KAT.TAL.322 Advanced Course in Labour Economics
April 4, 2024
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
Coworkers may discriminate in collaboration activity
Customers may discriminate in purchase decisions
First formalized by Becker (1957)
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 \(B\).
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.
Nondiscriminating 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 \(w_A\)
nondiscriminating firms hire everyone at \(w_A = w_B = w\)
Taste discrimination cannot persist under perfect 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 nondiscriminating firms are also lower.
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.
Two types of workers: high \(h^+ > 0\) and low \(h^ = 0\)
Employers use costless test to get more information about workers:
Employers know the overall share of efficient workers \(\pi(h^+) \equiv \pi\).
\[ \Pr\left(h = h^+  \text{pass}\right) = \frac{\Pr\left(h = h^+ \text{ and pass}\right)}{\Pr\left(\text{pass}\right)} = \frac{\pi}{\pi + p\left(1  \pi\right)} \]
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.
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.
\(\Delta\) Wage by nonproductive characteristics given same productivity.
Empirical challenges
What constitutes a productive vs nonproductive characteristic?
Is \(\Delta\) wage attributable to discrimination alone or worker preferences?
Does the discrimination arise from tastes or unobserved information?
Types of studies
Observational
Audit and correspondence studies
Lab experiments
Field experiments
Quasirandom experiments
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.
These are very strict assumptions, so the decomposition is a correlational (not causal) measure.
\[ \begin{align}\Delta_t  \Delta_s &= \left(\Delta X_t  \Delta X_s\right) \beta_{At} + \Delta X_s \left(\beta_{At}  \beta_{As}\right) + \\ &\quad + \left(\mathbb{E}x_{Bt}  \mathbb{E}x_{Bs}\right) \Delta\beta_t + \mathbb{E}x_{Bs} \left(\Delta\beta_t  \Delta\beta_s \right) \end{align} \]
Total \(\Delta_t  \Delta_s = 0.1522\) decomposed into (see Table 2)
Interpretation
Contribution
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
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
Challenges
CVs may not convey all relevant productive characteristics
cannot disentangle taste discrimination from statistical
hard to generalize to population
focuses on mean differences, overlooks other moments
Before 1970s, musicians in orchestras were handpicked by the director
In 1970s80s:
Staggered adoption of screen: differenceindifferences method
\[ P_{ijtr} = \alpha + \beta F_i + \gamma B_{jtr} + \color{#9a2515}{\boldsymbol{\delta}} F_i \times B_{jtr} + X_{it}\theta_1 + Z_{jtr}\theta_2 + \varepsilon_{ijtr} \]
Preliminaries



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
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 AfricanAmerican name
track callback/email rates in race/sex/city/quality cell
College degree  Years of experience  Volunteering experience?  Military experience?  Email 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)  
AfricanAmerican  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
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
Workers randomly matched to employers (\(5\times5\))
B  CV only  (baseline) 
V  CV +  (visual) 
O  CV +  (oral) 
VO  CV + +  (visual and oral) 
FTF  CV + +  (facetoface) 
Employers randomly told if their wage (next) adds to worker payoff
Captures tastebased discrimination
Employers set wages \(w_{ij}\) = # mazes could solve in 15 min
\(\Pi_i = 4000  40 \sum_{j=1}^5 w_{ij}  A_j\)
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 \[W_{ij} = \begin{cases}100w_{ij} & \text{with probability }80\%\\\bar{w} & \text{with probability } 20\%\end{cases}\]
Beauty does not affect actual performance, but increases confidence
There are beauty premia, but no evidence of tastebased 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
1520% of beauty premium due to confidence, 40% due to stereotype
Policy change in India: elite schools required to offer free places to poor students. Staggered implementation \(\Rightarrow\) diffindiff estimation
Results
Banthebox (BTB) policy
BTB “does nothing to address the average job readiness of exoffenders”.
Therefore, statistical discrimination may \(\uparrow\)
Use diffindiff to measure effect of BTB on employment of minorities
Full sample  BTBadopting  

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 
PreBTB baseline  
White  0.8219  0.8219 
Black  0.677  0.677 
Hispanic  0.7994  0.7994 
Source: Table 4
Quasirandom 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)
Outcomes: absences, time worked, scanning speed, time between customers
Absences  Overtime (min)  Scan per min  Intercustomer 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
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
Two main frameworks with different implications for labour markets
Simple decomposition to measure unexplained gap and its changes over time
Vast experimental and quasiexperimental literature
Next: Intergenerational mobility