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A Linear Rational Expectations Model of the
U.S. Soybean Oil Market
presented by

Ernesto Santiago Liboreiro

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6/01 c:/CIRC/DateDue.p65-p. 15

A LINEAR RATIONAL EXPECTATIONS MODEL OF THE U.S.
SOYBEAN OIL MARKET

BY

Ernesto Santiago Liboreiro

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Agricultural Economics Department

2000

ABSTRACT

A LINEAR RATIONAL EXPECTATIONS MODEL
OF THE U.S. SOYBEAN OIL MARKET

BY

Ernesto Santiago Liboreiro

In this study a linear rational expectations storage
model of the U.S. soybean oil market is estimated. An
inventory demand equation is specified to linearly depend
on the expected appreciation in stocks value. Model
estimation requires the solution of an expectational
difference equation and computation of the multi-step ahead
forecasts of exogenous variables. The later are solved
analytically by repeated substitution, making use of the
stochastic processes governing exogenous variables. The
simultaneous nature of prices and inventories determination
requires the use of FIML estimation method. Results
obtained show statistical significance in the speculative
inventory demand slope parameter and demonstrate that good
results can be obtained for soybean oil storage using a
linear model. A test of the rational expectation cross-
equation restrictions only gave a p—value of 0.01,
suggesting that these restrictions would be rejected at

conventional significance levels.

To Ernesto (Dad), Cristina (Mom),
Mariana and Christine

iii

ACKNOWLEDGMENTS

What started as a very interesting project became an
endless task full of frustrations, disappointments and
obstacles, only compensated with the constant help of my
Major Professor, Robert J. Myers. I only arrived to a safe
harbor, because of his help. My thanks to him. I am also
grateful to Steven Hanson and Jack Meyer, for their
valuable comments on the work done.

I want and must thank the three people that helped
decisively me to put an end to this project: Christine
Martin for her unconditional support throughout the last
four months, David Mather for his friendship and
"logistical" help and Nicolas Liboreiro, my son, whose mere
one and a half years of existence was the inspiration I
needed to get up every morning and work in what for moments
seemed to be an endless project.

My gratitude also goes to Michigan State University
and the MSU Agricultural Economics Department. You educated

and nurtured me. My deepest thanks to you.

iv

TABLE OF CONTENTS

LIST OF TABLES
INTRODUCTION
CHAPTER 1, THE U.S. SOYBEAN COMPLEX
1.1. Soybean market
1.2. Soybean oil market
1.3. Soybean meal market
CHAPTER 2, LITERATURE REVIEW
2.1. Soybean complex structural models
2.2. Rational expectations inventory models
2.3. Applications of dynamic programming
to soybean markets
2.4. Crushing rates and margins
CHAPTER 3, ECONOMIC MODELS OF COMMODITY MARKETS
3.1. Demand
3.2. Supply
3.3. Inventory demand
3.3.1. Speculative motivation
3.3.2. Convenience yield
3.4. Commodity market model
CHAPTER 4, MODEL SPECIFICATION
CHAPTER 5, ESTIMATION RESULTS
5.1. Data
5.2. Exogenous variables processes
5.3. The complete model
5.4. Econometric procedures
5.5. Results
5.6. A test of the rational expectations
restrictions
5.7. Limitations of the study
Chapter 6, Conclusions
Annex I
Annex II
Annex III
Bibliography

Page
vi

11
11
15
21
24
24
32

38
41
43
43
48
50
51
57
60
62
75
75
76
78
78
80

83
84
87
90
101
105
107

Table

Table

Table

Table

Table

Table

Table

Table

Table

LIST OF TABLES

U.S. Oils and fats usage, 1996

1995/96 Quarterly U.S. Soybean Oil Balance
Own Price elasticities

Inventory demand studies

U.S. Soybeans: Own Price elasticities
Exogenous variable AR(1) processes

ADE test on EXPEN, CRCAP and RFFR variables
FIML parameter estimates

R? and residuals tests

vi

16

21

27

36

49

76

77

80

81

INTRODUCT I ON

Much of the research in commodity price analysis
during the last twenty years has been devoted to
understanding the role of inventory demand on price
determination. Importantly, there is a simultaneous
determination of prices and inventories: inventory demand
affects current prices and current prices affect inventory
levels.

Inventories, in turn, are not just the mere
consequence of current production and consumption
imbalances, but are affected by specific factors like
speculative stockholding and "convenience yield".

If prices are expected to climb, storers may look for
increased stockholding in order to profit by carrying goods
forward in time while bidding up current period prices.
Thus, expectations about future prices affect current
prices through inventory demand (Muth, 1961; Gosh, Gilbert
and Hughes-Hallett, 1987; Wright and Williams, 1991).

Convenience yield is also considered an important
factor. Agents may want to hold stocks even with the
expectation of decreasing prices because the costs
associated with a "stock-out" are greater than the expected

speculative losses (Working, 1949; Brennan, 1959). Thus,

some minimum (pipeline) stocks would be held as a
cautionary measure.

This is important because much of the policy efforts
aimed at to price stabilization in commodity markets has
been made on the assumption that private inventory demand
does not play a significant price stabilizing role. Much of
the research of the 1950's and 1960's provided theoretical
support to buffer schemes on the assumption that there was
no private storage industry at all (Waugh, 1944; Oi, 1961).

A major concern in these research efforts has been
how to model price expectations. Much of the debate has
centered on whether expectations about future prices are
constructed looking backward in time or looking forward.
Muth (1961) provided reasonable arguments favoring forward
looking behavior (i.e. "rational" expectations). The
success of Muth's idea lies in the “elegance” of the
concept, in the sense that it provides a sensible approach
to making expectations endogenous. If agents are assumed
rational in choosing decision variables, they should also
be rational in making forecasts, thus using all knowledge
available about the actual model that determines market
price and quantity behavior. Much recent econometric work
has assumed that agents form expectations consistent with

the model (rational expectations).

Papers by Wallis (1980), Hoffman and Schmidt (1981)
and Chow (1981) provided the statistical underpinning for
rational expectations econometric models in a linear
framework. Since then, much econometric effort has been
devoted to studying inventory demand effects on market
equilibrium, implementing the so-called “linear rational
eXpectations inventory model” (Hwa, 1985; Gosh, Gilbert
and Hughues-Hallett, 1987; Trivedi, 1990; Gilbert and
Palaskas, 1990, Lord, 1991; Thurman, 1993; and Gilbert,
1995). The goal of these studies has been to show that the
speculative component of inventory demand plays a role in
spot price determination. The basis for all of these
studies has been Muth's (1961) commodity price model with
inventories.

The linear approach is subject to the criticism that
it does not account for the non-negative stocks
constraint. Although based on theoretical considerations
it is possible to argue that speculative inventory demand
increases linearly in respect to expected price
appreciation of stocks, it is also true that if the
expected price appreciation is zero or negative,
speculative inventory demand would be zero. Because stocks

cannot be negative for physical reasons, there is a

nonlinear relationship between expected price appreciation
in stocks and inventory demand levels.

Consequently, a linear representation of inventory
demand may not fit the actual characteristics of a
storable commodity market. This is sometimes blamed for
poor econometric results from linear rational expectations
storage models of commodity markets (Glauber and Miranda,
1993). Specifically, it has been rather difficult to
obtain statistically significant parameter estimates on
the speculative component of inventory demand. Researchers
have repeatedly failed to obtain statistically significant
evidence of inventory demand’s role in commodity price
determination (Gilbert and Palaskas, 1990; Trivedi, 1990).

Algorithms for estimating non-linear rational
expectations models appeared in the early eighties (Fair
and Taylor, 1983, 1991). The non-linearities in many
economic models do not allow a closed form solution. Thus,
numerical optimization techniques are required. The
implementation of these techniques in estimating commodity
market models that include non-linear inventory demand has
been successful (Miranda and Glauber, 1993).

However, the costs involved in this approach in terms
of computer power required and its intractability are quite

high. The computational costs grow quite rapidly as the

number of state variables increase. This has lead many
researchers to continue working in a linear framework
consistent with Muth’s work. In fact, stock-out episodes
are rare and researchers should expect to find evidence of
speculative inventory demand (Deaton and Laroque, 1990).
There are other problems besides a linear
specification that might explain poor econometric results
from rational expectations commodity storage models. In

particular:

1) Most studies used annual data (Gilbert and Palaskas,
1990, Trivedi 1990, Lord, 1991; Gilbert 1995). It may be
difficult to capture the inventory demand effect using
annual data. Although some commodities can be stored for
more than one year, it is reasonable to argue that
speculative demand is mostly a short run phenomena
(Trivedi, 1990). If this is the case, the use of expected
appreciation in annual prices as an explanation of the
end-of—period inventories may not be a sensible approach.
It is difficult to argue that speculators base their
storage decisions on expectations of annual average price
appreciation.

Also, when using annual data, the number of

observations may be small thus making it difficult to

uncover statistical evidence of relationships among
variables. Making use of long data series is an issue in
itself because the non-linear cross equation restrictions
implied by the rational expectations hypothesis clearly
calls for the use of non-linear estimation methods. If
maximum likelihood methods are used, large samples are
required, since standard errors are biased when working

with small samples.

2) The econometric implementation of the rational
expectations hypothesis has also brought problems in
previous studies. Much of the focus has been placed on the
price behavior implications of the model without
considering the remaining structural equations as
informative (Gosh, 1987; Gilbert and Palaskas, 1990;
Trivedi 1990). None (with the exception of Gilbert, 1995)
estimate a complete commodity market model imposing the
rational expectations cross-equations restrictions nor do
they recover the underlying structural parameter
estimates.

3) Some studies (Gilbert and Palaskas, 1989) have relied
on Ordinary Least Squares or Non Linear Least Squares
methods instead of Full Information Maximum Likelihood.

This fails to account for price and stock simultaneity and

results in biased and inconsistent parameter estimates.
The simultaneous nature of price and stock level
determination requires the use of simultaneous equation

estimation methods.

4) Other studies have essentially estimated/applied the
same model to different commodities, thus failing to take
account of the unique features of different commodity
markets (Gilbert and Palaskas, 1990; Trivedi 1990; Lord
1991). The unique features of each market must be
addressed in order to obtain good econometric results.
"One size fits all" is not a sensible approach because
misspecification in one equation may spill over and affect
parameter estimates in other equations when using

simultaneous estimation methods.

5) Other studies have estimated models for commodities
that have faced a great deal of government intervention,
such as price stabilization schemes (Trivedi, 1990).
Modeling these markets without accounting for government

actions may result in poor results

The present study estimates a model of the U.S.

soybean oil market assuming price expectations are

rational. The attempt is to study whether, overcoming many
difficulties of other studies, a statistically significant
and economically meaningful estimate of the parameter on
expected price appreciation can be obtained under a linear
specification of inventory demand. We show that the
linearity issue is not a major obstacle to obtain
statistically significant empirical estimates of the
inventory demand equation.

The U.S. soybean oil market is suitable for
conducting this study because there is evidence of stock-
out events and forward looking behavior among stock
holders (Lence, Hayes and Meyers, 1995).

Much of the existing empirical work on the soybean oil
market has relied on inventory demand specifications that
are not well supported by economic theory. In particular,
models of the soybean oil market have specified inventory
demand equations as a function of several variables that
enter in linear and unrestricted form, without imposing
rational expectations restrictions (Vandeborre, 1967;
Houck, Ryan and Subotnik, 1972; Meyers and Hacklander,
1979; Wesscott and Hull, 1985; Meyers, Helmar and Devadoss,
1986). Some studies have introduced an explicit price
expectation variable in soybean oil models and assumed

rational expectations. However, these studies (eg. Lence,

Hayes and Myeres, 1995) use futures prices to model price
expectations and assume futures prices as exogenous. The
present study is the first one to apply full linear
rational expectations storage model with endogenous price
expectations to the U.S. soybean oil market.

Our study also represents an improvement over
previous studies of linear speculative inventory demand
for several reasons. In this study we make use of a long
data series of 71 quarterly observations, and directly
estimate all structural parameters of the model. Both the
model and the exogenous variables stochastic processes are
estimated simultaneously, thus imposing the cross equation
restrictions and obtaining efficiency gains in parameter
estimates. We make use of FIML estimation methods to
account for simultaneity. In the course of estimation, we
impose the implied root restriction and we model supply I
and demand taking into account the particular features of
the soybean oil market (contemporaneous supply response,
no partial adjustment, etc.).

Estimating such a model calls for the solution of an
expectational difference equation in prices. Prices end up
being a function of the stable root of the polynomial in
the lag operator and the multi-step ahead forecast of

exogenous variables. The latter are turned into observable

variables by making use of the stochastic properties of
the variables. Multi-step ahead forecasts of exogenous
variables are computed by repeated substitution.

