This page, which was originally created because of press attention given to a $335 million settlement of the Department of Justice’s case against Bank of America’s Countrywide Financial Unit, addresses the way that federal enforcement of fair lending laws is based on a statistical perception that is the exact opposite of reality. Specifically, since the March 1994 issuance of an Interagency Policy Statement, the federal government has been encouraging or pressuring lenders to relax lending criteria because of the effect of standard criteria on minority mortgage loan applicants. The relaxing of lending criteria is akin to the lowering of cutoffs on employment tests, long regarded as a means of reducing the racial impact of such tests because lowering cutoffs tends to reduce relative differences in pass rates. But lowering cutoffs tends also to increase relative differences in pass rates (as illustrated, among other places, in Figure 2 of the 2009 Royal Statistical Society presentation). Similarly, relaxing lending criteria will tend to reduce relative differences in mortgage approval rates but increase relative differences in mortgage rejection rates. Nevertheless the federal enforcement agencies have continued to appraise compliance with fair lending laws on the basis of relative differences in mortgage rejection rates and other adverse outcome rates. Thus, federal enforcement of those laws is akin to pressuring employers to lower test cutoffs and then suing the employers that lower their test cutoffs the most. The matter is treated in three recent articles – “Misunderstanding of Statistics Leads to Misguided Law Enforcement Policies,” Amstat News, (Dec. 2012);
This page is closely related to the Discipline Disparities page, which also addresses a situation where federal law enforcement efforts are based on a statistical perception that is the exact opposite of reality. The page is generally related to the Scanlan’s Rule page of the site, which, along with its sub-pages, discusses the statistical pattern whereby the rarer an outcome the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding it. That and related patterns by which standard measures of differences between outcome rates tend to be affected by the overall prevalence of an outcome are also addressed on the Measuring Health Disparities (MHD), Mortality and Survival, and Measures of Association pages (and various MHD sub-pages). The Credit Score Illustrations sub-page of the Scanlan’s Rule page contains illustrations that are especially pertinent to the subject of this page.
This page has eleven sub-pages:
The Disparities – High Income sub-page addresses the erroneous perception that the fact that relative differences in adverse outcomes tend to be greater among higher-income than lower-income groups indicates that differences in income do not explain rejection rate disparities.
The Underadjustment Issues sub-page addresses the fact that efforts to adjust for racial differences in characteristics related to securing some outcome are invariably inadequate.
The Absolute Differences – Lending sub-page discusses issues concerning the measurement of lending disparities by means of absolute differences between rates as has been done in a number of studies by arms of the Federal Reserve System. The issue is treated more fully in Appendix A to the Bernanke letter.
The Disparities – High Income sub-page addresses the erroneous perception that the fact that relative differences in adverse outcomes tend to be greater among higher-income than lower-income groups suggests that differences in income do not explain rejection rate disparities.
The Underadjustment Issues sub-page addresses the fact that efforts to adjust for racial differences in characteristics related to securing some outcome are invariably inadequate.
The Absolute Differences – Lending sub-page discusses issues concerning the measurement of lending disparities by means of absolute differences between rates as has been done in a number of studies by arms of the Federal Reserve System (a matter now more fully treated in Section A of Appendix to the letter to the Federal Reserve Board).
The Lathern v. NationsBank sub-page discuses a putative class action brought against NationsBank Mortgage Corp. in Washington, DC on the basis of a study showing that NationsBank had comparatively large relative differences in mortgage rejection rates.
The United States v. Countrywide sub-page addresses several issues especially pertinent to the Department of Justice's lending discrimination case against Countrywide Financial Corp. that was the subject of a $335 million settlement announced in December 2011.
The United States v. Wells Fargo sub-page addresses several issues especially pertinent to the Department of Justice's lending discrimination case against Wells Fargo Bank that was the subject of a $175 million settlement announced in July 2012.
The Partial Picture Issues sub-page addresses a fundamental problem with analyses underlying claim of discrimination in assignment to subprime status and discrimination in loan pricing at issue in cases like United States v. Countrywide and United States v. Wells Fargo that was not present in analyses of rejection rate disparities – i.e., that the analyses of the claims fail to examine the entire universe of persons seeking the desired outcome. That matter was recently treated in my “Fair Lending Studies Paint Incomplete Picture,” American Banker, April 24, 2013
The Foreclosure Disparities sub-page addresses recent studies of disparities in foreclosure rates, explaining the measures that generally reduce foreclosures, while tending to reduce relative differences in foreclosure rates, will tend to increase relative differences in foreclosure rates.
