An analysis of alternative methodologies and interpretations of mortgage discrimination research using simulated data.

Brown, Christopher L. ; Simpson, W. Gary

INTRODUCTION

For the past several years, researchers have focused on investigating discrimination in the residential mortgage market. New data and methodologies have been employed and new theoretical lending models have been developed to explain why loan approval rates are higher for non-minority applicants than for minority applicants. There has been intense debate on the significance of default rates in identifying or ruling out discriminatory lending and on the appropriate methodology to use in testing for discrimination. This paper reviews the debate and uses simulated data to provide conclusive evidence on the merits of the alternative theories and methodologies. Understanding the relationship of default rates as potential indicators of discrimination and assuring that the methodology used in these studies is appropriate is very important because the findings of discrimination studies may be used to influence public policy.

The mortgage discrimination debate intensified with the release of a study conducted by researchers at the Federal Reserve Bank of Boston (Munnell, Tootell, Browne and McEneaney (1996)). The study employs the most comprehensive loan application information of any of the recent discrimination studies. The authors use a logit regression equation that includes all of the variables that should be relevant to the loan decision. The race of the applicant is included as an additional explanatory variable. If the coefficient on race is significant, it is interpreted as evidence of discrimination.

Munnell et. al. (1996) find minority applicants, on average, have greater debt burdens, higher loan-to-value ratios, and weaker credit histories than non-minorities. Furthermore, denied minorities have lower income and wealth, higher obligation and loan-to-value ratios, and worse credit histories than denied non-minorities. Despite these facts, the authors find evidence of discrimination against minorities. They find that minority applicants are rejected 60 percent more often than non-minority applicants when financial, employment, and neighborhood characteristics are held constant.

The findings of Munnell et. al. (1996) have received a great deal of attention from policymakers and academic researchers. Most of the debate focuses on perceived shortcomings in the study. Criticisms of the Munnell et. al. (1996) study include problems with the integrity of the data (Horne (1994), Liebowitz (1993), and Carr and Megbolugbe (1993)), the authors' failure to consider default rates (Becker (1993), England (1993), and Brimelow and Spencer (1993)), and problems with the use of a single-equation logit regression model of the probability of loan approval to detect discrimination.

More recently, Blank et al (2005) investigated racial discrimination in mortgage lending in Washington, DC. Using three different methodologies, a dissimilarity index approach, a three-way crosstabulation approach and a logistic regression. The adjusted dissimilarity index approach is based on the theory that, after considering for differences in neighborhood factors and using variables on the loan applicants that are available through HMDA, approval rates should be approximately the same across census tracts. Blank et al (2005) find there is a disparity between census tracts. They conclude that 10.64 percent of loans that should have gone to underserved census tracts were denied. That amounts to 1,315 loans. The crosstabulation approach simply evaluates whether there is a disparity in lending based on only income and race. After considering income, they find a significant difference in the proportion of loans denied between minorities and non-minorities across all income levels. The third approach is a logistic regression model. The model includes the race of the applicant along with neighborhood characteristics. They again find that minorities are less likely to receive loans, after accounting for the factors in the model.

The findings by Blank et al (2005) do not necessarily indicate discrimination. None of the methodologies employed by Blank et al (2005) include the credit history of the applicants. As explained in more detail in Section II, the distribution of credit quality may explain differences in loan approval rates even after considering all of the variables used in the Blank et al (2005) study.

Section II discusses the role of default rates in interpreting the results of mortgage discrimination research. A model of the relationship between loan denial and default rates and discrimination developed by Ferguson and Peters (1995) is presented. Section III discusses the criticisms of the use of a single-equation logit regression equation to measure mortgage discrimination. Section III also presents the reverse regression methodology LaCour-Little (1996) applies to the Munnell et. al. (1996) data to test for mortgage discrimination. Weaknesses in the reverse regression methodology are also discussed in Section III. Section IV presents the simulation analysis used to show the relationship between default rates and discrimination and to compare the performance of a single-equation logit regression model and the reverse regression model in identifying discriminatory lending. The simulation results are presented in Section V. The conclusion and recommendations for future research are presented in Section VI.

