Subprime Defaults: Measuring the Costs of Borrower BadBehavior�

Mark Jenkinsy

JOB MARKET PAPER

November 2008

Abstract

I study repayment behavior in the market for subprime auto loans using uniquedata on collections and vehicle recoveries from a large subprime auto lender. I begin byexamining borrowers�reasons for default in this market and their behavior immediatelyfollowing default. I �nd that 28 percent of defaulters disappear with their cars afterdefaulting and that this behavior imposes signi�cant costs on the lender and the otherparticipants in the market. I then estimate the impacts of policies designed to mitigatethis behavior. To do so, I develop and estimate a dynamic model of repayment behaviorin which borrowers trade o¤ the bene�t of using their vehicle with the cost of makingtheir loan payments, and borrowers� costs of disappearing are a form of unobservedheterogeneity. Counterfactual simulations show that policies that improve lenders�ability to screen out borrowers who are likely to disappear and policies that reduce thebene�ts of disappearing can reduce interest rates by up to 20 percent.

�I thank Jonathan Levin, Liran Einav, and Timothy Bresnahan for their guidance and advice. I alsothank Lanier Benkard, Jakub Kastl, Roger Noll, Peter Reiss, and Frank Wolak for valuable feedback, andWill Adams for his contributions to this project. I gratefully acknowledge support from the Hawley-ShovenFellowship, Stanford Institute for Economic Policy Research.

yDepartment of Economics, Stanford University, Stanford, CA 94305-6072. E-mail: mwj@stanford.edu.

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1 Introduction

In consumer credit markets, contract outcomes inevitably result from a combination of real-

ized uncertainty and individual choice behavior. Mortgage loans, for example, may default

due to unexpected events such as job loss or divorce, or borrowers�decisions to strategically

exercise their default option. The costs of these defaults, in turn, depend both on ran-

dom variation in house prices and borrowers�treatment of their property after foreclosure.

Micro�nance loans default due to unfavorable realizations of project risk, which can be in�u-

enced by borrowers�project choices and implementation e¤orts, as well as some borrowers�

predilections to take the money and run. Similar examples exist in insurance; for instance,

auto insurance claims are driven by the occurrence of unpredictable accidents or theft, as

well as the insured parties�e¤orts to avoid these events, their decisions to report them, and

their willingness to in�ate reported losses.

Disentangling the e¤ects of uncertainty and individual behavior on consumer lending

outcomes is di¢ cult to accomplish empirically. While lenders observe the incidence of default,

they do not observe much about the process that causes this event to occur. For example,

lenders typically do not observe the e¤ort that borrowers expend to earn income or limit

expenses, nor can they monitor the realized results of this e¤ort nor whether borrowers, given

their income and expense realizations, default because they are unable to pay or because

they are able to pay but choose not to. Nevertheless, understanding the roles of uncertainty

and individual choice behavior in determining contract outcomes is important for both �rm

and public policy, since both may be able to reduce the incentives for or otherwise mitigate

costly behavior.

In this paper, I study the impact of individual behavior on lending outcomes in the market

for subprime auto loans. Using unique data on payment collections and vehicle recoveries

from a large subprime auto lender, I begin by documenting two striking empirical facts.

First, 60 percent of borrowers in my sample default, and second, 28 percent of those who

default disappear with their cars after doing so. While the former fact is inevitably due to a

combination of borrowers�decisions and exogenous circumstances beyond their control, the

latter presents a unique opportunity to isolate the e¤ects of individual behavior on the cost

and availability of credit. Borrower disappearance, which is known in the subprime lending

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industry as �skipping�, is directly observable by the lender and is unconfounded by any

uncertainty beyond the borrowers�control. Moreover, this behavior imposes signi�cant costs

on the lender and the other participants in the market by, at least temporarily, preventing

the lender from recovering the car.

My analysis proceeds in several steps. I �rst examine the underlying causes of default

in the subprime auto loan market using data on reasons for default recorded by the lender

during the collections and vehicle recovery process. I show that the reasons that borrowers

default fall into two main categories: �nancial di¢ culties and vehicle failure. The former

category, which constitutes 36 percent of defaults, includes events such as job loss, death,

and divorce, as well as longer-term �nancial conditions such as overextended debt and bank-

ruptcy. The latter, which also makes up 36 percent of defaults, includes accidents, thefts,

mechanical problems, and vehicle con�scations for legal reasons. For the remaining 28 per-

cent of defaulters � those who disappear �no underlying reason for default is recorded.1

These �ndings suggest that borrowers weigh both the value of their car and their �nancial

circumstances when making their repayment decisions, a fact which guides much of my later

analysis. They do not, however, allow me to separate the e¤ects of uncertainty and behav-

ior on contract outcomes. For example, borrowers who default due to overextended debt

may have become overextended due to unexpected health care expenses or due to voluntary

overspending.

To isolate the impacts of individual behavior on loan outcomes, I next study borrowers�

behavior immediately following default. Borrowers who default on their auto loans can take

one of several actions. They can voluntarily return their cars to the lender, they can wait

for their cars to be repossessed, they can �le for bankruptcy, or they can disappear with or

otherwise hide their cars from their lender. I show that all of these actions are common and

that they impose very di¤erent costs on the lender. In particular, I show that although 97

percent of disappearing borrowers�cars are eventually recovered, these borrowers are able to

keep possession of their cars for an average of four months after defaulting. This increases

the lender�s losses in the event of default, because the lender must incur increased collections

1If borrowers who disappear default for �nancial reasons, then �nancial di¢ culties may account for upto 64 percent of defaults.

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costs to �nd the missing borrowers and because longer recovery times result in higher vehicle

depreciation. In addition, since borrowers who disappear are able to continue using their

cars in the event of default, they have less incentive to repay, meaning this behavior may

also increase the probability of default.

Having established the channels through which borrowers�behavior imposes costs on the

lender, I next seek to quantify the externality that individuals who disappear impose on

other borrowers in the market. To do this, I develop a stylized model of borrower repayment

behavior in which borrowers trade o¤ the bene�t of using their car with the cost of making

their loan payments. A full model of repayment is useful because it allows me to estimate

the e¤ects that eliminating borrowers�ability to disappear has on their incentives to repay.

I model the borrower�s repayment problem as a dynamic discrete choice model.2 In the

spirit of Ja¤ee and Russell (1976), borrowers in my model are one of two types: one type of

borrower disappears when he defaults, and the other does not. Borrower types are treated

as a form of unobserved heterogeneity.

The parameters of the model and the distribution of borrowers�types are identi�ed using

variation in the patterns of default timing for borrowers who disappear and borrowers who

do not, and are estimated using the Method of Simulated Moments. I �nd that approx-

imately 25 percent of borrowers are likely to disappear in the event of default, and that

these borrowers behave as if they expect to retain their cars for 15 months after defaulting.

After estimating its parameters, I use the model to conduct counterfactual simulations of

default and recovery outcomes under conditions where disappearing behavior is eliminated,

either through screening those likely to disappear from the market or through implementing

policies to reduce the bene�ts of disappearance. I �nd that disappearing behavior has a

signi�cant impact on interest rates, and that in its absence, interest rates could decline by

more than 20 percent. Most of this decline is due to increased recovery values in the event

of default, and a small portion is due changes in borrower incentives and the overall rate of

default.

From a policy standpoint, one implication of these �ndings is that consumer credit bu-

2Dynamic discrete choice models were pioneered by Wolpin (1984), Miller (1984), Pakes (1986), and Rust(1987) and recently surveyed by Aguirregabiria and Mira (2008).

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reaus should consider recording and reporting not only whether a borrower defaulted on a

secured loan, but also how he treated his collateral in the event of default. Such report-

ing could have two desirable e¤ects. First, it could reduce the frequency of costly behavior

by raising the costs of this behavior, and second, if borrowers who have disappeared with

collateral in the past are more likely to do it again in the future, documenting borrower

disappearance could allow lenders to better screen out of the market those who are most

likely to disappear.

