AN ECONOMETRIC ANALYSIS OF THE EFFECTS OF
IQ ON PERSONAL INCOME
BY
ABU ISHAQUE MAHBOOB JALAL
SUBMITTED TO PROFESSORS F. HOWLAND & J. BURNETTE
IN PARTIAL COMPLETION OF THE
REQUIREMENTS FOR ECONOMICS 31
26 APRIL 1999
1
Abstract
This paper mainly explores whether there is any statistically and economically
significant relation between IQ and personal income. Using a sample obtained from
National Longitudinal Surveys of Youth (NLSY), it finds a significant relation between a
person’s percentile score in an intelligence test called Armed Forces Qualification Test
(AFQT) and personal income in the year 1993. It also finds that the influence of
percentile IQ on personal income increases as the level of education increases. Moreover,
the empirical results show that IQ has influences of different magnitudes on personal
income depending on the levels of IQ itself. Thus, it suggests a non-linear relationship
between percentile IQ and personal income.
2
Table of Contents
I.
Introduction
4
II.
Literature Review
6
III. Theoretical Analysis
11
IV. Empirical Results
V.
A.
The Data
15
B.
Presentation and Interpretation of Empirical Analyses
21
Conclusion
40
Appendix A: Sample Questions: Armed Forces Qualification Test
Bibliography
42
44
3
I. Introduction
For years economists have been constantly trying to decipher the reasons behind
the inequality in the distribution of personal income. One of the strongest, and also the
most controversial explanations for the variations in people’s earnings is intelligence,
which is measured and often interchangeably referred to by Intelligence Quotient (IQ).
With an ever-widening gap between the earnings of the rich and the poor despite
seemingly equal opportunities offered by the society, the variations in intelligence level
have received an unprecedented amount of attention and momentum in the current
century. Limited success of the education programs in alleviating this inequality has only
strengthened the initiative to find some factors that is genetically determined, to a large
extent beyond the control of the mankind, and possibly account for the differences in the
ability of people to earn money. Moreover, extensive use of intelligence tests by
educational institutions, employers, and entrepreneurs as a measure of academic
excellence and skill has given rise to the concern that a cognitive elite based on
intelligence level is being created in the modern society1.
The relation between IQ and personal income has been under intense scrutiny.
Though the positive correlation between these two factors has been demonstrated in
many studies, IQ as a determinant of personal income is a problematic idea. A number of
factors other than intelligence level have been considered and demonstrated to be highly
significant in determining the income of an individual. Therefore, it would be an
interesting idea to explore whether IQ or intelligence level has any significant
relationship with personal income after controlling for some of the most important of
4
those factors. It will also provide us with an insight on how the relation (if any) between
IQ and personal income behaves.
This paper is intended mainly to explore statistically and economically significant
relationships between IQ and personal income. To this end, I will first provide a
discussion on some of the important studies conducted on this topic in the past. Then I
will go on to explaining some analytical backgrounds of my topic. Later in this paper I
will present the sample under consideration and the results of the empirical analyses.
Finally, I will draw a conclusion on the basis of my findings.
1
Herrnstein, Richard J. and Murray, Charles, The Bell Curve: Intelligence and Class Structure in American
Life, New York: The Free Press, 1994.
5
II. Literature Review
The relation between the level of intelligence, usually measured in IQ, and
income has been an issue of extensive discussion and research to economists as well as
other social scientists. Though very few researchers deny the importance of IQ in shaping
different aspects of a person’s life, the main debate centers on the types and magnitudes
of these effects. A careful study of the available literature on this topic would easily show
different kinds of conceptions about the effects of IQ on a person’s income. They range
from the viewpoint that IQ is the major determinant of a person’s earnings to the idea that
IQ has a minimal, if any, effect on income. There are also researchers who think that the
effects of IQ are important but that it works indirectly in determining income.
In their book The Bell Curve: Intelligence and Class Structure in American Life
(1994), psychologist Richard J. Herrnstein and political scientist Charles Murray provide
an extensive discussion on the effects of IQ on different aspects of American life. They
consider IQ to be mostly an inherited trait and connect differences in intelligence levels
to differences in wealth, income, education, unemployment, idleness, injury, family
structure, crime and such other issues. In their analyses Herrnstein and Murray use data
accumulated through National Longitudinal Survey of Youth (NLSY) – an ongoing
survey (starting in 1979) of a nationally representative sample of 12686 people who were
between 14 and 23 years of age in 1979. As a measure of cognitive ability2 they apply
percentile scores obtained from an intelligence test taken by all participants in NLSY
called Armed Forces Qualification Test (AFQT). It is worth mentioning that AFQT is
assembled from an average of four of the ten achievement tests designed to measure
2
Herrnstein and Murray use IQ and cognitive ability interchangeably.
6
proficiency in vocabulary, basic science, arithmetic operations, etc. in an armed forces
training program named Armed Services Vocational Aptitude Battery (ASVAB). From
their analyses Herrnstein and Murray obtain empirical results showing strong association
between low scores in AFQT and being in poverty. Results show that “whites with IQs in
the bottom 5 percent of the distribution of cognitive ability are fifteen times more likely
to be poor that those with IQs in the top 5 percent.” (Herrnstein and Murray, p. 127) The
authors also find poverty, unemployment, and welfare dependency to be more strongly
associated with IQ than socioeconomic status (which includes information about
education, occupation, and income of the parents of the participants). Using linear
logistic model of the form:
logit (p) = Log (p/(1-p)) =  +  x
in the analysis of NLSY data, they decide that low intelligence translates into a
comparatively high risk of poverty. Moreover, Herrnstein and Murray believe that ethnic
inequalities could be attributed, to a large extent, to the differences in their levels of
intelligence.
The viewpoints expressed by Herrnstein and Murray as well as their methods of
analyzing data have been under constant criticism by many researchers. Such a critique is
James J. Heckman’s article “Lessons from the Bell Curve” published in Journal of
Political Economy (1995). Though the author does not deny the important role of IQ in
determining the earnings of a person, he is not ready to accept it to be the most important
factor. He provides five main reasons that might disprove the claims of The Bell Curve.