The File Comparison Issues sub-page discusses the problematic nature of efforts to identify discrimination by means of comparisons of files of rejected and approved applicants.
The FHA/VA Steering Study discusses a study that regards the fact that a larger proportion of minority than white mortgage loans were FHA/VA loans as suggesting that minorities were steered to such loans but without providing an estimate of what the difference in proportions would be absent discrimination. It also discusses the fact that one of the entities authoring the study, after relying on relative differences in adverse outcomes as a measure of the comparative size of disparities, issued another study relying on relative differences in favorable outcomes as a measure of the comparative size of disparities.
The Holder/Perez Letter sub-page discusses an April 24, 2012 letter to the Department of Justice explaining to the agency, among other things, that statistical perceptions underlying its fair lending enforcement policies are incorrect.
The Federal Reserve Letter sub-page discusses the March 4, 2013 letter to the Board of Governors of the Federal Reserve System explaining to the agency, among other things, that statistical perceptions underlying its fair lending enforcement policies are incorrect.
The Disparate Treatment sub-page of the Discipline Disparities page addresses issues concerning determining the degree to which school discipline disparities may results from disparate treatment of similarly situated persons that are akin to issues concerning determining the degree to which school discipline disparities may results from disparate treatment of similarly situated loan applicants.
Listed below are my older articles pertaining to lending disparities issues. These were written when the focus on disparities in adverse lending outcomes was largely limited to disparities in mortgage rejection rates. But, as is somewhat reflected in recent items mentioned in the first paragraph above, the discussion would generally apply to disparities in any adverse lending outcome, including assignment to sub-prime and foreclosure.
Key points of the listed items, which points may be eventually elaborated upon on this page or sub-pages to this page, are discussed below, along with some recent developments and issues not previously considered in this context. To facilitate the reader’s use of this page, I list the topics immediately below. Highlighted items are also treated on separate sub-pages to this page. Some items are repetitive of things stated above.
There existed considerable sentiment that observed mortgage rejection rate disparities occurred not because (or at least not so much because) of intentional discrimination, but because standard lending criteria tended to disproportionately disadvantage minorities. Thus, banks were encouraged to relax those criteria. But the relaxing of criteria, while reducing disparities in approval rates, tends to increase disparities in rejection rates. Because few people understand this, however, banks that were most responsive to the encouragement to relax lending criteria became especially vulnerable to being singled out for litigation due to their large rejection rate disparities (as in the case of the suit against NationsBank discussed in the Lathern v. NationsBank sub-page and its references).
2. Underadjustment Issues
Anyone with the least understanding of normal distributions will recognize that in analyses of group differences in outcome rates efforts to adjust for differences in group characteristics associated with the outcome will invariably fail to fully address the role of those differences. A group that on average has lower qualifications relating to securing an outcome will be disproportionately represented within the lower reaches of each adjustment category. Thus, within high, medium, or low income categories (or more refined categories), the average incomes of minorities will tend to be lower than the average income of whites. And of course the differences in wealth of minorities and whites earning the same income are well-documented. Further, for every credit rating, however refined, the financial circumstances of minorities will on average be somewhat weaker than those of whites. But those who recognize the tendency toward underadjustment are often inclined to think that, even if there is some underadjustment, unaccounted for differences could not be great enough to explain what are perceived to be very large residual disparities in rates of experiencing an adverse outcome. Such thinking, however, fails to recognize that seemingly large relative differences in rare outcomes can be explained by seemingly small differences in average (and average unaccounted for) qualifications.
3. Implications of Large Relative Differences in Rejection Rates among High-Income Groups
During the 1990s it was asserted that claims that lending disparities could be explained by income differences were refuted by the fact that rejection rate disparities were found to be larger in higher-income categories than lower-income categories. Even if, properly measured, disparities were found to be larger in higher-income categories, such fact would have little bearing on the issue of whether there existed discrimination absent a showing that the differences between the financial circumstances of the groups were the same within each income category. Even then, I am not sure I see the logical basis for the contention. More pertinent to the principal statistical issues addressed on this page, however, the contention is based on relative differences in rejection rates. Because rejection rates tend to be comparatively low among higher-income groups, relative differences in rejection rates tend to be high (though relative differences in approval rates tend to be low) among such groups.
Since February 16, 2012, these issues have been more fully addressed on the High Income Group Disparities sub-page.
