«EFFECTS OF CCC S'E'QCKS ON THE CASH-FUTURE
PRiCE SPREADS m {363.1%

Thesis for flue Segree of M. S.
MtCHIGAN STATE UNIVERSWY
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Michigan State
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EFFECTS OF CCC STOCKS ON THE
CASH-FUTURE PRICE SPREADS

FOR CORN

BY

Robert N. Wisner

A THESIS

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

MASTER OF SCIENCE
Department of Agricultural Economics

1963

Approved i Cj7é:;:2§;1i /;7?é2rqéiuuj4i;dp

The object
price-support act:
corn through their
and (2) to obtain
stocks as a variab
were considered as
for corn storage.
Supply of storage 1
storage space. Eff
assumed to be throu
demand for corn.

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to be com consump:

 

other grains , inter

 

 

ABSTRACT

EFFECTS OF PRICE-SUPPORT PROGRAMS ON
THE CASH-FUTURE PRICE SPREADS FOR CORN

by Robert N. Wisner

The objectives of this study were (1) to determine whether CCC
price-support activities have affected cash-future price spreads for
corn through their effects on the commercial supply of corn storage
and (2) to obtain predictions of the cash-future spreads with CCC corn
stocks as a variable. In the economic framework, cash-future spreads
were considered as being determined by the commercial supply and demand
for corn storage. Price-support programs might affect the commercial
supply of storage through changes in the quantity of unoccupied grain
storage space. Effects on the commercial demand for storage were
assumed to be through changes in the current and future-supply and
demand for corn.

The main variables determining cash-future spreads were believed
to be corn consumption, commercial (non-CCC) corn stocks, stocks of
other grains, interest cost, the general price level and time. This
'relationship was studied at four separate dates during the year;
January 1, April 1, July 1, and October 1. Regression equations were
computed in pairs containing the same variables; one equation was based
on the 1927-1962 period and one was based on the 1934-1962 periodl

The longer period provided seven observations prior to the beginning of

Robert N. Wisner
CCC activities; more would have been desirable, but data for earlier
years were not available. If CCC activities have affected the commercial
supply of corn storage it was believed that the relationships between
spreads and the independent variables might be changed for the 1934-1962
period as compared with the longer period. Consequently, significant
differences in the correSponding regression coefficients for the two
time periods and significant coefficients for CCC stocks might be ex-
pected.

Within the limitations of the approach and the data, no evidence
was found that CCC activities have affected spreads through their effects
on the commercial supply of storage on January 1, April 1, or July 1.
However, the October 1 equations provided some evidence that CCC activ-
ities may have affected the commercial supply of storage at the beginning
of the marketing year. In each of three pairs of equations which were
computed for that date, the equation based on the shorter period pro-
vided a considerably better fit in terms of R2, R and Sy.x than the
equation based on the longer period. In addition, for the shorter
period, only the coefficients of the variable for CCC stocks were signif-
icant at the 10 percent level. Direct statistical tests, however, re-
vealed no significant differences in the corresponding coefficients of
October 1 equations for the two periods. This appeared due to the small
number of coefficients which were significantly different from zero.
’Effects of CCC activities on the commercial supply of storage would
appear to be through their effects on congestion in marketing firms at
harvest time rather than through a tightening up of the supply of un-
occupied grain storage space in total.

Predictions of cash-future spreads can be obtained from the

Robert N. Wisner
equations provided estimates of the independent variables are available.
However, the equations appear to be more useful as a framework for
determining the effects of changes in the independent variables on the
spreads. For January 1, significant relationships were found between
spreads and commercial corn stocks, corn consumption, and time. Corn
consumption and time were also important variables for April 1 and
July 1 equations. An additional variable, stocks of other grains, was
important for July 1. In the October 1 equations, the most important
variable determining spreads appeared to be CCC corn stocks, although

corn consumption was also of some importance.

EFFECTS OF CCC STOCKS ON THE
CASH-FUTURE PRICE SPREADS

FOR CORN

By

Robert N. Wisner

A THESIS

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

MASTER OF SCIENCE

Department of Agricultural Economics

1963

 

ACKNOWLEDGEMENTS

The author wishes to express his sincere appreciation to every-
one who has contributed to the completion of this thesis.

Special thanks are due Dr. Lester V. Manderscheid, the author's
major professor, for his encouragement and interest throughout the
development and completion of the study. Helpful suggestions from
Dr. David H. Boyne are also very much appreciated.

The author is grateful to Dr. Lawrence L. Boger for supplying
financial assistance in the form of an assistantship, thus making
graduate study possible at this time. Thanks are due the departmental
secretaries for typing the rough draft of the thesis. Assistance of
the statistical pool in computing the equations is also very much
appreciated.

The author wishes to thank Mrs. Lucille Wells for her expert
typing of the final of the manuscript.

Finally, the author wishes to express gratitude to his wife,
Marelene, for her constant understanding and encouragement while the

study was in progress.

ii

TABLE OF CONTENTS

Chapter Page
I. DEFINING THE PROBLEM . . . . . . . . . . . . . . . . . . l

The General Approach and Objectives . . . . . . . . . . l

The Characteristics of Corn . . . . . . . . 3

Price Support Operations for Corn Since 1933 . . . . . 14

II. REVIEW OF LITERATURE RELATED TO THE EFFECTS OF
GOVERNMENT PROGRAMS ON THE CASH-FUTURES PRICE

SPREAD . . . . . . . . . . . . . . . . . . . . . . . . 25
Descriptive Studies . . . . . . . . . 25

Factors Affecting the Quantity Placed Under
Price Support . . . . . . . . . . . . 32

Government Programs and the Cash- Future

Price Spreads . . . . . . . . . . . . . . . . . . . . 34
Summary . . . . . . . . . . . . . . . . . . . . . . . . 36
III. THEORY OF THE CASH-FUTURE PRICE SPREADS . . . . . . . . . 37
Hedging Purposes and Functions . . . . . . . . . . . . 37
The Supply and Demand for Storage . . . . . . . . . 42

The Introduction of a Government Supply and
Demand for Storage . . . . . . . . . . . . . . . . . 49
Hypothesis to be Tested . . . . . . . . . . . . . . . 55
IV. THE METHOD OF ANALYSIS . . . . . . . . . . . . . . . . . 57
The Approach . . . . . . . . . . . . . . . . . . . . . 57
The Data . . . . . . . . . . . . . . . . . . . . . . . 60
V. RESULTS OF THE ANALYSIS . . . . . . . . . . . . . . . . . 71
January 1 Equations . . . . . . . . . . . . . . . . . . 72
April 1 Equations . . . . . . . . . . . . . . . . . . . 91
July 1 Equations . . . . . . . . . . . . . . . . . . . 103
October 1 Equations . . . . . . . . . . . . . . . . . . 113
VI. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . . 126
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . 136
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

iii

Table

10.

ll.

12.

13.

LIST OF TABLES

Acreage Harvested and Production of Corn for
Grain in U.S., 1927-1962 .

Percentage of the Total Corn Crop Acreage Planted
With Hybrid Seed .

Percentages of the Total Corn Supply Accounted for
by Feed and Other Uses, 1958-1959

Price Support Program for Corn--l933 Through 1963

Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation l-l

Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 1-2 .

Actual Adjusted December Spreads and Spreads
Estimated With Equations 1-1 and 1-2 .

Simple Correlations Between the Variables, Standard
Errors and t Values of the Coefficients of
Equation 1-3

Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of

Equation 1-4 .

Actual Adjusted December Spreads and Spreads
Estimated With Equations 1-3 and 1-4 .

Standard Errors and t Values of the Coefficients
of Equation 1-5

Standard Errors and t Values of the Coefficients
of Equation 1-6

Actual Adjusted December Spreads and Spreads
Estimated With Equations 1-5 and 1-6 .

iv

Page

16

73

76

78

80

82

83

84

85

86

Table Page

14. Simple Correlations Between the Variables,
Standard Errors, and t Values of the Coefficients
of Equation 2-1 . . . . . . . . . . . . . . . . . . . . 92

15. Simple Correlations Between the Variables,
Standard Errors, and t Values of the Coefficients
of Equation 2-2 . . . . . . . . . . . . . . . . . . . . 93

16. Actual Adjusted March Spreads and Spreads Estimated
With Equations 2-1 and 2-2 . . . . . . . . . . . . . . . 94

17. Standard Errors and t Values of the Coefficients
of Equation 2-3 . . . . . . . . . . . . . . . . . . . . 95

18. Standard Errors and t Values of the Coefficients
of Equation 2—4 . . . . . . . . . . . . . . . . . . . . 96

19. Actual Adjusted March Spreads and Spreads Estimated
With Equations 2-3 and 2-4 . . . . . . . . . . . . . . . 97

20. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 2-5 . . . . . . . . . . . . . . . . . . . . . . 99

21. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 2-6 . . . . . . . . . . . . . . . . . . . . . . 100

22. Actual Adjusted March Spreads and Spreads Estimated
With Equations 2-5 and 2-6 . . . . . . . . . . . . . . . 101

23. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 3-1 . . . . . . . . . . . . . . . . . . . . . . 104

24. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 3-2 . . . . . . . . . . . . . . . . . . . . . . 105

25. Actual Adjusted June Spreads and Spreads Estimated
With Equations 3-1 and 3-2 . . . . . . . . . . . . . . . 106

26. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 3-3 . . . . . . . . . . . . . . . . . . . . . . 107

27. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 3-4 . . . . . . . . . . . . . . . . . . . . . . 108

28. Actual Adjusted June Spreads and Spreads Estimated
With Equations 3-3 and 3-4 . . . . . . . . . . . . . . . 110

V

Table Page

29. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 4-1 . . . . . . . . . . . . . . . . . . . . . . 114

30. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 4-2 . . . . . . . . . . . . . . . . . . . . . . 115

31. Actual Adjusted September Spreads and Spreads
Estimated With Equations 4-1 and 4-2 . . . . . . . . . . 116

32. Standard Errors and t Values of the Coefficients
of Equation 4-3 . . . . . . . . . . . . . . . . . . . . 117

33. Standard Errors and t Values of the Coefficients
of Equation 4-4 . . . . . . . . . . . . . . . . . . . . 118

34. Actual Adjusted September Spreads and Spreads
Estimated With Equation 4-3 and 4-4 . . . . . . . . . . 119

35. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of
Equation 4-5 . . . . . . . . . . . . . . . . . . . . . . 120

36. Simple Correlations Between the Variables, Standard
Errors, and t Values of the Coefficients of

Equation 4-6 . . . . . . . . . . . . . . . . . . . . . . 121

37. Actual Adjusted September Spreads and Spreads
Estimated With Equations 4-5 and 4-6 . . . . . . . . . . 122

vi

Figure

LIST OF FIGURES

The Supply of Storage

Equilibrium of the Supply and Demand for Corn in
Current and Future Time Periods

Equilibrium of the Supply and Demand for Storage
The Government Supply and Demand for Storage .
The Commercial Supply and Demand for Storage

Variables Determining the Quantity of Commercial
Corn Stocks Carried From Period t to Period t+1

vii

Page

48

49
49
52

52

56

CHAPTER I

Defining the Problem

 

During the past 30 years, American agriculture has been char-
acterized by high production and government price-support programs.
Government programs to stabilize farm prices evolved from a desire to
overcome an inherent weakness of the agricultural economy: the in-
flexibility of production processes in the short-run. The "Ever Normal
Granary" was set up to achieve that objective by storing grain from
large crOps as a reserve for years of small crops and unforeseen
national emergencies. This system was reasonably successful during
the 1930's and 1940's. However, from 1953 to 1961 the nature of govern-
ment price-support programs resulted in a steady increase in government
controlled stocks of grain. Doubts were raised as td whether the Com-
modity Credit Corporation (hereafter referred to as the CCC) would con-
tinue grain storage operations of the magnitude obtained in recent
years. Then, with the passage of the 1961 Feed Grain Program these
doubts were strengthened. In view of possible reductions in government
grain storage programs, questions arise as to what would be the impact

of such changes on firms in the grain trade.

The General Approach and Objectives

 

The logical approach to determining the effects of changes in
CCC grain storage programs on the grain trade appears to be an examination

1

2

of the effects of government storage programs in the past. Such an
examination should provide a basis for generalizations about the effects
of future changes in government programs. The purpose of this thesis
is to examine the effects of government price-support activities since
the introduction of the CCC on one aspect of the grain trade; the
cash-futures price spreads. The study will be limited to an examination
of the cash-futures price spreads for one commodity, corn, at a partic-
ular market. The market used, for reasons indicated in Chapter IV, is
the Chicago Board of Trade.

The approach used will be to expand upon a concept introduced
by Holbrook Working, that the cash-future price spread may be regarded
as a return for the creation of time utility, in other words a price of
storage.1 The link between cash and futures prices is stocks. This
provides a mechanism by which firms adjust current and future consump-
tion to levels at which the difference between expected future price
and current price is equal to the net marginal cost of holding inven-
tories of grain over time. Hence, cash and futures prices are intimately
related at all times. Using this theoretical construct, it should be
possible to postulate certain effects of government programs on the
supply and demand for corn storage, and to obtain quantitative estimates
of the magnitude of these effects by statistical analysis.

During the operation of the CCC, vast changes have been taking
‘place in corn production and utilization; consequently the study will

begin with an examination of the characteristics of corn and changes

 

1Holbrook Working, ”The Theory of the Price of Storage,” American_
Economic Review, Vol. XXXIX, December, 1949, pp. 1954-62.

 

3
which have occurred in the supply and demand for corn in the United
States during the period studied. This will be followed by a review
of CCC corn price-support operations since 1933. After a brief summary
of studies related to the effects of government programs on the cash-
future price Spreads for corn, the theoretical relationship between
cash and futures prices will be presented in detail. This will provide
a connection between the supply and demand functions for corn and the
supply and demand functions for corn storage. The theory will then be
expanded to include a governmental supply and demand sector for storage
and the interrelationships between the governmental and non-governmental
storage sectors. A statistical analysis will be attempted for the pur-
pose of separating the effects of various factors influencing the cash-
futures price spreads for corn.

Specifically, the objectives of the study are:

1. To determine whether or not CCC activities have affected the
relationship of cash-future price spreads for corn with commercial corn
stocks, corn consumption, and stocks of other grains.

2. To determine the effects of changes in CCC corn stocks on

the cash—future price spreads.

The Characteristics of Corn

 

Corn is the most important single crop grown in the United States.
Its value is closely related to the supply and demand for livestock.

The 1959 corn crop was worth 4.5 billion dollars, whereas the next most

 

2Unless otherwise indicated, this section is based on Richard J.
Foote, John W. Klein, and Malcolm Clough, The Demand and Price Structure
for Corn_§nd Total Feed Concentrates, U.S.D.A. Technical Bulletin No.
1061, October 1952.

 

 

.4
valuable crop, wheat, was worth 2 billion dollars.3 In this section,
factors determining the supply and demand for corn, and hence its value,
will be described.

Factors Affecting_theu§upply_g£_ggrn.--1n the United States,

 

 

most of the corn is planted during April and May and matures in
September and October, It is harvested during late fall and early
winter and either moves directly into marketing channels or into stor-
age. Production is largely concentrated in the "Corn Belt States" of
Iowa, Illinois, Indiana, and parts of Ohio, Wisconsin, Missouri, Kansas,
Nebraska, South Dakota, and Minnesota. This group produces around two-
thirds of the total United States output.

Corn production in 1950 accounted for about 48 percent of the
total supplv of feed concentrates, oats accounted for 13 percent, barley
and sorghum grains about 8 percent, bv~product feeds fed 12 percent,
domestic wheat, rye, and imported grains fed 2 percent, and stocks 1
percent. In 1960, corn production made up 42 percent of the total
supply of feed concentrates A During 1926-1945, stocks of the four
feed grains, in percentage terms, were about twice as variable as pro-
duction and exports were about three times as variable. On a tonnage
basis, changes in stocks accounted for more than 80 percent of the dif-
ference between changes in production and consumption, and net exports

accounted for about 20 percent Imports are relatively unimportant;

 

3Figures are from U S D.A , Agricultural Statistics, 1960, pp.
1, 29. They are obtained by multiplying total production of the crop
by the season average price per bushel.

4U S.D A., E.R.S., Grain and Feed Statistics through 1961,

Supplement for 1961 to Statistical Bulletin No. 159, p. 5.

 

 

5

they normally represent less than 1 percent of the domestic production.
A notable exception was the drought year of 1936 when imports equaled
7 percent of domestic production.

From 1909 to 1933, harvested acreage of corn was relatively con-
stant. However, since the near‘record of more than 97 million acres
was harvested for grain in 1932, acreage has declined. It has not ex-
ceeded 90 million acres since 1933, and since 1945 it has been below
79 million acres. During the post-war period, acreage of corn harvested
for grain reached a low of 57 million acres in 1962.,5

The longnterm downward trend in corn acreage has been more than
offset by a marked upward trend in yield per acre. The opposite trends
in acreage and production are shown in Table l. A major factor con—
tributing to the increased yield per acre since the early 1930's has
been the marked increase in the use of hybrid seed. By 1950 practically
all corn in the corn belt was planted with hybrid seed. As shown in
Table 2, 95.7 percent of the total corn crop acreage in United States
in 1960 was planted with hybrid seed. Other elements have contributed
greatly to higher yields and the expanded production of corn. Fertilizer
and the use of power machinery in corn production have expanded markedly.
The declining acreage also has been accompanied by a general with-
drawal of lower producing land from corn production. In addition,
weather conditions have been more favorable for corn production in

' recent years than during the 193095.

 

5U.S.D.A., E.R.S., Grain and Feed Statistics Through 1961,
Supplement for 1961 to Statistical Bulletin No. 159, p. 7, and
U.S.D A., A.M.S., Feed Situation, August 1963, p. 42.

 

 

 

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7

TABLE 2.--Percentage of the Total Corn Crop Acreage
Planted With Hybrid Seed*

 

 

 

Year Percent Year Percent
1950 78.0 1956 91.1
1951 81.5 1957 92.5
1952 84.6 1958 93.9
1953 86.5 1959 94.9
1954 87.3 1960 95.7
1955 89.4

 

*U.S.D.A., Agricultural Statistics, 1960 and 1961.

 

An indication of the trend in the use of fertilizer for corn
production is suggested by fertilizer use in Ohio, Illinois, Minnesota,
and Missouri. Four times as much fertilizer was used in these states
during 1948 to 1950 as in the late 193095. In these states plus
Indiana, Illinois, and Nebraska, the consumption of the three primary
plant nutrients rose an average of 8 percent per year from 1956 to
1960 and 5 percent from 1960 to 1961. Consumption of nitrogen rose
17 percent per year from 1956 to 1960 and 21 percent from 1960 to 1961.
Analysis of the 1959 census data shows that 69 percent of the three
primaryinutrients and 79 percent of the nitrogen fertilizer used in
these three states were applied to corn. Total primary plant nutrients

applied to corn rose from an estimated 63 pounds per acre in 1960 to
81 pounds in 1961. This was an increase of 18 pounds per acre compared
with annual increases averaging less than 2 pounds per acre from 1956

to 1960.6

 

6James Vermeer, An Economic Appraisal of the 1961 Feed Grain Pro-
gram, Agricultural Economic Report No. 38, U S.D.A., E.R.S., June 1963,
p. 21.

8

The increase in the number of tractors used in the corn belt has
been accompanied by an increased use of larger units of equipment for
seedbed preparation, planting, cultivating, and harvesting corn. This
mechanization has permitted an increased portion of the supply of feed
grains to go into the production of livestock and livestock products
for food and a relatively smaller part to go into the maintainance of
horses and mules for farm power. Mechanization has also made possible
more rapid and timely seedbed preparation and planting, particularly in
wet years. It has reduced the time required for harvesting corn, with
the result that corn is placed on the market earlier than in the past.

In short, acreage planted to corn has been reduced but increased
yields per acre have created an upward trend in corn production.
Mechanization, hybrid seed, and higher levels of fertilizer application
have been the major factors contributing to the increased production.
In addition, they have reduced the time required for harvesting and
have tended to place corn on the market earlier than in previous periods.

Factors Affecting the Demand for Corn.--A1most 80 percent of the
corn produced in the United States is fed to livestock on or near farms
where it is grown. Most of the remainder enters the so-called commercial
supply. Of the commercially sold corn, more than half is sold directly
as grain for feed or is used in mixed feeds. Thus, in total, about 90
percent of the corn produced is used for livestock feed. The remainder
‘ of the commercial supply is used for wet milling (cornstarch, sirup,
sugar, and oil), for dry milling (corn meal, grits, hominy, and break-
fast foods), for alcohol and distilled spirits, and for exports. These
corn processing industries provide the major sources of by-product feeds

fed to livestock, including gluten feed and meal, and distillers dried

9
grains. The percentages of the corn supply accounted for by various
uses in 1958-1959 are shown in Table 3. Of the non-feed uses, exports
have been most variable, ranging from less than 1 percent of the total
in many years to as much as 4 or 5 percent in a few years.

TABLE 3.--Percentages of the Total Corn Supply Accounted for by Feed
and Other Uses, 1958-1959*.

 

 

 

Use Percentage Use Percentage
Seed .4 Export 5.7
Alcohol .9 Livestock feed 86.2
Food 2.7 Wet milling 4.1

 

*Geoffrey 3. Shepherd, Marketing Farm Products, 4th Edition,'
The Iowa State University Press; Ames, Iowa, 1962, p. 435. Based on
U.S.D.A., Agricultural Statistics, 1960, p. 35.

 

 

The dry processing of corn for food is currently only about half
as large as at the turn of the century, reflecting a marked drop in
percapita consumption of corn meal and other dry-process products. In
contrast, the use of corn for producing starch, sugar, sirup, and other
wet-process products has more than doubled since 1909. In recent years
it has been a major non-feed use of corn. However, as Alfred Marshall
has pointed out, the derived demand for a factor of production will be
more inelastic the smaller the fraction of total cost accounted for by
the factor in question.7 For this reason, the demand for corn for non-
feed purposes is highly inelastic; there is practically no relationship
of corn for non-feed uses with its price. Factors connected with the

feed-livestock economy are the principal ones that affect the price

 

7Alfred Marshall, Principles of Economics, Eighth Edition,
Macmillan and Co.; London, 1920, pp. 385~386.

 

10
of corn.

Economic theory tells us that the profit-maximizing farmer will
feed corn up to the point at which the marginal value product of an
additional unit of corn is equal to the price of the additional unit.
Accordingly, it seems useful to briefly examine the factors determining
the marginal value product of corn fed to livestock. These include
livestock prices, the supply of other feed grains, the supply of pro-
tein supplements, and technological relationships in livestock pro-
duction.

A shift to the right in the supply of other feed grains, assuming
all other things remain constant, will reduce their prices. Producers
will then substitute larger amounts of other grains for corn; as a re-
sult the demand for corn will shift to the left. Year to year changes
in the production of other feed grains, however, tend to be associated
with changes in corn production. This should be expected since the
heavy-producing areas for corn and other feed grains coincide to a con-
siderable extent, thus making weather a common factor. In other words,
the supply of corn and the supply of other feed grains tend to move
together.

Livestock prices, which are directly related to the marginal
value product of corn, are determined by the supply and demand for
livestock. Looking first at the supply side, it is obvious that the
supply of livestock products is determined by the number of animals
fed and the level of feeding. The number of animals fed is in turn
related to the demand for livestock. If the demand for livestock pro-
ducts suddenly increases, livestock production and the demand for feed

are usually expanded in the short run by increasing the quantity of

ll
feed fed per animal. However, changes in livestock numbers are more
important than increases in the quantity fed per animal in increasing
livestock production and the demand for corn over a period of a year or
more. A second factor affecting the number of animal units fed is the
availability of feed. Profit-maximizing farmers will feed up to the
point at which the cost of producing an extra unit of livestock is
equal to the marginal revenue. The supply of feed enters since it
affects the cost of producing the additional output.

From these relationships we can see that feed prices and live-
stock numbers are interrelated. If the number of animal units on
farms at any given time is small, higher livestock-feed price ratios
(and therefore lower feed prices) are required to move a given supply
of feed into consumption than if the number of animal units is large.

Let us turn now to changes in the demand for corn over the
years. The increased consumption of livestock products as consumers
moved up the income scale has far overshadowed the decrease in con-
sumption of processed corn products. Technological factors would also
be of some importance except that they tend to be offsetting. Better
breeding and improved feeding practices would improve the efficiency
of production and in this way would increase the returns from a given
volume of corn fed. However, they would also reduce the quantity of
feed required to produce a given output of livestock and hence, would
reduce the demand for corn.

Benedict and Stine point out that the demand for corn has been
modified over the years by an increase in the production and use of
other feed grains such as grain sorghum, oats, and barley, along with

the increased use of byoproduct protein feeds such as cottonseed and

12
soybean meals. These changes also would appear to have been more than
offset by the increased demand for livestock products.

In recent years, the demand for prepared animal feeds has been
increasing rapidly. Over three times as much grain was processed and
manufactured into prepared animal feeds in 1959 as in 1939.9 The
total amount of corn utilized in prepared animal feeds in 1959 was
12.6 million tons.10 This would indicate that farmers are selling a
larger portion of their corn crop than in the past and buying back the
increased portion in the form of prepared feed. Although it should
not affect the total demand for corn, this trend would tend to increase
the total off-farm commercial grain storage requirements.

