LOAN PERFORMANCE AND RACE.

MARTIN, ROBERT E. ; HILL, R. CARTER

R. CARTER HILL [*]

Recent studies find evidence of racial discrimination in mortgage markets. Although these studies explore loan approval rates for whites versus minorities, they do not specifically consider loan performance, either in the form of default rates or loan administration costs. This study considers discrimination in the used car credit market, where the collateral is not subject to location externalities, collateral value and quality do not vary as much as in real estate, and the loan terms are shorter. We find administration costs and default rates are higher for minorities than for whites, controlling for age, income, home ownership, wealth, occupation, loan terms, and geographic location. (JEL K2)

I. INTRODUCTION

Credit discrimination occurs whenever minorities are denied credit on the basis of race or are offered loans at terms different than the terms offered similarly situated whites. [1] Economists identify two types of discrimination: preference (taste)-based discrimination and information (statistical)-based discrimination. [2] The legal definition of discrimination makes no such distinction. In their statistical studies, Munnell, Brown, McEneaney, and Tootell [1996], Carr and Megbolugbe [1994], and Gabriel and Rosenthal [1991] find evidence of discrimination, whereas most economic theorists, such as Becker [1993], and commentators, such as Brimelow [1993] and Brimelow and Spencer [1993], argue competition will greatly reduce, if not eliminate, discrimination.

In Section III, we demonstrate why, under regulation, statistical discrimination may increase with increasing competition. This anomalous result occurs because the legal definition does not distinguish between the two types of discrimination. Some economists implicitly assume credit markets are unregulated when considering the effect of competition on discrimination. Antidiscrimination regulation changes the effect of competition. In unregulated markets, taste-based discrimination is unprofitable and increasing competition will reduce this form of discrimination. If the industry's employees or white borrowers have a taste for discrimination, competition will not necessarily eliminate taste-based discrimination. When regulation is binding and the economic foundation for statistical discrimination exists, discrimination is profitable and increasing competition may increase discrimination. The effect of regulation and competition on discrimination depends critically on the information basis for discrimination (the relationship between loan performance and race). Therefore, the appropriate empirical question is Does a statistical basis for discrimination exist? This question cannot be answered by loan approval studies. Rather, it must be addressed by evaluating how loans perform after they are approved. Further, the appropriate public policy issue is Should society regulate statistical discrimination?

This article is an empirical inquiry into the relationship between race and loan performance. We measure loan performance by estimating the same marginal default rates that lenders use to score credit applications and by the variables that have the most impact on loan administration costs. We find that race matters, regrettably in the fashion suggested by stereotypes. In general, minorities have higher default rates and contribute to higher administration costs. In other words, the foundation for statistical discrimination appears to exist. Section II contains a review of the extant literature. A theoretical model of credit "scoring" with both taste and statistical discrimination is contained in Section III. The data are discussed in Section IV, and the empirical models are presented in Section V.

II. LITERATURE

As in Arrow [1973] and Becker [1957], an individual is said to have a preference, or taste, for discrimination if he is willing to pay a price, or forgo income, in order to practice discrimination. Given a distribution of preferences across individuals, one could rank order the strengths of those preferences by their respective reservation prices. The higher the reservation price, the stronger the preference for discrimination. This form of discrimination has little economic survival value, since some agents will have a zero reservation price for discrimination and others may have a negative reservation price. [3] Competition reduces the market impact of preference-based discrimination, since one lender's greed is sufficient to off-set the bigotry of many other lenders. A measurable credit market impact from preference-based discrimination may arise if (1) all lenders, and potential lenders, have positive reservation prices for discrimination; (2) the industry's employees, and potential employees, have positive reservation prices for discrimination; or (3) white borrowers have a taste for discrimination and are willing to boycott lenders who loan to minorities. If white borrowers do not care or do not know to whom lenders loan, then, free entry, potential lenders with zero reservation prices for discrimination, and potential employees with zero reservation prices for discrimination should eliminate the market effect of preference-based discrimination. Minority default rates and loan administration costs less than white default rates and loan administration costs constitute evidence of preference-based discrimination.

According to Phelps [1972] informational, or statistical, discrimination is based on measurable differences in behavior by group. For example, actuarial studies indicate young men, as a group, have more automobile accidents than do young women of the same age, education, and income. Consequently, insurance companies charge higher insurance premiums for young males than for young females. Since the cost of supplying insurance to young men is higher than it is for young women, this is not price discrimination. If default rates and loan administration costs differ between two groups, lenders have an economic motive for applying different lending criteria to different groups. The theoretical foundations for informational discrimination are contained in Stiglitz and Weiss [1981], Williamson [1987], and Jaffee and Stiglitz [1990].

Munnell et. al.'s [1996] [4] Boston real estate discrimination study refocused interest on this important social issue. Gabriel and Rosenthal [1991, 371] suggest discrimination in lending is serious and may be getting worse. This work prompted a vigorous response from some economists. Most recently, Day and Liebowitz [1998] report serious data irregularities in the Boston real estate study. When they correct the data, the evidence of discrimination disappears. Similarly, Harrison [1998] finds shortcomings in the statistical methods employed in the Boston study. When Harrison used the appropriate statistical methods, he found no evidence of discrimination in the data.

Gary Becker [1993] argues that the Munnell et. al. study is flawed, since it does not control for loan performance. Munnell et. al. counter that very little is known about loan performance and what is known does not suggest that minorities have higher default rates or higher loan administration costs [1996, 27]. They claim "The dearth of any evidence that minorities default more frequently, given their economic fundamentals, makes a conclusion of economically rational discrimination problematic" [1996, 45]. Further, "The hypothesis of statistical discrimination begs several questions,...; if such variables exist, why are the lenders not collecting them? And to use race as a signal, the lenders need evidence that race is correlated with outcomes, holding the rest of their information set constant; the default studies have yet to provide much support for this hypothesis" [1996, 47]. Munnell et. al. seem unaware of the serious legal liability any lender would face if they collect race-or gender-based data. Racial information in their credit-appraisal process would be a "smoking gun," much like a tape recording of senior executives making racial remarks. [5] Consequently, researchers cannot find detailed data sets to estimate loan performance and race, since no rational lender would collect that data. It is very important to note that in the current legal and political environment, lenders are prohibited by law from collecting the very data Munnell et. al. fault them for not offering in their own defense. Therefore, it is not at all surprising that the issue of loan performance and race is still an open question. However, as we see below, the loan performance [6] question goes directly to the heart of the discrimination issue.

