Statistical Inference for Aggregation of Malmquist Productivity Indices

The Malmquist Productivity Index (MPI) has gained popularity amongst studies on dynamic change of productivity of decision-making units (DMUs). In practice, this index is frequently reported at aggregate levels (e.g., public and private firms) in the form of simple equally-weighted arithmetic or geometric means of individual MPIs. A number of studies have emphasized that it is necessary to account for the relative importance of individual DMUs in the aggregations of indices in general and of MPI in particular. While more suitable aggregations of MPIs have been introduced in the literature, their statistical properties have not been revealed yet, preventing applied researchers from making essential statistical inferences such as confidence intervals and hypothesis testing. In this paper, we will fill this gap by developing a full asymptotic theory for an appealing aggregation of MPIs. On the basis of this, some meaningful statistical inferences are proposed and their finite-sample performances are verified via extensive Monte Carlo experiments