ANALYSIS OF THE TEXAS HIGH PLAINS COTTON MARKOV …

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 « 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, Â2-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* Â2-A2' ^^^ Â3-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 (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


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


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



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



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


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 ' Â1-A4' ^^^ Al-D* ^^^

equations were derived in the following manner: (1) P/ii AO ~ Â1-

A2,3 " Al-A2' ^ ^ Al-A4 " Al-A2,3,4 " Al-A2,3' ^"^^ ^^^ Âl-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 Â-IÂO' Â1-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.

^^^ Âl-A3 " Âl-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

Âl-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

^ ^ Âl-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

Âl-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 Â^-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

Âl-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' ^"^ Â4-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.

Documents

ANALYSIS OF THE TEXAS HIGH PLAINS COTTON MARKOV …