Sensitivity analysis of technical efficiency using bootstrap DEA and matrix based approach: with application to the Australian banking industry

Data Envelopment Analysis (DEA) is one of the commonly used non-parametric frontier analysis techniques for measuring the efficiency of Decision Making Units (DMUs). The lack of statistical precision and difficulties in the proper choice of variables are two significant challenges in applying DEA. To address these issues, this study firstly introduces a bootstrap procedure to estimate scale efficiency and the nature of returns to scale for individual DMUs. Secondly, this study improves the variable choice of the most commonly used DEA model in estimating both the pure technical and scale efficiencies of Australian banks. Moreover, the visualization of bootstrapped results using a novel efficiency matrix is introduced to present confidence intervals of pure technical and scale efficiency estimates as two determinants of technical efficiency. Such visualization facilitates any efficiency comparison between sample DMUs and provides a helpful tool for managers and policy makers to identify the source of technical inefficiency. Empirical applications are also given for Australian banks in two specific time periods including the post-Wallis period and the global financial crisis.