Risk-based Pricing of Interest Rates

Journal of Monetary Economics 53 (2006) 22832298

Risk-based pricing of interest ratesfor consumer loans$

borrowing as a whole either rose less or, sometimes, fell.

r 2006 Elsevier B.V. All rights reserved.

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www.elsevier.com/locate/jme

author and do not necessarily represent those of the Federal Reserve Board or its staff. I would like to thank

Pierre-Andre Chiappori, Lars Hansen, Erik Hurst and Annette Vissing-Jorgensen, for their direction and advice. I

also would like to thank the University of Chicago, the National Science Foundation and the Social Science0304-3932/$ - see front matter r 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.jmoneco.2005.09.001

Research Council for their nancial support. Of course, all errors are my own.

E-mail address: [email protected] classification: D12; E21; E51; G21

Keywords: Consumption; Borrowing; Debt; Consumer credit; Interest rates; Banking

$Federal Reserve Board, e-mail: [email protected]. The views presented are solely those of theWendy Edelberg

Received 17 June 2005; received in revised form 15 August 2005; accepted 12 September 2005

Abstract

By focusing on observable default risks role in loan terms and the subsequent consequences for

household behavior, this paper shows that lenders increasingly used risk-based pricing of interest

rates in consumer loan markets during the mid-1990s. It tests three resulting predictions: First, the

premium paid per unit of risk should have increased over this period. Second, debt levels should have

reacted accordingly. Third, fewer high-risk households should have been denied credit, further

contributing to the interest rate spread between the highest- and lowest-risk borrowers.

For people obtaining loans, the premium paid per unit of risk did indeed become signicantly

larger after the mid-1990s. For example, for a 0.01 increase in the probability of bankruptcy, the

corresponding interest-rate increase tripled for rst mortgages, doubled for automobile loans and

rose nearly six-fold for second mortgages. Additionally, changes in borrowing levels and debt access

reected these new pricing practices, particularly for secured debt. Borrowing increased most for the

low-risk households who saw their relative borrowing costs fall. Furthermore, while very high-risk

households gained expanded access to credit, the increases in their risk premiums implied that their

1. Introduction

ARTICLE IN PRESSW. Edelberg / Journal of Monetary Economics 53 (2006) 228322982284Credit industry literature suggests that by the early 1980s conventional lenders wereusing credit scores and the like to automate underwriting standards, but as late as the early1990s they still simply posted one house rate for each loan type and continued to rejectmost high-risk borrowers (Johnson, 1992). As data storage costs subsequently fell andunderwriting technology improved, however, lenders began to use estimates of default riskto price individual loans. This paper examines both the extent and consequences of thisincreased use of risk-based pricing of interest rates in consumer loan markets during themid-1990s.On the whole, the ndings are in keeping with the predictions that ow naturally from

these changes. First, for those obtaining loans, the premium paid per unit of risk becamesignicantly larger over this time period, with the difference between high- and low-riskborrowers interest rates nearly doubling for secured loans and increasing for mostunsecured loans as well. Second, changes in borrowing levels and access to debt reectedthese new pricing practices, particularly for secured debt. While lower interest ratesgenerally boosted borrowing in the late 1990s, the demand for credit increased most forlow-risk households who saw lower relative borrowing costs. Third, these changes inpricing practices led to increased credit access for very high-risk households (again,particularly for secured debt), but the increase in the very high-risk premium also causedtheir average borrowing levels to either rise less or, for some loan types, to fall. Finally,changes in risk-based pricing may account for one- to three-quarters of the increase in debtlevels for some secured loan types and may more than account for the increase in debt useby the highest-risk groups for secured debt.There has not been much scrutiny of the potential for credit terms to vary by borrower

risk, let alone empirical examinations of such variance in terms. On the theoretical side,Geanakoplos has written and co-written several papers showing the effect of default riskon loan terms in general equilibrium (some examples are Geanakoplos (2002) and Dubeyet al. (2003)). Riley (1987) argues StiglitzWeiss style rationing will not be empiricallyrelevant, as he postulates that lenders should vary interest rates by risk. However, using1983 mortgage rate data, Duca and Rosenthal (1993) nd no evidence of such interest ratevariation. My ndings are consistent with Ducas and Rosenthals, suggesting that risk-based pricing did not become a signicant factor in credit markets until more than adecade after 1983.Only in the 1990s did improvements in underwriting models and reductions in data

storage costs became sizeable enough to decrease the costs of risk-based pricing (Bostic,2002).1 Certain changes in consumer credit industry practices also spurred investment indeveloping new underwriting models. Canner and Passmore (1997) explain that in 1995bank regulators began putting greater emphasis on lending in lower-income neighbor-hoods and to lower-income borrowers in measuring compliance with the CommunityReinvestment Act. This increased the protability of developing a technology to lend tohigher-risk households. Furthermore, Fannie Mae, which previously bought only low-riskloans and essentially did not vary nancial terms with loan risk, introduced an improved,

1In addition, Peter McCorkell suggests insufcient data on defaults made risk-based pricing difcult prior to

1995. He also argues that until the late 1980s, mortgage lenders simply relied on their constantly appreciatingcollateral to moderate the costs of default (McCorkell, 2002).

