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8117266

S h ie l d s , J o h n R o b e r t

LABOR TIME ALLOCATION DECISIONS OF LOW FARM-INCOME
FAMILIES IN MICHIGAN

Michigan State University

University
Microfilms
International

PH.D. 1981

300 N. Zeeb Road, Ann Arbor, MI 48106

LABOR TIME ALLOCATION DECISIONS OF
LOW FARM-INCOME FAMILIES IN MICHIGAN

By
John R. Shields

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics
1981

ABSTRACT
LABOR TIME ALLOCATION DECISIONS OF
LOW FARM-INCOME FAMILIES IN MICHIGAN
By
John R. Shields

The central concern of this research has been to deter­
mine what Personal-Household attributes and Farm-Busines s
characteristics are statistically significant in their
association with annual hours-of-work for both on-farm and
off-farm labor supply.

First,

schooling,

number of children,

wage rate,

spouse labor income,

residence are examined.
assets,

debts,

Then,

the family attributes of age,
farming experience,
investment income,

market
and county

the farm characteristics of

acres rented in, and agricultural income were

included as explanatory variables.
The population studied consists of all small farm
households earning under $20,000 annually from gross agricul­
tural sales in 1973 and located in Michigan's lower peninsula.
A stratified random sample,
income households,

comprised of 243 low farm-

was drawn from the ten different counties

included in a general baseline survey of small family farms
conducted in 1974 under the auspices of the department of
agricultural economics.
The household production function model is used to
analyze the time allocation decisions of individual male and
female heads of households in an interdependent framework.
Consumer choice theory underlies the labor supply function

John R. Shields
while human capital theory is used to specify the wage
earnings function.
Multiple regression analysis using ordinary least
squares was selected as the optimal method of estimation,
given the complexity and cost of more sophisticated estima­
tion procedures as well as the inherent limitations of the
data utilized.

An instrumental variable technique was

employed to impute the off-farm wage rate for the entire
sample based on earnings information reported by the sub­
sample of working male and female heads of households,,
The Farm-Business model performed better than the

_2
Personal-Household model in terms of higher R values for the
on-farm and off-farm labor supply equations of both sexes.
The explanatory variables of the two models generally had
the correct signs;

that is, they are in conformity with the

theoretical expectations derived from a thorough review of
relevant literature.
sign,

The lone exception is the negative

significant at the

.01 level,

for the county residence

(in a Standard Metropolitan Statistical Area) variable in
the female off-farm equation of the Personal-Household model.
The addition of animal and crop enterprise variables
to the Farm-Business model substantially raised the explana­
tory power of the equations and gave the expected signs with
respect to their degree of labor intensity.

However,

for

lack of a strong theoretical base the results are reported
in an appendix.

Future explorations in the more complete „

formulation of this model might justify its validity.

John R. Shields
Labor supply decisions are more properly examined in a
life cycle c o n t e x t ; but in the absence of longitudinal data
the cross-section sample was stratified by three age
categories to approximate
correspond to entry,

'representative’ stages that

growth and disinvestment in agriculture.

The results do not support the proposition that life cycle
differences exist in the labor supply of household members.
But this may be due to a sampling design that produced too
few elements in the youngest age group.
By way of generalization the estimations of the
Personal-Household and Farm-Business models produced results
that are fully consistent,

not only with economic theory,

but also with the empirical findings of similar studies of
farm households in Illinois,

Iowa,

and North Carolina.

DEDICATION

To
All Those Languishing A.B.D.'s
Striving To Finish Their Ph.D. Dissertation
"The brain will not fail, when
the will to achieve is in earnest."
Don Juan in Hell
The Dream Sequence
Man and Superman
by George B. Shaw

ACKNOWLEDGEMENTS

First and foremost a special debt of gratitude is due
Professor Lester M a n d e r s c h e i d , my dissertation supervisor,
whose firm but compassionate guidance enabled me to complete
the Ph.D. program.

His thoroughly professional manner sets

a standard to be emulated.
Thanks also go out to Professors Einar Hardin,
Moser,

Collette

and Garland Wood for serving on my dissertation

committee and providing constructive criticism that substan­
tially improved the finished product.
No research is possible without data;

so I am truly

grateful for the cooperation of Professor Ralph Hepp in
granting me access to the Michigan Small Farm Family Program
survey information collected under his direction.
And for welcoming my initial expression of interest in
small farm research and encouraging me to pursue my speciali­
zation in labor economics in his capacity as the initial
Chairman of my dissertation committee before his departure
overseas,

I offer thanks to Professor Warren Vincent.

Computer programming assistance was absolutely essential
for the successful completion of this research,

and I was

fortunate to have had the instructive help of two very find
individuals —

Dave Zeitler and Hank Griffen.

Finally, putting pen to paper is only the start;
transforming the written scrawl into lasting print is what
gives the writer his ultimate satisfaction.

So,

for her

tireless efforts on my behalf a sincere vote of thanks for a
job well done goes to Sandy Bolton,

whose skills as a typist

are a marvel to behold.
*

*

*

*

*

Though words cannot possibly express the depth of my
heartfelt appreciation for her moral and financial support
during the writing of this dissertation over a few too many
Michigan winters,

I am compelled at the very least to

acknowledge the personal and professional sacrifices made on
my behalf by my loving wife Elizabeth.

To you,

I owe all!

TABLE OF CONTENTS

LIST OF T A B L E S ............................................

ix

LIST OF F I G U R E S ..........................................

x

Chapter
I.

Page
NATURE AND SCOPE OF RESEARCH
A.

PROBLEM DELINEATION
1.
2.

B.

C.

3

Underlying Propositions
Working Hypotheses
Research Objectives
.....................

5

.....................................

9

Research Rationale
Proposal Validity

SUMMARY

II.

..........................

RESEARCH JUSTIFICATION
1.
2.

1

Problem Statement
Investigative Boundaries

PROBLEM RESOLUTION
1.
2.
3.

.......................

REVIEW OF RELEVANT LITERATURE
A.

CONCEPTUAL FRAMEWORK
1.
2.

B.

........................

Theoretical Foundations
Analytical Paradigms

RESEARCH METHODOLOGIES
1.
2.

10

.....................

Data Bases
Estimation Techniques

v

40

Chapter
II.

Page
(Continued)
C.

..........................

EMPIRICAL STUDIES
1.
2.
3.

Classic Works
Recent Probes
Interdisciplinary Quests

S U M M A R Y .....................................

III.

60

DATA COLLECTION AND PROCESSING
A.

SURVEY P OPULATION
1.
2.

B.

C.

E.

65

Reference Period
Information Source
Factual Content
.......................

66

Consistency Checks
Remedial Assumptions

ESTIMATION ACCURACY
1.
2.

63

Sampling Method
Sampling Units
Sampling Frame
Sample Size

MISSING OBSERVATIONS
1.
2.

62

Subject Universe
Data Gathering

DATA C O M P O S I T I O N ............................
1.
2.
3.

D.

..........................

SAMPLING P L A N ..............................
1.
2.
3.
4.

........................

70

Sampling Error (Precision)
Non-Sampling Error (Bias)

S U M M A R Y .....................................

IV.

49

77

RESEARCH DESI GN AND STATISTICAL PROCEDURES
A.

ECONOMIC M O D E L ..............................
1.
2.

Functional Relationships
Hypothesized Associations

vi

79

Chapter
IV.

Page
(Continued)
B.

1.
2.
3.
C.

................

93

.......................

103

ECONOMETRIC SPECIFICATION
Parameterized Models
Equation Formulation
Estimation Methods

VARIABLE DEFINITION
1.
2.
3.

Response Variables
Explanatory Variables
Omitted Variables

S U M M A R Y ....................................

V.

PRESENTATION AND ANALYSIS OF RESULTS
A.

REPORTED FINDINGS
1.
2.

B.

..........................

129

Summary Statistics
Model Performance

INTERPRETED FINDINGS
1.
2.

.......................

150

Theoretical Conformity
Empirical Consistency

S U M M A R Y .....................................

VI.

128

156

SUMMARY AND CONCLUSIONS
A.

RESEARCH SYNOPSIS
1.
2.
3.

B.

157

Problem and Hypotheses
Theory and Model
Sampling and Estimation

GENERALIZED RESULTS
1.
2.

C.

..........................

.......................

159

Hypotheses Confirmation
Inference Limitations

FURTHER S E A R C H ..............................

vii

166

Appendix

Page
A.

MICHIGAN SURVEY QUESTIONNAIRE

...........

171

B.

MISSING DATA A D J U S T M E N T S ..................

183

C.

IMPUTED MARKET WAGE ESTIMATION

...........

190

Do

AGRICULTURAL ENTERPRISE MODEL

...........

207

E.

LIFE CYCLE LABOR SUPPLY ANALYSIS

BIBLIOGRAPHY

.........

220

..............................................

239

LIST OF TABLES
Table
IV-1

Page
Hypothesized On-/Off-Farm Variable Associations by Sex . . .

92

V-l

Sunmary Statistics of Data on V a r i a b l e s ...................

V-2

Male Labor Supply Estimations of Personal-Household Model

V-3

Female Labor Supply Estimations of Personal-Household Model.

139

V-4

Male Labor Supply Estimations of Farm-Business Model . . . .

143

V-5

Female Labor Supply Estimations of Farm-BusinessModel . . .

147

Estimated On-/Off-Farm Variable Associations bySex . . . .

160

VI-1

.

130
133

C-l

Imputed Market Wage Estimations for M a l e s .........

201

C-2

Imputed Market Wage Estimations for F e m a l e s .......

203

D-l

Male Labor Supply Estimations of Ag-Enterprise Model . . . .

212

D-2

Female Labor Supply Estimations of Ag-Enterprise Model . . .

216

E-l

Life Cycle On-Farm Labor Supply Estimations of Males . . . .

223

E-2

Life Cycle Off-Farm Labor Supply Estimations of Males

..

.

226

E-3

Life Cycle On-Farm Labor Supply Estimations of Females ..

.

232

E-4

Life Cycle Off-Farm Labor Supply Estimations of Females .

.

235

ix

LIST OF FIGURES
Figure

Page

II-l

Simple Labor /Leisure Choice M o d e l ......................

35

I1-2

Household Production Function Model

....................

37

11-3

HPF Farm Model and Work/Leisure Preference...............

x

39

CHAPTER I
NATURE AND SCOPE OF RESEARCH

In this beginning chapter the research problem is first
defined and circumscribed (section A) and then addressed in
terms of stated assumptions and working hypotheses, which
contribute to the formulation of research objectives for this
study (section B).

Finally,

the rationale and validity of

the proposed research is made explicit

A.

1.

(section C).

PROBLEM DELINEATION

PROBLEM STATEMENT
Briefly stated,

the central concern of this research is

to determine what Personal-Household attributes and FarmBusiness characteristics are statistically significant in
their association with annual hours of on-farm labor supply.
A related,

but subsidiary,

problem is to find out which

of the above mentioned type variables influence the amount of
annual hours of off-farm labor supply to wage employment —
full or part time.

Investigating this aspect of time alloca­

tion is symmetrical to the on-farm study and may offer
additional insights in understanding more completely the main
problem stated above.
The forces in question are identified as follows:

(a) Personal-Household attributes of the husband and wife —
age,

schooling,

number of children,

market wage rate,

farming experience,

spouse labor income,

investment income,

and

county residence.
(b) Farm-Business characteristics —

farm assets,

acres rented in, and agricultural income.

(NOTE:

farm debts,
These

variables will be formally defined in section C-2 "Explana­
tory Variables" of Chapter IV.)

2.

INVESTIGATIVE BOUNDARIES
The subject group was narrowly defined by Thompson

[1975], who collected the data,

to include only those farm

operations located in Michigan's lower peninsula whose enter­
prise type and levels would not normally have been expected
to generate more than $20,000 annual gross agricultural
sales as of the survey data year 1973.

The precise qualify­

ing definition used on the survey questionnaire was 10 acres
or more of land and enterprises smaller than:
Dairy —

25 milk cows + feed crops

Cash grain —

220 tillable acres

Beef cattle feeding —

100 feeders + feed crops

Beef cow and calf

—

80 cows + feed crops

Farrow and finish

swine —

30 sows - 2 litter system +

feed crops
Feeder pig production swine —

60 sows - 2 litter

system + feed crops
Feeder pig finish
Poultry —

swine —

3,500 laying

500 feeders + feed crops

hens + feed crops

3
Fruit —

40 acres

This definition of a small farm is taken as given,

though

extensive debate over what constitutes a 'small farm'

(or

even just a 'farm') has been widely reported in the litera­
ture —

without satisfactory resolution to all contesting

parties

[Brewster 1977;

Foote 1970; Hildreth and Worden 1976],

Our use of the term "low farm-income" families in the
title of this study reflects the choice of agricultural sales
classes as a criteria for sample selection.

However,

it

should be noted that although such low farm-income households
are what is more popularly referred to as small farmers,
latter are not necessarily low-income farm families —

the

given

the alternative sources of income available to an operator
and spouse.
No attempt was made to classify farms according to
established Agricultural Census categories of primary and
part-time based on the proportion of an operator's work time
spent on his agricultural enterprise.

B.

1.

PROBLEM RESOLUTION

UNDERLYING PROPOSITIONS
Two fundamental,

albeit untested,

premises are set

forth about the population from which the sample of small
farm operators was drawn and to which inferences will be made
as a result of this study.

They are:

(a) small farm house­

hold heads are individually rational in their actions
pursuant to their expressed goals;

(b) small farm households

4
possess an explicitly stated or implicitly understood goal
function which is presumed to be rooted in the maximization
of utility.
More specifically,
their land,
their

labor,

'efficient*

a fair return on the investment of

and capital resources is sought through
employment for a given state of managerial

and technical knowledge,
Admittedly,

which may vary among farmers.

such propositions cannot fully account for

farming as a leisure activity (e.g., especially among the
high total-income

'hobby'

farmers) where utility,

but not

necessarily further income, maximization is paramount.

But

in the main they have some reasonable basis as evidenced by
the findings of Olson who concluded that ''this research also
indicated that small farm operators reported a desire to
increase income from the small farm"
Moreover,

[Olson 1978, p. 123].

his study showed that "Tests of rationality indi­

cated that there was no significant difference between small,
medium,

and large farmers in terms of rationality of

decision making"

2.

[Olson 1978, p. 128].

WORKING HYPOTHESIS
Economic theory, past empirical work,

and logical

reasoning suggest certain and possible relationships between
some of the aforementioned variables and on-farm and off-farm
labor supply,

the anticipated directions (positive or

negative) of which are discussed more fully in the research
design chapter.

The expected signs (+, -, o) represent the

research/declarative form of hypotheses;

however,

the actual

5
estimation of these relationships will be in the form of the
statistical/null hypothesis (i.e.,

that the variables have

no significant effect on labor supply).

The reasoning behind

each of these hypotheses is presented in the DISCUSSION
paragraph immediately following the measurement description
of each "Variable Definition" in section C-2 of Chapter IV.

3.

RESEARCH OBJECTIVES
The primary aim is to determine what influence,

if any,

the foregoing factors may have on the amount of labor time
allocated to on-farm and off-farm work activity of small farm
operators and their spouses.

Of particular interest are the

variables for which some theoretical basis exists for
hypothesizing a relationship;
supply theory,

that is, does standard labor

developed with the urban dwelling,

holding population in mind,

also hold for the rural domiciled

farmer with multiple-job-holding opportunities.
reason to suspect not.

single-job­

There is no

Also of interest are the potentially

different influences of the same variables on male operators
and their wives with respect to labor supply decisions.
comparison of research results will be made with similar
previous studies for their empirical consistency.

C.

1.

RESEARCH JUSTIFICATION

RESEARCH RATIONALE
The M.S.U.

SMALL FARM PROGRAM reflects a nationwide

awakening to the special needs of small farmers and the

A

associated problems of low income.

Witness the titles of

Congressional Hearings held in the mid 1970's:
Family Farm Survive in America?"

(1975);

"Will the

and "Assistance to

Small Farmers in Upgrading Their Operations"

(1976).

These,

in part, were a response to the critical 1975 report to
Congress by the Government Accounting Office's (G.A.O.)
Comptroller General entitled "Some Problems Impeding
Improvement of Small-Farm Operations:
of Agriculture Could Do, But Doesn't!"

What the Department
The Report pointed

out t h a t :
The Department and land-grant colleges have not
made a concerted effort to solve problems im­
peding the economic improvement of small-farm
operations.
Also they have not adequately
(1) evaluated the economic and social impacts
of production-efficiency research nor (2) deter­
mined the assistance that small-farm operators
need to plan for and adjust to changes brought
about by such research.
[U.S. G.A.O.
Comptroller General 1975, p. ii]
The Michigan Cooperative Extension Service,

in conjunc­

tion with Michigan State University's Department of
Agricultural Economics,
farmers.

Accordingly,

has made a commitment to assist small
certain monies have been earmarked for

this client group in the late 1970s —

with specific ou t­

reach activities being initiated and supportive research
projects being undertaken.
Program goals have been formulated for meeting the needs
of full-time,
Halsey 1978].

part-retired,

and part-time farmers

[Hepp and

They include such broad aims as locating those

farmers not currently being served by existing agricultural
production and marketing programs;

helping farmers clarify

7
their personal goals and specify their economic objectives
for the farming operation; provide basic information on land
use,

enterprise selection, water management, machinery

purchase,

pesticide application,

estate planning,

etc.;

and

promote learning experiences to show these farm households
how to utilize their resources efficiently.
Among the research projects sponsored by the Agricultural
Experiment Station having an orientation toward limited
resource farmers were "The Role of Small Farmers in the
Agricultural Production System"

(Vincent 1973-78) and

"Analysis and Application of Farm Accounting and Business
Management Data"

(Nott 1973-76).

Doctoral dissertations

completed in the Department of Agricultural Economics are
"Description and Analysis of Limited Resource Farmers in
Michigan"

[Thompson 1975]

and "Non-Formal Education Delivery

Systems to Reach Limited Resource Farmers in Michigan"
[Olson 1978].

This dissertation involves further analysis of

the survey data collected by Thompson under the supervision
of Hepp.

2.

PROPOSAL VALIDITY
The research on labor time allocation decisions of low

farm-income families in Michigan proposed herein meets the
four basic criteria of a valid study:

(1) appropriateness —

it addresses a legitimate public policy issue of how the
Cooperative Extension Service can (no longer a matter of
'whether it should')

identify and assist more than the

current 30% of small-farm operators being reached,

and to

better understand what factors are associated with more or
less on-farm activity;

(2) uniqueness —

States of North Carolina,

Michigan, unlike the

Iowa and Illinois where similar

on-farm labor supply studies of farm households were con­
ducted,

is a highly urban-industrialized region with sub­

stantial off-farm job opportunities well dispersed
geographically so that a wide variety of employment positions
are generally within reasonable commuting distance of most
Michigan small-farm operators and spouses.

Such wage

employment possibilities constitute a competitive choice with
on-farm work for substantial numbers of the State's farm
population.

In addition,

this study is not narrowly focused

on the influence of supplementary income grants on labor
supply of farm households participating in a negative income
tax program (e.g.,

R.I.M.E.) but instead examines the

influence of a wide range of variables broadly classified as
Personal-Household attributes and Farm-Business characteris­
tics for which data is available;

(3) feasibility —

Consumer

choice theory underlying labor-leisure decisions is well
developed;

and household behavior models of labor supply are

generating consistent results.

Econometric estimation

methodology for cross section analysis of labor supply
equations is widely discussed in the empirical literature,
though admittedly there are many unresolved issues surround­
ing non-sampling error biases.

And relevant usable data is

available for analysis from a 1974 sample survey of 243 lower
peninsula small-farm households by Thompson

[1975] ;

9
(4) genera].izability —

By virtue of the geographic area

sampled the results can be inferred to the bulk of Michigan's
small-farm population.

These results can then be compared

with those found in other states.

Moreover,

replication

elsewhere of the research design is also possible.

SUMMARY

With the problem defined and its scope delimited to
discovering what household attributes and farm characteris­
tics are associated with changes in the on-farm labor supply
of Michigan operators and spouses in low farm-income house­
holds,

this chapter then sets forth the underlying

assumptions, working hypotheses,

and research objectives of

and justification for this dissertation.

It thus has

focused the following review of literature on hours-of-work
labor supply studies with particular reference to farmhousehold decision making.

CHAPTER II
REVIEW OF RELEVANT LITERATURE

This chapter constitutes a critical examination of the
general labor supply literature for both urban and farm
populations.

It provides an exposition of the theoretical

foundations and analytical paradigms (section A), discusses
the pros and cons of alternative estimation techniques for
available data bases

(section B),

and finally reviews the

various research that has special reference for the study
herein of Michigan farm households

A.

1.

(section C).

CONCEPTUAL FRAMEWORK

THEORETICAL FOUNDATIONS
The study of labor time allocation decisions is rooted

in the complementary economic theories of consumer demand and
human capital,
a.

explored below,

Consumer Demand Theory
The traditional theory of consumer behavior u n d e r ­

pinning labor supply analysis (i.e.,

labor/leisure dichotomy)

stems from Lionel Robbins classic article

[1930] on supply

of labor in terms of demand for leisure.

This led to fruit­

ful analyses of the effects of income and prices (i.e., wage
rates) on the supply of labor,
10

even though it subsequently

11
became apparent that the single category of

'leisure'

sole alternative to market work was inadequate.

as a

This

traditional theory rests on the view that an individual
attempts to maximize utility U, which is obtained directly
from the services provided by the goods x^ purchased in the
market —

all in a single period framework.
U = u (Xlf X 2 , . . ., X n )

The consumer's utility is subject only to his money income
(I) constraint:

I =

n
£ x .p .
i=l
1 1

The purchasing power of money income (I) is determined by
product prices (p^) prevailing in the market place.
tion of a good is, thus,

Consump­

determined by a person's income,

market prices of each good,

and the residual variable called

taste (T) which is included for sake of completeness,

D

x^

I pi
= d (-, — , T)
vp p
'

where p is a price index used to express variables in real
terms.

An important implication

price income-compensated

of the foregoing isthat

changes in the relative price

of

any good lead to changes in the opposite direction in the
quantity demanded of that good.
An inherent weakness of this received theory of consumer
demand (i.e.,

choice) is its inability to cope adequately

with behavioral decisions involving choices related to non­
monetary factors (e.g.,

allocation of a consumer's nonmarket

12
time;

deciding on family size), which necessarily restricts

its application to the market sector.

Moreover,

household

survey data analyzed heretofore show that the independent
variables,

income and prices,

explain only a small part of

the variation in the demand for specific goods, whereas the
proxies for taste (such as family size,
education,

occupation,

race,

family a g e - s t r u c t u r e ,

and socio-economic status)

exhibit systematic effects on behavior
This undue reliance on the catch-all

[Ferber 1973, p. 1315].

'taste'

as an explana­

tory variable in the demand function for market goods,
logical,

though

seems unwarranted inasmuch as neither economics,

nor any other discipline for that matter,

has a well-

developed theory of taste that can explain how it is formed
or predict its effects.
A modern reformulation of standard consumption theory
has been proposed by Becker
Lancaster [1966] and Muth
resurrects an earlier,

[1965] with variations by

[1966].

This 'new' approach actually

albeit rudimentary,

to anthropologist Margaret Reid

one attributable

[1934], who in her book

Economics of Household Production focused attention on the
unpaid activities of household members that substitute for
goods or services obtainable in the market.

The neo-house­

hold approach of Reid's successors is, thus, more noteworthy
for the formal development of its implications than for its
original conceptualization.
This household production function (HPF) approach con­
sists of three main components:

goods and services purchased

13
in the market place;

the time of a household member divided

between market work and aggregated non-market activities
(i.e., homework and leisure);

and the activities and/or

commodities produced by the household.
prised of its individual members,

The household,

is viewed as both a pro­

ducing and consuming unit that sequentially:
its capital assets (e.g.,
property derived;

com­

(1) draws on

savings) and nonlabor income (i.e.,

not government transfers),

some of its available time (i.e.,

and/or supplies

labor) to the wage market

in quantities sufficient to accumulate income needed to
acquire (i.e., buy) market goods and services;
goods and services are then combined as

(2) these

'inputs,'

sometimes

with portions of remaining household member time (t^) to
produce output called commodities (or characteristics);
(3) from these commodities utility is then directly obtainable
in consumption —

an activity for which additional time is

required.
The optimal allocation of time is quite analo­
gous to the optimal allocation of income.
One's time resource must be so distributed as
to give an equal yield in all sectors of use.
Otherwise, it would pay to transfer time from
an activity with a low yield to one with a
high yield ... until equilibrium had been
reached.
[Linder 1970, p. 3]
Under this formulation these household produced commodities
would also include what is popularly called

'leisure,'

that

is, pure time activities (such as beach combing) or time
intensive commodities (such as playing golf) which combine
physical goods with time inputs to "produce" recreation.
ever,

How­

no formal distinction is usually made between homework

14
and leisure.
Hence,

a consumer's demand for market goods/services are

not desired for their own sake (i.e.,

direct utility), but

only as inputs, usually in combination with time,

into the

home production of commodities which are then consumed by
the household.

They are not exchanged in the marketplace

and thus have no explicit market price;

though their value

(adjusted for product quality differences) may be determined
by pricing market equivalents.

Thus,

a production decision

also represents a consumption decision,
can be considered one and the same

and the two processes

[DeTray 1973,

p. v ] .

This type of decision is dependent upon the price of market
goods/services and the value or scarcity of time.

Note that

although the production/consumption decision is of a
simultaneous nature,

the production and consumption activities

are separate and sequential

[Pollack and Wachter 1975, p. 255].

The cost of producing these household commodities
depends upon the price of market goods/services
competitive market value),
(i.e.,

(i.e.,

the

the opportunity cost of time

the old "time is money" adage,

using either observed

market wages or asking non-market wages for those not w o r k ­
ing),
(e.g.,

and an imputed rate of return to household capital
interest on savings).

time is to the household,
goods/services,

For instance,

"the more valuable

relative to the price of market

the higher the cost of all commodities —

especially those whose production requires relatively large
amounts of time"

[Detray 1977, p. 2].

15
As households attempt to maximize their utility and
m inimize their production costs,

they respond to:

(1) changes in both the prices and productivity of factors,
(2) changes in the relative shadow prices of household
commodities

(i.e., only implicit prices can be used in the

absence of market prices),

and (3) changes in their full

real income.
Some examples of maintained hypotheses follow.

A

reduction in the price of some factor of household production
(e.g.,

a market bought good such as an automatic washing

machine) will shift the household production process toward
techniques that are more intensive in the use of that factor,
and away from methods that make intensive use of other
factors

(e.g.,

hand wringer wash tub and household time) as

well as toward commodities that use the newly lowered priced
factor relatively more intensively.
Alternatively,

if the price of one factor (e.g.,

a

household m e m b e r ’s time, measured in terms of an individual's
market wage rate representing the opportunity cost of time
or the money equivalent of marginal utility of work)
[Gronau 1970, pp.
(e.g.,

10-11]

rises relative to another factor

a market bought service such as automobile repair),

it will,

ceteris paribus,

cause a substitution in the p r o ­

duction process of a commodity

(e.g.,

automobile maintenance)

away from time intensive modes

(e.g.,

household members time

combined with a do-it-yourself tune-up kit) and towards a
more money-intensive method of production involving an

16
increased use of market bought goods/services as inputs
(e.g.,

commercial car repair service).

This relative factor price change will also result in a
substitution in consumption in favor of goods-intensive
activities

[Gronau 1970, pp.

saving microwave ovens.

10-11]

such as cooking with time

Cooking, by the way,

is also one of

those household activities akin to child rearing,

that is

difficult to distinctly identify as production versus
leisure.
unlike

It obviously can combine both elements,

’hobby'

farming!

not too

We should also point out here that

household time is not necessarily a required input for every
commodity produced at home.

(e.g., Heat can be produced

automatically by combining the market bought goods of a
furnace and gas as opposed to the old fashioned wood burning
stove which required time for log chopping and fire stoking.)
But, of course,

the acquisition of such market goods as

inputs to the household production and consumption processes
requires that more household member time be supplied to
market work in exchange for money with which to purchase
such goods and services.
Naturally,

one can also observe intrahousehold substitu­

tion among members'

labor as the value of time (i.e., offered

wage rate in the market) of one individual rises relative to
others in household production activity.

An example would

be a mother who turns over the care of a younger child to her
older children while she secures a wage market job.
Likewise,

if the marginal productivity of a m o t h e r ’s

17
time in household production
wage offer,

ceteris

is valued higher

than her market

paribus, she is likely to

opt for house­

hold production activity.

An example parallel to the last,

involves the commodity of intellectual skill development in
the early formative years of a child under 3, for which there
is no available market service (e.g.,

day care babysitting)

nor even a non-market substitute (e . g . , older child in
household) for the mother's input of time.

Of course,

the

ceteris paribus caveat ignores the impinging influences of
taste

for market versus non-market work, household

and other

income,

factors which would affect labor supply decisions.

By way of formal summary of the preceding exposition,
let the two person household's utility function be
U
where Z . stands for
3

= u (Zx ,Z 2 , . . ., Zn )
both the services from and the quantity

of the commodity Z ., each of which has a separate production
3

function (or technical constraint) of:
Z . = z . ( X . , H . , H - .,
j
j v i ’ m i ’ fi’
where

E)
y

is the vector of market bought goods/services,

where H

. and H „. represent home time of the male and female
mi
fi

heads of household in the production of Z. respectively,
1

and

where E represents a vector of environmental variables that
reflect the technology level of household production ( e . g . ,
education,

socio-economic background,

health status,

etc.)

[Michael and Becker 1973, p. 382].
The equilibrium condition for utility maximization is
that point at which the marginal utility of Z. is equal to

18
the sum of the marginal costs of using both time and goods/
services to produce Z ., which are the arguments of the
J
household's utility function,

instead of the market bought

goods/services in the conventional theory of consumption
behavior

[Ferber 1973, p. 1323].

In addition,

there are the total time (T) constraints

of the husband and wife:
T

m = N

T_p =
f

m+ H m + L m
N.p + H, + L_p
f
f
f

where N is market labor time,

H is home production time,

L is leisure/consumption time;

and there is the income (I)

budget (i.e.,

and

goods/services) constraint:

I =

=

T
Z R
t=l

Z

n
Z ( P ^ X . ).
i=l

R. (w ,H
+ w„.H„. ) + A
t v mt mt
ft ft
o

where p^ is the price of a unit of services of market goods
which both incorporates the discounted value of initial
assets and can be transferred between periods, w ^

and w ^

are the respective wage rates for males and females,

A q is

the discounted value of non-wage property income (i.e.,
initial assets), and where R. = l / ( l + r ) ( a + r )
’
t
o
o
(1 + r^)

. . . (1 + r^. - 1) is the discounted value at the

beginning of period zero of one dollar received at age t
[Ghez and Becker 1975, pp.

3-4 and 32].

These time and income constraints,
independent,

which are not

can be collapsed into a single household

19
constraint of full income (F) accounting for the total
resources of time and income:

F =

T
Z

T
=
Z
t=l

R.
t

R.

n
Z

[wT

[p X. + (w ,H , +
1 x
mt mt

+

wT-

w-.H-. )]
ft ft

+ A]

The left side of the equation shows how full wealth is
spent:

in part directly on goods,

using time for

consumption.

labor activity

(i.e., work) the

and in part indirectly by

If all time is spent at market
right side of the equation

would be the discounted value of money income called full
wealth,
pp.

the sum of human and property wealth

15-16;

[DeTray 1973,

Ghez and Becker 1975, pp. 2-4 and 32],

To elaborate,

full income is the potential money income

that would be earned if all available household time were
allocated entirely to its most profitable money generating
activity

[Becker 1965, p. 497].

For example,

time can be

converted into money via market work and hence into goods/
services,
labor.

thereby using less time in consumption and more at

The full income constraint represents the value of

time in both market work and home production.

The inclusion

of consumption and leisure under non-market time means that
for most households money income will be exceeded by full
income, the latter being a better indicator of welfare since
it reflects foregone earnings associated with labor time
withholding

[Fox 1975, p. 47].

Note that one family's

potential full income can be greater than another,

even

20
though it might conceivably have a lower money income —
perhaps by choice due to a different utility preference
function.

Full wealth,

then,

is the potential lifetime sum

total of all household resources,

including the total value

of time, whether or not that time is spent in the market
place working.

The distinction is an important one because

monetary earnings are not independent of how the household
allocates its resources over its lifetime and therefore does
not change from one period to another except for exogenous
changes in the household's economic condition brought about
by unanticipated gifts,

inheritances,

wage rate change,

etc.

Families obviously can alter their wealth through the invest­
ment decisions they make over a lifetime.

In this framework

these changes are not ruled out, but are assumed to be anti­
cipated with perfect foresight.

Operationally,

this means

that the household has some notion of its lifetime wealth
position that changes very little from time period to time
period and on which current consumption decisions are based
[DeTray 1972, p. 15].

It is important to reiterate that the

magnitude of this aggregate household resource constraint is
independent of the fraction of time the household chooses to
allocate to income earning activities in the wage labor
market, which in the traditional theory of choice forms the
basis of the income constraint.
The foregoing household production function approach is
analogous to the theory of the firm in that the household,
a producing unit,

invests in capital assets

(savings),

as

capital

21
equipment

(durable goods),

'labor force'

and training investments in its

(human capital of family members) while maximiz­

ing its objective function subject to technological and
resource constraints.

But it must also make complex

decisions in its capacity as an earning unit

(e.g.,

allocat­

ing resources to the most profitable opportunities for
members'

time and money assets) and as a consuming unit

(e.g., budgeting and investing wisely to raise the household
standard of living).
Moreover,

it must accept personal risks (e.g.,

and accidents to household members)

illness

and economic risks of

change inflicted by the cumulative effect of other household
decisions and in terms of fluctuation in aggregate incomes,
and prices,
Furthermore,

and employment

[Johnson 1975, pp. 47-48,

51].

an analysis of household decisions must consider

the social and economic institutional setting that influences
behavioral values and constraints

[De Tray 1977, p. 6],

The perceived advantages of the household production
function approach relative to traditional consumer choice
theory can be summarized as follows:
1)

Recognition that the family household,
members,

not its individual

is the appropriate basic unit of analysis for

examining decision making with respect to consumption
behavior
2)

[Johnson 1975, pp. 47-48].

Attention paid to the non-market sector of household
behavior by investigating changes in production technology
and corresponding output of commodities,

rather than

22
adherence to a restricted focus on market goods/services
only as the direct source of utility.
3)

Division of economic household behavior into production
and consumption activities such that preferences for
commodities are made distinct from the resources of
market goods/services and household time, thereby relat­
ing the utility function exclusively to the former.

