Between Black and White Population1. Comparing annual percent .docx
Effects of ability on determining wages of individuals
1. ECONOMETRICS
(ECON 330)
RESEARCH PAPER
Effects of ability
on determining wages of individuals
Arsalan Anwar 13020392
Gurbux Lohana 13020464
Nabeel Muhammad 13020313
Muhammad Farhan Anwar 14020391
We greatly appreciate the research assistance provided by TAs. The findings and conclusions of
this paper are those of the authors and may not reflect the viewpoint(s) of others.
2. 1
TABLE OF CONTENTS
1. Abstract ………………………………..………………. Page 2
2. Introduction and Literature Review …………………… Page 3
3. Data Analysis ………………………………………….. Page 4
4. Statistical Model ………………………………………. Page 5
5. Sensitivity Analysis …….……………………………… Page 7
6. Limitations, Issues and Remedies ……………………... Page 7
7. Conclusion ……………………………………………... Page 8
8. Bibliography ……………………………………………. Page 9
9. Appendix …….……….………………………………… Page10
3. 2
Abstract
This paper delves into discerning the effect of ability on wage, using IQ as a proxy for the
former, while controlling for other factors that could potentially influence wage and be correlated
with ability in some respect. The paper has been segmented into different parts to explain this
relationship. The first part is based on the introduction & literature review where we have
detailed our hypothesis and referenced previous studies that provide past findings pertaining to
our study. The following section on data description explains the data we have used for our
study. Next, we have formed a statistical model to gauge the causal relationship between wage
and ability while using several econometric tests to derive meaningful conclusions, before we
move to our sensitivity analysis. In the penultimate section, we provide data limitations, issues
and remedies. Finally, we conclude by providing our take on our model and the extent its
conformity to logic and relevance to previous studies.
4. 3
Introduction and Literature Review
(IQ as a proxy for ability)
In the past, a lot of research has been done on the causal effect of ability on wage.
Furthermore, different economists have used different variables to explain this relation. Some of
these variables include like IQ, interpersonal skills, level of education, sociability, and
experience. We believe IQ is the most suitable proxy amongst these, which led us to use it for
ability.
The model that we have formed in this paper is based on the data given to us. Variables
are included in wage regression equation based on intuition and analysis of past studies. Since
some of the variables in our data were irrelevant for this case, we ignored them altogether.
Econometric analysis part of the paper will further explain the variables for our model in detail.
A paper by (Cohan & Kiker, 1986) has attempted to establish a relationship between
wage, IQ and other contextual phenomenon. By accounting for IQ, they have controlled for
variables such as characteristics of family, high school friends, high school peers and their
families, and high schools to earnings at ages 35 and 53. According to them, IQ is not a
significant factor in explaining wage. Other factors count much more. Similarly, another study
by Cohn and Kiker in 1981, has measured cognitive ability for explaining variability in income
by establishing their model on Panel Study of Income Dynamics (PSID). Their findings also
concur that cognitive ability has negligible effects on earnings.
However, other studies have shown significant effects of IQ on wage. A study by
(Murnane, Willet & Levy, 1995) estimates that differences of mathematics achievement scores
have large effects on wage. This study is pertinent to our case because a large part of IQ tests
detects quantitative abilities. In addition, (Altonji, 1992) estimates augmented returns of 15
percent in wage for each standard deviation of IQ. He conducted tests of 692 individuals enrolled
in the Kalamzoo, Michigan school district between the years of 1928 and 1952.
Since our paper is based on effect of IQ on wage, variables which have a correlation with
IQ and an effect on wage, besides IQ itself, are also included in the regression model. A study
carried out in 1969 has shown that variables like parents’ education and good schooling have
positive effects on IQ. “Environment acts as a threshold variable to influence IQ” (Jensen,
1969).
The researches by (Datcher, 1982) and (Hauser and Megan, 1997) show that positive
environment and facilities provided to children at an early age play a significant role in
improving the performance on general IQ tests. Therefore, we have introduced variables such as
parents’ education, residence in metropolitan area besides access to newspapers, library and
magazines at an early age, in our model.
