BANKRUPTCY AND DELINQUENCY IN A MODEL OF UNSECURED DEBT

• Author: Kartik Athreya,Xuan S. Tam,Eric R. Young,Juan M. Sánchez
• Date: 01 May 2018
• DOI: http://doi.org/10.1111/iere.12281
• Published date: 01 May 2018

INTERNATIONAL ECONOMIC REVIEW

Vol. 59, No. 2, May 2018 DOI: 10.1111/iere.12281

BANKRUPTCY AND DELINQUENCY IN A MODEL OF UNSECURED DEBT∗

BYKARTIK ATHREYA,JUAN M. S ´

ANCHEZ,XUAN S. TAM,AND ERIC R. YOUNG 1

Federal Reserve Bank of Richmond,U.S.A.; Federal Reserve Bank of St. Louis,U.S.A.; City

University of Hong Kong, Hong Kong SAR; University of Virginia,U.S.A., and Zhejiang

University, China

This article documents and interprets a fact central to the dynamics of informal consumer debt default. We

observe that for individuals 60– 90 days late on payments, (i) 85% make payments during the next quarter, and

(ii) 40% reduce their debt. To understand these facts, we develop a quantitative model of debt delinquency and

bankruptcy. Our model reproduces the dynamics of delinquency and suggests an interpretation of the data in

which lenders frequently reset loan terms for delinquent borrowers, typically offering partial debt forgiveness,

instead of a blanket imposition of the “penalty rates” most unsecured credit contracts specify.

1. INTRODUCTION

Consumer debt delinquency, whereby borrowers delay debt repayment to smooth consump-

tion instead of invoking formal bankruptcy, is a quantitatively important phenomenon, with

open-ended delinquency accounting for up to half of all unsecured consumer debt default.

Delinquency, unlike bankruptcy, is informal default—it simply means nonpayment of debt

as initially promised. Interestingly, many borrowers classified as delinquent in a given quarter

somehow recover or improve their credit status within one quarter. This finding, detailed below,

emerges from recent credit bureau data. In particular, of individuals 60 or 90 days delinquent,

(i) 85% avoid getting past 90 days delinquent one quarter later, and (ii) 40% reduce their debt,

either because they made payments, received debt forgiveness, or both. The goal of this article is

to use data and theory to shed light on these two facts of informal default—especially to evaluate

the extent to which quantitative models of consumer default can be useful for understanding

the borrower-level short-term dynamics of delinquency.

The informality of delinquency complicates analysis and therefore the understanding of its

consequences for borrowers. In particular, a feature of many unsecured lending contracts is

a penalty rate on past-due debt.2Under such terms, a missed payment leads to an automatic

upward revision in the interest rate on existing debt. However, while most lenders might claim

to impose such rates, the proportion of consumers who face such terms is not clear, nor is it

necessarily clear to consumers. Industry observers, including consumer groups, have noted this

fact and pressed regulators to address what may constitute a violation of the 2009 CARD Act,

which places requirements on the disclosure of credit terms. As a result, an open question is

whether the data help us clearly discipline the interpretation of how borrowers are treated in

delinquency.

∗Manuscript received April 2013; revised December 2016.

1We thank the editors, Hal Cole and Dirk Krueger, for their detailed and clear guidance and four anonymous

reviewers for their extremely detailed and perceptive comments. This feedback led to very significant revisions that

we believe have greatly improved this article. We also thank Lijun Zhu and Helu Jiang for their research assistance in

the empirical part of the article. Please address correspondence to: Juan M. S´

anchez, Federal Reserve Bank Plaza, 1

Broadway, St. Louis, MO 63102. Phone: 8044264836. E-mail: vediense@gmail.com.

2Indeed, this structure is precisely how informal default was modeled in the early work on consumer debt default of

Livshits et al. (2007).

593

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(2018) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

594 ATHREYA ET AL.

Progress on this question first requires distilling data to capture key attributes. A primary

contribution of our work is to collect for the first time, to our knowledge, all publicly available

data on consumer debt delinquency and then use these data to establish two stylized facts that

describe individual-level dynamics associated with delinquency. Specifically, as noted above,

we first show that delinquency does not mean a persistent cessation of payment. Second, we

detail substantial dispersion in the change in the debt of delinquent borrowers. In addition,

we assemble previously undocumented facts regarding heterogeneity in the use of delinquency

(and bankruptcy) both by income group and across the life cycle.

Once we establish the facts, we lay out a model of debt delinquency and bankruptcy that is

theoretically and institutionally plausible—relative to current practice—and that nests a variety

of specifications for what delinquency implies for borrowers and lenders. We then derive the

predictions of two important polar cases of the model. The first case is where delinquency is met

with by the imposition of an exogenous penalty rate that is applied to all delinquent borrowers.

It is motivated by the letter of the contract that, in the unsecured credit market, typically spells

out a penalty rate for any late payment relative to the contract. The second case considered

is one in which lenders choose the terms of delinquent borrowers ex post (i.e., once they are

in delinquency) to maximize the market value of delinquent debt. This case is motivated by

both empirical and theoretical considerations. Empirically, we will show that the implicit terms

experienced by delinquent borrowers frequently do not mimic the terms prescribed by ex ante

agreements to impose a penalty rate. Of course, almost by definition, such resetting of interest

rates will not coincide except by accident with terms that borrowers and lenders might arrive

at in a renegotiation. Theoretically, our approach is motivated by the simple fact that, absent

commitment to imposing such rules, one would expect to observe such terms only when they

prove ex post valuable. Thus, a second natural case is one that does not impose anything purely

punitive but instead allows lender and borrowers to always renegotiate loans.

Due to their institutional and theoretical plausibility, and for the light they shed on how

delinquency affects borrowers, these two cases are each of independent interest. However, it is

clearly important to use these cases to understand the extent to which the data are driven by

either of these two models, first in their pure form and then when they are allowed to coexist. We

therefore provide, along with the development of each of the two cases, a systematic assessment

of the models’ ability (and in places, the inability) to account for the facts we establish.

We show first that the pure penalty-rate specification, although superficially accurate for

most of the credit card accounts given the standard description of lender behavior in the face of

default, leads to only partially accurate implications. In particular, we show that this specification

has reasonable implications for some of the characteristics of borrowers in delinquency, but it

fails strongly to provide reasonable implications for the facts on both short-term borrowing

dynamics following delinquency and the evolution of credit terms in delinquency.

We then assess the specification that features optimal resetting of loan terms. In this case, upon

the decision by the borrower to employ delinquency, lenders propose a revised debt obligation.

We note that, although in this case, lenders nominally propose the terms of renegotiation in

a take-it-or-leave-it manner, their market power is still significantly limited. This is because

borrowers always retain the option to refinance their debts in a competitive market as well as

to file for bankruptcy. We show that, although this model better matches the facts on borrower

dynamics following a delinquency, it fails to fully reproduce the evolution of credit terms during

delinquency. Thus, a conclusion of our model is that both types of consequences play a role

in accounting for the facts. Furthermore, our approach allows the two to be tractably nested

via the presence of a single parameter that specifies the probability that, in a given instance of

delinquency, a penalty rate or optimal resetting will be applied. Our preferred model suggests a

strictly positive probability (of roughly 40%) of optimal resetting, with the remaining probability

on a direct penalty rate.

1.1. Related Literature. Our work is related to several recent papers on unsecured consumer

credit markets. To begin, our approach is tied to Athreya et al. (2015), who study the implications