An Evaluation of the Federal Reserve Bank of Boston's Study 

	of Racial Discrimination in Mortgage Lending

	Dennis Glennon and Mitchell Stengel 

	Office of the Comptroller of the Currency

	Economic & Policy Analysis

	Working Paper 94 -2

	April 1994

Abstract:  In 1992, the Federal Reserve Bank of Boston (Boston Fed) released a now well-known study of mortgage lending practices in the Boston Metropolitan Statistical Area (MSA).  Using an

econometric model to examine extensive mortgage loan data collected from 131 financial

institutions in the Boston MSA, the authors of the Boston Fed study tried and failed to find

explanations other than racial discrimination for the significant disparities observed in the rejection

rates for white and minority loan applicants.

The Boston Fed study attracted considerable attention from Congress, the banking industry, the

civil rights community, bank regulators, and the news media.  But three follow-up studies have

raised a variety of problems with the Boston Fed study relating to data and methodology.

In this paper, we discuss and evaluate the problems cited by critics of the Boston Fed study.  We

focus our attention on three broad areas of concern:  model specification; data errors; and

differences in characteristics of the groups being compared. 

Our principal findings can be summarized as follows:

(i)	Several alternative model specifications perform better than the Boston Fed model in terms of various econometric performance measures; however, the race of the applicant continues

to have a large and highly significant effect on the outcome of the lending application

process.

(ii)	The results of the Boston Fed model are affected only slightly when some of the more obvious and easily correctable data errors are corrected.

(iii)	Allowing for different coefficients for whites and minorities, our analysis supports the Boston Fed's conclusion that approximately half the difference in denial rates can be

attributed to differences in the financial characteristics of the borrowers and the

neighborhood characteristics of the property; the remaining half can be attributed to differences in treatment by race.

We conclude with a qualified confirmation of the results of the Boston Fed study.  However, we

believe there are still several important specification issues that cannot be investigated and several

data problems that cannot be corrected using the data provided by the Boston Fed.  Additional

research at both the MSA and the individual bank levels is warranted. 

_____________________________________________________________________________

The opinions expressed are those of the authors and do not necessarily represent those of the Office of the Comptroller

of the Currency.  The authors would like to thank Jeffrey Brown, Michael Carhill, Julia Lane, Kevin Jaques, Daniel

Nolle, and Mark Winer for helpful comments.  Any errors are the responsibility of the authors.

Please address questions of substance to the authors at the Economic & Policy Analysis Department, Office of the

Comptroller of the Currency, 250 E Street, Washington, D.C., 20219, (202) 874-5240.

I.	Introduction

The Federal Reserve Bank of Boston's study of mortgage lending practices in the Boston MSA

(Munnell et al. 1992) has redefined the debate over the existence of racial discrimination in

mortgage lending.  Using a much more extensive data set than any previous study, the Boston

Fed analyzed differences in denial rates across races after controlling for wealth, credit and

employment histories.  The authors conclude that ". . . even after controlling for financial,

employment, and neighborhood characteristics, Black and Hispanic mortgage applicants in the

Boston metropolitan area are roughly 60 percent more likely to be turned down than whites"

(Munnell et al. 1992, p. 2).  They attribute the difference to discrimination on the part of the

lending institutions.  For many, the Boston Fed study seemed to answer ─ once and for all ─ the

question of whether racial discrimination exists in mortgage lending.  Moreover, the results of

the study were a major impetus in the renewed and intensified efforts of the federal government

to detect, punish, and eradicate such discrimination.

In recent months, however, three follow-up studies have identified several data and

methodological problems that appear to call into question the Boston Fed's central finding of

substantial discrimination against minorities (Horne 1994; Liebowitz 1993; Zandi 1993).  In this

paper, we discuss several of the issues raised by the follow-up studies.  We focus our attention

on three broad areas of concern, model misspecification, data errors, and differences in initial

endowments.  We find many of the criticisms of the Boston Fed's method of specifying and

assessing the accuracy of their model to be legitimate.  There are reasonable arguments

supporting alternative model specifications that may better capture the underwriter's decision-

making process.  Moreover, we find that there are unquestionably numerous data entry and data

reporting errors in the information supplied by the institutions that participated in the study. 

Nevertheless, using data provided by the Boston Fed, we test several alternative specifications

of the model and find their results ─ including the magnitude and significance of the race variable

─ to be quite robust with regard both to alternative specifications and to the correction of the

more obvious and easily correctable data errors.  Moreover, we find that approximately half of

the difference in observed denial rates can be attributed to differences in the initial endowments

(i.e., the basic characteristics of the applicants or the properties) associated with individual racial

groups, and that the remaining difference in the denial rates represents a discriminatory

differential of roughly the same magnitude as that found by the original study.

The follow-up studies also raise several other methodological and sample design problems that,

if valid, could substantially alter the Boston Fed's conclusion.  For the most part, however, those

issues cannot be tested using the Boston Fed data and therefore are speculative at best.  We

assess the validity of these criticisms as applied to the Boston Fed study, and where possible,

discuss the likely impact they would have on the results. 

The paper is structured as follows.  In the next section, we summarize the Boston Fed's

methodology and findings.  Section III introduces the issues of goodness-of-fit and separate

regression models for whites and minorities.  Section IV explores the question of differences in

endowments by race.  In section V, we discuss several alternative model specifications that we

believe better represent the underwriting procedure employed in the mortgage lending market. 

In section VI, a summary and discussion of some of the more troubling data errors are presented

and issues of model misspecification and omitted variables are also explored.  We conclude with

an overall assessment of the validity of the Boston Fed's findings with regard to the existence

of discrimination, and a discussion of future research efforts. 

II.	The Boston Fed model

The Boston Fed found that Home Mortgage Disclosure Act (HMDA) data consistently show that

non-Asian minority home mortgage application denial rates are two to three times higher than

those for whites.  This led Munnell et al. to argue:  

	[t]his pattern has triggered a resurgence of the debate on whether discrimination exists

in home mortgage lending.  Some people believe that the disparities in denial rates are

evidence of discrimination on the part of banks and other lending institutions.  Others,

including lenders, argue that such conclusions are unwarranted, because the HMDA data

do not include information on credit histories, loan-to-value ratios, and other factors

considered in making mortgage decisions.  These missing pieces of information, they

argue, explain the high denial rates for minorities (Munnell et al. 1992, p. 1).  

The Boston Fed sought to resolve this controversy, at least in the case of a single MSA, by

conducting a follow-up study.  With the voluntary participation of the lending institutions, they

collected information on the creditworthiness of applicants from all HMDA-reporting institutions

in the Boston MSA that received at least total 25 mortgage applications in 1990.  A final sample

of 3,062 files (2,340 white and 1,013 Hispanic and Black) was chosen from 18,838 total loan

applications.  An expanded HMDA data form was then sent to each institution, requesting information on 38 additional variables the researchers thought could influence the lending

decision for each loan application included in the sample.

The expanded HMDA sample data show that the minority applicants in the Boston MSA in 1990,

on average, had less wealth, higher loan-to-value ratios, and poorer credit histories than white

applicants.  (See Appendix 1 for details.)  As stated by the Boston Fed, "These differences tend

to support arguments that the higher denial rates experienced by minorities are attributable, at

least in part, to financial characteristics, credit histories, and other economic factors" ( Munnell

et al. 1992, p. 25).  Minorities were also more likely to have applied under special loan

programs and to have applied for private mortgage insurance.  While minorities had lower

incomes, they also applied to purchase less costly homes, so their obligation ratios were similar

to those of white applicants.

The centerpiece of the Boston Fed study consisted of the development of an econometric model

to assess the importance of these differences ─ and of the applicant's race ─ on the outcome of

the lending decision.  The model attempts to replicate the mortgage lending decision-making

process by estimating the probability of denial for each mortgage loan application, as a function

of the financial characteristics and credit and employment history of the applicant, the

characteristics of the home being purchased, and the neighborhood where the property is located. 

A dummy variable representing minority status is intended to test for discrimination.  That is,

after controlling for the relevant financial, credit, etc. characteristics, is there an unexplained

portion of the difference in denial rates that is correlated with the applicant's race? 

Since the outcome of the application process can take on only two possible values ─ approval or

denial ─ a logit limited dependent variable model is used.  The dependent variable (referred to

as the logit, or the log odds ratio) takes the form

			g(x) = ln[p/(1-p)]

where		 p = probability of denial.

