflated by the
CPI
(1967
=
100).
Cost statistics Indicate that about 13 percent of the final cost
of' a
loaf of bread Is due to the price of the flour. 1
other variables constant,
the effect of a change in the price of flour
on the price of bread is expected to be positive.
be a normal good as well,
Consequently,
Bread is presumed to
so that an increase In per capita disposable
income would result in an Increase in the demand for bread,
price
of bread.
However,
hence
It Is hypothesized that the income
the
effect
would be minimal,
A price
measure
between
for
index of potatoes is included in the bread equation as
a substitute commodity.
bread
particularly
and
potatoes
since the proportion
to potatoa purchases Is small,
since
of
Is
The
not
substitution
expected
to
be
relationship
very .large,
of consumer expenditures
However,
a positive sign is
allocated
expected
an increase in the demand for potatoes would increase the
potatoes
relative to bread,
a
leading consumers to substitute
bread in the diet.
U.S. Department of Agriculture. Economic Research Service. Wheat
Outlook and Situation. Statistical Bulletins WS-247-273.
Washington, D.C., Government Printing Office. 1981-1983.
price
mora
16
This
chapter
discusses the statistical concepts
and
econometric
methods used in parameter estimation of the models developed in Chapter
2.
Included are (I 1 distributed lags, 121 stochastic and nonstochastlc
difference
equations,
(3)
recursive
ARIMA models.
multivariate
systems,
and
141
Elementary aspects of market
Box-Jenkins
demand
and
supply theory are assumed to be understood.
Distributed Lags
Oftentimes
respond
For
functions
to changes In Independent variables over several time periods.
example,
effect
the dependent variables in demand and supply
the time adjustment between a change in
price
and
on quantity may not occur Instantaneously due to the natyre
the commodity,
its
of
imperfect knowledge, habits and technology, and/or time
required to make changes in consumption and production decisions.
This
particular form of dynamics (i.e. time lags in the adjustment of demand
and supply) is the basis of distributed lags.
lag
models
can
be
classified as
whether
a change in
finite
an
or
distributed
infinite.
difference
refers
influences
the dependent variable over a finite or infinite length
time.
to
either
In general,
independent
The
variable
of
17
A finite lag model can be specified as follows:
=a
Yt
where
Y
variable
+ ~OXt + ~!Xt-1 + ~2Xt-2 + • • .+ ~kXt-k +et
is the dependent variable,
and
•t
is a white noise
X is an
(10)
independent
disturbance
term.
(exogenous)
The
indicates that the order of lag coefficients higher than
~k
equation
are assumed
to be zero, so that the independent variable X does not affect Y beyond
k time periods.
Examples include the arithmetic lag,
and Almon polynomial lag.
to
statistically
proper
end
of
estimate
the
multicollinearity.
arbitrary,
precise
knowledge
period.
freedom
may
V-lag,
Finite distributed lag models are difficult
because of the problems
adjustment
process,
degrees
of
defining
the
of
freedom,
and
Usually, defining the end of the adjustment process
becomes
period
inverted
since
there
is little theoretical
basis
of the industry to identify the length of
If the order of lag structure is
large,
and/or
the
lag
degrees
of
are lost and multicollinearity between the lagged coefficients
result in small coefficient estimates relative to
their
standard
errors (Rucker 1980).
Three
weighted lag structure models,
Jorgenson's
geometric
rational
weighted
lag
the geometric,
are common examples
of
Pascal,
Infinite
lag model with one dependent variable
and
lags.
Y and
A
one
independent (exogenous) variable X is specified as:
( 11 )
where
•t is white noise and the sum of the
cannot
be
is finite.
be directly estimated due to an infinite number
and multicollinearity between the
can
~·s
estimated
via a Koyck
~·s.
However,
transformation
This model
of
parameters
the geometric series
(Kmenta
1971 ),
which
18
transforms equation (11) into the
following three parameter function:
(12)
The
difference
adjustment
of
equation
the
dependent
independent variable..
rate
parameter,
A_,
variable
indicates the time
Y given
a
change
rate
of
in
the
Thus, higher values of A indicate a slower
X.
of adjustment and lower values of A
indicate a more rapid
rate
of adjustment. Such results are illustrated in figure 1. Note also that
the
error
term
is
transformed into
a
first
order
autocorrelated
process.
Distributed lag models with geometrically declining weights may not
always
be
current
appropriate.
changes
It
may be more reasonable
to
expect
in an independent variable would display
more
that
of
a
polynomial weighted effect (i.e. an Inverted V-lag distribution) rather
than a geometric decline from the current period.
for
this
distribution
are by using the Pascal
Two ways of allowing
lag
and
Jorgenson's
rational lag. The Pascal lag model is specified as
( 1,3 )
where
L is a lag operator,
lag operator L.
W(L)
= w0
+
and W(L) represents a power series in
the
Specifically,
w1L + w2 L2 + w3 L3 + , , •
( 1 4)
Each weight corresponding to the model is
wi
where
:>-
=
[(i+r-1 )I I I l(r-1 )ll (1-A)r AI
( I =0, 1 , 2, .•. ) ,
is the time period in question, r is some positive integer, and
is a parameter to be estimated (Kmenta,
1971 l.
For r equal to one
the Pascal distribution is a geometric lag distribution.
than
(15)
one
For r greater
the result is an inverted V-lag distribution with
the
peak
19
- high "
- low 1-.
0
Figure 1.
Geometric Distributed Lags
20
2
0
Figure 2.
Pascal Density
3
21
weight occurring at period r-1.
Pascal
distribution
essence,
order
in
r
for
determines
Figure 2 shows the relationship ot the
different values of r with
a
the order of the difference equation
of correlation in the error term when the latter is
equation
(13) (Kmenta 1971).
A.
given
and
In
the
transformed
Its estimated value determines
the
rate of adjustment of the dependent variable, with the restriction that
all
roots
of the difference equation are real,
positive
rand A enter the estimation process nonlinearly,
Both
maximum
likelihood
procedures
are used to estimate
and
and
the
equal,
generally
Pascal
lag
( Judge, et a 1 • 1982 J .
A less restrictive distributed lag structure that allows
inverted V-lag is Jorgenson's (1966) rational lag model.
for
an
This model is
specified as
= bT(LlXt
Yt
+ <t
(16)
with the rational generating function
T(L) = A(LJ/P(L),
= a0
As given by Jorgenson,
A(L)
~0
- ~nln,
- ~ 1 L- ~ 2 L2- , , ,
Thus,
and
( 17)
+ a 1L + a 2 L2 + •••
+ amlm and ~(L)
with ~O normalized at a value of
=
one.
AIL) is an mth order polynomial lag on the independent variable,
~(LJ
is an nth order polynomial lag on the dependent variable.
~(L)
also determines the order of the difference equation and correlation of
the error structure.
the numerator
~(L)
For example, multiplying equation (16) through by
yields;
Yt + PtYt-1 + · · ·
+ PnYt-n
= a+
a1Xt-1 + • · •
+ amxt-m +
( 18)
m:;:n
22
The result Is an nth order. difference equation with an nth order moving
average error process.
Pascal
Jorgenson's model Is less restrictive than
lag since the roots may be Imaginary,
the
or real and unequal.
If
the order of m and n are of sufficient magnitude, Jorgenson showed that
any
arbitrary
This
lag function can be approximated by the
implies that the geometric and the Pascal functions
cases of the rational lag.
of
rational
However,
if
are
lag.
special
not too constraining, the use
the Pascal or geometric lag may be more suitable in dynamic
models
due to the estimation of fewer parameters.
Stochastic and Nonstochastlc Difference Equations
When there is a joint presence of a stochastic difference
and an autocorrelated error process,
ordinary least squares regression
results In Inconsistent parameter estimates.
to
equation
This Inconsistency is due
statistical correlation between the error structure and the
dependent
variable(s).
One method that can be used to alleviate this
problem is nonstochastlc difference equations (Burt,
Burt's definition,
lagged
1980).
Fo~lowlng
a first order nonstochastic difference equation can
be written as:
Yt =
= Pl't-1
where ~'t
error
purely
term.
O£
+ •t•
The
exogenous
EIYt-1)
= yt-1
the
EIYt-l)
structure
Is
Is
minus
difference
equation
Is
dependent
variable
Is
observed lagged
replaced by its lagged expected value.
variable,
and •t Is a white noise
- ~'t-1•
mean of the nonstochastlc
since
( 1 9)
+ llXt-1 + H(Yt-1) + l't
its
That Is,
random
misspecified in such a model,
the lagged
component.
consistent
If
and
dependent
the
error
unbiased
23
coefficient
process
estimates
are
still
obtainable
since
is removed from the systematic part of the
advantages
the
disturbance
equation.
in specifying nonstochastlc difference equations
Further
are;
(1)
the disturbance structure does not have to be correctly estimated as In
the
stochastic difference equation;
(2) the disturbance structure is
usually simpler because it does not have to be transformed;
and
(3)
distinction is made between the exogenous and endogenous components
the model,
of
The major advantage is that the parameter estimates of any
autocorrelated
disturbance are asymptotically uncorrelated with
parameters in the model (Burt 1980).
nonstochastic
not
a
difference
appropriate
since
other
Perhaps a minor weakness in using
equations is that ordinary least squares
the
specification
of
and/or
E(Yt-!)
is
an
autocorrelated error structure yields nonlinearities in the parameters.
Therefore,
nonlinear
for the model developed in this paper,
a modified Marquadt
least squares algorithm (maximum likelihood under normality)
is used to estimate the parameters.
Recursive Systems
Oftentimes
in agriculture,
particularly with short time
periods,
supply-demand interaction can be described by recursive systems
1953).
For
determines
example,
a
price determined at one market
price at another market level.
level
+
P2t =
+ b2X2t + clPlt + 't
(2 I
+ b3X3t + c2P2t + c3P1t + ~t
(22)
P3t
11 2
=63
et
(20)
Pit =a!
+
often
A recursive system can
illustrated as follows:
b1X1t
(Wold,
i
be
24
where the error terms let,
and
•t•
and
~tl
are assumed to be uncorrelated,
the error term in each equation Is uncorrelated with its
relevant
exogenous variable, Xt. Thus, a chain causality effect occurs
where an
endogeous
equation
variable determined In one equation feeds into the following
as
an explanatory variable.
described as having a triangular
matrix
(Johnston 1972).
