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When is "marginal effect" used to test for discrimination in credit decisions?
in Mathematics by Diamond (75,918 points) | 37 views

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ME is used when reviewing a binary, yes-no, decision such as loan acceptance. ME is the difference between the acceptance rate for a control group (often Whites or males) and a protected demographic class of interest, reported as a percentage:

$$100 \cdot (Pr(\hat{y} =1 | X_{c} = 1) - (Pr(\hat{y} = 1 | X_{p} = 1)$$
where  $\hat{y}$ are the model decisions,  $X_{c}$ and  $X_{p}$ represent binary markers created from a demographic attribute,  denotes the control group,  indicates a protected group, and $Pr(·)$  is the operator for conditional probability.

Importantly, ME can only be interpreted within the context of a given lending scenario.

As a hypothetical example, a male-female ME of 4% would often be a highly noteworthy difference in mortgage lending to a population of prime consumers, because class-control differences in credit quality among prime consumers is usually relatively small – particularly for this example because women often have higher average credit quality. On the other hand, a Minority-to-Non-Hispanic White ME of 4% might not be as unusual for something like a credit card offered to consumers across a wide spectrum of credit quality – particularly if the population includes those with thin credit files.

This is because some minority groups are more frequently found at the lower end of the spectrum of perceived credit quality as measured using traditional scoring systems. Thus, while minorities with a given model score would be treated the same as a Non-Hispanic White who had the same score, the average offer rate by class would be lower, leading to the higher ME.1
by Diamond (75,918 points)
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