This paper makes several contributions. First, it provides insight into the borrowing

and repayment behavior of low-income, under-banked borrowers, or subprime borrowers,

a topic that is of interest in its own right. While these borrowers are the focus of much

lending regulation, the empirical literature on their borrowing and repayment behavior is

fairly limited.3 The paper also adds a data point to the broad empirical literature on the

causes of delinquency, default, and bankruptcy by o¤ering some evidence on the reasons that

subprime borrowers default on their auto loans.

Second, this paper provides unique evidence of ex post moral hazard in consumer lending.

The literature on micro�nance distinguishes between ex ante and ex post moral hazard. The

former refers to incentive problems that a¤ect the borrower�s behavior before the realization

of any uncertainty (e.g., e¤ort in income generation) and a¤ects the borrower�s ability to

repay his loan. The latter refers to incentive problems that a¤ect the borrower�s behavior

after the realization of uncertainty (Besley and Coate (1995), Aghion de Armendariz (1999)),

but little empirical evidence exists on how common, or how costly, this form of moral hazard

is. Such empirical evidence is particularly scarce for credit markets in developed countries

such as the U.S.

By quantifying a speci�c form of moral hazard, this paper complements the growing

empirical literature on asymmetric information in consumer credit markets (Karlan and

Zinman (2007), Adams, Einav, and Levin (2008), and Einav, Jenkins, and Levin (2008a)).

These existing studies estimate the e¤ects of changes in contract terms (e.g., the interest

rate and minimum down payment requirement) on the probability of default, and separate

3See Adams, Einav, and Levin (2008) and Einav, Jenkins, and Levin (2008a,b) for additional studies inthe market for subprime auto loans and Skiba and Tobacman (2008) for a study of the market for paydayloans.

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these e¤ects into adverse selection e¤ects (borrowers who are more likely to default accept

higher interest rates and make smaller down payments) and moral hazard or repayment

e¤ects (borrowers with higher interest rates and larger loans are more likely to default), but

they do not attempt to separately quantify any form of ex post moral hazard.4

This paper also o¤ers an empirical counterpart to the theoretical literature on lending

with collateral, or secured lending. Collateral serves three primary functions in credit mar-

kets. First, collateral requirements can mitigate adverse selection if borrowers who are more

likely to repay are also able to pledge more collateral. For mortgages and auto loans, the

amount of pledged collateral is �xed, so adverse selection is instead dealt with through a min-

imum down payment requirement (Einav, Jenkins, and Levin (2008a)). Second, collateral

can mitigate moral hazard by increasing borrowers� incentives to repay. Third, collateral

reduces the lender�s losses given default. This paper provides empirical estimates of the

relative importance of the latter two e¤ects as they relate to borrower disappearance.

Finally, this paper o¤ers a �rst estimate of the deadweight losses associated with the

transfer of collateral in secured lending. Barro (1976) presents an early theoretical model

that shows how the transaction costs associated with the transfer of collateral in the event

of default can a¤ect market interest rates, but little empirical evidence exists about the

magnitude of these e¤ects. Deadweight losses due to property destruction after foreclosure

in the mortgage market suggest bad behavior is costly in this market, but no comprehen-

sive evidence about the magnitude of these costs is available. My �ndings show that the

deadweight costs associated with secured lending can indeed be quite high.

Several features of this market have been studied in previous work. Adams, Einav, and

Levin (2008) provide evidence of consumer liquidity constraints, showing that loan applicants

are extremely sensitive to minimum down payment requirements and that the demand for

loans increases substantially during tax rebate season, when applicants have more cash on

hand. These authors and Einav, Jenkins, and Levin (2008a) both provide evidence that the

market is subject to the problems of adverse selection and moral hazard, and the latter show

4Also related to this paper is the literature on insurance fraud, which is another consequence of expost moral hazard (e.g., see Crocker and Tennyson (1997), Crocker and Morgan (1998)). Like borrowersdisappearing with their cars, insurance fraud is a type of behavior that imposes costs on the insurer and theother participants in the market. .

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how di¤erent contract terms can be used separately deal with these two problems. Einav,

Jenkins, and Levin (2008b) also show how the implementation of credit scoring in this

market a¤ects lender pro�tability and the distribution of pro�ts across dealerships. While

these papers focus primarily on the borrowing decisions of consumers and the credit-granting

decisions of the lender, this paper utilizes signi�cantly more-detailed data on repayment and

recovery outcomes to study borrower behavior after the loan has been made.

The remainder of the paper is organized as follows. In Section 2 I describe my data

and the lending environment from which it is drawn. In Section 3 I present descriptive

evidence on the reasons that borrowers default, how they behave when they default, and

the impacts of their behavior on recovery outcomes. In Section 4 I develop a model of

borrower repayment behavior, motivated by the �ndings in Section 3, and describe the

identi�cation and estimation of the model�s parameters. In Section 5 I presents the results

of the estimation, and in Section 6 I present counterfactual estimates of market interest

rates under various counterfactuals in which borrowers�ability to disappear is reduced or

eliminated. Section 7 provides conclusions and suggestions for future work.

2 Data and Environment

My data are drawn from a large used car sales and �nancing company that operates deal-

erships in the U.S. The company primarily sells cars to customers with low incomes and

poor credit histories �so-called subprime borrowers �who want to purchase a car but are

unable to obtain credit at banks or traditional dealerships. Most customers put down a

small fraction of the car�s purchase price, often the minimum down payment required by the

company, and �nance the remainder of the purchase. The company provides the �nancing,

collects the loan payments, and recovers the car in the event of default.

My data include detailed information on all loans originated by the company between

June 2001 and December 2003. While the exact number of loans in my sample is proprietary,

it exceeds 10,000. For each loan, I observe data collected both at the time of sale and

over the subsequent repayment term. Data collected at the time of sale include borrower

characteristics (including monthly income), vehicle characteristics (including acquisition and

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reconditioning costs), and transaction characteristics (including loan size, interest rate, and

term). Data collected during the repayment term include the number of payments made, the

reason for default (if default occurred), and details about vehicle recovery (also conditional

on default). Repayment and recovery outcomes are observed through January 2008, meaning

the entire repayment term is observed for each loan.

Table 1 presents summary statistics on the borrowing population, loan terms, and re-

payment and recovery outcomes in my sample. Borrowers are characterized by low incomes

and poor or non-existent credit histories. The average borrower is 34 years old and has an

annual income of just under $30,000. Only 20 percent of borrowers have a FICO score above

600, the minimum threshold for a traditional bank loan, and 17 percent have no FICO score.

Most borrowers are renters, though 17 percent own their own home. Roughly 25 percent

have no bank account.

In a typical transaction, a customer makes a $900 down payment to purchase a car priced

at $10,000. After taxes and fees, the customer borrows just over $10,000 and agrees to repay

it in �xed installments over a term of (typically) 36 or 42 months. While interest rates vary

slightly with borrowers�credit quality and down payment, most loans have annual interest

rates at state-mandated interest rate caps, which are often 29.9 percent. The average annual

interest rate across all loans is 26 percent, yielding an average monthly payment of $388.

Borrowers who take out loans retain possession of their cars as long as they make their

loan payments on time. When borrowers miss one or more scheduled payments, they have

three courses of action. First, they can make up their payments within 90 days of the

scheduled due dates and maintain possession of their cars. Second, they can voluntarily

default by returning their cars to the lender. This action is reported to the credit bureaus

as a default, but presumably reduces other (non-pecuniary) costs to the borrower. Third,

borrowers who fall behind on their payments can keep possession of their cars until they

have o¢ cially been designated as defaulting by the lender. Loans are formally defaulted

at the end of the calendar month in which the borrowers�payments become 90 days past

due. Defaults are frequent and tend to happen early in the repayment term. Sixty percent

of borrowers default, and the average defaulter makes one third of his scheduled payments

before doing so.

