Group Title: effect of resource investment programs on labor employment
Title: The Effect of resource investment programs on labor employment
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Title: The Effect of resource investment programs on labor employment
Physical Description: 180 leaves : ill. ; 28 cm.
Language: English
Creator: Cato, James Carey
Copyright Date: 1973
 Subjects
Subject: Watersheds -- Economic aspects   ( lcsh )
Food and Resource Economics thesis Ph. D
Dissertations, Academic -- Food and Resource Economics -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1973.
Bibliography: Includes bibliographical references (leaves 175-179).
Additional Physical Form: Also available on World Wide Web
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by James Carey Cato.
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Bibliographic ID: UF00097568
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000420289
oclc - 37876239
notis - ACG8110

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RF

THE EFFECT OF RE50URCF INVEF>TMENT PROGRAMS
ON LABOR EMPLOYMENT





dft By
JAMES CAREY CATO









tON PRESENTED T IHE GR,DUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
1 FULFILLMENT OF THE REQUIRFjIENTS FOR TIE
DEGREE OF DOCTOR OF PHILOSOPHY






SITY OF











ACKNOWLEDGEMENTS


The author wishes to express appreciation to the Food and

Resource Economics Department, University of Florida, and the Economic

Research Service and Soil Conservation Service, United States Depart-

ment of Agriculture, for making this research possible. Sincere

appreciation is acknowledged to Dr. B. R. Eddleman, Chairman of the

Supervisory Committee, for his guidance and assistance during the

author's graduate program. Gratitude is also expressed to Drs.

J. E. Reynolds, K. C. Gibbs, and R. W. Bradbury who served as committee

members. Dr. W. W. McPherson also provided valuable comments.

Mr. Gene Harris provided valuable programming assistance.

Dr. Neil Cook, Economic Research Service, United States Department of

Agriculture provided excellent comments and guidance.

The author also wishes to express thanks to Mrs. Christine Ward

for her valuable assistance in typing the dissertation and to Mrs.

Phyllis Childress for her clerical and typing assistance in earlier

drafts. Appreciation is also due Miss Wanda Rhea who typed a complete

draft of the dissertation.

The greatest debt is due the author's wife, Diane, and sons

Kyle and Chad, for their unselfish devotion and sacrifice during his

graduate program.













TABLE OF CONTENTS




Page






LISTRO A BLES . . . . . . . . . . . . . vi




LIST OF ObGU EStiv.s. . . . . . . . . . . . ix
ABSTRACTe o. .L. .te.r. ture. . . . . . . . . . x

CHAPTER II

ITHEODUCTICAL .R . .RK. . . . . . . . . . 12





Mathematical Models of Equilibration Process . . . 12
Changes in Employment . . . . . . . 15
Economic Interpretation of Employment Effects . 16
Changes in Firm Numbers . . . . . . . 19
Economic Interpretation of Firm Number Effects . 21
Economic Interpretation of Exogenous Changes . . . 24
Factor Supplies . . . . . . . . . 25
Number of Firm Entrepreneurs . . . . . 32
Product Price . . . . . . . . . 32
Factor Price . . . . . . . . . 33
Firm Production Possibilities . . . . . 34

CHAPTER ill

STUDY AREA AND MODEL SPECIFICATION . . . . . . 3

Stildy Area . . . . . . . . . . . 35
selection OF Employml-ent Categorle! . . . . . 37
Cenera I MoUdel Spec.i f c ion . . . . 42
S trurctu ra I E S Lma tion . . . . . . . 45
REdvced Form Estim~atlon . . . . 45 .. M







Construction . . . . . . . . .
Manufacturing . . . . . . . .
Model Estimation Procedure. . . . . . .
Measurement of Variables and Empirical Expectations .
Employment . . . . . . . . . .
Firm Numbers . . . . . . . . .
Factor Supplies . . . . . . . .
Education investments (X1). . . . .
Corps of Engineers'natural resource
investments (X2)' . . . .
Soil Conservation Service PL-566
investments (X ). . . . . .
Agricultural Stabilization and Conservation


Service ACP investments (X4). .
Farmers Home Administration
investments (X ) . . . .
Crop allotment ( ) . . . .
Product Demand . . . . . . .
Agricultural product price (FP ).
Manufacturing product price (PPk)
Factor Price . . . . .
Agriculture wage rate (FP ) .
Manufacturing wage rate (FPk) . .
Technology . . . . . . . .
Agricultural technology (Z ).
Manufacturing technology () .
Farm Operator Supplies . . . . .
Agricultural wage opportunity (WW )
Agricultural employment opportunity
Farm operator age (WA) . . .
Manufacturing Labor Supplies . . .


* . i i
. . .
* . .
* . .
. *.
* .
* i *
. *.
. . .





(WE ) .
. . .


Manufacturing wage opportunity (WWV)..
Manufacturing employment opportunity (WE,)
Number of manufacturing firms (Mik) .


CHAPTER IV

ANALYSIS OF RESULTS . . . . . . . . .


Agriculture . . . . . . . . . .
Type of Equation . . . . . . .
Endogenous Variables . . . . . .
Exogenous Shifters . . . . . . .
Education investments . . . . .
Corps of Engineers' investments . .
Small Watershed Program investments .
Agricultural Conservation Program
investments . . . . . . .
Farmers Home Administration investimnts
Crop allotment . . . . . .
Agricultural product price . . .


I ( j





Page

Agricultural wage rate. . . . . .. 96
Agricultural technology . . . . .. 97
Agricultural wage opportunity . . ... 98
Agricultural employment opportunity ... . 99
Farm operator age . . . . . . . 100
Group differences . . . . . ... 100
Construction. .................. .. .. 100
Dependent Variable . . . . . . . . 102
Exogenous Shifters . . . . . . . . 102
Education investments . . . . . . 102
Corps of Engineers' investments. . . ... 103
Small Watershed Program investments ... 103
Agricultural Conservation Program
investments ............... 104
Farmers Home Administration investments . 104
Construction wage rate. . . . . .. 105
Construction wage opportunity . . . .. 105
Construction employment opportunity . . 106
Group differences . . . . . ... 06
Nondurable Manufacturing. . . . . . . ... 106
Dependent Variables. . . . . . . ... 107
Exogenous Shifters . . . . . . ... .11
Education investments . . . . ... .1
Corps of Engineers' investments . . ... 112
Small Watershed Program investments ... 113
Agricultural Conservation Program
investments . . . . . . . . 113
Farmers Home Administration investments .. 114
Manufacturing product price . . . . 114
Manufacturing wage rate . . . . .. 116
Manufacturing technology. . . . . ... 116
Manufacturing wage opportunity. . . ... 118
Manufacturing employment opportunity. ... 1!9
Number of firms . . . . . . . 1!9
Group differences . . . . . . . 120
Durable Manufacturing . . . . . . . . 121
Dependent Variables. . . . . . . ... 126
Exogenous Shifters . . . . . . . 126
Education investments . . . . . . 126
Corps of Engineers' investments . . ... 127
Small Watershed Program investments .... 127
Agricultural Conscrvation Program
investments . . . ... . . . . 128
Farmers Home Administratior. investrients . 128
Manufacturing product price . . . ... 129
Manrufscturing wage rate . . . . .. 131
Manufacturing technology. . . . ... !. 32
Manufacturing wage opportunity. . . . 134
Manufacturing employment opport'.it-. ... 13'
Number of fir rms ...... ............ 136
Group differences . . . . . ... 137




Page

CHAPTER V

SUMMARY AND CONCLUSIONS. . . . . . . . . ... 138

Summary . . . . . . . . ... . . .138
Conclusions . . . . . . . . ... . . 141
Limitations . . . . . . . ... . . 146
Need for Further Research . . . . . . . 147

APPENDIX A

SPECIFICATION OF AREA ADJUSTMENT MODEL . . . . . 149

APPENDIX B

MEANS AND STANDARD DEVIATIONS OF VARIABLES . . . ... 166

BIBLIOGRAPHY. . . . . . . . . . . . . ... 175

BIOGRAPHICAL SKETCH . . . . . . . . ... .... .180












LIST OF TABLES



Table Pagge

1 Industry identification and employment rankings for
the f ou r-s ta te a rea ( 1967) . . . . . . . 4o

2 Expected effect of changes in predetermined
variables on agricultural employment and


3 Expected effect of changes in predetermined
variables on manufacturing employment . . . . 55

14 Structural form and reduced form coefficients for
change in agricultural employment (E ) and number
of farm firms (N1I), all counties, 1910 to 1970 . . 77

5 Structural form and reduced form coefficients
for change in agricultural employment . . . . 79

6 Structural form and reduced form coefficients for
change in agricultural employment (El) and number of
farm firms (N 1), nonurban counties, 1560 to 19-70. .. 81

7 Regression equations for construction employment
change (E ) for all counties, urban counties,
and nonurarin counties, 1960 to )q70 . . . . . 101

8 Regression equations for textile mill product and
other fabricated textile products employment
change (E3) for all counties, urban counties, and
nonurban, counties, 11960 to 1S70 . . . . . 108

9 Regression equations for food and kindred products
emplo, ment change (Ej,) for all counties, urban
counties, and nonurban counties, 1960 to 1970 . . log

il0 Regression equations for nondurable manufacturing
em plIo yment change (END) for )IlI counties, urban
counties, and nonurban counties, 1960 to 1-570 110

11 Regression equatio,-ns for transportation products
,-mploymerit change ( 'E5) for all counties, urban
countie-, and nonurban couitic-sl 10,60 to, 970 . . 122


Vii





Table Page

12 Regression equations for furniture and lumber
and wood products employment change (E6) for
all counties, urban counties, nonurban counties,
1960 to 1970. . . . . . . . . ... ... 123

13 Regression equations for electrical equipment
products employment change (E7) for all
counties, urban counties, and nonurban
counties, 1960 to 1970. . . . . . . . . 124

14 Regression equations for durable manufacturing
employment (ED) for all counties, urban counties,
and nonurban counties, 1960 to 1970 . . . . .. 125

15 Definition and interpretation of terms
in equation (11). . . . . . . . . . 158

16 Definition and interpretation of terms
in equation (12). . . . . . . . . ... 162

17 Approximation of terms to represent a
change in residual return . . . . . . . 165

18 Means and standard deviations of employment change
variables for each county group of observations . . 167

19 Means and standard deviations of firm number change
variables for each county group of observations . .. 168

20 Means and standard deviations of factor supply
variables for each county group of observations . . 169

21 Means and standard deviations of product price
change variables for each county group of
observations. . . . ... . . ...... 170

22 Means and standard deviations of wage change
variables for each county group of observations . . 171

23 Means and standard deviations for technology change
variables for each county group of observations . .. 172

24 Means and standard deviations for wage opportunity
change variables for each county group of
observations . . . . . . . . . . 173

25 Means and standard deviations for employment
opportunity change variables for each county
group of observations . . . . . . . . 174


v ; ;












LIST OF FIGURES


Figure Page

I Illustration of the equilibration process th
resulting from a change in supply of the n
factor. . . . . . . . . ... .... 26

2 Illustration of the equilibration process in
the nth factor market resulting from a change
in supply of the nth factor . . . . . . . 27

3 Illustration of the equilibration process in
the firm entrepreneur market resulting from a
change in supply of the nth factor. . . . . ... 28

4 Illustration of the equilibration process in
the labor market resulting from a change in
supply of the nth factor. . . . . . . .. 29

5 Grouping of counties for the four-state study
area. . . . . . . . . ......... 38





Abstract of Dissertation Presented to the
Graduate Council of the University of Florida in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy

THE EFFECTS OF RESOURCE INVESTMENT PROGRAMS
ON LABOR EMPLOYMENT

By

James Carey Cato

December, 1973


Chairman: Dr. B. R. Eddleman
Major Department: Food and Resource Economics

This study examined the importance of investments in human and

natural resources along with several other variables in explaining

employment changes among counties comprising the four-state region of

Mississippi, Alabama, Georgia, and Florida over the time period 1960

to 1970. Counties in the study area were delineated into urban and

nonurban counties according to their human and natural resource endow-

ments. A theoretical economic model was developed that explains

changes in employment and firm numbers brought about by exogenous

shifts in the supplies of resources, demand for products, supplies of

other factors, firm production possibilities, and shifters of the

number of firms in an industry.

Empirical analysis was undertaken to determine the importance

of each exogenous shifter on industry employment changes. The

industries studied included agriculture, construction, textile mill

products and other fabricated textile products, food and kindred

products, transportation, furniture and fixtures, lumber and wood

products, electrical equipment, durable, and nondurable products

manufacturing. Changes in factor supplies included changes in per pupil






education expenditures, Corps of Engineers investments, Soil Conservation

Service investments in the Public Law 566 small Watershed Program,

Agricultural Stabilization and Conservation Service payments in the

Agricultural Conservation Program and loans and grants for community

water and sewer systems made by the Farmers Home Administration. Changes

in county product price indexes, allotment reductions, farm operator

age, wage rates technology indexes, number of firms, and alternative

wage and employment opportunities represented the other types of

exogenous shifters.

General equations for empirical analysis were specified for

each industry. A two-equation model was used for agriculture with the

number of farms considered endogenous. Single equation models were

specified for the remaining industries. Changes in the number of firms

were considered exogenous in these models. Two-stage and ordinary

least squares were used as empirical estimation procedures.

Results indicate that employment changes eminating from changes

in the exogenous shifters differed quite substantially among industries

and the county groups considered. Most employment effects were generally

consistent with expectations. Logical explanations were normally

apparent for employment effects that differed from initial expectations.

It was observed that some investm,-ents influenced employment in a parti-

cular industry and yet wiere not important in other industries. Location

of industries was also important. Effects differed between the urban

and nonurban counties for 5ome industries. The most satisfactory

res-ults were obtained for agricultural employment end farm number




changxst





Results indicated that any attempt to stimulate employment in

an area with investments in human and natural resource should take into

consideration not only the agricultural, urban, and nonurban character-

istics of the area, but the type of industry employment most evident

in the area.












CHAPTER I

INTRODUCTION



Investments in natural resources usually are for the expressed

purposes of conserving, developing, or managing the nation's supply

of soil, water, timber, mineral, and marine resources. Many public

investment programs in natural resources such as those associated

with the Tennessee Valley Authority (TVA) and the Small Watershed

Development Program administered by the USDA's Soil Conservation

Service contained explicit development objectives. These objectives

were concerned with alleviating depressed regional economic conditions

or improving the incomes of specific groups of people.

