Statistical discrimination and measuring discrimination

Statistical discrimination is the use of a group’s average characteristics to judge an individual whose productivity is hard to observe. It requires no prejudice and is profitable, so competition does not remove it. Measuring discrimination of any kind relies on splitting wage gaps into explained and unexplained parts, and on experiments that hold qualifications fixed.

Group averages as information

An employer sees a test score, an interview and a résumé, all noisy signals of productivity. When a signal is less informative for one group, for example because the employer cannot judge credentials from unfamiliar institutions, a profit-maximizing employer puts less weight on that group’s signal and more on the group’s average. Two applicants with the same score then receive different offers, without any animus on the employer’s part.

The model

Let $T$ be a test score measured in units of productivity, $\bar T_g$ the average score of group $g$, and $\alpha_g$, between 0 and 1, the reliability of the test for that group: the share of the variation in scores that reflects true productivity. In a competitive market a worker is paid expected productivity:

$$w = \alpha_g T + (1 - \alpha_g)\,\bar T_g .$$

A perfectly reliable test ($\alpha_g = 1$) pays each worker their score; a useless one ($\alpha_g = 0$) pays everyone the group average. Edmund Phelps formalized this argument.¹ Two cases matter.

• Same mean, noisier test for group B ($\alpha_B < \alpha_A$). B’s wage line is flatter and crosses A’s at the common mean. B workers who score above the mean are paid less than A workers with the same score; B workers below the mean are paid more. Each group is paid its own average productivity, so there is no gap between the groups’ average wages: Dennis Aigner and Glen Cain stressed that this case is not discrimination against the group as a whole, although individuals are treated differently by group.²
• Same reliability, lower mean for group B ($\bar T_B < \bar T_A$). The lines are parallel, and every B worker is paid $(1 - \alpha)(\bar T_A - \bar T_B)$ less than an A worker with the same score.

Reliability of B's test, α_B (noisier-test case)

0.25

B's average score (lower-mean case)

12

Score 30, group A

$27.00

Score 30, B with a noisier test

$22.50

Score 30, B with a lower mean

$24.60

Score 10, group A

$13.00

Score 10, B with a noisier test

$17.50

Open in Graph Lab

Figure 1. Wage offers by test score for group A (reliability 0.7) and for group B in two cases. With a noisier test and the same mean (red), a B worker scoring 30 is offered $22.50 against A's $27.00, while a B worker scoring 10 is offered $17.50 against $13.00. With equal reliability and a lower mean (purple), every B worker is offered $2.40 less than an A worker with the same score.

Three consequences follow. Statistical discrimination survives competition, because it is profit-maximizing given the information. A flatter wage line lowers the return to investing in skills for the group whose signals are discounted, which can make the lower average self-fulfilling. And employers judging individuals by averages treat many individuals unfairly even when each group’s average is paid correctly.

Key idea

Statistical discrimination is about information, not taste. When individual productivity is hard to observe, a group average is cheap information, and using it pays, which is why competition does not remove it.

Measuring discrimination: the Oaxaca-Blinder decomposition

Part of a raw wage gap reflects differences in skills. To separate it, estimate an earnings function for each group, here with schooling $s$:

$$w_M = \alpha_M + \beta_M s, \qquad w_F = \alpha_F + \beta_F s ,$$

where $\alpha$ is now an intercept, not a reliability. A least-squares line passes through the means, so $\bar w_M = \alpha_M + \beta_M \bar s_M$ and $\bar w_F = \alpha_F + \beta_F \bar s_F$. Subtract, then add and subtract $\beta_M \bar s_F$:

$$\begin{aligned} \bar w_M - \bar w_F &= (\alpha_M - \alpha_F) + \beta_M \bar s_M - \beta_F \bar s_F \\ &= \underbrace{(\alpha_M - \alpha_F) + (\beta_M - \beta_F)\bar s_F}_{\text{unexplained}} + \underbrace{\beta_M(\bar s_M - \bar s_F)}_{\text{explained}} . \end{aligned}$$