4)

Inclusion of production technology levels that avoids
confounding with undue dependence on taste variables for
interpreting observed household behavior,

thus strengthen­

ing reliance on changes in income as well as money and
time costs associated with acquiring market goods/
services,

producing commodities,

and eventually consuming

them.
5)

Incorporation of time,

the ultimate limited and non-

accumulative scarce factor,
hold behavior.

into the analysis of house­

Time becomes a fundamental unit of cost

(along with the money price of market bought goods/
services)

in individual allocation decisions with respect

to supplying wage labor toward acquiring the market
goods/services,
commodities,

processing them into home produced

and consuming same

[Johnson 1975, p. 22;

T. W. Schultz 1972, p. 844].
6)

Examination of interdependent behavior of household
members in a comparative advantage context whereby the
relative productive efficiencies and opportunity costs of
each family member enter the household decision making

23
function in determining time (i.e.,
among alternative uses.

labor) allocation

Such gains from trade within

the family are in accordance with well established trade
theory.
7)

Represents a much needed effort to learn about the
internal workings —
cesses —

8)

especially decision making pr o­

of family households.

Makes money income resolvable into the work time required
to earn it,

so that consumption and labor supply decisions

are both facets of the allocation of the basic resource
possessed by every individual —
9)

time.

Makes explicit the interdependence of several household
decisions a b o u t :
a)

family labor supply,

time,

and consumption expendi­

tures in a single time period;
b)

labor force attachments,

family size,

and expendi­

tures on goods and human capital investments (e.g.,
education,

on-the-job training) in a life cycle

analysis.
The foregoing advantages not-with-standing the household
production/consumption function (HPF) approach does have its
limitations,

the most general one of which is that it is

still in its formative exploratory stages with much refine­
ment necessary for empirical research on precisely stated
and refutable hypotheses

[DeTray 1977,

p. 2].

Some of the

principal drawbacks are:
1)

The presumed existence of a single household utility

24
function as an aggregation of all family members'
individual utilities is somewhat suspect.
2)

Another problem in the application of the HPF approach is
the assumption all household activities are production
processes, whereas they may well be expressions of
preference orderings.

Moreover,

it is difficult to

determine where production functions stop and utility
functions begin —
measures of

especially when direct empirical

'commodities1 produced and other relevant

variables are not available

[Pollack and Wachter 1975,

p. 274].
However,
Even if we have no observations on the produc­
tion of commodities by the household, we can
still study the allocation of time and goods
among household activities.
[That is to say,]
... We can still derive the demand function for
the activity inputs as functions of P, w, and
A.
(P = good's prices, w = wage rate, A =
non-labor income.)
[Pollack and Wachter 1975,
p. 275]
However,

the foregoing does depend on our being able to

distinguish the use of a market good/service or time in
one activity from its use in other activities;
time allocation,

and for

it must be possible to divide the day

into non-overlapping activities.

(i.e., Time cannot be

used simultaneously in two a c t i v i t i e s . )

Fortunately,

If this can be done, then the allocation of
goods among activities can be analyzed without
the household production function apparatus!
[Pollack and Wachter 1975, p. 276]
3)

Another serious difficulty is the prevalence of joint
production

(i.e., where an activity has more than one

25
commodity associated with it and hence reduces the cost
of producing each), most notably when time spent in a
production activity is also a direct source of utility
(i.e., work time may be a form of consumption as in the
"joy of cooking," the fun of gardening,
farming!).

Therefore,

or the love of

it is only in cases of household

indifference among alternative uses of their time that
(a) the price of time will equal the marginal wage rate
[Gronau 1970, pp.

10-11]

and that (b) the household

production/consumption function approach will provide a
satisfactory account of the allocation of time

[Pollack

and Wachter 1975, p. 256],
It is recommended that:
When household activities can more plausibly be
interpreted as directly producing a specific
type of utility or satisfaction, the appro­
priate alternative is to analyze the "inputs"
— the allocation of (market) goods and time
among household activities —
as a function of
(market bought) goods prices, the wage rate
(i.e., cost of time), and non-labor income.
[Pollack and Wachter 1975, p. 272]
Supposedly this framework still retains the insightful­
ness of the household production/consumption function
a p p r o a c h ’s emphasis on household produced commodities,
while dispensing with these two burdensome assumptions
that a r e n ’t critical to the study of allocation of time
and goods among activities —

provided only that these

allocations are themselves observable

[Pollack and

Wachter 1975, p. 276].
4)

The useful application of the HPF approach is also

26
contingent upon having the implicit commodity prices in
the demand function independent of the commodity bundle
consumed; but for this to be the case household produc­
tion technology must be assumed to exhibit constant
returns to scale and no joint production (i.e.,
bility) —

a restriction which,

separa­

if violated, would mean

that commodity prices depend on the household's consump­
tion pattern and hence on tastes;

that is, price

differences among households reflect differences in taste
as well as technology.

This would render inaccurate the

demand for commodities as a function of commodity
prices.

Yet,

this was the very situation the household

production/consumption function approach was designed to

5)

rectify

[Pollack and Wachter 1975, pp. 256 and 269-72],

Finally,

the HPF approach does not distinguish between

time spent at home work (i.e.,
time used in leisure (i.e.,

home production time) and

home consumption time).

These functions should be separable,

and not aggregated

into one entity called "non-market" or "home" time and
presented as a single alternative to market labor time
[Gronau 1976, p.

2].

pointed out by Mincer

The importance of this was first
[1962]

in his classic study of

"Labor Force Participation of Married Women" and con­
firmed in subsequent research

[Bloch 1973; Gronau 1976],

which showed that "changes in the socio-economic
environment
education,

(e.g.,

change in the wage rate,

income,

and number of children) have different effects

27
on work-at-home and leisure and on the allocation of
time of husbands and wives"
b.

[Gronau 1976, p. 3].

New Home Economics
In an effort to make modern consumer demand theory

more amenable to the practical difficulties of empirical
research,

Gronau

[1976] has revamped Becker's HPF approach

[1965], which allows only a dichotomous choice of time
allocation between market and non-market time,

to more

closely approximate the tripartite analysis of market labor,
housework,

and leisure time pioneered by Mincer

[1962],

whose labor supply model was revitalized into the broader
context of "new home economics" with implications for the
study of many other topics:
patterns,

health maintenance,

savings and investments,

education and training,
marriage choices,

consumption

transportation modes,

information search and migration,

fertility and family size,

child care,

etc.
Essentially, Gronau's model specifies that work-at-home
(i.e., home production time) generates services which have a
close substitute in the market, while leisure (i.e.,

home

consumption time) has only poor substitutes in the market.
It is assumed that personal work has at least some degree of
disutility and that available labor service substitutes will
be purchased in the market if the cost is sufficiently low.
Correspondingly,

use of a surrogate to enjoy leisure is

impractical if not impossible

[Gronau 1976, p. 6],

Using the HPF terminology,

a household is said to

28
maximize its welfare:
U = u (Z 1 , Z g , . . . , Zr )
by maximizing the amount of commodities,

Z., each of which
J

is a combination of goods and services (X) and consumption
time ( L ) :
Z . = z (X. , L . )
3

i

i

These goods can either be purchased in the market
or be produced at home (X^)-

(Xm )

It is assumed that Z is not

affected by the composition of X, to which the household is
indifferent in consumption.

In fact Z = z (Xm , X^, L) has

been demonstrated to have little predictive power
1976, p. 6].

[Gronau

It is further assumed for simplicity that the

commodity production functions (1) are linear homogeneous,
(2) differ between commodities,
each other (i.e.,

and (3) are independent of

the production process of Z^ is unaffected

by the level and method of producing Zg).
fully cognizant of Pollack and Wachter's
Gronau

[1976]

Moreover, while
[1975]

critique,

nevertheless reluctantly assumes for simplicity

sake that no joint production or consumption prevails.
(NOTE:

A detailed exposition is presented in section A-2

'Analytical Paradigms'
c.

of this chapter.)

Life Cycle Allocations
Consumer demand (i.e., utility) theory (e.g.,

optimizing goods and time allocation among alternative
activities) and human capital (i.e.,
(e.g.,

investment) theory

improving the mental and physical capabilities of

human stock) are but partial views of the world.

The effort

29
to integrate these approaches with reference to consumption
and labor supply decisions has principally involved examining
series of static utility maximizing choices over the life
cycle

[Ghez and Becker 1975]

that would provide variation in

consumption behavior with age.

A fundamental premise of this

life cycle approach is that households take account of
expected future events when making decisions

(e.g., goods

consumption patterns and labor force participation) as first
proposed in Fisher's

[1930]

theory of interest and planning

over time, during which the value of time changes according
to one's present life stage (i.e.,

age group) and thereby

affects the household production/consumption technology
chosen.

Time intensive modes are more likely during both the

early stage of schooling and the later period of retirement
when time has a lower opportunity cost

(i.e., value) and

less working hours are supplied to the labor market —
relative to the prime age working years, when the value of
time is higher (i.e., opportunity cost of leisure in terms
of foregone earnings) and goods-intensive household processes
predominate

[Michael and Becker 1973,

p. 389].

When wage rates are high, not only is the pro ­
duction of each commodity relatively goodsintensive, but consumption shifts towards
relatively goods-intensive commodities and away
from time-intensive commodities.
The latter
(e.g., children or grandchildren) would be con­
sumed more at younger and older ages if wage
rates or more generally the cost of time rose
at younger ages and fell eventually; conversely,
goods-intensive commodities would be consumed
more at middle ages.
These age patterns in the
consumption of time and goods intensive commo­
dities strengthen the tendency for consumption
time to fall initially (with age) and for goods

30
to rise initially with age.
p. 59]

[Becker 1975,

Life cycle patterns of goods consumption and time usage
have generally been analyzed by constructing "typical pro­
files" of a "representative" consumer
1976;

[Smith 1975; Heckman

Ghez and Becker 1975; Weiss and Blinder 1976; Ryder,

Stafford and Stephan 1976]

rather than by examining how a

cross section of consumers respond to variations in such
initial conditions as their wage rates,

human and financial

asset levels, market rates of interest,

tax rates,

identical ages in their life cycles
& 21].

etc.

at

[Heckman 1976, pp. Sll

The latter approach is one of "comparative dynamics"

whereby "at each age,

the consumer may be viewed as re-

maximizing remaining life time utility," given initial
conditions from previous optimal behavior

[Heckman 1976,

p. S 2 2 ].
Obviously a dynamic mode is more appropriate for what
is really a dynamic problem:
over an expected life span,

the allocation of resources
during which today's decisions

influence tomorrow's choices.

Unfortunately,

as more

variables are progressively endogenated into dynamic models,
it becomes increasingly difficult,
ble,

if not well nigh impossi­

to obtain explicit solutions to these models —

adequate longitudinal data were readily available
1975].

However,

even if

[Stephan

dynamic models can be useful in alerting us

to the interdependencies that exist and could possibly alter
the conclusions of the simple models more commonly employed;
as such,

the former can provide a rigorous test of the latter.

31
James P. Smith has done the most in advancing labor
supply research on "Family Decision-Making Over the Life
Cycle"

[Smith 1972,

1973,

numerous other researchers

1975].

Following Smith's lead

[DeTray 1973, p. 37; Da Vanzo

and Greenberg 1973, p. 73] have acknowledged the necessity
of a life cycle component by incorporating them into their
models.

However,

rarely can they go beyond a pro forma

inclusion for the lack of longitudinal data on which such
multi-period empirical research should appropriately be
done.

Basically, what the life cycle aspect of labor supply

attempts to account for is the effect of income generated by
the accumulation of assets over a lifetime.

It is thus p r e ­

sumed that during early periods of a household's work life,
individual members (especially male heads) will supply more
labor to the market when they are trying to get established
( e . g . , purchase of an initial home) than in later periods
when disinvestment of fixed assets (e.g.,

sale of an over­

sized home, when the children have grown up and gone) in
order to live off the more liquid capital gains and interest
thereon.
d.

Human Capital Theory
The other intellectual base, besides consumer choice

theory, upon which labor supply analysis rests is human
capital theory in terms of self investment decisions during
a particular time frame and/or spanning several periods.
Under Becker's revised specification

[Becker 1975, p. 63]

investment in human capital is the third major category (in

32
addition to market

labor force activity and aggregated non-

market production/consumption activity) to which time may be
allocated.
children)

Human resource investment in oneself

(or dependent

is a time-intensive activity that can take the form

of schooling,
migration,

on-the-job training,

etc.

personal health care,

and involves expenditures (i.e.,

actual

outlays for market goods/services as well as the opportunity
cost of foregone earnings associated with sacrificed labor
market time and earnings and/or home produced commodities)
that contribute to the creation of more productive human
stocks which can provide a stream of future services p o s se ss ­
ing both monetary and psychic value.

Assuming a person

knows his discount rate and probable remaining occupational
lifetime over which monetary returns will be garnered,

a

rational cost/benefit analysis can be employed for human
capital investment decisions.
Predictably,

time spent building human capital declines

with age as the present value of future returns decreases the
cost of investment and rises in terms of foregone earnings
(Becker 1975, pp. 64-65].

The psychic value return of human

capital investment constitutes personal satisfaction derived
from consumption activities, which in a HPF framework would
include the all important use of non-market time in p r o d u c ­
tion (e.g.,

children as human capital investment can contri­

bute to household production besides being objects of
personal gratification to parents).

Hence,

human capital

investments can expand the opportunity set of a household and

33
increase its "full real income" by raising the market value
of time (i.e.,

the wage rate) and by raising the productivity

of non-market consumption activities,

through which a lower

household commodity price index results

[Michael and Becker

1973, pp.

The increased

389-90; Becker 1975, p. 67],

productivity,

and thus value,

buted to two effects:

of human time can be attri­

a 'worker effect'

whereby improved

labor skills from human capital investment result in higher
efficiency in production,

and an

'allocation effect' whereby

improved management skills result in increased efficiency in
resource allocation in response to changing conditions
(i.e.,

technology, market,

etc.).

The ability to adjust

rapidly to disequilibrium has economic value,

as the litera­

ture on the adoption of innovations —

especially in agri­

culture —

Huffman 1974; T. W.

well documents

[Welch 1970;

Schultz 1975].
Human capital investments of education
ing) and experience

(formal school­

(on-the-job training) strongly influences

the efficiency with which people are able "to perceive,

to

interpret correctly and to undertake action that will
appropriately re-allocate their resources"
1975, p. 827].

[T. W. Schultz

Such "allocative ability" presumes a house­

hold has full knowledge of its production possibilities and
value thereof and uses rationality in the application of
decision criteria (e.g., balancing marginal costs and
marginal benefits) governing the allocation of household
resources,

the principal one of which is time —

34
proportionately more so, the poorer the household is in
terms of wealth and non-labor income resources.

The value

of this time in alternative uses therefore reflects not only
market conditions of demand and supply but also human
capital investments —

hence,

the contribution of Human

Capital Theory to the analysis of labor supply decisions of
households.
In terms of usual labor supply studies such human
capital variables as health/disability status,
experience (i.e., on-the-job training),

job market

and education (i.e.,

formal schooling) are included not only as determinants of
hours of work, but also as determinants of the wage rate/
earnings which has a price-quantity relationship with hours
[Mincer 1974].

The importance of human capital theory in

this regard will be seen later during the discussion of
instrumental variable techniques for imputing wages for both
those who don't work in the wage market as well as those who
do.

2.

ANALYTICAL PARADIGMS
While the previous sub-sections on theoretical founda­

tions included an exposition of not only consumer choice and
human capital theories, but also the household production/
consumption model,

this section will limit its focus to

specific illustrations of the latter as it pertains to
allocation-of-time decisions only.
The accompanying figures are merely modern extensions
of the text-book labor-leisure choice diagrams

(Figure II-l)

35

INCOME

w

o

T
LEISURE

Figure II-l.

WORK

Simple labor/leisure choice model

TIME

36
that now incorporate household production as the third
alternative in the decision framework.
In Figure II-2 we have on the vertical axis the composite
good Z, representing the bundle of goods that can be made in
the home or bought in the market as inputs for use (along
with household time)

in commodity production.

Time is

measured along the horizontal axis T, where OT would be a
corner solution of full-time leisure with no home production
and no purchased goods.

Any interior solution along the

concave opportunity frontier curve involves the use of time
in activities other than leisure.

Allowing for 8 hours of

sleep in a 24 hour day leaves 16 hours for allocation
between leisure,

home production and market work.

At point

A, where the real market wage rate line WA is tangent to the
opportunity frontier curve,

it can be seen that aT (3) hours

of time will be allocated to home production activity —
leaving Oa (13) hours for further allocation between leisure
and market w o r k .
The indifference curve 1^, signifying the household
utility function,

is drawn tangent to the real wage rate line

WA thus revealing the time allocation preference of the
decision maker.

(NOTE:

For purposes of simple exposition a

single person household is illustrated;

see Evenson

[1978]

for detailed presentation of the more complex graphical
analysis of the two person household,

complete with gains

from specialization achieved through application of the com­
parative advantage p r i n c i p l e . )

Tangency at point

indicates

37

COMPOSITE
GOOD

Z

w

o

o

a.
TIME
LEISURE
TIME

Figure II-2.

MARKET
WORK

HOME
PRODUCTION

Household production function model.

38
a decision to devote ba (8) hours to market work,
Ob

(5)hours for

Z axis, the more
intensive)

leisure.

leaving

The closer that point B is to the

goods-intensive (as opposed to leisure­

is production/consumption.

Farm production can easily be incorporated into the
basic household model already presented.

In Figure II-3

there are two opportunity frontiers drawn —

the familiar

home production curve HT, plus the combined home-and-farm
production curve FT.

The off-farm real wage rate line WC is

shown tangent to the farm-and-home production possibilities
frontier FL at point C, which divides available time into
cT

(7) hours for

farm-and-home production activities and

Oc

(9) hours of leisure and market work.

It is assumed here

for purposes of illustration that the returns to labor are
initially greater in agricultural production compared to
off-farm wage employment,

due to diminishing returns to labor

on-farm for a given level of complementary inputs in
production.

This makes farm employment his primary job and

off-farm employment his secondary job.

The farmer will con­

tinue to work at his primary farm job so long as the marginal
wage rate received from farming exceeds the wage he would
gain from off-farm employment.

However,

when the off-farm

wage offer WC rises above (i.e., becomes a steeper slope
than) the marginal wage rate FC from farm work,

the operator

will be induced to transfer some of his work time to the
off-farm job.

That

is, the farmer can move to a higher in­

difference curve tangent to the off-farm wage rate instead

39

COMPOSITE
GOOD
w

z

TIME
LEISURE
TIME
Figure I 1-3.

MARKET
WORK

FARM
LABOR

HOME
PRODUCTION

IIPF farm model and work/leisure preference.

40
of the on-farm wage rate.
The allocation of time between farm production and home
production is determined by the location point A on the home
production curve where its slope is equal to the real offfarm wage rate line WC.

Hence,

aT (3) and ca (4) represent

the hours spent in production activity in the home and on
the farm respectively.

The indifference curve I^ enables us

to discover the household's preference between market work
time be (7) and leisure time Ob (2), which is determined by
its tangency with the off-farm wage rate line WC at point

B.

1.

RESEARCH METHODOLOGIES

DATA BASES
Longitudinal or panel data is conspicuous by its

general absence in labor supply studies.

In light of recent

development of the household life cycle model of decision
making

[Smith 1975]

Unfortunately,

this type of data is badly needed.

such data that is available is usually of the

five to ten year range, which constitutes at most only one
stage of the full life cycle.

The best data available in

this regard is the University of Michigan's Income Dynamics
Panel data upon which only a few labor supply studies have
been conducted

[Wales and Woodland 1976,

1977].

Cross section data is by far the most prevalent avail­
able.

Many labor supply studies have been done on 1/1000

Census of Population data, mainly 1960 vintage
1966,

[Kosters

1968; Ashenfelter and Heckman 1974; Ghez and Becker

.

41
1975].

The 1967 S.E.O.

(Survey of Economic Opportunity)

data has been a popular sample population for numerous labor
supply studies —
compendium

especially those listed in one published

[Cain and Watts 1973].

The formulation of the

household life cycle model has highlighted the limitations
of cross-section compared to longitudinal data.
tions in sample stratification (e.g.,
statistical techniques,

But innova­

age cohort groups) and

in addition to economic modelling,

have helped make this type data more amenable to estimation.
In recent studies of off-farm and on-farm employment of
farm operators,

the data examined have included:

USDA survey of 960 tobacco farmers in Virginia,
Carolina and South Carolina

[Sexton 1975];

survey of 1400 farm operators in Illinois,

the 1973
North

the 1971 statewide
collected under

the auspices of the University of Illinois Department of
Agricultural Economics
1978];

the 1964 U.S.

[Sexton 1975; Barros 1976;

Census of Agriculture

Sumner

[Huffman 1973],

and the 1969-72 Rural Income Maintenance Experiment

(R.I.M.E.)

data on 250 Iowa and North Carolina farm family participants
(plus control group farmers)
Kerachsky 1975,

[Bryant and Hager 1977;

1977; Primus 1975,

1977].

Sub-optimal as it is to have no recourse but to conduct
analyses on data for purposes unintended by the original
survey designers,

it is even more distressing that the

reliability of such general data is questionable —

being

plagued with deficiencies like those noted for the regular
U.S.

Census of Agriculture

[Ingram and P rochaska 1972],

42
which in 1969,

compared to 1964,

provided less, not more,

detailed information on family members appropriate to the
household model of labor supply
the R.I.M.E.
error,

[Huffman 1976].

Even some of

data was subject to considerable measurement

requiring careful editing,

as,

for example, with the

net income variable which is of critical importance not only
for determining participation eligibility in the income
maintenance program,

but also for estimating household labor

supply responses to it

[Primus 1977, p. 864].

problems notwithstanding,
1975; Primus 1975]

the R.I.M.E.

studies

These data
[Kerachsky

have also been criticized for their

faulty specification of variables

[Huffman 1977].

Comparison of results among these studies is difficult
because the same variables are not consistently used in
each; moreover,

even for identical variables the measures

selected may differ for reasons of judgement and data limita­
tions .

2.

ESTIMATION TECHNIQUES
Selection of estimation procedures is influenced not

only by the substance and form of data available for analy­
sis, but also by the type of variables specified —
response variables,

especially

which are discussed below.

Labor supply studies are typically concerned with
examining the effects of explanatory variables on two
different kinds of response variables,
tinuous:

labor force participation,

Labor force participation

categorical and con­

and hours-of-work.

(LFP) is a discrete variable which

43
can be measured on the basis of aggregated data for a group
of individuals'

participation rate (L.F.P.R.) or disaggregated

data for each individual's participation status (L.F.P.S.).
LFP status is usually of a dichotomous (binary) nature
whereby a value of

*1 ’ is assigned to a person who is in the

labor force (i.e.,

employed) and a value of

'O' is designated

for the person not in the labor force (i.e., unemployed).
In symbol notation,

since labor force participation Yi can

only assume two different values,

1 and 0, the expectation

of Y is:
E(yi) =

[1 . fi(l)]

+

[0 • fi(0)]

= fi(l)

where fi(l) is the probability that a person with certain
(observable) characteristics and (unobservable) preferences
will enter the labor force.
The importance of labor force participation in a study
of annual hours of work is based on the idea that the latter
is conditional upon the former

[Heckman 1974,

1977].

Such a

formulation of labor supply decision making can thereby
include for estimation individuals reporting zero hours of
work as non-participants and thus avoid the possibility of
selectivity bias associated with selecting only a subsample
(i.e.,

those working) from the entire sample.

This relates

to the problem of truncation when observation of the response
variable is bounded at zero.
Labor supply measured in hours-of-work has a truncated
distribution of values;
worked is possible.

that is, no negative value of hours

This presents a problem,

especially when

44
there are a large number of observations concentrated at and
near zero.

This difficulty is most acute when estimating

the labor supply of secondary workers such as housewives and
potential multiple-job-holding farmers,

large proportions of

who m are not working in the wage sector.
There exist four basic methods for coping with this
situation.

One,

assume that the individuals with zero

hours-of-work are similar in every other respect to the w o r k ­
ing segment of the sample and exclude them from the sample.
Ordinary least squares is then used to estimate the hoursof-work equation based on the subsample of positive values
for the response variable.

This is a strong assumption and

much information is lost if the number of cases with zero
hours worked is relatively high.

Such sample censorship

results in selectivity bias.
A second method is to include nonparticipants and assign
them a zero value for hours-of-work.

The conventional O.L.S.

is then used to estimate hours-of-work for the entire
sample

[Greenberg 1972,

admit to truncation bias

p. 11].

Of course such studies

[T. P. Schultz 1975, p. 33].

The third method takes into consideration the zero
bounded distribution of observations on hours-of-work.
technique used to address this situation is TOBIT —

The

an

integration of PROBIT for the binary decision of whether or
not to work and ordinary least squares for the choice of the
non-zero levels of wage work.

It is designed to allow for

variation in the dependent variable that is limited

[Tobin

45
1958; Greenberg and Hosek 1976, p. 16].

However,

this can

be a computationally burdensome and costly procedure.
At this point it should be noted that the preceding two
methods usually involve some form of an estimated wage rate
imputed primarily on the basis of human capital characteris­
tics thought to determine wages and be common to the entire
sample,

regardless of labor force participation status.

The

wage rate is estimated on the basis of the job holding sub­
sample for which actual wage rates can be observed.

Then,

once the coefficients for the wage equation are known,
estimated wages can be assigned to the entire sample.
ever,

How­

this procedure is not used in the fourth method of

estimating hours-of-work.
This most recent method

[Heckman 1974,

1977]

of estimat­

ing a continuous labor supply function also involves
incorporating the labor force participation decision into
the hours-of-work decision.
[Boskin 1973, pp. 164-65]

But whereas the rudimentary form

is a two stage process whereby the

hours-of-work decision is made conditional on the decision
to participate in the labor force,
a three step process.

First,

this exposition involves

LOGIT analysis is used on the

entire sample, working and non-working,

to estimate the

probability that an individual is in the labor force.

Second,

for those in the labor force the probability that they are
working is calculated.

Third, using O . L . S . , an hours-of-work

labor supply function (but only for those actually employed)
that includes as regressors the probability of labor force

46
participation along with their actual wage rate is estimated.
No imputation of the wage rate is necessary to preclude
selectivity bias,

since the initial step in the procedure

utilized information from the entire sample —
those not participating

[Heckman 1976].

inclusive of

Unfortunately,

"Although Heckman's work represents a significant m e th od ol o­
gical advance,

it was computationally quite expensive and

his technique was,
research"

therefore, never adopted in applied

[Smith 1980, p. 9].

Rand Corporation comparisons

between Heckman's method and the alternative of imputing
wages to all women and estimating the hours equation over the
complete sample indicate much smaller systematic differences
are found between them than is true of the comparison with
the procedure of using only the subsample of working women
[Smith 1980, p. 10] .
The problem of zero truncation becomes unimportant

and

the slope of an ordinary least squares (OLS) function over
workers will closely approximate the TOBIT index function,
if discontinuity in labor supply is large.

Discontinuity

exists when observations of hours worked do not occur near
zero, but instead at some substantially higher number of
minimum entry hours.

Such discontinuity is attributable to

equality of the market wage with the reservation wage at a
positive quantity of hours, which in turn is due to the fixed
time

(e.g.,

commuting,

rest) and money

uniforms) costs of work.

(e.g.,

In other words,

gasoline, meals,

an individual will

work at least that minimum number of hours which will cover

47
his fixed expenses of being employed,
will be positive;

otherwise,

such that net earnings

why take a job at all.

It has

been noted that fixed time costs reduce observed hours worked,
while fixed money costs increase the hours worked.
discontinuity is sufficiently large,

When the

the importance of

selectivity may be severely diminished

[Smith 1980, pp.

14-

15, 20, and 22].
Experiments contrasting simple linear (OLS) estimates
and non-linear maximum likelihood (TOBIT) estimates
Schultz 1975]

found them to "produce quite similar results

at the sample means,

indicating that OLS is a good linear

approximation to TOBIT"
however,

[T. P.

[Smith 1980, p. 19].

They do,

diverge significantly away from each other at the

extreme (i.e.,

zero) end of the hours of work distributions

when the labor supply function does not exhibit discontinuity.
The advantages of the TOBIT framework are that:

(1) it

explicitly estimates the variance of the disturbances about
the TOBIT index,

(b) it provides estimates of the two

components of the expected labor supply:

the participation

rate and hours worked conditional upon participation
Schultz 1975],

[T. P.

and (c) it increases the reliability of

predictions for demographic groups (i.e., non-labor force
participants) that are not representative of the sample
means

[Smith 1980, p. 19],

A difficulty of using TOBIT is

that the estimates of the coefficients are not directly
interpretable,

at least not as the values of dependent

variables approach the bound,

nor are they easily transformed

48
into an interpretable form

[Kerachsky 1975, p. 87].

When it comes to actual empirical results,

the TOBIT

procedure in comparison with the linear ordinary least
squares method,

accounts for only a slightly increased share

of the variance of hours worked.

"In sum,

the TOBIT

technique seems a warranted application of more costly non­
linear estimation procedures to the study of labor market
behavior.

As a first approximation,

however,

are not likely to lead one far astray"

linear methods

[T. P. Schultz 1975 as

reported in Smith 1980, p. 81].
For essentially these reasons Kerachsky

[1975] elected

not to use TOBIT analysis of on- and off-farm labor supply
analysis, while Sexton

[1975]

and Sumner

[1978] opted for

the use of OLS in their analysis of farm household labor
supply.
Of the various techniques subsumed under the simple or
multiple linear regression model, Ordinary Least Squares
(O.L.S.) is the one technique most commonly used for estimat­
ing continuous and unbounded linear functions.

O.L.S.

is

known to yield best JLinear unbiased estimators (i.e.,
B.L.U.E.)

for both bivariate and multivariate regression

analyses,

if its assumptions are met.

Specifically,

the

estimated disturbance term is assumed to have the following
characteristics:

randomness of individual errors, homo-

skedastic (or constant) variance of the errors for all
observation of explanatory variables,
error terms.

and independence of the

If such assumptions are not violated,

O.L.S.

49
estimators have the desirable properties of unbiasedness
( i . e . , the expected value of the estimator coincides with
the true value),

efficiency (i.e., distribution of the

estimator is highly concentrated about the sample mean),
consistency (i.e.,

and

the estimator increasingly occurs closer

to the mean as sample size becomes larger).

Violation of

these and other assumptions will adversely affect such
desired estimation properties.

(NOTE:

This matter is more

fully discussed under section E "Estimation Accuracy" of
Chapter III.)

C.

1.

EMPIRICAL STUDIES

CLASSIC WORKS
Leaving aside the creative theoretical thinking of

Lionel Robbins,

Jacob Mincer, Gary Becker,

and Reuben Gronau

(among other distinguished labor economists) whose contribu­
tions to the field have already been discussed with reference
to "Conceptual Frameworks"

(section A),

the immediate focus

here is on the application of such models to actual data
with all its inherent and seemingly endless deficiencies.
Among the many pathbreaking studies,

there is one to

which all others repeatedly express an intellectual debt;

and

that is Jacob Mincer's 1962 paper entitled "Labor Force
Participation of Married Women:

A Study of Labor Supply."

In it he was the first to distinguish between work at home
and leisure,

at least for female householders.

He also

viewed a family's labor supply decision as being based on its

50
perception of potential income from labor and other sources
over an intermediate time horizon rather than just on actual
current earnings.

These two innovative ideas were followed

up by many researchers in the 1960s and 1970s, most of whom
were associated with either the National Bureau of Economic
Research (N.B.E.R.) or the Rand Corporation.
The first contribution of Jacob Mincer,

that of dis­

tinguishing between home work and leisure rather than lump­
ing it together as non-market time,

has been most energeti­

cally pursued by Reuben Gronau in his many studies on "The
Value of Time"
Again,

[Gronau 1970,

1973,

1974,

3976,

1977].

the difficulty has been with the lack of comprehensive

information on time use.

Not surprisingly it is the

anthropologists who are in possession of such data as a
result of their direct observations of households in other
cultures, usually less technically advanced.

Economists are

now gathering such information by field surveys and direct
observation,

but —

alas —

of less developed countries
the

'frontier'

mostly in the agrarian societies
[DeTray 1977].

Consequently,

literature is not likely to be on the U.S.

population with its keener sensitivity to intrusions upon
privacy in terms of direct observation and data collection.
One exception is the University of Michigan diary of time
use data.
The whole thrust of time valuation within the household
context is really an effort to reflect adequately the impor­
tant contributions of female heads rather than just

51
concentrating on male labor supply.

Hence,

literature of

the late 1960s and 1970s has been dominated by studies of
married women (as well as the many reports on low income
families —

female and male heads of household).

Moreover,

a good proportion of these labor supply studies is focused
on labor force participation decisions as opposed to hoursof-work, which is the response variable for this research.
Because of the different data bases,
variable measures,

the different

the different behavioral models,

different estimation procedures,

and the

it becomes well nigh

impossible to make consistent comparisons of research results
across the vast number of studies.

However,

the Rand

Corporation has conducted two sensitivity analyses of
studies having a common data base:
work

one on male hours-of-

[Da Vanzo, DeTray and Greenberg 1973]

and another on

housewive's labor force participation decisions

2.

[Cogan 1975],

RECENT PROBES
Capitalizing on all this theoretical and empirical

groundwork of the 1960s and early 1970s,

agricultural

economists began to examine the off-farm migration and
multiple-job-holding using a household behavior model.
Previous diagnostic examinations of on-farm labor supply are
minimal and, with one exception,

have been focused on the

impact of Rural Income Maintenance Experiments

(R.I.M.E.)

conducted in North Carolina and Iowa in the early 1970's
[Bryant and Hager 1977; Karachsky 1977;

and Primus 1977],

These studies examined the influence of government income

52
supplements on the labor supply decisions of farmers.

The

aforementioned exception was a study principally concerned
with off-farm employment that incidentally included on-farm
labor supply regression equations
[1975]

analysis of R.I.M.E.

[Sumner 1978].

Kerachsky's

data looked at self-employment

(as well as off-farm work) of husbands in a multiple-jobholding context

(while limiting his focus on wives to wage

employment in a single market framework).
investigation of R.I.M.E.

farm wives.

[1975]

data concentrated on the farm work

response of farm operators.
of the R.I.M.E.