The results of the Boston Fed statistical analysis are summarized as Boston I in Table 1.  (See

Appendix 2 for a list of variable definitions.)  Munnell et al. found that, after controlling for the

creditworthiness of the applicants, a minority applicant was still 56 percent more likely to be

turned down than a white applicant.  This result is reflected in the large, positive, and significant

coefficient on the race variable.  The authors tried numerous alternative specifications (see

Munnell et al. 1992, Appendix B, Tables 1 through 12), and found the magnitude and

significance of the coefficient on the race variable to be highly robust across all specifications.

We estimated the same model using the partial data set (2,932 observations) made available to

the public by the Boston Fed following the publication of the lending discrimination study.  The

results are presented as Boston II  in Table 1.  All coefficients and significance levels and the

percent correct predictions are nearly identical to those of the original study.

III.	Issues in evaluating the Boston Fed model

Goodness-of-fit

While certainly important, the robustness of the Boston Fed results in and of itself does not

validate the model or their finding of discrimination in mortgage lending in the Boston MSA. 

It does suggest that they are reasonably satisfied the model includes the "correct" variables,

specified with the appropriate functional form.  It does not, however, tell us how effective the

model is in predicting outcomes.  Like any statistical model, it must also be tested for goodness-

of-fit (i.e., to see if the model provides reasonably accurate estimates of the probability of

denial).  

Unfortunately, assessing the goodness-of-fit of a limited dependent model is difficult, since the

conventional method of assessing model reliability (using the distance between the observed and

the predicted values of the dependent variable) is complicated by the binary specification of the

dependent variable (1 if denied, 0 if approved).  Therefore, unlike least squares regression

models, limited dependent variable models have no generally accepted goodness-of-fit measures. 

One approach to the goodness-of-fit used by the Boston Fed is to measure the number of

"correct" predictions as a percent of the total number of observations.  A prediction is said to

be correct if the estimated probability of denial is greater than 0.5 (i.e., prob(y=1│x) > 0.5) for

an application that is actually denied, or if the estimated probability of denial is 0.5 or less (i.e.,

prob(y=1│x)  0.5) for an application that actually is approved.  By this measure, the Boston

Fed models consistently obtain an overall correct prediction percentage of roughly 90 percent

(with approximately 98 percent of approvals correctly predicted, but only 35 percent of denials correctly predicted).

This correct predictions approach, however, can be misleading.  First, despite the obvious

intuitive appeal, the choice of 0.5 ─ or any other value for that matter ─ as the cut-off that

distinguishes predicted approvals from predicted denials is arbitrary.  Second, this approach can

inflate the predictive power of a model in the very common situation where there are many more

occurrences of one outcome (in this case, approvals) than the other (denials).  For example, using

the Boston Fed data, 85.5 percent of all applications in the sample were approved.  So, a naive

"model" that simply says "approve every single application" (i.e., the estimated probability of

denial is set to zero for all observations) would correctly identify 85.5 percent of the outcomes. 

Even though the overall predictive power of the naive "model" appears good (85.5 percent

correct), it incorrectly predicts approval for every denied application.  Also, the predictive

accuracy of the Boston model, at 90 percent correct, is much more modest when compared to the

baseline of 85.5 percent for the naive "model."

We believe this method of evaluating a model's goodness-of-fit is inappropriate in a more

fundamental sense as well, since the objective of a logit model is not to correctly predict the

outcome for each individual observation, but to provide a reasonable estimate of the likelihood

an outcome will occur (for a given set of values for the independent variables).  We know by the

very nature of a probabilistic statement that some applications with very low predicted

probabilities of denial will in fact be denied and some with very high probabilities will in fact

be approved.  For example, if the probability of denial estimated by an accurately specified model

is 10 percent for each of 50 applications, we would expect 45 actual approvals and 5 actual

denials for the group.  The five denials are fully consistent with the nature of a discretionary

decision-making process, as accurately captured by the logit model.  They are not "incorrect" in

any meaningful sense.  Yet the correct predictions approach would classify them as incorrect and

would rank a model that predicts approval for all 50 of these applications as a better-fitting

model; such findings are clearly inappropriate.  For this reason, we believe a more accurate

method of assessing the goodness-of-fit of a logit model would rely on a measure that compares

the expected number of occurrences of a particular outcome (denials in this case) to the actual

number of such occurrences.  

Hosmer and Lemeshow (1989) have developed such a measure.  Their test statistic is derived by "calculating the Pearson chi-square statistic from the 2 by g table of observed and estimated

expected frequencies" (Hosmer and Lemeshow 1989, p. 141), where g is the number of groups. 

We calculated the Hosmer-Lemeshow test statistic for the Boston II model estimated using the

publicly available data.  The p-values presented in Table 1 are for a chi-square test with g - 2

degrees of freedom.  Each p-value indicates the probability that differences between the expected

and observed values as great as, or greater than, those derived from the model's estimated

probabilities, are due solely to random chance.  That is, if, Boston II is the true model of

mortgage loan decision-making, there is only a 16 percent probability of observing the pattern

of differences between the actual and expected numbers of denials that we see emerge from the

results of the Boston II model.  This relatively low p-value suggests the model is marginally

adequate. 

Separate models by race

Table 2 reports on separate models for whites and minorities.  Two interesting results emerge

from the separate models specification:  First, only six of the 12 coefficients in the minority

model are significantly different from zero; as compared to 11 of 12 in the white model.  Second,

though many of the variables in the minority model do not contribute to explaining the denial

decision, the model performs extremely well in predicting outcomes (as measured by the Hosmer-

Lemeshow test statistic).  Those results suggest that (i) minorities with characteristics identical

to whites are treated differently, as reflected in the difference in the estimated regression

coefficients across equations (i.e., different underwriting standards are applied ─ discrimination

exists); or (ii) the difference in the estimated parameters may only reflect the sensitivity of the

estimation procedure to the differences in initial endowments of minority applicants (e.g., higher

loan-to-value ratios, poorer credit history, and lower wealth), on average; or (iii) both i and ii. 

Munnell et al. support the first conclusion.  They reject the hypothesis of a difference in treatment

due to differences in factors unrelated to race.  This follows directly from their analysis of the

difference in the estimated coefficients across race equations.  In their Appendix B, they report

the results of an analysis of the difference in estimated parameters between the minority and white models.  They initially report that there exists a statistically significant difference in the

estimated parameters across equations.  They argue, however, that the difference can be explained

by the introduction of race as an explanatory variable (a simple shift parameter).  They therefore

conclude that the qualifying standards applied across the races are the same; that is, that the

weights assigned to measure the relative importance of each decision variable on the underwriter's

decision are, in a statistical sense, equal.  

Munnell et al. do not test for the possibility that the difference in treatment across equations is

associated with factors other than race.  Differences may arise, however, for several reasons:  (i)

the differences in initial endowments (financial and credit characteristics, etc.) between whites

and minorities, on average, may be large enough to distort the relationship between the likelihood

of denial and race;  (ii) there may be omitted variables or relationships correlated with the race

variable; (iii) there may be significant non-linearities embedded in the relationship between

the explanatory variables and the logit variable which have a disproportionately adverse effect

on minorities; or, (iv) there may be a more complex two- (or more) step procedure involved,

which would cause a single-step analysis to inadvertently assign too much weight to the race

variable and thus inappropriately implying discrimination where none exists.

In the discussion below we address the first three of these four possibilities.  We address the first

issue by testing the hypothesis that the difference in treatment is due to the significant differences

in the average values of the independent variables (i.e., initial endowments) by racial group.  Our

primary hypothesis is that the significantly lower wealth/liquid assets, poorer credit history, higher

loan-to-value ratios (LTV), and higher debt ratios of the minority group can account for a

significant portion of the difference in denial rate.  We test this hypothesis using a Blinder-

Oaxaca procedure.  This procedure decomposes the differences in the dependent variable between

the white and minority equations into two components.  The first is a measures of the difference

in the dependent variable associated with the difference in initial levels of the endowments by

groups; the second measures the difference due to differences in the estimated parameters across

equations (i.e., that associated with differences in treatment ─ discrimination). 

We address the second and third possibilities by testing several alternative model specifications

that include additional variables not investigated in the Boston Fed study and that incorporate

specific non-linear relationships between the dependent variable and the independent variables. 

More specifically, we use both higher order expressions for several of the independent variables

that are likely to have greater influence the greater their deviation from industry standards, and

step function relationships (e.g., different underwriter criteria are used if the LTV is .80 or

higher) that more closely approximate the procedures generally used in the industry.

