1. Statistical Concepts and Economics: Earnings and Education in Canada
Presentation to the Nepean High School Data Management Classes
Professor Christopher Worswick
Department of Economics
Carleton University
May 15, 2014

2. Basics of the Economic Approach to the Labour Market
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
However, workers differ in many ways:
Intelligence
Education
Work experience
These differences lead to variation in the wage
Natural to consider the statistical properties of the wage distribution

3. Measures of central tendency
Arithmetic mean or average
Useful in economics because we can think of this as the “expected” wage outcome for a worker.
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

4. Measure of spread 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.

5. Distributions Example: Normal distribution

6. Canadian Income Distribution

7. Skewness
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).

8. Differences in Means
Common in economics to compare the mean across two groups or across time for the same group.
Examples include:
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.)

9. Wage Returns to Education
Human Capital Theory:
more education will raise the person’s wage due to the increase in labour productivity from the skills gained in school.
Signaling Theory:
employers will pay more educated workers a higher wage since education is a signal of high (unobserved) ability.

10. Correlation Coefficient
A measure of the degree to which two variables are related
ranging from -1 to 1.
Correlation between the wage and the education level is predicted to be positive under either Human Capital Theory or Signaling Theory.

11. Wage Returns to Work Experience
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.
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.

12. Human Capital Wage Equation
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
The β terms are coefficients to be estimated and εi is a mean zero error term.

13. Linear Regression
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

14. Economics of University Education
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.
Simple case (work to age 65):
HS only: NPVhs=(65-18)Whs=47Whs
University: NPVu=(65-22)Wu-4T=43Wu-4T
If purely financial, the person would go to university if:
NPVu –NPVhs=43Wu-4T-47Whs>0

15. This simple approach can easily be extended to introduce:
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.
Returns to work experience complicate the analysis but are important
If β2>0, then both the Whs and Wu rise with X.

16. Wage-Experience Profiles

17. Net Present Value Calculations
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.

18. Access to Credit and University
Like all investments, the cost of post- secondary 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.
Without loans, the person might be unable to go to university even when it is a good investment.

19. Credit Market Imperfections
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.
Employers are unlikely to subsidize since worker could leave the firm without repaying
Notable exception?

20. Back to Statistics: Inference
So far, I have mainly talked about estimation.
Mean, Median
Variance
Regression coefficients
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

21. Normal distribution and Z-statistic
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.
However, the distribution of income is positively skewed so Normal distribution is likely an incorrect assumption.

22. Central Limit Theorem
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

23. Causality and Unobserved Ability
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.

24. Field of Study 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
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…
CLSRN Working Paper no. 109 “Economic Benefits of Studying Economics in Canada: A Comparison of wages of Economics Majors with those in Other Disciplines Circa 2005” Ather H. Akbari (St. Mary’s University) Yigit Aydede (St. Mary’s University)

25. Concluding Remarks
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.