Bootstrapping in Network Data Envelopment Analysis

Abstract

Data Envelopment Analysis (DEA) is a linear-programming method used to measure the relative efficiency of firms. The objective of this thesis is (i) to study the efficiency of the railway transport process in Europe considering its inner structure and the impact of railway noise on humans and (ii) to study the performance of bootstrapping approaches in obtaining DEA efficiency estimates when the production process has a network structure and the relation between the different stages is considered. First, the railway transport process is divided into two stages, related to assets and service provision, respectively. The negative impact of railways on people is measured as the number of people that are exposed to high levels of railway noise. The number of rail wagons in each country that is retrofitted with more silent braking technology is used as a proxy to measure the effort to reduce railway noise pollution. Data is extracted from Eurostat (2016), ERA 006REC1072 Impact Assessment (2018), and EEA (2020) and the additive efficiency decomposition approach is used. Based on the results, asset-efficient countries are usually service-efficient, but the inverse does not hold. Sensitivity analysis revealed that efficiency rankings are robust to alterations in the decomposition weight restrictions. Subsampling bootstrap was chosen as the most appropriate as it does not require any restrictive assumptions. The performance of subsampling is examined through Monte Carlo simulations for various sample and subsample sizes for general two-stage series structures. Results indicate great sensitivity both to the sample and subsample size, as well as to the data generating process-higher than in one-stage structures. A practical approach is suggested to overcome some result inconsistencies that are due to the peculiarities of the additive decomposition algorithm. The method is applied to obtain confidence interval estimates for the overall and stage efficiency scores of European railways.