Tootell [1993, 45] and Munnell et. al. [1996, 44] claim default rate studies add very little to our understanding of discrimination. They note that discrimination occurs "at the margin," so average default rate studies are not useful. [7] Tootell [1993] and Munnell et. al. [1996] do not consider the default rate analysis lenders use to make the accept/reject decision. They refer to aggregated average default rate studies. For example, one might calculate the average default frequencies within census tracts and then use these averages as independent variables in regressions that control for the racial composition of the census tract, along with other income, wealth, and demographic data. This is not the experience data that firms use to compute hazard rates in lending. The marginal probabilities are estimated from actual lending experience. The marginal default rates provide the foundation for "credit scoring." The default rates and loan administration cost estimates provided in this article are all marginal estimates based on actual loan experience for individual borrowers. [8] It is exactly the information firms use to make decisions at the margin.

III. THEORY

Credit Rationing

Stiglitz and Weiss [1981], Williamson [1987], and Jaffee and Stiglitz [1990] provide theoretical models that suggest equilibrium credit rationing can arise with asymmetric information. Under these conditions, prices may have adverse sorting effects. This is particularly important in credit markets, where rising interest rates may adversely effect the pool of potential borrowers. Prudent borrowers will be deterred by higher interest rates, while imprudent or dishonest borrowers may be undeterred. The adverse sorting causes expected profit per dollar lent to be concave in interest rates. This leads to a "bank-optimal" interest rate, beyond which the supply of credit is negatively sloped and where banks ration credit. Martin and Smyth provide statistical evidence that mortgage supply functions are backward bending in interest rates and that the "bank-optimal" mortgage interest rate is approximately 11% [1991, 1072].

If lenders ration credit exclusively by price, loan approvals could not be a discrimination issue. Therefore, the fact that loan approvals are a discrimination issue (rather than, say, loan terms) is evidence that lenders do use nonprice methods to ration credit. Suppose lenders used "risk-based pricing" for all loans; then, lenders rely exclusively on interest rates to ration credit. [9] No loans would be rejected. Instead, the lender would choose an interest rate for the loan that reflected the loan's risk. Borrowers would then accept or reject the loan offer. There are other reasons, beyond adverse price sorting, that help explain why lenders choose to ration credit via the loan approval process. If lenders used interest rates to ration credit and there were a statistical basis for discrimination, this practice would establish a prima facie statistical case that they were discriminating against minorities. This follows, since the statistical basis for discrimination means that default rates and loan administration costs are positively correlated with race. By using risk-based pricing, lenders would establish a statistical record that they charged higher interest rates to minorities. Again, the legal liabilities would be significant, since information-based discrimination is illegal. This is also the reason why lenders prefer "parsimonious" credit-scoring models. [10]

Evaluating Loans

Given nonprice credit rationing, the lender must have an objective criteria for sorting prospective loans. The technique employed by most lenders is credit scoring. Following Boyes, Hoffman, and Low [1989, 4-5], the marginal loan decision can be modeled as an expected profit calculation, where expected profit is net of the rate of return on government securities and loan administration costs. If [r.sup.o] is the rate of return on government securities, D is the default probability, w is the loss per dollar lent in the event of default, c is the loan administration cost per dollar lent, and r is the rate of return on the loan, then expected profit per dollar lent is

(1) [pi] = (1 - D)(r - [r.sup.o]) - Dw - c.

The lender should accept all loans such that [pi] [greater than] 0 and reject all loans such that [pi] [less than] 0. The threshold default rate is [D.sup.t] and is found where [pi] = 0. Therefore, [pi] [greater than] 0 for all D [less than] [D.sup.t] and [pi] [less than] 0 for all D [greater than] [D.sup.t].

Suppose there are two groups of borrowers, say group a and group b. Let the group a default rate be [D.sup.a] [equivalent to] [D.sup.a](s), where s is the borrower's "credit score," s [equivalent to] s(x), and x is a vector of borrower, loan, and collateral characteristics. Similarly, let [D.sup.b] [equivalent to] [D.sup.b](s) be the group b default rate. Both default rates are assumed to be decreasing in the credit score, s. Note, [D.sup.b] may be greater than, less than or equal to [D.sup.a]. The default rates represent the marginal default rates for members in groups a and b. Given the same age, income, occupation, education, and so forth, and if [D.sup.a] [greater than] [D.sup.b], then individuals in group a have a higher default probability than individuals in group b. Further, the expected profit function in equation (1) assumes the loan administration cost is the same for both groups. If one group misses more payments, writes more bad checks, or requires more extensions than the other, the threshold default rate such that [pi] = 0 will be different for that group. The lender assigns the group with higher administration costs a lower threshold for D and a higher threshold for s.

If [D.sup.b] does not equal [D.sup.a] (as in Figure 1, panel a), then the threshold credit scoring criterion will be different. In an unregulated market, the threshold scores for the two groups would be [s.sup.at] [less than] [s.sup.bt]. While the threshold scores are different, the default rates of the marginal borrowers are the same, [D.sup.t], when loan administration costs are the same. Pure taste discrimination against, say, members of group b occurs when the lender chooses a threshold score for group b that is higher than [s.sup.bt]. For example, a threshold score for group b such as [s.sup.*] in Figure 1 panel a would represent pure taste discrimination. Note, however, that the lender must be willing to forgo making some loans to members of group b where the expected real profit is positive. The expected profit from all loans to members of group b with scores between [s.sup.bt] and [s.sup.*] is positive. How much higher [s.sup.*] is than [s.sup.bt] depends on the lender's reservation price for discrimination. Any other lender with a lower reservation price will lend to all, or some, of the group b members whose scores are in the [s.sup.*]-[s.sup.bt] interval. Therefore, other things equal, pure taste-based discrimination will not persist in an unregulated competitive market. Further, statistical discrimination will persist only if the default rates between the two groups are in fact different.

