7. Labour market discrimination
KAT.TAL.322 Advanced Course in Labour Economics
Labour market discrimination
What is discrimination?
Discrimination arises when for the same level of productive characteristics, labour market outcomes differ based on nonproductive characteristics.
Employers may discriminate in hiring/firing decisions
Co-workers may discriminate in collaboration activity
Customers may discriminate in purchase decisions
Taste discrimination
Taste discrimination
First formalized by Becker (1957)
- There are two types of workers \(A\) and \(B\)
- Workers are perfect substitutes in production function \(F(A + B)\)
\(\Rightarrow\) equally productive \(F_A(\cdot) = F_B(\cdot)\)
A firm decides which worker to employ to maximise the utility
\[ \max_{A, B} PF(A + B) - w_A A - w_B B - d B \]
where \(d \geq 0\) is the disutility employer gets from worker \(B\).
Emphasize that both workers have same effect on profit (free of discrimination)
The disutility in this case has nothing to do with profit
Taste discrimination
Optimal labour demand conditions
\[ \begin{align} PF_A(A + B) &= w_A \\ PF_B(A + B) &= w_B + d \end{align} \]
Discriminating firm (\(d > 0\)) hires \(B\) workers iff \(w_A > w_B + d\).
Employment of \(B\) workers is lower than competitive level.
Taste discrimination
Perfect competition and free entry
Non-discriminating firms \(d = 0\) enters the market
Pay competitive wages to both groups \(w_A = w_B = P F_L(L)\)
Therefore,
discriminating firms hire \(A\) workers at \(w_A\)
non-discriminating firms hire everyone at \(w_A = w_B = w\)
Taste discrimination cannot persist under perfect competition
Discuss co-worker discrimination
- perfect competition: workers are free to move to firms that do not hire the other worker type \(\Rightarrow\) also can’t persist
Everyone is paid their marginal product
Taste discrimination
Imperfect competition
Monopsonistic employer
Lower wages and lower employment of discriminated group. The disadvantages persist as long as the employer does not compete with non- (or less) discriminating employers.
Market frictions (Black 1995)
Job search costs can lead to lower wages and longer unemployment spells in discriminated group.
Existence of prejudiced employers lowers reservation wage.
Therefore, wages of discriminated workers at non-discriminating firms are also lower.
Statistical discrimination
Statistical discrimination
Overview
Unobservable characteristics or imperfect measures of productivity.
Consider two workers with identical unobserved productivity \(F_A(\cdot) = F_B(\cdot)\) belonging to different groups \(A\) and \(B\).
The workers may give signals, such as education, past performance, etc. These are noisy measures of true productivities.
Employers may use average group characteristics to infer quality of signal and update their beliefs about workers.
The statistical discrimination may also change education decisions of groups and lead to persistent inequality among groups.
Statistical discrimination
Environment
Two types of workers: high \(h^+ > 0\) and low \(h^- = 0\)
Employers use costless test to get more information about workers:
- \(\Pr(\text{pass} | h^+) = 1\)
- \(\Pr(\text{pass} | h^-) = p\) where \(p \in [0, 1]\)
Employers know the overall share of efficient workers \(\pi(h^+) \equiv \pi\).
\[ \Pr\left(h = h^+ | \text{pass}\right) = \frac{\Pr\left(h = h^+ \text{ and pass}\right)}{\Pr\left(\text{pass}\right)} = \frac{\pi}{\pi + p\left(1 - \pi\right)} \]
Hence, wages of workers passing the test are
\[ \mathbb{E}\left(\text{productivity}| \text{pass}\right) = h^+ \frac{\pi}{\pi + p(1 - \pi)} \]
This wage is paid regardless of true type to anyone who passes the test
Wage is increasing in \(\pi\). Conversely, if someone is of type \(h^+\) but belongs to a group where \(\pi\) is very low, then their wage is much lower.
The wage is decreasing in the test error \(p\). The less precise the test is, the lower are wages!
Statistical discrimination
Self-fulfilling prophecies
Workers choose education to \(\max_e U(w, e) = \max_e w - e\)
If \(e = 1 \Rightarrow\) worker achieves productivity \(h^+\); otherwise, \(h^-\):
\[ \begin{align} \mathbb{E}\left(w^+\right) &= h^+ \frac{\pi}{\pi + p(1 - \pi)} \\ \mathbb{E}\left(w^-\right) &= pw^+ \end{align} \]
In equilibrium, \(\pi\) is equal to share of workers investing into education.
Statistical discrimination
Self-fulfilling prophecies
Worker invests into education iff
\[ w^+ - 1 \geq pw^+ \quad \Rightarrow \quad \pi \geq \frac{p}{\left(h^+ - 1\right)\left(1 - p\right)} \]
Workers invest into education if employers belief \(\pi\) is sufficiently high.
