Prefatory notes added May 11, 2014 (item otherwise not amended):
1. The subject of this page was recently treated in “The Perverse Enforcement of Fair Lending Laws,” Mortgage Banking (May 2014).Further, when I originally created this page, I had failed to recall that I had first described the pattern whereby relative differences in rejection rates tend to be larger, while relative differences in approval rates tend to be smaller in "Bias Data Can Make the Good Look Bad," American Banker (Apr. 27, 1992).I did so at the time simply as an illustration of the 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.It did not then occur to me that observers would mistakenly find significance in the fact that relative differences tend to be larger among more advantaged subgroups.My recent commentary “It’s easy to misunderstand gaps and mistake good fortune for a crisis,” Minneapolis StarTribune (Feb. 8, 2014) addresses the broader failure to recognize why relative differences in experiencing some outcome to be large in populations where the outcome it uncommon.
2. I have recently come to question the utility of the EES measure shown in the tables for analysis of appraising the size of a disparity in a subpopulation where the subpopulation is a segment of a larger population.The issue is akin to that addressed in the Truncation Issues subpage of the Scanlan’s Rule page of jpscanlan.com.I need to develop the issue further.For the present I merely note that the EES figures in the tables should be regarded with great caution.
One way in which the failure to recognize the 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 leads to a mistaken interpretation of data involves large relative differences in adverse outcomes among advantaged populations.“Race and Mortality” (Society 2000) discusses the attention given to large relative (racial) differences in infant mortality where parents are well-educated.“Can We Actually Measure Health Disparities?” (Chance 2006) and many comments or journal articles (see Section E.1 of the Measuring Health Disparities page (MHD)) discuss the attention given to the large relative (occupational level) differences in adverse health outcomes among British civil servants in the Whitehall Studies.Those providing various explanations for such patterns failed to appreciate that large relative differences in adverse outcomes are to be expected within groups where those outcomes are less common or that relative differences in the opposite, favorable outcomes tend to be small within those groups.
In the lending context, with regard to disparities in assignment to subprime loans[i] and disparities in mortgage rejection rates[ii] (as well as disparities in foreclosures), it was argued that the fact that relative differences in these adverse outcomes were larger among higher-income groups than among lower-income groups refuted claims that income differences accounted for disparities.Even if, properly measured, disparities were larger among higher-income groups, such fact would hardly be probative of discrimination. It would merely show that the factors driving the disparities, whether discrimination or differences in income and other credit-related factors,[iii] were more substantial among higher-income groups.And there is some reason to expect income variation within income level to be greatest in the highest-income group, where the grouping does not have an upper bound.
More to the point of this item, however, there is reason to expect relative differences in adverse lending outcomes to be greater among higher-income groups simply because such outcomes are rarer among higher-income groups.For the same reason, there is reason to expect relative differences in the favorable outcomes to be smaller among high-income groups.
In “Getting it Straight When Statistics Can Lie,” (Legal Times, June 23, 1993), I relied on publicly available data on rejection rates by income groups simply to illustrate the above pattern.To my knowledge, that was before observers were relying on the larger rejection rate disparities among higher-income group as evidence that income differences could not explain observed rejection rate disparities.
The studies referenced in the first two notes provide additional information to explore these patterns.The figures in Table 1 are from Graph 1 of the study on differences in assignment to subprime loans references in note i (Bradford).The adverse and favorable ratio columns show that, in accord with the distributionally-driven forces, as income increases and rejection rates becomes smaller, relative differences in rejection rates increase while relative difference in approval rates decrease.While not necessarily germane to the instant issue, the final column shows the difference between whites and blacks according to the method described on the Solutions sub-page of MHD that is theoretically unaffected by the overall prevalence on outcome.That column shows that the disparities were about equal in all four income categories.
Table 1 Percents of White and Black Home Loans That Were Subprime and Measures of Difference (Based on Bradford Graph 1) [ref B2612 a 1]
The patterns from the study on rejection rate disparities are a good deal less consistent with the distributionally-driven forces, both with respect to the larger relative differences in rejection rates at each higher-income level and with respect to decreasing relative differences in approval rates.These are functions of true differences at the various levels, as reflected in the final column.But whatever may be causing the differences within income level, that the differences vary by income category does not suggest that the differences are or are not functions of differing group characteristics within each income category.
Table 2 White and Black Mortgage Rejection Rates at NationsBank by Locale and Income Level and Measures of Difference (based on Bond Tables) [ref 2516 a 2]
The pattern of larger relative differences in rejection rates, but smaller relative differences in approval rates, among higher income applicants than lower income applicants could also be characterized in terms whereby increasing income reduces rejection rates proportionately more for whites than blacks, while increasing income increases mortgage approval rates more for blacks than whites.See the 1995 article by Kim and Squires,[iv] which happened to be examining approval rates rather than rejection rates and found that increasing income did more to improve approval prospect for whites than blacks.The authors opined (at 107-08) that this pattern occurred “perhaps because the income variable is a signal and the informational content of this signal is greater for African-American applicants than for white applicants.”
[ii] Bond, Patrick.1995. NationsBank and Community Reinvestment:The Denial of Black Loan Applicant in Atlanta, Baltimore, and Washington, DC. Commissioned by International Brotherhood of Teamsters.
[iii] Certainly at least some part of the difference is a result of income differences within each income level. Anyone with a basic understanding of normal distributions would recognize that within each broad income category the group that is disproportionately represented in the lower-income categories will be disproportionately represented in the lower levels of each category (or, put another way, will have lower average incomes within each category). See Adjustment Issues subpage of Lending Disparities page and .my “Statistical Quirks Confound Lending Bias Claims” (American Banker, August 14, 2012).