On the length of bank-firm relationships: an empirical application to a major French bank

Abstract

In this paper, we analyse whether the likelihood of the bank-firm relationships ending is dependent on their age or not and whether the respective behaviour is smooth or changes over their length. A parametric duration analysis is employed in this analysis. We start by estimating a continuous-time Weibull duration model over the duration of the relationships between 1185 firms and one of the major French banks. Our findings show that the likelihood of the relationships between them ending increases over their duration, but other specific factors to the firms, to the bank, to their own relationship and certain pricing conditions also play an important role in the duration of those relationships. Additionally, we extend the baseline Weibull duration model in order to allow for changepoints in the duration dependence parameter. The empirical findings support the presence of a change-point: positive duration dependence is observed for those relationships that last less than 23 years, but no evidence of duration dependence is found for longer events. Hence, we conclude that the likelihood of these relationships ending increases over time, but only until about 23 years of duration; then the relations become stronger and the likelihood of they ending is no longer dependent on its duration but on other conditionings.