### PT Presentation

```THE ECONOMIC RETURN ON
INVESTMENTS IN HIGHER
EDUCATION:
Understanding The Internal Rate of Return
Presentation
OISE, HEQCO, MTCU Research Symposium
Defining and Measuring Student Success
Toronto
November 22, 2013
Torben Drewes
Department of Economics
Trent University
Background
• Much public discussion about the financial viability of
(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?
Definitions
•
•
2011 NHS – average annual wage and salary income for:
–
–
–
•
•
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.
Definitions
•
•
•
•
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.
The IRR Calculation
•
Consider an annual series of cash flows, Ct, that can be negative or
positive.
•
The IRR solves for the value of ρ so that
•
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 +
•
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 +
•
Let’s try something a little more complicated ….
110
1+ 1

(1+)
=0.
= 0. So ρ = 0.10, or 10%
56
1+ 1
+
58
1+ 2
= 0.
ρ = 0.09, or 0%
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
Annual Earnings
High School College
Bachelor's
Age
18
31400
0
0
19
31400
0
0
20
31400
0
0
21
31400
50646
0
22
31400
50646
62340
23
31400
50646
62340
24
31400
50646
62340
25
31400
50646
62340
26
31400
50646
62340
27
31400
50646
62340
28
31400
50646
62340
29
31400
50646
62340
30
31400
50646
62340
31
31400
50646
62340
32
31400
50646
62340
33
31400
50646
62340
34
31400
50646
62340
35
31400
50646
62340
IRR to
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
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
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
Annual Earnings
High School College
Bachelor's
Age
18
31400
0
0
19
31400
0
0
20
31400
0
0
21
31400
50646
0
22
31400
50646
62340
23
31400
50646
62340
24
31400
50646
62340
25
31400
50646
62340
26
31400
50646
62340
27
31400
50646
62340
28
31400
50646
62340
29
31400
50646
62340
30
31400
50646
62340
31
31400
50646
62340
32
31400
50646
62340
33
31400
50646
62340
34
31400
50646
62340
35
31400
50646
62340
IRR to
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
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
\$19,246
\$30,940
University
College
15%
16%
Estimation
•
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
Earnings
•
High School
University
C2
18
C1
22
26
30
34
38
42
46
50
54
58
62
T
Age
The Caveats
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.)
The Caveats
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
The Caveats
7. Estimates are average rates of return. There will be large differences
across and within fields of study
\$120,000
\$100,000
\$80,000
\$60,000
\$40,000
\$20,000
1985
1990
1995
2000
2005
Social
Sciences
Commerce
Life Sciences Engineering
Health
1985
1990
1995
2000
2005
1985
1990
1995
2000
2005
Humanities
1985
1990
1995
2000
2005
1985
1990
1995
2000
2005
Fine Arts
1985
1990
1995
2000
2005
1985
1990
1995
2000
2005
Education
1985
1990
1995
2000
2005
1985
1990
1995
2000
2005
\$0
Math,
Computer,
&physical
Sciences
Distribution of real earnings (20th, 50th and 80th percentiles) by field of study for Canadian-born 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
Conclusions
•
•
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?
1996
2000
2004
2009
Women
7.3%
9.5%
9.1%
12.2%
Men
7.3%
8.7%
9.4%
12.3%
Sources: Boarini & Strauss (2010), OECD Journal
OECD, Education at a Glance, various years
```