THE ROLE OF DEFAULT RATES IN MORTGAGE DISCRIMINATION RESEARCH

Becker (1993) and England (1993) argue that, if discrimination exists, minorities should have lower default rates than non-minorities. They contend that failing to observe lower default rates for minority borrowers is evidence against racial discrimination in mortgage lending. Brimelow and Spencer (1993) also use this reasoning to challenge the findings of Munnell et. al. (1996). They cite the Boston Fed's finding that the average default rate for minority neighborhoods in Boston is the same as the rate for non-minority neighborhoods. Brimelow and Spencer (1993) argue that equal default rates for minority and non-minority neighborhoods contradicts the Munnell et. al. (1996) conclusion that Boston area lenders discriminate against minority applicants.

Munnell et. al. (1996), Tootell (1996), Browne and Tootell (1995), Galster (1993), and Ferguson and Peters (1995) argue that racial discrimination in the mortgage market will result in lower default rates for minority borrowers only if certain conditions hold. Tootell (1993) and Browne and Tootell (1995) argue equal minority and non-minority default rates can only be used as evidence of discrimination if the distribution of the quality of accepted minority applicants is identical to the distribution of accepted non-minority applicants.

Ferguson and Peters (1995) explain the relationship between denial rates, default rates, and the distribution of credit quality. They present a model where the distribution of credit quality is higher for non-minority applicants than for minority applicants. This is referred to as heterogeneous credit quality. Recent empirical evidence tends to support the hypothesis that the distribution of credit quality is heterogeneous.

Let q represent the probability of loan repayment. The distributions of credit quality for minority applicants, h(q), and for non-minority applicants, g(q), are shown in Table 1. For simplicity, assume q is measured without error. All applicants with q above some arbitrary cutoff point, [q.sup.*] are approved and applicants with q below [q.sup.*] are denied. All applicants face the same cutoff point, but the average credit score for approved minority applicants, [q.sub.h], is lower than the average credit score for approved non-minority applicants, [q.sub.g].

[TABLE 1 OMITTED]

The Ferguson and Peters (1995) model predicts that approved non-minority applicants will, on average, have higher credit quality than approved minority applicants. The Ferguson and Peters (1995) model indicates that if minorities have a lower distribution of credit quality than nonminorities, they may have higher default rates even if discrimination is present.

MODEL SPECIFICATION ISSUES IN MORTGAGE DISCRIMINATION RESEARCH

Rachlis and Yezer (1993) and Yezer, Phillips, and Trost (1994) argue that single-equation models cannot be used to test for discrimination because of the complexity of the mortgage lending process. The single-equation models do not take into consideration the borrower's choice of loan terms or the borrower's default decision. Yezer, Phillips, and Trost (1994) show the effects of simultaneity and self-selection bias that result from using a single-equation model of the loan approval decision to detect mortgage discrimination. They show that the coefficient on the discrimination variable will be biased upwards.

LaCour-Little (1996) also criticizes the methodology used by Munnell et. al. (1996). He also contends that the direct logit regression model produces a biased estimate of the discrimination coefficient. However, his line of reasoning is different than Yezer, Phillips, and Trost (1994). LaCour-Little (1996) implies that the logit regression methodology is inappropriate when one group of applicants has a lower distribution of credit quality than the other group. He states that differences in average credit quality require the use of a different methodology. He proposes reverse regression as an alternative methodology to detect discrimination in mortgage lending.

LaCour-Little (1996) uses reverse regression on the data from Munnell et. al. (1996) to test for discrimination. First, he estimates a direct logit regression equation with eleven independent variables used in Munnell et. al. (1996). The dependent variable, ACTION, equals 1 if the loan was denied. There is no race coefficient in this model. The coefficients generated from the regression are used to estimate the probability of loan denial for each observation. The predicted probabilities are considered the inverse qualifications index, Q-INDEX. The Q-INDEX variable is a measurement of the probability of loan denial, therefore higher values of Q-INDEX are bad.

The Q-INDEX values are used as the dependent variable in the following ordinary least squares regression:

Q-INDEX = [b.sub.0] + [b.sub.1] ACTION + [b.sub.2] RACE = e

where ACTION equals 1 if the loan was denied and 0 if the loan was approved, and RACE equals 1 if the applicant is a minority and 0 if the applicant is a non-minority. LaCour-Little (1996) contends the coefficient on RACE measures "the excess probability of default required to turn down a minority applicant." LaCour-Little (1996) also calculates a value, a*, that is a measure of the average qualifications of accepted minority applicants relative to accepted non-minority applicants. This measure is calculated as shown:

[a.sup.*] = -[b.sub.2]/[b.sub.1].

