Repayment decisions are important to borrowing behaviour meaning that understanding how consumers would like to repay their debts over time is an important information for many fields of economic research and consumer financial policy. Similarly, retrieving reliable estimates of time preferences is fundamental to applied and theoretical studies of financial and economic decision-makings. The majority of research that have studied time preferences rely on using stated choices that involve a trade-off between monetary rewards and the length of time required to wait to receive the reward, that is, over reward-time pairs. However, the discount rates that are measured in this way tend to be relatively high. This is attributed to present bias and hyperbolic discounting. Several methods have been used to reduce this bias, e.g., Double Multiple Price List (DMPL) approach and Convex Time Budget (CTB) method. It has also been explored using stated preference approaches that measure time preference and analysing the data using choice models. The literature of using this approach is rare, especially in financial contexts. This research will provide evidence to address this gap. In addition, we propose a new method to elicit time preferences and a novel modelling framework that incorporate latent class trajectory models. Furthermore, to date, the time preference literature has solely focused on eliciting discount rates in the context of receiving monetary rewards. However, in many settings it is more appropriate to identify time preferences in the setting of making repayment decisions. In this paper, we also explore this issue.
We employ a stated choice approach where participants were asked to make choices that involved a trade-off between alternative monetary rewards received at different times. Dissimilar to the past research, experiments in this research were asking participants to make trade-offs between repaying debt within different lengths of period, the longer period is, the more interests need to be paid. The data is composed of two treatments, one involving debt repayments of £500 and another of £5000. Participants from both treatments were required to complete the experiment designed, according to the manner of CTB, which consists of seven choice tasks. In each choice tasks, participants needed to choose one from 13 alternatives. The alternatives are presented as bundles of repayment amount and period length. The data collection was through an UK web-based survey, where 2,100 participants were recruited with approximate spilt between the two treatments.
The analysis is based on a latent class trajectory modelling framework that classifies the range of discounts rates among the sample and how this maps to distinct trajectories of choices in the CTB. Specifically, the latent class trajectory model used in this paper is a semi‐parametric technique used to identify distinct subgroups of participants who following a similar pattern of choice behaviour as they progress through the choice tasks. While each participant may have made a unique sequence of choices (due to differences in their individual discount rate) and, thus, had a unique trajectory, we summarise the heterogeneity in these trajectories by a finite set of unique polynomial functions.
Our approach is shown to provide a better understanding of variation between individuals’ repayment behaviour in certain features. In both treatments, our results suggest that three groups of choice participants that differ on the basis of their discount rate. Firstly, around 50 percent of the participants choose to repay the debt without paying any interests, which allows us to identify the optimal behaviour that refers to consumers minimize the interest charges depending on their financial circumstances. This behaviour has also been identified in optimal mortgage choices that individuals refinance over real options in the future according to time and risk preference. These participants are more likely to be elderly (over 60) and financially literate. The second type of behaviour is consistently repaying debt. Specifically, higher estimates of discount rates were identified along with shorter period of repayment. Compared with the participants preferred optimal repayment, this group tend to be younger (31-60),and less likely to get more financially literate questions correct. The third type of behaviour is reversal repaying. Generally, for these participants, the estimates of discount rate are variant in the length of repayment period. This behaviour tends to be exhibited by the participants who are between 18 to 30, and they tend to get less financially literate questions correct. The comparison between treatments discloses discount rates under same type of behaviour are variant depending on debt size. We also find that estimates of discount rate in our research is lower than the estimates that obtained from the design of over reward-time pairs.