Senate Document 97 [1], issued in 1962, also made explicit a

national policy of natural resource investments for purposes of

increasing income and employment in particular regions. The Appala-

chian Regional Development Act of 1965 [2] provided for the construction

of water resource projects to stimulate economic growth of the region.

Guidelines concerning principles and standards for the planning of

water and related land resource use, issued for review by the Water

Resources Council [3] in 1971, gave added emphasis to the role of water





This program, created by che Watershed Pr,:te.tion and Fiood
Prevention Act of 195L4, with its An.-ndnints, is zomnonly referred tc
as Pub ic Law 566.







resource investments in the development of a regional economy. This

orientation in policy has given added emphasis to natural resource

development programs and projects as instruments for dealing with

regional economic problems. Many other programs have evolved that focus

on goals of community improvement by concentrating on such areas as

increasing local employment and income, increasing public revenues, and

improving the quality of the environment.

Local employment and income of an area depend on many factors

other than investments in natural resources. Any explanation of employ-

ment and income changes occurring within a region requires analysis of

the many variables which interact to determine these changes. Identi-

fication and measurement of these complicated interdependencies are

necessary in order to assess previous or prospective effects of the

various programs in influencing the level of employment and income.

Changes in investment levels that shift the supplies of critical resources

often occur concurrently with changes in the demands for products,

supplies of other resources, firm production possibilities, and the

number of firms. An important element is the consideration of how

equilibration in product and factor markets is affected by programs

designed to change the supplies of resources and, in turn, how changes in

product and factor prices affect the level of output, resource employment

and income within the recipient region. Since similar investments in

heterogenous regions might have different effects on employment, dis-

similarities among regions need to be considered. These differences

could exist in the form of differino resource base or differing industrial

structure.

Planners and decision-makers need information on the effective-

ness of the small watershed and other natural reso r'ce projects in




3


fostering employment and income growth. Knowledge concerning the

relationships between natural resource investment and the other impor-

tant stimul i on changes in employment and income in a regional economy

is vital. Back [(41 has pointed out that assessment of the role of

natural resource investments in stimulating growth of a regional economy

will be a difficult task without information of this type.

Competition for the federal dollar between supporters of various

programs is very keen. Areas faced with employment and income problems

should utilize scarce resources in programs that would result in the

greatest rates of change in employment and income. Thus, information

on the effectiveness of natural resource investment programs in meeting

specified objectives is critical for future program planning. The

results of this evaluation will indicate that either small watershed

and other natural resource projects satisfy income and employment object-

ives or that program reform is necessary if objectives continue to

include income and employment goals. This research, chough conducted

for a sub-region of the Southeast, should provide answers applicable to

the entire Southeastern region. It is sufficiently broad to be indica-

tive of the national Small Watershed Program and otHer resource develop-

ment programs-


Objectives


The general objective of thi study is to evaluate the

effect iveness of ";ie Iel 4aterrshecl Program and other natural resource

investments in aceeaigepomn rwhin local recipient areas

The study include th-e Tour-szatc rec1Qn f Mississippi, Alabama, Geords.,








and Florida over the time period 1960 to 1970. More specifically, the

objectives are to:

1. Develop an economic model to explain changes in employment

and in the number of firms brought about by exogenous

shifts in the supplies of resources, demand for products,

supplies of other factors, firm production possibilities,

and shifters of the number of firms in an industry.

2. Empirically apply the model to selected industries in

order to determine the importance of changes in the above

factors on changes in employment and in the number of

farm firms.


Review of Literature


Previous studies concerned with the estimation and explanation

of the effects of investments in natural resources on employment,

income, and output are quite varied in purpose, objective and scope.

All previous work can be grouped into three basic categories consisting

of (1) case studies of individual projects and their impacts on local

areas, (2) studies proposing various procedures that could be used in

evaluating project effects, and (3) studies that attempt to determine

the effect of water resource investments over large multi-county or

multi-state areas. Some of these studies are reviewed in this section

to provide a cross section of previous work.

The first group consists of case studies of various small

watershed projects and the impact of the investment program on the

local economy and/or the sectors they were intended to benefit. Jarni.ia

and Back [53 estimated the local secondary effects of the construction







of watershed project structures for upstream flood protection in Roger

Mills County, Oklahoma. Through the use of an input-output analysis

they estimated income multipliers which were used to determine the

effect on the county's economy of increases in agricultural and

recreational income as a result of the watershed program. They found

that for each $100,000 in gross receipts to farmers in the county, there

was an estimated net (disposable) income to farmers of $26,867. This

$100,000 increase also generated $77,845 in gross receipts to other

sectors of the local economy and a net income of $16,457 to these

sectors. The local gross receipts multiplier of farm income was 1.78

and the local net income multiplier was 1.62. Net income receipts

from gross recreational receipts were about one-half those of gross

agricultural receipts. Gray and Trock [6] in an evaluation of the Green

Creek Watershed Project in Texas used traditional benefit-cost analysis

to compare the actual benefit-cost ratio derived from post-project

evaluation with the ratio estimated in the watershed work plan. They

found that the project failed to provide benefits in excess of costs

over the first eight years of the project. The ratio of benefits to

costs determined by the study was .919:1 as compared with an estimate of

1.49:1 made in the watershed work plan.

Input-output analysis was used by Kasal [7] to estimate the

local economic impacts in a four-county area as a result of five

Colorado watershed projects. Local net income arising from project

expenditures as well as benefits to the project users were estimated.

Kasal compared the original benefit-cost ratios for the projects with

those derived through the use O.: multipliers from the input-output








analysis and found that the local economic impact of all five projects
2
exceeded that estimated in the watershed work plan. Clonts is using

a similar analysis to measure the economic impact of the Cheaha Creek

Watershed on the local economy of Talledega County, Alabama. Cato

and Eddleman are evaluating the secondary impacts from the Taylor

Creek Watershed Project in a six-county area of South Florida. Work

in this study has been directed toward estimating the net increases

between the local impact area and the rest of the U. S., and among

groups within the local area. Several other studies not mentioned

were concerned mainly with benefits to primary project users, land use,

and increases in farmland values.

The second category of studies has been concerned primarily with

the introduction of suggested methodology for use in the evaluation of

water resource investments. The first of these methods as suggested by

Eidman [8] has had one empirical application. Eidman's presentation

described the linkages or interdependence of the various sectors and

subsectors of Southwestern Oklahoma with the use of a simple five-

equation economic model that employed economic base multipliers and

regression multipliers. This model was designed to explain employment

and income changes as a result of resource investments. Mazuera [9] used

the model to determine the secondary impact of using water in the Sugar

Creek Watershed floodwater prevention structures for irrigation develop-

ment and found that the project generated secondary effects amounting to




2
H. R. Clonts, personal communication.


"Work currently in progress.





7


less than a I percent change in both population and total income in the

watershed project area.

The work of Bromley et @1. [101 attempts to outline the role

of economic logic and method in analyzing the consequences of water

resource investments. Their work does not offer a concrete method

of project evaluation but rather is concerned with the many questions

raised in such an undertaking. A later study by Gibbs and Loehman [Hl]

deals with the evaluation of resource investment projects in terms of

multiple public goals. This study offers a model that might be used

to predict regional economic effects of resource investments which the

authors claim presents a more realistic view of the regional economy

than input-output or multiplier analysis.

The last category of studies has also been concerned with the

estimation of the impacts of water resource development at the local

level, but includes studies concerned with a much broader geographical

area than the local project area. Many of these studies used county

observations in various forms of econometric models to examine resource

investment effects oihile others examined regional differences in the

effects of resource investments. Haveman and Krutilla [121 looked at

both the national and regional effects of twelve types of water resource

projects with respect to their influence on various occupational and

industrial categories. Their analysis based on input-output models

constituted an effort to sort out the demands which public expenditures

for water resource developments imposed on the economy.

Water availability in relation to regional economic groWO) was

assessed by Howe L131 who determined that water deficit area~s did riot




8


were not guaranteed rapid growth. Howe's study suggested that water

resource developments are likely to be poor tools for accelerating

regional economic growth if markets, resources, and other factors

considered vital to development are lacking. Howe did not consider the

effect of water resource development on small regions.

Wiebe[14] attempted to evaluate the effectiveness of water

resource investment projects in alleviating regionally depressed

economic conditions. This study of the Tennessee River Watershed

consisting of 125 counties in parts of seven states suggested that (1)

residents in counties close to water resource investment projects enjoyed

a greater per capital income in the long run than did those living farther

away, (2) investments in water resources were in the long run associated

with increases in employment in counties removed from the project site

while nearer counties were associated with long run decreases in

employment, and (3) investments were not associated with an increase in

the level of living for people in low income and less educated groups

living near investment areas as compared to similar groups living in

areas removed from the investment site.

Another analysis by Cox et al. [15] was specifically designed to

assess broad based economic growth emanating from multipurpose projects

by the application of multiple regression analyses to many socioeconomic

indicators. Counties in the 13 Northeastern states of the United States

in which large .-:ater resource development projects had been constructed

between 1948 and 1958 were examined in 1960 to determine if changes had

occurred as a result of the projects. They concluded that there was no

relationship between project size and economic grc'-..th and that the

selection of project sites was biased toward urban areas where there is








a greater aprior likelihood of economic growth. They concluded that

it was dubious whether water resource projects served as a stimulus to

economic growth for the area studied. An index of economic growth

based on numerous income and employment variables were used to measure

economic growth.

Boxley and Harmon have recently worked on a study to determine

the relationship between Public Law 566 watershed investments and

economic growth in the Southeastern United States since 1959. Economic

growth was measured as income changes. They have attempted to use a

modified form of the shift-share analytical technique for the period

1959-1968. Tentative conclusions are that (1) there was no measurable

relationship between watershed investment and economic growth, and (2)

the selection of watershed sites for development appeared random when

measured in terms of rates and types of economic growth underway in the

study area. They have expressed limitations, however, as to the appro-

priateness of the statistical techniques used and thus offer these

conclusions in a qualified manner. They do point out that other

elements of capital infrastructure are probably necessary for economic

growth to occur.

Cato and Eddleman 5 are also concerned with the relation of

changes in income over th, last two decades to the level of investment

in natural resources for the same time period. Counties of a nine-state

region of the Southeastern United States have been delineated into

four groups on the bas i!s of the ir natural I and human resource endowments



4Robert F. Eoxley, and Marie Harmort, personal communication.







and level of economic activity. Multiple regression and correlation

analysis have been used to examine the effect of the level of natural

resource investment on changes in various income measures for the

four groups. The various types of water resource investments being

considered that are of interest to this study include water projects of

TVA, Corps of Engineers, and investments under the Small Watershed and

Flood Prevention Watershed Programs of the Soil Conservation Service.

Tentative results have indicated that with the exception of some invest-

ments by TVA and the Corps of Engineers, little effect is felt in local

income changes as a result of these water development projects.

Conflicting patterns have emerged as to the type of investment recipient

area that realizes the greatest impact.

This survey of the literature concerning the effect of water

resource investment on economic growth leads to two observations.

Either water resource investments are poor tools for stimulating economic

growth, or the methodology for measuring these effects falls far short

of accomplishing the goal for which it was designed. Many of the studies

cited have failed to consider the importance of interdependencies among

other important factors within a region which affect employment and

income changes. Changes in investment levels that shift the supplies of

critical factors, i.e., investments in water resources, often occur

concurrently with changes in the demands for products, supplies of other

resources, firm production possibilities, and shifters of the supply of

firms. Equilibration in product and factor markets is affected by

programs designed to change the supplies and/or productivity of resources

and this in turn causes changes in product and factor markets which affect

the level of employment and income within the recipient region.







A general approach that could be used in considering these
additional changes has been suggested by Tolley and Schrimper [ 16] and
Schrimper [ 17] This approach simultaneously considers aggregate and
micro adjustments in product and factor markets. Application of a
variant of the general model was performed by Schrimper [181 to deter-
mine the extent to which changes in various eognenous factors suggested

by the general model explained changes in the number of farms between
1954 and 1959 for six comparable groups of farms among states as well
as- among counties within North Crl in and. Ilio s
Eddleman and Cato [191 in a current study are using the same
variant of the general model as Schrimper to examine factors affecting
differential rates of change in the number of farms among counties in
Florida for the time period 1959-1969. Eddleman [20] has also proposed
the use of another variant of the general model to analyze the effects
ofivsmns nrsuc evlpetpogaso eina mlyet











CHAPTER II

THEORETICAL FRAMEWORK



All previous work using variants of the general model developed

by Tolley and Schrimper [16] has been concerned with measuring the rate

of change in employment or farm numbers. That is, employment and farm

number changes as well as changes in the exogenous variables were meas-

ured as percentage changes. The two-equation model developed in this

study is concerned with explaining absolute changes. The first equation

of the model explains changes in employment as a function of exogenous

changes in the prices of products, prices of factors having perfectly

elastic supplies, shifters of the supply of factors assumed to have other

than perfectly elastic supply functions for the region, shifters of firm

production possibilities, and changes in the number of firms. The second

equation of the model explains changes in the number of firms as a

function of these same exogenous variables and exogenous shifters of

firm supply functions in each industry.



Mathematical Models of Equilibration Process


Changes in the production of products and utilization of

resources in a region can be observed at several levels of aggregation

with each level providing a different insight about the impact of changes.

This dynamic process centers around three focal points. At the firm

level, product supplies and factor demands can be influenced by changes







in production possibilities or product and factor prices. The second

area concerns the aggregate effects of the micro adjustments reflected

in firms' product supplies and factor demands. Interaction of variation

in the number of firms with changes initiated at the micro or macro level

represents the third area.

Variation in product demands and factor supplies emanating from

the market level or from more disaggregated levels of specific types of

product demanders or resource suppliers can also be considered. For this

model, however, specification of the determinants of local employment and

firm number changes are under consideration and only variation at the ag-

gregate level for these two types of functions are considered as being

important to overall adjustments in a region's economy. Consequently,

product demand and factor supply functions, except for one critical fac-

tor (the nth factor), were assumed perfectly elastic.

