ANALYSIS OF THE TEXAS HIGH PLAINS COTTON
GINNING INDUSTRY STRUCTURE: A
MARKOV CHAIN PROCEDURE
by
DAVID WALLING MYERS, B.S.
A THESIS
IN
AGRICULTURAL ECONOMICS
Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
Approved
Accepted
December, 1982
l':3
- V f^--' ACKNOWLEDGEMENTS
I wish to sincerely thank Dr, Don E. Ethridge, my major advisor,
for his guidance and patience, as he often went above and beyond the
call of duty with me during my graduate studies. My gratitude is
also extended to my other committee members, Dr. Sujit K. Roy and
Dr. Hong Y. Lee, for their untiring help and support in this research
project and throughout my graduate years. The many hours they gave
me with their guidance, suggestions, and criticisms were invaluable.
Additional appreciation is extended to Glenn Bickei of Southwest
Public Service Company and Mack Bennett and Don Lewellen of the
USDA Cotton Marketing Service in Lubbock and Lamesa, Texas, respec
tively, for their help in gathering pertinent data.
Special appreciation is extended to Dale L. Shaw for his initial
guidance and continual encouragement and counseling with this
research effort. I also wish to thank Barbi Dickensheet and Mary
Ann Downing for their aid in typing and retyping the many drafts.
Others who assisted in this aspect included Theresa Alipoe, Shelly
Martinez, and Marie Wid. A note of acknowledgement must be extended
to Dr. Bob Davis for his ever present suggestions and counsel.
Lastly, I wish to express my deep appreciation to my family for their
encouragement and support during my academic years.
11
CONTENTS
ACKNOWLEDGEMENTS ii
LIST OF TABLES v
LIST OF FIGURES vi
I. INTRODUCTION 1
Cotton Gin Industry Changes 3
Objectives 8
II, REVIEW OF LITERATURE 9
Cotton Ginning Industry 9
Optimal Industry Structure 9
Cotton Ginning and Marketing Practices 11
Gin Capacity Utilization 12
Ginning Costs 14
Use of Markov Chains to View Industry
Structure 17
III, CONCEPTUAL FRAMEWORK 23
Market Structure Framework 23
Identification of Factors Causing Changes
in Structure 28
Demand for Ginning Services 28
Cost of Gin Operations 29
Hypotheses 35
IV. METHODS AND PROCEDURES 37
Markov Chain Model with Stationary
Transition Probabilities 38 • • • 111
Data Used 39
Gin Categories 40
The Transition Probability Matrix 41
Test of Constancy 43
Non-Stationary Markov Chain Procedure 43
Non-Stationary Probability Estimation 44
Exogenous Variables 45
Regression Data 45
Industry Structure Projections 49
V. FINDINGS 53
Stationary Transition Solutions 53
Non-Stationary Transition Solutions 57
Regression Results 58
Industry Structure Projections 61
VI, SUMMARY AND CONCLUSIONS 66
Summary 66
Conclusions 69
Limitations and Recommendations 73
BIBLIOGRAPHY 75
APPENDICES 79
IV
LIST OF TABLES
1. Percentage Increases in the Minimum Wage Rate 47
2. Percentage Changes in the Average Cost Per Kilowatt Hour of Electricity for Texas High Plains Cotton Gins 48
3. Percentage of Texas Cotton Ginned from Trailers and Modules 50
4. Stationary Transition Probability Matrix for Texas High Plains Cotton Gins Based on 1967-79 Projections 54
5. Projected Texas High Plains Cotton Gin Industry Structure: Stationary Transition Probability Markov Chain Model 56
6. Estimated Non-Stationary Transition Probability Regression Parameters and Statistics 59
7. Industry Structure Projections Under Alternative Conditions 62
LIST OF FIGURES
1. Location of the 23 County Texas High Plains 2 Study Area
2. Number of U.S. Cotton Gins and Their Bales Per Gin From 1900-1980 5
3. Number of Texas and Texas High Plains (23-County Area) Cotton Gins and the T.H.P. Per Gin Output From 1942-1980 6
4. Equilibrium for a Monopolistically Competitive Gin Firm with Excess Capacity (OC-OE) 25
5. Long Run Equilibrium for an Individual Gin in Monopolistic Competition 27
6. The Effects of an Increase in Demand 30
7. The Effects of an Increase in Input Costs 31
8. Technology Reducing Cost and Increasing Capacity 34
VI
CHAPTER I
INTRODUCTION
The United States cotton industry has undergone many changes
during the last three decades. Total acreage planted in cotton has
declined from 27.4 million acres in 1949 to 13.8 by 1979, while the
average yield during those same years has increased from 282 to 548
pounds per acre (31). There has been a major shift in cotton pro-
1/ 2/ duction within the United States, from the Delta— and Southeast-
3/ 4/ to the Southwest— and West— regions. In 1948, concentration of
production was: Delta 42%, Southeast 24%, Southwest 24%, and West
10%. By 1977, cotton production had shifted to the following:
Delta 26.6%, Southeast 3.6%, Southwest 41.2%, and West 28.6% (32,
p. 5). Within the four major regions of production, there are pro
duction sub-areas in which cotton production is especially concen
trated. The Texas High Plains, the area being studied here, is one
of them.
The Texas High Plains, represented here as a 23-county area
(see Figure 1), Is in the Southwest U.S. production region. In 1979^
— Missouri, Arkansas, Tennessee, Mississippi, Louisiana, Illinois, and Kentucky.
2/ — Virginia, North Carolina, South Carolina, Georgia, Florida,
and Alabama.
3/ — Texas, Oklahoma, and Kansas. 4/ — California, Arizona, New Mexico, and Nevada.
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18.7% of the total U.S. cotton production was grown in these counties.
With the High Plains area's economy being highly dependent on agri
culture, it is also dependent upon its major crop, cotton. In 1979,
the area's cotton production was valued at approximately $725,449,080,
which accounted for 33.41% of the High Plains total agricultural
production value (30).
The movement of cotton within the marketing system in the Texas
High Plains, after it has been harvested, is characterized by the
following:
1. On farm assembly of seed cotton and transportation to a
cotton gin.
2. Ginning of seed cotton and transportation to the warehouse,
3. Storage at the warehouse (and recompression for shipment,
if needed).
4. Merchandising services and market distribution as performed
by merchants in moving cotton to textile mills and export
outlets.
It is primarily market function 2 that is of concern in this study.
Cotton Gin Industry Changes
As suggested above, ginning is an extension of the farm pro
duction process. Thus, changes in the ginning industry usually have
occurred along with changes in production. The persistent trend in
yearly decreases in the mechanical harvest time has fostered the
adoption of greater peak-load ginning capacities in the ginning
industry. While the ginning season is usually defined as October I
to March 1, most of the volume ginned in the past has been done in
a 12-16 week period, creating a serious over-capacity problem for the
rest of the year (7, p. 5). A lack of storage capability for seed
cotton has been a major gin management problem, especially when the
harvesting rate exceeds the ginning rate. Another problem High Plains
gin managers have been faced with is rising fixed and variable costs.
Due to problems like these in the industry, certain trends have
occurred over time.
Since 1900 active gin numbers in the U.S. have declined from
over 30,000 to about 2,200 in 1980 (see Figure 2), while the average
gin size and volume ginned have increased (18). While these trends
were seen over the years, the amount of cotton being produced in the
U.S. has stayed relatively constant. During the years 1901-1910,
the average annual cotton production was 11,271,000 bales, while the
average between the years 1971-1980 was 11,559,000 (23).
Over the past 40 years, the same trend of declining gin numbers
has occurred in Texas also, with 2,713 active cotton gins in 1942
and only 759 in 1981 (see Figure 3). In 1942, the 23-county High
Plains study area produced approximately 20% of the state's cotton.
By 1981, over 60% was grown in the area. The percentage of Texas
gins in this area was 10.2% and 46.9%, respectively. The number of
active cotton gins in this 23-county area of the Texas High Plains
was 277 in 1942, and this number grew to a high of 437 in 1965.
But since 1965, gin numbers have declined along with the state and
national numbers. Figure 3 shows these trends, as well as the trend
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over time of increasing gin output, shown as bales ginned per gin
in the 23-county area of Texas High Plains. Thus, the tendency in
the High Plains was for the surviving gins to increase their
capacity levels. This was especially evident in the large gin cate
gory (capacity greater than 32 bales per hour) in the study area,
where gin numbers have increased from 8 to 20 for a 150% increase
during the 1967-79 time period. In the small gin category (less
than 9.0 bales per hour), the number of gins decreased by 45%. This
reflects both an increase in gin size and the industry drop-out rate.
While past trends and problems in the ginning industry are clear,
future changes are uncertain because the causes of adjustment are
not well understood. There has been little information available
concerning what economic factors are causing these trends and what
their individual impacts are.' There is a need to know what impact
particular changes in factors causing industry change would have on
future industry structure. In order for the industry to achieve
a high level of performance, it is necessary to adjust to changing
economic conditions, which supports the need to understand the rela
tive impacts of external forces on the industry. The competitive
position of the industry is highly dependent on aspects of production,
marketing, and utilization of gin capacity. Thus, it is important
to understand the impact of technological advances such as the
advent of module storage.
Information on the expected impact of different types of exter
nal forces on the different categories of cotton gins is of use to
8
gin managers as a management guideline so the necessary adjustments
can be made. Decisions can thus be based more upon expectations
rather than on past occurrences. Cottonseed oil mill and and other
related types of industries are also affected by changes in the cot
ton gin industry structure. The conditional projections of gin
industry structure can be useful to management in related industries
by offering insight into the future, depending upon what their expec
tations are. Special service industries involving companies related
to gin equipment and service, finance, insurance, and transportation
can also find this information useful in that they are all affected
by the ginning industry.
Objectives
The general objective of this study was to determine the major
economic factors affecting the cotton gin industry and provide
conditional projections of the future structure of the Texas High
Plains ginning industry. Specific objectives were to:
A, Construct data sets concerning the study area's ginning
industry with respect to individual ginning capacities,
volumes, and plant utilization rates.
B, Identify factors which affect changes in the gin industry
structure.
C. Develop procedures for conditional prediction of the High
Plains' gin numbers and sizes.
D. Analyze the impacts of changes in the selected external
variables on the future industry structure.
CHAPTER II
REVIEW OF LITERATURE
Two specific areas are emphasized in the Review of Literature.
The first section includes studies concentrating on the cotton ginning
industry, specifically in the Southwest region. The second section
includes studies dealing with the Markov process, specifically as it
applies to industry structure.
Cotton Ginning Industry
Studies on the cotton ginning industry have concentrated on four
major subject areas: 1) optimal industry structure, 2) marketing
practices, 3) gin capacity utilization, and 4) ginning costs.
Optimal Industry Structure
In a study on cotton gin industry structure in Louisiana, Hudson
and Jesse (18) indicated that the major problem in Louisiana's cotton
gins was plant over-capacity. They looked for a way to reduce the
overall costs by gaining the most efficient market adjustments with
the objective of improving net profits of both producers and pro
cessors. Using a spatial equilibrium model, Hudson and Jesse arrived
at a least cost structure of market organization of processing faci
lities by specifying the geographic location, number, and size of
potential cotton gins, warehouses, and oil mills. They found that
by decreasing the number of gins in the study area from 88 to 16,
there would be a cost reduction of $5.08 per bale in the ginning
sector. Overall total assembly costs would be reduced by $8.34 per
bale.
10
A similar study by Cleveland and Blakley (7) also recognized
over-capacity as the major problem in the industry. Concentrating
efforts on the area of the Texas and Oklahoma Plains, they set out
to simulate an optimal market structure. The purpose of the study
was to determine the size, number, and location of gins and ware
houses that would minimize the total cost of all seed cotton pro
cessing under two alternative ginning seasons and estimate the savings
incurred. In 1974 there were 289 gins and 37 warehouses, but for the
14-week ginning season the least-cost market structure reduced
the number of gin plants to 44 and warehouses to 10. This resulted
in an overall cost reduction of 29%. The least-cost market struc
ture for the 32-week ginning season included 22 gin plants and 11
warehouses. A cost savings of 32.8% was obtained with this simu
lated solution. The analysis supported the suggestion of a reorgani
zation of market facilities in the study area if costs are to be
minimized. Specifically, gin plant capacity must be increased and
a reduction must be seen in the number of gins and warehouses if
cost efficiency is the industry goal.
Fondren, Stennis, and Lamkin (12) evaluated the least-cost
spatial cotton industry structure in the Mississippi Delta area.
Using a linear programming technique, they found the least-cost
market structure to include fewer, but larger and more efficient
gins and warehouses. The model reduced the number of potential
gin sites from 73 to 23 and warehouse locations from 23 to 15.
Assessing a 10% oppportunity cost charge to reflect the loss to
11
producers for having capital tied up for a longer period of time in
a longer ginning season, those numbers changed to 24 and 16, thus
the charges were determined to have little impact. The major impli
cations from the study were: 1) a more efficient cotton marketing
organization was possible and 2) an extended ginning season might
help provide a more cost effective system.
In the early 1970*s, the cotton ginning industry in Lea County,
New Mexico, was utilizing only about 50% of its capacity and per bale
ginning costs were high. Fuller, Stroup, and Ryan (15) set out to
show how alternative marketing organizations could alter the situ
ation. They found that by reducing the number of gins, the result
would be a cost savings from the current (1973) system. At high
production levels, alternative systems using field storage were
found to realize greater savings.
Cotton Ginning and Marketing Practices
Another topic of concern in some studies has been the need for
a better ginning method or more efficient marketing procedure. One
topic of discussion is the processing of cotton through a central
ginning method. In this structure, gin owners acquire and store
enough seed cotton to allow gins to operate at near capacity levels
for several months instead of ginning only during the shorter gin
ning season. Central gin owners, according to Campbell C3), would
take title to harvested cotton before ginning. All seed cotton
of like quality is stored, mixed, and ginned together regardless of
12
grower identification. This was found to reduce gin costs by
three to seven dollars per bale from the conventional ginning method.
Lower labor and depreciation costs accounted for a large share of
this difference. The basic dissimilarity was that central gins
could operate at capacity levels regardless of how much seed cotton
was received on any one day. This reduced idle labor costs, as well
as depreciation and other fixed costs, per bale.
Fuller and Washburn (14) also studied centralized cotton gin
ning with the objective of determining the number, size, and
location of central gin plants that would minimize the total cost of
assembling and processing upland cotton production in New Mexico.
They discovered that gins presently use their variable inputs ineffi
ciently during most of the ginning season, so they hypothesized that
to invoke the greatest cost savings, the central ginning process
would be a viable alternative. Fuller and Washburn projected that
the Pecos and Rio Grande Valley regions would benefit from central
ginning with a $7.73 and $9.06 savings per bale, respectively, over
the conventional system. These were the cotton producing regions
of New Mexico that stood to benefit the most.
Gin Capacity Utilization
There is a concensus among studies concerned with gin plant
utilization that a major problem is the inefficient use of inputs.
In the cotton ginning industry, under-utilization of plant capacity
is the most prevalent form of inefficient input use according to a
study by Ethridge and Branson (11). In the report, the U.S. ginning
13
industry structure is examined and it is pointed out that from 1974-
1977, the industry utilized only 40% of its existing capacity. As
Fuller and Vastine (13) submit, this prevailing excess capacity
causes ginning cost per bale to be higher than necessary. In their
study on New Mexico cotton gins. Fuller and Vastine concluded based
on "potential ginning output", that during 1961-1971 excess capacity
or under-utilization of plant capacity existed even during the peak
harvesting season.
Most studies emphasize that excess capacity exists or at least --
is in large part caused by the short (average of 14 weeks) ginning
season. Cleveland and Blakley (6) conducted a study of this problem
in the Texas-Oklahoma Plains and compared cotton marketing costs
under alternative lengths of ginning seasons and differing gin sizes.
Two different marketing strategies were viewed with the first being
conventional seed cotton assembly (14-week season with short-term
storage at the warehouse). The second strategy involved a 32-week
season and storage on the farm. The latter was found to be the lower
cost strategy of the two because of a higher utilization rate of
plant capacity. It was discovered that per bale costs were less for
gins of larger size with higher rates of utilization and for the 32-
week season.