The fourth issue is much more complex.  It suggests that there may exist a two- (or more) step

process that initially evaluates the creditworthiness of the borrower using a reduced set of "key" 

qualifying variables instead of the broad spectrum of variables identified in the Boston Fed

study.  If a large proportion of the minority rejections take place at this level, for example

because a higher proportion of applicants have insufficient funds to close or poor credit histories,

a single step analysis may overemphasize the importance of race on the approval decision.  An

analysis of this sort is currently outside the scope of this paper.

IV.	The importance of the difference in endowments by race

An analysis of the sample statistics, by race, shows the financial characteristics of minorities in

the Boston MSA differ significantly from those of whites (see Appendix 1).  Minorities tend to

have less wealth, less income, a higher percentage of credit problems, and a lower percentage of

liquid assets in excess of closing costs.  Further, they generally borrow a larger percentage of the

value of the property and more often apply for private mortgage insurance (PMI).  By

themselves, lower wealth and income need not imply lower qualifications, since borrowers with

lower incomes and wealth tend to purchase less expensive homes.  Though the median loan-to-

income ratio of minorities is higher (2.45) than whites (2.03), monthly housing payments-to-

income ratios of minorities, in general, meet the secondary market guidelines.  The relationship

between white and minority applicants with respect to the other variables, however, supports the

argument that higher denial rates can be attributed to lower minority qualifications. 

The methodology used in the Boston Fed's model (i.e., the difference in treatment is confined

to an analysis of the difference in the intercept term through a simple dummy variable

specification) implicitly assumes that the groups have a similar endowment distribution.

Accordingly, the difference in denial rates unexplained by the augmented model must be

attributed to discrimination.  They find that approximately 56 percent of the difference in the

denial rates remains after controlling for wealth, employment, and credit history.  This remaining difference is attributed to discrimination.  

Because the Boston Fed model restricts the difference between races to the single shift term,

however, it is possible that a portion of the difference attributed to discrimination could be due

to differences in the distribution of endowments by groups; a likely result given the substantial

differences in endowments.  For this reason, we performed the Blinder-Oaxaca procedure (Berndt

1991; Blinder 1973), which decomposes the difference in the dependent variable into differences

associated with initial endowments and those associated with discrimination.

The procedure relies on the property that the fitted regression line passes through the regression

means.  This property holds for the logit of a multiple logistic regression model (i.e., the logit

is the log odds ratio, and is defined as:  g(x) = ln[p/(1-p)] = ßx ).  The decomposition of the

difference in the log odds ratios, by race, evaluated at the mean values of the independent

variables, is derived as follows:

	g(Xwa) - g(Xma) =  bw (Xwa - Xma)  +  Xma Δb	(1)

where

		g(Xia)	=	the mean log odds ratios, ln[p(y=1│Xia )/(1-p(y=1│Xia ))] for i =

m (minority), w (white), are calculated using the average values of

the independent variables, Xia, for each group; 

	    p(y=1│Xia)	=	probability of denial, given the mean values of the

independent variables;

		   bw	=	estimated coefficient from Table 2, Boston II, White;

		  Xia	=  	average value of the independent variables (i = m (minority), 

				w = (white)); and

		   Δb	=	difference in the estimated coefficient between the Boston II, White

and Boston II, Minority results reported in Table 2.

The first term on the right hand side of the equation represents the amount of the difference in

the log odds ratios associated with the differences in average endowments, and the second term

is that associated with differences in the estimated parameters.  A test of the null hypothesis of

equality of parameters across equations (whites only versus minority only) reveals that the

coefficients used in the Boston Fed model are indeed different, supporting the hypothesis that the

initial endowments are important determinants of the denial rate.   

The results suggest that 44 percent of the difference in denial rates is associated with

discrimination.  In other words, the "average" minority applicant (derived using the average

values of the independent variables), had an estimated probability of denial of 24.5 percent, while

the "average" white applicant's estimated probability of denial was 6.8 percent.  Controlling for

differences in the average initial endowments lowers the estimated probability of denial of the "average" minority applicant to 14.6 percent, thus explaining 9.9 percentage points, or 56 percent

of the initial difference in average estimated denial rates.  The remaining 44 percent of the

difference is attributed to differences in treatment by race.

Our results suggest that the degree of discrimination is lower than that found in the Boston Fed

study; a result we consider more accurate because the Blinder-Oaxaca procedure does not assign

the differences in denial rates exclusively to the intercept term, but also allows for variation in

the estimated slope coefficients.  However, and more importantly, our results show that the

difference in denial rates cannot be explained entirely by the difference in endowments.  This

substantive agreement with the Boston Fed's central conclusion should not be overshadowed by

the relatively minor difference in magnitude (56 percent versus 44 percent) between our results

and those of Munnell et al. 

An important caveat to this procedure, however, is that the model must include all relevant

decision variables.  If the model is misspecified, the second term on the right-hand side of

equation (1), Xma Δb, will overstate the degree of discrimination.  It is this issue we address in

the next section. 

V.	Specification of the Boston model

One of the most important issues related to the Boston model, and one that has been the subject

of considerable comment and criticism, is the question of the precise specification of the

regression model.  That is, which variables are included in the regression equation, and in what

form(s)?  Since the exact specification of the regression equation is not derived directly from a

theoretical model of mortgage lending, and since there is no well-established, standard model in

the previous literature, Munnell et al. had considerable leeway in their choice of specification. 

The Boston Fed collected data for a list of variables identified as the primary decision variables

through "numerous conversations with lenders, underwriters, and others familiar with the lending

process" (Munnell et al. 1992, p. 13).  A number of alternative specifications of the model were

explored (see Appendix B, Munnell et al. 1992) before the authors settled on the particular form

of the relationship between the independent variables and the decision to approve or deny a

mortgage application.  In this process, the authors chose both the variables to include and their

mathematical forms (e.g., linear or nonlinear, dummy or continuous) used in the final model.

While Boston Fed staff tried a large number of different specifications, there are reasons to

believe that the final model presented in the paper fails to capture all relevant aspects of the

relationship between the independent variables, including the race of the applicant, and the

outcome of the mortgage lending decision.  Therefore, it is fruitful to explore alternative

specifications they did not try ─ or, at least, did not report.  These alternative variables and

alternative forms of variables, are suggested by the model used in the Department of Justice case

against Decatur Federal, by the academic literature in the field, and by discussions with Office of the Comptroller of the Currency (OCC) examiners and fair lending and compliance staff.

The data

Table 1, above, presents our replication of the Boston Fed's basic model using the publicly

available dataset.  The Boston Fed also made available to each federal banking agency a set of

the raw data for participating institutions for which the agency is the primary federal regulator. 

The OCC and the Federal Deposit Insurance Corporation (FDIC) then agreed to exchange their

data sets (after removing all fields that could identify individual institutions or applicants).  This

yielded a combined data set of 1,603 observations, or slightly over half of the original sample

used by the Boston Fed.  These data were used for most of the analysis reported below.

Appendix 1 presents a comparison of the median values of a select group of series for the

OCC/FDIC sample and the full sample used in the published study.  As shown, the smaller

OCC/FDIC sample is very similar in almost all characteristics, with a few exceptions.  In the

OCC/FDIC sample denied applicants (both white and minority) had less net wealth and somewhat

lower monthly incomes; denied applicants (both white and minority) were more likely to have

applied for private mortgage insurance; and minority applicants (both approved and denied) were

more likely to be applying under special programs of some kind.

Table 3 compares the logit regression results, applying the same Boston Fed model specification

to the OCC/FDIC sample as to the publicly available sample.  Most of the estimated coefficients

are quite similar.  Of those that show substantial change for the smaller sample, mortgage credit

history and race are larger, while self-employment and rent/value are smaller.  Three of the

explanatory variables (probability of unemployment, self-employed, and rent/value) lose their

significance at the 5 percent level in the OCC/FDIC sample; all the others retain the same

significance, or lack thereof, as in the full sample regression.  Interestingly, the goodness-of-fit

of the model increases substantially for the smaller sample, suggesting that the model performs

better as a predictor of loan decisions for the sample of non-member state-chartered and national-

chartered banks than for the full sample. 

Alternative specifications

Alternative variables and alternative forms of the variables were explored to improve the

specification and goodness-of-fit of the Boston Fed model.  The alternative variables and forms 

that were significant, individually or in combination, or that improved the overall performance

of the model are discussed below.

One general issue that merits discussion relates to the nature of the mortgage decision-making

process, and how some of the most important underwriting standards are applied.  In particular,

it appears, from discussions with examiners, underwriters, and others familiar with mortgage

lending, that there are significant discontinuities and/or nonlinearities in the way underwriters

look at factors like the loan-to-value and debt ratios.  For example, loan-to-value ratios may

significantly affect the decision-making process only above certain levels; applications with very

high loan-to-value ratios may be automatically disqualified, regardless of how strong the rest of

the file may be.  Certainly a change in the loan-to-value ratio from 85 percent to 90 percent will

exert much more influence on the outcome of the underwriting process than a change from 50

percent to 55 percent. 

