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Stratified Sample Design for Fair Lending Binary Logit Models

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  • Judith A. Giles
  • Marsha J. Courchane

Abstract

Logistic regressions are commonly used to assess for fair lending across groups of loan applicants. This paper considers estimation of the disparate treatment parameter when the sample is stratified jointly by loan outcome and race covariate. We use Monte Carlo analysis to investigate the finite-sample properties of two estimators of the disparate treatment parameter under six stratified sampling designs and three data generating processes; one estimator is consistent irrespective of sample design while the other is not. Unfortunately the inconsistent estimator is employed inadvertently in fair lending studies. We demonstrate the gains in using the consistent estimator as well as providing recommendations on sample design. We also study the effect of sample design on the empirical power of a test for statistical significance of the disparate treatment parameter. We recommend adopting a sample design that approximately balances by outcome and racial group, when using the estimator that adjusts for the stratification scheme. However, if the standard logit estimator is employed, then our results suggest a sample design that balances by outcome and allocates across racial groups proportionally to the population. Though our study is framed in terms of fair lending applications, our results apply generally to the estimation of logistic regressions that use stratified or choice-based sample designs.

Suggested Citation

  • Judith A. Giles & Marsha J. Courchane, 2000. "Stratified Sample Design for Fair Lending Binary Logit Models," Econometrics Working Papers 0007, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0007
    Note: ISSN 1485-6441
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    File URL: https://www.uvic.ca/socialsciences/economics/_assets/docs/econometrics/ewp0007.pdf
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    References listed on IDEAS

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    4. Mitchell Stengel & Dennis Glennon, 1999. "Evaluating Statistical Models of Mortgage Lending Discrimination: A Bank‐Specific Analysis," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 27(2), pages 299-334, June.
    5. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    6. N. E. Breslow & N. Chatterjee, 1999. "Design and analysis of two‐phase studies with binary outcome applied to Wilms tumour prognosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(4), pages 457-468.
    7. Munnell, Alicia H. & Geoffrey M. B. Tootell & Lynn E. Browne & James McEneaney, 1996. "Mortgage Lending in Boston: Interpreting HMDA Data," American Economic Review, American Economic Association, vol. 86(1), pages 25-53, March.
    8. Day, Theodore E & Liebowitz, S J, 1998. "Mortgage Lending to Minorities: Where's the Bias?," Economic Inquiry, Western Economic Association International, vol. 36(1), pages 3-28, January.
    9. Calem Paul & Stutzer Michael, 1995. "The Simple Analytics of Observed Discrimination in Credit Markets," Journal of Financial Intermediation, Elsevier, vol. 4(3), pages 189-212, July.
    10. Stanley D. Longhofer & Stephen R. Peters, 1998. "Self-selection and discrimination in credit markets," Working Papers (Old Series) 9809, Federal Reserve Bank of Cleveland.
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    Citations

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    Cited by:

    1. McKinley Blackburn & Todd Vermilyea, 2006. "A Comparison of Unexplained Racial Disparities in Bank-Level and Market-Level Models of Mortgage Lending," Journal of Financial Services Research, Springer;Western Finance Association, vol. 29(2), pages 125-147, April.
    2. Jason Dietrich, 2005. "The effects of sampling strategies on the small sample properties of the logit estimator," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(6), pages 543-554.
    3. Fotios Pasiouras & Chrysovalantis Gaganis, 2007. "Financial characteristics of banks involved in acquisitions: evidence from Asia," Applied Financial Economics, Taylor & Francis Journals, vol. 17(4), pages 329-341.

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    More about this item

    Keywords

    Logistic regression; design efficiency; stratified sampling; choice-based sampling; case-control studies; balanced sampling; Monte Carlo experiment; mean squared error.;
    All these keywords.

    JEL classification:

    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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