Presentation
OISE, HEQCO, MTCU Research Symposium
Defining and Measuring Student Success
Toronto
November 22, 2013
Torben Drewes
Department of Economics
Trent University

• Much public discussion about the financial viability of investments made by young Canadians in higher education
(esp. university)
• The term “returns to higher education” occurs often in that discussion
– What exactly does that term mean?
– How are such returns estimated?
– How useful are such estimates?

• “Return to education” often used loosely.
• 2011 NHS – average annual wage and salary income for:
– high school graduates: $31,400
– college graduates: $50,646
– university graduates: $62,340
• Average college incomes are 61% higher than high school incomes.
The “return” to a college diploma is a 61% gain in income.
• Should be termed the “earnings premium”, not the return.
– After all, income comparisons do not consider the cost of the investment.
• The internal rate of return on an investment or project is the
"annualized effective compounded return rate" or discount rate that makes the net present value of all cash flows (both positive and negative) from a particular investment equal to zero.
– I.e. the interest rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits
(positive cash flows) of the investment.

• Why the confusion between earnings premium and irr?
• Regressing the natural logarithm of earnings against measures of schooling attainment produces the proportional increase in earnings for each unit change in education: the earnings premium.
• Jacob Mincer (HCEF): under certain assumptions (eg., no tuition, schooling is measured in years, etc.) the coefficient on the measure of education is the IRR.
• Those assumptions do not typically hold.
– earnings premium from a regression model are not equal to IRR.

• Consider an annual series of cash flows, C t
, that can be negative or positive.
• The IRR solves for the value of ρ so that 𝑁 𝑡
𝐶 𝑡
(1+𝜌) 𝑡
= 0 .
• Your brother-in-law wants to borrow $100. Promises to repay you $110 in one year. What is the IRR to you on this investment?
• Solve −100 +
110
1+𝜌 1
= 0.
So ρ = 0.10, or 10%
• Why is the IRR useful? The brother-in-law proposes a different repayment schedule: $56 in one year and $58 in two years. How to compare?
• Solve −100 +
56
1+𝜌 1
+
58
1+𝜌 2
= 0 . ρ = 0.09, or 0%
• Let’s try something a little more complicated ….

Internal Rate of Return Calculations
Assume Tuition =
Assume Schooling Takes
Decision year:
$6,000 University
$3,000 College
4 years University
3 years College
18 years old
Age
31
32
33
34
35
27
28
29
30
23
24
25
26
19
20
21
22
High School
Annual Earnings
College Bachelor's
18
Graduate
31400
Graduate Graduate
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
50646
50646
50646
50646
50646
50646
50646
50646
50646
50646
50646
50646
0
0
0
50646
50646
50646
0
62340
62340
62340
0
0
0
62340
62340
62340
62340
62340
62340
62340
62340
62340
62340
62340
Net Gains
College Bachelor's
-$34,400 -$37,400
-$34,400 -$37,400
-$34,400 -$37,400
$19,246 -$37,400
$19,246 $30,940
$19,246
$19,246
$30,940
$30,940
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
IRR to University
College
16%

Let’s Increase University Tuition
Internal Rate of Return Calculations
Assume Tuition =
Assume Schooling Takes
Decision year:
$10,000 University
$3,000 College
4 years University
3 years College
18 years old
Age
33
34
35
29
30
31
32
25
26
27
28
21
22
23
24
18
19
20
High School
Annual Earnings
College Bachelor's
Graduate
31400
Graduate
0
Graduate
31400
31400
31400
31400
0
0
50646
50646
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
31400
50646
50646
50646
50646
50646
50646
50646
50646
50646
50646
50646
50646
50646
0
62340
62340
62340
0
0
0
62340
62340
62340
62340
62340
62340
62340
62340
62340
62340
62340
Net Gains
College Bachelor's
-$34,400 -$41,400
-$34,400 -$41,400
-$34,400 -$41,400
$19,246 -$41,400
$19,246 $30,940
$19,246
$19,246
$30,940
$30,940
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$19,246
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
$30,940
IRR to University
College
15%
16%

• Use regression or other smoothing techniques applied to Census data to produce age-earnings profiles.
•
Out-of-pocket (C1) and opportunity (C2) costs are compared to earnings gains (B) to compute IRR.
B
C2
C1 22 26 30 34 38 42 46 50 54 58 62 T
Age
High School
University

1. Parameters Matter.
– Estimates use “prototypical” decision-maker – age 18.
– Eg.: returns to adult learning will be lower
2. Only earnings/tuition data are used.
– Non-monetary costs and benefits are important, but hard to measure
– Implies that IRR calculations are only part of the story.
3. Only private returns
– Correct if we are trying to model individual decision or inform young decision-makers.
– Incorrect if we are trying to evaluate public policy to promote higher education as social investment.
• Need to compare social costs (different than tuition) with social benefits (gross income, reduced health expenditures, implications for productivity of co-workers, etc.)

4. Future stream of earnings unknown.
– Proxied by current earnings of older workers.
5. The Missing Counterfactual
– The high school profile is what the university graduate would have earned had she entered the labour market after high school.
– University (and college) graduates may differ from high school completers in other ways that are related to earnings. The ability bias issue.
6. Average vs Marginal Returns
– Estimated returns are averages across all individuals participating in higher education.
– Policy question may need to estimate returns at the margin. Eg. should we expand access to higher education?

$80,000
$60,000
$40,000
$20,000
$0
7. Estimates are average rates of return. There will be large differences across and within fields of study
$120,000
$100,000
Education Fine Arts Humanities Social
Sciences
Commerce Life Sciences Engineering Health Math,
Computer,
&physical
Sciences
Distribution of real earnings (20 th , 50 th and 80 th percentiles) by field of study for Canadianborn male bachelor’s graduates in 2005 dollars, population aged 25-64 in the labour force: Census 1985 to 2005
Bell, King, Afshar, (2011), POSTSECONDARY EDUCATION AND THE LABOUR MARKET: THE EVOLUTION OF
SUPPLY AND DEMAND, 1985 TO 2005, HRSDC

• Given these difficulties, should we dump the IRR?
• No!
• Conceptually, IRR to higher education is a valuable theoretical construct in understanding demand for PSE
• For good policy design, statistical evidence trumps anecdotal evidence.
– More work needed on empirical implementation, but we need the estimates.
• What does that statistical evidence look like?

Women
OECD Estimates of IRR: Canada
1996 2000 2004
7.3%
Men 7.3%
Sources: Boarini & Strauss (2010), OECD Journal
OECD, Education at a Glance, various years
9.5%
8.7%
9.1%
9.4%
2009
12.2%
12.3%