Such a
system
technically
matrix and diagonal error covariance
~
As explained in Chapter 2,
hypothesized in the wheat,
is
flour,
this structure is
Terminal wheat
and bread markets.
price
is determined by certain exogenous and predetermined
variables.
Wheat
price then feeds into the flour price equation,
the
flour
of
price
and
price, in turn, feeds Into the bread price equation.
Time Series
An
alternative
behavior
by
time
to
structural price models is analysis
series methods.
Arguments for
pure
time
series
analysis Is that knowledge of the "true" structural model Is uncertain,
data collection is usually less costly,
history
of
past
The
prices.
prices may accurately
may
predict
current
and
future
time series method used in this study is the Box-Jenkins
autoregressive-integrated-moving
model
and lor an efficient market, a
average process (ARIMA).
start with a simple univariate
autoregressive
The
ARIMA
process
of
order q, given as AR(q):
Yt = elvt-1 + e2vt-2
where •t is white noise.
term
+. · .+
8 qYt-q + •t
123 l
If the order of q is large,
is weighted differently across time,
or if the error
then a moving average
process of order pis more appropriate (Judge,
et al.
1982).
(MAl
A MA(p)
25
is denoted as
Yt
= •t
(24)
+ at•t-1 + • · • + ap•t-p•
where equation (24) is merely a moving average of the white noise error
term, •t.
If both an autoregressive, and a moving average error structure are
present,
then an autoregressive-moving average (ARMA) process of order
q and p is appropriate.
= 8 1Yt-1
Yt
An ARMA (q,p) is noted as:
+ 8 2Yt-2 +
we assume a process where E(Ytl follows a linear trend equal
If
then
the series is nonstationary since the mean Is not
solve this
problem,
=
where
tot~,
constant.
To
Yt can be differenced up to some order d so
stationarity is obtained.
Wt
( 25 l
+ 8 qYt-q + •t + at•t-1 + · • • + ap•t-p
that
That is,
(1 - L)d Yt
L
(26)
is the lag operator and wt is stationary.
The result is that
Yt in equation (25) would represent an autoregressive-integrated-moving
average
process,
denoted as ARIMA (q,d,p),
where d is the
order
of
described
In
differencing.
The
Chapter
time
series
method applied to the price model
2 approximates the Box-Jenkins method.
That is,
approximates the Box-Jenkins ARIMA model by accounting for
with
and
binary variables,
tests
for
difference
is
multiplicative
an
in
study
seasonality
accounts for data trend with a trend variable,
autocorrelated
that
this
seasonality
the
Box-Jenkins
alternative,
the wheat,
multivariate
ARIMA processes.
error
is
structure.
additive
method
in
(Marsh,
The
this
primary
model
1983).
but
As
an
flour and bread price equations are tested as
The latter implies that various
lagged
26
endogenous
1983).
variables
are specified in the time series
system
(Chow,
The Individual ARIMA equations are represented in the following
form:
(PWHrt• PBRt, PKCF t) =
t 4 (D,T,PWHrt-i•PBRt-I•PKCFt-l•~t)
( 27)
where
D = monthly binary variables.
T = trend variable.
PWHrt-i
=
lagged price of the rth wheat.
PBRt-i
=
lagged price of bread.
PKCFt-i
=
lagged price of flour.
=
PJ~t-l + .••
Thus,
history
+ Pq~t-q + Et- e 1 £t-l - ... - epEt-p' which
represents an autoregressive process of order q and a
moving average process of order p.
each time series equation Is expressed as a function of the past
of the endogenous variables (i.e.,
error process.
would
i=l,2, ... ,k lags)
and
an
If the markets are relatively efficient, lagged prices
reflect important market Information and the order of lags would
be expected to be small.
27
CHAPTER 4
EMPIRICAL RESULTS
This chapter presents the statistical results of the structural and
multivariate
ARIMA
Determination
ot
models of the wheat,
the
flour,
and
bread
final model estimates was based
on
markets.
the
joint
criterion of the adjusted R2 's, asymptotic t-ratios, standard errors of
the
equations,
Therefore,
not
and
consistency
of the model with
all
variables hypothesized in the
economic
initial
theory.
equations
(Chapter 21 are included in the final version of the model.
Tables
through
equations
and
4 present the statistical results of the structural
their respective price flexibilities.
1
The latter are based on the
distributed lag patterns of the endogenous variables with given changes
in the exogenous variables.
of
the
Square
Table 5 presents the statistical
multivariate ARIMA models and Table 6 presents the
Errors
of
forecast
(RM5Es)
used
to
compare
the
results
Root
Mean
relative
predictive performances of the structural and ARIMA models.
Terminal Wheat Markets
The structural wheat prices of K.C.
HRW,
Minn. DNS, and Port. SWW
are estimated with a common set of independent variables since they are
hypothesized
example,
each
production,
to
be
wheat
and
influenced by
the
same
economic
price would be determined by
stocks.
Also,
the
wheat
factors.
exports,
prices
are
For
domestic
closely
28
interrelated
since they are substitutes in the milling process and are
partially utilized in livestock feed rations.
The
of
Pascal distributed lag was used to estimate all three
wheat
prices.
The final wheat price equations are
classes
estimated
as
functions of seasonal binary variables, exports of feedgrains (t and t1 ),
exports
government
estimates.
a
of
wheat (t and t-1 ),
plus
the contemporaneous
private wheat stocks,
and monthly
wheat
of
production
The nonstochastic difference equations are estimated up to
fourth order lag and each equation is also estimated
first
quantity
order
serial
coefficient
correlation.
estimates
Table I
presents
with
the
positive
regression
and statistical results for the three
terminal
wheat price equations.
The
Pascal distributed lag facilitated
wheat price models
in
parameter stability in the
that the parameter estimates varied little with
changes in model specifications.
The order of the difference equation,
determined by r in the Pascal density structure, Is not the same in all
equations.
difference
month
months
That is,
r=4 for PWH 1 and PWH 2 ,
and r=3 for PWH 3 .,
indicates that the distributed lag price effects
earlier
in the Portland market (I .e.,
compared
to
3
months for the
markets). Although this difference is not large,
role of white wheat in livestock feeding.
peak
Portland prices
Kansas
City
and
This
peak
one
2
Minneapolis
one reason may be the
Generally,
more soft white
wheat
(lower
grade) is fed to livestock compared to the hard
wheats.
Thus,
the shorter price peak period may reflect its relatively quicker
adjustments due to changing livestock feeding conditions In the Pacific
Northwest,
particularly
since lower quality white
wheat
suostitutes
29
with barley In concentrate rations.
The
t-1)
summation of the parameter estimates for wheat exports (t
is negative,
indicating larger quantities of wheat entering
and
the
export market occur at a reduced price. This would be in agreement with
negative
quantity effects for inverse demand.
Initially,
the
price
flexibilitles are positive since the contemporaneous parameter estimate
for
wheat
exports Is positive.
In a 3 month period,
Increase in wheat exports leads to increases in K.C.
and Port.
2).
HRW,
10
percent
Minn.
DNS,
SWW prices by .56, .16, and .44 percent, respectively (Table
These initial positive signs are likely due to an initial Increase
in demand for wheat at the terminal level.
of
a
wheat
exports
exports
(t-1)
relatively
coefficients
effects
are negative as the negative coefficient
dominates.
little
Beyond 3 months the effects
impact
However,
the
until about
12
price
on
wheat
flexlbllltles
months,
after
demonstrate a more significant effect.
Such
which
price
reliance
upon
For example, over
a 10 percent Increase In wheat exports reduces K.C.
HRW price by 6.8 percent but Port.
smaller
full
Note, also that soft white wheat prices are not as
affected by wheat exports as are hard wheat prices.
a 12 month period,
the
cumulative
appear to be more in line with an adjustment period of a
crop year or more.
show
flexibility
SWW price by only 1.8 percent.
may partly reflect white
livestock feeding,
wheat's
where the latter tends
to
The
greater
cushion
wheat price variability due to changes In exports.
The sum of the parameter estimates for exports of feedgralns (t and
t-1)
Indicate that an increase in the quantity of feedgrains
results in a decrease In all classes of wheat prices.
exported
Generally, this
30
reflects competition between wheat and feedgrains as wheat is partially
utilized
as
livestock
Note,
production.
feedgrain
feed
however,
exports
and some feedgrains
are
used
In
that a positive relation exists
food
between
and the price of soft white wheat for the
first
3
months and then the relationship becomes negative thereafter (Table 2).
The
Initial positive relation Is small and could mean that
teed9rain
exports
Northwest,
thus,
Extending
period,
Minn.
8.05
the
temporarily reduces feed supplies
boosting
time
in
additional
the
feed demand for lower quality white wheat.
analysis It can be seen that,
over
a
a 10 percent Increase In feedgraln exports reduces
DNS,
and Port.
percent,
Pacific
SWW prices by 9.96 percent,
respectively.
These
12
month
K.C.
HRW,
10.37 percent, and
results confirm the fact that
a
dominating Inverse demand relation exists.
The
contemporaneous
and
variables
lag parameters of
both
the
appear to alternate
In
sign.
wheat
feedgrain
export
reasoning
would Indicate that unusually high or low exports one
and
A priori
month
(I .e., due to unusual International events or problems with loadipg and
unloading
exports
ships at the dock) could be followed by opposite
the next month.
observations
seem
Upon examining the sample
to
confirm
this
pattern
for
data,
both
levels
the
wheat
of
export
and
feedgrains.
However, In the statistical model the combination of other
independent
variables
more
and the difference equation
coefficients
of a smoothening affect on the distributed lag patterns of
prices.
The
result
Is
to
preclude wheat
prices
from
have
wheat
displaying
corresponding month-to-month oscillations.
Government plus private wheat stocks display a negative correlation
31
with
all
three
theoretical
terminal wheat prices.
reasoning
since
This is
additional wheat
In
agreement
with
augment
total
stocks
supplies, thus, tending to decrease wheat prices. As shown by the price
flexibilities in Table 2,
impact
wheat stocks have a greater distributed
lag
on wheat prices compared to the impact of other variables.
For
example,
K.C.
over the long-run,
HRW
price
percent,
wheat
for wheat and feedgrain exports.
