We investigate the consistency of efficiency scores derived with two competing frontier methods in the financial economics literature: Stochastic Frontier and Data Envelopment Analysis. We sample 34,192 observations for all German universal banks and analyze whether efficiency measures yield consistent results according to five criteria between 1993 and 2004: levels, rankings, identification of extreme performers, stability over time and correlation to standard accounting-based measures of performance. We find that non-parametric methods are particularly sensitive to measurement error and outliers. Furthermore, our results show that accounting for systematic differences among commercial, cooperative and savings banks is important to avoid misinterpretation about the status of efficiency of the total banking sector. Finally, despite ongoing fundamental changes in Europe's largest banking system, efficiency rank stability is very high in the short run. However, we also find that annually estimated efficiency scores are markedly less stable over a period of twelve years, in particular for parametric methods. Thus, the implicit assumption of serial independence of bank production in most methods has an important influence on obtained efficiency rankings.Keywords: Cost Efficiency, Banks, Stochastic Frontier Approach, Data Envelopment Analysis JEL: D24, G21, L25
Non-technical summaryTo measure the cost efficiency of banks, one should compare observed cost-and output-factor combinations with optimal combinations determined by the available technology (efficient frontier). The method to implement this analysis could be either stochastic or deterministic. The former allows random noise due to measurement errors. The latter, on the contrary, attributes the distance between an inefficient observed bank and the efficient frontier entirely to inefficiency. A further distinction is made between parametric or non-parametric approaches. A parametric approach uses econometric techniques and imposes a priori the functional form for the frontier and the distribution of efficiency. A non-parametric approach, on the contrary, relies on linear programming to obtain a benchmark of optimal costand production-factor combinations.The most popular methods are Stochastic Frontier Analysis (SFA), which is stochastic and parametric, and Data Envelopment Analysis (DEA), which is deterministic and non-parametric. This study analyses on the basis of five criteria to what extent SFA and DEA yield consistent cost efficiency (CE) measures when applied to the same dataset. In particular, we check to what extent they provide different efficiency scores when stratifying the sample according to year, banking group or both dimensions simultaneously.Our results show very low consistency between SFA and DEA measures, especially when applied to the entire panel sample. First, mean CE according to SFA is substantially higher compared to DEA. This difference becomes smaller when stratifying the sample according to year, banking group or both dimensi...