In addition to the changes in the demand for corn already noted,
there has been a pronounced increase in corn consumption during the
second half of the marketing year.11 In the late 1920's, around 70
percent of the corn consumed as grain was consumed during October to
March and only about 30 percent was consumed during April to September.
The later percentage has gradually increased until in 1956 it was
about 40 percent of the total. From 1946 to 1956 much of the increase

occurred in the July-September quarter. The decrease in the first half

of the marketing year has been principally in the October-December

 

8Murray R. Benedict and Oscar C. Stine, The Agricultural Commodity
Programs - Two Decades of Experience, The Twentieth Century Fund; New York,
1956, p. 186.

 

9Walter G. Heid, Fr., Changing Grain Market Channels, U.S.D.A.,
E.R.S., Marketing Economics Division, ERS-39, November, 1961, p. ii.

1Orbid., p. 19.

1'lMalcolm Clough, "Changing Pattern of Corn Disappearance," U.S.D.A.,

A M 8., Feed Situation, May 21, 1956, p. 24-27.

 

 

13
quarter. At the present annual rate of domestic consumption, this would
mean that, as compared with the late 1920's, about 250 to 275 million
bushels of United States corn consumption has been shifted from the first
half to the second half of the marketing year.

There are several reasons for this change. A U.S.D.A. publica-
tion on seasonal patterns in marketing meat animals reveals that there
has been a marked increase in hog marketings in September, October, and
November since the 1920's, while marketings during January and February
have declined.12 This has increased corn consumption in the July-
September quarter and reduced the quantity fed from the new crop in the
October-December quarter. The trend toward year-round fattening of
beef cattle also has increased consumption in April to September rela-
tive to October through March. In addition, the relatively heavy
feeding of dairy cows during the summer has tended to increase corn
use during that period.

A pronounced increase in broiler production during the past 20
years also has added to corn consumption during April through September.
Commercial broiler production, which was practically nonexistent prior
to 1930 has expanded to the present level of over a billion head
annually. It is estimated that in recent years broilers are fed about
10 to 15 percent more feed during April through September than during
October through March.13 The declining number of farm chickens would

offset a small part of the influence of sharply expanding broiler

 

12Harold F. Breimyer and Charlotte A. Kause, Charting the

Seasonal Market for Meat Animals, U.S.D.A., A.M.S., Agricultural Hand-
book No. 83, June 1955, p. 28—30.

13Malcolm Clough, "Changing Pattern of Corn Disappearance,”
92. 915., p. 27.

 

 

14
production.

Summary of Factors Determining Corn Prices.--The purpose of this

 

section has been to present a general picture of the economic forces
determining corn prices and changes that have occurred in these forces.
Large changes have taken place in corn production and utilization con-
currently with CCC operations. In production, technological changes in
the form of hybrid seed, mechanization, and higher levels of fertiliza-
tion have occurred, thus shifting the supply of corn to the right. On
the demand side, there has been a shift to the right in the demand for
livestock, thus increasing the demand for corn. This effect has been
offset to a small extent by changes in the supply of other feed grains.
There has also been a technological change in livestock production
which would tend to both increase and decrease the demand for corn.
The two effects have tended to cancel each other. Finally the demand
for prepared livestock feeds has increased and the seasonal consumption
of corn has shifted toward a more uniform pattern throughout the year.
The following section will review price support operations for
corn since 1933. Chapter III will present the theory of the cash-
futures price spreads. This will provide a means of connecting the
current and future supply and demand for corn with the cash-future

spreads.

Price Support Operations for Corn Since 193314

In 1933 the newly created CCC was given power to make non-recourse

loans on corn stored under seal on farms where grown. Under the program,

 

14This section is based on Benedict and Stine, QR: Cit., unless

otherwise indicated.

15
farmers in the "commercial'r corn areas, could, if they chose, have
their corn appraised, measured, and put under seal, and could receive
a loan on it at a specific rate per bushel. The loans could be repaid
later with interest if they wished to reclaim the corn. If the market
price remained below the loan level and farmers did not choose to re-
claim it, they could turn it over to the CCC and be absolved from any
obligation to make up the loss. The "commercial" corn area is estab-
lished each year to include counties with a lO-year average production
per farm, exclusive of corn for silage, of 450 bushels or more and an
average of four or more bushels per acre of cropland.15 An additional
requirement for corn placed under price-support loans, since the loans
are based on shelled corn, is that the moisture content must be below
13.5% to insure safe storage. If it is above this level, corn is
likely to get out of condition, to become sour, musty, or heat damaged,
thus adversely affecting its feed value.16

The purposes of the price-support loan program were:

1. To relieve pressure on the corn market and encourage orderly
marketing of the crop.

2. To put money into the hands of farmers immediately without
forcing them to sell corn and hogs quickly in a glutted market in order
to get funds for meeting current obligations.

Price-support operations for corn are summarized in Table 4.
~ This summary will be supplemented by information in the following para-

graphs. The resealing provision is an extension of the loan for another

 

15U.S.D.A., A.M.S., Feed Situation, March 1958, p. 19.

 

16U.S.D.A. Miscellaneous Publication No. 692, Grain Production
and Marketing, p. 24-

 

 

 

 

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21

year or longer. Instead of delivering or redeeming the corn, the farmer
can renew his loan provided the corn is still of good quality.

Some additional government activities occurred during World War
II which are not brought out in Table 4. The United States Department
of Agriculture encouraged the expansion of pork and lard production by
selling government corn at prices below market value. Also 100 million
bushels of wheat were sold at feed prices (about the price of corn).
The program for feeding wheat to livestock was later expanded at the
direction of Congress, and the quantity of wheat fed during the war
period reached a total of nearly 1.5 billion bushels. Normal feed use
would have been about 500 million bushels for the five year period. In
January 1943 ceilings were imposed on corn prices at 100 percent of
parity. That tended to discourage speculative holding of corn for
further price advances. In addition, the demand for livestock products,
and consequently the demand for corn, was partially held in check by
rationing and prices were held down by price controls and consumer
subsidies.

In 1947 the CCC initiated a second form of price support; pur«
chase agreements. Under purchase agreements, the CCC purchases a
specified quantity, or any fraction thereof, of corn if it meets
certain quality specifications and if delivered by the grower during
a certain period. The price set in the purchase agreement is the same
' as the price at which loans are extended. The purchase agreement is
an option, issued without cost to the grower, which he can exercise or

not as he chooses.

 

1'7Lester V. Manderscheid, Influence of Price-Support Program on

Seasonal Corn Prices, Unpublished Ph.D. dissertation, Food Research In-

 

 

stitfife, Stanford University Library; Stanford, California, 1960, pp. 18-
19.

 

22

Until 1949 the CCC was not permitted to acquire any real property
except office space and that already leased when the CCC charter was
granted. In the fall of 1948 large crops caused a severe shortage of
storage facilities; consequently, on June 7, 1949 restrictions on the
ownership of storage facilities were relaxed. However, before the CCC
could construct new storage facilities, it was required to determine
that privately owned storage in the area concerned was not adequate.

In addition to its own purchase and lease program the CCC was directed
to make loans to grain growers in need of storage facilities.18

In the Agricultural Act of 1949, the following provisions were
made concerning CCC sales in the domestic market:

1. CCC sales policies should be worked out so as not to dis-
courage the private trade from acquiring and carrying normal inven-
tories.

2. CCC was not permitted to sell stored commodities at less than
5 percent above the current support price plus reasonable carrying
charges. This restriction did not apply to sales for new or by-product
uses, to sales made because of deterioration in quality, or to sales
for export.

The Agricultural Act of 1956 provided for an Acreage Reserve
Program under which soil bank certificates were issued for reducing
acreages of basic crops. These certificates could be redeemed for cash
'or exchange for CCC grain. The act also initiated a Conservation Re-
serve Program with contracts ranging from 3 to 15 years for land taken

out of production on which a cover crop was or was to be established.

 

18Murray R. Benedict, Can We Solve The Farm Problem?, The
Twentieth Century Fund; New York, 1955, p. 402.

 

23
The program provided payments for establishing conservation practices
and annual cash payments based on the value of the land for crop
production.19

The 1961 Feed Grain Program, approved on March 22, 1961, pro-
vided payments to corn producers who reduced their acreage by at least
20 percent of their base acreage for 1959 and 1960. The payments
ranged from 50 percent to 60 percent of the value of the production of
the diverted acres, figured at the county support price. Half of the
payment would be available immediately to the producer in cash upon
his declaration of intention to comply. Payment certificates were
redeemable either in cash or commodity. If the producer elected to
receive the cash equivalent of the grain, the Secretary of Agriculture
was authorized as the producer's agent to market from existing CCC
stocks the quantity of grain covered by the certificates.20 Thus, an
important aspect of the program was that it permitted CCC to sell
existing stocks of corn at market prices, above or below the support
level. This provision was continued until 1963. Under the 1963 pro-
gram the CCC is not allowed to redeem certificates at less than $1.07
per bushel plus an allowance for seasonal variation.

In summary, price support programs during the early years of
operation attempted mainly to even out fluctuations from year to year
and within year in the supply of corn. The war years were charac-

' terized by price ceilings, rationing, and attempts to expand production.

Following a post-war readjustment period, CCC stocks began to accumulate.

 

19U.S.D.A., A.M.S., Feed Situation,op. Cit., September 21, 1956,

 

p. 19.

20Commodity Exchange Authority, The Corn Futures Market 1961-62,
U S.D.A.; Washington, D. C., p. 7.

 

 

24

From 1953 to 1961, with high levels of corn production, large CCC
stocks were built up. Then in 1961 there was an abrupt shift in policy.
CCC was permitted to sell corn in the domestic market at the market
price even if the loan price was above the market price. In 1963, CCC
was again prevented from selling corn, other than that deteriorating
in quality, in the domestic market at less than a specific price.

The following chapter will review previous studies of the effects
of CCC price support programs on the demand for storage facilities,

marketing firms, and the cash-future price spreads.

 

CHAPTER II

Review of Literature Related to the ‘Effects of Government

“n-“ 0-“—

’ Programs on the Cash Futures Price Spread

 

The purpose of this chapter is to review and summarize previous
studies of the effects of government price—support programs on the
supply and demand for corn storage and on the cash-future price spreads
for corn. This information will complete the problem setting and will

provide a background for selecting the analytical approach.

Descriptive Studies

 

Several descriptive studies have attempted to determine the
impact of government programs on grain production and marketing. These
studies provide some idea of the nature and magnitude of the construc-
tion of grain storage facilities that has taken place in recent years
and problems in grain marketing that have arisen under government
price-support programs.

Schumaier, in a study of grain production and marketing in
Illinois, indicates that between 1955 and 1958, total off-farm grain
storage space in Illinois increased about 45 percent from 202 million
bushels to about 293 million bushels.21 During this period processor
storage space remained virtually unchanged. All of the space added
was located in country, subterminal, and terminal elevators. Total

21
t—- -.Il~r,:'l: r-r.‘ a---

Agricultural Experiment Station Bulletin No 637; Urbana, Illinois,
February 1959, p 103.

C P Schumaier, I11inois Crain Production and _Trade, Illinois

25

26

storage space in country elevators increased by about 84 percent, while
subterminal and terminal space increased by around 58 percent. During
the same period, CCC binsite storage increased by about 36 percent.
Information which was obtained on recent and planned additions at the
time of the 1955 survey indicated that much of the country elevator
space added since 1955 has been flat, steel, warehouse-type construction
with aerating equipment designed to store corn for the CCC.

In a 1954 survey Schumaier attempted to determine whether a
shortage of storage facilities existed in Illinois. The survey re-

vealed that the average occupancy of storage space at terminal, sub-

 

terminal, and processing plants was about 62 percent. For elevators

the occupancy level was 70 percent; for processors it was around 56
percent. Processors, terminal and subterminal elevators reported 19
percent of their average volume was stored for CCC and another 5 percent
for farmers largely on loan agreements that pass to the CCC upon their
expiration. Country elevators, in rough terms, carried stored-grain
inventories consisting of one-third for farmers, one-third for the CCC,
and one-third for themselves.22 The data upon which these estimates
were based was obtained from responsible executives in the firms inter-
viewed and was for one year only. Hence, Schumaier warns, it should

be interpreted with caution. However there did not appear to be any
shortage of storage space at the processor and terminal level in 1954.23

It is also interesting to note that CCC storage was most often reported

as long-term storage of a year or more. Processors, as would be

 

221bid., p. 59.
231bid., p. 49.

27

expected, stored predominately for their own accounts although some
space was rented to the CCC.24

CCC-owned facilities were found to be entirely flat storage that
requires filling, turning, and emptying with portable handling equip-
ment. Consequently, its use is economically limited to long-term
storage, of which CCC is almost the only user.

It should be recognized that storage space requirements are not
uniform throughout the year, particularly for elevators located in the

grain producing areas. For this reason, an average level of occupancy

may be misleading in attempting to ascertain whether adequate storage

 

facilities exist. At harvest time facilities are required for storing
large volumes of grain until they can be shipped to other links in the
marketing chain. Country elevators, river, and terminal elevators fre-
quently become temporarily filled when transportation is not immediately
available during favorable harvesting weather.

Schumaier reported that in Illinois, there were ample handling
facilities at the country elevator level, although handling problems
do arise in years when the bulk of the harvest arrives in a single week
and rail cars are short in supply. This results from the fact that
country elevators had a little over half enough space to store the
peak load as computed by Schumaier from 1949-53 average sales and 1955
storage space.25 For Illinois in total the available grain storage
space was slightly over twice as much as would be needed for the com-

puted peak load and about 3.5 times as much as would be needed for the

 

24Ibid., p. 50.

251bid., p. 56-57.

28
computed average load. The amount of storage space available, however,
varied greatly from region to region.26 It should be noted that a lack
of storage space at the local level at harvest time may limit the
quantity of corn going under loan.

Schumaier concluded, at the time the bulletin was published, that
grain storage space in Illinois was adequate to handle peak requirements
with space left over at the terminals for imported grain. Between 1951
and 1954 a large amount of storage was also constructed for the United
States in total. In February 1955 the U.S.D.A. indicated that from
1951 to 1954 a national increase of almost 645 million bushels of
capacity of commercial grain storage facilities took place. This does
not include government owned or farm storage facilities.27 For the
period 1951 to 1962, total off-farm commercial grain storage capacity
increased from 2,176 million bushels to 5,489 million bushels; in other
words, total commercial storage capacity has more than doubled since
1951. From January 1, 1961 until January 1, 1962 it has increased by
about 10 percent, nearly a half billion bushels.28 These figures
would tend to indicate that for the United States in total there has
been a definite lack of grain storage space.

A Great Plains Agricultural Council publication indicates that

there has been a lack of grain storage facilities in other states, at

 

 

least at harvest time. "Congestion at the local elevator at harvest
26Ibid., p. 57-58.
27U.S D.A. Press Release 491-55, February 28, 1955.
28

From U.S.D.A., S.R.S., Stocks of Grains in All Positions,
Washington, D. C., January 24, 1962, p. 11. Cited in Geoffrey S.
Shepherd, Marketing Farm Products, 4th Ed., The Iowa State University
Press; Ames, Iowa, 1962, pp. 437-38.

 

 

 

29
time is a common thing throughout the Plains States. This problem is
aggrevated if the local elevator finds itself filled with 'dead storage'
of grain which is owned by CCC or by farmers with loans who have not
yet decided whether to sell or whether to forfeit the grain."29 When
grain does not flow into use, the country or terminal elevator often
finds itself cramped for space to carry on its merchandising and pro-
cessing operations. Another factor which has contributed to congestion
at harvest time is the technological change in corn harvesting. This
along with improved roads and truck transportation have reduced the
main harvest period to three or four weeks.

A recent North Central Regional Research Publication was directed
toward finding the reasons for the large amount of storage construction,
whether excess storage capacity would exist if CCC acquisitions were
reduced or a series of poor crop years occurred, and what has been the
effect of government storage programs on marketing firm operations. In
the North Central region, construction of grain storage capacity in
selected terminal markets had increased while the volume of shipments
and receipts had decreased. "It is evident that this additional stor—
age space was not constructed in response to an increase in merchandising
activity. Rather, it was the result of an increase in the demand for

space to store CCC grain."3O

 

9Norris Anderson, Clarence Miller, Leonard Schrubben, Obed Wyum,
and Layton Thompson, Economic Aspects of Grain Storage in the Northern
Great Plains, Great Plains Agricultural Council Publication No. 14,
Montana Agricultural Experiment Station Bulletin 523; Bozeman, Montana,
August 1956, p. 32.

 

 

3OGeoffrey S. Shepherd, Allen Richards, and John T. Wilkin, Some
Effects of Federal Grain Storage Programs on Grain Storage Capacity,
Grain Stocks, and Country Elevator Operations, Indiana Agricultural
Experiment Station Research Bulletin 697, June 1960, (North Central
Regional Publication No. 114), p. 9.

 

 

30
An important reason for the large response to increased CCC de-
mands for storage was that several incentives have been provided to
encourage the expansion of storage facilities. The first of these were

occupancy contracts, which began as informal agreements between CCC and

 

warehousemen that CCC would not use its own storage facilities in a
local area if privately owned storage Space was available. In August
and September 1953 and from May through August 1954, formal occupancy
programs were in effect. The crucial point of these programs was
guaranteed occupancy.

A second incentive for storage construction was accelerated

 

amortization. The internal revenue code of 1954 provided for depre-

 

ciation of new and remodeled storage facilities over a five year
period.

Storage and handling agreements have provided an additional in-

 

centive for storage space expansion. These agreements are contracts
between CCC and individual warehousemen to handle and store CCC grain.
Stored CCC grain has provided revenue from receiving, storing, condi-
tioning, and loading out. In 1959 this amounted to a total of 21¢ per
bushel for one year's storage plus handling.33

Cooperative elevators were allowed financial aid from cooperative

 

banks for building grain storage facilities. such loans required that
the cooperative have a commitment from CCC guaranteeing utilization of

not less than 75 percent of the storage space constructed for at least

 

31Ibid., p. 4.

32Ibid., p. 5.

33Ibid., pp. 5—6.

A 1...? 2‘ 1'! I”
Ii .

 

31

three years if the structure was not an addition to the existing struc-
ture or for at least two years if it was. These loans could be made
for up to 80 percent of the cost of the storage facility.34

The study indicated that CCC tended to store most of its corn
stocks in CCC-owned facilities and the lowest proportion in terminal
storage, excluding processors. However, from 1956 to 1958 CCC corn
stocks rose considerably but only a small part of the increase was
stored in CCC-owned facilities; most of it was stored in commercial
subterminal and country elevators. In 1958, 33 percent of the total
CCC off-farm corn stocks was stored in subterminal and country elevator
facilities, 56 percent in CCC-owned or controlled facilities, and 11
percent in terminals. In contrast with corn, 54 percent of the CCC-
owned wheat was stored in subterminal and country elevators, 33 per-
cent in terminals, and 13 percent in CCC-owned or controlled storage.35
This latter information as we shall see in Chapter III, has relevance
for the quantity of corn storage which will be supplied since as
stocks of other grains increase, less storage space is available for
corn storage. From this information, it appears that a tightening of
available storage in subterminals, country elevators, and terminals
may have been occurring due to CCC wheat storage.

Apparently, CCC influence has been stronger in country areas
than in terminals, since construction of country elevator space between

1946 and 1954 increased at a greater rate than storage construction in

 

34Ibid., p. 6. From Allen E. Korpela, Federal Farm Law Manual;
Oxford, N. H., Equity Publishing Corp., 1956, p. 51.

 

35Geoffrey S. Shepherd, Allen Richards and John T. Wilkin, "The
Grain-Storage Picture,” Iowa Farm Science, 14, June 1960, p. 8-520.

 

 

32

selected terminal markets. In the terminal markets, any sharp reduction
in the wheat storage program could leave the elevators with excess
capacity not readily convertible to other uses.36

Grain storage construction has been of two general types: flat
storage (quonset type, for example) which can be converted readily to
alternative uses such as for storage of fertilizer, feed, and other farm
supplies, and permanent storage which has no important alternative uses.
In Iowa, on the average, almost as much flat capacity as upright capac-
ity exists. In addition, capital structures of Iowa cooperative

elevators indicated that managers expected adequate grain for merchan-

 

dising and storing to utilize the additional storage space in event

CCC storage operations were reduced.37

Factors Affecting the Quantity
Placed under Price Support

 

 

We have seen that CCC has encouraged a rapid expansion of grain
storage facilities. Government price support operations raise another
question: What determines the level of the CCC demand for these new
facilities? Allen Richards found that the main factors affecting the
quantity of corn placed under price support loan were:38

1. The demand for corn as evidenced by the number of livestock

on feed.

 

36Indiana Research Bulletin 697, QR: Cit., p. 9, from John Wilkin,
Impact of U.S.D.A. Support Program on Commercial Grain StoraggJ Unpub-
lished M.S. thesis, Iowa State University Library; Ames, Iowa, 1958,
p. 74.

 

37Indiana Research Bulletin 697, Ibid., p. 10.

38Allen B. Richards, "Factors affecting the Quantity of Corn
Placed under Loan," The Ninth Annual Symposium, Commodity Markets and
the Public Interest, Proceedings, The Chicago Board of Trade,
September 5, 6, 7, 1956, p. 147.

 

33

2. Corn supply conditions arising out of production each year.

3. The relationship between the market price and the loan price.

Richards found that the larger the corn crop in relation to the
demand for corn, the larger the quantity of corn sealed. For a given
supply of corn, an increase in the number of animal units on feed would
decrease the amount of corn available for sealing under the government
price support program. However, the most important factor affecting
the quantity of corn sealed is the difference between the market price
for corn and the loan price. The amount of corn sealed increases at
an increasing rate as the market price falls below the loan rate. The
reason for this is that if the loan rate is above the market price, the
marginal returns from feeding will be equated to the loan rate and any
corn not fed will be placed under support if it is eligible. The
further the loan rate is above a given market price the sooner the
marginal returns from feeding will be equated to the loan rate and the
greater will be the amount of corn resealed. If, on the other hand,
the loan rate is below the market price, there will be very little
incentive to put any corn under loan.

In addition, Gerald Gold points out that loan prices must be
above market prices before farmers will feel the difference is worth
the time and trouble of taking out a loan. Also, the amount of grain
eligible for loan may be limited due to high moisture content or for

other reasons.

 

391bid., pp. 149-154.

- 40Gerald Gold, Modern Commodity Futures Trading, The Commodity
Research Bureau, Inc.; New York, 1959, pp. 96-97.

 

34

Government Programs and the
Cash-Future Price Spreads

 

 

For the commodities wheat and cotton, Telser studied the supply
of storage during the operation of €00.41 For cotton the period studied
was 1934-1954; for wheat it was 1927-1954. The empirical supply curves
were constructed by regression analysis of interoption spreads, com-
mercial stocks, and consumption. An additional variable, stocks of
other grains, was included for wheat.

The effects of changes in the fraction of stocks held by CCC
seem to vary during the year. For cotton, at each date studied an in-
crease in the fraction of total stocks held by the government decreased
the spread. However, in most cases the coefficient of government
stocks was not statistically significant.

The wheat storage supply curve was studied for the dates July 31,
September 30, December 31, and May 31. On September 30 and December 31
an increase in government stocks relative to commercial stocks increased
the spreads. For the other two dates, an increase in government stocks
relative to commercial stocks decreased the spread. Perhaps the reason
for this, Telser suggests, is that during the middle part of the crop
year a considerable part of government stocks is held as loan collateral.
It is possible that the convenience yield of such stocks is quite
high.42

One other study has dealt directly with the effects of government

programs on the cash-futures spreads. Manderscheid, in an analysis of

 

41Lester G. Telser, "Futures Trading and the Storage of Cotton
and Wheat," Journal of Political Economy, Vol. 66, June 1958, pp. 233-
255.

 

42Ibid., p. 252.

35
the effects of government programs on the seasonality of corn prices,
used the cash—future price spreads to isolate the seasonal element of
corn prices. Consequently, one phase of his work involved an examina-
tion of the effects of government price-support programs on the seasonal
pattern of the cash-future price spreads. The time period studied was
1901 to 1954.

Manderscheid concluded that there has been an increase during
the price-support period in the level of the spread and also an increase
in the spread prior to harvest time. It should be mentioned here that
these spreads are cash price minus future price, while spreads in
Chapter III will be discussed as future price minus cash price. Hence
there has been an increase in the cash price relative to the future
price during the support period or a decrease in the level of Spreads
when considered as future price minus cash price. The larger spread
prior to harvest during the support period apparently has resulted from
a shortage of available corn supplies prior to harvest. This, in turn,
has resulted in a greater change in cash-futures price Spreads at har-
vest time. Technological developments which have allowed more rapid
harvesting and marketing have contributed to an earlier timing of the
seasonal low for the September spread during the support period.43

Following harvest there is less advantage in holding corn rela-
tive to the September future than there was in the pre-support period.
This is due to (l) the smaller average increase in the spread during
the year, and (2) the greater variability of the spread in the support

period years. This variability is partially related to uncertainties

 

43L, V. Manderscheid, op, 315., pp. 97-98.

36

about the effects of the program and changes in it.

Summary

We have seen that much descriptive work has been done on the
effects of government programs on the availability of storage facilities
and on marketing firms. In addition, one study examined the changes in
the seasonality of cash-future price Spreads which have been associated
with government price support operations. In the case of wheat and !
cotton, quantitative estimates have been made of the effects of govern- I

ment programs on the total supply of storage. However in the case of

 

corn, no quantitative estimates have been made of the relationship of
government storage to cash-future price spreads. As a prelude to
estimating this relationship, the economic relationships determining

the cash-future spreads will be specified in the following chapter.

 

11311., p. 98.