4. Higher Default Rates among Minorities as Putative Evidence of the Absence of Discrimination
During the 1990s, as discussed in the 1997 unpublished piece and the 1998 American Banker piece, a number of observers (including Nobelist Gary Becker) argued that the higher default rates among minority borrowers tended to refute claims of widespread credit discrimination. Those observers found in the higher minority default rates evidence that minorities had in fact been subjected to lower standards. (That same reasoning underlies claims that higher qualifications of Asians admitted to universities is evidence of discrimination against Asian applicants, as discussed in item a (“The Perils of Provocative Statistics”)). But in consequence of the same feature of normal distributions underlying points 1 through 3 above, a group that on average has weaker qualifications among applicants will tend to have weaker qualifications among those approved, even when the group has been discriminated against (as illustrated with regard to employment in Table IV of “Illusions of Job Segregation, Public Interest (Fall 1988)).
5. Foreclosure Disparities
Recently, in consequence of the foreclosures crisis, further attention is being given to the same sorts of disparities in defaults and foreclosures that in the 1990 led observers to regard (incorrectly, as discussed in item 4 supra) as evidence of the absence of credit discrimination.[ii] Now, however, the same disparities appear to be regarded as evidence that minorities were steered to higher risk loans. The study referenced in note iv gives much attention to the large racial disparities among higher-income groups in a manner somewhat akin to that discussed in item 3 supra, but, in any case, without recognition of the statistical forces leading toward large relative difference in adverse outcomes (though small relative differences in favorable outcomes) where adverse outcomes are less common. A central point of the study is that minorities have been especially impacted by the foreclosure crisis and policies should be implemented to reduce foreclosure rates.
I have not seen data on disparities in foreclosures prior to the foreclosures crisis (though there may be such data cited by the commentators referenced in item 4 supra). But the statistical forces described in the references mentioned at the outset are of a nature that would cause relative differences in foreclosures to be smaller (though relative differences in avoiding foreclosures to be larger) following the crisis than they were previously. Similarly, general efforts to reduce foreclosures, if successful, will tend to increase relative differences in foreclosure rates while reducing relative differences in rates of avoiding foreclosure. See item 7 infra.
The above-referenced works on differences in lending outcomes generally addressed perceptions about relative differences in adverse outcome rates. But the Department of Justice complaint in the Countrywide case discussed disparities in things like assignment to subprime loans in terms of odds ratios.[iii] The odds ratio is the standard output of common the statistical method (logistic regression) for attempting to adjust for differences in characteristics, which is presumably why the Justice Department employed the measure in its complaint. While the difference measured by the odds ratio is often regarded simply as an alternative formulation of the relative difference, it differs in certain respects. The key respect pertinent here is that the difference measured by the odds ratio is the same regardless of which outcome is examined.[iv]
But in order for a measure to provide useful information for comparing the size of two disparities, or even for abstractly appraising the size of one disparity, the measure must remain constant when there occurs a simple change in overall prevalence of an outcome akin to that effected by lowering a test cutoff. And, like two relative differences, the difference measured by odds ratios tend to change as the prevalence of an outcome changes, though in a more complicated way than the two relative differences.
Differences measured by the odds ratio tend to change in different directions at different points across the distributions and tends generally to change in the same direction as the larger relative difference. Roughly, as rare outcomes become more common, the difference measured by the odds ratio tends to decrease; as common outcomes become extremely common, differences measured by odds ratios tend to increase.[v] The important thing to understand about odds ratios in the instant context, however, is that adverse lending outcomes usually are in ranges where reductions in those outcomes tend to increase differences measured by odds ratios (as illustrated, for example, toward the right hand side of Figure 4 of the 2009 Royal Statistical Society presentation). Thus, things that reduce the prevalence of adverse lending outcomes – whether the outcome is the rejection of an application, receipt of a less advantageous type of loan, or foreclosure – will tend to increase both relative differences in rates of experiencing the outcome and differences measured by the odds ratio.
7. HAMP and Racial Disparities
The federal government’s Home Affordable Mortgage Program (HAMP), which provides assistance to persons whose mortgage payments exceed 31% of monthly gross income, presumably will result in a reduction in overall foreclosure rates. Such program thus, while tending to reduce relative differences between rates at which whites and minorities will be able to keep their homes, will likely increase relative differences in foreclosure rates.[vi]
But some attention is now also being given to racial differences in rate of successfully taking advantage of the HAMP program. A National Community Reinvestment Coalition (NCRC) survey found, based rates of securing HAMP assistance for 24.3% of black and 36.4% of white HAMP eligible borrowers, that whites were almost 50% more likely to receive assistance than blacks. Thus the study examined the matter in terms of relative differences in favorable outcomes.
