Elsevier

Research in Economics

Volume 67, Issue 4, December 2013, Pages 336-354
Research in Economics

Using bounds to investigate household debt repayment behaviour

https://doi.org/10.1016/j.rie.2013.09.007Get rights and content

Highlights

  • We investigate households debt repayment behaviour using a unique source of micro-data.

  • The data records households default and arrears, but also provides information on those households who are not given credit.

  • The data allows us to avoid implausible identification assumptions and provide partial identification for the effect of various factors on household repayment behaviour.

  • Among those factors, the results highlight a role for the availability of alternative credit sources in shaping repayment behaviour.

  • Other things equal, households who can rely on the financial help of relatives and friends, are predictably worse borrowers.

Abstract

Understanding the factors that influence arrears is crucial if policy makers wish to alleviate the problems caused by debt. But conventional estimates of repayment behaviour impose implausible assumptions about lender behaviour. However, an upper and lower bound for the effect of the determinants of repayment behaviour can be estimated. Reasonable assumptions about the behaviour of economics agents narrow these bands. We use administrative data from a leading Italian lender to the household sector to demonstrate the methodology, and we show that conventional estimates under-estimate the true default probability.

Introduction

The recent turmoil in the financial markets has focused the attention of policy makers and researchers on the issue of household debt. In particular, which households repay their debts? What factors affect repayment behaviour, and how large is the effects? This paper will provide some evidence on the issue using administrative data on Italian households. It also discusses how to provide a sensible estimate of the effect of any potential factor affecting default. We show that standard procedures to assess the probability of default, and to identify the causes of repayment, are potentially biased. A naive estimate which only uses the sample of actual borrowers fails to account for the fact that borrowers differ from those refused credit. However, standard procedures (such as selection models) impose implausible economic assumptions about the behaviour of lenders. We argue that the effect of any factor can, nonetheless, be bounded. Moreover, we show that merely assuming that lenders prefer to lend to those households more likely to repay the loan will narrow these bounds.

This paper is interested in understanding the underlying propensity to default, and what factors affect default. For some purposes, such as calculating the value-at-risk, the bank needs to evaluate the likely default behaviour of current borrowers. However, when the bank is making the lending decision, it needs to understand the likely behaviour of potential borrowers in order for it to decide which credit applicants should receive the loan and which should be refused. Basing the lending decision only on information about the default behaviour of current borrowers is likely to cause poor lending decisions (for example, a major reason for the sub-prime crisis was due to extending lending to households who were, hitherto, refused credit, without understanding how their default behaviour would differ from those previously given credit).1 Our methodology indicates that estimates of default risks using only borrowers overestimate the repayment probability. Since this is a crucial variable for the lending decision, underestimation of default risks can cause unexpected losses to arise on any given credit contract.

The underlying propensity to default is also the key variable of interest to policy-makers if they want to understand how a change in the policy variable affects the behaviour of borrowers. For example, we might be interested in the availability of alternative credit sources or the effect of bankruptcy exemptions.2 However, the overall effect of the variable of interest on the observed level of default will depend on how the lender changes the lending decision, since we will only observe an actual default if the borrower receives credit. To understand the true effect on default behaviour (e.g. the underlying propensity to default) of a policy change (such as a change in bankruptcy law) requires us to account for the change in lender behaviour: we need to predict the repayment behaviour of those whose application for credit was turned down before and after the policy change.3 However, there is a fundamental problem: the repayment behaviour of those who are denied credit is not observed. This raises an identification issue akin to that arising in many areas of the program evaluation literature where potential outcomes are not observable: focusing only on the non-rejected applicants yields only a partial picture of the effect of any policy change with the bias being larger if there is a bigger difference between those who are given credit and those who are refused. The non-rejected applicants are a selected sample of the applicant population, and the sampling process is silent about the potential repayment of the rejected applicants.

We are not the first to emphasize the importance of correctly estimating the probability of default by accounting for those refused credit. For example, Boyes et al. (1989) and Jacobson and Roszbach (2003) both obtained default probabilities in a fully parametric setting. A common solution to the identification problem (e.g. not observing the default behaviour of households refused credit) is to find some exclusion restrictions: variables that affect whether the lender provides the loan, but not whether it is repaid. However, our paper differs from those earlier contributions in an important way. While in a perfect information world, lenders would be able to screen out bad risks perfectly, with hidden types or actions, some good risks are screened out, which implies that some households refused credit would have repaid, had they been given credit. However, to the extent that the lender screens out bad risks, we expect the propensity to repay to be lower among the turned down applicants. This means that any variable that predicts whether the lender provides credit will be correlated with repayment behaviour, and hence will not satisfy the requirements for an exclusion restriction; any choice of exclusion restriction is ipso facto implausible. A key contribution of this paper is that the identification strategy we describe neither relies on incredible exclusion restrictions nor on some specific functional form for the default and credit granting probabilities. Instead, we describe an alternative identification method which places upper and lower bounds on the true effect. We also show how simple, and plausible, assumptions about the behaviour of the lender (that they lend to good risks and refuse credit to bad risks) can narrow the bounds on the estimates. In our second key contribution, we show that the repayment probability obtained from the sample of borrowers is really an upper bound to the true unobserved propensity to default.

