Estimating Malmquist productivity indexes using probabilistic directional distances: An application to the European banking sector

Abstract

Our paper by adopting the latest advances on the probabilistic characterization of directional distance functions as has been introduced by Daraio and Simar (2014), develops a Malmquist productivity index and presents its main decompositions. Specifically, the proposed productivity index is based on the probabilistic version of directional distance functions which are expressed as transformations of radial distances. We illustrate how these indexes can be computed and how different components can be derived. Specifically, we demonstrate how a probabilistic version of the following categories of change can be obtained: technical, efficiency, pure efficiency, scale efficiency, scale change factor and scale bias of technical change. Finally, we apply the probabilistic productivity indexes alongside with their decompositions to inputs/outputs data from a sample of 644 banks from 28 European countries between the years 2007, 2010 and 2014. The results suggest that the EU banks’ productivity levels remained relative unchanged from the initiation of U.S. prime crisis and during the EU sovereign debt crisis. Finally, during the U.S. prime crisis and the Global Financial Crisis, banks’ maintained their productivity levels by utilizing better their inputs and by exploiting scale economies. However, during the sovereign debt crisis banks maintained their productivity levels by investing on financial engineering competences.