CHAPTER III
Theory of the Cash-Future Price Spreads

In previous sections we have reviewed the major factors deter-
mining the supply and demand for corn. We have looked at CCC opera-
tions since 1933 and their effects on,the supply of corn. In Chapter
II, some major effects of government programs on grain storage capacity
and on marketing firms were examined. In addition, some effects of
government programs on the seasonality of cash-futures spreads for
corn were presented. The purpose of this chapter is to assemble these
factors into an economic framework that will indicate the interrelation-
ships between various variables and the price spread.

Since futures trading exists mainly for hedging purposes, this
chapter will begin with the purposes and functions of hedging. In the
first section the forces which cause cash and futures prices to move
together will be delineated. The following section will demonstrate
how these forces can be considered as a supply and demand for storage.
A final section will introduce government storage programs into the

economic framework.

Hedg1ng Purposes and Functions

According to the traditional concept, hedging consists of
matching one risk with an opposing risk. For example, millers or
other grain processors who sell their products at a fixed price for
future delivery before they can obtain needed grain, usually buy grain

37

38
futures contracts at the time of the forward delivery sales. Later,
when the grain is purchased, the futures contracts are sold. In such
transactions any loss caused by an advance in grain prices is expected
to be offset by gains made in the sale of futures contracts.45

At this point a definition of futures trading is in order.
Futures trading involves a contract in which a seller agrees to deliver
a certain class, quantity, and grade of grain, with provisions for
delivery of other classes or grades at differentials, at a stated place
at a designated future date, and a buyer agrhes to accept and pay for
such grain at the time of delivery. These contracts are between members
of an organized exchange and are subject to the rules and regulations
.of the exchange upon which the trade is made. Persons who are not
members of the exchange may carry on futures transactions through
members of the exchange.46 Normally less than 1 percent of all futures
contracts are actually held for delivery.

From the above example, it is apparent that the usefulness of
hedging in the traditional sense depends upon a reasonably stable rela-
tionship between cash prices and the prices of futures contracts. How-
ever, Holbrook Working has pointed out that hedging is done for a
variety of reasons other than simple risk-avoidance. He suggests that

there are five main types of hedging.47

Carrying;§harge hedgigg is done in connection with the holding

 

45U.S.D.A., Miscellaneous Publication No. 692, 9B: Cit. p. 60-61.
46Ibid., p. 59.
47

Holbrook Working, "New Concepts Concerning Futures Markets and
Prices,“ American Economic Review, Vol. LII, No. 3, June 1962, p. 438.

 

39

of commodity stocks for direct profit from storage. In contrast to the
traditional concept that such hedging is done only to reduce the risk of
stock-holding, the main effect of carrying-charge hedging is to trans-
form the operation to one that seeks profit from anticipating changes
in cash-futures price relationships. The decision the carrying-charge
hedger makes is not primarily whether to hedge or not, but whether to

48

store or not. '

Operational hedging normally entails the placing and "lifting" “

 

of hedges in such quick succession that changes in the cash-future price

relationship over the interval can be largely ignored; this is the main 1

 

fact which distinguishes operational hedging from carrying-change
hedging. Because of the short intervals over which operational hedges
are carried, the amount of risk reduction accomplished tends to be in-
sufficient to explain the observed frequency of such hedging. In view
of this the main use of operational hedging is apparently to simplify
business decisions and allow operations to proceed more steadily than
otherwise. For example, in the flour milling industry, buying and
selling decisions are made easier by judging prices on particular lots
of wheat in terms of their relation to wheat futures prices rather than
in terms of absolute level.49

Selective hedging involves hedging or not hedging stocks according
to price expectations. Because the stocks are hedged when a price de-

cline is expected, the purpose of such hedging is not risk avoidance, in

the strict sense, but avoidance of loss. Personal inquiry by Holbrook

 

481331., p. 38.

491bid., p. 439.

40
Working among large and well-managed firms in the grain trade has re—
vealed that, though hedging is their standard practice in most parts of
the country, they sometimes hedge incompletely.SO To the extent that
they allow circumstances in individual instances to influence the deci-
sion whether to hedge unsold stocks or not, they hedge selectively.
From an economic standpoint, selective hedging deserves appraisal as a
means of allowing handlers of a commodity to increase the efficiency
“of their participation in the price-forming process instead of largely
withdrawing from such participation, as in the case of routine carrying-

charge or operational hedging.

 

Anticipatory hedging is carried out when the futures contract is
not offset by either an equivalent stock of goods or a formal merchan-
dising contract. It takes either of two forms: (d)purchase contracts
in futures acquired by processors or manufacturers to cover raw material
"requirements," or (b) sales contracts in futures by producers, made in
advance of the completion of production. In either form, the anticipa-
tory hedge serves as a temporary substitute for a merchandising contract
that will be made later. The purpose of such hedging may be said to be
to take advantage of the current price.51

Pure risk-avoidance hedging, which involves avoiding the risk of
both price increases and price decreases, is unimportant or virtually
52

non-existent in modern business practice.

From these categories of hedging, an overall definition of hedging

 

50Ibid., p. 439.
51Ibid., p. 441.
52

Ibid., p. 442.

41
evolves. Hedging in futures can be defined as the process of "making
a contract to buy or sell on standard terms, established and supervised
by a commodity exchange, as a temporary substitute for an intended later
contract to buy or sell on other terms."53 Speculation, in the ordinary
usage of the term, refers to buying and selling (or more accurately, hold-
ing) purely for the sake of gain from price change, and not merely as
an incident to the normal conduct of a processing or merchandising busi-
ness. The importance of this definition can be seen in the objection
of business purchasing agents to being said to speculate when they seek
to time their buying, within reasonable limits, in accordance with their
judgment of price prospects.

According to the traditional concept of hedging, futures traders
are sharply divided into two classes, speculators and hedgers. Risk is
transferred from hedgers to Speculators. The question arises, do
speculators require a fee for their risk bearing services. This question
will be discussed in the following section. The significance of the
newer concepts is that hedging is not done solely for the reduction of
risk. Hedgers take part in many of the roles traditionally assigned to
speculators.' They also take more active roles in the price formation
process than was previously supposed. This is not to imply that specu-
lators are not important in futures markets. However they are not as

important as the traditional concept of hedging implies.

 

53Holbrook Working, "Hedging Reconsidered," Journal of Farm

Economics, Vol. XXXV, No. 4, November 1953, p. 560.
-54Holbrook Working, "New Concepts Concerning Futures Markets and
Prices," 92: Cit., p. 442.

 

42

The Supply and Demand for Storage

 

Holbrook Working has pointed out that continuous arbitrage be-
tween cash and futures prices results from the fact that if it appears
at any time that cash prices in the delivery month would be higher than
the present price of the future, more buyers than sellers of that future
would appear and the price of the future would be bid up to equality
with the expected price in the delivery month (except for variations in
the quality and location of the deliverable grain represented by the
futures contract as compared with the quality represented by cash
prices).55 This continuous arbitrage between cash and futures prices
makes it necessary in most considerations of price influences, to regard
the two sets of prices as determined in a single market.56 "At the
cash-grain tables buyers and sellers ordinarily do not discuss prices;
they bargain in terms of cents 'over' and cents 'under.‘ When agree-
ment is reached in these terms, the premium or discount settled on is
applied to the latest quotation for the 'basic' future to arrive at a
formal price."57

Futures trading, due to constant arbitrage between cash and
futures prices, provides a means of allowing cash prices to reflect
expectations regarding future events. Expectations influencing futures
prices should always affect both cash and futures prices, unless a

period intervenes when stocks from past and future production are ex-

pected to be non-existent. The reason for this is related to the fact

 

55Holbrook Working, "Theory of the Inverse Carrying Change in

Futures Markets,” Journal of Farm Economics, Vol. XXX, No. 1, February
1948, p. 5.

56Ibid., p. 5.

57Ibid., p. 7.

 

43

that futures prices equal or are closely related to cash prices expected
at the time the future matures. The difference between cash and futures
prices, then, provides a good approximate index of the return which can
be expected for providing storage of the commodity.58 When the expected
returns for storing are large, firms will store larger quantities of
the commodity than when the returns for storage are small. Since stor—
age is essentially a means of transferring part of the current supply
to the future supply of the commodity, it is apparent that if current
and future demands are given and all other factors determining current
and future supply are given, an increase in stocks will affect cash
prices and futures prices in opposite directions. For example, suppose
expectations of a short crop in the future period result in an initial
increase in the future price relative to the current price. This will
provide an incentive for larger stockholding, thus shifting current
supply to the left and raising the current price. At the same time the
future price will be reduced by a shift to the right in the future
supply.

Using this framework, we can think of the cash-future price
spread as a price of storage. The question arises, however, what is
the explanation for a large amount of storage space being supplied even
when the price of storage is zero or negative? One condition which makes
that possible is the fact that grain storage is an enterprise in which
most of the costs are fixed, from the short-run standpoint. Owners of
large storage facilities are generally engaged either in.merchandising

or processing and maintain storage facilities as a necessary adjunct to

 

58Holbrook Working, "Theory of the Price of Storage," American
Economic Review, Vol. XXXIX, No. 6, December 1949, p. 1254.

 

44

their merchandising or processing business. Consequently, the costs
of storage may be charged against the rest of the business, which re-
. . 59 . . 60

ma1ns profitable. As N1cholas Kaldor has p01nted out:
In normal circumstances, stocks, of all goods possess a yield,
measured in terms of themselves, and this yield which is a
compensation to the holder of stocks, must be deducted from
carrying costs proper in calculating net carrying cost. The
latter can, therefore, be negative or positive.

Kaldor also tells us that the marginal yield of such stocks falls
sharply with an increase in stocks above "requirements" and may rise
very sharply with a reduction of stocks below "requirements." There is
some level of stocks at which the marginal yield is zero. The yield
of stocks which are used up in production comes from the opportunity to
lay hands on them the moment they are needed, as well as from a re-
duction of the cost of frequent orders, deliveries, and delay.

With the introduction of a convenience yield, the net marginal
cost of storage can be considered as the marginal outlay minus the
marginal yield. For clarity, the yield will be referred to as the
marginal convenience yield. This explains why inventories are carried
when the apparent return is zero or negative.

There is one limitation which was hinted at in the first section
of this chapter that should be pointed out. The futures prices may be
discounted expected futures prices or may be reduced by a "risk premium"

which is necessary to persuade speculators to perform the risk-bearing

function. That problem cannot be dealt with here. The assumption will

 

591bid., p. 1260.

6ONicholastaldor, "Speculation and Economic Stability," Review
of Economics Studies, Vol. VII, 1939-40, p. 3.

 

45
be made that if such a "risk premium" exists, it should remain rela-
tively constant; hence the prices of futures contracts should be very
closely related to expected future prices. This does not appear to be
a serious limitation in view of an observation made by Roger W. Gray in
a study of corn futures prices at Chicago for 1921-1940 and 1947-1959
that "No 'downward' bias was evident in corn futures in either of these
two periods."61

Since it has been shown that cash and futures prices are in-
timately related at all times through stocks, the next step in devel-
oping a theory of the cash-future price Spreads is to specify the forms
of the supply and demand for storage.

The demanders of storage are an economic group who desire to
have stocks carried from one period in which they do not intend to con-
sume the commodity into another period in which they do intend to con-
sume it. Brennan suggests that, consequently, the demand for storage
of a commodity can be derived from the demand for its consumption.
Under the assumption that all variables affecting consumption except

price are exogenous, the demand function for consumption in period t

can be written as:

it.
69.

is consumption in period t, and Z

,
Pt = Et (Ct zit); < 0, where Pt is price in period t, Ct

it are I other "exogenous" variables

in period t. The subscripts indicate that the variables may shift

 

61Roger W. Gray, "The Search for a Risk Premium," Journal of
Political Economy, Volume LXIX, No. 1, June 1961, p. 255, For a dis-
cussion of the issues involved see: P. H. Cootner, "Returns to
Speculators: Telser vs Keynes," Journal of Political Economy, Volume
LXVIII, August 1960, pp. 396-404 followed by L. G. Telser, "Reply,"
P. H. Cootner, "Rejoinder," pp. 408-18. J. M. Keynes, A Treatise on
Money, 11, Macmillan and Co., London, 1930, pp. 142-47.

 

 

 

 

46

periodically.62 For convenience, the notation Zi will be dropped from

t
the other equations in this section. Given a fixed demand function for
period t, the price in period t is determined by the intersection of the

supply and demand for the commodity. This can be written as:

P = f (St_1 + X

t t represents stocks at the end

- St) where St-

t l

of period t-l, Xt is production t, and St is stocks at the end of t.
For convenience, it is assumed that current production and subsequent
levels of production and stocks are known.

Similarly, the price of the commodity in period t+1 can be

written as:

 

Pt+1 = ft+1 (St + Xt+1 - St+l)' An increase in St in period t

can be thought of as shifting the supply function for the commodity to
the left in period t, thus raising Pt’ assuming all other things are
constant. At the same time it will shift the supply function for the

commodity in period t+1 to the right, thus lowering P assuming all

t+1’

other things constant. The demand function for storage can now be
written'as:

Pt+1 ‘ Pt = ft+1 (C

Pt+1 ' Pt ft+1 (St + xt+1 ' t+1

t+1) ' ft <Ct) or

).

s ) - f (st_1 + xt - s

t t

The partial derivative of the above expression with respect to St is
assumed negative. Hence the demand for storage is a decreasing function
of the cash-future price spread.63 In general, the demand for storage

of a commodity from period t to period t+1 will shift to the right as

 

62Michael J. Brennan, "The Supply of Storage," American Economic
Review, Vol. XLVIII, No. 1, March 1958, pp. 51-52.

63Ibid., p. 52.

47
a result of (1) an increase in production in t, (2) a decrease in pro—
duction in t+1, or (3) an increase in stocks expected to be carried out
of t+1. Opposite movements of these variables will produce a shift to
the left.

Now let us examine the supply function for storage. This refers
not to the supply of storage space, but to the supply of commodities as
inventories. In a competitive industry in an uncertain world, a firm
seeking to maximize net revenue will provide storage of that quantity 4 "

of stocks at which the net marginal cost of storage per unit of time

. .thujr'

just equals the expected change in price per unit of time. As we have 14

 

already seen, the net marginal cost of storage is marginal outlay minus
marginal convenience yield. Brennan indicates that in addition, there
may be a marginal risk aversion factor for holding stocks over time.
If such a factor exists it can be deducted from the marginal convenience
yield to Obtain a net marginal convenience yield. The only change from
treating the risk aversion factor in this way would be that net marginal
convenience yield would eventually become negative rather than reaching
a zero minimum, since the marginal risk aversion factor, according to
Brennan, should be an increasing function of stocks.64

The total outlay on physical storage is made up of rent, handling
costs, interest, depreciation, insurance, taxes, etc. For an individual
firm, total outlay may increase either at a constant or an increasing
rate. However, in the aggregate, it seems reasonable to assume that the

marginal outlay for storage is approximately constant until total ware-

house capacity is almost fully utilized. Beyond this level, marginal

 

64Ibid., p. 53.

48

outlay will rise at an increasing rate.

Pt+1

The su l of stora e,'al
PP Y 8 ong _ Pt M . M

with its components, marginal outlay

and marginal yield, assuming no risk

 

I O O O o
aver31on factor, is shown in Figure l. o v

 

 

Quantity
The curve, Mcy’ represents the marginal S stored
convenience yield; M.o represents marginal
outlay. When stocks are small, MCy is
greater than M.o and storage will be Figure 1,

The Supply of Storage
supplied even at a negative price.

The supply of storage, SS, thus inter-
sects M6 at the quantity at which MCy = O, and for stocks larger than
this quantity SS and MD are identical. The introduction of a risk
aversion factor would cause SS to lie above MO beyond the point at
which Mty is zero; however for simplicity it will be assumed that
marginal risk aversion equals zero. Under the assumption of a competi-
tive industry, SS in Figure 1 will necessarily be the storage supply
function since expected change in price per unit of time is the dif-
ference between present price and the future price and SS is the net
marginal cost of storage.

The intersection of the supply and demand for storage can now be
considered as determining the cash-future price Spread. The equilibrium
of the commodity supply and demand functions in the two periods is

shown in Figure 2. The difference between Pt and Pt+ must just equal

1
net marginal storage cost between the two periods. At this point the

demand for storage intersects the supply of storage and determines the

cash-future price spread, W, as Shown in Figure 3.

49

  

    
   

 

 

 

 

 

Current Future
price price
P
storage t+1
Pt _--_____- _-___ses_t_ :ttj’.
I
I
I
I
I
|
I
0 1
Qt Qt+1

Figure 2. Equilibrium of the Supply and Demand
for Corn in Current and Future Time Periods

 

 

O 1
\\\D quantity
stored

 

Figure 3, Equilibrium of the Supply
and Demand for Storage

The Introduction of a Govgrnment Supp1y
and Demand for Storagg

Consider the introduction of a government storage sector into
the theory of cash-future price spreads. In particular, consider the
components of the storage supply function facing the government. The
marginal convenience yield of commercial stocks, we have seen, arises

from lower costs and reduced delay from holding stocks for normal

50

merchandising and processing activities. Firms providing storage for
CCC corn, however, do not have the privilege of using these stocks any
time the need for them arises. A partial exception to this is stocks
under price support loans. As we have seen, until a specific deadline,
July 31, of the marketing year, producers have the opportunity to re-
pay the loan with interest and use the corn. This amounts to selling
and later rebuying the corn, except that producers are given the oppor-
tunity to repay the loan even if the market price rises above the loan
price. In view of these facts, it appears that (1) corn owned by CCC
and stored either in commercial or CCC-owned facilities provides vir-
tually no convenience yield for the supplier of storage and (2) corn
under price-support loan may provide some convenience yield for pro-
ducers since it assures them of a maximum price they will have to pay
in the future for the quantity of corn stored and a minimum price they
will receive for their corn if they do not choose to repay the loan.

We can expect the marginal convenience yield of stocks under loan to
vary considerably from year to year and within years, due to variations
in the cash price relative to the support price.

Also in the case of CCC corn, the government bears all risks of
price changes so that there should be no marginal risk aversion factor
for such stocks. The remaining component of the government supply of
storage,.marginal outlay, is assumed to be the same as for the com-
mercial sector.

In view of the above considerations, the supply of storage
facing the government should be expected to have a different shape than

that of the commercial sector. It should be pointed out here that the

51

commercial sector is intended to include all non—government supply and
demand for corn Storage. An additional distinction between these two
sectors is that the intersection of the government supply and demand
for storage only determines the price which the government has to pay
for storage and not the cash-future price spreads. These considerations
make it desirable to separate commercial and government storage into
two sectors.

Now consider the demand for government storage. This is deter- I:
mined by the size of CCC inventories and the quantity of corn under loan

and purchase agreements. In general, we can say that it is not closely i

 

related to the cash-future price spreads or the cost of storage to the
government. Hence it is shown in Figure 4 as being perfectly inelastic
(D’D'). In Figure 4, PSg is the government price of storage, M'Cy the
government marginal convenience yield, M8 the total marginal outlay
function and S'S' is the government supply of storage. The corresponding
functions in Figure 5 represent the commercial demand for storage, the
commercial supply of storage, and its components. The commercial mar-
ginal outlay function has been drawn as a residual; it is the segment

of the total marginal outlay function M; in Figure 4 which lies to the
right of D’D?. This was done in view of the fact, as we have seen in
Chapter II, that CCC has maintained large inventories even at the end
of the marketing year. When the new crop moves into marketing channels,
a considerable portion of the total storage supply is already accounted
for by CCC stocks. Due to occupancy contracts, storage and handling
agreements, etc., CCC stocks cannot be removed from storage‘by the

individual firm even if the return for commercial storage were greater

than for CCC storage.

t+1

(P

t+1

58

Figure 4.

Figure 5

 

 

 

 

 

DH I D'
: fS’
l /
l M.
1 / O
%
I l//
l ,,/
l //
I
I
I
'Qi Q; Government
|

S' , Storage

I
Y
I
i
I
I
I
1

DH : D!
I
I

The Government Supply and Demand for Storage

 

 

 

 

D

Commercial
storage

The Commerical Supply and Demand for Storage

 

53
Using this theoretical framework, a reduction in government de-
mand to D"D" shifts the marginal outlay function for commercial storage

to the right to M3, thus changing the form of the commercial supply

- p )

function-from SS to SS* and lowering the price spread from (Pt+1 t o

P )

t+1 - t 1’ provided the demand for commercial storage remains

to-(P
hunchanged. This will increase the commercial quantity stored from QO
to Q1' An additional possibility is that CCC stocks under loan may
affect the marginal convenience yield of commercial stocks. In some
years, a considerable amount of corn placed under loan early in the
marketing year later is removed and moves into commercial channels.

In effect the government supplies free storage when this happens and
the result may be to reduce the quantity of stocks which firms will
carry when marginal returns for carrying stocks are zero.

Now let us examine the possible impact of changes in the govern-
ment demand for storage on the commercial demand for storage. As we
have seen previously the demand for commercial storage is:

8').

P = f t - t

Pt+1 ' t t+1

(S

It should be remembered that this demand function‘is based on the

+ Xt+ - S ) - f (St—l + X

t l t+1 . t

assumption of given demands for the commodity in'period t and period
t+1. A shift to the right of the demand in t+1, all other things held
constant, will increase future price and quantity, thus increasing the
demand for corn. A shift to the right of the current demand for corn
will decrease the demand for storage, all other things held constant.
Opposite shifts will have opposite effects on the demand for storage.
A shift to the right in the demand for corn would be brought about by

an increase in the price of substitutes, a decrease in the price of

 

54
complements, an increase in livestock numbers, or an increase in live-
stock prices, all other things held constant. Opposite changes in these
variables will produce a shift to the left of the demand for corn.

It can be seen then, that changes in government programs which
are expected to change the present or future supplies of other feed
grains will affect the commercial demand for corn storage.

Under the assumption of given present and future demands for
corn, recognizing the limitations of such an assumption, the commercial

demand for storage when government storage exists is:

P - P

t+1 t a ft+1 ] - f [S

[St+(X -s ) t

t+1 gt+l 1 + (xt ' Sgt) ' St]’

' St+1 t-

where St’ S and St are commercial stocks and S and S are

t+l’ -l gt+1 gt

additions to government stocks. From this function, it can be seen that
an increase in Sgt+l’ all other things constant, will shift the demand
for corn storage to the right. A decrease in Sgt will have a similar
effect. A decrease in Sgt+1 or an increase in Sgt’ all other things
constant, will Shift the demand for corn storage to the left. It is
apparent also, that in anticipating the impact of changes in government
programs on the commercial demand for corn storage, consideration must
be given to changes in acreage allotments, Conservation Reserve Programs,
and other policies designed to reduce corn production, both in current
and future periods.

In short, there are several possible effects of changes in CCC
corn storage on the commercial demand for corn Storage. Some of these
effects Should tend to cancel each other. In general, when no changes,
are expected in future price support programs, including CCC storage,

acreage allotments, and conservation programs, the main effect of a

decrease in CCC corn stocks, assuming normal production, is probably

56

 

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CHAPTER IV

The Method of Analysis

 

The first section of this chapter discusses the method of uti-
lizing the theoretical relationships outlined in the previous chapter I
to obtain a test of the hypothesis and to obtain the objectives stated

in the introductory chapter. The second section will consider what

 

data are appropriate for the analysis and the adjustments required in
the data in order to make them conform to the requirements of the

I

theory.

The Approach

 

It is apparent from the economic relationships presented in
Chapter III that annual observations of price spread and commercial
corn stocks will not necessarily trace out a storage supply function.
It appears reasonable to assume that such intersection points repre-
sent varying levels of both the supply of storage and the demand for
storage. Furthermore, it does not seem reasonable to assume that the
conditions required for the just-identified case are met. The con-
ditions are, in general, that the number of predetermined variables in
the model but not in the equation are equal to the number of endogenous

o o o a 65 ,
variables in the equation minus one. In View of these considerations,

 

65Richard J. Foote, Analytical Tools for Stgdying Demand and
Price Structures, Agricultural Handbook No. 146, U.S.D.A.; Washington,
D. C., August 1958, p. 62.

 

 

57

CHAPTER IV

The Method of Analysis

 

The first section of this chapter discusses the method of uti-
lizing the theoretical relationships outlined in the previous chapter
to obtain a test of the hypothesis and to obtain the objectives stated
in the introductory chapter. The second section will consider what
data are appropriate for the analysis and the adjustments required in
the data in order to make them conform to the requirements of the

f

theory.

The Approach

 

It is apparent from the economic relationships presented in
Chapter III that annual observations of price Spread and commercial
corn stocks will not necessarily trace out a storage supply function.
It appears reasonable to assume that such intersection points repre-
sent varying levels of both the supply of storage and the demand for
storage. Furthermore, it does not seem reasonable to assume that the
conditions required for the just-identified case are met. The con-
ditions are, in general, that the number of predetermined variables in
the model but not in the equation are equal to the number of endogenous

. . 65 . . .
variables in the equation minus one. In View of these con81derations,

 

65Richard J. Foote, Analytical Tools for Stgdying Demand and
Price Structures, Agricultural Handbook No. 146, U.S.D.A.; Washington,
D. C., August 1958, p. 62.

57

 

58
the following comments by Elmer Working in his classic article may have
. . 66
direct bearing on the problem.