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When borrowers default, the lender records a reason for default. In many cases, these rea-

sons are reported by the borrowers during conversations with the lender�s collections agents;

in others, they are determined by the lender based on the condition of the car. Reasons

reported by borrowers include personal or �nancial di¢ culties (e.g., job loss) and typically

cannot be veri�ed by the lender, except when a legal procedure requires veri�cation (e.g.,

bankruptcy). Reasons that relate to the value of the car (e.g., accidents) are generally veri-

�able by the lender, since the lender can observe the car. Exactly one reason for default is

recorded for every borrower who does not disappear with his car. A full list of recorded rea-

sons and additional discussion is provided in the next section. For borrowers who disappear,

no underlying reason for default is recorded.

After borrowers default, the lender closes their accounts and seeks immediate recovery of

their vehicles.5 Borrowers who default for reasons unrelated to car failures such as accidents

or breakdown may take one of several actions that a¤ect the lender�s ability to recover their

cars. They may (i) return their cars voluntarily, (ii) �le for bankruptcy, (iii) wait for the

lender to involuntarily repossess their cars, or (iv) disappear with their cars. In addition to

the type of recovery the lender records details about the recovered vehicle, including whether

or not a car was recovered, the number of days required to recover the car, and the value of

the car upon recovery. Over 80 percent of cars are recovered in the event of default, and the

average time between default and recovery is 75 days. Recovered cars are sold at auction and

typically sell at heavily discounted prices due to both above average wear-and-tear and the

perception that the company�s borrowers don�t maintain their cars. The average recovery

value is 38 percent of original car cost, or $2,200.

3 Descriptive Evidence on Repayment Behavior

In this section, I examine in greater depth my data on borrowers�reasons for default and their

behavior in the event of default. The goal of this section is threefold. First, I present evidence

5The company is obligated to recover the vehicle after a loan becomes 90 days past due to contractualagreements with its lenders and investors in its asset-backed securities. In rare cases, the company mayconduct an involuntary recovery before the loan is 90 days past due; this usually occurs if the lender has notreceived payments and has been unable to contact the borrower for several weeks.

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that borrowers default for two primary reasons: �nancial di¢ culties and vehicle failure. I

�nd that 36 percent of borrowers report defaulting due to �nancial problems, 36 percent

default due to problems with their vehicle, and 28 percent disappear without reporting a

reason for default. Second, I detail the heterogeneity in borrowers�post-default behavior and

show how borrowers�actions in the event of default lead to very di¤erent recovery outcomes.

Finally, I provide my de�nition of bad behavior, which I will use when measuring the impact

of behavior on the cost of credit in this market.

3.1 Reasons for Default

Table 2 provides a detailed list of borrowers� reasons for default. Thirty-six percent of

defaulters report defaulting for reasons related to their �nancial circumstances, including

loss of income, life events such as death and divorce, and overextended debt. If borrowers

who disappear did so in response to �nancial di¢ culties, the total could reach 64 percent.

The �nancial reasons for default listed in the table may not be mutually exclusive. For

example, borrowers who report overextended debt may have experienced a loss of income

or divorce that led to these �nancial conditions, though this is not something I observe in

my data. Similarly, these reasons do not allow me to distinguish between various underlying

causes of bankruptcy or overextended debt, such as unforeseen medical expenses, the addition

of a new family member, gambling losses, or consumption funded by high cost debt such as

payday loans. These limitations are not important for my conclusions, however, since the

remainder of my analysis does not rely on these data.

Another 36 percent of defaulters default due to problems with their vehicle. Several

negative shocks to a car�s value may lead to default. The �rst is mechanical failure, which

causes 9 percent of all defaults. The second is an accident or theft that is covered by

insurance. When a borrower who maintains collision insurance has an accident, the lender

collects the insurance settlement, which typically does not cover the full balance of the loan,

and the loan is terminated. Insured accidents cause 8 percent of all defaults. The third is

an accident or theft that is not covered by insurance.6 The fourth is that the vehicle may be

6The lender technically requires borrowers to maintain comprehensive insurance, but does not enforcethis requirement.

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con�scated due to accrued parking tickets or other legal violations. The latter two reasons

for default � uninsured accidents and vehicle con�scations � are grouped together in my

data; collectively, they account for 20 percent of all defaults.

The remaining 28 percent of defaulters disappear with their cars. For these borrowers, no

underlying reason for default is recorded. Delinquent borrowers are labeled as disappeared

when they have been out of contact with the lender for more than 20 days. Since the lender�s

attempts to contact the borrower typically include not only phone calls, but also visits to the

home and work and discussions with neighbors and co-workers, these borrowers are generally

thought to have made a conscious e¤ort to avoid the collections and recovery e¤orts of the

lender (and possibly other creditors).

3.2 Post-Default Behavior

Borrowers who default for reasons other than vehicle failures can take one of several actions in

the event of default. They can voluntarily return their cars, they can �le for bankruptcy, they

can wait for the lender to repossess their cars, or they can disappear or otherwise hide their

cars from the lender. Table 3 shows how three major recovery outcomes �the probability of

a nonzero recovery, the number of days to recovery, and the value of the recovered car net

of collections cost �vary with these types of behavior, as well as with the di¤erent types of

vehicle-related defaults.

The �rst panel of the table shows recovery outcomes for borrowers who defaulted due to

�nancial issues or life events and for borrowers who disappear with their cars. The panel

shows that borrowers who voluntarily return their cars tend to return them quickly and

with relatively high resale values. Borrowers who wait for repossession also have generally

favorable recovery outcomes, though slightly worse outcomes than borrowers who return

their cars. The probability of positive recovery is slightly lower for these borrowers than for

those who return their cars (98 percent vs. 100 percent) and the recovery times are slightly

longer (0.9 months vs. 1.0 months). The main di¤erence between borrowers who return their

cars and those who wait for repossession are the recovery values net of collections costs. The

average recovery value of returned cars is 40 percent of the those cars original cost to the

lender, compared to 31 percent for repossessed cars. At an average car cost of roughly $6,000,

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this equates to an approximate di¤erence of about $540.

Borrowers who declare bankruptcy are associated with a unique set of recovery outcomes.

They tend to keep their cars for a long period of time after default, due in part to the duration

of bankruptcy court proceedings, yet their cars yield very high resale values upon recovery.

While the long recovery time imposes costs on the lender, the collections expenses associated

with following a bankruptcy proceeding are much less than those of tracking down a missing

borrower. Also, although 10 percent of bankruptcy �lers in my sample had un-recovered

cars, I suspect this is due to censoring at the end of the observation period. Both of these

points suggest that bankruptcy �lers do not impose excessive costs on the lender in the event

of default.

I next consider borrowers who disappear with their cars. While the probability of recovery

for defaulters who disappear with their cars is (perhaps surprisingly) quite high at 97 percent,

these borrower keep their cars for on average 4 months, or 3 months longer than the average

borrower. This suggests that the costs imposed on the lender by disappearing borrowers is

not due to these borrowers�ability to permanently steal the car, but rather by the e¤ort they

force the lender to expend during recovery. The extended period of time that borrowers who

disappear keep their car after defaulting on the loan imposes several costs on the lender. First,

borrower disappearance imposes increased collections costs on the lender; tracing a missing

borrower is an expensive process and costs can easily exceed $1,000. Second, since used cars

are a rapidly depreciating asset, the additional time that a borrower keeps possession of the

time results in increased depreciation costs to the lender. As a result, recovery values net

of collections costs are substantially lower for borrowers who disappear than for borrowers

who take other actions at the time of default. Third, borrowers�ability to continue using

their cars in the event of default reduces their incentive to repay. This incentive e¤ect of

disappearing behavior may raise default rates and further increase costs to the lender.