Considerations of this type seem to be of particular importance in a model of the lending process,

yet the Boston model is conspicuous for the absence of variable forms that attempt to capture

such factors.  In our efforts to develop alternative specifications, we devoted considerable

attention to experimenting with forms that might capture these characteristics of the underwriting

process, in particular with regard to the loan-to-value, monthly housing expense-to-income 

and the total debt-to-income ratios.

Loan-to-value ratio.  While the loan-to-value ratio is highly significant in the Boston model, the

form in which it is cast in the model is subject to question.  In particular, the loan-to-value ratio

itself enters into the model, implying a linear relationship between the ratio and the dependent

variable (the logit).  Judging from the results reported in the Boston Fed study (Munnell et al.

1992, both text and Appendix B), it appears that no attempt was made to capture the kinds of

nonlinear or threshold effects discussed above. 

In order to better reflect the nonlinearities associated with the loan-to-value ratio, that variable

was replaced by a set of three variables designed to capture the threshold effect.  These are:  (i)

the excess above 80 percent (if 80 percent or less, the variable is set equal to zero), (ii) the excess

above 80 percent squared, and (iii) a dummy variable set equal to 1 if the ratio is above 90

percent.  The 80 percent level is generally regarded as an important threshold, since the secondary

market (Fannie Mae and Freddie Mac) requires private mortgage insurance for all loans above

80 percent.  The squared term allows for nonlinearities in the relationship between LTV and the

dependent variable, and the dummy variable differentiates loans with exceptionally high LTVs.

As shown in Table 4, for Model I all three alternative forms of the LTV specification are

significant at the 5 percent level.  The signs indicate, plausibly, that increasing LTV above the

80 percent level increases the probability of denial, although at a decreasing rate, and that

increases above the 90 percent level increase the probability of denial even further.  The

estimated coefficient for the variable that measures the impact of the race of the applicant is

somewhat smaller, suggesting that some of the unexplained difference in probability associated

with race is captured by the threshold effect of the loan-to-value ratio.  However, the race

coefficient remains highly significant.  The various measures of goodness-of-fit and predictive

ability all show marginal improvement over the Boston model ─ except for the percent of

correctly predicted denials, which shows a more substantial improvement.  Moreover, the log

likelihood ratio shows substantial improvement.  All of the remaining coefficients and

significance levels change only slightly.

Debt ratios.  The two standard debt ratios are used in the Boston Fed model to measure the

ability of the borrower to support the loan payments.  The ratio of proposed monthly housing

expenses to income was entered in the form of a dummy variable that was set equal to 1 if the

ratio exceeded 30 percent.  The total debt-to-income ratio was entered directly into the equation. 

The debt ratios are another area where discussions with examiners and underwriters, as well as

the logic of the underwriting process, suggest that there may be significant nonlinear and/or

discontinuous effects.  While the Boston model captures some of these with the dummy variable

formulation for the housing debt ratio, other studies have used other specifications that seemed

worth exploring.

Using the widespread secondary market standards (28 percent for the housing expense ratio and

36 percent for the total debt ratio), it is hypothesized that the likelihood of denial increases as a

function of the degree to which the ratios exceed these threshold levels.  Specifically, a set of

three variables was substituted for the Boston formulation:  (i) the excess of the housing debt

ratio above 28 percent squared, (ii) the excess of the total debt ratio above 36 percent, and (iii)

the excess above 36 percent squared.

As indicated in Table 4, for Model II all three of the new debt ratio variables are highly

significant.  The estimated coefficients imply that the probability of denial increases exponentially

at higher levels of housing debt; it also increases at higher levels of total debt, though at a

decreasing rate.  The impact of race is slightly larger in magnitude than in the Boston Fed

specification and remains highly significant.

The goodness-of-fit statistic, although still consistent with a well-specified model, shows a

considerable decline relative to the Boston model, while the measures of predictive ability show improvement, and the log likelihood ratio is virtually identical to that of Model I.  All of the

remaining coefficients and significance levels change only slightly.

Employment and education.  The Boston model used two variables ─ (i) the Massachusetts

unemployment rate for the industry where the applicant was employed, and (ii) a dummy variable

indicating if the applicant was self-employed ─ to represent employment status, history, and

stability.  The estimated coefficients were both positive, indicating that higher levels of

employment instability, as proxied by the unemployment rates and self-employed status, are

associated with higher probabilities of denial.  Although both coefficients were significant at the

2 percent level or better as reported for the full sample, when estimated for the combined

OCC/FDIC sample, neither was significant, even at the 10 percent level.

There are two problems with the use of the unemployment rate variable in the Boston model. 

First, the model does not make use of potentially useful information related to employment in

the loan file, for example the number of years in the current occupation.  Further, education

is also a useful proxy for employment and income stability; applicants with more years of

education are more likely to find and retain jobs, and have better potential for advancement and

income growth.  Second, the employment variable used in the Boston model assigns the same

probability of unemployment to everyone in the same industry (by two-digit standard industry

code (SIC)), whether clerk or chief executive officer.  

The potential weakness of the Boston approach is illustrated by the case of a loan file where both

the applicant and coapplicant were security guards with less than one year in the occupation; the

applicant had 1.5 years on the current job, the coapplicant less than one year.  Because the

applicant worked for a bank, however, the unemployment rate for the industry was relatively low,

and, partially as a result of this factor, the application had one of the lowest estimated

probabilities of the entire sample.  Yet the very short employment tenures of both the applicant

and coapplicant constitute a significant negative factor that should plausibly have contributed to

a higher probability of denial.  This was clearly not captured by the industry unemployment rate

specification used in the Boston model.

In an attempt to better model employment history and income stability, two variables were

substituted for the probability of unemployment:  (i) the number of years of education for the

person (applicant or coapplicant) with the higher employment income, and (ii) a dummy variable

set equal to one if the applicant's number of years in the current line of work was greater than

five.  The self-employed dummy variable was retained. 

Table 4.  Results of alternative regression models:  OCC/FDIC sample

Variable	OCC/FDICa	Model I	Model II	Model III	Model IV	Model V

	β	p-value	β	p-value	β	p-value	β	p-value	β	p-value	β	p-value

Constant	-6.8	0.0001	-6.4	0.0001	-5.48	0.0001	-5.29	0.0001	-6.35	0.0001	-2.48	0.0052

Ability to support loan

Housing expense ratio	0.48	0.0271	0.54	0.0153	  		0.35	0.1127	0.46	0.0494		

  Excess above 28%					0.0003	0.0176					0.0007	0.3430

Total debt ratio	0.04	0.0001	0.04	0.0001			0.05	0.0001	0.06	0.0001		

  Excess above 36%					0.13	0.0001					0.15	0.0001

  Excess above 36% sqd					-0.0008	0.0001					-0.001	0.1345

Net wealth	.00008	0.2615	.00009	0.1959	.00006	0.3563	.00008	0.2699	.00009	0.3103	.00008	0.2445

Risk of default						 						

Cons. credit history	0.34	0.0001	0.44	0.0081	0.34	0.0001	0.37	0.0001	0.34	0.0001	0.38	0.0001

Mtg. credit history	0.49	0.0024	0.35	0.0001	0.52	0.0018	0.52	0.0020	0.53	0.0023	0.49	0.0099

Public record history	1.3	0.0001	1.3	0.0001	1.18	0.0001	1.26	0.0001	1.41	0.0001	1.34	0.0001

Prob. unemployment	0.07	0.1078	0.06	0.1871	0.06	0.1296			0.07	0.1288		

Self-employed	0.38	0.1446	0.50	0.0644	0.29	0.2837	0.59	0.0248	0.28	0.3429	0.46	0.1389

Yrs. of education							-0.08	0.0066			-0.10	0.0033

Over 5 yrs. in occ.							-0.48	0.0184			-0.35	0.1292

Potential default loss

Loan-to-value ratio	0.51	0.0045			0.46	0.0122	0.52	0.0046	0.50	0.0064		

  Excess above 80%  			1.73	0.0302							1.76	0.0360

  Excess above 80% sqd			-0.23	0.0333							-0.23	0.0354

  Above 90 percent			0.92	0.0001							0.90	0.0008

Denied PMI	4.5	0.0001	4.4	0.0001	4.55	0.0001	4.42	0.0001	4.92	0.0001	5.02	0.0001

Rent/value in tract	0.12	0.7978	0.18	0.7155	0.24	0.6044	0.19	0.6828				

% moved in pre-1985									-0.02	0.067	-0.02	0.0471

Loan characteristics												

2- to 4-family home	0.56	0.0164	0.55	0.0201	0.47	0.0487	0.41	0.0822	0.54	0.0246	0.32	0.2248