The general regional model of adjustments consists of three basic

types of components. These are (1) product supplies and factor demands

for all firms in individual types of industries, (2) aggregate product

demand and factor supply functions, and (3) the number of firms in each

industry. Changes in any of the exogenous components can have substantial

effects on regional adjustments at all levels of aggregation because of

the relationships among the various functions. Primary causes of this

interaction are changes in the prices of products and factors which occur

at the aggregate level but still have an important impact on product out-

put and resource input decisions made by individual firms. Firm

adjustments emanating from changes at the aggregate level may result in


The complete od is specified in Appendix A.
The complete nodel is specified in Appendix A.







changes in the number of firms which lead to additional changes at the

aggregate level involving still further price adjustments. An equilib-

rium would exist when all product and factor prices and the number of

firms in the industry are consistent with their total demand and supplies.

For small areas or regions such as a county or group of counties,

the majority of product and factor prices might be realistically assumed

fixed since regional adjustments within the area would not likely have a

significant influence on the total market for these commodities. Feed-

back effects associated with adjustments would operate primarily within

factor markets since nearly all product prices, with the exception of

those products produced for local markets, would be mostly exogenous to

an individual region unless it accounted for a significant proportion of

the total national production of a commodity. Governmental price support

activities could also contribute to fixing some agricultural product

prices faced by farm firms in any given area. The probable existence of

fixed product prices in the analysis of regional adjustment or equilibra-

tion allows one to assume that the product demands and the supplies of

all but the critical factors are perfectly elastic for a region in which

firms in k different types of industries exist and produce m different

kinds of products with n-m different kinds of factors. Firms within

each of the k industry groups are assumed to have similar production

possibilities and be operated by basically the same type of entrepreneur.

The remaining part of this chapter is concerned with the discus-

sion of both changes in employment and firm numbers. First, an equation

explaining the effects of the various shifters on employment is discussed.

Then. a similar discussion of changes in firm numbers is outlined and fi-

nally, a discussion of both equations in a simultaneous context is given.








Changes in Employment

Using the assumptions discussed above, the change in demand for

labor (employment) in a g iven industry, k, cap in expressed as 2


t
(2.1) dQ E b S dX
Lk f 1 Lkn A f] f



+ d b III dp.
Lkj Lkn *j



+ d b d nki dp i
i M+l I Lki Lkn 1)

V
+ [d b d
h Lkh Lkn Zh


+ I q Lk b Lkn (71) nk d" ]k

where

b Lkn = change in quantity of lalww, demanded in the k th

industry associated with iD one-unit change ii

price of the n th factor.

A = difference in total quantity of the n th factor

demanded and supplied at z price one-unit abovc

the equilibrium price for the n th factor.

Sf = change in total quantity soopp] ied of the nth factor

associated with a one-unii change in the f th exog-

enous shifter for the n th actor supply,

2 The complete model from which equation (1.1) is derived and a
detailed treatment of the derivation and c-quMbsAtton process associated
with the exogenous shifters k presented in App**^x A. Table 15,
Appendix Agives a math-_matlcal def inition of t4-terms in the equatlon

am -







d = change in quantity of labor demanded in the kth
Lkj
industry associated with a one-unit change in
th
price of the j product.
th
d = change in quantity of the n factor demanded in
nkj
the kth industry associated with a one-unit change
.th
in price of the j product.

dLki = change in quantity of labor demanded in the kth

industry associated with a one-unit change in
.th
price of the i factor.
th
d k = difference in total quantity of the n factor
nki
supplied and demanded resulting from a one-unit

change in price of the i factor.

dLkh = change in quantity of labor demanded in the kth

industry associated with a one-unit change in the
th
h exogenous shifter of firm production

possibilities.

dnkh = change in quantity of the nth factor demanded in

the kth industry associated with a one-unit change

in the hth exogenous shifter of firm production

possibilities.

q = quantity of labor demanded by a firm in the kth
Lk
industry.

qnk = quantity of the nth factor demanded by a firm in

the kth industry.


Economic Interpretation of Employment Effects

Any discussion of the equilibration process on the demand for

labor associated with the exogenous shifters in the model must necessarily







be preceded by a discussion of the economic interpretation of the

various types of terms found in equation (2.1). Two terms appear in

each coefficient of the equation. The first of these is


b = oLk
Lkn k b-P

which represents the change in the total quantity of labor demanded in

the kth industry associated with a one-unit change in price of the nt
th
factor. Nk represents the total number of firms in the k industry,
bLk
while --- represents the change in quantity of labor demanded by a firm
Sn
in the kth industry associated with a one-unit change in price of the

n factor.

The second term is

r bq nk S
A = nk n
S1k ,P BP
k = 1 n n
th
which represents the amount by which the total demand for the n factor

would be less than the supply at a price one-unit above its equilibrium
r bqnk
level. The portion NW p represents the number of firms in the
k= k 6P
th n th
k industry times the change in the quantity of the n factor demanded

by a firm in the kth industry associated with a one-unit change in price
th n
of the n factor summed over all industries. The portion .-p- represents
th n
the total change in the quantity of the n factor supplied in the area

associated with a one-unit change in price of the th factor. The

absolute value of A (or -A) represents the increase in demand or decrease

in supply for this factor consistent with a one-unit change in price of

the factor. The negative reciprocal can then be interpreted as the ap-

proximate change in price for each unit increase in demand or decrease in

supply of the nt factor resulting from exogenous shifters in the model.







The magnitude of this reciprocal would ultimately depend on the

elasticities of the demand and supply functions involved since the elas-

ticities would determine the magnitude of the quantity change associated

with a given price change. Assuming constant elasticities within the

relevant range,(--) would represent the decrease in price for each unit

decrease in the demand or increase in the supply of this factor.

Three coefficients contain other terms that are very similar. The

terms dLkj d Lki, and dLkh represent the direct change in quantity of

labor demanded in the kth industry associated with a one-unit change in

the jh product price, i factor price, or h shifter of firm pro-

duction possibilities, respectively. Similarly, dnkj and dnkh represent

the change in quantity of the n factor demanded in the kt industry
th
associated with a one-unit change in price of the j product and in the

hth shifter of firm production possibilities, respectively. The term,
th
d ki represents the difference in total quantity of the n factor

supplied and demanded associated with a one-unit change in price of the
.th
i factor. The mathematical construction of these terms is similar to

that discussed for bLkn with the appropriate notational changes made as
L kn
shown in Table 15, Appendix A.

Interpretation of these terms becomes even more meaningful when

discussed simultaneously. For example,(- is the approximate change in
th
price of the nth factor associated with each unit change in total demand

or supply of the nth factor, and dnkj is the change in total quantity of

the nth factor demanded in the kth industry associated with a one-unit

change in price of the jth product. Their product, () dkj, represents

the total price change for the nth factor associated with a one-unit

change in price of the jth product. Final multiplication of this term by




19


b Lkn, which represents the change in quantity oF labor demanded in the k th

industry associated with a one-unit change in price of the n th factor,

gives b () d which may be interpreted as the total change in the
Lkn A nkj'
quantity of labor demanded in the k th industry resulting from a one-unit

change in the j th product price operating through the n th factor market,

This might be referred to as the indirect effect on labor demanded in the

k th industry resulting from an exogenous change in the j th product price.

The direct effect of this price term would be indicated by d Lk and would

complete the coefficient of dP.j. All other terms in each coefficient

would be interpreted in a similar manner.


Changes in Firm Numbers

Assuming only one critical factor, the change in the number of

firms in the k th industry can be expressed as3



(2.2) dN = S dX
k kn\/g f


+ +aD d]
d I kd kn B dd


+ 1akj + a kn t U dP

n-I
a .- a L, dP.
M Iki kn B

V
+ [Ck + a kn(i Mh dZh
h =


3The complete model from w,,hich equation (2.2) is dertved and a
detai -1ed treatment of the der iva ti on and equ ilIibr~im process assoc iated
w 'ith the exogenous shifters is presented in Appendix A. Table 16,
Appendix A,9i.,ies &. mathem-atica I def in it ion of the terms i n the equation.







where

akn = change in the number of firms in the k industry

associated with a change in residual returns

brought about by a one-unit change in the price
th
of the n factor.

B = excess demand for the nt factor associated with

a one-unit change in price of the nth factor.

Sf = change in total quantity supplied of the nt

factor associated with a one-unit change in the

f exogenous shifter of the n factor supplies.

Skd = change in the number of firms in the kth industry

associated with a one-unit change in the dth

exogenous shifter of firm entrepreneur supply.

Dd = change in total demand for the nth factor

associated with a one-unit change in the dth

exogenous shifter of firm entrepreneur supply.
th
akj = change in the number of firms in the k industry

associated with a change in residual returns

brought about by a one-unit change in price of

the jth product.
th
U. = change in demand for the n factor associated
J
th
with a one-unit change in price of the j product.

aki = change in the number of firms in the kth industry

associated with a change in residual returns

brought about by a one-unit change in price of

the ith factor.
the i factor.







th
L. = difference in total quantity of the n factor

that would be demanded and supplied resulting

from a one-unit change in price of the it

factor.

ckh = change in the number of firms in the kth industry

associated with a change in residual returns

brought about by a one-unit change in the hth

exogenous shifter of firm production possibilities.

Mh = change in demand for the nth factor associated

with a one-unit change in the hth exogenous

shifter of firm production possibilities.


Economic Interpretation of Firm Number Effects

Interpretation of the terms in equation (2.2) must also begin

with a discussion of those terms appearing in each coefficient and those

whose definitions are quite similar. Schrimper [18] provides a detailed

discussion of coefficients from a somewhat similar equation expressed in

terms of elasticities and percentage changes. Equation (2.2) represents

the sum of effects associated with shifters of factor supplies, shifters

of firm entrepreneur supply, product demands, factor supplies, and

shifters of firm production possibilities on the number of firms. Each

of these shifters operates through either a direct shift in the number of

firms or through changes in firm residual returns resulting indirectly

from these changes and from changes in use of the critical factor.

Two terms appear in each coefficient of the equation. The first

of these is

r kbN r ,b
a = -- qe N:' = -
ekn n ne e nP
e = 1 e e= n







as derived in Appendix A and shown in Table 16. This term represents the

change in the number of firms in the kh industry associated with change

in residual return brought about by a one-unit change in price of the

nth factor. The second term is defined as

B r 'q nk nn r o
B N k bP P E qnk kn
k = n n k = I

which represents the excess demand for the nth factor associated with a one-

unit change in price of the nth factor. The first portion of B is

identical to A as defined for equation (2.1). The second portion takes

into account some of the feedback effects on the quantity of the nt

factor demanded resulting from changes in the rnuber of firms that are

associated with a change in residual return brought about by a one-unit

price change for the nh factor. The reciprocal of this term, -) can

then be interpreted in the same manner as ( The negative reciprocal,

- ) can be interpreted as the approximate change in price of the n

factor for each unit decrease in total demand or increase in supply of

the nth factor after adjustments resulting from ,xegenous shifters in the

model.

The term Xkd represents the change in the number of firms asso-

ciated with a one-unit change in the dth shifter of firm entrepreneur

supply. Three additional terms that are very similar in nature are akj'

aki, and ckh. These terms are similar in mathematical construction and

interpretation to akn. They are interpreted as tOe change in the number

of firms associated with a change in residual return brought about by a

one-unit change in j product price, i factor price, and h shifter

of firm production possibilities, respectively. Each of these terms is

treated mathematically in Appendix A and Table 16.




23


The term D d may be interpreted as the change in demand for the n t+I

factor associated with a one-unit change in the d th shifter of firm entre-

preneur supply. Two terms that are similar to D d in that they represent

demand and supply relationship for Q n under alternative price changes are

U i and L Price changes in the j th product are considered in U The

r 0 tq nk
first part of U E N represents the change in demand for the
j, k = I k

n th factor associated with a one-un;t change in price of the j th product.

r
The second part, E q a a takes into account the feedback effects on
k = I nk kj' th
changes in the number of firms of a change in j product price as it is

felt through changes in the residual return. Both parts of this term

would have positive signs.

6S n r )qnk
The first part of L E No represents the
P i k k 6P

difference in supply and demand for the n th factor at its initial equi-

librium price after a one-unit increase in price of the i th factor,

assuming no change in firm numbers. The second part,

r 0 th
q nk a ki' takes into account the effects on demand for the n factor


resulting from changes i-n the number of firris brought about by a one-unit

change in P i as felt through a change in residual rturn. Both these

terms would tend to operate in the same -direction, The first part of L

differs from the f irst part of li i sinc-O factor suppies were assumed to

depend on possibly more than one factor price but b-- iadependent of
th ,
product prices. 'ExistIng relationship5 between the n factor supply

and changes in i th es, would requlate this movement to some

degree.







The last term, Mh, is also composed of two parts. The first

r bq
part, E N n, represents the change in quantity demanded of the
k = 1 h

nth factor associated with a one-unit change in the hth exogenous shifter

of firm production possibilities. The second part takes into account the
th
change in the number of firms as it affects the n factor demand. This

feedback effect is reflected through residual return changes resulting

from a one unit change in the hth shifter of firm production possibilities.

Changes in the hth shifter could be either output increasing and/or input

decreasing as explained and footnoted in Appendix A and Table 16.

Again, as in equation (2.1), the product of each term in the co-

efficients gives total meaning to each coefficient. For example, in

the coefficient of dXf, the product of (g) S would be interpreted as

the total price change for the nth factor associated with a one-unit

change in Xf, since Sf is the change in quantity of the nth factor sup-

plied as a result of a one-unit change in Xf and () is the n factor's

price change for each unit change in the quantity. Further multiplica-

tion by akn, which represents the change in the number of firms associated

with a change in residual return brought about by a one-unit change in

Pn, would then give the total change in the number of firms associated

with a one-unit change in Xf. The multiplicative effects of terms in

each of the other coefficients would be interpreted similarly.



Economic Interpretation of Exoqenous Changes


Changes in the demand for laborwvre expressed as a function of

changes in shifters of factor supplies, product prices, factor prices,

firm production possibilities, and the number of Firms. Changes in the








number of firms were then expressed as a function of the same shifters ot

factor supplies, product prices, factor prices, firm production possi-

bilities and shifters of firm entrepreneur supply. Each equation, (2.1)

and (2.2), was derived from the same basic model as shown in Appendix A.

Considered simultaneously, these equations then explain the changes oc-

curring in an area economy as the result of changes in the exogenous

variables. These processes are discussed separately in the following

sections.