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Table 1

Interest rate data

Standard deviation by origination year Observations

1989 1995 1998 All years

W. Edelberg / Journal of Monetary Economics 53 (2006) 22832298 2285automated underwriting system in 1995 and began to accept higher-risk loans subject tosome price discrimination. In 1996, Fannie Mae and Freddie Mac indicated that loanpackages must include a credit bureau score (McCorkell, 2002).In the mid-1990s, lenders could, and did, vary interest rates and issue higher-risk

mortgages (Freeman and Hamilton, 2002). As a result even credit unions began using risk-based pricing at this time as low-risk members complained that they were able to get lowerrates at conventional banks.2 The technology of risk-based pricing made its way frommortgage loans into other loan types, such as second mortgages, automobile loans andcredit card loans. For example, Black and Morgan (1999) nd demographic evidence thatmore high-risk households gained access to the credit card market in 1995 relative to 1989.(Indeed, this increased access appears to have been widespread: average household incomewent up about 20% more than the average income of those with any debt, pre-1995 versuspost-1995. Similarly, average education rose about 40% more overall than for those withdebt.) My results show that loans easily securitized, such as those mentioned above, havebeen affected the most these pricing changes, suggesting that secondary loan markets haveplayed a role in promoting risk-based pricing.

First mortgage ratea 1.16 1.26 1.49b 8,143

Second mortgage 2.21 2.82b 2.63 805

Auto loan 3.58 4.05b 4.53b 5,209

Credit cardc 4.18 4.43b 5.01b 4,007

Other consumer loan 4.47 6.07b 6.69 2,744

Education loan 3.37 4.05b 1.96 997

aOnly 30-year xed rate mortgages are considered.bDifference between current and preceding year is signicant with p-valueo0.1.c1983 is used in place of 1989.2. Data

This analysis uses the Surveys of Consumer Finances (SCFs) from 1983 to 1998. Firstand second mortgages, automobile loans, general consumer loans, credit card loans andeducation loans are considered. Loans in a category are summed and the highest interestrate is used.3 Table 1 shows the standard deviations for three loan originations years: 1989,1995 and 1998 (except for credit card loans, which substitutes 1983 for 1989 due to datarestrictions).4 Consistent with the increased use of risk-based pricing, interest rate variationgenerally increased over time, and often signicantly. Note that standard deviations of

2This point was made in conversations with the University of Wisconsin Center for Credit Union Research.3Credit card balances are considered loans when interest is paid on the balance. Note that Gross and Souleles

(2001) points out an underreporting of credit card debt in the SCF, which is problematic only if this

underreporting is signicantly correlated with risk, and this correlation changes over time.4Sampling weights are used for rst and second moments. Following Deaton (1997), the data are not weighted

in the empirical models as coefcients are assumed not to vary across the population.

monthly prime interest rates were similar in 1989 and 1995 and actually decreased between1995 and 1998. In addition, the table shows the total observations across the 5 years ofdata for the various loan categories, anticipating some of the differences in the resultsrobustness. For its more extensive data on bankruptcy, the Panel Study of IncomeDynamics (PSID) is also used for the wealth supplement years of 1984, 1989 and 1994.Total bankruptcies across all years prior to 1996 is 502, reecting a slightly lowerbankruptcy rate than in the population, a point made by Fay et al. (2002).

3. Empirical analysis

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5Maturity does not generally vary meaningfully within a loan type and was often found to have no real

W. Edelberg / Journal of Monetary Economics 53 (2006) 228322982286signicant effect on interest rates. For example, over one-half of mortgages have 30-year maturities, and nearly

60% of automobile loans have maturities between 4 and 5 years.6Note that this model essentially does not allow for a rejection by the lender. However, we can consider a loan

rejected any time RiIip0. For example, if a lender at least knows the upper bound for a households reservationinterest rate, it may choose to simply reject a loan rather than offer an interest rate above this upper bound.