It does not follow, that when conditions are such that shifts

of supply and demand are correlated, an attempt to construct

a demand curve will give a result that will be useless. Even
tho shifts of supply and demand are correlated, a curve which is
fitted to the points of intersection may be useful for purposes
of price forecasting, provided no new factors are introduced
which did not affect the price during the period of study. So
long as the shifts of supply and demand remain correlated in

the same way, and so long as they shift through approximately

the same range, the curve of regression of price upon quantity 1
can be used as a means of estimating price from quantity. '

With these statements in mind, consider a curve fitted to the

intersection points of the commercial supply and demand functions for r

 

storage from 1927 to date and a comparison of this curve with one
fitted to the intersection points from 1934 to date. The first curve
contains seven observations prior to the introduction of CCC price
support operations. We have seen that when government price support
operations are introduced, their effects on the commercial demand for
corn storage are through Shifts in the current and future supply and
demand functions for corn. Given the current and future levels of the
supply and demand for corn, the commercial demand for cornistorage
should be unaffected by government programs. Now let us assume that
current supply and demand for corn and expected future supply and de-
mand conditions are reflected by current consumption and consumption
in period t + 1. This assumption seems reasonable, since, as we have
seen in Chapter III, current and future consumption are factors that
the demanders of storage adjust in response to changes in current and

expected future supply and demand conditions. With this approach,

 

66Elmer Working, "What Do Statistical Demand Curves Show?“
Quarterly Journal of Economics, Vol. XLI, No. 1, February 1927, p. 227.

59

using the major variables determining the supply and demand for storage,
a regression analysis for each period should yield coefficients for the
various variables, with a very similar magnitude for both periods pro-
vided no new variables affecting the supply have been introduced during
the latter period. If the hypothesis is false, however, we might ex-
pect a difference in the size of the correSponding regression coeffi-
cients for the two time periods and a significant coefficient for CCC
corn stocks.

This is the approach which will be used. It will also provide
a basis for predicting the cash-future price spreads. Since the

approach will treat both (Ct) and C ) as exogenous, such predictions

t+1

will require an estimate of Ct+1 in order to be useful. Thus for

predictive purposes, the best available estimate of Ct+1 at the time
of the prediction should be used. The justification here for treating

it as exogenous is that Ct affects the price spread directly but is

+1
not "significantly” affected by the price Spread. In using this approach
for predictions, care should be exercised, since as we have seen in
Chapters I and II, some rather irreversible processes have been going

on during the operation of the CCC. One of the more important of these
is the construction of new storage facilities. If CCC stocks were re-
duced considerably, the marginal outlay function for commercial storage
would shift to the right to a position which had not been previously
attained, provided alternative uses for the new storage space are not
important. Fixed asset theory tells us that an asset will be used in
production as long as its marginal value product is less than its

acquisition cost but greater than its salvage value. Here the important

question is how much of the new storage space has an important salvage

60
value (alternative use)? This question cannot be answered, but it should
be pointed out that predictions based on the approach to be used here

are not valid for large decreases in CCC stocks.

The Data

From Chapter III, the variables required for a least-squares re-
gression of the intersection points of the commercial demand functions
for storage are:

l. The cash-future price spreads.

2. Commercial stocks of corn.
1_ l

3. Total stocks of corn under CCC control.

 

4. Total consumption of corn, domestic and export.

5. Stocks of other grains.

6. All available components of the marginal outlay for storage.

In addition to these it may be desirable to provide either a
variable which will account for the effects of variations in the general
price level or in some manner remove the effects of the general price
level from the cash-future price spreads.

In considering the appropriate time period to use, it is desir—
able to obtain the longest reasonably homogenious period available, but
at the same time considerable variation is required in the studied
variables. In order to determine whether CCC price support activities
have altered the direction or magnitude of the relationships between
other variables and the spread, several observations are required prior
to the introduction of CCC price support programs. With these consi-
derations in mind, the time period 1927 to date was chosen. The approach

will be to compare the effects of the relevant variables on the spread

61
for the complete period and for 1934 to date. A longer time period
would have been desirable; however some of the data needed were not
available prior to the fourth quarter of 1926. The war years, 1943-45,
and the immediate post-war years, 1946-48, were excluded from the
analysis. During World War II, as was pointed out in the introductory
chapter, government controls and other unusual conditions prevented the
operation of "normal" supply and demand relationships. The immediate '
post-war period represented a readjustment toward peace-time conditions.
During this period the demand for corn was unusually high and exports

were large. F

 

Since CCC activities may have different effects on the cash-
future spreads at different times during the year, the cash-futures
spread was studied at four different dates: January 1, April 1,

July 1, and October 1. These dates were selected because they coincide
with the dates for which quarterly grain stocks are published.

In computing the cash-future price spreads, cash prices for No. 2
corn at Chicago were used. The Chicago market provides prices for a
Specific grade, daily, from actual transactions, at a particular loca-
tion. Some measurement error exists in these prices due to quality
variations within grades, but this limitation is not serious and is un-
avoidable in any cash corn price series. The Chicago market also has
the advantage of providing opportunity to use futures prices determined
at the same location as the cash prices.

It is well to recognize that the cash-future spreads at other
markets may differ from the spreads at the Chicago market due to dif-
ferences in regional supply and demand conditions and availability of

storage Space. However, it is beyond the scope of this thesis to

62
consider regional variations in the cashefuture price spreads for corn.
The cash-future price spreads from 1927 to 1954 were obtained

from L. V. Manderscheid, Influence of Price-Support Program on Seasonal

 

7
Corn Prices.6‘ Consequently this section is based on Manderscheid's

 

work and explains the procedures used by him in collecting and adjusting
cash and future prices to obtain the cash-future spreads.
Cash and futures prices were obtained by Manderscheid from the

Annual Report of the Chicago Board of Trade, supplemented by information

 

from the Chicago edition of the Wall Street Journal and the Chicagg

 

Journal of Commerce. Cash and futures prices were compiled for each

 

Friday (except for war years) unless the market was closed on Friday
for a holiday or any other reason. In that case Thursday was used.

No particular Significance was attached to Friday; any other day might
be equally justified. The low price for No. 2 mixed or better cash
corn was recorded along with the low for a widely traded futures con-
tract.

In choosing the futures contracts used in deriving the spread
for a particular month, futures were selected which would always be
traded in the month for which they were chosen. The December future
is traded in volume in June and subsequent months; hence it was selected
for June. The May future was selected Since it has a large trading
volume and is used every year. The September future was used to pro-
vide an old crop future for the end of the marketing year.

Thus, from June through October, Manderscheid recorded the price

of the December future; from November through March the May future was

 

67Manderscheid, 9&3 SEE , pp. 55-62.

63

recorded, and from April through September, the September future was
recorded. In addition on the first Friday of November, both the December
and May futures were recorded. Similarly, on the first Friday of April,
both the May and the September futures prices were recorded.

Manderscheid then adjusted the futures prices to yield a synthetic
"September" future for a 16-month period extending from the June prior
to harvest to the September following harvest. The method used was
employed by Holbrook Working in a study of wheat prices.68 This method
assumes that a fairly constant inter-option spread has prevailed between
two particular future prices and that measuring the inter-option spread
at one properly chosen point allows us to adequately adjust a future
price so as to make it comparable to the price which might have pre-
vailed if the other future had been traded or had been recorded. This
assumption is probably not inconsistent with fact since traders tend
to keep inter-option spreads within a narrow range.

The procedure for adjusting the May future to yield a "September"
future involved adding to the price of the May future the premium of
the September future over the May future on the first Friday of April.
Similarly, the December future was adjusted by adding to it the premium
of May over December on the first Friday of November plus the premium
of September over May on the first Friday of April. In event the
premium was negative, it merely involved subtraction rather than addi-
tion. It should be noted that the transfer from one future to the next
was made one month prior to the beginning of the delivery month. The

switch was made at this point in order to remove possible effects of

 

8Holbrook Working, "Cycles in Wheat Prices,” Whgat Stud1gg,
Vol. VIII, No. 1, November, 1931.

 

64
any corners or squeezes.

A problem occurred in recording cash prices when the low quality
of the corn crop resulted in no trading of No. 2 mixed or better corn
on the Chicago market. Under these circumstances, Manderscheid obtained
market differentials between the No. 2 corn and the highest grade that
was traded by taking the difference between the low prices of these two
grades on the last day that both were traded. This differential was
then used to adjust the price of the lower grade corn to the level of
No. 2 corn. This adjustment should lead to as small an error as any
possible method which might be suggested.

The cash-future price spreads were obtained by subtracting the
"September" price from cash price. Both spreads and futures prices
were averaged to provide a series of average monthly prices. This
tended to smooth out small price changes while leaving larger, more
meaningful changes.

The price spreads used in this thesis were monthly averages for
December, March, the second June and the first September of each 16
month period. The September future in the second September of each
16-month period is an old crop future, at the delivery month for that
contract. The spread in the second September, consequently represents
a quality and location differential, rather than a price of Storage.
For this reason the spread for the first September of each period was
used. This spread represents the difference between cash price and
the expected future price of new crop in the following September. The
spread for the second June of each period was used Since it is based
on an old-crop future, and hence represents the difference between the

current price and the expected price in September of the same marketing

 

65
year.
These spreads were then compiled for 1955 through June 1963 by
the author, using the procedures discussed above. The prices were

obtained from the Annual Report of the Chicago Board of Trade and from

 

the Droversa Journal.

 

The cash-future spreads were adjusted to remove the effects of
two additional variables. The first of these was the general price
level. The monthly average spreads were deflated by dividing them by
the Bureau of Labor Statistics Monthly Index of Wholesale Prices for

all commodities (1957-59 = 100). These indexes were obtained from

 

monthly Federal Reserve Bulletins. The procedure for adjusting the

 

Wholesale Price Index for the base periods 1926 and 1947-49 to obtain

a 1957-59 base was based on five years for which both 1947-49 and 1926
bases were published and on five years for which both 1947-49 and 1957-
59 bases were both published. For these overlapping years, the monthly
index with the later base was divided by the monthly index with the
earlier base. These adjustment factors were then averaged for the
five-year period. The 1947-49 base index, when multiplied by .841
yields a 1957-59 base index. The adjustment factor to convert the

1926 base index to a 1947-49 base is .633.

The cash-future spreads were also adjusted to remove the effects
of variations in the interest rate. Interest cost, as previously noted,
is one of the components of the marginal outlay for storage. On the
aggregate level this is the only component of the marginal outlay which
is available. Published interest rates charged by banks to customers
for business loans do not take into account variations in conditions

under which loans are made; hence they do not provide an accurate

66
indication of the interest cost of holding stocks of corn. In addition,
the series of bank rates on short term business loans published by the

Federal Reserve Board of Governors in the Federal Reserve Bulletin was

69

 

revised in 1948. The revised series was extended back only to 1939.

In view of these considerations, the Short-term interest rate on four

to Six-month prime commercial paper in the New York money market was
selected as the basis for computing interest cost. This choice was

made on the assumption that the cost of a loan is highly correlated with
the interest rate in the New York money market.

The monthly interest rates were obtained from the Federal Reserve

 

Bulletin. Since the published rates are in percent per year, they were
converted to rates per month. These were then multiplied by monthly
deflated cash prices to obtain the interest cost per month. The in-
terest cost per month was multiplied by the number of months until
September, the date when the "September" future reached maturity, to
obtain the interest cost for each date studied. The interest cost

was then added to the cash-future spreads, since these spreads are

cash price minus future price rather than the future price minus cash
price called for by the theoretical framework of Chapter III. For the
statistical analysis, the signs of the deflated net spreads were re-
versed to convert them to future price minus cash price. Cash prices
for the years 1927 to 1954 were not directly available from Manderscheid's
dissertation. Hence, monthly average cash prices were obtained by re-
inflating average monthly future prices and adding these to the corres-

ponding average monthly spreads. The cash prices thus obtained were

 

9Federal Reserve Board of Governors, The Federal Reserve Bulletin,
March 1949, pp. 228-37.

 

67
then deflated by the Wholesale Price Index before computing interest
costs. It should be recognized that the deduction of interest cost from
the cash-future spreads, in practice, takes account of variations in
interest cost without using up an additional degree of freedom.
Total corn stocks for the United States in all positions quarterly
from 1927 to date were obtained from U.S.D.A., Grain and Feed Statistics

through 196170 and from various issues of the Feed Situation.71 Pub-

 

 

 

lished corn Stocks for United States in total are not available prior
to 1926. Since stocks of corn in interior mills, elevators, and ware-
houses are not available prior to 1943, the years before 1943 were ad-
justed to include an approximation of stocks in these positions. Ad-
justment was made by computing interior mill, elevator and warehouse
stocks as a percentage of farm and terminal stocks for the first five
years that interior mill, elevator, and warehouse Stocks were published.
These percentages were averaged for each quarter, and stocks for the
earlier years were increased by the corresponding percentages. The
adjustments are based on the assumption that the percentage of the
total corn supply stored in various positions remained reasonably con-
stant for the period 1927—43. Farm and terminal stocks multiplied by
.021 provided an approximation for interior mill, elevator, and ware-
house stocks for January 1. For April 1 the adjustment factor was
.034; for July 1 it was .043, and for October 1 it was .085.

Stocks of corn under loan and purchase agreements and in CCC in-

ventories quarterly from 1933 to date were obtained directly from the

 

70

Pt?
0
l"
('7‘

71

18
O
H
n

 

68

Agricultural Stabilization and Conservation Service. Commercial Stocks
of corn were then computed by subtracting total corn stocks under CCC
control from total corn stocks in all positions. Commercial stocks thus
include stocks of corn on farms. Although farmers probably do not base
their stockholding activities on the size of cash-future spreads, it
can be seen from the economic relationships presented in the previous
chapter that farm storage of corn should be expected to influence present
and future supply and demand conditions which in turn influence the
cash-future Spreads.

The major stocks of other grains are wheat, oats, and barley.
These stocks were included in the analysis because they provide an in-
dication of the level of occupation of total available storage facilities.
Stocks of rye, sorghum, and other grains were not included since they
comprise only a small percentage of the total supply of grains and should
be expected to have a very small effect on the supply of storage space
available for corn. Stocks of oats and wheat were obtained from the
same sources as total corn stocks. Since stocks are not available for
interior mills, elevators and warehouses prior to 1943 for oats and
prior to 1935 for wheat, only CCC stocks, farm, and terminal stocks
were used for these grains. It was assumed in so doing, that stocks
of wheat and oats in these positions would be highly correlated with
stocks in other positions. Beginning in 1960, all off-farm stocks of
both grains except CCC-owned stocks are combined into a single group.
Consequently an adjustment was required to obtain the approximate size
of Stocks held in terminal markets. For each quarter of the last five
years that terminal stocks were published, terminal stocks were computed

as a percentage of all non-farm and non-CCC stocks. These percentages

69
were averaged by quarter to obtain an approximation of terminal stocks
for 1960 to 1963.

In the case of barley stocks, the only published figures avail-
able for the years 1927-34 are visible supplies. For this reason,
visible supplies of barley were used. They consist of stocks in regu-
larly authorized warehouses at prominent grain centers of the United
States east of the Rocky Mountains, including quantities afloat on the
Great Lakes and the Barge canal. Here, the assumption was made that
visible supplies would be closely correlated with total stocks of

barley. Visible supplies were obtained from the Annual Report of the

 

Chicago Board of Trade from 1927 to date. CCC stocks of barley were

 

obtained from the same sources as corn stocks and were added to visible
supplies to obtain total stocks of barley. Total supplies of oats,
barley, and wheat were then combined into a single variable.

Quarterly domestic and export consumption of corn for grain only
was obtained from the same sources as total corn stocks; it is not
available prior to 1926. For the analysis, domestic and export con-
sumption were combined into a single variable. It would have been
desirable to subtract imports from total consumption; however quarterly
imports of corn into United States are not available. This is not a
serious limitation since annual imports normally amount to less than
1 per cent of corn production.

Two additional variables were believed to be useful in the
analysis. The first of these was production of corn for grain. The
second was the number of grain consuming animal units fed annually.
Both of these variables were obtained from the same sources as total

corn stocks; neither is available quarterly. The number of grain

 

7O
consuming animal units provides an additional measure of the demand for

corn, while production provides an additional measure of the total

supply.

 

CHAPTER V

Results of the Analysis

 

In this chapter the equations used to estimate the cash-future
price spreads will be presented for each of the four dates studied. l“-
The dates will be referred to as January 1, April 1, July 1, and October 1

Since these correspond to the times of the year for which U.S.D.A. stocks
bi’l

 

data are published. The procedure followed will be to present the equa-
tion, the regression coefficients, standard errors of the coefficients,
the standard error of estimate, R2, R, the degress of freedom, and the
simple correlations between the variables.72 In addition, comparisons
will be made of estimated and actual spreads, and the coefficients will
be tested for statistical significance with the t test. The reader who
is mainly interested in the results of the analysis should turn directly
to summaries of the equations for each date. These are presented on
pages 89, 102, 112 and 124.

For the first date to be studied, January 1, the variables will
be defined and discussed in terms of the reasons for inclusion where
these are not apparent from previous chapters. Since the same variables

will be used for each of the four dates studied, discussion of the

 

72

The cgefficient of multiple determination adjusted for degrees
of freedom is R2. Its formula is;

where D.F. is the number of observatigns minus the number of independent
variables minus one. The statistic, R is the square root of R .

71

72

variables will not be repeated for April 1, July 1, or October 1 equa-
tions. Equations for January 1 will be identified by the first number,
1. A second number identifies the number of the equation for the date
studied. For example, equation 1 - 3 is the third equation for
January 1. Even numbered equations are based on the time period 1934
through 1963; odd numbered equations are for the period 1927 through
1963. Equations for April 1 will be identified by the number 2; for
July 1 by the number 3; for October 1 by the number 4. Similar notation
will be used for the variables. For example, X31 refers to the first
variable for July 1 equations.

Economic theory and previous work have provided no indications
of the appropriate functional forms for the variables. Consequently,
functional forms for all variables were selected on the basis of pre-

liminary graphic analysis.

January 1 Equations

 

Three regression equations were computed for each of the two time.
periods for January 1. Each set of variables was included in one equa—
I,

tion covering the period 1927 through 1963 and in one equation for 1934

through 1963.

Equation 1 - 1. Time period: 1927 - 1963.

 

" l 2 3
Y11 - +34.9l - 106.28 iII-+ 71.56 X12 - 61.72 X12 + 20.133 X12
2
+ 10.07 X13 - 0.28 X13 + 0.47 X14 - 3.92 X15.
R2 = .72 RI: +.79' S = 9.76 D.F. = 22
y . x

Other important statistics of equation 1 - 1 are presented in Table 5.

 

73

TABLE 5.--Simple Correlations Between the Variables, Standard Errors
and t Values of the Coefficients of Equation l-l

 

fl
-

 

 

Simple Correlation With Standard t Value
Variable >x12 X13 X14 X15 Y CogffEZizitsa Coeffliients
x11 -.68 -.68 -.81 -.77 -.26 38.83 -2.74
x12 +.83 4.82 +.91 +.01 15.49 +1.94
x13 +.78 +.80 +.22 62.20 +0.16
x14 +.82 +.22 1.31 +0.36 l_
x15 -.15 0.91 -4.29 1

 

aThe formula for the variance of the coefficients of X1 taken
as a group was obtained from Dr. L. V. Manderscheid, Departmenf of
Agricultural Economics, Michigan State University. Where S§,x is the
squared standard error of estimate and C1 j is the i j th element of
the inverse sum of squares and cross products matrix,

2

12 + b13 + b14) — Sy.x (C22 + C33 + C44 +2C23 + 2C24 + 2034).
The combined standard error of the coefficients is the square root of
this formula. The variance of the coefficients of X taken as a

 

V (b

. 13
group is:
2
V (b15 + b16) - Sy.x (C55 + C66 + 2C56)°
/\
Y11 = estimated adjusted December spread. The adjusted spread refers to

average monthly Spreads (future price minus cash price), deflated,
minus interest cost, in cents per bushel.

X11 = million bushels of commercial stocks of corn on January 1 divided
by million bushels of total corn consumption for the preceding
quarter.

X12 = million bushels of corn in CCC inventories and under loan and pur-

chase agreements, divided by million bushels of total corn con-
sumption for the preceding quarter.

X13 = hundred million bushels of total corn consumption for the quarter
following January 1.

X14 = hundred million bushels of wheat, oats, and barley stocks.

X15 = time 1n years.

74

The reasons for dividing commercial and CCC corn stocks by con-
sumption during the previous quarter are twofold. First, current con-
sumption can be considered an indicator of the current supply and demand
for corn and is one of the variables affecting the demand for corn
storage. In the analysis, consumption in the quarter preceding January 1
was used as current consumption. Stocks were divided by consumption to
account for both variables Simultaneously. The second reason has been
suggested by Telser.73 He argues that it is not the absolute Size of
stocks, but their size relative to consumption that determines the

marginal convenience yield.

 

Consumption in the quarter immediately following January 1 was
included in the analysis as an indication of future consumption. This
provides a measure of expected future corn supply and demand conditions,
which, as we have seen previously, also affect the demand for corn
storage. Quarterly consumption was selected since expectations re-
garding future conditions may change considerably within the year. Con-
sumption during the three months immediately following the month in
which spreads were observed should provide a more accurate picture of
expectations at that time than would be provided by a longer unit of
time.

The last variable, was included to capture the effects of

X”,
changes through time in variables, such as technology, that were not
directly measurable. The level of X15 was one for 1927, two for 1928,

etc. This trend variable was not continued during the years omitted

from the analysis.

 

3Lester G. Telser, "Futures Trading and the Storage of Cotton
and Wheat," Op. Cit., p. 250.

75
From previous chapters it is apparent that the only variables
for which we can predict, a priori, the Sign of the coefficients are
X14 and X15. An increase in the stocks of other grains, all other things
remaining constant, should decrease the supply of unoccupied Storage
space, thus increasing the cash-future spread. From previous work by
Manderscheid, discussed in the review of literature, we should expect

15

the coefficient of X to be negative. [1
Values of t for 22 and 15 degrees of freedom, from a standard 1

table for two-sided tests are as follows:

 

 

 

 

level of significance 22 degrees of freedom 15 degrees of freedom F4
10% 1.72 1.75
5% 2.07 2.13
2% 2.51 2.60
1% 2.82 2.95

From Table 5 it can be seen that the coefficient of X11 is Significantly

different from zero at the 2 percent level and the coefficients of X12
are significant at the 10 percent level. Since the sign of the coeffi-
cient of X15 has been predicted in advance, a one-Sided test is appro-
priate for that coefficient. For a one-sided test, the coefficient of
X15 is Significant at the 1 percent level. Coefficients of the other
two variables are not significantly different from zero at the 10 per-
cent level. Also, Table 5 indicates that the independent variables are
highly intercorrelated. This would tend to increase the standard devia-
tions of the coefficients and consequently would reduce their statistical
significance.

Before comparing actual and estimated spreads from equation l-l,

let us examine equation 1-2, which contains the same variables as

equation 1-1, but covers a shorter time period.

76

Equation 1-2. Time Period: 1934 - 1963-

 

/\ l 2 3
Y11 — -52.39 -77.74 XI: + 65.52 X12 -47.88 X12 + 14.947 X12
. 2
+ 23.46 X13 - 0.99 X13 - 0.29 X14 - 4.09 X18.
R2 = .70 R4: +.74 S = 10 57 D.F. = 15
y.x

TABLE 6.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 1-2

 

 

j
L.—

 

 

 

Simple Correlation With Standard t Value '3"
Variable X12 X13 X14 x18 Y CogffEZiZEts Coeffifiients 1
x11 -.60 -.66 -.8O -.68 -.62 46.69 -l.67 1”“
x12 +.83 +.81 +.94 +.30 18.68 +1.74
X13 +.78 +.89 +.44 95.45 +0.24
X14 +.89 +.46 2.02 -0.14
X18 +.29 1.68 -2.44

 

The variable X18 is a trend variable beginning in 1934. All
other variables in equation 1-2 are the same as those in equation 1-1.

The simple correlations between the independent variables have
not been greatly affected by reducing the time period studied from
1927 - 1963 to 1934 - 1963. However, the simple correlations of the
independent variables with adjusted cash-futures spreads have been in-
creased considerably. The coefficient of X18 is significant at the
2.5 percent level; however none of the other regression coefficients
are Significantly different from zero at the 10 percent level. This
is partly due to a loss of degrees of freedom as compared with equa-

tion 1-1. The loss of degrees of freedom also contributed to the

reduction of R from +.79 in equation 1-1 to +.74 in equation 1-2.

77

Actual adjusted Spreads and spreads estimated with equations l-l
and 1-2 are compared in Table 7. The range of adjusted December spreads
fortfluaperiod 1927 - 1963 was 71.33 cents; for the 1934 - 1963 period
it was 68.27 cents. For 22 out of the 31 years studied, equation l-l
was in error by 7.51 cents or less. The largest errors were in 1934
and 1949. Errors were also large for the years 1936, 1935, 1928, and
1962. Errors from equation 1-2 were 7.91 cents or less for 13 out of
24 years. The three largest errors were for the years 1934, 1935, and
1936. Large errors were also obtained for 1949, 1950, 1953, 1956, 1959
and 1962.

At least five of the above years were somewhat unusual. The
year 1934 was characterized by the beginning of CCC activities, the
depression and with it a falling demand for corn, and a large corn crop
in 1933. The December 1934 spreads reflected the very short corn crop
of 1934 which was caused by the severe drought of that year. In 1949
some readjustment to peacetime conditions was probably still going on.
The December 1958 spreads were probably influenced by the removal of
acreage allotments on corn in November, 1958. In addition, the year
1962 was somewhat unuSual, since an abrupt change in policy permitted
CCC to dispose of corn in the domestic market at or below the market

price even if the support price was above the market price.