In the study by Ethridge and Branson (11), it was discussed how
certain technological innovations such as packing seed cotton into
modules and ginning it with the use of an automatic module feeder can
increase processing efficiency by 15%. They observed that the module
14
system improved storability of seed cotton, thus enhancing the feasi
bility of lengthening the ginning season. Consequently, ginning
capacity would be more fully utilized and per bale ginning costs
would decrease as plant size increases. Ethridge and Branson stated
that by using an automatic module feeder, reduced downtime, and
increased output per unit of operating time would be the result.
Additional possibilities included less energy usage and fewer laborers
required for ginning purposes. Break-even levels were estimated on
different sizes of gins for the automatic module feeder investment.
They estimated that as seasonal ginning volumes increased above break
even levels, per bale costs were significantly lower with the use of ...
this technology. Also mentioned was the fact that adding a feeder
may be considered as a means of increasing seasonal ginning volume.
Ginning Costs
In a study conducted by Laferney and Glade (20), it was esti
mated that ginning costs account for approximately 50% of the overall
off-farm costs between the cotton producer and the mill consumer.
Shaw C23) estimated that labor related costs account for about 40%
of this total ginning cost. Shaw also noted that gins typically have
some annual salaried management personnel and office employees, while
the bulk of the gin crew is normally seasonal hourly employees. The
number of seasonal workers employed depends upon gin size and techno
logy level, as well as management practices. Rapidly rising energy
costs have resulted in these costs increasing as a percentage of total
ginning costs. The major energy cost to a gin is electrical energy.
15
Almost all cotton gin machinery motors operate with electricity.
Cotton lint dryers, Shaw points out, are often run by natural gas,
although some gins use butane dryers. Other gin costs include bag
ging and ties, repairs, interest paid on working capital and capital
investment, insurance, taxes, and depreciation.
Observation of recent trends of revenue received for ginning
services increasing much more slowly than gin costs has caused gins
to become more cost conscious. Shaw (24) thus developed and pub
lished GINMODEL, which is a model for computer simulation of ginning
costs over a wide range of assumptions. Employing Shaw's economic-
engineering (or synthetic modeling) technique, the economic impact
of regulatory or technological changes can be analyzed by observing
the cost relationships resulting from the model. The model was
intended mainly to provide a tool to rapidly and economically analyze
the impact on ginning costs of the various alternatives facing the
cotton gin industry.
Shaw et al. (25) presented three applications of GINMODEL in
1979 to different cotton ginning problems. These cases exhibited
some of the possible uses of the model by gin managers, extension
specialists, and gin industry groups. Case 1 involved a problem
presented by a group of Texas ginners of estimating the effect on
ginning costs of changing from a 7-day to a 6-day workweek. Results
show an estimated total cost savings of 37 cents per bale, with 32
cents per bale savings on gin labor. Case 2 involved a question from
a gin firm in the Texas Rolling Plains on the cost effects of
16
consolidating their two plants into one. Results from the GINMODEL
suggested that total estimated ginning costs with the consolidated
plant would be higher than with the existing plants. The model
showed that while the variable costs would be lowered, the fixed
costs were much greater. A gin firm in Arizona which had been
operating at 66% efficiency, in Case 3, desired an estimate of
effects on ginning cost of their new plant resulting from improved
efficiency and greater annual volume. The results estimated that
if that efficiency rate could be increased to 85%, ginning cost
could be decreased from the previous year's $32.00 per bale to $17.00.
Ethridge et al. (10) analyzed the effects of different module
handling systems on ginning cost of -stripper harvested cotton. The
alternatives examined included two seed cotton handling systems
(trailers and modules) and three gin feeding systems (suction feeding,
automated module feeding using suction, and automated module feeding
using blowers). Using the computer simulation model, GINMODEL, on
five different plant sizes (7, 14, 21, 28, and 35 bales per hour
rated capacity), ginning costs were estimated and compared for the
alternative systems. Results indicated that when plant utilization
was greater than 50%, module handling systems lowered the ginning
costs below that associated with trailer handling, primarily due to
a large increase in the gin efficiency rate. Among large gin plants
(28 to 35 bales per hour) with above 70% capacity utilization, the
module handling system with blower module feeding was the least cost
method, assuming that cotton can be totally ginned from modules.
17
If a dual system is needed, accommodating both modules and trailers,
automatic suction feeding, in comparison with the module handling
suction feeding, has a lower cost per bale, but only for large gin
plants operating at near full capacity utilization. One important
observation in this study was the suggestion that gins can lower
their ginning costs and absorb the cost of module assembly only if
they can obtain a proportional increase in additional volume.
Use of Markov Chains to View Industry Structure
A mathematical tool, Markov Chains, has been used since the
late 1950's to review the past and predict future industry structure.
In its earliest applications to economics in projecting size distri
bution of firms, incorporation of an assumption that the probabili
ties of movement do not change significantly over time (stationary
transition probabilities) was used. In 1961, Collins and Prestion
(8) used this approach to analyze the size distribution and structure
of the largest industrial firms in the U.S. from 1909-1958. In this
study, the one hundred largest firms within the manufacturing,
mining, and distribution industries were identified in the years
1909, 1918, 1929, 1935, 1949, and 1958. Measuring the size of these
firms by their total assets, Collins and Preston used the Markov
Process to view the effect of relative size movements upon the
ultimate shape of these industrial firms' size distribution. The
changes in firm movements if the observed probabilities were assumed
to continue indefinitely as equilibrium distributions were projected
18
for each time period and compared to the others. Long-run trends
in the shape and stability of industry size structure during the
half century studied include 1) decline in the frequency of changes
in the relative size position among the giants, 2) decline in the
frequency of changes in the specific identities of these firms, and
3) the slight tendency for giant firms to become more nearly equal
in relative size. As a result, the authors point out that firms
now at the top are more likely to remain there than were their pre
decessors. This is supported by Adelman (1), who stated in a similar
study using the same methodology, that there is no decline, and
possibly a slight increase, in the relative importance of the large
coporate units in the economy over the first half of the century.
There have also been applications of the stationary probability
approach in agricultural economics. In one of the first applications
to this field in 1961, Judge and Swanson (19) reviewed some of the
basic Markovian properties and made some general suggestions con
cerned with how Markov Chains could be applied to agricultural
economics in the future. Stanton and Kettunen (27) later used the
Markov Chain model to project number and size of dairy firms in
New York. They concluded that the number of potential entrants to
an industry has a definite and measurable effect on subsequent pro
jections made for that distribution when Markov processes are used.
They also stated that:
. . . even though short-run projections may have more direct value in applied work, estimation of the equilibrium solution suggested by the use of Markov process analysis will provide an important bench mark for the evaluation of the transition matrix and its implications.
19
Power and Harris (22) applied Markov Chain methods of projection to
farm type structure data as taken from agricultural census reports
in England and Wales, They cautioned that their results were merely
projections with the basic assumption that the chief economic forces
influencing the number and type of farm holdings will continue to
affect them in the same pattern. Due to the short-term nature of
the projections, they concluded that the assumption is reasonable.
Power and Harris stated that use of Markov Chains has one large
advantage in that it allows the inter-sectoral movements to be traced,
thus amplifying the understanding of overall changes.
In an article by Smith and Dardis C26), Markov analysis was
employed to project the U,S, cotton fiber industry's competitive
potential. They projected cotton's market share to decline in most
of the crop's end uses as non-cellulose fibers were projected to
capture the majority of the markets. Smith and Dardis projected the
future state of the industry, incorporating the assumption that the
observed pattern of movement will continue Cstationary transition
probabilities). They reasoned that if cotton is to retain its mar
ket share, quality of cotton must increase, while the price must
become more competitive. Smith and Dardis say that for this to
happen, increased promotion and research by the industry (concerted
action) was necessary. The major question was whether voluntary
cooperation among the different interest groups was capable of
developing the appropriate competitive strategies.
20
Padberg (21), in 1962, incorporated Markov Chain stationary
transition probabilities to analyze the structural development within
the California wholesale fluid milk industry. His projections
revealed that fewer but larger firms would dominate the industry.
Padberg questioned whether the assumption of stationary transition
probabilities was realistic. Using a likelihood ratio test developed
by Anderson and Goodman (2), he indeed found that his hypothesis of
constancy was rejected. He concluded his study by stating that this
was just one indication of the need for modifying the stationary
assumption.
Colman's (9) research in 1967 applied the Markov Chain model to
the British dairy industry as he set out to predict the future indus
try structure. To support the conceptual validity of the stationary
assumption, Colman cited several points: 1) government policy of
fixing prices on milk, 2) capital investment in the dairy industry
is not often convertible to alternative uses, 3) much of the dairy
land is not suitable for farming, 4) lack of major resource avail
ability, and 5) a clear pattern of no movement in the dairy industry
in the past. The hypothesis of stationary transition probabilities
was then tested and was not rejected. The implication in this study
is that the Markov Chain model incorporating the stationary assump
tion can be a valid tool in viewing structural changes in certain
industries.
In a study by Hallberg (16) in 1969, it was found that when a
series of transitional probability matrices was found to be changing
21
over time, the Markov Chain model can be modified to incorporate the
variability. Hallberg, in his research on Pennsylvania frozen milk
product manufacturing plants, discovered that a priori information
suggested a functional relationship between the changing probabili
ties and certain exogenous factors. After testing for constancy
and having his hypothesis of stationary transition probabilities
rejected, Hallberg hypothesized that this functional relationship
was true. He then developed his own non-stationary Markov model
incorporating ordinary least squares statistical procedures.
Hallberg's approach uses a least squares regression equation for
each cell of the transition probability matrix. The major problem
with Hallberg's model lies in meeting two major Markov Chain require
ments: 1) that all of the transition probabilities were greater
than zero and 2) their sum for any particular row is equal to
one, because the least squares approach doe not deal directly
with these constraints. It is mathematically possible to arrive at
transition probabilities which are less than zero or greater than
unity. Hallberg dealt with this matter by stating if a negative
transition probability existed, it would be given a value equal to
zero.
A study by Stavins and Stanton (28) refined Hallberg's basic
structural approach and met the Markov requirements without the
use of ad hoc procedural assumptions. They recommended specifying
the required equations in a multinomial logit framework. Each row
22
of the transition probability matrices is handled as a separate
multinomial logit model (MNLM). By using the MNLM approach, incor
porating the use of an exponential function, it can be ensured that
all predicted values of the probabilities will be positive and sum to
unity. Therefore, both Markov constraints can be met without
resorting to arbitrary procedures. As with Hallberg's model, a simu
lation procedure was used for a series of matrix-vector calculations
which leads (recursively) to a conditional forecast of future indus
try structure. The major problem with this approach was that it
required a complete set of extensive data in order to be used, as
equations for each element in the matrices need to be estimated. It
appears to not be as flexible as Hallberg's approach if all equations
cannot be estimated.
CHAPTER III
CONCEPTUAL FRAMEWORK
The purpose of this chapter is to present a theoretical frame
work for examining the Texas High Plains cotton ginning industry and
identifying the factors causing structural changes in the industry.
The major components of any industry structure are the size, number,
and location of firms. A model of Texas High Plains gin industry is
developed in the first section. Factors causing changes in the
industry structure over time are then identified under two broad
categories: (1) demand for gin services and (2) ginning costs.
Market Structure Framework
The Texas High Plains cotton ginning industry appears to meet
the criteria of a competitive industry in several respects. Indus
try characteristics consistent with competitive market structure
include (1) numerous firms in the industry and (2) no artificial
barriers to entry and exit. However, as pointed out in the Review
of Literature, there is a major discrepancy with the competitive
model, namely the existence of industry-wide persistent excess plant
capacity.
Chamberlin (4, p. 109) states that excess capacity may develop
under pure competition, owing to miscalculation on the producer's
part or to sudden fluctuations in demand or cost conditions; but if
the industry is indeed purely competitive, there would be market
entry and exit and a movement toward full utilization. However, such
23
24
is not the case in the Texas High Plains ginning industry, because
what is seen here is chronic or permanent excess capacity. Producer
miscalculations or sudden fluctuations in cotton production are not
the only reasons for excess capacity, because the surplus capacity
of the ginning industry is rarely cast off. Chamberlin calls it
"wastes of competition", or wastes of monopoly elements in the indus
try. He says that it is basically a failure of pure price competition
to function that allows the permanent excess capacity situation to
develop with impunity, and this is a peculiarity of an economic
theory of the firm known as monopolistic competition. Clark (5, pp.
437-439, 464-467), concludes that excess capacity is a general char
acteristic of industry. He states that firms create a particular
level of plant capacity to take care of "peak" demand and it is
the lack of pure competition that allows firms to charge a higher
than normal price to compensate for the under-utilization of capacity
during the "non-peak" demand times. This occurrence is seen in the
Texas High Plains cotton ginning industry (Figure 4) as chronic
excess capacity, the difference between OE and OC, causes a higher
price (OM) to be charged and a lower volume ginned (OE) than v/ould
firms in pure competition (ON and OC, respectively).
The condition which prevents the occurrence of excess profits
or economic rent is the absence of barriers to entry and exit in the
industry. In such cases where excess profits exist, the immediate
result would be more sellers (because of the incentive to enter the
industry), thus reduced demand for each individual firm's services
25
Figure 4. Equilibrium for a Monopolistically Competitive Gin Firm with Permanent Excess Capacity (OC-OE).
26
until the reduced volume of each lowers profits back to the minimum
level. Even though the High Plains ginning industry is one of
relatively unrestricted entry and exit, there has not been many
entries into the industry.
In Figure 4, the gin firm in the Texas High Plains is shown
having a downward sloping demand curve. This is due to each firm's
product differentiation. With an individual gin's product being its
ginning services rendered, this product is different from others,
mainly due to spatial considerations. The product differentiation
comes from the dispersion of gins within areas of production. A
cotton producer may choose one gin over another because of lower
transportation costs of cotton from farm to gin and convenience of
the ginner's location. Cotton gins are established in almost every
community in the study area, because (1) producers prefer to haul
seed cotton short distances, (2) producers using trailers want them
emptied and returned with minimal delay, and (3) it is often felt
that the local gin will provide the highest quality of service (7,
p. 1). Even so, an individual gin in this industry usually does not
have a "spatial monopoly", because other gins are often close enough
to the producer to render some type of competitive force. Figure 5
depicts long run equilibrium for an individual gin in monopolistic
competition when there is free entry and exit. Therefore, if there
is free entry and exit, the firm achieves long run equilibrium with
out economic rent,
27
0
Figure 5. Long Run Equilibrium for an Individual Gin in Monopolistic Competition,
28
The problem of excess capacity might seem to have been getting
worse because of increased mechanization, especially that in the
form of moduling, causing the production harvest period of cotton
to decrease. This, in turn, causes the demand for ginning service's
time span to be shorter. However, the utilization of module builders
has also increased the gin's ability to store cotton and thus allow
for a higher utilization of plant capacity over a longer period of
time. This and other technological developments have aided cotton
gins in confronting the excess capacity problem, thus lowering cost
per bale. However, excess capacity still exists as a major problem
for the industry.
Identification of Factors Causing Changes in Structure
Demand for Ginning Services
A major cause for a gin manager's incentive to make changes in
gin operations is a perceived long-run change in demand for the
gin's services. The major factor in explaining changes in demand
is variation in the level of cotton production in the market area
at an individual gin. This factor is also a variable in the decision
process for entry or exit in the industry.
When the long-run level of cotton production increases, demand
for the gin's services rises as well and there are expectations of
a permanent demand increase. This expectation, ceteris paribus, will
encourage certain changes in industry structure: (1) new firms will
be induced to enter the industry and (2) existing gins already
29
utilizing their plant capacity at a high rate, will be induced to
enlarge their capacity. In Figure 6, Point A represents a gin's
operation at equilibrium with the level of demand at D and output
at OQ . When the demand for ginning services increases to D', the
optimum output and plant size for the gin firm changes to OQ^. How
ever, the existence of or potential for economic rent encourages
firms to enter the industry, which eventually causes a decline in
individual firm demand for ginning. Thus when the long-run level
of cotton production increases, there is pressure for individual
firms to expand capacity in order to maximize their profits and
there also is incentive for additional firms to enter the industry.
