Returns to schooling

The rate of return to schooling is the percentage increase in a worker’s wage from one more year of school, holding other characteristics fixed. It is estimated as the coefficient $b$ in a regression of the log wage on years of schooling, and estimates across countries average about 9 percent a year.¹ Comparing workers with different schooling overstates it when more able people stay in school longer; twins and natural experiments suggest the overstatement is modest.

The log-wage regression

The standard specification is

$$\ln w_i = a + b\,s_i + \text{other variables},$$

where $w_i$ is worker $i$‘s wage, $s_i$ is years of schooling, and the other variables (experience, region, sex) hold other differences fixed. The constant $a$ is the predicted log wage with zero schooling and has no economic interest.

Why the log. Differentiate with respect to $s$:

$$\frac{d \ln w}{ds} = b, \qquad\text{and since}\qquad d \ln w = \frac{dw}{w}, \qquad \frac{dw}{w} = b\,ds .$$

Setting $ds = 1$, $b$ is the proportional change in the wage, not the log wage, from one more year: the rate of return. A coefficient of 0.09 means a year of school raises the wage by about 9 percent. Logs also compress the scale of wages, so the few very high earners, who carry a lot of weight in least squares, distort the estimate less.

Exact versus approximate. The percentage reading is a first-order approximation. Exactly, $w(s+\Delta s)/w(s) = e^{b\Delta s}$. With $b = 0.09$, one more year raises the wage by $e^{0.09} - 1 = 9.4$ percent, and four more years by $e^{0.36} - 1 = 43.3$ percent, not 36: each year’s gain applies to a higher base. Differences in logs add up (four years are 0.36 log points); percentages compound.

Return to a year of schooling (b)

0.090

One more year, exact (e^b − 1)

9.4%

One more year, approximation (b)

9.0%

Four more years, exact (e^4b − 1)

43.3%

Four more years, approximation (4b)

36.0%

Open in Graph Lab

Figure 1. The hourly wage implied by $\ln w = a + bs$ when a worker with 12 years of schooling earns $20. With $b = 0.09$, 16 years predicts $28.67, 43.3 percent more; the shortcut $1 + 4b$ predicts $27.20 because it ignores compounding.

The simple specification imposes the same percentage return on every year. The investment model predicts a marginal rate of return that falls with schooling, and credential effects (sheepskin effects) add jumps at diploma years; adding $s^2$ or degree indicators to the regression allows both.

Ability bias

A regression of wages on schooling compares different people. If those who stay in school longer would have earned more anyway, because they are more able, more motivated or better connected, part of their wage advantage is credited to schooling. That is ability bias.

In the figure, Kai and Maya face different wage-schooling loci (the earnings each would receive at each level of schooling). Maya is more able: her locus is higher and steeper, so her marginal rate of return stays above their common discount rate for longer, and she completes 16 years while Kai stops at 12.

Maya's ability advantage at 16 years

$8.0k

Observed gap, M − K

$19.6k

Kai's true gain, K′ − K

$11.6k

Ability bias, M − K′

$8.0k

Return per year, comparing Maya with Kai

11.9%

Kai's true return per year

7.7%

Open in Graph Lab

Figure 2. Kai (lower ability) stops at 12 years (K) and Maya (higher ability) at 16 (M); the gap M − K of $19,600 is Kai's true gain from four more years, K′ − K = $11,600, plus Maya's ability advantage of $8,000, so the comparison puts the return at 11.9 percent a year instead of 7.7. With no ability gap the two share one locus and the comparison is exact.

In regression terms, suppose the true model is $\ln w = a + b\,s + c\,A + e$, where $A$ is unobserved ability and $c > 0$. Omitting $A$ gives an estimate that converges to

$$\hat b \;\to\; b + c\,\frac{\text{Cov}(s, A)}{\text{Var}(s)} .$$

Because able people get more schooling, $\text{Cov}(s, A) > 0$ and $\hat b$ overstates $b$. The bias matters for policy: a program that keeps Kai in school is worth his own gain, $11,600 a year, not the $19,600 gap between him and Maya.

Two other problems complicate the estimate. Errors in reported schooling bias $\hat b$ toward zero, and if returns differ across people, different methods estimate returns for different groups.

Key idea

If workers differ only in their discount rates, they sit on one wage-schooling locus and observed wage gaps trace it out without bias. Ability bias arises because differences in ability shift the locus itself.

Getting around ability bias

Measure ability. Add test scores to the regression as a control. The difficulty is that ability has many dimensions, any test measures it with error, and test scores are themselves raised by schooling.

