Case Study: Regression Analysis Conducted In Response to a Regulatory Inquiry

This case study details a fair lending review conducted by Premier Insights, Inc. for The Bank, analyzing loan application data to assess discriminatory lending practices. The analysis, submitted to the FDIC, involved statistical modeling of factors such as credit score, debt-to-income ratio, and loan-to-value ratio. The findings revealed no evidence of disparate treatment based on race, indicating that loan decisions were primarily based on objective, credit-worthiness criteria. Regression analyses confirmed the significance of these objective factors in determining loan approvals and denials, further supporting the absence of discriminatory practices. All data and code were provided to the FDIC.

Introduction

Premier Insights, Inc. assisted The Bank in analyzing data related to a regulatory fair lending review. This included formatting data for presentation to the FDIC and conducting statistical analyses. All requested data was collected and uploaded to the FDIC, along with the statistical analysis and programming code. The analysis found no evidence of disparate treatment, demonstrating the Bank relied on objective factors in making loan decisions.

Data and Scope

  • The analysis focused on a sample of 948 applications for first lien, 1-4 family, owner-occupied housing units.
  • The FDIC initially requested credit score, DTI (debt-to-income ratio), and LTV (loan-to-value ratio) to be added to the HMDA (Home Mortgage Disclosure Act) data.
  • Subsequently, the FDIC requested additional information including payment history with the Bank and others, and the applicant’s loan and deposit relationship with the Bank.

Underwriting Variables and Analysis

  • The Bank used a Fair Isaac credit scoring system, which is a common industry practice. However, the analysis noted that this system works well for typical situations, but applications still require individual review.
  • The Bank's use of loan origination determination software was not a definitive decisioning factor. Instead, it served as an alert system, signaling potential issues outside of credit policy parameters. For example, the determination might show "deny" due to a bankruptcy, but the Bank would not automatically deny a loan based on bankruptcy alone.
  • Premier Insights noted that the additional factors requested by the FDIC should be indirectly accounted for by the Fair Isaac credit score model. However, Premier Insights created variables from the data that the analysis suggested were pertinent.
  • The Bank's original data submission included override codes, which are used when the Bank deviates from core credit policy. Premier Insights corrected incomplete data and included these codes in the analysis.

Variable Coding

  • The FDIC identified black applicants as the target group and white, non-Hispanic applicants as the control group. Premier Insights coded applications where either the applicant or co-applicant was black as the target group and all others as the control group.
  • Applications with action codes of 1 or 2 were coded as approvals, and those with action codes of 3 were coded as denials.

Analysis and Findings

  • Premier Insights examined differences in key variables between loans that were denied and those that were approved, using t-tests to assess statistical significance.
  • Univariate Results: A significantly larger proportion of denials were for black applicants. However, denials also involved smaller loan amounts, lower income, lower credit scores, higher DTI ratios, and lower loan and deposit balances with The Bank. Denials were more likely for new home purchases and less likely for refinancing, and the denied applications were less likely to have previous loans or deposits with The Bank.
  • Black vs. Non-Black Applicants: The analysis showed that black applicants, on average, had smaller loans, lower income, lower credit scores, higher DTI ratios, and lower loan and deposit balances with the Bank, which were similar characteristics to those associated with denials.
  • Regression Analysis: Premier Insights used regression analysis to measure the role of race and other factors in loan decisions simultaneously. This allowed examination of the independent impact of each factor on loan decisions, holding other factors constant.

Overrides

  • Low-Side Overrides: These overrides were similar to overall approvals, involving larger loan amounts and applicants with higher income and credit scores. Low-side overrides were more likely for applicants with prior loans and for refinancing.
  • High-Side Overrides: High-side overrides had fairly good credit scores and DTI ratios, but lower incomes and were more likely for home purchases than refinancing. The credit scores were lower and DTI values higher than approvals, and therefore were denied based on other factors that increased overall risk.

Regression Results

  • Denials: When black was the only explanatory variable, it was significant. But, when credit score was added, the coefficient on black became insignificant. Adding other factors related to repayment ability showed that race was not significant in explaining denial. Key factors such as credit score, DTI, LTV, loan amount, and previous loans with the bank were significant in explaining loan approvals and denials.
  • Low-Side Overrides: Black applicants were more likely to receive a low-side override, other factors equal. Also, applicants with higher credit scores and lower DTI and LTV, and applicants with previous loans and those who were refinancing were significantly more likely to receive a low-side override.
  • High-Side Overrides: The analysis showed that race was not a significant factor in explaining high-side overrides. These overrides were driven by valid repayment factors. Credit score was a significant factor, as well as whether the applicant was refinancing and if they had prior loans with the bank.
  • Premier Insights provided detailed regression models to further analyze the factors driving loan decisions including models that included variables based on loan amount, previous deposits and loans, number of loans with the bank and the number of times an applicant had been late with payments.

Conclusion

  • Premier Insights' analysis confirmed that The Bank relied on objective factors in the loan decision process.
  • The data provided no evidence of discrimination based on the race of the applicants.
  • Premier Insights utilized detailed descriptive statistics and robust regression models to support the conclusions.
  • The analysis also supported that the Bank applied policy guidance as discussed during the onsite criteria interview.

Premier Insights' Expertise and Value:

  • Data Management: Premier Insights effectively formatted data for presentation to the FDIC and managed the complex data sets for the analysis.
  • Statistical Analysis: Premier Insights conducted detailed statistical analyses, including t-tests and probit regressions, to understand the relationships between variables and loan decisions.
  • Variable Creation: Premier Insights demonstrated its expertise by creating new variables that were pertinent to the analysis, ensuring a comprehensive review.
  • Override Analysis: Premier Insights provided detailed analysis of override codes to provide deeper insights into loan decision process.
  • Objectivity: Premier Insights' analysis was objective and unbiased, focusing on identifying the factors that influenced loan decisions using the data and modeling techniques to show that race was not a significant factor.
  • Technical Expertise: Premier Insights provided all the data, code and output in SAS format demonstrating expertise in advanced statistical software.

This detailed analysis provided The Bank with a clear understanding of their lending practices, demonstrating that their decisions were based on objective criteria and not on discriminatory practices. The work of Premier Insights was vital in showing the bank's adherence to fair lending regulations.