Applying the legal definition of discrimination to this market yields some surprising results. Under the current interpretation of the law, the lender must treat members of groups a and b the same with respect to access to credit and to credit terms. Further, any lender that collects group-based data is subject to costly litigation. To protect themselves from this litigation, lenders do not collect group-based data. From the lender's regulated perspective, there is only one group whose default rates are an average of the two, such as the dotted line in Figure 1 panel b. Given the same threshold default rate, [D.sup.t], for [pi] = 0, regulation requires a uniform threshold score for both groups, say, [s.sup.t]. If the two groups' default rates are different and the lender does not discriminate, the default rate for the marginal borrower in group b will be higher than the default rate for group a. Further, the expected profit from loans made to group b members in the interval from [s.sup.t] to [s.sup.b] is negative, whereas the expected profit from loans not made to group a members in the interval [s.sup.a] to [s.sup.t] is positive. Most important, the opportunity cost of taste-based discrimination is now negative--it pays to discriminate based on one's preferences. Lenders whose reservation price for discrimination is zero find it profitable to practice discrimination. Lenders who have a positive reservation price for discrimination have a double incentive to discriminate. Their expected profit increases if they discriminate, and discrimination increases utility. Ironically, antidiscrimination regulation in credit markets subsidizes bigots.

The two polar cases under regulation are (1) lenders practice neither statistical nor taste discrimination and (2) lenders practice both statistical and taste discrimination. In case 1, the outcome is [D.sup.a] [less than] [D.sup.b]. The data set obtained from the lender's loan experience will reveal default rates are higher for group b. The outcome is equally unambiguous in the opposite case, where [D.sup.a] [greater than] [D.sup.b]. The data set obtained from the fully discriminating lender's loan experience will reveal default rates are higher for group a.

There are an infinite number of possible outcomes between the two extremes. However, regulation creates a perverse incentive to discriminate. We start with complete compliance with the law, which is case 1. As the lender deviates from strict compliance and raises the threshold score for group b and/or lowers the threshold score for group a, expected profit increases until the threshold for group b rises to [s.sup.bt] and the threshold for group a falls to [s.sup.at]. Any increase beyond [s.sup.bt] or any reduction below [s.sup.at] decreases expected profit. Ironically, the most likely effect of increasing competition under regulation is an increase in discrimination. Deregulation of credit markets in the early 1980s may have contributed to an increase in "redlining." [11]

IV. DATA

Although very important, the real estate market is particularly ill suited for credit market discrimination studies. Real estate is a poor candidate, because of the nature of the collateral and the length of the loans. Real estate asset values are significantly influenced by the positive and negative externalities of the real estates' location. The marginal value of real estate improvements depends critically on these location externalities. Hence, "redlining" can represent either discrimination against an individual borrower or "discrimination" against a particular location. We should not be surprised to find a borrower rejected for a home loan at one location and subsequently approved by the same lender at another location. For example, a white couple wishing to purchase and renovate a home in a low-income minority neighborhood may experience considerable difficulty finding a lender willing to underwrite the project. The lender rejects the location, not the borrower, in this instance.

The used car credit market does not suffer from the inherent collateral problem one observes in real estate discrimination studies. Location externalities have a minimal influence on collateral asset values. [12] The mobility of the collateral suggests values will more closely resemble competitive prices, where the price and quality relationship is more uniform than is the case for real estate. [13] With less variation in asset values, the lender's decision to either accept or reject the loan in the automobile market reflects the borrower risk rather than collateral risk. In contrast to real estate, we would be quite surprised to find a lender who refuses to underwrite a loan on a specific car, regardless of who the borrower might be.

Our data come from a single lender who makes loans in the "C and D" used car market. The loans are, said to be "indirect paper," since the original loan application is generated by the used car dealer. [14] Most of the loans come from independent used car lots and the borrowers are, typically, high risk. Therefore, the loans are "C and D" paper rather than the "A and B" paper generated by franchised new car dealers. The lender data set contains more than 45,000 observations covering four years and nine months. There are nonracial borrower characteristics and multiple indicator variables for default and loan performance in the data. The loan performance variables allow us to study loan administration costs as well as default performance. Some loans may have high administrative costs yet never go into default.

The lender data set consists of borrower characteristics, loan characteristics, collateral characteristics, and the complete payment history of each loan. The original data set contains more than 120,000 loans. It was "aged" to include only loans that have an opportunity to run their complete natural course during the interval from January 1990 to September 1994. In fact, many of the sample loans did not run their entire natural course; they went into default or were prepaid. Prepaid or defaulted loans whose natural termination date occurs on or before September 1994 are included in the data set. If the natural termination date follows September 1994, the prepaid or defaulted loan is assumed to be from a later population of loans. After aging, there are 45,351 usable observations. This sample contains all loans from the interval that went successfully to term, were prepaid, were charged-off, or in which the car was repossessed.

Race

Lenders cannot collect racial variables. Hence, the original data set contains no racial variables. The lender avoids any contamination of the data by racially based variables. This is a serious problem for all loan performance studies and will remain so until lenders are allowed to defend themselves against discrimination charges. As a second-best solution, we merged the original data set with another data set containing racial variables. [15] The merging was accomplished by cross-matching zip codes between the lender data set and the zip code denominated data from the U.S. Bureau of the Census. [16]

Among other variables, the Census Bureau data reports racial variables as the number of white, black, Indian, Asian, and other residents in each zip code. The number of Hispanic residents in each zip code is an ethnic classification. The Hispanic residents are further classified by race, as white Hispanic, black Hispanic, and so forth. We wish to control separately for race and ethnicity. So, the racial variable is min, which is the proportion of the zip code population that is nonwhite. The ethnicity control variable is wh, the proportion of the zip code population that is white Hispanic. For each of the matched loans, the race and ethnic variables represent the probability the borrower is either a racial minority or a Hispanic person of white descent.