Should overall rates of receiving help under the program increase, the relative difference in receiving assistance is likely to decline, though the relative difference in failing to receive assistance will likely increase. At some point, the relative difference in adverse outcomes may exceed the relative difference in favorable outcomes, at which time some may be inclined to start to measure the disparity in terms of relative differences in adverse outcomes. That in fact is the approach of the Agency for Healthcare Research and Quality (as discussed, inter alia, in to the 2007 APHA presentation and its Addendum).
The 36.4% and 24.3% white and black assistance rates reported in the study translate into a difference between the hypothesized underlying means of approximately .35 standard deviations according to the procedure discussed on the Solutions sub-page of the Measuring Health Disparities page. Assuming that difference remained constant across the distribution, at the point where the white rate reached approximately 57%, the black rate would be about 43.6%, and the relative difference in the adverse outcome would start to exceed the relative difference in the favorable outcome. At the point where the white rate reached approximately 90%, the black rate would be about 82.6%. Thus, while the relative difference in the favorable outcome would be less than 10%, the black adverse outcome rate would be approximately 1.8 times the white rate. It is doubtful, however, that the program would ever achieve such substantial results.
On the other hand, if the program were contracted, the relative difference in the favorable outcome would tend to increase while the relative difference in the adverse outcome would tend to decrease. At the point where the white favorable outcome rate was reduced to 5%, the black rate would be about 2.3%. So, while the relative difference in the adverse outcomes would then be very small, the white favorable outcome rate would be more than twice the black favorable outcome rates.
The NCRC study also found that borrowers not eligible for HAMP received modifications of their loans more often than eligible borrowers. This presumably occurred because a smaller proportion of the HAMP-eligible borrowers were in a position to come to a workable arrangement with the lender. The study did not present black and white rates of loan modification among HAMP-eligible and non-HAMP-eligible borrowers. The study seemed to have far too few respondents to make such a breakdown useful. But in a larger-scale study one would likely find that among the non-HAMP-eligible (where loan modification rates were higher than among the HAMP-eligible), the relative difference between black and white loan modification rates would be smaller, and the relative difference between rates of failing to secure modifications would be larger, than among the HAMP-eligible borrowers. See the Higher Income sub-page.
8. Partial Picture Issues
Studies of minority-white white differences in assignment to sub-prime loan status and differences in loan terms, like those in the Department of Justice’s Countrywide and Well Fargo complaints involve examination only of whites and minorities who received loans. The entire universe of persons seeking loans also included persons who were not offered loans at all and did not receive loans at all. Thus the analyses underlying the claims are not minimally valid.
[i] Articles from this period involving other situations where observers failed to recognize the relationship between the infrequency of the outcome and large relative differences in experiencing the outcome include “An Issue of Numbers” (The National Law Journal, Mar. 5, 1990) (regarding, inter alia, the racial impact of NCAA eligibility requirements) and “Mired in Numbers” (Legal Times, Oct. 12, 1996) (regarding the racial impact of mandatory life sentences).
[iii]In its Countrywide complaint, the Department of Justice was careful always to state that it was describing differences in odds and not, as is common in medical literature, conflating differences in odds with differences in likelihood or chance. The complaint does, however, invariably refer to an odds ratio, for example, of 3.5 as indicating that one odds is “3.5 times higher than” rather than “3.5 times as high as” another. As that misusage predominates in all major scientific journals except for the New England Journal of Medicine (see the Times Higher sub-page of my Vignettes page), the Department cannot be faulted too much for that usage. But a legal pleading should be as precise as possible.
[iv] Depending on which outcome is used as the numerator in calculating the odds and which group’s odds is used as the numerator in calculating the odds ratio, the odds ratio can be greater than 1 or less than 1. But the value below 1 will be the reciprocal of the value above 1, the difference measured by the odds ratio is considered the same regardless of which approach is used. See the Semantic Issues sub-page of the Scanlan’s Rule page.
[v] The introductory material to the Scanlan’s Rule page discusses in some detail the pattern by which absolute differences between rates tend to change as the overall prevalence of an outcome changes. It also explains that the difference measured by the odds ratio tends to change in the opposite direction of the absolute difference.
[vi] Any program that reduces overall foreclosure rates (including, for example, a general reduction in mortgage principals as suggested by the head of the IMF, according to a Washington Post article of April 13, 2012) will tend to increase relative differences in foreclosure rates while reducing relative difference in rates of avoiding foreclosures. It is always possible that a program will be so focused on the circumstances of disadvantaged groups that it will reduce both relative differences in favorable outcomes and relative differences in adverse outcomes.