Dr. Radha Iyengar
Models of discrimination
Employer Preferences/Becker Model
Discrimination by average firm does not mean
discrimination by marginal firm
Competition will eventually eliminate discrimination
Groups with different means may get compensation
based on group-average productivity not individual
Can occur even with the same mean but different
variance in signals
Testing for Discrimination - 1
interpret the meaning of a race or gender coefficient in an
OLS model, typically a wage model.
use a Oaxaca- Blinder decomposition to interpret the
magnitude of findings.
Apply structural models to make inferences about what
employers believe initially and how they update beliefs as
productivity is revealed over time.
The key tool here is to use information known to the
econometrician at market entry (such as test scores) but not
known by employers except through its revealed effect on
productivity or its correlation with other observables.
Testing for Discrimination - 2
Quasi-experiments where race/gender is
alternatively revealed or concealed.
Audit studies: attempt to ‘randomize’ race to evaluate if
minorities are treated differently in job application,
housing search, vehicle purchases.
Lab experiments. In a non-market setting,
experimenters look for evidence of disparate treatment
of members of race or gender groups.
Yi ≡ the outcome of the process, such as income
earnings, or wage for the ith person.
Xi ≡ a vector of productivity characteristics of
the ith person that are independent of Y and of
the particular form of economic discrimination
under study (exogenous)
Zi ≡ 1[in the majority group]
ei ≡ random error term
Our Standard Earnings Equation is then:
Y = X'B + AZ + e
If A > 0 then there is evidence of discrimination
null is A = 0 with one-side alternative
we’re not considering “reverse discrimination” where A < 0
Define discrimination to be:
D (Y | X , Z 1) (Y | X , Z 0), ˆ
where Y E (Y | X )
Obvious Problem is, what to do with differences in
May be that investment in a given level of X has different
returns due to statistical discrimination: Remember the
TWM results from GED paper
Expectation of discrimination underinvestment (this is a
point Heckman makes in his review of the education lit)
The Regression Approach
Originally done by Oaxaca and repeated in
Key is to establish FACTS
Not entirely clear what the causal mechanism
underlying observed differences can be
Useful for defining classes of models that could
explain these differences
Race and Gender Earnings Differences
Black and Hispanic men, as well as white
women, earn about 2/3 that of white men.
Black and Hispanic women earn even less than
minority mean—only slightly over ½ of what
white males earn.
Wage trends reveal that women, particularly
white women, have experienced an increase in
their earnings relative to mean.
After declining in the 60s, wage gaps have
widended between race/ethnic groups.
Race and Gender Hours Differences
Among women: white women’s wages have risen
steadily since 1980.
Black women’s wages almost reached parity with white
women in the 1970s but diverged after that.
Hispanic women are doing relatively worse, although
that may be due to immigration and changing
Annual earning show an even large differential than
hourly wages, suggesting that weeks and hours worked
are lower among minorities and females. These
differences are less among full-time/full-year workers,
but are still substantial.
Women are more likely to work part-time.
Race and Gender Employment Differences
White men are more likely to ever be employed
and to be employed at any point in time.
Unemployment among white women has been as low or
lower than among white men since the early 80s.
Blacks have about twice the unemployment rate of
whites and this unemployment is more cyclical.
Female labor force participation rates have been
converging. Women, especially white women, have
been entering the labor force rates. They have reached
parity with black women.
These are more particular to US labor market
Thinking about Black-White Gap
How much of the B/W earnings gap is
explained by differences in skills that are
formed prior to market entry?
This is a great question because so much of
literature is focused on market discrimination
Ideal test: Look at identically skilled teens
before market entry and then again later in
life: What is the initial earnings gap and does it
grow over time.
Ideall, if there are no differences in tastes or
costs of skill investment, one could attribute
observed differences to discrimination.
Testing for observed race differences
Can’t assume differences are all due to
discrimination but can try to control for
unobserved innate productivity
Use NLSY. Sample 15 to 23 years old, who
took AFQT prior to age 18. Regress age effects
out of AFQT.
The basic result. ‘Pre-market’ skill appears to
explain a large part of racial earnings gap for
currently employed workers.
Military has done validation studies using objective
performance measures. Finds no evidence that test
systematically under-predicts performance of blacks.