5. 4
Data Analysis
The data provided to us is cross sectional in nature. It was obtained from the national
longitudinal survey of 1976 of youth in 1966; family demographics, locality and education level
of 5226 individuals ranging from 14-24 years old age group were included therein. Our
hypothesis states that, there exists a causal relationship between IQ and the wage of an
individual. The dependent variable, wage76, contains values ranging from 0 to 3.179, with a
mean of 1.65 which is irrational. So, we have introduced a new variable wages76 (i.e.
10,000*wage76) using Consumer income report of 1978, which says in 1976, on average, an
individual earns 15,000 dollars per annum. We have used wage instead of Log (wage) as our
dependent variable because the kdensity function of wage is placed rather normally around the
mean relative to that of log (wage). Our variable of interest (IQ) has values ranging from 50-158,
having a mean of about 101.
To examine the unbiased causal effects of IQ on wage, we have controlled for race,
parents’ education, educational level at the age of 25, number of siblings, residence of urban
area, and availability of magazines, library and newspapers.
There may be many other unobserved variables in our error term which affect wage but
do not affect our exogenous variables thus implying that, our OLS model assumes zero mean
conditionality of the error term. We have not used the simple regression model basing wage on
only IQ, so as to avoid the omitted variable bias.
Variable Description
Wage76 The wage of the individual in 1976
IQ Intelligence Quotient in 1976
Black =1, if the observed individual is black, and =0 otherwise
g25 Education level at the age of 25
Famed Father’s and Mother’s education level ranked from 1-9 in decreasing order,
1=highest…. 9=lowest
smsa66 =1 If living in a metropolitan area, =0 otherwise
num_sib number of siblings in 1966
mag_14 =1 if magazine was available at the age of 14, =0 otherwise
news_14 =1 if newspaper was available at the age of 14, =0 otherwise
lib_14 =1 if library access was available at the age of 14, =0 otherwise
The wages of a particular individual are significantly influenced by aforesaid variables,
all of which are factors that are correlated with IQ hence making it imperative for us to control
for them. The assumption in our model is that the individuals observed do not attain education
after the age of 25, the rationale behind which is explained later. We have included the dummy
variable black in our model to control for the changes in the wages due to race differences; this
data was collected in 1976 when concerns over racial discrimination were still very much
prevalent in the US society. It is also plausible to believe that the area of residence bears impact
6. 5
on the development of an individual justifying the inclusion of smsa66 to check the impact on
wage. In addition to these, we have used other dummy variables like availability of magazine,
newspaper and library at the age of 14 because numerous researches like Altonji, J. G. (1992)
and Cohan, E., & Kiker, B. F. (1986) show the existence of a causal relation of such
environmental factors with wages. To ascertain the ceteris paribus effect of IQ on wages, we
have controlled for the above mentioned variables. We have deleted some values of lib_14,
mag_14 and news_14, which have values other then 0 and 1.
Statistical Model:
We have used the ordinary least squares (OLS) method for our regression model which
is:
Wage76= β0 + β1(IQ) + β2(famed) + β3(smsa66) + β4(g25) + β5(num_sib) + β6(black) + β7
(mag_14) + β8(news_14) + β9(lib _ 14) + û
To satisfy the five Gauss-Markov assumptions, we have used several tests at the 95%
significance level.
To check for misrepresentation in the model, we used the Ramsey Reset test (ovtest). The
probability of F value came out be 0.2893 (Check in Appendix), thus we failed to reject our null
hypothesis, implying our model has no misrepresentation.
To satisfy MLR 5 we checked for heteroskedasticity by using Breusch-Pagan test (Check
in Appendix). The probability of our chi-square value is 0.0081; so we reject our null hypothesis
which shows there is heteroskedasticity in our model. Therefore, we are using robust standard
errors to correct this issue.
To test perfect multicollinearity in independent variables, we have looked at Variance
Inflation Factor (VIF) (Check in Appendix). All values are less than 2 implying the absence of
perfect multicollinearity in the model.
The R-squared value is 0.1048, which shows that our model explains about 10.48% of the
total variation in wages. The model gives a modest account of the variation because much of the
unexplained variation is accounted by other variables such as experience and tenure which is not
included in our model. The F-test value shows that variables in the model are jointly significant.
