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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.

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Bibliographic Info

Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0007.

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Length: 44 pages
Date of creation: 30 Jul 2000
Date of revision:
Handle: RePEc:vic:vicewp:0007

Note: ISSN 1485-6441
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Related research

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

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References

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  1. Paul Calem & Michael Stutzer, 1995. "The simple analytics of observed discrimination in credit markets," Working Papers 95-7, Federal Reserve Bank of Philadelphia.
  2. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
  3. James J. Heckman, 1998. "Detecting Discrimination," Journal of Economic Perspectives, American Economic Association, vol. 12(2), pages 101-116, Spring.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  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. Stanley D. Longhofer & Stephen R. Peters, 1998. "Self-selection and discrimination in credit markets," Working Paper 9809, Federal Reserve Bank of Cleveland.
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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, vol. 29(2), pages 125-147, April.

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