Discrimination: Empirical Evidence

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Discrimination Empirical Evidence

• Lent Term
• Lecture 7
• Dr. Radha Iyengar

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Last Time

• Models of discrimination
• Employer Preferences/Becker Model
• Discrimination by average firm does not mean
  discrimination by marginal firm
• Competition will eventually eliminate
  discrimination
• Statistical Discrimination
• Groups with different means may get compensation
  based on group-average productivity not
  individual productivity
• Can occur even with the same mean but different
  variance in signals

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Testing for Discrimination - 1

• Regression studies.
• 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.
• Learning models
• 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.

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Testing for Discrimination - 2

• Quasi-experiments where race/gender is
  alternatively revealed or concealed.
• Experimental Studies
• 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.

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Earnings Equation

• Define
• 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 1in the majority group
• ei random error term
• Our Standard Earnings Equation is then
• Y X'B AZ e

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Estimating Discrimination

• If A gt 0 then there is evidence of discrimination
  
• null is A 0 with one-side alternative
• were not considering reverse discrimination
  where A lt 0
• Define discrimination to be
• Obvious Problem is, what to do with differences
  in Xs
• 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)

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The Regression Approach

• Originally done by Oaxaca and repeated in many
  settings
• 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

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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 meanonly 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.

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Race and Gender Hours Differences

• Among women white womens wages have risen
  steadily since 1980.
• Black womens 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 composition.
• 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.

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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

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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.

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Testing for observed race differences

• Cant 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.

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Basic Results

• 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 return?
• 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 kids skills.
• 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?

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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 identified
• Less of the gap is explained once we condition on
  participation.

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Selection into Labor Market

• Notice that
• E(w) LFPR E( w participate)
• (1-LFPR)E( w dont participate)
• Comparing two groups
• We can rewrite this as

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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

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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
  non-employed,
• 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.

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Bottom line on Selection

• Appears that selection into pre-labor market
  characteristics has large explanatory affect
• We need to worry more about the determinant of
  the Xs
• This motivates much of the discussion on gender
  differences in preferences
• May be even more serious as incarceration rates
  and social welfare participation affect
  minorities
• Important interactions with signaling models

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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
  workers
• 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 the data

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Source Chandra (1998)
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Explaining trends in Wages

• Increase in the returns to skill that would occur
  in the 1980s
• 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-related convictions.
• Together could generate convergence in observed
  wages since they disproportionately affect
  low-skilled blacks.

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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 year
• Wages are not observed for 20 percent of prime
  age black men with annual rates at 40 percent for
  certain black skill groups.
• 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.

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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
• GObs E(wbtz 1) - E(wwtz 1) in year t
• This is a non-parametric version of the familiar
  Blinder-Oaxaca decomposition.
• no problem with overlapping supports since the
  skill cells are constructed separately by race
  but using the same Xs
• 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.

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Decomposing Observed Differences

• We can thus decompose observed outcomes as

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Adding the Time factor

• Looking over time and defining selection
  correction weights, we can then define

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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
  criminal activity
• 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.

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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 median respondent.
• This method does not rely on the presence of
  arbitrary exclusion restriction to identify the
  counterfactual distribution of wages for
  nonworkers.
• 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.

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Selection-Corrected Estimates

• 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.

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Differences in Selection Corrections
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Supply-Side Effects

• 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 employment,
• 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).

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Can discrimination explain differences?

• May be blacks are selecting out of labor market
  because of low expected wages or because of
  employers tastes
• Bertrand Mullinathan Apply for jobs by sending
  resume by mail or fax.
• Manipulate perceptions of race by using
  distinctively ethnic names.
• Otherwise, hold constant resume characteristics.
• Test Are callback rates lower for
  distinctively black-named applicants?

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Does implied race really matter?

• In most cases, names receive equal treatment but
  thats 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 they believe.
• Discrimination based on zip-code characteristics
  appears quite important, and does not
  systematically differ between white and non-white
  names.

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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 mother/birth
  characteristics.
• B-M response Not a surprise its not the name,
  and thats name is taken as proxy for race when
  race is shielded.

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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

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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
•  

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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
  capability.
• 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.

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Estimation Baseball

• BLACKit at b0 b1(Games Back)it-1,
  b2(Median Income)it b3 ( Nonwhite)it eit ,
• Where 
• BLACKit number of black players on team i in
  year t
• 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.

