Assessing the shape of the distribution of interest rates: lessons from French individual data

Estimating mixture models still raises numerous questions, both theoretical and empirical. However, this class of model appears quite powerful for a parcimonious modelization of ill-behaved distribution, as it is the case with loans rate vis-à-vis the private sector collected by the Banque de France from a panel of French credit institutions. Indeed, the heterogeneity of the credit market is a well-established fact which translate into high variability of interest rates at the micro level. Thus, we provide a detailed analysis of 11 categories of loans to non-financial corporations and households, and compare various procedures for the estimation of mixture models with a large number of components. The results allow us to identify modes in the distributions of interest rates and to clarify the nature of heterogeneity in the data in relation with the specialization of some part of the banking sector on particular instruments. Lastly, our methodology allows us to quantify the effects of the usury law on the upper side of the distribution, and to propose a preliminary estimate of eviction rates resulting from this regulation.