If there are expectations of a permanent demand decrease, the
opposite can be expected. With the utilization rate decreasing in
the short-run, this applies pressure for gin plants to decrease their
capacity, while some gins have added incentive to exit from the
industry.
Cost of Gin Operations
Changes in the cost of ginning affect the size and number of
cotton gins and in turn the size distribution of firms within the
industry. The consequence of a permanent increase in the level of
variable cost and its effect on an individual gin can be viewed in
Figure 7. As the short- and long-run cost curves shift upward, for
example due to a sudden increase in the cost of electricity, the
immediate effect on the individual gin firm is a decrease in quantity
ginned (from OQ to OQ ) and an increase in the price charged
30
0 Qi Qz \ Q 3 \
Figure 6. The Effects of an Increase in Demand
31
0
Figure 7, The Effects of an Increase in Input Costs.
32
(from OP to OP ). The major problem faced by these firms is that
their costs exceed revenues, as shown in Figure 7 by ECBP , or the
shaded area. Over time, firms cannot sustain this loss and some
will exit the industry, thus raising the demand curve for each sur
viving firm. As a result of this increase in costs, surviving
firms will expand their volume and charge a higher price for their
product. Thus the industry structure will likely be one of fewer
gins.
The two major variable costs to a cotton gin are labor and
energy costs. Recent studies show that employee salaries, hourly
wages, and other labor related costs account for about 40% of total
gin operating costs (23, p. 2). A gin in the Texas High Plains
typically will have some salaried management and office employees
(often the head ginner will be hired on a full-time salaried basis,
also), while the bulk of the gin crew is normally seasonal hourly
employees. The number of employees, employment length, and pay
scale varies greatly among gins and depends on many factors. These
factors include management philosophy, labor supply, gin size, geo
graphic region, gin volume, and technology level.
The major source of energy for a cotton gin is electricity, as
almost all of the motors operated by a typical gin in this region
use this energy source. Kilowatt demand for electricity varies
among gins depending mainly upon technology level, average cotton
quality, efficiency percentage, and amount of processing hours. It
must also be noted that the typical gin uses natural gas for drying
cotton, while some utilize propane or butane.
33
Changes in technology also have an effect on gin costs. Techno
logical changes within a gin can affect ginning efficiency, gin
capacity, or both. Those changes affecting efficiency only include
such cost reducing improvements as replacing old cotton dryers and
utilizing a more efficient gin press. Technological changes that
increase the capacity of a gin include the addition of higher
capacity gin stands and module feeders. The effect of these types
of changes is illustrated in Figure 8, as the gin firm which is seen
at Point A is operating at equilibrium. The introduction of addi
tional or new technology to this gin plant creates a situation where
the gin firm experiences reduced ginning costs and thus reduces
prices from OP to OP . Also, the gin will increase plant output
from OQ to OQ . This scenario leaves the industry with excess
profits (economic rent), and this will serve as an inducement for
new firms to enter the industry. Thus the demand curve for each gin
firm will shift downward until a new equilibrium is achieved.
Technological changes can be classified into two different
categories: (1) that which occurs gradually over time (a steady
progression of improvement) and (2) change that tends to occur peri
odically as a major new technological breakthrough. Improvements
in gin stands and types of equipment improvements are examples of
steady changes in technology. The addition of a module feeder, on
the other hand, is viewed as a type of periodic change in technology.
It represents a major new seedcotton handling/storage/ginning system.
The introduction of this type of technological change can present
34
LRAC
Figure 8. Technology Reducing Costs and Increasing Capacity
35
problems to smaller gins because of the large lump sum investment
required and the economic feasibility of its addition. While a
large firm may have no trouble acquiring the money necessary for
investment and cutting costs with the technological addition, small
firms may not have this capacity. Often because of smaller cash
flows, lack of capital, and access to financial markets, they cannot
expand plant capacity as readily as can larger gin firms. Thus with
the large lump-sum investment necessary for this type of technology,
small firms some times may be forced out of the industry.
Hypotheses
Based on the concepts previously discussed, variation in cotton
production, gin capacity, rate of utilization of ginning capacity,
cost of energy, cost of labor, time as an indicator of gradual tech
nological change, and percentage of cotton moduled as an indicator of
periodic technological change are expected to explain changes in the
Texas High Plains cotton gin industry structure. An increase in
variation in cotton production is hypothesized to accelerate the
exit of gins from the industry and favor the survival of large gins
more than small gins. As the gin capacity utilization rate increases,
an accelerated movement of small gins into the large gin categories
and a decrease in the rate of exit from the industry is expected.
An increase in the cost of energy is hypothesized to slow down
the movement into large categories and accelerate the exit rate. An
increase in the cost of labor is expected to affect the future
36
industry structure by causing an acceleration of movement out of the
small gin categories; some of these gins will exit while others will
increase their capacity. As periodic technological change (time)
increases, the number of active gins in the future industry struc
ture is expected to decrease, with many gins increasing their
capacity. The increased use of moduling is hypothesized to increase
the exit of small gins from the industry.
CHAPTER IV
METHODS AND PROCEDURES
The purpose of this chapter is to present the methods of research
and procedures used in the study. An explanation of the procedures
used in constructing the primary and secondary data sets and exami
ning cotton gin changes over time is presented. Also, the formu
lation of conditional projections of the industry structure and
identification of economic and industry factors affecting these
changes for the Texas High Plains cotton ginning industry are pre
sented in this chapter.
In general, the procedure used involved the use of a mathemat
ical tool known as Markov Chain Procedure. This procedure, as
adapted to the ginning industry, involved categorizing cotton gins
into different size groups. The relative size changes of gins in
the study area was then traced through time (1967-1979) and proba
bilities of movement in each transition were then estimated. These
transition probabilities were averaged and held stationary as they
were used to project future industry structure. This assumption
of stationary probabilities was then relaxed and an explanatory
model of how exogenous variables affect the probability of movement
between size groups was developed. Using least square regression,
parameters' of explanatory variables were estimated and used to
measure relative impacts of changes in these variables on the pro
babilities of gins moving between size groups. Projections of
37
38
industry structure with non-stationary transition probabilities and
projected values of explanatory variables were simulated and compared
to model solutions with the stationary transition probability
assumption.
Markov Chain Model with Stationary Transition Probabities
The major purpose of the Markov Chain model in this study was
to evaluate changes in the current and projected number and size
distribution of firms within the Texas High Plains cotton ginning
industry. The model implies four basic assumptions concerning the
cotton gin industry structure:
1) Cotton gins can be grouped into size categories according
to some valid criteria;
2) The movement of a cotton gin through the size categories
can be regarded as a stochastic process, i.e., there is a
random element associated with movement between size groups,
but the probabilities of movement can be estimated;
3) The transition probability of cotton gin movements between
size categories is a function only of the basic stochastic
process, i.e., the transition probabilities are determined
by forces external to the individual firm;
4) The transition probabilities remain constant over time.
Regarding the second assumption, Padberg (21, p. 191) states
that "if general environmental factors dictate a general type of
structural development within an industry, a probabilistic model may
approximate this development pattern." It is also understood that
39
if the structural change in the cotton gin industry is entirely the
result of actions by individual firms, then the probabilistic model
is inappropriate. Backed by these observations, it was initially
assumed that movements within the ginning industry of the Texas High
Plains were a stochastic process.
The assumption of stationary transition probabilities is a rigid
one, because it assumes that the movement of firms observed between
size categories over the specified time period will continue indefi
nitely. Thus, it is assumed that when attempting to project or
forecast, the (unspecified) exogenous forces will continue to act
the same way in the future that they did in the past.
Data Used
The major source of data used in this study was the USDA Cotton
Marketing Service Office in Lubbock, Texas. Total gin stand capacity
(bales per hour) was used as an indicator of cotton gin size. Data
on type and number of gin stands and saws were gathered from indi
vidual gin equipment schedule reports taken from the USDA office to
measure gin stand capacity. Using a formula determined by Ethridge,
Shaw, and Parnell— , each firm's total gin stand hourly rated
1/ GSC = X • • I2' '^" • /(2200 . 478)
where GSC = gin stand capacity in bales/hour, X = number of saws, D = diameter of saw in inches,
RPM = manufacturer's recommended revolutions per minute,
Y = saw loading factor in lbs. lint per hour, and
-n = 3.1416.
40
capacity was calculated. These measurements of size were then
categorized into five different size groups, to be discussed in a
following section.
Data on gin numbers in the study area were gathered from gin
identification reports from the USDA Cotton Marketing Service and
from a Texas Cotton Ginners Association publication. The Ginners'
Red Book.
Gin Categories
The movements of the 376 gins in the 23-county area were
recorded over time, and these gins were divided into size and activ
ity categories through the use of the hourly rated capacity figures.
The five size classes were: size group 1 == 0.1 to 9-0 bales, size
group 2 = 9-1 to 16.5, size group 3 = 16.6 to 21.0, size group 4 =
21.1 to 32.0, and size group 5 = 32.1 to 75.0. These particular
size categories were decided upon by arranging the hourly capacity
ratings in order and looking for logical breaks or gaps in the
rankings. It was noticed that gins grouped together in a size cate
gory often had similar characteristics. For example, most gins in
size group 5 were owned and operated as cooperatives and had similar
technology, such as type of gin stands and universal density presses.
The 2200 corresponds to peripheral speed in ft/min. for a 12" saw at 700 RPM. The 478 corresponds to the lint weight in a 500-lb. bale. For specifics, see Appendix A.
41
The four activity classes were: (1) new entries, (2) dead or
dismantled gins, (3) inactive gins, and (4) active gins. The new
entry activity included all gins that entered the industry after 1967,
while the dead gin classification included all gins that were dis
mantled and exited the industry. Inactive gins were defined as those
gins that had the capacity to gin cotton but were not in operation,
while the active gin class included those gins that had the capacity
and were actively operating.
These size and activity classes were then combined to form a
total of twelve gin categories. For example, Al was the designation
used for active gins in size group 1.
The Transition Probability Matrix
To be consistent with the assumptions and definitions of a
Markov Chain, let
n.. = the individual elements (number of gins) within the
twelve nxn transition matrices;
p.. = the individual elements within the twelve nxn transition
probability matrices;
p = the stationary probability matrix, computed by averaging
the p. .'s;
P = the individual elements within the stationary probability
matrix.
X = the initial starting state vector or the initial con-o
figuration of gin firms in the n states;
42
X = the configuration vector for year, t, and
X = the equilibrium configuration vector, i.e., the total
number of gins in each category during the year in
which equilibrium was reached.
The first step in projecting industry structure involved the
construction of 12 transition matrices for the period 1967-1979. A
12 X 11 matrix was developed for each individual transition (1967-68,
1968-69, etc.) with each n.. component containing information on the
number of gins which moved from state i to state j in a given annual
transition. A given state consisted of a gin's size group and its
status as inactive or active, an entering firm, or an exiting firm
(see Appendix B). From those transition matrices, twelve transi
tion probability matrices were formed of the same size, but with
p.. elements determined in the following fashion: P.. = n.. /Sn.. ,
where within a transition: i = beginning state, j = ending state,
and t = time period. Two constraints by Markov Chain definition
were imposed upon the elements of these matrices:
(1) 0 < p..^ < 1 for all i, j, t, and — ijt —
n (2) 2 P.. = 1 for all i and t.
j=l "- ^
These twelve transition probability matrices were then averaged to
form a stationary transition matrix, P, which constituted the con
stant or stationary probability assumption.
43
Given P and X , the projected future path of the stochastic pro
cess was:
(3) X^ = X^_^ • P.
Because P is a stochastic matrix satisfying constraints (1) and (2),
X eventually converges to X , or an equilibrium configuration of
gins after m time periods.
Test of Constancy
A test was conducted to see if the process of structural develop
ment within the Texas High Plains cotton ginning industry agreed with
the assumption of stationarity. This test was one of two tests
developed by Anderson and Goodman (2) specifically to test the con
stancy hypothesis in Markov Chains. It involved a chi-square pro
cedure, but was necessary to modify it slightly due to the common
occurrence of numbers of low frequencies in some transitions. The
null hypothesis for this test was p., = p.. , for t = 1,...T, or
otherwise stated that the twelve year annual transition probability
(p..) equals the transition probabilities derived for each of the
twelve transitions (p.. ) for i and j. Thus, the chi-square statis-
tic is calculated as:
2 (4) X = 2 n..^(p..^ - p..) /p.. .
ijt
Non-Stationary Markov Chain Procedure
The alternative procedure was a non-stationary Markov Chain
procedure that relaxes the assumption of constant transition proba
bilities. In this model, transition probabilities are allowed to
44
vary, and it was hypothesized, as explained in Chapter III, that
numerous factors determined movement among size and number of cotton
gins. These factors included changes in the cost of labor, changes
in the cost of energy, changes in utilization rate of plant capacity,
variation in county cotton production, time as a proxy for gradual
technological change, and percentage of cotton production moduled as
a proxy for periodic technological change.
Non-Stationary Probability Estimation
The non-stationary approach adopted followed Hallberg's Markov
Chain model (16), and it involved fitting a least square regression
of the form: /s n ^
(5) p.., = a.. + Z B... X, 131 ij ^^^ ijk Tc
where p.. ?= the estimated probability of a cotton
gin moving from state i to state j
in transition period t;
a.. = the estimated intercept term of the 13
equation;
B ., = the estimated parameter which shows 13 k
the effect of X, on the probability
of a gin moving from state i to
state j;
X^ = the exogenous variables, where k =
X, , ..., n.
Each cell of each of the 12 transition matrices has an estimated
45
probability value (p..), and these values viewed for a particular
cell over the thirteen year (12 transition) time period constitutes
the dependent variable observations (p.. ) for the regression
equation.
Exogenous Variables
The independent variables in this non-stationary Markov Chain
procedure used in estimating the regression equations were defined
as the following:
C = the annual percentage change in the minimum wage rate, IJ
used as a proxy for the changes in gin labor costs;
C = the annual percentage change in the electricity rate E
charged to gins, used as a proxy for changes in gin
energy costs;
U = the three-year moving average of the rate of plant
capacity utilization percentage;
PRD = the three-year moving average of the percentage change
in production in the county in which the gin is located;
T = the progression of time as a proxy for gradual techno
logical change, where T = 1 for the 1967-68 transition,
T = 2 for the 1968-69 transition, etc. ;
M = the percentage of seedcotton ginned from modules used as
a proxy for a periodic technological change.
Regression Data
Estimates approximating the annual percentage change in the cost
of labor were formulated from the minimum wage figures as reported
46
by the U.S. Department of Commerce, Bureau of Census (1980,
Statistical Abstract of the U.S.). These data are shown in Table 1.
Data from the Southwestern Public Service Company were used to
approximate ginning energy costs. Using their estimates on all-
electric gins' average cost per kilowatt hour, a data set was con
structed for the annual percentage change in the cost of energy
(see Table 2).
The percent utilization of cotton gin capacity was measured in
the following manner:
Percentage Utilization of Capacity = Seasonal Volume
SRC
SRC = HRC X ER X SOH
where SRC = seasonal rated capacity;
HRC = hourly rated capacity;
ER = efficiency rate; and
SOH = seasonal operating hours.
In the above formulas, SOH was assumed to be 1,000 and ER, the pro
portion of hourly rated capacity which a gin can maintain the period
of a season, was assumed to be .67 (10). Seasonal volume, the num
ber of bales each gin processed each year, was obtained from the
Lubbock Cotton Marketing Service Office.
Another data set measuring annual changes (variation) in cotton
production was constructed. Assuming that the variation in produc
tion in the area around a cotton gin is the same as the variation in
its county's production, cotton production data as reported by the
47
Table 1. Percentage Increases in the Minimum Wage Rate.
Year Percentage Change
1966-67 12.00
1967-68 15.00
1968-69 13.00
1969-70 11.50
1970-71 10.30
1971-72 0.00
1972-73 0.00
1973-74 18.80
1974-75 5.30
1975-76 10.00
1976-77 ' 4.60
1977-78 15.20
1978-79 9.40
Source: United States Department of Commerce, Bureau of Census 1980 Statistical Abstract of U.S., Washington, D.C.