Given this, do blacks underinvest in skills due to lower
In Table 2 and 3, no evidence of differences in return to AFQT.
But this is an endogenous comparison — conditional on having
attained a given level of skill.
Return may have been lower in prior eras, and this could affect
beliefs of black parents, who choose how much to invest in
How would you convincingly test this? What does this imply
that we should see for IV estimates of returns to school for
blacks versus whites?
Selection into Labor Market
Low scoring blacks noticeably less likely to
participate in labor market.
How do we deal with this? Two approaches:
Median regressions. If nonparticipants have
wage offers less than median for group with
similar observables (race, test score) and at
least half participate, then the median is
Less of the gap is explained once we condition
Selection into Labor Market
E(w) = LFPR *E( w | participate)
+ (1−LFPR)*E( w | don’t participate)
Comparing two groups
We can rewrite this as:
Adjusting for selection
Defining a selection factor
Can adjust the observed earnings ratio by
a selection factor.
OLS wage gap: −0.072
Median gap: −0.134
Adjusting for Selection - 2
We need to define a few other parameters
Making a symmetry assumption: kb = kw = 0.1
LFPRb = 0.91 and LFPRw = 0.94
Using this we can get:
Making an assumption on potential earnings of
we get back the observed ratio.
this calculation does not account for AFQT scores
if score gap is much larger among non-employed, this
suddenly does not seem so conservative.
Bottom line on Selection
Appears that selection into pre-labor
market characteristics has large
We need to worry more about the determinant
of the X’s
This motivates much of the discussion on
gender differences in preferences
May be even more serious as incarceration
rates and social welfare participation affect
Important interactions with signaling models
Effects of Selection into LFPR
Butler and Heckman (1977) : expansions in the
generosity of transfer programs over the decade
of the 1960s reduced LFPR for low-skilled
African-American men were more likely to be lower-
skilled, observed relative wages would increase.
a preoccupation with the wages of workers would cause
social scientists to overstate the success of Title VII
Legislation, or spuriously conclude that discrimination
against blacks had declined.
May not be that the Civil Rights Act (CRA) raising the
relative demand for black labor
selective withdrawal hypothesis could also rationalize
Source: Chandra (1998)
Explaining trends in Wages
Increase in the returns to skill that would occur in
a factor which would cause withdrawal to the extent that
reservation wages were relatively fixed over this period.
Massive growth in the US prison population as a
result of the “war on drugs” and the related
Sentencing Reform Act of 1984
Mandatory and longer sentencing guidelines for drug-
Together could generate convergence in observed
wages since they disproportionately affect low-
What do we know about selection?
Nonparticipation matters: across the entire skill
distribution, prime-age black men have withdrawn
from the labor-force at rates that exceed those for
comparably skilled whites.
By 1990, 30 percent of blacks versus 6.1 percent for whites
were not employed during a random reference week in the
Wages are not observed for 20 percent of prime age black
men with annual rates at 40 percent for certain black skill
Sample-selection criteria based on weeks worked or hours
worked also generate convergence in observed wages by
disproportionately excluding low-skill blacks and thereby
exacerbating the bias induced by ignoring nonparticipants.
Returning to the Oaxaca Decomposition
Differences in wages can be thought of as due to
differences between whites and blacks in observable skill
(“between skill differences”)
differences in unobserved skill as well as the possible contribution
of discrimination (“within skill differences”).
For those respondents with wages, we may write the observed
racial (log) wage gap
ΓObs = E(wbt|z = 1) − E(wwt|z = 1) in year t
This is a non-parametric version of the familiar Blinder-Oaxaca
no problem with overlapping supports since the skill cells are
constructed separately by race but using the same X’s
unlike the conventional decomposition where “counterfactual”
wages of blacks are typically estimated by extrapolating into a
region of no support, the nonparametric method does not suffer
from this limitation.