The approach followed in this study is subject to the
criticism that it is not “truly rational” in the sense
that expectations about the future path of exogenous
variables depend only on their past (their stochastic time
series properties). It has been suggested (Wright and
Williams, 1991), however, that this approach generates
consistent parameter estimates.

The study starts with a description of the U.S.
soybean complex focusing particularly on the soybean oil
market. The second chapter presents a review of the
literature. The third chapter covers commodity market
modeling and the fourth outlines the model specification
used in this study. Chapter five presents the estimation
results. In the last chapter we summarize and draw
conclusions. Annexes I and II present mathematical work,

and Annex III, introduces data descriptive statistics.

10

CHAPTER 1

THE U.S. SOYBEAN COMPLEX

1.1 Soybean market

Although soybeans have been cultivated in the U.S.
since the early 20”‘century, it was not until the early
1950's when they became an important part of American
agriculture, accounting for more than 10% of total
agricultural land devoted to corn, wheat and soybeans. By
1995 that share rose to 31% (U.S. Statistics Annuary,
1999), production value reached 14.6 billion dollars and US
soybean production represented 47.4% of world soybean
production (USDA, Oil Crops Yearbook, 1999).

Soybeans are an annual crop, cultivated at the end of
spring-early summer and harvested by the end of summer and
early fall. After harvest, the crop is consumed throughout
the year on a season that extends from September to August.
Good soil fertility, timely rains and good moisture
conditions are required for proper plant growth. Those
conditions are met in several U.S. states, including
Illinois, Iowa, Indiana, Michigan and Minnesota.

Soybean production has doubled every ten years from
the 1950's until the 1980's and in the first half of 1990's

has stagnated at near 2 billion bushels (bill. bu.). This

11

stagnation is, in part, due to the growth in south American
soybean production. More recently, worldwide income growth
and China's import demand sparked renewed growth in
American soybean plantings and production which reached an
all time high level of 2.75 bill. bu. in the 1998/89
season.

As for any storable good, soybean demand sources
include demand for current consumption and storage demand.
The bulk of current consumption demand comes from the
crushing industry. Soybeans are the main input for the
simultaneous production of crude soybean oil and soybean
meal, both of which are produced in almost fixed
proportions: 18% and 80% respectively (i.e. one soybean ton
crushed yields 180 kilos of oil and 800 kilos of meal).

Crushing is a rather simple process that originally
extracted the oil and meal content of soybeans using a
hydraulic pressing technique (mechanical extracting) and
latter evolved towards chemical extraction (solvent
extraction). Soybeans are cracked and de-hulled before they
are crushed and flaked. When crushed, some portion of the
oil contained by soybeans is extracted, although some oil
still remains in the flakes. The remaining oil is then
removed from the flakes by solvent extraction after which,

the flakes are de-solventized, toasted and ground to obtain

12

48% protein soybean meal. Lower protein contents are
obtained by mixing back the hulls into the meal. As part of
the process the oil is degummed to obtain degummed soybean
oil ready for refining. Hulls are mostly sold as feed
material and gums obtained from degumming are sold to
lecithin producers. Both hulls and gums represent a very
small portion of soybean crusher's revenue. In 1995/96
crushing accounted for 54.4% of total soybean demand in US,
with the remaining going to exports (33.8%), seed use
(2.8%), residual usage/shrinkage (1.4%) and inventories
(7.2%) according to USDA data (Oils Crops Yearbook, 1999).

The two main products obtained from soybean crushing
have very different characteristics regarding production
and inventory demand compared to the soybeans themselves.
First, although soybeans are an annual crop, both oil and
meal are continuously produced goods, since crushing
extends throughout the season. Second, while soybean oil is
a storable commodity, soybean meal is non-storable.

It is also very important to note that, since both
products (oil and meal) are the simultaneous result of
soybean crushing, not only soybean availability impacts the
supply of products (and their prices) but also demand'
conditions in one product have an impact in the supplies of

the other product. To illustrate, an increase in soybean

l3

meal demand would generate an increase in prices along the
supply curve of soybean meal, inducing expanded crushing
rates which in turn yields increases in soybean oil supply
and consequently lower oil prices.

Crushing takes place in very specialized factories.
Given the additional investment costs to be incurred for a
multi-seed operation, most soybean crushing facilities can
only crush one seed type, making it difficult to use
alternative inputs (cottonseed, sunseed, rapeseed, etc.).

Processing returns along with crushing capacity drive
crushing rates. Returns are composed of the difference
between revenue generated by sales of soybean oil and meal
minus the acquisition costs of beans. This difference is
usually called Gross Crushing Margin. Once processing costs
are deducted the Net Crushing Margin (the actual profit of
the operation) appears. Variable processing costs include
mainly labor, fuel, solvent and power.

Gross crushing margins averaged 95 cents per bushel
crushed over the 1988/89 to 1997/98 seasons based on 44%
protein soybean meal. The relative importance of oil and
meal sales in total annual revenue can be measured by the
oil share of product value, which averaged 34.8% and
fluctuated between 28% and 47% in the same period (USDA,

Oil Crops Yearbook, 1999).

14

Crushing capacity has grown since the sixties but the
number of crushing facilities has fallen, according to ERS
and Census data. Total annual soybean crushing capacity in
1995 was 1.8 billion bushels which compared to 1.4 billions
bushels in 1980, based on National Oilseed Processors
Association. Both years recorded utilization ratios near
74%.

Soybean price determination is the result of many
forces including carry-in stocks, current period’s soybean
production, exports, seed usage, crushing capacity, oil and
meal demand, and storage demand. Product prices are the
result of supply and demand forces evolving from each of
these different components of the soybean complex. Most
important is the issue that soybeans are the main input for
producing soybean oil. As such, soybean prices have a

strong impact on soybean oil supply.

1.2. Soybean oil market

In calendar year 1996 a total of 15,447 million pounds
(mill. lbs.) of crude soybean oil were produced of which
1,256 were exported and 13,658 were consumed domestically
(an increase of 618 mill. lbs. in stocks took place and
94.1 mill. lbs. were imported in the period). A total of

996 mill. lbs. were consumed in several other non—refined

15

uses and the remaining 12,662 mill. lbs. were consumed in
crude refining. That is, more than 90% of crude oil
domestic use is in the manufacture of refined oil products
for food consumption. Production of refined soybean oil
reached 12,274 mill. lbs. (there is about 5% weight loss in
refining). A total of 12,322 mill. lbs. were used in the
manufacture of end products (more refined oil was used than
produced because of a slight reduction in refined oil

stocks). Major soybean oil uses are shown in table 1.

Table 1

U.S. Oils and fats usage, 1996
(in million pounds)

 

 

Usage Manufac- Oils and Soybean Percen-
ture of fats use oil use tage

Salad and

Cooking oils 6,641 6,717 5,508 81

Baking and

frying oils 5,823 5,935 4,690 77

Margarine 2,480 1,847 1,694 91

Other , 361 125 51

Inedible 6,018 305 5

Total 12,322

 

Source: USDA, Oil Crops Yearbook, 1996 and Census Bureau of
Statistics, Industrial Reports, M20K9613

16

Table 1 shows the great importance of soybean oil in
the manufacture of salad and cooking oils, baking and
frying oils and margarine producing as it accounts for
about 80% of input usage in the manufacture of these
products. In fact, the mentioned products represent 84% of
total fats and oils domestic consumption in food products
(18,187 mill. lbs.).

Growth in domestic soybean oil consumption has been
due to population and per capita income growth, but also
has been fueled by the increasing use of vegetable fats as
a source of caloric intake. The increased consumption of
poultry and fish in place of red meats has reduced animal
fat intake.

Total domestic crude soybean oil consumption rose from
9,113 to 13,465 mill. lbs. in 1980/81-1995/96 seasons
period. Increased consumption was paralleled by increased
domestic production which rose by an accumulated annual
rate of 2% in the same period (USDA, Oil crops Yearbook,
1999).

Soybean oil faces competition from seed oils
(cottonseed oil and peanut oil mostly), as well as from
corn oil, olive oil and palm oil in the manufacturing of
salad and cooking oils. These same goods compete with

soybean oil in the making of baking and frying fats, as

17

also do lard and edible tallow. To a much lesser extent
soybean oil competes with other oils in manufacturing
margarine and the fabrication of paints, soaps, resins,
lubricants, etc.

The degree of substitution in the oils and fats
markets seems to be quite small. In particular, studies by
Chern and Yen (1992) and Chern, Loehman and Yen (1995) show
very low cross-price demand elasticities for soybean oil.

Exports are an important demand source although their
role has decreased in the last twenty years due to fast
production and export growth in South America. In the 1970-
74 period, exports represented 16.6% of total usage while
in 1990-94 period only 10%. Export demand variability,
however, appears to be an important source of price
instability in U.S. soybean oil.

After degumming (removing non-fatty materials),
processing crude soybean oil into refined soybean oil
consists of neutralizing the free fatty acids with caustic
acid (an alkali) and removing the resultant soap stock
(which is used in glycerin and soap production). Further
processing may include blanching, Winterizing,
hydrogenation and deodorization. An Alkali refining process

is the most common in US, accounting for 96% of total

18

refining capacity in 1975 and 95% in 1983 (USDA, Oil Crops,
Outlook and Situation Report, May 1985).

Stocks of soybean oil are therefore held in the form
of crude soybean oil by soybean crushers (as end product)
as well as soybean oil refiners (as inputs). Stocks of
refined soybean oil are held by refiners (as end products)
and brand product makers (as inputs). Many crushers,
however have integrated Operations that reach the consumer
in supermarket stores. Consequently they hold stocks of
refined soybean oil also.

Crushers hold crude soybean oil for speculative
purposes and due to opportunity costs. The former involves
the expectation of price appreciation from which a
speculative gain can be earned. The latter relates to the
“logistics” aspect of product distribution. Lacking storage
space involves the risk of stopping the crushing process.
It is not uncommon to face discontinuities in sales, not
only due to demand variability but also because of the lack
of coordination between production rates and current demand
rates. It is necessary to increase stockholding when sales
slow down because of the opportunity cost related to
stopping the factory, which in turn results in making no

profit on current operations.

19

Similar reasons motivate crude soybean oil refiner’s
stockholding. The “convenience yield” associated with
storing provides support to stockholding that otherwise
would not take place for purely speculative reasons.

No stockholding of soybean oil takes place in the
hands of the Government. Government intervention has been
limited to export donations and Credit subsidies in the
form of the PL-480 program and Export Enhancement Program
(EEP).

Some (small) portion of stocks is kept out of reported
statistics, the so called “invisible” stocks, that take
place while some portion of materials are in transportation
vehicles such as trucks, railroad, barges, etc.

During the last twenty years the soybean oil end-of-
season stocks to full-season-usage ratio averaged 10.8%
with a high of 16.3% in 1987 and a low of 5.5% in 1984. On
a quarterly basis, soybean oil stocks represented an
average of 35% of total demand with a high of 47% and a low
of 19% (according to USDA data). Table 2 shows 1995/96

quarterly and annual soybean oil balance.

20

Table 2

1995/96 Quarterly U.S. Soybean Oil Balance
(in million pounds)

 

 

 

 

Quarter
Concept 1 2 3 4 Total
Beg.Stocks 1,103 1,409 1,654 1,888 1,103
Production 4,096 3,888 3,677 3,578 15,239
Imports 11 34 36 14 95
Exports 371 354 155 112 992
Consumption 3,430 3,324 3,323 3,353 13,430
End Stocks 1,408 1,654 1,888 2,015 2,015
Demand 5,209 5,332 5,336 5,480 16,437
Usage 3,801 3,678 3,478 3,465 14,422
Stocks/Dem. 27 31 35 37 12
Stocks/Usage 37 45 55 58 14
Source: USDA, Oil Crops Yearbook, Oct. 1999

1.3 Soybean meal market
In the 1995/96 season, total domestic feed usage was
200.42 million short tons

(mst.) of which high protein

feedstuff was 35.6 mst. and soybean meal 26.5 mst. Soybean
meal use represented 33% of total domestic feed use and 74%
of high protein concentrates (USDA, Oil Crops Yearbook,

1998). Soybean meal feeding is the most important use

21

although it can also be used as food and fertilizer.
Soybean meal feed use is 98% of total soybean meal usage in
the US.

Soybean meal protein content can vary according to
product quality requirements. However, its variability is
limited between 43% and 50% per pound of weight,
constituting the highest protein content in all meal-feeds
available after groundnut meal. These features make soybean
meal feasible for livestock and poultry feeding in varied
proportions depending on the animal absorption
capabilities. Soybean meal is usually mixed with other
components in the ration depending on the animal, protein
content, nutritional content of other materials, and
prices. Given the varied characteristics of feeding
materials, they are not close substitutes. Moreover, a case
can be made for complementarity between soybean meal and
corn for example.

