University of Southern California Dissertations and Theses

The Influence Of Other People'S Schooling On An Individual'S Income

(USC Thesis Other)

The Influence Of Other People'S Schooling On An Individual'S Income

PDF

Download a page range

Download transcript

Copy asset link

Request this asset

Transcript (if available)

Content INFLUENCE OF OTHER PEOPLE'S SCHOOLING
ON AN INDIVIDUAL'S INCOME
by
Clarence Leroy Ham
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Economics)
June 1972
INFORMATION TO USERS
This dissertation was produced from a microfilm copy of the original document.
While the most advanced technological means to photograph and reproduce this
document have been used, the quality is heavily dependent upon the quality of
the original submitted.
The following explanation of techniques is provided to help you understand
markings or patterns which may appear on this reproduction.
1. The sign or ''target'' for pages apparently lacking from the document
photographed is "Missing Page(s)". If it was possible to obtain the
missing page(s) or section, they are spliced into the film along with
adjacent pages. This may have necessitated cutting thru an image and
duplicating adjacent pages to insure you complete continuity.
2. When an image on the film is obliterated with a large round black
mark, it is an indication that the photographer suspected that the
copy may have moved during exposure and thus cause a blurred
image. You will find a good image of the page in the adjacent frame.
3. When a map, drawing or chart, etc., was part of the material being
photographed the photographer followed a definite method in
"sectioning" the material. It is customary to begin photoing at the
upper left hand corner of a large sheet and to continue photoing from
left to right in equal sections with a small overlap. If necessary,
sectioning is continued again — beginning below the first row and
continuing on until complete.
4. The majority of users indicate that the textual content is of greatest
value, however, a somewhat higher quality reproduction could be
made from "photographs" if essential to the understanding of the
dissertation. Silver prints of "photographs" may be ordered at
additional charge by writing the Order Department, giving the catalog
number, title, author and specific pages you wish reproduced.
University Microfilms
300 North Zesb Road
Ann Arbor, Michigan 48106
A Xerox Education Company
I:
I
72-26,018
HAM, Clarence Leroy, 1923-
THE INFLUENCE OF OTHER PEOPLE'S SCHOOLING ON
AN INDIVIDUAL’S INCOME.
University of Southern California, Ph.D., 1972
Economics, general
University Microfilms, A XEROX Company, Ann Arbor, Michigan
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED.
UNIVERSITY OF SO UTHERN CALIFORNIA
THE GRADUATE SCHOOL
U NIVERSITY PARK
LOS ANGELES, CALI FO RN IA 9 0 0 0 7
This dissertation, written by
...........
under the direction of h.2r.?... Dissertation Com
mittee, and approved by a ll its members, has
been presented to and accepted by The Graduate
School, in partial fulfillm ent of requirements of
the degree of
D O C T O R O F P H IL O S O P H Y
D ate...Jm e..l912,
DISSERTATION COMMITTEE
Chairman
■ C
PLEASE NOTE:
Some pages may have
indistinct p r in t.
Filmed as received.
University Microfilms, A X erox Education Company
TABLE OF CONTENTS
Chapter
I.
II.
III.
INTRODUCTION ................................. 1
HUMAN CAPITAL RESEARCH ...................... 9
THEORETICAL MODELS .......................... 35
A. Competitive Theory Model
First Theoretical Model:
Perfect Competition
Model in Formula Format
Summary
Competitive Model in
Graphics
B. Separated Markets
Model With Separated
Markets
Illustration With
Indifference Curves
Implication of the Theory
C. Theory of Effects on Third Parties
Indirect Effects on Demand in
Product Markets
Indirect Effects on Supply in the
Factor Markets
Indirect Market Effects on People
as Consumers
li
iii
Chapter
Spillover Effects
D. Imperfections
IV. EMPIRICAL TESTING
88
Problems
Analytical Method
Majority Group Results
Contribution to.Reduction
of Variance
Minority Group Regression
Results
Further Evidence of Differences
Between the Groups
Interpretation of the Results
Evidence Concerning the Law
of Variable Proportions
Summary of Statistical Evidence
APPENDIX TO CHAPTER IV: LIST OF SYMBOLS. . 125
V. CONCLUSIONS 119
BIBLIOGRAPHY
126
LIST OF FIGURES
Figure
1. Competitive Model ......................... 51
2. Relative Marginal Productivities ......... 59
3. Relative Return to Factors ................ 62
4. Relative Return to People ................ 63
iv
LIST OF TABLES
j Table
I. Simple Correlation Matrix ................... 95
II. Order of Simple Correlation Coefficients. . 96
III. Regression Coefficients and Standard
E r r o r s ...................................... 101
IV. Means and Standard Deviations .............. 102
V. Regression Coefficients and Standard
E r r o r s ...................................... 108
VI. Ratio of Regression Coefficient Lo Mean
I n c o m e ...................................... 109
VII. Effect of One Standard Deviation
Difference in Position in Distribution. . Ill
v
CHAPTER I
INTRODUCTION
I
This is a study of the influence on the
| productivity of one individual of the human capital
j possessed by other people. The measure used for produc
tivity is income, and the measures used for human capital
are schooling and age, principally schooling.
I The issue has relevance because its answer has
| implications about the methods that are appropriate for
| financing the creation of human capital. If there are,
in fact, significant beneficial influences on others when
a person is schooled, then schooling is, at least in part,
a social overhead investment and is properly financed
through group expenditures, that is, by taxes.
Much research has been done in the last decade
and a half concerning the role of human capital. This
work was primarily in response to the discovery that the
conventional explanations of growth were able to explain
less than half the growth that had occurred in the
United States since reasonably reliable data has been
available. This concern with the human capital aspect of
growth has also received a great deal of attention in the
area of development economics. The other major impetus
2
came from the movement to convince everyone to continue
voluntarily in school beyond the legally required age
limit. The research, consequently, has been directed
along these two lines: the returns to the whole of
society and the private returns to the individual acquir
ing the schooling. No research has been done on the
returns to individuals other than those receiving the
schooling.
The null hypothesis of this study, then, is that
an individual's income is unaffected by the human capital
of others. The alternative hypothesis is that there is
an influence on an individual's income of the schooling
of those with whom he lives and works. The evidence of
this study is that there is an external influence of
schooling and that it varies for different subgroups of
the population. Estimates of the magnitude of the
influence are obtained in the study and reported in
Chapter IV.
The data used in the study are the appropriate
variables from the Bureau of the Census one-in-one-
thousand sample of the 1960 Census of the Population and
Housing.'*' The analytical method used is standard linear
stepwise multiple regression and correlation analysis.
! ^U. S. Department of Commerce, Bureau of the
| Census, U. S. Census of Population and Housing, 1960.
T
A basic canned program from the UCLA BMD series was
modified by personnel of the San Fernando Valley State
College Computer Center, and the analysis was accomplished
j on the Center's CDC 3170 computer.
1 The individual's reported income, age, sex, and
i
; level of school completed were the characteristics of
|
self used. They were designated: income (Y); age of
self (A ); schooling of self {S ); and sex { X), a dummy
s s s
with value one for male and zero for female. Calculations
were then made for the average school level completed in
the community (S ), average age in the community (A ),
c c »
percent minority members in the community (R ), average
school level completed by workers in the various jobs
(Sj), average ages of workers in the various jobs (A^),
and percent of minority members in the various jobs (Rj).
The specification of the mathematical model was of the
form:
Y = b0 + blAs + b2Ss + b3sX + V c + (1)
b5Ac + b6Rc + b7Sj + b8Aj + b9Rj‘
The stepwise process permitted testing with less than the
full set of independent variables. Also, when subsamples
were constructed by selection on the bases of categories
within any of the independent variables, the variables
so used would drop out of the equation.
4
This dissertation makes a distinction between
indirect market effect on others and spillover effect on
others. Two illustrations will help clarify the
l
i distinction. If A owns a resource and is selling in a
: market where B is a buyer, the supply and demand forces
i
; will result in a price that B must pay to get the desired
I
amount of the resource. If C now enters the market as
a new buyer, he will cause the demand to increase and the
j price to rise. B is now affected indirectly by market
|
j forces. B must pay a higher price (all others in the
I
market are also affected). Alternatively, C might do
something that destroys some of the resources — e.g.,
i
| polluting a stream. This would also cause the price that
i
B must pay to rise. This, however, is a spillover result.
It is not brought about by induced responses of all
parties to the decision making. An outsider has altered
the circumstance and was not party to initial decisions.
Or, from C's point of view, he made a decision that
affected others without the others having an influence on
his decision.
If W operated a record and hi-fi equipment store
and X established a similar shop next door, he could take
away much of W's business. That would be a market
response. On the other hand, if X established a noisy
production operation with a heavy stamping machine, or a
1
5
large truckline warehouse, producing such noise that
potential customers could not judge the hi-fi equipment
and, therefore, left, that would be a spillover effect.
; X took the action without reference to W, but it had
| consequences directly on W.
: The logical argument of the theoretical constructs
is really about human capital. However, education is
assumed to be the principal element in human capital, at
! least in the United States, and schooling is assumed to
j be the best available measure of education. Therefore,
i
the terms "human capital," "education," and "schooling"
have been used interchangeably throughout the text.
I
| This use of schooling introduces another problem,
though. What is the proper measure of schooling and how
shall it be used? The Census Bureau data is self-reported
schooling. No adjustment for potential incorrect
reporting has been made. A more significant question is:
Does a year of schooling always produce the same amount
of human capital regardless of where, when, or to whom
applied, and regardless of the character and quality of
the year of schooling? The number of days in an average
year of schooling has changed greatly in the past half
century and varies significantly among the regions of the
country. The quality variation must be as great. There
is also the question of whether eight years of schooling
6
applied two years each to four people who already have ten
years each of schooling would produce the same amount of
human capital as would the eight years if applied to one
j individual who already had eight years of schooling. The
1 logical implication of calculating average levels of
i
t
| schooling, as is done in the study, is a positive answer
i
to this question.
A possibly more serious limitation of the study
j is that there is no measure of the amount, or level, or
ability of the natural labor in people. This measure
would be of something in the genes that was inherited —
I something in the biology and physiology of the person.
This lack adds to the always serious problem of the
direction of causation. It may be that instead of
acquiring something from more schooled.fellow workers and
thereby becoming more productive, that those with more
natural ability and, therefore, more productivity are
permitted to work with those who have become more
productive by receiving more schooling. An then, are we
to consider psychological adjustment, family connection,
and the cultural results in attitudes and mores to be
natural labor or human capital?
There is also a problem in measuring productivity,
or income. Once again, the Census Bureau data is a self-
report of income for the year. The use of this measure
7
probably reduces the size of the regression coefficient
significantly and the size of the correlation coefficient
slightly.
I
i The fact that a complete production model is not
used might be looked upon as a serious problem. However,
! the objective was not a forecasting model, but only a
test of the influence of a specific variable. That means,
of course, an increase in the likelihood of a spurious
!
I correlation.
| This dissertation starts with a survey of the
i
| more important work in the field of human capital. The
| next chapter establishes the theoretical basis for expect
ing the relationship postulated in the alternative
hypothesis. This chapter will first analyze the implica
tions of the perfect competition model for the question
at hand. It will then investigate the implications of
geographical barriers to mobility. This will be followed
by the theoretical justification and expectations of
spillover and indirect market effects on others. The
final section of Chapter III will investigate the implica
tion of imperfections in markets on the theoretical
expectations. Chapter IV will report the empirical
findings, and Chapter V will discuss the implications of
the results.
-1
8
There is, of course, no implication in this study
that income, or material results, are the primary, much
less the only, results to be obtained from schooling.
CHAPTER II
HUMAN CAPITAL RESEARCH
There has been a significant increase in writing
and research concerned with the determinants of human
productivity in recent years. Growth theory and develop
ment economics both have been concerned with how to alter
that productivity while the fields of consumer economics
and education have become more quantitative in their
analysis of the results of schooling. The analogy with
the creation of physical capital goods has led to the
classification of most of this work under the title of
human capital.
While this work includes concern about the
health and mobility of people, it is concentrated in
studies of education — mostly within the sub-area of
formal schooling. This chapter will discuss only
materials in this narrow domain.
The failure to ask questions about these issues
in the past has left a legacy of very little data
directly related to the questions. In addition, some of
the data needed for definitive work is considered
personal and confidential. Other data involves the usual
9
problems associated with joint product and customarily
fixed coefficient of production. There is also massive
multi-collinearity of the variables and the ever-present
problem of apparently changing relationships with the
! passage of time. All of this means that ingenious use
must be made of the data that is available.
This research can be classified into three
categories according to the focus of its quantitative
results. First, there are studies trying to measure
the absolute returns to schooling. These are usually
defined in terms of changes in money income. Second,
there are studies of the rate of return to schooling;
that is, studies that add research on costs to the first
category. Third, there are studies of the effects on
society as a whole.
The primary works in human capital to date have
been those of T. W. Schultz, Edward F. Denison, and Gary
Becker.'*' Concentration here will be on these three, but
a few others will be mentioned.
The basic source of data for human capital
■**Gary S. Becker, Human Capital (New York:
Columbia University Press’ ^ 1964) ; Edward F. Denison, The
Sources of Economic Growth in the United States and
Alternatives Before Us (New York: Committee for
Economic Development, 1962); Theodore W. Schultz, The
Economic Value of Education (New York: Columbia
University Press, 1963’ )’ .
11
research about the United States is the decennial census
and special Census Bureau sampling studies. Herman P.
Miller is the principal user of the latter source. The
i common practice is to use the midpoint in each closed
income class as the mean of that class and various devices
for the location of the mean of the open ended (i.e., top)
class. Becker makes reference to studies that show that
people under-report income to the Census Bureau. He and
Houthakker,^ on whom several others rely for basic data,
make corresponding adjustments. Income under-reporting
is related to source of income, and, since sources of
income are not independent of income level, the adjust
ment is different for each income level. Miller, who
works for the Census Bureau, says, however, that sampling
of the same group several weeks apart will result in
4
individual answers that vary by "marked" amounts.
However, the switches cancel out and leave the mean and
pattern of the distribution unchanged.
Becker adjusted his data for variations in
^Herman P. Miller, "Annual and Lifetime Income in
Relation to Education: 1939-1959," American Economic
Review, Vol. L, No. 5 (December 1960), pp. 962-986.
^H. S. Houthakker, "Education and Income,"
Review of Economics and Statistics, Vol. 41 (February
1959), pp. 24-28.
^Miller, loc. cit.
5
unemployment so that his final results are applicable
to continuous high level employment. Once again,
unemployment incidence is related to income level so
that the adjustment varies with the level of income.
Since (in the tabulations by income level) the 1940
Census data omitted persons with more than $50 of income
from sources other than wages or salaries, Becker
obtained data on lawyers, dentists, and physicians from
another part of the Census data and integrated it into
the work.^
n
In his article, Miller is concerned with the
income ratios between levels of schooling finished and
with how those ratios have changed as the proportions of
the male population that have finished various levels of
schooling have changed. He found that the ratio of high
school graduate income to elementary graduate income for
the years 1946, 1949, 1956, and 1958 was 1.26, 1.34, 1.46,
and 1.48, respectively. The corresponding ratios for
college graduate income to high school graduate income
were (beginning with 1939) 1.57, 1.54, 1.63, 1.56, and
C
Gary S. Becker, "Under Investment in College
Education,” American Economic Review, Vol. L, No. 2
(May I960), ppT 346-354.
6Ibid.
^Miller, loc. cit.
1.65. During this same period the percentage of males
over 25 years of age with eight or fewer years of
schooling dropped from 62 to 39; the percentage with less
than a high school diploma dropped from 76 to 57; the
percentage of college graduates rose from 5 to 10; and
the percentage with a high school diploma rose from 12 to
23. As Miller points out, the law of variable propor
tions would predict, ceterus peribus, a decline in these
ratios as the relative supplies changed in this manner.
He explains the observed results' departure from this
prediction by offsetting changes in the demand side of
the market. The percentage of males employed in
managerial or professional jobs rose from 15.7 to 23.7
during this twenty-year period.
To eliminate the possible bias in the results
cited above that might have been caused by the effect
that aging has on income, Miller got corresponding data
on the 25-34 year age group at each data period. The
percentage of this age category with eight or fewer years
of schooling dropped from 45 to 20; college graduates
rose from 7 to 15 percent; and high school graduates,
from 20 to 33 percent. The high school graduate/elemen
tary graduate income ratio for the above stated years
was 1.16, 1.28, 1.31, and 1.34, and the college graduate/
1
14
high school graduate income ratio was 1.47, 1.39, 1.27,
1.31, and 1.46.
Miller also found that the percentage gain in
| income from the 25-34 age group to the 45-54 age group
was greater with more schooling, but that the ratio of
gain had been reduced for all school levels during the
twenty years under examination.
Miller attempted to verify that the income
differences were the result of the schooling by analyzing
the data concerning World War II veterans and their use
of educational benefits under the G. I. Bill. He found
j that veterans attended school in significantly larger
percentages than their peer group non-veterans. A decade
later the incomes of the veterans were significantly
greater. He points out that this could well have been
because they also differed in ways other than veteran
status. However, when a breakdown was made by age it
was found that younger veterans used the educational
benefits much more than older veterans and that ratios
of their incomes to the incomes of their peer non-veteran
groups were correspondingly greater — the younger
veterans achieving incomes 18 to 30 percent above their
non-veteran peers while the older veterans were only 6
to 17 percent higher than their non-veteran peers.
15
O