The results of the LaCour-Little (1996) reverse regression on the loan application data are shown in Table 2. LaCour-Little (1996) concludes the [a.sup.*] value of -.193 indicates that accepted minority applicants had average qualifications 19 percent lower than accepted white applicants. He interprets the RACE coefficient of .057 as the excess probability of default required to reject a minority applicant. He concludes that lenders appear to apply less stringent underwriting standards to minority loan applications, and that there is evidence of reverse discrimination.

The statistical analysis conducted by LaCour-Little (1996) may be accurate, but the conclusions derived from the analysis are questionable. LaCour-Little (1996) uses the finding that accepted minority applicants have average qualifications 19 percent lower than accepted non-minority applicants to conclude that there is evidence of reverse discrimination. However, the finding that accepted minorities have lower average qualifications than accepted non-minority applicants is not evidence of discrimination. This is the expected outcome based on the Ferguson and Peters (1995) model.

The correct interpretation of the reverse regression methodology employed by LaCour-Little (1996) is relatively straightforward. Since the ACTION and RACE variables are both binary, there are only four possible outcomes calculated by the model. Those four outcomes represent the average Q-INDEX values for (1) approved non-minority applicants (ACTION=0, RACE=0), (2) approved minority applicants (ACTION=0, RACE=1), (3) denied non-minority applicants (ACTION=1, RACE=0), and (4) denied minority applicants (ACTION=1, RACE=1).

LaCour-Little (1996) finds that approved white applicants have an average Q-INDEX of .0892 while approved minority applicants have a Q-INDEX of .1462. These results are consistent with the Ferguson and Peters (1995) model and the findings by Munnell et. al. (1996) that minority applicants, on average, have lower income levels, higher debt ratios, and worse credit histories than non-minority applicants. The findings do not indicate reverse discrimination or the absence of discrimination. The only way to prove discrimination (or reverse discrimination) is to use a model that will determine if the marginal cutoff point is the same for minority and non-minority applicants. When the distribution of credit quality is heterogeneous, calculations of differences in average credit quality do not provide useful information about the presence or absence of discrimination.

SIMULATION ANALYSIS

Simulation analysis is conducted to identify the role of default rates in identifying discrimination and to compare the performance of the reverse regression model and the logit regression model in detecting discrimination when non-minority and minority applicants have heterogeneous credit quality. Assume (following Ferguson and Peters (1995)) the screening process leads to a single credit score. The credit score reflects the probability of repayment, q. A uniform, nondiscriminatory credit policy requires that all applicants who meet some minimum required credit score, [q.sup.*], be approved.

Assume the lender collects all relevant information and inputs it into a logit regression equation to predict the probability the loan will be repaid if originated. The predicted value of the dependent variable from the logit regression is the credit score, q. To be consistent with LaCourLittle (1996), the credit score is converted from the probability of repayment to the probability of default (by subtracting the credit score from 100 percent). This variable, NSCORE, is used as the dependent variable in the reverse regression. It is equivalent to the inverse of the qualifications index used in LaCour-Little (1996). The independent variables in the reverse regression are the same as in LaCour-Little (1996); ACTION, which equals 1 if the loan was denied and 0 otherwise, and RACE, which equals 1 if the applicant is a minority and 0 otherwise. The logit regression model uses ACTION as the dependent variable, with NSCORE and RACE as the independent variables.

We use simulated data that contains 1000 observations on non-minority applicants and 500 observations on minority applicants. The average NSCORE for non-minority applicants is 26.4 percent with a standard deviation of 11.2 percent. The average NSCORE for minority applicants is 35.2 percent with a standard deviation of 13.4 percent. The first simulation contains no discrimination. All loans that have NSCORE's above 40 percent are denied and all other loans are approved. The rejection rate for non-minority applicants is 11.3 percent and the rejection rate for minority applicants is 36.2 percent.

The second simulation assumes discrimination exists such that non-minority applicants are approved with NSCORE's of 41 or below while minority applicants must have NSCORE's of 40 or below to be approved. The rejection rate for non-minority applicants in this simulation is 9.9 percent while the minority rejection rate remains 36.2 percent.

The third simulation assumes a wider range of discrimination exists, where non-minority applicants are approved with NSCORE's of 45 or below and minority applicants are approved with NSCORE's of 40 or below. For the third simulation, the rejection rate for non-minority applicants decreases to 5.0 percent, while the minority rejection rate remains at 36.2 percent.