Personal characteristics

Race	0.94	0.0001	0.80	0.0001	0.98	0.0001	0.86	0.0001	0.91	0.0001	0.71	0.0017

No. of observations	1603		1603		1603		1588b		1378c		1367d	

% correct predictions	89		90		89.6		89		89		91	

% correct approvals	97.6		97.7		97.6		97.7		97.9		97.4	

% correct denials	38.8		43.1		42.2		40.4		40.3		51.5	

-2 log likelihood	863.8		833.4		833.3		838.4		723.4		501.2	

Hosmer-Lemeshow test

(p-value)	0.82		0.83		0.49		0.66		0.72		0.50	

a OCC/FDIC model from Table 3 is reproduced for ease of comparison.

b Years of education was missing for 15 observations.

c 1990 Census tapes could be matched with loan applications for only 1378 observations.  See footnote  22 .

d Of the 1378 observations used for Model IV, years of education was missing for 11 observations.

As shown in Table 4, for Model III the dummy variable for self-employed applicants grows both

larger and considerably more significant.  The two new variables are both negative, as expected,

indicating that the probability of denial is lower for applicants with more education and with

longer experience in their current occupation; both estimated coefficients are significant.  The

race coefficient is slightly lower and still highly significant.  The goodness-of-fit statistic is less

than that associated with the Boston Fed specification; however, it still suggests the specification

of Model III is quite good.  The measures of correct predictions show modest improvement.

The estimated coefficients for the remaining variables, in general, show only slight changes in

magnitude.  There was, however, a substantial change in significance level of the coefficient on

the housing debt ratio.  The dummy variable indicating a housing debt-to-income ratio above 30

percent went from about 3 percent significance to about 11 percent.

Neighborhood effects.  It is widely believed that the location of the property being purchased

enters into the underwriting decision.  In particular, if the home is in an area where it can

reasonably be expected that property values may show little growth, or in fact decline, then a loan

is less likely to be approved, all other things being equal, because the probability of default is

higher and the position of the mortgagee is less secure.

Measuring this location effect, however, has proven to be difficult.  The Boston Fed study uses

a rather unusual proxy variable, the ratio of rental income to the value of the rental housing stock

in the Census tract where the property is located.  The estimated coefficient was positive,

indicating that higher rent-to-value ratios are associated with higher probabilities of denial.  The

estimate is highly significant in the published results for the full sample, but insignificant in the

combined OCC/FDIC sample.

The Boston Fed's choice was based on the presumption that landlords demand a higher return

on riskier properties.  While there is some logic to this line of reasoning, the authors do not

present any evidence to support the contention that this ratio is in fact higher in riskier or

deteriorating areas, or to prove that any such differential returns that might exist are, in fact, due

to differences in risk.  While the authors did try several other measures of neighborhood

effects, as reported in the Appendix, there are many other possible candidates that have been

used by other authors and that are readily available from the Census tapes. 

After matching the OCC/FDIC sample with 1990 Census tapes, the proportion of households

who had moved into their residences prior to 1985 was substituted for the rent-to-value ratio. 

The pre-1985 variable can be interpreted as a proxy for neighborhood stability, with the

presumption that the more households that stay in their residences for a long time, the more stable

the property values in an area and the lower the default rate and collateral risks to the lender. 

As shown in Table 4, for Model IV the estimated coefficient for the new variable, percent moved

in pre-1985, is negative, indicating that a location in a more stable neighborhood lowers the

probability of denial, as expected.

The estimate is significant at the 10 percent level only, which is marginal, yet far better than the

virtually total lack of significance for the rent-to-value variable.  In other respects as well,

comparison of the alternative to the Boston specification produces mixed results.  The goodness-

of-fit statistic is almost identical.  The overall percent correct predictions is slightly higher, but

that is due entirely to a better performance predicting approvals, while the percent of correct

denials is lower.  The race coefficient is slightly lower and still highly significant.  The remaining

coefficients and significance levels showed only slight changes.

Other variables.  A number of alternative specifications were also attempted in various other

categories such as gender, age, and marital status; property characteristics (e.g., condominium and

non-owner occupied); types of institutions (e.g., national banks, state banks, mortgage

subsidiaries); and a dummy variable for each separate lending institution.  Since these

specifications did not substantially alter the outcomes, they are not reported in detail here. 

Alternative specification:  Summary.  Table 4 presents, as Model V, regression results for a

specification combining all of the alternative variables discussed in the preceding sections.  The

signs of the new variables are all the same as when they were introduced separately, and the

magnitudes are approximately the same as well.  The significance of three of the new variables,

however, disappears when they are used in combination:  The excess of the housing debt ratio

above 28 percent squared, the excess of the total debt ratio above 36 percent squared, and the

dummy variable indicating more than five years in the same line of work.  The coefficient on the

race variable is lower than that in the preceding four models reported in Table 4, and also is

lower than the results when the Boston specification is run on the same sample.  This indicates

that the new specification is capturing some variation in outcomes that was previously attributed

to the race of the applicant.  The coefficient for race is still large and positive, however, and 

remains highly significant.

Table 5 reproduces the results from Model V and from the Boston Fed specification estimated

for the same sample (1,367 observations) for purposes of comparison.  The two specifications

have virtually identical goodness-of-fit statistics.  The log likelihood ratio for the alternative

specification, however, shows very substantial improvement, and the alternative specification does

better than the basic model in terms of the percent correct predictions.  Of particular note is the

large improvement in the percent of denials correctly predicted, from 40.7 percent to 51.5

percent.  Finally, there is little change in the signs, magnitudes, or significance levels of any of

the other variables.

An examination of the estimated probabilities of denial from the two specifications for individual

applicants reveals that the difference in results from the two models can be substantial in many

cases.  For about half of the observations, the two estimated probabilities are within two

percentage points; for 13 percent of the observations, however, the difference is greater than ten

percentage points and,for a few cases it exceeds 40 percentage points.  The probabilities estimated

by the original Boston specification exceed those from the alternative specification for about 60

percent of the observations; they are smaller for the remaining 40 percent.  Further, of those

applications that were actually denied and had estimated probabilities of denial of 0.5 or less in

the Boston model but more than 0.5 in the alternative specification, the amount of increase was

generally quite substantial.  Thus, the increase in the percent of denials correctly predicted,

discussed in the previous paragraph, is not due to probabilities that went from just slightly below

50 percent to just slightly above that level. 

Because of the form of the logit model, it is difficult to deduce the actual impact of changes in

the independent variables on the probability of denial directly from the regression results. 

Therefore, Table 6 presents the results of the alternative specification discussed above in a more

readily comprehensible format. 

The table shows the percentage change in the average estimated probability of denial as a result

of a change in the value of each independent variable.  For the dummy variables, the table shows

the impact of the presence of the particular attribute (e.g., self-employed) relative to an otherwise

identical application without the attribute (not self-employed).  For the continuous variables, such

as net wealth, the table shows the impact  of a one standard deviation change. 

Most of the variables common to both specifications show little change in their impacts on the

estimated probability of denial; the one exception is self-employment, which increases the average

probability only 22.9 percent in the alternative specification, down from 35.1 percent in the

original study.  As expected, the most significant changes arise in the cases of the variables that

have been transformed in the alternative specification:  The total impact of a one standard

deviation increase in the loan-to-value ratio has increased dramatically; the housing debt ratio has

much less impact, while that of the total debt ratio is approximately double what it was before.

Most importantly, the impact of minority status, although somewhat diminished, is still quite

large:  A Black or Hispanic applicant would have, on average, a 49 percent greater probability

of being denied than an otherwise identical white.

Conclusion:  Robustness of the race coefficient

The efforts to develop alternative specifications for the model were fruitful in terms of the results

for individual variables and groups of variables that seemed, a priori, to better approximate the

mortgage underwriting process, as well as in terms of improved predictive ability.  Nonetheless,

the one result of the Boston study that has attracted the most attention and that has the strongest

public policy implications, the estimated coefficient for the race variable and its significance,

remains highly robust across specifications.  Through many dozens of alternative specifications,

both those reported above and many others not reported, the coefficient is always positive, within

a narrow range (most often between 0.7 to 0.9), and very highly significant.  At least with the

alternative specifications that could be explored with the data provided by the Boston Fed, we

could not refute the Boston Fed's conclusion that mortgage lenders in the Boston MSA,

collectively, treated Black and Hispanic applicants differently from whites in 1990, and that, on

average, a Black or Hispanic applicant had an approximately 50 percent greater probability of

being turned down than a white applicant with otherwise identical characteristics.