Decomposing Observed Differences
We can thus decompose observed
Adding the Time factor…
Looking over time and defining selection
correction weights, we can then define
The effect of Data on Inference
In the US, a large amount of the inference is based on the
Current Population Survey, this is similar to the inference
based on the labor-force surveys
Most labor force surveys, including the CPS, have the advantage
of producing a fairly consistent yearly time-series which cover a
large section of the population
for example, the CPS is consistent from 1964 onward
The CPS also come with limitations
The CPS for example does not contain information on the
institutionalized population. This omission overstates the
convergence over time because it ignores the role of increasing
the Census provides a more accurate count of the Not in Labor
Force (NILF) group than does the CPS.
In 1990, ignoring the non-employed will be shown to understate
the racial wage gap by 11-16 percentage points; of this, 4-6
percentage points is the effect of incarceration which would be
omitted by the CPS.
Imputing Wages for Nonworkers
Wages for nonworkers are imputed
assuming that nonworkers are drawn from
points on the conditional wage offer
distribution that lie below that of the
This method does not rely on the presence of
arbitrary exclusion restriction to identify the
counterfactual distribution of wages for
Can construct a non-parametric identification of
the standard sample-selection model and a
non-parametric method to decompose the
mechanisms of convergence is provided.
Selectivity-corrected estimates of the
racial wage gap indicate large differences
Ignoring nonparticipation in segregated states
causes estimates of convergence in the 1960s
to be understated by as much as 15 percent as
a result of excluding a number of nonworking
blacks in 1960 from the analysis.
In contrast to the convergence in the observed
series from 1970-90, selectivity corrected
estimates indicate complete stagnation over
this period with a divergence of 5 percent
between 1980 and 1990.
Differences in Selection Corrections
The recent withdrawal of black men across the skill
distribution in recent years is a supply-side effect
by 1990 blacks in the lowest quartile of the offer wage
distribution had non-participation rates that were 20
percent higher than whites in the same quintile,
differences in offer wages explain 40 percent of the
overall difference in participation.
Over the 1960-90 period, differences in offer wages
explain a declining portion of the racial gap in
In 1990, wage elasticities of nonemployment imply that a
10% increase in offer wages would increase weekly
participation by 3.5 percent for blacks (about 50 percent
higher than comparable whites).
Can discrimination explain differences?
May be blacks are selecting out of labor market
because of low expected wages or because of
Bertrand & Mullinathan: Apply for jobs by
sending resume by mail or fax.
Manipulate perceptions of race by using distinctively
Otherwise, hold constant resume characteristics.
Test: Are ‘callback’ rates lower for distinctively black-
Does implied race really matter?
In most cases, names receive equal
treatment but that’s because in most cases,
applicants are not called back.
Black names appear to benefit less from
resume enhancements (such as honors,
more experience) than do whites.
Authors view this as evidence against statistical
discrimination — should work in opposite direction
Discrimination based on zip-code characteristics
appears quite important, and does not
systematically differ between white and non-white
Response Papers on Names
Response by Levitt and Fryer: detailed
birth records data that non-white names
not substantially correlated with life
outcomes once one conditions finely on
B-M response: Not a surprise; it’s not the
name, and that’s name is taken as proxy for
race when race is shielded.
Can this be eliminated by the market?
Economists typically study the economics of
discrimination but not the process by which
discrimination is remedied (through, for example,
shifts from segregation to integration)
Goff, McCormick and Tollison (AER, 2002) plan is to
model desegregation as innovation in order to
answer: What type of firm takes advantage of an
innovation early and why?
Use the case of professional sports
Easy to measure outcomes
Observable quality of both firms (e.g. teams) and individual
players in baseball and basketball
Theories of Integration - 1
Worst-first: The worst firms have the most to
gain from the recruitment of a larger pool of
talent that includes minorities.
The problem with this is that the poor performance
of these teams may be due to poor management,
which may also render them unaware of potential
profit gains from desegregation.
This hypothesis is based on competitive rivalry
Using league standing as a measure of
performance, this theory predicts that “the farther
a team is back in the league standings, the more
likely it is to be a leader in integration”
Theories of Integration - 2
Best-first: If these teams perform better
because of better management, then they
may better understand the profit
opportunities offered by integration.
This hypothesis is based on managerial
Using league standing again as a measure of
performance, “teams with the best winning
records and better management are more
likely to be leaders in the integration process.”