Other Borrower Characteristics

The lender data set contains the age of the borrower (bage), the borrower's combined monthly income (bcmi), a zero/one variable for home ownership (home), a zero/one variable for a cosigner (cosign), and a borrower occupation code. The occupation codes are clerical (cler), skilled labor (sl), unskilled labor (ul), and professional (prof). All of these variables come from the lender's data set and represent characteristics of the specific borrower.

The Census Bureau data contain other useful demographic variables. These additional demographic data offers the opportunity to control for unobserved differences in borrower wealth. For example, the 1989 median housing price (medhp) controls for real estate values. Similarly, the 1989 interest, dividend, and rental income per reporting household (idrinch) and the proportion of households reporting interest, dividend, and rental income (idrincp) are proxies for wealth. Finally, median household income (mhi) is included as a control for neighborhood income characteristics.

Collateral Characteristics

The lender's data set contains little direct information about the collateral. [17] There are two variables: the model year and a variable indicating whether the car is new or used. From the model year, we compute the age of the car at the time of loan origination measured in years (cage). We also define a zero/one variable for new cars (new).

Loan Terms

The lender's data set contains a variety of loan terms. The amount borrowed (amt), the interest rate on the loan (apr), the amount of the monthly payment (pay), the length of the loan measured in months (term), and the percent down payment (dp) are the primary loan terms. An estimate of the borrower's commitment to monthly fixed payments (fixpay) is computed from borrower characteristics, Census Data, and loan terms. The variable fixpay is equal to the monthly loan payment (pay) divided by the borrower's combined monthly income (bcmi) plus the median monthly homeowner cost (mmoc) divided by the median household income (mhi), and whether the borrower is a homeowner (home = 1). If the borrower is not a homeowner, the variable fixpay is equal to the monthly loan payment (pay) divided by the borrower's combined monthly income plus the median monthly gross rent (mgr) divided by the median household income. The variables mmoc, mhi, and mgr are data from the zip code data set.

Loan Performance

If the car is repossessed or if the loan is charged off, it is said to be a "bad" loan (bloan). The empirical study of default rates uses bloan as the criterion variable. Loan administration costs vary considerably from one loan to the next. Borrowers who always pay on time are the lowest-cost borrowers. Borrowers who skip payments, make partial payments, or make payments with bad checks increase collections cost. The number of months during the payment history in which no payments were made (nopmt) is one indicator of loan performance. The number of extensions given (numext), the number of partial payments (partpmt), and the number of payment reversals (revers) are other indicators of higher administration cost. Each of the loan administration cost variables (nopmt, numext, partpmt, and revers) are discrete count variables. A complete variable list is contained in the appendix.

V. LOAN ADMINISTRATION COSTS

The maintained hypothesis in this section is that loan administration costs are an increasing function of specific borrower behavior. Consequently, the lender's expected profit from a given loan decreases when the borrower fails to make a monthly payment (nopmt), makes partial payments (partpmt), writes bad checks (revers), or requires an extension of the loan (numext). All of the foregoing activities at least disrupt the timing of the lender's cash flow. The delay in the receipt of loan proceeds imposes an opportunity cost on the lender in the form of earnings foregone from reinvestment. There are direct costs in addition to the opportunity cost. Each borrower action requires a response from the lender. The lender response varies from a telephone call to written notice, collateral repossession, or legal fees.

The empirical question is what role, if any, does race play in missed payments, partial payments, bad checks, and loan extensions. Clearly, we must control for factors other than race that may contribute to this behavior. Nonracial borrower characteristics such as bage, bcmi, home, cosign, and the occupation variables sl, ul, prof, and cler may be important explanatory variables. The collateral characteristics, cage and new, are also included in the estimation. Further, there may be adverse incentive effects created by loan terms. Hence, we include apr, amt, pay, trm, dp, and fixpay as explanatory variables.

Seventy-one percent of the loans are concentrated in three states, and the remaining 29% are distributed over the rest of the continental United States. State laws may create different incentives, and variations in local competitive conditions may affect the quality of the loan portfolio, so we include zero/one dummy variables for the three states (st1, st2 and st3). "Compliance management" is an important part of risk management. State regulations governing rules for loan amortization, late fees, interest rate calculations, and collateral recovery vary by state. [18] Relatively small deviations from state regulations can leave the lender vulnerable to expensive class-action lawsuits. Compliance management consists of testing the computer-based loan calculations to determine whether they are in compliance with the regulations from the state of origin. This is a particularly important function when dealing with loans originated by third parties. In what follows, the omitted state dummy variable is the state that generates the most loans for the lender. To the extent that the lender faces less competition in the states where it does the most business, the state dummy variables will control for these effects.

The foregoing independent variables, along with the minority (min) and ethnic (wh) variables, were used as regressors explaining the four loan administration cost variables. The models are estimated by Poisson regression to account for the fact that the cost variables are "counts." The results are contained in Table I. Additional wealth variables from the Census Bureau's demographic data were included in the estimation. The coefficient estimate for the racial minority proportion is positive and significant at better than the .01 level in each equation. Higher concentrations of minorities are positively related to higher nopmt, partpmt, revers, and numext. The cost of administering loans increases for borrowers from neighborhoods with higher minority concentrations. The results for the white Hispanic variable, wh, are mixed. The coefficient is positive and significant at better than the .01 level for nopmt and partpmt. The coefficient is negative and significant at better than the .01 level for numext. The co efficient is insignificant in the revers equation.

A measure of the potential size of the minority effects can be obtained by sorting the original data set by racial concentrations in neighborhoods, estimating the administrative cost models separately on the two data sets, and comparing the results. The "white" data set consists of all zip codes in which the white proportion is greater than or equal to 98% of the total population. The "minority" data set consists of all observations for which the zip code minority population is greater than or equal to 85% of the total population. [19] Sorting results in 3,142 "white" observations and 957 "minority" observations.

