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Discrimination: Empirical Evidence. Lent Term Lecture 7 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

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discrimination empirical evidence

Discrimination: Empirical Evidence

Lent Term

Lecture 7

Dr. Radha Iyengar

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

Last Time
testing for discrimination 1
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.
testing for discrimination 2
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.
earnings equation
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≡ 1[in the majority group]
    • ei≡ random error term
  • Our Standard Earnings Equation is then:
  • Y = X'B + AZ + e
estimating discrimination
Estimating Discrimination
  • 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:
  • Obvious Problem is, what to do with differences in X’s
    • 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
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
race and gender earnings 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
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 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.
race and gender employment differences
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
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
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.
basic results
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?
selection into labor market
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.
selection into labor market17
Selection into Labor Market
  • Notice that:

E(w) = LFPR *E( w | participate)

+ (1−LFPR)*E( w | don’t participate)

  • Comparing two groups
  • We can rewrite this as:
adjusting for selection
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
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.
bottom line on selection
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 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 minorities
    • Important interactions with signaling models
effects of selection into lfpr
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
explaining trends in wages
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.
what do we know about selection
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.
returning to the oaxaca decomposition
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 decomposition.
    • 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
Decomposing Observed Differences
  • We can thus decompose observed outcomes as:
adding the time factor
Adding the Time factor…
  • Looking over time and defining selection correction weights, we can then define
the effect of data on inference
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.
imputing wages for nonworkers
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.
selection corrected estimates
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.
supply side effects
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).
can discrimination explain differences
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?
does implied race really matter
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 they believe.
    • Discrimination based on zip-code characteristics appears quite important, and does not systematically differ between white and non-white names.
response papers on names
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; 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
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
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
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.”
estimation baseball
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 iin year t-1;
    • Median Incomeit= median family income (in 1950 dollars) for team iin year t; and
    • Percentage Nonwhiteit= percentage of population that is non-white in year t for team i.
results baseball
Results Baseball
  • 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 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.
other results
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
shifting gears a little what about trends in gender differences
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
human capital explanations
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
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
testing for discrimination
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 wouldn’t be able to see the gender of a performer.
    • data on auditions for about four decades for 8 major US symphony orchestras.
estimating differences after blind auditions
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
glass ceilings
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 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
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
difference in response to 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
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
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.
choking evidence
“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
women and negotiations
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
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.
bottom line
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