78

TABLE 7.--Actual Adjusted December Spreads and Spreads Estimated With
Equations 1-1 and 1-2

 

 

 

A A A A
Years Y11 le Y Y-Y11 Y-Y12
1927 +20.33 -- +24.71 + 4.38 --
1928 +17.62 -- + 7.25 -10.37 --
1929 +15.05 -- + 8.77 - 6.28 --
1930 +10.4l -- + 7.23 - 3.18 --
1931 - 2.63 -- + 3.86 + 6.49 --
1932 +15.29 -- +18.72 + 3.43 --
1933 +16.07 -- +23.58 + 7.51 --
1934 - 3.32 + 2.78 +21.65 +24.97 +18.87
1935 —33.20 -34.84 -46.62 -13.42 -ll.78
1936 + 2.46 + 1.57 -ll.03 -13.49 -12.60
1937 ~46.00 -46.68 ~43.68 + 2.32 + 3.00
1938 + 0.27 - 2.28 + 2.74 + 2.47 + 5.02
1939 + 1.04 - 1.47 + 7.05 + 6.01 + 8.52
1940 + 2.60 + 3.87 + 5.05 + 2.45 + 1.18
1941 - 2.08 - 3.32 - 6.15 - 4.07 - 2.83
1942 +1l.31 +12.56 +18-26 + 6.95 + 5.70
1949 + 6.24 + 3.39 - 8.14 -l4.38 -ll.53
1950 - 0.23 + 1.76 - 9.25 - 9.02 -ll.Ol
1951 + 0.33 + 2.11 - 5.80 - 6.13 - 7.91
1952 - 5.74 - 1.78 - 9.62 - 3.88 - 7.84
1953 - 3.63 - 5.03 + 4.97 + 8.60 +10.00
1954 -ll.51 -l3.68 - 5.51 + 6.00 + 8.17
1955 - 0.19 - 4.21 + 0.77 + 0.96 + 4.98
1956 + 0.37 - 1.41 + 7.56 + 7.19 + 8.97
1957 + 3.25 + 5.54 + 1.85 - 1.40 - 3.69
1958 - 0.62 + 0.83 + 1.00 + 1.62 + 0.17
1959 + 1.21 + 1.63 - 7.32 - 8.53 - 8.95
1960 + 4.45 + 5.98 - 1.50 - 5.95 - 7.48
1961 +13.60 +ll.85 +12 46 - 1.14 + 0.61
1962 - 3.42 - 2.52 + 5.86 + 9.28 + 8.38
1963 - 5.46 - 6.92 - 4.87 + 0.59 + 2.05

.1 _.' _
I

Iran

 

 

79
In view of one of the objectives of the Study, let us compare

the coefficients of equations 1-1 and 1-2. They are as follows:

 

 

equation l—l equation 1-2
- * -
b11 106.28 77.74
b12 + 71.56* +65.52
- a -
b13 61.72 47.88
b14 . + 20.133* +14.947
b15 + 10.07 +23.46
b16 . - 0.28 - 0.99
b17 + 0.47 - 0.29
' - a - *
b18 3.92 4.09

The asterisk indicates that coefficients are significantly different
fqom zero at the 10 percent level of probability. Due to the lack of
significance of all the coefficients of equation 1-2 except b18 and
of three coefficients of equation l-l, it does not appear worthwhile
to test for significant differences between the coefficients of the
two equations.

The coefficient of X in equation 1-1 is positive, as would be

14

expected, while the coefficient of X in equation 1-2 is negative.

14
In view of the lack of significance of both coefficients, however, this
cannot be considered as a contradiction of the theoretical framework
of Chapter III.

The independent variables of equations 1-1 and 1-2 are highly
intercorrelated. This would tend to increase the standard errors and

reduce the significance of the regression coefficients. With this

problem in mind, two new variables were used in equations 1-3 and 1-4.

 

80

Equation 1-3. Time Period: 1927 - 1963.

 

‘0 l 2 3
Y13 — -426.8l - 113.57 XII + 62.93 X12 - 72.44 X12 + 27.880 X12
2 2 _
+ 347.73 Xl6 - 59.28 X16 + 10.21 X17 - 2.60 X15. R - .72 R - + .79
S = 9.74 D.F. = 22
y.x

Other important statistics of equation 1-3 are presented in Table 8.

TABLE 8.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 1-3

 

 

 

 

 

 

 

Simple Correlation With Standard t Value
Error of of

Variable X12 X16 X17 X15 Y Coefficients Coefficients P!
X11 -.68 +.61 -.80 -.77 -.26 39.84 -2.85
X12 —.l6 +.79 +.91 +.10 14.46 +1.27
X16 -.49 -.21 -.40 98.33 +2.93
X17 +.78 +.22 22.25 +0.46
X15 -.15 0.92 -2.82
X16 = million bushels of corn consumption in the quarter following

January 1 divided by ten millions of bushels corn production in
the corresponding marketing year.

X17 = ten millions of bushels oats, barley, and wheat stocks divided
' by millions of grain consuming animal units fed annually.

The variable, was included to provide a measure of the demand

X16

for corn relative to the supply and also as an attempt to reduce the
simple correlations with other variables by reducing the correlation

of the demand variable with time. The variable, was included in

x17,

view of the lack of significance of X as a measure of the supply of

14’
substitutes for corn relative to the demand for feed grains.

Equation 1-3 produced a slight decrease in the standard error of

estimate from 9.76 to 9.74 as compared with equation 1-1. The R2 and R

 

81

were unchanged. The main reductions in intercorrelations were as

 

 

follows:
equation 1-1 equation 1-3
X11 and X13 = -.68 X11 and X16 = +.61
X12 and X13 = +.83 X12 and X16 = -.16
X13 and X14 = +.78 X16 and X17 = -.49
X14 and X15 = +.82 X17 and X15 = +.78
X13 and X15 = +.80 X16 and X15 = -.21
From Table 8 it can be seen that the coefficients of X11, X16’

and X15 in equation 1-3 are significant at the 1 percent level.
Coefficients of the other two variables are not significantly different
from zero at the 10 percent level.

Now let us turn to equation 1-4, which contains the same vari-

ables as equation 1-3, but is based on the shorter time period.

 

Equation 1-4. Time Period: 1934 - 1963.
/Y\ --47653-10887—1—+5635X -7650X2+29077X3
14 " ~‘_ ‘ ' ' x11 12 ° 12 ° 12
2
7 - - -

+ 369. 0 X16 63.07 X16 6.38 Xl7 1.13 X18.

R2 = .71. RD: +.74 S = 10.41 D.F. = 15
y.x

Other important statistics of equation 1-4 are presented in Table 9.

 

82

TABLE 9.--Simp1e Correlations Between the Variables, Standard Errors,

and t Values of the Coefficients of Equation 1—4

 

 

 

 

Simple Correlation With Standard t Value
X X X X Error of of
Variable 12 l6 l7 l8 Coefficients Coefficients

X11 -.60 +.67 -.80 -.68 —.62 46.28 -2.35
X12 -.15 +.78 +.94 +.30 17.54 +0.51
X16 -.49 -.23 -.47 93.46 +3.28
X17 +.84 +.44 28.40 -0.23
X18 +.29 1.35 -O.84

 

From Table 9 it can be
significant at the 5 percent
significant at the 1 percent
cients are not significantly
level.

Equation 1-4 produced

estimate from 10.57 to 10.41

seen that the coefficient of X11 is

level and the coefficients of X16 are

level. The remaining regression coeffi-

different from zero at the 10 percent

a reduction in the standard error of

as compared with equation 1-2. The R2

and R were practically unchanged. The following reductions in inter-

correlations were obtained:

equation 1-2

X12 and X13 = +.83
X12 and X14 = +.8l
X13 and X14 = +.78
X13 and X18 = +.89
X14 and X18 = +.89

Spreads estimated with

equation 1-4

 

X12 and X16 = -.15
X12 and X17 = +.78
X16 and X17 = -.49
X16 and X18 = -.23
X17 and X18 = +.84

equations 1-3 and 1-4 are compared with

actual adjusted spreads in Table 10. In 20 out of 31 years studied,

‘1"?

 

83
equation 1-3 was in error by 6.61 cents or less. For the post—war
period the largest errors were in the years 1954, 1959, 1962, and 1963.
Equation 1-4 was in error by 7.37 cents or less in 19 out of 24 years.
The largest error in the post-war period was 8.51 cents in 1951.

TABLE 10.--Actual Adjusted December Spreads and Spreads Estimated With
Equations 1-3 and 1-4

 

 

 

A. /\ l\ I\
Years Y13 Y14 Y Y-Y13 Y-Y14

1927 +15.40 -- +24.71 + 9.31 --
1928 + 5.82 -- + 7.25 + 1.43 --
1929 +11.41 -- + 8.77 - 2.64 --
1930 + 9.56 -- + 7.23 - 2.33 --
1931 + 6.01 -- + 3.86 - 2.15 --
1932 +16.57 -- +18.72 + 2.15 --
1933 +12.35 -- +23.58 +11.23 --
1934 + 2.07 - 4.08 +21.65 +19.58 +25.73
1935 -41.73 -44.71 -46.62 - 4.89 - 1.91
1936 +13.21 + 7.05 ~11.03 -24.24 -18.08
1937 -37.07 -37.09 —43.68 - 6.61 - 6.59
1938 + 4.21 + 1.52 + 2.74 - 1.47 + 1.22
1939 + 8.31 + 6.37 + 7.05 - 1.26 + 0.68
1940 + 8.99 + 8.89 + 5.05 - 3.94 - 3.84
1941 + 3.17 + 0.41 — 6.15 - 9.32 - 6.56
1942 + 6.07 + 5.16 +18 26 +12.19 +13.10
1949 - 8.45 - 9.07 - 8 14 + 0.31 + 0.93
1950 ~ 4.93 - 4-10 - 9 25 - 4.32 - 5.15
1951 + 2.48 + 2.71 - 5,80 - 8.28 - 8.51
1952 - 8.17 - 4.95 - 9.62 - 1.45 ~ 4.67
1953 - 1.58 + 1.96 + 4.97 + 6.55 + 3.01
1954 -15 71 ~13.51 - 5.51 +10.20 + 8.00
1955 + 2.86 + 1.28 + 0.77 - 2.09 - 0.51
1956 + 3.67 + 0.19 + 7.56 + 3.89 + 7.37
1957 + 5.02 + 2.69 + 1.85 - 3.17 - 0.84
1958 + 2.26 + 1.59 + 1-00 - 1.26 - 0.59
1959 + 2.78 - 0.26 — 7.32 -10.10 - 7.06
1960 + 0.24 + 1.83 - 1.50 - 1.74 - 3.33
1961 +16.41 +13.67 +12 46 - 3.95 - 1.21
1962 - 3.52 - 0.45 + 5.86 + 9.38 + 6.31
1963 -13 88 ~ 7.37 - 4.87 + 9.01 + 2.50

In view of the lack of significance of the coefficients for X17

and the high simple correlations of this variable with other variables,

84

equations 1-5 and 1-6 were computed excluding

X17.

In omitting X

17

from the analysis, it should be pointed out that variables in the equa-

tion which are highly correlated with X

of that variable.

coefficients of

17

the remaining variables.

Equation 1-5. Time Period: 1927 - 1963.

 

Other important

-432.79 - 117.16 —-1——+ 63.38 x
X11

2
36 X16 - 61.51 X16 - 2.55 X15.

.72 R_=+.80 3 =9.57 D.F
y.x

12

. = 23

- 70.47 Xi

may carry part of the effect

This would be reflected by changes in the regression

3
2 + 26.880 X1

statistics of equation l—5 are presented in Table 11.

TABLE ll.--Standard Errors and t Values of the

Coefficients of Equation

l-5

 

 

Standard t Value
Error of of
Variable Coefficients Coefficients
X11 38.39 ~3.05
x12 13.87 +1.43
X16 94.50 +3.15
X15 0.90 -2.84

 

Equation 1-5 produced a reduction in the standard error of esti-

mate from 9.74 to 9.57 as compared with equation 1-3. The R2 remained

unchanged; however R increased very slightly from +.79 to +.80. From

Table 11 it can be seen that the coefficients of X

significant at the 1 percent level.

cant at the 2 percent level, but the coefficients of X

11

and X are

The coefficient of X

12

16
15 is Signifi-

are not

significantly different from zero at the 10 percent level. High simple

2

 

85

correlations of X12 with other variables could, in part, account for

the lack of significance of the coefficients of X12.

Equation 1-6. Time Period: 1934 - 1963.

 

IN 1 2 3
Yl6 — —477.01 - 105.96 iI;-+ 55.82 X12 — 76.66 X12 + 29.343 X12
2
+ 365.71 X16 — 62.29 X16 - 1.23 X18.
R2 = .71 i: +.76 s = 10.10 D.F. = 16. l
y.x
Other important statistics of equation 1-6 are presented in Table 12. ”

TABLE 12.--Standard Errors and t Values of the

 

 

 

 

Coefficients of Equation 1-6 5—1
Standard t Value
Error of to
Variable Coefficients Coefficients
Xll 43.09 -2.46
X12 16 92 +0.50
X16 103.87 +2.92
X18 1.24 -0.99

 

Equation l-6 produced a reduction in the standard error of esti-
mate from 10.41 to 10.10 as compared with equation 1-4. The coefficient
of multiple determination remained unchanged, while the B increased

from +.74 to +.76. The coefficient of X11 in equation l-6 is significant

at the 5 percent level, while the coefficients of X are significant

16

at the 2 percent level. The coefficients of X12 and X18 are not signif-

icantly different from zero at the 10 percent level. Again the high

simple correlation of X12 with other variables, especially X might

18’

account for part of the lack of significance of its coefficients.

86

Cashwfuture spreads estimated with equations 1—5 and 1-6 are
compared in Table 13. For 20 out of 31 years, equation 1-5 was in
error by 6.97 cents or less. For 18 out of 24 years studied, errors
from equation 1-6 were 6.70 cents or less. Equation 1-6 provided
slightly smaller errors for the post-war years than equation 1-5. The
average post-war error from equation 1-6 was 4.00 cents; for equation
1-5, it was 5.19 cents.

TABLE l3.--Actual Adjusted December Spreads and Spread Estimated With
Equations l-5 and 1-6

 

 

 

A. /\ /\ /\
Years Y15 Y16 Y Y-Y15 Y-Y16
1927 +15.75 -- +24.71 + 8.96 --
1928 + 5.78 -- + 7.25 + 1.47 --
1929 +10 59 -- + 8.77 - 1.82 --
1930 + 9.28 -- + 7.23 - 2.05 --
1931 + 5.01 -- + 3.86 - 1.15 --
1932 +16.22 -- +18.72 + 2.50 --
1933 +11.80 -- +23 58 +11.78 --
1934 + 2.77 - 3.86 +21 65 +18 88 +25.51
1935 -41.45 -44.75 -46.62 - 5.17 - 1.87
1936 +12.96 + 7.62 -11.03 -23.99 -18.65
1937 -36 82 -36.98 ~43.68 - 6.86 - 6.70
1938 + 5.30 + 1.13 + 2.74 - 2.56 + 1.61
1939 + 9.20 + 6.05 + 7.05 - 2.15 + 1.00
1940 +10.84 + 7.97 + 5.05 - 5.79 - 2.92
1941 + 4.12 + 0.14 - 6.15 -10.27 - 6.29
1942 + 5.92 + 5.18 +18 26 +12.34 +13.08
1949 - 9.12 - 8.83 ~ 8.14 + 0.98 + 0.69
1950 - 4.41 - 4.39 - 9.25 - 4.84 - 4.86
1951 + 2.42 + 2.79 - 5.80 - 8.22 - 8.59
1952 - 9.33 - 4.52 - 9.62 - 0.29 - 5.10
1953 - 2.00 + 1.97 + 4.97 + 6.97 + 3.00
1954 -16.29 -13.35 - 5.51 +10 78 + 7.84
1955 + 2.36 + 1-57 + 0.77 - 1.59 - 0.80
1956 + 2.16 + 1.19 + 7.56 + 5.40 + 6.37
1957 + 5.76 + 2.42 + 1.85 - 3.91 - 0.57
1958 + 3.31 + 1.07 + 1.00 - 2.31 - 0.07
1959 + 1.46 + 0.66 - 7.32 - 8.78 - 7.98
1960 + 1.35 + 1.15 - 1.50 - 2.85 - 2.65
1961 +15 68 +14 19 +12.46 - 3 22 - 1.73
1962 - 3.45 - 0-60 + 5.86 + 9.31 + 6.46
1963 ~13 31 - 8.08 - 4.87 + 8.44 + 3.21

 

87
The Durbin—Watson test for serial correlation of the residuals

was applied to equations 1-5 and 1-6. The statistic,

 

2
g (dt ' dt-l)
, t = 2 . .
d = 2 , for equation 1-5 was 1.29; for
t = 1 °

equation 1-6 it was 1.31. In the formula for d', d is the unexplained

t

residual of observation t. For both equations, the results were incon-

 

elusive.
Now let us examine the regression coefficients of equations 1-3, L4

1-4, 1-5, and 1-6. They are as follows:

 

 

 

 

 

eqqation 1-3 equation 1-4 equation 1-5 equation 1-6
b11 -113.57* -108.87* -117.l6* ~105.96*
b12 + 62.93 + 56.35 + 63.38 + 55.82
b13 - 72.44 - 76.50 - 70.47 - 76.66
b14 +27.88 + 29.08 + 26.88 + 29.34
b15 +347.73* +369.70* +359.36* +365.7l*
b16 - 59.28* - 63.07* - 61.51* - 62.29*
bl7 + 10.21 - 6.38 not included not included
b18 - 2.60* - 1.13 - 2.55* - 1.23

The asterisk indicates that coefficients are significantly different
from zero at the 10 percent level of probability. The variable, X17,
has a positive coefficient in equation 1-3 and a negative coefficient
in equation 1-5. However, neither coefficient is significantly dif-
ferent from zero, even at the 20 percent level. Consequently this can-

not be considered a contradiction of economic theory.

In Chapter III the null hypothesis was advanced that government

88
programs have affected cash-future spreads only through their effects
on the demand for corn storage. In Chapter IV it was suggested that
if the hypothesis is false, we might expect (1) a significant coeffi—
cient for CCC stocks and (2) a significant difference in the corres-
ponding regression coefficients of equations for the two time periods
studied. A t test was employed as a partial check on the latter con-
dition. Since X11 and X16 are the only variables that are significant
in the equations for both periods the test was applied only to those

two variables.

The formula for the t statistic is;

 

 

In applying the t test, S was assumed equal to zero. However,

i
b1 b1

since each set of regression equations is based on similar time periods,
the covariance of b1 and bi will tend to be positive. Consequently the
t test applied in this manner will give a conservative test of the
hypothesis. An approximate formula for the degrees of freedom of the

. . 74
test is given by Walker and Lev.

The t values of differences between the coefficients are as

follows:

 

74Helen M. Walker and Joseph Lev, Statistical Inference, Holt,
Rinehart, and Winston; New York, 1953, pp. 157—158.

 

89

equations 1-3 and l-4

 

 

 

coefficients t values degrees of freedom
- ' .-

b11 b11 0.077 51
- ' —

b15 b15 0.124 52
_ I

b16 b16 +0.124 52

equations 1-5 and 1-6

 

- ' -

b1]. bl]. 0.194 52
- ' -

b15 bl5 0.037 52

It is apparent that none of the t values are significant even at the
very low level of 50 percent, for which t = .68. With this test the
hypothesis cannot be rejected; however, it should be recognized that a
complete test of the hypothesis was not obtained. In view of the very
small t values obtained, the additional computing cost of obtaining a
more precise test does not appear to be justified.

Summary of January 1 Equations.--Six equations were computed

 

for January 1. Three of these were based on the observations from

1927 — 1963 and three were based on observations from 1934 - 1963.

The coefficients of multiple determination and adjusted multiple cor-
relation coefficients for the equations based on the longer time period
in every case were slightly larger than those for the corresponding
equations based on the shorter period. Similarly, standard errors of
estimate were smaller for equations based on the 1927 - 1963 period

than on the 1934 - 1963 period. Simple correlations between independent
variables were relatively large for all equations. This could account
for the lack of significance of several regression coefficients.

Equation 1-5 had a standard error of estimate of 9.57 cents;

 

90
this was the smallest standard error of estimate of the six equations.
For 20 out of 31 years studied, estimated spreads from equation 1-5
were in error by 6.97 cents per bushel or less. This should be compared
with a range of actual adjusted December spreads of 71.33 cents in the
period studied. For the shorter period, the range of actual adjusted
December spreads was 68.27 cents. Equation 1-6 was in error by 6.70
cents or less for 18 out of 24 years studied; however, its standard
error of estimate was 10.10 cents per bushel. l».
A t test for significant differences between the coefficients
of

and X in equations 1-5 and 1-6, assuming 8 equals zero, r4

X t
11 16 b1 b1

indicated that differences were not significant even at the 50 percent

 

level. Consequently, the author decided that the extra computational
cost of obtaining a more powerful test was not justified. Equation 1-5
would appear to give the best results for predictive purposes, since it
has the smallest standard error of estimate of the six equations and
its coefficients apparently are not significantly different from those
of equation 1-6.

In short, the hypothesis that CCC activities have influenced
cash-future price spreads only through their effects on the commercial
demand for corn storage was not rejected. Differences between regression
coefficients for the two periods were not significant and coefficients
of the variable for CCC stocks were not significantly different from
zero at the 10 percent level except in equation 1-1. It should be
pointed out that significant coefficients for CCC stocks might be ob-
tained even if the only effects of such stocks were on the commercial
demand for storage. In addition, an important reason for not obtaining

significant differences in regression coefficients for the two periods

91
may be the small number of observations which was available prior to
1934.
In the remainder of this chapter, the results of equations for
the other three dates studied will be presented. Assumptions underlying
these regression equations will be discussed in a section of the fol-

lowing chapter.

April 1 Equations

 

Variables used in the April 1 equations are defined in the same

'way as those for January 1 equations. However, the first subscript, 2, L

 

indicates that variables are based on observations for April 1. The
cash-future spreads used are March spreads. Corn consumption in the

quarter preceding March 1 is used in computing the variable, and

x21

X22. The variable,

April 1; the variable, X26’ is corn consumption in the quarter following

X23, is corn consumption in the quarter following
April 1 divided by corn production in the previous year. Stocks used
in X21, X22, X24, and X27 are April 1 stocks. The units for all vari-

ables are the same as those used in January 1 equations.

Equation 2-1. Time Period: 1927 - 1963.

A. 1 2 3
Y21 = -236.03 - 14.98 x21 + 29.39 x22 - 33.77 x22 + 13.964 x22

127 52 x 22 55 x2 + 1 251 x3 + 5 38 x + 0 03 x2
+ ° 23 ' ° 23 ' 23 ' 24 ‘ 24

2
- 0.011 x24 — 1.93 x25.
R2 = .71 E = +.74 s = 10.01 D.F. = 19
y.x

Other important statistics of equation 2-1 are presented in Table 14.

92

TABLE l4.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 2-1

 

 

 

 

Simple Correlation With Standard t Value
Error of of
Variable x22 x23 X24 X25 Y Coefficients Coefficients

X21 -.24 -.18 -.39 -.21 -.41 22.92 -0.66
X22 +.85 +.87 +.89 -.01 11.66 +0.82
X23 +.86 +.85 +.13 63.96 +1.66 I
X24 +.86 +.l6 89.38 +0.06 u-q
X25 -.15 0.87 -2.21

 

 

Simple correlations of X with the other independent variables

21
have been reduced considerably as compared with the January 1 equations.
However simple correlations between the other independent variables re-
main high. The coefficient of X25 is significant at the 5 percent
level; none of the other coefficients are significantly different from
zero at the 10 percent level.

Now let us examine equation 2-2 which is based on the 1934-1963

period.

Equation 2-2. Time Period: 1934 - 1963.

 

'\ 1 2 3
Y22 + -285.09 + 0.84 i;;‘+ 38.50 x22 — 43.96 x22 + 17.29 x22
182 15 x 29 81 x2 1 563 x3 24 14 x + 2 65 x2
+ ° 23 ‘ ° 23 + “ 23 ‘ ' 24 ° 24
3
- 0.087 x24 - 1.97 x28,
R2 = .73 8': +.69 s = 10.49 D.F. = 12
y.x

Other important statistics of equation 2-2 are presented in Table 15.

93

TABLE 15.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 2-2

 

 

 

 

Simple Correlation With Standard t Value
Variable x22 x23 X24 X28 Y CoiffiZizfits Coeffigients
X21 -.23 -.14 -.37 -.16 -.48 30.10 +0.03
X22 +.84 +.88 +.91 +.32 12.96 +0.89
X23 +.86 +.93 +.37 83.46 +1.84
X24 +.92 +.39 110.16 -0.20 an
X28 +.25 1.72 -l.l4

 

 

From Table 15 it can be seen that simple correlations between
the variables are approximately the same as for equation 2-1. The R2
is essentially unchanged, while B has been decreased and Sy.x has been
increased as compared with the 1927-1963 period. At the 10 percent

level only the coefficients of X are significant.

23
Actual adjusted March spreads and spreads estimated with equa-
tions 2-1 and 2-2 are compared in Table 16. For the 1927-1963 period
the range of actual adjusted March spreads was 73.26 cents. For the
shorter period the range was 65.77 cents. Spreads estimated with
equation 2-1 were in error by 10.16 cents or less for 24 out of 31

years studied. For 18 out of 24 years, estimate from equation 2-2 were

in error by 7.37 cents or less.