7Dollar values are deated using the CPI. For general consumer loans, current loan balances are better

predictors than original loan amounts. This may be due to the more informal nature of these loans. For example,

these loans may be renegotiated more easily so that current balance is also highly relevant for the terms.8The possible complication that l may be in part a function of dfor example, ex ante high-risk people inThe primary goal of this empirical analysis is to estimate the role default risk plays ininterest rate determination and also to see if that role has changed over time. Assume thata household has a reservation interest rate Ri(A,l,Pi), which is a function of a certain loanamount, A, with collateral to ensure a recovery rate, l, of the loan balance, and householdcharacteristics, P. Ii(A,l,di,o,f), the interest rate offered by the lender, is a function of A, l,default risk, d, the lenders discount rate, o, and xed costs, f.5 Because the SCF onlyreports interest rate data for households who successfully secure loans, selection bias isaccounted for. We can infer that R is greater than or equal to I for those consumers whohave positive loan balances. To formalize:

RiA; l;Pi I iA; l; di; o; f Hib ui,ProbRi I i40 FHib.

Hi is a vector of characteristics that helps predict whether the loan is observed forhousehold i. Ii and Ri, are subscripted i to allow for an idiosyncratic individual specicshock, eI:

I iA; l; di; o; f Xig i observed when Ri I i40.Note that the linearity in the equation above assumes lenders are risk neutral or are

diversied enough to appear risk neutral. Xi is a vector of characteristics that help predictI.6 X includes direct measures or proxies, where necessary, for the ve variables, A, l, d, oand f. First, A is included directly.7 Second, l should be roughly constant for each type ofnon-collateralized loan and hence captured by a varying constant term. For collateralizedloans, l should rise with collateral, and hence the equity in the collateral is included.8 Third,measures of d are described in detail below. Fourth, o is assumed constant over a year anddefault may be more difcult to collect from than low-risk people in defaultis not considered here.

is captured by year dummies.9 Finally, inasmuch as xed costs, f, are recovered throughthe interest rate, their effect should be captured by including A.H includes both supply and demand variables that inuence whether a household holds

a loan. On the supply side, H includes variables that help predict denial such as second-order polynomials of default risk. To account for demand, other nancial anddemographic characteristics, Pi, are included: an age polynomial, marriage status, thenumber of children, whether the family has a checking account, education, log of income,net worth, level of assets, race and variables that reect borrowing attitudes.10 Theattitudinal variables show whether households consider borrowing to be good, bad, or

zero), unemployment indicator, race, single parent indicator, and education. For the

ARTICLE IN PRESSW. Edelberg / Journal of Monetary Economics 53 (2006) 22832298 2287unconditional estimation, asset levels are used in place of debt and home ownershipstatus.13 Signicant time variation in coefcients is also included. Overall, the coefcientsare consistent with the bankruptcy literature. A detailed discussion of these results can befound in Edelberg (2003).

9This should in part reect the required rate of return to those supplying loanable funds. Ausubel (1991) nds

that credit card issuers earned possibly ve times the ordinary banking rate of return from 1983 to 1988. Here, no

specic rate of return is imposed, but it is assumed that markets are competitive.10Racial status may reect preferences for borrowing and potential lender bias (see Edelberg, 2002).11Numerous variables are included in H but not in X, such that the demands on the attitudinal variables as

appropriate instruments are less than they might be. However, robustness checks were still done. All the

signicant attitudinal variables from the probits were included in their respective regressions: For example, if an

attitudinal variable signicantly predicted mortgage use, it was included in the mortgage interest rate equation. In

all cases, most or nearly all of these coefcients in the interest rate regressions were insignicant.12The imputation of bankruptcy risk is based on a similar methodology in Jappelli et al. (1998).13Research used to identify explanatory variables includes Sullivan et al. (1989), Johnson (1992), Domowitz andokay and whether they believe borrowing is acceptable in certain circumstancessuch asfor a loss in income or to buy a house or jewelry. These variables ensure identication, asthey are excluded from X. Correlation estimates conrm that these responses are notsimple functions of borrowers debt portfolios.11

3.1. Default risk

Default risk is comprised of the risks of bankruptcy and delinquency. The SCF containsno bankruptcy data before 1998, so the PSID is used to estimate a model of futurebankruptcy, and bankruptcy risk is imputed for SCF households.12 A household is denedas bankrupt at time t if it declares bankruptcy during the period t to t+2. This futuremeasure allows for two forms of bankruptcy risk: conditional and unconditional on ahousehold holding debt. Conditional bankruptcy risk is relevant for lenders assessinginterest rates for loans, and thus will be included in X. Because the unconditionalbankruptcy risk measure does not include any debt measures, it is included in H, the vectorof characteristics predicting whether a household holds a certain loan. Note a full 14% ofthese bankrupt households have no debt at time t.In light of the extensive research on bankruptcy, the following variables are used in a

probit to predict bankruptcy risk: year, age, a checking account indicator, income, a selfemployment indicator, home ownership status, unsecured debt, an indicator of whether theratio of unsecured debt to income exceeds two, net worth (with negative net worth set toSartain (1999), Gross and Souleles (1999), Sullivan et al. (2000), and Fay et al. (2002).