Primus's

Bryant and Hager's

[1977]

study

data zeroed in on the unpaid farm work of

S u m n e r ’s

[1978]

examination of the Illinois

farm survey data pertained to the on-farm hours of work (in
addition to the off-farm labor supply) of operators

(while

restricting his analysis of wives to their decision to
participate in the wage market).

A detailed review of the

findings for these studies is deferred until Chapter V,
section B-2 "Empirical Consistency" where the results of the
research herein are analyzed with respect to their consistency
with other empirical works such as these.
A few other studies,

essentially using the same

methodology but devoted exclusively to off-farm labor supply
decisions of farmers,
few years

have also been published in the last

[Huffman 1973,

1977; Scott 1977;

1976,

Kada 1979].

1980;

Sexton 1976; Barros

Numerous other studies have

looked at the phenomena of multiple-job-holding and off-farm
employment generally

[Hathaway and Waldo 1964;

Loomis 1962,

53
1964,

1965; Hathaway and Perkins 1965];

and there are many

others examining non-farm income.
Why,

then,

the dearth of on-farm labor supply studies?

The answer may lie with the critical assumption that multiplejob-holding is a transitory,

rather than permanent,

adjust­

ment to the changing structure of agriculture and a prelude
to eventual complete off-farm migration.

This,

of course,

was a reasonable assumption in the past and many studies
seemed to confirm this phenomenon during the precipitous
decline in farm population during the quarter century follow­
ing World War II.

Thus the major concerns were with u n de r­

standing the nature of off-farm migration,
structural adjustment policies,

formulating

and designing manpower train­

ing programs for these farm leavers.

Consequently,

previous

studies examined off-farm labor supply with the implicit
assumption that less time was accordingly being supplied onfarm.

However,

knowing the extent of off-farm work and its

determinants can be no more than an indirect measure of onfarm labor supply.

This is especially so with reference to

limited resource small-farm operators,

for whom on-farm

and off-farm work are not mutually exclusive and may not even
have some precise ratio of hours trade-off.

This is not to

suggest that off-farm labor studies aren't indicative of
on-farm work time —
whole;

especially for the farm population as a

it is merely that they are insufficient,

if one's

principal focus is the farmer in the capacity of a selfemployed operator.

And this has become more apparent as

54
Agricultural Census figures for the 1 9 7 0 's indicate a sub­
stantial leveling off of rural and farm out-migration
1976,

1977].
In the case of Michigan,

past small-farm surveys have

provided evidence of a more permanent,

rather than transitory,

nature of multiple-job-holding among operators
1964,

[Beale

1965; Hathaway,

Hepp 1979].

Hence,

et al.

[Loomis 1962,

1966; Thompson and Hepp 1976;

the specific emphasis of this study is

with the on-farm labor supply decisions of low farm income
families in Michigan.

3.

INTERDISCIPLINARY QUESTS
a.

Seminal Writings
Sociology is the only other academic discipline to

study U.S.

farm households in detail.

Their studies can be

classified into three major categories:

(a) Conjugal power

structure and farm family decision making,
and value formation of farm families,

(b) Goal setting

(c) Career mobility and

off-farm migration of farm operators.
Conjugal power structure studies focus primarily on who
possesses authority to make decisions within the family.
Various types of power are identified (e.g.,
legitimate,

referent,

reward,

coercive,

expert) and theories are advanced to

explain why one spouse rather than another might exercise
more authority in decision making (e.g., whether wife should
work)

[Safilios-Rothschild 1970; Centers,

and Rabunsky 1972].

et al.

1971; Olson

The Resource Theory concerns how personal

attributes (e.g., years of schooling,

occupational status,

55
income level,

degree of social participation)

exercise of authority,

influence the

while the Exchange Theory relates how

personal possessions (e.g., money,

love) can be bartered

among household members in an effort to maximize one's
power.
Although these two theories have not been fully sub­
stantiated with respect to farm household studies
and Bharadwaj

1968;

[Wilkening

Wilkening 1968], they are mentioned

because they are concerned with family decision making which
presumably includes the allocation of time which is central
to the labor economist's models of the household.

Moreover,

some of their findings concerning involvement with farm
tasks (i.e.,

labor) —

especially of the wives —

potential interest to labor economists.

is of

Such discoveries

are reported in the next section "Pertinent Findings."
Goal setting and value formation,

the second area of

concern by sociologists studying farm families,

is one in

which Michigan Cooperative Extension Service agents found
small farm operators to be in need of counseling
1978].

[Olson

A review of sociological studies on decision making

relating to the field of consumer economics reports that "an
appreciable proportion (of farmers) do not have clear finan­
cial goals or plans in the sense of clearly enunciated
programs of allocation of income or acquisition of assets,"
although they were "much more common among
younger families,

those better educated,

... farmers in

and in families

where the wife was in a professional or managerial occupation"

56
[Ferber 1973, p. 1327].
The farm family studies in this area are concerned with
household members'

individual aspirations and how they are

associated with participation in decisions about the farm
business

[Wilkening and Bharadwaj

1968].

Generally,

farm

household studies have found that while husbands were the
most frequent deciders about operational matters (e.g.,
agricultural enterprises) decisions involving financial
investment

(e.g., buying farm land, borrowing money) are

usually of a joint nature

[Wilkening 1958; Wilkening and

Morrison 1963; Honey 1959; Ferber 1973, p. 1328].
Career mobility and off-farm migration constitute the
third category of sociological studies pertaining to farm
households.

They have identified some factors associated

with the reduction of on-farm labor and the corresponding
increase in off-farm labor as operators switch to part-time/
multiple-job-holding status or leave agriculture altogether,
b.

Pertinent Findings
One relevant finding is that "as (farm) income level

goes up so does the degree of task specialization and hence
less involvement of (the) wife in farm activities;" and
"with increasing size of the enterprise,

there is less ov er ­

lap of the family and the occupational areas of activity."
So "as the size of farm enterprises increases the wife is
less involved in both work and decision making roles in the
farm area.

At the same time the husband is less involved in

certain household tasks and decision making,

leaving these to

57
the wife"

[Wilkening 1968,

pp.

2-3] .

The influence of education on farm labor supply of
wives has also been noted:

"the more schooling,

she is expected to influence decisions,
she in involved in farm tasks."

the more

yet the less likely

Although "wives with higher

education relative to their husbands are more likely to be
involved in farm tasks"

[Wilkening 1968, p. 3].

In a separate study it was found that patterns of task
allocation are in conformity with the economists household
model of labor time allocation;

specifically,

"farm wives

who participate highly in the farm area do not participate
highly in household area"

[Wilkening and Bharadwaj

1967,

p. 710].
With respect to off-farm employment decisions of farm
wives the evidence indicates independence of choice;
is,

that

it is not a joint decision or even one dictated by or

requiring consent of the husband
p. 527; Wilkening and Bharadwaj

[Burchinal and Bauder 1965,
1967,

p. 708].

The signi­

ficance of this for labor economists is that a husband has
not been found to be a constraint on his wife's off-farm
labor supply.
As for farm operators

(i.e., male),

rural sociologists

have endeavored to identify the factors that are associated
with mobility out of full-time farming toward either parttime farming and/or complete exit from agriculture.
particular,

In

lower total farm income and farm income per

family member,

proximity to numerous non-farm jobs,

and

58
younger age are significantly associated with the shift
toward part-time farming

[Bennett 1967, p. 163].

Other reasons include health problems,
(i.e.,

lease renewal terms),

with limited acreage —

land tenure

and underemployment associated

though the reallocation of labor is

often solved via multiple-job-holding rather than abandon­
ment of farming

[Guither 1963, p. 570].

Another study found that people leaving agriculture
were not necessarily the small scale or part-time farmers.
"The people who are presently leaving agriculture are not
those with the lowest incomes,
poorest farmers,

the least efficient,

or the physically disabled."

the

Moreover,

since barriers to off-farm migration exist in the form of low
level job skills,
job information,

little wage work experience,

and lack of

the expected full impact of falling product

prices and resulting low incomes is somewhat mitigated.
"If it is a contest to see who can stay the longest without
starving,

it will more likely be the subsistence farmer with

a minimum of credit obligations;

not the larger, mechanized,

efficient organizations operating on credit with foreclosure
threats"

[Hill 1962, p. 426].

tives off-farm are not the

Those with attractive alterna­

'people left behind'

[National

Advisory Commission on Rural Poverty 1967] .
c.

Economics Interface
Aside from one article on farm adjustment problems

jointly authored by an agricultural economist and rural
sociologist

[Heady and Ackerman 1959]

and one other very

59
excellent article by a sociologist on farmer goals and
values

[Gasson 1973], which in part was addressed to agri­

culture economists,

little formal cooperative research of

the two disciplines has been reported —

at least in their

major professional journals.
Ironically,

the one such published study that does

attempt to integrate the findings of sociologists with those
of economists is concerned with labor supply decisions of
household members,
Supply"

"Family Power Structure and Family Labor

[Kushman and Scheffler 1975].

As the authors state

"we view the dichotomy between sociology and economics as
unfortunate.
the family,

The labor supply decision is important to
and labor supply behavior is likely to reflect

the way in which the decision is reached."

Their model of

labor supply allegedly provides evidence on sociological
theories of decision making.

Specifically,

the hypothesis of

male dominance by virtue of superior resources vis a vis
the female is not supported.

This result is consistent

with previous sociological findings already cited
and Bauder 1965; Wilkening and Bharadwaj

1967].

[Burchinal
The male

dominance hypothesis was tested by examining the impact of
spouse wage rates in the husband and wife's labor supply
equations.

The assumption is that the male makes his labor

supply decision prior to the female and that the wife takes
male labor supply as a constraint beyond her control.

No

cross substitution effect is expected in terms of female
labor supply response to a change in male wage rate,

though

60
it will demonstrate an own substitution effect for a change
in her wage rate.

The male model implies that in the female

labor supply function,

the response to a change in the male

wage will consist entirely of an income effect resulting
from the increased earnings of the male from his higher wage
rate.

SUMMARY

This chapter has presented an overview of the well
established economic theories of consumer choice and human
capital,
studies.

which constitute the foundation of labor supply
Moreover,

production principles derived from the

theory of the firm provide the framework for the recently
developed household production function model,

which can be

used to analyze labor supply decisions and suggest relevant
explanatory variables.

Comparison of least squares with

TOBIT and related estimation techniques indicates that while
the latter is more sophisticated in overcoming selectivity
bias of sample censorship,

the use of OLS with an instru­

mental variable for the wage rate can give comparable
results with less computational complexity and cost.

The

Rand Corporation studies cited herein have provided thorough
guidelines for the research design of this and similar
dissertations done on the labor supply of farm households.
An examination of these dissertations,
reading of rural sociology studies,

in conjunction with a

has contributed to a

realistic understanding of farm household decision making

61
dynamics in the interrelated matters of family goals,
come maximization,

and labor time allocation.

This leads to

the next step of scrutinizing the data in terms of its
adequacy and accuracy.

in­

CHAPTER III
DATA COLLECTION AND PROCESSING

This chapter provides an overview of the data utilized
for empirical analysis with reference to the survey subjects
(section A), how the sample was selected (section B), what
data was garnered and by what instruments (section C), why
and how the data was transformed from its original state
(section D),

and lastly the difficulties of statistical

estimation (section E).

A.

1.

SURVEY POPULATION

SUBJECT UNIVERSE
The theoretical,

albeit finite, population under con­

sideration consisted of all limited resource farmers* located
in Michigan's lower peninsula,

which contained 97% of all

such farmers in the entire State according to the 1969 Census
of Agriculture.

It is from this group that the sample was

taken and to which population the sample survey research

* Defined to include those farmers (1) who owned more
than 10 acres of land and earned a maximun of $20,000 but
more than $50 from agricultural product sales, and (2) who
owned less than 10 acres of land but grossed more than $250
in agricultural product sales.
62

63
results are to be generalized.

2.

DATA GATHERING
A field survey was conducted to assemble cross-section

data during a three week period in April of 1974.

The

information was obtained through the use of a written
questionnaire administered orally by interviewers,
subjects responded.

to whom

A copy of the questionnaire used in the

survey may be found in Appendix A.

A pretest of the

questionnaire was carried out in order to improve the quality
of data as well as refine the type of data collected in the
final revised questionnaire used.

B.

1.

SAMPLING PLAN

SAMPLING METHOD
A probability sample of the multistage stratified random

type was used by Thompson

[1975]

in gathering the field data.

This sampling method involved four steps.

2.

SAMPLING UNITS
First,

all counties of the lower peninsula were sorted

into 10 classes approximating "natural" groupings based on
such criteria as geographical contiguous regions (all except
one), plus principal agricultural enterprise activity,
numbers,

and urban area proximity.

(NOTE:

1975, p. 10 and Thompson and Hepp 1976, pp.
counties by groups.)

Second,

selected from each group.

See Thompson
3-4 for list of

one county was randomly

Third,

farm

three townships were

64
randomly selected from each county,
all small farms was sought.

from which a 3% sample of

In all counties a maximum of two

townships was sufficient to obtain the desired sample
percentage.

Fourth,

limited resource farmers were randomly

drawn from the previously selected county townships.

3.

SAMPLING FRAME
The township plat book listing farm owners was used as

the register from which potential small farmers were
identified (i.e.,

those owning less than 200 acres who were

reckoned to fall within the definition of limited resource
farmers).

The register was reviewed for accuracy by the

local county extension director and township board of super­
visors.

This corrected list formed the population from which

the sample was drawn.
The basic observation unit
the two member farm household.

(i.e.,

sampling element) was

Detailed data collection was

limited to the husband and the wife as heads of household,
although general information on the family was also gathered.

4.

SAMPLE SIZE
Personal interviews were obtained from 275 farm operator

households.
unusable,

After discarding 32 interview schedules as being

the final sample size equaled 243 households in­

cluding 239 men and 231 women.
of households is unknown,

The exact non-response rate

since no record was kept of the

total number of households contacted that could be compared
with the number of households for which questionnaires were

65
completed.

However, Hepp in a personal recollection to this

researcher in 1980 thought that it was very low —

under

five.
For purposes of the analysis herein this sample was
further divided into three sub-groups,
(age 34 and under) being the smallest

life cycle stage I
(36 men, 46 women),

stage II (age 35 to 54) being the largest (116 men,
women),

112

and stage III (age 55 and over) being intermediate in

size (86 men,

70 women).

The discrepancy between the aggre­

gate number of men (239) and women (231) and the disaggregated
age groups is due to the fact that specific age information
for one male and three females was not recorded in the
survey data.

Furthermore,

an examination of the "Life Cycle

Labor Supply Analysis" of Appendix E reveals the number of
cases for each age group to be less than reported here for
both sexes;

this is due to the loss of cases when missing

data occurred for variables entered in the multiple regression
equations.

C.

1.

DATA COMPOSITION

REFERENCE PERIOD
The time frame for which data was collected was the

calendar year 1973.

2.

INFORMATION SOURCE
Data was obtained from interview respondents on the

basis of personal recall;

although referral to any records or

66
documents in their possession was not precluded.

3.

FACTUAL CONTENT
Questions were asked under seven broad categories:

Personal demographics (section A) on the age and education of
the husband and wife,
children;
residence,

plus the number and ages of their

Family living information (section B) on-farm
own agricultural commodity consumption,

minimum required income;
land use,

Farm activities data (section C) on

crop and livestock enterprises,

of household members;

and

and on-farm labor

Off-farm employment figures (sections D

and E) of the husband and wife with respect to time worked
and wage rates; Farm business statistics
capital investments —

(section F) on

assets and debts; Household income

(section G) derived from agricultural sales,
ments and transfer payments.

(NOTE:

non-farm invest­

See section C "Variable

Definition" of Chapter IV for details about and analysis of
the variables selected from this data set.)

D.

MISSING OBSERVATIONS

In the course of examining the computer printout of raw
data transcribed from the survey questionnaire of 243 small
farm households,

it became apparent that many card/column

spaces were left blank by interviewers who should properly
have recorded zero or positive values for each question.
This meant that missing values existed for those variables
with blanks.

And if one of those variables is slated for use

67
in the analysis,

the whole case will be discarded by the

listwise deletion computer program and with it the informa­
tion on all other variables of the household.

Biased

coefficients of the regressors could result from such missing
observations,

a topic discussed in section E-2 "Non-Sampling

Error" of this chapter.
in nature.

The blanks were not always random

A close examination of the raw data computer

printout revealed that sometimes patterns of blanks occurred
for blocks or categories of related questions asked in a
sequence.

Curiously,

the patterns were observed for consecu­

tively numbered cases in specific counties,

thereby indicat­

ing a consistent failure by a single interviewer.

This does

not constitute prima facie evidence that all such blanks
could forthwith be converted to zeros.

Instead,

consistency

checks and remedial assumptions were relied on for making
any and all coding changes in the data.
It should be noted here that in one instance 22 blanks
for FARMDEBT occurred for all 22 cases in Cass county.

This

is due to the fact that in randomly selecting the counties
the surveyors decided to pretest the initial questionnaire
in Cass county before drafting the final version, which was
used in all the sample counties except Cass.

Rather than use

the final instrument in Cass they used data from the initial
questionnaire, which did not include data on the variable
FARMDEBT.

68
1.

CONSISTENCY CHECKS
To assess the true extent of the problem a missing data

file was obtained from the computer which listed the number
of blanks for each variable.
of information (i.e.,

Next,

so as to prevent the loss

reduction in the usable number of

cases from the original sample of 243 households) a series
of internal consistency checks were constructed such that it
could logically be deduced that at least some of the blanks
should rightfully have values of zero.

For example,

if a

blank existed for "off-farm hours of work" and a previous
question on "current employment" had a coded response of no
job,

then obviously the variable "off-farm hours of work"

should be assigned a zero value instead of a blank.
same token,

however,

By the

if a response to the "current employment"

question indicated an off-farm job was presently held,

then

a blank for the "wage rate" variable could not logically be
changed to a zero;

and the remaining information on that

case would not be retrieved if the variable with the blank
was included in the analysis.

(NOTE:

See Appendix B

"Missing Data Adjustments" for a complete description of the
consistency checks used).

2.

REMEDIAL ASSUMPTIONS
Where internal consistency checks were not possible for

the purpose of changing blanks to zero values in order to
retain information of household cases,

some reasonable

assumptions were made that allowed such a conversion.
example,

For

if a non-sensitive question such as the marital

69
status of an operator was blank it was assumed that no wife
was present and the blank left by the interviewer actually
represented a zero code.

(NOTE:

See Appendix B "Missing

Data Adjustments" for a complete statement of the assumptions
made for each variable.)
Of course,

there were some variables for which logical

consistency checks or reasonable remedial assumptions were
insufficient.

The principal ones were OPFARMYR (20),

WIFARMYR (20), OPFARMHR (9), WIFARMHR (14) OPWAGEST (10),
WFWAGEST (18), OPWAGINC (17), WFWAGINC (6), WFEDUCYR (17),
FARMDEBT (30),

and INVSTINC (11).

These variables are all

defined in Chapter IV.
In these situations the blanks remained such and infor­
mation was lost on those entire cases if the variable in
question was included in the analysis.

And because missing

values for most potential variables are not all concentrated
in a few cases in select counties,

but rather are seemingly

dispersed across many households in the survey,
in regressors tends to reduce the sample cases.
course,
However,

an increase
This, of

is an argument in favor of keeping the model simple.
some variables are essential to the model by reason

of economic theory,

regardless of this problem.

Consequently,

for both on-farm and off-farm analyses male cases fluctuated
in the 190's while female cases ranged from the 1 7 0 's to
180's.

This amounts to a considerable loss of cases from

the 239 men and 231 women of the 243 households.

70
E.

ESTIMATION ACCURACY

Accuracy of a survey takes into account sampling errors
as well as non-sampling errors,

and refers to how close a

sample estimate comes to the true population value.

However,

because the bias attributable to non-sampling error cannot be
measured,

the measurable precision

(e.g.,

standard error of

the mean) of sampling error approximates the accuracy of
estimation —

assuming little or no bias

[Spurr and Bonini

1973, p. 231; Moser and Kalton 1972, p. 68].

1.

SAMPLING ERROR (Precision)
Sampling error depends on the type of sampling design

used;

and on the size of sample.
a.

Sampling Design
The stratified multi-stage probability sample used

by the original survey researchers would seem to ensure
control of sampling error from the first source,

since "a

stratified sample generally has a smaller error ... than a
simple (without replacement) random sample of the same size"
[Spurr and Bonini 1973,
b.

p. 218] .

Sample Size
With regard to the second source of sampling error

"the reliability of a sample usually (i.e.,

except for small

populations) depends almost entirely on the absolute size of
the sample and not on the percentage of the population
sampled"

[Spurr and Bonini 1973, p. 234].

Nevertheless,

survey included "three percent of the number of limited

the

71
resource farms,

according to the 1969 Census of Agriculture,

in each of the designated counties
Unfortunately,

[Thompson 1975, p. 11].

no explanation is provided for emphasizing the

criteria of percentage instead of absolute size;

and no

reference is made to the relation between precision of the
sample mean and the size of the sample.
random samples a standard error S.E.

For stratified

(X) is calculated for

each stratum before combining the results into a weighted sum
for the whole sample

[Spurr and Bonini 1973, pp. 345-50;

Moser and Kalton 1972, p. 90].

2.

NON-SAMPLING ERROR (Bias)
Concerning the survey data adopted for the labor supply

analysis herein,

precautions were presumably taken by the

survey designers to minimize the potential (albeit
unmeasurable) bias that can arise in conjunction with imper­
fect data gathering procedures —
errors related to sample selection

in particular,
(e.g.,

inadequate frame

or population coverage) and variable measurement
defective instrumentation,

(e.g.,

unsound interviewing practices,

inexact respondent answers,
researcher cum data analyst,
data collector,

non-sampling

imprecise processing).

The

as distinct from the role of

is responsible for any additional bias stem­

ming from faulty judgements made with respect to econometric
modeling and statistical estimation choices.
Some of the more common problems associated with labor
supply analyses,

as reported in the literature and alluded

to in the earlier discussions of "Research Methodologies" in

72
section A of Chapter II, as well as in the whole of Chapter
IV on "Research Design and Statistical Procedures," are
briefly reviewed here in terms of their immediate relevance
to this study of on-farm labor supply.
a.

Unrepresentative Sample
Although the "sampling plan" was thoroughly dis­

cussed in section B of this chapter,
having an adequate sampling frame

the pertinent matter of

(i.e., population list) was

deferred until now.

In actuality,

identification of the very

small farmers (i.e.,

those with gross agricultural sales

less than $2,500 annually) has proven to be a difficult task
even for the U.S.

Census of Agriculture, which in 1974 failed

to collect detailed data on this,

the poorest segment of the

limited resource farm sub-population.

Similarly,

the use of

plat books, which may not include (or at least may not be
current on) small landholders,

and editing by the county

extension directors and township boards of supervisors, who
may not be aware of (or at least may not be in touch with)
this constituent group, make suspect any claim to complete
population coverage.

However,

it should be realized that the

cost of overcoming this deficiency tends to be prohibitive.
b.

Measurement Error
Otherwise known as reporting bias or errors in

variable,

this phenomena is an especially "well known and

much lamented problem in empirical research in economics,"
especially with respect to the income variable which tends to
be underestimated by respondents

[Cain and Watts 1973, p. 361].

73
In particular,

non-wage income such as farm revenue from

agricultural product sales is notoriously under-reported for
tax purposes

[Palmer and Pechman 1978, p. 20],

farm income (i.e.,

But,

since

gross sales) was used only as an upper

boundary in identifying the population of limited resource
farmers and not as an explanatory variable in the on-farm
labor supply function,
However,

the problem should not be acute.

gross farm income is used as an explanatory variable

in the analysis of hours worked off-farm.
Another related problem concerns the transitory

'noise'

that exists when reported wage rates deviate from the
theoretically desired permanent
the entire life cycle.

However, when the sample is broken up

into three life cycle stages
tion,

(or normal) wage relevant for

(i.e.,

age ranges) for estima­

use of reported market wages in calculating the off-

farm income variable is extrapolated for a narrower band of
years and may be less of a problem than might otherwise be
expected.
Unfortunately,

the most erroneous measurements may

possibly be in the annual hours-of-work on-farm,

since farm

operators were asked to informally estimate their annual
labor supply without calculating and reporting the separate
components that could account for seasonal and weekly
variability.

This is not to say there is measurement error,

but rather only to recognize its potential existence.
that as it may,

Be

it is equally important to realize that a

completely accurate tally of on-farm hours would require an

74
exhorbitant amount of time and money to regularly observe
(or at least periodically survey) labor by activities over a
year's time.

In that context,

this Michigan farm survey data

may be no different than the Illinois farm survey on which a
similar study was done

[Sumner 1978].

Moreover,

this same

difficulty also plagued the Rural Income Maintenance
Experiment
c.

[Palmer and Pechman 1978,

p. 12].

Missing Observations
When whole cases (i.e.,

households) must be discarded

for lack of data (i.e., blanks) on any one variable,
tion is lost on all other variables for the case.

informa­

This type

of bias is usually due to non-response to specific questions,
particularly those requesting sensitive information.

Such

may have been the case with FARMDEBT in 8 of the 30 cases of
missing data.

In other instances it may be more a matter of

faulty instrumentation whereby the interviewee is uncertain
of what response to give;
missing cases,

the FARMYR variable, with 20

asked for farming experience of heads of

household together instead of separately.

Alternatively,

it

could be inadvertent oversight by the interviewer or it may
be an inability to answer —

at least not with any reasonable

accuracy.
But,

for this survey the bulk of missing data is

probably attributable to the interviewers,

some of whom

seemingly let blanks represent zero values when "recording"
interviewee responses.
Because "it is very difficult to state rules of thumb

75
for dealing with missing observations,

there is no substitute

for careful thought on the part of the analyst"
Rubinfeld 1976, p.

194].

Hence,

[Pindyck

and

the situation was rectified

by constructing internal consistency checks and making
tightly reasoned remedial assumptions.

(NOTE:

See section D

of this chapter as well as Appendix B on "Missing Data
A d j u s t m e n t s .")
These corrective steps notwithstanding a solution to the
continued existence of missing observations in cross section
analysis is to drop the observations for a variable from
consideration,

if they appear to be missing at random ( e . g . ,

not available because of data reporting errors).
such circumstances,

Under

"the least squares estimator of the

slope estimator will be an unbiased and consistent estimator,
and the only effect of dropping the observations is a loss of
efficiency"

[Pindyck and Rubinfeld 1976, p. 194].

Only if

the missing observations were identical in value to the
sample mean of the available observations,

would the

variance of the estimated parameter not increase.
instances,

this is particularly unlikely.

This is because

Cass county, which includes 22 sample households,
for 16 of the FARMYR missing observations.

In two

accounts

This means that

the inclusion of this variable may effectively eliminate
Cass county households from the sample and cause selectivity
bias.
Another option,

besides dropping the missing obse rv a­

tions from analysis is to replace them with the sample mean

76
of the available observations.

In a multiple regression

model this procedure might yield different slope estimators
and more efficiency,

if only one of the several independent

variables has missing observations

[Pindyck and Rubinfeld

1976, pp.

the Michigan Small Farm

196-97].

Unfortunately,

Survey data involves the use of more than one variable with
missing observations;

thus,

able.

it cannot easily be assumed that for

Besides which,

rendering this solution question­

the variable FARMYR Cass county is representative of the
other counties from which the sample mean would be calculated.
An instrumental variable technique can also be used
whereby cases lacking observations for a variable are assigned
an estimate based on a regression analysis of cases which
have recorded values.

The difficulty is in the selection of

a proper instrument, which in the absence of economic theory
(as with imputed wage rates) is not obvious.

Also,

if

observations are missing for more than one right hand
variable such that more than one instrumental variable (i.e.,
imputed wage) is contemplated problems can arise
and Rubinfeld 1976,

p. 199].

Therefore,

[Pindyck

in those cases

where internal consistency checks of the data and remedial
assumptions about the data still leave blanks,

those cases

are reluctantly rejected for inclusion in the analysis.
d.

Omitted Variables
Certain explanatory variables, which economic theory

and supporting empirical work suggest are important deter­
minants of variation in response variables,

can render models

77
incomplete and thereby affect the estimation results.

The

exact patterns of bias that may occur are virtually impossible
to discern

[Kerachsky 1975, pp. 99-102].

Fortunately,

those

variables omitted herein for lack of information are not
critical to the model,
discussion of them.

but their potential effects warrant a

(NOTE:

See section A-3 "Omitted

Variables" in Chapter IV.)
e.

Sample Censorship/Selectivity
The extent to which the use of only a portion of

the entire sample is necessitated by data constraints and
thereby biases the results has been of paramount interest to
labor supply economists in recent years.
discussion of this,

(NOTE:

For a full

as it relates to estimation difficulties,

see section B-2 "Estimation Te ch ni q u e s ” of Chapter II.)

SUMMARY

Following a straightforward description of the survey
population,

sampling plan,

and data composition,

a discussion

of the data gathering process revealed that missing observa­
tions occurred through non-response and/or recording errors.
The ensuing coding changes used to correct for missing values
was successful for all but a few variables,

for which the

consistency checks and remedial assumptions were not
sufficient to completely eliminate the problem.

Implications

for biased results due to a variety of potential non-sampling
errors were then addressed in terms of securing accurate
estimates of the explanatory variable coefficients.

With

78
these concerns in mind,

the successive chapters on research

design and results analysis can be approached more critically.

CHAPTER IV
RESEARCH DESIGN AND STATISTICAL PROCEDURES

This chapter initially describes the general economic
model with respect to the functional labor supply relation­
ships and the hypothesized associations between classes of
variables for on-farm and off-farm work by sex (section A).
Next,

the Personal-Household and Farm-Business empirical

models are parameterized and appropriate estimation of
the equations is discussed (section B).

Finally,

the labor

supply response variable is defined with reference to its
possible alternative constructions;

and then the explanatory

variables are defined in terms of their measurement and
expected sign —

followed by a discussion of their validity

and complexity for estimation purposes (section C).

A.

1.

ECONOMIC MODEL

FUNCTIONAL RELATIONSHIPS
The general theoretical household behavior model

developed in section A-2 of Chapter II is adapted to the
case of agriculture whereby farm family members supply labor
to on-farm and off-farm work.

The amount of labor time

supplied by the farm operator (Lm ) will be influenced by the
wage rates received in his primary job (W^) and in his
79

80
secondary work (W2 ) if such an opportunity for multiple-jobholding exists within commuting distance of his residence.
Other factors will be the spouse market wage labor income
(I ) and non-labor income of the household derived from
capital holdings (C) —

with the prices of goods ignored by

assuming them to be constant in cross-section static analy­
sis.

Finally,

additional variables of Personal-Household

(H) and Farm-Business (B) models are included for analysis.
The general form of the labor supply model for the male
operator (Lm ) is thus expressed as:
Lm = f (Wr

W 2 , Is , C, H, B)

For the female head of household the general model for her
labor supply (L^) is written as:
L f = f (W1 , W 2 , W 3 , Ig , C, H, B)
where

stands for the home production wage rate of the

wife —

the remaining variables (W^, Wg,

I , C, H, B) being

the same type as for the male operator.
In adapting the general model to the agricultural
situation the self-employment wage rate for either a primary
or secondary job on-farm is not included in the analysis.
Hence,

only one wage rate is used;

market wage rate.

Also,

and that is the off-farm

for lack of an adequate measure

the home production wage rate of the wife is dropped in the
empirical estimation of female labor supply,
a.

Personal-Household Model
This model is essentially that of the general hou s e­

hold behavior model found in the labor supply literature

81
reviewed in Chapter II.

No distinguishing features unique

to the farm household are included.

For on-farm annual hours

of work of both sexes (OPFARMHR and WIFARMHR) the explana­
tory variables are:

age for the male operator (OPAGE) and

wife (WFAGE) used as a stratifier in the life cycle model
(in Appendix E),

educational level of the husband (OPSCHOOL)

and spouse (WFSCHOOL) as a binary variable indicating the
completion of high school,

the total number of children at

home for the father (HOMCHILD) or the number of young
children under five years old present in the household for
the mother (YNGCHILD), work experience in farming by years
for both heads of household (OPFARMYR and WIFARMYR),
farm wage rate of the man (OPWAGEST) and woman

off-

(WFWAGEST) as

estimated by the wage function (in Appendix C ) , spouse wage
income of the husband (OPWAGINC) and wife (WFWAGINC),
investment income (INVSTINC)
in the current period.

and

from non-labor related sources

The equation for annual off-farm

hours of work for both sexes (OPJOBHR and WFJOBHR) includes
the additional binary variable indicating residence in a
Standard Metropolitan Statistical Area county (SMSACNTY).
Each of these variables is discussed fully in section C
"Variable Definition" of this chapter,
b.

Farm-Business Model
This model is actually an extension of the Personal-

Household model,

and warrants considerable discussion given

that the literature review chapter emphasized the basic model
identified in the preceding section.

The additional variables

82
of farm assets (FRMASSET),
rented in (ACRENTIN),

farm debts (FARMDEBT),

acres

and gross farm income (FARMINC) have

been incorporated to reflect unique aspects of the farm
household;

although urban households with self-employment

in a family business would certainly be similar in nature.
The measurement,

expected sign,

and estimation difficulty

are discussed fully in section C "Variable Definition" of
this chapter.
The farm asset variable,

like the investment income

variable in the Personal-Household model described in the
preceding section,
on labor supply.

is included to estimate the wealth effects
But whereas the investment income variable

consists of non-wage labor earnings from liquid capital
holdings of stocks,

bonds,

and savings (as well as from

income derived from land rented out),

the FRMASSET variable

includes the value of agricultural property in the form of
real estate, buildings and machinery.

In empirical work

researchers have used variables measuring non-labor income
or assets to estimate pure wealth effects
p. 12].

[Smith 1980,

And although in this study the former does include

rental income from farm land (which is the major component
of the latter variable),

INVSTINC and FRMASSET can be con­

sidered distinct when viewed respectively in terms of cash
flow versus accrual accounting methods.

Specifically,

the case o f :
A hypothetical worker who owns ... land that he
rents to someone else.
His annual return from
the land will equal any rent payments he re­
ceives plus any increase in the value of the

take

83
land not reflected by the observed rent.
Ac­
cording to the accrual approach the worker ad­
justs his labor supply to the income that is
accrued during the year, no matter when this
income enters his cash stream.
The presumption
is that if he wishes, he could immediately
realize his full annual return by selling his
land.
The fact that he does not choose to do
so is assumed to be irrelevant to his alloca­
tion of time between market and non-market
activities.
The cash-flow variant is based on
the premise that a worker's current labor
supply ... is adjusted to the current cash in­
come stream."
[Greenberg 1972, p. 33]
It is interesting to note that,
expectations,

contrary to theoretical

empirical studies which included an asset

variable typically had positive estimated coefficients,
meaning that increasing assets increase market work
1975, p. 42; Smith 1980,

p.