Houthakker, using the same data as Miller,
combined 1949 pay rates for the various educational
levels with mortality rate tables to compute expected
lifetime incomes for various levels of schooling
completed. He then discounted these expected lifetime
income streams, both before taxes and after taxes, to
age 14. He discounted at several rates from ten percent
down. There was only one step of added school at which
the additional schooling did not add to expected life
time income in all of his calculations. That step was
to start but not finish college; and this was only if the
discount rate was less than eight percent for income
before taxes and less than six percent for income after
taxes.
The next section will be a discussion of rate of
return research and will focus on Hansen and Becker.
Schultz^ made the point that school budgets were
difficult to use because they contain so much that is
not truly schooling. It is necessary to extract the
pertinent figures. Hansen-*-® used Schultz's estimates
^Houthakker, loc. cit.
^Schultz, op. cit., p. 67.
•*-^W. Lee Hansen, "Total and Private Rates of
Return to Investment in Schooling," Journal of Political
Economy, Vol. 71 (April 1963), pp. 126-140.
16
of school costs and added to them his estimates of
income foregone. He constructed these estimates from
the tables of average income for each age group and
school level completed. He assumed in all cases the
student could have had an income equal to his peers in
age and schooling completed. With income from each
level of schooling completed accumulated over a life
time and with the costs just explained, Hansen computed
average rates of return for a school "plan" and marginal
rates for each year of progression. A "plan" for two
years of high school after the eighth grade would yield
a 12.7 percent return. A "plan" of four years of high
school would give a 15.3 percent return. A "plan" from
the eighth grade to finish college would give a 12.9
percent return. His marginal rates of return are: for
the second year of high school, 12.7 percent; for the
fourth year of high school, 18.6 percent; for the second
year of college, 6.2 percent; and for the fourth year of
college, 18.7 percent.
Becker‘ S took a much more complicated view of
how to derive valid data; or, perhaps, he was more
optimistic about the possibility of getting meaningful
numbers. (Or, perhaps, he got a grant and, therefore,
^-Becker, Human Capital
17
"had more time to devote to the work. Or, perhaps, he is
more able, or more diligent, or both.) Becker divided
the population into White Urban Male, Non-White Urban
| Male, White Rural Male, Non-White Rural Male, White
Female, and Non-White Female. Most of his work is with
the first group, White Urban Male. He argues that
students do earn some income from the age of 14 years.
He insists, however, that those who go on to school are
different in ability from those who do not.-^ Therefore,
it is not legitimate simply to assume they have foregone
the income received by those not in school. (He
correspondingly insists that if those who did not go on
to school had gone on, they would not receive the incomes
received by those who did, in fact, go on to school.)
He next adjusts the tuition and fees data for
scholarships and grants, and for part-time and extension
students. He uses data from a related sample study to
get the ratios of expenses for books and materials and
transportation to other expenses. (He later uses one-
half this ratio when working with high school data.) In
the end he comes out with about the same ratio of income
foregone to total college costs as do two or three others
who use somewhat different methods of calculations.
'*'^Ibid., p. 79 ff.
18
Using the income data and the cost data he has calculated,
he gets an after tax private return to a college education
of between 12 and 15 percent.
i
! He assumes that much of the difference in income
!
i between elementary and high school graduates really is
J due to ability differences but that only ten percent of
the college graduate-high school graduate difference is
ability related. To support this assumption, he cites
several studies about I.Q., high school grades, father's
occupation, and so on, having close correlations with
income and education (and with each other). He refers to
two studies that conclude that about twenty percent of
the difference in income between high school and college
graduates is due to ability. He concludes that about
eighty percent of the difference is due to the college
education, but only because these people have the ability
to benefit from college. That is, these people would
have more income than.the non-college people even if they
did not go to college, but only about ten or twenty
percent of the difference that does exist. On the other
hand, if the people who did not go to college had gone,
their incomes would have been increased much less by
that experience than was the incomes of those who did go.
He seems to say about twenty percent less.
College dropouts apparently get a return of eight
19
to ten percent on the investment they do make. By
comparison, this implies that those who finish get an
18 percent return on their last two years.
While non-white male college graduates receive
much less income than whites, their rate of return is not
that same proportion lower. Their foregone earnings are
also much lower. Thus, their rate of return is 8 to 12
percent. While the South discriminates against the Negro
(by an order of magnitude or so), the relative
discrimination against the college graduate is worse in
the North. The South has a separate market for the Negro
college graduate, while in the North he must face the
general market.
Becker objects to the use of average data as a
guide to individual decision making as the variation of
results is so great that the individual can do better for
himself by analyzing his own circumstances.
Hansen figures the total rate of return to a
college education as above ten percent. He compares this
to the rate on liquid assets as an alternative "invest
ment" and concludes that the country has been underin
vesting in schooling. Becker disagrees with this
conclusion in several ways. First, he feels the valid
alternative for comparison is an equally illiquid,
equally risky capital goods investment. Next, he feels
20
that the return from going through college to those who
do not now do so would be considerably less than the
return to those who now do. He uses data to show how
they differ in ability and social situation. He feels
i that the present dropouts would also have higher costs;
they would be from lower income families and would have
to borrow to finance their schooling and borrow in
markets that usually have high interest rates.
(Becker may be correct in this judgment, but it
seems to me that if his method of analysis had been tried
in 1900, or nearly any other time, and applied to the
question of high school, it would have led to the same
conclusion. Yet, he believes that society has gained
greatly from the great expansion of high schooling in the
past half or two-thirds of a century.)
Another of Becker's concerns is the difference
between the private and the social benefits of schooling.
There may be significant external benefits, he suggests.
It may be that widespread college education is the key
to technological progress. This could be as large as
the direct return. Denison does get the social return
to be twice the private return. On the other hand, it
may be that society overestimates the increase in
productivity. The higher pay for college graduates may
be the result of custom and may continue even though
21
there is no difference in productivity. Becker
ultimately concludes that ignorance precludes even a
tentative guess of whether the social return to college
education is higher or lower than the social return to
physical capital.
He concludes that the private rate of return for
finishing high school, before adjusting for ability, is
about eighteen percent. Ability, however, accounts for
from 40 to 60 percent of this gain over the elementary
graduate. With regard to the high school dropout, Becker
figures that 35 to 40 percent of his gain over the
elementary product is the result of ability. Thus, he
feels that while the unadjusted data shows diminishing
returns to increased schooling, the truth could be either
slightly diminishing returns or increasing returns.
Denison's^ objective was to ascertain the
quantitative importance of the various factors that had
contributed to economic growth in the United States from
1909 to 1959. One of the factors that he investigated
was education — as a substitute for "advance-of-
knowledge," schooling being something for which he could
get data. Since the data that does exist in this area
is of a very indirect type, any study is very dependent
13
Denison, op. crt., p. 308.
22
upon the assumptions and techniques used. Denison
assumes that mean incomes in large categories of people
are representative of their marginal productivities.
The Census data for 1940 and 1950 give the
j distribution of males 25 years of age and over by age
categories and years of school completed. Denison uses
the cohort survival method to construct the distribution
for each decennial year back to 1910. He corrects the
simple projection by an estimate of the extent to which
people claimed more schooling than they had. He obtained
this estimate by comparing the 194 0 and 1950 census data
for inconsistency. The evidence suggested that "self
promotion" increases with age and is higher at lower
levels of schooling.
Next, he gets a cross-classification of income
in 1949 by age and level of schooling completed. He
assumes that 60 percent of all increases in income
associated with increases in schooling is caused by the
schooling. (He also gives the final results that would
have been obtained if he had used one-half and two-
thirds.) He reconstructs the table using eighth grade
graduates as the reference point; that is, all incomes
are changed so that their difference from the eighth
grade graduate income of their age category is reduced
to 60 percent of the observed difference.
23
Now, having an income for every age level of
every schooling category and a distribution by age and
level of schooling for all the relevant years back to
! 1909, he is able to compute the mean income of males 25
I
i and over for each of those years (1909 to 1959). The
differences among these mean incomes could be inter
preted as a measure of the increase in productivity
resulting from the schooling. The rate of increase in
these computed mean incomes could be interpreted as the
rate of increase in productivity. Denison makes one
additional adjustment, however. This is for number of
days of attendance in a school year, which has had a very
large increase since 1909. Denison's reasoning is that
his income figures were calculated on the basis of a
school year as it existed in 1949 and that a day of
schooling results in the same change in income
(productivity) at one time and age level as it would at
any other time and age level. That is, a day of
schooling is a day of schooling, regardless — one year
of 200 days will produce twice the increase in
productivity as one year of 100 days will. And 200 days
in 1928 is equivalent to 200 days in 1948. Also, 200
days for a third grader does just as much as 200 days for
a college junior. Most other workers in these vineyards
have assumed a year of schooling to be a year of
24
schooling (they must be closer to the facts than
Denison). On the basis of his reasoning, the incomes for
the earlier years are reduced by a factor proportionate
to the difference in average daily attendance. The
result is that the growth rate of productivity is larger
to the same extent as the rate of increase in the
average days per school year.
The resulting adjusted rate of increase in his
computed mean incomes (interpreted as the rate of
increase in productivity attributable to schooling) is
0.94 percent per year. Since labor constituted about
73 percent of the inputs to production during these years,
this increase in labor productivity due to increased
schooling would have increased total output by 0.68
percent per year.
The actual annual growth rate in total output
during that period was 2.93 percent. The 0.68 percent
attributable to increased schooling in the labor force
is, thus, 23 percent of the growth that occurred. It
also constitutes 42 percent of the growth in per capita
income that occurred during that period.
If he had attributed one-half the 194 9 income
differences to the associated differences in level of
school completed (instead of 60 percent), he would have
found 19 percent of the growth resulted from increased
25
schooling of the population; if he had attributed two-
thirds, he would have obtained 26 percent.
Denison goes on to argue, but does not support
with data, that most of the taxes and other costs,
J including foregone income, which financed this schooling
I
came from reduced consumption. That is, there was a
trade-off between this type of investment and consumption
but not a trade-off between this and other types of
investment. Therefore, this source has not come at the
expense of other sources of growth.
Denison believes that since we now have such a
large fraction of our population having gone so far in
schooling, and with the length of the school year
unlikely to expand further, schooling as a source of
growth in the future will be limited mostly to improve
ments in the quality of schooling. (This is a great
potential, but probably a small hope. Notice also that
this is something Denison assumes has not occurred in
the past.)
The principle critical discussion of Denison’s
work is by Abramovitz.^ His overall evaluation is that
Denison has done a significant piece of work which is
14
Moses Abramovitz, "Economic Growth in the
United States: A Review Article," American Economic
Review, Vol. LII, No. 4 (September 1962), pp. 762-782.
26
a major contribution. However, he believes that the
contribution is mostly in the realm of "conception of
problems." He believes that Denison has done a
! remarkably astute job of handling the inadequate data but
i
| that the data are so inadequate that Denison's
quantitative results cannot be viewed as more than very
intelligent, reasonably informed guesses — much too
insubstantial to serve as the bases of a policy.
(Denison himself, of course, emphasizes the crucial role
that arbitrary assumptions play in his calculations.)
Basically, it is a starting point, in his view, for more
detailed research, and a call for better data collection
in the future.
His major specific criticisms are: (1) that
Denison ignores the difference between private and total
returns, attempting to measure only those that are
privately captured; (2) that he ignores knowledge
acquired outside of formal schooling; and (3) that he
assumes a day of schooling always to have the same effect.
Thus, a person with six years of 200 days per year would
have the equivalent of a person with twelve years of 100
days each. Within Denison's work he sees three factors
as crucial to the quantitative results: (1) the method
of construction of the age-schooling distributions for
the years in which they were not available; (2) the
27
assumption of the portion of income difference due to
schooling (the 60 percent assumption); and (3) the basic
J Census data, which has large sampling errors because of
j
j the small cell sizes and also has, apparently,
significant response errors.
Schultz discusses many different issues related
to the economic responses and consequences schooling
produces. Though he does not formulate a mathematical
model, as Becker does in the first part of his book,
Schultz does use conventional economic theory, in verbal
form. He is convinced that all studies of saving and
capital formation are grossly wrong and that most growth
theorizing has serious errors. Also seriously in error
are most wage theories and most explanations of the
pattern of personal income distribution. These areas,
in his opinion, all need reworking to fit in the results
of human capital formation.
He points out that theory would lead one to
expect the capital/output ratio to rise with develop
ment.^ Standard data, however, does not show this
result, and conventional theory does not have an answer
without considering human capital; for the human capital/
■^Theodore W. Schultz, "Investment in Human
Capital," American Economic Review, Vol. LI, No. 1
(March 1961), pp. 1-17.
physical capital ratio has been rising (it was four
percent in 1900 and 28 percent in 1956) and the total
capital/output ratio has, in fact, risen. Our
i
! conventional data indicate a large increase in the
I
marginal productivity of labor. This result, however, is
due to holding a unit of labor fixed in the statistical
studies when it has, in fact, grown through investment
in human capital.
The dramatic results of the Marshall Plan and the
rapid rate at which Europe recovered after World War II
compared with the low rate at which the poor countries
can absorb capital, while they are really starved for
capital, has intrigued many. Both these phenomena can
be explained by reference to the ratio of mixture of
various forms of capital, especially the human capital/
physical capital ratio. Physical capital was in the
increasing returns phase of the law of variable
proportions in Europe and is in the diminishing returns
phase in the less developed countries.
Schultz believes that schooling contributed more
to growth in the United States between 1929 and 1956 than
did material capital. The average years of schooling in
the labor force in 1929 was 8.41, and in 1957 it was
29
16
10.96 — that is, a one percent per year rate of
increase. The average daily attendance per year has also
increased at a one percent rate. Thus, schooling
| contributed two percent per year to United States growth
j from 1929 to 1957. (However, as more of our population
gets to higher levels of schooling, this rate of progress
cannot continue.)
Schultz1 basic method is to calculate the total
cost of schooling in a given year. This includes the
output foregone on the part of the students and the out
put foregone for the resources actually used in school
work in the schools (price adjustments are, of course,
made). This calculation gives him the investment in
human capital for that year. Accumulation of this data
over time gives him the stock of human capital in the
labor force at any one point in time. This stock has
been increasing at 4.09 percent per year and in 1957
added $22 billion to the stock of capital in the United
States. Reproducible tangible capital, according to his
figures, though larger in total quantity has been
increasing at only two percent per year and added but
$25 billion to the stock of capital in the United States
in 1957.
•j r
Schultz, The Economic Value of Education,
loc. cit.
30
Schultz argues that the degree of equalization of
income is much too large to be explained by the rather
trivial changes in the concentration of ownership of
physical capital plus the total of private and public
material transfer payments. It has its source in the
equalization of schooling opportunities in the last half
century. Schultz explains the Leontief Paradox (that the
United States exports wage intensive goods and imports
relatively more capital intensive goods) with human
capital. The wages should not all be looked upon as
payment to labor because a major portion of it is payment
17
to human capital.
The role of education in economic development
has been written about extensively. One such article
that is both more quantitative and has wider coverage
18
than most is an article by Bowman and Anderson. They
attempt to find a measure of education that will be a
good predictor of per capita income in the different
countries. They find that in current Europe the
17Theodore W. Schultz, "Investment in Man — An
Economist's View," Social Service Review, Vol. 33,
No. 2 (June 1959), pp. 109-117.
18Mary Jean Bowman and C. Arnold Anderson,
"Concerning the Role of Education in Development,"
Readings in the Economics of Education (Mayenne, France:
United Nations Educational, Scientific and Cultural
Organization, 1968), pp. 113-134.
31
percentage of youth with post-primary schooling in the
1930-1934 period is the best predictor. In Latin America
and Africa literacy is the best predictor.
! The literacy figures reveal some interesting
results. The literacy in Czarist Russia in 1914 was 40
percent of the male population. It was at least that
high in England and France just before the industrial
revolution. In 1955 all countries with literacy ratios
of less than 30 percent had per capita income of less
than $200; all with less than 40 percent literacy had per
capita income less than $300. Countries with literacy
between 40 and 70 percent showed little variation in per
capita income; what variation there was was not
correlated with literacy. Where literacy was between
7 0 and 90 percent the per capita income was usually, but
not always, higher than in the lower literacy categories.
It was usually one and one-half to two times the income
of the 40 to 70 percent literacy category. All countries
with literacy rates over 90 percent had per capita
incomes over $500.
As they see it, literacy is necessary but not
sufficient for movement to higher per capita output.
Percentage of school enrollment beyond the primary level