The table also includes information on recovery outcomes for borrowers who default

due to vehicle failure. Of particular interest are borrowers whose cars were abandoned

or con�scated, and in particular, the fact that probability of recovery for cars that were

abandoned or con�scated is only 51 percent. As discussed above, there are several reasons

why a car may be abandoned or con�scated; these include uninsured accidents or theft,

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mechanical failure, and con�scation due to unpaid parking tickets or other violations. There

are two primary reasons why an abandoned car may have recovery value. The �rst is that

the car was abandoned due to mechanical failure that left the car inoperable. The second

reason is that car was con�scated and the borrower was unwilling or unable to pay the �nes

to release the car, but the lender found it worthwhile to do so.

Abandoned cars that were not recoverable include cars that were wrecked or stolen with-

out insurance and cars that were con�scated but would require too high a payment in �nes

to justify recovering the vehicle. Both of these circumstances impose substantial costs on

the lender, and both are at least in part the result of adverse (to the lender) decisions by

the borrower. Borrowers who operate their car without insurance have made a conscious

decision to do so, and borrowers with impounded cars that are too expensive to recover have

likely made a series of unfavorable decisions to arrive in that situation. In both cases, these

decisions may have been predicated by negative �nancial shocks, and in the case of accident

or theft, some additional bad luck was likely involved.

3.3 De�ning Bad Behavior

The previous section documented a variety of borrower behavior in the event of default and

showed that these responses impose very di¤erent costs on the lender in the event of default.

It also documented several types of negative vehicle shocks and showed that these also impose

widely di¤erential costs on the lender. In this section, I use these �ndings to motivate my

de�nition of bad behavior. This de�nition of bad behavior will guide my modeling in the

next section, and my estimates of the costs of borrower bad behavior in this market.

There are several possible de�nitions of bad behavior in this market. The �rst is that

bad behavior includes all actions undertaken by the borrower that would not have been

undertaken if the borrower�s incentives were perfectly aligned with those of the lender. This

de�nition is extremely broad and would make the costs of bad behavior di¢ cult, if not

impossible, to quantify. A second de�nition is that bad behavior is all behavior that imposes

high costs on the lender after default. In this case, bad behavior might be de�ned by

a threshold level of recovery costs imposed on the lender. Based on this de�nition, bad

behavior could naturally be de�ned as either disappearing with one�s car or having one�s car

13

abandoned or con�scated; however, as discussed above, the latter may be a product of both

borrower decisions and realized uncertainty.

One speci�c borrower action that might be considered bad behavior is failure to maintain

comprehensive auto insurance. However, I don�t focus on this behavior for a two reasons.

First, it is not always clear from the lender�s perspective whether it is preferable for its

customers to pay for insurance or not. For borrowers who can�t a¤ord to make both their

loan and insurance payments, the lender would generally prefer to receive an additional $100

in loan payments instead of having their borrowers give that $100 to an insurance company.

Second, since uninsured accidents are grouped together with vehicle con�scations and some

mechanical failures in my data, it is di¢ cult for me to estimate exactly how many borrowers

experience uninsured accidents.

I de�ne bad behavior simply as disappearing with the car in the event of default. This

de�nition has several desirable features. First, this behavior is directly observable by the

lender and is not confounded by any underlying uncertainty. Second, the behavior would not

occur if the borrowers�incentives were aligned with those of the lender. Third, it imposes

clear costs on the lender and the other participants in the market.7

Based on the above de�nition, I �nd that 28.4 percent of defaulters are observed to

partake in bad behavior. Because I do not observe the post-default behavior of borrowers

who pay in full, I cannot compute a point estimate of the fraction of borrowers in the market

who will disappear without additional assumptions. Under the assumption that borrowers

who will disappear are at least as likely to default as those who will not, this provides an

upper bound on the total fraction of borrowers who may disappear. I can also calculate a

lower bound on this fraction by assuming that all borrowers who would disappear in the event

of default do in fact default. In this case, 17 percent (equal to 28.4 percent of defaulters who

disappear times 60 percent of defaulted loans) of all borrowers will disappear. Table 4 shows

how the personal characteristics of borrowers who disappear compare to borrowers who do

not. The table shows that borrowers who disappear appear similar based on observables to

borrowers who default but don�t disappear, though they do di¤er somewhat from borrowers

7A more stringent de�nition of bad behavior would include only borrowers that disappeared with theircar even when they had the ability to repay their loan, but I cannot distinguish these borrowers from thosewho disappear only in response to negative �nancial shocks in the data.

14

who pay in full.

Having de�ned bad behavior, the next question I seek to answer is: what is the e¤ect of

bad behavior on interest rates in this market? To answer this question, I need to quantify

the two primary impacts that this behavior has on lending outcomes: its e¤ect on recovery

costs and its e¤ect on the repayment incentives of borrowers. The latter requires a structural

model of repayment behavior, which I develop in the next section.

4 Empirical Model

In this section, I develop and estimate a stylized model of borrower repayment behavior.

The goal of the model is to estimate the underlying structural parameters of the borrower�s

repayment problem, which I will assume are invariant under counterfactual policies that

alter borrowers�bene�ts of disappearing with their car. The model has two key features.

First, borrowers derive utility from two sources: consumption and use of their car. Second,

in the spirit of Ja¤ee and Russell (1976), borrowers are assumed to be one of two types.

Borrowers of the �rst type return their car immediately upon default and receive utility only

from consumption of income after default. Borrowers of the second type are able to extract

value from the car in the event of default. While this is a stylized description of behavior

in this market, and it would be possible to estimate signi�cantly more complex models of

borrower repayment behavior than the one presented here, I chose this model because it best

matches the content of the data.

4.1 A Model of Repayment Behavior

I model the borrower�s repayment problem as a �nite horizon dynamic programming problem

with T periods. In each period t 2 f1; :::; Tg, borrower i makes a discrete choice dit 2 f0; 1gabout whether or not to continue making payments on his loan. If he chooses dit = 0, he

defaults and obtains a terminal value. If he chooses dit = 1, he makes his tth payment

and continues to the next period, until the loan is paid in full in period T . Each period t

represents a scheduled payment period, and T is the term of the loan.

15

A borrower�s �ow utility in period t depends on his choice of repayment behavior. If the

borrower chooses to make a payment in period t, he keeps the car and receives �ow utility

Uit(dit = 1) = vit + u(yit �mi); (1)

where vit is the consumption value of the car in period t, yit is the borrower�s residual

income, and mi is his scheduled loan payment. The function u(�) gives the utility from non-car consumption and is assumed to be increasing and concave, and to satisfy the boundary

condition u0(0) =1.If the borrower chooses to default, his utility depends on his type !i, which determines

whether he can derive utility from the car in the event of default. I assume that the amount

of utility that borrowers who disappear are able to extract from the car in the event of default

is equal to a constant � times the full consumption value of the car. This characterization is

consistent with my empirical �nding that borrowers who disappear keep their cars for several

months after defaulting, but is easier to work with analytically than assuming borrower�s

derive full utility from the car for K periods before it is recovered.8 Borrower�s �ow utility

functions in the event of default are given by:

Uit(dit = 0) =

8<: u(yit) if !i = Return

�vit + u(yit) if !i = Disappear: (2)

With these �ow utilities, the borrower�s dynamic problem can be written recursively as:

Vit(zit; �) = maxdit2f0;1g

fUit(zit; dit; �) + �E [Vit+1(zit+1; �) j zit; dit; �]g ; (3)

where zit = (!i; Li; yit; vit) is a vector of state variables with Markov transition probabilities

given by F!(zi;t+1jzit; dit; �), � is a vector of parameters governing the �ow utilities and statetransitions, and � is the borrower�s discount factor. The borrower�s type !i and per-period

payment amount mi are assumed to be constant over time, but yit and vit can vary over

time either deterministically or stochastically and may be serially correlated. The transition

8In fact, the two characterizations are identical; it is straightforward to write � in terms of K, theborrower�s discount factor, and the depreciation rate of the car�s value.

