Estimating global frontier shifts and global Malmquist indices

The Malmquist index is a measure of productivity changes, of which an important component is the frontier shift or technological change. Often technological change can be viewed as a global phenomenon, and therefore individual or local measures of technological changes are aggregated into an overall measure, traditionally using geometric means. In this paper we propose a way of calculating global Malmquist indices and global frontier shift indices which provides a better estimation of the true frontier shift and furthermore is easy to calculate. Using simulation studies we show how this method outperforms the traditional aggregation approach, especially for sparsely populated production possibility sets and for frontiers that also change shape over time. Furthermore, our global indices can be used for unbalanced panels without disregarding any information. Finally, we show how the global indices are meaningful for calculating differences between frontiers from different groups rather than different time periods as illustrated in a small case study of bank branches in different countries.