To provide evidence on the usefulness of our methodology for understanding the drivers of repayment, we use data from a leading lender of unsecured credit to the Italian household sector. Credit markets in Italy are small, but have grown rapidly over the past 20 years (see Casolaro et al., 2005). The trend is similar for consumer (non-housing) credit, which accounted for 8.1% of the GDP in 2003, and is largely unsecured. Theory predicts that incentives to repay depend crucially on how default is punished.4 There are several advantages in using lender's data to investigate the factors affecting repayment behaviour. First, since the data records the repayment history of applicants who were given credit, this allows us to observe default, which is a rare event in general household surveys. Even on the few occasions appropriate questions on default are included in such surveys, this is likely to be under-reported.5 Second, administrative data records all the variables that affect the decision to lend, while survey data typically includes only a subset of them. Third, the lender provides information on those applications that were refused. This information is crucial if one wants to draw reliable policy conclusions about household repayment behaviour, as it allows us to account for the fact that households granted credits are likely to be different from those which are refused.

In the empirical application, the paper analyses the role of several factors affecting repayment behaviour, including the quality of judicial enforcement, and the availability of informal credit markets. While the relation among credit contracts, law, and legal enforcement, is widely studied (see for instance Fay et al., 2002, Grant, 2001, Fabbri and Padula, 2004), much less has been said on the effect of non-market sources of credit. In a very different context, Banerjee and Newman (1998) show that these alternative credit sources can have important effects on development. They argue that in the formal sector informational asymmetries can be large, while they are much smaller in the informal sector in which agents behaviour can be much more easily observed: friends and family are likely to know whether people they know closely are reliable and will repay their debts. In contrast, our paper provides empirical evidence (albeit on credit to consumers not producers) showing that those types of household for which informal credit is more common are less likely to repay their debts in the formal sector, everything else being equal. Our identification method exploits the richness of the data, which provides detailed information on the characteristics of credit contracts, customers, repayment and, importantly, rejected applications. The paper confirms that a naive estimate, that neglects the lender's decision, understates default as it estimates only an upper bound to the repayment probability. Since default rates are rather low in the Italian market, our results indicate that the bias in countries, such as the US, might be considerably larger.

The rest of the paper is organised as follows. Section 2 discusses the selection issues, describes our approach to the identification of the effect of those factors that potentially influence repayment behaviour, and highlights the related data requirements. The data is presented in Section 3. Section 4 presents the results and Section 5 concludes. Details on estimation and inference and additional results are provided in Appendix.

Section snippets

The econometric model

Our aim is to investigate what drives repayment in the Italian consumer credit market, using data from a leading Italian lender. We estimate upper and lower bounds for all these drivers, and assess the factors that make a loan application likely to be rejected. To proceed, denote e as the repayment behaviour of the borrower, which takes the value one if the debt is repaid on schedule and zero if any scheduled repayment is missed. Denote by X a vector of observable characteristics that might

Data

We take data from three different sources, each described in turn. For information on borrowing, we have a unique data set which consists of a random sample of households that are in the full administrative database for the years 1996–1999 from the leading lender to the household sector in the Italian credit market. This lender specialises in non-mortgage lending to the Italian household sector, much of it (61% in our sample) via installment credit made available by the retailer at the point of

Results

The tables at the end of the paper report results for estimates of the bounds on the true effect on repayment. The upper bound, tightened upper bound, and lower bound are estimated by multivariate kernel regressions (using cross-validation to estimate the bandwidth).13

Conclusions

Using leading Italian lender's administrative data on credit applications, we are able to assess how features of the market affect repayment behaviour. Identifying the factors affecting the repayment behaviour of credit applicants is not trivial. A selection issue arises because we do not observe the repayment behaviour, had they been given a loan, of those households that are refused credit. Two popular methods for addressing selection require imposing the economic restriction that the

References (35)

  • G. Bertola et al.

    Dealer pricing of consumer credit

    International Economic Review

    (2005)
  • A. Bicakova

    Does the good matter? Evidence on moral hazard and adverse selection from consumer credit market

    Giornale degli Economisti e Annli di Economia

    (2007)
  • R. Blundell et al.

    Changes in the distribution of male and female wages accounting for employment composition using bounds

    Econometrica

    (2007)
  • A.W. Bowman et al.

    Applied Smoothing Techniques for Data AnalysisThe Kernel Approach with S-Plus Illustrations

    (1997)
  • F.A. Bugni

    Bootstrap inference in partially identified models defined by moment inequalitiescoverage of the identified set

    Econometrica

    (2010)
  • L. Casolaro et al.

    Regulation, formal and informal enforcement and the development of household loan marketlessons from Italy

  • V. Chernozhukov et al.

    Estimation and confidence regions for parameter sets in econometric models

    Econometrica

    (2007)
  • Cited by (3)

    Mario Padula gratefully acknowledges financial support of the Finance and Consumption Chair in the European Community which enabled this project to be started. The project was completed while the second author was visiting the Stanford University, Department of Economics on a Fullbright scholarship. We also would like to thank for comments and suggestions at various stages of this project Alberto Bennardo, Giuseppe Bertola, Agar Brugiavini, Richard Disney, John Duca, Burcu Duygan, Piero Gottardi, Luigi Guiso, Michael Haliassos, Stefan Hochguertel, Winfried Koeninger, Tullio Jappelli, Theresa Osborne, Frank Vella and Guglielmo Weber, and many other seminar participants. All errors are of course our own.

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