In the 1995/96 season, soybean meal production reached
a level of 32.5 mst. Domestic usage and exports were 26.6
and 6.0 mst., respectively (USDA, Oil Crops Yearbook,
1999).

Domestic soybean meal consumption has increased
rapidly in the last 20 years as a consequence of increased

livestock population and average weight per animal reaching

22

slaughter, but also has been fueled by increased poultry
consumption as part of the change in population's eating
habits regarding meats.

Exports have increased from 4.5 mst. in 1970-74 to 6.1
mst. in 1990-94 for a 35% increase. Faster SoUth American
production growth prevented exports from having a higher
share in total usage. In 1970-74 exports represented 26% of
total annual usage whereas in 1990-94 that percentage was
20%.

Soybean meal stocks are held by mills mostly. However,
they do not represent a major component of current demand.
During the period 1970-1995 end-of-season stocks to season—
usage ratio averaged less than 1% with a high of 1.8% in
1982 and a low of 0.4% in 1993. These numbers suggest
soybean meal non-storability.

Soybean meal pricing thus depends entirely on factors
affecting current supply and demand. Since inventories are
not a major source of demand, soybean meal prices depend on
crushing rates and demand factors such as number of
animals, feeding substitutes, export demand, etc. These
considerations are important as soybean meal is a major
output of soybean processing. Soybean meal prices determine
crushing rates to a great extent and consequently impact on

soybean oil supply and prices also.

23

CHAPTER 2

LITERATURE REVIEW

2.1. Soybean complex structural models

Vandenborre (1967) may be considered the first attempt
to estimate a complete model of the soybean complex. He
estimated an annual model, for the period 1948-1963. A
soybean supply response function was not estimated, and
supplies of soybean oil and meal were assumed to be given
each year. Soybean oil consumption demand was specified to
depend negatively on prices and availability of butter and
lard, and positively on cottonseed oil price. A time
variable was included to capture the effects of population
and taste changes. Soybean meal consumption demand was
specified to depend negatively on prices and availability
of other high protein feeds, positively on livestock prices
and high protein animal units. A time trend was added to
reflect technological change. Soybean oil ending stocks
were supposed to depend negatively on PL-480 exports and
positively on time and price of soybean oil. Soybean oil
beginning stocks plus current production were also
included. Soybean meal ending stocks were specified to
depend on time and prices of oil and meal. Crushing margins

were endogenous to the model, depending on a time trend

24

(standing for technological improvement) and prices of oil
and meal.

Results, from Vandenborre’s study were to a large
extent poor and suggested several specification errors,
with exception of the soybean meal equation which resulted
in a good fit. Crushing margins for example did not include
any variable referring to crushing capacity or soybean
availability. An equation for soybean meal ending stocks
was modeled in spite of existing evidence of non-
storability. Ending soybean oil stocks were modeled on
prices without providing any convincing reason for doing so
and this variable failed to be statistically significant.

Houck, Ryan and Subotnik (1972), Meyers and Hacklander
(1979) and Meyers, Helmar and Devadoss (1986) used annual
data in the soybean complex in an attempt to provide
improvements over previous efforts.

Houck, Ryan and Subotnik (1972) using data from 1946
to 1966, introduced an equation for soybean supply
response, although they assumed crushing margins to be
exogenous. Meyers and Hacklander (1979) built a model in
which crushing margins are endogenous for the period 1955-
1975. Meyers, Helmar and Devadoss (1986) expanded the model
by modeling the soybean complex in foreign countries and

introducing explicit export demand equations, for the

25

period 1966-1982. These models have in common several
specification features that are worthy of comment.

Soybean supply response is usually specified to depend
on expected own prices and expected prices of competing
products. Expected prices in turn are specified to depend
on previous period (observed) prices. Linear adjustment
costs are also modeled, which leads to a lagged dependent
variable in the model. Performance of this equation is
generally good with supply elasticities ranging between
0.60 and 0.84 (see table 3). These results suggest supply
adjustments do not totally occur in one period but are
spread out over several, and also suggest that farmer's
price expectation mechanism is backward looking.

Crushing rates (resulting in oil and meal supply) are
modeled to depend on soybean prices, prices of oil and meal
products, and crushing capacity. Although no other input
prices are included as explanatory variables, results are
remarkably good and conform with theory. An important
conclusion derived from these results is that crushing
rates respond instantaneously to prices of products and

soybeans (crushing margin).

26

Table 3

Own Price elasticities

 

 

Study Period Supply Soyoil Soymeal Crushing

Response Consump. Consump. Demand
Vanden(48-63) - -0.45 -O.28 -
HSR (46-66) 0.84 -0.28 -0.18 -0.21
MH (55-75) 0.60 -0.06 -0.21 -1.25
MHD (66-82) 0.71 -0.45 -0.41 -2.08
WH (66-81) — -0.33 -0.09 -
Henry (65-81) - -0.08 -0.23 -

 

Source: Vandenborre (1967); Houck, Ryan and Subotnik
(1972); Meyers and Hacklander (1979); Meyers, Helmar and
Devadoss (1986); Wesscott and Hull (1985) and Henry (1981)
Explanatory variables used in soybean oil consumption
demand equations are similar and include own price, income
and price of substitutes, although the actual specification
diverges to some extent. Houck, Ryan, and Subotnik (1972)
modeled consumption as a function of soybean oil price,
real food expenditures, cottonseed oil consumption and
wholesale price index of butter and lard obtaining
statistically significance in all variables but cottonseed
oil consumption. Meyers and Hacklander (1979) specified the
same equation to depend on real soybean oil price, real

consumer expenditures in non—durables and services, and all

27

other fats and oils consumption. Meyers, Helmar and
Devadoss (1986) used the same specification, although
expenditures are expressed in logarithmic terms.

Several issues can be mentioned related to the soybean
oil consumption equations specified in previous research.
Firstly, it is important to note refiner's demand for
soybean oil comes from consumer's demand for refined oil
products. Modeling crude soybean oil demand by introducing
some income variable as an explanatory implies demand
originates from consumers and thus should be conceived as a
derived demand form. Secondly, modeling soybean oil
consumption depending on all other oils and fats
consumption may be the source of biased estimators as long
as consumption of soybean oil and other oils and fats are
simultaneously determined. But most importantly, this
modeling approach fails to comply with economic theory. It
is not consistent to model the consumption of one good as a
function of the quantity consumed of another good. Yet,
introducing close substitutes prices instead of quantities
to account for substitution effects often results in
multicollinearity problems. In this sense it has been
difficult to obtain good estimates of the consumption

demand equation.

28

Soybean meal consumption demand equations included own
price, livestock prices, livestock units and price or
quantities of substitute products as explanatory variables,
with very minor differences in specification. The remarks
made above in respect to soybean oil also apply here.
Simultaneity bias can also be suspected in this equation as
quantities are used as explanatory variables.

Soybean and soybean oil end-of period stocks are
modeled in similar fashion in all three studies commented
above: 1) in an attempt to capture expectations about
future prices, next period's soybean production is included
as a proxy variable; 2) present period prices of the stored
good are included as an explanatory variable; 3) current
period production is included to capture convenience yield
effects; 4) stocks held by government are included as an
additional explanatory variable; 5) partial adjustment in
inventories is modeled; 6) dummy variables accounting for
outliers are also included; 7) all variables are specified
in linear form.

Although econometric results from the above
specification of the inventory demand equation seem to be
satisfactory from a purely statistical point of View, it is
difficult to reconcile them with theory. For a start, there

is no solid theoretical argument to support partial

29

adjustments in inventory demand. Second, specifying
expected price as a linear function of expected production
does not acknowledge the fact that prices also depend on
demand shifts. Third, it is evident that current period
production has a positive statistical relationship with
end-of—period inventories. To attribute the statistical
significance of this relationship to convenience yield may
be misleading. Fourth, although current prices are included
in the equation, this slope parameter is not restricted to
equal the one on expected price, thus the specification
does not enforce the speculative behavior of stockholders
during the estimation.

The inclusion of many variables with few restrictions
may very well result in a good statistical fit. For
example, the explanatory power of these equations, as
measured by its R2, is relatively high. In the case of
soybean oil equation, R2 figures are 0.80, 0.62 and 0.72 in
Houck, Ryan and Subotnik (1972), Meyers and Hacklander
(1979) and Meyers, Helmar and Devadoss (1986) studies
respectively. However, the actual economic relevance of
these results may be difficult to assess and accept. If
speculative inventory demand is to be modeled, the
specification should be based in solid economic theory and

the restrictions enforced.

30

Quarterly soybean complex models have also been
estimated. Wesscott and Hull (1985) modeled the soybean
sector using quarterly data for the period 1966-81.
Although soybean oil consumption demand follows a similar
specification to earlier works some seasonality was found.
Soybean meal consumption demand is specified as a function
of own price lagged one period, corn price, livestock
prices and seasonals variables. The Wesscott and Hull
(1985) study also specifies soybean meal demand as a
function of cattle placements and sows farrowings lagged
one and two periods. No inventory demand equation was
modeled since ending stocks were assumed to result from the
balance identity.

Monthly econometric models of the soybean sector have
also been estimated. Henry (1981) developed a partial
adjustment model for soybean oil and meal consumption in a
monthly model. Similar explanatory variables as in previous
studies were used in this work. Seasonal components were
found in both consumption equations. A very interesting
result, however, is that oil and meal expected prices were
found to be not statistically significant in explaining
crushing variability, in what seems to be a confirmation
that crushing rates depend on current product prices (not

the expected ones). Henry's (1981) work on the inventory

31

demand equations concluded that the speculative component
was irrelevant in both equations, thus challenging previous

efforts.

2.2. Rational expectations inventory models

Even though the origins of the rational expectations
hypothesis is dated to forty years ago with the seminal
work of Muth (1961), its application to agricultural
markets has taken place more recently. Until the late
seventies supply response analysis was dominated by several
backward-looking expectations formation hypotheses (naive,
extrapolative, adaptive, etc.) out of which adaptive
expectations was the one most commonly used. Nerlove's
adaptive expectations supply response model seemed to
provide a good explanation of the data in many applications
(see Askari and Cummings, 1979).

In the beginning of the 1980's a shift in the
literature took place towards the use of the rational
expectations hypothesis as an alternative to Nerlove’s
model. The attempts made by Sheffrin and Goodwin (1982) and
Eckstein (1984) showed that an alternative explanation was
able to explain the data without relying on ad hoc
mechanisms such as the partial adjustment process and

adaptive expectations.

32

In View of the U.S. government efforts to achieve
stabilization of grain prices in the mid 1980’s, a major
part of the literature was devoted to estimating the
“bounded price variation” model in which farmers'
expectations were modeled to include their expectations
about government actions and its effects on prices.
Shonkwiler and Maddala (1985), Holt and Johnson (1989) and
Holt (1992) are characteristic examples of this type of
research.

In the late 1980’s the rational expectations
hypothesis was also implemented to explain prices in
markets where inventories play a role in price
determination. The efforts in this area used the basic
specification in Muth's inventory model of three structural
equations and one equilibrium identity, in which previous
period inventory levels plus current production must equal
the current usage plus inventories carried into next
period. Following this basic structure several studies were
conducted: Hwa (1985), Gosh, Gilbert and Hughes-Ballet
(1987), Thurman (1988), Gilbert and Palaskas (1990),
Trivedi (1990) and Gilbert (1995).

Hwa (1985) made a first attempt to estimate a rational
expectations model in coffee, cocoa, sugar, copper, rubber

and tin. His model, however, modeled the “rational price

33

expectations” in a manner not consistent with the notion of
agents knowing the model. Hwa (1985) also introduced ad hoc
mechanisms such as partial adjustment in stocks and a price
equation implying that inventory holders incur in unplanned
storage.

Gosh, Gilbert and Hughes-Hallet (1987) who studied the
copper market found evidence of speculative behavior
without introducing convenience yield in their
specification nor enforcing the non-linear cross equation
restrictions. Thurman (1988) rejected the rational
expectations restrictions in a monthly copper model but the
model made better out-of sample forecasts than competing
models.

Gilbert and Palaskas (1990) (who investigated the same
commodities that Hwa worked on) confirmed previous results
in copper in an annual model but were unable to replicate
results on the other five commodities. They argued that
Imaybe the "production and consumption models were
insufficiently realistic to pick up future supply/demand
tnilances" and that the other five commodities had a great
deefil of government market intervention. It should also be
noted that they only used twelve observations in their

empirical model .

34

The latter three studies mentioned, studied a
simplified version of Muth's basic model structure, i.e.
that current production (supply equation) depends on
current price rather than expected prices as it is common
to assume in agricultural commodities. Significantly, these
models only estimated the pseudo-reduced form of the price
equation, not the full structural models.

Table 4 briefly summarizes the major characteristics
of studies mentioned here and their results.

