Central Limit Theorems for Aggregate Efficiency

Applied researchers in the field of efficiency and productivity analysis often need to estimate and make inference about aggregate efficiency, such as industry efficiency or aggregate efficiency of a group of distinct firms within an industry (e.g., public versus private firms, regulated versus unregulated firms, etc.). While there are approaches to obtain point estimates for such important measures, no asymptotic theory has been derived for it. This is the gap in the literature we fill with this paper. Specifically, we develop full asymptotic theory for aggregate efficiency measures when the individual true efficiency scores being aggregated are observed as well as when they are unobserved and estimated via the data envelopment analysis or the free disposal hull. As a result, the developed theory opens a path for more accurate and theoretically better grounded statistical inference (e.g., estimation of confidence intervals and conducting statistical tests) on aggregate efficiency estimates such as industry efficiency, etc.