Inference for aggregate efficiency: Theory and guidelines for practitioners

We expand and develop further the recently developed framework for the inference about the aggregate efficiency, extending the existing theory and providing guidelines for practitioners. In Monte Carlo simulations, we thoroughly examine the performance of the various improvement methods (compared with the original CLT results) for the aggregate input-oriented and output-oriented efficiency for different ranges of small samples and different dimensions of the production model. From the simulations, we conclude that: (i) when the sample sizes are relatively small (around 200 and less), the full variance correction method (adapted from Simar et al., 2023) with the data sharpening method (adapted from Nguyen et al., 2022) generally provides a better performance; (ii) when the sample sizes are relatively large, the full variance correction method without the data sharpening method is expected to perform better than the other suitable methods known to date. Finally, we use two well-known empirical data sets to illustrate the practical implementations and the differences across the existing methods to facilitate their use by practitioners.