1.3
Since
total
stocks measure a net balance between wheat production and
wheat
Its dominating effect is not surprising. An alternative
included
specifying
explanatory variable.
compared
there
decreases
by about 2.2 percent compared to I .2 percent and
respectively,
disappearance,
model
a I percent increase in stocks
to
was
However,
increase In the variance of
stocks
as
a
separate
the statistical results were inferior
those including total wheat stocks.
an
government
only private wheat stocks
were added,
the
One reason is
stock
that
variable
giving more explanatory power
when
to
the
latter.
The
forecast
an
of
next
year's crop
production
independent variable in each
(PRODt)
price
also
included
as
However,
positive signs of the parameter estimates resulted, which are
opposite of those hypothesized in Chapter 2.
wheat
is
equation.
Monthly data reveal that
wheat exports, feedgraln exports, and wheat stocks display considerable
variations about their means.
is
defined
phenomena),
estimates.
these
However,
on a crop year basis (I.e.,
relatively
Such
unexpected
lack
little
since the production variable
more nearly
variation
exists
reflects
in
of variation may at least partly
coefficient signs.
But due to
strong
its
yearly
monthly
account
for
theoretical
32
considerations,
wheat
price
production forecast variable was retained in
equations.
expectations
production
the
of
In
terms
of
demand
and
supply
future wheat production (as given by
estimates)
should certainly be
important
the
analysis,
U.S.D.A.
in
wheat
influencing
current cash wheat prices.
Overall,
the
significant.
monthly
seasonal
binary variables are
Calculation of F-ratios indicated that K.C.
not
highly
HRW was the
only terminal wheat price significant at a 90 percent confidence level,
indicating
that the seasonal variables contributed only little to
regression sum of squares in the Minn.
However,
making
certain
these
models,
individual
results
seasonal
DNS,
and Port.
asymptotic t-ratios
difficult
coefficients
to
lack
interpret.
the
SWW equations.
appear
significant
Often,
in
precise meaning
as
dynamic
the
binary
variables may be confounded with other economic and technical factors.
The
model
nonstochastic
are
prices.
(i.e.
an
difference equation coefficients in the
relatively large (in absolute values) for all
three
These large values indicate that the distributed lag
the
wheat
effects
adjustment period of a dependent variable given a change in
independent
dissipate.
Pascal
variable)
take
a
considerable
period
of
time
to
In the Pascal model, the time length of dissipation for at
least 80 percent of the distributed lag affects to be realized on wheat
prices
due to changes in the independent variables averaged 14 months.
This may not be unusually long since it only extends 2 months beyong
full
crop
sample
divided
year.
prediction
by
The Pascal model also performs reasonably
performance as the standard error of the
the respective means of the dependent variables
wel I
a
in
estimates
are
less
33
than 5 percent tor all three wheat price equations.
Kansas City Flour Market
The
Kansas City 'flour price equation is estimated as a function of
lagged
Kansas City wheat price,
per capita
quantity of flour mil led per capita,
first
order
nonstochastic
autoregressive
statistical
error.
rational lags,
the
parameter
equation
adjustment
period
income,
trend, and a
a
first
estimates
and
time
The structural equation was estimated by
The value of the
coefficient ( .7033) indicates the length
(the
order
while Table 4 presents the
yielding a Koyck geometric function.
difference
given
equation with
gives
results of flour prices,
related price flexibilities.
variable
3
disposable
seasonal variables,
difference
Table
U.S.
distributed lag
pattern)
of
a change in an independent variable.
the
On the
of
the
dependent
average,
flour prices tended to reach an equilibrium or dissipate within 6 to
8
months given a change in an independent variable.
The
hypothesis
evaluated
price
against
that
wheat
price
influences
the alternative of flour
flour
price
determining
in a structural and lagged price framework.
was
pri~e
wheat
The results of the
and adjusted R2 's indicated that changes in flour price
t-ratios
determined
by
wheat price movements with
little
feedback.
were
Because
1 ittle feedback occurred, wheat and flour prices were assumed not to be
jointly
dependent.
Consequently,
K.C.
HRW price entered the
price equation recursively In Its original form.
K.C.
HRW
significant
flour
Entering the original
price data was also supported by the fact that there was
correlation
(i.e.,
adjusted
R2 's were
less
than
no
.01)
34
Table 1.
Statistical Results of the Kansas City Hard Red Winter Wheat,
Minneapolis Dark Northern Spring Wheat, and Portland Soft
White Wheat Price Equatlons.a
Equations
Variable
PWH 1
PWH 2
PWH 3
.1499E+OO
( .1974E+01 l
.1149E+OO
( • 1482E+01 )
.2173E+OO
(. 3721 E+Ol l
-.5928E-02
(-.1091E+Ol)
-.6521E-02
(-.1599E+01 l
.9625E-02
(. 7758E+OO)
EXFGt_ 1
.2258E-02
( .3951E+00)
. 4178E-02
(.1019E+01)
-.I 732E-01
(-.1325E+Ol)
EXWHt
.2868E-06
(. !689E+01)
.1414E-06
(.1171E+01)
.2933E-06
( . 8838E+OO)
EXWHt_ 1
-.4420E-06
(-.2260E+01 l
-.2737E-06
(-.1920E+01 l
-.3865E-06
(-.1133E+01)
Kt
- .1669E-04
(-.3030E+O!J
-.8683E-05
(-.2848E+01)
-. 2971 E-04
(-.3055E+OI)
.2242E-03
(.2389E+01)
.1557E-03
( .1933E+OI l
.1829E-03
(, 7919E+00)
02
-.9126E-O!
(-.6533E+OOJ
-.1262E+OO
(-.8771E+00)
-. 1156E+OO,
(-.1462E+01 l
03
-.9534£-01
(- .1069E+01)
-.4524E-01
(-.4948E+00)
-.1205E+OO
(-.2107E+OI)
04
-.6723E-01
(-.6217E+00)
-.4297E-Ol
(-.3858E+00)
-.5390E-OI
(-.8787E+00)
Ds
- .1408E+OO
(-.I331E+01)
-.!363E+OO
(-.1252E+OI l
-.!539E+OO
(-.2495E+Ol l
06
-.3688E-01
(-.3471E+OOJ
-. 7092E-01
(-.6482E+00)
-.7604E-01
(-.1204E+01)
07
-.l262E+OO
(- .1160E+Ol l
-.5717E-01
(-.5125E+00)
-.8985E-01
(-.1415E+Ol l
Da
-.1474E+OO
(-.1425E+Oll
-. 2232E+OO
(-.2087E+OI)
-.1416E+OO
(-.24522E+01)
Intercept
EXFGt
PRODt
35
Table I ( cont l nued).
Equations
Variable
PWH 1
PWH2
PWH 3
.1048E+OO
(. !245E+O!)
.2431E+OO
( .2812E+O!)
-.4675E-01
(-.8095£+00)
0 to
-.2!26E+OO
(-.2391E+Ol)
-.2866E+OO
(-. 3211E+O!)
-.9204E-01
(-.1415E+OI)
011
.2157E-Ol
(.2494E+00)
-.3673E-01
(-.4211E+00)
-.3619E-01
(-.6308E+00)
012
-. 1930E+OO
(-.1364E+0!)
-.9294E-01
(-.6378E+00)
-.1610E+OO
(-.2037E+Ol)
E(DEP-1 )b
E(DEP-2)
E(DEP-3)
E(DEP-4)
. 2761 E+Ol
-.2859E+Ol
.!316E+Ol
-.2270E+OO
.2918E+Ol
-.3193E+O!
.1553E+Ol
-.2830E+OO
.2182E+Ol
-.1586E+01
.3850E+OO
Pt
.5731E+OO
(.6215E+Ol)
.5933E+OO
( . 6 551 E+00 )
.7902E+OO
(.1153E+02)
09
Statist Icc
Regression Results
-2
R
.9347E+OO
.9!92E+OO
.9380E+OQ
Sy/Y
.4260E-Ol
.4096E-01
.3891E-01
D.W.
.1872E+Ol
.1925E+Ol
.1852E+Ol
a The top figure represents the paramter estimate and the figures In
parentheses represent the respective t-ratlos for each variable.
b Represents the expected value of the lagged dependent variables,
which are determined by the estimated Pascal parameter. The Pascal
parameters and their asymptotic t-ratios for each equation are:
PWH 1 = .6903, t-ratlo = 20.462; PWH 2 = . 7296, t-ratio = 27.281;
PWH 3 = . 7272; t-ratio = 17.530.
cR2 = adjusted multiple R-squared statistic.
Sy/Y = standard error of the estimate divided by the mean
of the dependent variable.
D.W. = Durbin-Watson statistic.
36
Table 2. Estimates of Price Flexibilities for the Kansas City Hard
Red Winter Wheat, Minneapolis Dark Northern Spring, and
Portland Soft White Wheat Price Equations.a
Length of Run (months)
Variable
3
EXFG
EXWH
K
6
-.445
(-.455)
24
Long-Run
-1.301
(-1.454)
12
[-.218]
-.996
(-1.037)
[-.805]
[-1.214]
-1.329
(-1.537)
[-1.268]
.056
( .016)
[. 044]
-.075
(-. 140)
[-.006]
-.682
(-. 86 7)
[-.183]
-1.178
(-1.719)
[-.318]
-1.228
(-1.911)
[-.336]
-.16 7
(-.095)
[-.214]
-.623
(-.395)
[-.629)
-1.556
(-1.173)
[-1.312]
-2.122
(-1.896)
[-1.717]
-2. 1 7 5
(-2.051)
[-1. 768]
-. 1 37
(-. 144)
[ .019]
a The top figures represent the PWH 1 equation, the figures in
parentheses represent the PWH 2 equation, and the figures in brackets
represent the PWH 3 equation. The price flexibil ities are calculated
with respect to the means of each variable. Price flexibilities were
not computed with respect to the production variable because the sign
was not consistent with the original hypothesis.
between the residuals of the wheat price and flour price equations.
The effect of Kansas City wheat price is statistically
in both the contemporaneous and first order lag periods.
lag
could
relationship
between
from
The distributed lag effect of hard
winter price on flour price indicates there is always
material
The one month
indicate the time period needed for wheat to be moved
storage to the point of processing.
red
significant
the two prices (Table 4).
That is,
a
positive
as the
cost of wheat increases millers pass part of the cost
on
raw
in
37
the
form
of
higher flour prices.
For example,
the 6
month
price
flexibility indicates a 10 percent Increase In wheat price yields a 7. 7
percent
increase
in
flexibility for K.C.
per
capita
These
flour
price.
