Discrimination: Empirical Evidence

Lent TermLecture 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

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 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 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 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)

)|(ˆ where),0,|ˆ()1,|ˆ( XYEYZXYZXYD

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 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 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 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.

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 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 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 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 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 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 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

Source: Chandra (1998)

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?

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

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 gapΓObs = 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 We can thus decompose observed

outcomes as:

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 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 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 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

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? 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? 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 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? 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

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 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.

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.

Variable CoefficientIntercept 7.49 (7.96) *Games Black -0.03 (4.64)*Median Family Income -0.16 (-1.32)

Percentage Non-white -0.01 (-0.32)R2 0.58

21.10F-statisticYear Effects

1947 -5.88*(-7.74)

1955 -3.06*(-4.50)

1963 -1.19*(-2.03)

1948 -6.08*(-8.12)

1956 -2.08*(-4.19)

1964 -1.23*(-2.11)

1949 -5.79*(-7.85)

1957 -2.66*(-4.02)

1965 -0.68(-1.18)

1950 -5.67*(-7.78)

1958 -2.19*(-3.38)

1966 -0.05(-0.04)

1951 -5.09*(-7.10)

1959 -2.05*(-3.20)

1967 -0.24(-0.40)

1952 -4.85*(-6.09)

1960 -2.34*(-3.79)

1968 0.26(0.45)

1953 -4.70*(-6.73)

1961 -1.90*(-3.00)

1969 0.84(1.47)

1954 -3.58*(-5.18)

1962 -1.69*(-2.80)

1970 0.59(1.08)

Table 2: Estimates of Major League Baseball Integration, 1947-1971

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? 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 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 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 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

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 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?

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

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 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 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 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 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 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