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AN ECONOMETRIC ANALYSIS OF THE EFFECTS OF

IQ ON PERSONAL INCOME

BY

ABU ISHAQUE MAHBOOB JALAL

SUBMITTED TO PROFESSORS F. HOWLAND & J. BURNETTEIN 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.

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Table of Contents

I. Introduction 4

II. Literature Review 6

III. Theoretical Analysis 11

IV. Empirical Results

A. The Data 15

B. Presentation and Interpretation of Empirical Analyses 21

V. Conclusion 40

Appendix A: Sample Questions: Armed Forces Qualification Test 42

Bibliography 44

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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

1 Herrnstein, Richard J. and Murray, Charles, The Bell Curve: Intelligence and Class Structure in American Life, New York: The Free Press, 1994.

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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.

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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.

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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,

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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.

3 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.

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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

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(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)

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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

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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.

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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

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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.

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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 low-

income 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, non-

firm business, partnership, and professional practice. My sample excludes all the

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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

6 Center for Human Resource Research, The Ohio State University, NLS Users’ Guide 1995, Ohio: The Ohio State University, 1995.

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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 DESCRIPTIONPersonal Income 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.

Percentile IQ Percentile score in an IQ test AFQT.

Data represent Profiles, Armed Forces Qualification 7 Ibid.

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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.

0 = Not Totally Fit1 = Totally Fit

White It’s a Dummy Variable.

0 = Others (Black, Hispanic, Asian, etc.)1 = White

Male It’s a Dummy Variable.

0 = Female1 = Male

Family Size Data show total number of members in respondent’s family in year 1994.

Married It's a Dummy Variable.

Data show whether the respondents are married or not as of the year 1994.

0 = Others (Never Married, Divorced, Separated, etc.)1 = Married

Age 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

Education Education in years.

Data represent highest grade completed by the

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respondents as of May 1 of 1994.

Experience Experience in years as in 1994.

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

Percentile IQ 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

Table IV.A.2: Summery Statistic of the Variables.

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

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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

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.

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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 +


= 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.

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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.

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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

Variable

Coefficient

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

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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 p-

value 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.

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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:

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

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.

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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:

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Residual PERSONAL INCOME By PERCENTILE IQ

-50000

-30000

-10000

10000

30000

50000

70000

90000

110000

130000

150000

0 10 20 30 40 50 60 70 80 90 100PERCENTILE IQ

Linear Fit

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).

27

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 multi-

collinearity is that it inflates the SEs of the individual slope estimates. However, multi-

collinearity 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.

28

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:




* Experience + 13 * Experience2 + 14 * (Percentile IQ * Education) +


= an error term

The JMP output of this regression model is:

PERSONAL INCOME

Independent

Variable

Coefficient

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

Family Size * 471.30269 237.8925 1.98 0.0476

29

Male

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 *

Education

15.271646 2.947788 5.18 <.0001


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

Personal Income.

30

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 person

with 12 years of education is predicted to earn 32730.02 dollars per year, and the person

31

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:

Object 1


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.

32

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) +


= an error term

JMP output for the regression equation is:

33

PERSONAL INCOME

Independent

Variable

Coefficient

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 *

Male

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

Residency

2322.2252 430.2633 5.40 <.0001

Education 1632.1048 150.5992 10.84 <.0001

Education *

Male

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 *

Percentile IQ

200.20158 18.17221 11.02 <.0001

34

Bright *

Percentile IQ

126.95282 10.85655 11.69 <.0001

Normal *

Percentile IQ

120.60891 11.47342 10.51 <.0001

Dull * Percentile

IQ

136.69667 30.94712 4.42 <.0001

Very Dull *

Percentile IQ

-199.0129 159.4276 -1.25 0.2120


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 non-

linear relationship between Percentile IQ and Personal Income. To explore it further I

estimate the following model:




* Experience + 13 * Experience2 + 14 * Percentile IQ2 +


35

= an error term

The JMP output of the Model:

PERSONAL INCOME

Independent

Variable

Coefficient

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 *

Male

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

Residency

2340.2876 430.4786 5.44 <.0001

Education 1595.7637 151.5687 10.53 <.0001

Education *

Male

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

Percentile IQ2 0.2485844 0.26773 0.93 0.3532

36


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

37

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:

Object 2


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.

38

V. ConclusionThe 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

39

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.

40

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.

41

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

42

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.

43

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