Two-Stage Data Envelopment Analysis Models with Negative System Outputs for the Efficiency Evaluation of Government Financial Policies

The main purpose of this study is to provide a comparative analysis of several possible approaches to applying data envelopment analysis (DEA) in the case where some decision making units (DMUs) in the original sample have negative system outputs. In comparison to the traditional model of Charnes, Cooper, and Rhodes (CCR) and the CCR model with a scale shift to measure second-stage outputs, the range directional measure (RDM) model produces the most appropriate results. In this paper, an approach is proposed for estimating returns to scale. The study applies a two-stage DEA model with negative second-stage outputs to assess the public support for research, development, and demonstration projects in the energy sector in 23 countries over the period from 2010 to 2018. The assessment of government performance depends on its contribution to the growth of energy efficiency in the national economy and the reduction of its carbon intensity. Intermediate outputs (patents in the energy sector) are included in the analysis as both outputs of the first stage and inputs of the second stage. Taking the similarity between the calculations obtained without stage separation and the system efficiency calculations from the two-stage model as a measure of model adequacy, the RDM model shows the highest similarity scores.