48
Table 2. Percentage Changes in the Average Cost Per Kilowatt Hour of Electricity for Texas High Plains Cotton Gins.
Y^^^ Percentage Change
1966-67
1967-68
1968-69
1969-70
1970-71
1971-72
1972-73
1973-74
1974-75
1975-76
1976-77
1977-78
1978-79
6
- 5,
0,
5.
6,
3.
- 7.
25.
14.
8.
1.
27,
2.
.40
.30
.00
.20
.30
.30
.80
,40
.90
,10
,10
,10
30
Source: Southwestern Public Service, Summary of Southern Division All-Electric Gin Report, 1982.
49
U.S. Department of Commerce (Cotton Ginnings in the United States)
were gathered. Using the formula, CPV = CP - CP _-, where CPV =
cotton production variation, and CP = cotton production, this annual
variation was derived. Through the use of a three-year moving
average, the variable PRD was formed.
Data estimating the annual percentage of cotton production
moduled were taken from Ethridge, Shaw, and Robinson (10, p. 5).
Table 3 shov/s that the percentage of cotton moduled has been rising
since its advent and replacing the conventional trailer system. It
was assumed that the percentages moduled for the state of Texas were
representative of the percentage moduled in the study area. These
data were used as a proxy for the type of technology that changes
in a periodic rather than gradual fashion.
Industry Structure Projections
The industry structure projections, using the non-stationary
Markov Chain model described previously in this chapter, were esti
mated using the following procedure:
(6) X = X •?.., where P.. = f(X,). ^ t t-1 ij 13 K
In computing the series of matrix-vector calculations, the non-
stationary transition probabilities had to be estimated for each cell
in the matrices from the regression equations, using the exogenous
variables (X, ) previously conceptualized as causal factors. Noting
that the non-stationary transition probabilities could not be esti
mated for all cells due to reasons such as inadequate number of
50
Table 3. Percentage of Texas Cotton Ginned from Trailers and Modules.
Handling System 1973 1974 1975 1976 1977 1978 1979 1980
Trailer 100 97 95 87 81 77 67 59
Module 0 3 5 13 19 23 33 41
Source: "Changes for Ginning Cotton, Cost of Selected Services Incident to Marketing, and Related Information Season'.' Annual Reports. Economic Research Service and Agricultural Marketing Service-Cotton Division, USDA.
51
observations and cells for which the model was not significant, a
decision rule was applied to those cells otherwise unestimable. This
decision rule was applied in the following manner: those cells that
were not estimated singularly by regression procedures were given a
3/ value equal to their average percentage value.— This transition
probability value given to these cells is equal to their stationary
value.
The projections from this non-stationary model were made in
order to view the singular impact of the explanatory variables,
ceteris paribus, on the industry structure. Thus, for the cells
whose transition probabilities were estimated by the set of exogenous
variables (X, ), the levels of all these variables were held constant
at their average values, with the exception of one, the variable
whose impact was being examined. This variable was either held con
stant at a fixed level or varied at an assumed rate of change.
A projection in which T was allowed to change and other variables
were held either at their mean values or, in the case of moduling,
at its latest observed value was called the "baseline" solution
among the non-stationary projections. In other words, in this
scenario T constantly changed by one for each successive year of
projection. This meant that in the matrix-vector calculations
(Equation 6), a new P.. was being multiplied with each successive
transition. Each change of P.. was totally dependent on the change
— Average Percentage Value = ij In.
1
52
in T, or the progression of a year of time. As the cells with
transition probabilities that were estimated by regression procedures
were changed, this also changed the other cells' probabilities that
were determined by the decision rule. This occurs due to the con
straint (Equation 2) placed on Markov Chains , that the sum of the
transition probabilities within a given row must be equal to one.
These probabilities in question were thus adjusted to meet this
requirement.
The baseline projection was modified to incorporate selected
changes in the explanatory variables. In order to view the effect
on industry structure from different rates of change in the cost
of labor (C ), all conditions were constrained to those in the base-LI
line solution except for C , which was varied from the baseline C Lt LI
value. The resulting industry structure was then compared to the
baseline projection to show the effect of C on the industry. The
impact of a change in C was estimated in the same manner. For E
viewing the impact of a particular rate of change in the percentage
of cotton moduled on the cotton gin industry, the procedure was dif
ferent. The other variables (C and C ) were again held at their
mean values and T changed by one for each successive year, but the
percentage moduled value was changed by an assumed rate of increase
each year.
CHAPTER V
FINDINGS
The purpose of this chapter is to present the results of the two
Markov Chain procedures described in the previous chapter. In the
Markov Chain model with stationary transition probabilities, it was
assumed that the probabilities of transition between states remained
constant at the average of the probabilities observed in the thir
teen year period from which data were obtained. The forces which
previously affected the industry structure were assumed to continue
in the same pattern in the future.
Model results with stationary probabilities are presented first.
Results from the non-stationary transition probabilities Markov Chain
model are shown in the latter part of the chapter. In this model,
the probabilities of movements between states are expressed as a
function of exogenous variables, some of which vary through time.
Stationary Transition Solutions
Using the size and activity states of gins defined previously,
gin movements among states were traced through time and transition
probabilities of movement were estimated for the twelve transition
periods (see Appendix B). These transition probabilities were
averaged to form the stationary probability matrix shown in Table 4.
The probabilities in this 11 x 11 steady state matrix were assumed
to be constant through time. For example, the average probability
of an active gin in size group 1 staying in that same category in
53
54
CO c
•H o c o
o u CO
c • H CO
00 •H PC
CO CO >< CU H !-i O
14-1
X •H
.1 4-t CO S
•p •H i H •H .Q
CO .n o u
Pu
CO c o
• H CO
c CO
•H U
o
CO <y\
<» I
H NO C3N
> M H
CO C O
C o
•H ^3 4J (U CO CO 4J CO CO pq
CU r-t Xt
CO H
4-1 CO U cn 00
•r-t TJ
^1 r" C
T
4.
c 1 t -
<
<
CN <
i H <
LO h-f
IH
CN
'
1 - ^
Q
•1 0 0) H 4J J CO H 4J : CO ^
o o d o* o d d d d d d
8 8 § R S S r i « = ' ^ o o ^ S 2 * - ' O O O O C M i n r H O C D c D O i O O O O O d N O
o o d d d d d d d d d 8 8 O § S S J Q ^ « < ^ < ^ O O C D v O O O O O O N O O
o d d d d d d d d d d
. , '"t '^^ ^ <=><=> <^ O O Ci o d d d d d d d d d d
O O O O <D (D <0 G <D d d
o o o o o o o o o o o o o o o o o o o o o o O C D c D r - J O m o O O O O
o d d d d d d d d d d o o o S S S 2 < = 5 « ^ f ^ o S 2 S ^ < ^ c > o o o o o O O CD O o o o o o o o o o o o d d d d d d d
2 2 2 ^ < ^ C ) o o < j N o o o o o o o o o o o o o O O O c v J O O O O O O O
o o o o o o o o d o ' d
2 2 5 2 < = ' < = > O N O O O O O O P O O O O O r H O O O o o i n o o o o o o o o o o o o o o o o o d d
2 i C 5 g 2 2 ^ ^ c 3 o o o S ' ^ ^ S ^ ^ ^ O r o o o o o O t O O O O O O O O O O
O O O O O O O O O O O
2 i S K ^ 2 < ^ o < r r o o o o o c n v o o o o o o o o o o c N C N i o m m o o o o o r H O o o o d d d d d d
Q ; - I C M r o > d - i n r - i C N r o » ; r i O M M M M M < : < < < < 3
,
o 00 (U 4J CTJ
a
00
o c • 3 C
•H .H (U 00
(U
5:J > O - H
4-1 T3 a CO CO OJ c
TJ • H 11 II
Q M
CN
II
CN
o 4J .
v£> 4J • Ti
vO O iH CO a I I CO
o CO
m 4J • CO
NO M i H
O 3 •M O
x: r-t
CJN 0) a
II CO
CN (U r-t
* CO O Xi a\ o o m
O rH
II . CN
rH ( ^
It • •
• CO LO C Ci.
•H 3 t 3 00 O C
U CO 0) 00 >
•H (U O 4J N . a "H Csj
CO CO m
II II < lO
55
a transition was 0.919, while average probability of it going inactive
(II) or dead (D) was 0.031 and 0.004, respectively. The stationary
probability of this gin increasing to size groups 2, 3, and 4 was
0.040, 0.005, and 0.001, respectively. The interpretation is that
a gin in that category had a constant 0.919 probability of staying
in that same size and activity category (a 0.031 constant probability
of becoming inactive, etc.) the next year. The overall trend for
most active gins in a transition was for them to stay in their same
size and activity category. These stationary probabilities were
then used to determine conditional projections of industry structure.
The activity group, NE, was not included in the stationary or
steady state matrix, because the probabilities in this category were
conditional. The NE probabilities indicate the probability that a
new gin will enter a specific-group, given a new entry. The uncon
ditional probability that a gin will enter the industry structure
cannot be determined from available data. These stationary proba
bilities were used to determine conditional projections of industry
structure.
As shown in Table 5, the set of conditions results in major
changes in the number and size of gins in the Texas High Plains cot
ton gin industry. The trend of many gins exiting the industry, or
dismantling their equipment and ceasing operations, can be seen as
the number in the dead gin category grows from the 1979 total of
38 to a projected 84 by year 1999. The industry settles at an
56
G o
•H 4-1 •H
ans
u H
> . M CO C o •H 4J CO 4-1 C/D
• • 0) 5-1 3 4J
o 3 >-4 4-1 CO
> . }-l 4-1 CO 3
TJ C
IH
C •H O
C O 4J 4J • O i-i
U (U T3
CO o
c s •H CO C
rH -H fU CO
J2 rC U 00
•H > PC o
^ CO } . i CO CO X S (U
H ?>. 4-i
• 3 -H OJ rH 4-1 -H CJ ^ CU CO
•1—) j a
o o u u
P-. CU
• l O
(U r-t ^ CO
H
Ou 3 o •1
o >>
Xi
CO c
•rt O
M-l O
V4 CU
x> 3 z
1
t o <
S t < ;
m <
CN <
<
lO h-i
<r I H
ro M
CN M
T-i M
Q
Vi CO (U
>^
r-^ CO 3 •u a
<
C» rH O rH CN
VO CX) lO CM CN CN
NO <X) CJN CO CO >d-
rH t>v 00 r^ r^ vo
ON 0 0 CO rH CJN vO
o o o
rH O O
rH O O
r-\ r^
CO ".^ >d-
O f^ CX5 rH rH CO
r^ CM ON NO r^ r^ o^ ON ON
73 CU 4J o (U
1-1
o u
< N ^ r o c o < r ^ < r ^ ^ ^
J O i O i O i O i O i O i O i O i O i O C N C N C N C N c g c N C M C N C N C N
< 7 ) C T N < y s o O N O c O r H O N v O l O < r < t > c r s r - * < r < r r o c n o - )
^ ''^ ^ ^ ^ ^ VO NO lO S t CO Csj
^ <-i \o O CJN 0 0
^ ^ ^ ^ ^ : : ] ^ ^ < = ^ < ^
o o o o o o o o o o
o o o o o o o o o o
o o o o o o o o o o
NO lO lO lO lO >:t -ct
'sf - ^ CO CN CM
^ CO CO
r H C O ^ > 3 - ^ ^ ^ ^ - . < r i O N O r ^ o o o N o ; 5 ^ ^
0 < r C J N v 3 - ( 3 > ^ < y , ^ j j ^ C X 3 0 0 C X D C 7 N C 3 N O O r H r - 4 O N O N C J N O i C T v O O O O r H r H r H r H r H C N C N C N C N
CN O CN
e 3
•H U
X>
3 cr (U
>^
CO c o
CO 4J
57
equilibrium strucutre in 2022 with 125 of the gins that were in
operation in 1967 ceasing operation.
Another trend was the movement away from a small gin status
(gins in category Al and A2) to one of very large gin capacity
(category A5). In 1979, there were 63, 168, and 20 gins in size
groups Al, A2, and A5,. respectively. By the year 1999, the industry
structure was projected to have a total of 18, 131, and 40 gins,
respectively, in these categories.
The test of constancy was applied to test the assumption of
stationarity among the transition probabilities. Due to the lack
of clear and unbiased results, the null hypothesis, p.. = p.. , was 13 i3t
rejected (Appendix C), and the analysis was extended to examining
for non-stationarity in the probabilities.
Non-Stationary Transition Solutions
To incorporate non-stationary transition probabilities, least
square regression equations were estimated. Ten valid equations
were estimated, using the transition probabilities as the dependent
variable, and all were significant at the .10 level. Along with the
established decision rule, these equations were used to project
future industry structure. All inactive cells were assigned sta
tionary transition probabilities due to the lack of sufficient
numbers of observations and the row containing the A5 cells was also
stationary due to the lack of movement.
58
Regression Results
The non-stationary Markov Chain procedure incorporates the use
of ordinary least square regression equations to estimate the func
tional probability relationships within the different cells of
activity. In this study, there were two different types of regres
sion equations: (1) equations whose functional relationships were
directly estimable through the observations in one cell for the
twelve transitions and (2) equations whose functional relationships
were indirectly estimated or derived due to a lack of an adequate
number of observations in one cell for the twelve transitions. The
estimated equations and statistics are shown in Table 6, while an
explanation of how the derived equations were estimated can be seen
in Appendix D. The factors used in explaining the relationships were:
C = annual percentage change in the cost of labor; LI
C = annual percentage change in the cost of energy; E
T = time as a proxy for gradual technological change,
1967-68 transition = 1;
M = percentage of cotton production moduled;
PRD = three-year moving average of the annual percentage change
in cotton production; and
U = three-year moving average of the annual percent gin
capacity utilization.
The variable C , annual percentage change in the cost of gin LI
labor, was found to be a significant factor in five of the ten
equations. An increase in C had the tendency to increase the LI
59
c o
• H CO CO 0) u 00
Pi
Xi CO
XI o u
PH
c o
•H • u • H CO c CO u H •
CO
CO ^
c w O -H
•H -M 4J CO CO *-• 4-1 CO CO
o t^
=^ CO TJ !- o; a CO OJ
e E • H ^ 4-1 >-i CO n3
NO
CU
x^ CO
H
=1
I
I
X
o 0^
O rvi
00 O O
CO
r-i r^
oi _
O
OC
o
m O
tti ^
I
e n rj) c c
c o d I
d
o I
c o
' -- ^ ,—* CN r ^ (VI vO O
f~- iri m o ec '~. -•'• o ^ o -» o
~ J <N C - T o va
• o o •
CO o o
O iTi tN ^
• l A -a- O
- r ^ . OC f*l C r^ O
• ^ 0 0 n o o (N CO O CN c O -H o m o . o . o o •• O • o
\0 / -N CN PO
o o O ON
• O o •
en o O o
r-ccN CNvo m m ^/^^n O i / ~ O - j C m O o o O m O C N O o o O C N
• O • O . o . o O • C . c . o .
' N . ^ ^ I . ^ ^
" ^ ^ ^ m ^ . ^ \Oy-« •.Ty-v inON 00<T CNr^ vOr*. O C N O C O - ^ ^ ^
° ^ O - Or-, c S • O • o . O . O
O . o . O . O . ^ ^ I ^-- I s - . ^
-I ^ ^ ,-s <N <N f-. —I O u^ O *£ O u-\ C m
• o . O o . o .
—i p . . O <N O <J-• o
o •
o cc
o d
CNl 4-1
= a; i ; —I
• r ^
w -- 3. t. • ' . ' " !
CL >
-"- I
C
d
CN <
I
o o o o o o I
o o o o
m <r C >« O l A
d°
O
o I
• J
c u a.
3
O CL. r-
^ \n " —• 0) -D cr I—( O c (^ w
i i j I D
> J : — O
— a;
• — CN X >-
u . c c > . :c u m a) -« r^
a rz -•J C —
O J m
C u -" ( • > 1-O lA E b
-< o c C 3 u . O C O U C • 00 CN
tD m
> - . O m (0 4 j 4.1 ^ «, - I u C3 O .