Compare identical twins. Identical twins share genes and family background. Differencing the wage equation within a pair gives

$$\ln w_2 - \ln w_1 = b\,(s_2 - s_1) + \text{differences in other variables},$$

so ability drops out if the twins are equally able. Ashenfelter and Krueger surveyed twins at the Twins Days festival in Twinsburg, Ohio, and asked each twin about the other’s schooling to correct for reporting errors; their corrected estimates were 12 to 16 percent a year.² With about 700 identical twins, Ashenfelter and Rouse found about 9 percent and concluded that cross-section estimates are only marginally biased upward.³ In a large sample of Swedish identical twins, the within-pair estimate was 3.4 percent against 7.2 percent in the cross-section, and adding the twins’ adolescent IQ scores lowered it by about 15 percent, evidence that identical twins are not identical in ability.⁴ That is the method’s weak point: if identical twins chose different schooling, something differed between them. Differencing also magnifies the effect of reporting errors, because it removes much of the true variation in schooling but none of the errors.

Use a natural experiment. An instrumental variable shifts schooling without being related to ability. Angrist and Krueger used quarter of birth in the United States: children born early in the year start school older, so they reach the compulsory leaving age of 16 or 17 having completed less schooling. Roughly 25 percent of potential dropouts stayed in school because of these laws, and the estimated return for those compelled to stay, about 7.5 percent, was close to the least squares estimate.⁵ The instrument is weak, however: it explains little of the variation in schooling, and Bound, Jaeger and Baker showed that random numbers in its place produced similar-looking estimates.⁶ In Canada, Oreopoulos used changes in provincial school-leaving laws between 1920 and 1990. Students compelled to stay an extra year earned about 12 percent more a year, and the instrumental-variable and least squares estimates were close (12.1 and 12.7 percent).⁷

The verdict. Card’s survey concludes that twins studies imply an upward ability bias of about 10 percent of the least squares estimate, while instrumental-variable estimates are typically 20 to 40 percent above least squares.⁸ Instruments based on school-leaving laws estimate the return for students on the margin of dropping out, whose return may be above average, and least squares is also pulled down by measurement error.

Worked example

A regression on a sample of workers gives $\ln w = 1.90 + 0.08\,s$, with $w$ the hourly wage.

1. Interpret $b$. One more year raises the wage by about 8 percent; exactly, by $e^{0.08} - 1 = 8.3$ percent.

2. Predict wages. With 12 years, $\ln w = 1.90 + 0.96 = 2.86$, so $w = e^{2.86} = 17.46$ dollars an hour. With 16 years, $\ln w = 3.18$, so $w = e^{3.18} = 24.05$ dollars.

3. Compare. $24.05 / 17.46 = e^{0.32} = 1.377$: the 16-year wage is 37.7 percent higher. Four times 8 percent, 32 percent, understates the gap.

4. Measure ability bias using Figure 2. Comparing Maya ($51,800, 16 years) with Kai ($32,200, 12 years) gives a return of $\ln(51.8/32.2)/4 = 0.475/4 = 11.9$ percent a year. Kai’s own gain, from $32,200 to $43,800, is $\ln(43.8/32.2)/4 = 0.308/4 = 7.7$ percent a year.

5. State the bias. The comparison overstates the return by $11.9 - 7.7 = 4.2$ percentage points, more than half of the true return, because it credits Maya’s ability to her schooling.

Evidence: schooling and earnings in Canada

Median employment income by highest level of education, Canada

Median employment income in 2020, full-year full-time workers aged 25 to 54 (2021 Census)

No certificate, diploma or degree$44,800

High school diploma$54,000

Apprenticeship or trades certificate$60,800

College or CEGEP diploma$61,600

University certificate below bachelor's$63,600

Bachelor's degree or higher$81,000

Median employment income in 2020 of Canadians aged 25 to 54 who worked full year, mostly full time, by highest credential. Income rises with each credential, with the largest step to a bachelor's degree.Source: Statistics Canada, Table 98-10-0597-01, Employment income statistics by industry sectors, highest level of education, immigrant status and period of immigration, work activity during the reference year, age and gender (2021 Census of Population). Retrieved 2026-10-23.

Show the data and notes

The Labour Force Survey publishes no annual table of wages by education, so this uses the 2021 Census. Restricting to people who worked 49 or more weeks in 2020, mostly full time (30+ hours a week), holds hours roughly constant, so the gaps approximate differences in pay rates. Employment income = wages, salaries and commissions plus net self-employment income; both genders. Pandemic benefits such as CERB are government transfers and are not included. This table does not split degrees above the bachelor's level.