has a very weak relationship with per capita income and
the time pattern of the data showed that per capita
32
incomes rose before the expansion of post-primary
schooling. Bowman and Anderson conclude that there are
two breakthroughs: first, to get an adequate level of
| literacy; then, after a period on a plateau of per capita
income, a movement on to a highly educated society with
a high per capita income.
An educated elite seems to them to be necessary
but it can block development if it enforces a class
structured system. That is, the educational program can
have an incorrect structure. A polarized society without
social mobility and communications between classes can
block development. The time lags until responses to
improved education appear are in the order of 20 to 30
years.
There are, of course, the two outstanding
nineteenth century cases of the deliberate use of an
educational program to achieve rapid economic develop
ment — Germany and Japan. I want to mention two papers
19
about Japan. E. E. Hagen's paper discusses m non-
quantitative terms the importance of the pre-restoration
schooling that dealings with the Dutch had entailed.
.20
Koichi Emi gives data on the very large amounts that
19 . . .
E. E. Hagen, "The Japan Case," Public Opinion
Quarterly, Vol. XXII, No. 3 (1958)
0 0
Koichi Emi, "Economic Development and
33
the central government spent on education. These took
three forms: (1) the hiring of foreigners to train the
Japanese how to operate the new industrial facilities
being built; (2) the sending of students and government
officials abroad to study and observe; and (3) the
financing of the establishment of an internal school
system. Within fifteen years there was little need for
more foreigners. The central government expenditures on
the internal school system were, however, only from one-
eighth to one-fifth of the expenditures on this system.
The central government compelled local governments to
expand school facilities. The tax pressures were so
great that the peasants rioted against the schools. The
result, however, was a rate of growth of five percent in
the gross national product at a time when net physical
investment was less than ten percent of national income.
In conclusion, we can mention some of the
21
problems in this area of research that Vaizey dis-_
cusses. There is multiple correlation between parental
wealth, access to opportunity, motivation, access to
Educational Investment in the Meiji Era," Readings in the
Economics of Education (Mayeene, France: United Nations
Educational, Scientific and Cultural Organization, 1968),
pp. 94-108.
2^-John Vaizey, The Economics of Education
(London: Faber and Faber, 1962) .
34
education, and success in later life. In addition, the
wage and price system is a system of administered prices
in many respects. To use these prices as a measure of
productivity is a very questionable procedure. (But
what else do we have?) In answer we can, perhaps, say,
"We cannot help but have an educational policy; it should
be based on our best, and a consistent set, of guesses"
— or should it?
CHAPTER III
THEORETICAL MODELS
A. COMPETITIVE THEORY MODEL
Most people have a large concern about what they
i
receive from economic production, in both absolute amount
and in comparison with other people. Indeed this is
necessarily so, for if it were not, the species would not
have survived. Economics and economists have, over the
years, varied greatly in the amount of attention they
have devoted to that question directly. Interestingly,
the most widely accepted approach to the issue among
economists today is as a sideline, or byproduct, of the
theory of the firm, i.e., production theory, or price
theory. This line of reasoning assumes very broad
categories of "factors" of production; categories within
which the individual units are homogeneous, at least
with regard to all relevant economic characteristics.
Often as few as two fundamental factors are postulated:
Labor and Land, or, if you will, people and the rest of
nature, respectively. More often a tripartite structure
is used; one in which capital is added to the list.
Capital theory has proved one of the more intractable
35
subdivisions of economic theory, but all disputants and
searchers in the area seem to agree that it is a produced
means of production and that its cause and valuation are
inextricably mixed up with the real time process.
It would be desirable from the point of view of
the theorists if there were, in fact, the basic cate
gories of homogeneous land and homogeneous labor:
Fundamental indestructable nature (land) and basic
untrained labor, each of its own homogeneous character.
But, of course, this is not the way of the universe, as
many have commented (most of them with no apparent under
standing of the significance of their statement). Just
as different pieces of land have different specific
physical characteristics, so, too, do people have
different inherited constitutions. But differences of
these types are not difficult to fit into perfectly
competitive theoretical models as Frank Knight was,
apparently, the first to show.^ This conceptual ease is,
of course, dependent upon the other assumptions in this
perfectly competitive model (and as Vickrey points out,
we have to be very careful about just what is perfect or
^Frank H. Knight, Risk, Uncertainty and Profit
(New York: Harper and Row Publishers, Inc., Harper
Torchbook Edition, 1965).
37
the logic of the model becomes contradictory). The
result of the Knight reasoning is that in the "short run"
the differences in output, and therefore income, are
described as rents; and that in the "long run" they are
capitalized and the return to all factors, each unique,
is perfectly competitive. Even Euler's theorem can hold
instantaneously at one level, the competitive level. It
is important that the differences be "natural" rather
than contrived by man through special privilege, diffi
cult as that distinction may sometimes be. These true
economic rents resulting from the uniqueness of each
individual unit of each contributor to the output make
the explanation of the competitive model more wordy and
make it seem (to many people) to be much more complex,
but they do not change the essence of the theory.
The problem becomes more difficult to solve,
however, when we recognize that nearly every piece of
land has mixed with it, in an unscramblable manner, some
capital improvement, and that all units of labor have
mixed in them large amounts of learning; that is, human
capital (it uses resources, it increases the productivity
of the unit, and it requires a lapse of time before the
increase in productivity is realized).
^William S. Vickrey, Microstatics (New York:
Harcourt, Brace and World, Inc., 1964), p. 17.
38
The amount of land improvement that is
economically desirable is a problem to which a great deal
of study has been directed, starting, apparently, with
Jethro Tull, Charles Townsland, et al., in the early
1700's in England, though the Dutch may have studied it
3
earlier. The same is appropriate for what has come to
be called, within the last decade or two, human capital.
The problem of isolating the effects of capital improve
ments in land has been dealt with in a number of
different manners. Some studies deal with large numbers
of units of land and assume that the variability of the
natural characteristics of the land and the variability
of the capital improvements are independent. Properly
done, this is a satisfactory method. However, the
independence of the natural variation and the application
of capital is most likely not met in most situations.
Fortunately, land can be grouped by characteristics which
can be measured rather objectively. These are prin
cipally physical and chemical characteristics and
location. Within each major category it is possible to
3
S. B. Clough and C. W. Cdle, Economic History of
Europe (Boston: D. C. Heath and Company, 1952),
pp. 312-315, 421-426; Herbert Heaton, Economic History
of Europe (New York: Harper and Bros., 1948),
pp. 402-411; Dudley Dillard, Economic Development of
the North Atlantic Community (Englewood Cliffs: Prentice
Hall, Inc., 1967), pp. 145-147.
39
apply different modifications to different samples and
measure the results in yield. By this device it is
possible to advise what type and what amount of capital
improvement will be economically rewarding when mixed
with specific pieces of land when the characteristics of
the piece of land are known. We have learned to make the
predictions with a very high degree of accuracy. This
technique works well because we have a large number of
pieces of land of any given type and because people do
not get too emotionally concerned about what happens to
pieces of land; and the land cannot itself act to alter
the results. (It is unfortunate that our society is not
organized to get this information as widely circulated as
it could easily be, though it gets this type of in
formation dessiminated much better than almost any other
type of valuable information. And very few, if any,
societies have done better.)
With land, since it has a tendency to last longer,
and since people have less tendency to be emotional
about it, and since it does not have independent action
of its own, and since many of the capital modifications
will tend with time to disappear, we can often be even
more precise. We can work with a particular piece of
land. We can get data on it before the application of a
capital improvement, and also after the improvement, and
40
sometimes after the improvement has reverted. (Some
types of reversals are not possible, especially the
failure to stop erosion.) We also find that the result
! of different types of capital improvement depends on the
|
i characteristics of the land before the application.
(From an economic point of view in studies of this sort,
it is very important that the demand side of the market
and likely changes in it be considered.)
It is entirely appropriate that similar concern
about the application of capital to human beings be
j
studied, though the problem is much more complicated
and the benefits are in many forms that do not get
measured, and could not be run through a market. Also,
the deliberate testing is not socially accepted in our
culture.
There is another similarity. Just as it is
necessary to study what is happening to surrounding land
in order to isolate the effects of a capital application
to a given piece of land, there is need to try to
measure the consequences to an individual of the capital
that others have acquired. It is to this problem that
this dissertation is directed. We will begin by in
vestigating what economic theory would lead us to
expect.
41
First Theoretical Model:
Perfect Competition
If the supply side of a market is perfectly
competitive, all transactions will occur at the same
price. This is true of factors as well as of products.
If a higher rate of pay (all aspects of it considered)
were available from another employer, the resource would
immediately move to that employer, who would now find
I that he need not pay so high to get the volume of the
factor that he desired. Other firms would find they
must pay slightly more to retain the quantity they
desired. This partial investigation (of the factor
supply market only) is not sufficient for our purposes
for two reasons. It is not the completely competitive
model, and, more importantly, it does not require that
the factors be mixed in the same proportions in any given
type of production and that the marginal product of any
given type of factor be the same in all the firms that
use it. Therefore, it does not require, for instance,
that workers with the same natural labor and human
capital in them be paid the same when working with the
same type of fellow workers.
In the completely competitive model where factor
buyers also compete freely for factors and sell perfectly
competitively in output markets where the buyers are
42
perfectly competitive, the marginal product of each
factor is the same in all of its uses. This is true for
all categories of factors. (This sort of proposition is,
of course, tautological and useful only for logical work
and clarifications of ideas, for it is impossible in the
real world to identify true identity of factors, and
therefore proper classification, independent of the
reward given.)
Nevertheless, we will investigate what this
simplest of complete economic models would lead us to
expect.
The conventional microeconomic perfect
competition theory model says that when there are
several factors that combine to produce an output and
each of the factors can serve as an input to several
different products, the profit maximization motive of the
firms combined with the income maximization motive of the
resource owners will result in movement of the units of
the resources (both as contributors to output and as
receivers of income and, therefore, as cause of demand)
until the rates of reward of factors are exactly equal to
their marginal productivities, for each unit of each
factor. This means that all units of a given type of
factor will receive the same rate of pay regardless of
the type of output toward which it contributes. This, of
43
course, requires that the factors be combined in the
same proportions in the production of any particular
good. However, in the productions of different goods,
two, or a few, factors could be mixed in different
ratios because the other factors that were present would
be different. (This proposition encounters the logical
difficulty previously mentioned with reference to Frank
Knight and the uniqueness of each and every unit of all
things, with the differences being reflected as rents in
the short run — a model which, of course, is not subject
to verification because there is no independent way to
measure the difference.)
The equality of the rate of pay is derivable
from either the motive of cost minimization for a given
volume of output, from the maximization for output from
a given cost, or from the maximization of profit model.
It can be explained by use of total and marginal product
curves and the total and marginal revenue curves derived
when only one factor is varied, or it can be displayed
with the use of isoquants and budget lines for two
variable factors.
These types of analysis, however, are all partial
equilibrium approaches. They assume the price of the
output, and/or the price of the factors. They can
explain the equality of pay rate and marginal product in
44
any particular use, but they cannot prove the equality
of pay (and value of marginal product) in all uses, that
we obtained by assuming the mobility of resources in
search of highest income and the search of consumers for
maximum satisfaction from expenditure of income. To get
this equality from a mathematical model requires the
general equilibrium approach.
Model in Formula Format
the theory just given, some of the other techniques
mentioned will be illustrated. The first illustration
will be the mathematical derivation of the partial
equilibrium solution.
competitive market and its output can be symbolized by
the production function:
where V is volume of output and the x's are quantities
of various factors, its cost will then be the sum of
the fixed cost and the product of each factor quantity
times that factor price.
To be more precise than the verbal summary of
If a firm is maximizing profit in a perfectly
V = f(xlf x2,
( 2)
(3)
45
where CF is fixed costs and the r's are the prices of
the factor and C is total cost.
If C has a budget limit, CQ, the firm can
! maximize profit (if it sells in a perfectly competitive
i
j market) by maximizing the function:
m
V = f(xlr x2j . . . xm) - A(Cf + S r^i - CQ) (4)
i=l
The first order conditions for maximization can
be found by taking the partial derivative of the equation
with respect to each of the factor quantities and to
the Lagrangian multiplier and setting each derivative
equal to zero. The result of this is:
- f - Ar = 0 (5)
z 1 2 .
= f2 - Ar2 = ° (6)
9V = f - Ar = 0
3xm
3V _
m m
(7)
= CQ - CF - rlXl - r2x2 . . . - rmxm = 0 (8)
where f^# f2 . . . fm are, respectively, the derivatives
of the production function with respect to the input
variable of the subscript. That is, they are the
46
marginal productivities of the respective factors.
is, the ratio of prices between any two factors is equal
to the ratio of their marginal productivities. Or, again,
the ratio of marginal product to price is the same for
all factors. Lambda (A), the Lagrangian multiplier, is
the marginal productivity of money costs. That is, the
marginal dollar spent on any factor whatever will add the
same amount, A, to the value of output.
the total cost restraint and only a profit maximization
objective. Profit is the difference between total
revenue and total costs. Total revenue is output times
the unchanging competitive selling price; that is,
p[f (x-|-,x2,x3 . . . xm) 1 and total costs are fixed costs
plus the quantity used of each factor each multiplied
by the constant price per unit of the factor; i.e.,
With algebra we see that, e.g
f2 r2
That
The same conclusions can be found with release of
Cp + rxxx + r2x2 + r3x3 + . . . + rmxm .
(9)
Thus, profit is:
m
I I = p’f(x^iX2 • . • xm) - (CF + 2 r-j_x^) . (10)
i=l
The first order conditions for profit maximum
47
are found by taking the partial derivatives of the
function with respect to each of the factors and setting
them equal to zero. Thus:
I
I
= p fi-r-j_ - 0 for each (i = 1 to m)
or: MP^ x p = r^.
In English, the marginal physical product of each
factor multiplied by the price of the product must equal
the price of the factor per unit. Or, since the price
does not change with changes in output by a firm in a
purely competitive model, the marginal revenue product
of each factor must equal its price. (Note that if the
production function is homogeneous of the first degree,
the level of operation for a firm is indeterminate.)
In terms of the variables in this study, each
type or category of natural labor would constitute one
of the m categories of factors as would human capital.
Within 'each of these categories the pay rates would be
equal for all individuals and would be equal to that
category's marginal revenue product.
From the point of view of individual people, this
means that all with the same natural ability and capital
in them would receive the same pay. But, if the amount
of natural labor possessed by workers varies, each would
48
receive pay at the seme rate as others of his natural
ability level. Or, if each is unique then all would
receive a pay equal to the value of their marginal
i
! product — or value of next most productive use. Some
i
| people would analyze each individual1s excess of pay
over basic natural labor as rents in short-run analysis.
Looked at from an economic factor category point
of view, all natural homogeneous labor would be paid the
same and all capital would be paid the same. (Capital in
a worker works not only with labor in him but with labor
and capital in other workers as well; and with land and
other capital.)
This is the null hypothesis — what we hope to
reject; that all with the same capital in them receive
the same pay rate. We hope to do better than that,
however, for there are many possible types of deviations
from this ideal perfectly competitive model. We hope
to get more than just a rejection of this ideal. We
hope to get evidence that it is incorrect in a certain
way — or because of certain effects.
Summary. If the market for any particular factor
is perfectly competitive on the supply side, each unit
of that factor will receive the same rate of pay. By
definition, they are bidding against each other and will
move to higher pay or accept lower pay if willing. If
49
the market is also perfectly competitive on the demand
side, then this rate of pay will be equal to the
marginal revenue product of that factor, which will have
to be the same in all uses. If the output of all the
firms is sold in markets that are perfectly competitive
on both sides, then the marginal revenue products will
be, in all firms, the price of the output per unit
multiplied by the marginal physical product of the fac
tor. These prices will represent the value at the margin
of alternative products which could have been produced
with the resource under existing market arrangements.
If all other factors are also sold perfectly competitive
in markets where the demand is also perfectly com
petitive, then the above will be true for all.
Competitive Model in Graphics
The graphical exposition of these ideas can be
in the form of Figure 1.
In sectors 1 and 3 of the figure, the Ox axis
can measure the quantity of resource input. The Oy axis
in sectors 1 and 2 can measure the quantity of output.
The distance 00" would then measure the fixed factor
input and from O'x the variable factor. The curve O'A
would represent the generalized production function,
reflecting the law of variable proportions.
If the output is sold in competitive markets so
that the price for all units is the same and is always
equal to the alternatives foregone, the Oy axis can be
used to express the nominal value of output. The 00'A
i
i curve is the relationship between the resources used and
j
the value of income created: If the derivative of this
line were taken relative to the resource input, that is,
the slope with respect to the O'x axis, the result would
! be proportional to the marginal product of the variable
j factor. This has been drawn in sector 3 as the MP
curve.