16

probabilities F!(�) may depend on the borrower�s type. Speci�c state transitions for yit andvit are discussed in Section 4.2.

To complete the model, I must de�ne the terminal values that borrowers receive when

they exit the game, either through full payment or default. These terminal values are de�ned

by the �ow utility fuctions above. The terminal value that a borrower receives from full

payment in period T is given by:

V PAIDT+1 =

1X�=T+1

���T [vi� + u(yi� )] ; (4)

The terminal values for borrowers who default and return their cars and borrowers who

default and disappear with their cars in period t are given by, respectively:

V DEFt+1 =

8>><>>:1P

�=t+1

���t [u(yi� )] if !i = Return1P

�=t+1

���t [�vi� + u(yi� )] if !i = Disappear. (5)

This model of repayment behavior has several desirable properties. First, the model is

theoretically consistent with two pieces of empirical evidence presented in Adams, Einav,

and Levin (2008) and Einav, Jenkins, and Levin (2008a): the prevalence of early defaults

and the existence of moral hazard in the sense that, other things equal, borrowers with large

loans are more likely to default. Borrowers in the model are more likely to default early

in their loan term for two reasons: the selection of less risky borrowers (i.e. those with

higher incomes or car valuations) over the loan term and the increasing option value of full

payment. Conditional on an income and car value process, borrowers are also more likely to

default on larger loans, as larger loans decrease the borrower�s utility from payment relative

to that from default. Second, conditional on an income and car value process, borrowers

who disappear are more likely to default, and their probability of default is increasing in the

consumption they derive from the car after default.

Third, the model can be interpreted in terms of default costs instead of vehicle consump-

tion values. The �ow utility equations introduced above can be rewritten as: Uit(dit = 1) =

u(yit�mi) and Uit(dit = 0) = u(yit)� (1� �)vit, where (1� �)vit is the cost of default. Bor-rowers who disappear can be viewed as those with lower default costs. This renormalization

17

makes the model applicable to unsecured loans in addition to loans with collateral.

4.2 Econometric Speci�cation

The goal of the econometric model is to estimate the parameters of the borrower�s decision

problem and the distribution of types !i. As discussed above, I assume this distribution is

discrete with two points of support. The fraction of borrowers who disappear in the event of

default is given by the parameter �. In the remainder of this section, I specify the transition

probabilities F!(vi;t+1; yi;t+1jvit; yit; dit; �) and the functional form of the utility function u(�).The theoretical model presented above includes two state variables that vary over time

and are unobserved by the econometrician: the borrower�s utility from using his car vt and

his income yt. While borrowers may default due to negative shocks to either car value or

income, my data does not allow me to separately identify the distributions of these shocks.

To resolve this issue, I make two assumptions about vt. First, I assume that vt is equal to

a known function of the market value of the car, or vt = �v�t , where v�t represents the car�s

market value in dollars in period t. The parameter � represents the marginal utility that

the borrower derives from an additional dollar of market value of his car and is estimated in

the model.

Second, I assume that the market value of each car declines at a known depreciation

rate �, unless the borrower experiences a vehicle failure (e.g., an accident or breakdown), in

which case v�t = 0. Since initial market values v�0 are observed, these assumptions allow me

to treat vt as observed for all t. The transition equation for car market values is given by

v�it+1 =

8<: 0 with probability qt

(1� �)v�it with probability 1� qt: (6)

where qt is the probability of a vehicle failure in period . The depreciation rate and failure

probabilities are estimated outside of the model using observed depreciation rates and vehicle

failure frequencies. An assumption of the model is that these parameters are the same for

borrowers who return their cars and those who disappear. I discuss this assumption further

in the next section.

With this speci�cation, the state variable vt captures changes in the borrower�s marginal

18

utility of car consumption resulting from mean level vehicle depreciation and random vehicle

failure shocks. All other shocks that may a¤ect the borrower�s marginal utility of using his

car are captured in the unobservable term yt. As a result, yt in the econometric model should

not be interpreted strictly as income, but rather as an econometric error term that captures

all unobservables a¤ecting the borrower�s marginal utility of making his loan payment in

period t. In addition to unobservable car value shocks, these unobservables may include

shocks to income or expenses, or access to other forms of credit.

For the purpose of estimation, I assume that yt follows a stochastic process given by:

ln yit+1 =

8<: ln yit + �R"it if !i = Return

ln yit + �D"it if !i = Disappear: (7)

where the innovations "it � N(0; 1). This parameterization of the yt distribution incorpo-

rates two important features. First, yt is serially correlated, meaning borrowers with a high

marginal utility of payment in period t are also likely to have a high marginal utility of

payment in period t + 1: Second, the transition probabilities for yt may vary by type. This

assumption allows for the possibility that borrowers who are prone to disappearance may

have di¤erent likelihoods of default than other borrowers, even if their ability to disappear

were eliminated. Borrowers in the model are assumed to know their type and their respective

transition probabilities in all periods.

I make two additional assumptions to complete the econometric model. First, I assume

that the utility function u(�) = ln(�). While it would be possible to estimate a more �exibleutility function (e.g., CES), since yt is unobservable, changes in the utility function are not

identi�ed separately from changes in the transition probabilities for yt. Second, I assume,

rather than estimate, the borrowers�annual discount factor . I report results for biweekly

discount factors ranging from 0.99 (equivalent to annual discount factor of 0.77) to 0.80

(annual discount factor of 0.003). The low discount factors are based on the �ndings of

Skiba and Tobacman (2008), who estimate biweekly exponential discount factors of 0.72 to

0.85 for payday loan borrowers, a population that is likely to be similar to the one under

study here.9

9Skiba and Tobacman (2008) also present evidence that payday loan borrowers�behavior is consistent

19

4.3 Identi�cation and Estimation

The model is estimated using data on observed payment decisions dit for borrowers i 2f1; :::; Ng in periods t 2 f1; :::; Tg10, borrower types conditional on default (!ijdit = 0),

payment amounts mi, and initial per-period residual incomes yi0 and car values in dollars

vi0 recorded at the time of sale. The observed payment decisions de�ne a time to default

for each borrower given by: si =Pt

dit, where dit = 1 if the borrower makes a payment in

period t and dit = 0 if the borrower defaults in or before period t. Combined with the data

on borrowers�actions following default, these default times yield an observed distribution

of default times for borrowers who return their cars and for those who disappear. Kernel

density estimates of these distributions are shown in Figure 1.

The parameters of the model, � = (�; �; �; �2R; �2D), are identi�ed by the observed dis-

tributions of default times for both types of borrowers. The distribution of default timing

conditional on default for borrowers who return their cars identi�es the two parameters that

enter their decision problem: their income shock variance, �2R, and the marginal utility of a

dollar of car value, �. The distribution of default timing conditional on default for borrowers

who disappear identi�es two additional parameters: their income shock variance, �2D, and

the expected fraction of car value retained from disappearing, �. The �fth parameter �the

fraction of borrowers who would disappear in the event of default, � �does not a¤ect this

shape and is identi�ed from the total number of defaults of each type.

Several assumptions a¤ect identi�cation and estimation of the model�s parameters. First,

the model assumes that the marginal utility derived from an additional dollar of the car�s

market value, �, is the same for both types of borrowers. Data on default times and fre-

quencies e¤ectively identi�es di¤erences in the utility derived from the car�s market value

for both types of borrowers in payment and default, or �R and (1 � �)�D. As such, theassumption that �R = �D is not restrictive, but permits my interpretation of the parameter

� as the expected fraction of the car�s value that borrowers who disappear expect to retain

with partially naive quasi-hyperbolic discounting, rather than exponential discounting. Incorporating non-exponential discounting is a possible extension of my model.10The model must be estimated separately for borrowers with di¤erent payment schedules (i.e., biweekly,

weekly, semimonthly, monthly) and loan terms. Reported results are for biweekly loans with a 42-monthloan term.