12].

[Smith

This may reflect positive

serial correlation of work time with past work,

producing

the current assets.
For agricultural households one study found farm assets
to have a positive effect for hours worked on-farm and a
negative effect for hours worked off-farm
p. 58].
study

[Sumner 1978,

The off-farm hours results were the same in another

[Barros 1976,

p. 72].

Concern about life cycle influences on assets and labor
supply has been expressed by some researchers

[Smith 1975,

1980] who believe that assets at any particular age are a
result of past and expected future savings,
labor supply decisions.

consumption,

and

That is, the preference for accumu­

lating assets early in life (and thus above average wage
income in that period) is related to the preference for
working less later in life when non-wage income derived from

84
the accumulated assets is substituted for wage earnings.
As such assets are endogenously determined and "the empirical
relationship should not be interpreted as reflecting a
causal sequence from assets to market work"
p. 13],

[Smith 1980,

In other words "a substantial proportion of the

cross sectional variation in labor supply and asset levels
may merely be a reflection of variations in life cycle
positions,

time preferences,

patterns of market wages,

tastes for assets,

or lifetime

and may have nothing to do with

the causal relationship between income and labor supply"
[Da Vanzo, DeTray,

and Greenberg 1973, p. 28].

However,

transitory increase in labor force participation
well be an alternative to dissaving,
increasing debt.

"a

... may

asset accumulation,

or

One useful empirical implication of this

hypothesis for labor force behavior is that it should be
inversely related to the level of family assets, both in
the life cycle and in the short run sense"

[Mincer 1962,

p. 75].
Three approaches have been followed in purging assets
of whatever life cycle effects may exist.

First,

the sample

may be stratified by age to construct typical profiles of a
representative labor force participant for an age-cohort
group

[Ghez and Becker 1975; Heckman 1976;

and Stephan 1976;

Ryder,

Stafford,

Smith 1975; Weiss and Blinder 1976].

has been done herein.

(NOTE:

This

See section A-lc "Life Cycle

Allocation" in Chapter II and Appendix E "Life Cycle Labor
Supply Analysis.")

Second,

the sample may be chosen such

85
that the "individuals included all faced the same or similar
life cycle wage paths,

interest rates,

and other factors

that may affect intertemporal labor supply allocation"
[DeTray 1973, p. 26].

Such was the simplifying assumption

made for the aggregate cross section analysis herein —
given the relative homogeneity of a sample consisting of
small farmers in the same geographic region.

Moreover,

the

bulk of the farm assets for many operators is often inherited
and thus could be considered exogenous —

that is, not

dependent upon past or future labor supply.

.The third method

removes the effects of differing life cycle characteristics
by the regression technique of imputing age adjusted assets
using age,
status,
function

education,

total number of children,

homeowners

and locational variables as regressors in the asset
[Da Vanzo,

DeTray,

and Greenberg 1973, p„ 69].

This technique was judged inappropriate given the special
nature of the assets —

farm property that may have been

inherited and thus more a function of characteristics of the
present operator's parents for which not data is available.
Farm debt (FARMDEBT) is the second variable included in
the Farm-Business model.

Usually debt is combined with

assets as one explanatory variable, measured either as net
worth (assets - debts) or as a ratio (debts t assets).
Whereas the former is commonly found in general labor supply
studies it has not been used in farm household studies,
which have included either the debt-to-asset ratio

[Kerachsky

1975, p. 112; Primus 1975, p. 41] or total assets without

86
debts

[Barros 1976,

p. 44; Sumner 1978, p. 51].

The draw­

back of meshing debt with assets is that its distinct effect
is obscured;

and this is important when assets are non­

liquid and the debts are not merely a negative image of
assets.
Debt is considered significant because it is thought to
reduce the flexibility of altering one's work pattern for a
farm operation

[Primus 1975, p. 42],

In a multiple-job-

holding context such financial obligations should draw
forth additional labor supply, which may or may not be
devoted fully or even partially to agricultural self-employ­
ment;

that is because increased farm debt does not exclusively

reflect the acquisition of additional farm assets in the form
of acreage, buildings,

and machinery that require more labor

input to be optimally combined with such resources.

Instead,

farm debt can also result from inefficient management
practices and/or adverse market conditions that put a
farmer in the red,

in which case the regular earnings from

an off-farm job may be the most expedient method of paying
off creditors and subsidizing an unprofitable farm opera­
tion —

although among Illinois farmers it was found that

there was little variation in farm debt with the amount of
off-farm work or across types of farm.
variation by age did exist

But considerable

[Sumner 1978, p. 51].

The latter finding suggests the relevance of life cycle
effects whereby farm operators undertake indebtedness in
early years to accumulate assets.

Moreover,

"size of a

87
family's mortgage on the amount of stock it holds is
probably jointly determined along with other variables such
as those that reflect work choices"

[Greenberg 1972, p. 35].

Thus farm debt is treated in the same fashion as the farm
asset variable.
If rising debt were in fact due predominantly to asset
accumulation,

the two should be strongly correlated; but

such was not the finding among Michigan small farms sampled
in this study as FARMDEBT and FRMASSET did not demonstrate a
strong association in the cross section regressions.
The presumption behind the inclusion of the acresrented-in (ACRENTIN) variable is that small farmers who add
to their acreage are seeking to achieve economies of size
which may or may not require more work time.
North Dakota grain farms,
found that

A study of

not limited to small growers,

"the time allocated to labor activities by the

operator decreases with the size of farm while management
time increases.

The decrease in labor time with increases in

farm size is not exactly offset by increased management time
since the total time spent per day increased slightly with
size of farm"

[Johnson and Hvinden 1978,

p. 207].

Ther e­

fore, since the annual hours of farm work reported in the
Michigan Small Farm Survey presumably includes both labor and
management time,

on-farm labor supply is expected to increase

with additional acres of land rented in.

The possible

presence of simultaneity between these two variables is
recognized,

but it is not considered sufficient to justify

88
the use of a full information estimation technique.
Farm income (FARMINC)

is only used as a regressor in

the off-farm labor supply equation in which it is analogous
to the

'other income* or

'total family income'

discussed in the literature
Kerachsky 1975; Watts,

variables

[Ashenfelter and Heckman 1973;

et al.

1974].

In this study FARMINC

could have been combined with investment income and spouse
wage income variables to construct a total family income
variable.

Only one off-farm study included this type of

total family income variable encompassing farm income;
it was an imputed version

[Sumner 1978, p. 63].

and

An estimate

was used to purge it of potential simultaneity bias under
the assumption that at least some of its components were
jointly determined with labor supply.
While it is conceivable that the farm income component
could be jointly determined with off-farm hours of work in­
directly through on-farm hours if they are not independent
of each other,

the assumption made herein is that the tem­

porary or permanent part-time or full-time off-farm jobs
held by farmers and their spouses do not automatically
determine on-farm hours in a one-for-one tradeoff and
therefore determine farm income.

In fact,

"part-time

farmers work more hours per year than low income full-time
farmers" in Michigan

[Loomis 1965, p. 4].

must be recognized and allowed for.

Other influences

This is an important

point because flexibility in off-farm employment in terms
of hours per week (e.g.,

half-time jobs) and weeks per year

89
(e.g., paid vacation, unpaid leaves of absence,
of job),

not to mention evenings and weekends,

seasonality
will often

make possible an optimal allocation of labor to the farm —
even accounting for the peak period time requirements of
planting and harvesting.

The time requirements of the farm

business can also vary with the specific enterprises
selected,

the number of labor saving technologies adopted,

the type of cultural practices utilized,
work contracted for,

the amount of custom

the additional farm workers employed,

the differential productivity of individual farmers across
enterprise activities,

and the level of managerial skill

achieved by the operator.

Moreover,

substitutes for the

operator's time exist in the form of spouse and family labor,
which makes it imperative to also examine labor supply in
the context of the entire household rather than just the
traditionally identified head of household (i.e., male farm
o p e r a t o r ).
Indeed,

farm income is usually the result of work

efforts by the entire household,
member.

not just one individual

And in this context it is likewise assumed that,

although there may exist some degree of joint determination
of working hours among family members,

it is by no means

taken to be a tradeoff of a set ratio or to exclude other
influencing factors.
[Loomis 1965,

In fact,

another Michigan study

p. 4] found that for m ul tiple-job-holding

farmers "compared with low income full-time farms, more
custom work is hired,

family members contribute slightly more

90
farm work,

and mechanization is at a higher level per unit

of output."

With reference to the last point,

several

respondents in the study stated that "off-farm income enabled
them to have more and better machinery than when they were
farming full time."

Consequently,

it was decided to enter

FARMINC as an explanatory variable without imputing esti­
mates of i t .
Finally,

it should be noted that one recent study did

attempt the use of the more desirable simultaneous equations
model in estimating the labor supply of farm households
[Schaub 1980].

Unfortunately,

the results were inconclusive

with very few significant variables and the standard errors
generally larger than the coefficients.

Thus problems of

estimation remain for models that potentially contain
endogenous variables.

(See also section B-2b "Endogenous

Explanatory Variables" of this chapter.)
c.

Ag-Enterprise Model
The Farm-Business model has been extended to include

various animal and crop enterprises.

Labor supply equations

for male operators and their spouses for both on-farm and
off-farm hours-of-work are estimated.

The presentation and

analysis of these results are found in Appendix D since the
theoretical foundation of the Ag-Enterprise model is weak
and because of the potential endogenous nature of these
variables.

91
2.

HYPOTHESIZED ASSOCIATIONS
The reasoning modes behind the expected signs of the

explanatory variables identified in the previous section are
basically three:
models;

deductively via accepted theory and

inductively via established empirical knowledge;

intuitively via creative perception.

and

This last one is not

reasoning in the strictest sense, but it does account for
the reliance researchers must place on human judgements borne
more out of spontaneity than logic.

While the endeavor has

been made herein to exploit the contributions of theory and
models to their fullest extent and to utilize for guidance
the empirical findings reported in relevant labor supply
studies,

the fact remains that with so few studies of on-

farm and off-farm labor supply using the household behavior
approach being reported in the literature formal reasoning
may not be sufficient

in gaining full insight to the phe no ­

mena under scrutiny.

Nevertheless,

a summary of expected

signs for the included explanatory variables follows in
Table IV-1.

These variables are categorized under the

Personal-Household and Farm-Business models for on-farm and
off-farm hours of work by male operators and their spouses.
Precise definitions of these variables are provided in
section C of this chapter, where measurement,
and expected sign of each are discussed fully.

estimation,

92
Table IV-1.

Hypothesized on-/off-farm variable associations
by s e x ,

EXPLANATORY VARIABLES

RESPONSE VARIABLES
On-Farm Labor

Off-Farm Labor

By General Categories
operator

wife

operator

o

+
+

wife

PERSONAL-HOUSEHOLD
Education Level (Binary)
Children At Home
Young Children
Farming Experience
Off-Farm Wage Rate
Spouse Wage Income
Investment Income
S.M.S.A. Residence (Binary)

o
+
X

X
-

+
o
-

+
-

X

X

+
+
+

o
o
o

X

X

-

o
X

+
o
+

+
+

+
—

o
o
o
o

X

FARM-BUSINESS
Assets
Debts
Acres Rented In
Gross Income

SYMBOLS:
+
o
x

indicates
indicates
indicates
indicates

a positive relation.
a negative relation,
no hypothesized relation,
omission from model.

B.

1.

ECONOMETRIC SPECIFICATION

PARAMETERIZED MODELS
Two distinct, progressively expanded versions of the

basic economic model are estimated using the 1974 Michigan
SMALL FARM PROGRAM survey data.
a.

Personal-Household Model
This standard form of the household model is

specified such that the labor supply equation includes only
the Personal-Household variables.

This model closely approx­

imates many used in non-farm studies and forms a basis for
comparison with some of the empirical work mentioned in the
literature review.
The Personal-Household model of male operator labor
supply on-farm and off-farm is:
OPFARMHR =

aQ + a 1

OPSCHOOL + a2 HOMCHILD

+ a g OPFARMYR

OPWAGEST + a K WFWAGINC
5

+ ac INVSTINC
6

bQ + b x

OPSCHOOL + b 2 HOMCHILD

+ b 3 OPFARMYR

+ b.
4

OPWAGEST + b K WFWAGINC
5

+ b~ INVSTINC
6

+ a.
4

+ U1
OPJOBHR

=

+ b ? SMSACNTY + v 1
For the wives of farm operators the Personal-Household
model is specified for on-farm and off-farm labor supply as
follows:
WIFARMHR =

cQ + c ±
+ c„
4

WFSCHOOL + c2 YNGCHILD

+ c3 WIFARMYR

WFWAGEST + c K OPWAGINC
5

+ c~ INVSTINC
6

94
WFJOBHR

a.

= dQ

+d 1

WFSCHOOL + dg

YNGCHILD + dg WIFARMYR

+ d4

WFWAGEST + d &

OPWAGINC + dg INVSTINC

+ d?

SMSACNTY + z ±

Farm-Business Model
This model represents an addition of farm business

characteristics to the family household attributes already
specified in the Personal-Household model.

Variables deal­

ing with the financial structure of the farm operation are
considered important,

given the assumption of income utility

maximization by the household.

Accordingly, male operator

labor supply on-farm and off-farm is made explicit below:
OPFARMHR = a 1 +
+ a ? FRMASSET + a g FARMDEBT + a Q ACRENTIN

+ u2
where a^ through ag variables ( ..... ) are
the same as in the Personal-Household
model.
OPJOBHR

= bQ +
+ b g FRMASSET + b g FARMDEBT + b 1Q ACRENTIN
+ b 1± FARMINC + v 2
where b^ through b 7 variables ( ..... ) are
the same as in the Personal-Household
model.

The corresponding model for the wife's labor supply in
the self-employment and wage market sectors is:

WIFARMHR = c Q + ............................................
+ c? FRMASSET + cg FARMDEBT + cg ACRENTIN

+ y2
where

through cg variables

( ..... ) are

the same as in the Personal-Household
model.
WFJOBHR

= dQ + ............................................
+ dg FRMASSET + dg FARMDEBT + d 1Q ACRENTIN
+ d ix FARMINC + z2
where d^ through d^ variables ( .... ) are
the same as in the Personal-Household
model.

2.

EQUATION FORMULATION
a.

Jointly Determined Relations
The household labor supply model views the family,

rather than the individual,

as the decision making unit.

The labor supply choice of each household adult is not only
considered to be dependent on his or her own wage rate and
the total resources
household,

(i.e., potential full income) of the

but also quite possibly on the wage rate and

labor supply of other family members.

This raises the issue

of how the possible economic and other behavioral inter­
relations between family members should be treated.
If the labor supply equations of the male and female
heads of household are specified to exclude each member's
labor supply dependent variable from the right hand side of
the other m e m b e r s 1 equation as an explanatory variable,

then

96
Zellner's

[1962]

Seemingly Unrelated Regressions model

using Generalized Least Squares
priate.

Viewed as a system,

(SUR)

(GLS) estimation is appro­

these equations are estimated

as a single large equation with the anticipation that more
efficient estimates

(with smaller variance) will result

[Pindyck and Rubinfeld 1976, pp. 279-80].

The gain in

efficiency is achieved if the independent variables in the
different equations are not highly correlated and if the
disturbance terms in the different equations are highly
correlated.

The one known labor supply study which has com­

pared SUR with OLS found that the former resulted in only a
"small gain" in efficiency of the estimates and improved the
m o d e l ’s explanatory power just a "little bit"
pp.

88-97].

Accordingly,

[Muhammed 1979,

this estimation technique was not

utilized.
Alternatively,

a system of equations can be formulated

wherein each family member's labor supply is made explicitly
dependent upon both the wage rate (actual or potential) and
the labor supply of every other family member.

Full informa­

tion techniques can be used for estimating such a simultaneous
equations model;

however,

these techniques are "extremely

sensitive to both specification error and measurement error,"
such that the results "make the FIML estimator less
desirable than the limited information estimators" in that
the latter "estimates only one equation at a time,

confines

misspecification in one equation to that particular equation
and confines an error in measurement in one variable to

97
those equations containing that particular variable" rather
than allowing them to "propogate throughout the whole system
in the process of estimation"

[Intriligator 1978, p. 420].

Given the distinct possibility of measurement error due to
certain aforementioned inadequacies of the survey data and
of specification error due to the omission of relevant
explanatory variables as discussed in Chapter III, the above
concerns are germane.

Moreover,

full information techniques

are computationally complex and expensive to run and also
require larger samples than limited information techniques.
Consequently,

simpler alternatives to simultaneous equation

estimators have generally been used in labor supply studies
[Greenberg 1972, p. 53].
One of these simpler techniques involves the use of
imputed wage rates whereby a potential wage is estimated for
all members of a sample from a sub-sample of working indivi­
duals with an actual wage rate on the basis of human capital
and other characteristics possessed by the entire sub­
sample (e.g., males,

females).

Unfortunately,

problems can

arise with these potential wage rates, which are estimated
by a wage function using the above characteristics as
r e gr es so rs .
For instance,

some subgroups (e.g., wage earning wives)

are quite small relative to the total group and may be more
representative of one end of the wage distribution for such
characteristics facing all units of the sample.
result in biased estimates.

This could

Such is potentially the case in

98
this study with only 54 of 231 adult females reporting a
current wage rate.
Another weakness of using an imputed wage of one family
member in another member's labor supply equation is tho
possibility of bias due to the simultaneity between the wage
rate of one adult and the labor supply of the other whereby
"women with unusually strong tastes for non-market activi­
ties

[as opposed to market work]

seek out husbands with

unusually high market wages and they rely in
to a degree,
in the

[their]

search,

on the same objective characteristics included

[husband's]

1975, p. 8 3 ] o

wage function equation"

In other words,

woman's husband,

[T. P. Schultz

the characteristics of a

such as his educational level,

are not

independent of her own characteristics and tastes in the
selection of a marriage partner and therefore might affect
her own allocation of time.
A final difficulty with using the imputed wage is that
it does not account for the hours worked and thus the income
that will be earned in the context of part-time versus full­
time job opportunities

[Hall 1973, p.

106].

lead us to consider another alternative —

These obstacles
an earnings

variable.
The earnings (wage rate x hours worked) of household
individuals has been used by some researchers,
this one,

including

as an independent variable in the labor supply

equation of other family members,

while others have merely

added such wage income to non-employment income to construct

99
an

'other household income' variable

fn 47].

[Greenberg 1972, p. 54

The drawback of using earnings as an independent

variable is that the labor supply component

(i.e.,

hours

worked) may be endogenous and thus a potential source of
bias.
b.

Endogenous Explanatory Variables
Although this and numerous other studies are of the

cross section type, many aspects of family decision making
in the present are actually the result of past decisions and
events and of future plans and expectations.
explanatory variables,

Hence, many

taken as given by individuals in

the short run and assumed to be exogenous by researchers in
accounting for labor supply in a single period framework,
should realistically be viewed as endogenous in a m u l t i­
period framework.

For example,

level, work experience,

since family size,

net worth

education

(assets minus debts) and

investment income (as well as others like health that are
omitted from our analysis) are all behaviorally interrelated
with past,

current,

and future labor supply decisions,

it is

preferable to evaluate labor time allocation in a life cycle
model in addition to the usual short term context
Schultz 1975, pp. 25-30; Smith 1973],

[T. P.

This in fact is

accomplished by stratifying the sample into three age cohort
groups.

(NOTE:

See Appendix E "life Cycle Labor Supply

Analysis" for the results.)
It should be noted that two other variables utilized in
the analysis are possibly endogenous even in a single period

100
framework —
income,

namely,

farm income and acres rented in.

Farm

included only in the off-farm labor supply equation,

is generated by the combined work of the operator,
teenage children and hired hands;

spouse,

and to the extent that one

individual's on-farm labor is a sizable component of the
farm income variable and is actually interdependent with
their off-farm labor supply,
exist.

an endogenous relation may

The other explanatory variable,

acres rented in,

could also be considered endogenous if additional land in­
deed requires proportionately more labor to farm it.
it may not —

But,

depending upon whether or not the agricultural

operation is labor intensive, whether economies of scale
are achieved in the combination of labor and capital with
additional land,

and whether the efficiency of an individual's

present work effort
creased.

is below full capacity and can be in­

In any event,

farm income and acres rented in are

treated as exogenous variables in this analysis,

since for

the reasons stated both of these variables are probably more
nearly predetermined than truly endogenous.

Furthermore,

the models become far more complex if one tries to endogenize
all variables that might be considered such.

3.

ESTIMATION METHODS
a.

Multiple Regression Analysis
Estimation of the parameters of a multiple regres­

sion equation can indicate the direction, magnitude,
statistical significance of the association between a
response variable and an explanatory variable.

Using

and

101
non-experimental data in which the independent variables do
not stay constant across observations,

multiple regression

can obtain good estimates of their effects.

Thus it is

possible to estimate the effect of changing one exogenous
variable while the others are held constant.

"This makes

multiple regression a powerful and widely useful technique"
[Beals 1972,

pp. 294-95].

Of the various techniques subsumed under the simple or
multiple linear regression model, Ordinary Least Squares
(O.L.S.) is the technique most commonly used for estimating
continuous and unbounded linear functions.

O.L.S.

is known

to yield best I.inear unbiased estimators (i.e., B . L . U . E . ) for
both bivariate and multivariate regression analyses,
assumptions are met.

Specifically,

if its

the estimated distur­

bance term is assumed to have the following characteristics:
randomness of individual errors,
bution,

normality in their distri­

linearity of the expected values of errors,

homo-

skedastic (or constant) variance of the errors for all
observation of explanatory variables,
error terms.

and independence of the

If such assumptions are not violated O.L.S.

estimators have the desirable properties of unbiasedness
(i.e.,

the expected value of the estimator coincides with

the true value) efficiency (i.e.,

distribution of the

estimator is highly concentrated about the sample mean),
consistency (i.e.,

and

the estimator increasingly occurs closer

to the mean as sample size becomes larger).

Violation of

the assumptions may adversely affect desired estimator

102
properties.
b.

Limited Information Techniques
For Ordinary Least Squares (OLS) to yield unbiased

consistent estimates of the parameters in a single equation
the explanatory variables must be exogenous;

that is, they

should be uncorrelated with the stochastic disturbance term.
Two Stage Least Squares (2SLS) is an estimation technique
that compensates for the inclusion of two or more endogenous
variables in an equation.

It is a type of Instrumental

Variables (IV) estimation technique that is an appropriate
and commonly used single equation method for estimating a
structural equation of interest that is part of a jointly
determined system,
been specified

even when the rest of the system has not

[Da Vanzo and Greenberg 1973, p. 48].

In the first stage each right-hand side endogenous
explanatory variable is regressed on all predetermined
variables (i.e.,

those thought to be statistically independent

of the disturbances)

in the model.

This first stage generates

estimated values of the explanatory endogenous variables,
known as "reduced-form estimates" or "instrumental variables
estimates" that

(unlike the endogeneity of the variable in

its original form) are not correlated with the disturbance.
In the second stage the dependent variable is regressed on
the reduced form estimates of the explanatory endogenous
variables along with the exogenous variables in the equa­
tion.

Since the first stage purges the explanatory endogenous

variables of their correlation with the error term, 2SLS

103
estimators are consistent,

although their variances are

larger than those of corresponding OLS estimators.
As a summary judgement
ideal,

"the 2SLS estimator, while not

is a good compromise among the group of estimators.

Thus, 2SLS avoids the bias and inconsistency of OLS while at
the same time it avoids the sensitivity to specification
error and measurement error (and cost) of 3SLS and FIML"
tIntriligator 1978,

p. 420],

Not surprisingly 2SLS is the

mostly widely used technique for estimating simultaneous
equation systems in labor supply studies.

C.

1.

VARIABLE DEFINITION

RESPONSE VARIABLES
The hours-of-work labor supply response variable is

continuous in nature.

Here, we are interested in knowing

how many hours are w o r k e d in a week,
weeks are wor ke d in a year.
measure is most appropriate

in a year,

or how many

There is much debate on which
[Hanoch 1980],

especially when

annual labor supply estimates are made utilizing survey
(cross sectional) data as opposed to longitudinal panel
data.

In the case of " h o u rs -p er -w ee k ," seasonal

summertime vacation) and cyclical

(e.g.,

(e.g.,

recession layoffs)

factors can strongly influence the estimate of yearly hours
because it neglects the difference in the number of weeks
per year actually worked.

An alternative measure of "weeks-

per-year" is similarly deficient because it neglects
differences in hours-per-week

[Rea 1974, p. 284].

It's

104
advantages are that it is subject to less measurement error
than hours and is also less institutionally constrained than
the more rigidly defined half-time or 40 hour a week job
[Ghez and Becker 1975].

For that reason weeks-per-year has

fared better than hours-per-week for the same data set on
which both measures were used

[Ghez and Becker 1975, p. 120],

A combination measure of hours-per-week times weeks-per-year
is a logical solution to the drawbacks of each component
separately;

and it is the annual hours measure that is used

herein for both on-farm and off-farm labor supply.
This brings us to the matter of what variable construc­
tion to use,

'recall'

or

'budgeted'

hours when gathering data

[Primus 1977, p. 866].

This is especially true for self-

employed persons (e.g.,

farmers) from whom accurate estimates

of hours worked is sought.
is standard in surveys.

Relying on recall of the subject

The respondent is not asked to

provide the annual figure directly.

Instead,

the individual

is asked how many weeks per year he worked and how many
hours he worked in an average week during the year.

This

component approach to eliciting the desired aggregate data
facilitates recall and ensures more accurate accounting of
the hours measure of labor supply.
However,

despite such precautions,

occupational classifications (e.g.,

there exist certain

self-employed entre­

preneur) where "recall" hours of work may be suspect for
reasons of irregular work patterns (e.g.,

seasonality) and of

loosely defined business related labor that should be

105
disaggregated into relevant identifiable (e.g., production,
investment,

and "leisure") aspects.

Agriculture is a prime

example of this phenomenon with its peaks and troughs of
time-intensive activities (e.g.,

spring planting,

summer

spraying,

fall harvesting,

winter equipment overhaul).

Moreover,

farm work can also involve labor related to

current or future production,
all.

as well as to no production at

Greater precision in recall could be achieved by having

the surveyor ask the respondent to estimate the hours worked
on each of several activities, with the interviewer adding
up the total hours worked;

or an observer can record on a

regular basis throughout a period of time how many hours are
actually devoted to separate activities.
not easily done —

Such observation is

especially with respect to non-market

time.
Budgeted hours can be constructed by obtaining coeffi­
cients from independent data on which the number of hours
required for a particular agricultural enterprise have been
estimated.

The survey data examined herein includes the

prerequisite information on the number of acres grown for
each crop sold and/or on the number of different kinds of
livestock marketed.

However,

no reliable independent data

from which the required coefficients might be obtained
exists.

Consequently,

'recall'

hours is the measure of hours-

of-work used herein for both on-farm (OPFARMHR and WIFARMHR)
and off-farm (OPJOBHR and WFJOBHR) for male operators and
their wives respectively.

106
Survey respondents probably calculated the annual hours
on-farm by mentally or manually multiplying the number of
hours worked per we ek times the weeks worked per year in
accordance with the instructions to "estimate on weekly
bases if necessary to arrive at yearly total;" though these
component figures were not recorded on the questionnaire.
Several possible measurement errors exist.
on memory.

Then,

time operators,

2.

One is reliance

too, with farming a "hobby" for some part-

some hours may actually reflect

leisure.

EXPLANATORY VARIABLES
Fortunately,

this data set

the explanatory variables available from

[Thompson 1975]

are among those considered

important by theoretical postulations and found significant
by previous empirical analyses of labor supply.

Unfortunately,

there are also some important explanatory variables for which
no data was collected or for which measurements selected by
the original surveyors are inadequate.

These omitted

variables are described and their potential effects examined
in the next section,

"Omitted Variables."

What follows now

is a brief measurement description accompanied by a state­
ment about the expected sign and a discussion of the nature
of the explanatory variables.
Two main classes of explanatory variables —
Household,

and Farm-Business —

Personal-

form the rubric under which

may be found the potential causal factors associated with
variation in the on-farm hours-of-work labor supply response
variable.

Listed below are the variables included for

107
analyses in the labor supply regression equations.
a.

Personal-Household Model Variables

OPAGE:

Operator's Age (continuous)

WFAGE:

Wife's Age (continuous)
MEASUREMENT:

The age data was collected by six

age categories, but was entered as the midpoint
of the age category.
EXPECTED SIGN:

There is no prior expectation

regarding sign for either on-farm or off-farm for
operators or spouses.
DISCUSSION:

The age variable was not used in the

labor supply function directly.

Rather,

the

analysis includes a stratification of the sample
by age categories to approximate life cycle
stages of household members.

(See Appendix E

"Life Cycle Labor Supply Analysis" as well as
section A-lc "Life Cycle Allocations" of Chapter
II and section A-lb "Farm-Business Model" of
Chapter I V . )
OPSCHOOL

Operator's Years of Schooling (binary)

WFSCHOOL

Wife's Years of Schooling (binary)
MEASUREMENT:

A value of 1 is assigned for those

with twelve or more years of formal education;
and a value of 0 is assigned to those completing
eleven or less years of school.
EXPECTED SIGN:

There is no prior expectation

regarding sign for on-farm for either sex.

108
Off-farm a positive sign is expected for males,
but no prior expectation is found for females.
DISCUSSION:

Twelve years of schooling is equiva­

lent to a high school diploma and represents the
so-called "credential effect" repeatedly found in
studies of human capital.

It is the completion

of certified levels of education (i.e., primary
school certificate,
degree),

high school diploma,

college

not the incremental number of schooling

years (i.e.,

7, 11,

13) that matters in terms of

gaining employment.

Since a high school diploma

is a standard minimum requirement in t o d a y ’s work
world,

twelve years was chosen as the dividing

line for the construction of this binary variable.
Based on empirical research Michael

[1973]

found education to raise productivity of time in
market and non-market activity by approximately
the same percentage;

thus,

the increased education

of an individual has been assumed to be "Michael
Neutral" in terms of influencing the division of
the person's labor.

It is also assumed that

education raises the marginal productivity of all
inputs (not just time) by an equal percentage in
household commodity production.

Hence,

no change

in production technology is required to achieve
increased efficiency,

and therefore,

no change in

labor supply to market wage labor activity occurs

109
since the demand for purchased goods and ser­
vices (as inputs into home commodity production)
remains at a constant ratio with time
1973,

pp.

[DeTray

30-31].

In the context of agriculture an increased
on-farm wage rate (i.e.,

roughly formulated as

product sales revenues divided by h o u r s- of -w o rk ),
holding constant agricultural product prices,

can

be achieved by a declining number of man hours
required to produce the same level of output.
Thus,

an inverse relationship between education

and on-farm labor supply could be expected.

But,

if we assume that additional education imparts
skills that also increase his off-farm wage rate,
it will be the relative increase in the two
wages that will influence the effect on labor
supply in the alternative activities.
quently,

Conse­

in the absence of any information about

the specific orientation and content of schooling
( e . g . , an agricultural technology program emphasiz­
ing farm management skills) the "Michael Neutral"
assumption prevails.
HOMCHILD:

Children Living at Home (continuous)
MEASUREMENT:

The number of dependents who are

residing at home are included regardless of their
educational and employment status.
EXPECTED SIGN:

A positive relationship with both

110
on-farm and off-farm labor supply is expected
for husbands.

This variable is not used in the

wife's labor supply function.
DISCUSSION:

A father's labor supply is positively

related to both the number of children as well as
the age composition of the dependents because his
responsibilities increase —

given the man's

culturally defined role as the principal
winner'

of the household.

'bread

The magnitude of his

family obligations grows with the age composition
of the children, who become a more goods-intensive
commodity as they grow up and hence less time­
intensive in nature.

That is, the child requires

less parental attention in the form of personal
care as he becomes more self sufficient in feeding,
dressing and entertaining himself —

all the

while requiring more and more material possessions
such as games,

bicycles,

clothing,

food,

and

consumption goods generally.
YNGCHILD:

Young Children (continuous)
MEASUREMENT:

The number of children under the

age of five represents pre-schoolers requiring
personal time of the mother for care and feeding.
EXPECTED SIGN:

A negative association with on-

farm and off-farm hours is expected for wives who
are mothers.
DISCUSSION:

Like their husbands,

the labor supply

Ill
of wives also becomes more responsive to wage
rate as the children get older (i.e., past the
preschool age of 5 years),
degree as fathers.

though not to the same

But unlike them,

the m o t h e r ’s

labor supply is very responsive to the presence of
pre-schoolers in the home.

Children at this

formative age (and before they are eligible for
the free babysitting facilities of schools) are
very time-intensive commodities which require much
care —

a role society usually assigns the

mother.

Studies repeatedly show that the

presence of pre-schoolers has a negative effect
on mother's labor supply even for the highly
educated who have a high market opportunity cost
attached to their decision to remain outside the
labor force.

The explanation for this phenomenon

centers on three factors:
enjoy infants —

a taste preference to

mother and child bonding;

investment component whereby mothers,
those who are educationally aware,

an

especially

teach their

children intellectual and social skills in the
most critical first three years of life;

and a

high productivity level in home production of a
child commodity for the well-educated mother
[DeTray 1973, pp.

33-34;

Gronau 1973, p. S 1 9 2 ] .

As the children get older,
less time-intensive,

they not only become

but they also become

112
substitutes for mother in home production
h o u s e c l e a n i n g , cooking).

(e.g.,

This allows the mother

greater flexibility to respond to higher wage and
income opportunities

[Bryant 1976, p. 852].

OPFARMYR:

Farming Experience in Years (continuous)

WIFARMYR:

Farming Experience in Years (continuous)
MEASUREMENT:

The number of years the farm operator

and his spouse have continuously farmed together
is used.
EXPECTED SIGN:

It is positive for on-farm and

negative for off-farm for both sexes.
DISCUSSION:

This variable indicates the acquisi­

tion of specialized skills for higher productivity
in a particular line of work.

One drawback in­

volves the nature of the survey question which
asked for a joint response, which may understate
actual farm experience of the male operator before
he married his current wife.

Correspondingly,

the reliability of this figure for wives is also
open to doubt.