If a family of lines were drawn from the point
O' to the successive points along the line O'A and the
slopes relative to the O'x axis of each of these were
taken, the results would be proportional to the average
product of the variable factor. This has been plotted
as curve APV in sector 3 of Figure 1. This family of
curves reaches its maximum slope along line O’C in
sector 1. If a similar family of lines were drawn from
0 to the successive points along the 00'A line and their
slopes with respect to the Ox axis taken, the results
would be proportional to the average product to total
resource use, if we could get a common denominator by
which to measure the resource inputs. This is the curve
APt in sector 3.
51
y y
q
CD
d'
c'
b'
a'
ATC
A VC
MC
r x *z
0
AP,
MP
C3)
Fig. 1. — Competitive Model
52
If the resources and/or their products are being
sold in competitive markets, then a valuation in terms of
money can be established. The Ox axes can then be
: viewed as a cost of resource measure. The maximum that
i can be paid for the resources — and under competition
j this maximum will have to be paid — will be at the level
i
j of operation where the average product to total resources
I is at a maximum. This is at resource level 00' of fixed
i
I resource and O'c level of use of the variable resource
j (level c along the Ox axis). The variable factor will
|
then be paid at a rate equal to its marginal product at
| that level of operation. This is the level p in sector
! 3. The fixed factor will also be paid its marginal
product, something that cannot be shown in this graphic
framework. These together will exhaust the output
because Euler's theorem will hold in perfect competition
at the point of equilibrium.
Alternatively, we may express the problem in
terms of cost per unit of output rather than output per
unit of cost. The axis Ox in sector 1 then represents
money values and the axes Oy in sectors 1 and 2 represent
quantity of output, or, if the product sells in com
petitive markets and, therefore, at a constant price, the
value of output. The curve 00'A then represents the
relationship between costs of output and the output
53
resulting. The line OB then represents the relationship
between output and the value of the output when it is
i
j sold competitively. (This will be a 45-degree line if
: we convert output into monetary value and use the same
■ scale on the two axes.)
j If we take the derivative of the OO'A curve with
respect to output (the slope with respect to the Oy
axis), we will have the marginal cost per unit of output
i
; curve. This has been graphed in sector 2 of Figure 1
! as the MC curve. (The z axis of sector 2 measures
i
! money values, but on a very different scale from the Ox
j
axis of sector 1.) If we construct a family of lines
i from point 0 ' in sector 1 to each successive point on
line 0*A and calculate the slope of each of them to the
Oy axis, we will have a series that is proportional to
the average variable cost per unit of output. This has
been projected in sector 2 as the AVC curve. If we
construct a similar family of lines from the point 0,
their slopes will be proportional to the average total
cost per unit of output. These have been graphed in
sector 2 and labeled ATC.
If the output is sold in competitive markets,
the lowest price that will cover total costs will result.
Such a price is represented by the line OB in sector 1.
The slope of this line with respect to the Oy axis is
54
constant and is proportional to the level OP in sector 2.
The competitive level of output is then at the level of
output Oc1 and the level of use of resources of Oc.
In terms of this problem, the cost of a unit of
; human capital will equal its marginal product; or, the
| value of a unit of product will equal the marginal cost
of that unit. The appropriate amount of human capital
for an individual to acquire is the amount O'c.
I
j If all markets are perfectly competitive, the
j rate of pay for the marginal unit of human capital must
!
j be equal in all uses. This would imply that there was a
uniform ratio of mixture of natural labor and human
! capital in society. Everyone with the same amount of
natural labor would find it appropriate to have the same
amount of human capital; and the ratio of human capital
between two people would equal the ratio of natural labor
between the two. This is necessary to keep the ratio of
human capital to natural labor equal for everyone.
Since this would make natural ability and learned
ability perfectly correlated in the society, either one
would measure the effect of both in a statistical study.
We do not have an independent measure of natural labor,
but we can test to see if all the differences in output
(pay) are independent of the schooling and age of those
with whom an individual works and lives. This would be
55
sufficient to negate the hypothesis that this model is
a proper description of the world, unless all the
differences happen to be related to the variables which
! we have not included in our study. The latter seems to
■ be highly unlikely as a matter of subjective judgment.
i
| B. SEPARATED MARKETS
At this stage of the reasoning we must introduce
I
j imperfections into our economic model, for if the world
I worked like the model described we would find that all
|
j people with the same amount of schooling and the same
i
i age would have the same income. The first imperfectxon
we will consider is lack of perfect geographical
mobility, as measured by the market. We will assume
that there are imperfections that interfere permanently
with the mobility of factors, or that there are returns
to living in certain areas that are not measured by the
markets, i.e., returns in kind, e.g., friends, climate,
recreation. (A study of these latter factors would have
to avoid circular reasoning, not an easy task.) In any
event, there is a large body of evidence about the lack
of perfect geographical mobility of people.
To deal with this problem in this paper I will
assume that within each of the four principal geographic
regions of the nation and within each of the five
56
population sizes within each of these regions, there are
more or less homogeneous conditions. That is, each of
these will be considered as a market. This is not ideal.
! It is done because in the one-in-a-thousand sample the
■ Census Bureau has not identified the specific residence
; of the individual. It has merely identified the region
of the nation and the population category of the city of
residence.
i
! If these markets are internally perfect but there
| is immobility, or inadequate mobility (by the model
i
standards), between the markets, it is possible to find
factors mixed in different ratios in the production of
the same product in different markets. That is, we now
have the possibility of having two people who are similar
in all of their own characteristics but who are working
with groups in which the average schooling is different.
In this situation we would say that they are working
with different amounts of human capital and that the law
of variable proportions should operate.
Model With Separated Markets
If we make the comparison within one market
between the conditions before and after some of the work
force increased their schooling we should find that, if
the local market were perfect, the individual employers
57
each should attempt initially to readjust to the same
capital/natural labor ratio that prevailed before the
increase in schooling. This can be done by employing
! fewer workers with capital/labor ratios above the former
; average capital/labor ratio. (This adjustment is not
i possible if all workers now have ratios above the old
i
i ratio, or mixture ratios with the other factors of
l 9
J production cannot be appropriately adjusted.)
i
| This adjustment, if it could be made, would
I result in the marginal product of human capital and
i
j
| marginal product of natural labor being the same as they
!
j were before the increase in schooling (certeris peribus).
! In terms of personal pay, this would produce the same
pay for those who had not received the schooling because
they would have the same amount of natural labor and the
same amount of capital in each of them and the rates of
factor pay would be the same. The more schooled would
receive higher rates of pay because they would have more
units of capital in them.
However, this theoretical construct ignores the
supply side of the factor market (and also assumes that
the more schooled are going to demand in aggregate
exactly what they produce). The greater schooling means
that, from a factor point of view, there is a greater
supply of capital in the market; and from a people point
58
of view, there is a greater supply of more schooled
people.
If we make the comparison between two markets
; in which the human capital/natural labor ratios are
different, there is relatively more human capital in one
j of the markets, and this change in relative factor supply
cannot be ignored if we want sound analysis.
One way of reasoning is that with a greater
! supply of a factor, there would be a greater supply of
I all products toward which it contributed. The greater
j
| supply could be disposed of only if the products' prices
were reduced in proportion to the lowered relative
i marginal utilities (or in proportion to the change in
marginal rate of substitution) so that these prices
reflected equal satisfaction forgone in purchase of
other goods and services. This would lower the value of
the marginal product of a unit of the factor (and of
close substitutes) and the perfectly competitively profit
maximizing firm can pay only the marginal revenue product,
which in perfect competition is equal to the value of the
marginal product.
This, however, is only a partial view of the
problem. If we look at the physical process with the
law of variable proportions we find that if the firm is
able to, it will be operating within the ridge lines.
OUTPUT
MP.
TP =AP.
AP =TP.
AB
MP
a = human capital
b = natural labor
TP = total product
AP = average product
MP = marginal product
Subscripts indicate the appropriate factor.
RATIO
Fig. 2. — Relative Marginal Productivities
cTjfu
60
(This is a question of divisibility.) This means that
all factors' marginal product curves will be positive
and declining.
In terms of Figure 2, comparing two situations
’ with human capital/natural labor ratios of A and B, the
t
j marginal product of human capital will be less at B than
at A and the marginal product of natural labor greater.
(This would be true for all "normal" relationships; that
I
is, all except perfect substitutes — an empty term —
J and highly complementary factors. This latter implies
other factors against which both the factors under
consideration can move in the same relative direction.)
i This would imply for this study that in the markets with
more human capital, the return to additions of human
capital would be smaller than in markets with less human
capital. That is, the regression coefficients to
schooling should be smaller. (This would not be so if
schooling and natural labor were very close substitutes
and/or the mixture with other factors were in the
increasing rather than the decreasing portion of the
law of variable proportions.)
Illustration With Indifference
Curves
The change in relative reward can be demonstrated
61
by use of the indifference curve technique, too. Figures
3 and 4 will be used for this purpose. If we view the
problem as one of factors, then we use Figure 3: A, B,
' C, and D. If we view it as relationship between people
; with more and with less schooling (human capital), then
j we use Figure 4: A, B, C, and D.
In the factors analysis approach we compare a
position, a, which has a certain amount of natural labor
i and a certain amount of human capital, with another
I situation, b, which has the same amount of natural labor
I
i and more human capital. (That is, the difference in
j
j ratios of mixture of factors is illustrated by the
j
j simplification of holding natural labor at a constant
j level and varying human capital.)
■
In Figure 3-A, the production function
illustrated by the isoquants is one in which the two
factors are relatively close substitutes. In Figure
3-B, they are relatively distant substitutes, strong
complements. We see that in both cases the marginal
rate of technical substitution changes so that the pay
Pt
ratio — price of labor to price of capital (^) — is
increased but that the change is significantly greater
in the case of poor substitutes. This is, or course,
to be expected. When a factor becomes more abundant,
its price must fall significantly compared to its
62
Natural Natural
Labor Labor
Human
Capital
Human
♦ Capital
Natural
Labor
Natural
Labor
Human
Capital
Human
Capital
Fig. 3 Relative Return to Factors
63
Less
Schooled
ar
b'
0
ab
More
j Schooled
I
I
j Less
I Schooled
a'
b1
0
More
Schooled
Less
Schooled
a’
b’
0
a b
More
Schooled
Less
Schooled
More
Schooled
Fig. 4. — Relative Return to People
64
complements which now become more valuable per unit as
they have more of their complement with which to work.
A more abundant factor's price will not have to decrease
' ■ much to cause it to displace its substitutes. (Their
! prices might also fall, for that matter, in a multi-
j factor world. Such an occurrence would not be
inconsistent with the change in marginal rate of
technical substitution or in relative prices indicated.)
I
j Figure 3, C and D, presents two other possible
! production functions; Figure 3-D shows that it is
i
!
possible to have the price ratios change in the opposite
direction from that usually pictured. Note that this
I occurs in the case where the expansion path nearly
parallels one of the axes.
If we view the problem as one of different pay
rates for people rather than as one of functional factors,
then we find that as one level of schooling has an
increased relative supply, a lower level must have a
decreased relative supply. Figure 4, A and B, once
again compares the cases of close substitutes and of
factors dominantly complements. We see that in both
cases the pay ratio turns against the more educated, but
more so when they are complements. (If we make the
comparison between a level of schooling that has had a
change in its numbers and one that has not, Figure 3
65
(A, B, C, and D) is usable with appropriate changes in
what is measured along the axes.) Figure 4, C and D,
shows that it requires a more extremely asymmetrical
1
production surface to cause the pay ratio to shift in
' favor of the members of the more schooled group.
i
| Implication of the Theory
This analysis is in terms of ratios of pay,
! however, not of the levels of pay. From the point of
view of the whole economy, the increased supply of human
capital can find employment only if it offers its
services at a reduced rate of pay commensurate with the
I
J decline in its marginal productivity through the law of
j variable proportions. The rate of pay for natural labor
would be increased insofar as it is a complement of human
capital and decreased slightly insofar as it is a
substitute. The latter would cause the rate for human
capital to be reduced less.
With regard to people, the problem is more
complex. The labor in each person will cause him to
receive a pay increase when more human capital is
present, but the capital in him will cause a pay cut.
For a person who has no change (or, in comparing across
markets with different amounts of schooling, for two
people with the same amount of schooling and otherwise
66
the same), whether his pay is higher or lower when there
is more total human capital depends on the relative
elasticities and on the ratio of mixture within the
l
; person. The smaller the ratio of human capital in the
' person, the more likely a higher pay will result from
i
i
j increased human capital in the market, unless they are
very close substitutes.
However, in addition to these substitution and
I complementarity effects, there would also be an increase
I in total output and, therefore, in total income because
there is a larger supply of resources. This is relevant
with regard to the pay of people, for, though the pay
! rate for human capital may drop, or drop relative to the
pay to natural labor, a person may more than offset this
by his increased quantity of it.
This simple idea can be shown with algebra as
follows. Let subscript 1 refer to human capital and
subscript 2, to natural labor; p refer to price (or pay
rate) and q, to quantity. For a person who has not
changed his amount of capital, his pay, after some have
increased their capital (or in comparison across two
markets, similar persons, where one works in a market
with more human capital), is given by:
67
(P1 " Api)ql + (p2 + Ap2)q2 '
or his change in income, by:
; AY = -ipiqi + Ap2q2-
| If the pay changes were equal and the respective
! quantities were also equal, there would be no income
difference. A highly schooled person could expect a
loss of income unless the increase in the pay of labor
i
3
j greatly exceeded the reduction in the per unit pay of
i human capital; and vice-versa for a person with low
i
f
i schooling. So, we see it is a matter of the mixture
I
| ratio and the relative elasticities; the rates of
i
diminishing returns. The latter is dependent on the
precise shape of the production function. For a person
who has increased his level of schooling (or, comparing
across two markets where the average schooling is
different, an individual with more schooling compared to
one with less), the formulation would be:
(pl - APX) (qx + Aqx) + (p2 + AP2)q2‘
The change (or difference) in income is then:
AY = "AP1q1 + AP2q2 + plAql "
The additional elements for difference here, compared to
68
the previous case, are the terms with the change in
quantity in them. The sum of these two terms will be
positive. Thus, adding to one's schooling will be a
force for increased income or reduced loss of income.
The "income" effect is absorbed partially by the in-
j
j creased units of human capital.
I
i
With regard to the data available for this study,
the analysis of this section should lead us to expect
! greater income differential (increase) among lower
I schooled than among more schooled people when the market
i
j has more human capital in it. That is, we should expect
other people's human capital to have a larger marginal
impact in the lower ranges of schooling of self (Ss) than
in the more highly schooled. This means that the
regression coefficients of schooling of fellow workers
(Sj) should be larger for lower schooled than for highly
schooled people. In the context of my data, a smaller
regression influence is also more likely to be lost in
the "noise" in the data. This would result in lower
correlation coefficients, or in lack of statistical
significance.
C. THEORY OF EFFECTS ON THIRD PARTIES
The effects of any economic act can be
dichotomized in three convenient ways. One of these is
69
market vs. spillover effect; another is direct vs.
indirect; and the third is effects on decision makers
vs. effects on others. Some market effects are direct
! — the ones that have impact on the parties who make the
i
| decision. The immediate parties give up some things and
!
i gain some things. In a perfect market these are rational
! • 4
choices based on full information.
Some market effects are indirect. That is,
I
I
! people not parties to the economic decision are affected
because of changes in prices, supplies, or demands, and,
through market processes of adjusting to these changes,
these other parties are indirectly affected. This type
of case is the subject matter of the early writing, after
Marshall, on "externalities," the famous "empty boxes"
series of articles, and its lineage.
Some direct effects work through the market on
parties to the transaction, the decision makers, per
above. However, some of the direct effects have impact
on individuals who are not parties to the decision.
This happens because goods are not "packageable" and
infinitely divisible. There are spillovers of direct
impact on people in the "neighborhood" (hence, another
common term, "neighborhood effects"). (Notice, for
4
Vickrey, loc. cit.
70
instance, that insofar as a person’s actions subject him
to an undesirable side effect — e.g., identifiable
pollution in his own area — he, in the ideal model, will !
i
1 take this into consideration in his market decisions.
i This, of course, involves the perennial issues of
J
I knowledge and rationality.)
|
Goods which are "packageable" and divisible will
be easily handled by market processes and will have only
l
I market effects, direct ones on the decision maker and
| indirect ones through market responses. Goods which are
j
i
not divisible are not so easily handled by market
processes, many times cannot be satisfactorily dealt
with in this way at all. These goods will necessarily
affect large groups of people. If they are not to have
!
j spillover effects, it is necessary to bring all of those
affected into the decision making process. This is
difficult or impossible through market mechanisms.
[It would be most gratifying and would undoubted
ly contribute to problem understanding and problem
solving if the terms "private" and "social" costs and
benefits could be discarded. They should be replaced
by the two distinctions: (1) results to the decision
makers v£. results to others; and (2) market and non-
market results. They all happen to individuals and they
all happen to that aggregate of people called society.]