20

in the event of default.

Second, I assume that the vehicle depreciation rate and discount factor are the same

for both types of borrowers. These two parameters serve the same function in the model;

they both discount the amount of utility that borrowers derive from using their car in future

periods. If borrowers who disappear have higher vehicle depreciation rates or higher discount

rates (i.e., lower �) than those who return their cars, then my estimate of may overstate

the bene�t that these borrowers expect to derive from their cars in the event of default.

Intuitively, this is true because if borrowers�option value from repayment decreases through

higher depreciation or discounting, their current period bene�ts of repayment must increase

for the model to match observed repayment patterns. Higher current period bene�ts of

repayment equate to lower �.

Third, I assume that the vehicle failure probabilities are the same for both types of

borrowers. If borrowers who are prone to disappearance are also more likely to experience

vehicle failures such as accidents and breakdowns, then my estimates will underestimate

the fraction of borrowers who would disappear in the event of default. Moreover, since as

with higher depreciation rates, higher vehicle failure probabilities lower the option value

of repayment, this assumption may also lead to an overestimate of the parameter �. In

addition to a¤ecting the parameter estimates, the assumption that both types of borrowers

have the same vehicle failure probabilities, may a¤ect my estimates of the costs imposed by

disappearing borrowers. For instance, if these borrowers are also more likely to experience

high cost vehicle failures, such as uninsured accidents and vehicle con�scations, then my

results will also underestimate the impact of these borrowers on market interest rates.

I also note that these parameter estimates do not account for the selection of borrowers

into my sample. My estimate of �, for example, gives the fraction of borrowers that will

disappear in the event of default, not the fraction of applicants who would have done so had

they taken out a loan. If applicants who are prone to disappearance are also more likely to

borrow from this lender, my estimate will overstate the fraction of subprime auto borrowers

who will disappear in the event of default. Similar biases may exist for the other parameters.

I discuss the issue of selection further in Section 6, when I compute counterfactual interest

rates in which borrowers�ability to disappear is reduced or eliminated.

21

The goal of estimation is to recover the structural parameters: � = (�; �; �; �2R; �2D). I

estimate these parameters using the Method of Simulated Moments, as developed by McFad-

den (1989) and Pakes and Pollard (1989). The moments I match are the expected number

of defaults of each type that occur in K = 15 non-overlapping periods during the loan term

(for a biweekly loan with a 42-month term, each period equates to 12 weeks). Formally, each

moment is given by:

mk! =

1

N

NXi=1

1f!i = !; si 2 [(k � 1)TK

;(k)T

K)g; (8)

where ! 2 fR;Dg, k 2 f1; :::; Kg, K is the total number of moments for each type, T is

the term of the loan, and si the number of per-period payments made by borrower i before

default. This moment de�ntion yields 2K = 30moments (15 for defaults followed by a return

and 15 for defaults followed by disappearance). Matching all 30 moments is equivalent to

matching a histogram of default timing with K buckets for both types of default..

Estimation proceeds as follows. For each parameter draw �m, I compute the solution to

the dynamic game for all possible states in a discretized approximation of the state space.

I then simulate J = 1000 income and car value paths for all borrowers in my sample and

compute borrowers�simulated decisions in periods 1 through T . These simulated decisions

allow me to compute analogues to the empirical moments described above. The simulated

moments are given by:

mk!(�) =

1

N � J

JXj=1

NXi=1

1f!ji = !; sji 2 [

(k � 1)TK

;(k)T

K)g; (9)

where !ji and sji are the simulated analogs to !i and si above. I then seek the parameter

vector � which minimizes the weighted sum of squared di¤erences betwen the empirical

moments mk! and their simulated analogues m

k!(�); that is, I seek the � that minimizes the

objective function:

[mk! � mk

!(�)]0�1[mk

! � mk!(�)] (10)

where �1 is an (optimal) weighting matrix. In practice, I set = I:

22

5 Results

In this section, I discuss the results of the estimated repayment model. I divide the discussion

into two parts. First, I compare the simulated moments �t of the model to observed data on

the number and timing of defaults, Second, I discuss the estimates of the model�s 1structural

parameters.

5.1 Model Fit

The parameters of the model are estimated by matching 30 moments given by the fraction

of loans that end in defaults followed by returns and disappearance in each of �fteen 12-week

periods. Figures 2(a) and 2(b) show these moments in the form of a default timing histogram

for both types of defaults. The �gures show that the model reasonably matches observed

patterns of default timing, though there are some features of the data that the model does

not match particularly well. First, the model over-predicts the frequency of late defaults for

borrowers who return their cars. One reason for this might be that borrowers receive an

additional bene�t from repaying their loan beyond the full value of the car (e.g., paying the

loan in full may have a favorable impact on a borrower�s credit score), and that this bene�t

becomes particularly salient near the end of their loan term. Such a bene�t is currently not

included in the model. Second, the model fares poorly at matching the non-monotonicities

in the pattern of default timing for borrowers who return their cars. I am currently unaware

of a reason that these non-monotonicities exist, and developing a model that captures them

would add considerable complexity to the model.

5.2 Parameter Estimates

Table 5 presents estimates of the model�s structural parameters under the assumptions de-

scribed in the previous section. The fraction of borrowers who derive utility from disappear-

ing with their cars in the event of default is estimated to be 25 percent.11 This estimate

falls within the bounds of 17.0 percent and 28.4 percent computed in Section 3.3. The lower

bound corresponds to the case in which borrowers who are prone to disappearance default

11The discussion of results in this section assumes a biweekly discount factor of 0.99.

23

with probability one. In this case, the fraction of these borrowers in the sample is equal to

the number of observed defaults followed by disappearance divided by the total number of

borrowers, or 17.0 percent (see Table 2). The upper bound corresponds to the case in which

these borrowers default with the same probability as those who return their cars, meaning

the fraction of these borrowers in the sample is equal to the number of observed defaults

followed by disappearance divided by the number of total defaults, or 28.4 percent. Since

the point estimate from the structural model is closer to the upper bound, this suggests that

the probability of default for borrowers who disappear in the model is closer to the default

probability of borrowers who return their cars than it is to one.

There are two reasons why borrowers who disappear and those who do not may have

similar default probabilities. The �rst is that they may have similar income volatilities, and

the second is that borrowers who disappear may not derive much (expected) utility from

their cars in the event of default. I estimate that the variance of the shocks in the income

process, with income in thousands of dollars per biweekly period, is 0.062 for borrowers who

do not disappear and 0.071 for those who do. In dollar terms, these estimates suggest that

borrowers who do not disappear behave as if their standard deviation of biweekly income

shocks is about $250, or about 20 percent of average biweekly income. The equivalent

measure for borrowers who disappear is $270.

As noted above, because of the simpli�ed nature of the borrower�s decision problem,

these estimates are not representative of the true volatility of income for subprime auto

loan borrowers. In fact, my estimates may either understate or overstate income volatility.

Because my model does not allow borrowers to save or borrow, this behavior, to the extent

it is used to smooth consumption, may lead to estimates of a stochastic process that is

less volatile than the underlying income process. My estimates may also overstate income

volatility because, as estimated, my income process includes all non-car-value shocks that

may lead a borrower to default, not only shocks related to income.

I estimate the fraction of car value that borrowers who disappear expect to retain in

the event of default to be 39.7 percent. With an annual discount rate for borrower utility

of 23 percent and a vehicle depreciation rate of 12 percent, this equates to an expectation

of 15 months of car usage after default for borrowers who disappear. Since borrowers who

24

disappear are able to retain possession of the car for an average of approximately 4 months,

this estimate suggests that most borrowers who disappear do not have rational expectations

about their likelihood of successfully hiding the car from their lender. The �nal parameter

of the model, the per-period marginal utility that borrowers receive from each dollar of car

value, is estimated to be 1.338.