The explained part values the schooling difference at men’s return. The unexplained part is the difference in pay for the same schooling, evaluated at women’s average. This is the Oaxaca-Blinder decomposition, introduced by Ronald Oaxaca and Alan Blinder.³⁴

Women's average schooling, s̄_F

12.5

Women's intercept, α_F

$6.00

Raw gap, w̄_M − w̄_F

$7.50

Explained, β_M(s̄_M − s̄_F)

$2.25

Unexplained

$5.25

Share unexplained

70%

Open in Graph Lab

Figure 2. Wage-schooling lines for men, $w_M = 10 + 1.5s$, and women, $w_F = 6 + 1.4s$, with average schooling of 14 and 12.5 years. Of the $7.50 raw gap, $2.25 is explained by men's extra schooling (the rise along the men's line) and $5.25 is unexplained (the gap between the lines at women's average schooling). When women's average schooling exceeds men's, the explained part turns negative.

The unexplained part is not a measure of discrimination.

1. Omitted skills. Productive characteristics missing from the regression, such as years of full-time experience or field of study, end up in the unexplained part and overstate discrimination.
2. Tainted controls. Controls that themselves reflect discrimination, such as occupation when women are kept out of high-paying occupations, move discrimination into the explained part and understate it.
3. The index number problem. Valuing the skill difference at women’s returns instead of men’s gives a different split of the same gap.

Worked example

Men: $w_M = 10 + 1.5s$ with $\bar s_M = 14$. Women: $w_F = 6 + 1.4s$ with $\bar s_F = 12.5$. Wages are in dollars an hour.

1. Average wages. $\bar w_M = 10 + 1.5(14) = 31.00$ and $\bar w_F = 6 + 1.4(12.5) = 23.50$. The raw gap is $7.50.

2. Explained. $\beta_M(\bar s_M - \bar s_F) = 1.5(14 - 12.5) = 2.25$.

3. Unexplained. $(\alpha_M - \alpha_F) + (\beta_M - \beta_F)\bar s_F = (10 - 6) + (1.5 - 1.4)(12.5) = 4 + 1.25 = 5.25$. Check: $2.25 + 5.25 = 7.50$, so 70 percent of the gap is unexplained.

4. Women’s coefficients as the benchmark. Explained: $\beta_F(\bar s_M - \bar s_F) = 1.4(1.5) = 2.10$. Unexplained: $(\alpha_M - \alpha_F) + (\beta_M - \beta_F)\bar s_M = 4 + 0.1(14) = 5.40$. The same $7.50 gap splits differently: the index number problem.

Second example: the same wage equations, but women average 15 years of schooling. Decompose the gap using men’s coefficients.

Show the solution

$\bar w_F = 6 + 1.4(15) = 27.00$, so the raw gap is $31.00 - 27.00 = 4.00$. Explained: $1.5(14 - 15) = -1.50$. Unexplained: $4 + 0.1(15) = 5.50$. The explained part is negative because women have more schooling; on skills alone they would out-earn men, so the unexplained part exceeds the raw gap.

Audit and correspondence studies

Decompositions infer discrimination from what is left over. Experiments measure it directly. In an audit study, matched pairs of trained testers with equivalent qualifications apply for the same jobs. In a correspondence study, researchers send fictitious résumés that are identical except for a randomly assigned name or other group marker, and count callbacks. Random assignment means any gap in callbacks is caused by the marker.

Marianne Bertrand and Sendhil Mullainathan sent nearly 5,000 résumés to over 1,300 help-wanted ads in Boston and Chicago, with randomly assigned African American or white sounding names. White names received 50 percent more callbacks. A higher-quality résumé raised callbacks by 30 percent for white names and by far less for African American names.⁵

In Canada, Philip Oreopoulos sent 12,910 résumés to 3,225 job postings in Toronto and Montreal. Among applicants with Canadian education and experience, changing only the name from an English-sounding one to an Indian, Pakistani or Chinese one cut the callback rate by 4.4 percentage points from a base of 15.7 percent, a 28 percent drop. For such applicants with foreign education, Canadian work experience raised callbacks by 5.1 points from a base of 5.9 percent. In a small follow-up survey employers mentioned concerns about language skills, but listing fluency in several languages did not raise callbacks.⁶

Experiments measure callbacks, the first step of hiring, not wages or job offers, and they do not by themselves reveal whether employers act on taste or on beliefs about group averages.