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Table 2

Probability of default risk

Conditional bankruptcy Unconditional bankruptcy Delinquency

PSID SCFa PSID SCFa SCF

W. Edelberg / Journal of Monetary Economics 53 (2006) 228322982288Counterparts in the SCF that are close to the bankruptcy determinants in the PSIDare used in order to impute bankruptcy risk for SCF households. The necessarycorrection of the standard errors is done following Murphy and Topel (1985). Table 1shows bankruptcy risk in the PSID and imputed risk in the SCF, which areroughly similar. The bankruptcy risk is quite small: The 90th percentile household withdebt in the SCF still has only a 2.3% probability of declaring bankruptcy within the next 2years.Delinquency risk is the second measure of default risk. The SCF reports whether

respondents have been more than 60 days late on a loan payment in the previous year.14

Nearly 9% of the households report a delinquency, showing it is much more common thanbankruptcy. A probit is used to determine delinquency risk using the same determinantsthat are in the conditional bankruptcy model.15 A selection model is estimated, asdelinquency data only exists for households with debt. Again, the attitudinal variablesensure identication. And again, signicant time variation in coefcients is also included.

Percentiles 1% 0.0 0.0 0.0 0.0 0.1

10% 0.0 0.0 0.0 0.0 1.0

25% 0.2 0.1 0.2 0.1 2.6

50% 0.7 0.6 0.6 0.5 5.6

75% 1.4 1.3 1.2 1.1 11.8

90% 2.2 2.3 1.8 1.7 20.7

99% 5.1 5.3 3.4 3.3 47.9

Mean 1.0 0.9 0.8 0.7 8.9

Standard deviation 1.2 1.4 0.8 0.8 9.8

aBankruptcy risk in the SCF is imputed.Delinquency riskconditional on holding debtis reported in the last column of Table 2.Note that the correlation between bankruptcy and delinquency risk is only 0.35, showingthese are distinct measures of default risk.

3.2. Putting it all together

We now have three measures of default risk: delinquency risk, g, conditional bankruptcyrisk, fc, and unconditional bankruptcy risk, fuc. X and H are dened as follows:

X x; f cI95; f c; gI95; g; H h; f uc; f 2uc.

14As will be clear in the empirical analysis, a good bit of the information in late payments is indeed used by

lenders in pricing interest rates at loan origination. For every loan considered, average rates paid are higher for

those who made late payments versus those who had no late payments, with the differences ranging from a low of

0.2 percentage point for education loans to a high of nearly 2.5 percentage points for automobile loans.15The main results are robust to using either predicted or actual delinquencies. We might use actual

delinquencies given rational expectations, as lenders should predict correctly on average. In addition, if lenders

have superior data, their predictions of delinquency may be closer to the actual delinquencies than in this analysis.

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Table 3

Interest rates moments by origination year and risk class over time

High-risk versus low-risk spread

1989a 1995a 1998a

First mortgage rateb 0.53 0.59 0.69

Second mortgage 2.65 1.75 2.84

Auto loan 1.40 2.42c 3.94c

d c

W. Edelberg / Journal of Monetary Economics 53 (2006) 22832298 2289The indicator variable, I95, will determine whether the role of default risk in interest ratedetermination changed after 1995. The vectors x and h contain the remaining variables inX and H, respectively, aside from default risk. A default risk premium spread, s, measuresthe difference in interest rates between the highest- and lowest-risk groups:

s gf c f c;RI95 gf c f c;R gggRI95 gggRh i

gf c f c;LI95 gf c f c;L gggLI95 gggLh i

,

where the gs are the coefcients from the interest rate equation in the selection model. Theindicator function, I95, determines whether the risk premium is post- or pre-1995. R and Ldene averages of the default risk measures using conditional bankruptcy probabilities: thehighest- and lowest-risk groups are the 20% most and least likely to declare bankruptcy,respectively.16

Credit card 0.99 1.05 1.22Other consumer loan 0.08 3.03c 4.06

Education loan 0.02 1.30 0.26a1998 spreads computed from 1998 and 1997, 1995 computed from 1995 and 1996, and 1989 computed

from 1988 and 1987 (except for credit card rates which are computed for single years).bOnly 30-year xed rate mortgages are considered.cDifference between current and preceding year is signicant with p-valueo0.1.d1983 is used in place of 1989.4. Empirical results

Table 3 shows the differences in average interest rates paid by most and least riskygroups (as dened above) for 1989, 1995 and 1998.17 The clear trend is for the difference torise over time, consistent with an increased use of risk-based pricing. That the difference isnot always signicant reects the value of the more careful and extensive analysis discussedbelow.