Since the mean value for this

variable was 20 years,

late marriage or remarriage

may not be prevalent in this relatively more
traditional and stable population.
OPWAGEST:

O p e r a t o r ’s Estimated Wage Rate (continuous)

WFWAGEST:

Wife's Estimated Wage Rate (continuous)
MEASUREMENT:

The reported wage rate of the

individuals in the subsample that works off-farm

113
is regressed on the human capital (i.e.,
education,
mental

age,

and market work experience) and environ­

(i.e.,

residence in Standard Metropolitan

Statistical Area) characteristics which are
possessed by the entire sample.

Using the coeffi­

cients of these regressors wage rates are imputed
for those individuals not working and who other­
wise would of necessity be excluded from the
labor supply analysis.
selectivity bias.

This procedure avoids

Wage rates are also estimated

for the subsample that is working and are substi­
tuted for their actual wage rates.
EXPECTED SIGN:

It is negative for on-farm and

positive for off-farm hours for both sexes.
DISCUSSION:

Since wage rate is an important

theoretical variable in analyzing labor supply
but only a portion of the sample has an actual
wage to report,

it becomes imperative to estimate

the effects of wage rates of those individuals in
the sample population who are not employed.
Assigning a zero wage is unrealistic;

and asking

respondents what wage they would require to enter
the labor force and work a certain number of hours
(ceteris paribus) is unreliable.

One solution

widely used in recent labor supply studies has
been a technique that estimates an expected wage
for the non-working segment based on the working

114
segment of the sample, with the estimated wage
rate also being assigned to those with observed
wages

[Kalachek and Raines 1970; Hall 1973;

Boskin 1973].

The "imputed" actual wage is most

commonly found in labor supply studies of secon­
dary (e.g., married female),
household members —

rather than primary,

people who generally have

greater discretion in the decision whether or not
to work

[Scott, et al. 1977,

p. 271].

An ’instrumental variable'

technique is used

to impute the market wage rate variable

(i.e.,

OPWAGEST and WFWAGEST) by regressing the observed
wage rate on human capital variables common to
the entire sample regardless of employment status.
A natural logarithmic function is used, with the
equation being specified for males as follows:
LN(OPWAGE) = m Q + m ± OPAGE + m 2 OP A G E 2 +
m 3 OPEDUCYR + m 4 O P ED UC Y R2 +
m K OPMRKTYR + nv SMSACNTY + s
5

6

The corresponding equation for females is:
LN(WFWAGE) = w Q + w 1 WFAGE + w 2 W F A G E 2 +
w 3 WFEDUCYR + w 4 WF E D U C Y R 2 +
w K WFMRKTYR + w~ SMSACNTY + t
5
6
The wage estimates are then assigned to those
having an actual wage rate as well as to those not
working off-farm.

(NOTE:

For a complete desc ri p­

tion of this process and the results see Appendix C

115
"Imputed Market Wage Estimation.")
WFWAGINC:

Wife's Wage Income (continuous)

OPWAGINC:

Operator's Wage Income (continuous)
MEASUREMENT:

This earned income variable of the

spouse is a multiplication of hours-per-week
times weeks-per-year times the wage rate —

that

is, the midpoint of the wage range within which
respondents reported their wage.
EXPECTED SIGN:

No prior expectation regarding

sign exists for the wife's wage income in the
male labor supply on-farm or off-farm.

The sign

is expected to be negative for the husband's wage
income in female labor supply on-farm and offfarm.
DISCUSSION:

This constitutes a variation of the

Spouse Wage variable that is often included in
labor supply equations to approximate a household
decision-making framework, whereby the h u s b a n d ’s
(or wife's) market labor is open to influence by
the wife's

(or husband's) earning capacity.

Empirical results are mixed.

The coefficient for

the husband's wage rate in the wife's labor supply
regression is generally negative —
and strongly significant.

as expected —

On the other hand,

the

coefficient for the wife's wage rate in the
husband's labor supply equation has proven to have
a weak statistically insignificant effect

116
[Greenberg and Hosek 1976, pp. 23-24].

Spouse

income was used instead of spouse wage because
of the possibility of seasonal/limited work
opportunities (e.g., off-farm employment on a
neighboring farm,

school bus driving,

etc.) could

overstate the impact of the wage rate on an
annual basis
INVSTINC:

Investment

[Greenberg 1972, pp. 53-54],

Income of Household (continuous)

MEASUREMENT:

This non-labor income variable

consists of savings account interest,
bonds dividends,

and land rent.

stocks and

It excludes

transfer payments that are dependent upon employ­
ment status (e.g.,

unemployment insurance benefits,

welfare subsidy) or hours worked (e.g.,

social

security checks).
EXPECTED SIGN:

A negative relation with on-farm

and off-farm labor supply is expected for both
sexes.
DISCUSSION:

Empirical evidence seems to indicate

that this variable has little impact on husband's
labor supply
although,

[Scott, et al. 1977, pp. 268-72];

an expected negative relation has been

observed for wives

[DeTray 1973, pp.

15-16].

This is not to suggest that the variable lacks
theoretical importance;

its just that existing

measures are inadequate counterparts to the
theoretical concept

[Smith 1975].

117
The R.I.M.E.

studies

[Bawden and Harrar 1977]

indicate that the non-labor income (i.e., negative
income tax payments) had the effect of lowering
off-farm hours and raising on-farm hours of work.
So it is possible that investment

income could

result in a positive relation with on-farm hours
of work.
Attention is called to the fact that land
rent is included in the measure of this variable
and it is bound to be associated with the labor
required to work more or less land.

As such this

investment income variable has an endogenous
component,

the importance of which depends on the

proportion of investment income attributable to
land r e n t .
SMSACNTY:

Michigan County of Residence (binary)
MEASUREMENT:

Ottawa,

Cass,

Ionia,

and Livingston

counties were assigned a code of 1 because they
were part of or adjacent to a S.M.S.A.
EXPECTED SIGN:

It is positive for both husbands

and wives off-farm.

For on-farm labor supply this

variable is excluded.
DISCUSSION:
(i.e.,

Mileage to the nearest labor market

Standard Metropolitan Statistical Area)

represents a travel cost of working off-farm in
that the longer the distance,

the lower the net

wage for a given gross wage rate.

This is due to

118
direct outlays for gasoline or public transport
fares,

the cost of time with respect to its alter­

native uses in home production,

and the psychic

utility or disutility placed on this nonleisure
use of time.
Recent studies have illustrated the need to
be careful in the actual measurement of distance
so that it represents the distance from residence
to the nearest metropolitan labor market —

a

pre-determined figure that is exogenous to the
labor supply model.

If the actual distance from

home to the work place is taken as the measure,

a

simultaneity problem may arise due to the end o­
genous nature of the mileage.

This is because a

worker may choose among many jobs at varying
distances and the time and money costs of distance
travelled is optimized and jointly determined with
the wage offered

[Sumner 1976,

p. 20].

The

survey data utilized herein has data only on the
actual distance travelled to the place of off-farm
employment.

Unfortunately,

nearest S.M.S.A.

the distance to the

cannot be constructed,

since

the township location of the individual survey
respondent's residence is not known;

hence,

the

use of a binary proxy variable indicating resi­
dence in or close to a S.M.S.A.

county.

119
b.
FRMASSET:

Farm-Business Model Variables
Total Farm Assets (continuous)
MEASUREMENT:

This variable includes the estimated

value of land,

farm buildings,

and agricultural

machinery.
EXPECTED SIGN:
farm;

It is positive for husbands on-

but there is no prior expectation regarding

sign for wives on-farm.

A negative sign is

expected for husbands off-farm; whereas neither a
positive nor a negative relationship is expected
for wives off-farm.
DISCUSSION:

Figures reported for machinery and

equipment may vary among respondents because,
unlike land and buildings,

they depreciate in

value and the amount reported may not be consistent
across cases.

That is to say,

the dollar amounts

may reflect past acquisition price,
replacement cost,

estimated

current salvage value,

or tax

record values depending on how each respondent
views it.

This may impugn the reliability of

this variable,

yet to exclude this aspect of

assets could not be justified.

In any case the

land and buildings should dominate value of farm
assets.
"Monetary"

(i.e.,

liquid) wealth is used as

a proxy variable for "full" wealth in empirical
analysis.

It can be measured as assets alone,

as

120
net worth (i.e.,

assets minus liabilities),

as a ratio of debts to assets.
the measure selected,
systematically,
life cycle.

or

Irrespective of

observed assets may vary

rather than randomly,

For example,

over the

it has been suggested

that the early stage of working life is centered
on accumulation of wealth,

such that more labor

supply is associaced with more assets.
the later life stage of disinvestment,
decline and labor supply decreases

And in
assets

[DeTray 1973,

p. 23; Smith 1975],
If hours supplied do vary systematically over
time for the same or different reasons that
assets vary,

causation could be falsely attributed

to an observed relationship between assets and
hours worked in the market

[Smith 1975].

One way

of removing life cycle effects is to stratify the
sample according to age groups thought to reflect
distinct

life cycle stages

[Da Vanzo,

DeTray,

Greenberg 1973].
It should be noted that,
measure chosen,

regardless of the

empirical research has generally

turned up insignificant coefficients for this
variable

[Greenberg and Hosek 1976, p.

unexpectedly positive at that
FARMDEBT:

Farm Debt

12]

and

[Smith 1980, p.

12].

(continuous)

MEASUREMENT:

This variable specifically excludes

121
household consumer debt.

The information may

have been retrieved by use of business records
but more probably was obtained by recall.
EXPECTED SIGN:

It is positive for husbands, but

neither positive nor negative for wives on-farm.
No apriori expectation exists for either sex offfarm .
DISCUSSION:

This variable is potentially a strong

indicator of commitments made to self-employment
farming and is entered separately instead of as a
component of a net assets variable, wherein its
effect might be diluted.

Such might be the case

for young farmers whose financial liabilities for
the farm would approximately equal its value —
except

in the case of an inherited farm where

debts would be minimal relative to assets.

For

farmers in the middle and later life cycle stages
inflation of farm land values would greatly
exceed d e b t .
ACRENTIN:

Acres Rented In (continuous)
MEASUREMENT:

This land variable represents the

number of acres rented in for the purpose of
expanding the farm operation beyond the capital
investment and land availability constraints.
EXPECTED SIGN:

It is positive for husbands, but

neither positive nor negative for wives on-farm.
The expected sign is negative for husbands

122
off-farm with no apriori expectation for wives.
DISCUSSION:

An expansion of the land base may

bring forth additional labor supply from the
household to tend the enterprises put on such
acres.

Conversely,

sociologists have found that

individuals moving from full-time to part-time
farming generally reduce their acreages —
by renting less
FARMINC:

[Bertrand 1967,

usually

p. 301],

Gross Farm Income (continuous)
MEASUREMENT:
dollars,

This financial variable is in annual

representing the average gross farm sales

receipts for the preceding two years at the time
of the survey.

Respondent recall of this value

should be fairly accurate,

if actual income was

not underreported for income tax purposes.

Like­

wise overreporting of farm income is possible to
purposely give the "expected" impression of being
a successful farmer —
called

a variation of the so-

'Hawthorne E f f e c t ’ [Primus 1977, p. 866].

EXPECTED SIGN:

This variable is used only in the

off-farm equation where the sign is expected to
be negative for

husbands, but no

apriori expecta­

tion exists for wives.
DISCUSSION:

It is expected that this variable may

be highly correlated with
Also,

causality

the FRMASSET variable.

from farm income to on-farm labor

supply is somewhat implausible.

This variable is

123
hence more appropriately considered for inclusion
in the off-farm labor supply function.

3.

OMITTED VARIABLES
Variation in the annual hours of work might also be

attributed to some explanatory variables that are not included
in the analysis.

Race,

health status, work experience,

and

the local unemployment rate are the principal ones suggested
by a general review of the labor supply literature.
R a c e , for which no data was collected in the survey by
Thompson

[1975], would account for any discriminatory hiring

practices by employers and unions in the off-farm job market.
Accordingly,

less off-farm hours and more on-farm hours might

be observed for black farmers.

Thus,

non-caucasian farmers are present
(e.g.,

the extent to which

in appreciable numbers

Cass county in our sample) the omission of the race

variable represents a loss of potentially significant in­
formation .
Health status has proven to be a strong predictor of
regular wage employment

in rural labor markets

[Scott, et al.

1977, p. 271], though its influence on the supply of labor to
farm activity remains uncertain in the absence of empirical
evidence.

However,

given the strenuous nature of agricul­

tural production activity,

it can reasonably be assumed that

poor health would be negatively related to on-farm hours of
work.
losses,

Such disabilities as arthritis,
heart trouble,

vision and hearing

plus mental and nervous disorders are

the common measures of health status with reference to

124
employability.

Unfortunately,

this information is not

contained in the survey data.
Work e x p e r i e n c e , measured as the number of years in the
wage labor market,

has been found to express a predilection

or taste for employment and thus to be positively associated
with labor supply.

Unfortunately,

Thompson's

question on the length of time spent in the
tion'

[1975]

survey

’present occup a­

(coming as it did immediately after inquiries about

hours and wages of a 'currently held job') was sufficiently
ambiguous in definition and placement to allow for the
possibility of unreliable (i.e.,

inconsistent) data —

depending upon respondent interpretation of the question.
Consequently,

this variable was not directly included in the

labor supply function.

However,

as a probable measure of

accumulated human capital and increased productivity through
on-the-job training in a present position

(where skill train­

ing tends to be job specific), work experience is likely to
be an important determinant of wage rates.

Hence,

this

variable is included in the wage function, which is used to
generate estimated wages for all sample elements to be
plugged into the labor supply function.

(NOTE:

See Appendix

C "Imputed Market Wage Estimation.")
The unemployment rate is another variable that has been
found to affect the labor supply of men negatively with va r y ­
ing degrees of significance
p. 285],

The

[Cohen 1970,

'discouraged worker'

'additional worker'

hypothesis,

p. 44; Rea 1974,

effect,

as opposed to the

seems also to prevail for

125
women

[Cohen 1970, p. 85; Sweet 1973, p. 23]

women in particular
ever,

and for rural

[Heaton and Martin 1979, p. 72].

How­

certain weaknesses of this variable in the study of

non-metropolitan populations raise doubts about its useful­
ness .
First of all, the unemployment rate is likely to reflect
long run structural factors,

such that rises in the popula­

tion and labor force can keep the rate high over a period of
years and not reflect the shorter run changes in demand
opportunities

[Cohen 1970, pp. 21-22].

Instead,

change in

employment provides a better measure of existing job
opportunities facing job seekers.

For instance,

one of two

areas with identical unemployment rates might be experiencing
a substantial positive change in employment while the other
remains static.

And since the area with a low employment

change will have fewer chances for employment,
that the individual
the area will be

(e.g.,

it is likely

farm household member)

'discouraged'

living in

and either leave the wage

market labor force or refrain from entering it.
Secondly,

because the number of discouraged workers is

not counted in the unemployment rate,

this labor market

statistic does not accurately portray the degree to which
competition for scarce jobs prevails in non-metropolitan
areas.
Third,

farm operators who do view unemployment statistics

in various regions ( e . g . , Standard Metropolitan Statistical
Areas) as measuring the relative job opportunities may not be

126
able or willing to shift their supply of labor to those
markets where the demand seems greatest
lower unemployment rate).

(i.e.,

area with the

A previous study of operators in

Michigan found that "most part-time and full-time farmers
settled down to a permanent residence before they were 35
years old and became geographically immobile"

[Loomis 1965,

p. 3] .
Fourth,

characteristics of separate labor markets can

differ markedly,

especially in terms of the industrial

composition and therefore the types of jobs.

Thus,

same unemployment rate in two geographic regions,

for the

the demand

for labor by occupational skills and sex could vary
1973,

[Sweet

p. 23].
Fifth,

local area unemployment statistics in n o n ­

m etropolitan areas are inadequate.

"Measurement,

conceptual,

and definitional inaccuracies render comparisons of labor
market conditions in non-metropolitan areas, based on the u n ­
employment rate,
more,

inaccurate"

[Nilsen 1980,

p. 1].

Fur th e r­

the statistical rigor of non-metropolitan figures is

unknown since they are taken as the residual of metropolitan
estimates

[Nilsen 1980,

Sixth,

p. 5].

interpretation of the unemployment rate can be

difficult in non-metropolitan areas since a sizable pr o p o r ­
tion of the labor force is engaged in self-employment as a
secondary activity (e.g.,

farming).

And if unemployment

occurs in the primary activity (e.g., off-farm job),
unemployment statistics will not reflect this because of the

127
self-employed status

[Nilsen 1980, p. 33].

Although other variables besides race,

health status,

work experience and the local unemployment rate might also
be included to explain some of the variability in the
dependent variable,

control for all relevant variables is

seldom achieved.
The reason additional regressors,
by economic theory,

beyond those specified

are used is to control for the possible

effects of other independent variables that are assumed away
by the usual ceteris paribus assumption.

Although these may

serve to explain some of the variability in the dependent
variable,

control for all relevant variables is seldom

achieved.
First, all theories are simplifications.
It is
probably never possible to name all the varia­
bles that might affect Y; no matter how many
are taken into account, someone with ingenuity
can suggest another.
Useful theories focus on
important variables and ignore those with only
tiny effect.
Second, some of
the relevant
variables may be difficult or
impossible to
m easure or control.
Finally, economic theories
seldom give complete information about the form
of functional relationships.
So simplicity and
convenience are among the criteria for judging
empirical results.
[Beals 1972, p. 265]
The general guideline is, therefore,

to keep the model simple

and conserve degrees of freedom to strengthen the test on
other regressors.

Hence,

the argument is made for dropping

variables for which only weak apriori beliefs are held con­
cerning an hypothesized relation with the dependent variable
[Wonnacott and Wonnacott 1972, p.
which are theoretically important

300].

Of course, variables

in the testing of a

model

128
should be retained regardless of significance.
say,

Needless to

"There is a good deal of art and judgement involved in

empirical analysis"

[Beals 1972, p. 265] .

SUMMARY

With the adaption of the general household behavior
model to self-employment in agriculture combined with market
work in the wage sector the labor supply equations for onfarm and off-farm hours by sex were formulated.

Econometric

techniques were evaluated and multiple regression analysis
using ordinary least squares with an instrumental variable
technique was selected as the optimal method of estimation.
Finally,

the response and explanatory variables were

described with respect to their measurement and expected
signs.

The empirical results are reported and interpreted in

the following chapter.

CHAPTER V
P RESENTATION AND ANALYSIS OF RESULTS

The object of this chapter is to report the research
findings (section A) in terms of the descriptive summary
statistics of variables and the performance of the PersonalHousehold and Farm-Business models of on-farm and off-farm
labor supply.

These findings are then interpreted (section

B) with respect to their conformity to theoretical expecta­
tion and consistency with empirical findings of similar
studies.

A.

1.

REPORTED FINDINGS

SUMMARY STATISTICS
Comprehensive summaries of the survey data relating to

all the questions posed to Michigan small farm households
can be found elsewhere
1976].

[Thompson 1975;

Thompson and Hepp

The intent here is merely to provide mean values and

standard deviations for the variables used herein as a
reference for analysis of hours-of-work labor supply on-farm
and off-farm as well as for specification of the imputed wage
function.

These summary statistics in Table V-l are calcu­

lated on the basis of those reporting positive values,
excluding zeros and blanks.
129

130
Table V-l.

Summary statistics of data on variables.

Males

Variable
Name [c]

OPFARMHR

OPJOBHR

OPAGE

[183]

[156]

[238]

a

Females

Mean Values
(Std. D e v . )

Variable
Name [c]

1589.08
(1075.82)

WIFARMHR

1997.79
(605.31)
50.04
(13.16)

WFJOBHR

WFAGE

Mean Values
(S t d . D e v .)

[117]

[58]

[228]

OPEDUCYR

[239]

11.06
(2.13)

WFEDUCYR

[226]

HOMCHILD

[140]

2.81
(1.65)

YNGCHILD

[35]

OPFARMYR

[213]

21.07
(12.26)

WIFARMYR

[213]

OPMRKTYR

[156]

13.57
(9.21)

W FMRKTYR

[59]

4.48
(1.05)

WFWAGE

OPWAGE

[146]

[233]

4.13
(.61)

OPWAGINC [162]
(in hundreds)

90.18
(34.53)

INVSTINC [80]
(in hundreds)

12.88
(16.41)

FRMASSET [242]
(in thousands)

62.21
(36.13)

FARMDEBT [93]
(in thousands)

12.25
(12.22)

ACRENTIN

64.32
(52.45)

OPWAGEST

[35]

[54]

WFWAGEST

b

[225]

WFWAGINC [60]
(in hundreds)

1091.26
(1073.57)
1357.79
(704.02)
46.88
(12.81)
11.38
(1.74)
1.54
(.70)
21.07
(12.26)
9.35
(8.91)
2.94
(1.36)
2.16
(.67)
45.18
(31.85)

131
Table V-l.

(Continued)

Males

Variable
Name [c]

FARMINC [198]
(in thousands)

EL

a

Females

Mean Values
(Std. D e v . )

Variable
Name [c]

Mean Values
(S t d . D e v .)

8.55
(6.73)

The number of males in households is 239.

k The number of females in households is 231.
Means are calculated on the basis of those reporting p o s i ­
tive values; that is, n = 243 - (blanks and zeroes).
The
number in brackets represents the number of households
reporting such positive values for each particular
variable.

132
2.

MODEL PERFORMANCE
Looking first at the Personal-Household model and then

at the Farm-Business model,

the on-farm and off-farm regres­

sions for male and female heads of households respectively
are examined.
a.

Personal-Household Model
i.

Male Labor Supply
Ideally specified the Personal-Household model

wou ld include continuous measures of age,
market experience.

education,

and job

However these had to be dropped from the

equation due to strong correlations with the imputed wage
rate that was estimated using these variables.
time related,

Since age is

the presence of the farm experience (OPFARMYR)

variable in the equation picks up the effect of age without
being strongly correlated with the wage estimate.

The job

market experience (OPMRKTYR) variable was excluded because
of a high correlation with the imputed wage, which was
retained because of its theoretical basis as well as its use
as a means by which selectivity bias could be minimized by
inclusion of those not employed in the wage m a r k e t .

The

education variable is re-defined as a binary variable
(OPSCHOOL) to reflect the completion of high school;

so the

effect of education is expressed directly as OPSCHOOL and
indirectly through OPWAGEST, which also picks up the effect
of residence as well as age and job market experience m e n ­
tioned above.
As reported in Table V-2 the explanatory power,

adjusted

133
Table V-2.

Explanatory
Variables

Male labor supply estimations
household model.

ct

of personal-

On-Farm
Hours

Off-Farm
Hours

Intercept

1444.0668
(674.9125)

-1590.8782
(551.5824)

146.8114

OPSCHOOL

286.9588**b
(174.5007)

-162.7256
(142.4365)

124.2332

14.3820
(36.9718)

126.7964

HOMCHILD

112.4144****
(45.1784)

OPFARMYR

28.8030****
(7.2300)

OPWAGEST

-234.1134*
(153.0828)

WFWAGINC

-3.6468
(3.2931)

INVSTINC

-26.9490****
(6.4816)

Total
Hours

-15.9415****
(5.8620)

12.8615

789.3576****
(129.0048)

555.2442

.4634
(2.7521)

-3.1834

-3.2842
(5.2539)

-30.2332

165.4785
(132.2339)

SMSACNTY

R2

.16

.35

R2

.14

.33

n

198

200

a Coefficients are reported with standard errors in
parentheses.
b Significance levels:
**** = .01; *** = .05; ** = .10;
* = .15 for the null hypothesis that the parameter equals
zero.

134
—2
for degrees of freedom (R ), of the on-farm labor supply
equation of the Personal-Household model is not great at .14;
although it is higher than Sumner

[1978] obtained for

Illinois farmers with an equation which similarly excluded
farm business and agricultural enterprise variables.
The o p e r a t o r ’s completion of high school

(OPSCHOOL) is

associated positively with on-farm labor supply and is
significant at the
’credential effect'

.10 level.

While it was thought that the

of possessing a high school diploma

might tend to enhance employability off-farm and thereby
possibly,

though not necessarily,

reduce on-farm work,

the

sign and magnitude of the coefficient is not totally unex­
pected given the "Michael Neutral" assumption about the
increased productivity of education in all endeavors inclu­
sive of self-employment and home production as well as wage
work.
An increase in the number of children in the household
(HOMCHILD) is positively associated with on-farm labor supply
and is significant at the

.01 level.

An increase in labor

supply is expected as family responsibilities grow not only
in terms of the marginal expense of raising additional
children, but also with respect to the resulting change in
the composition of the family towards a more goods intensive
structure associated with the presence of older children
that a larger family implies.

Moreover,

the increased

availability of supplemental labor in the form of older
children, when combined with increased labor of the male head

135
of household, may reflect greater revenue opportunities as
the farm labor resource constraint

is overcome and increased

agricultural production possibilities are achieved.

But the

positive sign for this variable could also reflect a taste
factor whereby the father wishes to share the "joy of farm­
ing" with his children,
example,

to instill agrarian values in them by

and to increase their human capital in the form of

increased knowledge of agricultural production.
Years of experience in farming (OPFARMYR) is positive
and significant at the

.01 level,

indicating both a strongly

developed taste for farming and an accumulation of human
capital skills in agriculture are associated with increased
on-farm labor.
The estimated wage rate (OPWAGEST) has the expected
negative sign,
level.

though it is only significant at the

.15

This suggests that the higher the off-farm wage rate

rises relative to a given on-farm wage rate,

the more likely

is a lower supply of labor to agricultural work.
The sign of the wife's wage income (WFWAGINC) is nega­
tive but not significant at the

.15 level.

However,

this is

not surprising since empirical evidence indicates the
husband makes his labor supply decisions independent of his
wife's employment decisions.
Finally,

investment income (INVSTINC), which for some

farmers may include rent from land rented out, has the
expected negative sign that logically follows from a decrease
in farming acreage.

Of course, were this variable to be

136
purged of rental income and be comprised solely of stock
dividends and interest from bonds and savings,

then the

negative sign would imply that this type of income is not
used as a source of investment for an expanded farm opera­
tion requiring additional on-farm labor, but rather may
result in increased leisure activity at the expense of farm
pr od u c t i o n .
The explanatory power of the off-farm labor supply
equation is greater than for the on-farm equation.

This is

primarily due to the strong influence of the estimated wage
rate in explaining the variability in hours worked in the
wage m a r k e t .
OPWAGEST is significant at the

.01 level and has a

positive sign, which means time is allocated away from alter­
native uses of leisure,

home production,

or on-farm work.

The only other significant variable is OPFARMYR -—
at the

.01 level.

The sign,

as expected is negative;

also

thus

indicating that years of farming experience reflect a taste
for farm work and a lesser preference for off-farm employ­
ment as an exclusive labor activity.
0PSCH00L has an unexpected negative sign —

unexpected

in that it was thought that completion of high school might
provide operators greater opportunity for off-farm employ­
ment,

given employer preferences for

ever,

since the estimate is not much larger than its

standard error,

'credentials’ .

How ­

the results do not invalidate the "Michael

Neutral" assumption discussed earlier with reference to the

137
influence of schooling upon on-farm labor supply.
HOMCHILD,

although possessing the expected positive sign,

is not significant at the .15 level.
The finding that WFWAGINC has a coefficient less than
one that is not significant at the

.15 level is consistent

with the apriori assumption that no relationship exists
between a wife's employment and the husband's labor supply.
INVSTINC has the expected negative sign,
significant at the

.15 level.

though not

Such income makes employment

sources of income less necessary;

hence,

fewer hours are

worked off-farm.
A new variable,

SMSACNTY,

which indicates whether a farm

is located in or adjacent to a Standard Metropolitan Statisti­
cal Area,

turns out positive as expected,

cant at the

.15 level.

(NOTE:

but is not signifi­

The coefficient 165.4785 for

SMSACNTY in the labor supply equation does not express the
total effect,* which is actually 232,6527 when accounting for

* The total effect of SMSACNTY is calculated (1) by sub­
stituting the right hand side of the wage equation for
OPWAGEST in the labor supply equation, and (2) by combining
terms so that the coefficients are added.
Given the wage
equation
OPWAGEST = m n + ... + m^OPMRKTYR + m^SMSACNTY
0
5
6
which is substituted into the labor supply equation
OPJOBHR
= b n + ... + b.OPWAGEST + ... + b 7SMSACNTY
such that
OPJOBHR
= b Q + ... + b4 (mQ + ... + nigSMSACNTY) + ...
+ b 7SMSACNTY
= b Q + ... +[b4 (m0 + ... + mgOPMRKTYR) + b ^ S M S A C N T Y ]
+ ... + b SMSACNTY
= bQ + ... +[b4 (niQ + ... + rtigOPMRKTYR) ]+ ...
+[b4m g + b ? ]SMSACNTY

138
the Influence of SMSACNTY in the wage equation where the
coefficient is .0851 in Table C-l of Appendix C . )
Netting the effect of the explanatory variables in the
on-farm and off-farm equations in order to arrive at the
total labor supply gives signs that are not contrary to
theoretical expectation.

Although units of the explanatory

variables are not comparable,

it is worth pointing out the

large change in labor supply that results from a one unit
change in OPWAGEST whereby a one dollar increase in market
wage is associated with an increase of 555 hours (or approxi­
mately 14 forty hour work weeks) annually,
ii.

Female Labor Supply
The on-farm labor supply equation for females,

as reported in Table V-3,

shows results identical to the male

on-farm equation with regards to the direction of the
relationships of common explanatory variables with the hoursof-work response variable.
do differ,

However,

the significance levels

and the explanatory power of the equation is

lower.
The positive coefficient for wife's schooling (WFSCHOOL)
again illustrates the validity of the assumption that educa­
tion may increase productivity in all work activity and thus
raise the marginal value product of labor in farming.
However,

the number of young children (YNGCHILD) does

not have the expected negative sign that would indicate a
constraint upon involvement with the farm operation.
be that residence on the

'work site'

It may

allows the wife to

139
Table V-3.

Explanatory
Variables

Female labor supply estimations
household model.

On-Farm
Hours

Si

of personal-

Off-Farm
Hours

Total
Hours

-386.1087

Intercept

533.8517
(346.3638)

-919.9604
(207.9743)

WFSCHOOL

238.2922
(171.5049)

-225.4402***
(100.5362)

YNGCHILD

115.4990
(120.9875)

-219.9510****
(69.8835)

WIFARMYR

WFWAGEST

11.3604**b
(6.8982)
-24.4476
(126.3070)

1.7780
(4.0086)
827.9640****
(86.0216)

12.8520

-104.4520

13.1384

803.5164

OPWAGINC

-3.9916****
(1.5369)

-1.4487*
(.8924)

-5.4103

INVSTINC

-15.3967****
(5.7445)

-1.5358
(3.3340)

-16.9325

-512.6875****
(101.5777)

SMSACNTY

R2

.10

.38

R2

.07

.35

n

180

185

Si

Coefficients are reported with standard errors in
parentheses.

k Significance levels:
**** = .01; *** = .05; ** = .10;
* = .15 for the null hypothesis that the parameter equals
zero.

140
participate.
at the

In any case this variable was not significant

.15 level.

Years of farming experience (WIFARMYR) is positively
related to labor supply but is of weak significance.

This

variable does not measure the intensity of that experience
with respect to involvement;

rather,

for wives especially,

it may merely reflect the period of farm residence.
As with the male,

the estimated off-farm wage rate

(WFWAGEST) does have the expected negative sign but is not
significant at the

.15 level.

Interestingly the spouse's off-farm wage income
(OPWAGINC) does have the expected negative sign and is quite
significant.

This confirms the idea that the wife's labor

supply decisions take into consideration the monetary cont ri ­
bution to household well-being of the husband's wage market
income.
Investment income (INVSTINC),

inclusive of rentals from

farm land, decreases the labor supply as expected and is
significant at the .01 level.
The explanatory power of the off-farm labor supply
equation for females,

at

.35,

is slightly above that of the

male operator's equation.
The negative coefficient of WFSCHOOL, which is signi­
ficant at the .05 level seemingly does not support the
"Michael Neutral" assumption that education has an equal
effect on productivity in all productive endeavors, be they
in the home, on the farm,

or in wage employment.

Human

141
capital theory suggests that education increases productivity
of labor in farming activity relatively more than in market
wage work.

Most certainly the

operative for females.

'credential effect'

is not

The fact that the size of the

negative coefficient almost exactly matches the positive
coefficient

in the on-farm equation may indicate a compensa­

tory withdrawal from wage employment in favor of selfemployment .
YNGCHILD is significant at the

.01 level and the nega­

tive sign conforms to the expectation that an off-farm job
would require absence from the home where child care and
development are the commodities in need of production ala
the Household-Production Function model.
WFWAGEST is positive and significant at the

.01 level,

again illustrating that an increase in the market wage rate
does elicit an increased labor supply as predicted by
economic theory.
The negative sign for OPWAGINC, which is significant at
the .15 level,

confirms the expected dependence of the wife's

labor supply decisions upon the husband's employment status.
INVSTINC has the expected negative sign but is not
significant at the

.15 level.

The negative sign for SMSACNTY, which is significant at
the

.01 level,

is a surprise in that it was thought residence

in or near a Standard Metropolitan Statistical Area would
increase the likelihood of off-farm work in terms of greater
wage employment opportunities and shorter commuting distances

142
to off-farm jobs that would be compatible with home produc­
tion and child rearing responsibilities.

It should be noted

that the magnitude of the variable is reduced from a -512 to
-244 when the indirect effect of SMSACNTY expressed through
WFWAGEST is accounted for.

Still,

the negative sign is not

explained.
Netting the effect of the explanatory variables in the
on-farm and off-farm equations in order to arrive at the
total labor supply gives signs that are not contrary to
theoretical expectation.

As with male operators,

the

estimated wage had the greatest effect on labor supply for a
one unit change in the explanatory variable.
b.

Farm-Business Model
i.

Male Labor Supply
The explanatory power of the on-farm labor

supply equation of the Farm-Business model, found in Table
_2
V-4, is R = .24 which is almost twice that registered by
the Personal-Household model.

This increase can be attri­

buted to the effect of two variables,

farm assets (FRMASSET)

and acres rented in (ACRENTIN), which were both significant
at the

.01 level.

An increase in FRMASSET was found to be positively
related to on-farm labor supply, which means that as farmland
ownership and equipment investment is increased,

it draws in

more operator labor.
The positive sign for ACRENTIN indicates that as operat­
ing farm size is increased additional work effort is

143
Table V-4.

Explanatory
Variables

Male labor supply estimations
model.

