Subsampling bootstrap in network DEA

Data Envelopment Analysis (DEA), provides an empirical estimation of the production frontier, based on an observed sample of decision making units (DMUs). Except for the single input-single output case, the asymptotic distribution of the DEA estimator can only be approximated through bootstrapping approaches. Therefore, bootstrapping techniques have been widely applied in the DEA literature to make statistical inference for the cases when the production process has a single-stage structure. However, in many cases, the transformation of inputs into outputs has an inner structure that needs to be considered. This paper examines the applicability of the subsampling bootstrap procedure in the approximation of the asymptotic distribution of the DEA estimator when the production process has a network structure, and in the presence of undesirable factors. Evidence on the performance of subsampling bootstrap is obtained through Monte Carlo experiments for the case of two-stage series structures, where overall and stage efficiency estimates are calculated using the additive decomposition approach. Results indicate great sensitivity both to the sample and subsample size, as well as to the data generating process. Subsampling methodology is then applied to construct confidence interval estimates for the overall and stage efficiency scores of railways in 22 European countries, where the railway transport process is decomposed into two stages and the railway noise pollution problem is considered as an undesirable output.