First, he finds that AFQT fails to explain a significant portion of the variability in low
wages. The highest R2 explained by AFQT is less than 22 percent in log wages. Hence,
7
there must be factors other than IQ that explain a significant portion of the variability
across persons’ earnings. Secondly, AFQT scores are confounded by years of schooling.
In this context the author mentions the findings of Neal and Johnson (1994)3 that one
more year of schooling can raise AFQT scores by 0.22 standard deviations for men and
by 0.25 standard deviations for women. It brings forth the concern that maybe AFQT is
not an effective measure of the intelligence of a person. Moreover, the gap of AFQT
scores between whites and blacks can almost be eliminated through four additional years
of education for blacks. Thirdly, Herrnstein and Murray attribute inadequate importance
to the role of education in explaining the differences in income. Here the author quotes
the findings of Taber (1994)4: “on average, an extra year of schooling … increases
earnings by at least a substantial 6-8 percent.” (Heckman, 1111) Fourthly, Heckman
doubts the precision of Herrnstein and Murray’s use of the variable that describes
socioeconomic status of the participants of NLSY. The AFQT was conducted to persons
who were between 14 and 23 years of age in 1979. On the other hand, the variable
‘Socioeconomic Status’ (SES) includes education, occupation, and family income
measured in one year. Therefore, it is not likely that one year’s situation will describe 14
to 23 years of socioeconomic status of the participants. Finally, Herrnstein and Murray
misunderstand the ability of improvements in technology and management skills.
Through the use of better entrepreneurs and technology, even the low-skilled persons
could be utilized and included in the labor force. These kinds of changes would make the
effects of IQ on income comparatively smaller.
Neal, Derek and Johnson, William, “The Role of Pre-market Factors in Black-White Wage Differences”,
Manuscript, Chicago: University of Chicago, November 1994.
4
Taber, Christopher, “The Rising College Premium in the Eighties: Return to College or Return to
Ability?” Manuscript, Chicago: University of Chicago, November 1994.
3
8
Despite the vehement criticisms of the studies of Herrnstein and Murray, there are
many other studies that show a positive relation between the level of intelligence and
earnings. Such a study is illustrated in the article “Higher Education, Mental Ability, and
Screening” by Paul J. Taubman and Terence J. Wales published in The Journal of
Political Economy (1973). Here the authors operationally defined mental ability (or
intelligence level) to represent mathematical ability, coordination, verbal ability, and
spatial perception. In their analysis, the authors used regression analysis allowing for
non-linear effects of intelligence and included only the top half of the mental ability
distribution. They used scores from an intelligence test named Aviation Cadet Qualifying
Test (ACQT) as a measure of the IQ of the participants. ACQT is composed of seventeen
tests that measure abilities such as mathematical and reasoning skills, physical
coordination, reaction to stress, and spatial perception. Taubman and Wales (1973) found
that of the abilities mentioned above, only the mathematical ability is a statistically
significant determinant of a person’s income. It suggests limited overall influence of IQ.
They also found that though mental ability has very little influence on earnings in the
initial level, the influence grows over time. The rate of growth is higher for persons with
graduate training and higher mental ability.
One of the popular explanations offered to account for income inequality is that
additional years of schooling (up to a certain level) increase a person’s earnings.
However, there are debates whether this education – income relation is overestimated for
not including ability differences in the analysis. An attempt to explore this question after
controlling for ability is a central topic of the article “Education, Income, and Ability” by
Zvi Griliches and William M. Mason published in The Journal of Political Economy
9
(1972). They apply linear regression model on a 1964 sample of U. S. military veterans
accumulated through Current Population Survey (CPS). IQ scores from AFQT were used
as a measure of intelligence. The authors found that the coefficient of the variable
measuring education in the regression equation that did not include ability was 0.0528.
After including ability into the equation, the coefficient turned out to be 0.062. The
authors considered the difference (only 12%) to be not very significant. Moreover, the
results obtained by the authors show very little significance of intelligence level in
determining income. It suggests that leaving out ability (or IQ) does not necessarily lead
education – income relation to be overestimated. Thus, totally contrary to Herrnstein and
Murray's viewpoints, the authors decide,
“If AFQT is a good measure of IQ and if IQ is largely inherited, then the direct
contribution of heredity to current income is minute.” (Griliches and Mason, p.
S99)
10
III. Theoretical Analysis
Intelligence generally refers to the ability of a person to adapt effectively to his
surroundings and to exploit the available opportunities for his well being. In doing so an
intellectual individual brings about changes in himself, tries to change his environment
and/or shifts to a new setting. Social scientists agree that this kind of successful
adaptation essentially necessitates superiority in a number of cognitive processes –
perception, memory, reasoning, learning, creativity, faculty, problem solving etc.
However, intelligence is not necessarily considered an excellence in a single ability but
an effective combination of the abilities. Similarly, an individual’s income significantly
depends on his ability to demonstrate expertise in performing a job. It is theoretically
plausible to assume that a person with superiority in those cognitive processes would
have a better chance of performing the job efficiently. Thus, an employer would get
better return from employing a person with higher intelligence and would be ready to pay
more for his service. In other words, since Wage = Marginal Product of Labor, a person
with higher cognitive abilities will have higher productivity and thus higher earnings.
Therefore, we can assume that if it is possible to measure the intelligence numerically, we
will find a positive correlation between intelligence level and personal income.
The most prevalent means of measuring a person’s intelligence level is through
Intelligence Quotient or IQ. Most of the intelligence tests today measure abilities such as
problem solving, judgment, comprehension, and reasoning. The scores obtained in these
tests are computed on the basis of certain statistical distributions (usually Normal
Distribution). However, a large quantity of debates has centered on the measurability of
intelligence. Intelligence is mostly an abstract idea. It is also considered to be, in large
11
part, genetically determined5. Though a statistical measure of a person’s correct
responses to an intelligence test is attainable, it is hard to determine conclusively which
of the cognitive processes shape intelligence. Thus, no intelligence test can give a
definitive picture of a person’s intelligence level. However, most social scientists believe
that a well-designed intelligence test can give a good numerical measurement of the
intelligence level (obviously with a certain degree of error) of an individual.