94

TABLE l6.--Actual Adjusted March Spreads and Spreads Estimated With
Equations 2-1 and 2-2

__._ A

 

 

 

 

A A A. A
Years Y21 Y22 Y Y-Y21 Y-Y22
1927 +14.50 -- +21.12 + 6.62 --
1928 + 4.46 -- - 0.78 - 5.24 --
1929 +12.91 -- + 2.75 -10.16 --
1930 + 8.92 -- + 4.18 - 4.74 --
1931 + 1.02 -- + 2.48 + 1.46 --
1932 + 8.40 -- +22.82 +14.42 --
1933 +12.35 -- +12.7l + 0.36 --
1934 + 0.77 + 7.84 +15.09 +14.32 + 7.25
1935 -43.49 -44.78 -39 78 + 3.71 + 5.00
1936 + 0.32 - 2.63 - 6.41 — 6.73 - 3.78
1937 -38.70 -37.89 -50.44 -11.74 -12.55
1938 - 1.71 - 2.67 + 3.18 + 4.89 + 5.85
1939 + 1.02 — 7.54 + 4.70 + 3.68 +12.24
1940 - 1.31 + 1.55 + 1.49 + 2.80 - 0.06
1941 + 5.73 + 3.38 - 6.86 -12.59 -10.24
1942 + 1.62 + 2.92 +15.33 +13.7l +12.4l
1949 + 2.47 + 0.34 -l7.19 -l9.66 -17.53
1950 - 2.53 - 1.73 -l3.63 -11.10 -11.90
1951 - 3.95 - 3.42 - 2.74 + 1.21 + 0.68
1952 -10.12 - 6.56 - 6.54 + 3.58 + 0.02
1953 - 4.35 - 5.28 - 0.52 + 3.83 + 4.76
1954 - 4.89 - 5.19 - 5.44 - 0.55 - 0.25
1955 — 0.69 - 1.83 - 5.42 - 4.73 - 3.59
1956 - 1.07 - 0.05 + 2.85 + 3.92 + 2.90
1957 - 4.36 - 3.43 + 2.61 + 6.97 + 6.04
1958 - 4.70 - 4.97 — 3.95 + 0.75 + 1.02
1959 -lO.47 -10.68 - 8.10 + 2.37 + 2.58
1960 - 8.49 - 9.61 - 3.68 + 4.81 + 5.93
1961 +13.02 +13 43 + 6.06 - 6.96 - 7.37
1962 + 1.01 + 0.13 + 1.20 + 0.19 + 1.07
1963 — 6.40 - 5.32 - 5.79 + 0.61 — 0.47
In view of the lack of significance of the coefficients of X24

and the high simple correlations of this variable with other independent

variable, equation 2-3 and 2-4 were computed excluding X

24'

95

Equation 2-3. Time Period: 1927 - 1963.

 

/\ 1 2 3
Y23 — -235.41 - 30.70 i;;-+ 15.61 X22 - 17.89 X22 + 9.142 X22
2 3
+ 144.82 X23 - 24.63 X23 + 1.334 X23 - 1.44 X25.
R2 = .66 §'= +.73 S = 10 04 D.F. = 22
y.x

Other important statistics of equation 2-3 are presented in Table 17.

 

 

 

 

TABLE 17.--Standard Errors and t Values of the
Coefficients of Equation 2-3
Standard Error of t Value of

Variable Coefficients Coefficients .'

F—

1
X21 20.81 -1.48
X22 11.56 +0.59
X23 88 89 +3.13
X25 0.77 -l.86

 

As compared with equation 2-1, the R2 was reduced slightly,
but both E and Sy x were essentially unchanged. The standard errors
of all coefficients have been reduced. The coefficients of X are

23

significant at the 1 percent level; those of X are significant at

25
the 5 percent level. None of the other coefficients are significant
at the 10 percent level.

Now let us turn to equation 2-4 which is based on the 1934-1963

period.

Equation 2-4. Time Period: 1934 - 1963.

 

/\ 1 , 2 3
Y24 = -298.29 + 0.62 i_"+ 32 22 x22 - 35.16 x22 + 14.143 x22
21
2 , 3
+ 153.81 x23 - 25.26 x23 + 1.328 x23 - 1.43 x28.
R2 = .71 E = +.75 s = 9.62 D.F. = 15

y.x

96

Other important statistics of equation 2-4 are presented in Table 18.

TABLE 18.—-Standard Errors and t Values of the
Coefficients of Equation 2-4

 

 

 

Standard Errors of t value of

Variable Coefficients Coefficients
X21 24.90 +0.02
X22 11.83 +0.95
X23 39.07 +3.33
X28 1.15 -l.25

 

2
As compared with equation 2-2, the R is essentially unchanged,
while the H has been increased and Sy x has been reduced. The standard

errors of all coefficients have been reduced by omitting X The

24'
coefficients of X23 are significant at the 1 percent level; none of the
other coefficients are significant at the 10 percent level.

Spreads estimated with equations 2-3 and 2—4 are compared in
Table 19. Spreads estimated with equation 2-3 were in error by 9.20

cents or less for 23 out of 31 years studied. Equation 2-4 was in

error by 9.60 cents or less for 18 out of 24 years.

 

97

TABLE l9.-—Actua1 Adjusted March Spreads and Spreads Estimated With
Equation 2-3 and 2-4

 

 

 

 

A A A A
Years Y23 Y24 Y Y-Y23 Y-Y24
1927 +18.18 -- +21.12 + 2.94 --
1928 + 8.42 -- - 0.78 - 9.20 --
1929 + 8.63 -- + 2.75 - 5.88 --
1930 + 6.47 -- + 4.18 - 2.29 --
1931 - 8.83 -- + 2.48 +ll.3l --
1932 + 4.44 -- +22.82 +18.38 --
1933 +12.39 --- +12.7l + 0.32 --
1934 + 3.93 + 4.74 +15.09 +11.16 +10.35
1935 -40.89 -46.02 —39.78 + 1.11 + 6.24
1936 + 1.26 - 1.76 - 6.41 - 7.67 — 4.65
1937 -35.88 -37.42 -50.44 -14.56 -13.02
1938 + 6.21 - 1.65 + 3.18 - 3.03 + 4.83
1939 + 0.68 - 4.90 + 4.70 + 4.02 + 9.60
1940 + 2.75 + 3.19 + 1.49 - 1.26 - 1.70
1941 + 5.74 + 4.51 - 6.86 -12.60 -11.37
1942 - 2.58 + 0.77 +15.33 +17.91 +14.56
1949 + 2.14 - 1.23 -17.19 -19.33 —15.96
1950 - 1.19 0.33 -13.63 -12.44 -l3.96
1951 - 5.00 - 4.12 - 2.74 + 2.26 + 1.38
1952 -11.52 - 4.54 - 6.54 + 4.98 - 2.00
1953 - 4.79 - 4.63 - 0.52 + 4.27 + 4.11
1954 - 5.43 - 6.06 - 5.44 - 0.01 + 0.62
1955 - 2.50 - 5.14 - 5.42 - 2.92 - 0.28
1956 - 3.80 - 2.98 + 2.85 + 6.65 + 5.83
1957 - 3.63 - 1.83 + 2.61 + 6.24 + 4.44
1958 - 2.99 - 3.79 - 3.95 - 0.96 - 0.16
1959 -10.06 ~10.00 - 8.10 + 1.96 + 1.90
1960 - 7.10 - 8.13 - 3.68 + 3.42 + 4.46
1961 +11.48 +12.29 + 6.06 - 5.42 - 6.23
1962 + 1.76 - 0.51 + 1.20 - 0.56 + 1.71
1963 - 6.98 - 5.13 - 5.79 + 1.19 - 0.66

 

In view of the null hypothesis to be tested, let us examine the

coefficients of equations 2-1, 2-2, 2-3, and 2-4. They are as follows:

equation 2-1

 

98

equation 2-2

 

equation 2-3

 

equation 2—4

 

b21 - 14.98 + 0.84 - 30.70 + 0.62

b22 + 29.39 + 38.50 + 15.61 + 32.22

b23 - 33.77 - 43.96 - 17.89 - 35.16

b24 + 13.964 + 17.029 + 9.142 + 14.143

b25 +127.52 +182.15* +144.82* +153.81*
b26 - 22.55 - 29.81* - 24.63* - 25.26*

b27 + 1.251 + 1.563* + 1.334* + 1.328*
b28 + 5 38 - 24 14 not included not included
b29 + 0.03 + 2.65 not included not included
b210 - 0.011 - 0.087 not included not included
b211 - l.93* - 1.97 - 1.44* - 1.43

The asterisk indicates that coefficients are significant at the

10 percent level. The t test was used as a partial check for significant

differences in the coefficients, b b and b in equations 2-3 and

25’ 26’ 27’

2-4. Differences were not significant even at the 50 percent level of
probability.
Two additional equations were computed for April 1, using the

and X

26 27 and X

variables X 23 24

in place of X in an attempt to reduce

simple correlations between the independent variables. The variable,

X26’ is corn consumption in the quarter following April 1 divided by

corn production in the preceding year; the variable, is stocks of

X27,
other grains divided by the number of grain consuming animal units fed

annually.

 

99

Equation 2-5. Time Period: 1927 - 1963.

 

I“ 1 2 3
st - +35.42 - 13.45 X21 + 58.12 X22 — 55.22 X22 + 18.670 X22
2 2
- 125.32 X26 + 33.54 X26 + 357.34 X27 - 243.99 X27 - 2.95 X25.
R2 = .56 E = +.60 S = 11.77 D.F. = 21
y.x

Other important statistics of equation 2-3 are presented in Table 20.

TABLE 20.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 2-5

 

 

 

 

Simple Correlation With Standard t Value

Variable x22 x26 x27 x25 Y CogffEZizfits Coeffiiients
X21 -.24 +.42 -.40 -.21 -.41 27.36 -1.69
X22 +.44 +.86 +.92 -.01 13.24 +1.63
X26 +.26 +.50 -.33 124.96 -0.73
;X27 +.84 +.l6 37.63 +3.01
X25 -.15 0.95 -3.10

 

As compared with equation 2-1, simple correlations between the
independent variable have been reduced considerably. At the same time
the R2 has been reduced from .71 to .56 and H has been reduced from
+.74 to +.60. The Sy.x has been increased from 10.01 to 11.77.

In general, we might expect an increase in X27, stocks of other
grains divided by the number of grain consuming animal units, would in-
crease spreads. The reasoning behind this is that an increase in the
supply of substitutes for corn relative to the demand would shift the
demand for corn to the left, thus lowering the cash price relative to

the future price. Consequently, a one—sided t test could be used for

the coefficients of X27. However, in view of the functional form used

 

100

for X a two-sided test was applied. With a two-sided test, the

27’

coefficients of X2 are significant at the 1 percent level. The co-

7

efficient of X2 is significant at the 1 percent level; none of the

5
other coefficients are significant at the 10 percent level.

Now let us turn to equation 2-6 which is based on the 1934-1963

period.

Equation 2-6. Time Period: 1934 - 1963.

 

A 1 2 3 . “'1

Y26 = -49.39 + 5.33 XE; + 67.28 X22 - 67.92 X22 + 22.267 X22 i

2 2 .L}

- 83.43 X26 + 22.22 X26 + 383.99 X27 - 264.75 X27 - 2.47 X28. i+4
2

 

R = .55 E: +.52 s = 12.44 D.F. = 14
y.x

Other important statistics of equation 2-6 are presented in Table 21.

TABLE 21.--Simp1e Correlations Between the Variables,Standard Errors,
and t Values of the Coefficients of Equation 2-6

 

 

 

 

Simple Correlation With Standard t Values

Variable x22 x26 X27 x28 Y Cogff:::e::s Coeffigients
X21 —.23 +.56 -.37 -.16 -.48 38.83 +0.14
X22 +.32 +.87 +.91 +.32 15.06 +1.44
X26 +.19 +.4l -.21 153.71 -0.40
X27 +.89 +.38 61.23 +1.95
X28 +.25 1.61 -1.53

 

As compared with equation 2-2, simple correlations between the
variables have been reduced considerably. At the same time the R2 has
been reduced from .73 to .55 and H has been reduced from +.69 to +.52.
The Sy.x has been increased from 10.49 to 12.44. Only the coefficients

of X27 in equation 2-6 are significant at the 10 percent level.

101
Actual adjusted March spreads and spreads estimated with equa-
tions 2-5 and 2-6 are compared in Table 22. Spreads estimated with
equation 2-5 are in error by 9.22 cents or less for 21 out of 31 years
studied. Equation 2-6 was in error by 9.60 cents or less for 17 out
of 24 years.

TABLE 22.--Actual Adjusted March Spreads and Spreads Estimated With
Equations 2—5 and 2-6

 

 

 

 

.A A A .4
Years Y25 Y26 Y Y-Y25 Y-Y26
1927 + 9.80 -- +21 12 +11.32 -—
1928 - 7.12 -- - 0.78 + 6.34 --
1929 +13.71 -- + 2.75 -10.96 --
1930 + 6.80 -- + 4.18 - 2.62 --
1931 +11.54 -- + 2.48 - 9.06 --
1932 + 7.50 -- +22.82 +15.30 --
1933 +11.49 -- +12 71 + 1.22 --
1934 + 2.46 + 1.09 +15.09 +12.63 +14.00
1935 -32.11 -35.88 -39.78 - 7.67 - 3.90
1936 + 1.25 - 1.30 - 6.41 - 7.66 - 5.11
1937 -33.72 -35.10 -50.44 -16.72 -15.34
1938 -12.05 -16 91 + 3.18 +15.23 +20.09
1939 + 1.22 - 1.23 + 4.70 + 3.48 + 5.93
1940 - 7.38 - 8.11 + 1.49 + 8.87 + 9.60
1941 + 6.48 + 3.76 - 6.86 -13.34 -10.62
1942 + 0.52 + 0.85 +15.33 +14.81 +14.48
1949 + 4.03 + 2.78 -17 19 -21.22 —19.97
1950 - 1.87 - 1.89 -13.63 -11.76 -11.74
1951 + 3.32 + 3.56 - 2.74 - 6.06 - 6.30
1952 -10 77 - 4.82 - 6.54 + 4.23 - 1.72
1953 - 4.30 - 1.78 - 0.52 + 3.78 + 1.26
1954 - 0.94 - 0.99 - 5.44 - 4.50 - 4.45
1955 - 2.31 - 3.20 - 5.42 - 3.11 - 2.22
1956 - 6.04 - 5.69 + 2.85 + 8.89 + 8.54
1957 - 2.32 - 1.53 + 2.61 + 4.93 + 4.14
1958 + 5.12 2.63 - 3.95 - 9.07 - 6.58
1959 - 4.78 - 6.33 - 8.10 - 3.32 - 1.77
1960 - 6.31 - 5.45 - 3.68 + 2.63 + 1.77
1961 +-7.99 +-9.13 +-6.06 - 1.93 — 3.07
1962 - 4.91 - 5.76 + 1.20 + 6.11 + 6.96
1963 -15.01 -11.79 - 5.79 + 9.22 + 6.00

 

102
The Durbin-Watson test for serial correlation of the residuals
was applied to equations 2-3 and 2-4. For both equations the results
were inconclusive.
Now let us examine the coefficients of equations 2-3 and 2-4.

They are as follows:

 

 

equation 2-5 equation 2—6
b21 - 13.45 + 5.33
b22 + 58.12 + 67.28
b23 - 55.22 - 67.92
b24 + 18.670 + 22.267
b25 -125.32 - 83.43
b26 + 33.54 + 22.22
b27 +357.34* +383.99*
b28 -243.99* —264.75*
b29 - 2.95* - 2.47

The asterisk indicates that coefficients are significant at the
10 percent level. The t test was used as a partial test for significant

and b,

differences in the coefficients, b 28’

27 for the two equations.

Differences were not significant even at the 50 percent level.

Summary of April 1 Equatiqgs.--Three pairs of equations were

 

computed for April 1. In two of the three pairs, the equation for the
longer period provided a larger E, essentially the same R2 and a smaller
Sy.x than the equation for the 1934-1963 period. In the remaining

pair, the equation for the 1934-1963 period provided a larger R2,
essentially the same H, and a slightly smaller Sy.x than the equation
for the 1927-1963 period. Simple correlations between the independent

variables were relatively large and could account for the lack of

103
significance of several coefficients.

For predictive purposes, equation 2-1, based on the 1927-1963
period would appear to give the best results of the April 1 equations.
Coefficients of the variable for CCC corn stocks were not
significant at the 10 percent level in any of the six equations. In
addition, differences in the corresponding regression coefficients of

equations for the two periods were apparently not significant at the
50 percent level. In short, the equations provided no evidence that IE4
CCC activities have affected the commercial supply of corn storage for

April 1; consequently the null hypothesis was not rejected. twd

 

July 1 Equations

 

Four regression equations were computed for July 1. Variables
in these equations are defined in the same manner as those for January 1
equations. However, the first subscript of the variables, 3, indicates
that they are based on observations for July 1. The cash-future spreads

used for July 1 are June spreads. The variable, represents corn

X33 ’

consumption in the quarter following July 1; consumption used in com-

puting variables X31 and X32 is consumption in the quarter preceding

July 1. The variable, is corn consumption in the quarter following

X36’

July 1 divided by production for the preceding year. Stocks used in

and X are July 1 stocks. The

computing the variables X31, X32, X34, 37

units used for all variables are the same as those used in January 1

equations.

Equation 3—1. Time Period: 1927 - 1962.

‘3 l 2 3
Y31 — -67.60 - 5.11 X31 + 22.99 X32 - 30.95 X32 + 9.503 X32

2 3
+ 48.10 X33 — 9.98 X33 + 0.646 X33 + 3.05 X34 - 1.22 X35.

 

104

R2 = .83 8': +.87 s = 5.20 D.F. = 20
y.x

Other important statistics of equation 3—1 are presented in Table 23.

TABLE 23.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 3-1

 

 

 

 

 

Simple Correlation With Standard t Value
Variable X32 X33 X34 X35 Y CoiffiZizits Coeffiiients
x31 +.05 -.08 —.09 -.02 -.61 6.86 -0.75 1*?
X32 +.89 +.88 +.92 +.03 4.71 +0.33 7 1
X33 +.91 +.92 +.19 10.95 +3.54 1
x34 +.87 +.23 1.12 +2.73 5"
X35 -.04 0.42 -2.91

 

32, X33, X34, and X35 are

high. In spite of this, the coefficients of X

Simple correlations between the variables X
33 are significantly
different from zero at the 1 percent level. With a one-sided test,
the coefficients of X34 and X35 are also significant at the 1 percent
level; however, coefficients of the other two variables are not
significant at the 10 percent level.

Before comparing actual and estimated spreads from equation 3-1,

let us turn to equation 3—2, based on the shorter time period.

Equation 3-2. Time Period: 1934 - 1962

 

/\ 1 .
Y32 = -102.21 + 3.75 i;;’+ 20.89 x32 - 28.39 x3, + 8.929 x32
+ 61.26 x33 - 12.22 x33 + 0.775 x33 + 2.75 x34 - 1.69 x38.
R2 = .83 8': +.84 s = 5.63 D.F. = 13

y.x

Other important statistics of equation 3-2 are presented in Table 24.

105

TABLE 24.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 3-2

 

 

 

 

 

 

Simple Correlation With Standard t Value
Variable X32 X33 X34 X38 Y CogffiZiZEts Coeffiiients
X31 —.02 -.13 -.09 -.05 -.56 11.05 +0.34
X32 +.87 +.90 +.90 +.30 5.81 : +0.25
X33 +.91 +.97 +.38 18.49 +2.69
X,34 +.94 +.4l 1.53 +1.80 "
X38 +.28 0.97 -1.73 I 1

 

 

When compared with equation 3-1, the R2 of eqUation 3-2 is un-
changed, while E has been reduced slightly, from +.87 to +.84, and
Sy.x has been increased from 5.20 to 5.63. Simple correlations of X32,
X33, X3A, and X35 with Y have been increased considerably; however,
simple correlations between these variables remain high. The coefficients
of X33 are significant at the 5 percent level, while those of X34 and X38
are significant at the 10 percent level.

Cash-future spreads estimated with equations 3—1 and 3-2 are
compared in Table 25. The range of actual adjusted June Spreads for
the 1927 through 1962 period was 55 56 cents; for 1934 through 1962
it was 49.81 cents. For 25 out of 30 years studied, equation 3-1 was

in error by 4.97 cents or less. Equation 3-2 was in error by 3.30

cents or less for 16 out of 23 years.

106

TABLE 25.--Actual Adjusted June Spreads and Spreads Estimated With
Equations 3-1 and 3-2

 

 

 

/\ IA 74 74
Years Y31 Y3.2 1 Y-Y31 Y-Y32

1927 + 3.22 -- + 5.37 + 2.15 --
1928 - 8.53 -- -10.21 - 1.68 --
1929 + 2.73 ~~ - 3.60 - 6.33 --
1930 - 3.68 -- - 5.34 - 1.66 --
1931 -ll.88 —- -10.74 + 1.14 --
1932 + 4.46 -- + 3.78 - 0.68 --
1933 + 6.61 -- +13.54 + 6.93 -—
1934 —ll.22 - 8.85 - 3.08 + 8.14 + 5.77
1935 -24.66 -25.28 -26.29 - 1.63 — 1.01
1936 - 8.11 - 7.14 -10.01 - 1.90 - 2.87
1937 -39.41 -39.01 ~42.02 - 2.61 - 3.01
1938 - 2.86 - 3.39 + 1.44 + 4.30 + 4.83
1939 + 0.12 - 2.46 - 1.57 - 1.69 + 0.89
1940 -10.56 -10.41 -13.71 - 3.15 - 3.30
1941 - 2.52 - 2.20 + 2.45 + 4.97 + 4.65
1942 + 5.13 + 4.97 + 7.79 + 2.66 + 2.82
1949 - 3.15 - 3.09 -l6.86 -13.71 ~13.77
1950 ~12.86 -10.34 - 8.01 + 4.85 + 2.33
1951 - 5.47 - 5.68 - 6.55 — 1.08 - 0.87
1952 - 6.77 - 7.13 - 4.65 + 2.12 + 2.48
1953 - 8.59 - 9.48 - 9.76 - 1.17 - 0.28
1954 - 8.69 - 7.72 —12.47 - 3.78 - 4.75
1955 - 8.37 -10.29 - 9.59 - 1.22 + 0.70
1956 - 6.65 - 6.63 - 7.66 - 1.01 - 1.03
1957 - 7.09 - 7.12 - 4.92 + 2.17 + 2.20
1958 -l4.01 -13.62 -ll.69 + 2.32 + 1.93
1959 -11.24 ~12.18 «10.27 + 0.97 + 1.91
1960 - 9.22 - 9.51 - 4.79 + 4.43 + 4.72
1961 + 9.91 +10 32 + 4.50 - 5.41 - 5.82
1962 - 4.60 - 4.50 - 3.02 + 1.58 + 1.48

In equations 3-3 and 3-4, the variables X36 and X37 were included

and X. in an attempt to reduce the simple correlations

in place of X33 34

between the independent variables. The variable, is corn cone

x36’
sumption in the quarter following July 1 divided by corn production in

the preceding year, the variable, is stocks of other grains divided

X27’

by the number of grain consuming animal units fed annually.

107

Equation 3-3. Time Period: 1927 - 1962.

 

.A 1 2 3
Y33 — +9.77 - 19.54 2-(3—1- + 44.19 X32 - 51.94 X32 + 15.082 X32
2
- 6.66 X36 + 6.37 X36 + 6.00 X37 - 1.64 X35.
R2 = .68 §'= +.75 S = 6.92 D.F. = 21
y.x

Other important statistics of equation 3-3 are presented in Table 26.

TABLE 26.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 3-3

 

 

 

 

Simple Correlation With Standard t Value

Variable x32 x36 X37 x35 Y CoiffiZizfits Coeffiiients
X31 +.05 -.10 -.08 +.02 -.61 7.97 -2.45
X32 +.84 +.88 +.92 +.03 5.71 +1.28
X36 +.82 +.91 +.09 26.02 -0.01
X37 +.86 +.22 2.60 +2.31
X35 -.04 0.60 -2.74

 

Simple correlations between the independent variables have been
changed very little as compared with equation 3-1. However, the R2 has
been reduced from .83 to .68; E has been reduced from +.87 to +.75;

Sy x has been increased from 5.20 to 6.92. The coefficient of X37 is

35 18

is significant

significant at the 2.5 percent level; the coefficient of X
significant at the 1 percent level; the coefficient of X31
at the 5 percent level. Coefficients of the other two variables are
not significantly different from zero at the 10 percent level. The in-
creased t value of the coefficient of X31 is due mainly to an increase
in the absolute size of the coefficient from 5.11 in equation 3-1 to

19.54 in equation 3-3. This increase may indicate that part of the

 

108

effect attributed to X33 and other variables in equation 3-1 is now

being associated with X31.
Now let us examine equation 3-4, which contains the same variables

as equation 3-3 but is based on the shorter time period.

Equation 3-4. Time Period: 1934 - 1962.

 

 

A 1 2 3
Y34 - +15.69 - 19.43 XEI'+ 47.53 X32 - 55.58 X32 + 15.762 X32
- 29.94 X36 + 11.33 X36 + 5.47 X37 - 0.89 X38.
R2: .69 E=+.72 8 =7.22 D.F. = 14
y.x
Other important statistics of equation 3-4 are presented in Table 27. L a

 

TABLE 27.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 3-4

 

 

 

 

Simple Correlation With Standard t Value

Variable X32 X36 x37 X38 Y Cogff26izfits Coeffiiients
X31 -.02 —.16 -.07 -.05 -.56 9.48 -2.05
X32 +.77 +.90 +.90 +.30 6.71 +1.15
X36 +.82 +.91 +.29 31.36 -0.60
X37 +.92 +.39 3.08 +1.78
X38 +.28 0.95 -0.93

 

Simple correlations between the variables have not been greatly
changed as compared with equation 3-2. The R2, however, has been re-
duced from .83 to .69; the E has been reduced from +.84 to +.72; the
Sy.x has been increased from 5.63 to 7.22. As in equation 3-3, the
absolute size of the coefficient of X31 has been increased. In addi-

tion, its sign has been changed from positive in equation 3-2 to

negative in equation 3-4, and its standard error has been decreased

109
from 11.05 to 9.48. Here again, the change in the size of the coeffi-

cient may indicate that X is carrying part of the effect associated

31
with other variables in equation 3-2. In equation 3-4, only the coeffi-
cients of X31 and X37 are significantly different from zero at the

10 percent level.

