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Empirical Economics

Erschienen in:

23.08.2016

Hurdle models of repayment behaviour in personal loan contracts

verfasst von: José M. R. Murteira, Mário A. G. Augusto

Erschienen in: Empirical Economics | Ausgabe 2/2017

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Abstract

This paper proposes a hurdle model of repayment behaviour in loans with fixed instalments. Using information on previous and current contracts, the approach yields a model of customer behaviour, useful, for example, in assessing the impact of determinants of default, a natural concern for credit and behavioural scoring. Under plausible assumptions, a debtor in each period faces a number of missed payments, which depends on his previous repayment decisions; meanwhile, as most debtors are expected to meet financial obligations, the number of missed payments is bound to display excess zeros, with reference to a single-part law. Each sequence of missed payments is modelled by using the binomial thinning, a conceptual tool that allows for dependence between integers by defining the support of consecutive counts. Under suitable assumptions on heterogeneity, the model can be produced under a random effects approach, leading to a two-part panel data model, estimable by quasi-maximum likelihood. The proposed approach is illustrated using a panel data set on personal loans granted by a Portuguese bank.

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One alternative route to allow for dependence among discrete variables consists on assuming that these variables share common, often time-dependent, unobservable features. Such is the case of hidden Markov models, which is described and illustrated in detail in MacDonald and Zucchini (1997).

Binomial thinning constitutes the most popular form of thinning, a general probabilistic operation that can be applied to random counts—see Weiss (2008) for a survey of thinning operations.

These vectors may obviously include common covariates (indeed, they can be identical in view of the functional separability of the hurdle model—check (12).

Henceforth, unless required, the individual index, i, is omitted.

A likelihood ratio-type statistic is not valid because of a very probably incorrect variance assumption as well as neglected time dependence implied by the adopted likelihood.

In practice, the sample estimate for the covariance matrix to be used with the Hausman test may not be invertible, nor positive semi-definite, even if invertible—see Lee (1996, Ch. 5.9) for an estimator of the covariance matrix of \(\hat{\varvec{\theta }}-\hat{\varvec{\theta }}_{ML}\) that is positive semi-definite, by construction.

These observed differences suggest a deeper investigation into the small sample properties of both approaches in a wider range of situations—in any event, a hint that seems to reach beyond the scope of the present text, possibly justifying a separate note on his own.

No convergence was achieved with the NLS method, which prevented the presentation of the corresponding estimates. This setback notwithstanding, a sound alternative method is provided by pooled QML.

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Titel: Hurdle models of repayment behaviour in personal loan contracts
verfasst von: José M. R. Murteira
Mário A. G. Augusto
Publikationsdatum: 23.08.2016
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 2/2017
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-016-1140-2

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