71
If the effects are all of the same character,
these goods are usually tagged with the unfortunate title
of "public" or "social" goods. "Group goods" would
' appear to be a more truly descriptive title, and one
t without emotional-political overtones.
!
i The indivisibility of this type of goods means
|
that while the resources devoted to them can be varied,
or at least can be at different levels at an initial
i
j action, there can be only one of a given type for the
I group at one time (though the size of the group can also,
i
i
j in some cases, be varied). For example, more or less
I
i
| can be spent for police or war departments, but there is
i only one at one time to one group of people. And, the
size of a hydroelectric-irrigation - navigation-flood-
control project can be chosen at its installation. But
there can be only one project at one location at one
time.
Goods that are divisible but not packageable
present, perhaps, a worse problem — especially when the
spillover is of a different character than the effect on
the decision makers. These goods can be handled very
well by the market process, but only a portion of their
costs and benefits are used in the decision making.
Better economic decisions probably can be expected when
more of the affected parties are brought into the
72
decision making process, though the theory of second
best shows that this is not a certainty by the Pareto
optimality criterion. [But it is well to be careful in
thinking about how optimal Pareto optimality is. It
| does accept the starting ownership pattern of wealth and
r
other perquisites involved in the legal and other
institutions. And it is clearly self deception to call
this a "neutral policy" (an unfortunate term which is,
I after all, an empty set. One either has the capacity to
influence a thing or he does not. A policy to retain the
status quo is just as partisan a policy as any other.).]
If large groups of people are affected by an economic
action, it is then very difficult to handle it through
market operations and reach total marginal balance.
Cooperative action through agents can sometimes accomplish
this, however, if the effects are of the same type on a
group of moderate size; e.g., some farmers' cooperatives
and some consumer cooperatives.
The specification of these general comments to
the problem of this study concerns the extent to which
schooling in a society creates social overhead capital
and is, therefore, an economic function best performed
by the group through group processes if the goal of
optimal allocation is to be achieved.
It is the conception of this paper that the
schooling of an individual has three material results:
(1) direct effect on his own income; (2) indirect market
effects on the income of others; and (3) direct spillover
i
I effect on others.
i The first of these is what economic theory
|
assumes the individual knows and toward which he acts
rationally. It is what has been studied a great deal in
recent years, most especially by T. W. Schultz and Gary
t
! Becker.
i
The second of these includes the original dis
cussion and controversy following Marshall's comment and
Pigou expansion on externalities. With regard to
schooling, these indirect market effects can operate
through either the demand or supply side.
The third of these was largely ignored in
economic theory until the last two decades. It was
excluded by assumption from both the classical and neo
classical models. It was also largely ignored in public
policy and discussion until very recently, perhaps be
cause of the accepted theory.
Indirect Effects on Demand
in Product Markets
To the extent that schooling merely alters the
relative demand patterns, it will only alter the relative
J
74
prices of products, initially, and thus the relative
values of marginal products of the factors of production.
Since there is immobility of factors, these pay rate
; changes will not all be eliminated. But as long as there
| is no more demand, there can be no more factor payments.
Those resources that can, will shift; and, if all were
flexible enough to shift, all payments would be as
before except for the operation of the law of variable
i
i
I proportions. However, insofar as some cannot shift,
there will be changes in marginal value products.
Now, insofar as these changes in market demand
cause a change in the ratios of use of various factors,
there would also be called into operation the law of
variable proportions. The relative changes in factor
rewards (i.e., income payments to people with different
levels of human capital, schooling) would depend on the
relative income elasticities of various products,
relative price elasticities of those products, the
relative supply elasticities of the various factors, and
the elasticity of substitution of the factors, i.e., the
rate of change in the marginal rate of technical
substitution, which is dependent on the shape of the
production function.
If, -however, the increase in schooling increases
75
the productivity of those schooled and they do not take
the increase in reduced work time, it will also increase
aggregate demand (unless they hoard the resulting income
! payments). (In some countries the monetary arid
j financial institutions might be so inadequately, or
i
i
improperly, developed that no increased demand would
develop.) The increase in aggregate demand will increase
demand for all except inferior goods and, through
i derived demand, the value of the marginal physical
! product of factors, ceteris peribus. That is, the
marginal revenue product is changed by changing the price
of the output rather than by changing the volume of
output. Note that this is neither a spillover effect
nor the operation of the law of variable proportions.
The effect works through the operation of market pro
cesses, and it does not involve a change in physical
volume of resources or their output.
This process is sometimes thought of as the
operation of the law of variable proportions because it
is looked at on a society-wide basis. The reasoning is
that in the whole economy the quantity of human capital
has increased and, therefore, the marginal productivity
of natural labor is increased. But on the micro level
some of the results can accrue to people who have neither
acquired more human capital nor worked with those who
76
have. They simply have an increased demand for their
output.
These indirect market effects of human capital
i
: operating through changes in the demand for products
j should be measured by the regression coefficients of
j
l
average schooling in the community (S ) and/or the
c
average age in the community (Ac), insofar as those two
factors represent measures of human capital.
I
I
Indirect Effects on Supply
in the Factor Markets
! ----------------------------------------------------------------
The indirect market effects working through the
supply side of the market to change the income of
individuals other than the schooling receivers work by
changing the relative supplies of the various resources
and thus, through the law of variable proportions, the
marginal physical products and, therefore, incomes of
cooperating factors. The extent of the changes, once
again, will be dependent on the precise shape of the
production surface. This case was explained in Section B
of this chapter. These effects should be measured by
the average school level and average age of fellow
workers (S. and A,).
: 3
77
Indirect Market Effects on
People as Consumers
Notice that schooling can affect the welfare of
i
j those not participants to the schooling by affecting the
f prices of products. That is, it affects them as con-
i
! sumers, so that real but not money income is affected.
j
This effect can come from either the demand or the
supply side of the product market. That is, the
schooling can alter demand and, therefore, prices; or
l
J it can alter factor supply and, therefore, prices. The
non-participants can either gain or lose in real terms
from these price changes. The measurement of this gain
or loss would require knowledge of the spending patterns
of the affected parties. We have neither the tools to
isolate these particular effects on prices, nor the
knowledge of the required budgets.
Spillover Effects
Spillover effects may also operate from either
the supply or the demand side. The clearest case is
that of the schooling altering the supply of human
capital in the non-participants. By contact on the job
the non-participants, too, acquire human capital and,
therefore, have their income increased. This is not the
law of variable proportions at work, for in that case the
78
non-participant's productivity would return to its
former level if he were to cease to work with the more
schooled worker. When the non-participant has acquired
i
■ something he can take with him in a job transfer, it is
i
j a spillover effect. The school participant has not lost
i
|
anything by the non-participant's acquisition, but no
exchange has taken place. The non-participant has
surrendered nothing in order to acquire the additional
I skill. These effects should be measured by the
i
! regression coefficients of the schooling of co-workers
(Sj) and of their average age (Aj).
The spillover effect operating from the demand
side of the product market is more complex {perhaps we
are not able to measure it with the tools used in this
paper). However, as a result of increased schooling,
some people might alter their demand so that production
of more things from which the non-participants could
learn would occur; for example, "better" television,
educational toys, books, etc. This is not a repeat of
the indirect market effect case. They do not receive
more income because they sold to the more schooled, but,
as fellow consumers, are made more productive.
Note that in all the spillover effect cases
discussed in this paper to this point, where it was
possible to measure the effect, it is measured as a
79
change in the income of the non-participants. The fact
that this change of income is obtained from data about
what happens in markets does not make it a market effect
; and, therefore, the result of the operation of the law of
i
j variable proportions or of the interdependency
!
t
j characteristic of all variables in a general equilibrium
perfect competition model. The original changes were
made at a cost by individuals who evaluated the net
I
|
i return to themselves as positive; and the effect on other
people is because of a change in the supply circumstances
of the other people, not just a market interaction.
There is another kind of way in which one
individual's income may be higher as a consequence of his
working with a more highly schooled person that some
people would classify as a neighborhood effect. That is
a matter of definition. I would prefer to call it a
result of market imperfection. It may be that our
institutions, for quite a number of different reasons,
may pay people more simply because they have higher
schooling. This is sometimes done indirectly by setting
a higher pay rate for a group whose members have more
schooling. If someone happens to get himself into a work
group where the others have more schooling, he may get
higher pay as a result.
Neighborhood effects may also work from the
80
demand side, but, just as with the market effects from
the demand side, we do not in this work have the tools
to measure them. They would be illustrated by examples
■ wherein the schooled would alter their demand pattern
i
j among the items that have various different amounts of
i
j
j neighborhood effects, either increasing or decreasing
j
the total amount of neighborhood effects on the non
participants in the schooling.
i
I In terms of this study, the spillover effects
J should be reflected primarily in the regression co
efficients of the variables concerned with the contacts
on the job. These are the average school level of
fellow workers (Sj) and average age on the job (Aj).
However, insofar as the beneficiaries of the spillover
effects have shifted to new employment in the same
market, the effects would be reflected in the
corresponding characteristics of the community (Sc and
A,,). Insofar as the beneficiaries have moved into
different markets, they would cause the results of this
study to have coefficients of the wrong sign. These
latter cases, when mixed with those who have not moved,
would cause "noise" in the data, lowering both the size
of the regression coefficients and the measure of their
importance.
81
D. IMPERFECTIONS
There are three remaining issues to be explored.
One is the result to be expected from models that do not
i
i postulate perfect competition but which do have the
j conventional assumptions of an assumed pattern of owner-
j ship, an assumed pattern of demand which the sellers do
not try to modify, otherwise rational behavior and income
maximization as a goal, and possession of correct
I
| information. The second is the question of goals other
j than income maximization. The third is the consequences
of decision making that seems not to be directed toward
consistent goals, or, perhaps, any goals.
Conventional economic theory contains, in
addition to the competitive model, theories of monopoly,
duopoly, oligopoly, and monopolistic competition. The
middle two come in many versions. It does not seem
necessary to investigate these models in great detail;
the broad outlines of their results are sufficient.
Monopoly models and most determinate models of
duopoly and oligopoly indicate that a factor, or a
cooperating group of factors, can increase its income by
restricting its services below the competitive norm.
(Note that this is a virtual rather than a real
comparison, for in nearly all cases the competitive norm
82
is unattainable.) A difference is developed between
their average productivity and their marginal
productivity. If they are the employers of other factors,
: they may also react to the sloping nature of the other
j
| supply curves and reduce demand for the other factors
i
I
further and establish a difference between the average
cost (pay rate) and marginal product. Another way to
state the same proposition is that the private marginal
t
curves which are different from the social marginal
curves can be responded to in a case with monopoly
whereas they cannot be with full competition. (The
private marginal, private average and social marginal
values are forced into equality with the social average
value under competition.)
The result of the monopoly is that the factors
with monopoly-power receive a pay above their marginal
productivity. The complementary factors, which sell
their services competitively and whose pay rates are
fixed by the monopoly holders, receive a pay which is
below their marginal revenue product. In any particular
model with specified cost and demand functions, the pay
rates will have a systematic relationship to the marginal
productivities, even though they are not equal to them.
However, the size of the gap between pay rates and
marginal productivities will vary from one specific
83
cost-demand pattern to another, being dependent on the
specific elasticities in each case. This means that
some people with higher marginal productivity will
| receive pay below some other people with lower marginal
i
j productivity. In all cases, however, an increase in
I
t
j marginal productivity will result in an increase in pay,
| though by a smaller amount. Thus, the workers who had in-
j creased marginal productivity because of indirect market
i
I
I effects from the product market, indirect market effects
from the factor markets, or spillover effect in the
factor market would have higher pay than if they had not.
The critical issue for this study, however, is whether
i there is some systematic factor that would cause those
receiving benefit from others to be subject to larger or
smaller gaps between their marginal productivity and
their pay rates. This would require a systematic
patterning of the supply and demand functions between
gainers and non-gainers or a systematic pattern of
possession of monopoly positions. There seems no reason
to suspect the former. However, it may be that more
schooled and older people are more likely to have
monopoly positions. This would produce an increased
association between schooling of self (Sg) and income
(Y) and between age of self (A ) and income (Y).
s
Because of the multi-colinearity between these series
84
this might lead to a statistical increase in the
association of the Ss and As with Y at the expense of
! S and S-.
!
I However, the principle effect of monopoly
j positions that lead to the reduction of services offered
| would be expected to be a reduction of the association
postulated in this study. This would come from several
sources: first,-lack of perfect association between
I
i monopoly positions and schooling; second, lack of full
exploitation of such positions; third, the reduction in
the change in pay below the change in marginal
I
productivity when productivity is changed by gaining
from others' schooling; fourth, the lack of a systematic
relationship between the pattern of the supply-demand
functions and the acquiring of benefits from others'
schooling. Therefore, both the regression coefficients
and the correlation coefficients should be smaller than
in a world of perfect competition.
Some models of duopoly and oligopoly do not have
determinate solutions. However, they usually provide
boundaries between which the results should lie. Other
models, especially of oligopoly, postulate instability
and change until there is a modification in the details
of the market organization. Sometimes the models
indicate that, for at least short periods of time, the
pay rates can be widely divergent from marginal
productivity and can even be above marginal productivity.
i
! There seems no reason for an association between these
j phenomena and either the individual's own schooling or
i
I
I the schooling of others with whom he is associated.
I
I Therefore, if there were any individuals from situations
j where any of these models were a proper description, the
j
i effect on the statistical results of this study would be
a reduction in the size of the regression and correlation
coefficients.
j Another model which produces indeterminancy
within bounds is that of bilateral monopoly or oligopoly.
The specific results within the model depend upon
bargaining ability and power. Once more the ability to
have higher productivity does not necessarily result in
more pay.
Some writers have suggested that income
maximization is not the major goal of most economic
units. Other goals that have been suggested include:
growth of corporate size, labor peace, possession of the
most advanced technology, sinecures for family and
friends, social responsibilities, and others.
Conventional analysis would say that most of these would
not be possible without monopoly power to protect them
86
and that they are just alternate ways of taking the
results of that monopoly power instead of taking those
! results in the form of money income. Sometimes, of
I
j course, these actions may be taken in the belief that
i they will lead to maximum income. This is especially
| likely to be true of technology and labor peace. Some
i
of these goals obviously can result in pay that is not
closely related to productivity. However, it does not
I
l
j seem that they should have any systematic connection to
productivity acquired because of others' schooling and
productivity from any other cause. Individuals may also
take part of their productivity, from whatever cause,
in the form of leisure, or more pleasant working
circumstances, rather than in the form of higher income.
The individual maximized his utility rather than his
money income. Once again, the results for this study
are lower regression and correlation coefficients.
Many decisions are made without apparent ref
erence to productivity or maximization of anything. Rules
of thumb or seniority are used for job assignment or rate
of pay. Many decisions are made by union contract
according to formulas which often have only distant
relationships to productivity. Without unions, "company
politics" and personal prejudices often have large roles
to play. Some of these practices are, once again,
87
possible only because there is a monopoly to protect
them. Some of the practices exist because it is
impossible to obtain information that is more than a
1 very rough approximation to the productivity of the
j different workers. Here, also, there seems no reason
j to expect any of these actions to be systematically
!
related to the schooling of either the individual or
the individual's associates. These, then, are also
r
I forces to reduce the average influence in the economy of
I one person's schooling on the income of others.
There is one type of decision making that will
systematically affect the results of this study. That
is the growing practice of assigning job and pay rate on
the basis of schooling, without reference to pro
ductivity. This practice makes income less associated
with the schooling of associates.
CHAPTER IV
EMPIRICAL TESTING
|
j The data for the statistical testing are a
j subset of the one in one thousand sample taken from the
l
| 196 0 Bureau of the Census Reports.^- The data were
obtained on tape and the analysis was done at the
Computer Center at San Fernando Valley State College,
1
I Northridge, California.
i The total number of individuals on the tapes
I
| was nearly 180,000. Of these, over 64,000 were employed.
(