Of course these results are valid only insofar as the data truly reflects the underlying population. 

Several recent articles have suggested that the Boston Fed data is contaminated by numerous data

errors and inconsistencies.  They argue these errors could significantly influence the outcome of

the Boston Fed study.  In the next section, we address many of these issues.

VI.	Data entry/reporting errors

The Boston Fed states that they subjected the data to "careful visual inspection and computer edits and repeatedly called back lenders to verify that data items that seemed unusually large or small

actually reflected the contents of the lenders' files" (Browne 1993).  There are, however,

numerous instances in the partial data sets provided to the OCC and FDIC by the Boston Fed in

which the data remain suspect.  We discuss several examples of data errors we found in the

OCC/FDIC data and the implications those errors may have for the Boston Fed's results.

Analyzing the impact of data errors and inconsistencies

Duplicate files and coding errors.  Several of the more obvious data entry errors were easily

corrected.  For example, duplicate files were dropped from the data set, and the debt obligation

ratios entered as decimal values were converted to percentages.  There are relatively few of these

errors, and correcting them resulted in no substantive change in the Boston Fed's conclusions. 

It is not surprising these errors had so little impact on the results given that there is relatively low

leverage associated with extreme values in logit models (a statistical property of the estimating

procedure), so that even large changes in these values (i.e., converting the debt ratio from a

decimal to a percent) can have very small effects on the parameter estimates.

Correcting for other data entry problems, however, is more problematic.  Often it is difficult to

know if the correction itself introduces more error; and deleting the observation may bias the

sample if the errors are non-random across groupings.  Moreover, for errors of inconsistency it

is difficult to determine which data are false; therefore, the method used to correct the errors may

substantially influence the results.  We discuss several of these problems below.

Inconsistencies that suggest the debt ratios are underreported.  It is likely, given the large

number of files with monthly non-housing debt payments far below those consistent with the

level of outstanding liabilities, that the total debt obligation ratio is underreported in many

files.  Moreover, the proposed monthly housing payments for another 3 percent of the

applicants were below that required on a loan with a 6 percent mortgage interest rate (at a time

when market rates were above 10 percent).  This suggests that both the monthly housing expense

ratio and the total debt ratio were underreported for these observations as well.

In these cases, the applicant may appear qualified according to the model (that is, assigned a low

estimated probability of denial), yet appear unqualified to the underwriter, based on accurate

information concerning housing and non-housing debt payments.  Errors of this type reduce the

reliability of the model in general, and the importance of the housing expense and total debt

obligation ratios specifically as indicators of loan disposition.  There is no obvious way these errors can be corrected short of re-examining the loan files; a solution we believe is

impractical.

Including unverified data.  Two types of data verification errors are introduced in the Boston

Fed study:  (i) several banks reported data from the unverified, initial application, and (ii)

several applications contained information provided by the borrower that was not (or could not

be) verified by the bank.  Both of these data verification problems are especially troublesome for

it is difficult to know, a priori, how sensitive the coefficient of the race variable is to these

errors.

For example, including unverified data from the original, rather than the final, application form

may significantly affect the model's results if the unverified data tend to overstate the

qualifications of marginal borrowers (i.e., if the financial and credit history characteristics of the

denied applicants appear to approach those of the approved applicants).  The overstated

qualifications of marginal borrowers reduce the model's ability to accurately identify the

importance of each explanatory variable in the lending decision.  If the unverified data from the

original applications enter disproportionately from a single race category, a model that relies on

a single (categorical) variable to proxy for the race effect may wrongly attribute the difference

in denial rates to race.  The difference in denial rates will be more accurately reflected by

differences in financial and credit history characteristics of the applicant if the data used in the

model more accurately reflect the differences in qualifications.  The greater the difference

between the actual (verified) data and the reported data, the more likely the results of the

statistical model will be misleading.  Verification errors of this type are impossible to correct

without re-examining the loan files.

Data verification errors introduced by failing to incorporate information about the ability of the

bank to verify all (relevant) information on the application are less troublesome to correct.  The

Boston Fed data set contains an indicator variable (N56 - unverifiable information) that may

reduce the bias associated with overstated unverified data.  This variable identifies loan

applications containing credit, employment, income, residence, or "other" information that could

not be (or was not) verified by the loan officer.  Interestingly, unverified information was not

necessarily a fatal derogatory characteristic (see Table 7).  However, minorities with unverified information were 70 percent more likely to be denied than whites with unverified information.

Table 7.  Loan Files with Unverified Data by Race and Loan Disposition

	Approved	Denied	Percent

denied

Non-minority	26	24	48

Minority	9	41	82

Total	35	65	65

The Boston Fed data set identifies four categories of information that could not be verified: 

credit references, employment, income, and residence.  We tried several methods of incorporating

the unverified information dummy variable into the Boston Fed model.  We found the results to

be sensitive to the method used (see Table 8); however, the magnitude and significance of the

race coefficent are not affected.  Including the unverified information variable increases the

explanatory power of the model, suggesting either (i) the probability of denial increases if vital

information is not verified by the bank, or (ii) loan officers tend not to verify information if the

initial qualifications of the applicant are so poor that approval seems unlikely.  It is not clear

from the data if either or both of these are driving the result.  It is interesting to note, however,

that roughly 37 percent of the minority denials have unverified data, as compared to only 21

percent of the majority denials.  We return to this issue below.

Sufficient funds to close.  Having sufficient "funds to close" (that is, to cover the downpayment,

closing costs, and two months' payments) is a virtually universal underwriting requirement, and

lack of sufficient funds is often cited as a reason for denial.  The handling of this criterion in the

Boston Fed model, however, is problematic, and may not fully capture its impact on the lending

decision.

In the Boston Fed model, the downpayment amount is reflected in the loan-to-value ratio, which

proves to be a consistently important and significant variable.  In addition, the model attempts

to capture the sufficiency of funds to close through the use of net wealth and, alternatively, liquid

assets.  Neither of these latter variables, however, turns out to be significant, a result which,

according to the authors, appears "to support lenders' claims that they do not place much weight

on wealth . . . .  Pre-screening may also exclude people without enough cash to settle" (Munnell

et al. 1992, p. 30).

These explanations notwithstanding, it still seems curious that some measure of funds to close 

does not have significant explanatory power in the final model, in particular in light of the fact

that coming up with a downpayment has been found to be the primary obstacle to homeownership

for millions of American households (Apgar et al. 1990, Horne 1994).  On closer examination,

however, the treatment of this issue in the Boston model may be inadequate for several reasons. 

First, no attempt is made to measure available assets relative to the amount of money needed to

close.  Second, the various fees and points that must be paid by the buyer at closing are not taken

into account;  these can often constitute a substantial amount, especially for a marginal applicant

or first-time buyer who is struggling to come up with the necessary funds.  And finally, the way

that equity in a present home and gifts or grants were handled raises questions about the ability

of the model to fully capture the "funds to close" standard. 

While the amount of equity in a present home should, in principle, be captured in net worth, it

is likely that the net worth variable is misleading and inaccurate in this context.  Net worth

includes, among other things, real estate owned (which may include properties other than the

current home), net worth of businesses owned, autos, and furniture and personal property.  From

the total assets figure it is impossible to distinguish the amount of equity in the current home

(which is generally to be sold to move into the new home) from other assets the applicant may 

neither desire nor be able to liquidate in order to cover the closing costs of the new home.

There are similar questions with regard to gifts or grants used to meet part of the downpayment

and closing costs.  The data questionnaire in the Boston study included an item, "Did a gift or

grant account for any part of the down payment?" and a dummy variable reflecting the answer

was included in the model.  The estimated coefficient indicated a lower probability of denial for

applicants who had received gifts or grants, but it was not significant.  To the extent that gifts

actually received are accurately reflected in liquid assets, net wealth, downpayment amount, and

the loan-to-value ratio, this result, by itself, is not a cause for concern.  In fact, it is consistent

with lenders' contentions, as cited in the Boston Fed study (Munnell et al. 1992, pp. 14 and 30),

that wealth is not a significant factor in their decision-making.  