Factor Supplies

Changes in factor supplies in each equation are represented by

dXf. All changes in factor supplies occur in the supply of the factor

assumed to be other than perfectly elastic. Equilibration resulting

from an exogenous shift in factor supplies is demonstrated graphically

in Figures 1 through 4. Figure 1 demonstrates the entire process while

Figures 2, 3, and 4 outline in more detailed form the actual changes oc-

curring in three of the five segments of Figure 1.

The effect of a change in supply of the nt factor is indicated

in Figures 1 (b) and 2 as the shift from S to S' with the resultant in-
n n
0
crease in Qn to Q' and decrease from P to P'. Shown in Figure 2 is the
n n n n
total change in quantity of the nt factor indicated by

bS 1 S
bn dXf and the total price change as indicated by i- n dX.
ff

Since (-) represents the change in P associated vith a one unit change
An
in Qn (- would be negative as indicated since Q increases and the de-
th
mand curve for the n factor is negatively sloped. This decrease in P
n
th
would then cause an increase in residual returns to firms in the k in-

dustry as reflecLed in the shift from Rk to R: in Figures 1(d) and 3.
k K








P.

Qj k




P.
J








P.





P.


eQe Q /unit
n n n time

Sk









SR
*s \^


o e unit 1 /unit
Q, Q Q Q. u N F l /
ik ik k ik time k k k k time
(c) (d)
PLk

Lk


QLk QLk QLkQLk


-Sk
SSLk



Lk
/unit
Lk time


Illustration of the equilibration process resulting
from a change in supply of the nth factor.


o e u n i t 0
jk jk j Lk jk time n


Figure 1.




27











S
n




nS









nn e


nn


q dX d
A nk kk
nb
D

D


Figure 2 Illustation ofthe equlibratin poesi h t




















He
k

k

TI k


B bX F
f


a k (- )


bS
-XF dXf
f


I1


a (k 1 n dXf

Figure 3. Illustration of the equilibration process in the firm
entrepreneur market resulting from a change in supply
of the nth factor.


S k




29














PL
L k'







PL S Lk








D) 0 D D"
Lk Lk D L k Lk


Q Q QQ Q ,un i t
L k Lk L k QLk / Lie

qi kd k m

q 6S
N Lk I n d



k jP \A nk
n

Figure 4, 1Mustration of the- equilibration process in the- Ihbor
mark-et resu It ing f rom a change- i n supply of the nt
factor.







The effect of this shift would be the movement from Nk to NI as
k k


SSbs
indicated by akn (- -- dXf and the movement from ik to Hii as in-

BS
dicated by (- B) --j dXf in Figure 3. Resulting from an increase in the
-, f

th
number of firms would be an increase in the supply of the j product by

the kth industry, Sjk to Sk with the new quantity measured as Qjk as

shown in Figure l(a). Accompanying this increase would be an increase

in demand for the i factor shown in Figure 1(c) as the shift from Dik

to Di with Qi indicating the new quantity demanded. The final initial
ik ik
result would be an increase in the demand for labor as shown by the shift

from Dk to D- in Figures l(e) and 4. This total shift comes from two
Lk Lk
sources. The first is a direct result of the shift in Xf as shown by

bq bS
S Lk 1- n dX and indicated by the movement from Qk to Qk in
k 7P A N F Lk Lk
n f

Figure 4. The remainder of the increase in labor demand comes from an

increase in the number of firms resulting from increases in residual re-

turns through lower prices of P This increase is given by qL dNk as

the movement from Q to Q- in Figure 4.
Lk Lk
Entrance of new firms to the kth industry would ultimately in-

crease the demand for the critical factor as indicated by the shift from

D to De in Figures 1(b) and 2. The resultant shift in Q' to Qe is in-
n n n n
dictated in Figure 2 by q0k dN. Resulting from this would be a bidding
nk k'
upward of Pn to Pe as shown by (- + q dNk in Figure 2. Since

represents the decrease in price for each unit decrease in demand, an
e
increase in demand, i.e., the movement from D to D would cause a
n n

Drice increase as shown. Increases in P would then result in the exit
n
of some firms from the kh industry through a decrease in the residual







return to these industries. This decrease in return is shown by the

shift from R to Re in Figures 1(d) and 3. The effect of a price in-
k e
crease through -) then causes the movement from nk to Hk as

indicated in Figure 3. A similar response in the movement from Nk to

Ne is also shown. Resultant shifts would also occur in Sk and D.
k k ik
e e
Equilibrium positions would be indicated by S.k and De with equilibrium
jk ik
quantities indicated by Q and Q in Figures 1(a) and k(c),
jk ik
respectively.

The final movement requiring discussion concerns that in the

labor market. Changes in P resulting from increases in demand for the
n
th
n factor also cause a final shift in the labor demand function as in-

dicated by the shift from DL to De in Figures 1(e) and 4. Again
Lk Lk
since -~ represents the decrease in price of the n factor associated

with decreases in demand, the price increase occurring as a result of

the increased demand from new firms as felt through (- .) would partially

affect the earlier increase in the quantity of labor demanded as in-

o LK 1o o
dicated through the term, Nk bP- ) q dNk, with equilibrium quantity
n

demanded at Qek as shown in Figure 4.

A similar analysis could be performed for each of the remaining

four exogenous shifters in the model. Each discussion would center

around the equilibration process as reflected through the appropriate

terms in equations (2.1) and (2.2). However, due to their similarities

and the complete treatment given dXf, only a brief discussion is given

for the remaining shifters in the following sections.







Number of Firm Entrepreneurs

The initial effect of an increase in an exogenous shifter of the

number of firm entrepreneurs would, of course, be an increase in the num-

ber of firms in a given industry. Consequently, the residual return to

each firm in the industry would decline as the result of both increases

in the number of Firms and increases in demand for the nt factor which

would increase its price. The quantity of the jth product produced would
.th
initially increase along with the quantities demanded of the i factor

and labor. Ultimately, price increases for the nt Factor would result

in declines in residual returns to firms and lead to fewer numbersof firms.

Quantities of the jth product produced would then decline, along with the
.th
quantity demanded of the i factor and labor. Equilibrium quantities

would be expected to remain above their initial values as the result of

the initial upward shift outweighing secondary changes due to the reduc-

tion in the number of firms. The actual quantities of factors utilized

would depend on their substitutability for the nth factor and the increase

in the number of firms. Even though the nt factor and labor might pos-
th
sibly substitute, as the price of the n factor increased, the overall

effect should be an increase in quantity demanded of all factors as

well as in the number of firms.

Product Price

Increases in product prices (upward shifts in perfectly elastic

product demands) would directly affect the residual return to firms and

cause firm numbers to increase. As firm numbers increase, the demand

for the nth factor would increase, and since its supply function is

other than perfectly elastic its price would increase. Simultaneous in-

creases would also occur in the quantities of labor and the i factor
demanded. Ultimately, as the price of the nth factor increased the
demanded. Ultimately, as the price of the n factor increased the








residual return to firms would decrease accompanied by a decrease in the

number of firms. This would cause a decrease in the quantities demanded

of labor, the i th factor, and the n th factor. Equilibrium conditions

would be expected to result in an increase in the quantity of labor de-

manded as well as in the number of firms from the initial levels befor

the product price change.


Factor Price

Changes in factor prices, representing a shift in factor supplie

assumed to be perfectly elastic, operate in an opposite manner than prod

uct price changes. As factor prices increase, the residual return to



firms. Initially the quantity of the jth product produced, quantities



,crease. These decreases would be offset somewhat by their substitut-

ability for the i th factor. As the price of the n th factor declines a

the result of smaller quantities demanded, existing firms would expei

ence increased residual returns and, thus, new firms would be enticed

to enter the industry thus increasing the demand for the n th factor, h

i th factor, and labor, as well as increasing the quantity of product

produced. Depending on the elasticity of substitution among factors n

the relative magnitudes of the various changes occurring throughout

equilibration process, equilibrium increases in the quantities of lao

and the n th factor demanded might occur simultaneously with the decrt se

in the quantities of product output, i th factor demanded, and the nume







Firm Production Possibilities

Changes in firm production possibilities which are output

increasing and/or input decreasing result in higher residual returns to

firms and thus increases in firm numbers. Entrance of new firms would

increase the output of product, quantity of both labor and the th

factor demanded and bid up the price of the nt factor through increases
th
in its demands. Increases in the n factor price would ultimately lead

to a decline in returns and cause an offsetting effect by reducing the

number of firms. This decrease would then lead to a decrease in output,
.th
and decreases in quantities demanded of the i factor and labor.

Equilibrium quantities, however, would be expected to be greater than

the initial quantities.












CHAPTER III

STUDY AREA AND MODEL SPECIFICATION



One of the major objectives of this research was to determine

the importance of natural resource investments and other types of invest-

ments in influencing employment changes in recipient areas. Particular

interest was given to investments in critical resources including water

and other forms of capital investment. For research such as this to be

applicable in other areas some level of confidence must be maintained

that knowledge acquired through research in a particular geographical

area is transferable to other areas. If there is some question as L'o

the applicability of research results among areas then the information

becomes quite limited in use. Since regions differ in geographic, in-

stitutional, sociological, and economic characteristics one cannot

conclude that natural resource investments stimulate employment in gen-

eral without some regard to these different regional characteristics.



StudyArea


The four-state region of Mississippi, Alabama, Georgia, and

Florida containing 3,75 counties was chosen as the study area. The area

was delineated into togroups of homogenous subareas. Counties in the

four states were classified into two groups on the basis of a set of ten

variables depicting the county's human and natural resource endow'ments,

and its urban, industrlil, and agricultural structure. These ten







variables were 1960 measures of (1) population, (2) urban population,

(3) percent of persons 25 years old and over with a high school education,

(4) median age, (5) total employment, (6) total agricultural employment,

(7) total manufacturing employment, (8) land area, (9) land in farms, and

(10) value of farm products sold.

Discriminant analysis was used in this delineation. Counties were

grouped initially into two groups. A linear function of the differences

of the means between the two groups was found which discriminated most

successfully between the two groups. A general mean was then derived by

substituting the means of all variables into the function. The function

was then used to derive a mean for each county using county observations

on each variable. Counties having values above the general mean were

placed in one group and those having means below the general mean were

placed in the second group. The process was repeated until the number of

misclassified counties was minimal. Computational procedures of the tech-

nique are outlined b/ Martin [21]. Additional discussion of the discrim-

inant analysis technique is also provided by Tintner [22, pp. 96-102].

Several other variables were used with the above ten in grouping the

counties, but their relative lack of importance in the discriminant func-

tion excluded them from consideration in the final delineation process.

The most important variables in the delineation process were median age,

education level, land area, agricultural employment, and total employment.

Characteristics of the two groups were as expected. For example, the ur-

ban counties had higher average educational levels and higher average

total employment. The nonurban group had higher average agricultural

employment levels.

Some judgement was warranted as to the meaningfulness of the de-

lineations by persons familiar with the four-state region. Members of







the Southern Land Economics Research Committee from each of the four

states were asked to evaluate the initial classifications for their

state. These evaluations were used to adjust the mathematical delinea-

tions and resulted in the final grouping shown in Figure 5. About

one-fourth of the counties (91) represent the more urban-oriented group

while the remaining counties (284) exhibit a more rural orientation.

Analyses were carried out for three groupings of counties. All

counties in the four-state region constituted one group. The urban

counties and nonurban counties formed the remaining two groups. Effects

of similar investments in human, natural, and capital resources in these

dissimilar areas should provide results that would be expected in other

areas. For example, information on the effects of investments in urban-

oriented versus the rural-oriented areas could provide guidelines on

what types of investments should stimulate employment in the same types

of areas in other regions of the country.



Selection of Employment Categories


Some categorization of employment is necessary to insure a

meaningful analysis. Employment is reported on the basis of either oc-

cupational or industrial classifications. Occupational categories

include such classifications as the various types of laborers, crafts-

men, and professional workers, while the industrial classification

distinguishes among the various industries such as agriculture, construc-

tion, textile products, and metals. The various types of investment in


This committee consists of representatives from eleven southern
land-grant universities, several federal agencies, and is supported in
part by the Farm Foundation, Chicago, Illinois.



















































a,













n


0
1-
%- %-
O



En n n


4rJ L










0 0 -


ct
U U UP
a)






a, a O
Ci-


0 0
U-











L.1




3L 3
U U-In







human, natural, and capital resources could affect employment in each

occupational or industry category in a different way. Industrial classi-

fication lends itself to a more meaningful analysis from the standpoint

of the theoretical framework outlined in Chapter II. Also secondary data

on industrial classification are more readily available. The industrial

classification was, therefore, used to distinguish among employment cate-

gories in the analysis.

Industry selection was made primarily according to the number of

employees. Agriculture, construction, five individual manufacturing in-

dustries, and durable and nondurable manufacturing were selected for

analysis (Table 1). These industries are likely candidates for growth-

generating activities with growth in the remaining industries being

dependent on them. For this reason, and since data of the nature needed

for this study are not readily available for the more service-oriented

industries, the service industries such as wholesale and retail trade,

finances, and communications were not included in the analysis. Also,

the initial employment effects of investments in natural resources would

most likely be felt in the industries selected.

Industries three through seven accounted for approximately 57

percent (762,098 employees) of all manufacturing employment in the four-

state region in 1967 [23, pp. 1.7-1.11, 10.7-10.11, 11.9-11.13, 25.6-25.9].

The importance of construction and agriculture is shown in Table 1 where

these industries rank one (460,771 employees) and three (286,528 em-

ployees), respectively, when compared to employment in the individual

manufacturing industries [24, Table 54]. Employment data for construction

and agriculture were for 1969.






Table 1. Industry identification and employment
four-state area (1967)


rankings for the


Standard Total
Industry industrial four-
identification Industry classifica- state
for this tion code employment
study (SIC) rankb

SAgriculture 15-17 3

2 Construction 01, 07-09

3 Textile mill products and
other fabricated textile
products manufacturing 22, 23 2

4 Food and kindred products
manufacturing 20 4

5 Transportation equipment
manufacturing 37 5

6 Furniture, lumber, and wood
products manufacturing 24, 25 6

7 Electrical equipment
manufacturing 36 7

D Durable products
manufacturing 24-26, 32-34,
36, 37

ND Nondurable products
manufacturing 20, 22, 23, 28

Several industries were grouped together to make data from the
U.S. Census of Population and the U.S. Census of Manufactures comparable
for later uses in the study.