They were sorted into cells by region, size, and industry
of employment. For region, the Census Bureau divided
the United States into four parts: North East, North
Central, South, and West. Urbanization is indicated in
five categories: over one-half million, one-quarter to
one-half million, one hundred thousand to two hundred
fifty thousand, urbanized but less than one hundred
thousand, and not urbanized. All of the resulting cells
containing fewer than thirty people were then discarded.
The analysis was then performed on the remaining 58,874
^U. S. Department of Commerce, Bureau of the
Census, U. S. Census of Population and Housing, 1960.
88
89
individuals. There were 6,457 minority members (2,383
female and 4,074 male) and 51,874 majority members
(15,915 female and 35,959 male).
In each of the twenty cells established by the
intersection of the four region and five size categories,
i
j
| the mean school level finished, mean age, and fraction
of minority members were calculated. These calculations
have been referred to as: school level in the community
I
| (Sc), age in the community (Ac), and race in the
I community (R ). In each of the cells established by the
i ^
i
| region, size, and industry sort, similar averages and
j ratios were calculated. These calculations have been
referred to as: school level on the job (S^), age on the
job (A.), and race ratio on the job (R.). The rationale
J
for these calculations and their use in the analysis is
that within each size classification in each region,
market conditions are approximately homogeneous within
each industry. Thus, these averages represent the
corresponding characteristics of the group with which
each individual member of a group works. That is, they
describe, for the purposes of this paper, the relevant
characteristics of co-workers.
The theoretical basis of the analysis is that
human capital has effects, both spillover and indirect
market effects, on people other than its possessors. It
90
is assumed in the statistical analysis that the two best
measures of the human capital variable are schooling and
age, though it is assumed that schooling is the more
! important of the two. The community measures should
; show the influence of demand modification and the job
I
1
j measures should show the influence of supply mod
ification.
The race measures were included to keep the
I discrimination in the society from compromising the
I results being inspected. There is, of course, a problem
j
with the community measures. People may move to a
community because of its characteristics rather than get
i influence from it. The community measures may also be a
strong proxy variable for region.
1 ■
Problems
One important problem is that the data are all
"reported" data. This is really a small problem if we
assume that the sample sizes are large enough to "average
out" the variation in dishonesty and poor memory and
leave us with only an "adjustment" constant of some
unknown size. Other studies have dealt with this
adjustment constant.
The major problem of the study is that the model
is not a complete one. That is, several series of data
91
that are known to affect earnings are not available; for
example, family backgrounds and physical capital. But
the purpose is not a predictive model. The aim is only
; to test whether the variables under study have a
j significant influence and to get an order of magnitude
j idea of the influence, if it is found to exist. However,
!
there is the possibility that the variables found to be
significant are found so only because they are highly
|
! correlated with variables not included in the study.
! Outstanding among these, of course, is the amount of
i
physical capital in each work situation and the family
background of the employees under study.
Analytical Method
The statistical techniques used were very
conventional; only the sample size was unusual. A
standard stepwise regression program from the UCLA BMD
series was used. The program required modification to
take buffered input and very large sample size.
Linear relationships were tested because: first,
the complicated interaction in the theoretical model
precluded any conclusion about the precise shape of its
relationship; second, the rough approximation of the
proxy variables used to the theoretical variables of the
model; and, third, the sample size was so large that no
92
existing program would give a plot of the data to give
a preliminary view of the pattern. Over three hundred
hours of computer time had been used by the time the
linear models had been tested, and runs with trans-
i
i formations would have been given very low priority by
t
the Computer Center, as each run took approximately one
hour.
As was expected, the data quickly revealed that
| the relationships in the minority and majority groups
| were quite different. Therefore, these two groups were
separated for all the analysis. Each of these groups
was then analyzed with income (Y) as the dependent
variable and with independent variables of age of the
individual (A ), school level of the individual (S ),
s s
mean community school level (Sc), mean community age
(A ), community race ratio (R ), mean school level of
c c
co-workers (Sj), mean age of co-workers (Aj), race ratio
of co-workers (Rj), and a dummy, or shift, variable for
the sex of the individual (SX).
The results of the analysis of these two groups
serve as the basis for most of the results reported in
this study. However, there also appeared to be a
significant difference between the sexes. Therefore,
each of the racial groups was divided by sex. This
produced four basic tapes of data which were used for
93
the remainder of the analysis. Five series of regression
analyses were made on each tape. On each of the five
analyses each group was first sorted by another variable
| and the regression calculations were performed on each of
the sub-groups thus created. One of the sortings was by
level of school completed (S ). A second one was by age
b
(As) , with grouping by five-year intervals except for
intervals 41-50, 51-60, and over 65. A third sorting
was by income level (Y), with the distribution being
divided into fifths. The other two sortings were by
region and by size of urbanized area.
Majority Group Results
When a simple regression is run within the
majority group between reported income (Y) and average
school level completed by fellow workers (Sj) — that is,
those in the same industry, in the same geographical
region, and in the same sized urbanized area — the
regression coefficient obtained is $3 61, on the average,
per year of schooling. (The standard error was $11.)
However, the correlation coefficient is only .139.
(Both coefficients are highly significant as the sample
contains 51,874 individuals.) It is also clear that the
schooling of fellow workers (Sj) is carrying a c good
portion of the consequences of other variables with which
94
it is correlated. The simple correlation coefficient of
S • with the average school level in the community (S ) .is
J c
.336, and with the school level reported completed by the
individual himself (S ) the coefficient is .478. These
are the third and fifth highest simple correlation co
efficients in the matrix of 45 such coefficients, and the
two highest in which schooling on the job (Sj) is one of
the pair.
The entire matrix is presented in Table I, and
the highest thirty by order of rank in both the majority
and minority group are given in Table II.
The simple correlation coefficient between
schooling of co-workers (S■) and sex („X) is .188, which
J *
shows that in the majority group females work in groups
which have higher average schooling. When these four
independent variables (aX, S_, S_, and S j.) are entered
b SC J
into the regression equation, the regression coefficient
for Sj is reduced to $139, with a standard error of $12,
and the multiple correlation coefficient is raised to
.446.
While the individual’s own age (A_) has a simple
b
correlation coefficient with income that ranks
seventeenth in the matrix, it has the third highest
potential partial correlation coefficient and F value to
enter when Sj along has been regressed on income. When
TABLE I
SIMPLE CORRELATION MATRICES
Maj
Min
y X
Ss
Sc
Sj Rj
Rc
Aj
Ac
y
-.319
-.321
.142
. 066
.269
.256
.134
.369
.139
.385
-.075
-.381
.009
-.293
*.017
-.076
.013
.172
X
-.319
-,321
-.022
-.003
.064
.134
.034
.008
.188
-.011
.041
.381
.013
.037
-.035
.113
-.010
-.021
As
.142
.066
-.022
-.003
-.218
-.294
.002
-.028
-.044
-.062
.056
.068
-.019
-.017
.242
.207
.048
.027
Ss
.269
.256
.064
.134
-.218
-.294
.150
.267
.478
.463
-.109
-.179
-.003
-.161
-.061
‘ -.089
-.034
.111
SC
.134
.369
.034
.008
.002
-.028
.150
.267
.336
.471
-.156
-.284
-.365
-.519
-.032
-.053
.077
.121
Sj
.139
.385
.188
-.011
-.044
-.062
.478
.463
.336
.471
-.325
-.588
-.085
-.273
-.128
-.234
-.006
.108
Rj
-.075
-.381
.040
.381
.056
.068
-.109
-.179
-.156 1
-.284
-.325
-.588
.557
.437
.076
.207
-.332
-.280
Rc
-.009
-.293
.013
.037
-.019
-.017
-.003
-.161
-.365
-.519
-.085
. . . -.273.
.557
.437
-.143
. -.091
-.409
-.621
AJ
.017
“,076
-.035
.113
.242
.207
-.061
-.089
.032
-.053
-.128
-.234
.076
.207
-.143
-.051
.209
.222
Ac
.013
.172
-.010
-.021
.048
.027
-.034
.111
.077
.121
-.006
.108
-.322
-.280
-.£09
-.621
.209
.222
Level of Statistical Significance for Minority* 95% *= .025 t 99% “ *032
Level of Statistical Significance for Majority: 33% * = .0088; 39% * = .0114
M3
\J1
96
TABLE II
ORDER OF SIMPLE CORRELATION COEFFICIENTS
Majority Minority Minority Majority
1 Rc-A -.609 -.621 Rc-Ac -.621 -.609
2 Rj-Rc .557 .437
sr Rj
-.588
-.325
3
Ss-Sj .478 .463
sc-Rc -.519 -.365
4
sc-Rc
-.3 65 -.519
Sc-Sj
.471 .336
5 V*Sj .336 .471
V S j
.463 .478
6 Rj-A -.332 -.280 Rj-RC .437 .557
7
Rj“Sj
-.325
-.588
r -Sj
.385 .139
8 Y -X
-.319
-.321 Y -R4 -.381 -.075
9
Y -Ss
.269 .256 X -Rj
.381
.040
10 As-Aj .242 .207 Y -Sc .369 .134
11
As“Ss
-.218 -.294 Y -X -.321 -.319
12 Aj-Ac .209
.220 As-Sg -.294 -.218
13
X -Sj .188 —, 011 Y -Rc -.293 -.009
14
sc-Rj
-.156 -.284 Sc-R a -.284 -.156
15
Ss-S^ .150 .267
Ac-Hj
-.280 -.332
16 Rc-Aj -.143 -.091 Sj-Rc -.273
-.085
17
Y -As .142 , 066
ss-sc
.267 .150
18 Y -Sj
.139 .385
Y -Ss .256 .269
19
Y -Sc .134 .369
Sj“Aj
-.234 -.128
20
Sj~Aj
-.128 -.234 Ac-Aj .220 .209
21 Ss-R j -.109 -.179
As"Aj
.207 .242
22 Sj-Rc -.085 -.273
Rj’Aj
.207 .076
23
Sq-Ac
.077
.121 Ss-R a
-.179 -.109
2 4
Rj“Aj
.076 .20 7 Y -Ac .172 .013
25
Y -Rj
-.075
-.381 Ss-Rc .161 -.003
26 X -Ss .064 .134 X -Sg
.13^
.064
27
ss“Aj
-.061 -.089 Sc “Ac .121 .077
28
As“Rj
.056 .068 X -Aj
.113 -.035
29
As-Ac
.048 .027 S -Aq .ill -.034
30 X -Rj .040 .381
Sj”Ac
.108 -.006
95/6 Confidence Levels for Majority, ,0088} for Minority, ,025
99% Confidence Level: for Majority, .0114} for Minority, .032
97
the four variables mentioned above have all been entered,
it has a partial correlation four times as large as the
next most significant variable (Rc) and an F value to
enter thirteen times as large. The entry of age of self
into the regression lowers the regression coefficient of
Sj from $139 to $98 (with a standard error of $12), a
30 percent change. It changes the coefficient for the
individual's own schooling (Ss) by about 20 percent, but
the one for average schooling in the community (Sc) by
less than three percent and that for sex (SX) by less
than one percent. The resulting equation is:
Y = -8770 - 3003 X + 58A + 394S + 613S + 98S..
s s S C J
[34] [1.1] [5.8] [29] [12]
2
The multiple correlation coefficient is .488 (R = .238).
In a sample as large as this one, each of the
variables singly is almost certain to be significant,
even if the correlation coefficient is quite small.
That is true in this case. However, multicolinearity
is a severe problem and causes the regression coefficients
of some variables to behave in an erratic manner when
certain other variables are introduced into the equation.
For example, the percentage of minority group members in
a community (Rc) is quite highly correlated with average
age in the community (A ), -.609; with the percentage of
98
minority group members in the job group (Rj), .557; and
with the average school level of the community (S ),
c
-.365. These are the first, second, and fourth highest
of the 45 simple correlations in the matrix.
The result of this circumstance is that the
inclusion of other variables, even though they are
statistically significant when included, does not add
meaningfully to the proportion of variance explained.
The highest multiple correlation coefficient obtainable
2
in the majority group was .491 (R = .241), compared to
the .4 88 (R2 = .238) obtained when no average age or
race ratio variables were included.
The analysis does reveal something of the racial
discrimination in United States society in that the
whites receive higher income when they live in
communities with more minority residents but are similar
in their other characteristics. The regression including
R was of the form:
Y = -10,797 - 3013 X + 58A + 391S +
s s s
[34] [1.1] [5.8]
777S + 95S. + 34R .
C J c
[31] [12] [2.3]
The race coefficient is average change in reported income
per one percent of minority members in the community.
99
X is a shift parameter for sex and the regression
indicates that women in. the group average $3013 less
reported income than men in the same industries, in the
! same geographical region, in urbanized areas of the same
i
population size, who are the same age and who have the
same amount of schooling. The rest of the equation
indicates that the individual's income is on the average
higher by $58 for every year increase in his or her own
I
age and by $391, on the average, for every year of school
completed. A year of increase in the average school
level of the community in which the individual lives
will, on the average, increase his income by $777, and a
similar increase in his work group's schooling will
increase it by $95. He will also receive, on the
average, $34 more income for every one percent increase
in the fraction of his community that is of minority
groups.
The mean income of the majority group is $4 534
of reported income, with a standard deviation of $4 018.
The standard deviations of the dependent variables are:
for As, nearly 14 years; for Ss, 3.1 years; for Sc, .57
years; for Sj, 1.54 years; and for Rc, 7.2 percent.
Thirty and six-tenths percent of the sample were female.
100
Contribution to Reduction of Variance
The order of contribution to reduction of
variance in the stepwise process was: first, sex;
second, schooling of self; third, age of self; fourth,
schooling of co-worker; fifth, school level of the
community; and sixth, race ratio in the community. The
variables for average age in the community (A ) and
average age of co-workers (Aj) were seldom found to be
significant. The regression coefficients can be compared
quickly by the use of Table III; the means and standard
deviation of the independent variables are in Table IV.
It was possible to explain a larger proportion
of the simple variance of reported income among the
minority members of society than among the majority. In
addition, the characteristics of other people were more
closely associated with income among the minority than
among the majority. The characteristics of others were
also more important than the individual's own character
istics among the minority, whereas among the white
majority the individual's own characteristics were far
more important than were the characteristics of others.
Among the majority group, sex had the highest
increase in percentage of variance accounted for in
almost all orderings of introduction into the stepwise
process. The individual's own schooling usually made
101
TABLE III
REGRESSION COEFFICIENTS AND STANDARD ERRORS
MAJORITY
R, 2\
(Rz)
CONSTANT
sX As Ss Sc
sj
Rc
.139
(.019)
669 361
[11]
.446
(.199)
-6324 -3040
[35]
327
[6]
636
[30]
139
[12]
.488
(.238)
-8770 -3003
[34]
58
[1.1]
394
[6]
613
[29]
98
[12]
.491
(.241)
-10797 -3013
[34]
58
[1.1]
391
[5.8]
777
[31]
95
[12]
34
[2.3]
MINORITY
r (r2)
CONSTANT
sx As Ss Sc
Sj
Rc
.385
(.148)
-2026 452
[13]
.559
(.312)
-7252 -1459
[45]
85
[7]
685
[34]
237
[15]
.575
(.331)
-8090 -1485
[44]
22
[1.7]
113
[7]
676
[34]
223
[15]
.581
(.338)
-5939 -1465
[44]
21
[1.6]
111
[7]
530
[37]
220
[15]
-36
[4]
Standard errors are in brackets below their
respective regression coefficients.
102
TABLE IV
MEANS AND STANDARD DEVIATIONS
VARIABLE
MAJORITY MINORITY
Mean
Std.
Dev.
%
Female Mean
Std.
Dev.
%
Female
Y 4534 4018 2418 2069
40.80 14.00 38.96 13.35
10.90 3.10 8.54 3.53
Sc
10.60 .57 10.44 .72
sj
10.70 1.54 9.83 1.76
Rc
10.40% 7.20% 15.80% 5.86%
Rj
8.97% 10.20% 27.00% 21.30%
Ac
40.50 .67 40.20 .65
Aj
40.40 3.31
30.7%
40.85 3.03
36.9%
the second largest contribution.
Among the minority group, sex made approximately
2
the same amount of addition to R as it did among the
majority, but it was the largest addition in only about
one-half of the different orders of entry. Schooling on
the job (Sj), race on the job (Rj), or schooling in the
community (Sc) were usually the largest contributors when
sex was not. In those cases, sex was nearly always in
2
second place. The most common ordering of addition to R
was, first, sex by a distinct margin, followed by the
three school variables with nearly the same quantitative
addition, with their order usually being Sc, Sj, Ss.
These variables were followed by the age of the
individual (As).
In the majority group, sex was followed by
schooling of self (Ss) and by age of self (As). So, we
can see the individual's own characteristics are the most
important variables in the majority group. Average
reported school level in the community (Sc) and in the
cooperating work force (Sj) were about equal in their
average contribution to reduction of variance in the
majority, with Sc being the least variable from one
order of entering the variables to another.
104
Minority Group Regression Results
Within the minority group the simple regression-
correlation test between reported personal income (Y) and
the average school level of fellow workers (Sj) gave a
simple regression coefficient of $452 with a correlation
coefficient of .385. The standard error was $13. The
minority mean reported income was only $2418, with a
standard deviation of $2069. There were 6457 individuals
in the minority group.
The pattern of simple correlation coefficients
was quite different in the minority from that in the
majority. In the minority group Sj had the following
coefficients with the indicated variables:
R. . - .588; S . .471; Sof .463; Y, .385. These were the
J c s
second, fourth, fifth, and seventh highest, respectively,
of the 45 simple correlations in the matrix. This was
also the highest simple correlation with income. Other
correlations with income were: Rj, - .381; Sc, .369;
SX, - .321; Rc, - .293; Ss, .256. These were the eighth,
tenth, eleventh, thirteenth, and eighteenth, respectively,
in order of size among the 45 in the matrix.
When the four independent variables (SX, Sg, Sc,
and Sj) are entered into the regression analysis, the
resulting equation is:
105
Y = -7252 - 1459SX + 85Ss + 685SC + 237Sj
[45] [71 [34] [151
with R of .312. (The respective standard errors are
j indicated below the coefficients.)
i
{ When these variables have been entered, the next
highest partial correlation coefficient and F-to-enter
is that of age of self (A ). When A is entered, the
5 D
equation obtained is:
Y = -8090 - 1485 X + 22A_ + 113S„ + 676S.,
[44] [1.7] [7] [33]
+ 223Sj
[15]
with R^ of .331.
If Rc is then added to the regression analysis,
the equation becomes:
Y = -5939 - 1465„X + 21A,, + 111S_ + 530Sn +
[44] [1.6] [7] [37]
220Sj - 36Rc.
[15] [4]
The multiple R of the equation is .338.
For comparison with the majority group, the
simple correlations in the minority group of the minority
race percentage in the community follows: Rc-Ac, -.621;
106
Rc-Rj, .437; Rc-Sc, -.519. These are the first, sixth,
and third highest, respectively, of the simple
2
correlations in the matrix of 45. The highest R without
a race or age variable from the community or from the
job was .331; with race and/or age variables, the
highest obtainable was .339.
Of the 6457 members of this group, the mean age
(As) was 38.96 years with a standard deviation of 13.4
years. They had 8.54 years of schooling on the average
(Ss) with a standard deviation of 3.53 years. The
average level of school completed in the communities in
which they lived (Sc) was 10.44 years with a standard
deviation of .72 years. The average number of school
years completed by the work force with which they worked
(Sj) was 9.83 years with a standard deviation of 1.76
years. The group was 36.9 percent female.
The coefficients can be compared between
equations with different numbers of variables in Table
III. Comparisons can be made easily between the majority
and minority groups in Table V. The means and standard
deviations of all the variables for each group are given
in Table IV.
107
Further Evidence of Differences
Between the Groups
It was found that the independent variables,
especially the schooling of co-workers and of community
residents, were more important for the income of the
minority members than for the majority as revealed by
the size of the correlation coefficients. Another way
to show this same fact is to express the regression
coefficients as ratios to the mean income of the group.
This calculation will give the percentage of the mean
income that on the average is associated with a unit
change in the independent variable.
In Table VI the coefficients of Table V have