How intelligence level influences a person’s income is also subject to an
extensive debate. Herrnstein and Murray (1994) offer the idea of the formation of a
“cognitive elite” though screening of people on the basis of their intelligence level, who
finally end up being highly paid in their jobs. Through anecdotal descriptions of the
development of the American society in the second half of the current century, they
observe that America is too much dependent on IQ in making its decisions. This
screening based on IQ seriously starts at end of the high-school level when students apply
to Colleges. Since the number of institutions that offer quality education is remarkably
limited, a large number of students compete to get into these few ‘elite’ colleges. These
prestigious institutions pick the best and intelligent students depending on IQ scores
(such as SAT scores) and interview. When these students graduate, they get into
prestigious jobs and earn more money than students of normal intelligence level. Thus, a
cognitive class based on intelligence level is formed. On the other hand, the employers
always try to employ the best persons they can find for a job. Naturally, a person with
higher intelligence level will show better ability to master the job, to adapt to the new
5
Here it is necessary to distinguish between education and intelligence. Education is generally thought to
be a way of transmitting society’s knowledge and values from generation to generation. The characteristics
and directions of education are determined by the society. On the other hand, intelligence is a trait that is
mainly genetically determined and independent of society’s influences.
12
settings, to climb up the corporate ladder, and thus to be highly paid. Therefore, it is
possible to find a positive relation between IQ and personal income.
The relationship between IQ and personal income is often discounted through the
argument that it is almost impossible to unscramble the effects of education and
intelligence level on personal income. A person with a higher intelligence level has a
better chance of completing higher level of academic education. Moreover, it is an
established fact that up to a certain point, one additional year of education increases a
person’s earning by a statistically significant amount. Furthermore, education provides an
individual with vital knowledge and skill necessary to adapt to the environment. It also
trains a person to employ his cognitive processes more effectively.
It is, therefore, necessary to perform an empirical analysis to find out whether
intelligence level or IQ has a ‘significant’ effect on personal income after controlling for
Education and other confounding variables. A regression analysis is most appropriate in
such kind of analysis. A typical multi-variable regression model may be of the form:
Y = 0 +  1 * X1 +  2 * X2 +  3 * X3 + … … … … +  n * Xn + 
Where,
i
= Co-efficient parameters of the independent variables
 = an error term
Here, a box model is necessary to model the error term . We can use the
Standard Econometric Gaussian Error Box Model. However, some assumptions are
indispensable for the use of the GEB. We have to assume that the average of the box is
zero, the errors are identically distributed, independent of each other, and not correlated
with any of the independent variables. It is probable that there are violations of these
13
assumptions in the sample. However, we can easily find out the violations during the
empirical analysis and correct as much as possible by using different statistical tools.
Aside from the regression analysis, we can use other statistical methods, such as
correlation, elasticity, graphs, etc. to explore the statistical and economic significance of
the effects of IQ on personal income.
14
IV. Empirical Results
A. THE DATA:
The data I will use in my empirical analysis is obtained from National
Longitudinal Surveys: Youth 1979 - 1994 Public Codebook: Version 7.0.4. The National
Longitudinal Surveys of Youth (NLSY) is conducted by the U. S. Bureau of the Census
in cooperation with some other institutions such as U. S. Bureau of Labor Statistics,
NORC – University of Chicago, U. S. Department of Health and Human Services, U. S.
Department of Defense and Armed Services, U. S. Department of Education, etc. Now
the data is gathered by National Opinion Research Council (NORC) under the
supervision of the Center for Human Resources Research, Ohio State University. It is an
ongoing survey of nationally representative youths who were between 14 and 22 years
old in 1979 – the starting year of the survey. The number of participants was initially
12686. The sample includes significant number of participants (more than their national
percentile representation) from minority groups such as Blacks, Hispanics, and lowincome Whites. This database is particularly interesting in a sense that it is longitudinal
and thus helps us follow the changes in the same participants over time. It also allows us
explore information about a sample that combines a number of elements that otherwise
have to be studied separately.
The dependent variable in my empirical analysis is Personal Income. It shows
the amount in dollars each participant received from wages, salary, commissions, or tips
from all jobs (except for money received from military service), before deductions for
taxes or anything else in the year 1993. It also includes incomes from agriculture, nonfirm business, partnership, and professional practice. My sample excludes all the
15
participants who had income of 0 dollars in 1993. It is done mainly to eliminate the effect
of a large number of 0 dollars from my analysis. Here it is noticeable that the number of
participants with 0 dollars of income in 1993 is 412. Among them a significant portion
(186 participants) has completed 12 years of education. Thus, one of the possible reasons
for 0 dollars income is that the participants just have finished high school (or dropped out
of school or college) and have not got any job yet or doing something else. Moreover, if a
person is not in the labor force, we cannot tell what amount he might have earned if
working.
The independent variable that will be the main focus of my empirical analysis is
Percentile IQ. Data represent Profiles, Armed Forces Qualification Test (AFQT)
percentile score - revised 1989. The IQ scores mentioned here are expressed in
percentiles. The percentile scores for AFQT are obtained from a test referred to as the
“Profiles of American Youth” conducted by NORC representatives among almost all the
participants of the NLSY. Participants with age less than 17 years in 1980 were not
allowed to take the test. It is worth mentioning that “Profiles of American Youth” was
undertaken during the summer and fall of 1980 as an effort to update the norms of the
Armed Services Vocational Aptitude Battery (ASVAB) by the U. S. Departments of
Defense and Military Services. The ASVAB attempts to measure participants’ skill and
knowledge in the areas of (a) general science; (b) arithmetic reasoning; (c) word
knowledge; (d) paragraph comprehension; (e) numerical operations; (f) coding speed; (g)
auto and shop information; (h) mathematics knowledge; (i) mechanical comprehension;
and (j) electronics information6. The raw scores obtained in ASVAB are processed to
Center for Human Resource Research, The Ohio State University, NLS Users’ Guide 1995, Ohio: The
Ohio State University, 1995.