Calculated from: U.S. Bureau of the Census, Census of
Manufactures, Area Statistics: 1967 (Washington, U.S. Government
Printing Office), Vol. III, Part I, pp. 1.7-1.11, 10.7-10.11, 11.9-11.13,
25.6-25.9 and Census of Population: 1970 (Washington, U.S. Government
Printing Office), Vol. I, Parts 2, 11, 12, and 26, Table 54.







Water usage of each industry was also examined since two of the

natural resource investment programs included in the study are water

oriented. Water use data for construction and agriculture are not avail-

able. Agriculture should benefit from drainage, flood control and an

increased irrigation water supply. Analysis of national rank in water
2
use for manufacturing industries indicated that some of the largest

water using industries have not been included in the analysis. The pe-

troleum and coal industry is the third largest industrial water use in

the U.S. However, this industry provided only .3 percent of the total

four-state employment and thus was not included. Manufacture of stone,

clay,and glass products, nonelectrical machinery, and rubber and plastics

products accounted for only 5.5 percent of total four-state employment.

Additionally, these industries ranked low in total U.S. water use. Al-

though the stone, clay, and glass industry provides products required in

building water control structures, the combination of low employment and

inadequate county data provided sufficient basis for excluding these in-

dustries. Inadequate county data also resulted in the exclusion of both

primary and fabricated metal products, paper.and allied products, and

chemicals and allied products, although chemicals and fabricated metals

manufacturing rank one and two nationally in water use.

The five individual manufacturing industries included in the

analysis ranged from fifth to twelfth among the rankings for all indus-

tries in national water use. Water investment projects of the Soil

Conservation Service included in this study do not influence major in-

dustrial users of water. However, certain projects carried out by the



National water use data are available in the Census of
Manufactures [25, Vol. 1, pp. 7.16-7.17].






Corps of Engineers could influence the location and expansion of these

industries. Water use by these industries is important in assessing

employment changes due to investments in water resource programs.



General Model Specification


Economic interpretation of changes in the exogenous shifters in-

volved in equations (2.1) and (2.2) in the previous chapter made it

apparent that interaction occurs in both equations simultaneously.. Esti-

mation of the effects of exogenous changes on employment and firm

numbers could be considered using a system of equations. Figure I rep-

resents the simultaneous changes occurring as the result of a change in

resource supplies. Total interaction as the result of all changes in

the exogenous variables can be represented for each industry by a system

of equations. The availability of n county observations for each in-

dustry gives the following general system for the kth industry.


(3.1) dQLkt = 10 + PlldXft + 12dPkt + +13 ikt 14d hkt


+ lldNkt + Ulkt t = 1, 2, . ., n



(3.2) dNkt = 20 + 21dXft + 22dPkt + 23dPikt + dZhkt


+ 25dWdkt + U2kt t = 1, 2, . ., n

where the subscript t represents county observations, and

dQLkt = total change in the quantity of labor demanded

in the kth industry endogenouss).
th th
dXft = total change in the f shifter of the n

factor supply (exogenous).







dP. = total change in product demands in the kt
j kt
industry (exogenous).

dPikt = total change in factor supplies in the kth
ikt
industry for all factors other than the nt

factor (exogenous).

dZh = total change in firm production possibilities
hkt
for firms in the kth industry (exogenous).

dN = total change in the number of firms in the kt
kt
industry endogenouss).

dWdkt = total change in shifters of firm entrepreneur

supply for firms in the kth industry (exogenous).

The B coefficients and the parameters of the distribution are un-

known which leaves the problem of obtaining estimates of these parameters.

By rearranging equations (3.1) and (3.2) as


(3.3) -dQLkt + ylldNkt + ,0 + PlldXft + 1 dP + 3 dPkt


14dZhkt = Ulkt


(3.4) -dNkt + 20 + PdXft + 22dP.kt + 23dP.ik + 4dZhkt


+ 25dWdkt = U2kt


Estimates derived using the following model are consistent and
asymptotically efficient if the following assumptions are made:

E [(kt)] =


E[U(kt) U(kt+s)] if s
t U t = otherwise

E X(kt) U(kt 0







they can conveniently be written in matrix notation as


(3.5) -1 YIl dQLkt 010 oil 3 12 $13 314 0

0 -kt 20 21 [22 :23 24 25



SdXf dPjkt ikt hkt dkt
-U
U 2kt

and finally condensed to


(3.6) rY(kt) + X(kt) = U(kt)

where


r= D -_(kt) = dN



B o10 11 12 313 14 0

L20 21 B22 F23 e24 H25



X(kt)= dXft dPjkt dPikt dZhkt dWdk1


Ikkt
U(kt) =


The subscript k indicates that this particular system is for the

k industry. Each industry under study would be represented by an equa-

tion of this general form. Equation (3.6) presents the simultaneous

linear equation model in its structural form. Each of these sources pro-

videsa detailed discussion of simultaneous equation models, their

assumptions, limitations, and possible problems which might arise in

their application.







Structural Estimation

It is necessary that an equation in a set of simultaneous

equations be just or over-identified before estimates of the parameters

can be obtained. The order condition for identification can be used to

determine whether a given equation is identified. If A is equal to the

number of predetermined (exogenous) variables that do not appear in an

equation and B refers to the number of endogenous variables in the equa-

tion, then the following conditions determine the identification of the

equa t ion.

A = B 1 just identified

A > B 1 over identified

A < B 1 under identified


Reduced Form Estimation

The complete structural system may be written so that each endog-

enous variable is expressed as a function of all exogenous variables

appearing in the system. This representation of the system is referred

to as the reduced form and brings out the explicit dependence of the de-

pendent variables on the predetermined variables and the disturbances.

Premultiplication of equation (3.6) by F-1 and rearrangement gives

-1 -1
(37) Ykt= X(kt) + U(kt)


or (3.8) Ykt = nx(kt) + v(kt)


where -r1 I
10 11 . 15
-1
n =- r'P=

20 fl21 . 25

'Goldberger L26, pp, 352-372] and Johnston [27, pp. 241-252]
provide detailed discussions of the identification problem.







V1 V
-Ikt
V(kt) U (kt) V2kt
2kt

Estimates from the reduced form may be derived directly by

ordinary least squares since their disturbances are linear combinations

of the structural disturbances.5 However, in general practice the struc-

tural parameters are estimated first and then the reduced form parameter
-l
estimates are obtained by use of i = -Ir P.



Individual Industry Models


A two-equation system was specified for agriculture according to

the theoretical framework outlined in equations (2.1) and (2.2), and the

general estimation model outlined in equations (3.1) and (3.2). Single

equation models were specified for construction and the various manu-

facturing industries. These models are presented below with each

variable coded similarly to equations (3.1) and (3.2). That is, changes

in factor supplies are represented by X, changes in shifters of firm

supply by W, changes in product demands by PP, changes in factor prices

by FP, and changes in firm production possibilities by Z. Data sources

for each variable are given in the latter sections of this chapter and

the mathematical derivation is given in Appendix B.

5The assumptions for the reduced form disturbances are

E [V(kt)] = E [U(kt = 0

E/ V E 1 -1 =F for
E (kt) (kt) (kt) (kt)
t = t
= G otherwise
r [(kt v (k) = o
(kt) (kt)






Agriculture

The system of equations representing the agricultural industry is
6
(3.9.1.1) Eli = l + rl Xri + 711PP li + 811FPli


+ l911 li Z + 10, 11GRPi + ,11N i + Illi


6
(3.9.1.2) N; = 3012 + 1 X 7PPi + 2FP
r = 1

+ 912 li+ 10,12GRPi + 1,12 li + 1 i 1 22WE i


+ 13,12WAli + 112i

where the first subscript is the parameter number, the second

subscript is the industry number, the third subscript is the

equation number where

Eli = Change in agricultural employment for the period

.th
1960-1970 in the ith county.

Xli = Change in federal and state expenditures per pupil for

primary and secondary education during the period 1960
.th
to 1970 in the i county.

X2i = Change in total construction expenditures in water

development projects by the Corps of Engineers during
.th
the period 1960 to 1970 in the i county.

X3i = Change in total construction expenditures in the PL-566

Small Watershed Program by the Soil Conservation Service
th
during the period 1960 to 1970 in the i county.

X4i = Change in total investment in the Agricultural Conserva-

tion Program (renamed the Rural Environmental Assistance







Program in 1971) by the Agricultural Stabilization and

Conservation Service during the period 1960 to 1970 in
.th
the i county.

X5i = Change in total loans and grants for community water and

sewer systems and waste disposal systems made by the

Farmers Home Administration during the period 1960 to
.th
1970 in the h county.

X6i = Change in acreage of allotment crops due to reduction in

allotments between 1959 and 1969 weighted b/ the propor-

tion of the total value of the allotment crop to total
.th
value of crops and livestock in the i county in 1959.

PPIi = Change in price index of agricultural commodity groups

during the period 1959-61 to 1969-71 weighted by the

proportion of the value of the commodity group to the
.th
total value of crops and livestock in the i county in

1959.

FP = Change in the average annual wage per hired farm worker
.th
during the period 1959 to 1969 in the i count/.

Zli = Change in the Southeast index of agricultural output per

man-hour for corrmodity groups during the period 1959-61

to 1969-71 weighted b/ the proportion of the value of the

commodity/ group to total value of crops and livestock in
.th
the th county in 1959.

GRP. = Intercept shifter dummy variable

ith GRP. = I when urban-oriented county
Sw0 when rural-oriented county

N i = Change in the number of farms during the period 1959 to
1969 for the ith county
1969 for the county.







WW1i = Change in total annual nonagricultural wage payments

during the period 1960 to 1970 per agricultural
th
employee in 1960 for the i county.

WEli = Change in total nonagricultural employment during the

period 1960 to 1970 per agricultural employee in 1960
th
for the i county.

WAli = Change in the number of farm operators who were 55 or

more years of age during the period 1959 to 1969 in
.th
the i county.

U ll U i = Disturbance terms.
111i 1121
The Greek letters B and y represent the parameters to be estimated.

Variables endogenous to the system are Eli and N i. Equation (3.9.1.1)

is over-identified and equation (3.9.1.2) is just-identified.


Construction

Data availability on the construction industry precluded the

calculation of changes in the product price and technology variables.

Data on firm number changes also were inadequate. However, since the

construction industry would be one of the more important in evaluating

the primary employment effects of investments in natural resources a

single equation model was formulated in this industry. The equation for

the construction industry is

5
(3.9.2.1) E2 = 02 + X FP + 72GRPi
2r r2 ri 62FPi 72

+ 82"'+12 i + 92Ei + 2i

where

E 2 = Chanye 'n construction employment for the period 1960

to 1970 in the ith count%,.







Xli to X5i = Same as in equation (3.9.1.1).

FP2i = Change in average annual wages per construction

employee during the period 1958 to 1967 for the
.th
I county.

GRP. = Same as in equation (3.9.1.1).

WW2i = Change in total annual wage payments during the period

1960 to 1970 for all nonagricultural and nonconstruction
.th
employees per construction employee in 1960 for the i

county.

WE2i = Change in total nonagricultural and nonconstruction

employment during the period 1960 to 1970 per con-
.th
struction employee in 1960 for the i county.

U l2 = Disturbance terms.


Manufacturing

The remaining seven industries are manufacturing industries. A

two-equation model did not yield results comparable to those obtained

for agriculture. The number of manufacturing firms is much smaller and

the size of firms (measured in terms of the number of employees) is

generally larger than for the agricultural industry. Estimation of

changes in the number of manufacturing firms did not add to the interpre-

tive and explanatory power of the system of equations. Much of the

impact of changes in the exogenous variables for manufacturing industries

is transmitted through employment changes within existing firms rather

than change in the number of firms. Therefore, changes in the number of

firms in each manufacturing industry was treated as an exogenous variable

and a single-equation model was specified for each manufacturing industry.

This model is of the form







0 9.k.1) Eki Ok + rk Xri + 6k PPki +57k FPki
r = 1

+ 8kZk.+ GRP. + a W.+B W
kk 9k i lO~k'M + 11,kk ki


+ $12,k 14ki + ki

k = 3, 4, ,7, Do ND

where

E ki = Change in k th industry employment for the period 1960

to 1970 in the i th county.

X li to X 5i = Same as in equation (3.9.1.1).

PP ki = Change in price index for each SIC three-digit level

industry commodity group in the k th industry during

the period 1959-61 to 1969-71 weighted by the proportion

of value added by the coqimodity group to total value

added by the commodity group to total value added in

the k th industry in 1958 for the i th county.

FP ki =Change in average annual wages per production worker

for each SIC three-digit level industry group in the

k th industry during the period 1958 to 1567 weighted

by the proportion of production 'worker employment in

each Subgroup to total production worker employment in

the k th industry for the 1 th county.

Z ki =Change in the index of output per man-hour for each StC

three-digit level industry group in the k th industry

during the period 1959-61 to 1969-71 weighted by the

proportion of value added by the commodity group to

total value added in the k th industry for the it







GRP. = Same as in equation (3.9.1.1).

WWmi = Change in total annual nonagricultural and non-kth in-

dustry wage payments during the period 1960 to 1970 per
th th
k industry employee in 1960 for the i county.

WEki = Change in total nonagricultural and non-kth industry

employment during the period 1960 to 1970 per kth in-

dustry employee in 1960 for the i county.

Nki = Change in the number of firms in the kth industry during
th
the period 1959 to 1969 for the i county.

U ki = Disturbance term.

The symbols 0 and ,, represent the parameters to be estimated.



Model Estimation Procedure


Two-stage least squares was used to estimate the structural

parameters of equations having the form of (3.9.1.1) in the two-equation

system for agriculture. Ordinary least squares was used to estimate

equations having the form of equation (3.9.2.1) in each of the uses of

the two-equation models. This statistical procedure was also used for

all single-equation models. Estimates of the reduced form coefficients

for the two-equation models were derived from the structural parameter

estimates.








A computer program written by William James Raduchel [28] was used.

7Ibid.








Measurement of Variables and
Empirical Expectations


Changes in employment and firm numbers as defined in equations

(3.9.1.1) and (3.9.1.2) were considered as endogenous variables. In the

model that forms a system of equations, the endogenous variables are con-

sidered functions of some or all predetermined (exogenous) variables.

In the first equation employment changes were also considered as a

function of the endogenous variable for firm number changes. Predeter-

mined variables represent changes in exogenous shifters of product

demand, factor price, critical resource supply, firm production possibil-

ities or firm entrepreneur supply functions. Each of these general types

of shifters is represented by one or more variables in each equation.