Cash-future spreads estimated with equations 3-3 and 3-4 are
compared in Table 28. For 20 out of 30 years studied, errors from
equation 3-3 were 5.95 cents or less. Equation 3-4 was in error by
5.26 cents or less for 15 out of 23 years.

The Durbin-Watson statistic, d', for equation 3-1 was 2.74; for
equation 3-2, it was 3.29. Tables for interpreting d' for several
sample sizes and for k' ranging from one to five, where k' is the number
of independent variables in the equation, are given by Friedman and
Foote.75 However, neither Friedman and Foote nor the original article
by Durbin and Watson provide tables for k' = 9.76 Consequently, the
author used a linear extrapolation of the tabled values to k' = 9
testing the d of equation 3-2. The approximate rejection regions for
testing the hypothesis of no serial correlation in the residuals were
4-dg < 0.48 and d' < 0.48. Since the observed values of 4-d' and d'

were not near the rejection region, it appears correct to assume d'

falls in the inconclusive range. For equation 3-1, the d' was in the

 

inconclusive range for k” = 5; hence it would also be in the incon-
clusive range for k’ = 9.
75

Joan Friedman and Richard J. Foote, Computational Methods for
Handling Systems of Simultaneous Equations, U.S.D.A. Agriculture Hand-
book 94; Washington, D.C., 1955, pp. 77-78.

76J. Durbin and G. 8. Watson, "Testing for Serial Correlation
in Least Squares Regression," Biometrika, 1951, Vol. 38, p. 174.

 

 

 

 

110

TABLE 28.--Actual Adjusted June Spreads

and Spreads Estimated With

 

 

 

Equations 3-3 and 3—4
.A A. .A /~
Years Y33 Y34 Y Y Y33 Y-Y34

1927 + 1.60 —- + 5.37 + 3.77 -
1928 -14.48 -- -10.21 + 4.27 -
1929 - 0.37 -- - 3.60 - 3.23 -
1930 - 5.49 -- - 5.34 + 0.15 -
1931 - 1.71 -— -lO.74 - 9.03 -
1932 + 3.73 -- + 3.78 + 0.05 -
1933 + 3.89 -- +13.54 + 9.65 -
1934 - 7.40 - 6.53 - 3.08 + 4.32 + 3.45
1935 -17.67 -22.40 -26.29 - 8.62 - 3.89
1936 -10.24 -1l.99 -10.01 + 0.23 + 1.98
1937 -36.70 ~35.15 -42.02 - 5.32 - 6.87
1938 - 5.77 - 7.06 + 1.44 + 7.21 + 8.50
1939 + 3.17 + 3.05 - 1.57 - 4.74 - 4.62
1940 -14.63 -l3.58 -13.71 + 0.92 - 0.13
1941 - 5.82 - 6.79 + 2.45 + 8.27 + 9.24
1942 - 0.22 - 0.57 + 7.79 + 8.01 + 8.36
1949 - 5.48 - 4.34 -l6.86 -ll.38 -12.52
1950 —12.64 -14.95 - 8.01 + 4.63 + 6.94
1951 - 0.39 - 1.29 - 6.55 - 6.16 - 5.26
1952 - 3.69 - 3.16 - 4.65 - 0.96 . - 1.49
1953 - 8.25 - 7.23 - 0.76 - 1.51 - 2.53
1954 —13.42 -l3.12 ~12.47 0.95 + 0.65
1955 — 0.18 - 1.94 - 9.59 - 9.41 - 7.65
1956 - 1.71 - 3.78 - 7.66 - 5.95 - 3.88
1957 - 7.14 - 7.50 - 4.92 + 2.22 + 2.58
1958 -11.55 -ll.78 -11.69 - 0.14 + 0.09
1959 - 9.44 - 8.88 -10.27 - 0.83 - 1.39
1960 -10.64 - 9.49 - 4.79 + 5.85 + 4.70
1961 + 7.38 + 7.61 + 4.50 - 2.88 - 3.11
1962 -12.69 - 9.87 - 3.02 + 9.67 + 6.85

 

 

Now let us examine the regression coefficients of the four

equations.

They are as follows:

111

 

 

 

 

equation 3-1 equation 3-2
b31 - 5.11 + 3.75
b32 +22.99 +20.89
b33 -30.95 -28.39
b34 + 9.503 + 8.929
b3S +48.10* +61.26*
b36 - 9.98* -12.22*
b37 + 0.646* + 0.775*
b38 + 3.058 + 2.75*-
b39 - l.22* - l.69*
equation 3-3 equation 3-4
b31 -19.54* -l9.43*
b32 +44.l9 +47.53
b33 -51.94 -55.58
b34 +15.082 +15.762
b35 - 6.66 -29.94
b36 + 6.37 +ll.33
b37 + 6.00* + 5.47*
b38 - l.64* - 0.89

The asterisk indicates that coefficients are significantly dif-
ferent from zero at the 10 percent level. It should be noted that in

equations 3-1 and 3-2 the coefficients, b35, b36’ and b37 are for the

while b is for the variable,

X33, 38 In equations 3-3

variable, X34.
and 3-4, coeff1c1ents b35 and b36 are for variable X36; b37 is the

coefficient of X . The coefficient, is for the trend variable.

37

The variable,

b38’

X31, has a negative coefficient in equation 3-1

 

112
and a positive coefficient in equation 3-2. However neither coefficient
is significantly different from zero, even at the 40 percent level;
consequently this cannot be interpreted as a change in the relationship
of X31 with the cash-future spreads during the 1934-1962 period as com-
pared with the longer period.

The t test was again used to test for significant differences

in the corresponding regression coefficients of equations for the two

time periods. None of the differences in coefficients were significant I?”1
even at the very low level of 50 percent. In view of this and the fact i
that the coefficients of X32, the variable for CCC stocks, were not L“
significant at the 10 percent level in any of the four equations, the

 

hypothesis was not rejected for July 1.

Summary of July 1 Equations.--Two pairs of equations were com-

 

puted for July 1. One equation of each pair was based on the 1927-1962
period and one was based on the 1934-1962 period. In each pair of
equations, the largest E was obtained from the equation for the longer
period. The R2's were approximately the same for both periods, while
the equation for the longer period in each case produced the smaller
Sy.x' Simple correlations between the independent variables were rela-
tively large for both periods and could account for the lack of signifi-
cance of several regression coefficients.

Equation 3-1 had the smallest Sy.x of the four equations. For
25 out of 30 years studied, spreads estimated with it were in error by
4.97 cents or less. For predictive purposes this equation would appear
to give the best results of the July 1 equations.

A t test for significant differences in the corresponding re-

gression coefficients of each pair of equations indicated that

113
differences were not significant, even at the 50 percent level. In
addition, coefficients of the variable for CCC stocks were not signifi-
cant at the 10 percent level in any of the equations. Consequently
the hypothesis that CCC activities have influenced cash-future price
spreads only through their effects on the commercial demand for corn
storage was not rejected.

In the following section the results of equations based on the

fourth date studied, October 1, will be presented. I

October 1 Equations

 

Variables used in the October 1 equations are defined in the

 

same manner as those for January 1 equations. However, the first sub-
script, 4, indicates that variables are based on observations for
October 1. The cash-future spreads used are September spreads. Corn
consumption in the quarter preceding October 1 is used in computing the

variables X and X . The variable,

41 42 is corn consumption in the

x43’
quarter following October 1; variable, X46, is consumption in the
quarter following October 1 divided by corn production for the same
41, X42, X44, and X47 are October 1 stocks.

The units for all variables are the same as those used in January 1

year. Stocks used in X

equations.

Pairs of equations were again computed; one equation of each pair
was based on the 1927-1962 period and one equation was based on the
1934-1962 period. This was done so that comparisons could be made of
corresponding regression coefficients for the two time periods. If
the hypothesis is false, significant differences in the coefficients

might be expected.

114

Equation 4-1. Time Period: 1927 - 1962.

 

.A 1 2

Y41 = -540.18 - 0.27 i41l+ 15.18 x42 - 0.50 x42 + 117.81 x43
2

- 6.04 x43 - 1.59 x44 - 1.01 x45.

R2 = .49 = 24.94 D.F. = 21

§'= +.57 S
y.x

Other important statistics of equation 4-1 are presented in Table 29.

TABLE 29.-~Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 4-1

 

 

 

 

 

Simple Correlation With Standard t Values
Variable x42 x43 x44 x45 Y Cogffizizits Coeffifiients
X41 +.72 +.43 +.61 +.74 +.07 3.03 -0.09
x42 +.47 +.77 +.91 +.23 20.55 +0.71
x43 +.54 +.44 +.54 47.60 +2.35
X44 +.78 +.27 2.41 -0.66
X45 +.ll 1.77 -0.57

 

Simple correlations between several of the independent variables
of equation 4-1 are considerably lower than for the other dates studied.
However, the R2 is also considerably smaller than for other dates. The
coefficients of X43 are significant at the 5 percent level; none of the
other coefficients are significant at the 10 percent level. The co-
efficient of X44 is negative; however it is not significant at the 10
percent level. The negative sign may indicate that an increase in the
supply of other grains reduces the expected future demand for corn,
rather than affecting the supply of storage. Increases in stocks of
other grains would then depress the future price relative to the cash

price.

115
Before comparing September Spreads with spreads estimated from
equation 4-1, let us turn to equation 4-2, which is based on the shorter

period.

Equation 4-2. Time Period; 1934 - 1962.

 

Ai 1 . 2
Y42 = -349 61 - 0.24 iZI-+ 52 83 x42 - 14.54 x42 + 70.03 x43
2
- 3.63 x43 - 1.55 x44 + 0.07 x48.
R2 = .62 8': +.65 s = 23.03 D.F. = 14
y.x ~a

Other important statistics of equation 4-2 are presented in Table 30.

'.1
TABLE 30.-~Simple Correlations Between the Variables, Standard Errors, 1"
and t Values of the Coefficients of Equation 4—2

 

 

 

 

 

Simple Correlation With Standard t Value

Variable x42 X43 X44 X48 Y Coiffizizfits Coeffiiients
X41 +.69 +.50 +.57 +.80 +.25 3.27 -0.07
X42 +.64 +.77 +.88 +.60 21.10 +1.81
X43 +.68 +.73 +.58 52.93 +1.25
X44 +.86 +.54 2.96 -0.52
X48 +.52 2.93 +0.02

 

As compared with equation 4-1, the R2 has been increased from
.49 to .62 and E has been increased from +.57 to +.65. In addition,
the Sy.x has been reduced slightly. Table 30 indicates that simple
correlations of X43 and the trend variable with other independent vari-
ables have been increased. This would tend to increase the standard
errors of the coefficients for these two variables, and consequently

could account for part of the reduction in their respective t values.

Again, the coefficient of X44 has the wrong sign, but is not significant

116

at the 20 percent level. In equation 4-2, only the coefficients of
X42 are significant at the 10 percent level.

Adjusted September spreads and spreads estimated with equations
4-1 and 4-2 are presented in Table 31. The range of September spreads
for the 1927-1962 period was 125.77 cents; for the 1934-1962 period it
was 123.82 cents. For 16 out of 29 years studied, estimated spreads
from equation 4-1 were in error by 20.38 cents or less. Equation 4-2
was in error by 13.91 cents or less for 15 out of 22 years.

TABLE 31.-~Actual Adjusted September Spreads and Spreads Estimated With
Equations 4-1 and 4-2

 

 

 

 

A A A /\
Years Y41 Y42 Y Y-Y41 Y-Y42
1927 +12.16 -- +11.40 - 0.76 --
1928 + 4.54 -- -41.02 -45.56 --
1929 + 3.11 -— + 3.62 + 0.51 --
1930 -28.33 -- -10.13 +18.20 --
1931 —10.41 -— + 9.97 +20.38 --
1932 + 0.30 -- +28.77 +26.47 --
1933 + 8.48 -— +36.13 +27.65 --
1934 -59.92 -49.92 -36.01 +23.91 +13.91
1935 -55.30 —66.26 -61.65 - 6.35 + 4.61
1936 -66.07 -69.55 -89.64 -23.57 -20.09
1937 -42.86 -57.96 -89.54 -46.68 -31.58
1938 ~18.66 ~37.22 + 6.77 +25.43 +43.99
1939 + 8.47 + 1.27 + 5.09 - 3.38 + 3.82
1940 +12.18 + 7.78 —14.88 -27.06 -22.66
1941 + 3.71 + 2.10 +34.18 +30.47 +32.08
1949 - 6.70 ~12.93 -21.30 -14.60 - 8.37
1950 + 3.62 + 0.96 - 7.08 -10.70 - 8.04
1951 - 0.55 - 4.16 -12.18 -11.63 - 8.02
1952 - 8.63 -14.21 - 2.27 + 6.36 +11.94
1953 - 1.87 - 2.20 -27.19 -25.32 -24.99
1954 -23.81 -11.13 — 1.71 +22.10 + 9.42
1955 -15.14 ‘- 6.40 + 6.52 +21.66 +12.92
1956 — 8.70 - 3.14 ~16.71 - 8.01 -13.57
1957 + 2.89 - 0.63 - 1.10 - 3.99 - 0.47
1958 - 1.09 - 4.10 -12.64 -11.55 - 8.54
1959 + 3.92 + 3.03 ~10.70 —14.62 -13.73
1960 + 0.41 - 4.08 + 4.12 + 3.71 + 8.20
1961 -l3.00 -13.29 +10.44 +23.44 +23.73
1962 - 6.77 + 1.26 - 3.29 + 3.48 - 4.55

 

117
In view of the wrong signs obtained for the coefficients of X44
in equations 4-1 and 4-2 and the lack of significance of these coeffi-
cients, equations 4-3 and 4-4 were computed, excluding X44 from the

analysis.

Equation 4-3. Time Period: 1927 - 1963.

 

.A 1 2
Y43 = -482.46 - 0.42 iZ;-+ 16.43 X42 - 1.22 X42 + 100.51 X43
2
- 5.09 X43 - 1.49 X45. ',
.fi
2 _ I
R = .48 R = +.58 Sy x = 24.61 D.F. = 22 l
Other important statistics of equation 4-3 are presented in Table 32. +,fl

 

TABLE 32.--Standard Errors and t Values of the
Coefficients of Equation 4—3

 

 

 

Standard t Value
Error of of
Variables Coefficients Coefficients
X41 2.98 -0.14
X42 20.26 +0.75
X43 40.08 +2.38
X45 1.60 -0.93

 

As compared with equation 4-1, standard errors of all coeffi-
cients were reduced slightly. The R2 and E are essentially unchanged,
while Sy.x has been reduced from 24 94 to 24.61. Again the only co-
efficients which are significant at the 10 percent level are those for
X43; they are also significant at the 5 percent level.

Now let us examine equation 4-4, which is based on the 1934-

1962 time period.

118

Equation 4-4. Time Period: 1934 - 1962.

 

A l 2
Y44 = -317.59 + 0.06 £21- + 53.69 X42 - 14.70 X42 + 58.42 X43
2
- 2.99 X43 - 0.83 X48°
R2 = .61 E: +.67 s = 22.47 D.F. = 15
y.x

Other important statistics of equation 4-4 are presented in Table 33.

TABLE 33.—-Standard Errors and t Values of the
Coefficients of Equation 4-4

 

 

 

Standard t Value
Error of of
Variable Coefficients Coefficients
X41 3.13 -0.02
X42 20.54 +1.90
x43 47.38 +1.17
X48 2.31 -0.36

 

Again, the R2 and E were essentially unaffected by omitting X44
from the equation, but Sy.x was reduced from 24.04 to 22.57. The
standard errors of all coefficients were reduced slightly as compared
with equation 4-2; however only the coefficients of X42, CCC stocks
divided by consumption, are significant at the 10 percent level.

Cash-future Spreads estimated with equations 4-3 and 4-4 are
presented in Table 34. Spreads estimated from equation 4-3 were in
error by 18.65 cents or less for 18 out of 29 years studied. Equation

4-4 was in error by 18.45 cents or less for 16 out of 22 years.

 

119

TABLE 34.--Actual Adjusted September Spreads and Spreads Estimated With
Equations 4-3 and 4-4

 

 

 

 

A» A ‘A A
Years Y43 Y44 Y Y-Y43 Y-Y'44
1927 +11.41 -- +11.40 - 0.01 --
1928 + 6.76 —- ~41.02 -47.78 --
1929 + 2.86 -- + 3.62 + 0.76 —-
1930 -23.l7 -- -lO.l3 +13.04 —-
1931 - 7.41 -- + 9.97 +17.38 --
1932 + 3.86 -- +28.77 +24.91 --
1933 + 1.54 -- +36.13 +34.59 --
1934 —62.77 -52.24 -36.01 +26.76 +16.23
1935 ~53.38 -62.67 -61.65 - 8.27 + 1.02
1936 -67.86 -7l.19 —89.64 -2l.78 -18.45
1937 -43.01 -56.93 -89.54 -46.53 -32.61
1938 -21.31 -38.67 + 6.77 +28.08 +45.44
1939 + 2.06 - 3.69 + 5.09 + 3.03 + 8.78
1940 + 9.68 + 7.17 -l4.88 -24.56 -22.05
1941 + 3.34 + 2.57 +34.18 +30.84 +31.61
1949 - 2.65 - 9.46 -21.30 ~18.65 —11.84
1950 + 5.04 + 2.98 - 7.08 —12.12 -10.06
1951 - 0.02 - 4.01 -12.18 -12.16 - 8.17
1952 - 9.45 —15.56 - 2.27 + 7.18 +13.29
1953 - 1.67 - 3.12 -27.19 -25.52 -24.07
1954 -l9.30 - 8.30 - 1.71 +17.59 + 6.59
1955 -10.51 - 3.07 + 6.52 +17.03 + 9.59
1956 - 9.93 - 2.27 -l6.71 - 6.78 -l4.44
1957 + 0.63 - 3.51 — 1.10 - 1.73 + 2.41
1958 + 3.51 + 0.19 -12.64 -16.15 -12.83
1959 + 1.53 - 0.18 -lO.70 -12.23 -10.52
1960 + 0.75 - 3.12 + 4.12 + 3.37 + 7.24
1961 ~12.23 -12.68 +10.44 +22.67 +23.12
1962 -10.33 - 3.03 - 3.29 + 7.04 - 0.26
Two additional equations were computed for October 1, using the
variables X46 and X47 in place of X43 and X44. The variable, X46, is

corn consumption in the quarter following October 1 divided by corn
production in the same year; the variable, X47, is stocks of other
grains divided by the number of grain consuming animal units fed

annually.

 

 

120

Equation 4-5. Time Period: 1927 - 1962.

 

’\ 1 2
Y45 = ~228.31 + 0.25 i——-+ 38.39 X42 - 3.11 X42 + 141.37 X46
41
2 2
- 19.27 X46 - 19.27 X46 - 30.09 X47 - 2.08 X45.
R2 = .25 E'= +.O7 Sy x = 30.25 D.F. = 21

Other important statistics of equation 4-5 are presented in Table 35.

TABLE 35.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 4-5

 

 

 

 

 

Simple Correlation With Standard t Value
Error of of
Variable X42 X46 x47 X45 Y Coefficients Coefficients

X41 +.72 -.60 +.57 +.74 +.O7 3.54 +0.07
X42 -.66 +.72 +.91 +.23 25.26 +1.40
X46 -.87 -.75 -.13 95.59 +1.28
X47 +.74 +.l4 63.31 -O.48
X45 +.ll 2.28 —0.91

 

 

The R2 has been reduced from .49 to .25 as compared with equa-
tion 4~1. In addition, E has been reduced from +.57 to +.07 and the
standard error of estimate has been increased from 24.94 to 30.25.
None of the regression coefficients in equation 4-5 are significantly
different from zero at the 10 percent level.

Now let us compare equation 4-5 with equation 4-6, which is

based on the shorter time period.

Equation 4~6. Time Period: 1934 - 1962.

.A l 2
Y46 = -55.07 - 1.97 EZI-+ 73.65 X42 - 20.85 X42 + 47.48 X

2
- 8.07 X46 - 70.86 X47 + 1.37 X48.

 

46

 

121

RZ = .63 ii: +.66 s = 22.77 D.F. = 14
y.x

Other important statistics of equation 4-6 are presented in Table 36.

TABLE 36.--Simple Correlations Between the Variables, Standard Errors,
and t Values of the Coefficients of Equation 4-6

 

 

 

 

Simple Correlation With Standard t Value
Error of of
Variable X42 X46 X47 X48 Y Coefficients Coefficients

X41 +.69 —.55 +.52 +.80 +.25 3.17 -O.62
X42 -.57 +.69 +.88 +.6O 20.04 +2.64
X46 -.86 -.31 —.37 67.56 +0.58
X!+7 +.80 +.41 62.28 -1.14
X48 +.52 2.58 +0.53

 

 

Equation 4-6 produced a considerably larger R2 and E than equa-
tion 4-5. In addition the Sy.x was reduced from 30.25 to 22.77. The
coefficients of X42 and X47 were increased considerably, in absolute
terms, while the coefficients of X46 and X48 were reduced. Also,
standard errors of the coefficients of all variables except the trend
were reduced. However, only the coefficients of X42, the variable for
CCC Stocks, are significant at the 10 percent level; they are also
significant at the 5 percent level.

September Spreads estimated with equations 4-5 and 4-6 are com-
pared in Table 37. Spreads estimated from equation 4-5 were in error

by 19.26 cents or less for 17 out of 29 years studied. Equation 4-6

was in error by 18.63 cents or less for 17 out of 22 years.

122

TABLE 37.—-Actual Adjusted September Spreads and Spreads Estimated With
Equations 4-5 and 4-6

 

 

 

 

A A /\ A
Years Y45 Y46 Y Y-Y45 Y—Y46

1927 - 7.86 -- +11.40 +19.26 --
1928 - 5.98 -- ~41.02 -35 O4 --
1929 - 7.01 -- + 3.62 +10.63 --
1930 -15.23 -- -10 13 + 5.10 --
1931 -10.86 -- + 9.97 +20.83 --
1932 -11.76 -- +28.77 +40.53 --
1933 -17.48 -- +36.13 +53 61 --
1934 -43.81 -50.48 -36.01 + 7.80 +14.47
1935 -19.52 -59.42 -61.65 -42.13 - 2.23
1936 -45.49 -71.01 -89.64 -44.15 -18.63
1937 -30.80 -56.93 -89.54 -58.74 -32.61
1938 -18.34 -40.88 + 6.77 +25.11 +47 65
1939 +10.54 + 5.77 + 5.09 - 5.45 - 0.68
1940 +27.84 + 6.73 -14.88 -42.72 -21.61
1941 +12.29 + 5.57 +34.18 +21.89 +28.61
1949 - 8.61 -16.04 -21.30 -12.69 - 5.26
1950 + 4.31 - 1.85 - 7.08 -11.39 - 5.23
1951 - 6.29 - 8.07 -12.18 - 5.89 - 4.11
1952 -27.62 -18.74 — 2.27 +25.35 +16.47
1953 -12.45 - 5.56 -27.19 -14.74 -21.63
1954 -14.50 - 1.99 - 1.71 +12.79 + 0.28
1955 -15.65 - 4.68 + 6.52 +22.17 +11.20
1956 - 7.51 - 8.16 -16.71 - 9.20 - 8.55
1957 + 3.02 + 3.37 - 1.10 - 4.12 - 4.47
1958 - 7.84 -13.70 —12.64 - 4.80 + 1.06
1959 -11.88 + 6.14 -10 70 + 1.18 -16.84
1960 -14 34 -13.06 + 4.12 +18.46 +17 18
1961 + 6.61 - 7.11 +10 44 + 3.83 +17.55
1962 - 5.82 + 9.32 - 3.29 + 2.53 -12.61

 

The Durbin—Watson statistic, d', was computed as a test for
serial correlation of the residuals of equations 4-5 and 4-6. For both
equations the results were inconclusive.

In connection with the null hypothesis, it Should be noted that
in each pair of October 1 equations, the equation based on the 1934-
1962 period produced a considerably better fit in terms of R2, E, and

Sy x than the equation based on the longer period. The largest difference

123
in fit for the two periods was produced by equations 4-5 and 4-6. For
equation 4-5, the R2 was .25, E was +.07, and Sy.x was 30.25; for
equation 4-6, the R2 was .63, E was +.66, and Sy.x was 22.77. Equation
4-6 had the highest R2 of the six equations and its Sy.x was only
slightly larger than the Sy.x of equation 4-6, the smallest of the
October 1 equations.

A Significance test for R2, given by Walker and Lev, indicates
that the R2 of equation 4-6 is significantly different from zero at the
2.5 percent level, while the R2 of equation 4-5 is not significant at
the low level of 25 percent.77 For the other two pairs of equations,
however, R2"S for both periods were significant at the same level. A
smaller number of observations and consequently fewer degrees of
freedom apparently prevented the R2's for the 1934-1962 period from
being more significant than those for the longer period.

The better fit for the shorter period might indicate that a
change has occurred in the relationships between the independent vari-
ables and cash-future Spreads for the 1934—1962 period as compared with
the 1927-1962 period. This could be an indication that the null
hypothesis is false for October 1, even though direct statistical tests
are inconclusive. In addition, for the shorter time the only regression
coefficients that are Significant at the 10 percent level are those of
the variable for CCC stocks.