BLACKit = at + b0 + b1(Games Back)it-1, +
b2(Median Income)it +b3 (% Nonwhite)it + eit ,
BLACKit = number of black players on team i in
Games Backit-1 = number of games out of first
place by team i in year t-1;
Median Incomeit = median family income (in
1950 dollars) for team i in year t; and
Percentage Nonwhiteit = percentage of
population that is non-white in year t for team i.
We should see b1 > 0 if the worst teams
integrated first and b1 < 0 if the best
teams integrated first.
The negative coefficients are consistent
with the best-first hypothesis (managerial
These finding also suggests that competition in
the NL, led by the Brooklyn Dodgers, forced
other NL teams to integrate rapidly or lose,
absent Branch Rickey in the AL, the overall
pace of integration was slower.
Table 2: Estimates of Major League Baseball Integration, 1947-1971
Intercept 7.49 (7.96) *
Games Black -0.03 (4.64)*
Median Family -0.16 (-1.32)
Percentage Non-white -0.01 (-0.32)
1947 -5.88* 1955 -3.06* 1963 -1.19*
(-7.74) (-4.50) (-2.03)
1948 -6.08* 1956 -2.08* 1964 -1.23*
(-8.12) (-4.19) (-2.11)
1949 -5.79* 1957 -2.66* 1965 -0.68
(-7.85) (-4.02) (-1.18)
1950 -5.67* 1958 -2.19* 1966 -0.05
(-7.78) (-3.38) (-0.04)
1951 -5.09* 1959 -2.05* 1967 -0.24
(-7.10) (-3.20) (-0.40)
1952 -4.85* 1960 -2.34* 1968 0.26
(-6.09) (-3.79) (0.45)
1953 -4.70* 1961 -1.90* 1969 0.84
(-6.73) (-3.00) (1.47)
1954 -3.58* 1962 -1.69* 1970 0.59
(-5.18) (-2.80) (1.08)
They find similar results in college basket
ball, where good managers are the first
adopters of black players
Can think of this as “new technology”
Best managers adopt new productivity
enhancing technology faster
Then should be the case that black players in
professional baseball and college basketball,
around the time of integration, were better
than their white counter parts
Shifting Gears a little: What about trends
in Gender Differences?
The gender earnings ratio began to increase in
the late 1970s or early 1980s.
Convergence has been substantial: between 1978
and 1999 the weekly earnings of women full-
time workers increased from 61 percent to 76.5
percent of men's earning and flattened out by the
Could be that :
Women are encountering less discrimination than
an upward progression over time in the gender ratio
within given cohorts
Human Capital Explanations
Usually analyzed within the human capital
model (Mincer and Polachek, 1974)
The idea: division of labor by gender in the
family, women tend to accumulate less labor
market experience than men.
women anticipate shorter and more
discontinuous work lives, they have lower
incentives to invest in market-oriented formal
education and on-the-job training
choose occupations for which on-the-job training
is less important, gender differences in
occupations would also be expected
Non-human Capital Explanations
Shorter experience/tenure at firms
employers may be reluctant to hire women for such jobs
because the firm bears some of the costs of such firm-
specific training and fears not getting a full return on that
Labor market discrimination may also affect
women's wages and occupations.
"statistical discrimination," differences in the treatment of
men and women arise from average differences between
the two groups in the expected value of productivity
discriminatory exclusion of women from "male" jobs can
result in an excess supply of labor in "female"
occupations, depressing wages there for otherwise equally
Testing for Discrimination
Difficult to observe employer tastes
Can we separate human capital differences from some
form of discrimination
Set aside, for the moment, pre-market discrimination
Clever natural experiments by Goldin & Rouse
Symphony orchestras used to be all male in the past and
have slowly hired female musicians in the post-war period.
Many orchestras introduced screens during auditions in the
1970s, so that the judges wouldn’t be able to see the
gender of a performer.
data on auditions for about four decades for 8 major US
Estimating Differences after Blind Auditions
Simple difference in success rates in screened and
On average, women do worse on blind rounds
this could be due to changing composition of female pool.
Possible that only the very best women competed when
the game was lopsided.