Each variable, the type of shifter it represents, and the expected ef-

fects of changes in these variables on agricultural employment and the

number of farms are given in Table 2. A similar illustration of the ef-

fects on construction and manufacturing employment is given in Table 3.

Detailed discussion of each variable follows in the remaining sections

of this chapter.


Employment

Changes in employment for each county were computed for the time

period 1960 to 1970 as reported in the 1960 Census of Population [29,

Table 85] and the 1970 Census of Population [24, Table 123]. Employment

is reported in this source using basically the same industry categories

as suggested by the Standard Industrial Classification (SIC) of industries.

It was necessary to combine employment reported in some industries to con-

form to the industry classification shown in Table 1. Changes in

employment were used as dependent variables.














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A







Firm Numbers

Changes in the number of manufacturing firms for the period

1958 to 1967 were obtained from data reported in the 1958 Census of

Manufactures [30, State Table 7] and the 1967 Census of Manufactures

[23, State Table 9]. Firm numbers are reported for each two-digit SIC

industry in each county. Some industries were combined to conform to

the classification of industries used in this study.

Changes in the number of farms from 1959 to 1969 for each county

were obtained from the 1959 Census of Agriculture [31, County Table l]

and the 1969 Census of Agriculture [32, County Table 1]. Changes in the

number of farm firms were used as both predetermined and endogenous

variables. This distinction is discussed in a later section.


Factor Supplies

Changes in the supply of critical factors in a county should in-

fluence that county's labor employment. Investments that increase the

supply of a given factor would be expected to cause the price of the

factor to decline initially. A price decline would entice users to sub-

stitute more of the factor for other production inputs including labor.

With perfectly elastic product demands and a reduced price for the

critical factor, residual returns to firm operators should increase. In

the absence of any substantial barriers to entry of new firms into the

industry, new firms would be established, and this would increase in-

dustry output. Entrance of new firms would result in an upward shift in

the demand for all factors, including labor, causing the prices of those

factors having upward sloping supply functions to rise. Existing firms

would also expand output. Residual returns to firm operators would sub-

sequently fall, resulting in a cutback in factor employment. At the new







equilibrium, the quantity of labor employed would be greater or less

than the initial quantity, depending on the relative sizes of the demand

and supply elasticities as pointed out in the theory section. It would

also depend on the elasticity of substitution of labor for the other

factors whose prices varied. Labor could probably not be easily sub-

stituted for many of the natural resources considered in this analysis.

Therefore, investment programs to increase the supplies of these natural

resources should also increase the amount of labor required to complement

industry expansion resulting from either the initial project construction

phase or from users of the project.


Education investments (X1).--Federal and state expenditures per

pupil for education were considered to be exogenous to a county. Changes

in these expenditures over the period 1959-1960 to 1969-1970 were in-

cluded as a measure of exogenous shifts in the investment in a county's

human resources. Expenditure estimates were obtained from state educa-

tion agencies in Alabama [33, 34], Mississippi [35, 36], and Georgia [37,

38], and the Florida Statistical Abstract [39].

Increases in education expenditures should partially reflect an

increase in the number of persons in the recipient county attaining a

given educational level as well as an increase in the average productivity

level of the labor force. Unless outmigration from the counties of

people receiving the education occurs, an upgraded labor force should

attract potential employers and eventually result in increased employment

within the recipient counties.

The effect of increases in education levels or agricultural

employment and farm numbers should be opposite their effect on construction






and manufacturing employment. Since agricultural labor draws heavily

from the unskilled labor force it seems likely that increased educational

opportunities would reduce this labor force and lead to outmigration from

the more rural counties to more attractive job alternatives in urban areas.

This would lead to fewer agricultural workers and probable consolidation

of farms to gain operational efficiencies. Increased educational oppor-

tunity should, therefore, yield negative coefficients for agricultural

employment and farm numbers and positive coefficients for construction

and manufacturing employment as shown in Tables 2 and 3.


Corps of Engineers' natural resource investments (X ).--For this
2-
variable as well as the other types of natural resource projects, total

project expenditures by county over the period 1960 to 1970 were used as

the independent variable. Interpretation of the estimated coefficients

for these investment variables should provide insights into two components

of the analysis. First, the empirical significance of the various types

of natural resource investments on local employment and firm numbers can

be shown, and second, the relative importance of the various natural re-

source investment categories in influencing employment and firm numbers

can be appraised.

Investments by the Corps of Engineers in civil works and new

work construction were obtained For each county from the various district
8
offices which administer portions of the four-state area. Investments


Corps of Engineer personnel providing data through personal
communications were:

J. W. Dement, Chief, Engineering Division, Memphis
District, U.S. Army Corps of Engineers, Memphis,
Tennessee.
W. T. Moore, Chief, Engineering Division, Savannah









projects categorized into multipurpose, navigation, flood control, beach

control, and recreation projects. The major portion of expenditures was

for-flood control and navigation with a very small portion allocated to

beach control and recreation. Due to the large amount of the invest-

ments going into flood control and navigation projects, no distinction

among the above investment categories was made. Some expenditures by

the Corps for construction projects along the Mississippi River could not

be allocated to counties. Therefore, these investments were not in-

cluded in the analysis. Investments occurred in 148 of the 375 counties

comprising the four-state area.

Investments by the Corps of Engineers should also have con-

trasting effects on agricultural and manufacturing employment. Improved

flood control would be beneficial to agricultural areas by making more

,land available for use. This would bring about a two-fold reaction.

Both expansion of existing farms and the entrance of new Farms would

occur with the probable result being decreased residual returns to each

firm as the price of land is bid upward. The probable consequence would


District, U.S. Army Corps of Engineers, Savannah,
Georgia.
Powell Williams, Jr., As~st. Chief, Engineering Division,
Mobile District, U.S. Army Corps otF Engineers,
Mobile, Alabama.
George Marsh, Acting Chief, Engineering Division,
Jacksonville District, U.S. Army Corps of Enigineers,
Jacksonville, Florida,
J. L. Smith, Chief, Construction Division, New Orleans
District, U.S. Army Corps of Engineers, New
Orleans, Louisiana.
K. E. McLaughlin, Comptroller, Vicksburg District, U.S.
Army Corps of Engineers, Vicksburg, Mississippi.
F. P. Gaines, Chief, Engineering Divi lon, Nashville







be further expansion of the larger more established farms with the

overall effect being a reduction in farm numbers. It follows that the

larger farms might also operate with a smaller total labor force though a

more efficient operation realized as the result of the larger farm size.

The consequence would be reductions in farm numbers and agricultural em-

ployment as indicated by the coefficient sign in Table 2.

In contrast to the effect on agriculture, construction and manu-

facturing employment would likely increase as the result of Corps of

Engineers' investments. Employment would certainly increase in the re-

cipient area during the initial construction phase of the project.

Initial effects might also be felt in manufacturing provided that local

area materials were used. More importantly for manufacturing, however,

would be the effect occurring during the life of any project. Improved

transportation facilities, protection from flood damage, etc., would en-

courage the entrance of new firms and resultant employment increases.

Since firm consolidation in manufacturing does not occur as readily as in

agriculture, the indirect effect of decreases in firm numbers and employ-

ment is probably not large enough to offset the initial positive gains in

the recipient area. A positive coefficient for construction and manfac-

turing employment would be expected as indicated in Table 3.


Soil Conservation Service PL-566 investments (X ).--Construction
3-
expenditures by county from 1960 to 1970 for the Small Watershed Program

were obtained from personnel in each of the four-state offices of the

Soil Conservation Service. Data were tabulated from 239-B forms which


9Soil Conservation Service data were provided through personal
communications from:







gave actual dates of construction expenditures for each project.

Investments were then allocated to each county based on project location

as identified on maps prepared by the Soil Conservation Service. A total

of 111 counties received these types of investments during the study

period. Investments were measured in thousands of dollars.

The Small Watershed Program is designed to aid in the solution

of several types of problems. Of major importance among these is the re-

duction in floodwater damages to cropland, residences, businesses, and

protection of the health and lives of people from floods. Other poten-

tial and existing problems that this program attempts to alleviate

include erosion and sediment damage, improper drainage, and irrigation

needs. Recreation, fish and wildlife enhancement, and improvements in

the economic and social well-being of people have also received atten-

tion. These latter categories have been given increased emphasis in

recent years. PL-566 investments by the SCS which result in improve-

ments for the local recipient areas should provide conditions that

affect agricultural and manufacturing employment and firm numbers within

the local areas in a manner quite similar to that of Corps of Engineers'

investments. Reduction of floodwater damage to cropland should in

total reduce the number of farms and agricultural employment as indicated

in Table 2. Although some new farms might become established




Barbara Kennedy, Accounting Technician, Soil
Conservation Service State Office, Auburn,
Alabama.
Robert Salsman, Financial Manager, Soil Conserva-
tion Service State Office, Jackson, Mississippi.
George Adair, Accounting Technician, Soil Conserva-
tion Service State Office, Athens, Georgia.
Gertrude Griffin, Accounting Technician, Soil
Conservation Service State Office, Gainesville,
Florida.
I







the consolidation effect into larger farms to take advantage of

improvements made possible by the PL-566 project should be greater.

Construction employment should increase in the recipient area

during both the initial and secondary project phases and ultimately as a

result of the project in a manner similar to that discussed for Corps of

Engineers' investments. Also to be expected is an increase in manufac-

turing employment as indicated in Table 3. Increased output resulting

from project expenditures should provide a base for more manufacturing

employment in conjunction with increased enhancement for manufacturing

firm location resulting from the reduction in floodwater damages to

residences, businesses and through the effect of other firm location

attributes improved by the investment project.


Agricultural Stabilization and Conservation Service ACP

investments (X)..--Investments by the Agricultural Stabilization and

Conservation Service constitute a joint effort by the public sector,

farmers, and ranchers to share the cost of establishing needed conserva-

tion measures. These conservation programs include practices to

protect, improve, and renew soil, water, woodland, and wildlife resources

of private landowners. Data for the analysis were obtained from annual

state ASCS reports during 1960 to 1970 for Alabama [40], Mississippi

[41], and Florida [42]. Expenditure information included cash payments

to farmers and allowances paid to vendors for conservation materials

furnished farmers. Data for Georgia were taken directly from computer

printouts.0 A total of 374 counties had participants in the ACP



10Personal communication from the Data Division, Agricultural
Stabilization and Conservation Seivice, U.S. Department of Agriculture,
Washington, D.C.







Program during the study period. Investments were measured in thousands

of dollars.

Conservation measures which make land more available could also

influence the expansion of existing farms as well as encourage new farms.

The trend historically has been toward larger firms. Since this is a

cost-sharing program it seems logical to expect the larger farmers to

take advantage of this program opportunity and expand operations even

more. The indirect effect of entrance of new farms should be more than

offset by the consolidation of existing farms leading to a decrease in

total agricultural employment and farm numbers. Conservation measures

that remove land from production would provide a similar circumstance.

This negative overall effect is indicated in Table 2.

Since this type program requires some construction activity and

manufactured input which usually are purchased locally, a positive

effect on construction and manufacturing industry employment would be

expected as indicated in Table 3. Increased output would also be ex-

pected to result from the application of conservation measures leading

to a need for more processing and support facilities which in turn

should have some positive effect on manufacturing employment. Any

negative feedback effect on manufacturing employment should not be large

enough to affect the initial positive effect.


Farmers Home Administration investments (X) .--Loans and grants

for community water, sanitary sewer, arid solid waste disposal systems

were also considered to be investments that would influence employment

and farm numbers in each county as indicated in Tables 2 and 3. This

program provides financial assistance to communities in developing es-

sential new public service facilities and in expanding existing







facilities. Data for these investment loans in thousands of dollars were

obtained from the various state directors of the Farmers Home Administra-

tion.1 A total of 278 counties received financial assistance from FHA

during the study period.

Services and facilities provided by this type program are neces-

sary before a community can expand with regard to attracting new industry

and in turn services to support these industries. Communities demon-

strating adequate services will likely attract new industry and thus

expand employment in construction and manufacturing industries. Expan-

sion of existing firms in the community might also occur, and this

further supports the positive employment coefficient demonstrated in

Table 3. This program does not specifically influence a production in-

put used in agriculture such as land or water in the same manner as the

four earlier programs. A similar negative effect on agricultural employ-

ment and farm numbers as discussed for the earlier programs would be

expected. As community facilities become available and the community

begins to develop its manufacturing base, job alternatives for agri-

cultural employees and farm operators become more available. Smaller

farms are soon consolidated with the displaced operators assuming other

types of employment. Fewer employees are then required because of more

efficient operations and the negative effect occurs.


Crop allotment (XI).--Changes in crop allotments represent the

effect of shifts in a perfectly inelastic factor supply on the number of



State Directors, Farmers Home Administration, providing data
through personal communication were: S. B. Wise, Jackson, Mississippi;
John N. McDuffie, Atlanta, Georgia; John A. Garrett, Montgomery, Alabama;
and William Shaddick, Gainesville, Florida.









would beepced to increase the market price ofteallotment, or of

land, leading to lower residual returns to farm operators and ultimately

to a reduction in the number of farm firms. As the number of farms de-

cline aggregate demand for allotments would decline and thus lower their

market prices. The magnitude of changes in the number of farm firms and

consequently in agricultural employment due to a decrease in allotments

would depend on farm operators' responsiveness to changes in their

residual returns, the amount of allotments used in the production

process, and the actual level of operator returns.

Reduction s in acreage allotments between 1959 and 1969 for all

allotted crops were computed for all counties having acreages of these

crops. Annual reports for 1959 and 1969 from the Agricultural Stabiliza-

tion and Conservation Service in Alabama [401, Mississippi [411, Georgia

[433 and Florida [421 provide data on allotted crop acreages. County

reductions were weighted according to total value of sales of each

crop as a proportion of total value of crop and livestock sales in the

county in 1959 as derived from data available in the 1959 Census of

Agriculture [311. Declines in harvested acres in each county were also

computed using the same data sources that provided information on al lot-

merit reductions. The smaller of these two changes was then selected as

the effective cut in allotments. Allotment reductions w,ere not con-

sidered relevant for a county if its harvesting acreage in 10,59 was less

than the county's acreage allotment for the selected crop in 1969.
Posiivecoeficent ,oul beexpcte as how inTabe 2







Product Demand

Use of a product price as an indicator of product demand is

based on the assumption of perfectly elastic demand functions at the

county level. Producers in both agricultural and manufacturing in-

dustries at the county level are assumed to be price takers and thus

face perfectly elastic demand functions. An increase in product price

would initially increase residual returns to firm entrepreneurs. This

would have the effect of enticing new firms into the industry and

ultimately an increase in the quantity of resources employed in the pro-

duction process including labor. Also, existing firms would expand

output and hence increase their demands for production factors. In-

creases in demand for factors with upward sloping supply functions would

lead to increased factor prices and reduced returns to firm entrepreneurs.