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Results Baseball

• We should see b1 gt 0 if the worst teams
  integrated first and b1 lt 0 if the best teams
  integrated first.
• The negative coefficients are consistent with the
  best-first hypothesis (managerial ability).
• 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.

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Table 2 Estimates of Major League Baseball
Integration, 1947-1971
Variable Variable Coefficient Coefficient Coefficient Coefficient Coefficient
Intercept Intercept 7.49 (7.96) 7.49 (7.96) 7.49 (7.96) 7.49 (7.96) 7.49 (7.96)
Games Black Games Black -0.03 (4.64) -0.03 (4.64) -0.03 (4.64) -0.03 (4.64) -0.03 (4.64)
Median Family Income Median Family Income -0.16 (-1.32) -0.16 (-1.32) -0.16 (-1.32) -0.16 (-1.32) -0.16 (-1.32)
Percentage Non-white Percentage Non-white -0.01 (-0.32) -0.01 (-0.32) -0.01 (-0.32) -0.01 (-0.32) -0.01 (-0.32)
R2 R2 0.58 21.10 0.58 21.10 0.58 21.10 0.58 21.10 0.58 21.10
F-statistic F-statistic 0.58 21.10 0.58 21.10 0.58 21.10 0.58 21.10 0.58 21.10
Year Effects Year Effects Year Effects Year Effects Year Effects Year Effects Year Effects
1947 -5.88 (-7.74) -5.88 (-7.74) 1955 -3.06 (-4.50) 1963 -1.19 (-2.03)
1948 -6.08 (-8.12) -6.08 (-8.12) 1956 -2.08 (-4.19) 1964 -1.23 (-2.11)
1949 -5.79 (-7.85) -5.79 (-7.85) 1957 -2.66 (-4.02) 1965 -0.68 (-1.18)
1950 -5.67 (-7.78) -5.67 (-7.78) 1958 -2.19 (-3.38) 1966 -0.05 (-0.04)
1951 -5.09 (-7.10) -5.09 (-7.10) 1959 -2.05 (-3.20) 1967 -0.24 (-0.40)
1952 -4.85 (-6.09) -4.85 (-6.09) 1960 -2.34 (-3.79) 1968 0.26 (0.45)
1953 -4.70 (-6.73) -4.70 (-6.73) 1961 -1.90 (-3.00) 1969 0.84 (1.47)
1954 -3.58 (-5.18) -3.58 (-5.18) 1962 -1.69 (-2.80) 1970 0.59 (1.08)
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Other results

• 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

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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
  mid-1990s
• Could be that
• Women are encountering less discrimination than
  previous ones
• an upward progression over time in the gender
  ratio within given cohorts

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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

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Non-human Capital Explanations

• Specific Capital
• 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 investment.
• 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 productive workers

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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
  using orchestra
• 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
  wouldnt be able to see the gender of a
  performer.
• data on auditions for about four decades for 8
  major US symphony orchestras.

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Estimating Differences after Blind Auditions

• Simple difference in success rates in screened
  and not-screened auditions
• 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 policies.
• Modeling changes for the 3 orchestras that switch
  policies, can include musician and orchestra
  fixed effects

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Glass Ceilings

• One particular form of discrimination might be
  glass ceilings
• 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 SP 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 didnt
  study the announcement of hiring a female CEO
  instead

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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 outcomes?
• Preference for competition
• Negotiations

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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

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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 womens performance resembled that of
  mens, 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

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Testing Choking behavior

• Not quite the same but related question Do women
  perform differently (worse) than men in
  competitive environments?
• 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 entire match
• uses the classifcation of each points into
  winners, forced errors, and unforced errors,
• and focuses on unforced errors as evidence of
  choking.

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Choking Evidence

• Results
• 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 important points.
• More formally, including match fixed effects men
  actually make fewer unforced errors as the stakes
  get higher, women more.
• 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 these results
• Again, stylized setting, hard to interpret
  magnitudes or generalizability

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Women and Negotiations

• The Theory Its not preferences over
  competition/work environment/etc. its 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.

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Women and Negotiations - 2

• Some evidence
• 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 paid more.
• Internet survey of individuals negotiation
  behavior in real life. Women negotiate less often
  than men.

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Bottom Line

• 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