Presentation to the Nepean High School Data Management Classes
Professor Christopher Worswick
Department of Economics
Carleton University
May 15, 2014
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The wage paid to a worker is determined by the
demand for this type of work and the supply of
labour services by similar workers.
◦ Equilibrium wage is where labour supply = labour demand
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However, workers differ in many ways:
◦ Intelligence
◦ Education
◦ Work experience
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These differences lead to variation in the wage
Natural to consider the statistical properties of the
wage distribution
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Arithmetic mean or average
◦ Useful in economics because we can think of this as
the “expected” wage outcome for a worker.
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Median – 50% of the distribution has a wage
higher than this wage and 50% of the
distribution has a wage that is lower.
◦ Becoming more common in economics
◦ Useful if concerned about extreme values
 CEO salaries
 House prices
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Variance, standard deviation, etc.
If the wage distribution has a large variance
then this would indicate a high degree of
wage (or income) inequality.
Economists are concerned about income
inequality because:
◦ Normative: leads to inequality in consumption
◦ Efficiency: worse opportunities for children in
poorer families.
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Example: Normal distribution
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http://en.wikipedia.org/wiki/Normal_distribution
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The income distribution is not symmetric but
positively skewed.
Not consistent with the Normal distribution
but there are other distributions that can be
used to model this data
Also could use non-parametric estimation of
the underlying probability density function:
f(w).
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Common in economics to compare the mean
across two groups or across time for the
same group.
Examples include:
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Male/female wage difference
Immigrant/Canadian born wage difference
Growth in wage of Canadians across time
Cross cohort wage differences
 Baby boom cohort wage at say age 30 compared with
more recent cohorts at the same age (Gen X, Gen Y,
etc.)
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Human Capital Theory:
◦ more education will raise the person’s wage due to
the increase in labour productivity from the skills
gained in school.
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Signaling Theory:
◦ employers will pay more educated workers a higher
wage since education is a signal of high
(unobserved) ability.
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A measure of the degree to which two
variables are related
◦ ranging from -1 to 1.
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Correlation between the wage and the
education level is predicted to be positive
under either Human Capital Theory or
Signaling Theory.
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Human Capital Theory also predicts that the
wage a person receives will rise as s/he gains
more years of work experience.
◦ ‘learning-by-doing’ adds to the stock of human
capital.
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As firms compete for workers, the wage
offers should be higher for workers with
more human capital.
Creates a positive correlation coefficient
between the hourly wage variable, Wi, and the
years of work experience variable, Xi.
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A worker’s wage can be expressed as a
function of years spent in education, Si, and
work experience, Xi.
A simple version:
◦ Wi=β0 + β1Si + β2Xi + εi
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The β terms are coefficients to be estimated
and εi is a mean zero error term.
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One method for separately identifying the
effect of a number of variables (Si and Xi) on
the variable of interest (Wi).
εi captures any omitted variables such as
intellectual and physical abilities.
Many other factors can also be introduced on
the right hand side of the equation:
◦ Gender
◦ Place of residence
◦ Occupation
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Consider the decision of an 18 year-old:
◦ Work after high school with annual earnings, Whs
◦ Complete a four year university degree then
working with annual earnings, Wu, and tuition, T.
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Simple case (work to age 65):
◦ HS only: NPVhs=(65-18)Whs=47Whs
◦ University: NPVu=(65-22)Wu-4T=43Wu-4T
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If purely financial, the person would go to
university if:
NPVu –NPVhs=43Wu-4T-47Whs>0
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This will only be the case if Wu>Whs since the
person is foregoing 4 years of potential
earnings and paying tuition.
This simple approach can easily be extended
to introduce:
◦ discounting and
◦ preferences for education.
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Returns to work experience complicate the
analysis but are important
◦ If β2>0, then both the Whs and Wu rise with X.
50000
40000
Earnings
30000
HS
20000
UNIV
10000
0
-10000
18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63
Age
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The NPV from going to university
($1,759,828) is higher than for working after
high school ($1,599,724).
If the person discounts the future sufficiently,
then university may not b the right choice.
Studies typically find that post-secondary
education has a high return with the return
somewhat higher for university than for
college.
However, field of study matters.
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Like all investments, the cost of postsecondary education is upfront and the
benefits are in the future.
Can the person finance his/her education?
◦ help from family or loans which s/he must pay off
over the rest of his/her career.
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Without loans, the person might be unable to
go to university even when it is a good
investment.
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Banks are unlikely to make these loans
No collateral (e.g. house or car) only skills
Can’t force a person to work so risk of default
is high
Clear role for government
◦ low income individuals less likely to find financing.
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Employers are unlikely to subsidize since
worker could leave the firm without repaying
◦ Notable exception?
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So far, I have mainly talked about estimation.
◦ Mean, Median
◦ Variance
◦ Regression coefficients
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Statistical analysis in economics also involves
knowing when our estimates are “good” and
when they are “not so good”.
If we know the underlying distribution of the
variable of interest, Wi, then inference is easy
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If Wi is Normally distributed, then we can test
whether the sample mean differs from a value
of interest using the Z-statistic.
In our regression model:
◦ assume that εi is distributed normally
◦ test whether the return to education, β1, is
statistically significantly different from zero.
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However, the distribution of income is
positively skewed so Normal distribution is
likely an incorrect assumption.
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If the sample size is “large”, the distribution
of our estimate of each regression coefficient
can be approximated by the Normal
distribution.
This means that with large sample sizes,
testing is easy.
Coin toss example
◦ Sample fraction “heads” quickly approaches 0.5
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Is education exogenous?
If so, then a person should see an increase in
his/her wage after education because of the
skills s/he learns.
Alternatively, it could be that educate people
have higher ability and earn a higher wage
due to the fact that they have higher ability.
In the latter case, education does not “affect”
the wage
Estimated return to education biased
upwards.
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Akbari and Ayded (2013) - 2006 census micro
data
Undergraduate degree holders:
◦ 5 of the 50 disciplines earn more than those who hold a
degree in economics.
◦ Engineering, finance, computer science are also high
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Similar at the graduate degree level
Can use their sample means and regression
coefficients to compare the wage outcomes
across fields of study.
However, benefits of education only partly
involve wages…
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Statistical tools are important in all empirical
economic research.
Economic theorists employ mathematical
tools but statistics are also becoming very
important in their work.
Economics at the undergraduate level can be
a very rewarding area of study with very good
job prospects.
Also can complement other areas as an
elective or as a minor.