On-Farm
Hours

cL

of farm-•business

Off-Farm
Hours

Total
Hours

Intercept

955.6193
(633.7976)

-1573.1472
(549.9097)

-617.5279

OPSCHOOL

222.9907
(172.8185)

-80.8064
(144.2885)

142.1843

-8.0340
(38.7787)

111.9993

HOMCHILD

1 20. 0333****b
(45.9010)

OPFARMYR

27.3574****
(7.2647)

OPWAGEST

-211.6258
(146.4165)

WFWAGINC

-4.5964*
(3.1541)

INVSTINC

-23.9408****
(6.2421)

SMSACNTY

-10.0505**
(6.1580)
780.7794****
(125.7287)

17.3069

569.1536

.0930
(2.6912)

-4.5034

-5.2331
(5.2523)

-29.1739

140.8260
(133.5147)

FRMASSET

5.6631****
(2.1388)

.8903
(1.9460)

6.5534

FARMDEBT

-8.1165
(8.2052)

14.4141***
(6.7922)

6.2976

ACRENTIN

12.2448****
(2.6399)

-2.0621
(2.1668)
-31.2952****
(10.3818)

FARMINC

R2

.28

.41

R2

.24

.37

n

188

190

10.1827

144
Table V-4.

ct

(Continued)

Coefficients are reported with standard errors in
parentheses.

r_

Significance level:
**** = .01; *** = .05; ** = .10;
* = .15 for the null hypothesis that the parameter equals
zero.

145
required.
Farm debt
level.

(FARMDEBT) was not significant at the

.15

The negative sign was not expected as it suggests

that an increase in farm debt, presumably due to land and
equipment acquisition,
labor on the farm.

would call forth less rather than more

Potential explanations include:

in­

creased farm debt is not due to acquisition but to bad
management of existing assets and/or adverse product market
conditions;

the addition of advanced technology allows for a

less labor intensive production function;

refinancing the

mortgage to achieve increased cash flow for non-farm invest­
ment income.

Other interpretations are certainly possible.

Although the significance levels of the PersonalHousehold variables included in the Farm-Business model
change,

the signs remain the same.

OPSCHOOL and OPWAGEST

lose significance and WFWAGINC becomes significant at the

.15

level or better.

_2

The explanatory power (R ) of the off-farm labor supply
equation for males is only slightly increased (from

.33 to

.37) with the addition of the Farm-Business variables to the
Personal-Household model.

Of these only FARMDEBT and gross

farm income (FARMINC) are significant at the

.05 and .01

levels respectively.
The positive

sign for

FARMDEBT suggests the need for

off-farm income as a source of capital input to pay off lia­
bilities incurred
The negative

wit h the farming operation.
sign for

FARMINC implies less reliance upon

146
off-farm wor k to earn a livelihood.
The accumulation of FRMASSET does not have any signifi­
cant effect with a coefficient less than one in value.
ACRENTIN has the expected negative association with
off-farm hours of work, but is not significant at the .15
level or better.
In comparing the status of variables common to the
Personal-Household model and the Farm-Business model,

the

signs change only for HOMCHILD which becomes negative.
OPFARMYR and OPWAGEST remain the only variables that have
coefficients significant at the

.15 level or better.

Netting the effect of the explanatory variables in the
on-farm and off-farm equations in order to arrive at the
total labor supply of males gives signs —
tion —

with one excep­

that are not contrary to theoretical expectation.

The negative sign for WFWAGINC does suggest the possibility
of non-independence of male labor supply decisions with
spouse employment activity.
ii.

Female Labor Supply
The explanatory power of the Farm-Business

model's on-farm labor supply equation for females in Table

—2

V-5 remains virtually unchanged (R

= .07 versus

pared with the Personal-Household model.
common variables stay the same,
significance at the

.08) com­

The signs of the

though WFSCHOOL enters

.10 level.

FRMASSET is the only Farm-Business variable significant
at the

.15 level or better.

The positive sign indicates

147
Table V-5.

Explanatory
Variables

Female labor supply estimations
model.

£L

of farm-business

On-Farm
Hours

Off-Farm
Hours

Intercept

222.0467
(396.9871)

-696.1490
(223.2408)

WFSCHOOL

338.9064**b
(184.6125)

-234.4152***
(105.4219)

104.4912

YNGCHILD

134.0574
(126.5907)

-224.4471****
(71.2398)

-90.3897

WIFARMYR

WFWAGEST

13.2434**
(7.4030)
-26.2198
(131.6090)

OPWAGINC

-4.2608****
(1.6095)

INVSTINC

-15.0693****
(5.9217)

1.5397
(4.2162)
805.9528****
(85.5574)
-1.8629***
(.9346)
-2.7806
(3.4030)

Total
Hours

-474.1023

14.7831

779.7330

-6.1237

-17.8499

-563.1185****
(104.3429)

SMSACNTY

FRMASSET

3.4831*
(2.2354)

-.7367
(1.3426)

2.7464

FARMDEBT

2.3044
(7.5685)

-1.9476
(4.2502)

.3568

ACRENTIN

-1.5774
(2.5383)

2.4621**
(1.3740)

.8847

-12.5137**
(6.8212)

FARMINC

R2

.13

.41

R2

.08

.38

n

169

174

148
Table V-5.

cl

(Continued)

Coefficients are reported with standard errors in
parentheses.

k Significance levels:
**** = .01; *** = .05; ** = .10;
* = .15 for the null hypothesis that the parameter equals
zero.

149
that wives increase their on-farm labor contribution as the
value of land, buildings and equipment investments grow.
FARMDEBT and ACRENTIN have quite small coefficients and
are not significant at the .15 level or better.
The off-farm labor supply equation for females in the
Farm-Business model finds the variables common to the
Personal-Household model unaltered with respect to the co­
efficient signs and significance at the

.15 level or better.

_2

The explanatory power (R ) increases a bare

.03 to

.38 with

the model expansion.
Neither FRMASSET or FARMDEBT are significant,

and their

coefficients are quite small.
ACRENTIN is significant at the
positive sign.

.10 level and has a

One possible explanation for this somewhat

unexpected result can be found in the rural sociology litera­
ture reviewed in Chapter II, wherein a study
pp. 2-3]

[Wilkening 1968,

showed that "as the size of farm enterprises in­

creases the wife is less involved in both work and decision
making roles in the farm area."

Thus,

an increase in

ACRENTIN would mean an increased size of operation, which
would free up the wife to undertake more home production or
off-farm work.

This result could imply that larger farms

require more specialized roles and therefore more highly
developed skills, whi ch wives are not inclined to develop
vis a vis pursuit of traditional skills in home production
or of marketable skills for off-farm sector employment.
FARMINC is also significant at the .10 level.

The

150
negative sign suggests that increases in income from non­
wage market sources enables wives to reduce hours of work
supplied to the off-farm labor market.
Netting the effect of the explanatory variables in the
on-farm and off-farm equations in order to arrive at the
total labor supply gives signs that are not contrary to
theoretical expectation.

As with male operators,

the

estimated wage had the greatest effect on labor supply for a
one unit change in the explanatory variable.

B.

INTERPRETED FINDINGS

In this section the overall findings reported above for
sex aggregates are examined to see whether labor supply
theory is verified in the main and whether the empirical
results are consistent with those of similar studies.

1.

THEORETICAL CONFORMITY
Generally speaking,

the Personal-Household model is more

effective in explaining the variation in off-farm hours-ofwork than on-farm labor supply.
for males and was

.35 versus

—2

The R

was

.33 versus

.07 for females.

But,

.14

as the

Personal-Household model is extended to include FarmBusiness variables,

_2
the R of the on-farm labor supply equa­

tions dramatically approach the explanatory power of this
same model for off-farm hours-of-work by husbands and wives.
The Personal-Household model variables all had the
expected signs,

except for YNGCHILD for female on-farm labor

151
supply which has a non-significant positive (instead of
negative) sign, OPSCHOOL for male off-farm labor supply which
has

a

non-significant negative

(rather than positive)

sign, WIFARMYR for female off-farm labor supply which has a
non-significant positive (as opposed to a negative) sign,
and SMSACNTY for female off-farm labor supply which has a
significant negative (in place of a positive) sign.
A brief review of this model's seven variables of level
of schooling,
wage rate,

number of children,

spouse wage income,

farming experience,

investment income,

own-

and county

residence tends to confirm expectations derived from economic
theory regarding their relationships with labor supply both
to on-farm self-employment and off-farm wage employment.
The fact that on-farm hours-of-work increased for males
and females with graduation from high school is consistent
with the "Michael Neutral" assumption that education in­
creases labor productivity in all endeavors equally.
ever,

How­

even though possession of a high school diploma

enhances one's employability in the wage market,

off-farm

hours-of-work declines for both sexes which would seem to
suggest that the expected

'credential effect'

is not present

for either sex.
The number of children in a household, which indicates
additional male responsibility for goods-intensive consump­
tion,

is associated with an increase in on-farm and off-farm

hours worked —

presumably in order to earn more income with

which to purchase such goods.

The effect of young children

152
Is also in accordance with theoretical expectation in that
women are constrained from participating in labor away from
their residence.
The work experience variable for years farming supposedly
reflects human capital accumulation

(as well as taste

factors) which predicts that increased experience raises
productivity.

The estimated effects are significant and

positive for on-farm labor supply by males and females,

and

a significant negative relation with off-farm work by males.
A positive relation occurred for off-farm female labor
supply, but the coefficient was less than half the size of
the standard error.
The estimated wage rate has the expected positive sign
for off-farm labor and negative sign for on-farm work which
is what theory suggests is the logical relationship.
Spouse income in the male labor supply function was not
expected to have any effect,

given the independence of the

h u s b a n d ’s wage market decisions.

On the other hand, wives

are classified as secondary workers whose labor force par ti ­
cipation and hours-of-work are conditional upon the husband
as the primary worker in the household.

Indeed,

the results

bear this out with operator's wage income being negatively
associated with female labor supply both on-farm and offfarm.
Investment income reduced on-farm and off-farm labor
supply for both sexes as theory suggests,

although this

variable was significant only for on-farm labor supply of

153
both sexes —

which may be due to the effect of acres rented

out being a component of investment income.
Finally, while residence in a S.M.S.A.

county has a

positive effect for male off-farm labor supply as would be
expected with the increased job opportunities available,

the

sign is unexpectedly negative and significant for female
off-farm labor supply.
The Farm-Business model results show the variables to
have the expected signs with the exception of FARMDEBT for
on-farm male labor supply and FRMASSET for off-farm male
labor supply,

neither one of which had the value of its co­

efficient exceed the standard error."
Farm assets is positively related to on-farm labor
supply for both sexes and negatively related to off-farm
labor supply for females;
with theory.

and these results are consistent

The positive sign for male off-farm labor

supply, while not expected and not significant at the

.15

level or better, may be explained in terms of financing farm
expansion with off-farm earnings.
Farm debt,

contrary to expectation,

has a negative but

insignificant sign for on-farm labor supply —

perhaps

attributable to poor management or unfavorable market condi­
tions instead of reflecting capital investment in the farm.
However,

as expected it was positively related to male off-

farm labor supply and significant at the

.05 level thereby

indicating the importance of cross subsidization of farm
activity by off-farm sector income.

154
Acres rented in is positive and significant for male
on-farm labor supply,

as an expanded operation implies.

The

positive significant sign for female off-farm labor supply
suggests that larger farms may result in more specialized
activity by male operators,

but less for females who may

elect not to develop the expertise involved and accordingly
who supply less labor to the farm (negative,

non-significant

coefficient) and more to the wage market sector for which
she has salable skills.
Finally,

gross farm income is negatively related to

off-farm labor supply of both the male and female heads of
household, which is what theory would predict in terms of a
leisure preference choice.

2.

EMPIRICAL CONSISTENCY
The main studies with which the research results are

most directly comparable involve the Illinois farm studies by
Sumner

[1978]

and by Sexton
supply.

for both on-farm and off-farm hours-of-work
[1975]

The R.I.M.E.

and Barros
studies

[1976]

for off-farm labor

[Kerachsky 1975; Primus 1975]

with their emphasis on the experimental effects of income
transfers are less comparable,
a.

On-Farm Labor Supply

2

Sumner's male labor supply equations had R s of .10
and .18 for equations comparable to the two models estimated
herein

[Sumner 1978,

p. 74].

This represents a somewhat

lower explanatory power than the results reported in this
study for the Personal-Household (.16) and the Farm-Business

155
(.28) models.

Sumner's equations include age, education,

imputed wage,

health,

total family income,

farm assets,

and

regional location measures.
With respect to variables common and comparable in
measure to both studies,

the estimated market wage rate

showed a negative relation to on-farm labor supply in both
studies.

Similarly,

farm assets have a positive association

with on-farm hours in Illinois and Michigan.

Therefore,

the

results of the two studies are consistent with each other.
b.

Off-Farm Labor Supply

The imputed wage rate was positively related to off-farm
work in Sumner
this study.
and Barros

[1978, p. 74]

and Sexton

[1975, p. 91] as in

The non-employment income variables of Sexton
[1976, p. 66] were negative,

investment income herein.

as is the sign for

Farm assets had a negative sign in

Barros and a positive sign in this study, but neither were
significant at the

.15 level or better.

Years of farming

experience has negative coefficients for Barros and the
results reported here.
years,
Sexton;

Education, measured continuously in

had a positive sign in Sumner and a negative sign in
the binary measure of schooling used in this study

has a negative coefficient.

So once again the results are

generally similar for all four studies on comparable variables
for farmer operators in neighboring states where agriculture
is not too dissimilar.
The explanatory power (R
was

2

.58 for Sexton's equation,

values) for the three studies
.19 to .27 for Sumner's

156
specifications,
in.

and .35 to

.47 for the models reported here-

Barros did not report an R

2

value for his equation.

SUMMARY

The findings reported for on-farm self-employment and
off-farm wage work by both male operators and their spouses
were stable across progressively extended equations that in­
volved additional regressors of the Farm-Business model
beyond those of the standard Personal-Household model.

For

the most part the hypothesized relations prevailed with
expected signs occuring.

Moreover,

the coefficients on many

of these variables were significant at the

.01,

.05,

.10 or

.15 level.
An examination of theoretically specified variables of
the Personal-Household model conformed with human capital
theory (i.e.,

imputed wage function) and consumer choice

theory (i.e.,

labor supply function).

Furthermore,

a compari­

son of the findings reported herein were found to be consis­
tent with similar farm household studies conducted on
Illinois data for bot h on-farm and off-farm hours-of-work.

CHAPTER VI
SUMMARY AND CONCLUSIONS

This concluding chapter presents a brief overview of the
research conducted (section A),

an evaluation of the results

with respect to confirmation of hypotheses and the accuracy
of the findings (section B),

and finally some closing

suggestions for improved data gathering and estimation
procedures (section C).

A.

1.

RESEARCH SYNOPSIS

PROBLEM AND HYPOTHESES
The problem under investigation was the determination

of what Personal-Household attributes and Farm-Business
characteristics are associated with annual hours-of-work onfarm and off-farm by operators and their spouses belonging
to low farm-income households.

A review of relevant theory

and empirical literature in conjunction with deductive
reasoning about farming operations led to the formulation of
hypothesized associations between the aforementioned classes
of explanatory variables and the response variable of hoursof-work on-farm and off-farm (Table IV-1).

157

158
2.

THEORY AND MODEL
Consumer choice theory underlies labor supply analysis,

and human capital theory provides the foundation for labor
productivity analysis and the specification of wage earn­
ings functions.
The household production function model was used to
understand the interdependent relationships among individual
members of a single household.

In particular its applica­

tion to allocation-of-time decisions among alternative uses
of wage market work,
production,

self-employment farming,

home commodity

and leisure provided a conceptual framework for

examining labor supply of farm families.
This led to the specification of two labor supply models
or equations:

3.

Personal-Household and Farm-Business.

SAMPLING AND ESTIMATION
The data used were from a stratified random sample from

Michigan's lower peninsula.

A total of 243 low farm-income

households located in ten different counties were included
in the survey conducted in 1974

[Thompson 1975].

These

households were selected to be representative of small
farms, which were defined to have under $20,000 annual gross
agricultural sales.
Estimation of the labor supply functions involved the
use of an imputed wage rate for the entire sample in order
to avoid sample censorship that would occur if only the
actual reported wage rate was used.

By assigning an estimated

wage rate to non-workers they were included in the analysis.

159
The labor supply equations were then estimated using O L S .
This instrumental variable technique is also less
sensitive to measurement error and specification error than
is the alternative of using a simultaneous equations model,
which is designed to cope with potential endogenous relation­
ships among variables.

B*

1.

GENERALIZED RESULTS

HYPOTHESIS CONFIRMATION
The hypothesized relations between the P er sonal-House­

hold and Farm-Business explanatory variables and the hoursof-work response variables for on-farm self employment and
off-farm wage employment of operators and their spouses
prevailed for the most part, with coefficients for many
variables significant at the

.01,

.05,

.10, and

.15 levels.

The results for the aggregate sample by sex are summarized
in Table VI-1 and may be compared with the hypothesized
variable relations originally formulated in Table IV-1.
Table VI-1 also reports the sign and significance levels
for the animal and crop variables of the Ag-Enterprise
model,

the results of which are presented in Appendix D.

In appraising the findings according to the criteria of
whether they conformed to theoretical expectation and whether
they were consistent with the findings of similar empirical
investigations,
criteria.
task,

these results generally satisfied both

The models as specified are judged adequate to the

although incomplete to the extent that greater

160
Table VI-1.

Estimated on-/off-farm variable associations by
sex.

EXPLANATORY VARIABLES

RESPONSE VARIABLES

On-Farm Labor

Off-Farm Labor

By General Categories ---------------------------------------operator

wife

operator

wife

PERSONAL-HOUSEHOLD3,
Education Level
( B in ar y)
Children At Home
Young Children
Farming Experience
Off-Farm Wage Rate
Spouse Wage Income
Investment Income
S.M.S.A. Residence
(Bin a ry )

+ (.10)d

+

_

+ (.01)

X

+

X

X

+ (.01)
- (.15)
- (.01)

+
+ (.10)
- (.01)
- (.01)

X

X

+

(.01)

+ (.15)

(.01)

+
X

+
+
—
—

(.05)
X
-

- (.01)
+ (.01)
+

(.01)
+
+ (.01)
- (.15)

-

-

(.01)

FARM-BUSINESSb
Assets
Debts
Acres Rented In
Gross Income

+
+
X

—

(.05)
(.01)

+
—

(

_

(.05)

.10)
(.10)

AG-ENTERPRISE C
Layer Hens
Dairy Cows
Feed Cattle
Silage Corn
Grain Corn
Soybean
Wheat
Hay/Alfalfa
Fruit

Symbols:

+
x

+

+
+
+
+
+

(.01)
(.01)
(.01)
(.05)
(.15)

(.01)
+ (.01)
+ (.01)
+ (.01)
+
+
+

-

(.01)

+ (.05)
+ (.10)
+ (.05)

+

indicates positive relation.
indicates negative relation,
indicates omission from model.

161
Table VI-1.
£L

(Continued)

Estimations from Personal-Household Model in Tables V-2
and V-3.

^ Estimations from Farm-Business Model, inclusive of PersonalHousehold variables, in Tables V-4 and V-5.
Q

Estimations from Ag-Enterprise Model, inclusive of
Personal-Household and Farm-Business variables, in Tables
D-l and D-2.
^ The level at which the coefficient of the explanatory
variable is statistically significant in the respective
models estimated.

162
explanation of the response variable might have been achieved
had the survey data contained information on additional
variables of relevance to labor supply analysis.
The results of the empirical analysis showed that for
both sexes in on-farm labor supply the Farm-Business model
is only moderately better than the Personal-Household model
in explaining the variation in hours-of-work.

The differ­

ences are less pronounced for the off-farm equations.

_2
R

The

values for the on-farm labor supply equations of these

two respective models are
.07 for females.

.24 and

The values of

.14 for males and

.08 and

for the off-farm labor

supply equations of these same two models are .37 and .33
for males and

.38 and

.35 for females.

These figures also

point up the fact that the Farm-Business and PersonalHousehold models were better in accounting for the variation
of off-farm compared to on-farm hours-of-work.
speaking,

Generally

the explanatory power of these models compares

favorably with those of similar cross-section studies of farm
family labor supply to on-farm and off-farm activities.
The principal findings and conclusions of this empirical
study are summarized below:

first for on-farm labor supply,

then for off-farm labor supply,
v ariations thereof.

and finally for life cycle

Discussion is limited to those

variables for which the coefficients were significant at the
.15 level or better as reported in their respective models.
For males the variation in hours-of-work on-farm was
found to be a function of several variables.

Those operators

163
completing high school,
children,
assets,

supporting a larger number of

having mor e farming experience, possessing greater

and renting in acres were found to supply more labor

to their farming activities.

Those with investment income,

including rent from acres rented out,

supplied less labor

on-farm.
For females fewer variables were significant at the
specified levels.

Thus we are limited to stating with any

confidence that spouses of households where the husband's
wage income increases and investment income rises supply less
labor to the farm.

They supply more labor to the farm as

additional farming experience and farm assets are acquired.
Off-farm labor supply of males is positively affected
by a higher market wage rate and increased farm debts.

Less

hours are supplied to the off-farm sector when years of
farming experience accumulate and gross farm income rises.
Increased female labor supply to the off-farm sector
is associated with a higher market wage rate and an increased
size of operation due to additional acres being rented in.
Fewer hours-of-work are supplied off-farm for those spouses
who completed high school,
children in the home,
Statistical Area,

care for additional young

live in or near a Standard Metropolitan

and enjoy greater farm income.

An Ag-Enterprise model is also estimated for farm
operators and their spouses,

but it is relegated to

Appendix D since there is no sound theoretical basis for the
inclusion of crop and animal enterprises and there is good

164
reason to believe these variables may be endogenous with
labor supply decisions.
might be expected,

Briefly,

the results indicate,

as

that those enterprises characterized as

labor intensive are positively associated with on-farm hoursof-work and negatively related to off-farm labor supply.

_2

The R

of both the male and female equations increased sub­

stantially,

relative to the Farm-Business model, with the

addition of the agricultural enterprise variables.
Life cycle variations in the labor supply of farm
operators and their spouses are estimated and analyzed in
Appendix E.

In attempting to determine whether life cycle

effects are demonstrated by the results it is observed that
while the magnitude and signs of the coefficients for some
variables do change across age groups,

conclusive evidence

in the form of significant coefficients at the „15 level or
better in at least two age groups,

is generally lacking.

Only for the male off-farm equation is there support for
the presence of life cycle effects; while the male on-farm,
female on-farm,

and female off-farm equations are inconclu­

sive on this matter.

2.

INFERENCE LIMITATIONS
The purpose of any research study based on a scientific

sample is to make generalizations about the population from
which the sample was drawn.

Section F of Chapter III dis­

cussed the difficulties of obtaining accurate estimates.
With respect to potential sampling error the possibility
of this was m inimized by the nature of the sampling design

165
and sample size utilized.
However,

the potential bias from non-sampling error is

not so easily dismissed.

The possibility of an unrepresenta­

tive sample due to the probable missed households of
agricultural sales under $2,500 means that the results
reported herein cannot safely be generalized to the extreme
bottom end of the distribution of low farm-income households.
Measurement error is an obvious problem when mentioning
the effect of wage rates on labor supply since imputed wage
rates were assigned to all household members.

In particular,

the estimated wage rates are probably overestimated for the
non-wage market participants.
Farming experience reported jointly for husband and
wife is another potential source of measurement error —
especially for the wives.

Resulting estimated effects must

be viewed with some skepticism;

although this variable was

only significant for on-farm labor supply of wives.
Investment income should have been confined to stocks,
bonds,

and savings and have excluded rent from farmland

rented out for the purposes of examining labor supply onfarm;

this would lessen the chance of endogeneity with hours

of work.
Missing observations are by far the most serious source
of potential bias.
siderable detail.

It has already been discussed in con­
Suffice it here to reaffirm the notion

that with the loss of cases for analysis it is difficult to
infer the results herein to the entire population when

166
undetected patterns of exclusion from the sample may have
occurred.

Cass county households,

for instance, were

effectively excluded by virtue of the pervasive missing data
problem created by interviewers in that area.

Assuming

that the missing observations occurred randomly throughout
the sample (as was apparently the situation with the possible
exception of Cass county) inference can be made,

albeit not

with full confidence as to the accuracy of the coefficients
in terms of efficiency.
Certain variables were omitted from the analysis of
labor supply for lack of data,

though none of them was

especially crucial to the analysis with respect to economic
theory.

Race, health status, work experience,

and the

unemployment rate are the principal variables that might
have helped to better explain the variation in on-farm and
off-farm hours-of-work.
With these cautionary notes in mind,

the results can be

generalized to the population of low farm-income farmers in
Michigan's lower peninsula.

C.

FURTHER RESEARCH

The preceding limitations suggest improvements that
could be made in replicating and extending this study.
and foremost there is the data.

Ideally,

First

the data analyzed

in future research would be' comprehensive in nature with
respect to information on all variables prescribed by theory —
but especially those comprising the Personal-Household

167
model —

and to measurements of all variables that are

theoretically correct and correspond to similar empirical
research.

This would facilitate the construction of a more

complete and accurate model.
on individual health status,
wage rates,

on-farm and home production

commuting distance to the nearest S.M.S.A.,

local unemployment rates,
etc.

In this study the lack of data

career occupational work experience,

limited the scope of the models.
Given the missing observation problems due to reporting

and recording errors that blemish this research,

improved

data collection procedures and coding systems are also of
paramount importance.
So, too,

are more accurate measurements of variables

critically important —

particularly estimates of on-farm

labor supply for which the use of respondent's recall of
annual hours-of-work is less than satisfactory in terms of
reliability.
Longitudinal data is also preferred for analysis of
life cycle effects.

Obviously,

high collection costs

preclude the gathering of such data exclusively for house­
hold studies and necessitate reliance upon existing longitu­
dinal data sets —

the nature and scope of which labor

economists and policy makers might endeavor make more
relevant to their professional and public concerns.

Strati­

fication of the sample by age groups is a poor substitute
for historical data on individuals.

At the very least a

sufficiently large number of observations for each age group

168
in cross-section analysis is desirable so as not to have the
results open to question as is the case herein with the under
35 year old group.
With such improvements in data more thorough analyses
could be conducted (e.g.,

estimating the probability of off-

farm labor force participation using LOGIT),
could be minimized (e.g.,

potential biases

sample censorship) and the necessity

for additional compensatory estimation procedures could be
eliminated (e.g.,
sub-sample).

imputing a wage rate for the non-working

In connection with the last point the avoidance

of the instrumental variable technique would have permitted
the inclusion of the key variables of age and work experience
in the labor supply equations;

they were dropped because of

their high correlation with the imputed wage rate.

Addition­

ally, better data might justify the use of more sophisticated
estimation techniques that are computationally complex and
thus more costly (e.g.,

the three step Heckman approach or

the two step TOBIT procedure),

but which would help overcome

truncation bias due to the concentration of observations at
zero for off-farm hours-of-work.
To the extent that these aforementioned improvements
remain elusive and labor supply studies are not standardized,
disparity of judgements by researchers will continue to make
comparability of empirical findings difficult as alluded to
in the below quotation.
Estimation of this (l a b o r - l e i s u r e ) model re­
quires that researchers make many often arbi­
trary assumptions.
These include choices among
sample populations, alternative measures of the

169
variables whose relationships are to be esti­
mated-, and different estimation techniques.
Differences in the judgements of labor supply
researchers are in part responsible for a range
of parameter estimates far too large to be of
much use to policy makers trying to choose
among alternative income maintenance programs.
However, because the methodologies of these
studies have varied in several ways simultan­
eously, it is difficult to pinpoint the exact
causes of divergence in their empirical
results.
[Da Vanzo, DeTray, Greenberg 1976,
p. 313]
Turning to the matter of additional investigations
future researchers might want to concern themselves with,
consideration should be given to a comparison of the labor
supply responses of farm operator sub-groups such as those
employed full-time off-farm,
employed off-farm.

half-time off-farm,

and not

Another subject of interest would be the

redefinition of the response variable as total labor supply
adding the on-farm and off-farm hours in an effort to verify
labor supply theory.

This would help reconcile any conflict

of coefficient signs for a variable in the on-farm and offfarm labor supply analyses.

And finally,

although the

importance of household production was revealed in the litera­
ture review discussion of the "new home economics," a
formal incorporation of this alternative outlet for labor
into labor supply models is vital to allocation of time
studies —

particularly in the determination of the wife's

reservation price with respect to her participation in onfarm and off-farm activity.
In sum this study of labor supply decisions of low-farm
income households in Michigan by and large confirms what

170
other researchers have found in their studies of farm
populations in other states.
these analyses,

Taken in conjunction with

this research could well serve as a basis

for further investigation of labor time allocation decisions
of low farm-income families.

APPENDICES

APPENDIX A
MICHIGAN SURVEY QUESTIONNAIRE

CONFIDENTIAL
SMALL FARM FAMILY PROGRAM
SURVEY INFORMATION
Respondent

Name
Mailing Address
(Street or Rural Route)

(City)

(Zip Code)

Telephone No.
Farm Location

County
Township
Directions to Farm

Interviewer

Name _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Date

'

In a research project at Michigan State University, we are interested in your
suggestions and opinions regarding the needs of families living on small farms.
We would like to obtain information about your family and farm operation. The infor­
mation you give will be kept confidential.
It will be summarized with that from
other families and used to obtain a better understanding of the problems on a small
farm and programs to solve problems.
Before a schedule is completed, determine whether the farm qualifies
as a small farm according to the following definition._______________
Definition of a small farm —

10 acres or more of land and enterprises smaller

than:
Dairy - 25 milk cows + feed crops
Cash grain - 200 tillable acres
Beef cattle feeding - 100 feeders + feed crops
Beef cow and calf - 80 cows + feed crops
Farrow and finish swine - 30 sows - 2 litter system + feed crops
Feeder pig production swine - 60 sows - 2 litter system + feed crops
Feeder pig finish swine - 500 feeders + feed crops
Poultry - 3,500 laying hens + feed crops
Fruit - 40 acres

171

172

CONFIDENTIAL

-

ICard 1
(Col.)

1

-

Card

1

County Code

2

3-5

Farm No.
First, I will ask questions about your family.
A.

Family Data
1.

What are the ages of all persons in the family?
a)

b)

2

.

3.

(Circle answer)

Husband

Wife

None

0

Under 25

1

25-34

2

35-44

3

45-54

4

55-64

5

65 & over

6

None

0

Under 25

1

25-34

2

35-44

3

45-54

4

55-64

5

65 & over

6

c)

Children under 5 years old (Number)

8

d)

Children 5-8 years old (Number)

9

e)

Children 9-13 years old (Number)

10

f)

Children 14-17 years old (Number)

11

g)

Children 18 years old or over (Number)

12

h)

Other related adults

13

How many children are living at home?

14

(Number)

Was the living situation during school years of the
husband and/or wife in a rural area?
(Farm, country,
small town, etc.)

15
Neither
Husband
Wife
Both

173

-

4.

2-

ICard 1 I
(Col.)

What was the level of formal education attainment for the husband?
College grad

5

16

8 years or less
9-11 years
Completed high school
Some college or technical training

5.

What did the husband's high school education emphasize;

17

No high school education
General
Agricultural
Home economics
Business/secretarial
Vocational - other
College preparation
6.

What was the level of formal education attainment for the wife?
College grad

5

18

8 yM r s or less
9-11 years
Completed high school
Some college or technical training

7.

What did the wife's high school education emphasize;

19

No high school education
General
Agriculture
Home economics
Business/secretarial
Vocational - other
College preparation
B.

Family Living Information
1.

Do you have a vegetable garden each year?

Yes

20

No
2.

Do

you can or freeze vegetables for year round use?

Yes

21

No
3.

What percent of home consumed meat Is produced on the farm?

22
OZ
1-5 OZ
51-99Z
100Z

174

ICard l l
(Col.)

-34.

5.

6.

What percent of home consumed milk is produced on the farm?

23

02

0

1-502

1

51-992

2

1002

3
24

What percent of home consumed eggs are produced on the farm?

02

0

1-502

1

51-992

2

1002

3

Approximately how many dollars of monthly Income does your
family need to achieve a satisfactory or comfortable living
with prices at their present (March, 1974) level.

25-26
(Hundred* s
dollars)

7.

What is the minimum monthly income needed to support the
family?

27-28
(Hundred1s
dollars)

8.

How many years have you and your spouse lived on your
present farm?

29-30
(years)

9.

How many years have you and your spouse continuously
farmed?

31-32
(years)

10.

33

What are your reasons for living in a rural community?

For employment reasons

0

For retirement

1

Farm opportunity

2

Disdain for urban life

3

Appreciation for rural life

4

For health reason

5

Raise family

6

Other

7

Next, I will ask questions about your farm
1.

How many acres do you own?

34-36

2.

Of the owned land, how many acres are tillable?

37-39

175

Card ll
(Col.)

-43.

What is the major soil type?

40

Sand

1

Sandy-loam

2

Clay

3

Clay-loam

4

Loam

5

Loamy-sand

6

Muck

7

4.

How many tillable acres did you rent in 1973?______________ _

5.

If land was rented, what type of lease arrangement was
used on rented land?

41-43
44

Cash rent
Share rent
Cash and share rent
Other ______________

6

.

7.

S.

How many tillable acres of owned land did you rent out in 1973?
If land was rented out, what type of lease arrangement was used
on rented land?
Cash rent

45-47
48

1

Share rent

2

Cash and share rent

3

Other

4

______

How many acres of the following crops did you harvest in 1973?
a)

Alfalfa, clover or other hay harvested

___

49-51

b)

Corn for silage

___

52-54

c)

Corn for grain

55-57

d)

Wheat

58-60

e)

Other grain (i.e.:

f)

Soybeans

64-66

g)

Pasture

67-69

h)

Fruit

70-72

i)

Diverted or idle

73-75

j)

Other cash crops (Kind ________

76-78

k)

Other feed crops (Kind _____

79-80

Oats, rye)

61-63

176

ICard 2
(Col.)

-5-

9.

Card

1

County Code

2

Farm Number

3-5

What were the 3 year average yields per acre from the
following crops?
a)

6-7

Alfalfa, clover or other hay harvested (Tons)
(one decimal
place)

b)

C o m for silage (Tons)

8-9

c)

Corn for grain (Bu.)

10-12

d)

Wheat (Bu.)

13-14

e)

Soybeans (Bu.)

15-16

Ask questions about livestock production for the type of livestock
on the farm in 1973. If 1973 livestock production was not typical,
obtain the information for a typical year during the last three years.

