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.

我们开发了移动者-停留者模型的新扩展，以考虑宏观经济因素等时间相关变量，并将其应用于汽车贷款的还款过程。MS 模型假设了一种简单的总体异质性形式，它特别适合描述还款过程：一定比例的借款人始终按时还款（停留者），而互补比例则根据离散时间马尔可夫链（移动者）演变，具有吸收默认状态。与关注违约决定因素的文献相比，我们的扩展研究了信誉良好的借款人（逗留者）的决定因素。我们将借款人成为逗留者的概率建模为他们的时间固定协变量以及宏观经济变量的逻辑函数。从波兰银行获得的汽车贷款数据集，包含每个借款人的大量特征及其还款历史。MS 模型对这些数据的估计表明，年 GDP 增长是唯一对留守者概率产生重大影响的宏观经济变量：随着 GDP 的增加，留守者的比例也会增加。因为逗留者是最理想的借款人，所以提议的模型应该对机构贷款人有用。