If the two methodologies are reliable, they should not detect any discrimination in the first set of simulation data, but should detect discrimination in the second and third sets of simulation data. The findings should not reflect reverse discrimination for any of the three simulations.

The validity of default rate analysis is examined by comparing the average NSCORE of accepted minority applicants to the average NSCORE of accepted non-minority applicants for each simulation. Becker (1993) and others argue that, if discrimination is occurring, minorities should have lower default rates than non-minorities. Since the NSCORE variable measures the probability of default, according to Becker's (1993) theory accepted minority applicants should have lower average NSCORE's than accepted non-minority applicants if discrimination is occurring.

Since the required credit score is the same for all applicants in the first simulation, Becker's (1993) theory implies that the average NSCORE's for minorities and non-minorities should be the same for the first simulation. The second and third simulations result in lower marginal requirements for non-minorities, so Becker's (1993) theory indicates that non-minorities should have higher average NSCORE's than minorities for the second and third simulations.

RESULTS OF THE SIMULATION ANALYSIS

Default Analysis

The average NSCORE's for accepted minority and accepted non-minority applicants are shown in Table 3. The average NSCORE for accepted minorities remains 27.28 percent for all three simulations because the cutoff point does not change for minority applicants. The average NSCORE of accepted non-minority applicants is 24 percent when there is no discrimination (first simulation), 24.25 percent when there is slight discrimination (second simulation), and 25.21 percent when there is significant discrimination (third simulation).

Since the NSCORE is the probability of default, it is apparent that default rates for accepted minority applicants can be higher that default rates for accepted non-minority applicants even if discrimination is occurring. This finding is consistent with the Ferguson and Peters (1995) model. If the distribution of credit quality is higher for non-minority applicants than for minority applicants, default analysis provides no useful information on whether or not discrimination is occurring.

The Performance of the Logit and Reverse Regression Models in Identifying Discriminatory Lending

The results of the reverse regression, calculations of [a.sup.*], and the results of the logit regression are shown in Table 4. Using the reverse regression methodology, the RACE coefficient is positive and significant in all three simulations, and [a.sup.*] ranges in value from -.078 in the third simulation to -.156 in the first simulation. These findings are consistent with the results obtained by LaCour-Little (1996), which led him to conclude that there was evidence of reverse discrimination.

The logit regression model performs well in detecting discrimination. The coefficient on RACE is insignificant in the first simulation, where there is no discrimination. The RACE coefficient is significant at the .001 level for the second simulation, where there is a slight degree of discrimination, and the RACE coefficient is significant at the .0001 level for the third simulation, where there is significant discrimination.

From the simulation analysis, it is apparent that the reverse regression methodology adapted from labor discrimination research is inappropriate for use in mortgage research. The logit regression methodology clearly outperforms the reverse regression methodology in detecting discrimination.

CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH

The findings indicate that we cannot focus on default analysis to answer the question of whether or not discrimination is occurring. The findings also indicate that the reverse regression methodology is not appropriate for mortgage discrimination research and that a well-specified logit regression model may be used to identify one aspect of discriminatory lending. It is important to recognize that the logit model can only identify discrimination that occurs after the loan application has been completed. Discrimination in pre-screening applicants, or differences in the assistance provided to applicants in completing the application process cannot be measured using the single-equation logit methodology.

One recommendation for future research is to study the distributional characteristics of credit quality and attempt to measure the differences in the distribution of credit quality between minority and non-minority applicants. This will be a daunting task, but if the distributional properties are better understood, we can devise a better method for detecting mortgage discrimination.

REFERENCES

Becker, Gary S. (1993). The Evidence Against Banks Doesn't Prove Bias. Business Week, April 13.

Blank, Emily C., P. Venkatachalam,, L. McNeil, and R.D. Green (2005). Racial Discrimination in Mortgage Lending in Washington, D.C.: A Mixed Methods Approach. The Review of Black Political Economy, 33(2), 1-30.

Brimelow, P., and L. Spencer (1993). The Hidden Clue. Forbes, January 4.

Browne, L.E., and G. M.B. Tootell (1995). Mortgage Lending in Boston - A Response to the Critics. New England Economic Review, Sept./Oct., 53-78.