10. Beef Cow-Calf

11.

__

17-18

(Number)

__

19-20

(Number)

__

21-22

What was the selling weight of calves per head? (lbs)

23-25

a)

How many beef cows were in your herd?

b)

How many calves were born?

c)

How many calves were sold?

d)

(Number)

Feeder Cattle
__

26-27

a)

How many feeders were purchased? (Number)

b)

What was the ave. weight of feeders purchased
per head? (lbs.)

28-30

c)

How many feeders were sold?

31-32

d)

What was the ave. selling weight per head (cwt.)

33-35

a)

How many litters were farrowed during the year? (No.)_

36-37

b)

What was the ave» number of pigs weaned per litter?
(One decimal place)

38-39

c)

How many feeder pigs were sold?

__________

40-42

d)

How many feeder pigs were purchased?

____________

43-45

e)

How many market hogs were sold?

(Number)

12. Swine

13.

(Number)
(Number)

(Number)

46-48

Poultry
a)

What was the average number of laying hens?

49-52

b)

How many dozens of eggs were sold per hen?

53-54

[Note:

ESTIMATE TOTAL NUMBER OF DOZENS SOLD
AVERAGE NUMBER OF LAYING HENS ______

177

-

6-

&
14.

Dairy
a)

What was Che average number of milk cows in your
herd? (Number)

b)

Were you on a Grade A or B market?

c)
[Note:

What was the average annual milk production per
cow? (Cwt.)

55-56
Grade A

1

Grade B

2

__

57

58-60

USE ONE OF THE FOLLOWING TO ESTIMATE PRODUCTION]
Lbs. sold In 1973 __________+ Average number of cows
milking and dry ________
OR
Lbs. shipped on typical day

♦ Average number of

cows milking and dry ______

X 365

OR
DHIA, Owner Sampler or other'record
15.

16.

Other Livestock
a)

Kind ______________________________

b)

Number _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

c)

Production ________________________

DO
NOT
CODE

During 1973 what has been the total labor hours of farm work by the:
(Estimate on weekly bases if necessary to arrive at yearly total)
Hours/year
(Hundred's Hours)

D.

Off-Farm Employment

a)

Husband

61-62

b)

Wife

63-64

c)

Other family members

65-66

d)

Hired

67-68

Information for 1973
If the husband had off-farm work 1

1.

What kind of work was done?
69
None

0

Professional or Technical

1

Manager, official

2

or proprietor

Clerical

3

Sales

4

Craftsman or foreman

5

Operatives (semi-skilled)

6
(cont.)

178

-7-

Card 2
(Col.)

Nonfarm laborer

7

Service

8

Farm

9

2.

Ave. number of hours worked per week?

70-71

3.

Number of weeks worked in 1973?

72-73

4.

What is your regular hourly wage?
0-2.50

0

2.51-3.00

1

3.01-3.50

2

3.51-4.00

3

4.01-4.75

4

4.76-5.50

5

5.51-6.25

6

6.26-over

7

74

5.

How many years have you worked at the present occupation?

75-76

6.

How many miles do you drive to your present lob? Cone way)

77-78

7.

Are any of the following fringe benefits received?
a)

Life insurance

Yes
No

1
2

79

b)

Health/Hospital
Insurance

Yes
No

1
2

80

Card 3
(Col.)
Card

3

1

County Code

2

Farm Number

3-5

c)

Paid vacation time

Yes
No

1
2

6

d)

Retirement (not
social security)

Yes
No

1
2

7

e)

Other (specify)

If the wife had off-farm work
8.

What kind of work was done?

___________________

8

179

Card 3
(Col.)

-8-

9.

None

0

Professional or Technical

1

Manager, official

2

or proprietor-

Clerlcal

3

Sales

4

Craftsman or foreman

5

Operatives (semi-skilled)

6

Nonfarm laborer

7

Service

8

Farm

9

Ave. number of hours worked per week?

9-10
11-12

10.

Number of weeks worked in 1973?

11.

What is your regular hourly wage?
0-2.50

0

2.51-3.00

1

3.01-3.50

2

3.51-4.00

3

4.01-4.75

4

4.76-5.50

5

5.51-6.25

6

6.26-over

7

13

12.

How many years have you worked at the present occupation?

14-15

13.

How many miles do you drive to your present lob? (one wav)

16-17

14.

Are any of the following fringe benefits received?

15.

a)

Life insurance

Yes
No

1
2

18

b)

Health/Hospital
Insurance

Yes
No

1
2

19

c)

Paid vacation time

Yes
No

1
2

20

d)

Retirement (not
social security)

Yes
No

1
2

21

e)

Other (specify)

Yes
No

1
2

22

Did anyone else in your household work off-farm in 1973?

180

-9E.

ICard 3
(Col.)

Now, I would like to obtain an Indication of changes in the farm or off-farm
employment.
1.

23

Over the next two to three years, what changes would you like to make
in your farming operation? _____________________________________________

None

1

Do less farming

2

Expand farming operation

3

Retire from farming

4

Other __________________

5

| Ask questions 2-3 only if item 3 was checked in question 1 above
What changes would you like to make in expanding the farm operation?
(Detailed as possible - No. acres, kind and number of livestock, etc.)

24

Don't know
Increase crop yields
Increase acres farmed
Increase livestock production
Increase livestock numbers
Other ____________________ _ _ _
3.

How many additional hours of labor per year are available by the
family for this expansion?
(Hundred's
Hours)
ASK EVERYBODY I
4. What net cash farm Income are you attempting to achieve?
(Hundred's
Dollars)

25-26

27-29

If changes in off-farm work is anticipated by the husband ask
question 5-8.________________________________________________
5.

What kind of a job would you like to have in off-farm employment?

30

Don't know

0

Professional orTechnical

1

Manager, official orproprietor

2

Clerical

3

Sales

4
(cont.)

181

ICard 3 I
(Col.)

-10-

Craftsman or foreman
Operative (Semi-skilled)
Nonfarm laborer
Service
Farm

6

.

7.

How many hours would be worked per week?

31-32

How many weeks per year?

33-34

8 . What income is desired per year?

35-37
(Hundred1s
Dollars

If a change in off-farm work is anticipated by the wife ask
questions 9-12.____________________________________________
9.

10.

38

What kind of a job would you like to have in off-farm employment?

Don't know

0

Professional or Technical

1

Manager, official or proprietor

2

Clerical

3

Sales

4

Craftsman or foreman

5

Operative (Semi-skilled)

6

Nonfarm laborer

7

Service

8

Farm

9

How many hours could be worked per week

11.

How many weeks per year?

12.

What income is desired per year?

___

39-40

___

41-42
43-45

(Hundred's
Dollars)
F.

Capital Investment In Farm Business
1.

2.
3.

What is the estimated selling price for your land
and buildings?

46-48
(Thousand's
Dollars)
49-51

What is the approximate value of your machinery, on
Jan. 1, 1974?

(000)

What is the approximate value of your livestock on
Jan. 1, 1974?

(000)

52-54

182
-11-

G.

[Card 3
(Col.V

4. What is your approximate amount of debt for the
farm and farm personal property on Jan. 1, 1974?

(000)

5. What is your approximate debt for consumer items on
Jan. 1, 1974? (Cars, furniture, appliances, etc.)

(000)

55-57
58-59

Family Income
1.
2.
3.

4.

5.

What was the average per year gross agricultural sales
for the past two years?

(000)

What was your average per year cash farm expenses for
the past two years?

(000)

60-61
62-63

What was your family income from transfer payments in
1973? (i.e.: Social security, welfare, etc.)
What was your family income from investments in 1973?
(i.e.: farm rent, savings accounts, stock, bonds, etc.)
Other family income in 1973?

(i.e.:

64-66
(Hundred's
Dollars)
67-69

$

(Hundred's
Dollars)

pensions)

70-72
(Hundred's
Dollars)

H.

1.

State your suggestions and opinions regarding the needs of families
living on small farms. ___________________________________________

2.

State any other comments or observations.

APPENDIX B
MISSING DATA ADJUSTMENTS

The summary tally of responses to the survey question­
naire

[Thompson 1975]

indicated the presence of significant

numbers of non-responses to certain items on the instrument.
Because these became

'blank* when recorded on the computer

cards, potentially serious missing data problems arose for
some variables.

That is,

if just one variable

of many variables (e.g., work experience,

(e.g.,

income,

age)

etc.) for

a particular case (i.e., Michigan small-farm household) had
a blank instead of a zero or positive value,

then the whole

case had to be discarded with a resulting loss of informa­
tion on all other variables of that household for which data
was recorded.
In examining the format of the questionnaire and the
computer print-out of the raw data,

it was determined that

logical consistency checks and reasonable assumptions could
be used to convert blanks to zeroes for most, but not all,
variables selected for use in this study.

The nature of the

data correction and the change in the number of missing data
will be briefly explained for each affected variable.
all conversions blanks were changed to zeroes.

183

In

184
Consistency Checks
1)

OPFARMHR (Operator's Farm Hours —
blanks changed to zero;
Criteria:

card 2, col. 61-2) 10

25 remained.

If no operator is present in the household,

and if schooling is left blank,

or if tillable acres

rented out equals tillable acres owned,

or if gross

agricultural sales equals zero.
Logic:
2)

Self explanatory.

WIFARMHR (Wife's Farm Hours —
blanks changed to zero;
Criteria:

card 2, col. 63-4) 11

31 remained.

If no wife is present;

otherwise same as for

OPFARMHR.
Logic:
3)

Self explanatory.

OPSCHOOL (Operator's Schooling Years —
4 blanks changed to zero;
Criteria:
Logic:

4)

card

1, col. 16)

none remained.

If no operator present

in household.

Self explanatory.

WFSCHOOL (Wife's Schooling Years —
14 blanks changed to zero;
Criteria:

card 1, col.

18)

3 remained.

If no wife present;

otherwise same as for

OPSCHOOL.
Logic:
5)

Same as for OPSCHOOL above.

HOMCHILD (Children at Home —
changed to zero;
Criteria:

card 1, col.

none remained.

If no children are listed as present

of the various age groups under 18 years.
Logic:

14) 16 blanks

Self explanatory.

inany

185
6)

YNGCHILD (Children under 5 —

card 1, col.

8) 24 blanks

changed to zero; none remained.
Criteria:

If wife is

over 54;

and if operator is over age 54;

if no wife is present,
if total number of

children at home is zero or left blank.
Logic:

A woman over 54 is beyond child bearing age;

it

is unlikely that a widower or bachelor over age 54
would have young children;

it is presumed that a blank

for HOMCHILD really means zero due to interviewer
error,

as this is not

a sensitive question to which

interviewee would be reluctant to
7)

respond.

OPMRKTYR (Operator's Year in Market Work —
col.

75-6) 94 blanks changed to zero;

Criteria:

the

card 2,

7 remained.

If no job is presently held,

or if a blank

is recorded for work experience.
Logic;

The questions on present off-farm employment,

hours per week, weeks per year, wage rate,

and community

miles immediately precede the question on OPMRKTYR;

and

an inspection of the computer print-out of raw data
indicates a consistent pattern whereby if the initial
question was left blank,

all succeeding related que s­

tions were also left blank.

The presumption here is

that the interviewer meant the blanks to mean zeroes.
However,

it should be noted that this particular question

on how many years the individual has worked off-farm in
his occupation is actually independent of current
employment,

but may have been interpreted to refer to

186
the current job even though a separate question on this
was on the questionnaire.
8)

WFMRKTYR (Wife's Years in Market Work —
14-5) 183 blanks changed to zero;
Criteria:
Logic:

9)

1 remained.

Same as for OPMRKTYR above.

Same as for OPMRKTYR above.

OPWAGINC (Operator's Wage Income —
72-73

card 3, col.

card 2, col.

• 74) 77 blanks changed to zero;

Criteria:

70-71

17 remained.

If each of the components of this constructed

variable is blank (i.e.,

hours per week, weeks per

year, wage rate).
L og i c : See explanation for OPMRKTYR.
10)

WFWAGINC (Wife's Wage Income —
11-12

card 3, col.

9-10

•

• 13) 182 blanks changed to zero; 6 remained.

Criteria:

Same as for OPWAGINC above.

L o g i c : See explanation for OPMRKTYR.
11)

OPJOBHR (Operator's Off-Farm Job Hours —
70-71

card 2, col.

• 72-73) 80 blanks changed to zero;

Criteria:

If no job is presently held;

6 remained.
or if blanks

are recorded for current job and commuting miles.
Logic:
12)

Same as for OPMRKTYR above.

WFJOBIIR (Wife's Off-Farm Job Hours —
9-10

card 3, col.

• 11-12) 182 blanks changed to zero;

Criteria:
Logic:

•

Same as for OPJOBHR above.

Same as for OPJOBHR above.

3 remained.

187
Remedial Assumptions
1)

OPFARMHR (Operator's Farm Hours —
16 blanks changed to zero;
Criteria:

card 2, col. 61-2)

9 remained.

If the operator works 35 or more hours a

week for 48 or more weeks per year off-farm.
Rationale:

Given a full time,

year long wage job it is

likely that with commuting time added on little if any
labor was supplied to these farms.

It is recognized

that the assigned zero values may understate the true
value of on-farm labor, but this was judged preferable
to the loss of information on other relevant variables
for these 16 cases had they been left blank.
2)

WIFARMHR ( W i f e ’s Farm Hours —
blanks changed to zero;
Criteria:

14 remained.

Same as for OPFARMHR above.

Rationale:
3)

Same as for OPFARMHR above.

FRUIT (Fruit Enterprises —
blanks changed to zero;
Criteria:

card 2, col. 63-4) 17

card 1, col.

70-72) 227

none remained.

Recode blanks to zeroes.

Rationale:

Examination of the raw data, print-out

indicated that zero values were not recorded.

The

presumption is that interviewers meant blanks to signify
zero values.
4)

DAIRY (Dairy Enterprise —
blanks changed to zero;
Criteria:
Rationale:

card 2, col. 55-56) 209

none remained.

Recode blanks to zeroes.
Same as for FRUIT above.

188
5)

LAYERHEN (Layer Hen Enterprise —
207 blanks changed to zero;
Criteria:
Rationale:

6)

card 2, col. 49-52)

none remained.

Recode blanks to zeroes.
Same as for FRUIT above.

CROPNDEX (Index of Crop Enterprises —

card 1, col.

49-51 + 52-54 + 55-57 + 58-60 + 61-63 + 64-66 + 76-78)
166-201 blanks changed to zero;
Criteria:
Rationale:
7)

none remained.

Recode all crop enterprises to zero.
Same as for FRUIT above.

BEEFNDEX (Index of Beef Livestock Enterprises —
col.

card 2,

17-18 + 26-27) 177-191 blanks changed to zero;

none remained.
Criteria:
Rationale:
8)

Recode all beef enterprises to zero.
Same as for FRUIT above.

HOGNDEX (Index of Swine Livestock Enterprises —
col.

card 2,

36-37 + 46-48) 217-218 blanks changed to zero;

none remained.
Criteria:
Rationale:

Recode all swine enterprises to zero.
Same as for FRUIT above.

It should be noted that for some variables no consistency
checks or remedial assumptions are possible;
(20 blanks),

INVSTINC (11 blanks),

namely, FARMYR

and FARMDEBT (30 blanks).

In the case of farm experience it must be presumed that a
positive non-zero value should have been recorded.
investment income the blanks might be zeroes,

For

but they could

also reflect respondent reluctance to answer a sensitive
question.

Likewise for eight cases of farm debts where

189
people may have been unwilling to divulge what could be
considered privileged information.

The remaining twenty-two

blanks of this variable are genuine because no Cass county
household was asked about farm debts on the pretest question­
naire used.

APPENDIX C
IMPUTED MARKET WAGE ESTIMATION

This appendix is comprised of 3 sections:
of the instrumental variable technique,
estimated wage function,

a discussion

a description of the

and a report on the imputed wage

results.

INSTRUMENTAL VARIABLE TECHNIQUE
Essentially,

a wage function is estimated for the

employed sub-sample* using ordinary least squares (OLS).
Multiple regression analysis is run on a few critical
independent variables suggested by human capital theory and
previous empirical work

[Mincer 1974],

researcher's judgement dictates.

plus others as the

The main instrumental

variables are age, educational level, work experience,
health status —

and

all of which reflect labor productivity.

Variables like sex and race can also be included to reveal
the influence of such market forces as employer wage discrim­
ination policies

[Boskin 1973].

A locational variable is

sometimes used to reflect suspected differences in offered

* A wage function can also be estimated using an alter­
native data source based on the same approximate population,
if personal characteristics and labor market conditions are
similar [Sexton 1975, pp. 141-42].
190

191
wage rates across regional labor markets
and Greenberg,

1973, p. 111].

of the wage function,

Then,

[Da Vanzo, DeTray

using the coefficients

the specific values of each individual's

personal characteristics in terms of these variables (for
both the non-employed and employed subpopulations) are pl u g ­
ged into the wage function to calculate their appropriate
"imputed"

(i.e.,

estimated,

predicted,

potential) wage,

which in turn is to be inserted into the labor supply
f un c t i o n .
Econometrically speaking,

the first step of this two-

step IV procedure involves regressing the endogenous variable
(i.e., wage rate) on a set of predetermined variables thought
to be statistically independent of the disturbances.

This

first step generates estimated values of the explanatory
endogenous variable,
an

known as a 'reduced-form estimate*

'instrumental variable estimate,'

genous variable in its original form,
the disturbance term.
variable (i.e.,

or

that unlike the endo­
is not correlated with

In the second step the dependent

ho u rs - o f - w o r k ) is regressed on the reduced-

form estimate of the hitherto endogenous explanatory
variable (i.e., wage rate) and whatever other predetermined
variables are specified to directly affect the dependent
variable.

Although IV estimators are consistent,

their

variances are larger than those of corresponding OLS
estimators.

OLS estimators have a smaller dispersion than

IV, but it is around an asymptotically biased mean
and Greenberg 1973, pp. 48-49],

[Da Vanzo

192
This widely used technique addresses the complications
that can arise in labor supply studies with regard to the
inclusion of the theoretically important wage rate variable
in the labor supply function.
exists in wage rates

Measurement error often

[Hall 1973, p. 109].

This can be due to

the necessity for survey respondents to convert annual in­
come or monthly salary into the requested hourly wage rates.
Reporting errors can also occur when respondents signify
only the range within which their wages fall.
situations prevail with respect to the M.S.U.
Survey data.
do exist,

Both of these
Small Farm

When such errors in the measurement of wages

the classical estimation procedures are inappro­

priate because the wage variable and the error term are
likely to be correlated.

In this situation "the least

squares regression leads to biased,
estimates" of the beta coefficient
Second,

even inconsistent,
[Boskin 1973, p. 166] .

wage rates are not observed for individuals who

are not working in the labor force.

Omitting the data for

these persons would probably cause a downward bias in the
estimated wage response, because the omitted observations are
likely to have negative disturbances
This,

too,

[Hall 1973, p.

is a problem characteristic of the M.S.U.

109],
Small

Farm Survey respondents, many of whom did not report having
a job.
Third,

construction of an imputed wage rate is less

subject to life cycle effects (whereby a changing wage rate
is positively correlated with age and work experience) than

193
actual wage rates, which in a long run model of behavior are
endogenous to the system.
education,

training,

That is, past decisions regarding

and work experience will be reflected

over time in current market wage offers
1975, p. 13].
wage,

Hence,

"it is the lifetime average (permanent)

not the current wage,

[Da Vanzo, DeTray,
Fourth,

[T. P. Schultz

that is theoretically correct"

Greenberg 1973,

p. 65].

the imputed wage mitigates against transitory

influences on current actual wage rates.

To illustrate,

the wage rate reported during a particular survey period
may be atypical of the r e s p o n d e n t ’s normal work situation.
For example,

a temporary disequilibrium in hours worked can

cause a lowering of the wage rate (as with part-time employ­
ment and/or moonlighting jobs) or a raising of the wage rate
(as with seasonal employment and/or jobs requiring much
overtime work with time and a half pay)

[Greenberg 1972,

p. 41].
Fifth,

if the wage rate is recognized as not being

wholly exogenous in nature and determined jointly with hours
of work by such other factors as human capital investment
decisions,

choice of residence,

selection of occupation,

then the instrumental variable can minimize the biases
caused by these interdependencies
These,

then,

[Greenberg 1972, p. 48].

are the major justifications and advantages

of using the instrumental variable technique to impute wage
rates.

However,

satisfactory,

its success in empirical use is less than

as much of the literature reveals.

Still,

for

194
lack of an alternative approach that is not computationally
complex and expensive,

this remains a standard technique in

labor supply studies.

Some of the principal drawbacks

associated with the use of the instrumental variable technique
are set forth in the paragraphs that follow.
First of all,

imputing hourly renumeration for work

with a wage rate function is susceptible to variation
attributable to variables not included in the regression
equation such as unobserved and unmeasurable taste factors
or differences in the productivity of time in non-market
activities

[Greenberg 1972,

p. 49].

Moreover,

"the variables

that are included account for only a small fraction (15%) of
the variation in reported wages"
360].

[Cain and Watts 1973, p.

And much of that variation is attributable to age and

formal education which constitutes a "rather convincing case
for the instrumental variable often being little more than an
education variable scaled in wage units"
p. 49].

In fact,

the R

2

[Greenberg 1972,

values are low for such equations.

Studies on the general population ranged from .16 to .29
for males and from .15 to
and Greenberg 1973,
86].

pp.

.22 for females

111-23;

T. P. Schultz 1975, pp. 81-

Farm household studies using this same technique have

2

obtained even lower R s —
1976]

[Da Vanzo, DeTray,

and

.17

[Sumner 1978]

.05

[Sexton 1975],

for Illinois.

.09

[Barros

In another state

where farming is not too dissimilar from Michigan —
Iowa —
2
the R.I.M.E. study [Kerachsky 1975] obtained R s of .30 for
husbands and

.36 for wives;

however,

the use of over 20

195
variables in the wage function

(compared to the usual four

to six) probably pushed the value upwards.

Additionally,

since these empirically estimated equations tend to account
for such a moderate proportion of the variation in observed
wages,

there is a substantial risk that in using imputed

wages we are throwing away useful information in the form of
the unexplained residual.

Some of this unexplained variation

in wages could probably be traced to such factors as quality
of education and nature of experience,
measures are lacking
Second,

for which adequate

[Da Vanzo and Greenberg 1973, p. 35],

simultaneity bias may occur with the use of

actual/observed reported wage rates in the labor supply
equation.

This is because it is entirely possible for wage

rates to be a function of hours worked,
versa!

That is,

instead of visa

an employer who rationally takes into con­

sideration his fixed costs of employment
recruitment,
training,

personnel processing,

benefits administration,

(i.e., manpower

job orientation and
etc.) may elect to pay

part-time labor less than full-time workers in order to
recoup those expenses
and Hosek 1976,

p. 9].

[Greenberg 1972,

pp. 40-41; Greenberg

Since the M.S.U.

Small Farm Survey

data reveals a mixture of full-time and part-time off-farm
job holding,

the instrumental variable technique "may over­

estimate the wages facing part-time employees and/or under­
estimate those of full-time employees"

[Boskin 1973, p. 167,

fn. 1].
Third,

selectivity bias may result from the sample

196
censorship that necessarily occurs when using the employed
sub-sample (who have reported wage rates) as the basis for
imputing wages to the entire sample of working and non­
working individuals.

Such sample selection bias can cause

an overestimation of the actual wage offers non-labor force
participants are likely to face
p. 304,

fn. 13; DeTray 1973, pp.

[Shisko and Rostker 1976,
32-35; Gronau 1972;

Da Vanzo, DeTray, Greenberg 1973; Greenberg and Hosek 1976].
Moreover,

a person faces not one wage rate, but a distri­

bution of wage rates for the same bundle of characteristics.
Those job seekers finding high wage offers will work,

those

receiving low wage offers relative to their asking/reserva­
tion wage will choose not to work.

(It should be noted that

it is entirely possible that a non-worker will have a
greater potential wage than a worker,

yet stay out of the

labor force due to an even higher value of marginal product
in household production.

No attempt was made to estimate

the unobserved home wage rate.)

In imputing wages we only

observe the high wage rates offered to the employed —
a likely truncated wage offer distribution.

hence

That is, the

mean wage offer of the observed truncated distribution
probably exceeds the

'true' mean wage offer.

The magnitude

of the bias will be negatively related to the labor force
participation of the group under study
Greenberg 1973, pp.

34-35].

However,

[Da Vanzo and
the importance and

extent of this bias has been somewhat minimized as a result
of a comparative analysis of alternative wage estimation

197
procedures using only education and work experience as
independent variables.

"The effect of sample censoring,

which would bias the OLS estimate toward zero,
be trivial" for education,

appears to

although "it appears that

selectivity bias has a substantial effect" for labor market
experience

[Cogan 1975, p. 30].

Of course, one can assume away selectivity bias by
stating that all persons with a given set of market related
attributes face identical wage offers, which would thereby
ensure consistent and unbiased labor supply estimates
[Cogan 1975, pp.

17-18].

On one hand this seems not to be

an unrealistic proposition,

given the relative homogeneity

of the sample under study herein —
and spouses.

low farm-income operators

On the other hand it conveniently ignores the

fact that certain individuals with a given set of character­
istics choose to work while others with apparently the same
characteristics do not work
more,

[DeTray 1973,

p. 32],

Further­

these differences in work patterns between the working

and non-working sub-samples are probably "prima facie
evidence of important differences in the potential wage
rates of the two groups"

[Greenberg 1972, pp. 48-49].

And,

to the extent that selectivity bias does exist the parameter
estimates of the instrumental variable market wage equation
do not provide a consistent or asymptotically unbiased basis
to infer market wage offers for the population of workers
or non-workers

[T. P. Schultz 1975,

p. 14] .

198
ESTIMATED WAGE EQUATION
The wage function used by this researcher is restricted
to those variables which human capital theory suggest.
Accordingly,

the wage equation is specified identically for

both sexes:
LN(OPWAGE) = m Q + m ± OPAGE + m g O P AG E2 + m 3 OPEDUCYR +
m„ OPED UC YR 2
4

+ m K OPMRKTYR +
5

m c SMSACNTY + s
6

LN(WFWAGE) = w Q + V!± WFAGE + w g W F AG E2 + w g WFEDUCYR +
w. WFED UC YR 2 + w c WFMRKTYR +
4
5

w~ SMSACNTY + t
6

Taking the natural logarithm of the actual wage of those
working is fairly standard practice in the literature because

2
it tends to give a higher R .
In terms of the variables used,

age is thought to

affect earnings as a reflection of "vitality,

dexterity,

responsibility that vary over the life cycle"

[Kalachek and

Raines 1970,
variable,

p. 182].

and

And in the absence of a health status

it is likely to pick up the expected effect of

increasing disability with advancing age.

Age is also

entered as a squared term to account for a non-linear rela­
tionship whereby over time pay may rise to a maximum and not
increase with age or may even decline after age 45 with
respect to possible depreciation of human capital
1964,

pp.

138-44].

[Becker

The age variable may also pick up the

effect of on-the-job training which accumulates as human
capital with extended work experience,
variable is omitted from the equation.

if the work experience
(NOTE:

The age

variable is a continuous measure of age range category

199
m i d p o i n t s .)
The education variable should be indicative of the
economic value of additional schooling.
occasionally entered as a squared term,

This variable is
since beyond

generally recognized levels of achievement
diploma,
tion,

(i.e., high school

college degree) additional years of formal educa­

short of the next highest credential,

to be linearly related to wage increases.

are not thought
(NOTE:

The

education variable is a continuous measure of midpoints of
the years of schooling category.)
The experience variable is often included to account
for on-the-job training and skill acquisition that occurs
while working;

although there is no guarantee that is what

is being measured.

This job experience variable is theoreti­

cally important, because it is through work experience that
one informally accumulates human capital over time.

The

presumed higher productivity of such labor would likely
result in higher wage rates for that individual,
paribus.

Nevertheless,

some farm household studies have

omitted it from their estimated wage equations
1975;

ceteris

IKerachsky

Sexton 1975].
The last variable specified is the locational measure

indicating proximity to a Standard Metropolitan Statistical
Area where wage rates may generally be higher for similar
occupations compared to rural areas.

This is a binary

variable assigning 1 to counties classified as in or adjacent
to a S . M .S .A .

200
IMPUTED WAGE RESULTS
In Tables C-l and C-2 the results of the multiple
regression analysis of the wage equations are reported for
male and female heads of households respectively.

The wage

model was run using both the linear and natural log form of
the dependent variable as well as excluding and including
the square of education as a variable.
The signs of the coefficients yielded by the basic
equations for both male and female conform to theoretical
expectations;

but addition of the education variable as a

squared term does alter some of them.
With the exception of SMSACNTY,

all the explanatory

variables in the male equations are significantly different
from zero at a reasonable level of significance (i.e.,
.05,

.10).

By contrast,

.01,

only the WFMRKTYR and SMSACNTY

variables show up significant in the female equations.
2
The explanatory power (R ) of the female wage equations
is double that of the males in both linear and log form with
and without the squared term for education.

These R

2

values fall well within the range of other national and farm
household studies.

It would appear that the wage market work

experience variable is the most significant contributor to
explanatory power for both males and females; but the
locational variable SMSACNTY adds considerably to the
explanatory power of the female equation.

It may be that

for the type of w o r k available for women in the S.M.S.A.
counties (holding constant human capital qualities) the wage

Table C-l.

Imputed market wage estimations

Explanatory
Variable
Name

OLS-Linear
OPWAGE
1

Intercept

1.3865
(1.2432)

ct.

for males

OLS-Log
LN(OPWAGE)
2

.6698
(.3148)

Id

.

OLS-Linear
OPWAGE
3

8.2483
(2.5488)

OLS-Log
LN(OPWAGE)
4

2.0703
(.6532)

.0877**C
(.0476)

.0229**
(.0120)

.0792**
(.0463)

.0212**
(.0118)

OPAGE2

-.0010***
(.0005)

-.0002***
(.0001)

-.0010***
(.0004)

-.0002***
(.0001)

OPEDUCYR

.0957***
(.0450)

.0241***
(.0114)

-1.1290****
(.4031)

-.2258***
(.1033)

.0543****
(.0177)

.0111***
(.0045)

OPEDUCYR2

OPMRKTYR

.0255***
(.0102)

.0057***
(.0025)

.0248***
(.0099)

.0056***
(.0025)

SMSACNTY

.1602
(.1762)

.0657
(.0446)

.2554*
(.1738)

.0851**
(.0445)

R2

.12

.13

.18

o17

n

141

141

141

141

4.12

4.26

4.13

Mean wage^

4.24e

201

OPAGE

Table C-l.
SL

(Continued)

Coefficients are reported with standard errors in parentheses.
Estimated for 239 husbands.
The undercount from n = 243 households is due to absence
from the household (4 husbands).

c Significance levels:

**** = .01; *** = .05; ** = .10; * = .15.

Imputed wage is assigned to only 233 male operators due to 6 missing observations on
explanatory variables in the wage equation.
©

Mean of reported wage is $4.48 for the employed male subsample of 146.

Table C-2.

Imputed market wage estimation

Explanatory
Variable
Name

OLS-Linear
WFWAGE
1

Intercept

-.3629
(2.6100)

WIFAGE

si

for females

OLS-Log
LN(WFWAGE)
2

b

.

OLS-Log
LN(WFWAGE)
4

-.0066
(.9652)

.1256
(2.7299)

.2613
(1.0040)

.0469
(.0926)

.0053
(.0342)

.0342
(.0951)

-.0016
(.0350)

WIFAGE2

-.0007
(.0010)

-.0001
(.0003)

-.0006
(.0010)

-.0001
(.0003)

WFEDUCYR

.1546
(.1123)

.0562
(.0415)

.1691*
(.1151)

.0642*
(.0423)

-.0025
(.0039)

-.0014
(.0014)

WFEDUCYR2

WFMRKTYR

o0736****C
(.0227)

.0296****
(.0084)

.0712****
(.0231)

.0282***:
(.0085)

SMSACNTY

.7169***
(.3490)

.3605****
(.1290)

.7402***
(.3529)

.3733***:
(.1297)

R2
n
Mean wage**

.28

.32

.28

.34

54

54

54

54

2.20

2.32

2.16

2.34®

203

OLS-Linear
WFWAGE
3

Table C-2.
BL

(Continued)

Coefficients

are reported with standard errors in parentheses.

Estimated for 231 wives.
The undercount from n =
the household (12 wives).
C Significance levels:

243 households is due to absence

from

**** = .01; *** = .05; ** = .10; * = .15.

^ Imputed wage
is assigned to only 225 wives due to 6 missing observations on explanatory
variables in the wage equation.
0

Mean of reported wage is $2.94 for the employed female subsample of 54.

204

205
rates are probably higher than in rural counties.

However,

this difference is apparently not as important in determin­
ing male wage rates.
In deciding which specification and form of the equation
to use in generating estimated wage rates for the entire
sample,

the following criteria were employed:
high explana2
tory power (R ) and dispersion of the estimated wages.
With
respect to the first the R
the linear.

2

for the log form was higher than

This same phenomenon is reported in the litera­

ture, which may be the reason why the log form is convention­
ally used.
With regard to the second criterion it can be seen that
mean wages for alternative specifications remain virtually
unchanged with only a penny or two difference.

However,

inclusion of the quadratic of education achieves closer
correspondence between the estimated wage and the reported
wage at the high and low ends of the wage distribution of
those working off-farm.
The choice between the linear and the log form of this
particular specification again centers on the variability of
the estimates across individuals.

While the linear form

estimates are slightly closer to actual wage rates at the
higher end of the earnings distribution,

at the lower end

the linear form gives estimates considerably higher than
the reported wage rates.

And since it has been assumed that

those not participating in the wage market labor force are
probably at the lower end of the distribution,

use of the

206
linear estimates may over-estimate their wage rates compared
to the log form.

Hence,

the log form of the equation,

specified to include the square of education, was selected
to impute the wage rates for both the wage earning and non­
wage market subsamples.

APPENDIX D
AGRICULTURAL ENTERPRISE MODEL

Animal and crop enterprises have been added to the
Farm-Business model under the assumption that the selection
of such enterprises implicitly reflect use of time in those
farm activities having the highest marginal value product of
labor;

accordingly,

the agricultural enterprises can be

viewed as proxies for the on-farm wage rate,

for which no

reported values exist and none could reasonably be imputed.
One other farm household study

[Sumner 1978]

included

agricultural enterprises in on-farm and off-farm labor
supply functions, wherein they were considered to "measure
several effects which are not readily separable

...:

1) specific production functions with different demands for
labor,

skill,

given year]

etc.;

2) price and yield conditions in

relative to expected;

4) degree of specialization;

[a

3) inherent riskiness;

5) seasonality."