6
16
obtain AFQT scores. The percentile AFQT scores used in my analysis was calculated
through a five-stage process:
(a) computing a verbal composite score by summing word knowledge and paragraph
comprehension raw scores;
(b) converting sub-test raw scores for verbal, math knowledge, and arithmetic reasoning;
(c) multiplying the verbal standard score by two;
(d) summing the standard scores for verbal, math knowledge, and arithmetic reasoning;
and finally,
(e) converting the summed standard score to a percentile.7
In calculating percentile scores for AFQT, the scores from the following sections of
ASVAB were not used: (a) general science, (e) numerical operations, (f) coding speed,
(g) auto and shop information, (i) mechanical comprehension, and (j) electronics
information.
In my analysis I will also include a number of control variables. The control variables
are Totally Fit, White, Male, Family Size, Married, Age, Urban Residency,
Education, And Experience A short description of the variables are included in the
following table:
VARIABLE NAME
Personal Income
DESCRIPTION
Personal Income in 1993.
Data show amount in dollars received from wages,
salary, commissions, or tips from all jobs (except for
money received from military service), before
deductions for taxes or anything else. This sample
includes only persons with personal income greater
than 0 as in 1993.
7
Ibid.
17
Percentile IQ
Percentile score in an IQ test AFQT.
Data represent Profiles, Armed Forces Qualification
Test (AFQT) percentile score – revised 1989.
Totally Fit
It’s a Dummy Variable.
Data show whether health condition limits the amount
of work respondent can do. If it does limit, respondent
is considered not totally fit for work. If not, respondent
is considered totally fit for work. The data contains
information as of 1994.
White
0 = Not Totally Fit
1 = Totally Fit
It’s a Dummy Variable.
Male
0 = Others (Black, Hispanic, Asian, etc.)
1 = White
It’s a Dummy Variable.
Family Size
Married
0 = Female
1 = Male
Data show total number of members in respondent’s
family in year 1994.
It's a Dummy Variable.
Data show whether the respondents are married or not
as of the year 1994.
Age
0 = Others (Never Married, Divorced,
Separated, etc.)
1 = Married
Age in years at interview date.
Survey year: 1994
Age Range: 29 – 37
Urban Residency
Data show whether respondents’ current residence
urban or rural in 1994.
It’s a dummy variable.
0 = rural
1 = urban
18
Education in years.
Education
Data represent highest grade completed by the
respondents as of May 1 of 1994.
Experience in years as in 1994.
Experience
It’s a created variable.
EXPERIENCE = AGE – 6 – EDUCATION
Table IV.A.1: Description of the Variables
SOURCE: National Longitudinal Surveys: Youth 1979 - 1994 Public Codebook: Version
7.0.4.
The JMP outputs of the summery statistics of the variables are as follows:
Variable
Mean
SD
Max
Min
n
Personal Income
24568.72
19498.14
167697
6
6417
42.429
28.474
99
1
6417
Totally Fit
0.97
0.16
1
0
6417
White
0.668
0.471
1
0
6417
Male
0.527
0.499
1
0
6417
Family Size
3.138
1.553
14
1
6417
Married
0.576
0.494
1
0
6417
Age
32.908
2.234
37
29
6417
Urban Residency
0.806
0.395
1
0
6417
Education
13.275
2.388
20
1
6417
Experience
13.634
3.248
29
3
6417
Percentile IQ
Table IV.A.2: Summery Statistic of the Variables.
19
Here, one thing is noticeable that the minimum values of most of the variables
start at a very low number. For example, for Percentile IQ the minimum value is 1
percentile, for Personal Income 6 dollars per year, for Family Size 1, for Education 1st
grade completed, and for Experience 3 years. Moreover, in the case of Percentile IQ the
PERCE NTILE IQ
0
10
20
30
40
50
60
70
80
90
100
Picture IV.A.1: JMP output of the distribution of PERCENTILE IQ.
number of people below 50th percentile and above 50th percentile are not equal. These
are mainly due to the fact that NLSY sample includes significant number of participants
(more than their national percentile representation) from minority groups such as Blacks,
Hispanics, and low-income Whites and from special interest groups such as mentally
retarded, chronic alcoholic, etc.
20
B. PRESENTATION AND INTERPRETATION OF EMPIRICAL
ANALYSES:
The general form of the regression equation I will use to estimate and understand
the effects of a person’s IQ on his personal income is as follows:
Personal Income =  0 +  1 * Percentile IQ +  2 * Totally Fit +  3 * White +  4 *
Male +  5 * Family Size +  6 * (Family Size * Male) +  7 * Married +  8 * (Married
* Male) +  9 * Urban Residency +  10 * Education +  11 * (Education * Male) +  12
* Experience +  13 * Experience2 + 
Where,  i = Co-efficient parameters of the independent variables
 = an error term
In this case, as mentioned before, I am using a Standard Econometric Gaussian
Error Box Model to model the error terms. The error term  reflects the influences of
omitted variables, measurement error, and just pure luck. As requirements for the use of
the Gaussian Error Box Model, I assume that
a) the average of the box is zero,
b) the errors are identically distributed,
c) the errors are independent of each other, and
d) the errors are not correlated with any of the independent variables.
However, there may be violations of these assumptions in my sample. I will try to find
out and discuss possible violations of these assumptions during my empirical analysis of
the data.
21
There are many ways to address the questions whether IQ has any effect on
personal income and what the types of these effects are. The empirical section of my
paper will include the following three sections:
(1) A general discussion of the findings when I estimate the regression equation
using all the independent variables.
(2) In the second section, I will explore the question discussed by Taubman and
Wales (1973) that the influence of IQ on personal income increases as the
level of education increases.
(3) And finally, I will explore whether IQ has influences of different magnitudes
on personal income depending on the levels of IQ itself.
22
1. GENERAL FINDINGS:
In this section I use the general form of the regression model to estimate the
coefficients of the dependent variables.