However, it is possible that the net wealth and liquid assets data do not accurately account for

gifts received.  Often, for example, gifts are received just prior to closing, and the amount of the

anticipated gift may not be included in the liquid assets reported on the application form.  This

problem is even more likely to occur in those cases where data for the study was taken from the

initial, rather than the final, application form (Horne 1994, p. 7).  FDIC examiners also found

instances where gifts were indicated in the loan file, but not verified or received (Horne 1994,

p. 11).  These findings raise two possibilities:  that a gift actually received was not reflected in

reported liquid assets, or that a gift included in reported liquid assets was ultimately never

received.  In either case, the Boston Fed model would fail to accurately capture the effect of the

gift, or its absence, and the results of the model may be biased as a consequence.

The inability of the Boston model to accurately measure the true amount of assets available to

cover closing costs may explain the insignificant results obtained for net wealth and liquid assets. 

Further, it means that denials that arise entirely, or in large part, because of insufficient funds

may be attributed by the model to other factors.  As examples, if minorities are disproportionately

less likely to be current homeowners or if, as homeowners, they tend to have less equity in their

homes, or if they are disproportionately more likely to report anticipated gifts that fail to

materialize, these problems would result in an upwardly biased estimate of the race coefficient. 

We attempted to better capture the issue of sufficient funds to close, with a variable representing

the ratio of liquid assets to closing costs (defined for this purpose as the downpayment plus two

months' proposed housing costs); the results were not significant.  However, this may well have

been due to the measure used and to the problems with the Boston data.  To explore this issue

adequately, it would be necessary to collect data on the aspects of financial ability not included

in the Boston Fed's questionnaire:  verification and actual receipt of gifts or grants, equity in a

current home, and the amount of other closing costs (fees, points, etc.) 

Model misspecification and omitted variables

The model has also been criticized for failing to include several relevant decision variables that

are correlated with race, which implies that the model has omitted variable bias.  Of particular

interest, given the Boston Fed data, is the inclusion of information on special programs and

program guidelines.

Many mortgage lenders are developing special loan programs to assist first time homebuyers and

"other" specially qualified applicants (such as individuals who are unable to make a nominal

downpayment in spite of strong financial/credit histories); or are participating in programs developed by the Federal National Mortgage Association (Fannie Mae), the Federal Home Loan

Mortgage Corporation (Freddie Mac), or state or local government agencies.  The presumption

is that the underwriting criteria applied to these loan applications are different from those applied

to conventional loan applications.  The Boston Fed data set pools applications without respect to

whether they participate in a special program.  This may result in a comparison of loan

applications with very different underwriting standards.  Accordingly, we would have expected

the model to include a special loan program variable which would capture the change in the

weights applied to those applications made under a special loans program.

The results of the statistical model may be biased if the special loan program information is

ignored, especially if a disproportionate share of one racial group participated in special programs. 

(This is true with the Boston Fed's sample, where over 50 percent of minority applicants ─ 51

percent of approvals and 55 percent of the denials ─ applied under a special loan program, as

compared to only about 13 percent of the white applicants ─ 12.8 percent of approvals and 18.8

percent of denials.)  Because the Boston Fed model does not include a special loan program

variable, the race coefficient may capture the effect associated with the difference in underwriting

standards, not just the difference in treatment due to race.

A special program indicator by itself may not adequately capture the impact of less stringent

underwriting standards.  Interaction variables are used instead of a single indicator variable to

separate out the effects of the special loan programs' underwriting standards on debt ratios, credit

history, and loan-to-value ratio.  The special loan program variables are, in general, of the right

sign and are statistically significant (see Table 9 - Model VIII).  All else being equal, a borrower

who applies under a special program will tend to have a lower probability of denial.  However,

the sign on the total debt-to-income interaction variable suggests underwriters are more concerned

about a borrower's total debt burden when the borrower is applying under a special program. 

An applicant applying under a special loan program with high debt levels has a higher probability

of denial. (This result is consistent with special loan programs found at many lending institutions

today, such as first-time homebuyers programs, that allow very high loan-to-value ratios but

generally are strict on debt ratios and recent credit history.)

Though the inclusion of controls for special programs increases the explanatory power of the

model relative to the basic Boston specification (see Table 4), the impact on the race variable is

small.  Moreover, the goodness-of-fit falls dramatically.  Though the coefficients of the model

are plausible, the low p-value for the Hosmer-Lemeshow test suggests the accuracy of the model

is only marginal.

A related model misspecification issue concerns the failure to incorporate information on the

credit guidelines used by the bank to evaluate the loan application.  Misspecification may exist

due to (i) differences in underwriting standards across banks (some banks may be more flexible 

Table 9.  Results of regression model:  Special Loans Programs and Program Guidelines

Variable	Model VIII	Model 

	Coefficient	p-value	Coefficient	p-value

Constant	-6.88	0.0001	-1.00	0.0413

Ability to support loan				

Housing expense ratio	0.59	0.0099	0.68	0.0124

Total debt ratio	0.035	0.0001	0.027	0.0045

Net wealth	0.00008	0.2568	-0.00001	0.8924

Risk of default				

Consumer credit history	0.36	0.0001		

Mortgage credit history	0.48	0.0038		

Public record history	1.25	0.0001		

Probability of unemployment	0.06	0.1235	0.04	0.3932

Self-employed	0.40	0.1278	0.66	0.0301

Potential default loss				

Loan-to-value ratio	1.00	0.0070	0.55	0.0597

Denied private mortgage insurance	4.56	0.0001	4.41	0.0001

Rent/value in tract	0.59	0.0121	0.73	0.0084

Loan characteristics				

Purchasing 2- to 4-family home	0.12	0.8109	0.22	0.7071

  Total debt ratio x spec. pgm.	0.079	0.0005	0.11	0.0006

  Mort. credit history x spec. pgm.	-0.10	0.2974	-0.18	0.1073

  Housing exp. ratio x spec. pgm.	-0.07	0.0581	-0.11	0.0070

  Loan-to-value ratio x spec. pgm.	-0.97	0.0373	-0.48	0.2145

Personal characteristics				

Race	0.92	0.0001	0.74	0.0030

  Meets guidelines			-4.12	0.0001

Number of observations	1603		1601a	

Percent correct predictions	89.5		92.9	

Hosmer-Lemeshow test (p-value)	0.15		0.12	

a The "meets guidelines?" question was not answered ─ either yes or no ─ for two observations.

than others, especially if they anticipate selling the mortgage), (ii) banks rejecting well qualified

applicants that are overqualified under special program guidelines (see Horne 1994), and (iii)

banks approving marginally to poorly qualified applicants under the less stringent, special

program qualifying standards.  

Ideally, loan applications should be matched directly with the guidelines used to evaluate the

credit quality of the borrower.  Discrimination would exist if the guidelines were applied unfairly

across racial groups.  Unfortunately, this information was not collected for the Boston Fed study. 

The Boston Fed did, however, request that the banks indicate if the applicants' credit histories met the bank's loan policy guidelines for approval.  We use the "meets guideline" variable to

partially address the types of misspecification discussed in (i) and (iii).  The results are

reported in Table 9 as Model IX.  The coefficient on the race variable is significantly reduced

but is not eliminated after controlling for credit history guidelines.  This model, however,

performs poorly.

We combined the effects of unverified information, special programs, and program guidelines and

report the results in Table 10.  The coefficients for both the unverified information and the meet

guidelines variables are statistically significant.  However, the model performs poorly as indicated

by the very low Hosmer-Lemeshow statistic (see Model X).  Modifying the unverified

information variable by replacing it with an interaction term between race and unverified

information significantly improves the model's goodness-of-fit (see Model XI).  More

interestingly, the coefficient on the race variable is no longer significantly different from zero. 

This suggests minority applicants are treated the same as majority applicants, except those with

unverified information.  The difference in the denial rates is explained by the differences in

housing expense ratio, total debt ratio, credit history, loan-to-value ratio, denied PMI, and meets

guidelines.  

The results of Model XI certainly do not prove that discrimination did not exist in the Boston

mortgage market in 1990.  The fact that Model XI is the only specification, out of dozens

attempted, where race is not significant is probably more important than the lack of significance

itself; this is particularly true given the numerous problems, discussed above, with all three of

the variables (unverified information, special program, and meets guidelines) used in this model. 

Given the problems with the variables, and in the context of all the other specifications where

race was so consistently significant and robust, it is probably more accurate to characterize Model

XI as demonstrating that it is always possible, with sufficient effort, to find some formulation that

eliminates the significance of virtually any variable in virtually any model.  Moreover, Model XI

may even suggest an alternative hypothesis that discrimination may still exist, but in a different form.  That is, given that a large percentage of the denied minority applicants had unverified

information in their files, there may be a racial disparity in the "quality of assistance" given to

minority applicants.  Loan officers may spend more time working with white applicants than with

minorities to assure that they submit the documentation necessary to verify all the information

in their files. If that is the case, the lack of verified information may be masking this more subtle

form of discrimination.  In any case, the strongest conclusion that can be drawn from Model XI

is that this is an area that needs to be looked into more carefully in future research. 

