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Page 67
Appendix B
Audit Studies and the Assessment of
Discrimination
S.A. Murphy
The Housing Discrimination Study (HDS) uses primarily audit studies
to estimate overall-level discrimination against
ethnic/racial groups. Overall-level discrimination occurs when
there is ethnic/racial discrimination averaged across realtors,
applicants (i.e., auditors), and circumstances. By realtor is meant
housing realtors and other purveyors of housing; by circumstances
is meant the circumstances of the contact between the auditor and
the realtor. Overall-level discrimination is of course different
from individual-level discrimination, in which particular
auditors are discriminated against because of ethnic status. To
simplify the following discussion, the term “black” is
used to encompass racial minorities.
Discrimination here refers to adverse market
discrimination, which can occur in two ways. Discrimination
against blacks occurs when race = black is a direct reason for the
realtor to produce a negative outcome or when race = black
is used by the realtor as a surrogate for unobserved measures of
(renter/buyer) suitability that vary in distribution across the
racial groups. The former is direct discrimination, and the latter
is statistical discrimination.
Realtors should strive to ascertain all qualification measures
directly, including those that vary in distribution across racial
groups. Realtors are
S.A. Murphy works for the Department of Statistics and Institute
for Social Research at the University of Michigan.
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Page 67
Appendix B
Audit Studies and the Assessment of
Discrimination
S.A. Murphy
The Housing Discrimination Study (HDS) uses primarily audit studies
to estimate overall-level discrimination against
ethnic/racial groups. Overall-level discrimination occurs when
there is ethnic/racial discrimination averaged across realtors,
applicants (i.e., auditors), and circumstances. By realtor is meant
housing realtors and other purveyors of housing; by circumstances
is meant the circumstances of the contact between the auditor and
the realtor. Overall-level discrimination is of course different
from individual-level discrimination, in which particular
auditors are discriminated against because of ethnic status. To
simplify the following discussion, the term “black” is
used to encompass racial minorities.
Discrimination here refers to adverse market
discrimination, which can occur in two ways. Discrimination
against blacks occurs when race = black is a direct reason for the
realtor to produce a negative outcome or when race = black
is used by the realtor as a surrogate for unobserved measures of
(renter/buyer) suitability that vary in distribution across the
racial groups. The former is direct discrimination, and the latter
is statistical discrimination.
Realtors should strive to ascertain all qualification measures
directly, including those that vary in distribution across racial
groups. Realtors are
S.A. Murphy works for the Department of Statistics and Institute
for Social Research at the University of Michigan.
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not to use race as a surrogate for qualification measures. More work
is needed to assist well-intentioned realtors (with an imperfect
ability to assess qualifications) in avoiding the use of race as a
surrogate for qualifications.
Since individual-level discrimination and overall-level discrimination
are easily confused when discussing the utility of the audit model,
the two are discussed in turn below.
THE AUDIT MODEL AND
INDIVIDUAL-LEVEL DISCRIMINATION
Sometimes audit results are reported by audit pair (averaged over
realtors and circumstances of audit visits). Audit results reported
for a particular pair may be misconstrued as estimates of net or
gross individual-level discrimination. However, even under
extremely optimal conditions, audit results for a particular pair
cannot be interpreted as estimates of individual-level
discrimination. Suppose the audit coordinator is successful in
matching the audit pair on all possible qualifications (that vary
in distribution by race). One can expect there to be many
individual characteristics that do not vary across the two racial
groups (black/white), yet are used in assessing renter
qualifications. These characteristics may or may not be truly
indicative of one's qualifications. Moreover, since the
characteristics are equivalently distributed across racial groups,
their use does not constitute discrimination between racial groups.
The individuals in the audit pair may not be equal on these
characteristics; thus the realtor may treat the individuals in the
audit pair unequally, yet no discrimination occurs. Fallibility in
assessing qualifications may lead to this situation. To emphasize
this observation more strongly, even if both of the members of the
audit are white, it may be expected that audit results for one pair
(averaged over realtors and circumstances of audit visits) would
result in nonzero “estimates” of individual-level
measures of discrimination.
The conclusion is that audit results presented by audit pair do not
represent individual-level discrimination unless an extremely
strong assumption holds. This assumption is that the auditors are
matched on all qualifications and individual characteristics
regardless of whether these qualifications/characteristics vary by
race. This assumption appears impractical and unnecessary when the
goal is to ascertain overall-level discrimination. It is difficult
to see how this level of matching can be achieved in practice.
Indeed, this level of matching (i.e., the test coordinator has
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matched the members of the pair not only on all possible
qualifications that vary in distribution by race, but also on all
possible individual characteristics that vary in distribution by race)
will not hold even in optimal settings. The economic agent may treat
the members of the audit pair differently because of differing
individual characteristics that do not vary by race. Of course, if the
audit results for one audit pair are extremely gross, one may be
inclined to believe that there are no individual characteristics/
qualifications that could have produced such a gross effect.
THE AUDIT MODEL AND OVERALL-LEVEL
DISCRIMINATION
As long as audit pairs are matched on all qualifications that vary
in distribution by race, audit results averaged over realtors,
circumstances of the visits, and auditors can be viewed as an
unbiased estimate of overall-level discrimination (i.e., average
level of adverse market discrimination). This is because one
averages overall individual auditor characteristics (as opposed to
the case of individual-level discrimination, in which audit results
are to be averaged only over realtors and circumstances of the
visits).
