A Bayesian quantile regression model for insurance company costs data

Abstract

We examine the average cost function for property and casualty insurers. The cost function describes the relationship between a firm's minimum production cost and outputs. A comparison of cost functions could shed light on the relative cost efficiency of individual firms, which is of interest to many market participants and has been given extensive attention in the insurance industry. To identify and to compare the cost function, current practice is to assume a common functional form between costs and outputs across insurers and then to rank insurers according to the centre of the cost distribution. However, the assumption of a common cost–output relationship could be misleading because insurers tend to adopt different technologies that are reflected by the cost function in their production process. The centre-based comparison could also lead to biased inference especially when the cost distribution is skewed with a heavy tail. To address these issues, we model the average production cost of insurers by using a Bayesian quantile regression approach. Quantile regression enables the modelling of different quantiles of the cost distribution as opposed to just the centre. The Bayesian approach helps to estimate the cost-to-output functional relationship at a firm level by borrowing information across firms. In the analysis of US property–casualty insurers, we show that better insights into efficiency are gained by comparing different quantiles of the cost distribution.