16Here, s is calculated using xed risk classespresenting an economically useful summary of the coefcients ondefault risk. These premium spreads might change if we looked at the households actually using certain types of

loans pre- and post-1995, but this would make changes in pricing practices harder to isolate.17The spreads are taken from interest rates averaged for a 2-year period in order to have a reasonable number of

observations for each risk group. 1998 spreads are computed from 1998 and 1997, 1995 spreads are

computed from 1995 and 1996, and 1989 spreads are computed from 1988 and 1987 (except for credit card

spreads which are computed for single years and 1983 is substituted for 1989). Prime rate volatility is similar

across the time periods, though rates are a little more volatile from 1997 to 1998 then in the previous periods. For

rst mortgages, only 30-year xed-rate mortgages are used.

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Table 4

Default risk premium spreads

Pre-1995 risk premium spread Post-1995 risk premium spread

First mortgage rate* 0.50 0.98

Second mortgage rate* 0.98 3.97

Auto loan rate* 1.08 1.94

W. Edelberg / Journal of Monetary Economics 53 (2006) 228322982290Table 4 shows the default premium spreads for pre-1995 and post-1995.18 For the threetypes of secured loans, spreads at least nearly double over the sample, with the difference inthe spreads signicant at the 95% condence level in each case. The results are mixed forunsecured loans. The spread is positive but unchanged over the sample for generalconsumer loans, positive and statistically signicant for credit card loans only post-1995,and not statistically signicant for education loans before or after 1995.19

These results are quite robust. Default premium spreads were calculated using actualdelinquencies and then using slightly different cutoff years. Overall, spreads were a littlesmaller in the alternative models but still showed the same changes over time as in the basemodel.20 In addition, the models were estimated using only conditional bankruptcy anddelinquency predictions, in turn. While these models generally reect the base modelsresults, there is value-added from using both measures of default risk. For example,without delinquency risk, only the rst mortgage spread is truly consistent with the basemodel. For example, the second mortgage spread is insignicant post-1995. In addition,the automobile loan spread does not change over time, and the credit card spread issignicantly negative pre-1995.Fig. 1 shows these results graphically for rst mortgages, automobile loans, and credit

card loans. An interest rate function is plotted against conditional bankruptcy risk for pre-

General consumer loan rate 1.19 1.08

Credit card rate* 0.53** 1.30Education loan rate 0.03** 0.41**

*Difference is signicant at a 95% condence level.

** Spread is insignicantly different from zero.and post-1995 loan origination dates. For each loan type, interest rates are predicted by thesignicant measures of default risk, and other signicant variables are set to their meanvalues for the entire sample period. The effects of year dummies pre- and post-1995 areaveraged so that the predicted zero default interest rate reects the average discount rateover the period being considered. In total, 90% condence bands are also reported.Consistent with Table 4, the slopes are steeper in the post-1995 period, indicating that thedefault risk premium increased. A comparable gure for second mortgages is consistent

18Overall, the explanatory variables have the expected signs and are generally signicant. A more detailed

discussion can be found in Edelberg (2003).19For credit card loans, state usury laws may have constrained credit card rates more than other, generally

lower, consumer loan rates in 1983. These laws were rendered ineffective by a 1978 Supreme Court decision, but

there is evidence that lenders may have been slow to adapt. Using only 1995 and 1998, the premium is 0.70% in

1995, and it signicantly rises to 1.24% in 1998.20For mortgages, the inclusion of maturity, xed versus exible interest rates or FHA loan guarantees does not

signicantly alter the basic default risk premium spread results.

ARTICLE IN PRESSst ra

te

11

10

W. Edelberg / Journal of Monetary Economics 53 (2006) 22832298 2291with those for rst mortgages and automobile loans. For other consumer loans, the interestrate function is the same in both periods. The gure for education loans is similar to thecredit card loan gures, as it shows a at interest rate function pre-1995 and an upwardsloping function post-1995.