The following is a quantitative explanation in which:
f is used to denote densities.
e is race (black/white).
ea is realtor (realty, etc.).
r(ea) is the realtor's legitimate applicant
requirements/qualifications that vary in distribution by race
(income requirements, credit requirements, etc.).
ic is individual auditor characteristics that do not vary
in distribution by race. That is, f(ic|e) =
f(ic).
ice is individual auditor characteristics that may vary in
distribution by race and are not in r(ea). That is,
f(ice|e,r(ea),ic) is not identically equal to
f(ice|r(ea),ic). There is a dependence of
f on r(ea) since applicant requirements may vary
by realtor, and thus r(ea) may include more or less of the
set of all individual auditor characteristics varying by race.
c is circumstances of the audit visit unconnected with the
particular individual auditor (e.g., the apartment was rented in
the meantime).
X is 1 if the realtor says the advertised apartment is
available, 0 otherwise. X is indexed by all factors that
contribute to a result of 1 or 0. X is an unknown
nonparametric function: X(e,r(ea),ice, ic,ea,c).
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Technically, X = X(e,r(ea),ice,ic,ea,c) may be viewed as a
nonparametric structural equation in the terminology of Pearl (2000).
Suppose the audit pair is composed of one white and one black. The two
individuals are assigned the same realtor (same ea) and are
assigned or possess the same values as the realtor's legitimate
requirements, r(ea). They have different individual
characteristics, denoted by (ice′, ic′)
and (ice′′, ic′′),
respectively. Also, since they must visit the agent at different
times, the circumstances will be different as well (c′
and c′′).
The net average or overall-level discrimination estimate is then found
by averaging
X(e = w,
r(ea),ice′,ic′,ea,c′)
– X(e =
b,r(ea),ice′′,ic′′,ea,c′)
over circumstances, realtors, and audit pairs. This results in an
estimator for
ʃ(X(w,r(ea),ice,ic,ea,c)
f(ice|w,r(ea),ic) (1)
–X(b,r(ea),ice,ic,ea,c) f(ice|b, r(ea),ic)) f(c,ea)
f(ic) d(ea,c,ice,ic),
where f(c,ea) is determined by the selection of
advertisements and the visit times of the auditors (this density is
the same for both members of the audit pair since they ask about the
same advertisement, and the order of the visits is randomized); where
f(ic) is determined by the selection of the auditors; and
where f(ice|w,r(ea),ic) is determined by the
realtor's suitability requirements and the selection of the auditors.
In addition, f(ice|w,r(ea),ic) ≠
f(ice|b,r(ea),ic) since there are individual
characteristics that vary in distribution between the racial groups.
The above difference is zero if X(e,r(ea),ice,ic,ea,c) is
constant in both e and ice, that is, if the
realtor's judgment of suitability does not directly employ race or
employ race as a surrogate for individual characteristics (not in
r(ea)) that vary in distribution by race. This is exactly
what would be expected from a measure of overall discrimination.
COMMENTS
Audit pairs need only be matched on all qualifications that vary in
distribution by race to provide an unbiased estimate of average or
overall discrimination. Audit pairs may be matched on other
characteristics (to improve statistical power), but this is not
necessary to produce an unbiased
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estimator of net average or overall discrimination. Moreover, to
accumulate information about discrimination, one needs many audit
pairs. Multiple audits by audit pairs can be used to hold costs down,
but one does not thereby accumulate information about discrimination.
Information about discrimination is not accumulated because the
members of the audit pair may differ in ic, individual
characteristics that are distributed equally in the two races.
Differential treatment of the members of the auditor pair due to
ic is not adverse discrimination.
Improving the Matching on All Qualifications
that Vary in Distribution by Race
Estimation of net overall discrimination requires that the audit
pair be matched on all suitability qualifications that vary in
distribution by race. It can be expected that these qualifications
will vary by economic agent. Furthermore, it is unrealistic to
expect the HDS to be aware of all of realtors' suitability
qualifications. The HDS can assign qualifications to an audit pair
in a way that depends on the realtors. First, the customary
qualifications/requirements (such as creditworthiness, income, and
employer/occupation) are assigned. Then, after audit pairs have
been randomized to realtors and individuals within the audit pair
randomized by order, the first auditor should record all questions
asked and answers given that are not part of the assigned customary
requirements. The test coordinator can then use the additional
information requested of the first auditor to form a closer match
by maintaining a consistent life story for the second auditor. Thus
the realtor determines which individual characteristics (beyond the
customary suitability requirements and race) will be matched.
Determining Whether the Overall
Discrimination Effect Is a “Market-Level” Discrimination
Effect
It is of low utility to discover that agents handling homes for
which most blacks could not reasonably qualify are discriminatory.
It is much more useful to discover that agents handling homes well
within the reach of many blacks are discriminatory.
It appears that the distribution of the prices of the homes used in
the HDS should match the distribution of creditworthiness, income,
and employer/occupation among blacks rather than an overall average
distribution of creditworthiness, income, and employer/occupation.
This point is in
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line with the idea that it is important to ascertain discrimination in
situations in which blacks are qualified buyers. This is not the same
as saying that the impact of discrimination is most important at the
realties blacks choose to use, but that the impact of discrimination
is most important at the realties that sell homes blacks are qualified
to buy.
The above point can be seen from display (1), in which the differences
(X(w,r(ea),ice,ic,ea,c) f(ice|w,r(ea),ic) –
X(b,r(ea),ice,ic,ea,c) f(ice|b,r(ea),ic))
are weighed by the density f(c,ea). Thus large differences
can be paired with a small f(c,ea) weight and vice versa, and
so the definition of overall-level discrimination changes with the
distribution of realtors, ea.
How difficult would it be to match the market to the qualifications of
blacks; that is, to choose home advertisements (i.e., realtors) with
probabilities proportional to the “appropriate” segment of
the black population?
REFERENCE
Pearl, J. 2000 Causality: Models, Reasoning, and
Inference . New York :
Cambridge University Press .
Representative terms from entire chapter:
individual characteristics