The JMP output of the regression equation is:
PERSONAL INCOME
Independent
Coefficient
Variable
estimate
SE
t-ratio
p-value
Intercept
-6465.841
3563.593
-1.81
0.0697
Percentile IQ
147.49956
9.339927
15.79
<.0001
Totally Fit
4811.3633
989.0609
4.86
<.0001
White
917.5204
393.252
2.33
0.0197
Male
-2798.033
2158.105
-1.30
0.1948
Family Size
-1072.882
182.1491
-5.89
<.0001
Family Size * Male
475.78668
238.3705
2.00
0.0460
Married
226.84537
566.8916
0.40
0.6891
Married * Male
8972.4293
756.6521
11.86
<.0001
Urban Residency
2343.5024
430.46
5.44
<.0001
Education
1592.1921
151.5182
10.51
<.0001
Education * Male
361.60358
149.9005
2.41
0.0159
Experience
-1104.947
296.2332
-3.73
0.0002
Experience2
52.271735
9.598935
5.45
<.0001
Table IV.B.1: JMP output of the regression model
23
From the result we can see that the co-efficient estimate for the variable Percentile
IQ is positive. It suggests a positive relationship between Personal Income and Percentile
IQ. We can interpret the slope estimate as: holding every other control variables constant,
for every one-percentage point increase in Percentile IQ, Personal Income increases by
147.5 dollars per year give or take 9.34 dollars per year. This result agrees with the
notion that personal income increases as the IQ level increases, ceteris paribus. However,
to find out whether the parameter estimate of the independent variable Percentile IQ is
statistically significant, we can conduct a t-test:
Null Hypothesis:  1 = 0 meaning that ceteris paribus, Percentile IQ has no
effect on Personal Income.
Alternative Hypothesis:  1 ≠ 0 meaning that ceteris paribus, Percentile IQ
changes as Personal Income changes.
Here the t-statistic reported by JMP for this hypothesis testing is 15.79 and the pvalue is less than 0.0001. That means that if the null hypothesis were true, the probability
of getting such a result or more extreme results just due to chance is less than 0.0001.
Thus, we can comfortably reject the null hypothesis and decide that there is a statistically
significant association between Percentile IQ and Personal Income.
From the regression output we find a statistically significant relationship between
Percentile IQ and Personal Income. However, the question remains whether this
relationship has any economic significance. To find out the economic importance of this
association, I assume that there are two persons with percentile IQ 50 (normal) and 90
(bright). I also assume that both of them are totally fit to work, White married male with
family size of 4, and urban resident with 12 years of education and 2 years of experience.
24
After holding these situations constant, the person with a Percentile IQ of 50 earns
34439.12 dollars per year and the person with a Percentile IQ of 90 earns 40339.11
dollars per year. This is a difference of about 5900 dollars per year. This certainly has
economic significance. To further illustrate the situation we can draw a graph under the
same assumptions as before:
Personal Income ($)
Personal Income as a Function of Percentile IQ
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
Personal Income
0
20
40
60
80
100
Percentile IQ
Picture IV.B.1: Personal Income as a Function of Percentile IQ
We can also look at relative importance between Percentile IQ and Education.
The coefficient estimate for Percentile IQ is 147.50 and the coefficient estimate for
Education is 1592.19. It suggest that to compensate for decrease in Personal income due
to 1 less year of education one has to have about 11 more percentile units of IQ. We can
also look at some elasticities to find out the responsiveness of Personal Income for
percentage changes in Percentile IQ and Education. Here,
Percentile IQ elasticity of Personal Income is 0.6904
Education elasticity of Personal Income for male is 6.5243
Education elasticity of Personal Income for female is 11.5336
25
These results show that Personal Income is more responsive to percentage changes in
Education than to percentage changes in Percentile IQ. It contradicts the notion of
Herrnstein and Murray (1994) that IQ is the most important factor in determining
personal income. Percentile IQ is important in determining personal income, but it is not
the most important factor.
It is worth mentioning that I used (General Least Squares) GLS to estimate the
regression equation. The reasons are described in the next section where I explore the
validity of the box model.
26
THE VALIDITY OF THE BOX MODEL:
Now I would like to discuss the possible violations of the assumptions of the
Standard Econometric Gaussian Error Box Model. Again the assumptions are:
a) the average of the box is zero,
b) the errors are identically distributed,
c) the errors are independent of each other, and
d) the errors are not correlated with any of the independent variables.
These assumptions are necessary. Otherwise, this Ordinary Least Squares (OLS) model
no longer remains the most precise way to analyze data or the Best Linear Unbiased
Estimator (BLUE). The possible violations of this model include heteroscedasticity and
serial correlation. Moreover, multi-collinearity causes some problems with the
interpretations of the parameter estimates obtained from the regression model.
Heteroscedasticity occurs when the error terms for each observation do not have
constant standard deviations. It strongly violates the assumption that the error terms are
identically distributed. It often causes the OLS to estimate the standard errors of the
coefficient estimates imprecisely. Heteroscedasticity is generally found in cross-sectional
data. The graph of the residuals produced by JMP is as follows:
27
Picture IV.B.2: Residual Personal Income as a function of Percentile IQ
Eyeballing the graph of the residuals reveals the existence of heteroscedasticity in this
model. I also conduct the Goldfeld–Quandt test for detecting heteroscedasticity. The G–Q
statistic is 2.41319 and the p-value is virtually 0. It clearly demonstrates the existence of
heteroscedasticity in my sample. However, we have to remember that I included a large
number of independent variables in my regression model and my sample is obtained from
a nationally representative survey. Though there is apparently no simple way of getting
rid of the heteroscedasticity in such kind of model, I use trial and error method. Finally, I
came up with (Percentile IQ)-0.6 as weight. In this case the G–Q statistic is 0.986995 and
the p-value is 0.618553. It suggests that I have been, at least significantly, able to get rid
of the heteroscedasticity. It is noticeable here that due to the use of weight my model
goes from being called Ordinary Least Squares (OLS) to General Least Squares (GLS).