had this transformation performed upon them. The
information in this table that is most pertinent to the
thesis of this paper is the coefficients in the school
level in the community and school level on the job col
umns. These coefficients reveal that, with other
variables held constant, an increase of one year in the
average schooling of the co-workers will be associated
with over a nine percent change in income for minority
group members and with over a two percent change in
income for majority group members. The impact of a
difference of one year in average school level of the
community will be even more dramatic — approximately
108
TABLE V
REGRESSION COEFFICIENTS AND STANDARD ERRORS
V >
Constant
sX As Ss
S
c
S
s Rc
MIN. .385
(.148)
-2026 452
[13]
MAJ. .139
(.019)
669 361
[11]
MIN. .559
(.312)
-7252 -1459
[45]
85
[7]
685
[34]
237
[15]
MAJ. .446
(.199)
-6324 -3040
[35]
327
[6]
636
[30]
139
[12]
MIN. .575
(.331)
-8090 -1485
[44]
22
[1.7]
113
[7]
676
[33]
223
[15]
MAJ. .488
(.238)
-8770 -3003
[34]
58
[1.1]
394
[6]
613
[29]
98
[12]
MIN. .581
(.338)
-5939 -1465
[44]
21
[1.7]
111
[7]
530
[37]
220
[15]
-36
[4]
MAJ. .491
(.241)
-10797 -3013
[34]
58
[1-1]
391
[5.8]
777
[31]
95
[12]
34
[2.3]
Yw = 4534; Y0 = 2418
109
TABLE VI
RATIO OF REGRESSION COEFFICIENT
TO MEAN INCOME
(Expressed as a Percent)
SX/Y As/Y Ss/Y Sc/Y Sj/Y Rc/Y
MIN.
MAJ.
18.69
7.96
MIN.
MAJ.
60.34
67.05
3.52
7.21
28.33
14.03
9.80
3.07
MIN.
MAJ.
61.41
66.23
.91
1.28
4.67
8.69
27.96
13.52
9.26
2.16
MIN.
MAJ.
60.59
66.45
.87
1.28
4.59
8.62
21.92
17.14
9.10,
2.10
-1.49
+ .75
a one-fourth change in income in the minority group and
one-seventh change in income in the majority. The role
of the individual's own schooling is slightly more than
one-half as great for minority members as for majority
member s.
One of the dramatic results seen in Table VI is
that sexual discrimination appears to be worse than
110
usually measured. When the woman has the same character
istics and is living in communities with similar average
schooling, and she works in similar job settings, she
gets only slightly over one-third the pay of similarly
placed males.
A more meaningful comparison, for some purposes,
would involve comparing the ratios after they had been
multiplied by the standard deviation of the relevant
variable. This calculation would give a result that
told what percentage change in income was associated with
a difference of one standard deviation in placement of
the independent variable. These results are shown in
Table VII.
Interpretation of Results
It appears that the null hypothesis is in fact
false. We have highly significant regression and
correlation coefficients for both the average school
level of the co-workers and for the average school level
of the community. Apparently there are effects of the
schooling of some people on the income of others from
both the demand and the supply side. This effect also
seems to be more important for the minority group than
for the majority group. In the former the regression
coefficients are a larger fraction of the average income
Ill
TABLE VII
EFFECT OF ONE STANDARD DEVIATION
DIFFERENCE IN POSITION IN DISTRIBUTION
1
Ss sc
S j Rc
MIN.
MAJ.
32.89
12.26
MIN.
MAJ.
12.43
22.35
20.40
8.00
17.25
4.73
MIN.
MAJ.
12.15
17.92
16.49
26.94
20.13
7.71
16.30
3.33
MIN.
MAJ.
11.62
17.92
16.20
26.72
15.78
9.77
16.02 -8.73
3.23 + .54
of the group and are usually larger absolutely. The
correlation coefficients are also larger for the
minority group.
There is, however, difficulty in interpreting
the higher values for the minorities. Why have these
members of minority groups been selected? We do not
have an independent measure of "natural" labor. Perhaps
these individuals have more natural ability and, there-
112
fore, are permitted to overcome, or learn how to over
come, a portion of the discrimination to which minorities
are subjected. Perhaps one of the features of more
natural equipment is the ability to "pick up" more by
spillover effects.
Another possibility is that these individuals
have achieved better psychological adjustment and,
therefore, are able to function at a higher level and,
possibly, to gain more from potential spillover situ
ations as well. Another possibility is that they spent
their youths in a social setting, or accepted the ap
propriate aspects of their social setting, to produce
acceptance into better paying employment with the more
schooled.
Another possible explanation is that one form
that the discrimination against minorities can take is
the failure to increase their pay, or to promote them, or
to give them higher paying jobs simply because they have
finished certain levels of school regardless of their
productive effort or results — a practice that is so
common in our society. This failure to increase income
automatically when schooling of self is increased would
reduce the coefficient for schooling of self. The effect
of this social custom of automatic opportunity for the
more schooled is to reduce the reliance on productivity
113
in the determination of pay rates. If there are, in
fact, effects on others when someone is schooled, this
would be masked if pay rates were set by some social
rule of thumb.
One possible explanation can be eliminated. This
is the possibility that, in some way, the concentration
of the blacks in the south in combination with
differential treatment of the minorities causes a proxy
for regional difference to show up in the statistical
results. This explanation can be eliminated because for
every region and for both male and female, the co
efficients for Sj were larger for the minority group
than for the majority. These larger coefficients for
minorities also existed throughout all age levels, but
were much larger for females than for males. The
difference also existed for both sexes in all but one
level of schooling.
Returning to the null hypothesis and its
rejection, it may be that a type I error is being made.
Aside from the purely chance factors that produce type I
errors, there is the additional problem that we do not
have a complete model and, therefore, have more risk that
variables not entered into the analysis are having their
influence reflected by proxy. On the other side of this
114
argument, however, is the fact that most of the
deviations of the data from the ideal concept and most
of the deviations of markets from the competitive model
within the geographical district, as was discussed in
Section D of Chapter III, would tend to obscure the
effect we are trying to measure. That is, the effect may
well be stronger than our test shows.
Evidence Concerning the Law
of Variable Proportions
In addition to the basic alternative hypothesis
that there is an effect on other people when someone
increases his schooling, our theory led us to expect
that this effect would be relatively greater and stronger
among those with less schooling than among those with
more schooling. This conclusion was reached in Section B
of Chapter III and is stated on page 67.
The support for this proposition is quite strong
among the majority males. With only two small reversals
of order, the partial regression coefficient for
schooling of fellow workers (Sj) becomes progressively
smaller as the level of schooling of the individual (Ss)
increases. These two reversals occur at eight years
completed and at twelve years completed. The coefficient
becomes negative for college graduates. The level of
115
significance and partial correlation coefficients also
tend to a lower value as Sg increases until Sj becomes
statistically insignificant as a determinant of income
for persons with post-graduate collegiate schooling.
The evidence among the other three groups —
majority females, minority males, and minority females —
is not very strong, but it is not contradictory. These
categories have far fewer individuals in them, and this
contributes importantly to the fact that the level of
significance often is not reached. Within the majority
females there is the indicated decreasing coefficients
starting with the eighth year and continuing through
high school. Beyond high school the coefficient of Sj
becomes insignificant in the proper combination of
variables for comparison. This evidence is supportive.
Below the eighth year, however, the variable is also not
statistically significant.
Among the minority males there is good support
t
below the twelfth year, but above the twelfth year non
significance develops. Among minority females, the
smallest group, there is support through ten years of
schooling, but non-significance develops after twelve
years, again.
Other checks, less direct, were made by analysis
of sorts on other variables. The means of the schooling
116
of self (Ss) were compared with the partial regression
coefficients of schooling on the job (Sj)* The clearest
example of this is with the age sort where individuals
were grouped according to their age by five year
intervals, except for intervals 41 to 50, 51 to 60, and
over 65. For the majority males the coefficients moved
in inverse order to the mean schooling of self from
26 years through 60 years; and for the majority females,
31 years through 65 years. Among the minority the
evidence is not as good. Within the females, coeffi
cients with the correct progression are interspersed
with levels of non-significance. Within the males, the
inverse movement exists from 26 years through 50 years,
but there is direct ordering above and below those levels.
Within the sorts by region, one region is out of
order in three of the groups, and one group has random
order. With majority males, it is the North Central that
is out of order; with the majority females, it is the
West; and with the minority females, it is the South.
With the minority males, the ordering is random. In
the sorts by size of urbanized area (five sizes), the
majority males have moderate support, but the other
three groups give no support, though they do not contain
contrary evidence.
117
The summary of the evidence about the inverse
relationship between a person's own schooling and the
strength of the effect of others' schooling on his
income is positive. The most direct and relevant
evidence is good. Most indirect evidence is supportive
or not significant. Very little of it is contradictory.
Summary of Statistical Evidence
In Section A of Chapter III, the theoretical
basis of the null hypothesis — that schooling of an
individual would have no effect on the income of others
— was developed. In Section C of that chapter, the
theoretical basis for the alternative — that such
schooling would affect the income of others — was
given. This theory gave two mechanisms by which this
effect could be transmitted — indirect market effects
and spillover effects. Section B of Chapter III produced
a theoretical expectation that the influence postulated
would be stronger among those who had less schooling
themselves. Section D of that chapter argued that there
was a strong likelihood that the effect would be stronger
than measured by the data of this study, though there is
the possibility that a type I error will be made or that
the theoretical framework and data used will produce a
mistaken positive answer to the question.
118
The statistical evidence of this study does
overwhelmingly reject the null hypothesis. There is a
strong influence between Sj and Y, the schooling of
co-workers and income. There is also a strong as
sociation between schooling in the community (Sc) and
income. However, there is not a significant, reliable
relationship between income and the corresponding age
variables, the other proxy variable for human capital.
Statistical verification of the hypothesis that
the impact of the schooling of fellow workers would be
inversely related to the schooling of the individual
himself was also found.
In addition to these findings, it was also found
that the relationships within the minority communities
in the United States were significantly different than
among the majority. Especially important was the
discovery that the individual's own schooling was
relatively less important among the minority.
CHAPTER V
CONCLUSIONS
The theoretical basis of the null hypothesis of
this study was developed in Section A of Chapter III. If
markets were perfectly competitive and all goods and all
factors packageable and divisible, then the income of
people would be perfectly correlated with their own
possession of human capital. Therefore, the influence
of the human capital in others would have no relationship
to an individual's income unless different industries
had work forces that were grouped rather uniformly by
level of schooling. Even then, in a statistical analysis
there would be no additional variance left to explain
once the human capital within the individual had been
included in the equation.
The evidence of this study, however, is that
the average schooling both in the community and in the
cooperating work force has statistically significant
regression coefficients in a multiple regression
equation containing the individual's age and level of
schooling. This was true for both sexes in both races
and for nearly all of the dozens of subgroups for which
119
120
regressions were run.
The corresponding age variable for the community
and the job were found to have small coefficients and to
contribute very little to the reduction of variance when
very large samples were involved. When subgroups with
smaller numbers of individuals were involved, these age
variables were most likely to be statistically insigni
ficant. The age of the individual, however, was highly
significant.
In Section C of Chapter III (p. 76) a theoretical
basis was developed for the expectation of a relationship
between an individual's income and the average school
level in the community in which he lived. Such a
relationship was found.
Section B of Chapter III and pages 76-79 of
Section C gave two different reasons to expect the
schooling of fellow workers to have an impact on the
income of the individual. Such impact was found in the
empirical work.
In addition to those basic questions which were
the motivation of this research project, Section B of
Chapter III developed a theoretical basis for expecting
the impact of the schooling of others to be less the more
schooling the individual himself had. Clear evidence
to support this view was found.
121
In addition to these new theoretical results the
work also produced statistical evidence related to the
discrimination in United States society. First, it
appears the discrimination against women may be stronger
than the usual statistical citations would indicate.
These more common figures usually cite just the dif
ferences in the pay between the sexes when they work at
the same job. But, apparently, additional factors are
involved. One of these is that women are usually re
quired to have more education than men in the same jobs.
When the variables of this study were included in a
regression analysis, the coefficient for the sex variable
was a larger fraction of average income than had been
expected.
With regard to racial discrimination, the data
of this study showed that in addition to the much lower
pay rates for minorities when their other characteristics
were similar to the majority, the majority members
actually received more pay when they were otherwise
similar but lived in areas with more minority members.
The data also revealed that for minority members the
characteristics of others among whom they lived and with
whom they worked were much more important than these
characteristics were for majority group members. This
122
evidence is subject to several interpretations, however.
The principal significance of this study is to
give quantitative support to the widely held belief
that schooling is a form of social overhead capital and
that it should therefore be at least in part financed
by the group method, i.e., taxes. A person should be
willing to pay for part of the schooling of others
because he will receive some benefit from this ex
penditure. If schooling were left entirely up to
private decisions, there would be underinvestment in
it because the individual would not consider the return
that others would receive from his becoming more schooled.
The individual would invest in his schooling until the
marginal return to himself would just be equal to the
marginal value of what was given up to get the schooling.
We are concerned here with what Mishan^ calls a
collective good, one which has spillover effects of the
same character as the effects on the decision making unit.
There are many serious cautions and limitations
about the interpretation of these results. A number of
these have been discussed at various points in the text.
^*E. J. Mishan, "The Postwar Literature on
Externalities: An Interpretative Essay," Journal of
Economic Literature, Vol. IX, No. 1 (March 1971),
pp. 1-28.
123
There is, of course, the possibility that a Type II
error has been committed, either in the scatter of the
quantitative results of sampling or in the sense that
another theoretical explanation is just as consistent
with the results obtained and is correct. Then there
is the point that statistical association is always
ambiguous as to direction of causation, if there is any
causation. Other serious limitations are: the data are
self reported data; there is no independent measure of
natural labor; there is no use made of the amount of
physical capital or other resources used in the
production process; the method of identifying co-workers
and community residents is questionable; and the treat
ment of schooling as though a year of it was a homo
geneous item that produced the same effect regardless of
where, when, or on whom applied.
There is, on the other hand, the possibility that
there is more impact than this study shows. All the
"noise" in the system from bad data or random behavior
would cause the significance coefficients to be reduced.
Also, any curvilinear regression will fit data better
than a linear one unless the true relationship is
exactly linear and the sampling has been large and
"perfect." It seems very likely that at least some of
the relationships are not linear.
124
There is another point that can be made. There
may be more productivity impact than there are income
effects. All the monopoly elements in markets and all
the imperfection will cause incomes to differ from
productivity and usually in manners that would reduce
the coefficients of this study.
This seems to be a field worthy of more study.
Especially interesting would be tests to see how
different the relationships were in the 1970 Census.
APPENDIX TO CHAPTER IV
LIST OF SYMBOLS
Y - Income of individual
Ag = Age of individual
SX = Sex of individual
Sc = School level completed by individual
Sc = Average level of school completed
in the community
Ac = Average age of workers in the
community
R_, = Fraction of minority members in the
° community
S< = Average level of school level
completed by co-workers
Aj = Average age of co-workers
Rj = Fraction of minority members among
co-workers
125
BIBLIOGRAPHY
Books
I ---------
! Becker, Gary S. Human Capital. New York: Columbia
j University Press, 1964.
!
Bowman, Mary Jean, and Anderson, C. Arnold. Readings in
the Economics of Education. Mayenne, France:
United Nations Educational, Scientific and
Cultural Organization, 1968.
Clough, S. B., and Cole, C. W. Economic History of
I Europe. Boston: D. C. Heath and Company, 1952.
i
| Denison, Edward F. The Sources of Economic Growth in the
United States and the Alternative Before Us.
New York: Committee for Economic Development,
1962.
i
Dillard, Dudley. Economic Development of the North
Atlantic Community. Englewood Cliffs: Prentice
Hall, Inc. ,'"1967.
Heaton, Herbert. Economic History of Europe. New York:
Harper and Bros., 1948.
Knight, Frank H. Risk, Uncertainty and Profit. New York:
Harper and Row Publishers, Inc., Harper Torchbook
Edition, 1965.
Schultz, Theodore W. The Economic Value of Education.
New York: Columbia University Press, 1963.
Vaizey, John. The Economics of Education. London:
Faber and Faber, 1962.
Vickrey, William S. Microstatics. New York: Harcourt,
Brace and World, Inc., 1964.
126
127
Articles
Abramovitz, Moses. "Economic Growth in the United States:
A Review Article." American Economic Review,
Vol. LII, No. 4, September, 1962, pp. 762-782.
! Becker, Gary S. "Under Investment in College Education."
American Economic Review, Vol. L, No. 2, May, 1960,
pp. 346-354.
i
I
1 # *
Emi, Koichi. "Economic Development and Educational
Investment in the Meiji Era," in Bowman, Mary Jean
Anderson, C. Arnold, Readings in the Economics of
Education, pp. 113-13?^
Hagen, E. E. "The Japan Case." Public Opinion
| Quarterly, Vol. XXII, No. 3.
[ Hansen, W. Lee. "Total and Private Rates of Return to
! Investment in Schooling." Journal of Political
I Economy, Vol. 71, April, 1963, pp. 128-140.
|
I Houthakker, H. S. "Education and Income." Review of
Economics and Statistics, Vol. 41, February, 1959,
pp. 24-28.
Miller, Herman P. "Annual and Lifetime Income in
Relation to Education: 1939-1959." American
Economic Review, Vol. L, No. 5, December, 1960,
ppT-^F2-'9'8 6. --
Mishan, E. J. "The Postwar Literature on Externalities:
An Interpretative Essay." Journal of Economic
Literature, Vol. IX, No, 1, March, 1971,
pp. 1-28.
Schultz, Theodore W. "Investment in Man— An Economist's
View." Social Service Review, Vol. XXXIII, No. 2,
p p . 109-irr-----------------
_. "Investment in Human Capital." American
Economic Review, Vol. LI, No. 1, pp. 1-17.