1st m

ortg

age

inte

re

0 0.01 0.02 0.03 0.04 0.05Conditional Bankruptcy Probability

Auto

mob

ile lo

an in

tere

st ra

te


Cred

it ca

rd lo

an in

tere

st ra

te


post 1995 pre 1995post 1995 90% CI pre 1995 90% CI

9

8

7

16

14

12

10

20

18

16

14

12

Fig. 1. Interest rates by bankruptcy risk.

The change in the slopes can be summarized by measuring how much interest rateschange with an increase of 0.01 in bankruptcy risk. This change more than doubles for rstmortgages, going from 0.16 to 0.38 basis points.21 The change is up nearly ve times forsecond mortgages and more than doubles for automobile loans. There is no change in theslope of the interest rate curve for general consumer loans. Credit card and education loansgo from zero slopes to changes in interest rates of 0.48 and 0.30, respectively.The results for secured loans support the hypothesis that lenders increasingly used risk-

based pricing after 1995. For unsecured loans, credit card loans are the most robustlyconsistent with the hypothesis. Two potential reasons may have led to this negative result for

should have increased more (or decreased less) than levels for high-risk households.22 The

ARTICLE IN PRESSW. Edelberg / Journal of Monetary Economics 53 (2006) 228322982292following selection model is used to estimate these effects across households:

lnB_ g0 g1O95

X3i1

gi2 fic

X3i1

gi3O95 fic u,

PrB40 f b0 b1Y 95 X3i1

bi2 fiuc

X3i1

bi3Y 95 fiuc yA

!,

21The renancing boom after 1995 should not be driving the mortgage interest rate results. Loans are compared

by origination year, whether for purchase or renancing. Still, renancing booms may mean that borrowers who

receive bad shocks cannot renance to the new low rates. This may lead to less mortgage rate variation pre-1995

(i.e. if only high-risk households hold old loans), but not less variation as a function of risk.

In addition, mortgage interest rate results are not simply due to the addition of a subprime market, with little

spread within the prime and subprime markets. Instead of the implied bimodal distribution, we see a smooth bell-

shaped distribution of mortgage rates post-1995. For example, 50% of the post-1995 rates are between 7% and

8.5%, 20% are between 6% and 7%, and 20% are between 8% and 9%.22The change in the overall level of interest rates over time has a direct effect. For example, interest rates fell for

all credit card loans, and all risk classes increased credit card borrowing. However, interest rates fell more for low-education and general consumer loans. First, of the three unsecured loan types, credit cardloans have the highest incidence of loan securitization. As mentioned above, the secondarymarket for loans may motivate risk-based pricing. Perhaps, lenders of education and otherconsumer loans have yet to feel the pressures that led to risk-based pricing. Second, as lenderskeep better track of borrowers at risk of imminent bankruptcy, default losses may fall aslenders are more aggressive in obtaining partial payments and fees (Winton, 1998). Thesefalling default costs would offset the forces driving the increased use of risk-based pricing.

5. Implications for borrowing

If lenders declined to charge very high-risk households sufciently high interest ratesbefore the mid-1990s, lending to this group may have proved signicantly unprotable,and these households may have been rationed out of the market (Bostic, 2002). With risk-based pricing, lenders should offer these households debt with higher interest rates ratherthan reject them. If at least some of these borrowers have sufciently high reservationrates, debt use among very high-risk households should rise. Debt levels should alsochange in reaction to risk-based pricing. Before the mid-1990s, low-risk borrowers paidrelatively higher rates than their default risk justied, and high-risk borrowers paid lowerrates. As premiums adjusted to better reect risk, debt levels among low-risk householdsrisk borrowers, and this is where we can see the effect of risk-based pricing.

ARTICLE IN PRESSwhere B is the debt level for the various consumer loan types, in 1998 dollars, and A is the vectorof attitudinal variables. Accounting for changes in the cost of funds, O95 indicates if the loanorigination year is 1995 or later, and Y95 indicates if the survey year is 1995 or later. The thirddegree polynomial in bankruptcy risk allows debt use and levels to vary with default risk, andthe interaction terms measure how debt use and levels changed across risk classes over time.Fig. 2 shows predicted debt use and Fig. 3 shows predicted debt levels with 90% condence

bands. As the top panel of Fig. 2 shows, the very high-risk households have a higherprobability of holding a rst mortgage after 1995. Low-risk households also have a higherprobability of holding rst mortgages over time, perhaps as rates fell below some of theirreservation rates. Conversely, higher interest rates for high-risk groups lower the probabilityof rst mortgage use for this group. Consistent with these effects, the increases in mortgagelevels after 1995 are predicted to fall with default risk, shown in the top panel of Fig. 2.The increase in the use of automobile loans and credit cards loans is similar to that for rst