Trivedi (1990) who worked with annual data in tea,
cocoa and palm oil generated improvements over earlier
approaches. He modeled inventory demand to include a
speculative component and a transactions component, the
former specified as the expected change in prices and the
latter depending on expected consumption demand which
produced a positive convenience yield. He also modeled
supply to depend on current prices and expected prices
which is a specification that is rather difficult to
interpret. The results showed no evidence of a significant
relationship between inventory demand and expected prices.
An interesting conclusion of this study is that better
modeling of the process driving the exogenous variables may
be needed to provide a better fit. Based on his results the

author suggested that neglect of speculative inventory

35

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36

behavior in annual models may not be a serious
misspecification, while it may be important in the short
term.

Gilbert (1995) attempted to estimate an annual model
of the aluminum market. This study is the only one that
enforced the non-linear cross equation restrictions and
estimated the full market model. The study fails to reject
the rational expectations restrictions. The parameter on
expected appreciation of stocks value is significantly
different from zero. For estimation, the author constructed
estimates of expected long-term and short-term fundamental
imbalances, to account for the multi-step ahead forecasts
of exogenous variables, instead of exploiting the
stochastic properties of exogenous variables. Furthermore
the root restrictions implied by the second order
expectational difference equation was not imposed.
Importantly, his results critically depend on the fact that
the market that he studied does not show any evidence of
stock-out events. Gilbert's work is the only study, of the
several reviewed here, that obtained sound evidence (in a
linear framework) of inventory demand being explained by

expected price changes.

37

2.3. Applications of dynamic programming to soybean markets

More recently, the non-linearities involved in
inventory demand drove many researchers to the use dynamic
programming techniques.

Many researchers have studied the properties of price
stabilization in the context of dynamic programming when a
competitive storage industry exists (Helmberger and
Akinyosoye, 1984; Miranda and Helmberger, 1988; Glauber,
Helmberger and Miranda, 1989). A great majority of these
studies used the soybean market for those simulations.
Wheat to a lesser extent was also used.

The basic building block for these simulations is a
supply response function and a current consumption demand
function. From the parameters of those equations, a measure
of the inventory demand sensitivity to expected price
appreciation can be deduced. Convenience yield is mostly
not introduced in these models, however, since the main
goal is to analyze the effects of speculative storage
decisions on prices.

For the purposes of the simulations, estimation of the
above mentioned supply and demand functions were carried
out in many studies. The main feature of these supply
response estimations is that, instead of assuming backward-

looking expectations (as in almost every structural study

38

mentioned in section 2.1) they assume forward looking
behavior and consequently try to capture the response of
farmers to expected future prices. Because the best proxy
for future price expectations are provided by the consensus
of the futures markets, futures prices of deferred
contracts were used in almost all studies and showed
statistical significance. The results of these estimations

are summarized in Table 5.

Table 5

U.S. Soybeans: Own Price elasticities

 

 

Study Supply Crushing

Response Demand
Gardner (1976) 0.73 -
AH (1984) 1.02 -0.45
Lowry (1984) 0.89 -0.55
Glauber(1984) 0.64 -0.56
LGMH (1987) 0.89 -0.56
GHM (1989) 0.89 -0.61
MG (1993) 0.44 -0.55

 

Source: Gardner (1976); Akinyosoye and Helmberger
(1984); Lowry (1984); Glauber (1984); Lowry, Glauber,
Miranda and Helmberger (1987); Glauber, Helmberger and
Miranda (1989); Miranda and Glauber (1993)

39

These studies are important because they place a
question mark on previous econometric work in the soybean
complex using less sophisticated expectation formation
assumptions.

Irwin and Thraen (1994) reviewed several studies with
the objective of assessing how relevant is the rational
expectations hypothesis. The results of these studies are
mixed. Soybean farmers may use adaptive mechanisms as
pointed by Giles, Goss and Chin (1985), a perfect foresight
model according to Orazem and Miranowski (1980), the naive
model based on Shideed and White (1989), or the rational
conditional forecast or AR(2) model as stated by Holt
(1992).

The article by Miranda and Glauber (1993) provided
very interesting results in this respect because the
estimated elasticity of private stocks demand with respect
to expected price appreciation in the value of stocks was
4.78 (and statistically different from zero), which means
that storage decisions are very sensitive to changes in
current price, expected price and interest rates. The
results suggest that rational price expectations in soybean
inventory demand and acreage response functions may be a
very useful way to proceed. Also, a trend variable showed

statistical significance in the inventory demand equation

40

in what can be interpreted as a signal of the “scale of the
market” effect suggested by Muth (1961).

Gardner and Lopez (1996) carry on specific modeling of
convenience yield for their dynamic programming
simulations. For this purpose, a storage cost function was
fitted in soybean market, obtaining the best result with a

cubic representation on stocks levels.

2.4. Crushing rates and margins

Several articles have also been devoted to the
analysis of soybean crushing firms behavior, with special
focus on marketing margins.

Boyd, Brorsen and Grant (1985) worked on explaining
crushing margin as a function of non-soybean input prices
(a weighted average of natural gas and wages), a risk
variable, the amount crushed and a trend variable. Input
prices did not show explanatory power on crushing margins.
They found the risk variable to be statistically
significant. Increased risk measured by monthly product
price variability increased marketing margins. They
concluded that soybean crushing firms are risk averse.

Lence, Hayes and Meyers (1992) implemented a cash
crushing margins equation in which they included the amount

of soybeans crushed, risk variables and crushing capacity

41

as explanatory variables. They argued that previous
analysis was invalid since it ignored the risk management
possibilities existing by using futures markets. Making use
of a specification in which futures crushing margins are
used as dependant variable confirmed results of a sizable
effect of risk in marketing margins. Their work on crushing
rates shows that crushing margins and crushing capacity are
statistically significant explanatory variables of annual
crushing volume.

Lence, Hayes and Meyers (1995) argued that hedging in
the futures markets should reduce the risk on output
decisions. They concluded that futures prices had little
effect on crushing rates but a significant impact on
inventory levels suggesting that firms try to obtain
profits on basis speculation. Their analysis concluded that
soybean crushing firms do have forward looking expectations

which determine their storage decisions.

42

CHAPTER 3

ECONOMIC MODELS OF COMMODITY MARKETS

Microeconomic theory provides the theoretical
underpinnings for commodity market modeling. Since our
study requires the specification of demand and supply
equations, sections 3.1. and 3.2. are devoted to these
topics. In section 3.3. we review the relevant stockholding
theory for our model and in section 3.4. we present a
summary of a commodity market model for a storable

commodity.

3.1. Demand

Resource endowment, an individual's utility function
and prevailing prices of goods determine consumer choices
between goods. Consequently, consumer demand is modeled to
depend on own prices, prices of other goods, consumer
resources and tastes and preferences. Market demand is the
addition of individual consumer's demands. Equation (1)

depicts this relationship.

Qd = f (RP, OP, R, NI, TP, u) (1)

where Qd== Consumer's quantity demanded

43

RP = Retail price of the good

OP = Retail prices of other goods
R = Resource endowment

NI = Number of individuals

TP = Tastes and Preferences

f = Functional relationship

u = Random error term

Several other factors such as income distribution
among individuals and demographics also affect market
demand. These (not included in above equation) factors are
usually collapsed into a random error term. The random
error term may also account for optimization errors, and
errors in the functional form.

In specifying the above equation, it is common
practice among econometricians to use a per capita income
variable to measure resource endowments. Taxes play a role
in determining the amount of resources available for
consumption, thus a measure of disposable income is usually
used. Disposable income can be devoted to savings and
consequently be affected by interest rates. To avoid
introducing interest rates in the model specification it is
often the case that an expenditure variable is used instead

of an income variable.

44

The number of individuals is proxied by the
population. However, in order to simplify the
specifications, both the expenditure variable and
population number are generally collapsed into one single
per capita variable. Usually an aggregate measure of per
capita expenditure is used.

Consumer choices are made in the presence of an
immense array of goods available at different prices.
Because it is not usually feasible in econometric work to
introduce the prices of all goods, economists often revert
to the simplification of specifying the "other prices" with
the inclusion of close substitutes and complementary goods
prices only. However, in order to account for the existence
of an enormous amount of other goods, prices are usually
deflated by a general (consumer) price index.

Tastes and preferences are quite difficult to measure
and so the common econometric approach is to assume that
tastes and preferences change smoothly and relatively
slowly in time. It is common practice to proxy these
changes with a trend variable in linear or quadratic form.

The functional specification of the above relationship
is still subject of debate among economists, given that the
I true consumer's utility function is unknown. A linear

specification in the parameters is often used. To ensure

45

theoretical consistency in the parameter estimates,
homogeneity is often imposed in the course of estimation.

Many goods, however, are not directly consumed by
individuals but rather by firms, as intermediary goods
(inputs). These firms "transform" intermediary goods to
obtain a product suitable for retail consumption. The
firm's demand for the intermediary good is then a derived
demand from consumers.

Assuming that the firm's objective is to maximize
profits, input demand is modeled to depend on input price,
output price, other input prices, technology and the number
of firms in the market. This relationship is shown in

equation (2).

Qd = g (RP, WP, AWP, NP, T, v) (2)
where Qd== Processor quantity demanded

RP = Retail price of the good

WP = Wholesale input prices

AWP= Alternative wholesale input prices

NP = Number of firms

T = , Technology

g = Functional relationship

v = Random error term

46

The theoretical developments presented above are key
in deriving the wholesale commodity demand. The usual
procedures to obtain a complete description of wholesale
demand for an intermediary good is: a) to invert equation
(1) in order to obtain an expression for the retail price
as a function of the remaining variables, b) to substitute
the resulting expression into (2) in order to derive a
"reduced' form demand for an intermediate product at the

firm level. This results in an equation (3).

Qd = h (WP, AWP, NP, T, OP, R, NI, TP, 5) (3)
where Qd== Quantity demanded
WP = Wholesale input price
AWP= Alternative wholesale input prices
'NP = Number of processors
T = Technology
OP = Retail prices of other goods
R = Resource endowment
NI = Number of individuals
TP = Tastes and Preferences
h = Functional relationship
8 = Random term

47

It is clear from equation (3) that all exogenous
variables contained in equation (1) and (2) are also
contained in equation (3). The functional relationships f
and g of both equations are transformed into a new
functional relationship h. Also the random terms 2 and v

are now replaced by a new term s.

3.2. Supply

Based on output prices, firms choose the optimal
amount of inputs required to produce the planned output.
The profit maximization assumption leads to a model of
output supply that depends on output prices, input prices,
alternative output prices and technology. Market supply is
the addition of individual firm's supplies. Equation (4)

depicts this relationship.

Q8 = 1 (WP, AP, IP, N, T, w) (4)
where QS== Quantity supplied
WP = Wholesale output price
AWP = Alternative wholesale output prices
IP = Input prices
N = Number of firms

48

US

ma

f1:

IE

(1‘.

(n

if)

T = Technology
i = Functional relationship

w = Random error term

Other factors such as weather also affect output
supply. These (not included in above equation) factors are
usually collapsed into a random error term. The random term
may also stand for optimization errors or errors in the
functional form.

Some firms may produce different outputs depending on
relative output prices and select different combinations of
inputs to accomplish their production objectives. In these
cases (a plot of land suitable to producing either corn or
wheat, for example), several output prices are introduced.
Also, once the output decision is made, an input allocation
decision is required. Several input prices are generally
specified.

To empirically implement the above equation,
econometricians have assumed that physical characteristics
and technological standards (including manager's knowledge)
are similar among firms. Market supply is the addition of
single firms outputs. Processing capacity has been of
general use as a proxy variable for the number of firms in

the market.

49

Technological improvement is understood to mean a
change in the relationship between output produced and
input usage. If a higher output level can be reached with
no change in the input usage, it is said that a
technological improvement took place. Technological changes
are generally assumed to occur slowly, or at least to
spread slowly in the market (economy). This effect has
consequently been specified as a linear or quadratic trend.

The functional relationship of equation (4) largely
depends on the production function. Many different
functional specifications have been used to implement (4)

empirically.

3.3. Inventory demand

Stocks are held by producers, merchants, speculators
and consumers for precautionary, transactions, and
speculative motives. Stockholding theory attempts to
provide an explanation for why producers hold stocks of
end-products and merchants, processors and consumers hold
inventories of inputs. Speculators hold inventories with
the purpose of making speculative profits by changing the

temporal allocations of goods.

50

3.3.1. Speculative motivation

In its simplest representation, stockholding depends
on the difference between current and expected future
prices. Anyone (producers, processors or speculators) might
want to own stocks and carry them into the future for
speculative purposes. Producers and processors may want to
accumulate stocks in the anticipation of increased prices.
In such an event, producers would sell their products at
higher prices and processors would buy them at lower prices
than otherwise. Professional speculators would hold stocks
with the sole aim of making capital gains.

