Asymptotic Theory for Aggregate Efficiency

Applied researchers in the field of efficiency and productivity analysis often need to estimate and inference about aggregate efficiency, such as industry efficiency or aggregate efficiency of a group of distinct firms within an industry (e.g., public vs. private firms, regulated vs. unregulated firms, etc.). While there are approaches to obtain point estimates for such important measures, no asymptotic theory have been derived for it–the gap in the literature that we fill with this paper. Specifically, we develop full asymptotic theory for aggregate efficiency measures when the indi- vidual true efficiency scores being aggregated are observed as well as when they are unobserved and estimated via DEA or FDH. As a result, the developed theory opens a path for more accurate and theoretically better grounded statistical inference on aggregate efficiency estimates such as industry efficiency, etc.