Definitions

Difference in denial rates. Statistical Parity is satisfied if applicants from different groups are denied at the same rate. A violation of this measure is defined as the difference in denial rate between a target demographic group and the reference demographic group. For example, a Statistical Parity value of 10 for Black applicants means Black applicants are 10 percentage points more likely to be denied on their loan application than White applicants. Negative values indicate a lower denial rate relative to the reference group.

Difference in default rates. Predictive Parity is satisfied if borrowers from different groups default at the same rate. A violation of this measure is defined as the difference in default rate between a target demographic group and the reference demographic group. For example, a Predictive Parity value of 10 for Black borrowers means that Black borrowers are 10 percentage points more likely to default than White borrowers. Negative values indicate a lower default rate relative to the reference group.

Difference in lending standards. The Marginal Outcome Test is satisfied if borrowers at the margin default at the same rate across groups. Marginal applicants are defined as those who submit one application resulting in an approval and another resulting in a denial. See the technical report for more detail on our procedure to identify such applicants. A violation of this measure is defined as the difference in default rate between marginal applicants in the reference demographic group and marginal applicants in a target demographic group. For example, a value of 10 for Black borrowers means that Black marginal borrowers are 10 percentage points less likely to default than White marginal borrowers. This is because higher default rates at the margin imply lower lending standards among this group, relative to the reference group.

Difference in denial rates for non-creditworthy borrowers; captures a notion of unfair approvals. Equality of Goodwill is satisfied if non-creditworthy borrowers are denied at the same rate across groups. A violation of this measure is defined as the difference in denial probability between non-creditworthy applicants in a target demographic group and non-creditworthy applicants in the reference demographic group. We define non-creditworthy borrowers as those that defaulted on their loan. To estimate this measure, we use the set of applicants who apply multiple times (see the technical report for more detail on our procedure to identify such applicants), originate one loan, and later default. For example, a value of 10 for Black borrowers means that Black non-creditworthy borrowers are 10 percentage points more likely to be denied on their loan applications than White non-creditworthy borrowers.

Difference in denial rates for creditworthy borrowers; captures a notion of unfair denials. Equality of Opportunity is satisfied if creditworthy borrowers are denied at the same rate across groups. A violation of this measure is defined as the difference in denial probability between creditworthy applicants in a target demographic group and creditworthy applicants in the reference demographic group. We define creditworthy applicants as those that did not default on their loan. To estimate this measure, we use the set of applicants who apply multiple times (see the technical report for more detail on our procedure to identify such applicants), originate one loan, and do not default. For example, a value of 10 for Black borrowers means that Black creditworthy borrowers are 10 percentage points more likely to be denied on their loan applications than White creditworthy borrowers.

Conditional difference in denial rates. Conditional Statistical Parity is satisfied if applicants from different groups, conditional on the same attributes, are denied at the same rate. A violation of this measure is defined as the difference in denial rates between a target and the reference demographic group among those with the same attributes. For example, a value of 10 for Black applicants means that Black applicants are 10 percentage points more likely to be denied on their loan application than White applicants with the same set of attributes (e.g., credit score or loan amount).

The explorer includes two versions of this measure. “Small model” is a linear model and includes the conditioning variables: applicant income, loan amount, loan purpose, and an indicator for whether a coapplicant is present. “Large model” is a nonlinear model and includes an indicator for whether a coapplicant is present, loan purpose, the outcome of the automated underwriting system, and binned variables: applicant income, loan amount, credit score, debt-to-income ratio, and loan-to-value ratio.

In the underlying data available for download, we include several additional conditional statistical parity models:

• Large model (linear): includes an indicator for whether a coapplicant is present, loan purpose, applicant income, loan amount, credit score, debt-to-income ratio, and loan-to-value ratio. Available beginning in 2018.

• Large model, including AUS indicator (linear): includes the same variables as “large model (linear)” above and the outcome of the automated underwriting system. Available beginning in 2018.

• Large model (nonlinear): includes an indicator for whether a coapplicant is present, loan purpose, and binned variables: applicant income, loan amount, credit score, debt-to-income ratio, and loan-to-value ratio. Available beginning in 2018.

• Large model, including AUS indicator (nonlinear): equivalent to “large model” from the explorer

• Small model (linear): equivalent to “small model” from the explorer

• Small model (nonlinear): includes loan purpose, an indicator for whether a coapplicant is present, and binned variables: applicant income and loan amount.

Amount of under-representation among those approved; corresponds to the idea that approved applicants should be “representative” of qualified applicants. This measure is satisfied if the proportion of approved applicants from a group is equal to the proportion of qualified applicants from that group. We define qualified applicants as those who have low estimated default risk. A violation of this measure is the difference in the proportion of qualified applicants from a target demographic group and the proportion of approved applicants from the same demographic group. For example, a value of 10 for Black applicants means that there are 10 percentage points fewer Black approved applicants than Black qualified applicants. Thus, if Representativeness is positive, the group is “under-represented.”

In the underlying data available for download, we include two versions of Representativeness:

• Including race: includes race in the default risk model we use to define qualified applicants. This is the version included in the explorer visualizations.
• Not including race: uses the same model to estimate default risk and define qualified applicants as the above except race is excluded from the model.

Refers to the sex of the primary applicant, when known. We use these categories: female and male.

Refers to the first race or ethnicity category reported for the primary applicant (up to five can be), when known. We construct mutually exclusive categories: Hispanic (Hispanic), non-Hispanic White (White), non-Hispanic Black (Black), and non-Hispanic Asian (Asian).

The gross annual income of the applicant to the extent relied on by the lending institution reporting the application.

This variable is generated by the automated underwriting system (AUS) used by the institution to evaluate the application. Potential systems are the Desktop Underwriter, Loan Prospector, Technology Open to Approved Lenders, or some other system the lender uses.

The ratio as a percentage of the applicant’s or borrower’s total monthly debt payments to the total monthly income relied on in making the credit decision.

Ratio between the total amount of debt secured by the property and the value of the property, expressed as a percentage.

The number of months after which the legal obligation will mature or terminate, or would have matured or terminated.

A mortgage application that has been approved and for which loan capital has been issued.

The number of denied mortgage applications divided by the total number of submitted applications.

We consider a loan in default if its status is ever more than 90 days past due (i.e., three or more missed payments) within 24 months of origination. Default rate is equal to the number of mortgages in default divided by the total number of mortgages.

The sample size is the total number of individuals within a group who fit the criteria of the measure (e.g., for the Marginal Outcome Test among Black borrowers, the sample size is the number of Black borrowers who submitted multiple identical applications for a mortgage and were accepted at least once and denied at least once).