Note
that
the
long-run
HRW Is about 3 times larger than that for
quantity of flour milled or per capita disposable
price
either
Income.
economic results are consistent with the fact that wheat Is
the
dominant Input In the flour milling process.
Per capita disposable Income has a positive affect on flour
which
is
consistent with flour being a
magnitude
of
effect
of
slowly
over
normal
good.
However,
the
disposable income coefficient
Indicates
income
is relatively small and tends
to
time.
Given a 1 percent increase in
increase
disposable
price increases only about .3 percent over the long-run.
is
relatively smal I proportion of the cost of
retail
the
that
flour
a
price,
the
rather
income,
Flour
products
In
consumer budgets. Thus, the income effect is not expected to be strong.
In
addition,
income
flour
inelastic,
is utilized in numerous retail products that
precluding
a
strong Income effect
are
in
the. flour
negatively
correlated
market.
The
with
per capita quantity of flour milled is
flour price.
Its effect is not particularly large as can be seen
by the price flexibility coefficients in Table 4.
percent
price
For example,
a
increase in per capita quantity of flour milled decreases
of flour by only 1.6 percent over the long-run.
One reason
10
the
for
its minor importance may be the dominating effect of the level of wheat
prices.
relatively
That Is,
if monthly processing costs for making bread remain
constant,
the
price of flour is largely affected
by
the
38
price
of
This Is particularly true since the cost
wheat.
of
wheat
constitutes the largest share of miller raw material costs.
In
to
the original hypothesis a flour mill wage variable was included
proxy
the processing margin between the wheat and
flour
markets.
However, the result was a positive relationship between the flour price
and wage rate,
derived
demand (Tomek and Robinson 1972).
positive
margin
a
price
about
price.
monthly wage as a proxy for a processing
might be Inadequate for reflecting all processing
example,
due
flour
influence wage rates rather than wages impacting flour
in this case, using
on
Part of the reason for the
relationship may be that milling technology and
jointly
Also,
which was contrary to the effect of marketing costs
costs.
For
85 percent of the final cost of flour (at the mil 1) is
to the cost of wheat and most of the processing costs are
related
to capital investment in plant and equipment.
The
asymptotic t-ratios indicate that most of the seasonal
variables
are not statisticallY significant (different from
determining levels of flour prices.
since
wheat
is
life.
Consequently,
binary
zero)
in
Economic logic would bear this out
a nonperishable commodity with
considerable
storage
millers can continually draw upon wheat stocks to
satisfy monthly flour processing requirements.
In addition,
seasonal
retail consumption of flour based products is very weak at best.
The trend variable in the flour price equation indicates that
flour
real
prices experienced an upward trend throughout the sample period.
Though the variable Is statistically significant,
coefficient
( .0014)
Is relatively small,
the magnitude of the
Indicating
overshadowed by the effects of other regressors.
Its
Impact
Is
39
Retail Bread Market
The
retail
bread
price equation is also
estimated
by
rational
distributed lags (similar to that of the flour price equation).
bread
price
price,
per
seasonal
is
estimated as a function of lagged Kansas
capita
binary
disposable
variables,
Income,
trend,
Retail
City
flour
a price
index
of
potatoes,
and a first
order
nonstochastlc
difference equation with a first order autoregressive error.
Table
3
presents the associated parameter estimates and statistical results.
The rational lag form for the bread price equation was reduced to a
geometric
function.
0.907, indicates
than
The
estimated difference equation
that the distributed lag effects adjust
those found in the flour price equation.
average
length
of
period
for bread prices
coefficient,
more
slowly
More specifically,
to
dissipate
or
the
reach
equilibrium (given a change In any independent variable) is about 10-12
months (6-8 months for flour).
This may be due to the fact that
price Is not only subject to economic influences from the flour
but
also
consumers.
to
the
factors
that
purchasing
~arket,
behavior
of
The result could be to produce an underlying structure that
delays the distributed lag process.
reflected
determine
bread
in
Such distributed lag effects
are
the price flexibilities for different lengths of run
in
Table 4.
The
price
causal relationship of flour price influencing
was
evaluated against the opposite alternative to
hypothesized recursive structure (i.e.,
retail
verify
bread
the
similar to the relationship of
wheat and flour prices in the flour price equation).
Results of the t-
40
ratios and adjusted R2's showed that,
significant
on a monthly basis, there was no
joint dependency between the two markets,
flour
price only impacted bread price.
that
the
Kansas
City
flour
price
but rather that
The regression
Is
significant
results
in
contemporaneous period and in the period lagged one month.
be
due
next
both
the
The lag may
to an adjustment in price expectations from one month
or
show
to
tne
to a lag in the production process due to transportation
and
processing time.
The price flexibllltiy of bread price with respect to
flour price is .305 for a 3 month period and then decreases to .187 for
the long-run.
Indicates
This time decrease In the price flexibility coefficients
that
bread prices adjust to changes In flour
rapidly In the initial months,
prices
quite
which may be due to the very short time
horizon In bread production and sales.
Per
the
capita disposable income displays a positive correlation
price of bread.
hypothesis
that
This positive relationship supports the original
bread
Is
a
normal
good.
coefficient of .13 for a 3 month time period
The
price
flexibility
indicates that the· Income
effect Is not very significant for shorter time periods,
over
the course of a year to a value of .353.
but increases
Although small,
indicative that longer periods of time permit consumers to more
adjust
bread
flexibility
reflecting
purchases
coefficient
the
with
from
an
Income
change.
Also,
is still relatively smal 1 over the
fact that bread is a relatively
small
the
It
Is
freely
price
long-run,
proportion
of
total consumer food expenditures.
The
price
substitute
for
Index of potatoes is Included to measure potatoes as
bread.
A priori the degree
of
substitutability
a
is
41
hypothesized
to be weak,
which was confirmed withand a long-run price
flexibility coefficient of only .027.
theoretically correct;
in
The positive coefficient sign is
that Is, for substitute commodities an increase
the price of potatoes would lead to an increase in the
demand
tor
bread (hence, increase its price).
The
seasonal
significance.
continual
f~ct
and
The
trend
absence
variables
show
little
statistical
of seasonality In bread prices is due
available supplies of flour for bread manufacturing and
that consumption of bread Is nonseasonal.
The negative trend
to
the
in
real bread price could indicate there has been a steady Increase in the
efficiency of baking bread,
but lack of information makes the argument
weak at best.
Multivariate ARIMA Equations
Few
theoretical
consequently,
estimated
considerations
terminal wheat prices,
are
used in
the
ARIMA
models,
flour price, and bread price are
as a function of the same set of
variables.
They ,Inc 1ude
lagged prices, seasonal binary variables, trend, and an autoregressivemoving
average
error
structure.
FIna 1
parameter
estimates
and
statistical results for the time sarles equations are given in Table 5.
Stochastic
difference
equations are used since
values of the dependent variables are specified.
binary
lagged
observed
The specification of
variables and trend account for seasonality and time effects in
the data,
account
the
respectively.
for
conventionally
the
The autoregressive term (p) is estimated
fact that the data Is not first
done
In
the
Box-Jenking
differenced
framework.
as
However,
to
is
the
42
Table 3. Statistical Results of the Kansas City Flour Price and U.S.
Bread Price Equations.a
Equations
Variable
PKCF
PBR
Intercept
.6639E-01
( .4083E+OOJ
.5683E+OO
( .4384E+00)
.1605E+01
(. 1088E+02)
P\1Hl t-1
-.1040E+01
(-,3499£+01)
.9378£-01
( .3403E+01 l
.2869E+OO
(, 1930E+OI)
-.1690E+01
(-, 1009E+01)
.1743£+01
( '5240£+01)
-,1651E+01
(-,4749E+01)
PKCFt_ 1
.4800£-03
( , 2162 E+00)
PPOTt
E<DEP-1 ) 0
Trend
.7033E+OO
( .5904E+01 l
.9070E+OO
(.1112£+02)
.3160£+00
(. 2980E+OI l
. 7118E+OO
(. 9064E+OI)
.1143E-02
(.2133E+01)
-.3141E-02
(-.6600£+00)
-.7880E-02
(-.1252£+00)
.1300E-01
( ,5470E-01 l
-.1836E-Ol
(-.3156E+OOJ
-. 7768E-01
(-.3323E+OOJ
-. 7210E-01
(-.1255E+Ol)
.2395E-01
(. 1033E+OO l
43
Table 3 (continued).
Equations
Variable
Statist icc
PKCF
PBR
. 7232E-OI
( .1309E+Ol)
-.6253E-01
(-.2703E+00)
-.4488E-01
(-.7515E+00)
-.9063E-02
(-.3757E-01 l
.1610E+OO
(.267!E+OI)
.6572E-01
(.2607E+00l
.8969E-02
(. 1427E+OO l
. 1347E+OO
( .5531E+00)
- .!962E-01
(-.3144E+00)
.1 711E-01
(. 7104E-OI)
-.4443E-01
(-. 7420E+00)
.3063E-01
(. 1322E+OO)
-.4174E-01
(-.7007E+OO)
.2944E-01
(. 1248E+OO)
-.5243E-01
(-.8363E+00)
.2359E+OO
(. 9882E+OO l
Regression Results
.9616E+OO
.9587E+OO
Sy/Y
.2481E-OI
.1987E-01
D.W.
. 1976E+Ol
. 2l78E+Ol
a The top figures represents the parameter estimates and the figures
in parentheses represent the asymptotic t-ratios lor each variable.
b Represents the expected values of the lagged dependent variables.
c
R2
= adjusted multiple R-squared statistic.
Sy/Y = standard error of the estimate divided by the mean of the
dependent variable.
D.W. =Durbin-Watson statistic.
44
Table
4.
Estimates of Price Flexlblllties for the Kansas.City Flour
Price and u.s. Bread Price Equations.a
Length of Run (months)
Variable
3
6
12
24
PWH 1
.726
. 766
.784
. 787
.787
OFLM
-.102
-.137
-.153
-.156
-. 156
DINC
. 180
( . 1 30)
.243
(. 227)
.272
(.353)
.276
( . 462 )
.276
(.512)
PKCF
( . 305 )
(.275)
( . 2 36)
( . 203)
(. 187)
PPOT
(. 007)
( . 012)
( . 019)
( . 02 5 )
( . 02 7)
Long-Run
a The figures in parentheses represent the U.S. Bread Price Equation,
and the figures without parentheses represent the Kansas City
Flour Price Equation. Price flexibllitles were calculated with
respect to the means of the variables.
statistical
not
results showed that an autoregressive error structure
significant
consisting
in any equation,
and that the only
error
was
structure
of a moving average parameter in the soft white wheat price
equation.
The lagged price variables that were not statistically
significant
(in terms of their asymptotic t-ratios) were excluded from the original
ARIMA
seen
model (as given in Chapter 2).
As a general result,
that most of the equations nearly reverted back to
autoregressive
structure.
a
The individual fits of the ARIMA
It can be
univariate
equations
45
however, the adjusted
are close to those of the structural equations,
R2 •s and standard errors of estimates are slightly inferior.
Since
the
comparison
ARIMA
of
Generalization
seasonality
and structural
respective
their
of
is
the
very
methods
results
are
is
results would Indicate
weak,
highly
somewhat
that
appears
marginal
only strong In the soft
effects
Trend
equations.
In
the
in
In
no doubt due to lack of
requirements In monthly production and consumption.
models
hard
red
white
winter
both
models
seasonal
Trend In the ARIMA
wheat
wheat
equation,
and
variables,
in the ARIMA models rests
which
are
merely
with
bread
price
the ARIMA may be reflecting some of the
significance
dependent
tenuous.
strong
structural arguments found in the structural equations.
statistical
different,
weaker
Finally,
with
the
incorporating
the
lagged
historical
information implicit in the sample.
Such results suggest that the wheat,
relatively
efficient
in
flour,
and bread markets are
that past prices readily
capture
important
factors at work in the market. In the structural models, the
dif~erence
equation coefficients are also reflecting past history in wheat prices,
but
emphasis
is
shifted
toward
Independent
effects
by
certain
regressors that leads to understanding market structure.
Structural vs. Multivariate ARIMA
To evaluate the relative predictive performances of the
and
ARIMA
models,
Root
most
Mean Square Errors of forecast
calculated.
The
recent
sequentially
truncated and,
12 months of the
thus,
sample
structural
(RMSE)
were
period
were
forecasts were made on a month
by
46
month
parameter
suggesting
Error is
RMSE
the
process,
=[
structural
n
The formula for the Root Mean
~2
dependent variable,
size
standard
of 12).
Square
~ ei/n)l/2
i=l
ei is the difference between the actual and predicted
sample
the
that same models would have bean chosen even if
sample had been shortened.
where
truncating
estimates remained stable for both the ARIMA and
equations,
the
During the
basis for each equation.
value
and n is the number of periods tested
Table 6 presents the
RMSE,
adjusted
error of estimate associated with each equation in
of
(i.e.,
R2 ,
and
both
the
to
the
structural and ARIMA framework.
Generally
standard
errors
specification
usually
when
of
errors
revealed
the
size
forecast,
of RMSEs are
it
relative
is Indicative of
in the model (Marsh,
1983).
the
measure
of
Such
errors
are
in that the estimated parameters are
respect to a change in sample size.
of
large
unstable
In this model, however, the RMSEs
both the structural and ARIMA price equations are less
respective
standard
errors of forecast,
for the structural model,
than
and the parameter
remained quite stable in the truncation process.
particularly
with
This would
their
estimates
suggest,
that given the combination
of
data, sample size, and methodology, relative structural price stability
is present in the wheat, flour, and bread markets.
Overall,
the
comparative
results
equations appear to be close and mixed.
for the structural
and
AR!MA
For example, in examining the
price equation for hard red winter wheat, the RMSE statistical criteria
are close for the structural and ARIMA methods when comparing .0416
In
47
the
structural
slight
model with .0456 in the ARIMA
advantage for the structural equation).
method
(i.e.,
However,
only
a
in the soft
white wheat and bread price equations the RMSE's favor the ARIMA model.
Thus,
one
may conclude that if there is joint interest in
structural
information and price prediction in the market, the use of a structural
model
pure
would serve relatively well.
If one were merely interested
price forecasting in these markets,
the ARIMA model would
be
in
a
more efficient method since the costs of data collection and estimation
would be less with little concession of statistical precision.
48
Table 5.
Statistical Results for the ARIMA models of Wheat,
and Bread Prices."
F 1our,
Equations
Variable
PWH 1
PWH 2
PWH 3
PKCF
.3357E+OO
.2647E+OO
( .2398E+Ol) (-. 7698E+00)
PBR
Intercept
.8096E-01
-.1596E+OO
(. 8439E+OO) (-,8614E+00)
02
. 1088E-01
-.5214E-02
- .1684E-02
( .2761E+00) (-. 1411 E+00) (-.SOOOE-01)
03
.1389E+OO
(. 3507E+OO)
-.l857E-01
.IOOOE-01
( .2696E+00) (-.4923E+00)
.1978E-02
-.8112E-01
( .2313E-Ol) (-.3089E+00)
04
.3561E-01
( .9003E+00)
.6499E-01
( .1757E+01)
.1806E-01
( .4787E+00)
.3344E-02
( .3905E-Ol)
.1913E-01
(. 7278E-Ol)
Os
-.2252E-02
(-. 5661E-01)
.5803E-01
-.1846E-01
(. 1565E+OI) (-.4880E+00)
.8971E-01
( .1048E+01)
.8176E-01
(.3109E+00)
06
.2593E-01
(. 6280E+OO)
.4740E-01
( .1220E+01)
.5800E-02
(.1478E+00)
.1433E-01
-.3914E-01
( .1596E+OO) (- .1430E+OO l
07
.8412E-02
( .2032E+00)
.3947E-OI
( .1009E+01)
.2820E-01
(. 7160E+00)
.1611E+OO
(.I 793E+OI)
.1627E+OO
(. 5940E+OO)
-,3514E-02
-.3443E-01
-. 2721E-01
(-.8323E-01) (-.6990E+00) (-.8725E+00)
.1246E-OI
(.1376E+00)
. 7871E-OI
(. 2878E+OO)
Og
.!674E-Ol
(.1958E+00)
. 1848E+Ol
( .1599E+01)
.3964E-Ol
( .1510E+00)
Og
.4067E-OI
( .1006E+01)
.4325E-01
-.1581E-01
( .1167E+01) (-.4229E+00)
.3335E-01
(.3887E+00)
.6308E-Ol
(.2397E+00)
0 10
.4646E-01
( .1167E+01)
. 71 72E-01
-.1581E-01
(, 1938E+Ol) (-.4192E+00)
. 1898E-Ol
(.2213E+00)
.4806E-01
(.1827E+00)
011
.7882E-01
(. 1999E+01 l
.4622E-01
(, 1244E+OI)
.9437E-01
(.1101E+01l
, 1 776E+OO
( .6756E+OO)
0 12
-. 7192E-03
-.5291E-01
-.3048E-01
- .1688E-01
(-.1829E-01) (-,4546E+00) (-,1567E+01) (-.3554E+00)
.1688E+OO
( .6122£+00)
Trend
-.7155E-03
(-,l372E+01)
PWHI t-1
.8117E+OO
(. 1048E+02)
.1413E-01
(,3750E+00)
.1886E-03
- .1325E-02
( . 2850E+OO) (-.2305E+OI)
.6827E-03
-.5961E-02
( .4245E+00) (-.1454E+01)
49
Table 5 (continued)
Equations
Variable
PWH 1
PWH 3
PKCF
PBR
.8231E+OO
( .1387E+02)
PWH2t_ 1
PWH3t-l
PWH 2
.1361E+OO
( . 1441 E+0 I )
.8754E+OO
( .1598E+02)
PKCFt_ 1
. 7949E+OO
(.1134E+02)
.1993£-01
( .1860E+01)
P8Rt_ 1
.5228E-OI
(. 1925£+01)
.9157E+OO
(.1879E+02)
-.2094£+00
(- .1637E+OI)
e!
Statisticb
Regression Results
.9224E+OO
.9065E+OO
.9278E+OO
.8920E+OO
.9384E+OO
Sy/Y
.4629E-OI
.4388E-01
.4182£-01
.4167E-01
.2425E-01
o.w.
.!831E+Ol
.1771E+O!
.!955E+Ol
.2!95E+OI
.2053E+01
a The top figures represent the parameter estimate and the
figures in parenthesis represent the asymptotic t-ratios for each
variable.
b
R2
=adjusted multiple R-squared statistic.
Sy/Y = standard error of the estimate divided by the mean of
dependent variable.
D.W. = Durbin-Watson statistic.
the
50
Table
6.
Comparison of
Structural and
Equations.a
the Root Mean Square Errors of the
ARIMA Wheat, Flour, and Bread Price
Statistlcb
Equation
RMSE
-2
R
Sy
PWH 1
.0416
( . 0456)
.9347
( .9224)
.0675
( .0734)
PWH 2
,0400
( .0430)
.9192
( . 9065)
.0645
(.0691)
PWH 3
.0642
(.0401)
.9380
( .9278)
.0642
(. 0690)
PKCF
.0523
( .0782)
.9616
( . 8920)
.0952
( . 1 599)
PBR
.1 750
(.1325)
.9587
(.9384)
.4025
(.4912)
a The top figures represent the structural equations and
figures in parentheses represent the ARIMA equations.
b RMSE =Root Mean Square Error of forecast.
-2
R = adjusted multiple R-squared statistic.
Sy = standard error of the estimate.
the
51
CHAPTER 5
SUMMARY AND CONCLUSIONS
The
purpose
of
this study was:
(1)
to
determine
the
dynamic
structure of economic variables that impact short-term (monthly) levels
of wheat prices (K.C.
retail
bread
relationships
(3)
to
prices;
HRW,
Minn.
DNS,
Port. SWW), flour prices, and
(2) to measure and analyze the distributed
both within and between these market level
compare the price forecasting performance of
model
incorporating
difference
while
equations
rational
and
structural
An econometric
and
nonstochastic
structural
equations,
the time series equations were estimated by an approximation
were
used.
flexibilities.
patterns
12 month,
24 month,
was
to
price
These price flexibilities reflected the distributed lag
adjustment process.
dependency
used
and long-run
of the endogenous price variables which facilitated
their
prices,
6 month,
of
Monthly data from June of 1977 to May of
The structural coefficient estimates were
calculate 3 month,
of
lags
was used to estimate the
the Box-Jenkins ARIMA method.
