Multi-period productivity measurement under centralized management with an empirical illustration to German saving banks

In this paper, we revisit the structure of the centralized Malmquist indices which apply inter-temporal benchmark technologies coupled with a relaxed assumption that the technology remains unchanged between the start and the end of the analysis. From a theoretical point of view as well as with an empirical application to a panel of German savings banks over the time period 2006–2012, we discuss this premise as the technology—which is naturally under the influence of different external and internal conditions—can change over time. This may hence result in an inappropriate estimate of the benchmark technology, generate questionable sets of common-weights and lead accordingly to misleading results and managerial conclusions. To eliminate this pitfall, we propose a new centralized framework in which individual characteristics of the technology, represented by different contemporaneous technology sets over time, can be preserved and later traced in measuring productivity change. Details of our empirical results, determined by the proposed Malmquist index, reveal that the productivity of the group of German savings banks has always been increasing during the whole period analyzed. The positive rates of growth highlight the fact that this group had a stable financial system even when the financial crisis hit the international monetary and financial market. The best practice change component of the suggested Malmquist index also verifies the significant effect of change in the technology on the performance of these banks over time. Although the group of German savings banks reduced its fixed assets over time, our analysis of productivity change shows how successfully these banks could improve even in a highly customized and growing digital business environment. However, looking at the slowdown in the growth of productivity between 2011 and 2012, captured by our results, it seems advisable that they accelerate the adaptation of their business strategy, e.g., by investing more in high-quality and diverse internet-based products and services to catch up with the rapid developments in information technologies.