Table II contains the average values for the total data set, the white data set, and the minority data set by loan performance variables and the independent variables. In the white sample, 99.2% of the population is white. In the minority sample, 91.5% of the population is minority. The overall average for the total sample is 29.9% minority. The averages for bloan, nopmt, partpmt, revers, and numext are higher in the minority sample than in the white sample. Further, simple tests for differences in means reveal we reject the null hypothesis that the means are the same in each instance. Additional means tests reveal that minority borrowers receive lower interest rates, borrow larger amounts, have higher monthly automobile payments. They also borrow for longer periods of time, make lower down payments, maintain higher fixed-payments-to-income ratio, have the same combined monthly incomes as whites, are older than white borrowers, have the same homeowner representation as whites, have fewer cosigners, have lower valued homes than white borrowers, receive less income from interest, dividends, and rents, and tend to buy newer cars.

Controlling for the obvious differences in independent variables, a measure of the difference race makes in loan administration cost variables is obtained by estimating the models separately on first the white data set and then the minority data set. The "white" parameters are used in the minority data set and the "minority" parameters are used in the white data set to compute the predicted values for nopmt, partpmt, revers, and numext. The proportional average difference between the actual values and the predicted values is computed. [20] This analysis reveals that, after controlling for other variables, the minority data and minority parameters suggest proportionately higher values for nopmt, partpmt, revers, and numext when joined with the white parameters and white data, respectively. When we apply the "minority" coefficients to the "white" data set, the results reveal the predicted values are higher than the actual values by the following percentages: nopmt, 107.4%; partpmt, 110.0%; revers, 90.0%; and numext 40.0%. The minority coefficients lead to a higher predicted value in each case. In general, the minority coefficients lead to predicted values that are twice as high for the number of months with no payments, the number of partial payments, and the number of payment reversals.

The results when we use the "white" coefficients with the "minority" data are equally revealing. The predicted values are lower than the actual sample values as follows: nopmt, -35.7%; partpmt, -33.3%; revers, -56.0%; and numext, -25.0%. The predicted values are between 25% and 50% lower when we use the white coefficients with the minority data.

VI. DEFAULT RATES

Lender discrimination requires rejection of loans to qualified minorities. Hence, direct evidence of discrimination comes from the lender's loan portfolio as minority default rates that are lower than white default rates. Statistical discrimination with no taste discrimination suggests that default rates would be the same for whites and minorities. Higher minority default rates are consistent with a lender who has neither a taste for discrimination nor is statistically discriminating. Higher minority default rates are inconsistent with a lender who practices both taste and statistical discrimination.

The lender's risk of losing all or part of the loan principle is high in the "C and D" used car credit market. The cars are older and the borrowers have lower incomes than in the "A and B" used car credit market. In addition, almost all of the borrowers have troubled credit histories. Lenders use statistical "credit scoring" techniques to evaluate the default risk, an example of which can be found in Campbell and Dietrich [1983]. Boyes, Hoffman and Low [1989] demonstrated that probit analysis is a more efficient estimator of default hazard rates than other techniques, such as expert systems [21] and discriminant analysis.

The probit model is estimated using traditional credit scoring variables and the same racial variables used in the loan administration cost model. The traditional credit scoring variables are apr, amt, pay, term, dp, fixpay, deal, bage, bcmi, home, cosign, ul, sl, prof, cage, new, st1, st2, and st3. The results are contained in Table III. As expected, the default probability decreases with the borrower's age, the borrower's income, if the borrower is a homeowner, if there is a cosigner on the note, and with a higher down payment. The default probability increases as the interest rate increases, the size of the monthly payment increases, the length of the loan increases, and the fixed payment proportion of the borrower's income increases.

The effect of the minority proportion (min) on the default probability is positive and significant at better than the .01 level, as in the administration cost models. The co-efficient for white Hispanics (wh) is not significant. Holding age, income, home ownership, and occupation constant, minorities appear to have higher default rates than whites. The lender's data set suggests she is not discriminating against minorities. Discrimination would be evidenced by lower default rates for minorities than for whites.

Direct measures of borrower wealth are not reported, except for the borrower's combined monthly income (bcmi). However, it is possible to construct proxies for borrower wealth from the Census data set. One potential measure of wealth is the 1989 median housing price (medhp) in the zip code. Other measures are the amount, per reporting household, of other 1989 income from interest, dividends, and rentals (idrinch), the proportion of households reporting such income (idrincp), and median household income (mhi). The results for the probit default rate model with the wealth proxy variables are contained in Table IV. The signs and significance levels for min an wh are qualitatively the same as they were in Table III.

A measure of the size of the impact on default rates that differences in race may make can be obtained by an analysis similar to the impact analysis used on the measures of loan administration cost: the probit model is estimated separately on the white and minority data sets, and then the estimated coefficients are used to obtain the predicted default rate using the opposite sample. When the "minority" coefficients are used with the "white" data set, the predicted default rate is 10.1% higher than the actual default rate for the white sample. When the "white" coefficients are used with the "minority" data set, the predicted default rate is 11.1% lower than the actual default rate for the minority sample.

VII. CONCLUSIONS

The legal definition of discrimination does not distinguish between preference-based discrimination and statistical discrimination. Although the motives are different in these two types of discrimination, they are treated equally under the law. Without discrimination regulation, there are disincentives associated with preference-based discrimination and there are economic incentives associated with statistical discrimination. Discrimination regulation is binding in competitive markets only if the information foundation for statistical discrimination exists. The impact of competition is different in unregulated markets and in regulated markets. Competition reduces preference-based discrimination in unregulated markets, whereas competition may increase statistical discrimination in regulated markets.

Recent empirical studies suggest redlining in mortgage markets is increasing. This may be the natural consequence of the financial deregulation of lending institutions that began in the late 1970s. If redlining increases as competition increases, it is indirect confirmation of our results. An information basis for statistical discrimination must exist if competition increases redlining; otherwise, the entry of new lenders in the 1980s and early 1990s would have reduced preference-based discrimination.

We consider default rates and loan administration costs in our empirical models. Our results suggest minority loan default rates are higher than comparable white default rates and that minority loan administration costs are higher than comparable white administration costs. The measured differences are substantial. Regulation of statistical discrimination creates serious adverse incentive effects. It adversely selects for borrower behavior that increases default rates and raises loan administration costs. This adverse selection can result in "lemon effects" in credit markets and may result in a general deterioration in credit quality in the long run. Worst of all, regulation of statistical discrimination directly subsidizes bigoted lenders. These lenders can raise their profits by discriminating, in addition to realizing a utility gain from discrimination.

The empirical researchers who find evidence of discrimination claim there is little evidence that loan performance is different across racial groups. They are also puzzled by why lenders do not provide evidence of differences in group behavior. We note the rational lender will not collect racial data, since the legal liability would be substantial. Hence, data sets that contain both loan performance characteristics and race variables do no exist. Our results need to be confirmed or refuted in other data sets. This will require access by qualified researchers to other lender's loan data sets. Lender's will be reluctant to make this data available for study, since the simple pursuit of profit can establish a statistical record that suggests they are guilty of discrimination. If the information basis for discrimination exists, profits rise as the lender pursues statistical discrimination. Some "hold-harmless" agreement must be reached between lenders and regulators that allows the data to be studied.

Martin: Professor, Department of Economics, Centre College, Danville, Kentucky 40422, Phone 606-238-5260, Fax 606-236-7925, E-mail bmart@centre.edu

Hill: Department of Economics, Louisiana State University, Baton Rouge, Louisiana 70803, Phone 225-388-1490, Fax 225-388-3807, E-mail eohill@lsu.edu

(*.) This study is not part of any existing or pending litigation, and we received no compensation of any sort from the lender who provided the data. We are indebted to an anonymous referee, the members of the University of Kentucky's microeconomics workshop, and David Baumer for their comments and suggestions. A special debt is owed the referee for several important contributions. Any remaining errors are our own.

(1.) Tootell [1993, 46] contains a discussion of the legal definition of discrimination.

(2.) Arrow [1973] and Becker [1957] consider preference- or taste-based discrimination, whereas Jaffee and Stiglitz [1990], Phelps [1972], Stiglitz and Weiss [1981], and Williamson [1987] explore information- or statistics-based discrimination.

(3.) A negative reservation price suggests the lender would be willing to subsidize minority borrowers.

(4.) The study was originally released in 1992 by the Boston Federal Reserve Bank.

(5.) "Redlining" is the least detectable solution to the problem of economically motivated statistical discrimination under regulation. The lender need not contaminate her records with racial data. She can cease lending in minority neighborhoods and observe the impact on portfolio profitability. If minorities default more frequently and cause higher administrative costs, profitability will rise. If the hypothesis is incorrect, profits will fall. In any event, the lender does not need to collect racial data and discrimination is harder to prove.

(6.) Despite Munnell et. al.'s arguments to the contrary [1996, 44-45], loan performance is the central issue.

(7.) These authors also claim default rate studies suffer from omitted variable problems that prevent them from being useful. Omitted variable problems exist in every empirical economic problem, including "redlining" studies. Perfect variables and perfectly specified models do not exist. The degree to which omitted variables become a problem is always a judgment issue.

(8.) Each observation represents an individual loan, not a Census-tract average.

(9.) The Federal Reserve System recently encouraged lenders to use more "risk-based pricing," rather than rejecting loans.

(10.) A "parsimonious" credit-scoring model is one with a limited number of explanatory variables. As the number of explanatory variables increases, the lender runs the risk of unintentionally establishing a record of statistical discrimination, if the added variables are correlated with race. More variables add explanatory power to the model, and the cost of estimation and data storage are trivial compared with the benefits of lowering default rates. Again, this is a regulation effect.

(11.) Jayaratne and Strahan [1997] find that deregulation of banking in the 1970s and 1980s led to significant improvements in efficiency and that most of the cost reductions were passed on to consumers in the form of lower interest rates. Costs fell, and "nonperforming loans" declined significantly. Easier entry caused increased competition, leading to lower interest rates. The pressure on banks' margins cause them to reduce costs and improve loan portfolio performance. Under pressure from increased competition, banks would review those parts of the business that generate unprofitable loans. If there is a statistical basis for discrimination, groups of unprofitable loans would appear as geographic clusters based on minority concentrations. Therefore, more "redlining" would be a natural consequence of the increase in competition.

(12.) One exception may be the effect of salt corrosion in northern climates. Automobiles located in cold climates, or close to the coast, may suffer negative location extenalities from salt corrosion.

(13.) We are indebted to an anonymous referee for raising this point.

(14.) This practice varies little from national real estate lenders, who make home loans without ever meeting the borrower or who purchase mortgages originated by others. In both cases, the lender could use secondary data sources to infer the race of the borrower, if the lender was so motivated. Hence, we cannot rule discrimination out a priori.

(15.) Clearly, we would prefer to have the racial identity of each of the 40,000 plus individual borrowers. Since that does not exist in this data set or any other data set suitable for a loan performance study, we must use the Census data to augment our study. We take additional steps in the analysis to overcome this inherent problem by sorting the data set for those zip codes where it is almost certain the residents are white or almost certain the residents are minorities. This practice results in models with significant degrees of freedom, despite the sorting.

(16.) Obviously, the lender must have the borrower's zip code in order to administer the loan.

(17.) The absence of collateral data in the lender's information set reflects the fact that collateral risk is not the principle issue in the used car credit market.

(18.) Up-to-date details as to how state regulations vary are available from the Commerce Clearing House publications.

(19.) A lower criterion for the minority proportion was chosen in order to have sufficient degrees of freedom. Note, the 85% threshold for minorities results in an average proportion for the minority sample of over 90%.