Linked assets

University of Southern California Dissertations and Theses

Conceptually similar

PDF

An Investigation Into The Use Of The Cost-Benefit Method In Urban Design

PDF

A Constrained Price Discriminator: An Application To The U.S. Post Office

PDF

An Econometric Overhead Model Of An Aerospace Firm

PDF

On The Theory Of Value And Market Syndicalism

PDF

Cross-Sectional Analysis Of Manufacturing Production Functions In A Partitioned 'Urban-Rural' Sample Space

PDF

A Generalized Economic Derivation Of The ''Gravity Law'' Of Spatial Interaction

PDF

Some External Diseconomies Of Urban Growth And Crowding: Los Angeles

PDF

A Theory Of Regional Economic Growth: Growth Poles And Development Axes

PDF

An Econometric Analysis Of The Influence Of Money Supply And And Money Demand Relations In The Determination Of National Income

PDF

Differential Game Theory Approach To Modeling Dynamic Imperfect Market Processes

PDF

An investigation of the Cournot duopoly model with production lags and a lagged, noisy communication channel

PDF

Pollution, Optimal Growth Paths, And Technical Change

PDF

The Determinants Of Growth Differentials And Regional Concentration: A Theoretical And Empirical Investigation

PDF

Production Functions In Korean Manufacturing: An Analysis Of Trade Policyand Its Effect On Technological Change

PDF

On The Dynamics Of Planned Economy: General Theory With Empirical Analysis Of The Hungarian Experience

PDF

Planning For Stability And Self-Reliance: An Evaluation Of Policy Approaches For India

PDF

Some Effects Of Monetary And Fiscal Policy On The Distribution Of Wealth

PDF

A Simple Macroeconomic Model For The Chilean Economy

PDF

Regional Growth In The United States: A Production Function Approach

PDF

Towards A Socioeconomic Theory Of Socialism

Asset Metadata

Creator Ham, Clarence Leroy (author)

Core Title The Influence Of Other People'S Schooling On An Individual'S Income

Degree Doctor of Philosophy

Degree Program Economics

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Economics, General,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Niedercorn, John H. (committee chair), Fox, Frank H. (committee member), Tintner, Gerhard (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-499282

Unique identifier UC11364284

Identifier 7226018.pdf (filename),usctheses-c18-499282 (legacy record id)

Legacy Identifier 7226018

Dmrecord 499282

Document Type Dissertation

Rights Ham, Clarence Leroy

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA