Productivity growth in network models: An application to banking during the financial crisis

Stavros A Kourtzidis,Roman Matousek,Nickolaos G Tzeremes

doi:10.1080/01605682.2017.1421851

Abstract

We construct Malmquist Productivity indices for two-stage processes. A two-stage data envelopment analysis model with an additive efficiency decomposition is used for the modelling of the two-stage process. We incorporate prior information into the analysis using the Weight Assurance Region model. This model offers advantages such as the weights representing the contribution of each stage to the overall process are always positive and we also can restrict them into a region given the available prior information. We extend this model from efficiency analysis to productivity analysis and we calculate Malmquist Productivity indices using four alternative decomposition approaches. The model is applied to a panel of banks in Central and Eastern European countries and productivity change is evaluated for three periods of the financial crisis. The alternative decompositions allow us to examine the various sources of productivity change during the financial crisis. Convergence patterns are also examined.

Highlights

One of the key questions regarding two-stage data envelopment analysis (DEA) models is the level by which each stage contributes to the whole process
The Weight Assurance Region (WAR) model is an advancement of the original additive two-stage DEA model which can be considered as a special case of the WAR model with no additional information
The WAR model is a modification of the relational two-stage DEA model of Chen et al (2009) in order to incorporate assurance region-based weights regarding the contribution of each stage to the overall process

Summary

Introduction

One of the key questions regarding two-stage DEA models is the level by which each stage contributes to the whole process. Halkos et al (2015) notified an extreme case where the contribution of one stage is zero They proposed the Weight Assurance Region (WAR) model to overcome this problem. To the best of our knowledge this is the first time a network DEA-based MPI approach uses the four decompositions This is the first time that the dual of the WAR model is presented. The WAR model is a modification of the relational two-stage DEA model of Chen et al (2009) in order to incorporate assurance region-based weights regarding the contribution of each stage to the overall process. Note that here we omit the two additional constraints (4) for assurance region These constraints are used only in the overall model (5) in order to constraint the weights of each stage. The efficiency for the second stage based on (5) and (6) is calculated as: Ek2

Malmquist Productivity Index and decompositions

Test of convergence

Findings

Conclusions