(20.) For each observation, the predicted value is computed as described in the text. The actual value is subtracted from the predicted value, and the differences are summed and divided by the number of observations. The resulting average difference is then divided by the average actual value for the sample.

(21.) An expert system is one where each credit application is evaluated by an "expert" credit analyst, who renders an accept or reject decision. It represents a precomputing technology.

REFERENCES

Arrow, Kenneth J. "The Theory of Discrimination." in Discrimination in Labor Markets, edited by Orley Ashenfelter and Albert Rees. Princeton, N.J.: Princeton University Press, 1973.

Becker, Gary S. The Economics of Discrimination. Chicago.: University of Chicago Press, 1957.

-----. "The Evidence Against Banks Doesn't Prove Bias." Business Week, April 19, 1993, 18.

Boyes, William J., Dennis L. Hoffman, and Stuart A. Low. "An Econometric Analysis of the Bank Credit Scoring Problem." Journal of Econometrics, 40, 1989, 3-14.

Brimelow, Peter. "Racism at Work?" National Review, April 12, 1993, 42.

Brimelow, Peter, and Leslie Spencer. "The Hidden Clue," Forbes, January 4, 1993, 48.

Carr, James, and Isaac F. Megbolugbe. "The Federal Reserve Bank of Boston Study on Mortgage Redlining Revisited." Journal of Housing Research, 4, 1994, 277-314.

Day, Theodore E., and Liebowitz, S. J. "Mortgage Lending to Minorities: Where's the Bias?" Economic Inquiry, January 1998, 3-28.

Gabriel, Stuart A., and Stuart S. Rosenthal. "Credit Rationing, Race, and the Mortgage Market." Journal of Urban Economics, 29, 1991, 371-79.

Harrison, Glenn W. "Mortgage Lending in Boston: A Reconsideration of the Evidence." Economic Inquiry, January 1998, 29-38.

Jaffee, Dwight, and Joseph Stiglitz. "Credit Rationing." In Handbook of Monetary Economics, vol. 2., edited by B. M. Friedman and F. H. Hahn. New York: Elsevier Science, 1990, 837-88.

Jayaratne, Jith, and Strahan, Philip. "Entry Restrictions, Industry Evolution, and Dynamic Efficiency: Evidence from Commercial Banking." Journal of Law and Economics, April 1998, 239-73.

Martin, Robert E., and Smyth, David J. "Adverse Selection and Moral Hazard Effects in the Mortgage Market: An Empirical Analysis." Southern Economic Journal, April 1991, 1071-84.

Munnell, Alicia, Lynn E. Browne, James McEneaney, and Geoffrey M. B. Tootell. "Mortgage Lending in Boston: Interpreting HMDA Data." American Economic Review, March 1996, 25-53.

Phelps, Edmund S. "The Statistical Theory of Racism and Sexism." American Economic Review, September 1972, 659-61.

Stiglitz, Joseph, and Andrew Weiss. "Credit Rationing in Markets with Imperfect Information," American Economic Review, June 1981, 393-410.

Tootell, Geoffrey M. B. "Defaults, Denials, and Discrimination in Mortgage Lending." New England Economic Review, September/October 1993, 45-51.

Williamson, S. "Costly Monitoring, Loan Contracts, and Equilibrium Credit Rationing." Quarterly Journal of Economics, February 1987, 135-45.