mortgages, as shown in the lower panels of Fig. 2. However, for both loan types, thecondence bands are wider, particularly as risk increases. In addition, the predicted debt levelsfor automobile loans are quite consistent with the hypothesis, shown in the middle panel ofFig. 3. Indeed, high-risk households (as opposed to very high-risk households), which saw nosignicant increase in access but saw relative borrowing costs rise, are predicted to holdsignicantly lower levels of automobile debt post-1995. The overall increase in popularity ofcredit card borrowing overwhelms the effects of risk-based pricing, and all credit cardborrowers are predicted to increase debt levels after 1995, shown in the lower panel of Fig. 3.Equivalent gures for the other debt types are not shown. Second mortgages are only

held by households with rst mortgages, making results on its use less informative. Otherconsumer loans and education loans showed no signicant increases in their premiumspreads, so there is little reason for the hypothesis to hold in these cases, and indeed noconsistent story emerges from the graphs. In addition, a number of aggregate debtcategories were considered but are also not shown, though they bear out the hypothesis.For example, very high-risk households have a higher probability of holding any debt,post-1995. Low-risk borrowers increase total debt levels more than high-risk borrowers do,and in some cases very high-risk borrowers actually decrease borrowing levels. Finally,consistent with interest rates falling below or rising above reservation rates, low-risk (high-risk) households have a higher (lower) probability of holding any form of debt.

6. Access to debt markets

The increase in the use of debt and debt levels in the 1990s has been the subject of muchpopular discussion. To isolate the role of risk-based pricing, a counterfactual of a pre-1995world with the increased use of risk-based pricing is estimated by the following model forthe various types of consumer debt, where B is the borrowing level for each household:

lnB^ g0 g1O95 X4i1

gi2Q5i X4i1

gi3O95Q5i u,

PrB40 f b0 b1Y 95 X10i2

bi2Q10i X10i2

bi3Y 95Q10i yA !

.

For this analysis, default risk quantiles replace continuous measures of risk: (Q5)i

W. Edelberg / Journal of Monetary Economics 53 (2006) 22832298 2293represents the ith of ve quantiles, and (Q10)i represents the ith of ten quantiles. Risk is

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ebt 1

W. Edelberg / Journal of Monetary Economics 53 (2006) 228322982294t Mor

tgag

e D

0.8

0.6measured this way since the many households with near-zero default risk should not berepresented by zero. Using zero would obscure the effects of any changes in the coefcientsfor this risk group.23

Prob

abilit

y of

1s

0 0.01 0.02 0.03 0.04 0.05Unconditional Bankruptcy Probability

Prob

abilit

y of

Aut

omob

ile D

ebt


Prob

abilit

y of

Cre

dit C

ard

Debt



0.4

0.2

0

0.5

0.4

0.3

0.2

0.1

0

1

0.8

0.6

0.4

0.2

Fig. 2. Predicted debt use by bankruptcy risk.

23The preceding sections analysis on the heterogeneous effects of risk-based pricing across risk groups suggests

which risk groups should be excluded in order to identify this model. Robustness checks show that the choices

ARTICLE IN PRESS

ls200.000

W. Edelberg / Journal of Monetary Economics 53 (2006) 22832298 2295e De

bt L

eve 150.000

100.000Fig. 4 plots the predicted changes for borrowing levels and debt use for rst mortgagesand all debt for a pre-1995 world with and without the increased use of risk-based pricing.Probability of debt use is plotted against bankruptcy risk, whereas predicted debt levels are

Mor

tgag


Auto

mob

ile D

ebt L

evel

s


Cred

it Ca

rd D

ebt L

evel

s



50.000

0

20.000

15.000

10.000

5.000

2.500

2.000

1.500

1.000

500

Fig. 3. Predicted debt levels by bankruptcy risk.

(footnote continued)

made are quite reasonable. The selection equation uses additional risk quantiles to better estimate increased debt

use among the very high-risk groups. The tenth quantile is even further divided into four ner divisions of risk.

ARTICLE IN PRESSW. Edelberg / Journal of Monetary Economics 53 (2006) 228322982296plotted against bankruptcy risk quantiles. Quantiles are used as the signicant changesoccur for households in the rst quantile, which have nearly zero variation in bankruptcyrisk.24

Fig. 4. Effects of risk-based pricing.

24These condence intervals reect the prediction error in the coefcients and not the error associated with the

residual. These plots do not represent genuine forecasts of levels and use of debt, only the levels and use predicted

by risk-based pricing as summarized by the coefcients. Including the error associated with the residual generally

makes the condence intervals so large as to include pre- and post-1995 point estimates.