Consequently, firm numbers would decline and this would result in a re-

duction in labor employment. Existing Firms would also reduce their out-

put and cause reductions in resource demands. The net change in labor

employment would depend on the relative magnitude of both the initial

and indirect effects of these changes in output of existing firms and in

the number of firms. A product price variable was not included for

the construction industry since output is not easily defined in terms of

a product with an established market price.


Agricultural product price (PPl).--Changes in price indexes were

computed for each of the seven major agricultural commodity groups pro-

duced in the study area using three year averages centered on 1959 price

indexes [44] and 1969 price indexes [45]. These changes were weighted

by the 1959 value of each commodity group as a proportion of the total




67


value of crops and livestock produced in each county. The resulting

measure was a weighted change in product prices faced by farm producers

at the county level. Value of products sold was obtained from the 1959

Census of Agriculture 131, County Table 51. A prior! specification of

the net result of increases in agricultural product prices on employment

is difficult. It is quite possible that increases in Agricultural

product prices could lead to a reduction in agricultural employment and

farm numbers due to farm consolidation. Since some agricultural opera-

tions do allow fairly easy entry, the opposite effect could occur under

certain conditions.


Manufacturing product rice (PPk).----Changes in national whole-

sale price indexes as reported by the Bureau of Labor Statistics [46] for

three-digit level (SIC) industries between 1959-61 and 1969-71 were used

in computing a county product price for each two-digit level industry.

For each industry, county price changes were obtained by weighting the

change in the three-digit national wholesale price indexes by the-1958

value added by manufacturing for each three-digit level industry as a

proportion of the total value added for the two-digit industry in the

county. Data used to calculate value added for each industry were ob-

tained from published data made available by the US. Bureau of the

Census [30, 471 .

Expected effects of product price increase in the manufacturing

industries are also difficult to specify. Existing firms wo 1d be ex-

pected to expand output and new firms enter the industry as the result

of a product price incerase. This assumes there ae no barriers to

entrance. Increases in employment should occur. Output increases







expansion being offset. With manufactured products, unlike agricultural

commodities, some apparent downward inflexibilities of prices would help

support in part a conclusion that the indirect effect of decreasing em-

ployment would not completely offset the direct effect leaving a positive

overall effect on manufacturing employment. It does remain possible that

decreased residual returns to firms as the result of entry by new firms

would be substantial enough to cause an actual decline in employment.

Both alternatives are indicated to demonstrate the effect of product

price increases on manufacturing employment in Table 3.


Factor Price

Changes in the price of factors whose supply is assumed to be

perfectly elastic would affect the net returns to firm entrepreneurs and

consequently the number of firms. Indirectly, the level of labor employ-

ment would be affected. As the price of factors having perfectly elastic

supply functions increased, labor as well as other production factors

would be substituted for these inputs to the extent possible. This would

result in an increase in the price of all factors having upward sloping

supply functions. As these factor prices increased, residual returns to

firm entrepreneurs would decrease and consequently the number of firms

would decline. A reduction in firm numbers would decrease factor de-

mands, resulting in a decline in factor prices. Increases in residual

returns to firm entrepreneurs would entice some new firms into the in-

dustry with resultant increases in labor employment. Employment levels

under new equilibriumr conditions would depend on the relative magnitudes

of these various changes. The more inelastic the supply function of

critical factors, other than labor, the larger the price increase will







be for that factor as demand for it increases. Consequently, labor

whose supply function is more elastic would be substituted for the

higher priced factor with a resultant employment increase.


Agriculture wage rate (FPI1.--A proxy variable was used as the

annual wage rate for agricultural employees. Total expenditures for

hired farm labor in 1959 and 1969 for all farms in each county were

divided by the total number of hired farm laborers working 150 days or

more each year in that county to obtain an annual wage per worker. The

change in this wage was then computed. These data were obtained from

the 1959 and 1969 Censuses of Aqriculture [31, 32]. Employment effects

of increases in hired farm labor wage rates should be negative as shown

in Table 2. Wage increases would result in higher factor costs to op-

erators. This would encourage substitution of other factors for labor.

Smaller farms would not be able to make sufficient substitutions and

would not be able to compete with larger and more efficient farm opera-

tions. Farm numbers would then decline through consolidation and

expansion of existing farms.


Manufacturing waqe rate (FPk).--Changes in average annual produc-

tion worker wage rates between 1959 and 1970 for each two-digit level

manufacturing industry in each county were used for manufacturing wage

rate changes. Data were obtained from the 1959 and 1970 County Business

Patterns for each state [48, 49]. If the two-digit level industry wage

was not reported for a county due to disclosure problems, the change in

average annual production worker wage for all manufacturing industries in

the county was used. Increases in an industry's wage rates would be ex-

pected to result in a decrease in labor employment within the industry as







indicated by the negative coefficient sign in Table 3. Other production

factors would be substituted for labor as the price paid to labor in-

creased.


Technology

Changes in technological forces that affect agriculture and manu-

facturing industries should have an effect on the amount of labor

employed. Similar to the other types of shifters discussed previously.

technology changes would also affect factor demand, product supplies,

and the number of firms. Increases in technology that were output in-

creasing and nonlabor input decreasing would cause the quantity of

products produced to increase with subsequent decreases in the use of

inputs. Prices of those inputs having inelastic supply functions would

decrease since demand for them would decline. Further substitution of

the lower priced inputs for labor could cause a decrease in employment.

If technology changes had been labor decreasing, the quantity of labor

would have decreased initially. The indirect effect of these changes

would be an increase in the number of firms concomitant with an increase

in residual returns as a result of the change in technology. flew firms

would then increase the demand for all factors and reduce firm residual

returns. Equilibrium quantity of labor demanded could be either smaller

or larger than the initial quantity demanded depending on the degree of

factor supply inelasticity, substitutability of labor for the other

factors used, and the magnitude of changes in the number of firms.


Agricultural technology (Z.).--Changes in output per man-hour in

agriculture were used as indicators of changes in agricultural technology.

Changes in the index of output per man-hour for six major commodity groups







in the Southeast were computed using three-year averages centered on

1959 and 1969 [50, p. 8]. These changes were then weighted by the 1959

value of each commodity group produced as a proportion of the total value

of crops and livestock produced in each county obtained from the 1959

Census of Agriculture [31, County Table 5]. The resulting measure was

a weighted change in labor productivity for each county. Trends in out-

put per man-hour and advances in agricultural mechanization suggest that

technology increases in agriculture are likely to be labor decreasing.

A negative effect on agricultural employment should be indicated as sug-

gested in Table 2. Similar effects would be expected on farm numbers.

Technology advances should enable the operation of larger farms with

resultant decreases in farm numbers.


Manufacturing technology (Zk).--Changes in technology for each

manufacturing industry were computed in a manner similar to that for

agriculture. Changes in national output per man-hour indexes between

1960 and 1970 for three-digit level industries were used in computing a

county technology change variable for each two-digit level industry.

These indexes are published by the Federal Reserve System [51]. Changes

in the national output per man-hour indexes for the three-digit level

industry were weighted by the 1959 value added of each three-digit level

industry as a proportion of the total value added by the two-d;git level

industry in the county. The same value added data used in calculating

industry product price was used in the weighting procedure. Technology

changes in the manufacturing industries have employment effects similar

to those in agriculture. The negative effect indicated in Table 3 im-

plies that technology changes are probably labor decreasing. A technology








variable for the construction industry was not included since output per

man-hour indexes for construction were not available.


Farm Operator Supplies

Changes in farm operator supplies affect agricultural employment

in various ways. Several variables used in this study are quite unique

with respect to the types of shifters discussed earlier. These shifters

are thought to affect farm operator supplies which in turn affect agri-

cultural employment. Changes that increase the number of farms indirectly

cause increases in the amount of products produced and factors used in-

cluding labor. Ultimately, the price of factors having less than

perfectly elastic supply functions would increase with concomitant de-

creases in the number of farms, quantity of products produced, and

quantity of labor employed. Equilibrium employment levels would depend

on the relative magnitudes and effects of the described changes. In

general, declines in farm operator numbers should cause declines in

agricultural employment.


Agricultural waqe opportunity (WW1).--Wages in industries other

than agriculture represent changes in the opportunity cost to farm op-

erators of remaining in present employment as a result of changes in

wages in other employment alternatives. Initially, wage increases in

employment alternatives would decrease the number of farm operators re-

naining in agriculture. As the larger farms realize greater residual

returns some increase in farm numbers might occur. This effect should

be minimal with an overall decline in farm numbers expected as indicated

in Table 2. The movement to fewer, larger, and more efficient farms

should then cause a negative effect on agricultural employment as

indic.i-red in Table 2.







Change in agricultural opportunity wages between 1960 and 1970

in each county was determined using data on employee wages obtained from

County Business Patterns [48, 49] and the Census of Population [29].

Change in annual nonagricultural wages between 1959 and 1970 per agri-

cultural employee in 1960 was used as the indicator of wage opportunity

for agricultural employees. Changes in county unemployment levels would

have provided an alternative measure for this variable.


Agricultural employment opportunity (WEl).--Increases in employ-

ment opportunity in alternative employment situations would be expected

to decrease the number of farm operators remaining in agriculture in a

manner similar to that of increases in wages in employment alternatives.

Changes in employment alternatives were calculated using employment data

obtained from the 1960 and 1970 Censuses of Population [24, 29]. Changes

in nonagricultural employment between 1960 and 1970 per agricultural em-

ployee in 1960 indicate employment opportunities for agricultural workers

and farm operators.


Farm operator age (WA).--Farm operator age represents the change

in the number of farmers who were 55 or more years of age during the

period 1959 to 1969. This variable is intended to reflect the relative

effects of potential operator retirements on the number of farms during

1959 to 1969. The greater the number of farmers who are reaching an

older age, the greater should be the decline in farm numbers and employ-

ment during the entire period. This variable was calculated for each

county from the 1959 Census of Acriculture [31, County Table 5] and the

1969 Census of Agriculture [32, County Table 3]. A positive coefficient

sign would be expected as shown ir. Tablr- 2. Declines in the number of







older farm operators would be expected to cause declinesin farm numbers.

Implicit in this is the assumption that farm consolidation occurs rather

than operator replacement.


Manufacturing Labor Supplies

Changes in the supply of labor available to a particular manu-

facturing industry certainly affect employment in that industry.

Shifters of labor supplies would logically cause changes in the number

of firms in the industry which would in turn affect employment. Changes

in the number of manufacturing firms for a given manufacturing industry

were considered exogenous, however, and shifters of manufacturing in-

dustry labor supplies are discussed below as a direct effect on

manufacturing industry employment.


Manufacturing wage opportunity (WWl)k.--Wages in manufacturing in-

dustries other than the industry of present employment (kth) represent

changes in the opportunity cost to employees of remaining in present em-

ployment as a result of changes in wages in other employment alternatives.

Initially, wage increases in other industries would entice employees to

leave their present industry if their skills were transferable. Their

present industry might bid wages upward and regain to some extent but an

overall negative effect would be expected as indicated in Table 3.

Change in opportunity wages between 1960 and 1970 in each county

was determined for construction and manufacturing using data on employee

wages obtained from County Business Patterns [48, 49] and the Census of

Population [29]. It was hypothesized that employees would not be moving

into the agricultural industry because of its low average wage level.

lhe char.o in annual nonagricultural wages between 1959 and 1970 per




75


construction worker in 1960 in each county was used to indicate the wage

opportunity for construction industry employees. A similar measure was

c31culated per manufacturing employee in each county.


Manufacturing employment opportunity (WE. --increases in employ-

ment opportunity in alternative employment industries would be expected

to af f ec t the nuribe r of em p 1 oyee5 i n the 9 iven i ndu s t ry i ri a wa nne r

similar to that of increases in wages in other industries. Changes in

alternative manufacturing employment were calculated for each county

using employment data obtained from the 1960 and 1970 Census of

Population [24, 201 by computing the change in all employment other than

agriculture and industry of present cmployment per worker in industry of

present cfTiployment. Increases in employment opportunity in other manu-

facturing industries should decrease employment in the industry of

present employment as shown in Table 3. Growth in industries that are

complementary in nature would be expected to positively affect employ-

ment in each other.


Number oF nianuacturinq firms (N Changes in the number of

manufacturing firms were used as predetermined variables in the con-

struction and manufacturing models. An increase in the n6mber c firms

in general would be expected to bring about an increase in employment.

Some cases would exist where intrafirm expansion could bring about an

employment increase while firm -.unibers were declining. In general, a

pos i t; ve s i gn s hou I d be expec ted f or th i s coef f t c tent as s hown 1 n Table

3. Data sources for firm numbcr5 were outtltned earlier.














CHAPTER IV

ANALYSIS OF RESULTS



Parameter estimates in equations identical to those presented in

Chapter III were made for agriculture, construction, and the various

manufacturing industries. Equations (3.9.1.1) and (3.9.1.2) were used

for agriculture. Equation (3.9.2.1) was used for construction and equa-

tion (3.9.k.l) was used for the manufacturing industries. All equations

were estimated for each of the three groupings of counties. Counties

were excluded if no employment was reported in both 1960 and 1970. In

this chapter a comparison is made of parameter estimates obtained from

estimating the relationships for each of the three groups. Effects of

the predetermined variables on employment in each industry and farm firm

numbers for agriculture are discussed. General comparisons of the

results obtained for all three groups are made.


