In the Fall 2015 edition of the CFPB’s
Supervisory Highlights, they discussed
two measures of risk that they may
use in their credit decision fair lending
exams: ( 1) odds ratios and ( 2) marginal
effects. While odds ratios are likely
familiar to anyone who has worked in
fair lending since the beginning of time,
marginal effects may be a relatively
unfamiliar concept. Since the CFPB
article in 2015, there have been other
articles that mention the CFPB’s use of
marginal effects, but none discuss the
concept in detail.
Here we’ll explain the concept of
marginal effects in lay terms, discuss
why the CFPB uses marginal effects in
addition to odds ratios, and describe
how financial institutions that choose to
incorporate marginal effects in their fair
lending analyses can reduce file review
costs and fair lending risks. This article
begins with a brief review of odds ratios
then introduces marginal effects and discusses how they are different from odds
ratios, and how these differences can
benefit your institution.
Odds Ratios
An odds ratio is the ratio of a particular
outcome occurring versus not occurring
for one group versus another. Regulators
use odds ratios as one way to quantify
fair lending risk. For example, a denial
rate odds ratio of 2.0 indicates that an
applicant group’s declined-to-approved
ratio was twice the declined-to-ap-
proved ratio of their comparator group.
There are disadvantages to using odds
ratios, including these two, which are
mentioned by the CFPB in their 2015
Supervisory Highlights article:
■ ■ ■ Regulator’s experience is that “…the
magnitudes of odds ratios can be
difficult to interpret.” 1 In particular,
some people confuse odds ratios for
differences in denial probabilities.
However, as their name suggests,
odds ratios are ratios and consider
denial probabilities, as well as approval probabilities. As stated by the
CFPB, “An odds ratio in the context
of an underwriting analysis is the
ratio of the odds of a loan application
denial—that is, ‘the probability of
being denied’ divided by ‘the probability of not being denied (that is, approved)’—for the test group and the
control group, respectively.” 2
■ ■ ■ Odds ratios are not unique. An odds
ratio of 2.0 could be the result of the
target group having a denied rate of
66% and the control group having a
denied rate of 50% or the target group
denied rate being 80% and the control
group having a denied rate of 66%. 3
Despite these short comings, odds
ratios remain a part of the regulator fair
lending arsenal due in a large part to
their familiarity in the industry. Another
benefit of odds ratios is their ability to
analyze small datasets. Unlike, regres-
sion analyses, which recommend at least
30 target group applications, 30 control
group applications, and 100 combined
applications to produce meaningful
results, odds ratios requirements are less
strenuous, and their results are accept-
able if there are 5 target group applicants
and 25 control group applicants. Never-
theless, to overcome the odds ratio limi-
tations and legacy status, regulators may
utilize an additional fair lending risk
measurement called marginal effects.
Marginal Effects
In credit decision analyses, marginal effects are a measure of the difference in
denial probabilities typically focusing
on the denial probability difference between the scenario where an application
possesses a prohibited basis attribute
and the scenario where the application
does not. For example, suppose the
denial probability of a Hispanic applicant was determined to be 66%, but
if that same applicant was White, and
his/her denial probability was found
to be 50%. The marginal effect for this
applicant would be 16% (66% – 50% =
16%). Thus, marginal effects as used in
underwriting fair lending analysis are
used to express the absolute change in
the denial probability associated with a
loan containing a prohibited basis group
attribute versus not containing a prohibited basis group attribute.
So why do the regulators use marginal effects in their analyses, and similarly,
aside from the fact that the regulators
use marginal effects, why should compliance officers include them in the
analyses they perform for their institutions? One reason why is, unlike odds
ratios, marginal effects results actually
show the difference in denial probability
between two groups or applications.
Despite some individuals believing, or
at least articulating, that odds ratios do
Marginal Effects
You may not know me, but your regulator does!
MARGINAL EFFECTS are a regression-based process, used for many years as an analytical tool. The Consumer Financial Protection Bureau (CFPB) has been and continues to use marginal effects in its fair lending exams. Aside from the fact
that regulators utilize marginal effects in their exams, financial institutions may
choose to use marginal effects in their fair lending analyses as well for three
additional reasons: ( 1) lowering review costs and ( 2) reducing fair lending risk,
and ( 3) enhancing analytical versatility.