Allowing for the increased use of risk-based pricing in a pre-1995 world predicts one- tothree-quarters of the actual increases in debt levels seen across the 1990s. For example, themodel predicts that risk-based pricing would have added over $7,000 to the average

ARTICLE IN PRESSW. Edelberg / Journal of Monetary Economics 53 (2006) 22832298 2297mortgage amount excluding any economy-wide changes (in 1998 dollars). Actualmortgages originated after 1995 versus those originated before 1995 increased about$30,000. Similarly for automobile loans, the model predicts an increase of nearly $1500 inthe average loan size, whereas actual automobile loans increased over $2000. (Figures forautomobile loans are not shown for brevity, but can be seen in Edelberg (2003).) Themodel predicts an increase in the average debt burden for households with debt of nearly$6000 over the mid-1990s. The actual average rose about $14,000.The model over-predicts the increased use of debt. For rst mortgages, the model

predicts an increase of nearly 8 percentage points of households holding mortgages frombefore 1995 to after 1995. The actual increase was 3 percentage points in the SCF. Forautomobile loans, the model predicts an increase of nearly 0.5 percentage point ofhouseholds holding automobile loans, and the actual increase was only 0.1 percentagepoint. Note that the highest risk group saw much larger changes. For these households, themodel predicts an increase of 3.2 percentage points in those holding automobile loans. Theactual increase was 2.6 percentage points. For all debt, the model predicts an increase ofalmost 7 percentage points in the number of borrowers, and the actual increase was 2percentage points.25

7. Conclusion

Lenders increasingly used risk-based pricing of interest rates in consumer loan marketsduring the mid-1990s. Risk premium spreads for secured loans rose over time by asignicant amount. The case for unsecured loans is less clear. The premium spread forcredit card loans more than doubled, but education loan and other consumer loanpremiums are statistically unchanged. The evidence suggests that variations over time inhouseholds debt levels and use of debt instruments are consistent with this change inpricing practices. For example, while very high-risk and very low-risk households havebeneted from these changes, high-risk households have seen their relative premiumsincrease and have changed their borrowing in response.

References

Ausubel, L., 1991. The Failure of Competition in the Credit Card Market, American Economic Review, 81(1).

Black, S.E., Morgan, D.P., 1999. Meet the New Borrowers. Current Issues in Economics and Finance. Federal

Reserve Bank of New York.

Bostic, R.W., 2002. Trends in equal access to credit products. In: Durkin, T., Staten, M. (Eds.), The Impact of

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Banks, Finance and Economics Discussion Series. Federal Reserve Board, Washington, DC.

Deaton, A., 1997. The Analysis of Household Surveys. Johns Hopkins University Press, Baltimore, MD, World

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25Other changes that were similarly heterogeneous across risk-classes could also account for the models

predictions. For example, if attitudes towards risk changed in the same manner that risk-based pricing affected

various risk groupsif only the lowest risk groups became exogenously more amenable to high debt levels overthe time periodsuch changes could not be rejected as alternative reasons for the predictions.

Domowitz, I., Sartain, R.L., 1999. Determinants of the consumer bankruptcy decision. Journal of Finance 45 (1),

403420.

Dubey, P., Geanakoplos, J., Shubik, M., 2003. Default and punishment in general equilibrium. Cowles

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Conference on Credit Scoring and Credit Control, Organized by the Institute of Mathematics and Its

Applications and held at the University of Edinburgh in August 1989. Oxford University Press, New York.

McCorkell, P.L., 2002. The impact of credit scoring and automated underwriting on credit availability. In:

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Murphy, K., Topel, R., 1985. Estimation and inference in two-step econometric models. Journal of Business and

Economic Statistics 3 (4), 8897.

Riley, J.G., 1987. Credit rationing: a further remark. The American Economic Review 77 (1), 224227.

Sullivan, T.A., Warren, E., Westbrook, J.L., 1989. As We Forgive Our Debtors: Bankruptcy and Consumer

Credit in America. Oxford University Press, New York.

Sullivan, T.A., Warren, E., Westbrook, J.L., 2000. The Fragile Middle Class: Americans in Debt. Yale University

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Winton, E.W., 1998. Games Creditors Play: Collecting from Overextended Consumers. Carolina Academic Press,

North Carolina.

Risk-based pricing of interest rates for consumer loansIntroductionDataEmpirical analysisDefault riskPutting it all together

Empirical resultsImplications for borrowingAccess to debt marketsConclusionReferences

Documents

Risk-based Pricing of Interest Rates