1984
distributed
prices;
each
equation with an alternative multivariate AR!MA model,
lag
Statistical tests revealed
nonexistent between monthly wheat,
flour,
but rather that a recursive structure existed.
analysis
that
joint
and
bread
That is, wheat
price determined flour price and flour price, in turn, determined bread
price.
economic
This stands in contrast to many agricultural commodities where
conditions in the higher market levels
(i.e.,
retail)
feed
52
Into the lower market levels (i.e., farm).
The
seasonal
terminal market wheat prices were estimated as a function
of
variables,
of
feedgrfilns,
fourth
exports
of
wheat,
lagged
exports
U.S.D.A. monthly wheat production estimates, and third and
order
difference
lagged
nonstochastlc
equation
was
difference
equations.
estimated for Port.
difference equations were estimated for K.C.
SWW
The
and
third
order
fourth
order
HRW and Minn.
DNS.
All
equations were estimated as Pascal distributed lags with positive first
order
serial correlation.
Exports of wheat and exports of feedgralns
Included contemporaneous values and lags of one period.
and
feedgrain
terminal
export
wheat
variables
prices,
indicating
occurred at lower market prices.
relatively
role
in
positive
exerted a
negative
Increases
In
Both the wheat
Impact
quantity
probably due to
The wheat production variable
relationship
wheat
expectations.
Total
prices,
stocks
which
of wheat
variable in determining monthly wheat prices.
flexibility
coefficient
demanded
wheats
livestock feeding.
theoretical
the
However, the asymptotic t-ratlos were
weak for feedgraln exports,
with
on
exceeded
was
minor
exerted
contrary
was
the
a
to
dominant
In particular, its price
twice the value of those
of
other
regressors.
Kansas
City
variables,
Income,
first
flour price was estimated as a function
lagged Kansas City wheat price,
estimated
by
autoregression
nonstochastic
rational
difference
distributed
a trend variable,
equation.
lags with
in the error structure.
seasonal
per capita U.S. disposable
quantity of flour milled per capita,
order
of
and a
The
structure
positive
first
order
Red
Winter
Kansas City Hard
was
53
Wheat price (contemporaneous and one period lag) was the most Important
variable
the
In determining flour price.
fact
This result Is consistent
that wheat Is the dominant raw product Input In the
with
milling
process and constitutes the largest portion of variable costs.
Retail
bread
variables,
per
price
was
estimated
as
a
function
contemporaneous and lagged Kansas City flour
capita
variable,
disposable
and
Income,
a price Index of
of
seasonal
price,
potatoes,
a first order nonstochastic difference
U.S.
a
trend
equation.
The
equation was likewise estimated by rational lags with a positive
order autoregressive error.
that K.C.
first
Basically, the statistical results showed
flour price was the most influential variable in determining
levels of bread prices within a sixth month period. However, beyond six
months
effects
disposable Income was most Important,
of demand (i.e.,
Indicating that
secular
as opposed to the Input side of the
market)
are more important In establishing bread price.
All
of
of the multivariate ARIMA models were estimated as a
the same set of lagged stochastic price variables,
seasonality
and
trend variable,
statistically
result
reverted
accounting
for
time effects In the data with binary variables and
a
respectively. The lagged price variables that were not
significant were omitted from each price
was that the price equations for Port.
back
function
to a univariate
autoregressive
SWW,
equation.
and retail
structure.
The
The
bread
price
equations for K.C. HRW, Minn. DNS, and K.C. flour more nearly reflected
a
multivariate
autoregressive
structure since an
price variable was included (Port.
SWW price,
additional
lagged
retail bread price, and
retail bread price, respectively). These results suggest that the ARIMA
54
models
are relatively efficient since past
wheat,
flour,
and
bread
prices appear to capture relevant economic and technical Information In
the market.
In
the
structural
observations
and ARIMA models,
made for each estimation method.
were
evaluated
the
multivariate
model
via
standard
price
prediction
performances of
Both
the
sample
predictions
prediction
ARIMA models were relatively close,
performances
of
forecast.
structural
with the
and
structural
demonstrated
parameter
In the truncation process and all RMSEs were less than their
errors
of
estimation
may
concluded
(for
this
efficient
if
short
researcher.
ana 1yzed
Their
calculated Root Mean Square Errors
performing only slightly better.
stability
recent
were sequentially truncated and then monthly
were
Overall,
the 12 most
be
forecast.
less
However,
(i.e.,
the
Since data
costly for
model)
term
that the
prediction
time
collection
series
ARIMA
were
and
equations,
approach
the
parameter
only
may
it
be
goal
Is
more
of
the
if the effect of grain policy decisions must be
impact
of a change In
the
government
.storage
program on wheat price) then a structural model is superior since there
is a description of cause-effect relationships.
Several concluding remarks are In order.
relationship of wheat,
short
run
framework.
First, in this model the
flour, and bread prices Is cast in a relatively
Consequently,
price studies based
on
longer
periods, such as quarterly or annual models, might negate the recursive
structure
and yield more of a jointly
dependent
system.
Second,
a
further refined model could provide additional Information for terminal
wheat prices determined by quantities divided Into different classes of
55
wheat;
however,
the
necessary data was not
available.
Third,
the
interpretation of the effect of wheat exports may be relatively obscure
since
it
income
farm
also
captures the effects of other variables
of importing countries,
programs.
Fourth,
ocean freight rates,
as
three
involved
however,
the
and six months may be valuable
parameter
equations
were
the
indirectly,
longer forecast periods
because
in producer grain marketing and holding
overall,
and
as
the Root Mean Square Errors of forecast were
estimated on a month to month basis;
such
such
estimates
In
the
of
the
decisions.
structural
not highly significant though most of the
time
Lastly,
wheat
price
coefficient
signs were theoretically correct and the adjusted R2 's were high.
The
strength
the
in
these
equations,
according to
the
t-ratios,
was
negative impact of stocks. However, its effect goes beyond the terminal
market
since wheat prices are instrumental in the
indirectly
equations
in the bread market.
flour
One can conclude that the
market,
structural
would serve as a base for likely direction and magnitude
wheat price changes (due to changes in the independent variables),
such measurements need to be interpreted with caution.
and
in
but
56
LITERATURE CITED
57
LITERATURE CITED
Arzac, E.R. "An Econometric Evaluation of Stabilization Policies for
the U.S. Grain Market." Western Journal of Agr. Econ. 4
(July 1979): 9-22.
Barr, T.N. "Demand and Price Relationships for the U.S. Wheat
Economy." Wheat Situation. United States Department of
Agriculture, Economic Research Service. WS-226, 1973, pp. 15-25.
Burt, O.R. "Nonstochastic Difference Equations,
Distributed
Lags, and Agricultural Supply." Dept. Agr. Econ. and Econ. Staff
Pap. No. 78-9. Montana State University, Bozeman. October 1978.
Burt, O.R. "Estimation of Distributed Lags as Nonstochastic
Difference Equations." Dept. Agr. Econ. and Econ. Staff Pap.
No. 80-1. Montana State University, Bozeman. January 1980.
Chow, G.C. Econometrics, McGraw-Hill, New York, 1983, pp. 188-189.
Jorgenson, D.W. "Rational Distributed Lag Functions."
Volume 32, No. 1, January, 1966, pp.135-149.
Econometrica,
Judge, G.G., R.C. Hill, W.E. Griffiths, H. Lutkepohl and T. Lee.
Introduction to the Theory and Practice of Econometrics,
First ed. New York: John Wiley and Sons, Inc., 1982, pp. 737-741.
Kahlon, A.S. "The Domestic Demand and Price Structure for Different
Classes of Wheat In the u.s.• unpublished doctoral dissertation,
Kansas State University of Agriculture and Applied Science, 1961.
Kmenta, J. Elements of Econometrics.
1971' pp. 487-491.
New York: Macmillan Co.,
Marsh, J.M. "A Rational Distributed Lag Model of Quarterly Live
Cattle Prices." Amer. J. Agr. Econ. 65 (August 1983): 539-547.
Rucker, R.R. "The Dynamics of Montana Beef Inventories."
unpublished Master's Thesis, Montana State University, Bozeman,
Montana, December, 1980.
Sims, C.A. "Distributed Lags.• Frontiers In Quantitative Economics,
Vol. II, M.D. Intrilligator and D.A. Kendrick, editors, NorthHolland Publishing Co., Amsterdam, 1974, pp.308-310.
Tomek, W.G., and Robinson, K.L. Agricultural Product Prices.
Seconded. Ithaca, NY, Cornell University Press, 1981.
58
U.S. Department of Agriculture. Economic Research Service.
Agricultural Outlook. A0-18-102. Washington, D.C., Government
Printing Office. 1977-1984.
U.S. Department of Agriculture.
Economic Research Service. Wheat
Outlook and Situation. Statistical Bulletins WS-247-273.
Washington, D.C., Government Printing Office. 1981-1983.
U.S. Department of Commerce. Bureau of Economic Analysis. Survey of
Current Business. Volumes 58-65. Washington, D.C., Government
Printing Office. 1977-1984.
U.S. Department of Labor. Bureau of Labor Statistics. Monthly Labor
Review. Volumes 100-107. Washington, D.C., Government Printing
Office. 1977-1984.
Vannerson, F.L. "An Econometric Analysis of the Postwar United
States Wheat Market.• unpublished doctoral dissertation,
Princeton University, 1969.
Wang, V.B. "The Demand and Price Structure for Various Classes
of Wheat.• unpublished doctoral dissertation, Ohio State
University, 1962.
Wold, H., and Jureen, L. Demand Analysis.
and Sons, 1953, pp. 60-70.
Westcott, P., D. Hull,
Quarterly Wheat Prices
Report, United States
Service, WS-268, 1984,
New York: John Wiley
and R. Green, "Relationships Between
and Stocks.• Wheat Outlook and Situation
Dept. of Agriculture, Economic Research
pp.9-13.
59
APPENDIX
60
Table
OBS
2
3
4
5
6
7
8
9
10
11
12
J3
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
n
33
34
35
36
37
38
39
40
41
7. Original Data Used in the K.C. HRW, Minn. DNS, Port.
SWW, K.C. Flour, and Retail Bread Price Equations.a
Consumer
Price
Index
.18180£+03
. 18260£+03
.18330E+03
. 18400E +03
.18450E+03
.18540E+03
.18610E+03
.18720E+03
. 18840E+03
.18980£+03
.19150E+03
.19330£+03
.19530E+03
.19670E+03
. 19780E+03
. 19930E+03
.20090£+03
. 20200E +03
. 20290E +03
.18720£+03
.18840£+03
. 18980E +03
.19150E+03
.19330E+03
.19530E:J"03
.19670£+03
.19780E+03
.19930£+03
.20090£+03
.20200£+03
.20290£+03
.23320E+03
.23640£+03
.24490£+03
.24250£+03
.24490£+03
.24760£+03
.24780£+03
.24940£+03
.25170E+03
.25390E+03
K.C.