28
A problem with using a large number of independent variables and interaction
terms is the existence of multi-collinearity. Multi-collinearity occurs when two of the
independent variables are highly correlated. However, usually a correlation of 0.8 or
lower does not cause any statistical concern. In case of my model, there are several
incidents where there are high correlations between two of the independent variables. For
example, the correlation between Percentile IQ and Percentile IQ*Education 0.9695,
between Percentile IQ and Percentile IQ2 0.9653, between Male and Education*Male
0.9652, and between Experience and Experience2 0.9847. The main effect of multicollinearity is that it inflates the SEs of the individual slope estimates. However, multicollinearity does not bias the parameter estimates or estimates of the SEs. A large data-set
offsets some effects of multi-collinearity. Moreover, the JMP estimates of my regression
equations do not show the existence of any multi-collinearity.
29
2. DOES THE INFLUENCE OF IQ ON PERSONAL INCOME INCREASE AS
THE LEVEL OF EDUCATION INCREASES?
One of the findings in the study conducted by Taubman and Wales (1973) is that
the influence of IQ on personal income increases as the level of education increases. In an
effort to duplicate their result I estimate the following regression model:
Personal Income =  0 +  1 * Percentile IQ +  2 * Totally Fit +  3 * White +  4 *
Male +  5 * Family Size +  6 * (Family Size * Male) +  7 * Married +  8 * (Married
* Male) +  9 * Urban Residency +  10 * Education +  11 * (Education * Male) +  12
* Experience +  13 * Experience2 +  14 * (Percentile IQ * Education) + 
Where,  i = Co-efficient parameters of the independent variables
 = an error term
The JMP output of this regression model is:
PERSONAL INCOME
Independent
Coefficient
Variable
estimate
SE
t-ratio
p-value
Intercept
-6704.573
3556.722
-1.89
0.0595
Percentile IQ
-61.32484
41.37175
-1.48
0.1383
Totally Fit
4781.0326
987.0885
4.84
<.0001
White
971.32375
392.5983
2.47
0.0134
Male
-3017.152
2154.179
-1.40
0.1614
Family Size
-1110.126
181.9247
-6.10
<.0001
30
Family Size *
471.30269
237.8925
1.98
0.0476
Married
255.95844
565.7791
0.45
0.6510
Married * Male
8957.6212
755.1353
11.86
<.0001
Urban Residency
2311.9904
429.6371
5.38
<.0001
Education
1169.8261
171.7908
6.81
<.0001
Education * Male
367.57373
149.6033
2.46
0.0140
Experience
-285.3075
335.3083
-0.85
0.3949
Experience2
24.033374
11.02175
2.18
0.0293
Percentile IQ *
15.271646
2.947788
5.18
<.0001
Male
Education
Table IV.B.2: JMP output of the regression model
In the output of the regression model we can see that the slope estimate for the
interaction term Percentile IQ * Education is positive. The estimate is 15.27. It means
that ceteris paribus, for every one-year increase in education level, the slope estimate of
the variable Percentile IQ increases by 15.27 units give or take 2.95 units. If Education is
0, the slope estimate of the variable Percentile IQ equals to –61.325, which implies no
positive influence of IQ on income. However, as education level increases, the effect of
percentile IQ on income becomes positive and keeps getting bigger. To find out whether
the parameter estimates of the independent variable Percentile IQ and interaction term
Percentile IQ * Education are statistically significant, we can conduct an F-test:
Null Hypothesis:  1 =  14 = 0 meaning that ceteris paribus, Percentile IQ or its
interaction with Education has no significant influence on
31
Personal Income.
Alternative Hypothesis: At least one of  1 and  14 is not zero meaning that ceteris
paribus, at least Percentile IQ or its interaction with Education has
significant influence on Personal Income.
In this case, the Unrestricted Model is the same as the one used to estimate the model in
this section. For the Restricted Model we assume that the values of  1 and  14 are zero.
The F-statistic is 138.618. The p-value for an F – distribution with 2/6402 degrees of
freedom is virtually 0. Therefore, we reject the null that  1 =  11 = 0 and decide that at
least Percentile IQ or its interaction with Education has significant influence on Personal
Income.
From the above discussion, we find support for the comment of Taubman and
Wales (1973) that the influence of IQ on personal income grows as the level of education
increases.
To estimate the economic significance of the findings I assume that there are three
person with same IQ level (50 in percentile unit) but different Education levels – 8th
grade completed, high school graduate (12 years of education), and college graduate (16
years of education). I also assume that all of them are totally fit to work, White married
male with family size of 4, and urban resident with 2 years of experience. The person
who completed 8 years of education is predicted to earn 22942.84 dollars per year, the
person with 12 years of education is predicted to earn 29071.97 dollars per year, and the
person with 16 years of education is predicted to earn 38275.90 dollars per year. Now, if
we change the IQ level to 80 percentile units (with the same assumptions), the person
who completed 8 years of education is predicted to earn 24768.29 dollars per year. The
32
person with 12 years of education is predicted to earn 32730.02 dollars per year, and the
person with 16 years of education is predicted to earn 43766.54 dollars per year. It is
clear that as the level of Percentile IQ increases, the differences among the three persons
get wider. It shows that the influence of IQ on personal income grows as the level of
education increases. To further illustrate the situation we can draw a graph under the
same assumptions as before:
Personal Income as a Function of Percentile IQ for
Different Levels of Education
Personal Income ($)
50000
45000
40000
35000
Education 8 yrs
30000
Education 12 yrs
Education 16 yrs
25000
20000
15000
0
20
40
60
80
100
Percentile IQ
Picture IV.B.4: Personal Income as a Function of Percentile IQ
In estimating this regression model, I used GLS. I did not encounter any biased
estimate that could have existed due to the high correlation between the variables
Percentile IQ and Percentile IQ * Education.
33
3. DOES IQ HAVE INFLUENCES OF DIFFERENT MAGNITUDES ON
INCOME DEPENDING ON THE LEVELS OF IQ ITSELF?