Modeling speculative activities is not different to
modeling any other economic activity. A risk-neutral
speculator will seek to maximize expected profits as the
difference between expected revenue and costs involved in
the storing operation. Since storing of non-perishable
goods is only a temporal reallocation of commodities, no
"physical transformation" takes place. Consequently the
expected revenue is nothing else but the expected future
value of stored goods.

Storing operations require monetary resources to
acquire inputs, of which the raw material is the main cost.
Physical costs of storage include payments for insurance of

storage facilities and stored goods, rent, wages, energy,

51

and loading and unloading costs. Other costs of storage are
physical deterioration and opportunity costs, i.e. the
returns that could be achieved by allocating storage
resources to alternative uses.

Agricultural commodities may experience some
deterioration of their physical condition, or may very well
loose (by vaporization) some of their moisture content to
yield a product with no different characteristics than the
one originally stored but of lesser weight. These losses
are costs that should also be modeled.

In the short run, a risk neutral speculative firm that
maximizes expected profit in a competitive market for

storage would maximize:

3.4).“: [(l-a) Eth - (1+rtiPtis. - (1+r.)C(s.,w.) (5)
where Ek¢U4 = expected profits at time t

EkPUI = expected future price at time t

Pt = price at time t

St = stock level at time t

rt = interest rate at time t

a = deterioration factor (0<a<1)

C(St,wt) = total physical cost of storage function

wt = vector of input prices

t = time

52

Total physical costs of storage may be classified into
fixed costs and variable costs, the latter depending on the

total amount of stocks held:

C(Stlwt)= FC + VC(Stlwt) (6)

where FC fixed costs of physical storage

VC(SUvn) = variable costs of physical storage

The first order condition (FCC) to maximizing (5) is:

(1‘3) EtPt+l "' Pt = rtPt + (1+rt)C' (Stlwt) (7)

where C'(St,wt)) = marginal physical costs of storage

If a is assumed to be zero, equation (7) can be

expressed as:

at EtPt+1 " Pt = C' (Stlwt) (8)

where St = 1 / (1 + rt)

The left hand-side of (8) is referred to as the “cost

of carry”. Equation (8) says that in equilibrium the firm

53

 

m:

maximizes profits at the stock level where expected
discounted marginal revenue equals storing marginal costs.
From (8) we can solve for the optimal level of storage
St, obtaining a functional relationship that depends on the
form of C'(St). VC(St) is usually considered to be a linear
function, and so, marginal storage costs are constant, at
least until total warehouse capacity is almost fully
utilized. If total physical costs of storage are assumed
linear (and consequently marginal costs of storage are

assumed constant), (8) can be expressed as:

Br EtPt+l ’ Pt = C0 3 St > 0 (9)

where co = marginal physical costs of storage

which states that when speculative storage levels are
positive, the cost of carry should equal the constant (per
period of time) marginal physical costs of storage. That
is, marginal revenue must equal marginal costs, the usual
condition for profit maximization.

This condition implies that when stocks are positive
carrying charges would be positive and equal to the

marginal physical storage cost

54

Implicitly, equation (9) also says that whenever Bt
Ethu - Pt is greater than co storers would choose to store
an infinite amount of the commodity whereas zero levels
would be stored when 8t Edfii1-'Ek < co. In reality we see,
however a much smoother inventory behavior (which may be
explained by convenience yield).

If marginal physical costs of storage are linearly

increasing, the optimal level of storage can be obtained as

follows:
8t Ethu - Pt = mm + nu St ; or (10)
St = C0 + C1 (Bt EtPt+l " Pt) (11)
where co = -mo/m1

C1 = (l/ml)

which says that the storage level depends linearly on the
expected discounted price appreciation.

Assuming risk neutrality, however, may not be a
realistic assumption since speculative storage is in fact a
risky activity. Thus modeling speculative demand for
inventories may require the assumption that firms maximize

expected utility instead.

55

A similar expression for inventory demand equation
(11) can be obtained when risk aversion plays a role in
speculative behavior. Under uncertainty a risk averse firm
would maximize expected utility of profits EU [ ¢U4 ]. It is
possible to show that under EU decision making, inventory
demand can be expressed as a linear function of expected
price appreciation if certain assumptions are made
(constant conditional variance of prices and constant risk
aversion) (Muth, 1961, Gosh, Gilbert and Hughes-Hallett,
1987).

In many instances, risk averse speculators can manage
price risk by hedging with futures contracts. Under an EU
decision framework, a similar result to equation (11) can
be obtained as long as we assume no basis risk and unbiased
futures markets (Chavas and Helmberger, 1996). When price
risk can be hedged in futures markets a risk averse firm
would choose the amount to store as a linear function of
expected appreciation in cash prices.

Although it may be difficult to provide support for an
equation of the type depicted in equation (8) on the
grounds of constant conditional variance of prices and
constant risk aversion, it is no less true that price risk
management is a sensible possibility in U.S. soybean oil

market. Soybean oil futures contracts have traded in U.S.

56

since 1958 at the Chicago Board of Trade and have grown in
volume through the years. In fact, Lence, Hayes and Meyers
(1995) provide evidence that futures prices play a role in
determining soybean oil inventory levels. On these grounds,

explicit modeling of price risk aversion can be avoided.

3.3.2. Convenience yield

Stocks are also held by producers, processors and
consumers for transactions and precautionary reasons. It is
well documented that goods may be carried into the future
even in the expectation of price depreciation. When such a
thing happens it is said that stocks are held not for
speculative purposes but because of the "convenience"
return from holding stocks.

The functional form of the relationship between
convenience yield and stock levels is assumed to increase
at a decreasing rate as the level of stocks increase.
Therefore, at high levels of stocks held, marginal
convenience yield approaches zero and at low levels of
stocks marginal convenience yield is very high.

Given the enormous variability of firm sales rates, a
commodity producer firm looks to have as many outlets as
possible to sell their products. Creating new commercial

relationships requires time to evaluate the financial

57

conditions of buyer and seller and contract execution
performance. Typically, building confidence between each
other to reach a successful commercial relationship takes
years. Once it is established, a consistent flow of
commercial transactions are required to keep relationships
"going on". The availability of product to sell is
therefore a key to maintaining "good" commercial
relationships.

A crusher might want to hold high stock levels of end-
products, because this would allow sales of big quantities
to clients with which commercial deals can only be done on
that basis. The stock levels should not be as high,
however, as to reach the maximum storage capacity, due to
its implications for the production process. Full storage
impedes production from continuing. To prevent this, a
permanent flow of sales must be possible, the only
guarantee being a diversified portfolio of clients. On the
other side, crushers may not want to have stocks lower than
a certain "working" level, because there are clients whose
product needs must be fulfilled, at least in small volumes.

A refiner might want to keep input stock levels above
a certain "working level", due to the costs of running
under capacity, or having to stop the production process in

the case of a stock-out. This may evolve into an inability

58

to provide refined material to customers, which in turn
must look for other supply sources. This may jeopardize a
commercial relationship and, most important, reduce profits
from the refining operation. In brief, some level of stocks
are held not for speculative purposes but to allow
continuos transactions to take place.

Convenience yield is therefore a function of the
stocks level. The exact nature of the functional
relationship is one that must be determined empirically.

Formally:

II
H)

CY (S) (12)

where CY = Convenience yield

Convenience yield modeling has differed among
researchers. Some researchers have reasoned that including
a trend variable in the inventory demand equation would
account for “coverage yields” a related concept to the
“transactions” motivation for stockholding (Lord, 1991). As
a matter of fact Muth (1961) had suggested that inventory
demand would also depend on the “size of the market”.

A more realistic approach (Trivedi, 1990) specified

that inventory demand would linearly depend on expected

59

consumption. In his own terms this factor would “reflect
transactions demand for inventories which produce a
positive convenience yield”.

The two sources of inventory demand introduced in
section 3.3. may be integrated into a single framework.
Producers and processors would hold stocks of products and
input materials for either of both reasons, making it
difficult to determine the exact reason why some portion of
stock is held. Suffice to say that in what follows we
assume that some portion of stocks is held for one reason
and the remaining portion for the second reason, to obtain

an additive formulation to obtain:

St = C0 + Cl (Br EtPt+l " Pt) + CY (13)

which says that expected profits are the result of expected

speculative profits plus convenience yields.

3.4. Commodity market model

On the grounds of the work presented above, a
commodity market model would include a demand equation, a
supply equation, an inventory demand equation and a market
clearing condition. The latter, when dealing with non-

storable commodities is usually expressed as the equality

60

between quantity supplied and demanded. When dealing with
storable commodities the condition transforms to include
inventory demand. That is, beginning inventories plus
current's period output supplied must equal current's
period demand for consumption plus demand for storage. If
the market is open to foreign trade, imports and exports
should be modeled and be included in the market clearing
condition. The market model then consists of equations (3),

(4), (13) and the market clearing condition (15).

Market model

Qd = h (WP, AWP, NP, T, OP, R, NI, TP, 5) (3)
Q5 = i (WP, AWP, IP, N, T, w) (4)
st = co + c1 (13t Eth - P.) + CY (13)
Std + Q5: QS+ st (15)

In our work, the wholesale price refers to crude

soybean oil price.

61

CHAPTER 4

MODEL SPECIFICATION

On the grounds of the literature review conducted in
Chapter 2, the work developed in Chapter 3, and Muth's
(1961) inventory model, we specify the following model of

the U.S. soybean oil market:

DISSt = a0 + a1 RSBOPt + a2 EXPENt + a3 RLARDP + 8y: (1)

PRODt be + b1 RSBOPt + b2 RSBMPt +

b3 RSBPt + b4 CRCAPt +

51 D1 + 52 D2 + S3 D3 + 82: (2)
CO: = C0 + C1 [Et RSBOPul - RSBOPt] +

C2* T + C3 RFFRt (3)
CObq + PROD: = DISSt + Xt + COt (4)

where DISS = Domestic soybean oil consumption
RSBOP = Real crude soybean oil price
EXPEN = Personal consumption expenditures
RLARD = Real wholesale lard price
PROD = Soybean oil production
RSBMP = Soybean meal price
RSBP = Real soybean price

62

CRCAP
D1,D2,d3
CO

E

RFFR

Et RSBOPt+1

Crushing capacity

Seasonal dummy variables
End-of-period soybean oil stocks
Expectations operator

Real interest rate

Trend variable

Soybean oil exports

error term

time, quarter

Et [RSBOPHl I Q ]

The expectation formed about RSBOP“)
conditional on information available

at time t. Expectations are rational.

The model resembles the typical structure of Muth's

model and includes three behavioral equations, (1) to (3)

(consumption demand,

production and inventory demand), and

one market clearing condition (4) (the material balance

identity). Behavioral equations are specified linearly in

levels as is the material balance identity. All price

variables are real as they are deflated by the Census

Bureau of Statistics producer price index.

Equation 1, stands for current period consumption

demand, which is modeled to depend on soybean oil prices

63

lard prices and personal consumption expenditures. Although
it is reasonable to believe that prices of other oils would
affect soybean oil demand, several aspects leads us to the

simplification of including only a not-so close substitute.

Firstly, it is important to recall that equation (1)
refers to demand at a wholesale level, which derives from
demand at a retail level. In this sense retail prices of
bottled soybean oil competing products might be included
such as bottled rapeseed oil and bottled corn oil. Also
retail prices of margarine competing products like butter
might be included and retail prices baking and frying fats
alternatives to soybean oil, such as lard and edible
tallow. We opted for including lard prices in our
specification. We used wholesale lard prices as a proxy
variable for retail prices.

On the other hand, wholesale prices of alternative
inputs to soybean oil might also be included. The
representation of processor's input demand introduced in
Chapter 3, fits well to different processing activities in
the soybean oil market such as refining and bottling, the
making of salad dressings, margarine, products for
industrial use (paints and lubricants) and others.

In the making of margarine, soybean oil inputs only

marginally compete with cottonseed oil and corn oil. More

64

important is the substitution effect that may take place
between soybean oil and cottonseed in the making of baking
and frying fats. But still, out of the total oil usage in
the manufacturing of baking and frying fats, soybean oil
constituted 80 % of total input demand.

Salad dressing, and cooking oils also use soybean oil
in their makings. Salad dressings use alternative vegetable
oils according to their prices and as is the case in the
production of blended bottled oils. However, it is
important to note that institutional factors (regulations)
and consumer tastes severely limit the range of
substitutions among alternative inputs. In brief, although
soybean oil may be substituted for other inputs, it is
limited to a narrow range.

- Second, the inclusion of many other wholesale oil
prices would introduce a high degree of multicollinearity.
As a matter of fact, soybean oil is the major oil consumed
in the U.S. so its supply and demand conditions are the
major factor explaining edible oil price variability.