Category	Median employment income
No certificate, diploma or degree	$44,800
High school diploma	$54,000
Apprenticeship or trades certificate	$60,800
College or CEGEP diploma	$61,600
University certificate below bachelor's	$63,600
Bachelor's degree or higher	$81,000

Median employment income was $81,000 for full-year workers with a bachelor’s degree or higher and $54,000 for high school graduates: 50 percent more, or 0.41 log points. Spread over four years of university, that is about 10 percent a year, close to the 9 percent average across countries. It is not a causal estimate. The gap includes differences in ability and motivation, and the top category includes graduate degrees, which take more than four years.

Common mistakes

Traps on exams

• Misreading $b$. In a log-wage regression, $b = 0.08$ means about 8 percent per year: not 8 cents, and not 0.08 percent.
• Treating $b\,\Delta s$ as exact for large changes. It is the change in log points. The exact percentage is $e^{b\Delta s} - 1$.
• Calling every schooling gap a return. Workers with more schooling are usually more able; the raw gap mixes the two.
• Mixing up the two sources of different schooling. Different discount rates move workers along one locus (no bias); different abilities put them on different loci (bias).

On the exam

Draw two concave wage-schooling loci, the more able worker’s higher and steeper. Mark each worker’s chosen point and the less able worker’s counterfactual point at the higher schooling level, then split the observed gap into the true gain and the ability bias.

Check yourself

1.

A regression on a sample of Canadian workers gives $\ln w = 1.6 + 0.07\,s + \text{other variables}$, where $w$ is the hourly wage and $s$ is years of schooling. What does the coefficient 0.07 mean?

1One more year of schooling is associated with a wage about 7 percent higher, other variables held fixed2One more year of schooling raises the hourly wage by 7 cents3One more year of schooling raises the wage by 0.07 percent4Schooling explains 7 percent of the variation in wages

Check answer

2.

Kai completes 12 years of schooling and earns $32,200 a year. Maya, who is more able, completes 16 years and earns $51,800. With 16 years of schooling, Kai would earn $43,800. Which statement is correct?

Maya's ability advantage at 16 years

$8.0k

Observed gap, M − K

$19.6k

Kai's true gain, K′ − K

$11.6k

Ability bias, M − K′

$8.0k

Return per year, comparing Maya with Kai

11.9%

Kai's true return per year

7.7%

1Comparing Maya with Kai overstates the gain from four more years of school by $8,0002Comparing Maya with Kai understates the gain, because Maya earns more than Kai would3Kai's true gain from four more years of school is $19,6004The comparison is unbiased, because both workers face concave wage-schooling loci

Check answer

3.

Instrumental-variable estimates of the return to schooling based on compulsory schooling laws are often as large as or larger than least squares estimates. Which explanation fits this pattern?

1The laws change schooling only for students near the leaving age, whose return may be above average, and least squares is pulled down by errors in reported schooling2The instruments introduce ability bias that pushes the estimates up3Compulsory schooling laws raise students' innate ability4Least squares estimates are always too low, because ability bias works downward

Check answer

Practise more questions on this topic

Sources

1. Psacharopoulos, G. and H. A. Patrinos (2018). Returns to investment in education: A decennial review of the global literature. Education Economics, 26(5), 445 to 458. The 9 percent figure is the average private return across 1,120 estimates from 139 countries. ↩

2. Ashenfelter, O. and A. Krueger (1994). Estimates of the economic return to schooling from a new sample of twins. American Economic Review, 84(5), 1157 to 1173. ↩

3. Ashenfelter, O. and C. Rouse (1998). Income, schooling, and ability: Evidence from a new sample of identical twins. Quarterly Journal of Economics, 113(1), 253 to 284. ↩

4. Sandewall, Ö., D. Cesarini and M. Johannesson (2014). The co-twin methodology and returns to schooling: Testing a critical assumption. Labour Economics, 26, 1 to 10. ↩

5. Angrist, J. D. and A. B. Krueger (1991). Does compulsory school attendance affect schooling and earnings? Quarterly Journal of Economics, 106(4), 979 to 1014. NBER working paper 3572. ↩

6. Bound, J., D. A. Jaeger and R. M. Baker (1995). Problems with instrumental variables estimation when the correlation between the instruments and the endogeneous explanatory variable is weak. Journal of the American Statistical Association, 90(430), 443 to 450. ↩

7. Oreopoulos, P. (2006). The compelling effects of compulsory schooling: Evidence from Canada. Canadian Journal of Economics, 39(1), 22 to 52. ↩

8. Card, D. (1999). The causal effect of education on earnings. In O. Ashenfelter and D. Card (eds.), Handbook of Labor Economics, vol. 3, chapter 30, 1801 to 1863. Elsevier. ↩