Evidence: Canada’s gender wage gap

Among full-time employees, women’s average hourly wage rose from 83 percent of men’s in 1997 to 90 percent in 2025. In 2025 the averages were $40.45 for men and $36.32 for women. These are raw ratios with no controls.

Gender wage ratio, Canada

Women's average hourly wage ÷ men's, full-time employees aged 15 and over

Women's average hourly wage divided by men's, full-time employees. The raw gap narrowed from 17 percent to 10 percent between 1997 and 2025.Source: Statistics Canada, Table 14-10-0064-01, Employee wages by industry, annual. Retrieved 2026-10-23.

Show the data and notes

Computed from the published annual average hourly wages of full-time employees (all industries). A raw ratio: it does not control for occupation, industry, experience, education or hours. Statistics Canada cautions that 2006 changes to LFS processing introduced a level shift in average wages; compare across 2006 with care. The LFS recorded sex before 2022 and gender from 2022; Statistics Canada combines them in one series. From 2022 "Men" and "Women" are its Men+ and Women+ categories, each of which includes some non-binary persons. The Labour Force Survey covers the 10 provinces; it excludes the territories, people living on reserves, full-time members of the Canadian Armed Forces and people living in institutions.

Period	Women ÷ men
1997	0.830
1998	0.827
1999	0.826
2000	0.820
2001	0.822
2002	0.834
2003	0.841
2004	0.849
2005	0.855
2006	0.850
2007	0.847
2008	0.844
2009	0.857
2010	0.863
2011	0.870
2012	0.871
2013	0.872
2014	0.873
2015	0.876
2016	0.876
2017	0.874
2018	0.880
2019	0.881
2020	0.890
2021	0.891
2022	0.886
2023	0.886
2024	0.890
2025	0.898

Average hourly wage by gender, Canada

Full-time employees aged 15 and over, current dollars

• Men
• Women

Average hourly wages of full-time employees by gender, in current dollars. Both rose steadily; women's rose faster.Source: Statistics Canada, Table 14-10-0064-01, Employee wages by industry, annual. Retrieved 2026-10-23.

Show the data and notes

Annual averages, all industries, not adjusted for inflation. Statistics Canada cautions that 2006 changes to LFS processing introduced a level shift in average wages; compare across 2006 with care. The LFS recorded sex before 2022 and gender from 2022; Statistics Canada combines them in one series. From 2022 "Men" and "Women" are its Men+ and Women+ categories, each of which includes some non-binary persons. The Labour Force Survey covers the 10 provinces; it excludes the territories, people living on reserves, full-time members of the Canadian Armed Forces and people living in institutions.

Period	Men	Women
1997	$17.83	$14.79
1998	$18.10	$14.96
1999	$18.59	$15.35
2000	$19.21	$15.76
2001	$19.84	$16.30
2002	$20.31	$16.93
2003	$20.69	$17.39
2004	$21.12	$17.94
2005	$21.72	$18.58
2006	$22.98	$19.53
2007	$23.98	$20.32
2008	$25.03	$21.12
2009	$25.85	$22.16
2010	$26.31	$22.70
2011	$26.75	$23.26
2012	$27.43	$23.90
2013	$28.05	$24.46
2014	$28.54	$24.92
2015	$29.24	$25.60
2016	$29.89	$26.19
2017	$30.36	$26.53
2018	$30.96	$27.25
2019	$31.81	$28.02
2020	$33.44	$29.77
2021	$34.22	$30.48
2022	$35.75	$31.66
2023	$37.53	$33.25
2024	$39.29	$34.98
2025	$40.45	$36.32

