Rigorous methods have recently been developed for statistical inference of Malmquist productivity indices (MPIs) in the context of nonparametric frontier estimation, including the new central limit theorems, estimation of the bias, standard errors and the corresponding confidence intervals. The goal of this study is to briefly overview these methods and consider a few possible improvements of their implementation in relatively small samples. Our Monte-Carlo simulations confirmed that the method from Simar et al. (2023) is useful for the simple mean and aggregate MPI in relatively small sample sizes (e.g., up to around 50) and especially for large dimensions. Interestingly, we also find that the “data sharpening” method from Nguyen et al. (2022), which helps in improving the approximation in the context of efficiency is not needed in the context of estimation of productivity indices. Finally, we provide an empirical illustration of the differences across the existing methods.
