Further Improvements of Finite Sample Approximation of Central Limit Theorems for Weighted and Unweighted Malmquist Productivity Indices

Various methods recently have been proposed to further improve the finite sample performance of the developed central limit theorems (CLTs) for the simple mean and aggregate efficiency estimated via non-parametric frontier efficiency methods. We thoroughly investigate whether these methods are also effective to improve the finite sample performance for the recently developed CLTs for the simple mean and aggregate Malmquist Productivity Indices (MPIs). The extensive Monte-Carlo experiments confirmed that the method from Simar et al. (2023a) is useful for the simple mean and aggregate MPI in relatively small sample sizes (e.g., up to around 50, perhaps 100) and especially for large dimensions. Interestingly, we find that the better performance of the data sharpening method from Nguyen et al. (2022) observed in the context of efficiency is not obvious in the context of productivity. Finally, we use one well-known empirical data set to illustrate the differences across the existing methods to guide the practitioners.