Examination of Decomposition Weights in the Additive Two-Stage Network Data Envelopment Analysis Model: An Application to UK Investment Trusts

This paper investigates issues regarding the decomposition weights in the additive two-stage network Data Envelopment Analysis model. The issues under investigation include the non-increasing decomposition weights, the impact of decomposition weights on the stage efficiencies, the zero weight to one of the two stages, and the infeasibilities or peculiar results due to weight restrictions. We extend the previous work of Despotis et al. (2016) and Ang and Chen (2016) to the case of variable returns to scale, for alternative specifications of the model including simple and generalised structures. In addition, we develop the necessary conditions under which there can be a reversal in the decomposition weights for the two stages. A General Weight Assurance Region model is introduced for weight restrictions. The proposed model can handle multiple input, output, and intermediate variables at both stages, including leakage variables in the first stage and inputs that enter the system in the second stage. The empirical investigation is undertaken using a dataset of 91 UK investment trusts for 2019. The overall fund efficiency is decomposed into operational management efficiency in the first stage and portfolio management efficiency in the second stage. Generalised structures with an external input in the second stage, and models assuming VRS tend to produce results which do not suffer from the issues under investigation.