Limited to musicians (male and female) who
auditioned both blind and non-blind suggest that
women did relatively better in blind rounds (diff-
females minus diff-males)
All of these models exclude orchestra fixed effects
because there is no ‘within’ variation in orchestra blind
Modeling changes for the 3 orchestras that switch policies,
can include musician and orchestra fixed effects
One particular form of discrimination might be
women not being promoted to higher level jobs.
If this is due to discrimination, then we would expect the
women who do get promoted to be particularly able.
Wolfers (2006) looks at the stock returns to
female headed S&P 1500 firms
very slightly negative returns for female headed firms
(though not many observations)
This result implies either there is no discrimination, or if
there is discrimination, the market completely
understands how much better the women are and
values the firms correspondingly
May be incorporated in stock prices and didn’t study the
announcement of hiring a female CEO instead
Can we explain differences with preferences?
Hard to do in a non-experimental setting
Rarely observe controlled enough conditions to
isolate preference related response
Typically want to have more stylized setting
What might generated differences in
Preference for competition
Difference in Response to Competition
Gneezy, Niederle, and Rustichini (2003): lab experiment.
Students at and Israeli engineering school were asked to solve
mazes on a computer.
The experimental sessions were run with six students at a time
working in a room. They were paid according to how many
mazes they solved using different payment schemes:
An individual piece rate: 2 shekels per maze solved
A piece rate with randomization: Among a group of six subjects,
only one was selected randomly to be paid at the end, and that
individual received 12 shekels
A single sex tournament: Only the participant in the group solving
the most mazes was paid 12 shekels for every maze solved, and
groups consisted of six men or six women
A mixed tournament: Only the participant in the group solving the
most mazes was paid 12 shekels for every maze solved, and
groups consisted of three men and three women
Gender Differences in Competition
Performance was the same for piece rates and
piece rates with randomization.
Men solved significantly more mazes in either of the
tournaments, and their performance was similar in the
single sex and mixed tournaments.
Men solve slightly more mazes than women.
Otherwise women’s performance resembled that of
men’s, except in the mixed
In the tournament were women performed only as well as
in the piece rate scheme.
Results suggests that women compete less in
mixed gender environments.
This may be rational because they expect the slightly
better men to win anyway or due to stereotypes
Testing “Choking” behavior
Not quite the same but related question: Do women
perform differently (worse) than men in competitive
Paserman analyzes data from tennis Grand Slam
tournaments, played by professional tennis players for
rather high stakes.
He analyzes how the performance of men and women in
singles matches varies with the stakes within a tournament
To do this, he assigns each point a significance based on the
how winning the point affects the probability of winning the
uses the classifcation of each points into winners, forced
errors, and unforced errors,
and focuses on unforced errors as evidence of choking.
Simple comparison of outcome of a play and the
importance of a point: Not much of a relationship for
men, but women make more unforced errors in more
More formally, including match fixed effects: men actually
make fewer unforced errors as the stakes get higher,
Women become more conservative on both measures,
men hit faster first serves, slower second serves, and also
have longer rallies.
Higher risk aversion of women could possibly explain
Again, stylized setting, hard to interpret
magnitudes or generalizability
Women and Negotiations
The Theory: It’s not preferences over
competition/work environment/etc. it’s
failure to ask for money that generates
differences in observed outcomes
Babcock and Laschever (2003) suggest
that women expect lower salaries and are
less likely to ask for higher salaries in the
workplace. They present some evidence
that this results in lower pay for women.
Women and Negotiations - 2
Survey of starting salaries of Carnegie Mellon
Students. Women earn 8% less. 7% of women
negotiated but 57% of men negotiated. Those who
negotiated were able to raise their starting salaries
by about 7%.
Lab experiment where participants were told they
would be paid between 3 and 10 dollars at the end.
Everybody was actually offered only 3 dollars at the
end. 9 times as many men as women asked to be
Internet survey of individuals negotiation behavior
in real life. Women negotiate less often than men.
There is some “discrimination”. In recent data, this is
probably more important with respect to race/ethnicity than
with respect to gender, although there was probably a lot of
gender discrimination in the past.
It is less of a settled issue what the causes for
discrimination are, i.e. whether it is statistical or taste
based. However, evidence for rational statistical
discrimination is weak
Particularly for women, other things seem to matter a lot.
Different preferences, potentially different skill sets,
different opportunity costs all seem to play a role