6 The Costs of Bad Behavior

Having computed estimates of the fraction of subprime auto borrowers who are likely to

disappear in the event of default, I next seek to quantify the externality that these borrowers

impose on the other borrowers in the market, as measured by the e¤ect of this behavior on

break-even interest rates. I proceed in two steps. First, I describe how to compute the

lender�s break-even interest rate, and derive the lender�s pro�t function that gives rise to it.

Second, I compute counterfactual interest rates under two scenarios in which disappearing

behavior is eliminated.

6.1 Lender Pro�ts

The lender�s expected pro�ts for an applicant depends on the applicant�s type ! and the

lender�s o¤ered interest rate r and collections policy �. Expected pro�ts from each applicant

are a function of �ve components: (i) the applicant�s probability of sale G(r; �; !), (ii) down

payment DP (r; �; !), (iii) expected loan payments PMT (r; �; !), and (iv) expected net

recoveries REC(r; �; !), and (v) the cost of the car C. The expected pro�ts from lending to

a borrower of type ! is given by:

�(r; �; !) = G(r; �; !) � [DP (r; �; !) + PMT (r; �; !) +REC(r; �; !)� C]. (11)

Total �rm expected pro�ts are then given by:

�(r; �) =Xi

[��i�(r; �;D) + (1� ��i )�(r; �; R)]� F , (12)

25

where the probability that an applicant will disappear in the event of default is denoted ��i

and the �rm�s �xed costs are denoted by F . I assume that the break-even interest rate is

that which sets total expected �rm pro�ts equal to zero. Existing interest rates allow me

to back out the level of �xed costs F , which I then use to compute zero-pro�t rates under

counterfactual policies toward disappearing behavior.

As suggested by the equation for expected pro�ts per applicant, policies toward disap-

pearing behavior can a¤ect lender pro�ts through four channels. First, through their di¤ering

e¤ects on the probability of sale for each type, such policies may a¤ect the fraction of bor-

rowers who are prone to disappearance. Second, these policies may impact the borrower�s

choice of down payment D. Third, they may a¤ect the expected �ow of loan payments for

borrowers who would disappear in the event of default. This e¤ect occurs because changing

these borrowers�ability to disappear with the car changes their incentives to repay, and thus

the expected number of payments they will make. Fourth, policies that impact disappearing

behavior may a¤ect expected recovery values net of collections costs.

In what follows, I focus on the latter two e¤ects. The borrower�s decision about whether

or not to purchase a car, and conditional on purchase, how much to put down are made at the

time of sale and are not modeled explicitly in this paper (see Adams, Einav, and Levin (2008)

and Einav, Jenkins, and Levin (2008a) for additional details about these decisions). One

advantage of my structural model is that it allows me to separately quantify the payment

incentive and recovery value e¤ects of bad behavior on interest rates. I also quantify an

additional e¤ect that results from the fact that the lower interest rates that result from the

elimination of bad behavior lead to still lower default rates due to the e¤ect of payment size

on default.

6.2 Counterfactuals

I evaluate two counterfactuals. In the �rst, I consider the e¤ect on market interest rates of

policies that reduce or eliminate borrowers�bene�t from disappearing with their cars in the

event of default. In terms of the model developed in the previous section, this equates to

reducing the magnitude of the parameter �. In practical terms, such policies might include,

at the �rm level, introducing technology that allows the lender to quickly locate the car

26

(e.g., a satellite tracking device), or at the public policy level, increasing the penalties from

disappearing, either through recording this behavior at the credit bureaus, which imposes

an additional cost of this behavior because it can restrict borrowers�future access to credit,

or through stricter explicit legal penalties.

In the second counterfactual, I consider the e¤ects of screening disappearing borrowers

from the market. This counterfactual is similar to the �rst, but incorporates an additional

e¤ect; namely, since borrowers who disappear have more volatile incomes than those who

do not, screening these borrowers from the market decreases default rates more than sim-

ply eliminating their bad behavior. I consider the e¤ect of �perfect�screening in which all

disappearing borrowers are screened from the market. In terms of the model, this counter-

factual equate to removing all borrowers were observed to disappear with their cars after

defaulting and assuming all other borrowers would not disappear. While this counterfactual

would be di¢ cult to reach in practice, it provides a measure of the size of the externality

that borrowers who are prone to bad behavior impose on others in the subprime auto loan

market.

The results of the counterfactual simulations are presented in Table 6. The table shows

that zero-pro�t interest rates would be reduced 22 percent and 24 percent, respectively,

in the two counterfactuals in which disappearing behavior was eliminated. The table also

shows that the primary impact of eliminating disappearing behavior is through increasing

the lender�s net recovery in the event of default. This e¤ect accounts for nearly 75 percent of

the total reduction in interest rates that would result by eliminating disappearing behavior.

The e¤ect of eliminating this behavior on expected loan payments, due either to changes in

incentives or due to screening out disappearing borrowers with higher income volatilities, is

considerably smaller.

7 Conclusion

This paper studies the impact of borrower behavior on lending outcomes in the market

for subprime auto loans. I present unique evidence on subprime borrowers� reasons for

default and their behavior in the event of default, and show that certain types of behavior,

27

in particular disappearing with one�s car, impose high costs on the lender. I quantify

these costs and demonstrate that if this behavior were eliminated, interest rates could fall

by as much as 20 percent. This �ndings suggest that policies that reduce the bene�ts of

disappearing or improve lenders�ability to screen borrowers who are likely to disappear from

the market could have substantial welfare e¤ects. One policy that could accomplish these

goals is credit bureau reporting that includes information not only about whether a borrower

defaulted but how he behaved after default.

This paper also sets the stage for future work on understanding consumer repayment

behavior in this and other consumer credit markets. It is the �rst paper to my knowledge

to apply a structural dynamic discrete choice model to borrowers�repayment decisions on

individual consumer loans. This methodological approach presents a promising way to ad-

dress a number of questions about consumer lending, including how to set optimal contract

terms and design optimal collections, deferment, and loan modi�cation policies. Better un-

derstanding the trade-o¤s inherent in modifying existing loans, in particular, would be of

interest in the current mortgage market. Another bene�t of the approach is that it provides

a framework for evaluating consumer welfare, though this would require that the model be

extend to the time of purchase. This is an area for future work.

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29

Table 1: Summary Statistics

Obs* Mean Std. Dev. 5% 95%

Borrower CharacteristicsAge N 34.4 10.8 20 54Monthly Income N 2,487 1,050 1,378 4,500FICO Score > 600 N 0.20 - - -No FICO Score N 0.17 - - -Home Owner N 0.17 - - -Live With Parents N 0.15 - - -Bank Account N 0.75 - - -

Vehicle Characteristics Total Cost N 5,790 1,181 3,965 7,549 Car Age (years) N 4.6 1.9 2.0 8.0 Odometer N 72,156 22,576 31,993 104,868 Lot Age (days) N 35 47 1 127 Car Price N 10,330 1,613 7,995 12,949

Loan Terms Down Payment N 904 541 400 2,000 Loan Amount N 10,293 1,673 7,777 12,989 Interest Rate (APR) N 26.8 4.1 17.8 29.9 Loan Term (months) N 40 4 34 42 Monthly Payment N 388 48 310 467

Loan Outcomes Default N 0.60 - - - Fraction of Pmts Made (if default) 0.60N 0.35 0.25 0.04 0.86 Car Recovered (if default) 0.60N 0.88 - - - Days to Recover (if recovery) 0.53N 75 125 9 303 Recovery Value (if recovery) 0.53N 2,202 1,558 305 4,879

Notes: * To preserve the confidentiality of the company that provided the data, we do not report the exact number of loans.All values based on uncensored loans originated between June 2001 and December 2003.