After we run the regression the average returns to ability for wages, while controlling for
other factors, comes out to be 19.89 dollars. This shows that IQ, which we used as a proxy for
ability, has a significant impact on determining individuals’ wages. This finding is corroborated
by studies which show that “people with higher aptitudes for comprehending and quantitative
applications earn better wages“(Jensen, 1969)
7. 6
Coefficient of g25 indicates that, ceteris paribus, average returns of education on wages
are 233.3 dollars. This coefficient is highly economically significant. This is in accordance with
the intuition that wages increases with the level of education. A study by (Bartik, 2000) has
shown that there is a positive correlation between wages and level of education.
The co-efficient of famed is counter-intuitive, the data has accounted for parents’
education level by assigning 1 to the highest rank and 9 to the lowest; getting a significantly
positive coefficient of 78.97, as is our case, does not support intuition. The coefficient indicates
that, ceteris paribus, one rank decrease in the parents’ education will increase individuals’ wage
by 79 dollars. A study (Corcoran, Gordon, Laren & Solon, 1990) has shown that highly educated
parents are able to give more facilities and better nurturing environment to their children. This
leads us to believe highly educated parents’ children have higher chances of earning better
wages.
The co-efficient of black indicates that the difference of wage between blacks and whites,
on average, is -1637, which is highly significant. Controlling for everything else, Black
individuals earned $1637 less wage, on average, than their non-black counterparts. This relation
is acknowledged by a research carried by US Labor Bureau of Statistics ("Consumer income,"
1978).
The co-efficient of num_sibs is -170.9 indicating, an expected decrease in wage due to an
increase in the number of siblings by 1, ceteris paribus. A possible explanation for this could be:
as number of siblings increase, the resources and attention of parents per child decrease which
eventually lead to a decreased capability for earning wages ("Consumer income," 1978).
The co-efficient of smsa66 is 1388, very highly significant, is also in line with our
assumption that people living near the metropolitan areas, on average, earn higher than those of
non-metropolitan areas, ceteris paribus. The effect of this dummy variable may be accounted by
factors such as relatively higher employment opportunities in metropolitan areas and the
grooming effects of metropolitan areas ("Consumer income," 1978).
All above mentioned variables are statistically significant at 5% significance level.
Although the dummy variable news_14 is statistically insignificant, it bears a coefficient
of 467.1 in our model. We have included it in our model with the presumption that the
availability of newspaper develops the habit of reading newspaper, creating general as well as
job-related awareness among individuals since an early age, potentially enabling them to earn
higher wages in the future.
lib_14 has a negative co-efficient of 50.18 in our model, which is not plausible in theory.
We would like to believe that the availability of libraries should have a positive rather than
deterrent effect on wages. However, the statistical insignificance on lib_14’s co-efficient in the
model suggests library availability bears no significant effect, neither positive nor negative, on
one’s wages.
8. 7
mag_14 has a coefficient of 64.29 which is again statistically insignificant. It shows that
availability of magazine at age 14 does not affect the wage of an individual. Again our result of
coefficient is against our assumption for magazine availability’s effects, which should be
positive.
Sensitivity Analysis
For sensitivity analysis we introduced a new dummy variable named IQ2, which takes a
value of 1 when the observed individual has an IQ higher than or equal to the mean (101) and 0
otherwise; when we replace IQ in our original model by the new IQ2 variable, its coefficient is
530 which indicates that, after controlling other factors the individuals with higher than average
IQ will, on average, earn more than the individuals with below average IQ. The coefficient on IQ
tells us that the average returns to IQ are just 20 which are way less than 530. Most prominently,
the coefficient of IQ2 comes out to be significant.
We now test for the significance of racial discrimination prevalent in the returns of IQ on
wage structure according to our model. It is a statistically insignificant claim that the returns to
wages of IQ differ for blacks and non-blacks. To check for this, we introduce an interaction term
IQ*black, which tells us the difference in returns to IQ from black to white. But the coefficient
of this interaction term not only comes out to be insignificant but also increases multi-
collinearity.