The literature review conducted in Chapter 2, on the
other hand, suggests modeling consumption demand should
depend on some income measure. However, some work also

proved satisfactory with the specification of an

65

expenditure variable as a proxy variable for resource
endowments. In this study we follow the latter approach.

There is no available data for the number of refiners
(processors) thus we were unable to include this variable
in the course of estimation. We also considered it
inappropriate to include a trend line accounting for such a
variable, as a trend would be correlated with the
expenditure variable. We have also assumed that there has
been no major technological change.

We have also assumed, following previous research,
that demand contemporaneously responds to prices and
expenditures. No lag structure is specified.

The signs in equation 1 are expected to be negative on
prices, and positive on expenditures and lard prices.

The seasonal behavior of consumption demand seems to
be fairly well explained by prices. That is, seasonality in
consumption demand is induced by supply through the price
mechanism thus no seasonal dummy variables are incorporated
in the specification of this equation.

Equation 2, specifies current period production as a
function of output prices (oil and meal) input prices
(soybeans), and crushing capacity (proxy variable for the

number of firms).

66

Soybean oil is produced in almost fixed proportions
from soybean crushing. About 180 kilos of oil are obtained
per 1,000 kilos of soybeans crushed. This relationship
marginally varies through the years according to soybean
vegetative growth conditions (temperatures, moisture, etc).
Thus we may substitute soybean oil production for.crushing
rates and maintain the same equation specification used for
soybean crushing rates.

Soybean crushing rates, depend largely on crushing
margins, i.e. the difference between product value and
soybean prices. Product value is the revenue from oil and
meal sales weighted by their production yields. Although
there are many other inputs related to soybean crushing,
soybeans account for the bulk of them. In our specification
we assume other input costs are fixed.

Most work on crushing rates assumes a specification of
crushing margins that we do not fully enforce in this
study. The need for a specific soybean oil price in the
supply equation (in order to study soybean oil inventory
demand), requires that each component of the crushing
margin (soybean oil price, soybean meal price and soybean
price) be specified separately. Still, the specification

losses no theoretical support.

67

No technological change took place in the last 20
years in the soybean oil extraction industry. Solvent
extraction factories were the standard production
technology then as now.

In specifying equation (2) we follow previous research
in modeling contemporaneous supply response without partial
adjustments mechanisms. Soybean oil output decisions depend
on current prices, not expected prices. The literature has
consistently shown that this specification is a good
representation of reality. Also, as mentioned in Chapter 2,
no study has been conducted to asses whether partial
adjustment mechanisms play a role in soybean oil output
(i.e. soybean processing). However, the presumption is that
if they exist they are marginal and are not modeled here.

Most soybean crushing facilities do not have the
ability to crush other types of seeds, so alternative
output prices are not specified.

We make used of crushing capacity as the proxy
variable for the number of firms in the market. The
literature reviewed in Chapter 2, has placed a big emphasis
on the explanatory power of crushing capacity on annual
crushing rates. In this study we incorporate crushing

capacity as an explanatory variable of soybean oil output.

68

F9

The strong seasonal component in soybean oil
production is captured by specifying seasonal dummy
variables.

Equation (3), the soybean oil inventory demand
equation, specifies a linear functional relationship
between inventory demand and the expected appreciation in
stocks value. Although it has been shown that inventory
demand may depend as well on higher moments of the price
probability distribution, we have assumed that price risk
management is possible in the soybean oil market.

In equation (3) we assume that price expectations are
formed rationally. Although it is still a matter of debate
whether rational expectations properly depicts the
formation of expectations by agents, there is evidence
supporting this hypothesis in soybean inventory demand
(Glauber and Miranda, 1993) and soybean oil inventory
demand (Lence, Hayes and Meyers, 1995).

Given that convenience yields are in essence non-
monetary (and non-observable) benefits to stockholdings it
may be difficult to find any variable that properly
captures the convenience yield effect. Thus researchers
have oriented their efforts to hypothesize about the actual
shape of the storage function cost by introducing

quadratic, cubic and hyperbolic functions. The result of

69

this effort has been the introduction of a nonlinear
relationship between expected appreciation of stocks value
an the inventory level (Gardner and Lepez, 1996; Glauber
and Miranda, 1993).

The trade-off between the two approaches is high. The
econometric tractability of a linear specification is hurt
by its lack of realism. On the other hand, a non-linear
specification of convenience yield would require the use of
non-linear rational expectations estimation techniques. As
discussed in the Introduction of this study we have opted
for the first approach.

Inventory demand is also affected by the size of the
market as pointed out by Muth (1961). A linear trend
variable was included to capture the effect of “scale of
the market” growth. The linear specification allows for
negative stocks. Previous research has considered that this
specification accounts for "transactions" convenience yield
and we take this to be the specification for convenience
yield.

We specify equation (3) to depend linearly on interest
rates. Although the work conducted here, leads to a
specification where the discounting factor is
multiplicative in respect to expected prices, the non-

linearities introduced by such a representation, leads to

70

model complexities that could not be solved in a linear
framework. We thus opted for including the discounting
factor in a linear fashion.

Equation (4) is the material balance condition where
initial inventories plus current period’s production must
equal current period's consumption plus export demand and
current period’s inventory demand.

Import demand is not modeled because they are almost
non-existent. Export demand, on the other hand is assumed
exogenous at every period in order to reduce the complexity
of the model. The exogeneity assumed here allows us to
avoid modeling government actions in the form of PL-480
donations and the Export Enhancement Program (EEP).

When expectations about future prices are assumed
rational in a rational expectations model a solution for
the expectations variable is needed, i.e. an expression for
the non-observable variable Et RSBOPPH.

By substituting equations (1), (2) and (3) into the
market clearing condition (4) and after rearranging terms
an expectational difference equation results. Solving this
equation results in an expression for qu RSBOPt as a
function of the stable root (A) of the polynomial in the

lag operator, the structural equations parameters and the

71

multi-step ahead forecasts of exogenous variables (see

Annex I and II for procedures).

15..1 RSBOPt = A RSBOPt-1 + c1'1(bo-ao)A / (A-l)

- c1“1 b2 A 2110 xi Et-1 RSBMP...
- cl'l b3 A 21:0 A1 15..l RSBPt+i
- of1 b. x 21-0 A1 13..1 CRCAP...
+ cl‘l a2 A 21:0 Ai EH EXPEN...
+ cl'l a3A 21:0 xi 13..l RLARDP.+1
+ cl'l A 21:0 xi Et-1 x..i

+ c1'1 c2 A 21:0 Ai Et-1 T,t+i

+ c1“1 c3 A 21-0 A1 Et-1 RFPR...i
+ c1'1 81 A 21:0 Ai Et-1 Dlt+i

+ cl’l sz A Ei=o Ai Et-1 D2t+i

+ c1'1 s3 2. 21=o 2.1 EH D3... (5)

In order to obtain an observable form for E, RSBOPuq we
compute the multi-step ahead forecasts of exogenous
variables by repeated substitution. This requires a
previous assessment of the stochastic processes governing
each of the exogenous variables. Once this is assessed and

an expression for Et RSBOPU4 is obtained, it is substituted

72

into equation (3) and estimated simultaneously. In Annex I
and II we go over mathematical procedures.

If we specify that RSBMP, RSBP, CRCAP, EXP, RLARD and
X follow autoregressive processes of order one and that
RFFR fellows a random walk with no drift, we obtain an
estimable expression for Et RSBOPtn which we substitute into

the inventory demand equation:

CO); = C0 + (bo’ao-C2)A / (A’l) ‘|" C1 (A-l) RSBOPt

‘ b2 A th /((1'A) (1-Ah11))

(b2 A hn /(1'Ah11)) RSBMP:

- 133 A h2o /((1‘A)(1‘Ah21)) (b3 A h21 /(1'Ah21)) RBP:
‘ b4 A hao /((1’A)(1-Ah31)) ’ (b4 A 1131 /(1-Ah31)) CRCAPt
+ a2 A hoo /((1"A) (1'Ah01l) ' (b3 A h01 /(l-Ah01)) EXPENt

+ 33 A hso /((1‘Al (1'Ah51))

+

(a3 2. h51 /(1-Ah51)) RLARDPt
+ x hqo /((1-A) (1-Ah41)) + ( 2. h,1 /(1-Ah41)) xt

+ cth

+ c3 RFFRt

- 51 A / (l-A")

- s2 2.2 / (1-x4)

- s3 2.3 / (1-A‘) + e.. (6)

As is common in rational expectations models, the

structural equation (inventory demand) containing

73

expectations variables (expected prices) not only contains
its own shifters but also the solution for the multi-step
ahead forecasts of those shifters (both of them in terms of
t time). It is immediately clear from equation (6) that the
rational expectations hypothesis leads to imposing non-
linear cross equation constraints in the estimation. This
obviously also leads to the use of non-linear estimation
methods.

Testing whether the restrictions hold (are supported
by the data) calls for a likelihood ratio test comparing
the unrestricted maximum likelihood to the restricted one.
An alternative procedure is a Wald test. An estimation of
the unrestricted model is needed. Then, it is studied how
much the unconstrained estimates fail to satisfy the
restrictions. For that purpose analytical expressions of
the restrictions are required, these being quite complex to
obtain. In Chapter 5 we estimate the model and conduct a

likelihood ratio test.

74

CHAPTER 5

ESTIMATION RESULTS

The linear rational expectations inventory model
specified in Chapter 4 was estimated for the U.S. soybean
oil market and a test of the rational expectations
restrictions was conducted. In what follows we present the

results of this analysis.

5.1. Data

Quarterly data are used, starting in the first quarter
of 1980 and ending in the third quarter of 1997 for a total
of 71 observations. Table 6 details the variables names,
units of measurement and the corresponding sources. Price
variables are real (in dollar/cents of October 1997),
deflated by the Producer Price Index (PPI); personal
consumption expenditures are in billions of (1996) dollars
and interest rates are real, computed by subtracting the
quarterly inflation rate (as per PPI) from the nominal
interest rate. Quarterly crushing capacity (three month
agregate) is reported in million bushels by the National
Oilseed Processors Association. In Annex III data

descriptive statistics are presented.

75

5.2. Exogenous variables processes

Of great importance for model estimation is the
determination of the data generating processes for
exogenous variables. Exploratory work conducted with
different stochastic processes specifications lead us to
the conclusion that, for most variables, autoregressive
processes of order one are appropiate representations of
the data generating processes. Table 6 shows OLS estimates

of AR(1) processes for all (seven) exogenous variables.

Table 6. Exogenous variable AR(1) processes

 

 

Param EX PEN RS BMP RBP CRCAP X RFF R RLARD
Const -0.81 28.76 115.22 1.71 257.08 0.77 272.4
{-0.04) (2.08) (2.43) (0.20) (5.70) (1.74) (2.23)
.AR(1) 1.00 0.88 0.84 1.00 0.27 0.88 0.87
(211.5) (15.0) (13.5) (47.3) (2.4) (15.9) (15.5)

Q(10) 14.12 12.48 12.06 12.57 7.30 9.83 13.15

 

Note: t statistics are in parenthesis. Q is Box-Pierce
statistic at the 5% level. The chi-square critical value is
18.30

Results obtained also leads us to conclude that all
but three (EXPEN, CRCAP and RFFR) exogenous variables

follow stationary autoregressive processes of order one.

For the three mentioned variables it is not possible to

76

reject the hypothesis of pure random walks. In Table 7
results of Augmented Dickey-Fuller for the mentioned
variables are presented. The test included a constant,

trend variable and one period lagged first differences.

Table 7. ADF test on EXPEN, CRCAP and RFFR variables

 

 

Param EXPEN CRCAP RFFR
Slope -0.04 -0.15 -0.10
ADF Stat. -l.19 -1.60 -2.75

 

Note: MacKinnon critical value is -3.47 at 5%
significance level

We modeled EXPEN, CRCAP as AR(1) and allowed for the
AR parameter estimates to be generated in the course of the
estimation. In contrast, the RFFR stochastic process
restriction was analytically imposed.

The seasonal component in the supply equation, as well
as the trend component in inventory demand equation were
assumed to be known with certainty and the multi-step ahead
forecasts drawn upon these variables were computed using

this assumption.

77

5.3. The complete model

The model estimated is:

Structural equations

 

DISSt = a0 + 31 RSBOPt + a2 EXPENt + a3 RLARD 4' en (1)

be + b; RSBOPt + b2 RSBMPt + b3 RBPt + b4 CRCAPt

PRODt
+51Dl+SzD2+S3D3+€2t (2)

COt = C0 + c1 [Et RSBOPt+1 - RSBOPt] + c2 T + C3 RFFR + e3t (3)

Exogenous variable processes

 

EXPENt = hog + 1101 EXPENt-1 (4)
RSBMPt = 1110 + hll RSBMPt-1 (5)
RBPt = hzo + h21 RBPt-1 (6)
CRCAPt = 1130 + h31 CRCAPt-1 (7)
Xt = h4o + h“ Xt_1 (8)
RLARD: = hso + 1151 RLARDt-1 (9)

Market clearing condition

 

COt-1 + PROD: = DISSt + Xt + COt

5.4. Econometric procedures
Price expectations are non-observable which calls for

transformation of the model into an estimable form based

78

only on observed data, as described in Chapter 4. Once this
is done econometric estimation of the model is possible. In
this study, due to the simultaneous nature of the model,
the Full Information Maximum Likelihood (FIML) method was
used applying GAUSSX software.

