Efficiency under quantile regression: What is the relationship with risk in the EU banking industry?

This study estimates cost efficiency under a quantile regression framework. Our purpose is to investigate whether cost efficiency differs across quantiles of the conditional distribution. Efficiency scores are derived using the distribution‐free approach. Results show that for higher conditional distributions, efficiency scores are lower. In a second stage analysis, we examine the relationship between efficiency and risk, measured as distance to default. Cross section regressions show that the higher the risk, the lower the level of efficiency. The magnitude and the significance of the coefficient of the distance to default increases for conditional distributions associated with lower levels of efficiency.