VII.	Conclusions

Was the Boston Fed right?  Most of the commentary and controversy over the Boston Fed study

has focussed on the central conclusion.  Was there really significant discrimination against

minorities in the mortgage lending market in Boston in 1990?  Or, do the data and

methodological shortcomings of the study so undermine the validity of the results as to cast doubt

on the existence of discrimination?

The results of our analysis of the Boston Fed's methodology and data permit us to answer the

first question with only a qualified yes.  To the extent that we could correct the most obvious

data problems, explore alternative specifications, and subject the model to additional econometric

tests ─ that is, going as far as was possible using the Boston data ─ the model overall and the

race coefficient in particular were remarkably robust.  Our results could not refute the findings

of the Boston Fed concerning differences in treatment between minorities and whites.  The

coefficient on the race variable remains statistically significant and of approximately the same

magnitude as that found in the original study. 

However, as pointed out above, there were numerous data errors that could not be readily

corrected and alternative specifications that could not be tested with the available data.  Thus, it

is not possible to definitively reaffirm, or to repudiate, the results of the Boston Fed study.  The

only way to do so would be to go back to the original loan files at all 131 participating

institutions to verify the original data, correct data errors, and collect data on additional variables

(or different forms of some variables).  However, given the intense publicity and controversy

generated by the release of the Boston Fed study, as well as the federal and state enforcement

actions that have ensued as a direct consequence of the study, it is virtually certain that such a

follow-up effort will never take place.

Where do we go from here?  While setting the record straight once and for all about the Boston

Fed study would certainly be important for its own sake, the impossibility of doing so does not

necessarily affect the research agenda in this area.  Even if the Boston study were completely

beyond reproach in the unanimous opinion of the research community, it still represents only one

study, in one city, at one point in time.  As such, it calls out for replication in other times and

places.  We should be careful not to draw conclusions about the existence or pervasiveness of

discrimination in mortgage lending until and unless we find consistent and systematic evidence

in repeated studies.

Moreover, in the process of carrying out other studies, researchers can extend and modify the Boston Fed methodology in two important respects.  First, we can learn from their problems and

shortcomings and can make every attempt to avoid the data problems, for example, and to collect

data on additional variables.  Second, we can explore the possibility of adapting the econometric

methodology to requirements of the examination procedures employed by the federal bank

regulators, in order to develop a statistical tool that can assist bank examiners in detecting the

existence of discrimination in any single lending institution. 

These tasks will constitute the principal objectives of the next phase of our research.

	 Appendix 1.  Key characteristics of mortgage applicants, by race and loan disposition

		     Full Boston sample (3,062 observations) and OCC/FDIC sample (1,603 observations)

Variable	White	Black/Hispanic

	Approved	Denied	Approved	Denied

	Boston	OCC/FDIC	Boston	OCC/FDIC	Boston	OCC/FDIC	Boston	OCC/FDIC

Ability to support loan

Housing expense/income (%)a	26.0	26.0	26.6	26.0	26.0	26.0	28.0	29.0

Total debt/income (%)a                	33.0	32.5	37.0	37.0	34.0	34.0	38.0	38.0

Net wealth ($000)a	93	94	75	59	39	37	33	29

Monthly base income

(applicant plus coapplicant) ($)a	4,666	4,691.5	4,471	4,260	3,333	3,412	3,600	3,254

Liquid assets ($000)a	38	40	28	23	19	18.75	15.5	13.85

Risk of default					

Percent with poor credit historyb	14.6	12.7	38.9	41.9	23.4	21.4	51.5	50.4

Probability of unemploymenta	3.2	3.2	3.2	3.6	3.2	3.2	3.2	3.2

Percent self-employed	12.0	12.9	22.4	21.4	7.5	7.6	7.4	6.9

Potential default loss					

Loan-to-value (%)a	77.3	75.1	83.1	83.5	85.0	84.3	90.0	89.7

Rent/value in tract (%)a	4.6	4.6	4.9	5.1	7.3	7.2	8.9	9.1

Percent applied for PMI	21.6	22.2	17.1	23.9	42.2	42.0	26.6	36.5

Percent denied PMIc	0.7	0.8	75.0	82.0	1.3	1.8	82.5	73.8

Loan characteristics					

Percent purchasing 2- to 4-family home	7.7	7.8	18.3	19.6	24.8	24.8	34.4	31.3

Percent fixed-rate loans	68.6	60.7	62.8	56.4	60.6	46.6	69.6	63.5

Percent 30-year fixed-rate loans	85.9	87.5	83.3	82.9	91.1	94.3	91.3	95.6

Percent in special loan programs	12.6	12.8	16.1	18.8	40.6	50.0	40.3	54.8

Personal characteristics					

Agea	34.0	34.0	35.0	35.0	36.0	36.0	36.0	37.0

Percent married	63.0	61.7	53.2	54.7	53.7	57.2	55.0	50.0

Percent with dependents	37.6	35.5	39.9	42.7	52.6	55.0	52.2	46.1

	  a Median value.

	  b Poor credit history is defined as more than two late mortgage payments or delinquent consumer credit histories (more than 60 days past due) or bankruptcies 

    or other public record defaults.

	  c Based on number applying for private mortgage insurance.

Appendix 2.  Variable Definitions

Housing expense ratio 	Equals 1 if proposed monthly housing

payment to income ratio is greater than .30;

otherwise equals 0.  

Excess above 28 percent	Equals proposed monthly housing payment to

income ratio minus .28 if the result is

positive; otherwise equals 0.

Total debt ratio	Equals total monthly debt payment divided

by monthly income.

Excess above 36 percent	Equals total debt ratio minus .36 if the result

is positive; otherwise equals 0.

Excess above 36 percent squared	Equals total debt ratio minus .36 if the result

is positive, squared; otherwise equals 0.

Net wealth	Equals total assets minus total liabilities.

Consumer credit history	Equals 1 if no "slow pay" accounts, 2 if one

or two slow pay accounts, 3 if more than two

slow pay accounts, 4 if insufficient credit

history, 5 if account shows delinquent credit

(60 days past due), and 6 if account shows

seriously deliquent credit (90 days past due).

Mortgage credit history	Equals 1 if no late payments, 2 if no

payment history, 3 if one or two late

payments, and 4 if more than two late

payments.

Public record history	Equals 1 if any public record of credit

history; otherwise equals 0.

Probability of unemployment	Equals the 1989 Massachusetts

unemployment rate for the applicant's

industry.

Self-employed	Equals 1 if the applicant is self-employed;

otherwise equals 0.

Loan-to-value ratio	Equals the loan amount divided by the

appraised value.

Excess above 80 percent	Equals the loan-to-value ratio minus .80 if

the result is positive; otherwise equals 0.

Excess above 80 percent squared	Equals the loan-to-value ratio minus .80 if

the result is positive, squared; otherwise

equals 0.

Excess above 90 percent	Equals 1 if loan-to-value ratio is greater than

.90; otherwise equals 0.

Denied private mortgage insurance	Equals 1 if the applicants applied for and

were denied private mortgage insurance;

otherwise equals 0.

Rent/value in tract	Equals rental income divided by value of

rental housing stock in the Census tract in

which the property is located.

Purchasing 2- to 4-family home	Equals 1 if the applicant is purchasing a two-

to four-family home; otherwise equals 0.

Race	Equals 1 if the applicant is Black or

Hispanic; otherwise equals 0.

Years of education	Equals the number of years of education for

the applicant (if there is a coapplicant, equals

the number of years of education for the

person with the greater base monthly income

from wages. 

Over five years in occupation	Equals 1 if the applicant has been in the

recorded line of work more than five years;

otherwise equals 0.

Percent moved in pre-1985	Equals the number of households in the

Census tract that moved in before 1985

divided by the total number of households in

that tract that  report a date moved in.

Unverified information

	Income

	Employment

	Credit References

	Residence

	Other	Equals 1 if reported information could not be

verified by the underwriter (an aggregate and

individual verificiation series were created for

income, employment, credit, residence, and

other); otherwise equals 0.

Special program	Equals 1 if the applicant applied under a

special loan program; otherwise equals 0. 

Meets guidelines	Equals 1 if the applicants' credit history met

the lender's loan policy guidelines for

approval; otherwise equals 0.

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