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Implications of Stratified Sampling for Fair Lending Binary Logit Models


  • Judith Clarke


  • Marsha Courchane



We examine the effect of sample design on estimation and inference for disparate treatment in binary logistic models used to assess for fair lending. Our Monte Carlo experiments provide information on how sample design affects efficiency (in terms of mean squared error) of estimation of the disparate treatment parameter and power of a test for statistical insignificance of this parameter. The sample design requires two decision levels: first, the degree of stratification of the loan applicants (Level I Decision) and secondly, given a Level I Decision, how to allocate the sample across strata (Level II Decision). We examine four Level I stratification strategies: no stratification (simple random sampling), exogenously stratifying loan cases by race, endogenously stratifying cases by loan outcome (denied or approved), and stratifying exogenously by race and endogenously by outcome. Then, we consider five Level II methods: proportional, balanced, and three designs based on applied studies. Our results strongly support the use of stratifying by both race and loan outcome coupled with a balanced sample design when interest is in estimation of, or testing for statistical significance of, the disparate treatment parameter. Copyright Springer Science + Business Media, Inc. 2004

Suggested Citation

  • Judith Clarke & Marsha Courchane, 2004. "Implications of Stratified Sampling for Fair Lending Binary Logit Models," The Journal of Real Estate Finance and Economics, Springer, vol. 30(1), pages 5-31, October.
  • Handle: RePEc:kap:jrefec:v:30:y:2004:i:1:p:5-31 DOI: 10.1007/s11146-004-4829-5

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    References listed on IDEAS

    1. Harrison, Glenn W, 1998. "Mortgage Lending in Boston: A Reconsideration of the Evidence," Economic Inquiry, Western Economic Association International, vol. 36(1), pages 29-38, January.
    2. 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.
    3. Helen F. Ladd, 1998. "Evidence on Discrimination in Mortgage Lending," Journal of Economic Perspectives, American Economic Association, vol. 12(2), pages 41-62, Spring.
    4. 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.
    5. 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.
    6. Robert Avery & Patricia Beeson & Paul Calem, 1997. "Using HMDA Data as a Regulatory Screen for Fair Lending Compliance," Journal of Financial Services Research, Springer;Western Finance Association, vol. 11(1), pages 9-42, February.
    7. 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.
    8. Paul S. Calem & Michael J. Stutzer, 1995. "The simple analytics of observed discrimination in credit markets," Working Papers 95-7, Federal Reserve Bank of Philadelphia.
    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. Calem, Paul S & Longhofer, Stanley D, 2002. "Anatomy of a Fair Lending Exam: The Uses and Limitations of Statistics," The Journal of Real Estate Finance and Economics, Springer, vol. 24(3), pages 207-237, May.
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    Cited by:

    1. Judith Clarke & Nilanjana Roy & Marsha Courchane, 2009. "On the robustness of racial discrimination findings in mortgage lending studies," Applied Economics, Taylor & Francis Journals, vol. 41(18), pages 2279-2297.
    2. Judith A. Clarke & Nilanjana Roy & Marsha J. Courchane, 2006. "On the Robustness of Racial Disrcimination Findings in Motgage Lending Studies," Econometrics Working Papers 0604, Department of Economics, University of Victoria.
    3. Yongheng Deng & Stuart Gabriel, 2005. "Are Underserved Borrowers Lower Risk? New Evidence on the Performance and Pricing of FHA-Insured Mortgages* (Revised)," Working Paper 8579, USC Lusk Center for Real Estate.


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