 Poisson Models: Administrative Cost Variables [a]
 Number of Number of
 No-Pay Partial-Pay Number of
 Months Months Pay Reversals
Independent Variable (nopmt) (partpmt) (revers)
Intercept 0.09 -2.06 -7.05
 (2.86) (23.61) (20.24)
Interest rate 0.001 -0.004 0.01
 (1.95) (2.33) (1.92)
Loan amount -0.00006 0.00001 -0.00003
 (11.05) (1.62) (0.61)
Payment 0.001 0.003 0.004
 (13.24) (15.21) (3.94)
Term 0.03 0.02 0.04
 (38.55) (13.63) (5.95)
Down payment -0.002 -0.008 -0.0002
 (11.30) (11.65) (0.09)
Fixed payment ratio 0.002 -0.0001 0.001
 (18.19) (0.33) (1.50)
Buyer's age -0.05 -0.005 -0.003
 (24.05) (8.26) (1.42)
Buyer's income -0.00002 -0.00006 0.00004
 (8.18) (9.22) (1.86)
Homeowner -0.15 -0.21 -0.23
 (23.00) (11.45) (3.25)
Cosigner 0.005 0.03 -0.28
 (0.60) (1.14) (2.57)
Unskilled labor 0.14 0.30 0.17
 (14.43) (11.05) (1.68)
Skilled labor 0.13 0.13 0.02
 (13.42) (4.62) (0.15)
Professional 0.15 0.03 0.12
 (11.44) (0.69) (0.90)
Car age -0.01 -0.01 -0.02
 (10.54) (2.62) (1.06)
New car -0.05 -1.03 -3.44
 (0.20) (6.35) (2.27)
State 1 0.17 -0.03 0.17
 (23.27) (1.65) (1.94)
State 2 0.10 -0.05 0.44
 (10.12) (1.97) (4.44)
State 3 0.16 0.19 0.47
 (22.60) (9.77) (5.85)
Minority 0.36 0.42 1.07
 (23.88) (10.08) (6.67)
White Hispanic 0.39 0.51 0.32
 (9.93) (4.70) (0.79)
Median house price 0.0000005 -0.0000002 0.000003
 (2.57) (0.39) (1.73)
Interest, dividend, 0.000001 -0.000003 0.00001
 rent per house (1.08) (1.12) (1.16)
Interest, dividend, -0.02 -0.07 0.26
 rent proportion (0.78) (0.98) (1.03)
Median household 0.000007 0.000008 0.00002
 income (10.34) (4.37) (2.74)
Log-likelihood -142,621 -44,908 -5,759
 observations 45,361 45,361 45,361
 Number of
 Extensions
Independent Variable (numext)
Intercept -3.80
 (28.41)
Interest rate 0.006
 (2.38)
Loan amount -0.00004
 (2.50)
Payment 0.003
 (10.94)
Term 0.04
 (16.29)
Down payment -0.007
 (6.39)
Fixed payment ratio 0.002
 (4.46)
Buyer's age -0.001
 (1.23)
Buyer's income -0.00002
 (2.77)
Homeowner -0.02
 (0.61)
Cosigner 0.05
 (1.06)
Unskilled labor 0.24
 (5.76)
Skilled labor 0.18
 (4.24)
Professional -0.17
 (2.84)
Car age -0.06
 (9.90)
New car -1.19
 (4.23)
State 1 0.15
 (4.73)
State 2 -0.05
 (1.22)
State 3 0.29
 (9.59)
Minority 0.38
 (6.01)
White Hispanic -0.67
 (2.81)
Median house price 0.0000002
 (0.24)
Interest, dividend, -0.00001
 rent per house (1.78)
Interest, dividend, -0.26
 rent proportion (2.43)
Median household 0.00001
 income (5.16)
Log-likelihood -21,893
 observations 45,361
(a.)t-values in parentheses.
 Means: Total Sample, White Sample
 and Minority Sample
 Total White Minority
Variable (n = 45,361) (n = 3,142) (n = 957)
Performance variable:
 Bad loan (%) 14.7 13.9 20.8
 No payment 3.2 2.7 4.2
 Partial pay 0.4 0.3 0.6
 Reversal 0.029 0.02 0.05
 Extensions 0.2 0.1 0.2
Independent variable:
 Interest rate (%) 27.9 28.8 26.9
 Amount ($) 3,949 3,410 4,456
 Payment ($) 200 180 215
 Term (mo) 25.9 24.5 27.4
 Down payment (%) 15.5 17.9 11.9
 Fix payment ratio 2.1 1.5 3.2
 Buyer's age (yrs) 36.6 36.0 38.0
 Income ($) 1,719 1,716 1,699
 Homeowner (%) 27.0 26.6 28.3
 Cosigner (%) 10.8 16.2 10.1
 Unskilled (%) 50.9 58.0 50.1
 Skilled (%) 32.3 25.0 33.1
 Professional (%) 6.6 8.0 3.4
 Car age (yrs) 3.3 4.3 2.6
 New car (%) 0.6 0.5 0.4
 State 1 (%) 26.9 2.6 11.9
 State 2 (%) 15.8 14.2 13.4
 State 3 (%) 28.5 47.2 47.8
 Minority (%) 29.9 0.8 91.5
 White Hispanic (%) 1.6 0.6 0.1
 Median house price ($) 60,337 57,848 42,309
 Interest, dividend, rent per house ($) 5,735 5,533 3,474
 Interest, dividend, rent proportion (%) 41.0 46.7 15.9
 Median household income ($) 24,823 23,917 15,600
 Probit Default Rate Model: bloan
 Default Probability
Independent variable Coefficient p-Value
Intercept -1.44 0.0001
Interest rate 0.005 0.0020
Loan amount -0.00005 0.0051
Payment 0.17 0.0001
Term 0.01 0.0001
Down payment -0.006 0.0001
Fix payment ratio 0.003 0.0001
Buyer's age -0.008 0.0001
Buyer's income -0.00004 0.0001
Homeowner -0.20 0.0001
Cosigner -0.11 0.0001
Unskilled -0.004 0.8797
Skilled 0.03 0.2200
Professional -0.02 0.6075
Car age -0.001 0.6805
New car -0.16 0.1387
State 1 0.13 0.0001
State 2 0.16 0.0001
State 3 0.22 0.0001
Minority 0.13 0.0002
White Hispanic -0.14 0.2380
Log-likelihood observations -18,261.76
 45,361
 Probit Default Rate Model with Wealth
 Variables: bloan
 Default Probability
Independent variable Coefficient p-Value
Intercept -1.44 0.0001
Interest rate 0.005 0.0017
Loan amount -0.00004 0.0055
Payment 0.17 0.0001
Term 0.01 0.0001
Down payment -0.006 0.0001
Fix payment ratio 0.0003 0.0001
Buyer's age -0.008 0.0001
Buyer's income -0.00004 0.0001
Home owner -0.19 0.0001
Cosigner -0.11 0.0001
Unskilled -0.0009 0.9729
Skilled 0.04 0.1971
Professional -0.02 0.6333
Car age -0.001 0.6872
New car -0.15 0.1472
State 1 0.12 0.0001
State 2 0.17 0.0001
State 3 0.21 0.0001
Minority 0.09 0.0284
White Hispanic -0.27 0.0293
Median housing price 0.02 0.0004
Interest, dividends, rent, per house 0.0002 0.5505
Interest, dividends, rent, proportion -0.15 0.0277
Median household income -0.000003 0.1577
Log-likelihood observations -18,253.52
 45,361

List of Variables

Performance Variables:

bloan - "bad" loan, a loan that has been written off and/or the car has been repossessed, (1,0).

nopmt - number of months during payment history when no payment was received.

partpmt - number of months during payment history when a partial payment was received.

revers - number of months during payment history when payments were reversed.

numext - number of extensions given.

Independent Variables:

apr - annual percentage interest rate on loan.

amt - amount borrowed.

pay - monthly payment.

term - length of loan measured in months.

dp - percent down payment.

fixpay - ratio of monthly fixed payments divided by monthly income.

bage - borrower's age.

bcmi - borrower's combined monthly income.

home - home ownership, (1,0).

cosign - cosigner on loan, (1,0).

ul - unskilled laborer.

sl - skilled laborer.

prof - professional worker.

cage - car age, measured in years.

new - new car, (1,0).

st1, st2, and st3 - state of residence control variables, (1,0).

min - minority population as percent of zip code.

wh - white Hispanic population as percent of zip code.

medhp - median housing price in zip code.

idrinch - average interest, dividend, and rental income reported per household in zip code.

idrincp - proportion of households in zip code reporting interest, dividend, and rental income.

mhi - median household income for zip code.