We introduced another interaction term black*g25 to check whether economic returns to
education at age 25 differ from black to white, but its coefficient also comes out to be
insignificant.
Limitations, Issues and Remedies
The education level in 1966 is given for individuals for age group 14-24 but, later in
1976, many of the observed individuals would be more than 25 years of age rendering it
impossible for us to ascertain whether they continued or finished their education at 25 years of
age; we are only provided with g25 educational level of our observations. Therefore, we have
assumed that g25 is the terminal level of education, an assumption necessitated by a limitation of
our data.
Another problem in our data is that variable famed is ranked from 1 to 9 (1 for highest,
and 9 for lowest). This created a problem in regression because we do not know the method of
this ranking system. To counter this problem, we summed up the highest grade of mother and
father’s education. Though our assumption was valid for values greater than 30, but for the
values less than and equal to 30, there were multiple ranks given to a single summed value so we
had to use the ranking system used in the given data, although admittedly we were not sure of the
9. 8
ranking method. The remedy to this problem can simply be to rank parents according to the sum
of their highest level of education with maximum of 9 given to the best and 1 given to the lowest.
Conclusion
We had set out to determine the relationship between wage and ability, using IQ as a
proxy for the latter. Our model confirmed our hypothesis that each point increment in IQ causes
statistically significant positive wage differences. However, other variables have more
economically significant coefficients, thus creating relatively higher influence on wage than IQ
in terms of magnitude. These results lead us to conclude that other variables such as residence in
metropolitan areas, race, and years of education bear more impact on wages.
There were certain results in our model that worked against logic. According to the
model, a higher level of education for parents affected the wages negatively; we could not come
up with a logical explanation for this phenomenon. We are of the view that relatively higher
education for their parents should enable individuals to earn at least as high wages as their
counterparts, if not more because famed66 could not possibly deter wage rates. Similarly, the
availability of newspapers, and magazines was not a significant factor according to the model,
which came as a surprise since these can be taken as tools for a better nurturing which should
improve grooming and eventual wage earning for observed individuals.
Our OLS model proves that our hypothesis is consistent with the findings of the previous
studies conducted by several researchers as discussed earlier in the paper. We have concluded
from our findings that though IQ affects wage but there are also other variables that have more
economically significant impact on wages. We can further extend our research by taking another
hypothesis that whether after certain ideal level of IQ, does the effect of IQ on wages vary or
does not vary economically.
10. 9
Bibliography
Altonji, J. G. (1992). The effects of high school curriculum on education and labor market
outcomes. Journal of Human Resources, 409-12.
Cohan, E., & Kiker, B. F. (1986). Socioeconomic background, schooling, experience and
monetary rewards in the united states . Economica, 497-53.
Corcoran, M., Gordon, R., Laren, D., & Solon, G. (1990). The american economic
review. POVERTY AND THE UNDERCLAS, 80(2), 362-366.
Datcher, Linda (1982) "Effects of community and family background on achievement"
Review of Economics and Statistics, Vol. 64, February, 32-41.
Hauser, Robert M. and Megan, M. Sweeney (1997) "Does poverty in adolescence affect the
life chances of high school graduates" Consequences of Growing Up Poor, Duncan, Greg J.
and Jeanne Brooks-Gunn, eds., Russell Sage Foundation, New York, 541-595.
Jensen, A. R. (1969). How much can we boost iq and scholastic achievement?. Harvard
Educational Review, 111-13.
Murnane, R. J., Willet, J. B., & Levy, F. (1995). The growing importance of cognitive skills in
wage determination. Review of Economics and Statistics, 251-66.
US Census Bureau, (1978). Consumer income (Series P60, No.109)
11. 10
APPENDIX
GRAPH A (WAGES76):
GRAPH B (LWAGE):
0
.00002.00004.00006.00008
.0001
Density
0 10000 20000 30000 40000
wages76
Kernel density estimate
Normal density
kernel = epanechnikov, bandwidth = 779.8797
Kernel density estimate
0
.5
1
1.5
2
Density
7 8 9 10 11
lwage
Kernel density estimate
Normal density
kernel = epanechnikov, bandwidth = 0.0472
Kernel density estimate
