Statistical Inference for Hicks–Moorsteen Productivity Indices

The statistical framework for the Malmquist productivity index (MPI) is now well-developed and emphasizes the importance of developing such a framework for its alternatives. In this paper, we try to fill this gap in the literature for another popular measure, known as the Hicks–Moorsteen productivity index (HMPI). Unlike MPI, the HMPI has a total factor productivity interpretation in the sense of measuring productivity as the ratio of aggregated outputs to aggregated inputs and has other useful advantages over MPI. In this work, we develop a novel framework for statistical inference for HMPI in various contexts: when its components are known or when they are replaced with non-parametric envelopment estimators. This will be done for a particular firm’s HMPI as well as for the simple mean (unweighted) HMPI and the aggregate (weighted) HMPI. Our results further enrich the recent theoretical developments of nonparametric envelopment estimators for the various efficiency and productivity measures. We also examine the performance of these theoretical results for both the unweighted and weighted mean of HMPI for a finite sample, using Monte-Carlo simulations and also provide an empirical illustration along with the computation code.