In the course of the estimation, the model and the
processes governing exogenous variables were simultaneously
estimated. Also, and importantly, the root restriction
implied by the model was imposed in the course of the

estimation, according to following formula:
A = 1+0.5(b1-a1)/c1-0.5( (bl-a1)/c1) (1+4c1/b1-a1) )0-5 (10)

Starting parameter values of equations (1) and (2) are
based on OLS estimates. Starting values for equations (4)
to (9) are based on FIML estimates of these equations.
Starting parameter values in equation (3) are 1670 (mean
carry over), 0.5, 0 and 0 for the constant term, ch ch and
c3 respectively. Several combinations of different starting
values in this equation resulted in similar results in all

cases .

79

5.5. Results

In Table 8 we report results of the model estimation.

Table 8. FIML parameter estimates

 

 

Variable No. Param. Estimate pIValue
Consumption

Constant 1 a0 506.21 0.08
RSBOP 2 a1 -0.170 0.00
EXPEN 3 a2 0.584 0.00
RLARD 4 a3 0.137 0.03
Production

Constant 5 b0 -304.50 0.66
RSBOP 6 bl 0.889 0.00
RSBMP 7 b2 15.670 0.00
REF 8 b3 —7.558 0.00
CRCAP 9 b4 8.509 0.00
D1 10 51 -47.225 0.62
D2 11 52 —371.167 0.00
D3 12 53 -608.317 0.00
Inventories

Constant 13 c0 3340.595 0.00
Price Aprec. 14 c1 18.117 0.00
Trend 15 c2 -17.974 0.14
RFFR 16 c3 -100.112 0.03
Processes

Constant 17 h00 1.805 0.93
EXPEN 18 h01 1.007 0.00
Constant l9 h10 11.108 0.10
RSBMP 20 hll 0.952 0.00
Constant 21 h20 8.167 0.63
REP 22 h21 0.986 0.00
Constant 23 h30 3.504 0.76
CRCAP 24 h31 0.996 0.00
Constant 25 h40 253.871 0.00
X 26 h41 0.378 0.00
Constant 27 h51 332.627 0.11
RLARD 28 h52 0.885 0.00

 

80

A total of 28 parameters were estimated. The
estimation reached convergence in 95 iterations with a
tolerance level of 0.001 and a log-likelihood value of
-3514.192.

All structural parameter estimate signs are in
accordance with economic theory. The own price elasticity
of demand is -0.159 computed when computed at the means,
which is in the range of previous studies.

The crucial parameter in the model, c1, which measures
the inventory demand response to expected price
appreciation in stocks is positive at 18.12 and is
statistically significant at a 5% significance level. The
parameters c2 on the Trend variable is negative but not
statistically significant. The parameter c3 on the interest
rates is also statistically significant at a 5%

significance level.

Table 9. R? and residuals tests

 

 

Equation R2 D.W. Order
DISS 0.85 1.537 -
PROD 0.84 0.927 1
CO 0.79 1.566 -

 

Table 9 shows R? statistics for equations (1), (2) and
(3) at 0.85, 0.84 and 0.79 respectively. Results on

equation (3) show the important explanatory relevance of

81

speculative inventory demand. Our results compare favorably
to about an average R? of 0.71 in previous studies (Houck,
Ryan, and Subotnik, 1972; Meyers and Hacklander, 1979; and
Meyers, Helmar and Devadoss, 1986). The results are not
strictly comparable as these studies used different
specifications and data.

Table 9 also show Durbin-Watson statistics. There is
no strong evidence of autocorrelation on equations (1) and
(3) as the test statistics lie in the indecisive area.
There is, however, evidence of serial autocorrelation in
equation (2). Correlogram analysis leads us to believe
residuals are follow an AR(1) process.

The inventory demand elasticity with respect to
‘expected price is 28.26 when computed at data means.

The root parameter was estimated, based on the
restrictions implied by formula (10), at 0.147. The
estimate is consistent with a priori expectations (higher
than zero and lower than one) and is consistent with a low
degree of serial autocorrelation in quarterly prices.

The results obtained are consistent with economic
theory and support the hypothesis that expected future
price appreciation plays a role in spot price
determination, through inventory demand in the soybean oil

market.

82

5.6. A Test of the rational expectations restrictions

A likelihood ratio test was conducted to test whether
the data and our model specification support the rational
expectations hypothesis imposed in this study.

The likelihood ratio test as described by Wallis (1980) and
Hoffman and Schmidt (1981) consists of comparing the log-
likelihood of the restricted and unrestricted model.
Specifically, the test statistic is two times the
difference between the unrestricted and restricted log
likelihood values, under the null that the rational
expectations hypothesis is true. The asymptotic
distribution of the test statistic is Chi-square with
degrees of freedom equal to the number of restrictions
being tested. Importantly, the test is a joint test of the
rational expectations restrictions and the proposed model
specification (the structural equations and exogenous
variables stochastic processes).

We conducted an estimation of the unrestricted model
under FIML. A total of 34 parameters were estimated.
Convergence was achieved in 89 iterations. The log-
likelihood is -3506.12.

The critical Chi-square value for 6 degrees of freedom

(the number of restrictions) is 12.59 at a 5% significance

83

level. The test statistic value is 16.08, and rejects the
null of rational expectations and model specification. The
computed test statistic p-value is 1.4%

The test result suggest that the model specification
and the rational expectations hypothesis jointly are not

supported by the data.

5.7. Limitations of the study

The most important limitations of this study are
related to model specification. In particular, the
variables are in levels not logs, the latter being the norm
in previous studies. The need for consistency between the
structural equations and the material balance identity
forced our research effort to assume linearity in the
levels of the variables. Some studies, however, have relied
on log-linear specifications of consumption demand and
supply equations.

The convenience yield specification that we used is a
very simplified one. Although assuming that inventory
levels should increase as the market size increases (in the
long run) is a reasonable representation of reality,
convenience yield also has short run implications that our

simple trend-line specification may not have captured.

84

Exports were assumed exogenous, in spite of evidence
suggesting that they are endogenous.

There is also a limitation on the supply equation.
Research efforts tend to show that crushing margins have
explanatory power over supply of soybean oil. Our
specification, although in line with this approach, did not
impose the corresponding parameter restrictions in the
supply equation (i.e. b1= m 0.225, b2= m 0.011 and b3=-m) .
This may explain the resulting autocorrelation evidence.

Finally, our results may be subject to simultaneous
equations bias as the prices of soybeans and soybean oil
are simultaneously determined with soybean oil prices.

These aspects may explain why the rational expectation
restrictions were rejected even though significant
parameter estimates in the inventory demand equation were
obtained.

Given that rejection of the rational expectations
restrictions is a common feature in econometric work it
might be worth to explore alternative ways to judge the
model performance.

In particular, we have not conducted a test of how
well the estimated model predicts (out of sample) price
behavior compared to models where inventory demand is not

specified or simpler models based on the stochastic

85

properties of the time series. This would also help to
assess the model's practical use as a predictive

instrument.

86

CHAPTER 6

CONCLUSIONS

In this study we estimated a linear rational
expectations storage model following the tradition of Muth
(1961). Our study is the first one to apply this analytic
framework to the estimation of a model of the U.S. soybean
oil market.

The estimation of such a model requires an observable
form of the rational expectation of future prices. To do
so in a model-consistent framework, an expectational
difference equation must be solved. This results in
expected prices depending on multi-step ahead forecasts of
exogenous variables. To obtain the later we exploit the
time series properties of exogenous variables.

Estimation results are in agreement with theory. Most
importantly, the parameter on expected price appreciation
of stocks value in the inventory demand equation is of the
correct sign and statistically significant, providing
evidence of speculative inventory demand. Also, a good fit
of the inventory demand equation was obtained.

The results support the hypothesis that expected
future prices impact on current prices through inventory

demand. This finding contradicts claims made by previous

87

studies indicating that anticipated future market
conditions may be unimportant in assessing price prospects
for primary commodities.

Our work supports the view that soybean oil inventory
demand behavior contributes to price stability.

However, a likelihood ratio test rejected the
rational expectations restrictions. It is our view that,
although this fact casts doubts on whether the rational
expectations hypothesis is a sensible way to model
expectations in the soybean oil market, the specification
limitations commented in Chapter 5 may be at least part of
the explanation.

Importantly, this study shows that statistically
significant estimates of the relevant inventory model
parameters can be obtained in a linear framework while
imposing the rational expectations restrictions in the .
course of estimation. The non-linearity issue is not a
major obstacle to getting reasonable results.

Further work might include an assessment of out-of-
sample forecasting power compared to simpler model
specifications, since it is important to assess the extent
to which price forecasting improves when inventories are
modeled. Work should also be oriented towards the

estimation of the non-linear inventory model making use of

88

the stochastic dynamic programming algorithm embeded in
the maximum likelihood estimator. It would be important to
compare results of both estimates of the Cl parameter and
check whether the claim made in the introduction of this
study (about the approach implemented in this study to be

a reasonable estimator) is actually correct.

89

1. ..

90

ANNEX

I

Model

d
t

a0 + a1 Pt 4' a2 Xlt + Vt
Qst = b0 + 131 Pt + b2 xzt + ut
It = C0 + Cl [Br Pt+1 " Pt] + C2 X3t + C3 X4t

1H + OS. = th + xot + I.

she—re.

Qfi; : Consumption demand

Qfi; : Production

It : Inventory demand

Xlt : Consumption demand shifters
X2t : Production shifters

X3t : Inventory demand shifter

X4t : Inventory demand shifter

X0t : Exports

vt : Random error term
ut : Random error term
t : Time

91

(1)
(2)
(3)

(4)

To obtain an estimable form of the model we:

substitute (1), (2) and (3) into (4)

 

C0+C1(Er-ipt'Pt—l]+C2X3t-1+C3X4t-1+bo+b1Pt+b2X2t+Ut =

ao+a1Pt+azx1t+Vt+XOt+C0+C1 [Etpt+l-Pt] +c2X3t+C3X4t

and operate

 

ClEt-ipt’CTPt-1+C2X3t-1+C3X4t-1+bo+b1Pt+b2X2t+ut =

ao+a1Pt+a2X1t+vt+X0t+co+clEtPt.1-c1Pt+c2X3t+c3X4t

We rearrange

 

ClEt-lpt‘clPt-1+b1Pt‘aTPt'ClEtPt+1+C1Pt =

ao'bo'C2X3t_1'C3X4t_1"b2X2t+azxlt+X0t+C2X3t+C3X4t-ut+vt

And regroup

 

ClEt-lPt-ClEtPt+l+ (bl-81+C1)Pt‘C1Pt-l =

ao-bo-C2X3t-1-C3X4t-1-b2X2t+a2X1t+X0t+C2X3t+C3X4t-ut+Vt

We take expectations as of t-l

 

C31Et-l[Et-1 Pt] "ClEt-i Pt+l+(k:)l-al'+’cl)Et--1Pt-ClEt-1Pt-1 =
ao‘bo‘CzEt-1X3t-1‘C3Et-1X4t-l'szt-1X2t+azEt-1 X1t+Et-1X0t+CzEt-1 X3:

+C3Et-IX4t-Et-lut+Et-lvt

92

.-.““T.{

l

By the law of iterative expectations

 

ClEt-lpt-ClEt-lpt+l+ (bi-81+C1) Et-IPt—ClEt-lpt-l =
aO—bO—CZEt-1X3t-l-C3Et-1X4t-l-b2Et-1X2t+aZEt-let+Et-1X0t+CZEt-1X3t

+C3Et-1X4t“Et-1Ut+Et-1Vt

Rearranging

 

'ClEt-1Pt+1+(bi-a1+2ci)Et-lpt’CiEt-TPt-l ’-

aO—bO-CZEt-lx3t-l-C3Et-1X4t-l-bZEt-1X2t+aZEt-lXlt+Et-1xot+C2Et-1X3t
+C3Et—1X4t
which is

Et-1Pt+1—Cl-l (bl’a1+2C1)Et_1Pt+Et-1Pt-1 =
(31-1(bO-ao)+Cl-1C2Et-1X3t-1+Cl-1C3Et-1X4t-1+Cl-lb2Et-1X2t”Cl-lazEt-IXIt -

Cl-l Et-1X0t-C1-1C2Et-1-X3t-C1-lC3Et-1X4t

We operate on the LHS with lagged polynomials

 

E.-.P..1 L"E.-1P.