Statistical discrimination
Multliple equilibria and persistent inequalities
- If employers believe that \(\pi = 0\), there is no incentive to get educated \(\Rightarrow\) everyone gets wage = 0
- This can arise when testing is very imprecise such that too many uneducated people able to pass the test \(p > \frac{h^+ - 1}{h^+}\). Then, the right hand side of the inequality on last slide is >1 and no \(\pi\) can exceed it.
- If employers believe that \(\pi = 1\), then all workers want to get educated.
- There is some \(\pi_0\) in the middle where all workers (since they are ex-ante identical) are indifferent between getting educated or not \(\Rightarrow\) mixed strategy with \(\pi_0 = \Pr(e = 1)\)
- This equilibrium is unstable, because if employers believe \(\pi+\epsilon\) for some very small \(\epsilon > 0\), then all workers get educated \(\Rightarrow\) collapse to rightmost equilibrium with \(\pi = 1\)
- For \(\epsilon < 0\), same argument leads to leftmost equilibrium with \(\pi = 0\)
- Therefore, if employers believe that \(\pi_A < \pi_0\) and \(\pi_B > \pi_0\), then group A never gets education, group B always gets education and wage inequality between groups is very sticky!
Empirical results
Measuring discrimination
\(\Delta\) Wage by non-productive characteristics given same productivity.
Kitagawa-Oaxaca-Blinder^{1} decomposition
Wages in two groups (\(A\) and \(B\)) can be written
\[ \begin{align} \ln w_A &= \mathbf{x}_A \boldsymbol{\beta}_A + \varepsilon_A, \quad \mathbb{E}\left(\varepsilon_A\right) = 0 \\ \ln w_B &= \mathbf{x}_B \boldsymbol{\beta}_B + \varepsilon_B, \quad \mathbb{E}\left(\varepsilon_B\right) = 0 \\ \end{align} \]
Then, average wage differential
\[ \Delta = \mathbb{E}\left(\ln w_A\right) - \mathbb{E}\left(\ln w_B\right) = \color{#288393}{\left[\mathbb{E}\left(\mathbf{x}_A\right) - \mathbb{E}\left(\mathbf{x}_B\right)\right]\boldsymbol{\beta}_A} + \color{#9a2515}{\mathbb{E}\left(\mathbf{x}_B\right)\left(\boldsymbol{\beta}_A - \boldsymbol{\beta}_B\right)} \]
decomposed into explained and unexplained components.
Explained part is essentially composition effect.
Unexplained part: what would \(B\) workers get if their returns were same as \(A\)’s?
The unexplained part on its own is not an evidence of discrimination!
Also show that decomposition is sensitive to the reference group!
Kitagawa-Oaxaca-Blinder decomposition
Interpretation
- Common support: \(\mathbf{x}_A\) and \(\mathbf{x}_B\) contain same set of variables
- Conditional mean independence: \(\mathbb{E}(\varepsilon_A) = \mathbb{E}(\varepsilon_B) = 0\)
- Invariance of conditional distributions: distribution of \(\mathbf{x}_B\) remains unchanged if \(B\) workers receive returns \(\boldsymbol{\beta}_A\)
These are very strict assumptions, so the decomposition is a correlational (not causal) measure.
Kitagawa-Oaxaca-Blinder decomposition
Point out the differences between different bases
Kitagawa-Oaxaca-Blinder decomposition over time
Blau and Kahn (1997): swimming upstream
\[ \begin{align}\Delta_t - \Delta_s &= \left(\Delta X_t - \Delta X_s\right) \beta_{At} + \Delta X_s \left(\beta_{At} - \beta_{As}\right) + \\ &\quad + \left(\mathbb{E}x_{Bt} - \mathbb{E}x_{Bs}\right) \Delta\beta_t + \mathbb{E}x_{Bs} \left(\Delta\beta_t - \Delta\beta_s \right) \end{align} \]
Total \(\Delta_t - \Delta_s = -0.1522\) decomposed into (see Table 2)
2nd term
3rd term
4th term
Interpretation
Change in prices
Moving along distribution
Unexplained change
Contribution
0.0997
-0.1420
0.0143
Total wage differential fell by \(\approx\) 15 percentage points.
The 4th term is crucial for the swimming upstream interpretation. If women did not move up along the distribution, i.e., their characteristics stayed at \(\mathbb{E}x_{Bs}\), then the gender wage gap would have risen by 1.4pp.
Kitagawa-Oaxaca-Blinder decomposition
Summary
Unexplained differences in earnings may be large (about 10%)
They have also risen over time, so gender wage gap did not fall as much as it would have.