• —4 C 9 ( (N / \
O • C u
— >T lU -^
CO O C
O e^j —
>, o - * m
cd . m
o . a
I < I
(I)
CO 4)
•3
E
< m <
< <
— c-
A
C
0)
«; IK 41
JC
c 41 u n Q.
3 2
i - I
60
probability of a small, active gin becoming inactive or exiting the
industry (P^^_p, P^^.J-L, ^A2-I2^' W^lle being significant in only
two equations, an increase in C , the annual percentage change in
the cost of gin energy, was shown to have a direct effect on keeping
a small gin in Al from increasing in size. Time was a significant
variable in all but one of the equations, An increase in T was seen
to heighten the probability of a gin increasing its plant capacity
to another size category (P , . P P and P 'J uhnlp ^ ^ ^ A1-A2' A1-A3' A1-A4' ^^^ A4-A5^ * vti±Le
it decreased the probability of a gin staying in the same active
size group (P j . j , A2-A2' ^^ A3-A3^ * ^^ increase in the per
centage of cotton moduled, M, had the tendency to increase the
probability of a gin staying active in the same size category
• Al-Al* ^A2-A2' ^^^ ^A3-A3^ ' while it decreased the probability of
gin movement away from its size category (P., -.» ?.<, -p , and P ).
Two factors that were conceptualized to have explanatory power
in viewing the non-stationary transition probabilities of movement
were found to not be significant factors in any of the equations.
The variables were U, the annual percent utilization gin plant
capacity, and PRD, the annual percentage change in cotton production.
Both of these variables were estimated by using a three-year moving
average embodying the assumption that management decisions regarding
these two factors were made on long-run changes and not on annual
variations. Using a three-year moving average may have reduced the
variation in these variables and diminished their explanatory power
on the dependent variable.
61
Industry Structure Projections
The baseline non-stationary probability projections consisted
of the following conditions: T, time as a proxy for gradual techno
logical change, varied by one for each successive year of projection,
while C and C were held constant at their mean values (C = 9.425
and C = 6.733), and M was held constant at its latest observed value
(M = 33). Beginning with the existing industry structure for Texas
High Plains cotton gins in 1979, the baseline structure was projected
for 20 years. The starting state for 1979 was the following: D = 38
(gins that were active at the beginning of the study, 1967, but
defunct by 1979), II = 4, 12 = 7, 13 = 0, 14 = 0, 15 = 0, Al = 63,
A2 = 168, A3 = 49, A4 = 25, and A5 = 20. By 1999, the simulated
industry structure had changed in the following manner: D = 156,
II = 1, 12 = 21, 13 = 2, 14 =*0, 15 = 0, Al = 2, A2 = 67, A3 = 23,
A4 = 16, and A5 = 88. As shown in Table 7, the trends in this simu
lation (baseline) point to a swift movement of gins out of the small
gin active categories (Al and A2). Most of the gins in Al quickly
exit the industry as do gins in A2, (although A2 gins often go
inactive (12) before exiting). Most of the surviving gins in Al and
A2, as well as many in A3 and A4, are seen to increase their capacity
levels. The number of gins in A5 is seen to increase from 20 to
1979 to 80, twenty years later.
In Table 7, where a comparison of all of the projected scenarios
is shown in five-year intervals, the projected gin movements in the
baseline are compared with that of the stationary scenario.
Table 7, Industry Structure Projections Under Alternative Conditions.
62
Scenario
1979
Sratlonary
Baseline
C^- 5%
C, = 50%
C_ = 15% E
M = 50%
M = 5%
Year
—
1984 1989 1994 19P9 2022 1984 1989 1994 1999
1984 1989 1994 1999
1984 1989 1994 1999
1984 1989 1994 1999
1984 1989 1994 1999
1984 1989 1994 1999
D
38
53 64 74 84 125
58 92 126 156
62 104 137 165
81 123 156 184
62 97 132 165
49 72 102 132
58 83 105 122
11
4
4 3 2 n
1
3 2 1 1
2 1 1 1
1 1 1 1
7 3 1 1
5 4 2 1
5 3 2 1
Number
12
7
6 5 5 5 3
10 19 22 21
9 16 20 20
14 19 21 20
13 21 23 20
2 11 19 23
9 12 12 12
of Gins
13
0
0 0 0 0 0 1 1 2 2
0 0 0 0
0 0 0 0
1 • 2
2 2
1 1 2 1
1 1 1 1
by
14
0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
Group
15
0
0 0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
Al
63
45 33 23 13 9 34 11 2 2
41 18 5 2
34 11 2 1
24 7 2 1
44 20 5 2
35 15 6 3
A2
168
161 151 141 131 86
170 143 104 67
154 127 97 70
145 115 84 60
169 139 99 63
170 160 137 108
165 152 135 119
A3
49
49 49 48 46 35
46 40 32 23
49 49 49 44
47 47 47 42
44 38 30 22
55 49 34 20
50 45 36 31
A4
25
25 25 25 25 25 29 27 22 16
24 16 10 5
23 14 9 5
28 25 20 15
28 35 31 22
30 35 40 45
A5
20
25 30 35 40 42 24 40 63 88
'25 38 49 38
27 41 51 59
26 43 66 90
20 25 44 69
21 26 31 35
63
Both solutions show gins moving out of size groups Al, A2, and A3
and into the D and A5 categories. However, there is a difference
in the degree or amount of movement. By 1999, gin numbers were much
greater in D (156 to 84) and A5 (88 to 40) in the baseline, while the
stationary solution showed greater numbers in the Al, A2, A3, and A4
categories. This indicates that the baseline scenario projects
swifter changes, but in the same direction as the stationary solution.
The baseline was then modified to allow for a change in the cost
of labor (C ), The average increase (mean value) in the cost of labor
over the study time period was 9.425% in the baseline solution. This
variable was allowed to change at 5.0% (a decrease in the increase)
based on the assumption that inflation, thus wage increases will
decrease and stabilize at a lower level in the future. This scenario,
when compared to the baseline, brought about a more rapid exit of
gins (D = 165) and increased the number of gins moving into A3 (44,
compared to the baseline's 23 by 1999), but projected fewer gins
moving into A5. This indicates that a 5% increase in C , ceteris
paribus, will induce a flight out of Al and A2 (concurring with the
baseline) and into D, A3, and A5 (baseline shows more of an increase
into A5). The change in cost of labor was then adjusted to a 15%
level, based upon the assumption that inflation will continue to
increase at higher rates. This scenario projected an increased
movement of gins out of Al and A2 and into D, while all other size
categories stayed relatively stable with the C = 5% projection.
64
There was an exit of 184 gins by 1999, leaving only one gin active
in size group one.
The baseline was modified by an alteration in the level of
change in cost of energy (C ) to a 15% increase per annum. The mean E
value for C during 1967-79 was 6.733%, but for the last six years of
the study, 1974-79, the average increase was 13.15%. Thus, the C_ =
15% scenario embodied the expectation of a continuation of high
energy cost increases. This scenario does not change the baseline
projection much. Basically, it shows an acceleration of gins out of
Al and into D, as one gin is left in Al and 165 are projected to exit
the industry (compared to 2 and 156) by 1999.
Assuming the level of cotton moduled would level off at 50%, the
baseline was modified with M = 50%. This situation altered the base
line solution 1999 projections the most in the D; A2, and A5 cate
gories. Fewer gins exited the industry (D = 132), while more gins
entered and stayed in A2 causing fewer large gins (A5 = 69) to be
projected. The baseline scenario was then altered by allowing the
percentage moduled to increase by 5% per annum.' Overall, fewer
movements between categories were viewed, as the projections seen in
this scenario exhibited (see Table 7) much alteration from the base
line solution. The twentieth year of projection (1999) shows that t
under this situation, more gins stayed in the Al, A2, A3, and A4
categories, thus fewer gins moved to D and A5 size groups.
65
This moduling scenario projected gin numbers in 1999 for the above-
mentioned categories as follows: D = 122, Al = 3, A2 = 119, A3 = 31,
A4 = 45, and A5 = 35, compared to the baseline's: D = 156, Al = 2,
A2 = 67, A3 = 23, A4 = 16, and A5 = 88.
CHAPTER VI
SUMMARY AND CONCLUSIONS
Cotton gins have been operating under a situation over the years
where the total cost per bale of ginned cotton has been increasing.
Many studies exist that point out that the majority of variable costs
are labor and energy related, but few show the specific impact of
these costs on industry structure. Gin operators have tried to
manage these inputs and utilize their capacity more efficiently, but
face the perennial problem of a short ginning season and volatile
cotton production. Use of more energy efficient technology, such as
higher-rated capacity gin stands and larger diameter saws, and labor-
replacing technology has been well documented, while its impact on
the number and size of cotton gins has not. The advent of another
type of technological innovation, cotton modules, has been shown by
studies to increase the efficiency of the ginning operation; however,
measuring its impact on the industry has received little attention.
Therefore, managers of ginning operations and other related indus
tries, such as cottonseed oil mills, textile mills, gin service
companies, equipment companies, and cotton producers, have little
information in order to gain greater knowledge of the relative impor
tance or impact of these factors on the industry.
Summary
The general objective of this study was to determine the major
economic factors affecting the cotton gin industry and provide
66
67
conditional projections of the future structure of the Texas High
Plains ginning industry. Specific objectives were to: (1) construct
data sets concerning the study area's ginning industry with respect
to individual ginning capacities, volumes, and plant utilization
rates, (2) identify factors which affect changes in the gin industry
structure, (3) develop procedures for conditional projection of num
bers and sizes of gins in the High Plains, and (4) analyze the effects
and impact of changes in the explanatory variables on the future
industry structure.
The study area included 23 counties with 376 cotton gins. Data
on ginning volumes and individual technological changes were gathered
at the USDA Cotton Marketing Service Office in Lubbock for years
1967-79. Gin capacity was estimated from each gin's equipment make
up and utilization rates were.estimated based on the assumption of
1,000 hours of seasonal operation time. These data sets that were
constructed were all primary data except for the gin volume figures
which were secondary.
Using a stationary Markov Chain procedure, after gins (capacity
level) were categorized into twelve different size and activity
groups, changes in gin size and number were traced from year to year.
Probabilities of movement were estimated and then used to extend the
overall trends into the future. Thus, assuming stationarity of fac
tor changes and transition probabilities, the future industry
structure was projected.
68
Incorporating a least square approach to estimate probabilities
of gin movements among size groups, a non-stationary Markov Chain
model was developed. Ten different equations were estimated, and
the relative impacts of selected industry and economic factors on
the probabilities of movement were estimated. With the use of these
equations, the future industry structure was simulated up to a time
period of 20 years, constraining all factors but time at their base
levels and projecting a baseline industry structure. Explanatory
variables were changed to evaluate the effects of those changes on
industry structure. The alternate scenarios developed were (1)
a 5% increase per annum in the cost of gin labor, (2) a 15% increase
per annum in the cost of labor, (3) a 15% increase per year in the
cost of energy to gins, (4) extent of moduling set at 50%, and (5)
a 5% annual increase in the rate of moduling. Of these five simu
lation scenarios plus the baseline and the stationary transition
probability scenarios, there were three that showed dramatic changes
in the industry. The second scenario (C = 15%) showed that of the LI
325 gins that were active in 1979, only 51.4% were active 20 years
later. Only one out of 63 and 60 of 168 remained in active size
groups one and two, respectively. Most of these gins were seen to
exit the industry as the dead gin category increased by 146 over this
timeframe. In the simulation, where C was set equal to an annual
increase of 15%, many of the same trends were seen but with more
of the small (Al and A2) and medium (A3) size gins moving into the
very large gin size category (A5), A5 was seen to increase from 20
69
in 1979 to 90 by year 2000. The advent of moduling, as seen in
scenario 5, exhibited the same industry trends of gins either getting
larger or exiting the market structure, but to a lesser degree as
fewer movements between categories were seen.
Conclusions
These conclusions are based on the results of the study and they
embody the assumption that the procedure used and results shown are
correct and accurate for the cotton gin industry in the study area.
Four major factors were causes of movements or changes in gin size
and number within the Texas High Plains cotton gin industry as
approximated by data on the 23-county study area during the 1967-79
time period. These factors were: (1) changes in cost of labor, (2)
changes in cost of energy, (3) progression of time as an indicator
of gradual technological change, and (4) proportion of cotton pro
duction moduled.
The impact of the progression of time on the industry structure
is one mainly of an accelerated movement of the small and medium
active gins toward a large gin status and an exiting of gins from
the industry. In other words, as time progresses, there will be
fewer cotton gins in the industry, but most of the active gins will
be larger. Technological change over time is expected to accelerate
the movement when compared to an extension of the past based on
annual averages.
An increase in the cost of labor affects the industry structure
in a manner as to increase the number of gins exiting the industry.
70
Labor cost increases have a much greater impact on small gins than
on gins of larger sizes. A large increase in the cost of labor
decreases the number of small gins at an accelerated rate as most
of these gins will either increase their capacity to a medium gin
status or exit the industry. This signals the small gin manager of
a need to increase capacity and decrease cost per bale of ginned
cotton if he plans to stay active in the industry. The gin equip
ment and gin service industries face the likelihood of increased
sales of new technology (especially the large capacity gin stands
and module feeders) and demand for servicing them. The High Plains
cotton producer faces the problem of greater declines in the number
of active gins in conjunction with the large labor cost increases.
This means that he could possibly be traveling a longer distance
to get his cotton ginned in the future. It must be noted that if
inflation continues on its downward trend, cost of labor can be
expected to increase at a slower rate. This will help more small
and medium gins stay active, with fewer forced to increase to large
gin size.
A large increase in the cost of energy will force many small
and medium size gins in the industry to exit. Many of the surviving
gins will increase their capacity as this scenario provides the
highest number of gins moving to a large gin capacity. Again, gin
equipment companies, if they expect this scenario to occur, should
view this as an increase in future demand for additional technology
per gin.
71
In this study, the increased use of cotton moduling tends to
have the effect of inducing fewer movements among active gins, as
well as enabling more gins to stay active. However, it must be
remembered that size in this study is measured according to gin
stand capacity. Thus, a gin cannot, under this measurement, increase
its size unless it increases its gin stand capacity. Since the
advent of moduling, the investment of capital into moduling equip
ment (module feeders, module movers, etc.) has replaced the invest
ments into other technology (gin stands) and the addition of this
type of equipment increases gin plant capacity. However, there are
no data available with which to include plant capacity increases due
to moduling. Also, gins are aided by the additional ability to store
cotton for longer periods of time, enabling them to lengthen their
ginning season. Gin management will thus pay less overtime to labor
and spread their variable costs over a longer period of time. Cot
ton producers will benefit from this scenario in lower ginning cost
and less transportation expenses (due to more gins staying active).
Gin equipment and service companies will profit from the sales and
servicing of these module builders and feeders, as well as from the
fact that more gins were projected to continue being active.
Thus, there are several implications to be reached from this
research. Small gin managers and owners need to review their
situation and decide on the future path in which they plan to
operate. If management foresees either cost of energy or cost of
labor to continue increasing at a high rate, it must be realized
72
that to survive as an active gin, it most likely must enlarge its
capacity and lower its cost per bale of cotton.
Cotton producers, cottonseed oil mills, and cotton distribution
specialists, depending upon what they expect of the future industry
and economic factors, must anticipate the movement of many gins to
larger capacity and the fact that more gins will drop out of the
industry. Producers must be willing to pay higher transportation
costs, but realize that in many cases, using a module builder can
cut their ginning costs.
Industries related to the ginning industry like the gin equip
ment and gin service industries, are also affected by these projec
tions. Many gin firms will increase their capacity and, in doing
this, buy new technology from gin equipment companies, much of it
probably labor-replacing. On the other hand, fewer small gins in
the industry will result, which would cause a permanent drop in
demand for particular types of gin equipment and service. For those
equipment companies that sell and/or service module builders and
feeders, the advent of moduling is especially important to them.