Et-lPt+l = L Et-lPt

to obtain:

 

L-lEt-lPt—Cl—l(bl-al+2Cl)Et-lPt+LEt-1Pt = (L-1+9+L) For-1P:

93

where

cl'l (bl-a1+2c1) = e

We pre-multiply in both sides of the equation by L

L (L'1+e+L)E.-1P. = Lc."(bo - a0)
+ cl-1C2LEt-1X3t-1+C1-lc3LEt-1X4t-l
+ cl'lszEt-1X2t —c1'1a2LE.-1 Xlt-cl’lLEt-1X0t

- cl'lchEt-1X3t-c1’1c3LEt-1X4t

to obtain

 

(L+eL+L2) Et-1Pt = Lc1'1(bo—ao)
+ Cl-lCZEt-1X3t-2+Cl-lCBEt-1X4t-2
+ Cl-leEt-1X2t-l-Cl-la2Et-l Xlt-l-ClfilEt-lXOt-l

-1 -1
" C1 CzEt-1X3t-1’C1 C3Et-1X4t-l

The LHS can be expressed as:

(l‘AlL) (1'A2L)Et-lpt

where

A1+A2 = e and AlAz = l

which implies

A1 = A2-1

94

—
r.
A.

T... .__....-_

Thus

 

(1-A1L) (1-A2L)E.-1P. = Lc.’1 (be-ao)
4" Cl-1C2Et-1X3t-2+C1-1C3Et-1X4t-2
+ cl-lb2Et-1X2t-l’Cl-laZEt-l Xlt-l_cl-1Et-1XOt-l

-1 -1
" C1 CzEt-1X3t-1’C1 C3Et-1X4t-l

Pre-multiplying both sides by -(AflrJ)/(l-Afl54)yields

(1->.2L)i«:..1Pt = -A2L-1Lc1'l (bo-ao) / (1-A2L‘l)

+(Azc1'1c2)/ (1-A2L")Et-1x3.-2+ (Azcl‘lcn/ (1-A2L'liE.-ix4.-z
+ (A2C1-lb2) / (1-A2L'1)E.-ix2.-1- (Azcl‘laz) / (1-A2L'1)Et_1 x1.-.
" (A2C1-1)/(l-AzL-1)Et-1X0t-1 - (A2C1-1C2) / (1‘A2L-1)Et-1X3t-1

—(A2c1'1c3)/(1-A2L'1)Et-lx4t-1

Note that:

 

-(A2L—')(l—AZL)/(1-AZL'1) = 1

Also that:

 

-A2L-1Lc1'1(bo-ao)/(1-A2L'1) = c." (bo‘ao) A2/ (AZ-1)

95

. “1

1‘1“

Thus we obtain (dropping the subscript on A2)

 

Et_1Pt = A Pt-1 + c1’1(bo-ao)A/ (A-1)
+ Acl’laz 21-0 )8 E.-. x1...
- Acl‘lbz 21-0 A1 E.-. x2...
+ Acl'lcz [i=0 Ai Et-1 X3“)
+ Acl’lcz 21:0 Ai Et-l X4t+i

4* AC1.l 21:0 Ai Et—l X0t+i

n-

- AC1-1C2 [i=0 A1 E:t-l X3t+i-1

ILAA—‘l .

- AC1-1C3 21:0 Ai Et-l X4t+i-l

If we assume that X0, X1 and X2 follow AR(1) processes such

that:

X01: = hqo + 1141 XOt-l 4' eo:

Xlt h10 + hll Xlt-1 4' en

h20 + 1121 XZt-l + 92:

X2t

then (see Annex II):

 

AC1.1 21:0 Ai Et-l X0t+i = (Act-11140) / ( (l'A) (l‘Ah4o))

+ ((Aci'lh...) / (1-Ah41) mo.-.

Aci‘laz 21-0 >3 E.-. x1... = (Ac1'1h10a2>/<(1—A) (1"Ah10))

+ ((Acl'lhuaz) / (1‘Ah11) )x1.-,

96

Acl'lbz Z.-. A1 E.-. x2... = (Ac1'1h20b2)/((1-A) (l'Ahon

+ ((Aci'lhmbz) / (1-Ah21) )x2.-.

If a component of the X2t vector is a seasonal dummy

 

variable (see Annex II), then;

 

AC1-151 £i=0 Ai Et-l D1t+i = AC1-151/ (1-r4)

If we assume that X3 is a trend variables and X4 follows a

 

random walk (see Annex) then:

 

Acl'lcz )3.-. A1 E.-. x3... = (Ac1'1c2)/(l-A)2

+ ((Ac1‘1c2) / (1-2.) )x3.-.

Acflc. 21:0 20 E.-. x3“.-. = (Azci'lcz) / (1-2.) 2

+ ((AC1'1C2i/(l-A))X3t-1

AC1-1C3 21:0 A1 Et-1 X4t+i = ( (AC1-1C2)/(1-A) )X4t-1

Ac1'1c3 [i=0 A1L Et-l X4t+i-1 = ((AC1-1C2)/(1-A))X4t-1

Thus we obtain following expression for Equt

 

EHP. = 2. P.-. + c1"(bo-ao)A/(A-1)

+ (AC1-1hioaz)/((1'A) (l’AhioH + ( (AC1-1h1182)/ (1-Ah11) )Xlt-l

97

- (Aci'lhzob2)/((1-M (l-Ahon — ((Aci'lhmbzi/(l-Ahzn)xz.-1

+ (Aci'lhmi/(u—M(1-Ah.o)) + ((Acl'lhnwu—Ahm)xo.-1
- (Aci'lsl/(l-r“))

+ (Aci'lcn/(l-A)2 ‘ (Azci'lczwu-MZ

which we lead one period

 

Eth = A Pt + c1'1(bo-ao)A/(A-l)

+ (Ac1'1h10a2)/((1-A) (15.1.10)) + ((Ac1'1h11a2)/(l-Ah11))Xlt
- (Ac1’1h20b2)/((l-A) (1-Ah20)) - ((Acl'lh21b2)/(l-Ah21))X2t
+ (Ac1’1h4o)/((1-A)(l-Ahqo)) + ((Acf'huwu—xmlnxot

- (Acl'lsl/(l-r4))

+ (Acl'lcn/(l-A)2 - (Azcl‘lcn/(l-AV

Note that

 

(Acl‘lczi/(l—M2 - (Azcl'lcn/(l-M2

= -(Ac1"c2)/(A-1)

We substitute EQ§.1in equation (3) to obtain

 

 

It = C0 + C1[A Pt + C1-l(b0'ao)A/(A2‘l)
+ (Aci'lhloazwiil-A)(1—Ahloii + ((Aci'lh11a2)/(1-Ah11))Xlt

" (AC1-lh20b2)/((1"A) (1-Ah20)) ’ ((AC1-1h21b2) / (1"Ah21) )X2t

98

£4

+ (Aci'lhmi/(u-A)(1%.th + ((Aci'lhnHu—Amnixot
- (Acl'lsi/(l-rm -((Ac1'lc2)/(A-1)) - Pt]

+ C2X3t + C3X4t

which is

It = Co + CLAPt + (rm-ao-c2)A/(A-l)

+ (Ah10a2)/((1-A)(l-Ahlo)) + ( (Ah11a2)/(1-Ah11))X1t
- (Ah20b2)/((1-A) (1-Ah20) ) - ( (Ah21b2)/(l-Ah21) )X2t
+ (Ah4o)/((1'A)(1-Ah4o)) + ((Ah41)/(l-Ah41))X0c

- (Asl/ (1-r4))

+

C2 X3t + C3X4t

Thus estimate the model

 

(1) th = 80 + al Pt + 32 Xlt + Vt
(2) Qst = b0 + b1 Pt + b2 X2t + U:
(4) It = C0 + C1(A-1)Pc + (bO'aO‘C2)A/(A'1)

+ (Ah1082)/( (1‘A) (l'Ah10)) + ((Ah1132)/(1‘Ah11))X1t

(Ah20b2)/((1-A) (l-Ahon - ( (Ah21b2)/ (1-Ah21) )X2t

+

(A1140) / ( (l-A) (1—Ah40) ) + ((Ah41)/(1-Ah41) )XOt

(Acl‘lsi/ (1-r‘))

+ C2 X3t + C3X4t

99

(5) XOt = 1140 + 1141 XOt-l + 80c
(6) X1: = h10 + hll Xlt-l + elt

(7) X2t = h20 + h21 X2t-1 + 82:
and impose the root restriction

A = 1 + 0-5<b1-a1>/cl - 0.5((b1-a1)/c1) (1+(4c1/(b1-a1))°'5

100

 

ANNEX I I

101

We look for an estimable form if the multi-step ahead

 

forecasts of exogenous variables:

 

£130 AiEt-1Xt+i where (AI < 1

If we assume that X follows an AR(1) process:

 

X. = ho + hllqu + et ; where Ihll < 1; et~D(0,o)

 

then

Et-lxt = Et-l[h0 + hl Xt-l + er]

= ho + hl Xt-1

Et-1Xt+1 = Et-l[h0 + hl Xt + ecu]

ho + 1'11 Et-lxt

ho + h1[ho + hi xt-l]
= ho + hlhO + 1112 xt-l

= ho(1 + h1)+ hf x.-1

Et-lXt+2 = Et-l[h0 + hl Xt+1 + €t+21

ho + hl Et-lxt+l

ho + h1[ho + hlho + hf x.-.)
= ho + mm. + hizho + hf x.-.

= ho(1 + 111+ 1112) + hl3 Xt-l

102

Et-lxt+i = ho(1 + h1+ hTZ-oo-h11)+ hi1+1 Xt-l

Now

21-0 A1 Et-1Xt+i = zinc Ai[ho(1 + 111+ 1112- . - -h11)+ him Xt-l]

£1=o A1 Et-lxt+i = £i=0 Ai [ho(1 + h1+ 1112. - . ohli) 1+ £1=o A1 hlhl Xt-l

21-0 A1 mix... = (ho/((1-A)(1'Ah1)) + (hi/(l-Ahn) x.-.

If Xt = hy4Xp4 + e. ; where Ihll < 1; et~D(0,o), then

 

 

 

21-0 >3 mix... = (hi/(l-Ahn) xm

If Xt = l + Xtd + et ;where et~D(0,o), then

 

 

2.3. x' me... = 1/(1-2.)2 + (1/(1-Ai) x.-.

If Xt = X94 + et ;where et~D(0,o), then

 

£10 A1 max... = (1/(l-Ai) x.-.

The seasonal components muti-step ahead forecasts are:

 

21:0 Ai Et-1D1t+i ’-
21-0 A1 Et-1D2t+i =

21-0 A1 Et-1D3t+i =

103

where

£i=0 Ai Et-lDltH'. = A0 Et-1D1t+0 + A1 Et-1D1t+1 + A2 Et-1D1t+2

x3 13.4131...3 + x4 3.431... xi E.-1D1.+1

Since D1 is defined such that

 

Dluo = 1 ;(first quarter)
DIUJ = 0 ;(second quarter)
D1“. = 0 ;(third quarter)
Dlug = 0 ;(fourth quarter)
Then:

 

Zi=oA'E.-101..i= A0 (1) + 2.1 (0) + 28- (0) + 2.3 (0)

A4 (1) + x5 (0)...

which is

{1:0 A1 Emma. = A0 + A4 + x8 ...= l/(l-A")

In the same fashion we can compute

 

[i=0 >3 Emma. A1 + 2.5 + 2.9... = A/(l- 2.4)

21-0 A1 EHDB... A2 + A6 + 2.10... = AZ/(l- A4)

104

ANNEX III

105

Descriptive statistics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable name Acronym Mean Std. Dev Minimum Maximum
Carry In CI 1666.5 534.7 632.0 2893.0
Production PROD 3235.9 454.7 2316.0 4303.0
Imports M 3.4 7.6 0.0 36.0
Exports X 415.7 191.6 72.0 1149.0
Dissapereance DISS 2818.3 424.1 2064.0 3810.0
Carry Out CO 1671.8 529.9 632.0 2893.0
Real SBO RSBOP 2637.8 561.0 1887.5 4365.0
price

Real SBM RSBMP 233.5 45.1 151.2 354.1
price

Real Bean RBP 750.8 129.9 581.0 1132.4
price

Real Lard RLARD 2114.4 581.2 1375.5 3725.1
price

Expenditures EXPEN 4222.7 674.8 3149.2 5453.1
Crush CRCAP 407.3 32.0 347.1 482.7
capacity

Real F.F. RFFR 7.2 3.3 2.0 16.9
Rate

 

 

 

 

 

 

 

 

106

 

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