A bootstrapping dynamic two-stage SBM model: An application to assess industrial water use and health risk systems

Despite the great number of applications of bootstrapping data envelopment analysis (DEA) with a one-stage structure, there are limited attempts for approximating the distribution of the DEA estimator considering the two-stage structure across multiple periods. This research develops the dynamic two-stage non-radial DEA model based on smoothed bootstrap and subsampling bootstrap. Then, we run the proposed models on assessing the efficiency of China's industrial water use and health risk (IWUHR) systems and compare them with the bootstrapping results on standard radial network DEA. The results are as follows. (1) The proposed non-radial DEA model based on smoothed bootstrap can adjust original over-estimated and under-estimated values. (2) China's IWUHR system has good performance, and its HR stage performs better than the IWU stage for 30 provinces from 2011 to 2019. The poor performance of the IWU stage in Jiangxi and Gansu needs to be noticed. The provincial differences of the detailed bias-corrected efficiencies expand in the later period. (3) The rankings of IWU efficiency in the three regions are in agreement with that of HR efficiency: eastern, western, and central regions in this order. Particular attention should be paid to the downward trend of the bias-corrected IWUHR efficiency in the central region.