Over the observed range for October 1, an increase in the ratio
of CCC stocks to corn consumption increased cash-future spreads. From

the theoretical framework of Chapter III, this could be explained in

 

7'7Walker and Lev, 92: Cit., p. 324.

 

124
two ways: (1) an increase in October 1 CCC stocks shifts the expected
future supply of corn to the left, thus increasing future price rela-
tive to the cash price, or (2) an increase in CCC stocks reduces the

supply of unoccupied storage space, thus changing the commercial supply

 

function for storage. In reality, a combination of these two effects
may have occurred.

Summary of October 1 Equations.-—Three pairs of equations were
computed for October 1. In each pair, the equation based on the shorter
period provided a considerably better fit in terms of R2, E, and Sy x

than the equation based on the 1927-1962 period. Simple correlations

 

between the independent variables, except for X41, with all other in—
dependent variables were somewhat lower than for the other three dates
studied. However they were still relatively large and could account
for the lack of significance of several regression coefficients.

Equation 4-4 had the smallest Sy.x of the six equations. For
predictive purposes, it would appear to provide the best results of
the October 1 equations.

Although direct statistical tests of the hypothesis were not
conclusive, the better fit obtained for the 1934-1962 period as com-
pared with the longer period provided some evidence that it may be
false. In addition, the only coefficients which were significant at
the 10 percent level in equations for the Shorter period were those
of the variable for CCC stocks. In every equation, an increase in CCC
corn stocks relative to consumption increased cash-future spreads.
This could be due either to reductions in the expected future supply
of corn or reductions in the supply of unoccupied storage space. In

reality, a combination of these effects may have occurred.

125
In Short, though a precise test of the hypothesis was not pos-
sible, there iS evidence that at the beginning of the marketing year

CCC activities may affect both the commercial supply and demand for

 

corn Storage.

 

CHAPTER VI

Summary and Conclusions

 

The objectives of this thesis were (1) to determine whether CCC
. price-support activities have affected the cash-future price spreads
for corn through their effects of both the commercial supply and the
commercial demand for corn storage, and (2) to obtain predictions of
the cash-future spreads with CCC corn stocks as a variable. In the
analysis, cash-future Spreads were treated as a price of storage that
is determined by the intersection of the commercial supply and demand
for corn storage. The supply of storage is determined by the marginal
cost of holding inventories through time minus the marginal convenience
yield of those inventories in terms of reduced cost and delay to the
stockholder. The prices of futures contracts were considered to be
expected future prices of the commodity. Commercial stocks, then, pro-
vide a mechanism by which the grain trade, given the current and ex-
pected future demand for corn, can adjust current and future corn
supplies to a level at which the cash-future spread is equal to the net
marginal cost of storing corn from one period to the next.

The main variables determining the cash-future spreads were be-
lieved to be corn consumption in the quarter preceding the date at
which Spreads were observed, corn consumption in the quarter following
the date at which spreads were observed, CCC controlled corn stocks,
commercial (non-CCC) corn stocks, stocks of other grains, interest
cost, the general price level, and time. Corn consumption preceding

126

 

127
the date at which spreads were observed was considered to reflect cur-
rent supply and demand conditions, while corn consumption following the
date at which spreads were observed was considered to reflect expected
future supply and demand conditions.

The first objective of the thesis was restated in the form of a
null hypothesis that CCC activities have affected cash-future spreads
only through their effects on the commercial demand for corn storage.
The analytical approach consisted of least-Squares regression equations
of the intersection points of the commercial supply and demand for corn
storage. The variables were studied at four separate dates during the
year: January 1, April 1, July 1, and October 1. The equations were
computed in pairs containing the same variables; one equation was
based on the 1927-1962 period and one was based on the 1934-1962 period.
For both periods, war and immediate post-war years were omitted from
the analysis. If the null hypothesis is false, it was believed that
significant differences in the coefficients of variables for the two
periods might be obtained.

With the use of a t test described in the preceding chapter, no
evidence of Significant differences between coefficients for the two
periods was found in any of the equations. It should be emphasized,
however, that a complete test of the hypothesis was not obtained, and
also that the limited number of observations prior to the beginning of
CCC activities might prevent detection of significant differences in
the relationships even if the hypothesis is false.

With these limitations in mind, we should note that a significant,
positive relationship was found between July 1 stocks of other grains

and June cash-future Spreads. Originally, stocks of other grains were

 

128
included in the analysis to provide a measure of the quantity of un-
occupied grain Storage Space. It was believed that a positive relation-
ship between stocks of other grains and Spreads would indicate a
shortage of unoccupied storage space. However, in View of the lack of
Significance of the variable for CCC corn stocks in the July 1 equa-
tions, it appears more reasonable to assume that stocks of other grains
represent supplies of substitutes for corn. An increase in these stocks
would shift the current demand for corn to the left, thus lowering the
cash price relative to the future price, and increasing spreads. In
short, CCC stocks do not appear to have created a shortage of unoccupied
grain Storage space on July 1.

The October 1 equations provided some evidence that CCC stocks
may have affected the commercial supply of corn storage at the beginning
of the marketing year. In each pair, the equation based on the 1934-
1962 period provided a considerably better fit than the equation based
on the longer period. This might indicate that a change has occurred
in the relationships between variables specifying the commercial supply
of storage and the cash future price spreads for the 1934-1962 period
as compared with the 1927-1962 period. In addition, for the 1934-1962
period, only the coefficients of the variable for CCC stocks are
significant at the 10 percent level. An increase in the ratio of CCC
stocks to corn corn consumption, over the observed range, was associated
with an increase in spreads. This could reflect expectations that in-
creases in CCC stocks would shift the future supply of corn to the left,
thus increasing the future price relative to the cash price, or it
could indicate that increases in CCC corn stocks caused a tighting up

of the supply of unoccupied storage space. In effect, a combination

 

129
of these two conditions may have occurred.

It Should be noted that the coefficient for stocks of other
grains was not Significant at the 10 percent level in any of the
October 1 equations. This would seem to indicate that CCC corn stocks
have not resulted in a shortage of unoccupied storage space in total at
the beginning of the marketing year. However, in the review of litera-
ture it was noted that CCC stocks have contributed to congestion in
country, subterminal, and terminal elevators at harvest time. Con-
sequently, an increase in October 1 CCC stocks might increase congestion
at these points in the marketing chain, thus depressing cash price rela-
tive to the future price and increasing the spreads. It was also noted
in the review of literature that technological changes in production
and marketing have tended to place corn on the market earlier and in a
shorter time period than in the past. This would tend to magnify the
effects of CCC stocks on congestion in marketing firms at harvest.

In short, though direct statistical tests were not conclusive,
there is some evidence that CCC corn stocks may have affected the cash-
future spreads through the commercial supply of storage at the beginning
of the marketing year. Their effects would appear to be through in-
creases in the congestion of country, subterminal, and terminal elevators
rather than through a tightening up of the total supply of unoccupied
storage space. For the other three dates studied, January 1, April 1,
and July 1, within the limitations of the data and the approach, no
evidence was found that CCC activities have affected the commercial
supply of corn storage. For these dates, the main effects of CCC stocks
on the cash-future spreads are probably through their effects on the

available supply of corn.

 

130

Given the current and expected future demand for corn, an in-
crease in CCC corn stocks, all other things remaining constant, should
produce a shift to the left of the available supply of corn. This, in
turn, would increase the cash price relative to the future price, and
consequently would decrease cash-future spreads. However, if an in-
crease in current CCC stocks is associated with an expected increase
in future CCC stocks, the future price will also be affected. The
change in spreads will depend upon the size of the increase in current
CCC stocks relative to expected increases in future CCC stocks.

In connection with the second objective of the thesis, it would
be well to take a brief look at the assumptions underlying least-
Squares regression. The main assumptions are as follows:78

1. Error terms are independent and randomly distributed with
constant variances. For tests of significance they are

assumed normally distributed.

2. The independent variables are a set of fixed numbers with
no measurement error.

3. The number of observations exceeds the number of parameters
to be estimated and there are no exact linear relationships
between any of the independent variables.
The Durbin-Watson test provided a partial check on assumption
1. However, in connection with assumption 2, several adjustments which
were made on the stocks data were pointed out in Chapter IV. These
adjustments obviously will introduce errors into the data. In addition,
there will always be errors in any statistical series of stocks and

consumption. These errors will bias least-squares regression coeffi-

cients toward zero. Under such conditions the regression coefficients

 

78J. Johnston, Econometric Methods, McGraw-Hill Book Company,
Inc., New York, San Francisco, Toronto, London, 1963, pp. 107-108.

 

 

131
are inconsistent; even as the sample Size becomes infinitely large the
expected value of the estimated coefficients will not converge to the
true population value. However, provided the errors are random, least-
squares regression is still appropriate for prediction.79

In connection with assumption 3, the high Simple correlations
between independent variables create problems in attempting to obtain
reasonably precise estimates of their relative effects. However,
Johnston suggests that these problems may not be too serious for fore-
casting purposes, provided the high intercorrelations of the independent
variables can reasonably be expected to continue in the future.

There are two additional requirements for least-squares pre-
dictions to be valid: (1) the variables must be within the range upon
which the equation is based, and (2) there must be no new variables
affecting the spread during the period for which the prediction is
made. As was pointed out in Chapter IV, estimated spreads from the
equations also would not be valid for large reductions in CCC stocks
because certain irreversible process may have been occurring during
the period studied.

Within the restrictions imposed by the above assumptions, the
equations may be used to predict cash-future spreads provided estimates
of stocks and consumption are available at the time predictions are to
be made. The equations will then provide a range within which the ex-
pected value of the spread should fall for given values of the inde-
pendent variables. However, the equations appear to be more useful as

a frame of reference for explaining the direction and approximate size

 

79Ibid , pp. 163-164.

 

 

132
of the effects of changes in the independent variables on the cash-
future Spreads. With this purpose in mind, the discussion now turns
to the best equations which were obtained for each of the dates studied.

The best predicting equations for the four dates studied appear

 

to be equation l-S, equation 2-1, equation 3-1, and equations 4-4 and
4-6. The E for these equations were respectively, +.80, +.73, +.87,
+.67, and +.66; the Sy.x's were 9.57, 10.49, 5.20, 22.77, and 22.47.
These should be compared with a range of actual adjusted December

spreads of 71.33 cents, March spreads; 73.26 cents, June spreads;

 

55.56 cents, and September Spreads; 123.82 cents.

In the above equations, the ratio of commercial corn stocks to
corn consumption in the preceding quarter was a significant variable
only in equation 1-5. Its coefficient was negative; thus an increase
in commercial stocks relative to consumption would appear to be caused
mainly by a shift of the commercial supply of storage to the right
along the demand curve. For the rest of the above equations, except
for equation 4—4, the coefficient was also negative. In equation 4-4,
the coefficient was +0.06 and was not significantly different from
zero at the 10 percent level.

The ratio of CCC corn stocks to consumption in the preceding
quarter had significant coefficients only in equations 4-4 and 4-6.

In these equations, an increase in CCC stocks was associated with an
increase in cash-future spreads. For the other three dates studied,
the results for this variable indicated that an increase in CCC stocks
was associated with an increase in spreads and that the size of the
relationship between Spreads and CCC stocks divided by corn consumption

varied with the level of CCC stocks relative to consumption. There

133
are several possible explanations for this result. Initially, an in-
crease in CCC stocks might influence expectations regarding future corn
supply and demand conditions more than it does current supply and demand
conditions. Then, over some range, current supply and demand conditions
may become more important relative to expected future supply and demand
conditions. Still larger increases in CCC stocks might again focus
attention on expected future conditions. An alternative explanation
is that due to steady increases in CCC stocks through time, the variable
for CCC stocks is highly correlated with time. Consequently, the effects
of other variables changing concurrently with CCC stocks, such as the
level of the commercial demand for corn storage, may be partly reflected
in the coefficients for CCC stocks relative to consumption in the pre-
ceding quarter.

In equations 2-1 and 3-1, there was a significant relationship
between corn consumption in the following quarter and spreads. The
coefficients for this variable indicated that an increase in corn con-
sumption in the following quarter was associated with an increase in
cash-future spreads and that the size of the relationship depended up-
on the level of corn consumption. Again, the result could be due
partly to intercorrelations of consumption with other variables which
have been changing over time. An alternative explanation might be that
increases in corn consumption during the following quarter represent
shifts of the commercial demand for storage to the right along the
commercial supply of storage.

In equation 1-5, a significant relationship was found between
corn consumption in the quarter following January 1 divided by corn

production during the preceding year and cash-future spreads. Over

134

the observed range, an increase in this variable was associated with
an increase in Spreads.

Two other variables were useful in the above equations. AS was
noted earlier, a significant relationship was found between stocks of
other grains and spreads in equation 3-1. In addition, time was a
significant variable in equations 1—5, 2-1, and 3-1. Time was included
in the analysis to capture the effects of variables changing over time,
such as technology, which were not directly measurable. As previous
work suggested, the coefficient of the time variable was negative in
almost every case.

In examining the residuals from the above equations, it should
be noted that errors tend to be large for the years 1942, 1949, 1959,
1961, and 1962. One explanation for this is that cash-future spreads
tend to be very sensitive to expectations concerning future supply and
demand conditions. Consequently, in making predictions of the spreads
it is important to take into consideration unusual expected future
Supply and demand conditions as reflected by drought, war, and other
factors which might affect both the foreign and domestic supply and
demand for corn. It Should be emphasized also that cash-future spreads
are likely to be affected by expectations concerning the effects of
changes in acreage allotments, conservation programs, and other policies
which will affect corn production and the production of other feed
grains. In general, programs designed to reduce corn production will
shift the expected future supply of corn to the left thus increasing
the future price relative to the cash price and increasing Spreads.
Programs designed to reduce the production of other feed grains will

tend to increase the expected future demand for corn, thus increasing

 

135
cashwfuture spreads.

Finally, it should be emphasized that the regression coefficients
obtained are not structural coefficients; however, they will provide
estimates of the cash-future spreads for given values of the independent
variables taken as a group.

Future work might utilize a method of estimating regression co-
efficients suggested by Arnold Zellner.80 At the time this study was
done, computational facilities for the method were not available. By
using the Zellner approach, the efficiency of estimators in separate
equations may be improved considerably when the disturbance terms of
equations for the different dates are highly correlated. Disturbance
terms in the equations studied are probably highly correlated since
they reflect some of the same unstudied fluctuations. However, the
effects of high correlations between the independent variables of the

different equations on the gain in efficiency are not clear.

80Arnold Zellner, "An Efficient Method of Estimating Seemingly

Unrelated Regressions and Tests for Aggregation Bias," Journal of the
Amerigann§tatistical Association, Vol. 57, No. 298, June 1962, pp.
3484368,

 

 

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Review, Volume XXXIX, No. 6, December 1949, pages 1254-1262.

 

Zellner, Arnold, "An Efficient Method of Estimating Seemingly Unrelated
Regressions and Tests for Aggregation Bias," Journal of the
American Statistical Association, Volume 57, No. 298, June 1962,
pages 348-368.

 

 

 

 

 

 

 

APPENDIX

 

 

 

 

 

 

2.3+ 2.2+ :.2+ 3.2.. 2-3:
Ho.om- wo.m - ao.ma+ mo.aw+ sm-mmaa
mo.zo- a~.6~- wa.am- «6.66. mm qmaa
so.am- Ho.oH- as.6 - mo.aa- em-mmaa
sm.am- No.~s- 44.om- w6.ms- am-omaa
aha.6 + 64.a + wa.m + aa.~ + mm-amaz
sao.m + an.z - 04.4 + mo.a + am-mmaa
6mm.sz- Ha.mz- as.a + mo.m + os-amaa
nwz.sm+ mq.N + sm.6 - ma.s - aq-osaz
-- ma.a + mm.mz+ 6~.mz+ ~6-asaa
nom.am- 6w.6a- ma.aa- 4H.m - a¢-wqaa
nwo.m . Ho.w - mo.m~- mm.m - omumqmfi
an.NH- mm.o . qm.m - ow.m - Hm-ommH
SNN.N - m6.6 - 6m.6 - N6.a - mm-amaz
nafi.nmu om.a - mm.o - No.6 + mm-mmm~
HM QHN.H - sq.~H- q¢.m . Hm.m - qmummmfi
1. nwm.o + mm.o - Nq.m . “5.0 + mm-¢mmfi
nan.ofi- oo.m - mm.N + om.m + omummmfi
noH.H . ~m.¢ - Ho.~ + mw.H + unnommfi
nqo.~H- mo.HH- ma.m - oo.~ + wmunmma
205.0H- AN.oH- 0H.w . mm.m - mmuwmmfi
BNH.¢ + ma.6 - mo.m - om.a - oo-amaH
nq¢.oH+ om.q + 00.0 + oq.ma+ Honooma
nmN.m - o~.m - o~.H + om.m + No-HomH
6 6 aa.n - 4w.a - ms-N6aH
umnEouaom mean Soyuz umnsoomo mummw

Afimsmsm pom mucmov

 

kmm<mw m<31HmOm MH<HQMZZH Qz< m<3 UZHQDAUxm .momH mobommfi ommfi
.Hmoo HmmMMHzH wm Qmobamm Qz< QmH<Ammn nmonm mm<o szHZ monm MMDHDM

H mqm<H Nanmmm<

 

 

 

142

 

.cucoE one you vomofio mmS muaunm wonsouaom aw wowwmuu ouommn vmuosv moowum do wommmn

.bmfiwaeoo mm3 manna osu cons ofiamfiflm>m uo: opus muons

 

.cwuofiaam o>uommm Hanovmm .muocuo>ow mo bumom o>ummom Hmuovom osu mo

moammw mdowum> cam .Hmaudow muo>oun 63H .muuomom stcc< ovmuH mo vumom owmowzu .oomH ponouoo

.mHQHOMHHmo .ouomcmum mhumunflq huwmuo>wab whomamum .mDSuHumCH noummmmm boom a:oHumuuomme

.a.:m bosmwfin3dos .mmowum cuoo Hmcommow so Emumoum uwommsm1mowum mo mucoSHmcH .vwmaomuovcwz
.> woummq Scum Umcwmuno mums mama .>H noummno CH ponwuommv wvonume onu an wmuDQEoox

 

 

 

 

.2... . «.2 .

oq.HH+ mm.m + NH.HN+ Hm.¢m+ mm1onH
No.H¢1 HN.oH1 mm.o 1 mN.m + wN1mNmH
mo.m + oo.m 1 mm.N + mn.w + mN1wNaH
mH.oH1 qm.m 1 wH.¢ + mm.m + OM1mNmH
mm.m + ¢N.OH1 w¢.~ + ow.m + Hm1ommH
mm.wm+ mm.m + N®.NN+ ¢N.wa+ NM1HM¢H

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T... J... H: ...1 .I...1......a
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A... 7 x n... . a L1 (N. N T .xn . 1

a. .no
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3
4
1

 

 

 

 

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oaa.mmm 404.606 msm.oao.a moo.aam.a Name
ONH.66z ma6.mam 6mm.awo.a awm.oaw.a Seas
mam.mAN Nam.oa6 Oa6.oam.a 66N.oma.N mama
mam.mmz Ham.mqa m66.on ~66.mmm.a mama
sw6.mma awo.mza zao.60m.a amm.Sas.N mama
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wHo.~mN am¢.aaa sam.eom.a ~6m.mHo.N Hmaa
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64¢.mm maa.aam auo.smm.a a66.omo.m meme
6 a amam.mam.a mwmm.wao.m mama
H meOOUO H kHSH H HHHQ< H zumjcmh mummy

Awamemsm cocav

 

 

 

. 1mm<m> ma: oszzaoxm .moaa mueomea Amos
.mmaaem omeaz: mom mmmymazo 5m meuoam zmoo aaaommzzoo

N mHm<H xHozmmm<

 

 

 

 

.onHdEoo mmB oHnmu can Cons oHanHm>m uoc mums mamas

.humcHeHHoumm

144

 

.GOHumSOHm boom ..m.z.¢ ..<.n.m.D mo mmsmmH msoHHm>
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.omma an: 6664>6m .ama .oz ausmaasm Hmuaumaumum .omaa awsouea moaumaumum 6664 666 cameo ..m.m.m

 

 

 

a .<.Q.m.D EOHM UQCHMUDO 0H0»? Mumm—

.>H woummno :H vmnwuommv vaSuoE onu he vousasoos

 

cam.mm~ 6mm.aom asm.ona maa.mmm.a NNSH
NNH.~oH mam.aam mmo.waa m66.mme.a mNaH
aou.ama ama.N~a 464.08w 6mm.~a¢.a auaa
mao.ama Hom.uam mam.aaa «ma.aua.a omaH
ama.~ma Nam.aem mmo.mao oao.waa.a Emma
6mm.mmm 6am.aom Hwa.N6a sow.moo.a «mas
mas.aaa wmq.6~a 6mm.om~.a 4mm.a~m.a mama
Ham.qmu 46a.mmu waN.oaa oom.amm.a «mos
mam.oN mom.oam ooa.qoa oma.aow mmma

- . .n .u:. .1.
.1... 1 -—4v
......'..»..

CI: . 3.... 7

l

-----

 

 

 

000 000.00 000.00 000.00 0000
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mNH com
Non pmq¢ 0mm aoN “mafi
qom «mm Koo qam mmmfi
«KN umq mqo mww mmafi
own mNc 5mm mow oqmfi
mom oqm mwm mum quH
“mm mmm mow Hoo.H mqafi
qu «no oqm ¢om o¢m~
own qu moo 0mm Nqafi
qmq oqm #05 “mm mqmfi
mam Hem qqfi mNo.H mqmfi
mam mam #05 com ommH
qu mqm omw moo.H Hmafi
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moo mam ~H¢ mam wmmfi
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wow mqw mNo.H woo.~ oomfl
«mm «Hm oHH.H mqu.H Hoofi
o mqma mqu.H mooonfi Noafi
umnEmuamm wCSh scum: pmnEmqu wcflccwwmm
stounu zwsoucu swsounu fiwsounu ummw
mHsh kua< mumscmh umnouoo wcfiumxumz

 

 

«mm<m» m<3 ozHosgoxm .N@aH masomze ommfi Ammg<am amaHz: mom mmmam<so wm
a$sz28 .zmoo mo moz<m<mmm<mHn Hmomxm oz< oHammzon mo mgmmmsm onggHz

q mqm<H xHQ2mmm<

 

 

148

 

 

 

 

.UmHHQEOU mm»? mHDMU 0:“ C®£3 OHSQHHWPN HOG 0Hm3 MUNQU

.mamcmdn 000.00m cmsu mmmfi mums munoaxmn

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.mmH .oz aflumfifism Hmowumflumum .HomH awaoucu wowumflumum vmmm can :fimuo .om.m.m ..<.n.m.:«

 

 

 

mom mm¢ mum «Na omafi
NHN nqq co“ mmm NN¢H
mmm Noe one mfio mNmH
mHN oH¢ mmo «mm amafi
mmH own How qqm om¢H
«mm nwm oqo “mm amafi
on mmq Noe moo «mad
NaH moq «do o¢m mmofi
mofi QNON mfiq qu «mofl

0mm HN¢ qmm 000 mmmfi

149

 

 

 

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.humafiBmeumm

.uuommm Hmscc< mvmua mo vumom owmowno mSH van .aoflumnuwm 0mmm ..m.2.< ..<.n.m.0 mo mmSmmw

 

 

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..<.0.m.0 Scum wmchuao mum3 mama

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151

 

 

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154

.UmHHQEOU mw3 mHflmu m5“ C®£3 QHDQHMNNVN UOC mhm3 wumnm

.mmwmum>m 00:0:05 mum mmuswwm
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.cfluwHHSm m>ummmm

 

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155
APPENDIX TABLE 8

CORN PRODUCTION AND GRAIN-CONSUMING ANIMAL UNITS FED ANNUALLY
FOR UNITED STATES, 1926 THROUGH 1963, EXCLUDING WAR YEARS*

 

 

Grain-Consuming

 

 

Production Animal Units

Years (1000 bushels)a (Millions)
1963 3,861,640b 176.0b
1962 3,643,615C 173.2C
1961 3,625,530 168.9
1960 3,908,070 167 6
1959 3,824,598 165.7
1958 3,365,205 167.7
1957 3,045,355 160.0
1956 3,075,336 161.0
1955 2,872,959 165.3
1954 2,707,813 161.6
1953 2,881,801 156.9
1952 2,980,793 158.8
1951 2,628,937 167.3
1950 2,765,071 168.1
1949 2,946,206 163.8
1948 3,307,038 158.6
1947 2,108,321 153.1
1946 2,916,089 159.6
1942 2,801,819 192.2
1941 2,414,445 167.1
1940 2,206,882 155.8
1939 2,341,602 156.1
1938 2,300,095 148.3
1937 2,349,425 137.8
1936 1,258,673 137 8
1935 2,001,367 138 7
1934 1,146,734 131.2
1933 2,104,725 153 9
1932 2,578,685 159.7
1931 2,229,903 156.4
1930 1,757,297 152 8
1929 2,135,038 154 1
1928 2,260,990 153.2
1927 2,218,189 153 7
1926 2,140,207 153.1

 

*Sources: U.S.D.A., E.R S., Grain and Feed Statistics Through
1961, Statistical Bulletin No. 159, Revised June 1962, pp. 3-5, 9, and
U.S.D A , A.M.S., Feed Situation, August 1963, pp. 10, 43.

 

 

aProduction for grain only.
bAugust l, 1963 indications.

c . .
Preliminary.