But the unexplained differences \(\neq\) discrimination
- Selection into labour force, occupations, unobserved preferences
- Counterfactual labour market returns can affect HC investments
Audit (correspondence) studies
Send fictitious CVs nearly identical except in group membership
Measure callback from firms or probability of getting interviews/offers
RCT \(\Rightarrow\) group differences can be interpreted as discrimination
Remember that for statistical discrimination we want to get \(\boldsymbol{\Delta}\) beliefs even if people are identical in every respect (observable and unobservable)
Therefore, if there are actual differences in unobservable characteristcs, it is not statistical discrimination, but correct economic decision!
for CVs completeness:
how can reflect great interpersonal skills or stress resilience other than face-to-face, probably repeated, interaction?- so, the group membership may convey some information about productive characteristics
for generalization
the total discrimination effect may be larger if people try to compensate bysending out more CVs
being selective about firms
for other moments
Even if both groups are identical on average in observable and unobservable way, it can still be that unobservables are narrower in one group than the other. If employer knows that then the expected variance of unobservable distributions will also be picked up by the group dummy.
Goldin and Rouse (2000)
Before 1970s, musicians in orchestras were handpicked by the director
In 1970s-80s:
- auditions became more “open and routinized”
- musicians were hidden behind screen at some stage of audition
Staggered adoption of screen: difference-in-differences method
Auditions were advertised widely attracting 5x more applicants
Selection committee consisted of orchestra members, “not just conductor and section principal.”
Goldin and Rouse (2000)
Difference-in-differences approach
\[ P_{ijtr} = \alpha + \beta F_i + \gamma B_{jtr} + \color{#9a2515}{\boldsymbol{\delta}} F_i \times B_{jtr} + X_{it}\theta_1 + Z_{jtr}\theta_2 + \varepsilon_{ijtr} \]
\(F_i\) - gender
\(B_{jtr}\) - indicator if screen is used
\(X_{it}\) - other individual characteristics
\(Z_{jtr}\) - other orchestral characteristics
Goldin and Rouse (2000)
Results
Without semifinals | With semifinals | Semifinals | Finals | |
---|---|---|---|---|
Female x Blind | 0.111 | −0.025 | −0.235 | 0.331 |
(0.067) | (0.251) | (0.133) | (0.181) | |
Obs. | 5,395 | 6,239 | 1,360 | 1,127 |
R2 | 0.775 | 0.697 | 0.794 | 0.878 |
Source: Table 6
Bertrand and Mullainathan (2004)
Created templates for CVs of jobseekers in Boston and Chicago
high and low quality types based on experience, skills, career profiles
randomly assign distinctively White or African-American name
track callback/email rates in race/sex/city/quality cell
College degree | Years of experience | Volunteering experience? | Military experience? | E-mail address? | Employment holes? | Work in school? | Honors? | Computer skills? | Special skills? | |
---|---|---|---|---|---|---|---|---|---|---|
White names | 0.720 | 7.860 | 0.410 | 0.090 | 0.480 | 0.450 | 0.560 | 0.050 | 0.810 | 0.330 |
(0.450) | (5.070) | (0.490) | (0.290) | (0.500) | (0.500) | (0.500) | (0.230) | (0.390) | (0.470) | |
African-American | 0.720 | 7.830 | 0.410 | 0.100 | 0.480 | 0.450 | 0.560 | 0.050 | 0.830 | 0.330 |
(0.450) | (5.010) | (0.490) | (0.300) | (0.500) | (0.500) | (0.500) | (0.220) | (0.370) | (0.470) |
Source: Table 3
Bertrand and Mullainathan (2004)
Callback \(\neq\) job offer or wage
Race is only communicated via names
There may be more discrimination once employers can see applicants. For example, not all African-Americans have distinct African-American names.Ignores other channels of job search (networks)
Mobius and Rosenblat (2006)
Lab experiment to measure taste discrimination based on beauty
Participants randomly assigned as workers (5) and employers (5).
Workers answer survey and solve simplest maze game
Survey + practice time = digital CV
Workers predict # mazes solved in 15 min (private)
\(100 A_j - 40 |C_j - A_j|\), where \(A_j\) actual and \(C_j\) predicted performance
Measures confidence
Mobius and Rosenblat (2006)
Workers randomly matched to employers (\(5\times5\))
B CV only (baseline) V CV + (visual) O CV + (oral) VO CV + + (visual and oral) FTF CV + + (face-to-face) Employers randomly told if their wage (next) adds to worker payoff
Captures taste-based discrimination
Employers set wages \(w_{ij}\) = # mazes could solve in 15 min
\(\Pi_i = 4000 - 40 \sum_{j=1}^5 |w_{ij} - A_j|\)
Highlight the logic after the next slide!
an employer with taste for beauty might want to sacrifice earnings by giving higher \(w_{ij}\). But if she knows her wages won’t affect the worker, she has no incentive to do so.