Carr, J. H., and I.F. Megbolugbe (1993). The Federal Reserve Bank of Boston Study on Mortgage Lending Revisited. Journal of Housing Research, 4(2), 277-313.

England R. S. (1993). Washington's New Numbers Game. Mortgage Banking, September, 38-54.

Ferguson, M. F., and S. R. Peters (1995). What Constitutes Evidence of Discrimination in Lending? Journal of Finance, 50, 739-748.

Galster, G. C. (1993) The Facts of Lending Discrimination Cannot Be Argued Away by Examining Default Rates. Housing Policy Debate, 4(1), 141-146.

Horne, D.K. (1994). Evaluating the Role of Race in Mortgage Lending. FDIC Banking Review, 7(1), 1-15.

LaCour-Little, M. (1996). Application of Reverse Regression to Boston Federal Reserve Data Refutes Claims of Discrimination, Journal of Real Estate Research, 11, 1-12.

Liebowitz, S. (1993). A Study That Deserves No Credit. Wall Street Journal, September 1, A14.

Munnell, A.H., G.M.B. Tootell, L.E. Browne, and J.E. McEneaney (1996). Mortgage Lending In Boston: Interpreting HMDA Data," American Economic Review, 86, 25-53.

Rachlis, M.B., and A.M.J. Yezer (1993). Serious Flaws in Statistical Tests for Discrimination in Mortgage Markets. Journal of Housing Research, 4(2), 315-336.

Tootell, G.M.B. (1996). Redlining in Boston: Do Mortgage Lenders Discriminate Against Minority Neighborhoods? Quarterly Journal of Economics, November, 1049-1079.

Yezer, A., R. Phillips, and R. Trost (1994). Bias in Estimates of Discrimination And Default in Mortgage Lending: The Effects of Simultaneity and Self-Selection. Journal of Real Estate Finance and Housing, 9, 197-215.

Christopher L. Brown, Western Kentucky University

W. Gary Simpson, Oklahoma State University

Table 2: LaCour-Little (1996) Reverse Regression Results

      Variable          Parameter Estimate

Intercept                     .0892
ACTION                         .296
RACE                           .057

[a.sup.*] = -.057/.296 = -.196

Table 3: Average NSCORE for Accepted Applicants

                 Simulation 1    Simulation 2    Simulation 3

Minority             27.28           27.28           27.28
Non-Minority         24.00           24.25           25.21

Table 4: Results of the Simulation Analysis

Reverse Regression Results

Simulation 1: No Discrimination

  Variable     Parameter Estimate   T-Statistic        P-Value

Intercept            .2397             84.7            <.0001
ACTION               .2167             36.6            <.0001
RACE                 .0339              6.8            <.0001

[a.sup.*] = -.0339/.2167 = -.156 Adjusted [R.sup.2] = .528

Simulation 2: Slight Discrimination

  Variable     Parameter Estimate   T-Statistic        P-Value

Intercept            .2425             84.9            <.0001
ACTION               .2187             35.5            <.0001
RACE                 .0303              5.9            <.0001

[a.sup.*] = -.0303/.2187 = -.143 Adjusted [R.sup.2] = .514

Simulation 3: Significant Discrimination

  Variable     Parameter Estimate   T-Statistic        P-Value

Intercept            .2529             84.7            <.0001
ACTION               .2255             30.7            <.0001
RACE                 .0175              3.1             .0019

[a.sup.*] = -.0175/.2255 = -.078
Adjusted [R.sup.2] = .451

Logit Regression Results

Simulation 1: No Discrimination -2logL = 1461 w/2 df p<.0001

  Variable     Parameter Estimate   Chi-Square         P-Value

Intercept            167.8             23.85           <.0001
NSCORE              -418.8             23.81           <.0001
RACE                  -0.8              0.01            .9133

Simulation 2: Slight Discrimination -2logL = 1410 w/2 df p<.0001

  Variable     Parameter Estimate   Chi-Square         P-Value

Intercept            111.8             35.46           <.0001
NSCORE              -272.9             35.42           <.0001
RACE                  -2.5             11.36            .0007

Simulation 3: Significant Discrimination -2logL = 1257 w/2 df p<.0001

  Variable     Parameter Estimate   Chi-Square         P-Value

Intercept            107.9             31.16           <.0001
NSCORE              -239.9             31.11           <.0001
RACE                 -11.9             28.79           <.0001