Advertisement

Empirical Economics

, Volume 53, Issue 2, pp 641–667 | Cite as

Hurdle models of repayment behaviour in personal loan contracts

  • José M. R. MurteiraEmail author
  • Mário A. G. Augusto
Article
  • 226 Downloads

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.

Keywords

Loan repayment Panel count data Binomial thinning Beta mixture Hurdle 

JEL Classification

G21 C23 C25 

References

  1. Adke S, Gadag V (1995) A new class of branching processes. In: Heyde CC (ed) Branching processes. Springer, New York, pp 90–105CrossRefGoogle Scholar
  2. Al-Osh MA, Alzaid AA (1987) First-order integer valued autoregressive INAR(1) process. J Time Ser Anal 8:261–275CrossRefGoogle Scholar
  3. Brännäs K (1994) Estimation and testing in integer valued AR(1) models. Umeå Economic Studies 355. University of UmeåGoogle Scholar
  4. Brännäs K (1995) Explanatory variables in the AR(1) model. Umeå Economic Studies 381. University of UmeåGoogle Scholar
  5. Cameron AC, Trivedi PK (2005) Microeconometrics methods and applications. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  6. Cameron AC, Trivedi PK (2013) Regression analysis of count data, 2nd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  7. Chamberlain G (1980) Analysis of covariance with qualitative data. Rev Econ Stud 47:225–238CrossRefGoogle Scholar
  8. Chamberlain G (1985) Heterogeneity, omitted variable bias, and duration dependence. In: Heckman JJ, Singer B (eds) Longitudinal analysis of labor market data. Cambridge University Press, Cambridge, pp 3–38CrossRefGoogle Scholar
  9. Cragg JG (1971) Some statistical models for limited dependent variables with application to the demand for durable goods. Econometrica 39:829–844CrossRefGoogle Scholar
  10. Freeland RK, McCabe B (2004) Analysis of low count time series data by Poisson autoregression. J Time Ser Anal 25:701–722CrossRefGoogle Scholar
  11. Gouriéroux C, Monfort A, Trognon A (1984) Pseudo maximum likelihood methods: theory. Econometrica 52:681–700CrossRefGoogle Scholar
  12. Hall BH, Cummins C (2005) TSP 5.0 user’s guide. TSP International, Palo Alto (CA)Google Scholar
  13. Hausman J, Hall BH, Grilishes Z (1984) Econometric models for count data with an application to the patents–R&D relationship. Econometrica 52:909–938CrossRefGoogle Scholar
  14. Heckman JJ, Willis RJ (1977) A beta-logistic model for the analysis of sequential labor force participation by married women. J Polit Econ 85:27–58CrossRefGoogle Scholar
  15. Honoré B, Kyriazidou E (2000) Panel data discrete choice models with lagged dependent variables. Econometrica 68(839):874Google Scholar
  16. Jazi MA, Jones G, Lai C-D (2012) First-order integer valued AR processes with zero inflated Poisson innovations. J Time Ser Anal 33:954–963CrossRefGoogle Scholar
  17. Joe H (1997) Multivariate models and dependence concepts. Chapman & Hall, LondonCrossRefGoogle Scholar
  18. Jung RC, Kukuk M, Liesenfeld R (2006) Time series of count data: modelling, estimation and diagnostics. Comput Stat Data Anal 51:2350–2364CrossRefGoogle Scholar
  19. Jung RC, Ronning G, Tremayne AR (2005) Estimation in conditional first order autoregression with discrete support. Stat Pap 46(2):195–224CrossRefGoogle Scholar
  20. Lee M-J (1996) Methods of moments and semiparametric econometrics for limited dependent variable models. Springer, New YorkCrossRefGoogle Scholar
  21. MacDonald IL, Zucchini W (1997) Hidden Markov and other models for discrete-valued time series. Chapman & Hall, LondonGoogle Scholar
  22. McKenzie E (1985) Some simple models for discrete variate time series. Water Resour Bull 21:645–650CrossRefGoogle Scholar
  23. McKenzie E (1988) Some ARMA models for dependent sequences of Poisson counts. Adv Appl Prob 22:822–835CrossRefGoogle Scholar
  24. McKenzie E (2003) Discrete variate time series, stochastic processes: modelling and simulation. In: Shanbag DN, Rao CR (eds) Handbook of statistics, vol 21. North-Holland, Amsterdam, pp 573–606Google Scholar
  25. Mullahy J (1986) Specification and testing of some modified count data models. J Econom 33:341–365CrossRefGoogle Scholar
  26. Pagan A, Vella F (1989) Diagnostic tests for models based on individual data: a survey. J Appl Econom 4:29–59CrossRefGoogle Scholar
  27. Ramalho EA, Ramalho JJS, Murteira J (2011) Alternative estimating and testing empirical strategies for fractional regression models. J Econ Surv 25:19–68CrossRefGoogle Scholar
  28. Ramsey JB (1969) Tests for specification errors in classical linear least squares regression analysis. J R Stat Soc B 31:350–371Google Scholar
  29. Santos Silva JMC, Murteira J (2009) Estimation of default probabilities with incomplete contracts data. J Empir Finance 16:457–465CrossRefGoogle Scholar
  30. Schweer S, Weiß CH (2014) Compound Poisson INAR(1) processes: stochastic properties and testing for overdispersion. Comput Stat Data Anal 77:267–284CrossRefGoogle Scholar
  31. Stanghellini E (2009) Introduzione ai metodi statistici per il credit scoring. Springer, MilanoCrossRefGoogle Scholar
  32. Steutel FW, VanHarn K (1979) Discrete analogues of self-decomposability and stability. Ann Probab 7:893–899CrossRefGoogle Scholar
  33. Sun J, Zhao X (2013) Statistical analysis of panel count data. Springer, New YorkCrossRefGoogle Scholar
  34. Thomas LC, Edelman DB, Crook JN (2002) Credit scoring and its applications. SIAM, PhiladelphiaCrossRefGoogle Scholar
  35. Weiss C (2008) Thinning operations for modelling time series of counts—a survey. Adv Stat Anal 92:319–341CrossRefGoogle Scholar
  36. Windmeijer F (2006) GMM for panel count data models. CeMMAP working papers CWP21/06, Centre for Microdata Methods and Practice, Institute for Fiscal StudiesGoogle Scholar
  37. Winkelmann R (2004) Health care reform and the number of doctor visits—an econometric analysis. J Appl Econom 19:455–472CrossRefGoogle Scholar
  38. Wooldridge J (1997) Multiplicative panel data models without the strict exogeneity assumption. Econom Theory 13:667–678CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • José M. R. Murteira
    • 1
    Email author
  • Mário A. G. Augusto
    • 2
  1. 1.CEMAPRE-ISEG Universidade de LisboaFaculdade de Economia da Universidade de CoimbraCoimbraPortugal
  2. 2.Institute of Systems and RoboticsFaculdade de Economia da Universidade de CoimbraCoimbraPortugal

Personalised recommendations