Mobius and Rosenblat (2006)
Workers complete 15 min “employment”
The actual \(A_j\)s are realized.
Payoffs
Firms receive \(\Pi_i\) as on previous slide
Workers receive \(\Pi_j = 100 A_j - 40 |C_j - A_j| + \sum_{i=1}^5W_{ij}\) where \[W_{ij} = \begin{cases}100w_{ij} & \text{with probability }80\%\\\bar{w} & \text{with probability } 20\%\end{cases}\]
Mobius and Rosenblat (2006)
Results
Beauty does not affect actual performance, but increases confidence
There are beauty premia, but no evidence of taste-based discrimination
B V O VO FTF BEAUTY 0.017 0.131** 0.129** 0.124** 0.167** (0.040) (0.042) (0.034) (0.036) (0.043) SETWAGE −0.010 −0.072 0.098* −0.046 0.033 (0.055) (0.052) (0.046) (0.048) (0.057) SETWAGE x BEAUTY −0.058 −0.099+ 0.005 −0.022 −0.044 (0.057) (0.053) (0.048) (0.050) (0.058) N 163 161 163 162 163 Source: Table 4
15-20% of beauty premium due to confidence, 40% due to stereotype
Stereotype = beauty making a worker appear more able in eyes of employers
Rao (2019)
Field and lab experiments eliciting taste-based discrimination
Policy change in India: elite schools required to offer free places to poor students. Staggered implementation \(\Rightarrow\) diff-in-diff estimation
Results
- exposure to poor classmates makes students more prosocial
- it also reduces discrimination (teammate choices in race)
- when stakes (prizes) are high, only 6% choose slower rich student over faster poor student
- when stakes are low, 33% discriminate against poor students
- past exposure \(\downarrow\) taste discrimination WTP by 12pp
The prosocial effect is really driven by changes in fundamental notions of fairness and generosity.
Doleac and Hansen (2020)
Quasi-random policy experiment measuring statistical discrimination
Ban-the-box (BTB) policy
- Banning prior criminal convictions box on job applications
- Hawaii in 1998 \(\longrightarrow\) 34 states + DC in 2015
BTB “does nothing to address the average job readiness of ex-offenders”.
Therefore, statistical discrimination may \(\uparrow\)
Use diff-in-diff to measure effect of BTB on employment of minorities
Obama banned the box in federal job applications in 2015
Doleac and Hansen (2020)
Results
Full sample | BTB-adopting | |
---|---|---|
White x BTB | −0.003 | −0.005 |
(0.006) | (0.008) | |
Black x BTB | −0.034** | −0.031** |
(0.015) | (0.014) | |
Hispanic x BTB | −0.023* | −0.020 |
(0.013) | (0.015) | |
Obs. | 503,419 | 231,933 |
Pre-BTB baseline | ||
White | 0.8219 | 0.8219 |
Black | 0.677 | 0.677 |
Hispanic | 0.7994 | 0.7994 |
Source: Table 4
Glover, Pallais, and Pariente (2017)
Capturing self-fulfilling prophecy of statistical discrimination
Quasi-random assignment of new cashiers to managers in French stores
Do minority cashiers perform worse with biased managers?
Measure manager bias using Implicit Association Test (IAT)
- 66% moderate to severe bias
- 20% slight bias
Outcomes: absences, time worked, scanning speed, time between customers
Minority = North or Sub-Saharan Africans (25-29% of new cashiers)
Glover, Pallais, and Pariente (2017)
Results
Absences | Overtime (min) | Scan per min | Inter-customer time (sec) | |
---|---|---|---|---|
Minority x Mngr bias | 0.012*** | −3.237* | −0.249** | 1.360** |
(0.004) | (1.678) | (0.111) | (0.665) | |
Obs. | 4,371 | 4,163 | 3,601 | 3,287 |
Dep var mean | 0.0162 | -0.068 | 18.53 | 28.7 |
Sources: Tables III and IV
Similarly, Carlana (2019)
Doleac and Stein (2013)
Customer discrimination
Post ads selling iPods on 300 geographically local online markets
Black sellers get:
18% fewer offers
$5.72 (11%) lower avg offer
$7.07 (12%) lower best offer
Similar (sometimes larger) effect for tattooed
Summary
Two main frameworks with different implications for labour markets
- Taste-based discrimination
- Statistical discrimination
Simple decomposition to measure unexplained gap and its changes over time
Vast experimental and quasi-experimental literature
Next: Intergenerational mobility
References
Footnotes
Formerly, Oaxaca-Blinder (Oaxaca and Sierminska 2023)↩︎