HRW
Price
.23100£+01
.23500£+01
.23100E+01
.24700E+Ol
.25600E+01
.28100E+01
.28000E+01
.28200E+01
.28400£+01
.30700E+01
.32100E+01
.31200E+01
.31200E+01
.31400£+01
.31400£+01
.32400E+01
.34200E+01
.34800£+01
.33900£+01
.34200E+01
.35000£+01
.35200E+01
.35300£+01
.36400E+01
.41700£+01
. 43400£+01
.41200£+01
.42600£+01
.43900£+01
.45300E+01
.45100£+01
.43300£+01
.43200£+01
.40700E+01
.39000£+01
.41000£+01
.40700£+01
.42100£+01
.43100£+01
.44500£+01
.47000£+01
Minn.
DNS
Price
Port.
.24300£+01
.22900£+01
.22200£+01
.25100£+01
.26100£+01
.27100E+01
.26800E+01
.27300E+01
. 27200£+01
.28600£+01
.30800E+01
.31000£+01
.30600E+01
.29500E+01
.29600E+01
.30700E+01
, 32100E+01
.33200£+01
.31500£+01
.31200£+01
.31200E+01
.31800E+01
.32900£+01
.36200E+Ol
.42300E+01
.43100E+01
.41000£+01
.41800£+01
.43100£+01
.42700£+01
.41800E+01
.41600E+01
.41300£+01
.40400E+01
.39400E+01
.42100£+01
.41900£+01
.45400E+01
.42200£+01
.41700E+01
.46200£+01
.27900£+01
.28800E+01
.28800E+01
.28000E+01
. 27500E+01
.29100E+01
.29700£+01
.31700£+01
.33300£+01
.34100£+01
.36200E+01
.36000E+01
.36000E+01
. 37400£+01
.37200E+01
. 37700E+01
.37600E+Ol
.37600E+01
.37100£+01
.37000E+01
.36500E+01
.37000£+01
.37000£+01
.39100E+01
.44600£+01
.46700£+01
.44500E+01
.43100£+01
.41300£+01
.41600£+01
.41000E+01
.41000E+01
.42600£+01
.41300£+01
.40200£+01
.39100£+01
.39200E+01
.41500E+01
.40600E+01
.42300E+01
.44800E+Ol
sww
Price
K.C.
Flour
Price
.55800E+01
.58500E+01
.59100E+01
.60900E+01
.63200£+01
,65800E+01
.64900E+01
.69900£+01
.66800£+01
.69600£+01
. 72500E+Ol
.74600£+01
. 72300£+01
.76000£+01
. 75800E+01
. 75500E+Ol
. 76000£+01
. 79200£+01
. 77900E+Ol
. 75500E+01
. 77800E +0 1
.81800£+01
.81200£+01
,88000E';01
.90800£+01
. 10390E +02
. 10090E +02
. 10080E +02
.10100£+02
. 10600E +02
. 10460E +02
. 1OOOOE +02
. 10260E +02
,98100E+Ol
.94900£+01
.10010E+02
.98100E+01
. 10000£+02
.10110£+02
. 10480E +02
.10600E+02
a Observations 1-84 represent months of June 1977 to May 1984.
61
Table 7 (continued),
OBS
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
Consumer
Price
Index
K.C.
Minn.
Port.
HRW
DNS
sww
Price
Price
Price
.25620E+03
.25840E+03
.26050£+03
.26320E+03
.26900E+03
.26680£+03
.26900E+03
.27130E+03
.27440£+03
.27650E+03
.27930E+03
. 27990E+03
.28070E+03
.28150E+03
.28250E+03
.28340E+03
.28310E+03
.28430E+03
.28710E+03
.29060E+03
. 29220E+03
.29280E+03
.29330E+03
.29410E+03
.29360E+03
.29240£+03
.29310£+03
.29320E+03
.29340£+03
.29550E+03
.29710E+03
.29810E+03
.29930E+03
.30030E+03
.30180E+03
.30260£+03
.30310E+03
.30350E+03
.30520£+03
.30660£+03
. 30730£+03
.30880E+03
.30970E+03
.48900£+01
.45400£+01
.46000E+OI
.44700E+OI
.43500£+01
.44800E+OI
.43600E+OI
.42400£+01
.42500£+01
.41400£+01
.41900E+01
.43100£+01
.44600E+01
.43500E+01
.43300E+01
.42600E+01
.42500E+OI
.42800E+Ol
.42200E+Ol
.40600E+01
.37400E+Ol
.37000E+01
.37500E+01
.36100£+01
.38600£+01
.39800E+Ol
.40000E+OI
.40800£+01
.41800E+01
.42100E+Ol
.40500E+01
.39200£+01
.37100E+01
.38800E+01
.39000E+01
.38400E+01
.38200E+01
.38500£+01
.38100£+01
. 37100E+Ol
.38500E+Ol
.39300E+OI
.37200E+01
.47800£+01
.46200E+Ol
.46500E+OI
.45300£+01
.43200£+01
.44100E+Ol
.44400E+01
.42900E+01
.41800E+01
.40300E+Ol
.40700E+Ol
.42200£+01
.42900£+01
.41500E+01
.42100£+01
.41700E+01
.41000E+Ol
.42100E+Ol
.41600E+01
.40800E+Ol
.40800E+01
.37800E+Ol
.37900£+01
.37800£+01
.38500E+01
.37600E+Ol
.38000£+01
.38200E+01
.40100E+01
.43400E+01
.42500E+01
.41500E+Ol
.40700E+01
.42100£+01
.43000E+01
.43300£+01
.42300E+01
.42100E+01
.41500E+Ol
.40600£+01
.42000E+Ol
.42800E+01
.43900E+01
.46800£+01
.44000E+OI
.45200E+OI
.45200E+OI
.44100£+01
.45100E+OI
.44100£+01
.42600E+OI
.42700£+01
.42500E+01
.42100E+01
.43800£+01
.44200£+01
.40000E+01
.41200E+OI
.40900E+01
.41200E+01
.41400E+Ol
.42400E+Ol
.41800E+Ol
.41300E+01
.41600E+01
.42900E+01
.42900E+01
.44400E+Ol
.44500£+01
.45200E+01
.45900E+OI
.46800E+01
.46200E+Ol
.43500£+01
.41500E+01
.40800£+01
.40600E+01
.41200E+01
.40300£+01
.39000E+01
.38100£+01
.37900£+01
,36900£+01
.37300£+01
.40300E+Ol
.40500E+OI
K.C.
F 1our
Price
. 10680£+02
. I 0350E+02
. I 0660E+02
. I 0400£+02
.10280£+02
.10530£+02
.10310E+02
.10530£+02
. I 0280E +02
. 10300E +02
.10200E+02
• 10020£+02
. I 031 OE +02
. 10050E +02
.10640E+02
. 10700E+02
. I 0640E+02
.10420E+02
.10330E+02
• 10260E +02
.10210E+02
.99800E+01
.10120E+02
.99600£+01
.99200E+Ol
. 10300E +02
. 10200E+02
. 10490E+02
. 10500E +02
.10160E+02
.10350E+02
.10390E+02
.10380£+02
. 10340E +02
.10330£+02
. 10300E +02
.10020£+02
.96800£+01
.98700E+Ol
. 10030E +02
.10120E+02
. 10070E+02
.10120E+02
62
Tab 1e 7 (continued).
OBS
Population
Quant lty
of Wheat
Stocks
1
2
3
4
5
6
7
8
9
10
II
12
13
14
15
16
.21667£+03
.21682£+03
.21699£+03
.21716£+03
.21733£+03
.21748£+03
.21761E+03
.21774£+03
.21784£+03
.21794£+03
.21809E+03
.21822E+03
.21836E+03
.21850£+03
.21867E+03
.21886E+03
.21903E+03
.21919£+03
.21934E+03
.21953£+03
.21967£+03
.21978£+03
.21993£+03
.22009£+03
.22025E+03
.22058£+03
.22078£+03
. 22099E+03
.22118£+03
.22136E+03
.22155E+03
.22172E+03
.22187£+03
. 22200£+03
.22217E+03
.22235E+03
.22261E+03
.22281E+03
.22301£+03
.22324E+03
.22345£+03
.22848£+03
.11108£+04
.14322£+04
.17536£+04
.20750£+04
.23965£+04
.22623£+04
.21281£+04
.19938£+04
.18384£+04
.16830£+04
. 15277£+04
.13522E+04
.11767£+04
.14168£+04
. 16569E+04
. 18970£+04
.21370E+04
. 19686E +04
. 18002£+04
.16318£+04
. 14963£+04
.13606E+04
.12249£+04
.10747£+04
.92450£+03
.12611£+04
. 15977£+04
• 19343€+04
. 22708£+04
.20859£+04
. 1901 OE+04
.17162£+04
.15525E+04
.13888£+04
.12251E+04
. I 0635E+04
.90200£+03
.12946£+04
.16872£+04
.20798£+04
.24723£+04
.22826E+04
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
Quant lty of
Feedgraln
Exports
Quantity
of Wheat
Exports
u.s. Wheat
Production
Estimate
.39000£+01
.41000£+01
.41000£+01
.46000£+01
.38000£+01
.46000E+OI
.53000£+01
.42000E+01
.43000E+OI
.51000E+01
.51000E+OI
.60000£+01
.58000£+01
.50000£+01
.52000£+01
.48000£+01
.39000£+01
.44000E+OI
.45000E+01
.42000£+01
.43000£+01
.49000£+01
.53000£+01
.58000£+01
.61000£+01
.60000£+01
.62000£+01
.54000£+01
.63000£+01
.65000£+01
.65000£+01
.59000£+01
.58000£+01
.61000E+01
.65000E+OI
.51000£+01
.57000£+01
.57000£+01
.59000£+01
.58000£+01
.69000E+01
. 70000E+OI
• 77073£+05
.83657£+05
. 93432£+05
.11063£+06
.69107£+05
.57565E+05
.87368£+05
.64819£+05
.94669E+05
.10547E+06
. I 0329E +06
.12006E+06
. 10893E +06
.10611 E+06
.13192E+06
.11961E+06
.11552E+06
.92392E+05
.90027£+05
. 70400£+05
.67106£+05
.75548£+05
. 76961£+05
.78306£+05
.10461 E+06
.13328£+06
.11779£+06
.12962£+06
.14904£+06
. 10888E+06
.11488£+06
.82683£+05
.89526E+05
.94735£+05
.98327£+05
.88579£+05
.96193£+05
.12360£+06
. 14141 E+06
.13732£+06
.11695£+06
.11220£+06
.55100E+02
.55600£+02
.55600£+02
.55200E+02
.55200£+02
.55200£+02
.55200£+02
.55100£+02
.55100E+02
.48100£+02
.48100E+02
.48800E+02
.48800£+02
.49500£+02
.49500£+02
.48700E+02
.48400E+02
.48400£+02
.49000E+02
.49000E+02
.49000E+02
.49000£+02
.49000£+02
.49000£+02
.49000£.;.02
. 5 7200£+02
.58100£+02
.57800£+02
. 5 7500E +02
.57500£+02
.57500£+02
.58300£+02
.58300£+02
.58300E+02
.58300£+02
.61800£+02
.61800£+02
.63100£+02
.63300£+02
.64100£+02
.64300£+02
.64300£+02
63
Table 7 (continued).
