A new framework for examining creditworthiness of borrowers: the mover-stayer model with covariate and macroeconomic effects

Abstract

We develop a novel extension of the mover-stayer model to allow for time-dependent variables such as macroeconomic factors and apply it to the repayment process for car loans. The MS model postulates a simple form of population heterogeneity, which is particularly well suited to describing the repayment process: a proportion of borrowers always repay on time (stayers), and a complementary proportion evolves according to a discrete-time Markov chain (movers), with an absorbing default state. In contrast to the literatures focus on the determinants of defaults, our extension examines the determinants of creditworthy borrowers (stayers). We model the probability of borrowers being stayers as a logistic function of their time-fixed covariates as well as of macroeconomic variables. The car-loans data set, obtained from a Polish bank, contains a large number of characteristics for each borrower and their repayment histories. The MS models' estimation from these data indicates that annual GDP growth is the only macroeconomic variable exerting a substantial effect on the stayers' probability: as GDP increases, so does the proportion of stayers. Because stayers are the most desirable borrowers, the proposed model should be useful to institutional lenders.

Keywords:

• Mover-stayer model
• Macroeconomic variables
• Creditworthy borrowers
• Car loans data
• EM algorithm

Acknowledgments

We thank both referees for very helpful comments and suggestions that significantly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The original mover-stayer model was proposed by Blumen et al. (1955). Frydman (1984) developed maximum likelihood estimation of its parameters.

2 For an extension of the MS model that does not include covariates, see Frydman and Schuermann (2008).

3 For theory of deviance test, see Homer et al. (2013). We got ‘Residual deviance’ and ‘degrees of freedom’ numbers from R's ‘glm’ function, and calculated the p-value using R's ‘pchisq’ function.

4 See Homer et al. (2013) for a discussion of odds ratios for discrete and continuous variables.