As mentioned before, if these company managers expect the percent
age of cotton moduled to keep increasing as one projection shows,
72% of all cotton gins active in 1979 will still be active by year
1999, and many will have purchased other equipment, such as gin
stands and presses. This could mean more equipment sales of tradi
tional technology as well as more sales of moduling equipment,
because of more firms staying in the industry.
73
A smaller number of active cotton gins coupled with existing
gins replacing labor with technology may mean less total emplojnment
and less income for townspeople. Towns that lose some or all of
the nearby cotton gins, especially due to increases in labor or
energy costs, could suffer economically. However, the region as
a whole, especially cotton producers, will benefit from the industry
adjustment in the form of lower ginning charges and a more efficient
market structure than would be the case without the adjustment.
Among the various scenarios examined, a steady increase in the
percentage of cotton moduled will likely have the most favorable
impact on the Texas High Plains economy. One of the conclusions is
that the procedure used to reach the objectives of the study was
successful in that the results were clear and conceptually correct.
The procedure, however, was limited in its scope due to data
limitations.
Limitations and Recommendations
The findings in this study are subject to several limitations.
One of these limitations is due to the fact that in the estimated
regression equations within the non-stationary Markov Chain pro
cedure, the number of observations ranged from 9 to 12. More
observations would have been preferable and possibly more conclusive.
This study was limited to the time period of 1967-79, as these were
the only years for which data on size groups were available. Also,
more complete data on moduling and other operations of gins, wage
rates, and other cost items would strengthen the analysis.
74
Because new entry observations provided information only on
conditional probabilities, i.e., the state into which an entering
gin would enter, given a new gin in entry, new entries, were not
included in the projection process. This left a void in that the
projections were made from existing industry structures and their
gins' movements.
While information gathered and projections made in this study
contribute to the understanding of the Texas High Plains ginning
industry, there are other major information and research needs.
More specific data are needed on labor costs, levels of technology
in use, equipment use, operating practices, energy usage, and other
related information. A study on the advent of module storage, its
trends and impact on the industry is needed, as this factor alone
could change industry permanently, and not much information is avail
able. Also, a study on the substitutability of the different types
of technology for each other is needed by the industry. Follow-up
research from this study could include a study viewing the projec
tions that were made and their specific impacts on other related
industries, such as cottonseed oil mills and cotton merchants.
BIBLIOGRAPHY
1. Adelman, I.G. "A Stochastic Analysis of the Size Distribution of Firms." Journal of the American Statistical Association. 43: 893-904, 1958.
2. Anderson, T.W., and Goodman L.A. "Statistical Inference About Markov Chains." The Annals of Mathematical Statistics. 28: 89-110, 1957,
3. Campbell, J.D. Central Cotton Ginning: Cooperative Cost, Use in Other Countries, and Potential Use in the United States. Farmer Cooperative Service, United States Department of Agriculture, Washington, D.C, 1969.
4. Chamberlin, E.H. The Theory of Monopolistic Competition. Cambridge, Massachusetts: Harvard University Press, 8th ed., 1962.
5. Clark, J.M, "Law and Economics of Basing Points." American Economic Review, 39: 430, 1949.
6. Cleveland, O.A,, Jr., and Blakley, L.V. Costs of Marketing Cotton Under Alternative Gin Size and Length of Season Operations in the Oklahoma-Texas Plains. Agriculture Experiment Station. Research Report P-7604. Oklahoma State University, Stillwater, Oklahoma, 1976.
7. Cleveland, O.A,, Jr., and Blakley, L.V. Optimum Organization of Cotton Ginning and Warehouse Facilities in the Oklahoma-Texas Plains. Agriculture Experiment Station. Technical Bulletin T-144. Oklahoma State University, Stillwater, Oklahoma, 1976.
8. Collins, N.R., and Preston, L.E. "The Size Structure of the Largest Industrial Firms, 1909-1958." The American Economic Review. 51: 986-995, 1961.
9. Colman, D.R. "The Application of Markov Chain Analysis to Structural Change in the Northwest Dairy Industry." Journal of Agricultural Economics. 18: 351-361, 1967.
10, Ethridge, D.E., Shaw, D.L., and Robinson, J.A. An Analysis of Effects of Moduling Handling Systems on Ginning Costs with Stripper Harvested Cotton. Department of Agricultural Economics, Texas Tech University, College of Agricultural Sciences Publication No. T-1-198, Lubbock, Texas, August, 1981.
75
76
11. Ethridge, M.D., and Branson, R.E. Operating Cost for United States Cotton Gins by Location, Plant Size, and Utilization Rates: Impact of an Automatic Feeding System. Texas Agriculture Market Research and Development Center. Department of Agricultural Economics, Texas A&M University, MRC 77-5, College Station, Texas, 1977.
12. Fondren, T.H. , Stennis, E.A., and Lamkin, CJ. Optimum Organization of Gins and Warehouses for Marketing Cotton in the Mississippi Delta Area of Mississippi. Mississippi Agricultural and Forestry Experiment Station, Mississippi State University, AEC-33, Mississippi State, Mississippi, December, 1981.
13. Fuller, S., and Vastine, W. Utilization of New Mexico's Cotton Ginning Capacity, 1970-71. New Mexico Agricultural Experiment Station, Research Report 232, 1972.
14. Fuller, S., and Washburn, M. Centralized Cotton Ginning: A Locational Analysis, New Mexico Agricultural Experiment
- Station, Bulletin 646, 1975.
15. Fuller, S., Strop, M., and Ryan, J. Cost of Assembling, Storing, and Processing Seed Cotton in Lea County as Affected by Altering the Number of Operating Gins. New Mexico Agricultural Experiment Station, Research Report 247, 1973.
16. Hallberg, M.C "Projecting the Size Distribution of Agriculture Firms - An Application of a Markov Process with Non-Stationary Transition Probabilities." American Journal of Agricultural Economics. 51: 289-302, 1969.
17. Hart, P.E., and Prais, S.J. "The Analysis of Business Concentration: A Statistical Approach." Journal of Royal Statistical Society, Series A. 119: 150-181, 1956.
18. Hudson, J.F,, and Jesse, R.H. Optimum Number, Size, and Location of Processing Facilities for More Efficient Marketing of Louisiana Cotton. Louisiana State University, Department of Agricultural Economics and Agribusiness, Research Report No. 438, Baton Rouge, Louisiana, 1972.
19. Judge, C C , and Swanson, E.R. Markov Chains: Basic Concepts and Suggested Uses in Agricultural Economics. Department of Agricultural Economics, University of Illinois, AE RR 49, Urbana, Illinois, 1961.
77
20. Laferney, P.E., and Glade, E.H., Jr. Off-Farm Costs of Moving Cotton in the 1969-1970 Marketing Season. United States Department of Agriculture, Economics Research Service, 1971.
21. Padberg, D.I. "The Use of Markov Process in Measuring Changes in Market Structure." Journal of Farm Economics. 44: 189-199, 1962.
22. Power, A.P., and Harris, S.A. "An Application of Markov Chains to Farm-Type Structural Data in England and Wales." Journal of Agricultural Economics. 22: 163-177, 1971.
23. Shaw, D.L. "Cotton Ginning Costs: With Emphasis on Labor, Energy, and Impact of Changes." Unpublished speech presented to Cotton Gin Manpower - Horsepower Conference, Lubbock, Texas, 1978.
24. Shaw, D.L. Economic-Engineering Simulation of Cotton Ginning Costs. GINMODEL: Program Documentation and Users Guide. United States Department of Agriculture, Economics, Statistics, and Cooperative Service, Commodity Economics Division, and College of Agricultural Sciences, Texas Tech University, T-1-174, Lubbock, Texas, 1978.
25. Shaw, D.L., Ethridge, D.E., Childers, R.E., Jr., and Sartin, M.O. "GINMODEL: Some Case Study Applications." 1979 Beltwide Cotton Research Conference Proceedings. National Cotton Council, Memphis, Tennessee.
26. Smith, B., and Dardis, R. "Inter-Fiber Competition and the Future of the United States Cotton Industry." American Journal of Agricultural Economics. 23: 209-216, 1972.
27. Stanton, B.F., and Kettunen, L. "Potential Entrants and Projections in Markov Process Analysis." Journal of Farm Economics. 49: 633-642, 1967.
28. Stavins, R.N., and Stanton, B.F. Using Markov Models to Predict the Size Distribution of Dairy Farms, New York State, 1968-1985. Cornell University Agricultural Experiment Station, Department of Agricultural Economics, A.E. Res. 80-20, Ithaca, New York, 1980.
29. Texas Cotton Ginners Association. Ginners' Red Book. Various editions, Dallas, Texas,
30. Texas Crop and Livestock Reporting Service. 1980 Texas Field Crop Statistics. Texas Department of Agriculture, Austin, Texas.
78
31. United States Department of Agriculture. Agricultural Statistics, 1980. Washington, D.C.
32. United States Department of Agriculture. Statistics on Cotton, 1920-1978. Economic Research Service, Washington, D.C.
33. United States Department of Agriculture. Cotton Ginnings in the United States, Crop of 1980. Washington, D.C
APPENDICES
A, Gin Stand Properties, Manufacturers, and Capacity Equations
B. Transition Probability Matrices for Markov Analysis of Texas High Plains Cotton Gins
C Modified Application of the Chi-Square Test in Testing Stationary Transition Probability Assumption
D. Derived Regression Equations
79
80
c 0) e a
•H
cr
• H O CO
a CO
CJ
d CO
CO
u u O
•Ul a CO
»4H
C CO
S CO 0)
u CU a o }-)
PL,
c CO • p C O
C •H O
•H
c (U a
CO c o
CO 3 ol
M
X r-i CN O
CO
o
CU
3 i H a c
CO
C CO
4-1 CO
CN r-i ^
OS I , O
cJ CN
CN W rH K
r O * C N 00 CN rH
rH I S I o O CN
• O rH
m CJ csi w rH ffi " I «N
*v^ ^ r-i C N l CN I
<6 rH O r^ I CN
- •^ O rH r H | O i
o u s
CO
73 C CO CO
4-> eg CO 3
o C U4
•H O o
1 i-> 0)
CO . u -o <u C 6 CO CO • W -H S CO TJ Oj
C = •H CN O
rH
a 3 O M
O
O rH O r^
'X3 r-i r-i ,-i U O CO CO
X
.029
II
CJ CO 05
^ CN CN r-i r-i
178-
224-
PC PC ^ «\
CN CN CN rH rH r H
r 1 r r^ O CN
HE 17
HE 20
HE 25
1 rH r-i
CO CO
CO U 4-t (U CO 4-1
a e • H CO • CJ -H S • * ' ^ f ^ 15 Od, CO :
CO CN O CN rH O
r-i r^ a CO rH 3 3 rH 4J O Q CO CO
u o
X
m c
•
1!
CJ CO
o
«.CN CN r-i rH f
I 00 C30 lO
- O rH rH
H-I
.^CN CN rH 1—1 1
L 88-:
L 128-
r-i T3 rH 4J (U to CO (U
CO r-i r rH
.c to
wit
tors
er.
(0 CO 4J ^ 3 4J (U
c -H e . CO GO CO S •W < : -H PL,
CO CO "TS Pd rH
D. C rH r i n 3 -H O CN CSI O CJ Oii rH 00
:5r
.05X
II
CJ
79-16
Gs
100-16,
141-16, M 80-18
0-18, M 142-18
CJ CN CJ CJ rH
S • • VO S vO - r H rH VO r *
r rH O 00 m f sr rH • ^ CO rH 1
o» <j-CJ o o% S u S „
s
MG 75-14,
MG 90-16,
C 119-16,
M 90-18,
saws,
u OJ
S -
iamet(
0 RPM
73 TJ O C r^ CO z 4J VO 4J
« * CO r H CO
(X G r-i T-i 0 "H ,-i r-i O C J CO CO
CJ
CO CO • E O 3 U
1 ^ C
a, L =
Gordo
& C CO C CO CO CO
• 3 ^
Co., M = Murray Pirati
ick Etter Co., and MG =
c ^ •H 'O CJ i-i
CO rH K CO •u II
c <U W
•u «. C -o o
CJ CJ It c
•H CJ CJ
• t 3
CO c J-i CO 0) 4J J-I CO 3 *J M a (u
inufa
ws p
^ CO e CO
TS «4-l
CO (U
Gin
Numt
1 ^ * ^
CO (U
.c o c •H
c •H > - •
U (U
amet
•H TJ
^ CO
CO
Iraate,
•u CO (U
>^ 4-1 •H CJ CO
CO o
and
i j
CO
c •H O
' - ^1 «N( c O | ^ (
81
Appendix B. Transition Probability Matrices for Markov Analysis of Texas High Plains Cotton Gins.
NI.I Transition No.
CatPgf>rv
NE
D
ISl
IS2
IS3
IS4
IS 5
AS I
AS2
AS 3
AS 4
ASS
D
0
10
0
0
0
0
0
0
0
0
0
n
PIJ Transition No
Category
NE
D
ISl
rs2
IS3
IS4
TS5
ASl
AS 2
AS 3
AS4
AS 5
D
0.000
1.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
n.ooo
. 1 from l<?67
ISl
0
0
1
0
0
0
0
4
0
0
0
0
IS2
0
0
0
1
0
0
0
0
3
0
0
0
. 1 from 1967
ISl
0.000
0.000
0.333
0.000
0.000
0.000
0.000
0.034
0.000
0.000
0.000
0.000
IS2
0.000
0.000
0.000
1.000
0.000
0.000
0.000
0.000
0.017
0.000
0.000
0.000
to 1968
IS3
CO
1
0.
0,
0,
0,
0,
0.
0.
0,
0.
0,
0,
0,
0
0
0
0
0
0
0
0
0
0
0
0
1968
[S3
.000
,000
.000
,000
,000
,000
,000
,000
,000
,000
.000
.000
IS4
0
0
0
0
0
0
0
0
0
0
1
0
:
IS4
0,000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.038
0.000
IS5
•]
0.
0,
0,
0,
0.
0,
0,
0,
0.
0.
0.
0.
0
0
0
0
0
0
0
0
0
0
0
0
:s5
.000
.000
,000
,000
.000
.000
.000
.000
.000
,000
.000
.000
ASl
0
0
2
0 •
0
0
0
114
0
0
0
0
ASl
0.000
0.000
0.667
0.000
0.000
0.000
0.000
0.958
0.000
0.000
0.000
0.000
\9 2
0
0
0
0
0
0
0
1
168
0
0
0
AS2
0.000
0.000
o.coo
0.000
0.000
0.000
0.000
0.008
0.983
0.000
0.000
0.000
AS3
0
0
0
0
1
0
0
0
0
36
0
0
AS 3
0.000
0.000
0.000
0.000
1.000
0.000
0,000
0.000
0.000
1.000
0.000
0.000
AS4
0
0
0
0
0
1
0
0
0
0
25
0
AS4
0.000
0.000
0,000
0.000
0,000
1,000
0,000
0,000
0.000
0.000
0.962
n.ooo
AS5
0
0
0
0
0
0
0
0
0
0
0
8
AS 5
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0,000
0.000
0.000
1,000
Appendix B, Continued.
82
NIJ Trans i t ion No
C a t e g o r y
NE
D
I S l
IS2
IS3
IS4
IS5
ASl
AS 2
AS 3
AS4
AS 5
D
0
9
1
1
0
1
0
0
0
0
0
0
P I J T r a n s i t i o n No
C a t e g o r y
NE
D
I S l
IS2
IS3
IS4
IS5
ASl
AS 2
AS 3
AS 4
ASS
D
0 . 0 0 0
1 ,000
0 . 2 0 0
0 , 2 5 0
0 , 0 0 0
1 .000
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
. 2 from 1968
I S l
0
0
3
0
0
0
0
3
0
0
0
0
IS2
0
0
0
2
0
0
0
0
0
0
0
0
. 2 from 1968
I S l
0 . 0 0 0
0 . 0 0 0
0 . 6 0 0
0 , 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 , 0 2 6
0 . 0 0 0
0 . 0 0 0
0 , 0 0 0
0 . 0 0 0
IS2
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 5 0 0
0 . 0 0 0
0 , 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
t o 1969
IS3
t o
0
0
0
0
0
0
0
0
0
0
0
0
1969
I S 3
0,
0.