Statistics Canada applied the Oaxaca-Blinder decomposition to hourly wages of employees aged 25 to 54, using men’s coefficients as the benchmark. The gap narrowed from 18.8 percent ($5.17 an hour) in 1998 to 13.3 percent ($4.13) in 2018. The narrowing was largely explained by changes in the occupations of women and men, women’s rising education and the decline of unionized employment among men. In 2018 the largest explained factors were the distribution of women and men across industries and women’s greater share of part-time work, and nearly two-thirds of the gap was unexplained.⁷

Common mistakes

Traps on exams

• Equating the unexplained part with discrimination. Omitted skills push it up; controls that reflect discrimination push it down.
• Assuming statistical discrimination creates an average gap. With equal means and a noisier test, each group is paid its own average; the harm falls on high scorers in the discounted group.
• Mixing benchmarks. With men’s coefficients as the benchmark, the explained part is $\beta_M(\bar s_M - \bar s_F)$ and the unexplained part is evaluated at $\bar s_F$. Mixing the two leaves a remainder.
• Reading callback gaps as wage gaps. Correspondence studies measure the chance of an interview, not pay.

On the exam

For the decomposition, draw both wage-schooling lines, mark each group’s average, and show the unexplained gap vertically at $\bar s_F$ and the explained part as the rise along the men’s line from $\bar s_F$ to $\bar s_M$. Write the formula and check that the two parts add up to the raw gap.

Check yourself

1.

Two groups have the same average productivity, but an employer's test predicts productivity less well for group B than for group A. In the statistical discrimination model, how are B workers paid compared with A workers who get the same score?

Reliability of B's test, α_B (noisier-test case)

0.25

B's average score (lower-mean case)

12

Score 30, group A

$27.00

Score 30, B with a noisier test

$22.50

Score 30, B with a lower mean

$24.60

Score 10, group A

$13.00

Score 10, B with a noisier test

$17.50

1B workers with high scores are paid less, and B workers with low scores are paid more2Every B worker is paid less than an A worker with the same score3Every B worker is paid more than an A worker with the same score4B and A workers with the same score are paid the same, because average productivity is equal

Check answer

2.

Wage equations are $w_M = 8 + 1.6s$ for men and $w_F = 5 + 1.5s$ for women, with $w$ in dollars an hour and $s$ in years of schooling. Men average 13 years of schooling and women 14. Using men's coefficients as the benchmark, what is the unexplained part of the wage gap, in dollars an hour?

Your answer (dollars per hour)

Check answer

3.

What did Bertrand and Mullainathan (2004) find when they sent résumés with randomly assigned names to employers in Boston and Chicago?

1White-sounding names received about 50 percent more callbacks, and better résumés helped white names much more than African American names2Callback rates were equal, but African American applicants were offered lower wages3Better résumés closed the gap for African American names4The gap appeared only for jobs requiring a university degree

Check answer

Practise more questions on this topic

Sources

1. Phelps, E. S. (1972). The statistical theory of racism and sexism. American Economic Review, 62(4), 659 to 661. ↩

2. Aigner, D. J. and Cain, G. G. (1977). Statistical theories of discrimination in labor markets. Industrial and Labor Relations Review, 30(2), 175 to 187. ↩

3. Oaxaca, R. (1973). Male-female wage differentials in urban labor markets. International Economic Review, 14(3), 693 to 709. ↩

4. Blinder, A. S. (1973). Wage discrimination: Reduced form and structural estimates. Journal of Human Resources, 8(4), 436 to 455. ↩

5. Bertrand, M. and Mullainathan, S. (2004). Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination. American Economic Review, 94(4), 991 to 1013. NBER working paper 9873. ↩

6. Oreopoulos, P. (2011). Why do skilled immigrants struggle in the labor market? A field experiment with thirteen thousand resumes. American Economic Journal: Economic Policy, 3(4), 148 to 171. Summary: J-PAL. ↩

7. Pelletier, R., Patterson, M. and Moyser, M. (2019). The gender wage gap in Canada: 1998 to 2018. Labour Statistics: Research Papers, Statistics Canada catalogue no. 75-004-M. Statistics Canada. ↩