Table 2: Reasons for Default

Percent of All Loans

Percent of Defaults

[1] [2]

Financial Problemsa Loss of Income 4.1 6.9 b Other Life Events * 2.8 4.7 c Overextended Debt 9.3 15.6 d Bankruptcy 5.0 8.4

21.2 35.5 Vehicle Failure

e Accident / Stolen with Insurance 4.6 7.6 f Mechanical Problem 5.1 8.5 g Abandoned / Confiscated ** 11.9 20.0

21.6 36.1 Unknown

h Disappear with Car 17.0 28.4

Total 59.8 100.0

Notes: (a) Reported by borrower, not verified by lender.(b) Reported by borrower. Includes death, divorce/separation, and legal problems.Death and some legal problems verified by lender.(c) Reported by borrower, not verified by lender.(d) Reported by borrower and verified by lender.(e) Directly observed by lender. Lender collects insurance claim.(f) Directly observed by lender.(g) Directly observed by lender. Includes three types of vehicle failure: uninsuredaccidents, cars abandoned due to mechanical failure, and cars impounded for legalreasons (e.g., parking tickets).(h) Directly observed by lender. Borrowers are classified as disappearing if theyhave defaulted, have not been in contact with the lender for 20 days, and cannot belocated at their listed residence or place of work. No underlying reason fordisappearing is recorded.

Table 3: Recovery Outcomes

Percent of Defaults

Probability of Vehicle Recovery

Months to Recovery

Recovery as Pct. of Initial

Cost[1] [2] [3] [4]

Post-Default Behaviora Return Car 15.0 1.00 0.9 0.40 b Wait for Repossession 12.2 0.98 1.0 0.31 c File for Bankruptcy 8.4 0.90 5.9 0.47 d Disappear with Car 28.4 0.97 4.0 0.10

Vehicle Failuree Accident / Stolen with Insurance 7.6 1.00 1.0 0.80 f Mechanical Problem 8.5 0.99 0.9 0.31 g Abandoned / Confiscated ** 20.0 0.51 0.9 0.14

Total 100.0 0.88 2.2 0.28

Notes: [1]: For (a) and (b), the sum of values in this column equals the sum of (a), (b), and (c) in Table 2, column [2]. For (c)through (g), values equal the corresponding values in Table 2, column [2]. [2]: Probability that a car with a nonzero resale value was recovered. [3]: Average number of months between the date of default and the date the recovered car was sold at auction.Approximately 1 month is due to a lag between the time when the lender takes possession of the car and when it resells it. Months beyond the first reflect additional time it takes for the lender to find and repossess the car.[4]: Average value of recovered car, not conditional on recovery, minus collections costs. Collections costs arecalculated assuming a constant monthly rate and average collections costs of $1200. Values are reported as a percentof the initial cost of the car.

(a) Car voluntarily returned by borrower (e.g., borrower dropped car off at dealership).(b) Car repossessed involuntarily at known place of residence.(c) Car repossessed through bankruptcy proceedings (same loans as Table 2, row (d)).(d) Car repossessed involuntarily after locating missing borrower (same loans as Table 2, row (h)).(e) Same as Table 2, row (e).(f) Same as Table 2, row (f).(g) Same as Table 2, row (g).

Table 4: Borrower Characteristics by Behavioral Group

Payers

Defaulters Who Don't Disappear

Defaulters Who

Disappear

P-Value for Columns[2] vs. [3]

[1] [2] [3] [4]

Personal CharacteristicsAge 35.3 34.2 33.1 0.000Income ($/month) 2,564 2,461 2,395 0.000Home Owner 0.19 0.17 0.12 0.000Lives w/ Parents 0.14 0.15 0.16 0.000Bank Account 0.79 0.74 0.70 0.000Has Dependents 0.32 0.35 0.34 0.009

Credit VariablesFICO Score (if avail.) 472 438 413 0.000No FICO Score 0.16 0.17 0.18 0.000Recent Credit Inquiries 7.2 8.4 8.2 0.028 Debt to Income Ratio 39.3 43.6 44.1 0.480 Proprietary Credit Grade

Low Risk 0.40 0.27 0.21 0.000Medium Risk 0.43 0.50 0.51 0.000High Risk 0.17 0.24 0.28 0.000

Choice BehaviorCar Cost 5,854 5,743 5,751 0.185 Down Payment 981 909 886 0.000Put Minimum Down 0.41 0.52 0.53 0.000

Notes: [1]: All borrowers who paid loan in full (40.2 percent)[2]: All borrowers who defaulted and did not disappear, including car failures (42.8 percent)[3]: All borrowers who defaulted and disappeared (17.0 percent)[4]: P-value of difference in means between columns [2] and [3].

Table 5: Parameter Estimates

Estimate Std. Err. Estimate Std. Err. Estimate Std. Err.[1] [2] [3] [4] [5] [6]

ParametersFraction of bad types (π) 0.250 (0.025) 0.238 (0.024) 0.251 (0.026)Variance of income shocks (R) 0.062 (0.006) 0.040 (0.004) 0.036 (0.006)Variance of income shocks (D) 0.071 (0.009) 0.058 (0.007) 0.059 (0.005)Car value utility (α) 1.338 (0.081) 1.882 (0.114) 2.039 (0.129)Default value for bad types (φ) 0.397 (0.071) 0.327 (0.059) 0.328 (0.052)

Biweekly discount factor β = 0.99 β = 0.90 β = 0.80

Notes: Point estimates and standard errors based on simulated method of moments estimator (see Section 4.4), assuming annual vehicledepreciation rate of 0.12. Biweekly discount factors equate to 0.77, 0.06, and 0.003 annual discount factors, respectively.

Table 6: Counterfactuals

Counterfactual A:Elimination of Bad

Behavior

Counterfactual B:Perfect Screening of Bad

Borrowers[1] [2]

Existing Average APR 26.0 26.0

Decomposition of APR ReductionRecovery Effect (4.3) (4.3)Incentive Effect (0.4) (0.4)Income Variance Effect n/a (0.3)Payment Size Effect (1.1) (1.1)

Counterfactual Average APR 20.2 19.8Percent Change from Existing (22%) (24%)

Notes: [1]: Counterfactual A considers the effect of eliminating borrowers'ability to disappear with their cars in the eventof default. In terms of the model presented in Section 4, this equates to setting φ=0 .[2]: Counterfactual B considers the effect of screening all borrowers who would disappear with their cars in theevent of default from the market. This is similar to Counterfactual A, but incorporates an additional effectresulting from the fact that good and bad borrowers have different income processes.Both counterfactuals computed using biweekly discount factor of 0.99.

Figure 1: Kernel Density of Default Timing by Type of Default, Conditional on Default

0.0

0.5

1.0

1.5

2.0

2.5

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Fraction of Payments Made

Den

sity

Defaults followed by ReturnDefaults followed by Disappearance

Notes : Based on raw data for all loans. The solid line gives the density of default timing for loans that defaulted and were followed by a car return. The dashed line gives the density ofdefault timing for loans that defaulted and were followed by a car return. Fraction of payments made before default is equal to the total # payments made / total # of payments due.

Figure 2(a): Timing of Defaults Followed by Return

0.00

0.01

0.02

0.03

0.04

0.05

0.06

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Period (12 Weeks)

Perc

ent o

f All

Loan

s

ActualModel

Figure 2(b): Timing of Defaults Followed by Disappearance

0.00

0.01

0.02

0.03

0.04

0.05

0.06

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Period (12 Weeks)

Perc

ent o

f All

Loan

s

ActualModel

Notes : Based on raw data and model output for all loans. Each bar in Figure 2(a) gives the fraction of all loans in the sample thatdefaulted in a given 12-week period and were followed by a car return (including defaults due to vehicle failure, such as accidents ormechanical problems). Each bar in Figure 2(b) gives the fraction of all loans in the sample that defaulted in a given 12-week period andwere followed by a disappearance. Bars represent raw frequencies, not conditional on default. Those labeled "Actual" give observedfrequencies, and those labeled "Model" give simulated at outcomes at the estimated parameter values in Table 5.