Agriculture


Tables 4 through 6 contain the parameter estimates for the two-

equation models used for agriculture. Each table presents three equa-

tions for one of the three groupings of counties. Table 4 presents the

results for all counties, Table 5 the results for the urban counties and

Table 6 the results for the nonurban counties. !n the following dis-

cussion each agricultural equation in the tables is not referred to

separately as the poramete: estimateF are discu'-,ed. Each para.neter and




77
Table 4. Structural form and reduced form coefficients for change in
agricultural employment (El) and number of farm firms (N,),
all counties, 1960 to 1970.
Endogenous var abea

PredtermnedStructural Derived reduced
Preetrmiedform coefficients form coefficients
variales aAgricultural Number of Agricultural




Constant -8.69 14.63 3.03

Education (X 1) -.1476 .2055* .0169
(.2906) (.1073)

CE (X 2) -.0033 -.0005 -.0037
(.0038) (.0014)
PL-566 (x 3) -.0741 .0314 -.o489
(.1003) (.0307)
ACP (X 4) -.5671 --3 8 8 2* -.8770,


FHA (X 5) -.0527 -.-05 96 -.1004
(.0309) (.0105)
Allotment (Y .1577 07 63** .2187
(.0747) (.0268)
Product price (PP 1) 2.4475 7.4334-***,, 8.3083
(3-9030) (1-3790)

Wages (FP,) -.0070 .0031 -.0045
(.0093) (.0030)
Technology (Z 1) 1.9176 -1.0211* 1.1002
(1.4180) (.5400)

Wage opportunity (WWJ) ---1.1679 -.9350
(2.6060)

Employment opportuni ty
(WEI) ---.4192 -.3356
(1.0110)







Table 4 (Continued)

Endogenous variables
Structural Derived reduced
Predetermined form coefficients form coefficients
variables Agricultural Number of Agricultural
employment farm firms employment
(El) ( 1ll)C E(E1)



Number of farms (I1) .8006
(.1251)

Dummy (GRP) 297.4100 29.5200 321.0400
(58.2700) (23.4800)

-2
R2 .82

R -- .81

aComplete variable definitions can be found in Chapter III.

Change in agricultural employment was estimated with two-stage
least squares. Figures in parentheses for this equation are asymptotic
standard errors. Levels of significance are not indicated since they are
approximations.

CChange in number of farm Firms was estimated by ordinary least
squares with figures in parentheses indicating standard errors. Since
this equation is just-identified and contains all predetermined vari-
ables the structural coefficients are identical to the derived reduced
form coefficients.

-:'Significant at 10 percent level.

-'-Significant at 5 percent level.


-''.-"'Significant at 1 percent level.






Table 5. Structural form and reduced form coefficients for change in
agricultural employment (EI) and number of farm firms (I1),
urban counties, 1960 to 1970

Endoqenous variables
Predetermined Structural Derived reduced
Predetermined
form coefficients form coefficients
a
variables
Agricultural Number of Agricultural
employment farm firms employment
(E )b (N )c (El)


Constant


268.80


-78.21


263.30


Education (X1)


CE (X2)


PL-566 (X3)


ACP (X4)


FHA (X5)


Allotment (X6)


Product Price (PPI)


Wages (FP1)


Technology (Z1)


Wage opportunity (WW1)


Employment opportunity
(WEl)

Farm operator age (WA)


.8879
(.8316)

-.0058
(.0104)

.3388
(.2186)

-.8410
(.2107)

-.0682
(.0595)

.1843
(.3383)

-14.4830
(9.5980)

.0343
(.0427)

-1.1216
(3.2520)


.399 1-':
(.1619)

.0018
(.0021)

.0804:-
(.0433)

2482'"
(.0427)

.03 1 '1 :
(.0121)

.0580
(.0688)

4.9352 -
(1.9490)

.0131
(.0088)

-.1356
(.6920)

-.3720
(2.5290)


.1350
(.7820)

1.911 1--':1
(.0965)


.9159


-.0057


-.8584


-.0703


.1884


-14.1364


.0352


-1.2014


-.0261



.0095


.1342







Table 5 (Continued)

Endogenous variables
Structural Derived reduced
Predetermined .
riForm coefficients form coefficients
variables
Agricultural Number of Agricultural
employment farm firms employment
(E1)b (N1)c (El)


Number of farms (NI) .0702
(.2503)

R2 .93
-2
R -- .92


Complete variable definitions can be found in Chapter III.
b
Change in agricultural employment was estimated with two-stage
least squares. Figures in parentheses for this equation are asymptotic
standard errors. Levels of significance are not indicated since they are
approx imat ions.

CChange in number of farm firms was estimated by ordinary least
squares with figures in parentheses indicating standard errors. Since
this equation is just-identified and contains all predetermined variables
the structural coefficients are identical to the derived reduced form
coefficients.

"'Significant at 10 percent level.

"-Significant at 5 percent level.


*;,-,-Significant at 1 percent level.







Table 6. Structural form and reduced Form coefficients for change in
agricultural e7pioyment (EI) and nu'-Iber of farw firml (10.
nonurban counties, 1.960 to 1970

Erdo2enous variables a

Predetermined Sructural Derived rQduced
varlAbles form coefficients form coefficients
Agricultural Number of Agricultural
criployment farm firms C'mployment
(E I )b (N I )c (El)


Constant -47o.6o 58-59 -390-70

Education (X 1) -.3154 .1246 -,1454
(.2515) (.1312)

CE IX .0007 -.0021 -.0022
2 (.0034) (-OC17)

PL-566 (x 3 -.1474 -.Clog -.1623
.0959) (.0481)
ACP (X 4) -.2659 .4153-,,-,' -8324
(.C940) (.0352)

FHA (X 5 .0456 0 7 9 6 C63,0
(.0334) (.0143)
Allotment (x 6) ..0821 0 7 7 1884
(.0595) (.0290)
Product price (PP 4.284o 8 5 8 9 16.OOZ9
0-5910 0-7430)
Wages (FP -.CO58 .0020 -.003C
(-oO73) (.0037)
Technology (Z 1) 7.;C522 -i.4802'- 5.0328
(1.498o) (-7969)

Wage opportunity WW,) .1759 .2400
(4,1390)

Employment opportunity
(Wy 9.09,93* 12.4128
(47030)

Farm operator age (WA) I 4 0 2 7 1-9137
(.01947)




mola,







Table 6 (Continued)

Endoqenous variables
Structural Derived reduced
Predetermined form coefficients form coefficients
variablesa Agricultural Number of Agricultural
employment farm firms employment
(El)b (N1)c (El)


Number of farms (NI) 1.3643
(.1322)

R2 .80

-2
R -- .80

aComplete variable definitions can be found in Chapter III.

b
Change in agricultural employment was estimated with two-stage
least squares. Figures in parentheses for this equation are asymptotic
standard errors. Levels of significance are not indicated since they are
approximations.

Change in number of farm firms was estimated by ordinary least
squares with figures in parentheses indicating standard errors. Since
this equation is just-identified and contains all predetermined vari-
ables the structural coefficients are identical to the derived reduced
form coefficients.

*Significant at 10 percent level.

**-Significant at 5 percent level.


'--'-Significant at 1 percent level.








the comparisons that are made can be found in the three tables. Means

and standard deviations of each variable are given in Appendix B.


Type of Equation

Tables 4 through 6 contain both structural equations and derived

reduced form equations. Each structural equation for changes in

employment was estimated by two-stage least squares. The equation is

over-identified in each model and contains two endogenous variables.

Coefficients of these equations can be interpreted as the direct effect

on changes in agricultural employment of a one-unit change in the pre-

determined variable. Figures in parentheses are asymptotic standard

errors. These can be examined in relation to each coefficient to provide

an approximation of the statistical reliability for each coefficient

using standard normal test procedures.

The equation for changes in the number of farm firms was esti-

mated by ordinary least squares. It is one of the two structural

equations of each two-equation model. The equation contains only one

endogenous variable (change in the number of farm firms) and all of the

predetermined variables in the model.

Each table also contains a derived reduced form equation for

employment changes. Reduced form equations express an endogenous

variable as a function of all exogenous variables in the model. Coeffi-

cients in this equation can be interpreted as the partial derivative of

the endogenous variable with respect to any predetermined variable with

all other predetermined variables held constant at their mean values.

This coefficient indicates the total effect of a change in the

endogenous variable after taking into account the interdependencies

among all current predetermined variables. This coefficient can be









referred to as a multiplier in contrast to a structural coefficient which

indicates only a direct effect. For this particular model the structural

form equation and reduced form equation for changes in the number of farm

firms are identical. The structural equation contains all predetermined

variables in the model expressed as a function of changes in the number

of farms. This is also the reduced form equation of the model by

definition.


Endogenous Variables

Changes in agricultural employment and in the number of farm

firms from 1960 to 1970 represented the two endogenous variables in the

agricultural equations. The trend in agricultural employment during

this time period was generally downward. Although some counties did

experience increases the average change was negative. The urban counties

experienced the smallest average decline per county in agricultural

employment while the nonurban counties had the largest average decline

(Appendix B, Table 18). Urban counties had fewer agricultural employees

and had already experienced larger declines in some earlier time period.

Employment decline in the urban counties averaged slightly less than

one-half the decline in the nonurban group. Average decline for all

counties was approximately twice that of all urban counties.

The number of farm firms per county also declined for each of the

three groups with the magnitude of the declines for each group having the

same ordering as employment declines. Relative differences were not as

large as experienced in employment. Large variation among counties was

indicated for both farm number changes and agricultural employment

changes (Appendix B, Tables 18 and 19).





85


A decline in farm numbers would be expected to cause a decree

in the number of agricultural employees. Fewer farms would cause a

decline in farm operators and decrease employment. Larger and more efi

cent farms should also require fewer employees. This relationship wra

supported without exception by positive coefficients for changes in ith

number of farm firms when this variable was included in the employment

change equation. Standard errors for this coefficient were relatively

small in relation to the coefficient for both the all county group and

nunurban group. The larges efec of Ua decriease in one farm firmon

agricultural employment occurred for the nonurban group of counties %,,hl

the smallest effect was indicated for the urban group. Since the struc

tural form equation for changes in the number of farm firms was estimate

by ordinary least squares the coefficient of determination (R 2) becomes

a valid measure of the proportion of total variation explained by the

predetermined variables in the system. The exogenous variables explaied

80 percent of the total variation in farm numbers in the nonurban count

group, 82 percent using all counties, and 93 percent using urban counts

Examination of corrected R 21s showed very little decline in explanatory

power when the results were adjusted for degrees of freedom.

While explan-ntory power wshigh for all groups a difference

existed among the various groups of counties with respect to the statis-

tical significance of the predetermined variables. Some of the variabe

that were important for one group of counties were not important for

other groups. Multicollinearity was never a serious problems. Very fe

simple correlations among the independent variables exceeded an absolut

value of .5 and in no cases were these coefficients extremely large.
Idntfiaio o tevaiale n hih h smpe oreato








coefficients exceeded .5 will be made in later sections when each inde-

pendent variable is discussed.


Exogenous Shifters

All predetermined variables included in Tables 4 through 6 were

discussed in Chapter III. Each estimated coefficient reflects the effect

of the shifter it represents according to the type of equation in which

the coefficient is found.


Education investments.--Changes in per capital education expendi-

tures did not appear to be a very important variable affecting agricul-

tural employment changes. Negative coefficients were found for all

counties and the nonurban group of counties. The coefficients indicate

that a one dollar increase in per pupil education expenditures was

accompanied by changes in agricultural employment of the magnitude of

the estimate. Changes in per pupil expenditures were smaller for the

two groups having negative coefficients than for the urban group

(Appendix C, Table 20). The urban group indicated a positive effect from

education expenditures. A more skilled work force resulting from higher

education levels would be expected to migrate to urban areas to realize

their employment potential. This migration effect is supported by the

negative coefficients for the nonurban counties. It appears possible

that the migration effect was large enough to support a positive coeffi-

cient for the urban group. Education expenditures appeared most impor-

tant in the nonurban counties upon examination of the standard errors of

each coefficient.

Somewhat different results were obtained for changes in the

number of farm firms. Increases in per capital education expenditures








were significantly associated with increases in farm numbers for both the

urban group of counties and the group consisting of all counties while a

positive but nonsignificant coefficient was experienced in the nonurban

group of counties. The opposite relationship was expected. Increases in

per pupil education expenditures would be expected to enable farm opera-

tors to attain more skills and take advantage of other employment alter-

natives in a given area. This would be particularly true with operators

of smaller and more marginal farms. The strong positive relationship for

the urban counties suggests one possible effect that may be occurring.

Higher educational expenditures in the urban counties coupled with higher

incomes may encourage an increase in the number of small and part-time

farms. This could occur even though the total number of farms might

decline for a given area.

Reduced form coefficient signs and magnitudes indicate the total

effect on employment as a result of education expenditures. The effect

was positive for all counties and for the urban counties group. For the

nonurban group where the direct negative effect on employment was largest

and the positive effect on farm numbers was small the total effect was

negative.

A correlation coefficient of -.50 between changes in per pupil

education expenditures and technology change was noted in the urban group

of counties. This must represent some form of spurious correlation.

Increased technology levels would normally be associated with increases

in educational skills.


Corps of Engineers' investments.--Investments by the Corps of

Engineers demonstrated a negative effect on agricultural employment

change for all groups except the nonurban group. A major portion of









investments by the Corps in the four-state study area was for flood

control. Effective flood control should make more land available for

agricultural use. Expansion of existing farms to benefit from this

should enable more efficient labor saving operations with resultant

declines in agricultural employment. Displacement of existing farms by

expansion would also contribute to employment declines. It appears that

this occurred in the two groups having negative coefficients. Any

employment increase due to new farms in the recipient area was offset by

reduction in employment as the result of farm expansion. The standard

error for the positive coefficient associated with the nonurban group

was quite large. Average investment in the nonurban counties was approx-

imately one-half that in the urban counties.

The effect of a one thousand dollar change in investments on farm

numbers was not significant for any of the three groups. Negative effects

occurred for all counties and the nonurban group. Fewer farms would be

expected if existing farms expand to take advantage of more flood pro-

tected land.

Examination of the geographical pattern of Corps of Engineers'

investments gives further indication as to why positive coefficients

occurred for employment in the nonurban group and for farm number changes

in the urban group. A large proportion of these investments occurred

in the delta area of Mississippi and in an area in east-central Alabama

which are predominately nonurban areas. These areas have traditionally

been areas where large numbers of small farms were in existence. Flood

protection provided by Corps of Engineers' projects could have made new

land available which was suited for mechanized agricultural use. This

undoubtedly created a movement to larger farms through both the effect




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