To answer the question whether IQ has influences of different magnitudes on
personal income depending on the levels of IQ itself, I divided percentile IQ into five
different levels according to the way described by Herrnstein and Murray. The groups are
as follows:
COGNITIVE GROUP
PERCENTILE IQ
Very Bright
95% and above
Bright
75% to 95%
Normal
25% to 75%
Dull
5% to 25%
Very Dull
5% or below
In this case the regression model is:
Personal Income =  0 +  2 * Totally Fit +  3 * White +  4 * Male +  5 * Family
Size +  6 * (Family Size * Male) +  7 * Married +  8 * (Married * Male) +  9 *
Urban Residency +  10 * Education +  11 * (Education * Male) +  12 * Experience +
 13 * Experience2 +  14 * (Percentile IQ * Very Bright) +  15 * (Percentile IQ *
Bright) +  16 * (Percentile IQ * Normal) +  17 * (Percentile IQ * Dull) +  18 *
(Percentile IQ * Very Dull) + 
Where,  i = Co-efficient parameters of the independent variables
 = an error term
34
JMP output for the regression equation is:
PERSONAL INCOME
Independent
Coefficient
Variable
estimate
SE
t-ratio
p-value
Intercept
-6720.99
3571.357
-1.88
0.0599
Totally Fit
4865.095
988.685
4.92
<.0001
White
1044.14
392.1765
2.66
0.0078
Male
-2335.62
2160.633
-1.08
0.2797
Family Size
-1084.071
182.1176
-5.95
<.0001
Family Size *
477.30041
238.2786
2.00
0.0452
Married
280.72311
566.7436
0.50
0.6204
Married * Male
8918.4328
756.4119
11.79
<.0001
Urban
2322.2252
430.2633
5.40
<.0001
Education
1632.1048
150.5992
10.84
<.0001
Education *
323.74371
150.1831
2.16
0.0311
Experience
-1071.752
298.3667
-3.59
0.0003
Experience2
51.274385
9.686319
5.29
<.0001
Very Bright *
200.20158
18.17221
11.02
<.0001
Male
Residency
Male
Percentile IQ
35
Bright *
126.95282
10.85655
11.69
<.0001
120.60891
11.47342
10.51
<.0001
136.69667
30.94712
4.42
<.0001
-199.0129
159.4276
-1.25
0.2120
Percentile IQ
Normal *
Percentile IQ
Dull * Percentile
IQ
Very Dull *
Percentile IQ
Table IV.B.3: JMP output of the regression model
In the estimate of the regression model, we can easily see that the parameter
estimates of the interaction terms get bigger and bigger as the cognitive groups go from
Normal to Very Bright. The p-values for Percentile IQ * Very Dull is not very low.
However, for the terms Percentile IQ * Very Bright, Percentile IQ * Bright, Percentile IQ
* Normal and Percentile IQ * Dull the p-values are extremely low (less than 0.0001) and
thus statistically significant. Therefore, it implies that generally the effect of IQ on
income is bigger when the IQ level itself is higher. It suggests the possibility of a nonlinear relationship between Percentile IQ and Personal Income. To explore it further I
estimate the following model:
Personal Income =  0 +  1 * Percentile IQ +  2 * Totally Fit +  3 * White +  4 *
Male +  5 * Family Size +  6 * (Family Size * Male) +  7 * Married +  8 * (Married
* Male) +  9 * Urban Residency +  10 * Education +  11 * (Education * Male) +  12
* Experience +  13 * Experience2 +  14 * Percentile IQ2 + 
Where,  i = Co-efficient parameters of the independent variables
36
 = an error term
The JMP output of the Model:
PERSONAL INCOME
Independent
Coefficient
Variable
estimate
SE
t-ratio
p-value
Intercept
-6539.134
3564.505
-1.83
0.0666
Percentile IQ
127.10112
23.87248
5.32
<.0001
Totally Fit
4808.8317
989.0753
4.86
<.0001
White
954.08849
395.2235
2.41
0.0158
Male
-2790.967
2158.142
-1.29
0.1960
Family Size
-1078.196
182.2409
-5.92
<.0001
Family Size *
477.39633
238.3794
2.00
0.0453
Married
243.24757
567.1729
0.43
0.6680
Married * Male
8963.4662
756.7218
11.85
<.0001
Urban
2340.2876
430.4786
5.44
<.0001
Education
1595.7637
151.5687
10.53
<.0001
Education *
357.48313
149.9678
2.38
0.0172
Experience
-1068.709
298.7962
-3.58
0.0004
Experience2
50.964214
9.701786
5.25
<.0001
Male
Residency
Male
37
Percentile IQ2
0.2485844
0.26773
0.93
0.3532
Table IV.B.4: JMP output of the regression model
In the estimate of the regression model, we can easily see that the slope estimate
for the independent variable Percentile IQ is 127.10 with an SE of 23.87 and the slope
estimate for the term Percentile IQ2 is 0.248584 with an SE of 0.26773. Both the
estimates are positive. Though the regression estimates suggest a non-linear fit for
Percentile IQ and Personal Income, we need to find out whether the parameter estimates
of the terms Percentile IQ and Percentile IQ2 are statistically significant. We can conduct
an F-test:
Null Hypothesis:  1 =  14 = 0 meaning that ceteris paribus, Percentile IQ or
Percentile IQ2 has no significant influence on Personal Income.
Alternative Hypothesis: At least one of  1 and  14 is not zero meaning that ceteris
paribus, at least Percentile IQ or Percentile IQ2 has significant
influence on Personal Income.
In this case, the Unrestricted Model is the same as the one used to estimate the model in
this section. For the Restricted Model we assume that the values of  1 and  14 are zero.
The F-statistic is 125.122. The p-value for an F – distribution with 2/6703 degrees of
freedom is virtually 0. Therefore, we reject the null that  1 =  14 = 0 and decide that
ceteris paribus, Percentile IQ or Percentile IQ2 has statistically significant influence on
Personal Income. Therefore, we can say that IQ has influences of different magnitudes on
income depending on the levels of IQ itself.