085
Population
Quantity
of Wheat
Stocks
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
.22865£+03
.22883£+03
. 22898£+03
.22912£+03
.22928E+03
.22944£+03
.22962£+03
.22980£+03
.23003£+03
.23026£+03
.23048£+03
.23067E+03
.23084£+03
.23101E+03
.23118£+03
.23138£+03
.23154£+03
.23170E+03
.23188E+03
.23206£+03
.23228E+03
.23250£+03
. 23270E+03
.23290E+03
.23308£+03
.23327E+03
.23343£+03
.23357£+03
.23374E+03
.23389E+03
.23407£+03
.23423£+03
.23467£+03
.23488E+03
.23522£+03
.23538£+03
.23555£+03
.23571£+03
.23588£+03
.23603E+03
.23620£+03
.23636E+03
. 20929£+04
.19032£+04
.17117E+04
.15202£+04
. 13286£+04
.11587£+04
.98880£+03
.14254£+04
. 18620£+04
.22986£+04
.27352£+04
.25495£+04
.23638£+04
.21780£+04
.19710£+04
.17640£+04
.15571E+04
.13605E+04
.11639E+04
.16197£+04
.20755£+04
.25313£+04
. 29871 E+04
.28315£+04
.26759E+04
.25210E+04
.23060E+04
.20920E+04
.18770E+04
.17090£+04
.15410£+04
.18973£+04
.22535E+04
.26098E+04
.29660£+04
.27527£+04
.25393£+04
.23260£+04
.21360E+04
.19460E+04
.17560E+04
.15660E+04
77
78
79
80
81
82
83
84
Quantity ot
Feedgrain
Exports
Quantity
ot Wheat
Exports
U.S. Wheat
Production
Estimate
.68000E+01
.62000£+01
.61000E+01
.60000E+01
.53000E+01
.60000E+Ol
,46000£+01
.47000£+01
.47000£+01
.49000£+01
.61000E+01
.51000£+01
.54000£+01
.48000£+01
.44000£+01
.56000£+01
.54000£+01
.58000E+01
,50000E+01
,37000£+01
.37000£+01
.34000£+01
.48000E+01
.49000E+01
.52000E+Ol
.53000E+01
.46000£+01
.49000£+01
.42000£+01
.41000E+01
.42000£+01
.36000£+01
.37000£+01
.46000£+01
.47000E+OI
.57000E+Ol
,53000£+01
.53000£+01
.48000E+O!
.54000E+OI
.50000E+01
.46000E+Ol
. 13205£+06
. 12998E +06
.12440£+06
.12877£+06
.12765£+06
. 78030E+05
.12452£+06
.13817£+06
.14543£+06
.19415£+06
.15699£+06
.12749£+06
.13776£+06
.12416£+06
.13872£+06
.14908E+06
.14818E+06
.11660E+06
.14591£+06
. I 1791£+06
.12434E+06
. 13099E +06
.98520E+05
.94638£+05
.88457£+05
.14314£+06
. 14659E+06
.13113£+06
.11245E+06
.96235E+05
.11351£+06
.11670E+06
.87823E+05
. 11926£+06
.11481£+06
.10288E+06
. 1 2889E+06
.11836E+06
.11110£+06
.1!871£+06
.97132£+05
.11281E+06
.64300£+02
.64500E+02
. 64500E-t02
.64500£+02
.64500£+02
. 73600£+02
. 71800E+02
.76500E+02
.74800£+02
.74800E+02
.74800£+02
.74800£+02
. 74800E+02
.76000£+02
.76000£+02
.76000£+02
. 76000£+02
. 721 OOE+02
. 73900£+02
.73800£+02
.75400E+02
.76600E+02
.76500£+02
. 76500£+02
.76500£+02
. 76400£+02
.76400E+02
.76400£+02
.76400£+02
.64000£+02
.63800E+02
.66300E+02
.66000£+02
.65500£+02
.65500E+02
.65500E+02
.65500E+02
.66000£+02
.66000E+02
.66000£+02
.66000£+02
.69400E+02
64
Tab 1e 7 (continued) .
OBS
2
3
4
5
6
7
8
9
10
11
12
I3
14
I5
16
I7
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
Disposable
Income
Ret a i 1
Bread
Price
Wage of
Flour Mi 11
Workers
. 13026E+04
.13222E+04
.13317E+04
.13424E+04
.13558E+04
.13679E+04
.13799E+04
.13825E+04
.13949E+04
.14166E+04
.14330E+04
. 14399E+04
.14493E+04
.14702E+04
.14825E+04
.14936E+04
.15!31E+04
.15294E+04
.15504E+04
.15648E+04
.15785E+04
.15972E+04
.16024E+04
.16105E+04
.16254E+04
.16503E+04
. 16664E+04
.16747E+04
.16944E+04
.17109E+04
.17251E+04
.17569E+04
.17633E+04
.17751E+04
.17756E+04
.17838E+04
.17930E+04
.18249E+04
.18377E+04
.18592E+04
. 18802E+04
.18977E+04
.40200E+02
.40600E+02
.40600E+02
.40700E+02
.40500E+02
.40400E+02
.40900E+02
.39900E+02
.40100E+02
.40200E+02
.40300E+02
.41200E+02
.41900E+02
.42000E+02
.42400E+02
.42400E+02
.42800E+02
.43500E+02
.44000E+02
.44400E+02
.44600E+02
.44900E+02
.45200E+02
.45400E+02
.45700E+02
.46600E+02
. 47700E+02
.48200£+02
.48600£+02
.49100E+02
.49800E+02
.50100E+02
.50700E+02
.50200E+02
.50700E+02
.50400E+02
.50300E+02
.51100E+02
.50700E+02
.51100E+02
.51400E+02
.51900E+02
.58300E+01
.59300E+OI
.60300E+OI
.62000E+OI
.62100E+Ol
.64000E+Ol
.63900E+OI
.64000E+OI
.63800E+OI
.64300E+OI
.64400E+OI
.64900E+Ol
.65300E+OI
.66800E+Ol
.68500E+OI
. 71100£+01
. 70800E+01
.71700E+01
. 71100E+Ol
.69400E+01
.69900E+Ol
.69200E+Ol
.68300E+01
.68900E+Ol
.69000E+Ol
.70400E+OI
. 71700E+Ol
.73700E+01
. 75000E+O!
.76100E+Ol
. 75800E+OI
.73600E+Ol
, 73600E+Ol
. 74600E+Ol
.75800E+OI
.75400E+Ol
. 76200E+01
.78300E+Ol
. 79100E+Ol
. 79200E+Ol
. 79200E+Ol
.81500E+Ol
65
Table 7 (cont l nued J o
OBS
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
Disposable
Income
o19131E+04
o19314E+04
o19466E +04
19654£+04
o19756E+04
o19849E+04
o19963E+04
o20554E+03
o20432E+04
o20573E+04
20804£+04
o20929E+04
o20921E+04
o21092E+04
o21175E+04
o21244E+04
o21463E+04
o21525E+04
o21556E+04
o21948E+04
o21967E+04
o22027E+04
o22119E+04
o22287E+04
o22323E+04
o22532E+04
o22482E+04
o22665E+04
o22868E+04
o23038E+04
. o23124E+04
o23518E+04
o23644E+04
o23861E+04
o24103E+04
o24269E+04
o24487E+04
o24822E+04
o25045E+04
o25197E+04
o25452E+04
o25541E+04
0
0
Retail
Bread
Price
Wage of
Flour Mill
Workers
o51900E+02
o53100E+02
o53300E+02
o53800E+02
o51900E+02
o52500E+02
o52300E+02
o52100E+02
o51900E+02
o52400E+02
o52100E+02
o52700E+02
o52100E+02
o53700E+02
o53400E+02
o52600E+02
o52600E+02
o52900E+02
o52500E+02
o53400E+02
o53400E+02
o53600E+02
o53400E+02
o53400E+02
o53700E+02
o53800E+02
o54000E+02
o54400E+02
o54500E+02
o54600E+02
o54700E+02
o54900E+02
o54700E+02
o54600E+02
o55000E+02
o55500E+02
o55600E+02
o56000E+02
o55600E+02
o55900E+02
o55800E+02
o56200E+02
o80200E+01
o80000E+01
o80100E+01
79700£+01
o80400E+01
o80300E+01
o81900E+01
o82200E+OI
o84400E+01
o85500E+01
o84600E+01
o84600E+01
o85500E+01
o86400E+01
o87500E+01
o87800E+01
o88300E+01
· o87800E+01
o87200E+OI
o91400E+01
o93100E+01
o94200E+01
o93600E+OI
o94500E+01
o93800E+OI
o93800E+OI
o94400E+OI
o94600E+01
o94400E+01
o95500E+01
o95500E+OI
o97200E+01
o98700E+01
o99700E+01
o99400E+Ol
o10040E +02
o10110E+02
oi0150E+02
o10130E+02
oI 0060£+02
o10180E+02
o99900E+Ol
0