Time envelopment analysis: A new method for effectively incorporating time series in data envelopment analysis

Data envelopment analysis (DEA) is a non-parametric tool for empirically evaluating the relative efficiency of homogeneous organizational units, i.e., decision-making units, by estimating the production frontiers. Time series analysis is a statistical technique that considers a series of data collected chronologically over time intervals. This study introduces a three-stage method, Time Envelopment Analysis (TEA), to effectively integrate time series analysis into DEA. The three-stage method includes a first-order autoregressive (AR(1)) model followed by DEA and ordinary least squares (OLS). The performance of the TEA method with four different values for the AR(1) parameters is compared with the DEA-OLS procedure using extensive Monte Carlo simulations. The simulation results show that the TEA method outperforms the DEA-OLS procedure. We further demonstrate that TEA is more accurate when the autoregressive parameter is smaller, particularly in scenarios defined by a progressive decrease in the impact of technical inefficiencies. We evaluate the proposed TEA method using a real-world healthcare dataset from 63 countries by estimating the effect of contextual variables on each country’s productivity.