0,
0,
0,
0.
0.
0,
0.
0.
0.
0.
,000
,000
,000
,000
.000
.000
,000
,000
,000
,000
,000
,000
IS4
:
0
0
0
0
0
0
0
0
0
0
0
0
IS4
0.
0,
0,
0.
0,
0,
0,
0,
0,
0,
0,
0.
,000
,000
.000
,000
,000
,000
,000
.000
,000
,000
.000
,000
I S 5
0
0
0
0
0
0
0
0
0
0
0
0
IS5
0,
0,
0,
0,
0,
0,
0,
0.
0,
0,
0.
0.
,000
.000
.000
.000
,000
.000
,000
.000
.000
.000
.000
.000
ASl
1
0
1
0
0
0
0
108
0
0
0
0
ASl
1.000
0 . 0 0 0
0 ,200
0 , 0 0 0
0 . 0 0 0
0 .000
0 . 0 0 0
0 . 9 3 1
0 , 0 0 0
0 , 0 0 0
0 , 0 0 0
0 . 0 0 0
AS 2
0
0
0
1
0
0
0
5
167
0
0
0
AS2
0 . 0 0 0
0 . 0 0 0
0 .000
0 . 2 5 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 4 3
0 .988
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
AS 3
0
0
0
0
0
0
0
0
1
36
0
0
AS 3
0 ,000
0 , 0 0 0
0 . 0 0 0
0 .000
0 .000
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 6
0 ,972
0 , 0 0 0
0 . 0 0 0
AS4
0
0
0
0
0
0
0
0
1
1
26
0
AS 4
0 , 0 0 0
0 . 0 0 0
0 , 0 0 0
0 , 0 0 0
0 .000
0 . 0 0 0
0 , 0 0 0
0 , 0 0 0
0 . 0 0 6
0 , 0 2 8
1,000
0 .000
ASS
0
0
0
0
0
0
0
0
0
0
0
8
ASS
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 . 0 0 0
0 , 0 0 0
0 . 0 0 0
0 . 0 0 0
0 , 0 0 0
1.000
Appendix B. Continued,
83
NIJ Trans
C.:itegory
N'E
D
I S l
IS2
TS3
IS4
IS5
ASl
AS 2
AS 3
AS 4
AS 5
——
i i t i on No.
D
0
12
2
1
0
0
0
0
0
0
0
0
3 from
I S l
0
0
1
•0
0
0
0
2
0
0
0
0
1969
IS2
0
0
0
1
0
0
0
0
1
0
0
0
to 1970:
IS3
0
0
0
0
0
0
0
0
0
0
0
0
IS'*
0
0
0
0
0
0
0
0
0
0
0
0
IS5
0
0
0
0
0
0
0
0
0
0
0
0
ASl
0
0
3
0 •-
0
0
0
104
0
0
0
0
AS 2
0
0
0
0
0
0
0
4
172
0
0
0
AS 3
0
0
0
0
0
0
0
0
0
36
0
0
AS4
0
0
0
0
0
0
0
0
0
0
26
1
ASS
0
0
0
0
0
0
0
0
0
1
2
7
PIJ Trnnsicion No. 3 from 1969 to 1970:
Categorv ISl IS: IS3 IS4 IS5 ASl AS 2 AS 3 AS4 ASS
NE 0.000 0.000 0.000 0.000 0.000 0.000
D 1.000 0.000 0.000 0,000 0.000 0.000
ISl 0.333 0.167 0.000 0.000 0.000 0.000
[S: 0.500 0.000 0.500 0.000 0.000 0.000
153 0,000 0.000 0,000 0.000 0.000 0.000
154 0,000 0.000 0.000 0.000 0.000 0.000
155 0.000 0.000 0.000 0.000 0.000 0,000
ASl 0.000 0.013 0.000 0.000 0.000 0.000
AS2 0.000 0.000 0.006 0.000 0,000 0,000
.\S3 0,000 0.000 0.000 0.000 0.000 0.000
AS4 0.000 0.000 0.000 0.000 0.000 0.000
ASS 0,000 0.000 0.000 0,000 0,000 0,000
0,000 0,000 0.000 0.000 0,000
0.000 0.000 0.000 0,000 0.000
0.500 0.000 0.000 0,000 0,000
0.000 0,000 0.000 0.000 0,000
0.000 0.000 0.000 0.000 0.000
0.000 0,000 0.000 0,000 0,000
0.000 0.000 0.000 0.000 0,000
0,946 0.036 0.000 0.000 0.000
0.000 0,994 0.000 0,000 0,000
0.000 0,000 0,973 0.000 0.027
0.000 0.000 0.000 0.929 0.071
0.000 0.000 0,000 0.12S 0.875
Appendix B. Continued.
84
NIJ Transition No. 4 from 1970 to 1971:
Category
NE
D
ISl
IS2
IS3
IS4
IS5
ASl
AS 2
AS 3
AS 4
.\S5
D
0
13
3
2
0
0
0
1
0
0
0
0
ISl
0
0
0
0
0
0
0
3
0
0
0
0
IS2
0
0
0
0
0
0
0
0
1
0
0
0
IS3
0
0
0
0
0
0
0
0
0
0
0
0
IS4
0
0
0
0
0
0
0
0
0
0
0
0
ISS
0
0
0
0
0
0
0
0
0
0
0
0
ASl
0
0
0
0 .
0
0
0
97
1
0
0
0
AS 2
1
0
0
0
0
0
0
5
172
0
0
0
AS 3
0
0
0
0
0
0
0
1
2
36
0
0
AS 4
0
0
0
0
0
0
0
0
0
0
27
0
ASS
0
0
0
0
0
0
0
0
0
0
0
10
PIJ Transition No, 4 from 1970 to 1971:
Cicegorv D ISl IS2 IS3 IS4 ISS ASl AS2 AS3 AS4 ASS
NE 0.000 0.000 0.000 0.000 0.000 0,000
D 1,000 0.000 0.000 0.000 0.000 0.000
151 1.000 0.000 0,000 0.000 0.000 0.000
152 1.000 0,000 0.000 0.000 0,000 0.000
153 0,000 0.000 0.000 0.000 0,000 0,000
TS4 0,000 0.000 0.000 0.000 0,000 0,000
IS5 0,000 0.000 0,000 0,000 0.000 0.000
ASl 0.009 0,028 0.000 0,000 0,000 0.000
AS2 0.000 0.000 0.006 0.000 0.000 0.000
AS3 0.000 0.000 0.000 0.000 0.000 0.000
AS4 0.000 0.000 0.000 0.000 0.000 0.000
ASS 0.000 0,000 0.000 0.000 0.000 0.000
0,000 1.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0,000
0,000 0,000 0,000 0,000 0.000
0,000 0,000 0,000 0,000 0.000
0.000 0.000 0.000 0.000 0.000
0.907 0.047 0.009 0.000 0.000
0.006 0,977 0.011 0,000 0,000
0,000 0,000 1,000 0.000 0,000
0.000 0.000 0.000 1.000 0.000
0.000 0.000 0.000 0.000 1,000
Appendix B. Continued.
85
NIJ Transition No
Category
NE
D
ISl
IS2
IS3
IS4
ISS
ASl
AS 2
AS3
AS 4
ASS
PIJ Transi
Category
NE
D
ISl
IS2
TS3
IS4
IS5
ASl
AS 2
AS 3
AS 4
ASS
D
0
19
0
0
0
0
0
0
0
0
0
0
tion No
D
0.000
1.000
0.000
0.000
0.000
0,000
0,000
0.000
0.000
0.000
0.000
0.000
. 5 from 1971
ISl
0
0
3
0
0
0
0
1
0
0
0
0
IS2
0
0
0
0
0
0
0
0
1
0
0
0
. 5 from 1971
ISl
0.000
0,000
1,000
0,000
0.000
0,000
0,000
0.010
0.000
0.000
0.000
0.000
IS2
0.000
0.000
0.000
0.000
0.000
0.000
0,000
0,000
0.006
0.000
0.000
0.000
to 1972
IS3
to
1
0,
0,
0,
0,
0,
0.
0,
0,
0,
0,
0,
0,
0
0
0
0
0
0
0
0
0
0
0
0
1972
CS3
,000
.000
.000
.000
.000
.000
.000
.000
,000
.000
.000
,000
IS4
:
0
0
0
0
0
0
0
0
0
0
0
0
IS4-
0.
0.
0,
0,
0,
0
0,
0,
0,
0.
0,
0,
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
,000
. [SS
0
0
0
0
0
0
0
0
0
0
0
0
ISS
0,
0,
0,
0,
0,
0,
0,
0,
0.
0.
0,
0,
.000
.000
.000
.000
.000
.000
.000
.000
.000
,000
.000
.000
ASl
0
0
0
0
0
0
0
97
1
0
0
0
ASl
0.000
0,000
0.000
0.000
0.000
0.000
0.000
0.990
0.006
0,000
0.000
0,000
AS2
0
0
0
1
0
0
0
0
176
0
0
0
AS 2
0.000
0.000
0,000
1.000
0.000
0,000
0,000
0,000
0,983
0,000
0.000
0.000
AS 3
0
0
0
0
0
0
0
0
1
37
0
0
AS 3
0,000
0.000
0.000
0.000
0,000
0.000
0.000
0.000
0.005
0,949
0,000
0.000
AS4
0
0
0
0
0
0
0
0
0
2
26
0
AS4
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.051
0.963
0.000
ASS
0
0
0
0
0
0
0
0
0
0
1
10
ASS
0,000
0.000
0,000
0,000
0,000
0,000
0,000
0.000
0,000
0.000
0.037
1.000
Appendix B. Continued.
86
NIJ Transition No.
Category
NE
D
ISl
IS2
IS3
IS4
ISS
ASl
AS2
AS 3
AS 4
ASS
D
0
17
1
0
0
0
0
2
2
0
0
0
6 from
ISl
0
0
2
0
0
0
0
3
0
0
0
0
1972
IS2
0
0
0
1
0
0
0
0
3
0
0
0
to 1973:
IS3
0
0
0
0
0
0
0
0
0
1
0
0
154
0
0
0
0
0
0
0
0
0
0
0
0
ISS
0
0
0
0
0
0
0
0
0
0
0
0
ASl
0
0
1
0
0
0
0
91
0
0
0
0
AS2
0
0
0
0
0
0
0
2
166
0
0
0
ASS
2
0
0
0
0
0
0
0
6
36
1
0
AS4
0
0
0
0
0
0
0
0
0
1
26
0
ASS
0
0
0
0
0
0
0
0
0
0
1
11
PIJ Transition No. 6 from 1972 to 1973:
Category ISl IS2 IS3 IS4 ISS ASl AS2 AS3 AS4 ASS
NE
D
ISl
IS2
IS3
IS4
ISS
ASl
AS 2
AS 3
AS4
ASS
0.000
1,000
0.250
0,000
0,000
0.000
0,000
,0,020
0.011
0,000
0,000
0,000
0.000
0.000
0,500
0.000
0.000
0.000
0.000
0.031
0.000
0.000
0.000
0.000
0.000
0.000
0.000
1,000
0.000
0.000
0.000
0.000
0.017
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.026
0.000
0.000
0.000
0.000
0,000
0,000
0,000
0,000
0.000
0.000
0.000
0,000
0,000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0,250
0,000
0,000
0,000
0.000
0.929
0.000
0.000
0,000
0,000
0,000
0.000
0.000
0,000
0.000
0.000
0.000
0.020
0.938
0.000
0.000
0.000
1.000
0.000
0.000
0.000
0,000
0.000
0.000
0.000
0.034
0,948
0.036
0.000
0.000
0.000
0.000
0,000
0,000
0.000
0.000
0.000
0.000
0,026
0,928
0.000
0.000
0,000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0,000
0.036
1.000
87
Appendix B. Continued.
NIJ Transition No. 7 from 1973 to 1974:
Category
NE
D
ISl
IS2
IS3
IS4
ISS
ASl
AS 2
AS 3
AS4
ASS
D
0
20
1
3
0
0
0
0
2
0
0
0
ISl
0
0
4
0
0
0
0
6
0
0
0
0
IS2
0
0
0
1
0
0
0
1
-
0
0
0
IS3
0
0
0
0
1
0
0
0
0
1
0
0
IS4
0
0
0
0
0
0
0
0
0
0
0
0
IS5
0
0
0
0
0
0
0
0
0
0
0
0
.\S1
0
0
0
0
0
0
0
80
0
0
0
0
AS2
1
0
0
0
0
0
0
5
155
1
0
0
AS 3
1
0
0
0
0
0
0
0
4
42
0
0
AS 4
0
0
0
0
0
0
0
0
0
1
24
0
ASS
0
0
0
0
0
0
0
0
0
0
3
12
P[J Transition No. 7 from 1973 to 1974;
Cat .".;ory
N'c
0
ISl
rs2
ISl
1S4
1S5
ASl
AS 2
AS 3
AS 4
ASS
D
0.000
1.000
0.200
0.750
0.000
0.000
0.000
0.000
0.011
0.000
0.000.
0.000
ISl
0.000
0.000
o.soo
n.ooo
0.000
0.000
0.000
0.066
0.000
0.000
0.000
0.000
IS2
0.000
0.000
0.000
0.250
0.000
0.000
0.000
O.Oll
0.042
0.000
0.000
0.000
IS3
0.000
0.000
0,000
0.000
1.000
0.000
0.000
0.000
0.000
0.022
0,000
0.000
-IS4
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
o.noo
ISS
0.000
0.000
0.000
0.000
n.ooo
0.000
0.000
0.000
0,000
0.000
0.000
0.000
ASl
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.869
0.000
0.000
0.000
0.000
AS2
0.500
0.000
0.000
0.000
0.000
0.000
0.000
0.054
0.923
0.022
0.000
0.000
AS 3
0.500
0.000
0.000
0.000
0.000
0,000
0,000
0.000
0.023
0.934
0.000
0.000
AS4
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.022
0.889
0.000
ASS
0.000
0.000
0.000
0,000
0,000
0,000
0.000
0.000
0.000
0.000
0.111
1.000
88
Appendix B. Continued.
NIJ Transition No. 8 from 1974 to 1975:
Category
N'E
D
ISl
IS2
IS3
IS4
ISS
ASl
AS 2
AS 3
.\S4
AS 5
D
0
25
0
0
0
0
0
0
0
0
0
ISl
0
0
6
0
0
0
0
2
0
0
0
0
IS2
0
0
0
5
0
0
0
0
3
0
0
0
IS3
0
0
0
0
0
0
0
0
0
2
0
0
IS4
0
0
0
0
0
0
0
0
0
0
0
0
ISS
0
0
0
0
0
0
0
0
0
0
0
0
ASl
0
0
•4
0
1
0
0
73
0
0
0
0
AS 2
0
0
0
3
0
0
0
4
156
1
0
0
AS 3
0
0
0
1
1
0
0
1
1
42
0
0
AS4
0
0
0
0
0
0
0
0
0
2
23
0
ASS
1
0
0
0
0
0
0
0
0
0
1
IS
PIJ Tr.Tnsitlon Nu. 8 Fmm 1974 to 1975:
Category D ISl IS2 IS3 IS4 ISS ASl .A.s: AS3 AS4
NE 0.000 0.000 0.000 0.000 O.COO 0.000
D 1.000 0.000 0.000 0.000 0,000 0.000
TSl 0.000 0.600 0.000 0.000 0.000 0.000
IS2 0.000 0.000 0.556 0.000 0.000 0.000
TS3 0.000 0.000 0.000 0,000 0.000 0.000
154 0.000 0.000 0.000 0.000 0.000 0.000
155 0.000 0.000 0.000 0.000 0.000 0.000
AS] 0.000 0.025 0.000 0.000 0.000 0.000
AS2 0.013 0.000 0.013 0.000 0.000 0.000
AS3 0.000 0.000 0.000 0.043 0.000 0.000
AS4 0.000 0.000 0.000 0.000 0,000 0.000
ASS 0.000 0.000 0.000 0.000 0.000 0.000
ASS
0.000 0.000 0.000 0.000 1.000
0.000 0.000 0.000 0.000 0.000
0.400 0.000 0.000 0.000 0,000
0.000 0.333 0.111 0.000 0.000
0.500 0.000 0.500 0.000 0.000
0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000 0.000 0,000
0.913 0.050 0.012 0.000 0.000
0.000 0.963 0.006 0.000 0.000
0.000 0.021 0.893 0.043 0,000
0,000 0.000 0.000 0.920 0.080
0.000 0.000 0.000 0.000 1.000
89
Appendix B, Continued,
NIJ Transition No.