To illustrate this finding I consider a number of people who are totally fit to work,
White married male with family size of 4, and urban resident with 12 years of education
38
and 2 years of experience. That is, they are exactly similar in their physical fitness, race,
marital condition, family size, residency, years of education and experience level. In their
case, the relationship between Percentile IQ and Personal Income behaves in the
following way:
Personal Income as a Function of Percentile IQ
Personal Income ($)
45000
40000
35000
30000
Personal Income
25000
20000
15000
0
20
40
60
80
100
Percentile IQ
Picture IV.B.5: Personal Income as a Function of Percentile IQ
I used the GLS to get rid of heteroscedasticity while estimating the regression
model. I did not encounter any biased estimate that could have existed due to the high
correlation between the variables Percentile IQ and Percentile IQ2.
39
V. Conclusion
The level of IQ of a person appears to have a positive influence on his personal
income. This article inquires whether this relationship is statistically and economically
significant and how these two elements behave mutually. To this end, I try to explore
three hypotheses designed to shed some light on this topic. First, I estimate a General
Least Squares (GLS) multivariate regression model to find out the magnitudes of the
effects of IQ on personal income after controlling for some of the most important factors
considered to be significant determinants of a person’s income. I obtained my sample
from an ongoing survey of nationally representative youths – National Longitudinal
Survey of Youth (NLSY). The regression estimate of the model finds a statistically
significant relationship between percentile IQ and personal income. In the discussion that
followed I notice that this relationship also translates into economic importance.
However, I find, contrary to Herrnstein and Murray’s concept, that IQ is not the most
important determinant of personal income. Personal income, on average, is far more
responsive to percentage changes in education.
As the second hypothesis I examine the question discussed by Taubman and
Wales (1973) that the influence of IQ on personal income increases as the level of
education increases. I estimate a General Least Squares (GLS) multivariate regression
model. The results find this notion to be true. The level of IQ is more significant for a
person who has higher level of education. For people with low levels of education, IQ
does not matter much.
And finally, I explored whether IQ has influences of different magnitudes on
personal income depending on the levels of IQ itself. In the estimate of a General Least
40
Squares (GLS) multivariate regression model I find that the relationship between
Percentile IQ and Personal Income is non-linear. It assumes an increasing concave up
shape. It means that the effect of IQ on personal income increases in an increasing rate.
A main concern related to my model is the presence of heteroscedasticity. Though
I have been able to get rid of a significant portion of this heteroscedasticity, it does not
necessarily mean that I have been able to get rid of it completely. Further statistical
manipulation involving improved means of eliminating heteroscedasticity would
certainly increase the quality of my estimates.
My study finds statistically and economically significant relationships between
the level of IQ and a person’s income. However, it still could not provide satisfactory
answers to some of the statistical and theoretical concerns related to the conception of
intelligence as a determinant of income. I could not include the confounding effects of a
person’s socio-economic status in determining his income. Moreover, the use of AFQT as
a measure of IQ is still not beyond debate. These concerns deserve more attention in
future studies on this topic.
41
Appendix A
SAMPLE QUESTIONS:
ARMED FORCES QUALIFICATION TEST (AFQT)8
Arithmetic Reasoning:
1. If a cubic foot of water weighs 55 lbs., how much weight will a 75½-cubic-foot tank
trailer be carrying when fully loaded with water?
(a) 1,373 lbs.
(b) 3,855 lbs.
(c) 4,152.5 lbs.
(d) 2,231.5 lbs.
Word Knowledge:
1. “Solitary” most nearly means
(a) sunny
(b) being alone
(c) playing games
(d) soulful
Paragraph Comprehension:
People in danger of falling for ads promoting land in resort areas for as little as
$3,000 or $4,000 per acre should remember the maxim: You get what you pay for. Pure
pleasure should be the ultimate purpose in buying resort property. If it is enjoyed for its
8
Fischer, Claude S., Hout, Michael, Jankowski, Martin S., Lucas, Samuel R., Swidler, Ann, and Voss,
Kim, Inequality by Design: Cracking the Bell Curve Myth, New Jersey: Princeton University Press, 1996,
pp. 41 – 42.
42
own sake, it was a good buy. But if it was purchased only in the hope that land might
someday be worth far more, it is foolishness.
Land Investment is being touted as an alternative to the stock market. Real estate
dealers around the country report that rich clients are putting their money in land instead
of stocks. Even the less wealthy are showing an interest in real estate. But dealers caution
that it’s a “hit or miss” proposition with no guaranteed appreciation. The big investment
could turn out to be just so much expensive desert wilderness.
The author of this passage can best be described as
(a) convinced
(b) dedicated
(c) skeptical
(d) believing
Math Knowledge:
1. In the drawing below, JK is the median of the trapezoid. All of the following are true
EXCEPT
(a) LJ = JN
(b) a = b
(c) JL = KM
(d) a
b
43
Bibliography
1. Fischer, Claude S., Hout, Michael, Jankowski, Martin S., Lucas, Samuel R., Swidler,
Ann, and Voss, Kim, Inequality by Design: Cracking the Bell Curve Myth, New
Jersey: Princeton University Press, 1996.
2. Goldberger, Arthur S. and Manski, Charles F., “Review Article: The Bell Curve by
Herrnstein and Murray”, Journal of Economic Literature, 1995, Volume 33, June
1995, pp. 762 – 776.
3. Griliches, Zvi and Mason, William M., “Education, Income, and Ability”, The
Journal of Political Economy, Chicago: University of Chicago, 1972, Volume 80,
Issue 3, Part 2, pp. S74 – S103.
4. Heckman, James J., “Lessons from the Bell Curve”, Journal of Political Economy,
Chicago: University of Chicago, 1995, Volume 103, Issue 5, pp. 1091 – 1120.
5. Herrnstein, Richard J. and Murray, Charles, The Bell Curve: Intelligence and Class
Structure in American Life, New York: The Free Press, 1994.
6. Taubman, Paul J. and Wales, Terence J., “Higher Education, Mental Ability, and
Screening”, The Journal of Political Economy, Chicago: University of Chicago, 1973,
Volume 81, Issue 1, pp. 28 – 55.
7. Woodbury, Robert M., “General Intelligence and Wages”, The Quarterly Journal of
Economics, MIT Press, 1917, Volume 31, Issue 4, pp. 690 – 704.
44