However,

"the

variables used have only gross indicators and have obvious
deficiencies for measuring any of the effects listed"
[Sumner 1978,

p. 44].

The specific agricultural enterprises examined were:
(1) animal:

layer hens (LAYERHEN), milking cows (DAIRYCOW),

beef cow (BEEFCOW),

feeder cattle sold (FEEDCATL),

207

hogs

208
sold (H0GS0LD),

and feeder pigs farrowed (FEEDPIG) —

measured in actual numbers;

and (2) crop:

hay and alfalfa (HAY/ALFA),

grain corn (GRNCORN),

corn (SILCORN), wheat
beans (SOYBEAN),

(WHEAT),

fruit

all

(FRUIT),
silage

rye and oats (RYE/OAT),

soy­

and miscellaneous cash crops (MISCROP) —

all measured in acres harvested.

Consistent with the MVP
J_j

criteria,

it is expected that those enterprises earning the

most revenue for the least amount of labor will be pursued
by multiple-job-holders while the more labor intensive
enterprises will be less characteristic of part-time farmers.

ESTIMATION OF MODEL
The inclusion of these agricultural enterprise variables
in the labor supply equations does raise the question of
whether farmers take agricultural enterprises and their
labor requirements as a given and then allocate some of their
remaining time to off-farm work (e.g.,

part-time versus

full-time,

seasonal versus

temporary versus permanent,

annual) or whether farmers take their off-farm job and its
labor requirements as a given and then choose the type and
level of agricultural enterprises whose labor intensities
(e.g., grain versus livestock,

and beef cows versus dairy

cows) are congruent with the permanently held off-farm job.
Despite the potential for endogeneity of decision
making,

the feasibility of the simultaneous equations model

has not been fully demonstrated in previous related empirical
work —

witness the inconclusive results of S c h a u b 's [1978]

farm household study reviewed in Chapter IV, section A-lb

209
"Farm-Business Model" as well as the sensitivity of simul­
taneous equations models to specification error and m e a s u r e ­
ment error discussed in Chapter IV, section B-2a "Jointly
Determined Relations."
With the aforementioned in mind a simplifying assumption
is made for this cross section study —
evidence —

with supporting

that in the short run farmers are fixed in their

particular type of farming by virtue of family tradition,
personal preferences,

technical knowledge,

farming experience,

soil type, machinery specialization, market outlets,

etc.

that limit their flexibility of switching among various
agricultural enterprises.

In other words,

farmers are

thought to take their agricultural enterprises and corres­
ponding labor requirements as given and then over the course
of a year they allocate
work,

their remaining time among off-farm

household production,

and leisure activities.

assumption is backed up by a previous study
p. 4] of Michigan full-time,
part-time,

This

[Loomis 1965,

low farm-income operators and

multiple-job-holding farmers, wherein two-thirds

of the latter group reported no change in their farm opera­
tion resulting from work off the farm.

Moreover,

two-thirds

said they worked

[of these part-time farmers]

"nearly

off-farm because farming did not yield sufficient income"
[Loomis 1965, p. 8] and "off-farm income enabled them to
have more and better machinery than when they were farming
full-time"

[Loomis 1965,

income preference'

p. 4].

Furthermore,

the

'money

for farming expressed by part-time

210
operators indicates that the amount of income farmers would
be willing to forego to farm only (i.e., quit non-farm job)
is less than the income they would be willing to sacrifice
to work at a non-farm job only (i.e.,
1965, p. 10].

Thus,

quit farming)

[Loomis

it would appear that off-farm work is

instrumental to agricultural self-employment,

which —

even

if the secondary occupation in terms of the number of hours
worked —

is considered by multiple-job-holding farmers to

be the primary and initially determined labor activity.
Another potential estimation problem is the so-called
'perfect fit'

that results from a deterministic relationship

between two variables.

That is,

for a given time budget,

the selection of a particular type and specific level of
agricultural enterprise activity would automatically determine
not only the amount of on-farm labor supply but also in­
directly the number of hours worked off-farm as a residual.
However,

while it is true that on-farm and off-farm hours

are not independent of each other,
fit.

neither are they a perfect

Besides the reasons for this already explored in the

context of possible endogeneity of the farm-income variable
with off-farm labor supply in Chapter IV, section A-lb
"Farm-Business Model"

(e.g.,

the influence of other forces

on labor supply on and off the farm;
allocation over a year;

the flexibility of time

and the existence of household

production and leisure activity from which time might also
be subtracted in pursuit of increased work on or off the
farm),

it should additionally be pointed out that measurement

211
error in reporting labor supply hours on-farm and off-farm
as well as different productivities of time in various
agricultural enterprises across individuals in the sample
mitigate against a perfect fit.
A final quandary centers on the selection of an appro­
priate measure for agricultural enterprise variables:
binary,

percentage,

or continuous.

A binary measure,

essentially a qualitative indicator,

ignores magnitude such

that subsistence levels of enterprise activity are not
distinguishable from commercial levels.
measure

[Sumner 1978]

A percentage

of the relative size of one enterprise

to another or to total farm activity also ignores magnitude
since base levels will vary across farms such that a higher
percentage for one farm relative to another could actually
constitute a lower absolute level of activity.

Moreover,

it

is not simple to construct a common denominator for diverse
enterprises (e.g.,
measure,

animal,

crop).

the third alternative,

A continuous quantity

was chosen because it most

accurately reflects the magnitude of the enterprise,

although

the hours of work required by the enterprise may vary across
individual farm operators —
function (i.e.,

depending upon the production

labor versus capital intensive) and upon the

differential labor efficiencies of the household members.

RESULTS OF MODEL
The Ag-Enterprise model for males in Table D-l doubles
the explanatory power of the Farm-Business model for on-farm
—2
—9
labor supply (R = .24 to R = .52) but only slightly

212
Table D-l.

Male labor supply estimations
model.

ct

of Ag-Enterprise

On-Farm
Hours

Off-Farm
Hours

Intercept

884.8531
(532.4200)

-1534.6243
(530.6973)

-649.7712

OPSCHOOL

226 .7624*b
(145.4126)

-86.3958
(139.9527)

140.3666

HOMCHILD

58.7097*
(37.3664)

-11.6091
(37.0843)

47.6091

Explanatory
Variables

OPFARMYR

17.1845****
(5.9685)

OPWAGEST

-155.3044
(117.2978)

WFWAGINC

-3.9424*
(2.5656)

INVSTINC

-15.1840****
(5.0894)

SMSACNTY

-10.7272**
(6.0080)
772.9419****
(121.1305)

Tot a lC
Hours

6.4563

617.6375

.9830
(2.6007)

-2.9594

-4.6289
(5.0232)

-19.8129

55.9020
(129.8469)

FRMASSET

-.4907
(1.9814)

.0437
(1.8718)

-.4470

FARMDEBT

-6.1812
(6.6418)

14.6166***
(6.5594)

8.4354

ACRENTIN

5.1737***
(2.3885)

-3.4790*
(2.3994)

1.6947

-23.9588***
(11.6587)

FARMINC

LAYERHEN

6.5722****
(2.3854)

DAIRYCOW

72.7891****
(10.8481)

FEEDCATL

8.2942
(5.9357)

-41.6006****
(11.6590)

31.1885

213
Table D-l.

Explanatory
Variables

(Continued)

On-Farm
Hours

FRUIT

16.8441***
(7.5130)

SOYBEAN

7.9797*
(5.0706)

GRNCORN

7.8840***
(3.2715)

SILCORN

27.8877****
(6.3839)

Off-Farm
Hours

WHEAT

10.9787***
(5.5129)

HAYALFA

6.7528**
(3.5829)

R2

.56

.47

R2

.52

.42

n

188

190

T o t a lc
Hours

a Coefficients are reported with standard errors in parentheses.
k Significance levels:
**** = .01; *** = .05; ** = „10;
* = .15 for the null hypothesis that the parameter equals
zero.
c The total hours coefficient is the sum of the on-farm and
off-farm coefficients.

214
increases it for off-farm work (R

2

= .37 to R

2

= .42).

With the exception of FRMASSET in the on-farm equation all
variables common to the two models retained their signs for
on-farm,

off-farm and net total labor supply.

In terms of

significance levels HOMCHILD and ACRENTIN become less
significant while FRMASSET is no longer significant at the
.15 level for on-farm labor supply.

The farm asset variable

is probably diluted in its effect by the inclusion of the
agricultural enterprises.

In the off-farm labor supply

equation ACRENTIN becomes significant at the

.15 level.

The final equations of the Ag-Enterprise model include
only those farm activities that showed up significant at the
.15 level or better first in the on-farm equations of
either sex,

and second in either the male or female off-farm

equations.

This was done to facilitate a comparison of the

male operator and spouse with respect to agricultural enter­
prises that were significant for at least one of the two
heads of household.
RYE/OAT,

Consequently,

BEEFCOW,

H O G S O L D , FEEDPIG,

and MISCROP were eliminated in preliminary regres­

sion analyses.
As might be expected for the on-farm hours-of-work
equation,

all the included enterprise variables had positive

signs.

LAYERHEN and DAIRYCOW are significant at the

.01

level.

Their positive association with on-farm hours-of-

w ork is consistent with the labor intensive nature of these
two enterprises.
at the

The fact that SILCORN is also significant

.01 level may reflect a complementary relationship

215
of silage corn with a dairy operation for home grown feed.
GRNCORN and FRUIT production are significant at the .05
level;

and SOYBEAN is significant at the

.15 level.

In the off-farm equation the DAIRYCOW variable is
significant at the .01 level and the negative sign merely
confirms the time intensive nature of that enterprise and
its lack of seasonality such that off-farm work is not
practical.

Other explanations point up the stability of

yield and price and the economies of scale achieved up to a
full-time dairy operation

[Sumner 1978,

p. 57].

Two crops

that never appeared in the on-farm equations for lack of
anything approaching significance are in fact positively
related to off-farm employment.
significant at the

.05 and

WHEAT and HAY/ALFA are

.10 levels respectively.

The

inherent nature of cultivating these crops may require
little in the way of regular care (i.e.,
other crops,

time) vis-a-vis

thus permitting farm operators free time to

pursue work off-farm.
As with the Ag-Enterprise model for males,

the female

on-farm labor supply equations in Table D-2 register a su b­
stantial increase in the explanatory power compared with the
Ag-Business model (R

2

— 9

= .33) while the off-farm
_2
hours equation remains virtually the same (R = .38 to

_2
R

= .39).

= .08 to R

For the on-farm and off-farm labor supply the

signs of the variables common to both models remain as b e ­
fore,

though the variables that were significant at the

.15

level or better in the on-farm equation lose that status with

216
Table D-2.

Explanatory
Variables

Intercept

Female labor supply estimations
model.

of Ag-Enterprise

On-Farm
Hours

Off-Farm
Hours

236.8586
342.9707)

-732.7665
(221.7743)

-495.9079

T ot a l C
Hours

WFSCHOOL

159.9552
(164.6181)

-268.4359****
(105.6967)

-108.4807

YNGCHILD

31.7781
(111.7545)

-196.7266****
(71.8226)

-164.9485

WIFARMYR

5.3206
(6.5013)

WFWAGEST

-39.9949
(115.3889)

OPWAGINC

-1.2462
(1.4797)

-1.7996***
(.9259)

-3.0458

INVSTINC

-6.9854
(5.2285)

-2.6454
(3.3703)

-9.6308

SMSACNTY

1.7134
(4.1758)
830.1158****
(85.5334)

7.0340

790.1209

-561.6714****
(103.3243)

FRMASSET

-.6984
(2.1978)

-.8601
(1.3308)

-1.5585

FARMDEBT

-2.6931
(6.7583)

-2.4587
(4.2160)

-5.1518

ACRENTIN

-7.8296****^
(2.4471)

3.0074***
(1.3862)

-4.8222

-9.5039
(6.9116)

FARMINC

LAYERHEN

10.4138****
(2.7500)

DAIRYCOW

48.4416****
(12.6124)

FEEDCATL

22.0207****
(6,2492)

-3.6806***
(1.7922)

6.7332

217
Table D-2.

Explanatory
Variables

(Continued)

On-Farm
Hours

FRUIT

9.4464
(7.7091)

SOYBEAN

3.7945
(5.4122)

GRNCORN

2.9260
(3.4222)

SILCORN

23.8481****
(6.5734)

Off-Farm
Hours

R2

.39

.43

R2

.33

.39

n

169

174

To t a l c
Hours

a Coefficients are reported with standard errors in parentheses.
k Significance levels:
**** = .01; *** = .05; ** = .10;
* = .15 for the null hypothesis that the parameter equals
zero.
c The total hours coefficient is the sum of the on-farm and
off-farm coefficients.

218
the addition of Ag-Enterprise variables.
equation WFSCHOOL,

ACRENTIN,

In the off-farm

and FARMINC change their level

of significance.
In the on-farm labor supply equation the agricultural
enterprises LAYERHEN, DAIRYCOW,
cant at the

.01 level.

and SILCORN are all signifi­

Since these were also equally

significant for the male operators it would appear that
these enterprises by their labor intensive nature may involve
joint participation on the part of the couples.

Observations

of some Michigan small farms are consistent with such
empirical results.

Additionally,

the number of young cattle

fattened and sold in feeder cattle operations (FEEDCATL) is
positively related to the w i f e ’s on-farm hours-of-work at the
.01 level.
Only one variable,

LAYERHEN, was at or even near signi­

ficance in the off-farm labor supply equation.

The negative

sign for the coefficient is compatible with the labor inten­
sive nature of this enterprise and the high level of involve­
ment wives have in such an operation.

SUMMARY

The Ag-Enterprise model explains substantially more of
the variation in hours-of-work than either the Farm-Business
or the Personal-IIousehold models.

The Ag-Enterprise model

was more effective in explaining the variation in on-farm

—2

than off-farm labor supply as evidenced by the R

value of

.52 and .33 for the males and females respectively on-farm

219
compared with
off-farm.

.42 and

.39 for men and women respectively

The principal findings are as follows:

for on-farm and then for off-farm labor supply.

first
Males

involved with such enterprises as layer hens, dairy cows,
fruit production,

soybeans,

grain corn,

and silage corn were

found to supply more labor to their farming operation.
Females supplied more labor on-farm when layer hen, dairy
cow,

feed cattle,

and silage corn enterprises are pursued.

Off-farm the growing of wheat and hay plus alfalfa is
associated positively with male labor supply, whereas an
increase in the number of dairy cows is negatively associated
with wage market work.

Females who raise layer hens are

found to supply fewer hours-of-work to wage sector employ­
ment .

APPENDIX E
LIFE CYCLE LABOR SUPPLY ANALYSIS

Labor supply literature suggests the distinct possi­
bility that present

labor supply decisions are made in a

lifetime framework, whereby the goals of individuals and
households with respect to consumption patterns and asset
accumulation change over the years;

and so too does the

value of time change as human capital skills are acquired
and then depreciate with age.

Thus,

it is thought that dur­

ing the early periods of one's work life, when a person is
attempting to get on his/her financial feet,

he/she will

supply more labor to the work force compared to later periods
in the life cycle* by which time the consumption of market
goods is less imperative (i.e.,

goods-intensive children

have grown up and the desire for consumer durables is
satisfied if not saturated).
In terms of agriculture these periods roughly correspond
to the "entry or establishment" stage,
survival" stage,
life

the "growth and

and the "exit or disinvestment" stage of

[Boehlje 1973, p. 23].

During the first stage the

* See section A-lc "Life Cycle Allocation" in Chapter II
for a more detailed exposition of the theoretical framework
for this subject.
220

221
farmer evaluates the opportunities in farming compared with
other occupational alternatives and determines whether or
not an agricultural occupation is preferred.

The new entrant

concentrates on acquiring capital resources and managerial
ability in an effort to establish a viable economic unit
that will generate a competitive income and good growth
potential.

The second stage conforms to the "growth and

survival" years when the entrepreneur strives to extend his
resource constraints and achieve increased production effi­
ciency by expanding sales and reducing costs.

The third

stage is characterized by "exit or disinvestment," either
through retirement from production and management activities
while maintaining control over income earning assets,

or

through intergenerational transfer sale of the farm.

These

three stages have been marked off in this study by the
following age groups:
stage two,
over.

stage one,

35 to 54 years of age;

34 years old and under;
stage three,

55 years and

This means altogether twelve life cycle regression

equations will be estimated —

a set of three age category

equations each for farm operators' on-farm and off-farm
labor supply and another set of three age category equations
each for spouses'

on-farm and off-farm labor supply.

The

use of age to stratify the sample precludes its use as an
explanatory variable in the on-farm labor supply function,
in whic h it would likely be correlated with other variables
reflecting life cycle decisions of the farm firm (e.g.,
asset accumulation,

investment income,

farm size-tillable

222
acres) and life cycle phenomena of the farm operator ( e . g . ,
off-farm and on-farm work experience,

health status,

age and

number composition of children).
Multiple regression analysis was used with the AgEnterprise model,

inclusive of the Personal-Household,

Farm-Business variables.

and

Those Ag-Enterprise variables that

were not statistically significant at the
dropped from each equation.

Thus,

.15 level were

there are some differences

in the variables included in the several equations estimated.
On-farm and off-farm labor supply results are reported
first for husbands and then for wives.
a.

On-Farm Labor Supply (Male Age Groups)
Because the farm experience variable is time

related it was dropped from the equations for the age
groups.

Other than this one variable,

the Personal-Household

and Farm-Business components of the Ag-Enterprise model are
identical to those used in the analysis of the aggregate
samples for operators and spouses.

The findings are reported

in terms of age group comparisons for each variable.*
In Table E-l an examination of the male age groups
shows that the middle and older age groups correspond with
each other in terms of coefficient signs for all common
variables save one,

FRMASSET;

but it is not significant at

the .15 level for either group.

Similarly,

when comparing

* it should be noted that tests of differences between
coefficients were not made.

223
Table E-l.

Explanatory
Variables

Intercept

OPSCHOOL

HOMCHILD

Life cycle on-farm labor supply estimations
males.

Age Group
under 35

-115.4050
(1153.6215)
- 8 1 3 . 9606***b
(377.9354)
156.4520**
(90.9777)

OPWAGEST

237.0403
(251.5096)

WFWAGINC

-4.6422
(8.3981)

INVSTINC

FRMASSET

FARMDEBT

-52.6779***
(23.0071)
13.1612****
(4.2529)
-28.0546***
(13.2274)

Age Group
35-54

ct

of

Age Group
over 54

2445.2321
(943.8749)

1889.6325
(862.4703)

198.6447
(188.0747)

190.5045
(220.2309)

53.7126
(42.9323)
-420.5120***
(204.2059)
-4.2776
(3.3061)

255.7305**
(144.2728)
-334.5008
(862.4703)
-5.2386
(4.4127)

-7.3729
(7.4093)

-14.0888***
(6.8157)

-.0867
(2.5881)

2.3589
(2.8281)

-.9763
(7.7981)

-27.7212
(21.3259)

6.3965***
(2.6634)

23.0093****
(7.9999)

35.1769***
(15.4171)

94.9826****
(17.9164)

LAYERHEN

8.6565***
(3.7849)

9.1521****
(3.4629)

SILCORN

27.7869****
(9.3735)

GRNCORN

9.6699* * *
(3.9313)

ACRENTIN

DAIRYCOW

.7873
(5.2666)
91.2344****
(28.1094)

32.1132***
(15.4132)

MISCROP

-24.6267***
(10.7487)

HOGSOLD

78.0335****
(18.7696)

224
Table E-l.

Explanatory
Variables

(Continued)

Age Group
under 35

Age Group
35-54

Age Group
over 54

R

.70

.53

.74

—2
R

.57

.46

.68

31

88

68

n

ct

Coefficients are reported with standard errors in paren­
theses .

k Significance levels:
**** = .01; *** = .05; ** = .10;
* = .15 for the null hypothesis that the parameter equals
zero.

225
the 35-54 and 55 + age groups with the aggregate sample,

the

signs of the coefficients match for all the variables with
the exception again of FRMASSET,

for which the coefficient

is positive for the oldest age group.
The under 35 group differs from the other age samples
and from the male aggregate results with regards to the
schooling and imputed wage rate variables.

OPSCHOOL has a

negative coefficient significant at the .05 level.

And the

coefficient for OPWAGEST is positive, but not significant at
the .15 level.

These results would seem to suggest that

within the youngest group the completion of high school may
indeed have a 'credential effect'

—

except that no corres­

ponding positive sign occurred in the off-farm estimation
for this age group (Table E-2).
this generation,

Thus,

it may be that for

the completion of high school leads to the

continuance of post-secondary schooling,

a taste for more

leisure time, or even higher labor productivity,
capital theory,
efficiently.

ala human

such that less hours are required to farm

Then,

too, with such a small sample

'noise,1

not rationality, might better explain the results.
The same may be said of the imputed wage rate.

Its

positive non-significant sign for on-farm labor supply,
coupled with its negative significant sign at the .10 level
for off-farm labor supply (Table E-2) leads this researcher
to conclude that the unobserved on-farm wage rate must be
higher than the off-farm wage rate and/or the taste for farm
work has a stronger counter influence than off-farm earning

226
Table E-2.

Explanatory
Variables

Life cycle off- farm labor supply estimations
males.

Age Group
under 35

Age Group
35-54

ct

Age Group
over 54

Intercept

3422.2210
(919.5644)

-1267.0922
(903.6100)

-4225.4048
(804.5753)

OPSCHOOL

-225.4936
(327.1347)

-225.7749
(175.1857)

42.6325
(188.6845)

HOMCHILD

-19 2. 8210***b
(75.9617)

OPWAGEST

-367.4366**
(197.7977)

9.5062
(39.1228)
653.9609****
(197.5507)

-272.6566***
(118.6677)
1473.9679****
(240.0469)

WFWAGINC

2.2194
(7.2379)

-1.3116
(3.2233)

5.5418*
(3.7972)

INVSTINC

27.8223*
(18.6788)

4.1548
(6.7459)

-8.5387*
(5.8607)

SMSACNTY

FRMASSET

748.3919****
(235.6811)
-1.6146
(4.4921)

323.3533**
(173.9521)

-310.6883*
(191.3419)

4.7334**
(2.5613)

-2.4982
(2.5338)

FARMDEBT

40.7507****
(12.0935)

-1.8204
(7.0608)

ACRENTIN

10.1017***
(4.2551)

-4.1851*
(2.5921)

FARMINC

-28.9282*
(17.6904)

DAIRYCOW

SILCORN

SOYBEAN

HAY/ALFA

-16.0208*
(10.4359)

of

48.5801***
(19.9145)
-4.8007
(7.1009)

-49.8635****
(17.9610)

1.6321
(15.2717)

-45.1156****
(14.6383)

-48.0752****
(15.9368)

18.5298***
(8.9955)

25.3676***
(12.2324)

-21.2027****
(7.6133)
8.7128***
(4.0360)

227
Table E-2.

Explanatory
Variables

(Continued)

Age Group
under 35

Age Group
35-54

OAT/RYE

Age Group
over 54

-25.5225***
(10.1373)

MISCROP

30.1175****
(8.2051)

R2

.74

.57

.63

R2

.59

.49

.54

31

89

70

n

EL

Coefficients are reported with standard errors in paren­
theses .

k Significance levels:
**** = .01; *** = .05; ** = .10;
* = .15 for the null hypothesis that the parameter equals
zero.

228
ca p a c i t y .
Aside from the aforementioned two differences the
only other life cycle comparisons worthy of mention are
differences in significance of the coefficients for variables
across age groups.
at the

In particular,

INVSTINC is significant

.05 level for the young and old age group,

significant at the

but not

.15 level for the middle age group.

Since acres rented out may be a substantial part of this
variable measure,

it wou ld appear that older farmers may be

part-retired and younger farmers may not be ready, willing or
able to fully utilize their land resources, whereas for
middle age farmers rental of land out to neighbors is less
likely.
FARMDEBT is another variable having a negative coeffi­
cient that is significant at the

.05 level.

Thus,

as farm

debts increase among young farmers in their initial "entry
and establishment" stage they supply less labor to the farm
and correspondingly more labor to off-farm work (Table E-2).
Apparently,

off-farm work is a capital generator for this

age group.
Interestingly,

only one agricultural enterprise, DAIRYCOW,

is significant at the
age category.

In sum,

.15 level or better for the under 35
life cycle variations are not really

in evidence for male on-farm labor supply when considering
those variables that are significant at the
better.

.15 level or

229
b.

Off-Farm Labor Supply (Male Age Groups)
A comparison among male age groups for off-farm

labor supply reveals differences with respect to coefficient
signs for every one of the Personal-Household and FarmBusiness variables,

although for many the coefficients are

not significant at the

.15 level or better.

Concentrating on the variables whose coefficients are
significant,

an increase in HOMCHILD decreases the work off-

farm for the youngest and oldest age groups,

but not for the

middle age group.
OPWAGEST has positive coefficients significant at the
.01 level for the middle and older age groups,
sign that is significant at the
age group.

but a negative

.10 level for the youngest

While no additional explanation for this latter

group is offered besides those mentioned under on-farm labor
supply,

the results for the two older age groups are as

expected.
The coefficients for INVSTINC are significant at the
.15 level for the youngest and oldest age groups,
opposite signs.

but with

The positive coefficient for the under 35

age group suggests that as farm land is rented out the
operators supply more hours off-farm to further increase
their capital accumulation efforts,

but that for older

operators such investment income enables them to "retire” by
cutting back their off-farm work.

These results are consist­

ent with the life cycle hypothesis.
Residence in or near a S.M.S.A.

for the young and middle

230
age groups has a positive sign and is significant at the
.01 and .10 levels respectively.

Close proximity to job

centers does not increase off-farm labor supply for the
oldest age group, which has a negative sign that is signi­
ficant at the

.15 level.

Given the possibility of pensioned

retirement from off-farm jobs held in preceding life cycle
stages these results are consistent with each other.
Only for the middle age group is the FRMASSET variable
significant —

at the

.10 level and positive.

The idea

that an increase in assets would be associated with an in­
crease in off-farm labor supply is unexpected.

A possible

explanation is that since our sample is limited to small
farms,

an increase in off-farm hours is compatible with

operating a larger farm.

Alternatively,

farm assets are

being partially paid for by off-farm wage employment income.
The positive coefficients for FARMDEBT at the

.01 and

.05 levels for the youngest and oldest age groups respectively,
suggest that regardless of the life cycle stage an increase
in debts brings forth an increase in labor supply off-farm,
perhaps to help reduce their liability position as they are
getting started and as they approach retirement after which
mortgage payments on land relative to declining income
become

a financial burden.

ACRENTIN is significant at the
the young and middle age groups,

.05 and .15 level for

though with opposite signs.

While the negative sign is expected and occurs for the middle
age group,

increased acreage for the youngest group is

231
surprisingly associated with an increase in off-farm employ­
ment.

Possible explanations include the necessity of off-

farm work in order to finance expansion of their operation,
which is not so great within the limits of a small farm to
preclude increased involvement in both sectors.

Or, the

results may be meaningless given the small sample and
possibility of

'noise.'

As expected the sign is negative for FARMINC and signi­
ficant at the
groups.

.15 and

Thus,

.01 level for the young and middle age

as more on-farm labor is required to generate

more agricultural product sales revenue,

operators supply

less hours of work to the off-farm sector.
Some interesting results occurred with the agricultural
enterprise variables.

SILCORN, HAY/ALFA,

and MISCROP have

significant positive signs for the middle and older age
groups.

These results suggest that these activities may not

be particularly time consuming on a regular basis (as is the
case with DAIRYCOW which has the expected negative sign)
and thus may be compatible with the holding of off-farm jobs
which provide vacations that can be timed to coincide with
peak labor requirement periods of planting and harvesting.
In sum,

some life cycle variations do seem to occur for

male labor supply off-farm, but the evidence is not strong,
c.

On-Farm Labor Supply (Female Age Groups)
A comparison of the younger, middle, and older age

groups for females in Table E-3 reveals identical signs of
the coefficients for most of the common variables.

In only

Table E-3.

Explanatory
Variables

Life cycle on-farm labor supply estimations
females.

Age Group
under 35

Age Group
35-54

SL

of

Age Group
over 54

Intercept

1092.1822
(654.9304)

245.9791
(481.3534)

323.3717
(386.5340)

WFSCHOOL

243.3957
(373.6863)

320.3521
(228.2465)

283.0465
(265.6667)

YNGCHILD

34.4017
(96.7501)

200.4110
(336.4399)

WFWAGEST

-3 5 7 . 3267*b
(230.2204)

-24.6965
(158.8172)

OPWAGINC

-.0982
(2.2767)

INVSTINC

170.6664
(257.5102)

-3.9684**
(2.0349)

-4.0270
(3.2897)

-19.5734*
(13.0015)

-4.3478
(7.7066)

-4.8536
(7.5241)

FRMASSET

2.8717
(3.5042)

3.4981
(2.7834)

-6.7912*
(4.1180)

FARMDEBT

-21.9154***
(9.6399)

-13.1068**
(7.8933)

-.0240
(17.0307)

-7.2127**
(4.5204)

-14.3788
(8.6816)

ACRENTIN

-2.9587*
(1.9132)

LAYERHEN

5.9466***
(2.3937)

15.1244****
(5.5914)

DAIRYCOW

84.7132****
(18.5493)

FEEDCATL

27.5519****
(6.4685)

FRUIT

21.6705****
(5.1019)
79.6146****
(13.4207)

SILCORN

WHEAT

41.9063****
(16.3308)

233
Table E-3.

Explanatory
Variables

(Continued)

Age Group
under 35

MISCROP

Age Group
35-54

Age Group
over 54

-64.8975****
(22.7215)
14.8808**
(8.8658)

SOYBEAN

R2

.55

.54

.55

R2

.38

.46

.45

37

79

54

n

Si

Coefficients are reported with standard errors in paren­
theses .

k Significance levels:
**** = .01; *** = .05; ** = .10;
* = .15 for the null hypothesis that the parameter equals
zero.

234
two instances, both for the over 54 age class compared to
the middle age and young groups,
WFWAGEST has a negative sign,
.15 level or better.

are the signs opposite.

though not significant at the

FRMASSET has a negative sign on the

coefficient and is significant at the

.15 level, "which is

consistent with the previously mentioned findings of sociolo­
gists that as farm operations become larger the wife tends
to withdraw her participation while the male increasingly
specializes in farming activity.
In comparing the results for age groups with the aggre­
gate sample,

the signs on the coefficients are the same for

all age groups save for WFWAGEST in the older age group
equation and FRMASSET for the younger and middle age
groups.
the

In neither case are the variables significant at

.15 level or better.
Of the many animal and crop enterprises that enter

significance at the

.15 level or better,

only LAYERHEN is

significant for more than one age category —

the youngest

and o l d e s t .
As with male age groups on-farm labor supply,

female

age groups do not demonstrate any life cycle variation for
those variables entering significance at the .15 level or
better.
d.

Off-Farm Labor Supply (Female Age Groups)
For females there is consistency of signs across

age groups for the various Personal-Household and FarmBusiness variables found in Table E-4.

In no instance do we

235
Table E-4.

Explanatory
Variables

Intercept

WFSCHOOL

YNGCHILD

WFWAGEST

Life cycle off-farm labor supply estimations8- of
females.

Age Group
under 35

-6705.2844
(893.4800)
- 5 2 1 . 6264 ** b
(294.2171)
-53.2623
(69.7319)
3704.2688****
(466.2718)

OPWAGINC

-.5499
(1.7406)

INVSTINC

-14.7572*
(9.8599)

Age Group
35-54

Age Group
over 54

-528.3698
(352.3498)

-692.7713
(196.9022)

-444.5163****
(148.8329)

-65.8271
(136.5498)

28.4456
(228.7764)
917.5406****
(125.3151)

911.3572****
(133.8844)

-3.8040***
(1.7288)

.5897
(1.6962)

-3.2358
(5.2364)

1.3913
(4.0762)

SMSACNTY

-3221.1810****
(464.6645)

-624.1094****
(158.1994)

FRMASSET

4.0011
(2.8462)

.5011
(2.1487)

-4.0512***
(1.8426)

-6.1568
(5.4264)

.7084
(8.5055)

-.4935
(2.0203)

2.8511
(3.1139)

6.1094
(4.2841)

-15.2651
(10.9379)

-16.9616
(13.2879)

-5.5568
(9.2411)

FARMDEBT

ACRENTIN

FARMINC

-17.1963***
(8.1223)

-13.9494****
(4.3532)

LAYERHEN

PIGLITTR

-34.6721**
(17.9886)

FEEDCATL

31.2780***
(13.8952)

BEEFCOW

-649.6326
(141.2763)

-15.5127*
(9.5440)

236
Table E-4.

Explanatory
Variables

(Continued)

Age Group
under 35

SOYBEAN

R2
—2

ir
n

cl

Age Group
35-54

Age Group
over 54

-10.5073*
(6.4527)
.80

.53

.62

.70

.45

.54

38

80

57

Coefficients are reported with standard errors in p a r e n ­
theses .

k Significance levels:
**** = .01; *** = .05; ** = .10;
* = .15 for the null hypothesis that the parameter equals
zero.

237
find coefficients significant at the

.15 level or better but

with different signs for different age groups.

Moreover,

the signs on these variables match those for the aggregate
female sample.

Hence,

life cycle variations are not so much

in evidence for females as for males in off-farm employment.

SUMMARY

The life cycle estimations of representative farm
operators and their spouses by age group categories was dis­
appointing in that little variation among the under 35, 35
to 54, and over 54 years old classes was observed except
for the off-farm male operators.
residence in or near a S.M.S.A.

Here we found that for
the young and middle age

groups supplied more labor off-farm but the older group
supplied less.

A higher market wage rate was associated

with increased labor supply for the middle and older groups,
but less hours for the young group.

Increased investment

income resulted in an increase in labor supply for the young
age group but a decrease for the older group.

Additional

acres rented in is associated with an increased labor supply
for the under 35 group,
years of age class.

but a decrease for the 35 to 54

And finally,

increased size of the

silage corn enterprise resulted in a decrease in labor
supply for the young males and an increase in labor supply
off-farm for the older males.

Since all of the life cycle

differences involve a comparison of the young age group with
either the middle or older age groups,

the reader is

238
cautioned that because of the small sample size of the young
males

(i.e.,

substance,

31) the results may reflect more noise than

thereby calling into question the validity of

even these life cycle results.

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