Category
NE
D
ISl
IS2
IS3
IS4
ISS
ASl
AS 2
AS 3
AS4
ASS
D
0
26
1
2
0
0
0
0
0
0
0
0
9 from
ISl
0
0
7
0
0
0
0
6
0
0
0
0
1975
IS2
0
0
0
6
0
0
0
0
6
0
0
0
to 1976:
IS3
0
0
0
0
0
0
0
0
0
1
0
0
IS4
0
0
0
0
0
0
0
0
0
0
0
0
ISS
0
0
0
0
1
0
0
0
0
0
0
0
ASl
0
0
0
0 "
0
0
0
67
0
0
1
0
AS 2
1
0
0
0
0
0
0
5
157
o
0
0
AS 3
0
0
0
0
1
0
0
0
0
42
0
0
AS4
0
0
0
0
0
0
0
0
1
1
22
0
ASS
0
0
0
0
0
0
0
0
0
0
2
18
PIJ T r a n s i t i o n No. 9 from 1975 to 1976:
ISl IS2 IS3 -IS4 Category
NE
D
ISl
TS2
IS3
1S4
ISS
ASl
AS 2
AS 3
AS4
ASS
ISS AS] AS2 AS3 AS4 ASS
0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 .000 0 . 0 0 0
1.000 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 .000
0 . 1 2 5 0 . 8 7 5 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0
0 . 2 5 0 0 . 0 0 0 0 , 7 5 0 0 . 0 0 0 0 . 0 0 0 0 ,000
0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 5 0 0
0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 , 0 0 0 0 , 0 0 0 0 , 0 0 0
0 , 0 0 0 0 . 0 0 0 0 . 0 0 0 0 , 0 0 0 0 .000 0 . 0 0 0
0 . 0 0 0 0 . 0 7 8 0 . 0 0 0 0 , 0 0 0 0 , 0 0 0 0 , 0 0 0
0 , 0 0 0 0 , 0 0 0 0 , 0 3 6 0 . 0 0 0 0 , 0 0 0 0 . 0 0 0
0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 .022 0 , 0 0 0 0 . 0 0 0
0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 .000 0 . 0 0 0
0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0
0 .000 1.000 0 .000 0 .000 0 . 0 0 0
0 ,000 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0
0 . 0 0 0 0 . 0 0 0 O.OOC 0 . 0 0 0 0 , 0 0 0
0 , 0 0 0 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 , 0 0 0
0 , 0 0 0 0 , 0 0 0 0 , 5 0 0 0 . 0 0 0 0 , 0 0 0
0 , 0 0 0 0 . 0 0 0 0 , 0 0 0 0 . 0 0 0 0 . 0 0 0
0 . 0 0 0 0 . 0 0 0 0 , 0 0 0 0 . 0 0 0 0 , 0 0 0
0 , 8 5 8 0 .064 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0
0 . 0 0 0 0 .957 0 . 0 0 0 0 . 0 0 6 0 , 0 0 0
0 ,000 0 , 0 4 3 0 , 9 1 3 0 . 0 2 2 0 . 0 0 0
0 , 0 4 0 0 , 0 0 0 0 , 0 0 0 0 . 8 8 0 0 , 0 8 0
0 . 0 0 0 0 . 0 0 0 0 . 0 0 0 0 , 0 0 0 1,000
Appendix B, Continued.
90
NIJ Transition No
Category
ME
D
ISl
IS2
IS3
IS4
ISS
-ASl
AS 2
.AS 3
AS 4
ASS
D
0
29
3
0
0
0
0
0
0
0
0
0
PIJ Transition No
Category
NE
D
ISl
IS2
IS3
IS4
ISS
ASl
AS 2
AS 3
AS4
ASS
D
0.000
1.000
0.230
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
o.noo
. 10 from
ISl
0
0
6
0
0
0
0
0
0
0
0
0
, 10 from
ISl
0.000
0.000
0,462
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
]
0
0
0
0
0
0
0
0
0
0
0
0
1976
[S2
0
0
0
7
0
0
0
0
0
0
0
0
1976
[S2
000
000
000
583
000
000
000
000
000
000
000
000
CO 1977:
IS3 1
0
0
0
0
0
0
0
0
0
0
0
0
to 1977:
IS3
0,000
0.000
0.000
0.000
0.000
0,000
0,000
0,000
0.000
0.000
0.000
0.000
[S4
0
0
0
0
0
0
0
0
0
0
0
0
IS4
0
0
0
0
0
0
0
0
0
0
0
0
000
000
000
000
000
000
000
000
000
000
000
000
ISS
0
0
0
0
0
0
1
0
0
0
0
0
ISS
0
0
0
0
0
0
1
0
0
0
0
0
000
000
000
000
000
000
000
000
000
000
000
000
ASl
0
9 4
0
0
0
0
64
0
0
0
0
ASl
n.ooo
0.000
0.308
0.000
0.000
0.000
0.000
0,941
0.000
0,000
0.000
0.000
AS 2
0
0
0
5
0
0
0
2
161
0
0
0
AS 2
0.000
0,000
0,000
0,417
0,000
0.000
0,000
0.029
0,976
0.000
0.000
0.000
AS 3
0
0
0
0
1
0
0
1
4
43
0
1
AS 3
0.000
0.000
0.000
0.000
1.000
0.000
0.000
0.015
0.024
1.000
0.000
0.050
AS 4
0
0
0
0
0
0
0
1
0
0
23
0
AS 4
0.000
0,000
0,000
0.000
0.000
0.000
o.ooo
0.015
0.000
0.000
0.958
0.000
ASS
0
0
0
0
0
0
0
0
0
0
1
19
ASS
0.000
0,000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.042
0.950
Appendix B. Continued,
91
NIJ Transition No
Category
NE
D
ISl
IS2
IS3
IS4
ISS
ASl
.\S2
AS 3
AS 4
ASS
PIJ Transi
Category
NE
D
ISl
IS2
rs3 TS4
ISS
ASl
AS 2
AS 3
AS4
ASS
D
0
32
3
3
0
0
1
0
0
0
0
0
tion No
D
0.000
1.000
0.300
0.428
0.000
0.000
1.000
0.000
0,000
0.000
0,000
0,000
, 11 from
ISl
0
0
2
0
0
0
0
2
0
0
0
0
1977
IS2
. 11 from
ISl
0.000
0.000
0.333
0.000
0. ono
0.000
0.000
0.029
0.000
0.000
0.000
0.000
0
0
0
4
0
0
0
0
3
0
0
0
1977
IS2
0
0
0
0
0
0
0
0
0
0
0
0
000
000
000
572
000
000
000
000
018
000
000
000
to 1978:
IS3
0
0
0
0
0
0
0
0
0
0
0
0
IS4
to 1978: - • • — - » • 1
IS3
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
]
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
[S4
000
000
000
000
000
000
000
000
000
000
000
000
1
0
0
0
0
0
0
0
0
0
0
0
0
LSS
0
0
0
0
0
0
0
0
0
0
0
0
[SS
000
000
000
000
000
000
000
000
000
000
,000
.000
.ASl
0
0
i 0
0
0
0
62
0
0
0
0
ASl
0.000
0.000
0.167
0.000
0.000
0.000
0.000
0.912
0.000
0.000
0.000
0.000
AS 2
1
0
0
0
0
0
0
3
165
0
0
0
,\S2
1.000
0.000
0,000
0.000
0,000
0,000
0.000
0.044
0.982
0.000
0.000
0.000
.
AS 3
0
0
0
0
0
0
0
1
0
48
0
0
AS 3
0.000
0.000
0.000
0.000
0.000
0.000
0,000
0,015
0.000
0,960
0.000
0.000
AS4
0
0
0
0
0
0
0
0
0
2
23
0
AS 4
0,000
0.000
0.000
0,000
0.000
0,000
0.000
0.000
0.000
0.040
0.958
0.000
ASS
0
0
0
0
0
0
0
0
0
0
1
20
ASS
0.000
0.000
0.000
0,000
0,000
0.000
0.000
0.000
0.000
0,000
0.042
1,000
Appendix B. Continued.
92
NIJ Transition No
Category
NE
D
ISl
IS2
IS3
IS4
ISS
ASl
AS 2
AS 3
AS 4
ASS
D
0
38
0
0
0
0
0
1
0
0
0
0
PIJ Transition No
Category
NE
D
ISl
IS2
IS3
IS4
ISS
ASl
AS 2
AS 3
AS 4
ASS
D
0,000
1.000
0.000
0,000
0,000
0,000
0,000
0.016
0.000
0.000
0.000
0.000
. 12 fr
ISl
0
0
3
0
0
0
0
2
0
0
0
0
om 1978
IS2
. 12 from
ISl
0.000
0.000
0.750
0,000
0,000
0.000
0.000
0.032
0,000
0.000
0.000
0,000
0
0
0
5
0
0
0
0
2
0
0
0
1978
IS2
0
0.
0.
0
0
0
0
0
0
0
0
0
000 -
000
000
714
000
000
000
000
012
.000
.000
.000
to 1979:
IS3 IS4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
to 1979:
IS3
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
IS4
0.000
0.000
0.000
0.000
0.000
0,000
0,000
0.000
0.000
0.000
0.000
0.000
ISS
0
0
0
0
0
0
0
0
0
0
0
0
ISS
0
0
0
0
0
0
0
0
0
0
0
0
000
000
000
000
000
000
.000
.000
.000
.000
.000
.000
ASl
0
0
1
0
0
0
0
55
0
0
0
0
ASl
0,000
0,000
0.250
0.000
0.000
0.000
0.000
0.873
0.000
0.000
0,000
0,000
AS 2
0
0
0
2
0
0
0
5
164
1
0
0
AS 2
0.000
0,000
0,000
0,286
0.000
0.000
0.000
0.079
0.976
0.020
0,000
0,000
AS 3
0
0
0
0
0
0
0
0
2
46
0
0
AS 3
0.000
0,000
0.000
0.000
0,000
0.000
0.000
0.000
0.012
0.939
0.000
0.000
AS4
1
0
0
0
0
0
0
0
0
2
25
0
AS 4
1.000
0.000
0.000
0.000
0.000
0.000
0.000
0,000
0.000
0,041
1,000
0,000
ASS
0
0
0
0
0
0
0
0
0
0
0
21
ASS
0,000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
1.000
Appendix C. Modified Application of the Chi-Square Test In Testing Stationary Transition Probability Assumption.
The chi-square goodness of fit test, defined as,
2 _ 2 X - 2] n ( p . - p . ) ^ w i t h n ( n - l ) d . f . , was s e l e c t e d
•t A 4- -^J ^ I J t i l t ijt
"ijt
for application to the Texas High Plains cotton ginning industry (2).
However, due to an inadequate number of observations in many cells
(there were a large number of observations that had observed values
of P^. = 0), the original 11 x 11 stationary probability matrix
could not be tested. The matrix was modified (9) in order to apply
the chi-square procedure to aggregated groupings of cells. The modi
fication consisted of condensing the 11 x 11 matrix to a 2 x 3 matrix
aggregation, with all inactive gins grouped into one category, all
active gins into one category, and a dead gin category. Thus, the
aggregated or partitioned matrix which resulted can be illustrated
in the following manner:
I A D
where I denotes inactive gins, A denotes active gins, and dead or
defunct gins were denoted as D. This matrix was the most detailed
matrix which had all cells with sufficient numbers of non-zero obser
vations with which to apply the chi-square procedure. The individual
93
94
cells were evaluated with the above X^ relationship to test the
hypothesis of stationary transition probabilities. The basis of
2 the X calculated values was that the p.. consisted of observed
111
annual transition probabilities for cells and the p.. consisted of
the average or stationary probabilities over the 12 transitions.
Results from the test showed that hypothesis of stationary proba
bilities was not rejected. This indicates that the probabilities
in the individual cells were constant, i.e., the probability of
active gins remaining active is stationary and does not change over
time. Thus, the individual movements between the activity groups
(I, A, and D) from transition to transition were not significantly
different from the stationary transition probabilities. However,
this test and its results did not allow for any evaluation of
whether the probabilities of movement between size groups was con
stant because of the data limitations. Thus, the stationary assump
tion for all the movements among activity and size groups could not
be tested. Examination of the movements between size groups (see
Appendix B) reveals that there was much variation in the stationary
probabilities from year to year. Thus, it was reasoned that the
transition probability matrix was not stationary.
Appendix D. Derived Regression Equations
Equations for certain cells that could not be estimated directly
by regression, due to an inadequate number of observations, were
derived by grouping cells and their observations together, estimating
equations for groups of cells, then subtracting to estimate indivi
dual cells. Equations and relationships were derived for three such
cells' transition probabilities, P A I A Q ' ^A1-A4' ^^^ Al-D* ^^^
equations were derived in the following manner: (1) P/ii AO ~ ^A1-
A2,3 " Al-A2' ^ ^ Al-A4 " Al-A2,3,4 " Al-A2,3' ^"^^ ^^^ ^Al-D "
^ - Al-A2,3,4 - Al-Al " Al-Il' ^1-A2,3 ""^ "^ "^^"^'°" °' '^"
combined cells with the elements P. .„ and P. . , while P _ . 0 0 / A1-A2 A1-A3 A1-A2,3 ,4
was an equation of the combined cells with elements ^A-I^AO' ^A1-A3'
and P ,. The third derivation was based on the constraint placed A1-A4
on each row (discussed earlier); that the sum of a row's elements
equal one. The derived equations, concise explanations of relation
ships, and statistics are detailed below.
^^^ ^Al-A3 " ^Al-A2-3 " • Al-A2
= (0.0152 + 0.0044 T) - (0.0161 + 0.0036 T)
= -0.0009 + 0.0008 T
where P .. .., = the probability of a gin in
active size group 1 increasing to
size group 3 in an annual transition.
In this equation, an increase in time was seen to have the effect of
increasing P^^_^3_
95
96
The suporting statistics for P , .„ were: A1-A2,3
^Al-A2 3 " 0-0152 + 0.0044 T
(.0196)
F-Value: 7.70 PR > F • 0.0196 R^: 0.4350
D-W: 1.94 n = 12
^ ^ ^Al-A4 " Al-A2*,3,4 " Al-A2,3,
= (0.0142 + 0.0047 T) - (0.0152 + 0.0044 T)
= -0.0010 + 0.0003 T
where P A I A A ~ ^^^ probability of a gin in active
size group 1 increasing in size
group 4 in an annual transition.
This equation indicated that an increase in time had the effect of
increasing V^j__^^_
were: The supporting statistics for P A I A O -J A
^Al-A2,3,4 = 0.0142 + 0.0047 T
(.0115)
F-Value: 9.52 PR > F: 0.0115 R^: 0.4878
D-W: 1.91 n = 12
(2) P = 1 - P - P - P ^^ Al-D Al-A2,3,4 Al-Al Al-Il
= 1 - (0.0142 + 0.0047 T) - (1,0787 - 0.0076 C +
0.0026 C^ - 0.0219 T + 0.0043 M) - (0.0117 + E
0.0021 C^)
= -0,1947 - 0.0026 C^ + 0.0055 C + 0.0172 T -E L
0.0043 M
97
where ^A^-D ~ ^^^ probability of a gin in active
size group 1 exiting the industry in
an annual transition.
In this equation, an increase in C and T had the effect of increasing LI
^Al-D' ^^^^^ ^^ increase in C and M had inverse effect on PAI.C*
Regression equations for transition probabilities of other cells
were tried but could not be estimated frequently due to lack of ob-
servations. Some cells (P^^.^^, P^^,^^. 7^^_^^. P^^.AS' ^"^ ^A4-A4>
had enough observations, but none of the hypothesized variables were
statistically significant. Thus, ten estimated equations for non-
stationary transition probabilities resulted from the analysis.